\r\n(x^2)y + (y^2)z + (z^2)x = 100\r\nx+y+z = 9\r\nz-y-x = 1\r\nxyz = 0\r\n(x^2)(z-1) = 64\r\nx((z^2)-1)+z((y^2)-3)-x(yz-xy) = 81\r\n2xz+x+z = 49\r\nx((z^2)+x)+z(y^2)-(x^2)(z-y) = 36\r\n
\r\nSo (4,0,5) is indeed a solution and there are no others...',NULL,0); INSERT INTO comment VALUES (3688,701,1756,'Rajat','Solution','2003-03-29 08:01:09',0,'x = 4\r\ny = 0\r\nz = 5\r\n\r\n(x^2)(z-1) is a square. So, (x)√(z-1) = whole number. since x is whole number, √(z-1) must be whole. Therefore, (z-1) is a square less than 10.\r\n\r\nThe values of z can be 5, 2, 1. z is greatest of all three numbers chosen since (z - y - x) is a square. So, z cannot be 1 (x and y cant be assigned values). Similary if z is 2, then x+y+z = 3 which is not a square.\r\n\r\nOnce we have z = 5, then x can be either 4 or, 1 to satisfy \"2xz+x+z is a square\". If x = 1, then xyz cannot be satisfied.\r\n\r\nTherefore x is 4.\r\n\r\nNow, \"xyz is a square\" can only be satisfied if y = 0.',NULL,0); INSERT INTO comment VALUES (3689,687,1756,'Rajat','','2003-03-29 08:05:31',3,'It will float down normally.',NULL,0); INSERT INTO comment VALUES (3690,471,1301,'Charlie','re(7): regarding posted solution','2003-03-29 09:59:35',0,'It is not required that the maximum and minimum numbers be known in order for the posted strategy to need a modification. What I stated previously in clarifying Cory\'s point was an example of 100 slips. The only thing we know about the maximum is that it is at least 100; it might be 10,000,000 for all we know. The only thing we know about the minimum is what we see come up. But it still holds true that if every one of the first 37 was under 50, it still makes no sense to accept an 80. This is even though we do not know the distribution and do not know the maximum, all we know is that because each slip has a unique number, that the maximum, whatever it is, is at least 100 and maybe more (maybe a lot more). But we dont know what it is, just that it\'s at least 100. \r\n\r\nAs Cory said it\'s the uniqueness of the slips, and not the knowing of the min and max, that changes the nature of the strategy.',3679,0); INSERT INTO comment VALUES (3691,688,1811,'dan','vibration','2003-03-29 10:31:10',0,'OK, so what if the sound from the speakers caused the yolk to vibrate and heat up. the heat may have been sufficient to coagulate the fluid inside',NULL,0); INSERT INTO comment VALUES (3692,633,1709,'silvis','','2003-03-29 10:42:26',3,'When the water turns into ice, it gets colder and the molecules expand so the density goes down.',NULL,0); INSERT INTO comment VALUES (3693,701,1767,'Fernando','re: Solution','2003-03-29 20:53:49',0,'very nice SHORT solution, Rajat!!',3688,0); INSERT INTO comment VALUES (3694,689,1821,'montana hingis','i fink?','2003-03-30 04:16:08',0,'3 red, 3 blue',NULL,0); INSERT INTO comment VALUES (3695,689,1301,'Charlie','In fact...','2003-03-30 05:54:11',3,'It didn\'t make any difference what the make-up of the first die is. The half-and-half nature of the second die (3 red, 3 blue) assures that whatever the first die shows, there\'s a 50% chance of a match on the second.',NULL,0); INSERT INTO comment VALUES (3696,689,153,'TomM','','2003-03-30 06:11:51',3,'The first die has a 1/6 chance of showing blue and a 5/6 chance of showing red.\r\n\r\nIf r = the number of red faces on the second die, and b = the number of blue faces, then r = 6 - b and the second die has an (6-b)/6 chance of showing red and a b/6 chance of showing blue.\r\n\r\nWhen thrown together, the dice have a 1/2 chance of showing the same color. This happens when both dice show red (5/6 * [6-b]/6) or (+) when both sides show blue (1/6 * b/6)\r\n\r\n(5/6 * [6-b]/6) + (1/6 * b/6) = 1/2\r\n(30 -5b)/36 + b/36 = (30-4b)/36 = 1/2\r\n30 - 4b = 18\r\n4b = 12\r\nb = 3\r\nr = 6 - b = 3',NULL,0); INSERT INTO comment VALUES (3697,693,1301,'Charlie','Posted Solution Not Minimum','2003-03-30 06:19:56',3,'The posted solution requires 8 weighings even when it is assumed that the ancients knew they had 120 grams of clay to begin with. My first comment on this puzzle shows that with this assumption, the 5 weights can be produced in 6 weighings.\r\n\r\nIn the second step, after using the 1-g and 3-g weights together to measure out 4 g of clay, instead of weighing out another 4 g of clay and then another 1 g of clay, just use the original 1-g weight with the first 4 g measured to get 5 g of clay in one step. Then combine the 4+5 into a 9-g weight, rather than 4+4+1.\r\n\r\nLikewise, to get the 27-g weight just weigh out 13 grams once (not twice), then measure out 14 grams using the 1-gram weight and the 13 grams of clay on one side, and combine the 13+14 to get a 27-gram weight.\r\n\r\nThen with the assumption that these ancients actually KNEW they had 120 grams of clay, it\'s done with only 6 weighings, rather than 8.\r\n\r\nBut how did these ancients actually know they had 120 grams of clay to begin with?',NULL,0); INSERT INTO comment VALUES (3698,179,1822,'Tim Axoy','Dunno','2003-03-30 07:46:17',0,'Dunno.',NULL,0); INSERT INTO comment VALUES (3699,225,1822,'Tim Axoy','Dunno','2003-03-30 07:49:19',0,'Dunno.',NULL,0); INSERT INTO comment VALUES (3700,45,1822,'Tim Axoy','Of course not','2003-03-30 07:55:45',1,'It certainly is not an octagon.',96,0); INSERT INTO comment VALUES (3701,689,1822,'Tim Axoy','Timothy\'s and Urban\'s game','2003-03-30 08:02:08',0,'I love the name Timothy!!',NULL,0); INSERT INTO comment VALUES (3702,111,1822,'Tim Axoy','soluTion,not soluCion','2003-03-30 08:04:56',0,'NM',1813,0); INSERT INTO comment VALUES (3703,689,1822,'Tim Axoy','5-1','2003-03-30 11:24:55',3,'Of course,5 red and 1 blue.',NULL,0); INSERT INTO comment VALUES (3704,104,1822,'Tim Axoy','Simple','2003-03-30 11:28:01',0,'Simple!!!!!\r\nX-1',NULL,0); INSERT INTO comment VALUES (3705,689,1824,'Eric','Solution (don\'t peak!)','2003-03-30 11:57:32',3,'Basic algebra solves this one:\r\n\r\n1st die:\r\n5 red\r\n1 blue\r\nRequirements: matches = non-matches\r\n\r\nr = red sides of second die\r\nb = blue sides of second die\r\nr + b = 6\r\n(5 x r) red matches, (1 x b) blue matches\r\n(1 x r), (5 x b) = non-matches\r\n(note, fractions were removed as a function of the algebra for clarity)\r\n\r\n(5 x r) + (1 x b) = (1 x r) + (5 x b)\r\n5r + b = r + 5b\r\n5(6-b) + b = 6-b + 5b\r\n30 - 5b + b = 6 - b + 5b\r\n24 - 4b = 4b\r\n24 = 8b\r\nb = 3\r\n\r\n6 - 3 = 3 = r\r\n\r\nsecond die = 3 blue; 3 red\r\n',NULL,0); INSERT INTO comment VALUES (3706,266,1822,'Tim Axoy','-9 months','2003-03-31 01:25:38',4,'The son has not gotten born yet,but I do not know where the father is.\r\nWhere is he?',NULL,0); INSERT INTO comment VALUES (3707,485,1822,'Tim Axoy','Part 1,Reverses of squares','2003-03-31 02:36:06',2,'First,I reverse every two digits.\r\n01,04,09,16,25,36,49\r\nSecond,I see that these are the squares,so the next two reversed numbers are 64 and 81.\r\n\r\n\r\n\r\n',NULL,0); INSERT INTO comment VALUES (3708,485,1822,'Tim Axoy','Part 2,Reverse 64 and 81','2003-03-31 02:36:51',1,'Now,Ireverse 64 and 81 to get 46 and 18.',NULL,0); INSERT INTO comment VALUES (3709,211,1831,'gavin','a question of logic, my perception','2003-03-31 02:47:39',0,'We first must realise that a rubber band in this case is presumed to be oval, thus no end. So for the ant to reach the end, the rubber band must break. Which leads into the next assumption that the ant does not fall off the rubber band when it breaks. Having found data from www.chemheritage.org/EducationalServices/ faces/teacher/poly/activity/feat.htm , whichs shows in an experiment that a 10cm long rubber band breaks at 58.9 cm, I make the assumption that a 1 metre long rubber band breaks at 5.89 metres.\r\n\r\nNext; the lifespan of an \"ant\", roughly maxuimum being hammer.prohosting.com/~penz/encycl/lifespan.htm <\r\nAn ant can live up to 5 years, so\r\n\r\nThe rubber band will break at 5.89 meters and at 1 millimetre per second will take the ant 5890 seconds or 98 minutes and 10 seconds to reach the end of \"he\" doesn\'t fall off. The lifespan of an ant being 5 years, I say yes the ant reaches the end of the rubberband. :-)',NULL,0); INSERT INTO comment VALUES (3710,469,1831,'gavin','who lost in the transaction?','2003-03-31 03:32:20',0,'My answer is that 100 rupees was lost by whomever dropped the note on the park bench. The rest is a zero-sum game, no one wins, no one loses.',NULL,0); INSERT INTO comment VALUES (3711,234,1822,'Tim Axoy','Yes,good and bad','2003-03-31 04:23:33',0,'Marriage should be happy.\r\nYour Mother-in-law should not be a woman Hitler.\r\n\"Stop banging the pots\" is an anagram of \"The sap bangs toot gin.\"',3129,0); INSERT INTO comment VALUES (3712,702,1831,'gavin','solution?','2003-03-31 04:24:39',0,'The back of an open/closed sign eg like one hanging in a shop window',NULL,0); INSERT INTO comment VALUES (3713,689,1831,'gavin','i agree with montana hingis','2003-03-31 04:41:20',0,'regardless of no of colours on the first die there will be 3 blue, 3 red on the second',NULL,0); INSERT INTO comment VALUES (3714,701,1567,'Bryan','Zero?','2003-03-31 05:49:08',4,'I thought zero was not considered a whole number...',NULL,0); INSERT INTO comment VALUES (3715,34,1707,'Jonathan Waltz','well,','2003-03-31 08:55:08',0,'i see both points of view, that it would be an infinite game, and also the last unit left standing would be zero. on one hand, once a zero appears, it would make zeros out of all of the other numbers. even if you didn\'t make a zero with the multiplications, then the random digits would eventually turn up a 0, which is why i belive that levik even added that portion of the problem',NULL,0); INSERT INTO comment VALUES (3716,233,1707,'Jonathan Waltz','solution','2003-03-31 08:59:32',0,'well, always on a standard six sided die, opposite sides add up to seven, so 1 is paired with 6, 2 with 5, and 3 with 4. that means that one from each pair must be showing, and the only one number that doesn\'t have a dot in a corner is one, so therefore six must be represented on this picture.',NULL,0); INSERT INTO comment VALUES (3717,705,1301,'Charlie','solution','2003-03-31 09:10:40',3,'Three of the dodecahedron’s pentagonal faces meet at each vertex. Erect a small sphere around one vertex. Each of the three faces that meet there intersects the circle in a segment of great circle arc, forming a spherical triangle. The arc length of each side of this spherical triangle is the angle at the vertex of the regular pentagon, which is (5-2)*180/5 = 108°. The angles between the sides of the spherical triangle are equal to the dihedral angles between the faces of the dodecahedron, so we must merely solve for the angles of the spherical triangle. That can be accomplished through the law of cosines for spherical triangles (i.e., in spherical trigonometry):\r\n\r\ncos a = cos b cos c + sin b sin c cos A, where lower case represents a side and upper case an angle, and side a is opposite angle A. \r\n\r\nIn this case all the sides are 108°, so cos 108 = (cos 108)^2 + ((sin 108)^2) cos x. Therefore cos x = (cos 108 – (cos 108)^2) / (sin 108)^2 = -.447213595499954, so x = 116.5650511770777 degrees, which is the answer, to the precision shown.\r\n',NULL,0); INSERT INTO comment VALUES (3718,705,1567,'Bryan','re: solution','2003-03-31 09:37:00',0,'Good job, Charlie! Your solution (correct, BTW) is just one fourth as long as mine. It helps that you used spherical trig; I used planar trig. Heck, I never even heard of spherical trig! Guess I have more reading to do. lol',3717,0); INSERT INTO comment VALUES (3719,705,1301,'Charlie','re(2): solution','2003-03-31 10:21:09',0,'When I first heard of spherical trigonometry, by reading Lancelot Hogben\'s Mathematics in the Making (illustrated with lots of pictures), I wondered why it wasn\'t covered in H.S. trig courses (at least in the U.S.). It\'s of much use in converting astronomical coordinates, finding times of sunrise/set, etc. It seems a neglected area, as is the subject of continued fractions.',3718,0); INSERT INTO comment VALUES (3720,685,1,'levik','re(2): oopss... I forgot...','2003-03-31 10:42:30',0,'Gautam > I will soon post the solution.\r\n\r\nHow soon? I\'m kinda anxious to see it myself.',3634,0); INSERT INTO comment VALUES (3721,483,1834,'hj','possible sol','2003-03-31 11:42:38',3,'(a) 11\r\n(b) 10',NULL,0); INSERT INTO comment VALUES (3722,469,1834,'hj','possible sol','2003-03-31 11:54:37',3,'you lost 100 rupees, the rupees you borrowed the lady',NULL,0); INSERT INTO comment VALUES (3723,688,1126,'Bedhed','i think so...','2003-03-31 12:12:32',1,'i think there is either one of 2 solutions:\r\neither the music, assuming it was extremely loud, caused strong enough vibrations to break down the emulators in the yolk and caused it to bind to itself, or...\r\nthe heat of all the bodies, with the eggs being exposed to it for over an hour, began to go rotten, as sam\'s last name suggests',NULL,0); INSERT INTO comment VALUES (3724,488,1072,'Alan','Crazy guess','2003-03-31 13:39:12',0,'could it be grammer? grammar has spelling but there are almost always exceptions to every rule.',NULL,0); INSERT INTO comment VALUES (3725,672,1838,'Linda','just a thought','2003-03-31 15:08:59',0,'but what if the swords bearers don\'t strike the sheilds? like... if they hit their feet or something? the sheild folks can only protect so much of their body at once right? so like... if the sword guys surrounded the shelid guys, they could manage to get a few people down right? they could slowly pick away at them... and then they\'d win. But thats what i think :D',NULL,0); INSERT INTO comment VALUES (3726,488,1253,'Brian Nowell','Remember Me','2003-03-31 15:16:14',0,'This site has many more of this.\r\n\r\nhttp://www.xs4all.nl/~jcdverha/scijokes/11_2.html#subindex\r\n\r\nThis is a Mneumonic for the value of Pi.\r\n3.14159265 .... etc',NULL,0); INSERT INTO comment VALUES (3727,701,1767,'Fernando','re: Zero?','2003-03-31 16:09:41',0,'well, if i\'m not wrong, whole numbers are integer numbers. Integer numbers are:\r\n
\r\n...., -3, -2, -1, 0, 1, 2, 3, .........',3714,0); INSERT INTO comment VALUES (3728,701,775,'Cory Taylor','re(2): Zero?','2003-03-31 17:18:41',0,'In Canadian Classrooms anyways (there are discrepancies between systems unfortunately), the set of \"Natural\" numbers is more commonly known as counting numbers, Whole numbers include the counting numbers and zero (easily remembered by considering the \"o\" in whole as a zero), and integers are counting numbers, zero and the negatives of the counting numbers. I apologize if this nomenclature is not standard in the US or elsewhere.',3727,0); INSERT INTO comment VALUES (3729,469,979,'Ravi Raja','re: The Solution','2003-03-31 23:25:39',0,'Charles, you have mentioned the following in your comment: \"The guy who discovered the bill was counterfeit could potentially now go on to buy something else with it, since its obviously a good enough forgery for four people not to catch it.\" But because of the same reason his neighbour paid her the same amount borrowed from him using the same counterfeit note. So, what happens if everytime he goes on to buy something and the note comes back to him after a few (after a finite number of) transactions ?',3660,0); INSERT INTO comment VALUES (3730,469,979,'Ravi Raja','re: who lost in the transaction?','2003-03-31 23:34:40',0,'Okay gavin please tell me one thing, that suppose you had a \"COUNTERFEIT\" 100 Rupee note and you left it or misplaced it or dropped it somewhere, then will you ever say that you lost 100 Rupees ? ',3710,0); INSERT INTO comment VALUES (3731,469,979,'Ravi Raja','re: possible sol','2003-03-31 23:37:27',0,'In that case you lost 100 Rupees hj but what do you have to say about the money that you were supposed to pay to your plumber ?',3722,0); INSERT INTO comment VALUES (3732,483,979,'Ravi Raja','re: possible sol','2003-03-31 23:42:14',0,'I am sorry hj, this is not the correct solution. If you say that this is correct, then can you please show it how you arrived at it ?',3721,0); INSERT INTO comment VALUES (3733,51,1822,'Tim Axoy','1/18','2003-04-01 02:46:45',3,'The father gave the sons 9/18+6/18+2/18=17/18 with 1/18 not given.',NULL,0); INSERT INTO comment VALUES (3734,123,1707,'Jonathan Waltz','easy','2003-04-01 03:25:45',0,'well, it takes three minutes for one to split into two, and since that is what we start with for our second problem, it should take 57 minutes, because we subtracct the amount of time needed to get from 1-2 amoebas. and now, for another question. what does a glass full of amoebas look like?',NULL,0); INSERT INTO comment VALUES (3735,154,1707,'Jonathan Waltz','open a new mint','2003-04-01 03:44:29',0,'if they know how much money is in the safe, and have records of who the money goes to, then they could just blow the money, and print out all new money, and hand that to the owner, taking those certain bills out of circulation, as well as existance.',NULL,0); INSERT INTO comment VALUES (3736,690,1072,'Alan','guess','2003-04-01 04:04:02',3,'The oil. If you dump the steel in the water it woulkd actually heat up the water to water vapour before it makes contact with the water thus being cooled after a slight delay. Where as oil has a higher boiling temperature (i think) and wil make contact with the steel before the water.',NULL,0); INSERT INTO comment VALUES (3737,690,1517,'jude','I would say','2003-04-01 04:11:22',1,'bucket \'o oil. Assuming both buckets sizes and quantities of water/oil are the same, the oil should not be as effected by the heat as quickly as the ice water.\r\n\r\nThere\'s no mention as to the type of oil, but I\'m thinking heavy motor oil. I think if you use a lighter oil (like for cooking) the times might be closer.',NULL,0); INSERT INTO comment VALUES (3738,99,1707,'Jonathan Waltz','bigger than nicks','2003-04-01 04:21:59',0,'i believe that i have found a bigger number than nicks entry of \"(.1^-2e3)!\" if you consider π (pie) and e as matematical symbols, then couldn\'t you do this:\r\n(.1^((-2e3)πe))!\r\nif it is, you may have to change the verdict. ',NULL,0); INSERT INTO comment VALUES (3739,99,1707,'Jonathan Waltz','re: bigger than nicks','2003-04-01 04:23:41',0,'though this is bigger than his, i must give most of the credit to nick for coming up with the base part of the equation, i just added pie and e to his equation, so if you come to a verdict that pie and e can be used, give him credit also',3738,0); INSERT INTO comment VALUES (3740,99,1707,'Jonathan Waltz','re(2): bigger than nicks','2003-04-01 04:31:30',0,'you can discount everything in my past two comments, i am sorry, i didn\'t read all of the comments, and missed the fact that we discounted pi and e because they are numbers, merely in a differen\'t form.',3739,0); INSERT INTO comment VALUES (3741,690,775,'Cory Taylor','material property','2003-04-01 04:38:05',0,'Materials have many properties that are unique to them, and help people separate or distinguish materials from one another. One of these properties is called specific heat capacity, and it refers to the amount of energy that is required to affect a specific temperature change to a specific volume (I believe in SI units it is the number of Joules required to change 1 gram by 1 degree). This is the property which will govern this situation, as the process of cooling is in fact simply an energy transfer, from the hot steel to the cool liquid.\r\n\r\nI am not aware of the relative values of the specific heat capacioties of various oils or water, but I do know that the value of water is considered very high in general, so I would suspect that the values of most oils (if not all) would be less than that for the water. This leads to my belief that water would be a better coolant in this case. Further to this is the temperature difference. Thermodynamics says that the rate of cooling between materilas of different temperatures is proportional to the temperature difference. As the oil is a t room temperature and the water is at the freezing point (20 C less), the rate of cooling would initially be faster based on this characteristic when using the water.\r\n\r\nFinally, the actual material used since man began turning iron into steel is in fact water, done in a process called (if I remember coprrectly) Martinizing. This process makes the steel stronger but less durable (flexible) than it would be if slow-cooled.',NULL,0); INSERT INTO comment VALUES (3742,99,775,'Cory Taylor','re: bigger than nicks','2003-04-01 04:47:59',0,'also this method wouldn\'t work, as the factorial can only operate on positive integers. Nicks prefactorial number is the same as 10^8, wheras yours is 10^68.3178..., which is certainly smaller (so far so good), but the result is not an integer, so that factorial cannot be computed.\r\n',3738,0); INSERT INTO comment VALUES (3743,99,775,'Cory Taylor','bigger than Nicks the sequel','2003-04-01 04:51:47',0,'So nick created this monster number using \"-2^3\", but cannot this number become larger by switching the 2 and the 3?',NULL,0); INSERT INTO comment VALUES (3744,114,1301,'Charlie','Excel Agrees','2003-04-01 05:06:02',3,'The Excel solver function agrees with the posted answer of the minimum P being 7.5, when x=y=z=0.5, when using the constraints given, though x>0 has to be coded as x>=.0000001, etc.',NULL,0); INSERT INTO comment VALUES (3745,690,1301,'Charlie','Perhaps...','2003-04-01 05:19:29',1,'Perhaps he should dump it in water first, to make use of its high specific heat and heat of vaporization, and then when all the water has boiled away, use the oil.',NULL,0); INSERT INTO comment VALUES (3746,83,1707,'Jonathan Waltz','solution i think','2003-04-01 05:40:55',0,'well, since we are looking for the least amount of assistants, i will start with one assisstant. the only way that he would be any good is if he turned back after the first day, and the general could only carry one more days worth of supplies. so if we go with two, then you could have one turn back after the first day, leaving the general and the other assistant with four days worth each. then, after the second day, the second assistant turns back leaving the general with four days worth of food, which is enough, so the answer is 2',NULL,0); INSERT INTO comment VALUES (3747,469,1707,'Jonathan Waltz','re(2): who lost in the transaction?','2003-04-01 05:51:26',0,'if you were going to use that 100 rupee note, and could have used it somewhere, and you didn\'t know that it was conterfeit, then yes, they would have lost. another thing, if the person purposely put it down because he found out that it was fake, he would have lost 100 rupees when he was paid that at some other time, or if he gave change for it.',3730,0); INSERT INTO comment VALUES (3748,132,1707,'Jonathan Waltz','oh, too easy','2003-04-01 06:01:12',0,'16, 66',NULL,0); INSERT INTO comment VALUES (3749,488,1842,'Mick','Answer','2003-04-01 07:14:28',0,'I think it might be a start because the key-words are celestial and relate.≥∞±±∑∞≤<²√',NULL,0); INSERT INTO comment VALUES (3750,250,1707,'Jonathan Waltz','re: surely a paradox','2003-04-01 07:33:34',0,'just because something is false, doesn\'t mean the exact opposite is true. just like saying he runs everywhere is false, but he runs sometimes is true, so therefore, the statement could be false, he doesn\'t lie all of the time, but he does lie.',1513,0); INSERT INTO comment VALUES (3751,689,1843,'Luke','Solution to similar problem about coins','2003-04-01 07:35:32',0,'If you have a collection of coins, you can use the entire collection as one coin by flipping them all, and announcing heads if an even number of heads turn up, tails otherwise.\r\n\r\nRESULT: The entire collection of coins simulates a fair coin precisely if any one of the coins is fair.\r\n\r\nPROOF: Given a coin, let the BIAS be the probability of heads minus the probability of tails. This is a number between -1 and 1 inclusive. \r\n\r\nThe BIAS is zero if the coin is fare. The BIAS of the simulated coin is equal to the products of the BIASes of the coins in the collection.\r\n\r\nThis can be seen as a negative result: you cannot create a fair coin this way without having a fair coin to start with. However since all the BIASes are numbers in the range [-1,1], the more coins you use, the less Bias there will be.',NULL,0); INSERT INTO comment VALUES (3752,692,1301,'Charlie','In vacuum or in air...','2003-04-01 09:09:11',3,'In a vacuum it doesn’t matter what the weight of the object is. At 10 m/s, with gravity accelerating it at 9.8 m/s^2, the object will take 10/9.8 seconds to reach its apex. At an average speed of 5 m/s, it will have traveled 5.102 m up.\r\n\r\nIn air, at a density of 1.24 kg/m^3, atmospheric resistance, in general, but dependent on shape, would amount to 1.24 A V^2 / 2, where A is the cross sectional area of the object and V is the speed at which it is going, directed opposite to the current motion. When A and V are measured in the MKS system, the force will be in kg-m/s, or Newtons.\r\n\r\nIf the object is a bowling ball with a diameter of 20 centimeters, being a sphere the air resistance is only about 1/2 that mentioned above, and the ball reaches 5.031 meters at t=1.01 seconds.\r\n\r\nIf the object has a more irregular shape and is say 1 square meter in cross sectional area, it will get only 2.914 meters up, at t= 0.71 seconds.\r\n\r\nThese are of course approximate and based on a numerical integration.',NULL,0); INSERT INTO comment VALUES (3753,692,1567,'Bryan','Conserve energy','2003-04-01 09:18:12',0,'When the 7kg object is released (or any object of mass m, for that matter), it has kinetic energy Ek=.5mv², where v is its velocity of 10 m/s. When the object attains its maximum height, it\'s velocity (and therefore its kinetic energy) will be zero, but what it has instead is potential energy Ep=mgh, where h is its height above a reference point. Since energy is conserved between these two states, we know that
Ek=Ep
.5mv²=mgh
Solving for h,
h=v²/2g
h=10²/(2*9.8)
h=5.1 m
So, regardless of its mass, any object thrown upward at a rate of 10 m/s will rise 5.1 m above the height at which it was released. This calculation ignores losses to wind resistance etc., but these are negligible for this scenario.',NULL,0); INSERT INTO comment VALUES (3754,672,1844,'Brian Allen','request for clarification','2003-04-01 09:19:53',0,'Can I assume that we are operating under the definition that a shield which has been sliced through is \"destroyed\"?\r\n\r\nIf the Shield\'s property of \"cannot be destroyed\" is clarified as always being able to repair itself, it would still leave open the possibility of the sword slicing through it freely wouldn\'t it? (almost as if the shield were intangible at any point it was in contact with the sword)',NULL,0); INSERT INTO comment VALUES (3755,692,1301,'Charlie','re: In vacuum or in air...','2003-04-01 09:20:25',0,'The numerical integration:\r\nDEFDBL A-Z \' this version is for the larger object\r\nCLS\r\npi = ATN(1) * 4\r\nA = 1\r\nV = 10\r\nm = 7\r\np = 0\r\ndt = .0001\r\nDO\r\n acc1 = -9.8\r\n acc2 = -1.24 * A * V * ABS(V) / m\r\n acc = acc1 + acc2\r\n p = p + dt * (V + V + dt * acc) / 2\r\n IF p > pMax THEN pMax = p\r\n V = V + dt * acc\r\n t = tPrev + dt\r\n IF INT(t * 10) > INT(tPrev * 10) THEN\r\n PRINT USING \"##.## ##.###\"; t; p\r\n END IF\r\n IF p < pMax AND fl = 0 THEN\r\n PRINT USING \"##.## ##.###\"; tPrev; pMax\r\n fl = 1\r\n END IF\r\n tPrev = t\r\nLOOP UNTIL p <= 0\r\nPRINT USING \"##.## ##.###\"; t; p\r\n\r\nFor the bowling ball, we set\r\nA= pi * (1 / 10) ^ 2 due to its size\r\nand\r\nacc2 = -.62*A*V*ABS(V)/m due to its spherical nature.',3752,0); INSERT INTO comment VALUES (3756,99,1575,'DJ','Hmm','2003-04-01 12:53:10',0,'',NULL,0); INSERT INTO comment VALUES (3757,692,1846,'Timothy','Gravity','2003-04-01 13:00:50',0,'Gravity goes at the speed you said.',NULL,0); INSERT INTO comment VALUES (3819,711,1301,'Charlie','solution','2003-04-04 10:52:10',3,'The first thing to do is to find the radius of the ball. A right triangle can be formed from bottommost point in the depression to the point 1 cm above that, at the center of the circle made at top-of-jello level, along a radius of that circle to some point on that circle, and then straight back to the bottom point. It has legs of 1 cm and 3 cm, and so the hypotenuse, extending from the bottom of the depression to the rim is √10 in length\r\n\r\nThe center of the whole ball lies along a perpendicular bisector of that hypotenuse where it meets a vertical line above the center of the depression. That line, an extension of the 1-cm side of the first rt triangle, forms a radius of the sphere and is the hypotenuse of a larger rt triangle similar to the first as they share a common angle at the bottom of the depression. The shorter side of the new triangle is half the hypotenuse of the old: (√10)/2. As it is similar, the ratio of the shorter leg to the hypotenuse is still √10, so the hypotenuse is ((√10/2)(√10) = 5, which is the outer radius of the ball, which we\'ll call R.\r\n\r\nAt this point we can either use a pre-built formula for the volume of the cap of a sphere (which is what the depression is) or use calculus directly. The formula is (1/3)πh²(3R-h), where h is the 1-cm height of the cap. This comes out to 14π/3.\r\n\r\nTo be continued due to lack of space...',NULL,0); INSERT INTO comment VALUES (3759,488,1575,'DJ','oh?','2003-04-01 14:15:55',0,'It\'s a device for remembering the digits of pi.\r\nThe number of letters in each word represents a digit (sir=3, I=1, bear=4, a=1, rhyme=5, etc). This verse gives us 21 digits (20 decimal places). There are also two more lines that I have seen to this mnemonic:\r\n\r\nOr locate they who can cogitate\r\nAnd so finally terminate. Finis.\r\n\r\nOr, 26433832795, giving us pi to 31 places:\r\n3.1415926535897932384626433832795.\r\n\r\nInteresting to note: the next digit is zero, usually represented by a ten-letter word.\r\n\r\n=)',NULL,0); INSERT INTO comment VALUES (3760,692,1549,'Lucifer','Physics','2003-04-01 14:33:01',0,'Im glad people are solving it, its an interesting problem. The reason I didnt specify air resistance is because both cases can occur, and I wanted to spark discussion on it. What\'s interesting as well, is when something falls from a vacuum into an air occupied zone.',NULL,0); INSERT INTO comment VALUES (3761,702,1575,'DJ','ehh...','2003-04-01 14:41:11',0,'',NULL,0); INSERT INTO comment VALUES (3762,702,1575,'DJ','ehh...','2003-04-01 14:52:10',0,'A circle (or any other shape, for that matter)? When the shape is closed, it has no endpoints and could be considered an open set of points. But when the shape is open or \'broken,\' it has two included endpoints, which are then a closed set of points.\r\n\r\nYeah, it\'s a stretch...',NULL,0); INSERT INTO comment VALUES (3763,685,834,'Gautam','re(3): oopss... I forgot...','2003-04-01 16:28:57',0,'Hi Lev,\r\n The solution is posted...',3720,0); INSERT INTO comment VALUES (3764,432,1847,'Eirene','solution','2003-04-01 18:27:17',0,'it was quite easy, it think... ALan stole the money... that would make him a liar together with Carl leaving Barry the sole soldier... right?',NULL,0); INSERT INTO comment VALUES (3765,488,1253,'Brian Nowell','re: oh?','2003-04-01 18:53:27',0,'Please note my \"Remember Me\" comment. Check this out for more of the same.',3759,0); INSERT INTO comment VALUES (3766,692,979,'Ravi Raja','Solution','2003-04-01 20:10:03',1,'We first use the formula:\r\nV = U - gT, where U is the initial velocity, V is the final velocity, T is the time of flight of the object and g is the acceleration due to gravity.\r\nHere, V = 0, U = 10 and g = 9.8\r\nSo from here we can solve for T and then using the formula:\r\nH = U*T - (1/2)*g*(T^2), we can calculate the required height.\r\nIs it correct ?',NULL,0); INSERT INTO comment VALUES (3767,692,1183,'fwaff','re: Solution','2003-04-01 20:32:00',3,'Yep, that\'s one way of getting it Ravi. As I\'m sure you know you\'ve used the first two equations of motion, alternatively you can use the third equation of motion directly: \r\n\r\nv^2 = u^2 + 2as\r\nWhere v is the final velocity, u is the initial velocity, a is acceleration and s is distance.\r\n\r\nSolving for v=0, u=10, a=-9.8 gives s = 5.102m\r\n\r\nClearly this assumes that gravity is the only factor considered regarding the deceleration of the object. When air friction is considered then you get Charlie\'s more complex answer. To further complicate Charlie\'s answer you could also introduce spin to the object......\r\n\r\n\r\nOne minor point of pedantry, the gravitational constant in the question should read -9.8m/s/s or -9.8m/(s^2) as it is an acceleration (-9.8m/s is a velocity).',3766,0); INSERT INTO comment VALUES (3768,489,158,'Ender','thoughts','2003-04-02 02:51:03',0,'Shouldn\'t there be an added stipulation that n is greater than 1? If n equals 1, then the solution is trivial: n=1 and m = whatever year they were born in plus one.\r\n\r\nAlso, m = 1 will cause the equation to return negative values for any positive n, so since the year is positive, m = 1 can be eliminated.\r\n\r\n',NULL,0); INSERT INTO comment VALUES (3769,489,1301,'Charlie','Computed','2003-04-02 03:22:19',3,'m, n and year:\r\n3 7 1844\r\n2 11 1927\r\n\r\nfound by\r\n\r\nCLS\r\nn = 4\r\nDO\r\n FOR i = 1 TO n / 2\r\n j = n - i\r\n li = LOG(i) * j\r\n IF li < 55 THEN\r\n y = i ^ j - j ^ i\r\n IF y > 1700 AND y < 1980 THEN\r\n PRINT i, j, y\r\n END IF\r\n END IF\r\n NEXT\r\n n = n + 1\r\nLOOP\r\n',NULL,0); INSERT INTO comment VALUES (3771,703,1567,'Bryan','How about ...','2003-04-02 07:49:53',0,'Weigh 1 pearl from bag 1\r\n100 pearls from bag 2\r\n10,000 pearls from bag 3\r\n1,000,000 pearls from bag 4\r\n100,000,000 pearls from bag 5
\r\nIf every bag held pearls from blue oysters, the total weight should be 1010101010 grams (\"10\" repeated 5 times). If any of the pairs of digits reads 09 or 11, the corresponding bag holds fakes or pearls from black oysters, respectively. There are other solutions that use far fewer pearls, but this one is easy to explain.',NULL,0); INSERT INTO comment VALUES (3772,703,1301,'Charlie','conserving pearls','2003-04-02 09:12:36',3,'On the scale, place 1 from bag 1, 3 from bag 2, 9 from bag 3, 27 from bag 4 and 81 from bag 5. From the total weight, subtract the 1089 that the total would be if they were all fake.\r\n\r\nExpress the result in base 3 numbers. The first position on the right contains a 0, 1 or 2 depending on whether bag 1 contained fake pearls or pearls from blue or black oysters respectively. The next position to the left (the 3\'s position) has the same significance for the second bag. The next position to the left (the 9\'s position) does so for the third bag, etc.\r\n\r\nTo convert a number to base-3 (ternary), divide the number by 3 and place the remainder on the extreme right of your answer. Take the quotient and divide it by 3. Place the remainder just to the left of the preceding remainder, and continue with the new quotient. Keep repeating until you get a quotient of zero (of course place the corresponding remainder on the left of the answer).\r\n\r\nFor example, if the total weight were 1300 grams, you\'d subtract 1089, giving 211. Convert this to ternary: 211/3 = 70 w/rem 1; 70/3 = 23 w/rem 1; 23/3 = 7 w/rem 2; 7/3 = 2 rem 1; 2/3 = 0 w/rem 2. Thus the ternary representation is 21211, and the 5th and 3rd bags contain pearls from black oysters and the rest contain pearls from blue oysters, and there were no fakes.',NULL,0); INSERT INTO comment VALUES (3773,17,1846,'Timothy','No way!','2003-04-02 11:12:59',0,'5*4 is not 10!',NULL,0); INSERT INTO comment VALUES (3774,703,1846,'Timothy','Infinity','2003-04-02 11:15:19',0,'Is it infinity?',NULL,0); INSERT INTO comment VALUES (3775,432,1846,'Timothy','Alan','2003-04-02 11:41:13',3,'Since Barry contradicts Carl,one is a knight and one is a liar.\r\nIn either case,Alan is lying and guilty.\r\nBy the way,Barry is a knight.',NULL,0); INSERT INTO comment VALUES (3776,469,979,'Ravi Raja','re(3): who lost in the transaction?','2003-04-02 22:46:07',0,'Yes I agree Jonathan that if the person who left it has given any change for that note (counterfeit), then obviously he loses 100 Rupees but nothing of that sort is mentioned in the given problem. ',3747,0); INSERT INTO comment VALUES (3777,469,979,'Ravi Raja','re(3): who lost in the transaction?','2003-04-02 22:51:38',0,'One more thing Jonathan, as you have stated in your comment: \"if you were going to use that 100 rupee note, and could have used it somewhere, and you didn\'t know that it was conterfeit, then yes, they would have lost\", is also correct unless the others use the note in a similar manner. I mean purchasing something worth Rupees 100 using that note. ',3747,0); INSERT INTO comment VALUES (3778,469,979,'Ravi Raja','Regarding The Solution','2003-04-02 23:00:41',0,'Levik you had asked me to make a few changes in the solution of this problem and I had done that and at the same time I had asked you to check whether the changed solution is correct or not but unfortunately I did not get any replies from you regarding this. I understand that may be that you did not notice it after that or may be due to some other reasons but Please if you see this then please reply to this comment of mine and do let me know if I am supposed to make any more changes in this problem\'s solution. Thank You.',NULL,0); INSERT INTO comment VALUES (3779,686,1821,'montana hingis','ok, a rly bad guess...','2003-04-03 01:46:32',0,'cuz he was the murderer/victim?',NULL,0); INSERT INTO comment VALUES (3780,686,1821,'montana hingis','re: ok, a rly bad guess...','2003-04-03 01:48:38',0,'sorry, i meant murderer. (couldn\'t have continued on if he\'s dead ;)',3779,0); INSERT INTO comment VALUES (3781,686,1183,'fwaff','Solution','2003-04-03 02:06:37',3,'Because the police aren\'t particularly interested in ornithology!\r\n\r\nMurder is the collective pronoun for crows. Clem saw a murder of crows and in the next field he could well have seen a flock of sheep.\r\n\r\nLet\'s just hope that Clem doesn\'t work with a boredom of accountants or a confusion of planners.',NULL,0); INSERT INTO comment VALUES (3782,686,979,'Ravi Raja','I Think....','2003-04-03 03:00:49',1,'Was it the shooting of some film/movie in which the hero or any actor in the movie was murdering some other actor. Thus everything being just artificial (I mean ACTING) Clem did not notify the police about this.',NULL,0); INSERT INTO comment VALUES (3783,686,103,'friedlinguini','re: Solution','2003-04-03 03:19:38',3,'<simpsons>\r\nMarge: I\'m not comfortable with a gang of crows living in our bedroom!\r\nHomer: Murder, honey. It\'s a murder. A group of crows is called a murder.\r\n</simpsons>\r\n\r\n\'nuff said.',3781,0); INSERT INTO comment VALUES (3784,483,1854,'Manoj Nair','i got it!','2003-04-03 03:21:56',3,'hello,\r\ni think its the possible solution.\r\nA = original number ( and the number the first man dealt with) = 5p+1\r\nRemaining number after the first man hides his share = 4p = 5q+1\r\nprocedding this way, 4q=5r+1\r\n4r=5s+1\r\n4s=5t+1\r\nand of course, 4t=5u (considering the second case)\r\nby solving all these equations, we will get the final equation as,\r\noriginal number, A = (15625u+8404)/1024, where \'A\' and \'u\' should be integers.\r\nI solvedit by iteration and got the value as,\r\nu=204 and A=3121\r\n\r\nin the first case, only the last equation changes as, 4t=5u+1\r\nsolving again, we get, A = (15625u+11529)/1024\r\nwhere \'A\' and \'u\' should be integers\r\nagain, by iterations, i got the values as,\r\nu=1108 and A =16918\r\n\r\nI would like know whether it\'s the right answer or not...also, i wish to know whether Ravi Raja belongs to Kerala or not, as I\'m a keralite...thank you',NULL,0); INSERT INTO comment VALUES (3785,483,979,'Ravi Raja','re: i got it!','2003-04-03 03:41:32',0,'Manoj your answer 3121 is correct but not the other one, which is supposed to be equal to 15621 and not 16918. So please do check your solution. \r\n\r\nManoj, I am from Gujarat (I mean I am a gujarati) but I stay in Calcutta (West Bengal).',3784,0); INSERT INTO comment VALUES (3786,686,1686,'DuCk','Does this count???','2003-04-03 04:50:15',0,'Well, if he\'s in the country he could have seen one animal kill another for food. I\'m not certain that an animal can commit a murder, but it\'s just something that crossed my mind. I\'m always looking for animals when I\'m in the country. ',NULL,0); INSERT INTO comment VALUES (3787,684,1854,'Manoj Nair','9 persons could be saved!','2003-04-03 04:53:50',3,'Hello i got a nice way out of this puzzle. here is it...\r\nNOTE : i\'m giving 1....10 for persons from last to front\r\nas somebody said earlier 1 will say BLACK iff he sees odd number of blacks, and he will say WHITE iff he sees odd number of whites (either will be the actual case, as he can see only 9 hats. so ther is no possibility of two odds)\r\nI\'m beginning with a hypothetical condition of 7W (7 white hats) and 2B(2 black hats) in front of 1. so he will say W. (he may get killed or may be saved). then, 2 can see either 7W+1B or 6W+2B. If it\'s the first case, he will definetley say his hat as B, to make B to an even mumber. If it\'s the second case, he will say W to make W an odd number.\r\nwe can proceed further with the first case (2 sees 7W+1B and tells as B). here 3 can have two probabilities - he can see either 7W or 6W+1B). If it\'s 7W, he will add one B to it, as identified by 2 as the colour of his cap. so it becomes 7W+1B. now both W and B became odd numbers. actually this was not the case. so he will say B as the colour of his hat, to make B an odd number. Again, if it\'s 6W+1B, he will add B to it as said by 2. then it becomes 6W+2B. to make W an odd number, he will say W as the colour of his hat.\r\nI think there is no need to explain it further. So all the 9 people (from 2-10) can say the colour of their hats correctly and escape from the mouth of the monster. 1 has a probaility of 50% to escape.\r\nI think it makes a reasonable solution. If there is anything wrong in this, plz feel free to contact.\r\nmanojezz@yahoo.co.in',NULL,0); INSERT INTO comment VALUES (3788,686,1846,'Timothy','The murderer','2003-04-03 06:01:42',0,'Clem was the murderer!',NULL,0); INSERT INTO comment VALUES (3789,61,1846,'Timothy','Saturday','2003-04-03 06:20:43',3,'The knight had a horse named Saturday.',NULL,0); INSERT INTO comment VALUES (3790,281,1846,'Timothy','Author unknown','2003-04-03 06:25:58',4,'Why do you put author unknown?\r\nWhy not Friedlinguini?',NULL,0); INSERT INTO comment VALUES (3791,686,1645,'luvya2003','re: Solution','2003-04-03 11:07:43',0,'sounds right to me',3781,0); INSERT INTO comment VALUES (3792,24,1645,'luvya2003','re(4): the solution posted is WRONG!!!!','2003-04-03 11:19:32',0,'In PROPER American English, \"and\" reprsents a decimal point, but most Americans say \"point.\" Even though I\'m not very grammar oriented, I thought I should point out the meaning of \"and\" in American English. Also in PROPER American English, numbers after decimal are said different. \r\nFor example, 1.4 is said \"one and four tenths.\"',3662,0); INSERT INTO comment VALUES (3793,707,1575,'DJ','some kind of start...','2003-04-03 13:07:39',1,'This type of multi-level logic problem used to make several appearances in Games magazine. They would always supply a chart to use, which is helpful in exclusive-elmination logic problems. I created one to print off and write on, and then thought, hey, maybe it\'ll make it easier for someone else to use, too. Unless, of course, all you geniuses come up with some super simple way that solves this (I haven\'t even consider the actual clues yet). Anyway, I uploaded it to http://www.clarkson.edu/~broadbdj/logic.doc in Word format. I was going to make a neat little javascripted page with a table on it you could click on to figure it out...but we don\'t see enough of these types of problems, and it would be more trouble than it\'s worth.\r\n\r\nOkay, now to start figuring out the problem!\r\n\r\n=)',NULL,0); INSERT INTO comment VALUES (3794,117,1567,'Bryan','Trial and error','2003-04-03 13:15:34',0,'For what it\'s worth,
Draw an arc centered on angle A
Set the compass to a very short arc
Place the point of the compass on the intersection of the first arc with one ray of A
Mark off the length of the short arc on the first arc
Mark a second short arc off the end of the first, and a third off the second
If the third short arc doesn\'t exactly intersect the other ray of A, adjust your compass and try again.
When the three small arcs exactly extend along the first arc from ray to ray, you have the points through which you can now draw your trisecting lines.
There may or may not be a more formal way to solve this, but with a sharp pencil lead, this is as accurate a method as any.',NULL,0); INSERT INTO comment VALUES (3795,707,1861,'john','Chart 2 Hey DJ','2003-04-03 14:47:42',0,'Hey DJ\r\n\r\nI made a chart too, using excel though. I maitained the spacial logic and numbered the floors from 5 to 1 instead of 1 to 5 and the floors from a to b horizontally. I used floors as my main horizontal row and apt letter as my main vertical column. (instead of the names, which in some ways may be easier too). It can help in the logic. I started like yours but screwed up my logic, I think this will help. Of course once you make one mistake early, it can screw up everything else.',NULL,0); INSERT INTO comment VALUES (3796,218,1861,'john','Re: solution','2003-04-03 16:22:31',0,'The problem does not state that only one bag is fake therefore, we need to add that if the weight comes to 303 grams i.e. 7 grams light that must mean bags 1,2,and 3 are fake (1+2+4=7) or any other odd combination i.e. 18 means bags 5 and 2 are fake etc. etc. alll possible combinations can be solved\r\n',NULL,0); INSERT INTO comment VALUES (3797,686,1862,'mary','answer','2003-04-03 17:56:46',0,'a murder of crows',NULL,0); INSERT INTO comment VALUES (3798,702,1862,'mary','haha','2003-04-03 17:58:35',0,'a vending machine food portal',NULL,0); INSERT INTO comment VALUES (3799,429,1862,'mary','answer','2003-04-03 18:01:33',0,'the ice was poisoned and didn\'t melt until later',NULL,0); INSERT INTO comment VALUES (3800,707,1821,'montana hingis','just want to clarify sth','2003-04-03 18:05:04',0,'in the puzzle, there are 5 occupations given so that means that no one is retired, right? then they are all under 70, and the youngest man is 12. How can he be working?',NULL,0); INSERT INTO comment VALUES (3801,427,1862,'mary','','2003-04-03 18:05:11',0,'credit card?\r\n',NULL,0); INSERT INTO comment VALUES (3802,707,1821,'montana hingis','another point','2003-04-03 18:10:18',0,'when you say \"below\" does it mean one floor below or just anywhere below? and the same with \"right/left of\".',NULL,0); INSERT INTO comment VALUES (3803,383,1862,'mary','garr','2003-04-03 18:14:19',0,'snowmen don\'t have necks',NULL,0); INSERT INTO comment VALUES (3804,382,1862,'mary','?','2003-04-03 18:18:12',0,'bodies of water, ocean sea..',NULL,0); INSERT INTO comment VALUES (3805,379,1862,'mary','guess','2003-04-03 18:23:20',0,'germ, bacteria, virus',NULL,0); INSERT INTO comment VALUES (3806,378,1862,'mary','durh','2003-04-03 18:25:35',0,'a coffin/casket',NULL,0); INSERT INTO comment VALUES (3807,686,1859,'Quicksilver','Solution :)','2003-04-03 18:36:00',3,'A Murder is a group or flock of crows.\r\nObvious to anyone who has memorized every Simpsons. :)',NULL,0); INSERT INTO comment VALUES (3808,707,1821,'montana hingis','not quite sure if it\'s rite...','2003-04-03 19:44:04',0,'Edgar Loomis - zookeeper - 60 - 5B\r\nDan James - nurse - 12/24/36 - 4A\r\nCalvin Nash - banker - 24/36 - 3C\r\nBlake Knight - electrician - 12/24/36 - 2D\r\nAlbert Masse - pastry chef - 48 - 1E\r\n\r\ni\'m not certain bout the ages of Dan Calvin and Blake.\r\nalso made the assumption with (5) that Mr. Nash could live anywhere right of the man on the fourth floor.',NULL,0); INSERT INTO comment VALUES (3809,686,1863,'Pat','I think I have it','2003-04-03 20:53:05',0,'Did Clem see a murder of crows?',NULL,0); INSERT INTO comment VALUES (3810,708,103,'friedlinguini','Most of a Solution','2003-04-04 02:31:38',1,'Let p be the probability that we\'re looking for. In order for the colony to die out, either the amoeba must die in the first minute, or whatever amoebas are remaining must all die out. If n amoebas are alive at one instant, then they can all be considered different independent colonies, so the odds of all of them dying out is p^n. This gives the framework for the answer.\r\n\r\nFor each case, weight the probability of the colony dying out with the probability of the case occurring. Since each case is equally likely, use a weight of 1/4. Thus:\r\n\r\np = 1/4 + p/4 + p²/4 + p³/4\r\n4p = 1 + p + p² + p³\r\np³ + p² - 3p + 1 = 0\r\n\r\np is the solution to a cubic equation. I don\'t have the analytic solution for a cubic handy, but I can probably generate a numerical one quickly enough unless someone else wants to kill this one off.',NULL,0); INSERT INTO comment VALUES (3811,708,103,'friedlinguini','re: Most of a Solution','2003-04-04 03:26:59',3,'So that nobody has to click back, the equation that I\'m trying to solve is:\r\n\r\np³ + p² - 3p + 1 = 0\r\n\r\nOne obvious solution for p is 1. Is this the answer we\'re looking for? I don\'t think so. If you start with one amoeba, the expected number of amoebae (is that right) in the next minute is:\r\n\r\n0/4 + 1/4 + 2/4 + 3/4 = 3/2\r\n\r\nThis means that the colony wants to increase in size. If you have a large number of amoebae, then the tendency is for the colony to keep growing geometrically. I don\'t think that the colony\'s dying out is a certainty given the rules of the problem.\r\n\r\nFortunately, cubics can have multiple solutions; we just have to look for another one that makes sense. If 1 is a solution to the equation, then (p - 1) is a factor of the polynomial. I\'ll spare everybody the details of synthetic division (If anybody wants an explanation of this, let me know and I\'ll post it in the Reference forum) and just say that\r\n\r\n(p³ + p² - 3p + 1) / (p - 1) = p² + p - 1.\r\n\r\nApplying the quadratic formula to p² + p - 1 = 0 gives\r\n\r\n-1 ±√2.\r\n\r\nThe probability can\'t be negative, but -1 + √2 is a plausible probability.\r\n\r\nSimplifying that a bit, I\'d say that the solution is √2 - 1, or roughly 0.414.',3810,0); INSERT INTO comment VALUES (3812,707,1567,'Bryan','re: not quite sure if it\'s rite...','2003-04-04 04:44:04',0,'Sorry, this answer is not right.
Start again by figuring out the five ages. Once you have those you will see that at least one of the men is retired. True, an occupation is listed for each man, but people often continue to think of themselves in terms of a life-long occupation even after they retire. Perhaps the problem should have stated \"occupation or former occupation.\" Sorry for the confusion.',3808,0); INSERT INTO comment VALUES (3813,707,1861,'john','some questions Bryan','2003-04-04 06:10:36',4,'I have looped myself into impossibilities a few times. These are some logic assumptions I have made. Please let me know if they are true, false, or irrelevant because it can be solved without them. \r\n\r\n1)Their ages are sequential and do not start at 12. (i.e. 24,36,48,60,72 or 36,48,60,72,84). This will make a difference; either way Albert is 48 (clue7), but is he 2nd or 3rd oldest). \r\n\r\n2)Can I assume that in the mathematical relationships (i.e. clue 3), that you did not use the same number (i.e. person) twice, or is this a false assumption.(It is not definitively true like blake not banker not mr. Masse in clue 4).\r\n\r\nPlease let me know, as these may be my false assumptions that are trapping me.\r\n',NULL,0); INSERT INTO comment VALUES (3814,489,1626,'Gamer','That\'s good','2003-04-04 06:29:14',0,'That\'s a cool way to do it. Is there a way to do it using super-math? I don\'t know, I was just wondering',NULL,0); INSERT INTO comment VALUES (3815,707,1567,'Bryan','re: some questions Bryan','2003-04-04 06:41:05',0,'John: yes, clue (3) refers to all five men; none are mentioned twice in that clue. I see now that this clue is vague in that regard, and I will have to send a clarification to Levik.
As for your first assumption, I will give you a hint. Since we are talking of men with occupations and retired occupations, 12 is not a viable age. From clues (3) and (7) and the information given up front, it can be deduced that 48 is a mathematical impossibility (can you figure out why?), and in fact all five ages can be figured out from this same information.
I hope this helps. I\'ll be monitoring the comments to see what else isn\'t clear :P lol\r\n',3813,0); INSERT INTO comment VALUES (3816,708,227,'Dulanjana','re(2): Most of a Solution','2003-04-04 06:54:57',0,'it should be p² + 2p - 1 = 0\r\n\r\nTherefore (p - 1)² = 0\r\n\r\nHence p = 1 ',3811,0); INSERT INTO comment VALUES (3817,708,103,'friedlinguini','re(3): Most of a Solution','2003-04-04 07:25:32',0,'That\'s what I thought at first until I looked closer.\r\n\r\n(p - 1)² = p² - 2p + 1, not p² + 2p - 1.',3816,0); INSERT INTO comment VALUES (3818,707,1861,'john','re(2): some questions Bryan','2003-04-04 08:29:10',0,'I do not understand, 48 is mathematically impossible.\r\n\r\nI am working in circles. I am trying to figure out where I went wrong by seeing where my contradictions lie. Perhaps more clarification may help or I may know when I see the solution posted. I can see where I am wrong if I am even close. For fun my contradictions are Jones zookeeper clue 6, Nash electrician clue 5, calvin electrician clue 8, and dan banker clue 9. I figured with occupations being the commonality they are probably wrong but I can not figure out how to fix them. Anyway, when the answer is posted I will work backwards.',3815,0); INSERT INTO comment VALUES (3820,711,1301,'Charlie','re: solution','2003-04-04 11:00:19',3,'... continued\r\n(btw, in the previous post, make ((√10/2)(√10) = 5 read ((√10)/2)(√10) = 5)\r\n\r\nThe volume of the plastic in the ball is (4/3)π(R³-r³) where r is the inner radius. We set this equal to half the volume of the depression (spherical cap) as the density of the plastic is twice that of the jello and we need to make the volumes match. So\r\n(4/3)π(125-r³)=(14π/3)/2). Solving this for r, gives ³√(125-7/4) or 4.97656. Subtracting this from the outer radius, 5, gives .02344 cm as the thickness of the plastic shell, or 234.4 micrometers or microns.\r\n\r\n',3819,0); INSERT INTO comment VALUES (3821,707,1869,'Dan','Solution?','2003-04-04 11:19:01',0,'Here\'s my stab at an answer. Back to the drawing board or did I get it right? ;)\r\n\r\nBlake Knight/24/Electrician/1D\r\nAlbert Loomis/36/Zookeeper/5B\r\nEdgar James/48/Pastry Chef/4A\r\nDan Masse/60/Nurse/3E\r\nCalvin Nash/72/retired Banker/2C\r\n',NULL,0); INSERT INTO comment VALUES (3822,711,1301,'Charlie','re(2): solution','2003-04-04 11:24:18',0,'Since this is a Calculus question, if we did not use the pre-built formula for the cap of a sphere, we could have gotten that volume from:\r\n\r\n∫{4 to 5} π(5²-x²)dx\r\n\r\nas we need to integrate π(radius)² where the square of this radius is 5²-x².\r\n\r\nThis comes out to π[25x - x³/3] evaluated from 4 to 5, which comes out to the same 14π/3.',3820,0); INSERT INTO comment VALUES (3823,707,1869,'Dan','re: Solution?','2003-04-04 11:27:02',0,'Scratch that. I just found a flaw in the solution. Let\'s try this again.',3821,0); INSERT INTO comment VALUES (3824,707,1567,'Bryan','re: Solution?','2003-04-04 11:32:37',0,'You are close but ... no.
Albert\'s age is the difference between the youngest and oldest ages (7), and all the ages are different (given). Even if all the ages were consecutive multiples of 12, that would make Albert\'s age 48. 36 is too small a number to meet the above requirements.',3821,0); INSERT INTO comment VALUES (3825,711,103,'friedlinguini','re(3): solution','2003-04-04 11:49:02',0,'*applause*',3822,0); INSERT INTO comment VALUES (3826,405,1870,'Brian P','re(2): more difficult','2003-04-04 12:22:56',0,'haha, that\'s funny',3142,0); INSERT INTO comment VALUES (3827,686,1709,'silvis','A guess','2003-04-04 13:41:31',3,'It was roadkill.\r\n',NULL,0); INSERT INTO comment VALUES (3828,82,1873,'mary','','2003-04-04 14:13:22',0,'if he had an infinite number of demons then how did he give orders to all the demons? thats impossible so theres no answer!',NULL,0); INSERT INTO comment VALUES (3829,488,1868,'Brelon Crumbley','ooo....creepy','2003-04-04 15:27:37',0,'ooo....creepy...that was very smart of u 2 come up with that.',NULL,0); INSERT INTO comment VALUES (3830,690,1868,'Brelon Crumbley','hmmm','2003-04-04 15:30:46',0,'perhaps the oil',NULL,0); INSERT INTO comment VALUES (3831,488,1253,'Brian Nowell','re: ooo....creepy','2003-04-04 22:04:51',0,'Er .. smart? Just happened to surf in the \'right\' place! A search engine for another word actually directed me to the location. Smart? No .. Coincidental.',3829,0); INSERT INTO comment VALUES (3832,707,1877,'ZG','Solution','2003-04-05 00:42:06',3,'Blake Knight is an 84-year old retired electrician living in Apartment 1D.\r\nCalvin Nash is a 36-year old banker living in Apartment 2C.\r\nDan Masse is a 72-year old retired nurse living in Apartment 3E.\r\nEdgar Loomis is a 24-year old pastry chef living in Apartment 4A.\r\nAl James is a 60-year old zookeeper living in Apartment 5B.\r\n\r\nThis solution brought to you by ZephyrSkater, PBS, and the number 3.',NULL,0); INSERT INTO comment VALUES (3833,707,1877,'ZG','re: Solution','2003-04-05 00:53:23',1,'Al just wanted me to come back and let you all know that his full name is \"Albert\", and that \"punk kids\" like me are ruining society, and that he doesn\'t like being called \"Al\". But he\'s still 60. And he\'s still a zookeeper. So don\'t worry.',3832,0); INSERT INTO comment VALUES (3834,29,1873,'mary','another way?','2003-04-05 03:59:23',0,'how about asking \"if i were to ask u which direction to knightville, what would u tell me\"\r\n\r\nthey would both point to knightville, knights b/c they are honest and liars bc it is a double negative, they would have to lie twice, therefore telling the truth',NULL,0); INSERT INTO comment VALUES (3835,686,1873,'mary','PONDRER','2003-04-05 04:20:16',0,'',NULL,0); INSERT INTO comment VALUES (3836,686,1873,'mary','SRY','2003-04-05 04:21:56',0,'ok that last thing was supposed to say that ...i think i know\r\n\r\ni think that he was one of those country guys and it was a pig murder or something bc someone was gonna eat the pig for dinner....yea',NULL,0); INSERT INTO comment VALUES (3843,707,1861,'john','THE solution (so I hope)','2003-04-05 12:08:58',3,'Hey Bryan,\r\n\r\nAlbert Loomis 60 Zookeeper Apt 5B\r\nBlake Knight 84 Electrician Apt 1D\r\nCalvin Nash 36 Banker Apt 2C\r\nDan Masse 72 Nurse Apt 3E\r\nEdgar James 24 Pastry Chef Apt 4A\r\n\r\nI did not get any conflicts on my chart, now I will reread the clues with the answers and see if they are all true.',NULL,0); INSERT INTO comment VALUES (3838,490,1575,'DJ','Umm','2003-04-05 05:56:26',0,'I\'m not sure exactly how to prove it, but those numbers are squares of 7, 67, 667, 6667, etc.\r\n\r\nThe 9 comes from the square of 7, then there will as many 8s as there are 6s in the root, and the remaining digits will all be 3s (from 6²=36) with a carryover digit. So, there are as many 4s in the answer as the rest of the digits; ie, the same number as of 8s plus one for the 9.\r\n\r\nThat\'s not much of a proof, just a bunch of observations. I have to collect my thoughts.\r\n\r\nI just woke up.',NULL,0); INSERT INTO comment VALUES (3839,707,1575,'DJ','welp','2003-04-05 06:36:05',0,'I\'m pretty sure I could have made a bunch of assumptions and figured out everything using trial and error. I am trying, though, to form not only a solution, but an explanation for everything I am doing. So far, my solution is woefully incomplete, and I have elimated a number of possibilities, but with not one specific match proven yet. Is it possible to solve this, without assuming anything besides what explicitly stated above? I\'m sure I have missed a few things, but there still remains a lot to be deduced. Maybe I\'ll post my thoughts thus far.',NULL,0); INSERT INTO comment VALUES (3840,707,1575,'DJ','Okay','2003-04-05 08:26:57',0,'Okay, I have now worked everything out except for the ages. Here is my process, clue by clue:\r\n\r\n',3839,0); INSERT INTO comment VALUES (3841,707,1567,'Bryan','re(2): Solution','2003-04-05 09:38:14',0,'Sorry ZG, but if Al is a zookeeper like you say, then his last name is not James. Clue 6 sez the zookeeper lives above Mr. James.',3833,0); INSERT INTO comment VALUES (3842,683,1413,'dave domingo','Holy cow -- it\'s correct','2003-04-05 10:33:28',0,'I always had a problem with this puzzle because all my life I thought \"women\" was pronounced \"wemmen.\" But lo and behold, dictionary.com\'s pronunciation guide says the \"O\" in this word has a short \"I\" sound, as in \"pit.\" Etymology: \"Middle English, from Old English \'wimman,\' variant of \'w*fman\'\" [The * represents a symbol for the long \"I\" sound, as in \"pie.\"] ',NULL,0); INSERT INTO comment VALUES (3844,707,1861,'john','re: THE solution (so I hope)','2003-04-05 12:16:05',1,'Verified all statements hold true; therefore this is a viable solution. HooYah Who\'s the man?',3843,0); INSERT INTO comment VALUES (3845,686,1879,'John DuWors','A Guess','2003-04-05 12:34:27',0,'He didn\'t notify the police because he was the murderer.',NULL,0); INSERT INTO comment VALUES (3846,686,1879,'John DuWors','Guess','2003-04-05 12:38:24',3,'He was the murderer.',NULL,0); INSERT INTO comment VALUES (3847,488,1626,'Gamer','Great riddle!','2003-04-05 12:55:01',0,'I gave up after not knowing what the poem meant (what does elucidate mean?) and read the answer. That sounds like a great ridde! :)',NULL,0); INSERT INTO comment VALUES (3848,490,1301,'Charlie','solution','2003-04-05 13:42:37',3,'Thank to DJ\'s noting that the square roots are in the form 6...67, the proof can proceed from there forward to the squares.\r\n\r\nFirst note that 10^n-1 is a number represented by n 9\'s, so (10^n-1)/9 is represented by n 1\'s, and ((10^n-1)/9)d is represented by n occurrences of the digit d.\r\n\r\nSo let\'s start with a number in the form DJ found:\r\n(((10^n-1)/9)6 + 1), where the +1 changes the last 6 to a 7. The square of this number is given by\r\n\r\n((10^(2n)-2(10^n)+1)/81)36 + ((10^n-1)/9)12 + 1\r\n\r\nThen as 36/81=4/9, this becomes\r\n\r\n((10^(2n)-2(10^n)+1)/9)4 + ((10^n-1)/9)12 + 1\r\n\r\nThen as we wish to combine the terms involving 10^n together, we make this\r\n\r\n((10^(2n)-2(10^n-1)-1)/9)4 + ((10^n-1)/9)12 + 1\r\n\r\nThen, actually moving those over,\r\n\r\n((10^(2n)-1)/9)4 + ((10^n-1)/9)(12-(2)(4)) + 1\r\nor\r\n((10^(2n)-1)/9)4 + ((10^n-1)/9)4 + 1\r\n\r\nBut ((10^(2n)-1)/9)4, as mentioned at the beginning, is represented in the decimal notation by 2n 4\'s, while ((10^n-1)/9)4 is represented by n 4\'s. These two terms then represent a 2n-digit number of all 4\'s plus an n-digit number of all 4\'s, therefore converting the second half of the string to all 8\'s. The unit term at the end changes the last 8 to a 9.\r\n\r\nThis accounts for any value of n (or k in the statement of the puzzle).',NULL,0); INSERT INTO comment VALUES (3849,489,1880,'Camaris','Grandfather and Father','2003-04-05 14:01:48',0,'Can the average length of a generation be 41 1/2 years? Are you sure it wasn\'t his great grandfather?\r\n',NULL,0); INSERT INTO comment VALUES (3850,707,1567,'Bryan','re(2): THE solution (so I hope)','2003-04-05 15:31:30',0,'John, YOU da man. My hat\'s off to you.
I\'ll have to find time to make another logic problem :P',3844,0); INSERT INTO comment VALUES (3851,490,979,'Ravi Raja','re: solution','2003-04-06 04:12:57',0,'Charlie, suppose that DJ did not note that the square roots of the given sequence of numbers are of the form 7, 67, 667, 6667, ....etc. then how would you proceed to prove the numbers of the given form to be perfect squares ?',3848,0); INSERT INTO comment VALUES (3852,490,979,'Ravi Raja','re: solution','2003-04-06 04:18:56',0,'This method Charlie, that you have used to prove the result is actually back-calculation or manipulation what I would say, since you came to know the form in which the square roots of the numbers in the sequence are. ',3848,0); INSERT INTO comment VALUES (3853,490,979,'Ravi Raja','re: solution','2003-04-06 04:23:41',0,'Suppose the digits from 0 through 9 occurred in random order in the square roots of the numbers of the given sequence, instead of following a definite pattern like 7, 67, 667, 6667,....,etc., then how would you have proceeded to solve the given problem ? I need that kind of a proof Charlie. \r\n\r\nAnyway, I am not saying that your method is wrong. it is absolutely correct and nice one too but all I want is a different approach and a shorter method. That\'s it. :)',3848,0); INSERT INTO comment VALUES (3854,490,1626,'Gamer','re(2): solution','2003-04-06 04:44:16',0,'I was thinking about 4((10^x)+2)*(x 1s) + 1 for how to do that sequence.\r\n\r\n(\'x 1s\' is the sum of (10^x)+(10^x-1)+...+(10^1))\r\n\r\nWould that help at all or is it too complicated?\r\n',3853,0); INSERT INTO comment VALUES (3855,490,1626,'Gamer','Partial idea','2003-04-06 05:03:37',1,'This also goes from the square roots up, but can be worked the reverse way as well.\r\n\r\nSince (a+1)² =a² +2a+1, 7² =6² +2(6)+1, 67² = 66² +2(66)+1, 667² = 666² + 2(666) + 1,\r\n\r\nSince (x 6s)² =( x 4s then x 5s) - x 9s (Or, (x-1) 4s, then a 3, then (x-1) 5s, then a 6), adding 2(x 6s ) will just change the 3 to a 4 (adding 1), the 5s to 8s (adding 3) and the 6s to 8s (adding 2). You get (x 4s then x 8s) as a result, and adding 1 to the end gives 9 at the end instead of an 8. So you get (x 4s, then (x-1) 8s, then a 9) which is what the problem asks for.\r\n\r\nI haven\'t found how to prove the 36, 4356, 443556, 44435556 sequence, which is the next problem with this. ',NULL,0); INSERT INTO comment VALUES (3856,281,1626,'Gamer','re: Author unknown','2003-04-06 08:23:09',0,'I think it\'s because nobody knows who first created this puzzle-type.',3790,0); INSERT INTO comment VALUES (3857,707,1626,'Gamer','re: THE solution (so I hope)','2003-04-06 14:19:09',0,'I get nervous and shaky when I even look at these logic problems. *Shakes* I don\'t know how you people do these! :)',3843,0); INSERT INTO comment VALUES (3858,252,1626,'Gamer','Board Rules','2003-04-06 14:24:10',0,'Um Tim Axoy, + turns into 4 is exactly what \"If posting a solution, don\'t give it away in the subject\" means!\r\n\r\nAnyway, I interpreted \"The following equation\" as interchangable with \"The problem below\", but maybe that isn\'t what the author meant. So I came up with Charlie\'s solutions',NULL,0); INSERT INTO comment VALUES (3859,696,1626,'Gamer','Different blocks?','2003-04-06 16:07:33',4,'If I was using MAY for May, could I put MAY all on one cube or would I have to put it on 3 seperate cubes?',NULL,0); INSERT INTO comment VALUES (3860,696,1301,'Charlie','Attempt at a solution (probably too naive)','2003-04-06 16:28:35',0,'On the face of it, it would seem the month cube could handle only 6 months of the year, as I can\'t see any way of representing one month as the upside down version of another or similar trick. The date cube could have 6 figures, but if one of the m is a 6 it could serve as a 9 also. So we\'d have 7 dates in each of 6 months, for 42 dates within the year that could be represented.',NULL,0); INSERT INTO comment VALUES (3861,696,1183,'fwaff','re: Attempt at a solution - more combinations','2003-04-06 22:48:14',1,'By using the same font as on a calculator it is possible to further increase the number of invertible numbers since 12 inverts to 21.\r\n\r\nThis increases Charlie\'s answer to 6(months) x 8(days) = 48\r\n\r\nIf we also allow the number format to be flexible as to whether or not there is a leading zero for single digit numbers then we can have 10 inverting to 01 and 20 inverting to 02.\r\n\r\nSo now the total increases to 6(months) x 10(days) = 60\r\n\r\nOn the number cube we have 01/10,02/20,6/9,12/21, if we make the remaining two faces 17 and 27 and make one of the faces on the month cube show \"JU\" for June. Then if we invert 17 it becomes L1 turning JU 17 into JUL 1 (similarly JU 27 becomes JUL 2) which adds another 2 onto the total. I\'m not sure if this violates the rules as it puts the month across the two cubes - the last sentence of the problem \"one month symbol...can be on 1 face of 1 cube\" can be taken to mean \'no repeats\' (in which case the solution is valid) or it can be taken as \'the month must appear on only 1 cube\' (in which case these last two are not valid).\r\n\r\nOK so the max I\'ve got to so far is 62. Who\'s got the next bright idea?',3860,0); INSERT INTO comment VALUES (3862,281,1183,'fwaff','re(2): Author unknown','2003-04-06 22:54:42',0,'Also putting \'author friEdlinguini\' would destroy the problem.\r\n\r\nPutting \'author fwaff\' would be ok though, apart from it being a total lie :-)',3856,0); INSERT INTO comment VALUES (3863,492,1183,'fwaff','Solution','2003-04-07 03:01:03',3,'Neat seasonal problem Ravi! I guess this shows how long the problem queue is.\r\n\r\nFrom front to back the reindeer are:\r\n\r\nPrancer\r\nCupid\r\nRudolph\r\nDasher\r\nBlitzen\r\nVixen\r\nComet\r\nDonder\r\nDancer\r\n\r\nTo get the solution I wrote down the list and used a kind of \'bubble sort\' principle to move names up and down. I needed to run through the clues a few times before I had a run through where there were no changes.\r\n\r\nOne minor point of pedantry, traditionally \'Donder\' is actually \'Donner\'. Donner and Blitzen are the German words for thunder and lightning.\r\n',NULL,0); INSERT INTO comment VALUES (3864,492,1896,'molly','solution','2003-04-07 03:14:00',0,'prancer\r\nrudolph\r\ncupid\r\nblitzen\r\nvixen\r\ndasher\r\ndonder\r\ndancer\r\ncomet',NULL,0); INSERT INTO comment VALUES (3865,492,103,'friedlinguini','re: Solution','2003-04-07 03:30:50',0,'One minor point of pedantry, traditionally \'Donder\' is actually \'Donner\'. Donner and Blitzen are the German words for thunder and lightning.\r\n\r\nI got bitten by this while the problem was in the queue. I was pointed (I\'m sorry - I don\'t remember by who) to www.donder.com.',3863,0); INSERT INTO comment VALUES (3866,696,1183,'fwaff','re(2): Attempt at a solution - 2 more combinations','2003-04-07 03:34:09',1,'Ok now this is getting tenuous so bear with me.... \r\n\r\nInstead of the \'calculator font\' where 2 is represented with 5 straight lines, draw it with 3 straight lines such that it looks like Z. It\'s still horizontally symmetrical so Z0/0Z and 1Z/Z1 remain valid.\r\n\r\nNow take the ZO face and turn it 90deg clockwise so that it shows NO reading vertically downwards. Now we have a month on the \'day\' cube, so what we need are some days on the \'month\' cube. The only two that I can see are S (for September) looks like 5 (giving NO 5 - bonfire night) and if you take the letter M (for March or May) and rotate it 90deg clockwise it looks like 3 (for NO 3).\r\n\r\nSo far the cubes have:\r\n\r\nCube 1: 01(10), 02(20,NO), 6(9), 12(21), 17(L1) and 27(L2)\r\nCube 2: JU, S(5), M(3), ???, ***, @@@\r\n\r\n...which give 64 combinations. Only 302 left to find now!!!',3861,0); INSERT INTO comment VALUES (3867,492,1183,'fwaff','re(2): Solution','2003-04-07 03:53:46',0,'Thanks fried. Ravi, please accept my apologies. My parents have a very old copy (circa 190?) of a book which contains this poem and it refers to \'Donner\'.\r\n\r\nThat link just goes to show that some people have way too much time on their hands, but not quite as much spare time as this chap....\r\n\r\nhttp://www.pixyland.org/peterpan/index.html',3865,0); INSERT INTO comment VALUES (3868,492,1897,'luana','solution','2003-04-07 04:28:05',0,'Dancer, Donder, Comet, Vixen, Blitzen, Dasher, Rudorph, Cupid, Prancer',NULL,0); INSERT INTO comment VALUES (3869,490,979,'Ravi Raja','re(3): solution','2003-04-07 04:29:26',0,'Yes Gamer, in \"one of the methods\" by the help of which the problem can be solved this sequence,\".... the sum of (10^x)+(10^x-1)+...+(10^1))....\" that you have posted in your comment is required. I meant that of courlse that will help.',3854,0); INSERT INTO comment VALUES (3870,686,1900,'Charming','could it be?','2003-04-07 07:21:28',0,'because he was on his way to the police already',NULL,0); INSERT INTO comment VALUES (3871,469,1900,'Charming','could it be?','2003-04-07 07:33:18',0,'no one as if the woman didnt remember that she owe him 100 rupees, he wouldnt had got the counterfeit note.... likewise if she remembers to return him the money, he would in turn got the counterfeit which still has no monetary value....which in turn means he still didnt get anything in return.... so he may not lose anything at all in fact',NULL,0); INSERT INTO comment VALUES (3872,358,1900,'Charming','nice','2003-04-07 07:47:58',0,'great riddle',NULL,0); INSERT INTO comment VALUES (3873,686,1903,'Evonne','Juz a wild guess','2003-04-07 09:13:43',0,'He was the victim',NULL,0); INSERT INTO comment VALUES (3874,68,1626,'Gamer','','2003-04-07 09:45:05',0,'That\'s what I was always like on some of the boring math problems. I was like, Yes I can...\r\n\r\nI can NOW, but I spent so long on this problem and still didn\'t get it *sigh*',NULL,0); INSERT INTO comment VALUES (3875,45,1626,'Gamer','re: no really...','2003-04-07 09:56:57',0,'That\'s a good way to think about it :)',3575,0); INSERT INTO comment VALUES (3876,712,1567,'Bryan','Aha!','2003-04-07 12:08:19',3,'Take one part observation, one part perception, three parts patience (while the subconscious does its thing), and about ten parts luck, and the sequence becomes
104 = 53 base 7
125 = 53 base 6
203 = 53 base 5
311 = 53 base 4
1222 = 53 base 3
The next number in the sequence is 110101 (= 53 base 2).',NULL,0); INSERT INTO comment VALUES (3877,686,1905,'Karen','hunter','2003-04-07 12:09:15',0,'He was hunting, and he saw someone shoot an animal.',NULL,0); INSERT INTO comment VALUES (3878,205,1906,'Eric','re(2): A different approach','2003-04-07 13:02:38',0,'I believe that Alonso asked if Bertrand ate MORE apples than he. If Alonso had had one apple then Bertrand may very well have had one apple also since that would be an EQUAL amount, not more.',1727,0); INSERT INTO comment VALUES (3879,686,1896,'molly','solution?','2003-04-07 14:03:36',0,'the police were already there',NULL,0); INSERT INTO comment VALUES (3880,686,1907,'Tahlia','I HAVE THE SOLUTION! :)','2003-04-07 14:20:47',0,'Clem saw a group of crows.... thus a group of crows is called a MURDER! ',NULL,0); INSERT INTO comment VALUES (3881,61,1907,'Tahlia','MOVIE DEJAVU','2003-04-07 14:27:49',0,'His horse\'s name is Saturday',NULL,0); INSERT INTO comment VALUES (3882,686,1761,'jPs','Easy!!!','2003-04-07 14:53:00',3,'Cauze he\'s a chiken dude! \r\nhahaha ... :P',NULL,0); INSERT INTO comment VALUES (3883,686,1761,'jPs','Easy!!!','2003-04-07 14:54:19',3,'Cauze he\'s a chicken dude! \r\nhahaha ... :P',NULL,0); INSERT INTO comment VALUES (3884,492,1821,'montana hingis','reindeer','2003-04-07 17:11:16',0,'prancer\r\ncupid\r\nrudolph\r\ndasher\r\nblitzen\r\nvixen\r\ncomet\r\ndonder\r\ndancer',NULL,0); INSERT INTO comment VALUES (3885,492,1821,'montana hingis','re: solution','2003-04-07 17:12:31',0,'its the other way round (prancer is first)',3868,0); INSERT INTO comment VALUES (3886,492,979,'Ravi Raja','re(3): Solution','2003-04-08 00:25:52',0,'No apologies please fwaff. that was just like a suggestion from your part and everyone makes mistakes. isn\'t it ? :) ',3867,0); INSERT INTO comment VALUES (3887,491,1626,'Gamer','Idea','2003-04-08 01:48:11',2,'My guess is 11,111,111,100. Since the number is divisibly by 9, you have to make the number divisible by 9. Since it has to be divisible by 225, you need to add on the 2 zeroes. (49,382,716 x 225=11,111,111,100)',NULL,0); INSERT INTO comment VALUES (3888,491,1301,'Charlie','re: Idea','2003-04-08 03:50:39',3,'I agree with the answer 11,111,111,100. As 225 is 9*25, the number of ones has to be 9 (or a multiple of 9, but that would make it bigger), and since 2\'s and 5\'s are not permitted in the answer, the number must end in two zeros to be divisible by 25.',3887,0); INSERT INTO comment VALUES (3889,712,775,'Cory Taylor','re: Aha!','2003-04-08 03:56:55',0,'holy cow theres some smarties aroiund here',3876,0); INSERT INTO comment VALUES (3890,491,1915,'John','Zeros and Ones','2003-04-08 05:51:52',0,'If veiwed as a binary problem then the smallest interger evenly divisible by 225 is 001011111',NULL,0); INSERT INTO comment VALUES (3891,491,1915,'John','Zeros and Ones','2003-04-08 06:00:18',0,'I have a coorection to my earlier attempt\r\nthe binary solution should read 010000111',NULL,0); INSERT INTO comment VALUES (3892,732,1715,'Jonny Doe','Solution','2003-04-08 06:48:30',3,'Drew (I) is the liar and Mohammed is not a liar',NULL,0); INSERT INTO comment VALUES (3893,732,1567,'Bryan','Not so fast','2003-04-08 08:13:41',4,'Considering the statement, \"Mohammad and I are both liars,\" the obvious line of logic is as follows:
- If the statement is true, then Drew is a liar, which is a contradiction
- Therefore Drew is a liar
- If Drew is a liar and his statement is a lie, then Mohammad must not be a liar
When I saw that transcendental numbers were acceptable, I thought \"heck, who needs zeros?\". But if we eliminate them as well, we can still get 24 from
[cos(0) + sec(0) + cosh(0) + sech(0)]!',3929,0); INSERT INTO comment VALUES (3933,137,1933,'michael','algebraic route','2003-04-09 06:51:38',3,'All variables are minutes prior to 12:00\r\nx = original plane arrival time\r\ny = friend\'s departure time\r\nz = time spent walking\r\n\r\nSince the friend\'s travel speed is constant, we know that time to and from airport are equal.\r\n\r\nx - y = 0 - x\r\n\r\n0 being 12:00\r\n\r\nFrom the actual travel info, we know that\r\n\r\n(x - 60 + z) - y = -20 - (x - 60 + z)\r\n(pick up time)\r\n\r\n2x = y solves out both x and y and leaves z = 50\r\n\r\nThere are an infinite pair of x and y values consistent with the scenario, only constrained by realistic bounds on car and foot travel speeds.\r\n\r\nI applaud the intuitive method, I wish it would have occurred to me.',NULL,0); INSERT INTO comment VALUES (3934,732,1933,'michael','Hmmm','2003-04-09 07:00:46',3,'Four possibilities:\r\nI Mo\r\nL L\r\nL T\r\nT L\r\nT T\r\n\r\nThe first is out, because I\'d be telling the truth, yet I\'m a liar.\r\nThe third and fourth are out, because I\'d be telling a lie, yet I\'m a truthsayer.\r\nThe second is right, because I lied and I\'m a liar.\r\n\r\nNow I can go back and read the other posts.',NULL,0); INSERT INTO comment VALUES (3935,457,1902,'Hank','wording and my solution','2003-04-09 07:02:49',1,'I interpreted the problem to be: \r\n1)when you went in, you had twice as many R than P or R=2P\r\n2)when you left, you had just as many P as R or R=P\r\n3)you spent half of your money at the store\r\n\r\nMy solution was: 404R and 202P when entering (406.o2 total); 201R and 201P when leaving (203.01 total)\r\n\r\nAfter reading your solution, I accept that I misunderstood the wording. Just letting you know my interpretation.',NULL,0); INSERT INTO comment VALUES (3936,493,1686,'DuCk','Solution','2003-04-09 07:14:19',3,'Here\'s one way it\'s possible:\r\n\r\n=(0!+0!+0!+0!)!\r\n=(1+1+1+1)!\r\n=(4)!\r\n=4*3*2*1\r\n=24\r\n\r\nThanks!',NULL,0); INSERT INTO comment VALUES (3937,714,1902,'Hank','No clue','2003-04-09 07:15:09',0,'I\'ve never seen a problem like this.\r\n\r\nMy solution: ummm...True, i guess\r\n\r\nHere\'s another one for you: kdfahdkahjslkseiekd?',NULL,0); INSERT INTO comment VALUES (3938,714,1517,'jude','two thoughts','2003-04-09 07:55:21',1,'if internet speak\r\nhemawawsalwgcsi2alwgcscswa (but I don\'t know what do to with the 2)\r\n\r\nif you use the numerbers to correspond to the letters in the alphabet\r\nhcmdwdweaawiceibaawicecewd\r\n\r\nSo now what? a word scramble/jumble?',NULL,0); INSERT INTO comment VALUES (3939,714,1902,'Hank','re: two thoughts','2003-04-09 09:10:33',1,'OR \r\nthe letter could represent the first letter of the word and the number could represent the length of the word (eg: how many will watch a w...)\r\nOR\r\nI\'ve seen problems like 26LA --> 26 Letters in the Alphabet or 6FU --> 6 Feet Under',3938,0); INSERT INTO comment VALUES (3940,714,1517,'jude','re(2): two thoughts--Possible Solution','2003-04-09 09:25:38',0,'thanks to Hank\'s thought, I think I have it\r\n\r\n\r\n\"How much wood would a woodchuck chuck, if a woodchuck could chuck wood?\"\r\n\r\n\r\n',3939,0); INSERT INTO comment VALUES (3941,714,1301,'Charlie','re(3): two thoughts--Possible Solution','2003-04-09 09:33:31',3,'And of course, the easy part now: the title is An Old Tongue Twister.',3940,0); INSERT INTO comment VALUES (3942,421,1937,'Chad','really..','2003-04-09 11:52:34',0,'You dummy. Turn the square upwards and diagnol, it will fall right through the hole.',3203,0); INSERT INTO comment VALUES (3943,427,1666,'bik88','i\'ve heard this one','2003-04-09 13:13:49',3,'i ought too owe nothing for i ate nothing',NULL,0); INSERT INTO comment VALUES (3944,714,1626,'Gamer','re(4): two thoughts--Possible Solution','2003-04-09 13:53:12',0,'Wow... I didn\'t get this one at all... had to look at solution... Seems so easy now! :)\r\n\r\nI actually submitted a problem based on this (but not similar to the coding process) Hopefully it\'s not too easy.',3941,0); INSERT INTO comment VALUES (3945,714,1846,'Tim Axoy','Word code','2003-04-09 14:07:22',3,'It is a sequence with numbers and letters.\r\nThe letter is the first letter of the word.\r\nThe number is the number of letters in the word.\r\nTitle=An old tongue twister\r\nProblem=How much wood would a woodchuck chuck if a woodchuck could chuck wood?',NULL,0); INSERT INTO comment VALUES (3946,492,1846,'Tim Axoy Disn1','What??????????','2003-04-09 14:39:10',0,'Your problem is so hard it should be rated 5 and not 3.',NULL,0); INSERT INTO comment VALUES (3947,491,1626,'Gamer','re: Decimal Representation ( Base 10 )','2003-04-09 15:46:24',0,'That is what I think.... Otherwise we would have to say too many common sense type things',3921,0); INSERT INTO comment VALUES (3948,491,1301,'Charlie','re(5): Idea','2003-04-09 16:27:10',0,'The table of 1\'s and 0\'s numbers in other bases was correct in showing such numbers divisible by 225 in that base, but the ones for bases 16 and 18 were not the smallest. The correct table with the smallest for each base is:\r\n6 11001 ( 1513 89 )\r\n7 1011 ( 351 117 )\r\n8 11101101101 ( 1225032257 149 )\r\n9 11011011 ( 5321710 185 )\r\n10 11111111100 ( 11111111100 225 )\r\n11 1001010011 ( 2359733905 269 )\r\n12 100011 ( 248845 317 )\r\n13 1100001 ( 5198103 369 )\r\n14 110101101 ( 1581743325 425 )\r\n15 1101110 ( 12153615 485 )\r\n16 10111000011 ( 1104091807761 549 )\r\n17 100101011 ( 6977182229 617 )\r\n18 10000101001 ( 3570469122025 689 )\r\n19 11010101110101 ( 44272446480796725 765 )\r\n20 1110010 ( 67360020 845 )\r\n21 1011011011 ( 796167105007 929 )',3911,0); INSERT INTO comment VALUES (3949,492,1941,'shaun','first timer','2003-04-09 21:06:33',0,'I think the order is as follows, from front to back\r\nPrancer\r\nCupid\r\nBlitzen\r\nRudolph\r\nDasher\r\nVixen\r\nComet\r\nDonder\r\nDancer',NULL,0); INSERT INTO comment VALUES (3950,492,1941,'shaun','re: first timer','2003-04-09 21:18:48',0,'oops, Blitzen should be 5th behind rudolph and dasher',3949,0); INSERT INTO comment VALUES (3951,693,1930,'Irina','re: Posted Solution Not Minimum','2003-04-10 00:56:10',0,'why not easier:\r\nsplit the 120 grams into 2 equal lots, both of sixty grams\r\nput one aside then split the other one into 2 lots of 30 grams\r\nput one aside then split the other one into 2 lots of 15 grams\r\nput one aside then split the other one into 2 lots of 7.5 grams\r\n\r\nis there something wrong with this solution?\r\nThanks , Irina',3697,0); INSERT INTO comment VALUES (3952,714,1575,'DJ','a6t3q8..','2003-04-10 01:12:49',1,'Answer the question..\r\nI\'ll admit, I was stumped for this one, until I saw jude\'s interpretation. No one answered the question posed, though; so:\r\n\r\na1w9w5c5a2m4w4a2a1w9c5c5i2a1w9c5c5w4!\r\n\r\n(A woodchuck would chuck as much wood as a woodchuck could chuck if a woodchuck could chuck wood!)',NULL,0); INSERT INTO comment VALUES (3953,732,979,'Ravi Raja','re(2): Solution','2003-04-10 01:21:59',0,'Yes Tim I understood at once that it was the problem which we have been discussing in the chatterbox. \r\nBut still I made a mistake but then I corrected it.',3925,0); INSERT INTO comment VALUES (3954,494,1575,'DJ','Solution','2003-04-10 02:51:15',3,'We want the statements on the three envelopes to evaluate to TT, FF, and TF (or FT) for the correct location of the formula.\r\n\r\nIf the formula were in the first envelope, Then the statements on the three envelopes are:\r\n1-FF, 2-FF, 3-TT. This cannot be the case.\r\n\r\nIf the formula is in evelope 2, the statements evaluate to:\r\n1-TT, 2-TF, 3-TF. This is also not it.\r\n\r\nWith the formula in envelope 3, the statements are then:\r\n1-TF, 2-TT, 3-FF; the formula must be in envelope three.',NULL,0); INSERT INTO comment VALUES (3955,494,1686,'DuCk','answer','2003-04-10 03:08:08',3,'The formula is in envelope #3 (3rd envelope has two false statements, 2nd envelope has two true statements, and 1st envelope has one true and one false statement). If the formula was in any of the other envelopes these True/False constraints would be violated.\r\n\r\nThanks\r\n',NULL,0); INSERT INTO comment VALUES (3956,714,1517,'jude','re: a6t3q8..','2003-04-10 04:35:04',0,'HAHAHA\r\n\r\nThanks DJ....I forgot to answer it',3952,0); INSERT INTO comment VALUES (3957,494,1928,'The Mighty Puck','entertaining','2003-04-10 06:45:27',0,'it was an entertaining riddle of sorts',NULL,0); INSERT INTO comment VALUES (3958,421,1902,'Hank','huh...','2003-04-10 07:02:54',0,'I was just thinking of posting the same question today.',NULL,0); INSERT INTO comment VALUES (3959,494,1946,'austin','solution','2003-04-10 08:13:20',0,'The formula is in the first envelope. The statements on the first envelope are true and false. The statements on the second envelope are both false, and the statements on the third envelope are both true so therefore the formula is in the first envelope. Thanks.',NULL,0); INSERT INTO comment VALUES (3960,494,1946,'austin','re: solution','2003-04-10 08:19:19',0,'I was wrong and am big enough to admit that. It was my first time out though folks. I\'ll read a little more carefully next time before I answer the question.',3959,0); INSERT INTO comment VALUES (3961,717,1920,'Brian Smith','Solution','2003-04-10 08:21:48',0,'A always lies and does not like strawberries\r\nB always tells the truth and does not like strawberries\r\nC alternates and does not like strawberries',NULL,0); INSERT INTO comment VALUES (3962,717,1902,'Hank','New Solution and clarification','2003-04-10 08:35:07',3,'If C always lies, then he is currently telling the truth -- impossible\r\nIf C always tells truths, then he is currently lying -- impossible\r\nThe only other option is that C alternates between Ts and Ls.\r\nA says that C never lies, which is a lie, making A the liar.\r\nB must be the teller of truths.\r\n\r\nClarification:\r\nDoes C alternate Ts and Ls by sentence? I would assume so because that is the easiest way to distinguish alternates. In addition, it would not be pointed out that one alternates, if it did not pertain to the problem. So, Cs first sentence is a lie, his second must be the truth.\r\n\r\nSolution: No one likes strawberries.',NULL,0); INSERT INTO comment VALUES (3963,717,1946,'austin','giving it a go','2003-04-10 08:37:31',0,'A is the habitual liar and does not like strawberries\r\nB is telling the truth and does not like strawberries\r\nC alternates and does not like strawberries.',NULL,0); INSERT INTO comment VALUES (3964,717,1919,'Lewis','answer','2003-04-10 09:07:07',3,'A = Liar\r\n Doesn\'t like strawberries\r\nB = Truth-Teller\r\n Doesn\'t like strawberries\r\nC = Alternater\r\n Doesn\'t like strawberries',NULL,0); INSERT INTO comment VALUES (3965,432,1919,'Lewis','solution','2003-04-10 09:27:36',3,'If Barry was the guilty one, Alan and Carl would both be telling the truth, so thats wrong.\r\n\r\nIf Carl was the guilty one, Alan and Barry would both be telling the truth, so thats also wrong.\r\n\r\nIf Alan was guilty, that would mean that Barry is the Knight and Alan and Carl are liars.\r\nTherefore, Alan is the guilty one.',NULL,0); INSERT INTO comment VALUES (3966,717,1660,'Tim Axoy','C tells the truth and lies.','2003-04-10 09:48:23',3,'C\'s first statements cannot be true for the same reason Drew cannot be a knight in Drew and Mohammad.\r\nAlso,using the same logic,C\'s second statement was true.',NULL,0); INSERT INTO comment VALUES (3967,717,1660,'Tim Axoy','Who? Who? Who likes strawberries?','2003-04-10 09:51:30',3,'C does not like strawberries because his second statement is true.\r\nA certainly lied about C never telling a lie(C\'s first statement was).\r\nA cannot be the alternater,so A always lies.\r\nTherefore,his second statement is a lie,so A does not like them either.',NULL,0); INSERT INTO comment VALUES (3968,717,1947,'Jon','my guess','2003-04-10 09:52:00',0,'no one likes strawberries. C is obviously the alternater because his first statement would be a paradox if he wasn\'t. C\'s first statement then becomes a lie so his second is a truth. C doesn\'t like strawberries. A said that C never lies. This being a lie, A has to be the liar. A also doesn\'t like strawberries. B must then be the truth teller. B doesn\'t like strawberries. no one likes strawberries.',NULL,0); INSERT INTO comment VALUES (3983,717,1,'levik','re: C tells the truth and lies.','2003-04-10 18:27:01',0,'Tim, \r\n\r\nplease do not post clues or solutions in subjects. Others have asked you not to do this before. It asks you not to do this when posting a comment. Now, I\'m asking you specifically as a webmaster.\r\n\r\nThis site has certain guidelines that exist to make it interesting for all the visitors. I do not want one person ruining the experience of all the other users. If you cannot apply common sense and see what would spoil other peoples\' experience, at least listen to them when they tell you straight out.',3966,0); INSERT INTO comment VALUES (3970,494,1947,'Jon','easy way to solve this type of problem','2003-04-10 10:03:22',0,'the easiest way to solve this is to skip logic all together. just do a simple test by picking one of the envelopes as the TRUE envelope. it becomes very easy to realize that 2 only works putting the formula in the 3rd envelope.',NULL,0); INSERT INTO comment VALUES (3971,717,1575,'DJ','TIM....','2003-04-10 10:14:25',0,'We\'re glad that you can give the answer to the problem three times. Really. But please stop putting your answers in the subject of your comments! It\'s no fun for anyone to come here and see the solution that you copied before getting a chance to solve it themselves..please.',3969,0); INSERT INTO comment VALUES (3972,696,1072,'Alan','What?','2003-04-10 10:38:22',0,'Ok i know this problem only got two votes but its at 1? is there any justification behind this reasoning? just to start off you guys (I\'m not angry at those who didn\'t vote)did not find the maximum number of combinations, secondly there is simply one genious concept you have to come across. I honestly don\'t think this problem should be a 1 and if you think differently vote on it.',NULL,0); INSERT INTO comment VALUES (3974,191,1660,'Tim Axoy','Zoom!!!!','2003-04-10 11:52:02',0,'I dunno.',NULL,0); INSERT INTO comment VALUES (3975,696,1942,'benard','low rating','2003-04-10 12:11:25',0,'I gave this problem a low rating because the rules are not at all clear to me. ie how many letters or numbers are allowed on 1 face of 1 cube (I defaulted to 1). Is it supposed to be letters on one cube, numbers on the other? Are we expected to use numbers in place of letters? Is M a good substitute for 3?\r\n My solution (with substitutions) calls for 213 days, all months covered: JAUMFD on one cube, 0-5 on another. Without subs the number drops to 167.',NULL,0); INSERT INTO comment VALUES (3976,717,1626,'Gamer','re: DO NOT CRITICIZE ME!','2003-04-10 12:37:11',0,'We aren\'t criticizing you even if that\'s what you think! But if you continue to flood the chatterbox with pre-checked problems, the subjects with message answers and the comments with multiple of the same solution, we would have reason to.',3973,0); INSERT INTO comment VALUES (3977,717,1949,'Mac','answer?','2003-04-10 12:40:55',3,'A is the liar and doesnt like strawberries\r\nB tells the truth and doesnt like strawberries\r\nC alternates and likes strawberries',NULL,0); INSERT INTO comment VALUES (3984,159,1253,'Brian Nowell','Software Solution','2003-04-10 21:08:38',0,'This explortion utilises many of the understandings established in my comment “Eureka!! – Squares Anyway” in which an x – y orientation was unnecessary because of the nature of length of sides.\r\n\r\nI have chosen an 8 x 5 grid as an arbitrary base model around which all rectangles may be addressed. It is labelled x from A to H across the top and y = 1 to 5 downwards. The grid is then boldly divided horizontally between Rows 3 & 4 and vertically between Columns 3 & 4 and F & G. Cells B2 to E5 on the ‘diagonal’ are shaded as are cells D1 to G4. Also shade G1, H2 A4 and B5.\r\n\r\nThe visual pattern is repeated in multiples of 3 whether by column or row. Note that the ‘Diagonal’ beginning at A1 has an initial blank cell as the adjacency property is preserved by this arrangement. Similarly a ‘diagonal’ that would end as in the case of H5 also terminates with a clear cell.\r\n\r\nNote too that the block of cells F3 to H5 is important in determining the final outcome.\r\n\r\nTo begin: For any multiple of 3 columns, every row will have an identical number of black cells, that being int(x/3). However the first cell of Row 1 is exempt and may be represented by the value of [-1] in a final calculation.\r\n\r\nBlack cells for all rows to column int(x) will be y* int(x/3) –1.\r\n\r\nFor additional columns (and there will be either 1 or 2) there will be int(y/3) black cells.\r\n\r\nThe remaining cells of those columns (part of the F3-H5 black) will be 1, 2 or 4, depending upon rows and columns in excess of the multiple of 3. Mod(x,3)*mod(y,3) will evaluate to 0, 1, 2 or 4.\r\n\r\nThe following are conditions and implications surrounding the F3-H5 block.\r\n\r\nIn Following Table:\r\nDescription is Columns (C), Rows (R), Multiple of 3 (Mlt_3)\r\nAdd – describes number of cells added for cells as generated within the F3-H5 block.\r\nShade describes shading for the condition.\r\nBlack is the Black Cells value to show in the formula.\r\n\r\nDescription Add Shade Black \r\n1. C & R are Mlt_3 0 F3 = White -1 \r\n2. Only 1 C or R\r\n of Mlt_3 added 0 F3 = Black 0\r\n3. 2 C or 2 R Rows \r\n of Mlt_3 added 0 F3 = Black 0\r\n4. Both 1 C and \r\n 1 R added 1 G4 = White 0\r\n5. 2 C & 1 R, or \r\n 1 C & 2 R added 2 G4 = Black +1\r\n6. 2 C & 2 R are 4 G4 = Black\r\n both added H5 = White +1\r\n G4 = Black\r\n \r\n\r\nSo the formula looks like this:\r\n Black Cells = y*int(x/3) + mod(x,3)*int(y/3) + [Cells of Condition].\r\n\r\nCells of Condition?\r\nI can only see a Software Solution. \r\nBecause of the differences in Syntax, ‘Nesting’, etc, programmers need to manipulate this according to their programming language.\r\n\r\nI define a variable “Cond_Cells”. This is the value [Cells of Condition] which would be calculated by a properly constructed programming module which evaluates the following 9 conditions:\r\n\r\n1. If (mod(x,3) = 0 AND mod (y,3) = 0) then Cond_Cells = -1\r\nElse If\r\n2. If (mod(x,3) = 1 AND mod (y,3) = 0) then Cond_Cells = 0\r\nElse If\r\n3. If (mod(x,3) = 0 AND mod (y,3) = 1) then Cond_Cells = 0\r\nElse If\r\n4. If (mod(x,3) = 2 AND mod (y,3) = 0) then Cond_Cells = 0\r\nElse If\r\n5. If (mod(x,3) = 0 AND mod (y,3) = 2) then Cond_Cells = 0\r\nElse If\r\n6. If (mod(x,3) = 1 AND mod (y,3) = 1) then Cond_Cells = 0\r\nElse If\r\n7. If (mod(x,3) = 2 AND mod (y,3) = 1) then Cond_Cells = 1\r\nElse If\r\n8. If (mod(x,3) = 1 AND mod (y,3) = 2) then Cond_Cells = 1\r\nElse If\r\n9. If (mod(x,3) = 2 AND mod (y,3) = 2) then Cond_Cells = 1\r\n\r\n\r\n',NULL,0); INSERT INTO comment VALUES (3979,274,1942,'benard','more solutions','2003-04-10 15:15:35',0,'fill in the line to become a point. extend said point. Also, the king did not specify that he couldn\'t dig up and move floor tiles',NULL,0); INSERT INTO comment VALUES (3980,458,1942,'benard','check math on solution','2003-04-10 15:45:52',0,'Don\'t post \"the\" solution before you double check your math',NULL,0); INSERT INTO comment VALUES (3981,417,1942,'benard','this is not a sequence','2003-04-10 15:51:29',0,'This is not a sequence. Look up the word \"sequence\". This is a trick question, and belongs in a different category.',NULL,0); INSERT INTO comment VALUES (3982,491,1951,'Andrew','I think i got it!!!!','2003-04-10 17:23:39',0,'1000110?',NULL,0); INSERT INTO comment VALUES (3985,494,979,'Ravi Raja','re: solution','2003-04-10 22:24:08',0,'Austin: If the formula is in envelope 1 then both the statements written on the first envelope are false and so also the two statements on the second envelope which contradicts the conditions of the problem. So, please do check your solution once again. Thank You.',3959,0); INSERT INTO comment VALUES (3986,696,1183,'fwaff','re: low rating','2003-04-10 22:24:50',0,'So how do you get 213 days?\r\n\r\nI can see how you could get 37 from the faces you describe (6 months x 6 days = 36 + using the 5 as S and the M as a 3 to get 3rd September). Where do the other 176 come from?',3975,0); INSERT INTO comment VALUES (3987,696,1183,'fwaff','re: What?','2003-04-10 22:52:35',1,'Although it is not stated explicitly the implication is that each cube shows one full face. If we are allowed to display the cubes such that one or two faces are visible then other combinations appear. For example, if we have j, u, a, m, o, f on the faces of one cube then it can be positioned to show:\r\n\r\nOne face showing\r\nj - july\r\na - april\r\nn - november (turn the u upside down)\r\no - october\r\nm - march\r\nf - february\r\n\r\nTwo faces showing\r\nja - january\r\nju - june\r\nau - august\r\nma - may\r\n\r\nSimilarly, having 1 and 2 on opposite faces of the other cube and the numbers 3,4,5,6 on the other faces it\'s possible to get:\r\n\r\nOne face\r\n1,2,3,4,5,6,9\r\n\r\nTwo faces\r\n13,14,15,16,19,23,24,25,26,29\r\n\r\nWhich gives a total of 17x10 = 170 combintions (not counting combinations using letters as numbers and vice versa eg the 5 as an S and the M as a 3, etc)\r\n\r\nConversely, if the cube holder is constructed in such a way that only half a face is visible (like the one Nick Reed\'s nan has - see his comment in the orginal Calendar Cubes problem) then it\'s easy to have all twelve months on one cube. Similarly make the day cube such that only one corner of a face is visible, then 24 days are easily possible.\r\n\r\nThis gives 12x24 = 288 combinations.\r\n\r\nAlan: are either of these the \'genius concept\' you had in mind?\r\n',3972,0); INSERT INTO comment VALUES (3988,270,1660,'Tim Axoy','More than 2 babies','2003-04-11 02:00:44',3,'There were more than 2 babies,so they are certainly not twins.\r\n',NULL,0); INSERT INTO comment VALUES (3993,495,1947,'Jon','ummm...........','2003-04-11 05:44:44',0,'no clue. This is a really hard one because it is almost impossible to think about. How would telling eachother they didn\'t know their number effect the out come of who guessed first. Since I assume they know they have to be consecutive numbers, then eventually one might guess, but saying I don\'t know over and over again doesn\'t change the fact that it could be one higher or one lower than the card on the other\'s forehead.',NULL,0); INSERT INTO comment VALUES (3990,476,1947,'Jon','weird answer for fun','2003-04-11 04:26:51',0,'I think if you tell them that their mother\'s belly turns purple when rubbed, they might just let you go until they can find out for sure.',NULL,0); INSERT INTO comment VALUES (3991,732,1947,'Jon','hmmm.....','2003-04-11 04:33:39',0,'Drew is obviously a liar of sorts, but there isn\'t enough info to solve the problem. There is a few possibilities. Mohammud could either be a liar or tell the truth. If the statement were in two sentences like this, Mohammud is a liar, I am a liar, then the mohammud part becomes solvable assuming they either have to lie or tell the truth both. Since drew has to lie and tell the truth both in order to get away with saying I am a liar, this still puts Mohammuds honesty in question. I love paradoxes.',NULL,0); INSERT INTO comment VALUES (3992,732,1947,'Jon','re: hmmm.....','2003-04-11 04:37:08',0,'oops, I made a mistake. Mohammud tells the truth and Drew lies. Since the statement says both, if Drew calls Mohammud a liar, it doesn\'t matter what he says about himself, if he lied about that the rest would still be a lie. Since Drew lies, Mohammud then tells the truth. Either that, or Drew is just as confused as I am.',3991,0); INSERT INTO comment VALUES (3994,495,1575,'DJ','Attempt','2003-04-11 05:50:45',3,'I am assuming that both logicians know that the numbers are consecutive positive integers, and they both know that the other is going to think the problem out correctly.\r\nIf the first logician saw a 1, then he would know that his number was two (as zero is not positive).\r\nIf the second logician then saw a 1, he would similarly know he had a 2. If he saw a two, then, he would know that his number was 3 (if it was 1, the first logician would have been able to correctly guess a 2).\r\nIf the first logician, then, saw a 3, he would know that his number was a 4; like above, if his number was 2 the other logician would have correctly deduced a 3 on his own head.\r\n\r\nGoing on as such, after n \'statements of ignorance,\' the logician who sees the number n+1 on the other\'s forehead will be able to deduce that his own card bears the number n+2.',NULL,0); INSERT INTO comment VALUES (3995,434,1947,'Jon','umm my guess again','2003-04-11 05:57:33',0,'One draw is needed. Take one ball out of the box marked BW and you will get either a black or white ball. If you get a Black, then it has to contain two black balls because it can\'t contain one black and one white. Since the box marked WW can\'t have both white and we know where both black is, we know white has one of each color. Since the last box remaining is BB, and the last balls remaining is the white-white combination, they have to go together. When you pull a ball out of the BW box that is white, the same reasoning applies except switch everyy black from the previous explanation to white, andd all white to black.',NULL,0); INSERT INTO comment VALUES (3996,495,1947,'Jon','re: Attempt','2003-04-11 06:21:55',3,'This seems rigth, but I think there is more. Each logician knows the others number then they wait for n to reach the other fellows number. Assume x is equal to the number on the other logiacians head. As soon as x-1=n or x=n, then automatically, the logician knows his own number. Since in any situation (I tested this) the logician with the higher number will always see the x-1 or x =n situation first, the logician with the higher number will win. It does not matter if the numbers are even or odd or that A went first.',3994,0); INSERT INTO comment VALUES (3997,472,1947,'Jon','','2003-04-11 06:26:41',0,'I assume that the canon ball is denser than water since I haven\'t seen one that isn\'t. The water level will go down. A floating object displaces it mass in water when a sinking object displaces its volume. Since water is less dense than the canon ball, it has more volume for the same mass. So more water is displaced when the canon ball is in the boat then when the canon ball is at the bottom of the pool. This causes the drop in the water level.',NULL,0); INSERT INTO comment VALUES (3998,495,158,'Ender','My attempt','2003-04-11 06:37:44',3,'The first few iterations:\r\n\r\nA has a 2 on his forehead, B has a 1\r\nA:y \r\nA thinks \"B has a 1, so I must have a 2\"\r\n\r\nA-1, B-2\r\nA:n, B:y\r\nB thinks \"A has a 1, so I must have a 2\"\r\n\r\nA-2, B-3\r\nA:n, B:y\r\n\"A has a 2. If I had a 1, A would have already answered, so I must have a 3.\"\r\n\r\nA-3, B-2\r\nA:n, B:n, A:y\r\n\"B has a 2. If I had a 1, B would have already answered, so I must have a 3.\"\r\n\r\nA-4, B-3\r\nA:n, B:n, A:y\r\n\"B has a 3. If I had a 2, B would have already answered, so I must have a 4.\"\r\n\r\nA-3, B-4\r\nA:n, B:n, A:n, B:y\r\n\"A has a 3. If I had a 2, A would have already answered, so I must have a 4.\"\r\n\r\nA-4, B-5\r\nA:n, B:n, A:n, B:y\r\n\"A has a 4. If I had a 3, A would have already answered, so I must have a 5.\"\r\n\r\nA-5, B-4\r\nA:n, B:n, A:n, B:n A:y\r\n\"B has a 4. If I had a 3, B would have already answered, so I must have a 5.\"\r\n\r\nA-6, B-5\r\nA:n, B:n, A:n, B:n A:y\r\n\"B has a 5. If I had a 4, B would have already answered, so I must have a 6.\"\r\n\r\nFor each \"no\" heard, that player knows the number on their head must be higher than that number of no\'s (e.g., hearing 4 no\'s means that the number on their head must be at least 5.)\r\n\r\nSo they say \"no\" until they have heard either the number they see on the other\'s head, or one less than that number. They then say yes, and add one to the number they see for their number.\r\n\r\nSo if n statements of ignorance have passed before someone says yes, then the number said will be either n+1 or n+2, depending on if the other person\'s card is n or n+1.\r\n',NULL,0); INSERT INTO comment VALUES (3999,288,1919,'Lewis','ummmm','2003-04-11 06:42:21',3,'well, i think pretty much everyone has heard this one - IT CONTAINS EVERY LETTER OF THE ALPHABET',NULL,0); INSERT INTO comment VALUES (4000,281,1919,'Lewis','re(2): Answer','2003-04-11 06:45:47',0,'Well if its called \'answer\' most people would assume that it contains some answer, and that would most likely be for the one its commenting on....its quite obvious, really',1710,0); INSERT INTO comment VALUES (4001,493,1947,'Jon','','2003-04-11 06:46:11',0,'while we are at different solutions, (e^0+pi^0+e^0+pi^0)! very similar to others, but I like actually using to the zeroth power.',NULL,0); INSERT INTO comment VALUES (4002,263,1947,'Jon','paradox','2003-04-11 06:53:27',0,'this is really something of a approaching a limit. Each time Achilles reaches the point where the tortoise was last, the tortoise has moved on. This will not actually go on forever but the idea is that Every time Achilles reaches the spot, the tortoise doesn\'t make it quite as far from it as the last time. This will go on in distance wise forever, but Achilles will pass the tortoise when he reaches the limit of this distance. Even though he reached the limit, the mathematics of the distances could be computed as if he didn\'t.',NULL,0); INSERT INTO comment VALUES (4003,693,1947,'Jon','re(2): Posted Solution Not Minimum','2003-04-11 07:41:29',0,'This solution divides the weights, but it does not make them able to be added to make all possible intiger masses between 1 and 121. ',3951,0); INSERT INTO comment VALUES (4004,7,1947,'Jon','re(2): It\'s not 1/3 the way the problem was posed.','2003-04-11 08:19:44',1,'I agree with Bryan. You are told that one coin is tails, but not which coin is tails giving you the three ppossible outcomes instead of the two. t-t, t-h, h-t are all different possibilities, only one being favorable.',3617,0); INSERT INTO comment VALUES (4005,495,1301,'Charlie','My Nitpicking Note','2003-04-11 08:33:10',0,'The puzzle says \"n statements of ignorance later\" after 4 statements of ignorance have already been made. Does that mean there are n+4 statements of ignorance? The prior comments assume n statements of ignorance in all.\r\n\r\nJust nitpicking on my part.',NULL,0); INSERT INTO comment VALUES (4006,103,1947,'Jon','bob is right','2003-04-11 08:36:23',0,'The answer is to try and divert you from the obvious, but I don\'t see why his solution doesn\'t work, nicely done bob. 32 bars is done by 8x3 little bars. seperate each of the 8 rows first gives you seve breaks then divide the remaining rows individually into the one third chunk. At two breaks a row, and eight rows, you get 16 more breaks. 16+7=23 breaks in all.',NULL,0); INSERT INTO comment VALUES (4007,7,1301,'Charlie','re(2): It\'s not 1/3 the way the problem was posed.','2003-04-11 08:54:30',0,'You say \"Trying to read into the psyche of the puzzle\'s narrator introduces artificial constraints on the problem, resulting in a distorted answer.\", but in order to get the answer of 1/3, one must assume that the narrator, when faced with one head and one tail, would never choose to announce \"at least one tail\". That in fact is trying to read into the psyche of the narrator and assumes something that was not given in the problem statement. Where does the problem say that when faced with one of each, he\'d always report only the head?\r\n\r\nA better phrasing of the problem would have been \"When asked if there was at least one head, I replied \'yes\',\" placing the choice to prefer heads upon someone who didn\'t know the outcome, and explicitly stating in the puzzle a preference for reporting heads.',3617,0); INSERT INTO comment VALUES (4008,7,1301,'Charlie','re(3): It\'s not 1/3 the way the problem was posed.','2003-04-11 08:57:28',0,'Make that \"tails\" in my preceding post, but the argument is the same.',4007,0); INSERT INTO comment VALUES (4009,307,1626,'Gamer','Not really','2003-04-11 09:52:01',0,'Can you say pi=E? I don\'t think you can.',NULL,0); INSERT INTO comment VALUES (4010,469,1947,'Jon','an new idea in the subject','2003-04-11 10:14:32',0,'actually, everyone gains 100 rupes. since none of the debts depended on someon paying them back, all people received 100 rupes a value that would otherwise come out of their pocket. The final result would be the same if the bill was real. However, the last person to have the note, the author, would have gained 200 rupes except the second time he saw it he realized it was a fake. In truth, even though it was counterfeit, it earned everyone 100 rupes. ',NULL,0); INSERT INTO comment VALUES (4011,103,1301,'Charlie','re: bob is right (where did the other row go?)','2003-04-11 10:16:31',0,'8 x 3 is only 24 little bars. The puzzle calls for 8x4 little bars. You have 3 breaks to break apart 4 strips of 8, and each of those 4 strips of 8 requires 7 breaks. That\'s 3 + 4 x 7 = 31.\r\n\r\nThe other way, making 8 strips of 4, requires 7 breaks initially, and then each of the 8 strips of 4 requires 3 breaks, so 7 + 8 x 3 = 31.',4006,0); INSERT INTO comment VALUES (4012,469,1947,'Jon','re(2): The Solution','2003-04-11 10:17:45',0,'When the note comes back to him he can report the note the the FBI or something and make the person who paid it to him give him real money. Not honest, but very plausible.',3729,0); INSERT INTO comment VALUES (4013,722,1947,'Jon','don\'t spill','2003-04-11 10:27:04',0,'take the 11 and dump it into the three until the three is full giving you 8 gallons. dump the 11 into the 6 giving you 6 in the 6, 3 in the 3 and two in the 11. dump the three gallon bucket, then place the 2 from the 11 in it. refill the 11 and dump out the 6. 11 + 2(in the three bucket)= 13',NULL,0); INSERT INTO comment VALUES (4014,722,1947,'Jon','re: don\'t spill','2003-04-11 10:38:42',0,'oops, I didn\'t read close enough. Sorry, let me revise.',4013,0); INSERT INTO comment VALUES (4015,722,1947,'Jon','trying again','2003-04-11 10:53:45',0,'11 6 3 needed\r\n0 0 0 13\r\n0 6 0 7\r\n6 0 0 7\r\n6 6 0 1\r\n11 1 0 1\r\n11 0 1 1\r\n5 6 1 1\r\n5 4 3 1\r\n8 4 0 1\r\n8 1 3 1\r\nThis is the only way I saw to do it, but divide the 6 bucket and 3 bucket evenly by sight.\r\n8 2 2 1\r\n10 0 2 1\r\n11 0 2 0',NULL,0); INSERT INTO comment VALUES (4016,722,158,'Ender','Bad joke solution','2003-04-11 11:13:17',0,'First fill the 11 gallon container. Then use the meter on the gas pump to fill 2 gallons on one of the other containers.\r\n\r\n*Dodges rotten vegetables*\r\n\r\nHonestly, when was the last time you saw a gas station that didn\'t have meters on the pumps? This gas station owner needs to get with the times!\r\n',NULL,0); INSERT INTO comment VALUES (4017,722,1567,'Bryan','re: Bad joke solution','2003-04-11 11:35:21',0,'Ho, Ender <grin>. Nothing wrong with stating the obvious asnwer. Heck, if he\'d gone to full service, he would have just said, \"13 gallons, please.\" ',4016,0); INSERT INTO comment VALUES (4018,722,1567,'Bryan','Alternate solution','2003-04-11 11:55:16',3,'The man cannot dispose of any extra gas, but perhaps he can find or borrow another container at the gas station to hold some gas for a minute. If so, he can top off the 11-gallon container, then use it to fill the 6 and 3. He can then pour the remaining 2 gallons into the spare container, pour the 6 and 3 into the 11, top it off, pour the 2 gallons back into the 6 or 3, and go back to his car.',NULL,0); INSERT INTO comment VALUES (4019,722,1626,'Gamer','Use the liquid?','2003-04-11 12:08:53',2,'That was actually the solution I was thinking of... but what if he found a liquid that didn\'t mix with gasoline, but instead seperated and floated on top... Would this be legal?\r\n\r\nMy idea is fill up the 6 container with this liquid, dump it into the 11, fill it up again and put in all possible in the 11. You would have 1 gallon of liquid in the 6. Put this liquid into the 3. \r\n\r\nThen do the same thing with gasoline after you pour out/give back the liquid in the 11. You would then have 1 gallon liquid in the 3 and 1 gallon gasoline (in addition to 11 gallons in the 11)\r\n\r\nPut 1 more gallon of gasoline in the 3 (fill it up) and pour out/give back the 1 gallon in the 3, then carry it back in the 3 and the 11, and give them the 6 gallon container for letting you use the liquid :)',NULL,0); INSERT INTO comment VALUES (4020,722,1947,'Jon','another solution','2003-04-11 12:45:11',0,'the man could fill the 11 container, then dump as much as possible into the 6 container, leaving him 5 in the 11. Then dump from 11 to 3. He now has 2 left in the 11. Return this amount to his car. bring the empty 11 back, dump both the 3 and 6 into the 11. Add more gasoline til the 11 is full. Return to his car again with the 11 and add it to the two in his tank allready. This gives him 13 gallons. It just gives the man a reason to have a fourth container. (Unless he left his car at home?)',NULL,0); INSERT INTO comment VALUES (4021,492,1947,'Jon','I like this problem.','2003-04-11 13:10:34',0,'This problem is fun to figure out. my answer is:\r\n1 prancer \r\n2 cupid\r\n3 rudolph\r\n4 donder\r\n5 dasher\r\n6 blitzen\r\n7 vixen \r\n8 comet \r\n9 dancer\r\nI thought rudolph led the sleigh',NULL,0); INSERT INTO comment VALUES (4022,27,1626,'Gamer','Liar liar!','2003-04-11 13:32:52',0,'It\'s not really a paradox... The students know the teacher is lying about it being a complete surprise, so they can just assume there will be a test some time next week.',NULL,0); INSERT INTO comment VALUES (4023,491,1626,'Gamer','re: I think i got it!!!!','2003-04-11 13:35:57',0,'But how can it be? 2 and 5 are undefined in binary... Check out the solution below \\|/ (or the \"basic\" solution of 11,111,111,100)',3982,0); INSERT INTO comment VALUES (4024,86,1626,'Gamer','Problem with 2 Solutions','2003-04-11 15:14:20',0,'The two solutions I have seen so far:\r\n\r\nThe one given:\r\n\r\nSince multiplying by 10 just moves the decimal point, since we are in base 10, 39.99... has the same number of digits as 3.999... But .999... = .999 and so must have the same number or digits. (reflexive property) But 39 has 2 digits and 3 has one. So 3.999... x 10 must not equal 39.999...\r\n\r\nAnd I haven\'t yet found any PROOF that 1/9 = .1111... You can prove that .25 is 1/4 because .25*4 = 1 (exactly) but .111... x 9 = .9999... and that is circular reasoning to try to prove it is equal to 1. (I am not saying it can\'t be done, but we were trying to prove this in the first place!)',NULL,0); INSERT INTO comment VALUES (4025,494,1960,'Andrew F','Is it that straightforward?','2003-04-11 17:20:55',0,'What if we assume the problem tells us the answer?\r\n\r\nIf \r\n1 is true\r\n2 is false \r\n3 is true\r\n\r\nThe formula is in 2 and nothing is contradicted.\r\nThis would be a valid solution then, right?',NULL,0); INSERT INTO comment VALUES (4026,494,1960,'Andrew F','re: Is it that straightforward?','2003-04-11 17:30:45',0,'oops. misread. sorry\r\n1 mixed 2 true 3 false\r\n\r\n1 the formula is not in 1 (tue), nor in 2(so a flase assertion) (mixed if in 3)\r\n\r\n2 The formula is not in 1(true), but in 3(true) (true if in 3)\r\n\r\n3 the formula is in 3(so, not not in3-false) and not in 1 (also a false) (therefore 3 is both false)\r\nGot it. Sorry about the last post.\r\n\r\n',4025,0); INSERT INTO comment VALUES (4027,722,1964,'Marie','solution','2003-04-11 19:03:16',0,'He is at a gas station. He uses the register on the pump.',NULL,0); INSERT INTO comment VALUES (4028,494,1966,'Jessica Price','My thought','2003-04-11 21:04:38',0,'It is in envolope three',NULL,0); INSERT INTO comment VALUES (4029,722,775,'Cory Taylor','you guys are brlliant','2003-04-11 21:47:41',0,'my apologies for being intoxililcated but it is friday night...\r\nBrilliant asking for just asking for 13 gallons. I spent about 25 minutes on this one looking for a solution without success, so your solution works for me.',NULL,0); INSERT INTO comment VALUES (4030,491,1951,'Andrew','re(2): I think i got it!!!!','2003-04-12 02:48:09',0,'Yea i punched in 255 instead of 225.. and i don\'t understand what u mean by simple solution.',4023,0); INSERT INTO comment VALUES (4031,307,1933,'michael','No no','2003-04-12 04:31:45',0,'To get to a=a+b, one has to divide through by (a-b). But a=b, which means dividing by zero. End of algebraic validity.',NULL,0); INSERT INTO comment VALUES (4032,496,1301,'Charlie','First figure out...','2003-04-12 04:40:10',3,'First figure out what each of the four types of mathematicians would say about themselves (Use of \"he\" is made as a grammatical convenience):\r\npure and insane: says he\'s applied, says he\'s sane\r\npure and sane: says he\'s pure, says he\'s sane\r\napplied and insane: says he\'s applied, says he\'s insane\r\napplied and sane: says he\'s pure, says he\'s insane\r\n\r\nSince A says he\'s insane he must be applied.\r\nSince B says he\'s pure he must be sane.\r\nSince C says he\'s applied he must be insane.\r\nSince D says he\'s sane he must be pure.\r\n\r\nTherefore D is saying a falsehood when he says C is sane. Since D is pure, D must be insane.\r\n\r\nSo B is telling the truth that D is insane, and since B is sane, B must be pure.\r\n\r\nSo C is saying what is false when he says that B is applied, and since C is insane, C must be pure.\r\n\r\nSo A is telling the truth when he says C is pure, and since he\'s applied he must be insane.\r\n\r\nFinal result:\r\nA: applied & insane\r\nB: pure & sane\r\nC: pure & insane\r\nD: pure & insane',NULL,0); INSERT INTO comment VALUES (4033,496,1567,'Bryan','re: First figure out...','2003-04-12 08:59:41',0,'Charlie, you found a great way to disect this problem. I didn\'t take your word for it, but rather used the same technique and verified the same results (guess I was too lazy this morning to do the figuring myself).',4032,0); INSERT INTO comment VALUES (4034,702,1969,'Christian','Re:Solution','2003-04-12 10:22:04',4,'True, it could indeed be a drawbridge because when the drawbridge is open it is closed to traffic and when it is closed it is open to traffic, but think about this, when it is open it is also open to boat traffic and when it is closed it is closed to boat traffic.... can we think of a better answer?!?!',NULL,0); INSERT INTO comment VALUES (4035,429,1969,'Christian','re: Death Riddle','2003-04-12 10:29:53',0,'True, the poison could have been in the ice and so that man didn\'t get poisoned before it melted, but how do we know that some ice had not already melted into the punch, for the eat from the punch would transfer to the ice and the ice would melt in just a few minutes and we don\'t know quite how long the man had been at the party, just that he had left early. Also, how do we know that the man had no ice in his punch? I like to have ice in my drinks and it is a normal thing, so we must consider other things because you cannot assume that the ice has or has not melted by the time he drank it and you cannot assume that the man did not have any ice in his glass.',2796,0); INSERT INTO comment VALUES (4036,378,1969,'Christian','I think...','2003-04-12 10:38:17',0,'Could it be a coffin? For who makes it does not need it(or else they wouldn\'t be making it now would they?!?! lol), who buys it has no use for it(for they couldn\'t buy it now could they?!?!), and who uses it can neither see nor feel it so they must be dead! ',NULL,0); INSERT INTO comment VALUES (4037,342,1969,'Christian','There is one and it goes by the rules..','2003-04-12 10:42:11',2,'Play the piano to find the key, and use the key to unlock the door.',NULL,0); INSERT INTO comment VALUES (4038,329,1969,'Christian','Hmm..','2003-04-12 10:51:04',0,'In the solution, it states this:One letter is missing: a \"J\" - for June. There are a total of three months in a year starting with a \"J\", and of them, only \"June\" is also a woman\'s name. So Jason\'s gilrfriend\'s name is June. \r\nBut June is not the only woman\'s name, July is also a woman\'s name. Hasn\'t anyone ever paid attention to the orphan\'s names in the musical Annie?!?! Annie, Katie, Tessie, Duffy, Pepper, JULY**, Molly! I agree with the person who said the J in Jason is July because then the months go in order and it makes more sense.\r\n',NULL,0); INSERT INTO comment VALUES (4039,496,153,'TomM','','2003-04-12 12:53:01',3,'First, cobsider the statements about themselves. (Note that pure mathematicians are Knights and Applied mathemeticians are Liars)\r\n\r\nNo sane mathematician can claim to Applied. No insane mathematician can claim to be Pure. No Pure mathematician can claim to be insane. No Applied mathematician can claim to be sane.\r\n\r\nThus: A is Applied; B is sane; C is insane and D is Pure.\r\n\r\nD\'s second statement is false. Since D is pure, he is telling the truth as he believes it, so D is insane.\r\n\r\nB\'s second statement is true. Since B is sane, B is also pure.\r\n\r\nC\'s second statement is false. Since C is insane, he believes it to be true, and so C is Pure\r\n\r\nA\'s second statement is true. Since A is Applied, he believes he is lying, and so A is insane.\r\n\r\nIn Summary:\r\nA is Applied and insane\r\nB is Pure and sane\r\nC is Pure and insane\r\nD is Pure and insane ',NULL,0); INSERT INTO comment VALUES (4040,717,1861,'john','I agree','2003-04-12 13:19:45',0,'I agree with Brian, Austin, Hank, Lewis, and Jon.\r\nAlthough the solution is not yet posted, I would say five agreements makes it pretty well right. Sorry Mac, C alternates as you say, but the first statement has to be the lie. therefore statement two is the lie and he does not like strawberries. What is wrong with strawberries.',NULL,0); INSERT INTO comment VALUES (4041,43,1626,'Gamer','Easily done','2003-04-12 13:34:27',1,'Actually, when I looked in a few math books, it says divisible means you would need to have a remainder of 0. So your nitpicking is actually incorrect.\r\n\r\nThe way I did it was looked at numbers that were perfect squares, cubes and square, cube roots were prime... I got 2^4 as one (just by luck) and noted 17 was close too, so I got it quickly',NULL,0); INSERT INTO comment VALUES (4042,494,1861,'john','re: easy way to solve this type of problem','2003-04-12 15:38:49',0,'Unless I misunderstand you, this logic is flawed, or your post is incomplete. If I simply pick an envelope to be true and look at that only, then results would be as follows: True envelope/formula envelope--1/2,2/3,3/1 \r\nall envelopes could be true and this would be inconclusive, you had to look further to see that only 2/3 woulb de the possible solution==>it is not as easy as you would make it out to be. I do believe however that you came to the correct conclusion.',3970,0); INSERT INTO comment VALUES (4043,494,1861,'john','re: Solution','2003-04-12 15:42:41',0,'I like this way of looking at it. I examined all twelve possibilities of t/f rather than only three of env 1, 2 or 3. I did it the long way, you did it the smart way. Same answer though.',3954,0); INSERT INTO comment VALUES (4044,469,1971,'Steven','here\'s a go','2003-04-12 19:46:06',0,'I am a new-comer, I just joined today, but here goes. Really the problem has no answer because I am sure that all of the various articles purchased did not cost exactly 100 Rupees. In fact, if each individual got change when he bought a good or service, he actually made money. but then he lost when he accepted the note in payment for his service or good. so the answer would depend on how each person viewed both of his transactions, then the totals of each person would be the overall loss or gain.',NULL,0); INSERT INTO comment VALUES (4045,494,1971,'Steven','re: solution','2003-04-12 20:03:27',0,'if, in the first envelope one is true and one is false, no matter how you work it, that puts the formula in a different envelope',3959,0); INSERT INTO comment VALUES (4046,494,1971,'Steven','HAHA! i think i got it','2003-04-12 20:13:52',3,'the formula is in the third envelope. \r\nFirst Envelope (a)true (b)false \r\nSecond Envelope (a)true (b)true [has to be true because the only other options are true-true and false-false.\r\nCHECK: Third Envelope (a)false (b)false\r\nthe answers to the Third Envelope correspond to the answers to the other two envelopes. Is this right?',NULL,0); INSERT INTO comment VALUES (4047,168,1919,'Lewis','Other Solution','2003-04-13 00:14:21',1,'It could be an arabic book, because they go from right to left...',NULL,0); INSERT INTO comment VALUES (4048,732,1660,'Tim Axoy','You are correct!','2003-04-13 02:09:07',3,'You got the correct answer,but you need to focus on what Drew says about himself.\r\nJust look at the solution.',3992,0); INSERT INTO comment VALUES (4049,29,1660,'Tim Axoy','My strategy:How it works','2003-04-13 02:16:47',3,'A knight would point to Knightville if you asked him where it was,but a liar would point to Liarville.\r\nHowever,a knight tells the truth and points to Knightville meaning he would point to Knightville,but liars lie and will not say they will point to Liarville,but Knightville,so they point to Knightville. ',3834,0); INSERT INTO comment VALUES (4050,712,1919,'Lewis','re: Aha!','2003-04-13 02:41:23',4,'What the hell do you mean by \'base #\'?',3876,0); INSERT INTO comment VALUES (4051,469,979,'Ravi Raja','re: could it be?','2003-04-13 04:04:27',0,'Yes that\'s true Andrew that if he gets back the counterfeit note then he does not lose anything but he does gain a hundred rupees if the woman, as you have mentioned, does not remember that she owed him a hundred rupees.',3871,0); INSERT INTO comment VALUES (4052,494,979,'Ravi Raja','re: Is it that straightforward?','2003-04-13 04:05:20',0,'No, I am sorry Andrew, the answer you have arrived at is not correct. The formula is not in Envelope 2.',4025,0); INSERT INTO comment VALUES (4053,494,979,'Ravi Raja','re(2): Is it that straightforward?','2003-04-13 04:07:12',0,'Yes Andrew. This time you got it correct. ',4026,0); INSERT INTO comment VALUES (4054,469,979,'Ravi Raja','re: an new idea in the subject','2003-04-13 04:09:37',0,'How can you say Jon that everyone earned 100 rupees at the end of the transaction. Everybody got something worth rupees 100 from the next person thus forming a complete circle and then returning back to the one who had found the note. So is it not that nobody earned anything ?',4010,0); INSERT INTO comment VALUES (4055,496,1660,'Tim Axoy','People who say they are this are that.','2003-04-13 04:13:09',3,'All people believe they are sane.\r\nSane people truthfully and insane ones falsely.\r\nTherefore,A does not believe he is insane,but says it,so A is applied.\r\nAlso,C believes and says he is sane,so C must be pure.\r\n',NULL,0); INSERT INTO comment VALUES (4056,469,979,'Ravi Raja','re(3): The Solution','2003-04-13 04:14:50',0,'Then just think about the situation when the plumber also registers a complaint against that man saying that the man who had found the note settled his (the plumber\'s) account with the same note and as a rsult he would also have to pay his plumber real money. ',4012,0); INSERT INTO comment VALUES (4057,494,979,'Ravi Raja','re: My thought','2003-04-13 04:15:20',0,'Yes Jessica you are absolutely correct.',4028,0); INSERT INTO comment VALUES (4058,469,979,'Ravi Raja','re(3): The Solution','2003-04-13 04:17:53',0,'I hope in doing so, the man, finds himself standing behind the \"Bars\" !! lol. :)',4012,0); INSERT INTO comment VALUES (4059,494,1660,'Tim Axoy','Hunting for the formula','2003-04-13 04:18:55',3,'Suppose it is in Envelope 1.\r\nThen,both statements on both 1 and 2 would be false,but only one envelope has two false statements,so it is not in 1.',NULL,0); INSERT INTO comment VALUES (4060,494,979,'Ravi Raja','re(2): Solution','2003-04-13 04:19:49',0,'I agree John. A problem can always be solved in more than one way but people do prefer the shorter method and leave out the longer ones. ',4043,0); INSERT INTO comment VALUES (4061,494,1660,'Tim Axoy','1 and 2,true and true.','2003-04-13 04:21:59',3,'The first statements on both 1 and 2 are true,so 3 has two false statements.\r\nThat includes statement (a),which means 3 has the formula.\r\nBy the way,1 has one true and one false while 2 has two falses.',NULL,0); INSERT INTO comment VALUES (4062,469,979,'Ravi Raja','re: here\'s a go','2003-04-13 04:22:46',0,'Steven here in this problem we are assuming that everyone (as mentioned in the problem) had to pay every other (the next ones until they ate back to the one who found the note) person exactly the same amount and that amount here is taken to be \"Hundred Rupees\". Now I think you can proceed with your reasoning and give the appropriate answer. ',4044,0); INSERT INTO comment VALUES (4063,469,979,'Ravi Raja','re: SOLUTION','2003-04-13 04:27:49',0,'Levik, you have not yet replied to my comments yet. You had asked for a change in the solution and I made the necessary changes and had asked you to check them and let me know if that is alright or do I have to make any more changes. But unfortunately I do not see any replies from your part. How do I know whether the changes I have made are correct or not. So please do check the solution of this problem and then let me know. Thank You. ',3578,0); INSERT INTO comment VALUES (4064,496,1660,'Tim Axoy','D,not C!!','2003-04-13 04:29:41',0,'I made a mistake.',NULL,0); INSERT INTO comment VALUES (4065,494,979,'Ravi Raja','re: HAHA! i think i got it','2003-04-13 04:44:30',0,'Yes Steven, your answer is absolutely correct.',4046,0); INSERT INTO comment VALUES (4066,718,1660,'Tim Axoy','UHH!','2003-04-13 04:46:47',3,'The smallest positive number that can be made I think is (1/2)/3=1/6.\r\n\r\n\r\n\r\n',NULL,0); INSERT INTO comment VALUES (4067,494,979,'Ravi Raja','re: Hunting for the formula','2003-04-13 04:48:23',0,'Okay this is correct but you have to find out the envelope in which the formula is, Tim.',4059,0); INSERT INTO comment VALUES (4068,714,1660,'Tim Axoy','I do not know the answer.','2003-04-13 04:52:17',3,'I do not know the answer.',3956,0); INSERT INTO comment VALUES (4069,494,979,'Ravi Raja','re: 1 and 2,true and true.','2003-04-13 04:54:38',0,'Yes, Tim you got it this time, but why don\'t you post everything in just one place ?',4061,0); INSERT INTO comment VALUES (4070,718,979,'Ravi Raja','This is my Guess........','2003-04-13 05:00:57',1,'The smallest positive number that I can suggest using the digits 1,2 and 3 is : \r\n\r\n[(21)^(-3)]! \r\n\r\nWhich is equal to one divided by the cube of 21 and then the factorila of that result, so that the numerator is equal to 1 and the denominator is equal to (9261)!, thus giving us the result :\r\n\r\n[1/(9261)!] \r\n\r\nwhich is the smaallest number that I could think of till now, using the digits 1,2 and 3 only, i.e., [(21)^(-3)]! \r\n\r\nLet\'s see if anybody else has any other number in his/her mond.\r\n',NULL,0); INSERT INTO comment VALUES (4071,99,1660,'Tim Axoy','This puzzle is Level 9261.','2003-04-13 05:02:23',3,'21^3=9261 might work.\r\n',NULL,0); INSERT INTO comment VALUES (4072,718,979,'Ravi Raja','re: This is my Guess........','2003-04-13 05:05:42',0,'Oops I am sorry. The last line of my previous comment should be: \"Let\'s see if anybody else has any other number in his/her mind \", and not, : \" Let\'s see if anybody else has any other number in his/her mond \". \r\n\r\n',4070,0); INSERT INTO comment VALUES (4073,718,1,'levik','re: This is my Guess........','2003-04-13 05:06:33',0,'Ravi, I don\'t think that \r\n\r\n[(21)^(-3)]! \r\n\r\nis equal to \r\n\r\n[1/(9261)!]\r\n\r\nIn the first equation, the factorial is applying to the whole number, so the second would be (1/9261)!\r\n\r\nAnd I am not sure that factorial is defined for fractions.',4070,0); INSERT INTO comment VALUES (4074,718,979,'Ravi Raja','re(2): This is my Guess........','2003-04-13 05:12:50',0,'Yes Levik. In that case I\'ll think of something else. I mean some other solution, \" IF FACTORIALS ARE NOT DEFINED FOR FRACTIONS \".',4073,0); INSERT INTO comment VALUES (4075,718,979,'Ravi Raja','How About This Guess ?','2003-04-13 05:15:44',1,'The smallest positive number that can be made using the digits 1, 2 and 3 only is (according to me): \r\n\r\n[(21)!]^(-3)\r\n\r\nI hope there is nothing wrong with this one.',NULL,0); INSERT INTO comment VALUES (4076,718,1660,'Tim Axoy','Smaallest','2003-04-13 05:23:50',0,'It is the smallest,not smaallest.',4070,0); INSERT INTO comment VALUES (4077,228,1660,'Tim Axoy','Paradoxes','2003-04-13 05:27:36',0,'This is more of a paradox than a riddle.',NULL,0); INSERT INTO comment VALUES (4078,718,1301,'Charlie','re(2): This is my Guess...(factorials of fractions).....','2003-04-13 05:48:40',0,'While there is a generalization of the factorial function that extends to fractions, it does not lead to (1/n)! being equated with 1/(n!). In general, x! = Γ(x+1), where Γ() represents the Gamma function. A good discussion is at www.rskey.org/gamma.htm. In the case of (1/9261)!, the result comes out as approximately .999937683957. This is very close to 1 (one), as would be expected since 0! is defined as 1 (one) and 1/9261 is very close to zero.',4073,0); INSERT INTO comment VALUES (4079,718,1928,'The Mighty Puck','smaller than UHH! i think.','2003-04-13 06:48:47',1,'try (1/2)^-3 = 1/8',4066,0); INSERT INTO comment VALUES (4080,718,1928,'The Mighty Puck','re: smaller than UHH! i think.','2003-04-13 06:50:01',1,'strike that last one\r\n\r\nmake that (1/2)^3',4079,0); INSERT INTO comment VALUES (4081,718,1928,'The Mighty Puck','never mind both of those...','2003-04-13 06:51:52',1,'(1/3)^2 = 1/9',NULL,0); INSERT INTO comment VALUES (4082,718,1928,'The Mighty Puck','i don\'t suppose this is legal is it?','2003-04-13 06:53:24',4,'1/23 \r\n\r\nit uses all the digits...they just aren\'t seperate. and im assuming we aren\'t considering 0 a positive number.\r\n\r\n',NULL,0); INSERT INTO comment VALUES (4083,718,1928,'The Mighty Puck','after seeing ravi raja','2003-04-13 06:58:32',0,'i kinda wish i hadn\'t posted. *grins*',NULL,0); INSERT INTO comment VALUES (4084,718,1301,'Charlie','re: How About This Guess ?-- a better guess','2003-04-13 07:56:43',1,'[(31)!]^(-2) is much smaller than [(21)!]^(-3).\r\n[(31)!]^(-2) is about 1.48x10^-68, while [(21)!]^(-3) is about 7.50 x10^-60.',4075,0); INSERT INTO comment VALUES (4085,732,1660,'Tim Axoy','Only Level 1','2003-04-13 08:14:55',0,'This puzzle is only Level 1.\r\nI thought it would be too simple.\r\nBy the way,you got a correct answer.',3894,0); INSERT INTO comment VALUES (4086,732,1919,'Lewis','answer','2003-04-13 09:12:50',3,'Drew is a liar and Mohammad is a knight. Simple',NULL,0); INSERT INTO comment VALUES (4087,732,1660,'Tim Axoy','Good,my friend','2003-04-13 09:16:10',0,'That is it.',4086,0); INSERT INTO comment VALUES (4088,718,1626,'Gamer','re(2): How About This Guess ?-- Does this work?','2003-04-13 12:22:13',0,'My guess is 2^(-(31!)) or 3^(-(21!)), although I don\'t know how to figure out what they would be.',4084,0); INSERT INTO comment VALUES (4089,348,1975,'iris','Hmm...','2003-04-13 13:16:11',0,'I don\'t really like the \"water gives me life\" line because when the \"sun brings him death,\" it becomes water.',NULL,0); INSERT INTO comment VALUES (4090,249,1660,'Tim Axoy','Is it?','2003-04-13 13:34:14',4,'Is 1113213211 correct?\r\n \r\n',NULL,0); INSERT INTO comment VALUES (4091,99,1660,'Tim Axoy','I did not think of thit.','2003-04-13 13:40:33',0,'That is really clever(sarcasm).',351,0); INSERT INTO comment VALUES (4092,84,1660,'Tim Axoy','No! You cannot! You cannot overtake the last person! No,no,no!','2003-04-13 13:57:31',3,'If you overtake the last person,then you are behind the last person,but nobody is behind the last person.',NULL,0); INSERT INTO comment VALUES (4093,84,1660,'Tim Axoy','Agreement','2003-04-13 13:58:36',0,'I agree.',1496,0); INSERT INTO comment VALUES (4094,313,1660,'Tim Axoy','Simple Simon met a Pieman who gave Simple Simon a problem called Sugar Cubes.','2003-04-13 14:00:48',3,'Just add 1,8,and 64 to get 73.\r\nIt is as simple as that.',NULL,0); INSERT INTO comment VALUES (4095,189,1626,'Gamer','Another idea','2003-04-13 14:27:45',1,'The same number in the alphabet',NULL,0); INSERT INTO comment VALUES (4096,718,1301,'Charlie','re(3): How About This Guess ?-- Does this work? Yes that works.','2003-04-13 14:54:27',0,'Wow! indeed, the first of the two is indeed smaller. 2^(-(31!)) is about 1/(10^(2.5*10^33)) while 3^(-(21!)) is about 1/(10^(2.4*10^19)).\r\n\r\nSo the tiniest so far is 2^(-(31!)), and extended precision arithmetic tells us this is about 1.02192753424799x10^-2,475,321,084,412,797,072,581,101,485,711,599.\r\n\r\nIn fact I don\'t think both sets of parentheses are needed in your formulation. If they were, they\'d run into Alan\'s prohibition on any symbol\'s being used more than once.',4088,0); INSERT INTO comment VALUES (4097,718,1301,'Charlie','Better solution','2003-04-13 15:11:58',0,'Even better is .1^(32!). This is \r\n10^-63,130,836,933,693,530,167,218,012,160,000,000',NULL,0); INSERT INTO comment VALUES (4098,718,1567,'Bryan','Let\'s not reinvent the wheel','2003-04-13 18:04:09',2,'C\'mon, everybody! The answers proposed so far aren\'t even within orders of orders of magnitude of our best efforts. It seems to me that the place to start is with Nick\'s solution to \"Make the Most of These Digits\". In this problem, it was shown that the largest number we could think to make using the digits 1, 2, and 3 and the same limitation of not repeating any symbols was
(.1^-2e3)!
where 2e3 = 2000, e being the symbol for exponent in scientific notation. So a STARTING point for our search of the smallest positive number we can get might be
.1^2e3! (which = .1^2000!)
Some improvements on this include
Tan(.1)^2e3!
In degrees, not radians, Tan(.1) = 0.001745331024189
Sin[Tan(.1)]^2e3!
Sin[Tan(.1)] = 3.046177290459e-5
We could keep on in this vein using hyperbolic trig functions, but we might run out of types of brackets to use.
Now, does anyone have any ideas for improving on this? And can someone with a really big calculator tells us what the last expression is equal to?
I better tell Nick there\'s a bigger number than his solution, while I\'m at it.\r\n',NULL,0); INSERT INTO comment VALUES (4099,718,979,'Ravi Raja','I Think This Is The \" SMALLEST \"','2003-04-13 21:18:08',3,'Here is the smallest number that I could get using the digits 1, 2 and 3 only:\r\n\r\n[(.1)]^[(2)^(3!)]!\r\n\r\nWhich is equal to (.1) raised to the power of (64!) (factorial of 64). Since (3!) = 6 and [(2)^(3!)] = 64 and therefore [(2)^(3!)]! = (64)!. This will give us a number which will contain (64!), that is, (factorial 64) zeros between the \'Decimal Point\' and the digit 1(One), and this I believe is the \"SMALLEST\" of all the numbers yet obtained/derived using the digits 1, 2 and 3 only.\r\n\r\nDoes anybody else agree with me ? ',NULL,0); INSERT INTO comment VALUES (4100,718,979,'Ravi Raja','re(3): This is my Guess...(factorials of fractions).....','2003-04-13 21:27:28',0,'Well I think you need to check your calculations Charlie. Since we know that 1/9 = .11, 1/99 = .01...., and so on. So as the denominator keeps on increasing, the numerator always remaining fixed and equal to 1, we see that the value of the fraction gradually approaches 0(ZERO), then how can you say that 1 divided by (9261)! will give you a result which is close to 1(One) and not to 0(ZERO). So could you please perform the calculations again Charlie. ',4078,0); INSERT INTO comment VALUES (4101,718,979,'Ravi Raja','HELP !!!! HELP !!!!','2003-04-13 21:39:32',3,'Charlie , or anybody else please could you help me out with this one? I have found out two different solutions but I cannot just figure it out which one of the two is smaller. Could you please perform the calculations for me as you do and let me know. Thank You. Here are the two different numbers (smallest positive) that I have obtained using the digits 1, 2 and 3 only once:\r\n\r\n(a) [(3!)]^[-{(21!)}], which is equal to (1/6) raised to the power of 21 factorial. So that we have 1 in the numerator and 6 raised to the power (21!) in the denominator. And here is the next one.\r\n\r\n(b) [(.1)]^[(2)^(3!)]! \r\n\r\nWhich is equal to (.1) raised to the power of (64!) (factorial of 64). Since (3!) = 6 and [(2)^(3!)] = 64 and therefore [(2)^(3!)]! = (64)!. This will give us a number which will contain (64!), that is, (factorial 64) zeros between the \'Decimal Point\' and the digit 1(One).',NULL,0); INSERT INTO comment VALUES (4102,718,153,'TomM','re: HELP !!!! HELP !!!!','2003-04-13 22:03:16',0,'Ravi-\r\n\r\nSorry, but...\r\n\r\nBoth of those expressions use the factorial symbol (!) twice. The problem states that we can only use each symbol once.',4101,0); INSERT INTO comment VALUES (4103,72,1660,'Tim Axoy','DJ,I just... ...wanted to... ...do it because... ...of so and so. OOOOOOOOOKKKKKKKKK? AGREEMENT?','2003-04-14 02:36:57',0,'OK,DJ?\r\nI apologize.',3483,0); INSERT INTO comment VALUES (4104,68,1660,'Tim Axoy','8 5 4 9 1 7 6 3 2 0. 8 5 4 9 1 7 6 3 2 0. 8 5 4 9 1 7 6 3 2 0.','2003-04-14 02:42:53',3,'I start out with the first letters.\r\nEFFNOSSTTZ\r\nThe next letters.\r\nIIOINEIHWE\r\nIt is in alphabetical order.',NULL,0); INSERT INTO comment VALUES (4105,718,1660,'Tim Axoy','I agree! I agree!','2003-04-14 02:51:10',3,'That is big. I think it is as big as 640!.',4099,0); INSERT INTO comment VALUES (4106,497,1301,'Charlie','solution','2003-04-14 03:28:56',3,'Let the distance between Reno and Las Vegas be the unit of distance, and the time it takes the bird first leaving Reno (the R bird) to get to Las Vegas be the unit of time. Call the speed of the bird originally starting at Las Vegas (the LV bird) s. Let x miles be y units of our distance measure.\r\n\r\nWhen the two birds meed for the first time, the LV bird has traveled a distance of 2y (we can convert to miles later if necessary, but right now we\'re using Reno-LasVegas units), and has been traveling at rate s, and so has taken 2y/s units of time. Meanwhile the R bird has traveled 1-2y units traveling as speed 1. Therefore (2y/s)=(1-2y).\r\n\r\nWhen they meet the second time, the LV bird has traveled the full distance plus y, that is 1+y units at rate s, totalling (1+y)/s units of time. At that same time the R bird has traveled the whole distance plus 1-y, or a total distance of 2-y, at speed 1, so the time is 2-y, and therefore (1+y)/s = 2-y.\r\n\r\nSo we have \r\n2y/s = 1-2y\r\nand\r\n(1+y)/s=2-y\r\n\r\nDivide the former by the latter to get\r\n2y/(1+y) = (1-2y)/(2-y)\r\n\r\nThis leads to \r\n4y-2y²=1-y-2y²\r\n5y=1\r\ny=1/5\r\nThen as 2y/s=1-2y,\r\ns=2y/(1-2y)=(2/5)/(3/5)=2/3\r\nTherefore the LV bird is traveling at 2/3 the speed of the R bird. A diagram with the appropriate slopes bouncing off the two sides, shows that the next time they meet, the R bird will have made 3 full one-way trips while the LV bird will have made 2, so they will both be at Las Vegas when this happens.',NULL,0); INSERT INTO comment VALUES (4107,696,1183,'fwaff','Posted solution does not work','2003-04-14 03:38:29',4,'There are two errors within the solution. \r\n\r\nFirstly, you are using A to represent both April and August which is expressly forbidden in the rules. Since you created 11 numbers on the number cube then by losing a month your solution reduces by 11.\r\n\r\nSecondly, at the end of the first paragraph you say \"This gives us 8 months\". Then in the middle of the second paragraph you say \"Now we add 9 because only 9 of the months on the cube have 30 days\". Since you only found 8 months your solution reduces by a further 1.\r\n\r\nI make it that your solution gives 78 possibilities.',NULL,0); INSERT INTO comment VALUES (4108,718,1301,'Charlie','re(4): This is my Guess...(factorials of fractions).....','2003-04-14 03:45:58',0,'Ravi, did you read the beginning of the post? I did not say that 1/(9261!) is close to 1, I said that (1/9261)! is close to 1. That is, using the definition of x!=Γ(x+1), when you take the fraction 1/9261, which itself is quite close to zero, and apply this generalized factorial function to that small number, the result is close to one, and that this is analogous to 0! itself being 1. It is you who have mistakenly stated that 1/(9261!) = (1/9261)!. It is the latter of this pair that I am saying is close to 1. The former is certainly close to zero, as you say.\r\n\r\nWhat I said, copied:\r\nIn the case of (1/9261)!, the result comes out as approximately .999937683957. This is very close to 1 (one), as would be expected since 0! is defined as 1 (one) and 1/9261 is very close to zero. \r\n',4100,0); INSERT INTO comment VALUES (4109,718,1301,'Charlie','re: I Think This Is The','2003-04-14 03:47:43',0,'[(.1)]^[(2)^(3!)]! \r\nuses the factorial symbol and the power symbol twice each and the problem calls for each symbol to be used only once.',4099,0); INSERT INTO comment VALUES (4110,718,1301,'Charlie','re: Let\'s not reinvent the wheel','2003-04-14 04:11:35',0,'My calculator is not big enough for the factorial power, but note that Tan[Sin(.1)] is smaller than Sin[Tan(.1)] .\r\n\r\nTan(Sin(.1)) is 3.046172652279979e-5\r\n\r\nso if someone wants to pile function upon function, be sure to find the most efficiently minimizing sequence.',4098,0); INSERT INTO comment VALUES (4111,497,1183,'fwaff','re: solution','2003-04-14 04:14:31',4,'Isn\'t this one of several possible solutions?\r\n\r\nWhat about the cases when at the second \'crossing\' both birds are travelling in the same direction? ',4106,0); INSERT INTO comment VALUES (4112,696,775,'Cory Taylor','all twelve months','2003-04-14 04:22:30',0,'you could get all 12 months onto one die. Assuming for sake of description simplicity that both cubes are of equal size, write the three letter abbreviation of a month near the top of a cube face. Then, looking at teh face with writing on in, rotate the cube 180 degrees, keeping the written face viewable, and write the next three letter abbreviation on the top of the same face (the first month is showing upside down on the bottom half of the face), giving you two months on the first face. This method can be repeated on six faces giving you all 12 months on one die. A similar procedure could be used to get 12 day numbers as well (though I\'m not sure this can\'t be beaten).\r\nFinally, you need to construct a little groove that the dice can fit in which will obscure bothe of their bottom halves. This gives me 144 days of the year on two dice.',NULL,0); INSERT INTO comment VALUES (4113,722,1920,'Brian Smith','12, 14 but no 13','2003-04-14 04:27:28',0,'I got 12 and 14 gallons, but not 13 yet. This puzzle will keep me occupied for a while.',NULL,0); INSERT INTO comment VALUES (4114,497,1902,'Hank','don\'t ask me how','2003-04-14 05:42:40',1,'but I got .2x from Las Vegas',NULL,0); INSERT INTO comment VALUES (4115,497,1301,'Charlie','re(2): solution--another solution','2003-04-14 05:56:00',3,'Here\'s one additional solution, where the LV bird is slow enough so that the R bird on its return from Las Vegas passes the LV bird still on its first leg. The other possibility would be if the LV bird were so fast it was the one to pass the R bird. That case I think would require the LV bird to be much much faster than the R bird in order that the first distance from LasVegas be twice the second distance from Reno. Perhaps someone else can figure that case.\r\n\r\nBut in the case of a slower LV bird, my equations become\r\n2y/s=1-2y\r\n(1-y)/s=2-y\r\n\r\n2y/(1-y)=(1-2y)/(2-y)\r\n1-3y+2y²=4y-2y²\r\n4y²-7y+1=0\r\ny=(7±√33)/8\r\nUsing the + gives a solution above 1, contrary to the situation, so y=(7-√33)/8 = 0.156930 and s = 2y/(1-2y)=0.457427.\r\n\r\nThe next time they meet, will be shortly thereafter as the R bird bounces back from Reno, starting out his 3rd one-way trip while LV is still completing his 2nd. Let this distance be called z. Then\r\n(1-z)/s = 2+z\r\nz=(1-2s)/(s+1) = 0.058422\r\nbut this is the fraction of the way back to Las Vegas. As y is 0.156930 (which is x miles), z converts to 0.372281 y, in our units, or 0.372281 x miles.',4111,0); INSERT INTO comment VALUES (4116,496,1947,'Jon','my guess at this one','2003-04-14 07:27:10',0,'A cannot say he is insane unless he is either a liar, or very confused. If he beleived he was insane and was pure, he would be sane, but then be wrong about his guess which doesn\'t work. If If he believed he was sane and pure, he would be sane and would say so. If he was Applied and beleived he was insane, he would say sane, and actually be insane which he is so that is also a contradiction. So A is an Applied Sane person.\r\nA says C is pure. This is a lie so A believes C is applied. A is always right about his beliefs so C is Applied. C says he is applied so he beleives he is pure. this isn\'t true so C is insane. C says B is applied. This is a lie so C believes B is pure. C is insane so this is incorrect. B is also applied. B says he is pure. Since we know he is a liar, he believes he is applied. Being correct about his belief, B is sane.B says D is insane which is a lie so B believes D is sane. B is right always so D is sane.D says C is sane. This is wrong so either D is lying or he doesn\'t actually know. We know D is always correct so he has to be lying. D is Applied.\r\n\r\nA is applied sane.\r\nB is applied sane.\r\nC is applied insane.\r\nD is applied sane.',NULL,0); INSERT INTO comment VALUES (4117,496,1947,'Jon','re: People who say they are this are that.','2003-04-14 07:29:14',0,'I know you meant D not C so here is my counter argument. If D were right insane, he would believe himself sane and therefore could easily tell himself to be sane truthfully. P.S. my answer is wrong so don\'t look at it.',4055,0); INSERT INTO comment VALUES (4118,496,1947,'Jon','Got it now.','2003-04-14 07:37:24',3,'My answer works perfectly until you look at what D says about himself. I D is applied sane he would say himself insane. so he must be pure. So he believes C is sane which is wrong so D is insane and just believes himself sane. B has to be either Applied insane or pure sane in order to say he is pure. C says B is applied which is a lie so he believes B is pure which would be wrong so B is applied. Froom before we now know that B is insane. From my first answer we know that A is Applied sane, there is no other answer there. This just agrees with th e rest of this answer so here it is.\r\nFinal answer is \r\nA Applied sane\r\nB Applied insane\r\nC Applied insane\r\nD Pure insane\r\n',4116,0); INSERT INTO comment VALUES (4119,496,1947,'Jon','I am wrong twice, lol.','2003-04-14 07:43:56',0,'Charlie you are right and I am wrong, my B doesn\'t work because it disagrees with himself. K get it now',4032,0); INSERT INTO comment VALUES (4120,719,1947,'Jon','odd solution','2003-04-14 07:47:47',3,'They could count all the grains of sand and then divide that number by 121, because of their tube they know the weight of all the sand. Take the answer of their division and count the number of grains of sand out and use those for the weight.',NULL,0); INSERT INTO comment VALUES (4121,672,1947,'Jon','quite simple really','2003-04-14 08:16:41',0,'the sheild maker, knowing about the swords would make a sheild with two handles that the sword maker would slice in half. this gives the sheild maker two sheilds instead of one neither of which is able to be destroyed, but have been sliced through by the sword. Done.',NULL,0); INSERT INTO comment VALUES (4122,719,1902,'Hank','question','2003-04-14 08:18:41',4,'how did they know that they had 121g of sand in the first place?',NULL,0); INSERT INTO comment VALUES (4123,469,1301,'Charlie','The solution','2003-04-14 08:40:16',0,'The \"Another possible reasoning\" section claims that \"everybody stands in relation to his/her debtor just where he/she was before I picked up the note\". How could that be? Looked at in that light, the tailor now has a sewing machine for which he owes 100 rupees, where beforehand he didn\'t owe anything and did not have this sewing machine?\r\n\r\n',NULL,0); INSERT INTO comment VALUES (4124,719,1567,'Bryan','Do they have to?','2003-04-14 08:51:37',1,'The ancients had to create a 1 gram weight, but maybe they don\'t need to weigh out one gram of sand to do it.
Say they have a balance, and they reconfigure it so the lengths of the balance arm on either side of the fulcrum have a 121:1 ratio. They place the empty tube on the short arm, and make a weight that counters the empty tube when placed on the long arm. Next, they fill the tube with sand and put it back on the short arm of the balance. They leave the first weight on the long arm (this counters the weight of the tube), and fashion a new weight to counter the 121g of sand. If balanced, this new weight will be 1g.',NULL,0); INSERT INTO comment VALUES (4125,719,1902,'Hank','would it be better','2003-04-14 09:07:59',0,'They can\'t know that they have 121g. what they do know is that they have a tube of sand. and they want to find out what 1/121 of the sand is.\r\n\r\nIf this is the case, then the previous comment by Bryan may be valid.',NULL,0); INSERT INTO comment VALUES (4126,719,775,'Cory Taylor','my solution','2003-04-14 09:09:46',0,'since there is no precendent set for the weight of one gram, the ancients could simply portion whatever amount of sand they thought might provide a convenient measure, and call it \"one gram\". Then they\'d have to lock it away in a safe in a foreign country to guarantee its longevity for comparitive measurement purposes...',NULL,0); INSERT INTO comment VALUES (4127,719,1626,'Gamer','The problem says:','2003-04-14 09:51:49',1,'For this, you have to KNOW that the tube holds 121 grams of sand. We don\'t know how they know this, but they must know that.\r\n\r\nThen, to know they have 121 grams of sand, they just pour it all in the tube and see it exactly fits.\r\n\r\nWhat you are trying to do is find 1/121 of what will fit in the tube, since 1 gram/ 121 grams = 1/121.\r\n\r\n\r\nI don\'t know how to do this without a scale or measurements on the tube... So I don\'t know if I ruled out something in the problem',NULL,0); INSERT INTO comment VALUES (4128,719,1902,'Hank','re: my solution','2003-04-14 10:01:32',0,'This sounds sound',4126,0); INSERT INTO comment VALUES (4129,690,885,'np_rt','Inaccurate solution','2003-04-14 10:24:53',0,'Ice water is the better choice of the two, assuming the steel is hotter than 100 degrees C.\r\n\r\nBtw, it\'s Fourier\'s law of heat transfer that says that the rate of heat transfer is proportional to the temperature gradient, not thermo.\r\n\r\nUsing either bucket does not change the fact that the steel loses heat by means of conduction, assuming you don\'t move the steel too much. It only changes the boundary condition of the governing differential equation (Laplace Operator on the temperature is zero, assuming roughly constant properties).\r\n\r\nThe boundary condition is Newton\'s law of cooling, q\'\'=h*deltaT or q=h*A*deltaT. It is true that the fact that water evaporating will cause the steel to contact vapor (100 degrees C) slightly more.\r\n\r\nBut because of this, the mechanism of heat transfer has changed from natural convection to natural convection with boiling/evaporation. This means that the h is greatly increased (typically about 100-10,000 times larger), which more than balances the change in T (~50 degrees or so). Of course, other fluid properties have to be taken into account such as viscosity, density, thermal diffusivity, heat capacities, and beta (which I won\'t go into detail).\r\n\r\nWhen the lower portion of the steel touches the water, the water vapor will rise up and take away heat from the higher portions steel (which I assume to be hotter than 100 degrees). Then the upper portion of the steel will be cooled down completely as it\'s submerged into the bucket. Although the water vapor will only cool the steel for a few seconds, this will make it a better choice.\r\n\r\nAnd for those of you who are still in doubt, you can check anywhere that using water with evaporation (equipment safety issues though) or steam with condensation is one of the best ways of heat transfer. That\'s why it\'s used in most industrial plants, not only because it\'s cheap.',NULL,0); INSERT INTO comment VALUES (4130,494,1981,'tony','this is easy','2003-04-14 10:38:09',0,'its in the second envelope. 1st-both true, 2nd both false, and the third, the first statement is true, and the second is false.',NULL,0); INSERT INTO comment VALUES (4131,469,1660,'Tim Axoy','Yes,an idiot. A stupid idiot.','2003-04-14 10:54:20',0,'Yes,Robert!\r\nWho was it?',3511,0); INSERT INTO comment VALUES (4132,35,1626,'Gamer','Ok','2003-04-14 11:33:05',1,'Except if you think that the or is an xor type... Either 17 OR 23 but not both... Since 00 is divisible by both, you wouldn\'t be able to use it.',NULL,0); INSERT INTO comment VALUES (4133,150,1626,'Gamer','Problem with Solution','2003-04-14 11:39:10',0,'The puzzle said a grid of PEOPLE... And since one person isn\'t people, I don\'t think you can have a 1x1 grid.',NULL,0); INSERT INTO comment VALUES (4134,719,1626,'Gamer','re: my solution','2003-04-14 13:35:01',0,'The problem I see with this is we are already given 121 \"grams\" to measure by (the tube), so unless the decided measurement = this one, we are stuck. Is this right?',4126,0); INSERT INTO comment VALUES (4135,690,775,'Cory Taylor','re: Inaccurate solution','2003-04-14 16:55:17',0,'Im so glad that someone agrees with me on this one. I can say all day that the actual material that has been used for this purpose for the last (well, many) years has been water and that there would\'ve had to be a good reason for it, not to mention all the other pros I came up with.\r\n\r\nThank you np_rt',4129,0); INSERT INTO comment VALUES (4136,722,1839,'Rajeev','13 the lucky number','2003-04-14 21:05:49',0,'11-(3+6) + 11 = 13',NULL,0); INSERT INTO comment VALUES (4137,733,1301,'Charlie','solution','2003-04-15 03:44:41',3,'Let\'s assume that if for example the triangle\'s vertex that lies to the north is the one that has two edges joined to opposite ends of an edge of the square, and that it connects to both ends of the north edge of the square. \r\n\r\nEach horizontal slice will be a trapezoid (that is, in the U.S.; in England it would be called a trapezium) with two parallel edges. At the extremes they are degenerate, as the square, with two sets of parallel edges, and the triangle where one of the parallel edges has length zero.\r\n\r\nFirst we need to find the volume. To simplify the math, let x range from zero at the bottom to 1 at the top. The differential of volume is therefore 200 dx (measured in centimeters).\r\n\r\nThe larger (south in our setup) side of each trapezoid will be 20-4x cm, while the smaller (north) side will be 20-20x cm. These average to 20-12x cm. The altitude of each trapezoid will be 20-(20-8√3)x cm.\r\n\r\nThe area of each trapezoid will be (20-12x)(20-(20-8√3)x). We need to integrate this from zero to one and multiply that by 200 to get the volume.\r\n\r\nThis comes out to 200 ∫{0 to 1} (400 - (640-160√3)x + (240-96√3)x²)dx\r\n\r\nWe get 200[400x - ((640-160√3)/2)x² + ((240-96√3)/3)x³]{0 to 1}\r\n\r\nwhich evaluates to 48627.68775...\r\n\r\nWe need to multiply by the 2.8 g/cm³ density. Blindly multiplying we\'d get 136157.5... grams, but 2.8 g/cm³ was given to only 2 significant figures. Allowing for the fact that the answer begins with a lower digit, we can stretch and allow 3 significant digits in the answer, and conveniently say 136 kg.',NULL,0); INSERT INTO comment VALUES (4138,733,1102,'Robin Gatter','My solution','2003-04-15 03:52:34',0,'My answer is: 236.957 Kg.\r\n\r\nThe horizontal cross-section varies between a square at the bottom and an equilateral triangle at the top. Typically this is a trapezium with parallel sides length 20-x/50 and 20-x/10 and the perpendicular distance between them is 20 - x(1/10-sqrt(3)/25), where x is the height of the cross-section above the base in cm. The area of a trapezium is the average of the 2 parallel sides multiplied by the perpendicular separation. Integrating this area over the range corresponding to the pillar\'s height gives the pillar\'s volume, 84627.69 cc, and hence the mass.',NULL,0); INSERT INTO comment VALUES (4139,733,1102,'Robin Gatter','re: solution','2003-04-15 04:01:05',0,'Charlie I like your solution much better than mine, which fails a simple sanity check. I\'m still looking for my slip...',4137,0); INSERT INTO comment VALUES (4140,733,1902,'Hank','a solution','2003-04-15 04:22:19',3,'(this may be the same as previous, I have not yet looked)\r\nthe volume of the pillar would be the average of two pillars (one with the triangle base, one with the square base)\r\nV of pillar with triangle base = .5*16*13.85*200 = .5bhd = 22160\r\nV of pillar with square base = 20*20*200 = 80000\r\nThe mean of the two would be = (80000+22160)/2 = 51080 cm^3 * 2.8g/cm^3 = 143024g',NULL,0); INSERT INTO comment VALUES (4141,279,1920,'Brian Smith','function f(x) = x+1','2003-04-15 04:22:56',0,'This puzzle got me thinking, but for some of the trouble spots in my list I used the trig identity sec (arctan (sqrt x)) = sqrt (x + 1).\r\nUsing that identity I came up with a system to generate every number 6 to infinity.\r\n\r\n(sec (arctan (sqrt 2)))^(0!+0!) + 3 = 6\r\n(sec (arctan (sec (arctan (sqrt 2)))))^(0!+0!) + 3 = 7\r\n(sec (arctan (sec (arctan (sec (arctan (sqrt 2)))))))^(0!+0!) + 3 = 8\r\n(sec (arctan (sec (arctan (sec (arctan (sec (arctan (sqrt 2)))))))))^(0!+0!) + 3 = 8\r\n\r\nRepeatedly applying sec (arctan (x)) increases the value of the expression by 1.',NULL,0); INSERT INTO comment VALUES (4142,352,1686,'DuCk','my answer','2003-04-15 04:57:54',0,'8, 1, 15, 10, 6, 3, 13, 12, 4, 5, 11, 14, 2, 7, 9\r\n\r\n-- I started by listing #s 1-15 and what they could stand next to. After some observation you realize 8 can only border 1 to make a perfect square and 9 can only border 7. Therefore, these must be the end digits. Pretty much after that you work your way inside; matching up what #s border each other. The sequence above is the end result and satisfies the requirements.\r\n\r\n-Thanks levik, this was enjoyable...',NULL,0); INSERT INTO comment VALUES (4143,733,1301,'Charlie','','2003-04-15 05:02:05',0,'',NULL,0); INSERT INTO comment VALUES (4144,733,1301,'Charlie','A Twist','2003-04-15 05:02:49',3,'The puzzle states that the edge of the triangle opposite the vertex that has two of the non-horizontal edges, is parallel to two edges of the square but does not actually state which two. In my previous solution I had assumed that the north vertex of the triangle connected to both ends of the north side of the square and the south side of the triangle was parallel to the north and south edges of the square. But if the top is twisted 90 degrees, say ccw as seen from above, what is now the west vertex is now still connected to the two ends of the north side of the square and the opposite edge of the triangle is parallel to the east and west sides of the square (i.e., running north-south). The twist is not severe enough to entangle the edges, as it would in a 180-degree twist, and so a column is still formed.\r\n\r\nI\'d hate to have to formulate this for integration, so I chose to integrate this numerically.\r\n\r\nEach level except the top and the bottom is an irregular quadrilateral. Near the triangular top it in fact becomes non-convex. The best way to get the area of the quadrilateral is to split it into two triangles, each of whose areas can be found using Heron\'s formula. In doing so it is important that the diagonal dividing the quadrilateral connect the concave vertex to its opposite (when such concave vertex exists), as if the other two vertices are connected, area outside the bounds of the actual quadrilateral would be included.\r\n\r\nHeron\'s formula states that the area of a triangle equals √(s(s-a)(s-b)(s-c)) where a, b and c are the lengths of the sides of the triangle, and s = (a+b+c)/2. This avoids the necessity of finding a base and altitude.\r\n\r\nBy setting coordinates for the vertices for the base and the top of the column, intermediate coordinates can be interpolated.\r\n\r\nThe following program evaluates the volume for both the non-twist and twist cases:\r\nDEFDBL A-Z\r\nDIM topx(4), topy(4)\r\nDIM botx(4), boty(4)\r\nbotx(1) = 0: boty(1) = 0\r\nbotx(2) = 20: boty(2) = 0\r\nbotx(3) = 20: boty(3) = 20\r\nbotx(4) = 0: boty(4) = 20\r\n\r\npi = ATN(1) * 4\r\ndr = pi / 180\r\nCLS\r\nFOR twist = 0 TO 90 STEP 90\r\n PRINT twist,\r\n topx(1) = 0: topy(1) = 0\r\n topx(2) = 16: topy(2) = 0\r\n topx(3) = 8: topy(3) = 8 * SQR(3)\r\n topx(4) = 8: topy(4) = 8 * SQR(3)\r\n\r\n FOR i = 1 TO 4\r\n x = topx(i) * COS(twist * dr) - topy(i) * SIN(twist * dr)\r\n y = topx(i) * SIN(twist * dr) + topy(i) * COS(twist * dr)\r\n topx(i) = x: topy(i) = y\r\n NEXT\r\n\r\n volume = 0\r\n stepSize = .00001\r\n FOR i = stepSize / 2 TO 1 - stepSize / 2 STEP stepSize\r\n \' PRINT USING \"#.## \"; i;\r\n FOR j = 1 TO 4\r\n midx(j) = botx(j) * (1 - i) + topx(j) * i\r\n midy(j) = boty(j) * (1 - i) + topy(j) * i\r\n \' PRINT USING \"###.### ###.###; \"; midx(j); midy(j);\r\n NEXT\r\n\r\n \'Triangle Area=SQRT(s(s-a)(s-b)(s-c)),\r\n \'where s = (a + b + c) / 2 OR perimeter / 2!\r\n FOR j = 1 TO 4\r\n k = (j MOD 4) + 1\r\n dist(j) = SQR((midx(k) - midx(j)) ^ 2 + (midy(k) - midy(j)) ^ 2)\r\n NEXT\r\n dist(5) = SQR((midx(1) - midx(3)) ^ 2 + (midy(1) - midy(3)) ^ 2)\r\n s = (dist(1) + dist(2) + dist(5)) / 2\r\n area = SQR(s * (s - dist(1)) * (s - dist(2)) * (s - dist(5)))\r\n s = (dist(4) + dist(3) + dist(5)) / 2\r\n area = area + SQR(s * (s - dist(4)) * (s - dist(3)) * (s - dist(5)))\r\n \' PRINT USING \"###.##\"; area\r\n volume = volume + area * stepSize * 200\r\n NEXT i\r\n PRINT volume\r\n PRINT\r\nNEXT twist\r\n\r\nFor the zero and 90-degree twists the program finds the volumes:\r\n0 48627.6871924711\r\n90 34056.7495513749\r\n\r\nSo for the twisted case, 34057*2.8 = 95360 g, or, with allowed precision 95 kg.',NULL,0); INSERT INTO comment VALUES (4145,127,1686,'DuCk','my guess','2003-04-15 05:09:55',0,'I\'m thinking there is definitely more cream in the coffee, since you pure a spoonful of 100% cream into the coffee. Now when when you pour the coffee/cream mixture back into the cream, you have a diluted (so to speak) solution of coffee going in. Since you stirred the coffee before returning the spoonful, I think that the amount of cream that goes back into the cream cup is very small. This leads me to believe there is more cream in the coffee than coffee in the cream.',NULL,0); INSERT INTO comment VALUES (4146,127,1686,'DuCk','re: my guess','2003-04-15 05:13:39',0,'i am definitely wrong. it was definitely too early to be thinking. especially proportionally! =)',4145,0); INSERT INTO comment VALUES (4147,159,1920,'Brian Smith','Upper bound formula','2003-04-15 05:25:06',1,'After a little thought on this problem, I came up with a formula which gives a strong upper bound on the number of black squares.\r\n\r\nThe ideal tiling on an infinite board is a diagonal pattern.\r\n\r\nXOOXOOXOOXOOXOO\r\nOXOOXOOXOOXOOXO\r\nOOXOOXOOXOOXOOX\r\nXOOXOOXOOXOOXOO\r\nOXOOXOOXOOXOOXO\r\nOOXOOXOOXOOXOOX\r\n\r\nEvery white square borders exactly 2 other white squares.\r\n\r\nThis pattern can be applied to any rectangle. The number of black squares in the rectangle is ceil(x*y/3).\r\n\r\nOne black square can be removed by situating a diagonal to end in the upper left corner.\r\n\r\nThe total number of black squares in the rectangle now is ceil(x*y/3) - 1.\r\n\r\nIf a diagonal ends in the lower right corner another black square can be removed. A diagonal will end in the lower right corner if (x-y) mod 3 = 0.\r\n\r\nThe total number of black squares in the rectangle now is:\r\n ceil(x*y/3) - 1 if (x-y) mod 3 != 0\r\n and\r\n ceil(x*y/3) - 2 if (x-y) mod 3 = 0\r\nThis formula works for all x,y >= 4\r\nIt gives 20 black squares for the 8x8 board.\r\n\r\nAll the white squares except half of the border squares touch exactly two other white squares. The remaining white squares touch only one other white square.\r\n\r\n*ceil is the ceiling function. ceil rounds a non integer up to the next integer. \r\nceil (1.9) = 2, ceil (2) = 2, ceil (2.1) = 3\n\nEdited on December 2, 2003, 11:53 am',NULL,0); INSERT INTO comment VALUES (10088,159,1920,'Brian Smith','Solution','2003-12-02 12:03:59',3,'Cases 1 by x and 2 by 2:\r\nZero black squares\r\n- Every square borders at most two squares so the conditions of the problem are already met.\r\n\r\nCases 2 by x for x>=3:\r\nfloor(n/2) black squares\r\n- Uses the following pattern (X=black squares):\r\nOOOXOOOXOOOXOOOXOOOXOO ....\r\nOXOOOXOOOXOOOXOOOXOOOX ....\r\n\r\nCases 3 by x for x>=3:\r\nx-2 black squares\r\n- The black squares are the x-2 squares NOT along the border.\r\n\r\nCases x by y for x>=4 and y>=4: \r\nif (x-y) mod 3 != 0 then ceil(x*y/3)-1 black squares\r\nif (x-y) mod 3 = 0 then ceil(x*y/3)-2 black squares\r\n- See this comment.',NULL,0); INSERT INTO comment VALUES (4148,494,1971,'Steven','re: this is easy','2003-04-15 06:53:38',0,'if in the second envelope (a) is false, that means the formula IS in the first envelope. a contradiction',4130,0); INSERT INTO comment VALUES (4149,741,1928,'The Mighty Puck','guess','2003-04-15 07:20:16',1,'we know that De Morgan\'s age was between 41 and 44, assuming that there even is a solution. Let\'s finish by listing all the squares in this range \r\n\r\n41^2 = 1681, \r\n42^2 = 1764, \r\n43^2 = 1849, \r\n44^2 = 1936. \r\n\r\nSo, the only possible age, consistent with the given information and our assumption of the age of De Morgan when he died, is 43 years old. he was born when the year was 1849. So the answer is x = 43. \r\n\r\nthe only resonable answer i can think of for jim is that he was born in 1980 and will be 45 in 2025. \r\n\r\nam i off here?',NULL,0); INSERT INTO comment VALUES (4150,714,1920,'Brian Smith','Cs and Qs: Different answer','2003-04-15 08:17:37',3,'I found a different answer to this puzzle.\r\n\r\nh2c5c3a1q5o2c7f3a1q7e5q5o2c7h2c3\r\n\"He could cut a quart of coniper for a quarter every quart of coniper he cut.\"',NULL,0); INSERT INTO comment VALUES (4151,279,775,'Cory Taylor','re: function f(x) = x+1','2003-04-15 09:36:30',0,'subtly invalididates rule d. Also, It looks like the final sum you\'ve shown is 9, not 8, but that\'s just semantics...\r\n\r\nMy method (in progress) is to define trig functions in degrees rather than radians and use the arccos and arcsin of numbers less than one to give me fractions, which can be rounded up or down according to other posters. Still working on a couple of the larger ones.\r\n\r\nAlso, I came up with a previous method to calculate any number to infinity, but it was rejected due to its notation.',4141,0); INSERT INTO comment VALUES (4152,741,1567,'Bryan','re: guess','2003-04-15 09:56:46',3,'I agree Jim was born in 1980 and will be 45 in the year 45^2 (2025).
De Morgan was 43 in the year 43^2 (1849), so he was born in 1806.',4149,0); INSERT INTO comment VALUES (4153,719,233,'Zach Bolinger','Viable approach','2003-04-15 13:03:04',1,'The problem goes to great lengths to assure us that the sand is a homogenous mixture with a constant density. It seems to me that if you marked off the tube in 1/121 increments, the sand between each tick would weight 1 gram. It would be difficult to calculate where the ticks belong. If the number were 128, you could just divide by 2, 7 times. If you could accurately divide the tube into 11 sections, and then divide each section by 11 again, you would have a 1 gram mark.\r\n\r\nDo we have a balance that will allow us to split the collection of sand in half? I\'m not sure if that knowledge would help.',NULL,0); INSERT INTO comment VALUES (4154,154,1989,'Vicky','re: open a new mint','2003-04-15 20:40:27',0,'Good idea, but I think you can\'t do that... Something about a government thing, and plus, since it\'s the owner\'s fault he locked it in the safe, shouldn\'t they not give him or her the money? Heh, sorry it\'s totally off subject, but yeah... And why would they put it in the safe? Can\'t you use drills to break open the top? Or lasers? Argh. So is the guy saying there\'s more than one possible combination? We just need to find the shortest... O boy. ',3735,0); INSERT INTO comment VALUES (4155,741,979,'Ravi Raja','First Possibility','2003-04-15 21:32:27',3,'We can calculate and see that: \r\n(42)^2 = 1764, (43)^2 = 1849, (44)^2 = 1936 and (45)^2 = 2025. \r\nSo, it is obvious that 43 years old in the Year 1849, which implies that he was born in the year 1806, whereas Jim will turn 45 years in the year 2025 implying he was born in the year 1980.\r\n\r\nSo, in AUGUSTUS DE MORGAN\'s case, x = 43 and in JIM\'s case, x = 45. This was the first possibility.',NULL,0); INSERT INTO comment VALUES (4156,741,979,'Ravi Raja','Second Possibility','2003-04-15 21:35:08',3,'We can calculate and see that: \r\n(42)^2 = 1764, (43)^2 = 1849, (44)^2 = 1936 and (45)^2 = 2025. \r\nSo, it is obvious that 43 years old in the Year 1849, which implies that he was born in the year 1806, whereas Jim will turn 44 years in the year 1936 implying he was born in the year 1892.\r\n\r\nSo, in AUGUSTUS DE MORGAN\'s case, x = 43 and in JIM\'s case, x = 44. This was the second possibility. \r\n\r\n',NULL,0); INSERT INTO comment VALUES (4157,494,979,'Ravi Raja','re: this is easy','2003-04-15 21:45:24',0,'No Tony, the formula is not in the second envelope. Please do check your anser and reasoning again. ',4130,0); INSERT INTO comment VALUES (4158,469,979,'Ravi Raja','re: The solution','2003-04-15 21:55:14',0,'Charlie: Now, what value do you assign to a counterfeit note ? Irrespective of whether it is a 100 Rupees note or a 500 Rupees note. It\'s value I suppose always should be considered to be equal to zero. \r\n\r\nSo, when the milkman paid the tailor for the garments he had made, he was at a loss of 100 rupees, that is you can say (-100). After that he (the tailor), used the same note (whose value we are assuming to be equal to zero) to purchase a sewing machine for himself worth Rupees 100. So, here he has gained 100 Rupees, that is (+100).\r\n\r\nSo, now the net loss or gain will be calculated by adding the two values, that is (-100) and (+100), which will give us the result 0, which implies no profit, no loss.',4123,0); INSERT INTO comment VALUES (4159,469,979,'Ravi Raja','re: Yes,an idiot. A stupid idiot.','2003-04-15 21:55:48',0,'That was the author, that is me, Tim. :) lol :)',4131,0); INSERT INTO comment VALUES (4160,494,979,'Ravi Raja','re(2): this is easy','2003-04-15 21:57:40',0,'Exactly Steven. You are absolutely correct. Tony must have made some mitake in his reasoning or might be he lost track and was confused. :)',4148,0); INSERT INTO comment VALUES (4161,732,979,'Ravi Raja','re: Solution','2003-04-15 22:10:54',0,'You are correct Jonny Doe but explain how you arrived at the result.',3892,0); INSERT INTO comment VALUES (4162,732,979,'Ravi Raja','re: Not so fast','2003-04-15 22:17:59',0,'how can you say that statement Bryan ? If you are Truth teller, the you can never say that comment.And if you can then you are a liar and the person whom you are speaking of has to be a truth teller. \r\nOr may be I am not getting what you are trying to say. ',3893,0); INSERT INTO comment VALUES (4163,732,979,'Ravi Raja','re: Seems too simple','2003-04-15 22:25:14',0,'You are absolutely correct DuCk. That is the actual reasoning. ',3894,0); INSERT INTO comment VALUES (4164,732,979,'Ravi Raja','re: Answer','2003-04-15 22:33:32',0,'You are absolutely correct Lewis.',3902,0); INSERT INTO comment VALUES (4165,732,979,'Ravi Raja','re: answer','2003-04-15 22:42:20',0,'Absolutely Correct. ',3912,0); INSERT INTO comment VALUES (4166,732,979,'Ravi Raja','re: Hmmm','2003-04-15 22:46:59',0,'Yes Michael, your answer is correct but here in your solution \"I\" has to be Drew. So the answer is Drew is a Liar and Mohammad is the Truth Teller, and not \"I\" am a Liar.',3934,0); INSERT INTO comment VALUES (4167,718,979,'Ravi Raja','That\'s it. This is the SMALLEST. I got it.','2003-04-15 23:07:54',3,'Okay now I think I have finally obtained the smallest positive number which can be formed using the digits 1,2,and 3 once only and any mathematical symbols that we are aware of, and also no symbol being used more than once. Here is how I figured it out, though I do not know whether it is the smallest or not. So I might need help once again from Charlie or anyone who can help me with the calculations.\r\n\r\nIt has been observed from the previous comments that: 2^(-(31!)) is about 1/(10^(2.5*10^33)) while 3^(-(21!)) is about 1/(10^(2.4*10^19)), so the tiniest so far is 2^(-(31!)), and extended precision arithmetic tells us this is about 1.02192753424799x10^-2,475,321,084,412,797,072,581,101,485,711,599. \r\n\r\nNow all I have to do is use a sine function because I know that sin(x) approaches 0 (zero) as x approaches 0 (zero). \r\n\r\nTherefore the smallest positive number which can be formed using the digits 1,2,and 3 once only and any mathematical symbols that we are aware of, and also no symbol being used more than once is as given below: \r\n\r\nsin [2^{-(31!)}].\r\n\r\nThat is, sin(x), where x = 2^(-(31!)) \r\n\r\n',NULL,0); INSERT INTO comment VALUES (4168,718,979,'Ravi Raja','HELP !! I think I found out the SMALLEST Number','2003-04-15 23:12:14',3,'Okay now I think I have finally obtained the smallest positive number which can be formed using the digits 1,2,and 3 once only and any mathematical symbols that we are aware of, and also no symbol being used more than once. Here is how I figured it out, though I do not know whether it is the smallest or not. So I might need help once again from Charlie or anyone who can help me with the calculations. \r\n
\r\nIt has been observed from the previous comments that: 2^(-(31!)) is about 1/(10^(2.5*10^33)) while 3^(-(21!)) is about 1/(10^(2.4*10^19)), so the tiniest so far is 2^(-(31!)), and extended precision arithmetic tells us this is about 1.02192753424799x10^-2,475,321,084,412,797,072,581,101,485,711,599. \r\n
\r\nNow all I have to do is use a sine function because I know that sin(x) approaches 0 (zero) as x approaches 0 (zero). \r\n
\r\nTherefore the smallest positive number which can be formed using the digits 1,2,and 3 once only and any mathematical symbols that we are aware of, and also no symbol being used more than once is as given below: \r\n
\r\nsin [2^{-(31!)}]. \r\n
\r\nThat is, sin(x), where x = 2^{-(31!)}\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (4169,498,1626,'Gamer','Seen before','2003-04-16 01:51:31',3,'I remember this one :) I never solved it... spent at least an hour trying to figure it out.\r\n\r\n1 is given\r\n\r\nSo far there are 1 1s = 11\r\n\r\nNow so far there are 3 1s = 31\r\n\r\nNow so far there are 4 1s, 1 3 = 4113\r\n\r\nNow so far there are 6 1s, 2 3s, 1 4=612314\r\n\r\nNow so far there are 8 1s, 1 2, 3 3s, 2 4s, 1 6, = 8112332416 (the answer)',NULL,0);
INSERT INTO comment VALUES (4170,741,1626,'Gamer','re: Second Possibility','2003-04-16 01:56:40',0,'Doesn\'t \"The other day...\" mean Jim said it recently? So Jim would have to be 111 years old for that to be true... and I thought that was out.',4156,0);
INSERT INTO comment VALUES (4171,741,979,'Ravi Raja','re(2): Second Possibility','2003-04-16 04:09:29',0,'Well you are trying to say that a person can never be 111 years old ? \r\nIf that is so then my solution is wrong but if you agree that, yes, a person can be 111 years old, then I think there is nothing wrong with the second possibility. ',4170,0);
INSERT INTO comment VALUES (4172,741,979,'Ravi Raja','re(2): Second Possibility','2003-04-16 04:19:46',0,'By the way Gamer, how did you get that ? I mean how can you say that Jim would have to be 111 years old for my second answer to be true ? Can you please explain ?',4170,0);
INSERT INTO comment VALUES (4173,722,775,'Cory Taylor','re: 13 the lucky number','2003-04-16 04:33:39',0,'When I first looked at your solution I wondered how I could have missed something so simple, but on further inspection, your method requires a fourth container to hold the 2 gallons left in the 11 gallon tank so that you can put the 9 gallons in the other two tank back into the 11.\r\n\r\nOr have I overlooked something obvious?',4136,0);
INSERT INTO comment VALUES (4174,741,979,'Ravi Raja','re(2): Second Possibility','2003-04-16 04:38:08',0,'Gamer, this was what was stated in my comment \" SECOND POSSIBILITY\" : \r\n
\r\nWe can calculate and see that: \r\n(42)^2 = 1764, (43)^2 = 1849, (44)^2 = 1936 and (45)^2 = 2025. \r\nSo, it is obvious that Augustus De Morgan was 43 years old in the Year 1849, which implies that he was born in the year 1806, whereas Jim will turn 44 years in the year 1936 implying he was born in the year 1892. \r\n
\r\nSo, in AUGUSTUS DE MORGAN\'s case, x = 43 and in JIM\'s case, x = 44. This was the second possibility. \r\n
\r\nSuppose \"The other day....\" as referred in the problem is SOMEDAY, say, in the year 1912 (arbitrarily chosen, and can be any year between 1892 and 1936), so that only in that interval he can say that he will be \'x\' years in the year \'x^2\', where x = 44. And in the year 1902, Jim would have been 20 years old and not 111. So could you please explain how did you get that ? I mean how can you say that Jim would have to be 111 years old for my second answer to be true ? \r\n',4170,0);
INSERT INTO comment VALUES (4175,741,979,'Ravi Raja','re(2): Second Possibility','2003-04-16 04:44:16',0,'Gamer, this was what was stated in my comment \" FIRST POSSIBILITY\" : (Very Similar To Second Possibility)\r\n
\r\nWe can calculate and see that: \r\n(42)^2 = 1764, (43)^2 = 1849, (44)^2 = 1936 and (45)^2 = 2025. \r\nSo, it is obvious that Augustus De Morgan was 43 years old in the Year 1849, which implies that he was born in the year 1806, whereas Jim will turn 45 years in the year 2025 implying he was born in the year 1980. \r\n
\r\nSo, in AUGUSTUS DE MORGAN\'s case, x = 43 and in JIM\'s case, x = 45. This was the first possibility. \r\n
\r\nSuppose \"The other day....\" as referred in the problem is SOMEDAY, say, in the year 2000 (arbitrarily chosen, and can be any year between 1980 and 2025), so that only in that interval he can say that he will be \'x\' years in the year \'x^2\', where x = 45. And in the year 2000, Jim would have been 20 years old and not 111. So could you please explain how did you get that ? I mean how can you say that Jim would have to be 111 years old for my second answer to be true ? \r\n\r\nThis case is similar to the \"Second Possibility\" Case which has also been discussed in one of my replies posted.',4170,0); INSERT INTO comment VALUES (4176,741,1301,'Charlie','Direct approach','2003-04-16 04:57:34',3,'√1871=43.255... We want a date before 1871, so go with x=43 and born 43²-43=1806 for De Morgan.\r\n\r\n\"The other day\" implies recency, and the speaking is for the future, so calculate √2002 = 44.74... As it\'s in the future, round up to x=45 and the year of birth is 45²-45=1980 for Jim.',NULL,0); INSERT INTO comment VALUES (4177,469,1301,'Charlie','re(2): The solution','2003-04-16 05:07:39',0,'Yes, I also agree that the net loss to those persons is zero, but didn\'t see how that was concluded from the interpretation \"We can also say that all the transactions carried out through the counterfeit note are invalid\". The puzzle assumes that the tailor still owns the sewing machine, rather than being treated as fraudulent ownership.\r\n\r\nMy only disagreement with the overall \"no net change\" is that indeed, the woman is no longer in possession of the sewing machine she once had, and the narrator has had his debt to the plumber paid off. Thus the woman\'s debt to the narrator has been paid off, by in effect paying one of the narrator\'s bills.',4158,0); INSERT INTO comment VALUES (4178,741,979,'Ravi Raja','re: Direct approach','2003-04-16 05:16:37',0,'So according to you Charlie, x = 43 in case of De Morgan and x = 45 in case of Jim.\r\n\r\nIt is also posible that x = 44 (in case of Jim), whereas x remaining the same for De Morgan.',4176,0); INSERT INTO comment VALUES (4179,741,1301,'Charlie','re(2): Direct approach','2003-04-16 05:29:07',0,'The possibility of x=44 depends on \"The other day\" referring to a time before 1936, so that the future tense is warranted in Jim\'s statement. If someone were talking to me and said something about \"the other day\" and I later found out they were talking about something that happened that long ago, I would feel as if whoever said it was trying to deceive me.\r\n\r\nAlso, the possibility of x=44 would imply that pleasance was old enough in 1936 to understand perfect squares. And I thought that I was one of the older flooblers and even I wasn\'t yet born in 1936.\r\n\r\nAs a probability problem I\'d put P(x=44) << .01, where << means is much less than.',4178,0); INSERT INTO comment VALUES (4180,498,1947,'Jon','ummm...','2003-04-16 05:47:11',3,'this is like the 1, 11, 21, 1211, ... problem only with more of a total overall feeling about it, next two would be 8112332416, 11132113342618\r\njust count the number of times any digit appears and place them in a sequence. 8 1\'s, 1 2, 3 3\'s,..... and so on counting the total for all times in the sequence. I don\'t know what you would do if you reached 1,432 1\'s.',NULL,0); INSERT INTO comment VALUES (4181,718,1567,'Bryan','re: HELP !! I think I found out the SMALLEST Number','2003-04-16 06:09:59',0,'Ravi, read my post \"Let\'s not reinvent the wheel\" and Charlie\'s reply.',4168,0); INSERT INTO comment VALUES (4182,741,153,'TomM','re(3): Direct approach','2003-04-16 06:30:28',0,'The real question becomes how old is the puzzle itself? If it is older than 1936, then x = 44 and x² = 1936 is correct. If it is newer than 1980, then x = 45 and x² = 2025. If it dates from between 1936 and 1980, either answer suffices',4179,0); INSERT INTO comment VALUES (4183,712,1567,'Bryan','re(2): Aha!','2003-04-16 06:36:37',0,'Lewis, bases are a confusing topic when you first learn of them. Let\'s start by first considering how people count. Normally when we count, our numbers go
1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and
10, 20, 30, 40, 50, 60, 70, 80, 90, 100 etc.
The biggest single digit we have is \"9\", and there are nine numbers before we get to the double digits. But one could instead count in base 3, for example, where the numbers go
1, 2, 10, 11, 12, 20, 21, 22, 100, 101, 102, 110 ...
In base 3, the largest single digit is \"2\", and then one would have to start over in the double digits.
In base 10, if we consider the number \"468\", the 8 is said to be in the ones\' place, the 6 is in the tens\' place, and the 4 is in the hundreds\' place. In base 3, considering the number \"201\", the 1 is in the ones\' place, the 0 is in the threes\' place, and the 2 is in the nines\' place (9 of course is 3 squared).
Why use different bases other than base 10? Because it\'s easier for computers, that\'s why. The most common bases are hexadecimal (base 16, where the numbers go 1 thru 9, A, B, C, D, E, F, 10), octal (base 8), and binary (base 2, which only uses zeros and ones, like switches turned on and off).
For a good website on the topic, check out
http://www.dsgb.orbix.co.uk/doggie.htm',4050,0); INSERT INTO comment VALUES (4184,722,1,'levik','re: Bad joke solution','2003-04-16 07:36:51',0,'This is actually what the submitted solution is. :|\r\n\r\nI wonder if there\'s an actual way of doing it without relying on the potentially crooked gas station meter.',4016,0); INSERT INTO comment VALUES (4185,736,1902,'Hank','Half of the solution','2003-04-16 08:02:24',0,'I stink at and despise proofs, so I leave that to another puzzler.\r\n\r\nBut as for part B...(I think) it goes like this:\r\nx = the smaller integer\r\ny = the larger integer\r\na = the larger perfect square\r\nb = the smaller perfect square\r\n\r\na = ((x+y)/2)^2\r\nb = (y-((x+y)/2)^2\r\n\r\na-b=x*y',NULL,0); INSERT INTO comment VALUES (4186,736,1991,'jennifer','I think I got it.','2003-04-16 08:07:59',0,'The solution is:\r\n\r\n(sqrt a + sqrt b) * (sqrt a - sqrt b)= x = a - b\r\n\r\nWhere:\r\na is the largest of the squares,\r\nb is the smallest of the squares, and \r\nx is the product/difference\r\n \r\n',NULL,0); INSERT INTO comment VALUES (4187,736,1301,'Charlie','solution','2003-04-16 08:29:39',3,'If ab = k²-j² then by factoring, ab = (k+j)(k-j).\r\n\r\nIf we let k+j=a and k-j=b, adding the equations we get\r\n\r\n2k=a+b\r\n\r\nsubtracting the equations we get\r\n\r\n2j=a-b\r\n\r\nso \r\n\r\nk=(a+b)/2 and j=(a-b)/2\r\n\r\nIf a and b are both odd or both even, the numerators will be even, so k and j will be integers as required.\r\n\r\nSo, for example, if we seek 3*5=15, we can use k=(5+3)/2 and j=(5-3)/2, that is, 4 and 1, so 4²-1²=16-1=15, as needed.',NULL,0); INSERT INTO comment VALUES (4188,736,1991,'jennifer','re: solution','2003-04-16 08:34:01',0,'That is what I originally came up with. But does the question not state that a and b are the perfect squares not the integers?',4187,0); INSERT INTO comment VALUES (4189,736,1567,'Bryan','Solution','2003-04-16 08:51:53',3,'For any two numbers a and b,
[(a+b)/2]²-[(a-b)/2]² = [(a²+2ab+b²)/4] - [(a²-2ab+b²)/4] = 4ab/4 = ab
Thus the product of a and b equals the difference of the squares of (a+b)/2 and (a-b)/2. If a and b are both even or both odd, these will be perfect squares.',NULL,0); INSERT INTO comment VALUES (4190,736,1301,'Charlie','re(2): solution','2003-04-16 10:18:56',0,'Oh, Oh, I used misleading letters, not using a and b the way the problem called for. I write below what I should have had:\r\n\r\nLet the required a = p² and b = q² where p and q are integers so that a and b would be perfect squares.\r\n\r\nIf kj = p²-q² then by factoring, kj = (p+q)(p-q). \r\n\r\nIf we let p+q=k and p-q=j, adding the equations we get \r\n\r\n2p=k+j \r\n\r\nsubtracting the equations we get \r\n\r\n2q=k-j\r\n\r\nso \r\n\r\np=(k+j)/2 and q=(k-j)/2 \r\n\r\nIf k and j are both odd or both even, the numerators will be even, so p and q will be integers as required. \r\n\r\nSo, for example, if we seek 3*5=15, we can use p=(5+3)/2 and q=(5-3)/2, that is, 4 and 1, so that a = p² = 16 and b = q² = 14²-1²=16-1=15, as needed. \r\n',4188,0); INSERT INTO comment VALUES (4191,719,1072,'Alan','Ok','2003-04-16 10:51:35',0,'Well since i was asked about gamers comment to see if they\'re right- no. There is a solution, some of you might not like it but it will work, is feasible and is justified witl logic and certain principles',NULL,0); INSERT INTO comment VALUES (4192,736,1626,'Gamer','Other uses as well','2003-04-16 11:15:51',0,'In my solution, I used the integers and not the perfect squares... Just substitute sqrt(a) for a and sqrt(b) for b if you want to get the perfect squares and not the roots.\r\n\r\nThis is especially useful for easy multiplication. If asked what 23^2 was, you could just figure out what 20*26+(3^2) which is just 520+9 = 529',4190,0); INSERT INTO comment VALUES (4193,88,1994,'Tiffy','Ta Da!','2003-04-16 16:24:36',3,'They would both bring water, but the $ dude would drink a week poison before hand. They both only drunk water there, so the $ dude died.',NULL,0); INSERT INTO comment VALUES (4194,88,1994,'Tiffy','But Wait...','2003-04-16 16:25:55',4,'But does the $ dude find out about the pharm. dude\'s plan...?',NULL,0); INSERT INTO comment VALUES (4195,722,775,'Cory Taylor','re(2): Bad joke solution','2003-04-16 19:28:44',0,'I was beginning to wonder. It doesn\'t usualy take this group very long to come up with the answer to these types of problems...',4184,0); INSERT INTO comment VALUES (4196,718,979,'Ravi Raja','re(2): HELP !! I think I found out the SMALLEST Number','2003-04-16 22:11:10',0,'Yes Bryan I went through those two comments \"let\'s not reinvent the wheel\" and Charlie\'s reply to that post but I still do not understand why you asked me to check those comments. Is there anything wrong with my answer ? That is: sin [2^{-(31!)}], and if yes then what is it ? Please do let me know.\r\n\r\n\r\n\r\n',4181,0); INSERT INTO comment VALUES (4197,734,1301,'Charlie','solution without spherical trig','2003-04-17 03:55:24',3,'Take the 5 equilateral triangles that meet at one of the vertices, and cut them from the remainder of the icosahedron while still maintaining the same contact with each other. Lay this cap down on a base to form a pyramid with a regular pentagonal base. Choose any diagonal of the base; it forms a triangle with two sides of the pentagon. Let the sides of the pentagon be length 1. The angle at the vertex of the triangle that the diagonal creates is 108 degrees. Bisect this angle to form two right triangles and find that half the length of the pentagon’s diagonal is sin(54°).\r\n\r\nNow draw a median of one of the two triangles of the pyramid directly above the chosen diagonal, from one end point of the diagonal on the pentagon to the middle of the edge of the pyramid that lies above the diagonal. Then connect that midpoint to the midpoint of the diagonal. The result is a right triangle, with half the diagonal included as a leg. The right angle is at the midpoint of the diagonal on the base, as a line directly up from the base has to be merely rotated about the diagonal as an axis, as the slant edge of the pyramid is at right angles (but skew) to the diagonal.\r\n\r\nThe leg of the right triangle is half the diagonal, that is sin(54°). The hypotenuse is the slant height of the pyramid, that is, the altitude of the equilateral triangle, which is sqrt(3)/2. The angle at the edge is in fact half the dihedral angle as the plane of the triangle is perpendicular to the edge, by symmetry. That half dihedral angle is therefore arcsin(sin(54°)/(sqrt(3)/2) = arcsin(2 sin(54°)/sqrt(3)) = 69.09484255211072 degrees. Twice this is 138.1896851042214 degrees, which is the sought dihedral angle.\r\n',NULL,0); INSERT INTO comment VALUES (4198,734,1301,'Charlie','But, for the record','2003-04-17 03:59:45',3,'An icosahedron has five triangular faces meeting at each vertex. Erect a small sphere centered upon one vertex. The five faces intersect the sphere in five arcs of great circles forming a spherical regular pentagon. As each side of the pentagon is the arc subtended by one angle of a plane equilateral triangle, each is 60 degrees. The angles of the spherical pentagon are the dihedral angles of the original icosahedron.\r\n\r\nConnect the center of this spherical pentagon (on the sphere) to each of the pentagon’s corners and to each of the centers of the five sides, forming 10 congruent spherical right triangles (5 of each handedness).\r\n\r\nThe angle of each right triangle that is located at the center of the pentagon is 360/10 degrees, or 36 degrees. The angle at the midpoint of each side is 90° by symmetry. The leg opposite the 36-degree angle is half the length of the side of the pentagon, and therefore 30 degrees.\r\n\r\nIn spherical trigonometry there is a version of the law of cosines that relates three angles and one side:\r\n\r\ncos A = -cos B cos C + sin B sin C cos a, where capital letters refer to angles and lower case to sides, and side a is opposite angle A.\r\n\r\nAs the angle and side pair we know are 36 degrees and 30 degrees, and we know the angle adjacent to the 30-degree side is 90 degrees, we get\r\ncos(36) = - cos(90) cos C + sin(90) sin C cos(30)\r\nand as cos(90)=0, we can solve\r\nsin C = cos(36)/cos(30)\r\n\r\nAngle C is half the angle of the spherical pentagon, that is, half the dihedral angle sought, and therefore acute. The dihedral angle is twice this, and therefore 2 arcsin(cos(36)/cos(30)) = 138.1896851042214… degrees.\r\n',NULL,0); INSERT INTO comment VALUES (4199,734,1567,'Bryan','re: solution without spherical trig','2003-04-17 04:41:25',0,'Thanks for humoring me, Charlie. lol',4197,0); INSERT INTO comment VALUES (4200,497,775,'Cory Taylor','my solution','2003-04-17 08:19:18',0,'I really looked forward to this one, and finally got to it.\r\n\r\nThe way I see it, there are three possible ways that the birds can meet twice, once if the LV bird reaches its destination and meets the R bird again before the R bird has completed its first journey, one with the opposite happening, and one where both bird have completed one full journey and are on their return flight.\r\n\r\nThe formulas I used work out to be similar in all three cases which made checking each scenario fairly easy.\r\n\r\nHere we go - I\'ll just give the basics of my method, if you want to chekc it out go ahead! This problem actually turned out to be much easier than I expected it to be (Don\'t worry though Ravi - I think the 4 was still justified!)\r\n\r\nThis problem related to the RATIO of two velocities - the actual velocities are irrelevant. This means that we can assume values for certain (combinations) of variables, which is of great value. I chose to assume that the time elapsed at the first crossing was known and labelled it t(1). Also, the distance between Reno and Las Vegas should be treated as a known, which I called D. The velocities of the birds are v(lv) and v(r), for las vegas and reno respectively. Now using the general physics formula that v=d/t, out pop expressions for the velocities in terms of d (known), x (unknown) and t(1)(known).\r\n\r\nv(lv)=2x/t(1) and v(r)=(d-2x)/t(1)\r\n\r\nNow considering the most likely case first (that both birds complete one full trip and are returning), we can (since the birds each have a CONSTANT velocity) equate these with similar equations created when looking at t(2), namely;\r\n\r\nv(lv)=(d+x)/t(2) and v(r)=(2d-x)/t(2)\r\n\r\nNow equating these two sets of equations and cancelling (a lot) where possible, we get two equations both in the form t(2)=t(1)*some other stuff. Combining these and cancelling the time factors results in the following simple equation;\r\n\r\n(d+x)/2x=(2d-x)/(d-2x)\r\n\r\nWhen this equation is solved, it yields an x value of one fifth that of d (again it\'s simply the ratio here that is important, as we\'re treating d as a known value), which can then be used to solve the actual problem.\r\n\r\nAs it turns out, two of the three initial cases coincide as the birds meet for the second time at the instant that one of the two birds is completing its first journey.\r\n\r\nChecking the third possible case (following the same steps) yields the following quadratic;\r\n\r\n(4)(x^2)-(4d+3)(x)+(d^2)=0 While this is certainly solvable, it gives only negative values for the \"known\" variable d, which isn\'t possible under the boudaries of this question, which, finally leaves us with just the one solution.\r\n\r\nThis means that the only allowable solution is that the third meeting is at the tunaround point in Las Vegas.\r\n\r\n',NULL,0); INSERT INTO comment VALUES (4201,497,775,'Cory Taylor','re: my solution','2003-04-17 08:23:24',0,'gah - mistakes! I meant that the birds meet for the third time just as one of the birds is completing its second journey.\r\n\r\nThis means that the solution isn\'t on the border of two cases. However, evaluation of the fast reno bird has its only solution d=0 (which is what confused me), while my evaluation of the fast Las Vegas bird remains correct.\r\n\r\nUnless I\'ve made other mistakes....',4200,0); INSERT INTO comment VALUES (4202,735,1902,'Hank','Solution (long and complicated version)','2003-04-17 09:30:41',0,'so you want the distance from the center point, (C), to the center of one of the sides, this will be the shorter, (r). the distance from C to a vertex where three planes meet will be (R).\r\n\r\ntake any two planes of the tetrahedron and draw a line perpendicular to the center point of a triangle (t). Now you will have two lines that intersect. the intersection point is (C) of the tetrahedron. \r\n\r\nline Ct = r; line C to the vertex = R\r\n\r\nknowing that all of the angles in the tetrahedron are 60*, half would be 30*. the intersection at t is known to be 90*. making a 30-60-90 triangle.\r\n\r\nin such a triangle we know that the hypotenus(?) to the short leg is 2:1. in this case R = the hypoteneus(?) and r = the short leg.\r\n\r\nSo 2:1\r\n\r\nThank goodness I\'m not a teacher',NULL,0); INSERT INTO comment VALUES (4203,735,1902,'Hank','Solution (short version)','2003-04-17 09:31:11',3,'2:1',NULL,0); INSERT INTO comment VALUES (4204,735,1517,'jude','I get','2003-04-17 09:41:56',0,'Rad inner = (1/2)tan30 ==> sin30/2cos30\r\nRad outter = (1/2cos30) ==> 1/2cos30\r\n\r\nDropping denoms, it\'s \"sin30:1\" or like Hank said \"1:2\"\r\n',NULL,0); INSERT INTO comment VALUES (4205,735,1301,'Charlie','This is the solution','2003-04-17 09:42:15',3,'Erect the medians (which are also angle bisectors) on each of the four faces. Choose one face as the base. A vertical line through the meeting point of the medians (the center, equidistant from each vertex and each side) of the base will pass through the centers of the inscribed and circumscribed spheres, as will any line drawn perpendicular to any of the faces at their centers.\r\n\r\nThe center of the base divides each median line in a 1 to 2 ratio—one unit away from the edge and two units from the vertex. (Let’s keep that unit of measure: the distance from the center of the triangle to the edge.) The one-unit segment from the center of the base to one of the edges, together with the median of the adjacent face at that edge, and the vertical line from the center of the base to the top vertex of the tetrahedron, forms a right triangle, with the 1-unit segment on the base being the shorter leg and the median going up the adjacent face being the hypotenuse. That median has length 1+2=3, just like all the other medians. Call this the median of the second face.\r\n\r\nA smaller right triangle can be constructed within this larger one. This time the longer leg will be the portion of the median extending from the top vertex of the tetrahedron, down the slant-height median to the center of the second face. The short leg is the perpendicular to the second face at its center extending to the center of the tetrahedron. This right triangle is similar to the larger one as they share their acute angle, but the hypotenuse is now along the vertical centerline, extending from the top vertex to the center of the tetrahedron (as the perpendiculars from each of the centers of the faces meet there as stated previously). The short leg is the radius of the inscribed sphere and the hypotenuse is the radius of the circumscribed sphere. As this smaller triangle is similar to the larger one, the ratio of the short leg to the hypotenuse is again 3, which is now seen to be the ratio of the radii of the two spheres: 3:1.\r\n',NULL,0); INSERT INTO comment VALUES (4206,735,1301,'Charlie','re: Solution (long and complicated version)','2003-04-17 10:04:54',0,'Regarding \"knowing that all of the angles in the tetrahedron are 60*, half would be 30*. \", those are only the angles on a face that are 60°. C, the center of the tetrahedron, is not on a face. One of the angles in the rt triangle through the center is the dihedral angle between two faces of the tetrahedron and is arccos(1/3) = 70.528779... degrees.',4202,0); INSERT INTO comment VALUES (4207,191,1666,'bik88','i think i got it','2003-04-17 10:32:25',1,'the bus is not moving',NULL,0); INSERT INTO comment VALUES (4208,311,1660,'Tim Axoy','Dances and Wolves','2003-04-17 11:16:59',0,'Funny names!',NULL,0); INSERT INTO comment VALUES (4209,494,1660,'Tim Axoy','Explanation...','2003-04-17 11:33:26',0,'You should have an explanation.',4130,0); INSERT INTO comment VALUES (4210,469,979,'Ravi Raja','re(3): The solution','2003-04-17 23:34:52',0,'Obviously Charlie, if you carry out transactions using a counterfeit note, then would you call such a thing valid ? ',4177,0); INSERT INTO comment VALUES (4211,469,979,'Ravi Raja','re(3): The solution','2003-04-17 23:41:03',0,'Also Charlie, I had mentioned in my comment \"re: The solution\" that : (copied): Now, what value do you assign to a counterfeit note ? Irrespective of whether it is a 100 Rupees note or a 500 Rupees note. It\'s value I suppose always should be considered to be equal to zero\". \r\nIsn\'t this what I had written in that comment. So still everyone is yet to pay a hundred rupees to the ones whom they are supposed to. \r\n',4177,0); INSERT INTO comment VALUES (4212,499,1567,'Bryan','One solution','2003-04-18 04:31:53',3,'The four men are dealers at a casino, each working a different table on the night shift, and each paid a fair wage for their work.',NULL,0); INSERT INTO comment VALUES (4213,499,979,'Ravi Raja','re: One solution','2003-04-18 05:01:32',0,'Okay, that I cannot say is not correct, but the answer is something else. ',4212,0); INSERT INTO comment VALUES (4214,499,1920,'Brian Smith','Two Solutions','2003-04-18 05:10:13',3,'Solution 1: They played against other people, not each other.\r\nSolution 2: They were band members.',NULL,0); INSERT INTO comment VALUES (4215,499,775,'Cory Taylor','my solution','2003-04-18 06:28:56',0,'there was a fifth member who played with them who lost a pile..',NULL,0); INSERT INTO comment VALUES (4216,499,1626,'Gamer','re: my solution','2003-04-18 06:41:42',3,'My idea is they didn\'t play eachother. There were 4 \"1 on 1\" games, and each of the four men won their game',4215,0); INSERT INTO comment VALUES (4217,311,1626,'Gamer','Easier solution?','2003-04-18 06:54:14',3,'The way I thought was:\r\n\r\nSuppose the track was divided into 60 units. Then, in 20 seconds, Dances would be 20 units away.\r\n\r\nWolves would have to make up the other 40 units to meet Dances. So Wolves moves twice as fast. Since 1/2 of 60 is 30, Wolves takes 30 seconds.',NULL,0); INSERT INTO comment VALUES (4218,499,1567,'Bryan','Two solution','2003-04-18 08:39:31',0,'The four men worked at the mint, and each played (fed) metal ingots into machines that stamped coins of different denominations. Sorry, but they didn\'t get to keep the money they made!',NULL,0); INSERT INTO comment VALUES (4219,702,1666,'bik88','lightbulb!','2003-04-18 08:58:26',3,'isnt it a drawbridge',NULL,0); INSERT INTO comment VALUES (4220,722,1666,'bik88','some thoughts','2003-04-18 09:17:11',1,'fill up the 6g. pure it in the 11g. do this again.\r\nyou can only pure i 5g, and the 6g container will be left with 1g. mark the level of 1g and then pure it into the 3g. now you can fill the 6g container up to the level of 1g. this gives you 13g.',NULL,0); INSERT INTO comment VALUES (4221,469,1301,'Charlie','re(4): The solution','2003-04-18 09:29:12',0,'I agree that if each person were to give 100 rupees to the next person in line (narrator to plumber, ... , woman to narrator), that all accounts would be settled.\r\n\r\nBut de facto, that\'s not necessary as it merely is making a circle back to the narrator.\r\n\r\nBut, more to the point, before the incident this had not been the case. The only owing that existed before the incident was the woman owed 100 rupees to the narrator and the narrator owed 100 rupees to the plumber. The situation now is, de facto, that the woman has paid off the narrator\'s plumbing bill, settling both debts. De jure, it would require the actually pointless passing around of a 100-rupee note.',4211,0); INSERT INTO comment VALUES (4222,718,1301,'Charlie','re(3): HELP !! I think I found out the SMALLEST Number','2003-04-18 09:42:40',0,'Ravi, Bryan\'s point is that 2e3!, being 2000!, serves as a much larger power than 31!, and starting with .1 instead of what amounts to 1/2 (because of the negative exponent) is using a better (smaller) base.\r\n\r\nI, myself, do have problems with the 2e3, as I don\'t really consider that standard mathematical notation. But even .1^(32!) is a better replacement for 2^{-(31!)} within the solution you propose. Also, looking at what Bryan suggested, shows that one should not stop at sin(tiny expression), but pile other functions on top of it, like tan(sin(tiny expression)), with the caveat we seek the most efficient sequence of the piling on of functions.\r\n\r\nI don\'t know whether we can use indefinitely many variations on parentheses to get around the 1-use-of-each-symbol restriction.',4196,0); INSERT INTO comment VALUES (4223,741,1626,'Gamer','re(4): Direct approach','2003-04-18 10:29:59',0,'No answer is particularly WRONG, but I wouldn\'t think of someone living to 111... I would think they would die earlier. \r\n\r\nThe way I got 111 was 2003-1892.\r\n\r\nWhat TomM says is true too... I assumed this puzzle was recent... This may not be right.',4182,0); INSERT INTO comment VALUES (4224,732,1660,'Tim Axoy','If you liked this','2003-04-18 12:30:45',0,'If you liked this,then maybe you would like Drew and Mohammad come back.\r\nIt is one of my pending problems.',NULL,0); INSERT INTO comment VALUES (4225,733,1660,'Tim Axoy','solution','2003-04-18 12:54:46',3,'As stated in the problem, since the base of the pillar has 4 sides and the top has 3, two of the edges running the length of the pillar must meet at one of the corners of the triangle. Since the edge of the triangle opposite this corner is parallel to one of the edges of the bottom, every cross section of the pillar between the top and bottom is a trapezoid. To find the volume, we can integrate the trapezoidal cross sections along the height of the pillar. \r\nFor a trapezoid with parallel sides B1 and B2 and height H, its area is \r\n\r\nA=.5(B1 + B2)H \r\n\r\nAt the square base, B1 = B2 = H = 20cm\r\nAt the top, B1 = 16, B2 = 0, & H = 8*sqrt(3) \r\n\r\nAll three values change linearly from the base of the pillar to its top 200cm above. Let y = 0 at the base and y = 200 at the top. Then \r\n\r\nB1 = f(y) = 20 – y*4/200 = 20 – y/50\r\nB2 = f(y) = 20 – y*20/200 = 20 – y/10\r\nH = f(y) = 20 – y*20/200 + y*8*sqrt(3)/200 = 20 – y/10 + y*sqrt(3)/25 \r\n\r\nA = f(y) = .5(20 – y/50 + 20 – y/10)(20 – y/10 + y*sqrt(3)/25) \r\nA = y^2*(15 – 6*sqrt(3))/2500 + y*(4*sqrt(3) – 16)/5 + 400 \r\n\r\nTo find volume V: \r\n\r\nV = integral[A dy] from 0 to 200\r\nV = 1/3 *y^3*(15 – 6*sqrt(3))/2500 + .5*y^2*(4*sqrt(3) – 16)/5 + 400y ] from 0 to 200\r\nV = 200^3*(15 – 6*sqrt(3))/7500 + .5*200^2*(4*sqrt(3) – 16)/5 + 80000\r\nV = 48627.7 cm^3 \r\n\r\nTherefore the weight W of the pillar is \r\n\r\nW = 48627.7*2.8 = 136157.6 g = 136.16 kg\r\n\r\nNote: Whether the triangular top of the pillar is centered above the square base or not will have no effect on the pillar’s volume.\r\nv',NULL,0); INSERT INTO comment VALUES (4226,734,1660,'Tim Axoy','solution','2003-04-18 12:55:41',0,'Each side of the die is an equilateral triangle. Consider two adjacent sides sharing one edge, and on each triangle draw an altitude from the middle of the shared edge to the corner opposite. If we connect the ends of these two lines with a third line, and find the lengths of all three lines, we can calculate the angle X between the two triangular sides using the law of cosines. \r\nSet the length of each edge of the icosahedron arbitrarily to 1. The height of the altitude on each triangle is then sqrt(3)/2. \r\n\r\nEvery vertex of the icosahedron consists of five triangles meeting at one point. The perimeter created by the outer edges of these five triangles is a regular pentagon with length of sides = 1. For any two adjacent triangles in this group, one end of the shared edge falls on a corner of the pentagon, and the corners of the pentagon immediately on either side are coincident to the corners of the triangles opposite their shared edge. A line between these two corners will have a length L where \r\n\r\nL^2 = 1^2 + 1^2 – 2*1*1*cos(108) = 2.61803 \r\n\r\nPlugging in the lengths of the three sides of our mystery triangle, \r\n\r\nL^2 = [sqrt(3)/2]^2 + [sqrt(3)/2]^2 – 2* sqrt(3)/2* sqrt(3)/2*cos(X)\r\nX = arccos [(L^2 – 3/4 – 3/4) / (-2*3/4)]\r\nX = arccos(-0.74535)\r\nX = 138.189 degrees \r\n',NULL,0); INSERT INTO comment VALUES (4227,499,2008,'Steve','Here it is','2003-04-18 13:08:55',0,'They are musicians.',NULL,0); INSERT INTO comment VALUES (4228,743,1567,'Bryan','Okay odds, but a sucker\'s bet','2003-04-18 17:59:32',3,'For two 6-sided dice, there are 36 permutations. The number of permutations that yield each number is as follows: 2 or 12: 1, 3 or 11: 2, 4 or 10: 3, 5 or 9: 4, 6 or 8: 5, and for 7: 6. Thus the odds are 8/36 that one would roll a 7 or 11 (wins immediately), and 4/36 that one would roll 2, 3, or 12 (loses immediately).
If any of the six other numbers come up, 2, 3, and 12 are harmless, and in fact any subsequent rolls other than 7 and the desired number can be ignored. For 4 or 10, the odds of winning are 3 to 6 against, or 3/9. Similarly, the odds for 5 or 9 are 4/10, and the odds for 6 or 8 are 5/11.
Now the total odds of winning can be calculated by multiplying the odds of rolling a number with the odds that it will win, and summing the lot. So for 2 through 12, the odds of winning are
1/36*0 + 2/36*0 +3/36*3/9 + 4/36*4/10 + 5/36*5/11 + 6/36*1 + 5/36*5/11 + 4/36*4/10 + 3/36*3/9 + 2/36*1 + 1/36*0
= 0.492929
These odds are very nearly 50%, which means that for any one series of rolls that ends in success or failure, one has a nearly even chance of coming out on top. However, a lengthy stay at the craps tables will wipe out all but the luckiest shooters. Why? Because if the cold streak comes first, the player has to have enough money to get through it to be there for the hot streak (this is true for all games against the house). If you want good odds in Vegas, buy some real estate there. ',NULL,0); INSERT INTO comment VALUES (4229,743,1626,'Gamer','re: Okay odds, but a sucker\'s bet','2003-04-19 02:30:59',0,'Looks good... There always is the \"slightly under 1/2\" chance you will win in many of these games... That\'s why I don\'t like gambling... You will not win more than you will win.',4228,0); INSERT INTO comment VALUES (4230,499,2010,'OutKazt','Outkazt\'s solution','2003-04-19 02:53:56',3,'THEY ARE ALL MUSICIANS',NULL,0); INSERT INTO comment VALUES (4231,499,1645,'luvya2003','re: Here it is','2003-04-19 03:01:39',0,'I didn\'t think of this answer at first but now that I think about it...it\'s the most correct answer.',4227,0); INSERT INTO comment VALUES (4232,743,775,'Cory Taylor','re(2): Okay odds, but a sucker\'s bet','2003-04-19 05:46:12',0,'yah - a personal favorite quote of mine;\r\n\r\n\"Gambling is a tax on people who are bad at math\"',4229,0); INSERT INTO comment VALUES (4233,733,979,'Ravi Raja','Oh My God !!!!','2003-04-19 07:56:01',0,'A 9 Year Old Kid solving a problem of Calculus using \"Integration\" ? Is that possible? Should I call it a \"Nightmare\" ?',NULL,0); INSERT INTO comment VALUES (4234,499,2014,'Senlron','re: Here it is','2003-04-19 09:40:34',0,'I agree too',4227,0); INSERT INTO comment VALUES (4235,743,1626,'Gamer','re(3): Okay odds, but a sucker\'s bet','2003-04-19 10:33:28',0,'Yep... I like that lots too.\r\n\r\nOf course, some people gamble in skill games (like poker and such) just because they know they can sucker others who are worse into playing with them... It\'s a little immoral, but all\'s fair in love, war, and gambling right? ',4232,0); INSERT INTO comment VALUES (4236,154,2005,'Aamir Rashid','its haunting','2003-04-19 13:10:32',0,'My God! I have lost my head only reading it....\r\nI hope I will think over it some other time esp when I am unable to sleep.',NULL,0); INSERT INTO comment VALUES (4237,469,979,'Ravi Raja','re(5): The solution','2003-04-19 22:54:24',0,'Charlie, you have stated in your last comment the following: \"....before the incident this had not been the case. The only owing that existed before the incident was the woman owed 100 rupees to the narrator and the narrator owed 100 rupees to the plumber\". But it was not so I believe. The plumber too owed the milkman the same amount, that is 100 rupees and the milkman owed 100 rupees to his tailor for his garments. \r\nYes one thing is true that you cannot say that the tailor owed the lady (the narrator\'s neighbour) 100 rupees before the incident, but the rest as mentioned above are! ',4221,0); INSERT INTO comment VALUES (4238,469,979,'Ravi Raja','re(5): The solution','2003-04-19 23:04:12',0,'One more thing Charlie. again regarding your comment in the last post where you have stated the following: \"....that the woman has paid off the narrator\'s plumbing bill, settling both debts. De jure, it would require the actually pointless passing around of a 100-rupee note\". I agree with you when you say that the passing around of the 100 rupee note was pointless, but how do you say that the woman settled \"BOTH\" the debts. Which \"Both\" debts you\'re talking about Charlie ?',4221,0); INSERT INTO comment VALUES (4239,29,1660,'Tim Axoy','Lying twice is not telling the truth.','2003-04-20 03:24:57',0,'It is not telling the truth.\r\nThe liars lie about their lie and just say they would tell the truth.',NULL,0); INSERT INTO comment VALUES (4240,29,1660,'Tim Axoy','A puzzle about Drew','2003-04-20 03:27:02',0,'I made one called Drew and Mohammad.',1636,0); INSERT INTO comment VALUES (4241,154,1660,'Tim Axoy','What opens?','2003-04-20 04:07:09',3,'Find an X that is related to itself because if it jams,then it is neutral and if it is neutral,then it jams.\r\nObviously,X can neither jam or be neutral,so it opens.\r\nHere is how we find such an X.\r\nCall the norm of a number X the number X2X2(Example:The norm of 59 is 592592).\r\nThen,we need a number N such that if x is related to y,then Nx is related to the norm of y,or basically y2y2.\r\nNow,2N2 is related to N,so N2N2 must be related to the norm of N,which is the very number N2N2.\r\n\r\n',NULL,0); INSERT INTO comment VALUES (4242,154,1660,'Tim Axoy','Finding our number','2003-04-20 04:13:48',3,'We need to find the number N from the rules given.\r\nI will denote x\' to be the reverse of x.\r\nAlso,x\'\' is x itself(It is the reverse of the reverse of x).\r\nAlso,the reverse of xy\',x in front of y\' is yx\',y in front of x\' and the reverse of x\'y,x\' in front of y is y\'x,y\' in front of x.\r\nWell,if x is related to y,then 5x is related to the y\',15x is related to 2y\',515x is related to y2,and 9515x is related to y2y2,so 9515 is such an N.\r\nSince N2N2 is related to itself,9515295152 is related to itself.',NULL,0); INSERT INTO comment VALUES (4243,469,1301,'Charlie','re(6): The solution','2003-04-20 04:36:10',0,'The woman owed the narrator 100 rupees. She no longer owes the narrotor 100 rupees, not because of the worthless 100-rupee note, but rather, because of a chain giving that has resulted in the plumber being paid off, again not in the form of that worthless 100-rupee note, but rather value received in garments.\r\n\r\nThus two debts have been paid off: the one the woman owed to the narrator, and the one the narrator owed to the plumber.\r\n\r\nLooked at in a short-circuited way, you could even consider the previous situation one in which the woman owed the plumber 100-rupees, with the narrator as an intermediary.\r\n\r\nBut in any case, previously the plumber was owed 100-rupees. Now he has received 100 rupees worth of garments and so is de facto paid off, relieving the narrator of his debt. The narrator was owed 100 rupees by the woman and now no longer is, but in turn no longer owes the plumber. And the woman, is out the sewing machine, but rightfully so as her debt to the narrator is now de facto discharged.\r\n\r\nDe Jure, they\'d have to pass around a real 100-rupee note, but it would make no material difference. But the incident did result in the settling of debts.',4238,0); INSERT INTO comment VALUES (4244,500,153,'TomM','D*mned if you do and d*mned if you don\'t.','2003-04-20 07:41:46',3,'Suicide is against the law, but if successful you are beyond the government\'s justice. Attempted suicide, like an attempt at any other violent crime, can be prosecuted, although it rarely is any more.',NULL,0); INSERT INTO comment VALUES (4245,500,1626,'Gamer','Catch-22','2003-04-20 07:47:43',2,'Named after a book I read, I think this is another good subject.\r\n\r\nI got this! Yay... Now I feel happy. :)\r\n\r\nI think the other reason is we have such new stuff that suicide is lots harder to catch. Just shooting yourself is one way. (I know that adolescents are twice as likely to commit suicide if a gun is kept in the house)',4244,0); INSERT INTO comment VALUES (4246,500,1951,'Andrew','I agree','2003-04-20 08:08:29',0,'I agree the answer is suicide.',NULL,0); INSERT INTO comment VALUES (4247,469,1626,'Gamer','re(7): The solution','2003-04-20 09:17:54',0,'Sorry, I didn\'t want to take the time to read all 95 messages... I just read the most recent ones.\r\n\r\nWhat I think is although the transaction isn\'t strictly legal in the \"paying-for-things\" sense, money is just a way to pay for things instead of bartering.\r\n\r\nThink of it this way. The narrator took a 100 rupee note from the ground, and passed it around. Then the narator put it back on the ground. Thus, everyone is how it should be, as well as the ground, since it got its 100 rupee note back.\r\n',4243,0); INSERT INTO comment VALUES (4248,469,1626,'Gamer','re(8): The solution','2003-04-20 09:23:13',0,'If the counterfeit note isn\'t used:\r\n\r\nThe narrator exchanges a household appliance to the plumber for a good plumbing fixture.\r\n\r\nThe plumber exchanges a household appliance (which he now has)to the milkman for the milk.\r\n\r\nThe milkman exchanges the household appliance to the tailor for the garments.\r\n\r\nThe tailor exchanges the household appliance to the neighbor for the old sewing machine.\r\n\r\nNow each person has what he/she had at the end of the story. Does this show that nothing was gained or lost? Sorry if I missed one of your reasons...',4247,0); INSERT INTO comment VALUES (4249,500,2005,'Aamir Rashid','','2003-04-20 11:17:03',1,'Yes, I cannot think anything else than suicide...\r\nm i right Ravi...',NULL,0); INSERT INTO comment VALUES (4250,130,2005,'Aamir Rashid','re(3): Close but....','2003-04-20 13:03:06',0,'yah thats really interesting and that reminds me of the famous Maths Rule.\r\n Inverse of an inverse of a number is the original number.\r\n\r\nI hope that rule will do a lot of help in Knights and Liars problems.',597,0); INSERT INTO comment VALUES (4251,130,2005,'Aamir Rashid','making knight out of a liar','2003-04-20 13:03:56',0,'yah thats really interesting and that reminds me of the famous Maths Rule.\r\n Inverse of an inverse of a number is the original number.\r\n\r\nI hope that rule will do a lot of help in Knights and Liars problems.',597,0); INSERT INTO comment VALUES (4252,741,1575,'DJ','welp','2003-04-20 14:34:57',0,'The problem itself isn\'t much to get your mind around, just find a year that is a perfect square and subtract its square root.\r\n\r\nRavi, you\'re just being argumentative for the sake of arguing. The problem on my screen says \"Posted on 2003-04-15\" and begins with the words \"the other day,\" and Jim is talking entirely in present tense, as is the question posed at the end of the problem. Supposing this puzzle is from before 1936, and for some reason was preserved verbatim until today, I think it probably would have been made clear in the problem, but sure, Jim could have been turning 44. If the puzzle is from between 1936 and 1980, you can\'t say that either answer is valid; rather, both answers are invalid because either Jim has already turned 44, or he hasn\'t been born yet. So either the problem is more than 67 years old, or it is relatively recent and is worded accordingly. To me, there shouldn\'t be much of a pressing debate here...',NULL,0); INSERT INTO comment VALUES (4253,722,1575,'DJ','ehh','2003-04-20 14:45:07',0,'usually problems like this are figured out so that it is actually possible to solve the problem using only the containers with the measurements specified, and the only actions you can do are fill each container all the way, either from it being empty, or from having some left over in it after filling another container.\r\n\r\ngenerally, it is allowable to completely empty a container at any point in the problem, but this one specificlly states otherwise. that, to me, was an indication that there was a specific solution that could be attained without having to use more than 13 gallons.\r\n\r\nafter working on it for a while, i began to suspect that it was impossible, but i was looking forward to seeing a real solution. guess i\'m just stuck being disappointed..\r\nworse, the posted solutions are just links to people\'s guesses that break the rules of the problem.\r\n\r\nso, my suspicions were correct, but..why bother making a specific problem like this without any idea how (or if) it can be done?\r\n\r\ni don\'t get it... *sob*',NULL,0); INSERT INTO comment VALUES (4254,500,2029,'Jay Stone','solution','2003-04-20 14:50:52',0,'suicide',NULL,0); INSERT INTO comment VALUES (4255,500,1575,'DJ','or','2003-04-20 14:55:12',0,'How about the murder or incapacitation of every single form of law-enforcement official on the face of the earth? \r\nIf completely successful, there would be no one to punish him.\r\n\r\nOr, maybe you\'re excaping from prison to go live in seclusion in a non-cooperative foreign country?\r\nIf successful, you won\'t get punished.\r\n\r\nI suppose both of those are still punishable, but i can\'t just say the same thing as everyone else..',NULL,0); INSERT INTO comment VALUES (4256,500,2029,'Jay Stone','re: or','2003-04-20 15:30:32',0,'ESCAPING (that\'s how it\'s spelled) from prison is not a crime. You cannot be arrested trying to escape from prison.',4255,0); INSERT INTO comment VALUES (4257,500,2032,'robby','I KNOW THIS ONE','2003-04-20 19:03:11',0,'suicide',NULL,0); INSERT INTO comment VALUES (4258,500,979,'Ravi Raja','re: Catch-22','2003-04-20 21:58:50',0,'How about hanging oneself, diving in a body of water (provided the one who does that does not know how to swim), jumping off from a tall building....etc. are other ways of comitting a Suicide.',4245,0); INSERT INTO comment VALUES (4259,500,979,'Ravi Raja','re:','2003-04-20 22:14:36',0,'Yes Aamir. You\'re absolutely correct.',4249,0); INSERT INTO comment VALUES (4260,500,979,'Ravi Raja','re: Catch-22','2003-04-20 22:23:01',0,'Well Gamer I believe that there are less chances to find a gun at a normal person\'s place and so the other ways of committing a suicide, that I have suggested in my previous comments is more likely to be accepted by them.',4245,0); INSERT INTO comment VALUES (4261,498,2005,'Aamir Rashid','The solution','2003-04-20 23:07:04',3,'The next two numbers are as below:\r\n\r\n8112332416 1113253342618\r\n\r\nActually any number in the sequence is just the count of the digits used in the sequence so far. For example if we start with 1, 11 represents that uptil now there is only one digit(that is ofcourse \"1\") used in the sequence and it appears only once.(Remember the first 1 in \"11\" shows the number of occurences and the second 1 shows the actual digit which has occured). Following the same strategy it is quite easy to show that 31 means that 1 has appeared in the sequence thrice so far. But here, we have a new number introduced in the sequence and that is 3 so it\'s count is to be managed as well, which is apparent from 4113.\r\nNow 4113 tells that now there are 2 digits in the sequence \"3\" and \"1\", where 3 comes once and 1 is repeated 4 times and so on.......This is how I think it works.\r\n\r\nPlz do let me know if there is a bug. ',NULL,0); INSERT INTO comment VALUES (4262,469,1919,'Lewis','solution','2003-04-20 23:22:25',3,'Everybody who got paid the note lost 100 rupees because the note was counterfeit.\r\nEverybody who paid the note to somebody else gained 100 rupees because the note was counterfeit.\r\nBecause evrybody used it and everybody got paid it, they were all even - no gains & no loses.\r\n',NULL,0); INSERT INTO comment VALUES (4263,500,1919,'Lewis','re: or','2003-04-20 23:26:56',0,'Or maybe the crime was getting away with murder, stealing etc. If he got away with it he couldn\'t be punished.',4255,0); INSERT INTO comment VALUES (4264,229,1919,'Lewis','hmmmm.....','2003-04-20 23:29:40',0,'um.... because they both exist on Earth? No?\r\n\r\nAnyway, its a stupid riddle. How can a desk write? Oh...',NULL,0); INSERT INTO comment VALUES (4265,738,1920,'Brian Smith','The 5th degree vs. The interrupted sequence','2003-04-21 05:52:35',0,'Two ideas came to me soon after seeing this problem.\r\n\r\nIdea 1\r\nThe sequence can be interpreted as a series of points: (1,1),(2,4),(3,9),(4,16),(5,25),(6,pi)\r\n\r\nConstruct a polynomial passing through those points: f(x) = (x-1)*(x-2)*(x-3)*(x-4)*(x-5)*(pi-36)/120+x^2\r\n\r\nf(7) = 6*pi-167\r\n\r\nIdea 2\r\nThe sequence is the perfect squares with pi substituted for 36. The next term is then 49.',NULL,0); INSERT INTO comment VALUES (4266,500,1517,'jude','or how about','2003-04-21 06:02:57',0,'overthrowing a \"government\"?',NULL,0); INSERT INTO comment VALUES (4267,503,1301,'Charlie','solution','2003-04-21 09:01:01',3,'Let x be the horizontal component of the distance of the crossover point from the wall where the base of the 10-meter ladder rests. Let y be the height of the crossover point. \r\n\r\nThe top of the 10-meter ladder rests 8 meters above the ground (the triangle is a 3,4,5 rt triangle with dimensions doubled), and the top of the 12-meter ladder is 12√3 meters up (as it makes an angle of 60 degrees with the ground).\r\n\r\nThe equation of the 10-meter ladder is therefore\r\ny=8x/6\r\nand the 12-meter ladder is\r\ny=(12(√3)/6)(6-x)\r\nsubstituting and multiplying by 6,\r\n8x = 12(√3)(6-x)\r\nand\r\nx=72(√3)/(8+12√3) \r\nand y=8x/6 = 5.7765896... meters above the ground.',NULL,0); INSERT INTO comment VALUES (4268,503,1517,'jude','Interesting problem','2003-04-21 09:05:33',0,'Drawing a graph of how I interpret this problem, I get two lines (for 0 < x < 6):\r\n1) y=-(4/3)x + 8\r\nand\r\n2) y=((sqrt108)/6)x\r\n\r\nSubstituting 2) into 1), then the result back into 2), I get a height of (8*sqrt(108)) / (8 + sqrt(108)) or approx 4.5m',NULL,0); INSERT INTO comment VALUES (4269,503,1567,'Bryan','re: solution','2003-04-21 09:12:45',0,'Charlie, my solution confirmed jude\'s answer, which differs from yours. I believe your equation for the 12-meter ladder should have been
y = (6(√3)/6)(6-x)
and all else would follow correctly.',4267,0); INSERT INTO comment VALUES (4270,503,1301,'Charlie','re(2): solution','2003-04-21 09:23:22',0,'You\'re absolutely right.\r\n',4269,0); INSERT INTO comment VALUES (4271,738,1517,'jude','as Arsenio Hall said....','2003-04-21 09:48:56',0,'Things that make you go hmmmmmmmm...\r\n\r\nok another observation is that each of the numbers listed (not pi) make up the first 7 numbers after the decimal point of pi, only scrambled to resemble a series of squares\r\n3. 1 4 1 5 9 2 6\r\nextending pi a few places, \r\n3. 1 4 1 5 9 2 6 5 3 5 8 9... you don\'t another 6 to make 36 for about another 8 places\r\n\r\nthis one really has me stumped because it\'s in \"Word problems\" yet we\'re asked to create a mathematical function\r\n\r\nAt first thought it had something to do with cooking, like 6 squares = 36 which if multiplied by 10 equals 360 which equals a pi(e) but maybe I\'m grasping at straws here...',NULL,0); INSERT INTO comment VALUES (4272,500,1626,'Gamer','re(2): Catch-22','2003-04-21 10:07:59',0,'I think you misread me. I am just saying that such other ways of killing ones self are harder to do... You can shoot yourself anywhere...\r\n\r\nI like the other ideas that were listed as well. My new idea is paying of the authorities to not turn your previous crimes and your bribe in, without anyone knowing.',4258,0); INSERT INTO comment VALUES (4273,79,1626,'Gamer','Plurals caution','2003-04-21 13:55:12',1,'Careful with plurals. Namely that he needs to take each pile of BILLS and shuffle them. This sounds like there needs to be at least 2 bills in each pile.\r\n\r\nWhat I would do is be all nice to the uncle if he just has over 1000 dollars in cash just laying around the house!!!!!!\r\n\r\nI like your proof though TomM',254,0); INSERT INTO comment VALUES (4274,503,2041,'annij','solution','2003-04-21 17:24:28',0,'The height of the intersection is 4.52 metres from the ground. Fun Problem!',NULL,0); INSERT INTO comment VALUES (4275,738,1183,'fwaff','Word problem???','2003-04-21 22:00:33',1,'OK so p is the 16th letter of the alphabet and i is the 9th, so we have...\r\n1 4 9 16 25 p(=16) i(=9) \r\nthen d(=4) and a(=1) would be the last two values of the sequence\r\n\r\nI doubt this is what was wanted, but a \'word problem\' asking for a mathematical function has left me bemused!',NULL,0); INSERT INTO comment VALUES (4276,738,1183,'fwaff','re: Word problem??? - maths bit','2003-04-21 22:29:44',3,'Sorry, I should have put this on the end of my previous post...\r\n\r\nA mathematical function that gives the sequence is:\r\n\r\n(floor(n/6))pi + (1-floor(n/6))n^2\r\n\r\nfor n=1 to 5 this is equivalent to 0pi + 1n^2 = n^2\r\nfor n=6 this is 1pi + (1-1)6^2 = pi\r\nfor n=7 to 11 this is 1pi + (1-1)n^2 = pi\r\nfor n=12 this is 2pi - 144\r\n\r\nAgain I guess that this is A solution rather than THE solution.',4275,0); INSERT INTO comment VALUES (4277,485,1919,'Lewis','Annoying','2003-04-21 22:40:38',0,'Tim, PLEASE stop giving the answers away in your comment\'s subjects :)',NULL,0); INSERT INTO comment VALUES (4278,342,1919,'Lewis','Saw','2003-04-21 22:45:46',1,'And if you didn\'t have a saw, you could rub your hands together until they got a little soar and then use the little saw to saw the table.\r\n\r\nBut when you get out you can\'t be bothered to walk all of the way home. So you shout and shout until your throat gets a little hoarse, then you get on that horse and ride home. (By the way, this doesn\'t actually work :)',NULL,0); INSERT INTO comment VALUES (4279,718,1660,'Tim Axoy','1 of each symbol','2003-04-22 02:17:25',0,'Yes.\r\nFor example,3/(((12!)!)!) would be really big.\r\nWe could add more and more symbols on!',4222,0); INSERT INTO comment VALUES (4280,501,1517,'jude','How about','2003-04-22 04:39:17',0,'Stars?',NULL,0); INSERT INTO comment VALUES (4281,501,1902,'Hank','i dunno','2003-04-22 04:46:35',0,'dreams?',NULL,0); INSERT INTO comment VALUES (4282,738,1567,'Bryan','re: Word problem???','2003-04-22 05:03:54',0,'Sorry for the confusion. I submitted this as a sequence, not a word problem. Perhaps the topic was changed during the recent hacking episode. I must admit, given some of the creative answers I\'ve seen so far, maybe I should put the wrong topic on problems more often <grin>.',4275,0); INSERT INTO comment VALUES (4283,503,1686,'DuCk','my solution','2003-04-22 05:38:11',0,'I\'m getting 4.52 metres above the ground at 2.6097 metres from the left wall. I just set the origin as the bottom left corner of the alley and used the equations of the lines to find the intersection points. It had been so long since I did geometry, I couldn\'t believe how stumped I was at first about finding the intersection point. Thanks Ravi!',NULL,0); INSERT INTO comment VALUES (4284,501,1686,'DuCk','a quickie guess','2003-04-22 05:42:15',0,'This was the first thing that popped in my head, but it is probably wrong. Stars...\r\nJust decided to go with the gut on this one.',NULL,0); INSERT INTO comment VALUES (4285,159,1920,'Brian Smith','3 x n','2003-04-22 06:20:52',0,'3 x n\r\nOOOO...OOO\r\nOXXX...XXO\r\nOOOO...OOO\r\nNumber black squares = n - 2',NULL,0); INSERT INTO comment VALUES (4286,766,1517,'jude','Trey Anastasio???','2003-04-22 07:27:52',0,'Cleopatra and Marc Anthony are fish. They were in a fish bowl on a table that got knocked over.\r\n\r\nAAhhhhh but who knocked over the table?',NULL,0); INSERT INTO comment VALUES (4287,766,1902,'Hank','Maybe','2003-04-22 08:06:02',3,'They died because they were unable to breathe outside of the water in their fish tank.',NULL,0); INSERT INTO comment VALUES (4288,501,2046,'Rebecca Howard','?','2003-04-22 09:15:38',0,'Shadows maybe? The fingers of darkness?',NULL,0); INSERT INTO comment VALUES (4289,61,2046,'Becky','Another solution','2003-04-22 09:59:15',0,'He stayed for a few days, just not the few days immediately after the drink!!',NULL,0); INSERT INTO comment VALUES (4290,82,2046,'Becky','Who needs demons?','2003-04-22 10:18:54',0,'Maybe the men killed him at exactly 1:00 because he was trying to get the fire back...',NULL,0); INSERT INTO comment VALUES (4291,31,2046,'Becky','Spinning?','2003-04-22 10:22:17',0,'Maybe it was facing both ways at once?',NULL,0); INSERT INTO comment VALUES (4292,501,1301,'Charlie','My vote is for...','2003-04-22 10:40:48',0,'dreams',NULL,0); INSERT INTO comment VALUES (4293,501,1626,'Gamer','My idea','2003-04-22 11:15:42',0,'My idea was sleep. Sleep comes at night and is lost when the day wakes you up.',NULL,0); INSERT INTO comment VALUES (4294,766,1301,'Charlie','re: Trey Anastasio???','2003-04-22 12:09:24',0,'It should ease levik\'s mind that it wasn\'t people.',4286,0); INSERT INTO comment VALUES (4295,501,1575,'DJ','yeah','2003-04-22 15:24:21',0,'I was thinking dreams, just because sleep doesn\'t really qualify as a \'they\'',NULL,0); INSERT INTO comment VALUES (4296,766,2029,'Jay Stone','solution','2003-04-22 16:04:34',0,'they are fish',NULL,0); INSERT INTO comment VALUES (4297,154,1575,'DJ','The Real Solution (Part I)','2003-04-22 16:13:48',3,'I had \'proved\' an 8-digit solution before, but my oversight was that the reverse of x is not necessarily x. So, I will redo the problem, with the invented notation of X being the reverse of x (if x=123, X=321). As before, I will attempt to prove that a number relates to itself, which by property E means that it must be a solution and open the lock. The shortest solution still presumably has the form of xx2 or x2x2, where x is a series of 1s, 5s, and 9s that enumerates the steps needed to find that very arrangement.\r\nFirst, for xx2, lets work backwards:\r\nxx2 - 2XX - XX - xx - x\r\nor\r\nxx2 - 2XX - XX - X - x.\r\nA consecutive reversal (5) and repetition (9) are interchangeable. This yields the following proof:\r\n2x2 ~ x\r\n92x2 ~ xx\r\n592x2 ~ XX\r\n1592x2 ~ 2XX\r\n51592x2 ~ xx2\r\n:. x must equal 51592, and this shows that 51592515922 relates to itself and therefore is a combination that opens the safe. Also (using the 5-9 commutability), 51952519522 opens the safe by similar proof.',NULL,0); INSERT INTO comment VALUES (4298,154,1575,'DJ','The Real Solution (Part 2)','2003-04-22 16:15:41',3,'Now, work backwards again to find x2x2:\r\nx2x2 - 2X2X - 2X - X - x\r\nor\r\nx2x2 - x2 - 2X - X - x.\r\nThus we have the proofs:\r\n2x2 ~ x\r\n52x2 ~ X\r\n152x2 ~ 2X\r\n9152x2 ~ 2X2X\r\n59152x2 ~ x2x2\r\n:. x = 5915, and 5915259152 relates to itself and must open the safe. Also:\r\n2x2 ~ x\r\n52x2 ~ X\r\n152x2 ~ 2X\r\n5152x2 ~ x2\r\n95152x2 ~ x2x2\r\n:. x=9515, and 9515295152 also relates to itself and must open the safe.',NULL,0); INSERT INTO comment VALUES (4299,154,1575,'DJ','The Real Solution (Part 3)','2003-04-22 16:17:28',3,'Such solutions were come upon previously by myself and other people. These combinations do indeed relate to themselves, and therefore must open the safe, but they are not the shortest and are not the solution to the problem.\r\nAn inspection of the latter two valid combinations reveals that both are repeats of some number. A simple proof, from the definitions, shows that:\r\n2y2 ~ y\r\n92y2 ~ yy\r\nSo, for any repeated number yy, 92y2 is related to it. And, if yy opens the safe (see where I\'m going now?), then 92y2 must also open the safe, to conform to property E. Therefore, the solutions 9515295152 and 5915259152 each yield another solution, and we have that:\r\n2951522 ~ 95152\r\n92951522 ~ 9515295152\r\nand\r\n2591522 ~ 59152\r\n92591522 ~ 5915259152.\r\nTherefore, we have found two 8-digit solutions, 92591522 and 92951522.\r\n\r\n!!',NULL,0); INSERT INTO comment VALUES (4300,501,2049,'Sarah','um i know what it is','2003-04-22 17:52:35',0,'stars',NULL,0); INSERT INTO comment VALUES (4301,766,1183,'fwaff','Hmmm','2003-04-22 21:41:40',3,'Given how long this riddle\'s been going around, my guess is that they died of old age.\r\n\r\n:-)',NULL,0); INSERT INTO comment VALUES (4302,766,2050,'Zephia','well.....','2003-04-22 23:45:16',0,'They\'re fish. Their fish bowland the table it was on, were blown over by a gush of wind through the open window (hence the broken glass)...without water the wee fishies died.',NULL,0); INSERT INTO comment VALUES (4303,501,979,'Ravi Raja','re: ?','2003-04-23 00:06:58',0,'Rebecca you stand under the Sun at any time of the day and then post a comment telling us whether you saw your shadow or not.',4288,0); INSERT INTO comment VALUES (4304,501,979,'Ravi Raja','re: My idea','2003-04-23 00:08:24',0,'Many people feel sleepy even during the day time and are awake at nights.',4293,0); INSERT INTO comment VALUES (4305,501,979,'Ravi Raja','re: i dunno','2003-04-23 00:09:38',0,'Don\'t you, or any other person \"Day-Dream\" ? lol. ',4281,0); INSERT INTO comment VALUES (4306,501,979,'Ravi Raja','re: ?','2003-04-23 00:11:04',0,'And one more thing, Rebecca. You in a completely dark room then let us know whether you saw your shadow or not.',4288,0); INSERT INTO comment VALUES (4307,766,1839,'Rajeev','sounds fishy','2003-04-23 00:22:45',0,'Cause both were fish out of water',NULL,0); INSERT INTO comment VALUES (4308,502,1517,'jude','mmmkay?','2003-04-23 04:02:56',3,'\r\nany \"thousand\" number\r\n\r\n',NULL,0); INSERT INTO comment VALUES (4309,766,1517,'jude','re: well.....','2003-04-23 04:06:17',0,'wouldn\'t the broken glass be from the broken fish tank/bowl?\r\n',4302,0); INSERT INTO comment VALUES (4310,502,1301,'Charlie','re: mmmkay?','2003-04-23 04:06:40',3,'Specifically, one thousand is as high as you have to count.',4308,0); INSERT INTO comment VALUES (4311,502,1902,'Hank','Other solutions??','2003-04-23 04:40:03',3,'0.001 (one thousandth) (actually, if we are counting non-integers, I\'m sure that there are smaller numbers)\r\n\r\none hundred and one (like the dalmations) (not technically correct, but it is how it is spoken)',NULL,0); INSERT INTO comment VALUES (4312,502,1902,'Hank','re: Other solutions??','2003-04-23 04:41:38',0,'or in other languages? quatro, etc.',4311,0); INSERT INTO comment VALUES (4313,502,1928,'The Mighty Puck','simple','2003-04-23 06:12:55',0,'one thousand',NULL,0); INSERT INTO comment VALUES (4314,501,1947,'Jon','ummm','2003-04-23 06:18:45',1,'so far all the answer but stars have been ruled out, but the sun is indeed a star so there goes that one too. I know I am being picky but oh well. ummmm..... How about everyone try really hard to forget that there are bugs in the day and we can use them as an answer?',NULL,0); INSERT INTO comment VALUES (4315,502,2054,'entelecheia','Spelling them out?','2003-04-23 09:17:08',0,'If you were to write out each number as you were to say it... a hundred, a hundred and one, a hundred and two...',NULL,0); INSERT INTO comment VALUES (4316,429,2054,'Entelecheia','Alternate Answer','2003-04-23 09:56:38',0,'He poisoned the punch.',NULL,0); INSERT INTO comment VALUES (4317,765,1301,'Charlie','solution','2003-04-23 13:12:14',3,'If we number the coins 1-39, we’d like to place the coins on the left (L) or right(R) according to the following schedule for the four weighings:\r\n\r\n 1 LLLL\r\n 2 -LLL\r\n 3 RLLL\r\n 4 L-LL\r\n 5 --LL\r\n 6 R-LL\r\n 7 LRLL\r\n 8 -RLL\r\n 9 RRLL\r\n 10 LL-L\r\n 11 -L-L\r\n 12 RL-L\r\n 13 L--L\r\n 14 ---L\r\n 15 R--L\r\n 16 LR-L\r\n 17 -R-L\r\n 18 RR-L\r\n 19 LLRL\r\n 20 -LRL\r\n 21 RLRL\r\n 22 L-RL\r\n 23 --RL\r\n 24 R-RL\r\n 25 LRRL\r\n 26 -RRL\r\n 27 RRRL\r\n 28 LLL-\r\n 29 -LL-\r\n 30 RLL-\r\n 31 L-L-\r\n 32 --L-\r\n 33 R-L-\r\n 34 LRL-\r\n 35 -RL-\r\n 36 RRL-\r\n 37 LL--\r\n 38 -L--\r\n 39 RL--\r\nwhere a hyphen indicates to leave that coin off for that weighing.\r\n\r\nThese are based on the ternary representation of one less than the coin number, with L representing 0, - representing 1, and R representing 2, and presented low order to high order. Note that no two lines exist where one is the same as the other with L\'s replaced by R\'s and vice versa, so for example, if the left pan went down every time except for the 3rd weighing, we\'d know that coin 19 was heavy as there is no line that has RRLR which could indicate that its coin was light.\r\n\r\nHowever there is a problem: the second weighing has three more coins on the left pan than on the right; the third has 9 more on the left than the right; and the fourth has all 27 of its coins on the left.\r\n\r\nThis can be remedied, however. After the first weighing, there are either 13 or 26 coins that we know to be good. During the second weighing, any three of these can be reallocated: if one was to appear on the left, it can be left out, or if it was to be left out it could be put on the right. The same applies to weighing 3, as the imbalance is only 9 and we have 13 to work with.\r\n\r\nOn the fourth weighing, there are 27 coins scheduled to appear on the left pan. But at least 19 of those can be known from one of the previous weighings or another to be good. And instead of leaving any one of those off, it can be switched to the right pan, and that counts for two in balancing the sides. As an odd number must be accounted for, one can be merely not placed on a pan.\r\n\r\nThen simply find the pattern of Ls and Rs on the above chart. Only one will be found, and it will apply to the given pan either going up or going down (as mentioned before, there is no corresponding negative value of, say, LLR- vs RRL-).\r\n\r\nSo, for example, if the left pan went up, you\'d know that all those that weren\'t weighed in the first weighing are good. So in weighing 2 you\'d place the coins as per the second column above, except you\'d leave, say, coins 2, 11 and 20, known to be good, off, instead of on the left pan. Say this time the pans balanced. All the coins on each balance are now known to be good, so in the next weighing, number 3, place all the coins as per the third column except 2, 3, 5, 7, 8, 9, 28, 29 and 30, as these would be scheduled for the left pan but can be left off as they are knwon to be good from either not being weighed in weighing 1, or being weighed in weighing 2. Say in weighing 3, the left side goes down again. Then place coins 1-27 on the left pan, except for 1, 2, 3, 5, 7, 8, 9, 10, 11, 12, 13, 14 and 15, which are to be placed on the right pan instead, and 16, which is to be left off, as these are known to be good from the previous weighings and allow an equal number of coins on the two pans. Now, if neither side goes down, we match the results to line 31 representing coin 31, and since the corresponding side, L, went down each time, it is heavier than the rest.',NULL,0); INSERT INTO comment VALUES (4318,765,1715,'Jonny Doe','THE SOLUTION','2003-04-23 15:28:19',3,'Divide the 39 into 3 piles of 13 coins. Put the first two piles on each side of the scale, if the scales are even then the fake coin is in the third pile otherwise the coin is in the pile that weighs less.\r\n
\r\nTake pile with the fake coin and divide it into two piles of 6 coins leaving one coin out. Weigh the two piles if the scales are even then the coin you left out is fake, otherwise the coin is in the pile that weighs less.\r\n
\r\nTake pile with the fake coin and divide it into three piles of 2 coins. Put the first two piles on each side of the scale, if the scales are even then the fake coin is in the third pile otherwise the coin is in the pile that weighs less.\r\n
\r\nTake the last two coins and weigh them. The one that weigh less is the fake.\r\n
\r\nIn theory it is possible based on this method to find the coin after two weighs but if we must weigh 4 times we can always grab a few coins and weigh them just for fun.\r\n',NULL,0); INSERT INTO comment VALUES (4319,765,1301,'Charlie','re: THE SOLUTION','2003-04-23 18:21:50',0,'The problem did not state that the fake coin weighs less than the others; it might weigh more instead.\r\n\r\nAlso, 2 weighings (the last paragraph remark) are enough to differentiate only 9 possibilities (3 possibilities for result of first weighing x 3 possibilities for second).',4318,0); INSERT INTO comment VALUES (4320,766,2058,'Anna','??','2003-04-23 22:04:30',0,'There was a storm which knocked over the table which had a glass of water on it. Cleopatra and Marc Anthony were struck by lightening?',NULL,0); INSERT INTO comment VALUES (4321,494,2059,'Michael','re(3): this is easy','2003-04-23 23:10:16',0,'Could it be that there are two ways to solve this problem?',4160,0); INSERT INTO comment VALUES (4322,738,1983,'Ahmed','re: Word problem???','2003-04-24 02:02:49',0,'O.K. fwaff, I note that your sequence (p is the 16th letter of the alphabet and i is the 9th...etc) can\'t explain why 25 is included?. Also, Bryan commented that this needs a mathimatical relations. however it was a smart observation. ',4275,0); INSERT INTO comment VALUES (4323,504,1902,'Hank','A different angle','2003-04-24 04:05:50',0,'It might help to think of it as liars and knights:\r\nA: \'B is a liar\'\r\nB: \'A is a knight\'\r\n\r\nIt is still the same solution. or paradox.',NULL,0); INSERT INTO comment VALUES (4324,504,979,'Ravi Raja','re: A different angle','2003-04-24 04:21:31',0,'You can verify that on your own Hank. As there are only a few possibilities (I think only four).',4323,0); INSERT INTO comment VALUES (4325,504,2060,'Katherine','Just a Question.','2003-04-24 04:40:02',4,'Are these statements referring to each other?',NULL,0); INSERT INTO comment VALUES (4326,504,979,'Ravi Raja','re: Just a Question.','2003-04-24 04:54:20',0,'Yes Katherine. The two statements are referring to each other.',4325,0); INSERT INTO comment VALUES (4327,501,1902,'Hank','re: ummm','2003-04-24 06:11:25',1,'fireflies or lightning bugs',4314,0); INSERT INTO comment VALUES (4328,279,1920,'Brian Smith','Using trig functions: Zero to 150 completed','2003-04-24 06:15:39',3,'I managed to generate all values 0 to 150 using only the following:\r\n+ - * / ! ^ ( ) sqrt sin cos tan floor ceil\r\n\r\n0= 2*0*0*3 \r\n1= (2+0)^(0*3) \r\n2= 2+0*0*3 \r\n3= 2*0*0+3 \r\n4= 20^0+3 \r\n5= 2+0+0+3 \r\n6= (2+0+0)*3 \r\n7= 20^0+3! \r\n8= 2+0+0+3! \r\n9= (2+0+0!)*3 \r\n\r\n10= 20/(-(0!)+3) \r\n11= (2+0!)!-0!+3! \r\n12= (2+0!+0!)*3 \r\n13= (2+0!)!+0!+3! \r\n14= 2*(0+0!+3!) \r\n15= ((2+0!)!-0!)*3 \r\n16= 2^(0+0!+3) \r\n17= 20+0-3 \r\n18= 20+0!-3 \r\n19= 20-(0*3)! \r\n\r\n20= 20+0*3 \r\n21= 20+(0*3)! \r\n22= 20-0!+3 \r\n23= 20+0+3 \r\n24= 20+0!+3 \r\n25= 20-0!+3! \r\n26= 20+0+3! \r\n27= 20+0!+3! \r\n28= (floor sqrt 20)+(0!+3)! \r\n29= (ceil sqrt 20)+(0!+3)! \r\n\r\n30= (2+0!)!+(0!+3)! \r\n31= ceil [-2*(tan (0!+0!))/sin 3] \r\n32= 2^(0!+0!+3) \r\n33= (2+0!)*floor [(tan (0!))/(sin 3)] \r\n34= 2+0!+ceil [(tan tan (0!))/(sqrt 3)] \r\n35= -2+floor [(tan tan (0!))/(-(0!)+3)] \r\n36= (2+0!)!*(0+3)! \r\n37= ceil [cos 2+(tan tan (0!))/(-(0!)+3)] \r\n38= floor [sqrt 2+(tan tan (0!))/(-(0!)+3)] \r\n39= 2+floor [(tan tan (0!))/(-(0!)+3)] \r\n\r\n40= 20*(-(0!)+3) \r\n41= -2+0+floor [(tan tan (0!))/(sqrt 3)] \r\n42= ((2+0!)!+0!)*3! \r\n43= 2*0+floor [(tan tan (0!))/(sqrt 3)] \r\n44= 20+(0!+3)! \r\n45= 2+0+floor [(tan tan (0!))/(sqrt 3)] \r\n46= 2*(-(0!)+(0!+3)!) \r\n47= 2+ceil [(tan tan (0!))/(tan (0!))]-3 \r\n48= (2+0)*(0!+3)! \r\n49= floor [2*(tan tan (0!))/(0+3)] \r\n\r\n50= 2*(0!+(0!+3)!) \r\n51= -2+floor[(tan tan (0!))/(tan (0!))]+3! \r\n52= 2+floor[(tan tan (0!))/(tan (0!))]+3 \r\n53= 2+ceil[(tan tan (0!))/(tan (0!))]+3 \r\n54= (ceil[-(tan 2)]^(0!+0!))*3! \r\n55= -2+0+ceil[(tan tan (0!))/(sqrt sqrt 3)] \r\n56= 2*0+floor[(tan tan (0!))/(sqrt sqrt 3)] \r\n57= (20-0!)*3 \r\n58= 2+0+floor[(tan tan (0!))/(sqrt sqrt 3)] \r\n59= 2+0+ceil[(tan tan (0!))/(sqrt sqrt 3)] \r\n\r\n60= 20*(0+3) \r\n61= floor[(sqrt 2)*(tan tan (0!))/(tan (0!))]-3! \r\n62= -2+(0!+0!)^(3!) \r\n63= (20+0!)*3 \r\n64= (2+0+0)^(3!) \r\n65= -2-0!+floor[tan tan (0!)]-3! \r\n66= 2+(0!+0!)^(3!) \r\n67= -2+0+ceil[tan tan (0!)]-3! \r\n68= 2*0+floor[tan tan (0!)]-3! \r\n69= 2*0+ceil[tan tan (0!)]-3! \r\n\r\n70= -2-0+ceil[tan tan (0!)]-3 \r\n71= 2*0+floor[tan tan (0!)]-3 \r\n72= (2+0!+0!)!*3 \r\n73= 2+floor[tan tan (0!)]+0-3 \r\n74= 2+ceil[tan tan (0!)]+0-3 \r\n75= -2+floor[tan tan (0!)]+0+3 \r\n76= 2+floor[tan tan (0!)]+0*3 \r\n77= 2*0+floor[tan tan (0!)]+3 \r\n78= 2*0+ceil[tan tan (0!)]+3 \r\n79= 2+floor[tan tan (0!)]+0+3 \r\n\r\n80= 2+ceil[tan tan (0!)]+0+3 \r\n81= (2+0!)^(0!+3) \r\n82= 2+floor[tan tan (0!)]+0+3! \r\n83= 2+ceil[tan tan (0!)]+0+3! \r\n84= 2+ceil[tan tan (0!)]+0!+3! \r\n85= floor[(sqrt sqrt 2)*(tan tan (0!))]+0-3 \r\n86= ceil[(sqrt sqrt 2)*(tan tan (0!))]+0-3 \r\n87= ceil[(sqrt sqrt 2)*(tan tan (0!))]+0!-3 \r\n88= floor[(sqrt sqrt 2)*(tan tan (0!))]+0*3 \r\n89= ceil[(sqrt sqrt 2)*(tan tan (0!))]+0*3 \r\n\r\n90= floor[(sqrt sqrt 2)*(tan tan (0!))]-0!+3 \r\n91= 20+floor[tan tan (0!)]-3 \r\n92= 20+ceil[tan tan (0!)]-3 \r\n93= floor[20*tan (0!)]*3 \r\n94= ceil[20*(tan (0!))*3] \r\n95= 20-floor[(tan tan (0!))/(cos 3)] \r\n96= ceil[20*tan (0!)]*3 \r\n97= 20+floor[tan tan (0!)]+3 \r\n98= 20+ceil[tan tan (0!)]+3 \r\n99= ceil[-(cos 2)*(tan tan (0!))+0!]*3 \r\n\r\n100= 20*(-(0!)+3!) \r\n101= 2+0+ceil[(tan tan (0!))*(sqrt sqrt 3)] \r\n102= floor[(sqrt 2)*(tan tan (0!))]+0-3 \r\n103= ceil[(sqrt 2)*(tan tan (0!))]+0-3 \r\n104= ceil[(sqrt 2)*(tan tan (0!))]+0!-3 \r\n105= floor[(sqrt 2)*(tan tan (0!))]+0*3 \r\n106= ceil[(sqrt 2)*(tan tan (0!))]+0*3 \r\n107= ceil[(sqrt 2)*(tan tan (0!))]+(0*3)! \r\n108= floor[(sqrt 2)*(tan tan (0!))]+0+3 \r\n109= ceil[(sqrt 2)*(tan tan (0!))]+0+3 \r\n\r\n110= ceil[(sqrt 2)*(tan tan (0!))]+0!+3 \r\n111= floor[(sqrt 2)*(tan tan (0!))]+0+3! \r\n112= ceil[(sqrt 2)*(tan tan (0!))]+0+3! \r\n113= ceil[(sqrt 2)*(tan tan (0!))]+0!+3! \r\n114= (20+0!)*3! \r\n115= -2+0+ceil[(tan tan (0!))*(sqrt sqrt (3!))] \r\n116= 2*0+floor[(tan tan (0!))*(sqrt sqrt (3!))] \r\n117= ((2+0!)!-0!)!-3 \r\n118= -2+(0!+0!+3)! \r\n119= -2+0!+(-(0!)+3!)! \r\n\r\n120= 20*(0+3!) \r\n121= 2-0!+(-(0!)+3!)! \r\n122= 2+(0!+0!+3)! \r\n123= ((2+0!)!-0!)!+3 \r\n124= -(2+0!)!+ceil[(tan tan (0!))*(sqrt 3)] \r\n125= ((2+0!)!-0!)^3 \r\n126= (20+0!)*3! \r\n127= -2-0+floor[(tan tan (0!))*(sqrt 3)] \r\n128= 2^(0+0!+3!) \r\n129= 2*0+floor[(tan tan (0!))*(sqrt 3)] \r\n\r\n130= 2*0+ceil[(tan tan (0!))*(sqrt 3)] \r\n131= 2+0+floor[(tan tan (0!))*(sqrt 3)] \r\n132= 2+0+ceil[(tan tan (0!))*(sqrt 3)] \r\n133= 2+0!+ceil[(tan tan (0!))*(sqrt 3)] \r\n134= -2+ceil[(tan tan (0!))/(cos (0!))]-3 \r\n135= -2+ceil[(tan tan (0!))/(cos (0!))-(sqrt 3)] \r\n136= floor[(sqrt 2)+(tan tan (0!))/(cos (0!))]-3 \r\n137= 2+floor[(tan tan (0!))/(cos (0!))]-3 \r\n138= 2+ceil[(tan tan (0!))/(cos (0!))]-3 \r\n139= -2+floor[(tan tan (0!))/(cos (0!))]+3 \r\n\r\n140= 20*(0!+3!) \r\n141= 2*floor[tan tan (0!)]-0!-3! \r\n142= 2*floor[tan tan (0!)]+0-3! \r\n143= floor[2*(tan tan (0!))]-0-3! \r\n144= (2+0!+0!)!*3! \r\n145= 2*floor[tan tan (0!)]+0-3 \r\n146= floor[2*(tan tan (0!))]+0-3 \r\n147= 2*ceil[tan tan (0!)]+0-3 \r\n148= 2*floor[tan tan (0!)]+0*3 \r\n149= floor[2*(tan tan (0!))]+0*3 \r\n150= 2*ceil[tan tan (0!)]+0*3\n\nEdited on December 2, 2003, 11:40 am',NULL,0); INSERT INTO comment VALUES (4329,504,1567,'Bryan','Solution, of sorts','2003-04-24 06:26:43',1,'Call the two statements A and B, and assume they can only be true or false.
If A is true, B is true, but A says B is false: A cannot be true.
If A is false, B is false, but not A implies B is true: A cannot be false.
If B is true, A is false, but B says A is true: B cannot be true.
If B is false, A is true, but not B implies A is false: B cannot be false.
From this seeming paradox, we see that the original assumption is incorrect, and in fact both statements are neither true nor false.',NULL,0); INSERT INTO comment VALUES (4330,279,775,'Cory Taylor','re: Using trig functions: Zero to 150 completed','2003-04-24 06:28:20',0,'well done Brian - you beat me\r\n\r\n:(',4328,0); INSERT INTO comment VALUES (4331,504,1660,'Tim Axoy','Sorry,Ravi.','2003-04-24 07:45:20',0,'My A knights and liars paradox was a dupe of this one(though not intentionally).',NULL,0); INSERT INTO comment VALUES (4332,504,979,'Ravi Raja','re: Sorry,Ravi.','2003-04-24 07:57:44',0,'Tim why do you have to say Sorry for that. There are many problems submitted by someone or the other which turns out to be a dupe of some problem on this site, but that doesn\'t mean you have to aologise for that. ',4331,0); INSERT INTO comment VALUES (4333,768,1660,'Tim Axoy','This IS cool!','2003-04-24 08:02:54',0,'It is cool like it says!',NULL,0); INSERT INTO comment VALUES (4334,768,979,'Ravi Raja','I Got It !!','2003-04-24 08:11:31',3,'Let the first number of the sequence be taken as 1.\r\nNow, the next number will be 1 multiplied by (2!), which is equal to 2.\r\nThe third number will be equal to 2 multiplied by (3!), which is equal to 12.\r\nThe fourth number will be equal to 12 multiplied by (4!), which is equal to 288.\r\nThe fifth number will be equal to 288 multiplied by (5!), which is equal to 34560.\r\nSo we see that the \'N\'th number of the sequence is obtained by multiplying the \'(N-1)\'st number by (N!), that is N factorial.\r\nTherfore the next number of the sequence has to be equal to 34560 multiplied by (6!), which will give us the result 24883200.\r\nIsn\'t this correct ?\r\n',NULL,0); INSERT INTO comment VALUES (4335,768,1660,'Tim Axoy','No!!!!','2003-04-24 09:40:16',0,'You asked if it was not correct.\r\nI answered \"No\" because it is correct.',4334,0); INSERT INTO comment VALUES (4336,504,2066,'David','a thought','2003-04-24 13:37:29',0,'The first statement does not say whether the second is true. It says that the first is false, but leaves the true answer open to question. The second however, says plainly, that the first is true. ',NULL,0); INSERT INTO comment VALUES (4337,504,1626,'Gamer','re: Sorry,Ravi.','2003-04-24 14:15:24',0,'Yes don\'t worry... That\'s why we have Journeymen and such... so that the dupe puzzles just get deleted :)',4331,0); INSERT INTO comment VALUES (4338,504,1575,'DJ','Well..','2003-04-24 18:52:19',1,'The quotation marks make the difference.\r\n\r\nThe first statement says that the next statement (the second one) is \"False\", but it is not \"False\". It is \"The previous statement is \"True\".\" Therefore the first statement is false, since the second statement is not what it says that it is.\r\n\r\nSimilarly, the first statement is not \"True\", but it is \"The next statement is \"False\", therefore the second statement (which refers to the previous statement, the first one), is also false.\r\n\r\nBoth statements are False (Neither statement is \"True\" or \"False\").',NULL,0); INSERT INTO comment VALUES (4339,502,1299,'Anoop','A little tricky?','2003-04-24 19:11:27',0,'i think maybe the answer should 101. since technically when u spell out 101, it is hundred and one => it contains an a in the \"and\"\r\n\r\notherwise the simple answer is 1000 as it contains an a.',NULL,0); INSERT INTO comment VALUES (4340,502,1575,'DJ','Pedantry','2003-04-24 19:16:20',3,'Counting each number \'correctly,\' and counting only whole numbers, as is implied but not stated in the problem, you have to count to \"one thousand,\" since 100 is \"one hundred,\" not \"a hundred,\" and 101 is \"one hundred one,\" not \"a hundred and one.\"\r\n\r\nIf you count in increments of anything other than an integer (still assuming only rational numbers), the next number you say will have the word \"and\" in it, since that is the correct way to pronounce it (ie, \"one and one third\" or \"four and three eights\").\r\n\r\nThe only exceptions there would be if you are counting backwards (or by a negative number). Then, the next fractional number you say may be between zero and one (ie, two thirds), and may not have an \'a\' in it. Once you are below zero, any number will work since you say the word \"negative\" before each value (one, zero, negative one, negative two. . .). Since the problem does specify \"how high,\" that can probably be ruled out.\r\n\r\nRegardless, the immediate and technical answers are the same: one thousand.',NULL,0); INSERT INTO comment VALUES (4341,279,1575,'DJ','ehm..','2003-04-24 20:04:33',0,'I\'m still not too big on saying that \'floor\' and \'ceil\' should be considered \"mathematical symbols.\" Maybe no one else agrees, but it doesn\'t set right with me. Trig functions I can swallow, and it appears that may be necessary to tackle this problem, but I hope not to have to round off any sloppy numbers.\r\nMy list is still largely incomplete, but, I have quite a few numbers with solutions simpler than those Brian came up with by rounding. I am sure that there are quite a few more that I have overlooked as well.\r\n\r\nMy list to date is now on a flooble notepad, so anyone can go look, and add any numbers you may have solved for as well. The point, at least my goal, is to not use the rounding functions in the solutions.\r\nhttp://www.flooble.com/cgi-bin/mypad.pl?id=2003\r\n\r\nWhat does everyone else think?',NULL,0); INSERT INTO comment VALUES (4342,499,1575,'DJ','hmm','2003-04-24 20:18:01',0,'Another plausible solution, that fits the riddle in every way, is simply that the men were playing cards, but not against each other, or that another party (or parties) were playing with the men and lost money to them. If the intended solution is that they were musicians, maybe it could be stated somewhere that they were playing together and with no one else. That rules out playing separate card games, and, coupled with the line of \"separate scores,\" might make a more challenging riddle with a \'cleaner\' answer. Otherwise, it\'s hard to say that other solutions are \'wrong\' just because they\'re not what you were thinking of.',NULL,0); INSERT INTO comment VALUES (4343,502,1183,'fwaff','re: Pedantry','2003-04-24 22:05:45',1,'Hmmmm... this is a similar argument to the one in the \'Division by three\' problem. Since Ravi has already given us the start point of \'one\' it rules out languages other than English, but the issue becomes which \'English\'. \r\n\r\nFrom my understanding in American English the convention is as DJ states above (ie 101 is written as \'one hundred one\'), but in modern English English the convention is different such that 101 is written \'one hundred and one\'. To further confuse matters, archaic English has a numbering convention similar to German such that 21 is written one and twenty - (think of the \'Sing a song of sixpence\' nursery rhyme). I have no idea what conventions are used in other types of English (eg Australia, New Zealand, Canada, etc).',4340,0); INSERT INTO comment VALUES (4344,501,2072,'Jake','Live, from Iraq','2003-04-24 23:54:35',3,'As I recall the Stars come out at night and are lost by the day (except for the sun of course). I may be wrong though, haven\'t read all of the other posts yet, but this is the answer as I remember it.',NULL,0); INSERT INTO comment VALUES (4345,504,979,'Ravi Raja','re: a thought','2003-04-25 00:05:39',0,'David how can you say that the first statement says that it itself is false?',4336,0); INSERT INTO comment VALUES (4346,502,979,'Ravi Raja','re: Other solutions??','2003-04-25 00:06:41',0,'In that case you can say ONE TENS AND ONE (for 11), if what you have said for 101 is true.',4311,0); INSERT INTO comment VALUES (4347,502,979,'Ravi Raja','re(2): Other solutions??','2003-04-25 00:10:59',0,'No Hank in English language of course. Since nothing has been mentioned regarding that. ',4312,0); INSERT INTO comment VALUES (4348,504,979,'Ravi Raja','re: Well..','2003-04-25 00:20:28',0,'Don\'t you think DJ that here, in this problem, the words True and False within quotes have the same meaning as we use it in general. Their meanings do not change if the words are put within quotes.',4338,0); INSERT INTO comment VALUES (4349,500,2074,'Dan','I have anser','2003-04-25 02:01:49',0,'sucide',NULL,0); INSERT INTO comment VALUES (4350,505,1301,'Charlie','solution','2003-04-25 03:56:11',3,'Let the ages of the Father, Mother, Son and Daughter be F, M, S and D respectively.\r\n\r\nThe father was the same age as the mother is now (F-M) years ago at which time the daughter was D-(F-M). So\r\n\r\nM = 3(D-(F-M))\r\n\r\nThe mother was twice the age the daughter is now (M-2D) years ago, at which time the father was F-(M-2D). Also, the daughter will reach half the age the mother is now in M/2 - D years, at which time the son will be S + M/2 + D, so \r\n\r\nS + M/2 + D = (F-(M-2D))/2\r\n\r\nThe daughter was the same age the son is now D-S years ago, at which time the mother was M-(D-S). The father will reach twice that age 2(M-(D-S))-F years from now, at which time the daughter will be D+2(M-(D-S))-F, so\r\n\r\nD+2(M-(D-S))-F = 4S\r\n\r\nSimplifying:\r\n\r\n3F - 2M -3D = 0 (A) \r\nF/2 - M - S + 2D = 0 (B)\r\nF - 2M + 2S + D = 0 (C)\r\n\r\nCombining (B) and (C), we get\r\n\r\nS = 3D/4\r\n\r\nCombining (A) and (C) we get\r\n\r\n2F - 2S - 4D = 0,\r\n\r\nand given the relation of S and D,\r\n\r\nF = 11D/4\r\n\r\nUsing these we get\r\n\r\nM = 21D/8\r\n\r\nSo D must be a multiple of 8:\r\n\r\nIf D=8, F=22, M=21 and S = 6. None of these is a perfect square.\r\n\r\nD=16 is already a perfect square, and then F=44, M=42 and S=12, which is the solution, as the next multiples of 8,22,21,6 do not include perfect squares until unreasonable ages.\r\n\r\nFather = 44\r\nMother = 42\r\nSon = 12\r\nDaughter = 16',NULL,0); INSERT INTO comment VALUES (4351,505,1301,'Charlie','re: solution -- Correction','2003-04-25 04:34:46',0,'Where I said \r\n\r\n\"in M/2 - D years, at which time the son will be S + M/2 + D, so \r\n\r\nS + M/2 + D = (F-(M-2D))/2\" \r\n\r\nthe S + M/2 + D should of course be S + M/2 - D.\r\n\r\nThe equations which followed from this are correct as the mistake was in typing in what I had on paper.',4350,0); INSERT INTO comment VALUES (4352,279,1920,'Brian Smith','re: ehm..','2003-04-25 04:48:01',0,'You have a very nice start on your list.\r\n\r\nIn my list, I try to minimize the number of operators and functions used in the expression. Your list had some entries using fewer functions than mine. I updated my list with some entries from your list and gave you credit. (11 entries) I am still deciding on the decimal point and the subfactorial, but I will probably put them in.\r\n\r\nThere are symbols for floor and ceil. Floor and ceil each have a pair of symbols. Unfortuneately, I can not find a font with those symbols.\r\n
\r\nceil\r\n+- -+\r\n| 2.1 | =3\r\n\r\nfloor\r\n| 2.9 | =2\r\n+- -+\n\nEdited on December 2, 2003, 11:36 am',4341,0); INSERT INTO comment VALUES (4353,504,2072,'Jake','Answer from Iraq','2003-04-25 04:51:59',3,'Here we go:\r\nBy capitalizing the words True and False they would appear to be proper nous, meaning they can be names of objects (think of coding a computer it doesn\'t care what you call things). Thus the paradox tells us the answer.\r\n\r\nThe first statement is \"True\" (thats the statements name according to the 2nd statement. The 2nd Statements name is \"False\" according to the 1st statement.\r\n\r\nAs to if either is true or false, I would have no idea :-)\r\n\r\nAt least that is this poor soldiers solution to the problem.',NULL,0); INSERT INTO comment VALUES (4354,504,979,'Ravi Raja','re: Answer from Iraq','2003-04-25 05:05:51',0,'I think that everyone understands what I mean here when i am using the words True and False within Quotes. Obviously I am not assigning names to the statements.',4353,0); INSERT INTO comment VALUES (4355,718,1920,'Brian Smith','A small idea, an even smaller number','2003-04-25 05:40:38',0,'Using a trig identity, I can get an incredibly small number from the very large number (.1^-2e3)! [The solution to Make The Most Of These Digits.]\r\n\r\ncot tan x = 1/x, so: cot tan [(.1^-2e3)!] is my very small number',NULL,0); INSERT INTO comment VALUES (4356,718,1920,'Brian Smith','re: A small idea, an even smaller number','2003-04-25 05:43:06',0,'I made a mistake. My equations should read:\r\ncot arctan x=1/x\r\ncot arctan [(.1^-2e3)!]',4355,0); INSERT INTO comment VALUES (4357,766,2076,'Christy','Farfetched but possible','2003-04-25 06:32:56',0,'Marc Anthony (the singer mind you) hit a really high note shattering the glass and Cleopatras ears causing her death. Then he died of a heart attack and fell into the table. LOL',NULL,0); INSERT INTO comment VALUES (4358,504,2066,'David','re(2): a thought','2003-04-25 06:44:03',0,'sorry, i said it wrong, i meant:\r\nThe first statement does not say whether itself is true. It says that the second is false, but leaves the true answer open to question. The second however, says plainly, that the first is true. It makes sense to me that you would go with the one that tells the answer plainly. Dunno though. \r\n',4345,0); INSERT INTO comment VALUES (4359,502,2066,'David','','2003-04-25 06:56:53',0,'So the number 1000 was NOT the solution? Is it a trick question?',NULL,0); INSERT INTO comment VALUES (4360,500,2066,'David','a possible answer','2003-04-25 07:02:14',0,'if you commited xenocide - i think its called that - and completely wiped out the human species it would not be punishable, or at least not on this earth. ',NULL,0); INSERT INTO comment VALUES (4361,504,979,'Ravi Raja','re: a thought','2003-04-25 07:58:35',0,'Also David you have mentioned that the second statement however states that the first is true. But you do not know whether the second statement itself is true or not! ',4336,0); INSERT INTO comment VALUES (4362,504,979,'Ravi Raja','re(3): a thought','2003-04-25 08:07:52',0,'David: Just like you are saying that - The second statement however, says plainly, that the first is true and so we should go with the statement that tells the answer plainly. Similarly, I can say that even The first statement, says plainly, that the second is false. This means we should go with this too and that implies both the first and the second statements are true. Isn\'t it ?',4358,0); INSERT INTO comment VALUES (4363,500,2078,'amanda','maybe.....','2003-04-25 08:08:14',0,'suicide',NULL,0); INSERT INTO comment VALUES (4364,769,1301,'Charlie','solution','2003-04-25 09:56:25',3,'The largest tetrahedron that will fit within a given cube has each of its 6 edges as a diagonal of one of the cube\'s 6 faces. Suppose one edge of the tetrahedron is a diagonal of the top face of the cube. Another edge of that tetrahedron would be a diagonal of the bottom face, but at right angles to the one on top (but of course skew as they are on parallel planes). The other 4 edges of the tetrahedron are then the diagonals of the side, front and back faces of the cube that connect up each of the two ends of the top diagonal to each of the two ends of the bottom diagonal.\r\n\r\nHalf the vertices of the cube are also vertices of the tetrahedron. The other half (numbering 4) are the right-angled vertices of right tetrahedra. Each of these smaller tetrahedra has 3 isosceles right triangular faces (each of which is half a face of the cube), and one equilateral triangular face where it adjoins the central regular tetrahedron.\r\n\r\nLet the edges of the cube have length 1, so the cube\'s volume is 1.\r\n\r\nConsider one right triangular face of a small tetrahedron to be the base. It\'s two equal legs have the same length as the edge of the cube, which we have taken as 1. The area of the base is therefore 1/2. The altitude of the small tetrahedron is one of the edges of the cube, and therefore 1. As it is a pyramid, the volume is equal to the area of the base times the height divided by 3, which therefore comes out to 1/6.\r\n\r\nAs there are 4 of these small tetrahedra, their total volume is 4/6, or 2/3. Together with the regular tetrahedron whose volume we seek, that makes up the whole of the volume of the cube. So our regular tetrahedron has volume 1 - 2/3 = 1/3. That is the tetrahedron has 1/3 the volume of the cube.\r\n\r\nI don\'t know of a mathematical proof that this tetrahedron is the largest that will fit in the cube -- the same as saying the cube is the smallest that will fit around the tetrahedron-- but it is hard to imagine a larger tetrahedron fitting.',NULL,0); INSERT INTO comment VALUES (4365,769,1567,'Bryan','re: solution','2003-04-25 10:44:00',0,'Charlie, good solution to this problem - more elegant than mine! ',4364,0); INSERT INTO comment VALUES (4366,505,1626,'Gamer','re(2): solution -- Correction','2003-04-25 13:48:03',0,'Sigh... I can never do these \"The son was half as old as the mother when the mother was half the age of the daughter when the daughter was twiice the age of the son\" problems... They are just way too confusing to me.',4351,0); INSERT INTO comment VALUES (4367,766,2076,'Christy','This is all I got','2003-04-25 17:07:47',3,'Cleopatra and marc anthony were someones pet goldfish and someone or something or some event knocked the table over that the fish tank or fish bowl was on. There for they died of suffocation.',NULL,0); INSERT INTO comment VALUES (4368,501,2076,'Christy','um maybe','2003-04-25 17:35:27',0,'dreams?',NULL,0); INSERT INTO comment VALUES (4369,501,2076,'Christy','hmmmm','2003-04-25 17:37:03',0,'ghosts?',NULL,0); INSERT INTO comment VALUES (4370,504,1983,'Ahmed','re: Solution, of sorts','2003-04-25 20:37:31',0,'Well. I have nothing to add. I think that Bryan\'s solution is a complete one. Isn\'t it??',4329,0); INSERT INTO comment VALUES (4371,507,979,'Ravi Raja','Rewording Of The Problem','2003-04-26 04:34:43',0,'Sorry friends, I think there is a bit of confusion regarding the Language of the problem and so one of my friends had asked me to change it when it was in the queue but unfortunately when I logged on next, the problem was pushed up on the site. So I would like to clear everything here. I mean the problem is written now in a different form (but the meaning remains the same):\r\nHere is how it goes: \r\nThere is a four-digit number,all of whose digits are different and is equal to the difference between the two numbers formed by its digits arranged in descending and ascending order. \r\nI think this is alright. \r\nSorry for that again.',NULL,0); INSERT INTO comment VALUES (4372,507,1626,'Gamer','My solution','2003-04-26 05:50:01',3,'This is actually a good problem, :) I have come to various conclusions about the numbers, and my answer is 6174.\r\n\r\n7641\r\n1467\r\n----\r\n6174\r\n\r\nI am still working around with how to prove it.',NULL,0); INSERT INTO comment VALUES (4373,765,1072,'Alan','Solution','2003-04-26 07:18:01',2,'Well first divide the coins into three piles. First weigh pile one against pile 2, then pile 2 against pile 3. This will tell you whether the coin is lighter or heavier. On top of that you will know which pile contains the fake coin. so know you have 13 coins and two weighings. then divide the 13 coin group, into 3 groups 4, 4 and 5. then weigh the 4 against the other 4. t worst you\'re left with the group of 5. Now heres where I\'m stuck. you can divide it into 2 groups of 2 and a single coin. Any other thoughts?',NULL,0); INSERT INTO comment VALUES (4374,507,1301,'Charlie','re: My solution -- exhausive search uniqueness shown','2003-04-26 09:17:17',0,'Proof of uniqueness of the solution is obtained by the following program that looks at all numbers formed with four different digits in ascending sequence and subtracting that from it\'s reverse and sees if the result has the same four digits. It includes the possibility that the leading digit is zero. Only 7641 - 1467 = 6174 is found by the program.\r\n\r\nFOR i = 0 TO 6\r\n FOR j = i + 1 TO 7\r\n FOR k = j + 1 TO 8\r\n FOR l = k + 1 TO 9\r\n diff = l * 1000 + k * 100 + j * 10 + i - (i * 1000 + j * 100 + k * 10 + l)\r\n s$ = LTRIM$(STR$(diff))\r\n IF LEN(s$) < 4 THEN\r\n s$ = RIGHT$(\"0000\" + s$, 4)\r\n END IF\r\n s1$ = LTRIM$(STR$(l * 1000 + k * 100 + j * 10 + i))\r\n DO\r\n ix = INSTR(s1$, LEFT$(s$, 1))\r\n IF ix = 0 THEN EXIT DO\r\n s1$ = LEFT$(s1$, ix - 1) + MID$(s1$, ix + 1)\r\n s$ = MID$(s$, 2)\r\n LOOP UNTIL s$ = \"\"\r\n IF s$ = \"\" THEN\r\n d = l * 1000 + k * 100 + j * 10 + i\r\n a = i * 1000 + j * 100 + k * 10 + l\r\n PRINT d; \"-\"; a; \"=\"; d - a\r\n END IF\r\n NEXT\r\n NEXT\r\n NEXT\r\nNEXT\r\n',4372,0); INSERT INTO comment VALUES (4375,507,1626,'Gamer','Proof :)','2003-04-26 11:26:20',3,'Looking at the problem, it can be proven that the answer\'s first number + fourth number = 10, and its second and third number = 8.\r\n\r\nThe difference between the greatest and least number in the answer has to be the first number in the answer.\r\n\r\n9 and 8 can\'t be in the middle, or you would get -1 and 0 as the other number, which are illegal.\r\n\r\nNeither x nor y can be the largest or the smallest, since that would end up with a 0 (as largest or smallest) So x and y have to be between the other numbers. This means that the numbers in the middle have to be the largest and the smallest, and this means that the first number is the difference of the middle ones. Since the first and last number equal 10, you can figure out what numbers could work.\r\n\r\n044T The first number is 0, and that is excluded. (Also, T isn\'t a valid number in base 10)\r\n\r\n2358 or 2538 The first number is 5-3=2, so the last number is 10-2=8, But this isn\'t allowed, since the first and last numbers have to be between the middle numbers\' values.\r\n\r\n4266 or 462 The first number is 6-4=2, and the last number is 10-4=6. But this isn\'t allowed, since the first and last numbers have to be between the middle numbers\' values.\r\n\r\n6174 or 6714 The first number is 7-1=6 and the last number is 10-6=4. This seems to work so far, so to check it, you get 7641-1467=6174, and you see that the first one works.\r\n\r\nSo the answer must be 6174.',NULL,0); INSERT INTO comment VALUES (4376,502,1971,'Steven','A High Number To Spell To','2003-04-26 11:36:01',3,'1000. One ThousAnd. Just spell 1-19, then pick up with 20, then count by tens until you reach 100, then count by hundreds \'til you reach one thousand.',NULL,0); INSERT INTO comment VALUES (4377,766,1971,'Steven','Circumstancial','2003-04-26 11:49:13',1,'From the evidence presented, they would appear to be fish. But was the water all over, or was it in a glass sitting somewhere, or what? As people, they could have died from a number of natural causes. With the violence indicated in the riddle, it could be shock with a heart attack from seeing or hearing something or somebody they had double-crossed or thought dead that they had in their bloody and not too nice past.',NULL,0); INSERT INTO comment VALUES (4378,81,2080,'Tristan','I concur with the original','2003-04-26 11:51:46',3,'15 of 36, after manually working out all the cases using a simple \"yes and no\" method. There are 15 cases where the sum of B is Greater to the Product of A, and 19 cases where the Product of A is greater than the sum of B, this leaves 2 cases, ehich are those where the equal the same ( 2 cases in A = 12, 1 case in B = 12) 15/36 is the correct answer',NULL,0); INSERT INTO comment VALUES (4379,304,1626,'Gamer','re(2): simple guess','2003-04-26 12:16:42',0,'The way I think about it is: Start with 9=9, Each time you add 9, you are just adding 1 to the tens place and subtracting 1 from the ones place. Once you get 99 (or 97, another like number), you just subtract 1 from the ones place and add 1 to the hundreds place, and make the other number(s) (which should be 9) 0.\r\n\r\nSo, you have either added a net amount of 9,0,-9 each time. This means the sum of the digits will be a multiple of 9.\r\n\r\nThis is the same idea with the divisible by 3 idea. You are adding a net amount of 9, 6, 3, 0, -3, -6, -9...',1902,0); INSERT INTO comment VALUES (4380,298,1626,'Gamer','That\'s a fun idea','2003-04-26 16:19:40',0,'I don\'t think I would have gotten that... too hard! :)',NULL,0); INSERT INTO comment VALUES (4381,507,1567,'Bryan','re: Proof :)','2003-04-26 17:29:12',0,'Gamer, I want to understand your proof. You make a mention of x and y without defining them. Did I miss an earlier partial proof?',4375,0); INSERT INTO comment VALUES (4382,507,1567,'Bryan','Interesting!','2003-04-26 17:36:06',2,'An observation that may be of interest to others:
Take any four consecutive digits. Subtract the ascending number from the descending one, and the answer will be 3087. Repeat the subtraction process (descending minus ascending) with these digits and the answer is 8352. Repeat the process a third time with these digits, and the answer is 6174',NULL,0);
INSERT INTO comment VALUES (4383,507,1301,'Charlie','re: Interesting!','2003-04-27 04:06:07',1,'In fact, take any four digits, consecutive or not, and so long as they are not all equal, and keep repeating the process, and you will eventually get 6174 after at most 7 iterations.\r\n\r\nFor example, start with 2631. Applying this procedure produces successive values of 5085, 7992, 7173, 6354, 3087, 8352 and then 6174 interminably.\r\n\r\nIt even works considering smaller number as having leading zeros: 343 produces (via 0343) 3996, 6264, 4176, 6174.\r\n\r\nOf course if all the digits are the same, then you get all zeros right away and that\'s the end, but only one digit need be different, as in 1112 leading to 0999, 8991, 8082, 8532, 6174.\r\n',4382,0);
INSERT INTO comment VALUES (4384,777,1301,'Charlie','solution','2003-04-27 04:08:59',3,'Choose any equilateral triangle on the plane, with sides equal to one meter. As there are only 2 colors to go around, two of the vertices must lie on points of the same color and are one meter apart.',NULL,0);
INSERT INTO comment VALUES (4385,496,1660,'Tim Axoy','He-she','2003-04-27 04:39:25',4,'Ravi,in your solution,some of A,B,C,and D were called a he once and a she another time.\r\nWhy?',NULL,0);
INSERT INTO comment VALUES (4386,766,2076,'Christy','ok im trying again','2003-04-27 05:13:53',4,'did they die of choking? ',NULL,0);
INSERT INTO comment VALUES (4387,504,1660,'Tim Axoy','Both false','2003-04-27 09:44:32',3,'The statements are not named \"True\" and \"False\",so both are false.',4354,0);
INSERT INTO comment VALUES (4388,777,1,'levik','re: solution','2003-04-27 17:33:01',0,'Nice!\r\n\r\nI would not have thunk of solving this one with the pigeon-hole principle :)',4384,0);
INSERT INTO comment VALUES (4389,504,979,'Ravi Raja','re: Both false','2003-04-28 01:12:02',0,'Tim, since the problems were not named True and False, then obviously the words have heir usual meanings. SO how can you say that both are false ?',4387,0);
INSERT INTO comment VALUES (4390,507,1626,'Gamer','re(2): Interesting!','2003-04-28 01:37:10',0,'\r\nThat\'s cool...\r\n\r\nHere are the sequences from before (in your last post), used as an example.\r\n\r\n2631, 5085, 7992, 7173, 6354, 3087, 8352 6174 \r\n \r\n0343, 3996, 6264, 4176, 6174. \r\n\r\n1112, 0999, 8991, 8082, 8532, 6174. \r\n\r\n\r\n\r\n2631, 5085, 7992,\r\n\r\nNow the middle two numbers add up to 8, and the outsides add up to 10.\r\n7173, 6354, 3087, 8352 6174 \r\n\r\nIt works with other sequences too.\r\n\r\n0343, 3996, \r\n\r\nNow the middle numbers (2,6 1,7 1,7) add up to 8, and the outside numbers (6,4 4,6 6,4) add up to 10\r\n6264, 4176, 6174. \r\n\r\n\r\n1112, 0999, 8991, \r\n\r\nHere is where it begins again.\r\n8082, 8532, 6174. \r\n',4383,0);
INSERT INTO comment VALUES (4391,507,1626,'Gamer','More about Proof','2003-04-28 01:39:25',0,'Sorry about that. I must have deleted the part where I explained it. x and y are the first and last number of the possible four-digit number. ',NULL,0);
INSERT INTO comment VALUES (4392,506,1301,'Charlie','solution','2003-04-28 03:53:56',3,'There are 25 sets of factors of 180, and they could add up as follows:\r\n\r\n3 + 3 + 4 + 5 = 15\r\n2 + 3 + 5 + 6 = 16\r\n1 + 5 + 6 + 6 = 18\r\n2 + 2 + 5 + 9 = 18\r\n2 + 3 + 3 +10 = 18\r\n1 + 4 + 5 + 9 = 19\r\n1 + 3 + 6 +10 = 20\r\n1 + 3 + 5 +12 = 21\r\n1 + 2 + 9 +10 = 22\r\n2 + 2 + 3 +15 = 22\r\n1 + 3 + 4 +15 = 23\r\n1 + 2 + 6 +15 = 24\r\n1 + 2 + 5 +18 = 26\r\n1 + 3 + 3 +20 = 27\r\n1 + 1 +12 +15 = 29\r\n1 + 1 +10 +18 = 30\r\n1 + 1 + 9 +20 = 31\r\n1 + 2 + 3 +30 = 36\r\n1 + 1 + 6 +30 = 38\r\n1 + 1 + 5 +36 = 43\r\n1 + 2 + 2 +45 = 50\r\n1 + 1 + 4 +45 = 51\r\n1 + 1 + 3 +60 = 65\r\n1 + 1 + 2 +90 = 94\r\n1 + 1 + 1+180 =183\r\n\r\nOnly two of the totals, 22 and 18, have more than one set of four factors that add up to them, and so would be ambiguous if the professor\'s teaching years were equal to one of them. But those adding to 22 both have terms with two digits.\r\n\r\nThose adding to 18 have only one with two digits: 2, 3, 3 and 10. So this is the number of years of study of the four students.',NULL,0);
INSERT INTO comment VALUES (4393,506,1301,'Charlie','re: solution','2003-04-28 03:59:00',0,'The list of ways to factor 180 into 4 factors was produced from sorting the output of the following program by total:\r\nDECLARE SUB factorit (n!, lev!)\r\nDIM SHARED fact(4)\r\nn = 180\r\nOPEN \"factors.txt\" FOR OUTPUT AS #1\r\nfactorit n, 1\r\nCLOSE\r\nEND\r\n\r\nSUB factorit (n, lev)\r\n IF lev = 1 THEN strt = 1: ELSE strt = fact(lev - 1)\r\n IF lev = 4 THEN\r\n IF strt <= n AND n >= fact(lev - 1) THEN\r\n strt = n:\r\n ELSE\r\n EXIT SUB\r\n END IF\r\n END IF\r\n FOR i = strt TO n\r\n IF n \\ i = n / i THEN\r\n fact(lev) = i\r\n IF lev = 4 THEN\r\n tot = 0\r\n FOR j = 1 TO 4\r\n PRINT #1, USING \"###\"; fact(j);\r\n IF j < 4 THEN PRINT #1, \"+\"; : ELSE PRINT #1, \"=\";\r\n tot = tot + fact(j)\r\n NEXT\r\n PRINT #1, tot\r\n ELSE\r\n factorit n / i, lev + 1\r\n END IF\r\n END IF\r\n NEXT\r\nEND SUB\r\n\r\n',4392,0);
INSERT INTO comment VALUES (4394,113,1920,'Brian Smith','re: Most of a solution - Solution confimed.','2003-04-28 04:13:15',1,'There are two maximum points on A. They are given by y=4/sqrt 31 and y=-4/sqrt 31. These are the only maxima on the curve A. \r\nx=7/sqrt 31 y=4/sqrt 31 z=20/sqrt 31 A=8\r\nx=-7/sqrt 31 y=-4/sqrt 31 z=-20/sqrt 31 A=8\r\nThis has been confirmed by solving dA/dy for all cases.',3898,0);
INSERT INTO comment VALUES (4395,769,1686,'DuCk','My shot at a solution','2003-04-28 05:02:00',0,'Let\'s start with getting the volume of a tetrahedron. A tetrahedron is a pyramid on a triangle base, so the volume of the object would be V=1/3*Ab*H (where Ab=area of base, and H=height). The height is obtained by H=1/3*√6*a (where a=the length of a side of the tetrahedron). The area of the base is obtained by Ab=1/4*√3*a². Substituting into and compounding volume equation we obtain V=1/12*√2*a³. \r\n\r\nNow we will find the volume of a cube. That\'s pretty easy as it is the side of the cube, we\'ll call it s, cubed. Therefore V=s³.\r\n\r\nNow, we must realize that the largest tetrahedron that will fit inside a cube will do so when the sides of the tetrahedron, a, run along the diagonal of the faces of the cube. Therefore the relationship between s & a is ==> a=√2*s. \r\n\r\nFinally, we put the ratio together and substitute with the a=√2*s relationship. From this we get:\r\n\r\n Ratio=(1/12*√2*(√2*s)³) / (s³)\r\n\r\nand reduce that down to Ratio=1/3. Sorry about the poor description, but hopefully this might help someone. ',NULL,0);
INSERT INTO comment VALUES (4396,769,1920,'Brian Smith','solution','2003-04-28 06:25:58',0,'The smallest cube around a tetrahedron is equivalent to the largest tetrahedron in a cube.\r\n\r\nThe tetrahedron with the largest volume will have verticies coinciding with the verticies of the cube. The four verticies of the cube are all sqrt 2 units apart. A tetrahedron with an edge of sqrt 2 has a volume of (sqrt 2)^3*(sqrt 2)/12=1/3. The cube has volume 1^3=1. The ratio of tetrahedron to cube is (1/3)/1=1/3.',NULL,0);
INSERT INTO comment VALUES (4397,783,1301,'Charlie','Ooooohhhhhh! Now I get it.','2003-04-28 07:41:13',3,'It just hit me: the lower case omega is like a 3 turned 90 degrees. As that approaches an infinity sign, which is like an 8 turned ninety degrees, we could say that the original 3 becomes an 8. It\'s more like a symbolic analogy.',NULL,0);
INSERT INTO comment VALUES (4398,783,1299,'Anoop','hmmm','2003-04-28 08:24:52',0,'well the answer is 3. if theres no mathematical relation b/w w and 3, since its a constant , the limit should be 3. \r\n \r\nYou could of course say that w looks like 3 turned sideway and infinity looks like 8 sideways so the answers should be 8...but thats more like just plain fun...which mite be the point of the problem here.',NULL,0);
INSERT INTO comment VALUES (4399,783,1686,'DuCk','my guess','2003-04-28 08:38:25',0,'8',NULL,0);
INSERT INTO comment VALUES (4400,783,1,'levik','Reminds me...','2003-04-28 09:18:48',0,'This reminds me of that old geek joke:\r\n\r\n\"One plus one is equal to three for large values of one.\"\r\n\r\nTee-hee. Makes me laugh just thinking about it.',NULL,0);
INSERT INTO comment VALUES (4401,506,1575,'DJ','well','2003-04-28 10:32:48',0,'I won\'t bother posting a redundant solution, though I solved the problem.\r\n\r\n..It seems that no matter what time of the day I get on here Charlie has already been through all the new problems. I knew the answer to this one, sadly, because it is very similar to the first problem I submitted, I think around two months ago, which is still sitting in the queue for probably another month and a half before it gets to be voted on.\r\n\r\nohwell\r\n\r\nOn a side note, what language are you using there? I\'ve seen it around on this site, but it\'s unfamiliar and dissimilar to any of the C-based languages I know.',NULL,0);
INSERT INTO comment VALUES (4402,504,1575,'DJ','See the difference?','2003-04-28 10:41:27',2,'1. The next statement is \"1+1=3\".\r\n2. 1+1=3\r\n3. The previous statement is \"False\".\r\n4. The previous statement is False.\r\n3. The first statement is True.\r\n4. The first statement is \"True\".\r\n\r\n1 - T\r\n2 - F\r\n3 - F\r\n4 - T\r\n5 - T\r\n6 - F',NULL,0);
INSERT INTO comment VALUES (4403,502,1575,'DJ','Miscellany','2003-04-28 10:57:33',0,'While many people insist on saying the word \'and\' for numbers above one hundred, I have never seen anything saying that it is the correct way to say it for any English dialect. Correct me if I\'m wrong, please, but I haven\'t seen it.\r\n\r\nWhile I was trying to find something to the contrary of what I said before, I found a page with some interesting facts:\r\n\r\nEight is the first number alphabetically. Zero is the last.\r\n\r\nFour is the only number that, spelled out, has as many letters.\r\n\r\nForty is the only number whose letters are in alphabetical order. One is the only number whose letters are in reverse alphabetical order. First also has its letters in alphabetical order.\r\n\r\nEighty-six, nine letters long, is the longest number that is normally typed using strictly alternating hands (ignoring the hyphen).\r\n\r\nInterchangeability is the word in the English language that contains the letters to form the most numbers. Its letters can form the words three, eight, nine, ten, thirteen, thirty, thirty-nine, eighty, eighty-nine, ninety, and ninety-eight.\r\n\r\nOne thousand is the first number that, when spelled out, contains an a.\r\nOne billion is the first number that contains a b. \r\nOne octillion is the first number that contains a c. \r\nOne hundred is the first number that contains a d. \r\nZero is the first number that contains an e. Starting from one, it\'s one. \r\nFour is the first number that contains an f. \r\nEight is the first number that contains a g. \r\nThree is the first number that contains an h. \r\nFive is the first number that contains an i. \r\nThe letters j and k do not appear in the English spelling of any cardinal number. \r\nEleven is the first number that contains an l. \r\nOne million is the first number that contains an m. \r\nOne is the first number that contains an n. \r\nZero is the first number that contains an o. Starting from one, it\'s one. \r\nOne septillion is the first number that contains a p. \r\nOne quadrillion is the first number that contains a q. \r\nZero is the first number that contains an r. Starting from one, it\'s three. \r\nSix is the first number that contains an s. \r\nTwo is the first number that contains a t. \r\nFour is the first number that contains a u. \r\nFive is the first number that contains a v. \r\nTwo is the first number that contains a w. \r\nSix is the first number that contains an x. \r\nTwenty is the first number that contains a y. \r\nZero is the first and only number that contains a z. (One zillion is not a real number.)\r\n\r\nSeven is the first number not to contain any letter for the first time.\r\n\r\nOne octillion, the first number containing a c, is the largest number to contain any letter for the first time.',NULL,0);
INSERT INTO comment VALUES (4404,71,2092,'Allison Smetana','An interesting way','2003-04-28 11:08:08',0,'la la la la la la la la la la la la la la la la la la la la la la la la la la la la la la la la ',NULL,0);
INSERT INTO comment VALUES (4405,159,1253,'Brian Nowell','One Equation','2003-04-28 16:07:01',3,'Nick wondered if an \"x,y\" equation could be formulated to describe the minimum number of shaded tiles for a given rectangle; parameters are within the descriptor.\r\n\r\nI offered a solution for squares \"Eureka!!! - Squares Anyway\" and later followed up with a Software solution; useless for a calculator!!\r\n\r\nBrian Smith has used a CEILING function (which rounds fractional parts upwards to the next integer) as against INT (which I chose, which rounds downwards).\r\n\r\nBrian Smith\'s contribution is 2 formulae. These are great, but Nick sought one.\r\n\r\nNow with many Maths situations there will be exceptions, like \"if A = 0 ...\". \r\nBrian identified these but probably lowered his by one; I think that his condition should be for x,y>3 not x,y >= 3. He produced these three exceptions as:\r\nOOOOOOOOOO, for a single row which needs no Black tiles,\r\n\r\nOOOXOOOXO\r\nOXOOOXOOO, for 2 rows and requires int(length/2) Black tiles,\r\nand\r\nOOOOOOOOO\r\nOXXXXXXXO\r\nOOOOOOOOO, for 3 rows requires just the length-2 Black tiles.\r\n\r\nBrian\'s formulae, which are: ceil(x*y/3)-1 if (x-y) MOD 3 != 0 and ceil(x*y/3)-2 if (x-y) MOD 3 = 0, differ by a value of 1.\r\n\r\nWhen (x-y) MOD 3 != 0, the value is either 1 or 2. Using the following device (x-y) will return either Zero or a One: MOD((MOD(x-y,3))^2,3); this syntax is used in MS Excel.\r\n\r\nApplying this to ceil(x*y/3)-2 creates the formula: ceil(x*y/3)-2 + mod((mod(x-y,3))^2,3).\r\n\r\nI have not seen the Ceiling function on any calculator so it would be great to have this formula using only the Int and mod functions. Int(x*y/3)-1 produces the same results as ceil(x*y/3)-2, except where either x or y, or both are a multiple of 3.\r\n\r\nAnyway here is one formula that appears to do what is required for all x,y values greater than 3: n=ceil(x*y/3)-2 + mod((mod(x-y,3))^2,3).\r\n\r\nUsing Excel as a calculator and cells A1 and B1 holding the respective values of x and y,\r\nthe syntax would read as: =CEILING(A1*B1/3)-2+MOD((MOD(A1-B1,3))^2,3)',NULL,0);
INSERT INTO comment VALUES (4406,506,1301,'Charlie','re: well -- the computer language','2003-04-28 16:58:40',0,'It\'s Quick Basic, a DOS-based language Microsoft had a few years back. It shares much syntax with versions of Visual Basic up to 6.0.',4401,0);
INSERT INTO comment VALUES (4407,783,979,'Ravi Raja','Two Possible Solutions','2003-04-28 23:31:09',3,'Firstly is we consider the proper method for dealing with such Limit problems, then we see that since 3 is a constant and there is no term/function omega, of which the limit is to be found, so the final value of the limit should be equal to 3. That is, Limit of 3, as omega tends to infinity is equall to 3.\r\n\r\nSecondly, this problem can be solved on the basis of the category assigned to the problem. We see that omega when turned through an angle of 90 degrees in the anticlockwise direction, resembles the digit 3 and infinity (∞) when turned through the same angle (90 degrees) in the same direction (anticlockwise) resembles the digit 8, thus implying that 3 tends to 8 and therefore the value of the given limit is equal to 8. That is, Limit of 3, as omega tends to infinity is equall to 8.',NULL,0);
INSERT INTO comment VALUES (4408,443,2094,'x','re: Solution attempt','2003-04-29 00:14:06',0,'Excellent approach',3024,0);
INSERT INTO comment VALUES (4409,504,2097,'itduzntmatter','re(2): Both false','2003-04-29 04:56:49',0,'its up to the reader to define what the problems are named as they werent named in the original question.',4389,0);
INSERT INTO comment VALUES (4410,504,2097,'itduzntmatter','','2003-04-29 05:02:48',0,'but if true and false are their proper meanings, then theres no way of determining the answer (unless of course the meanings are changed.)',NULL,0);
INSERT INTO comment VALUES (4411,27,2097,'itduzntmatter','','2003-04-29 05:26:52',0,'they concluded there cant be an exam.. but that means there can be one and it will be a surprise... but repeating the original argument there cant be one... so it just goes round in circles like the other paradoxes!',NULL,0);
INSERT INTO comment VALUES (4412,337,2097,'itduzntmatter','','2003-04-29 05:53:55',0,'aren\'t you forgetting twenty seconds (22nds)',NULL,0);
INSERT INTO comment VALUES (4413,780,153,'TomM','Nesting Allowed?','2003-04-29 08:47:10',3,'If \"nesting\" (placing one or more bags inside another and countint the marbles inside the nested bag toward the outer bag\'s total) is allowed you get 101 bags all with a different number of marbles within:\r\n\r\nThe first bag is empty. It has 0 marbles.\r\nThe second bag contains the first plus one marble. It has one marble.\r\nThe third bag contains the second plus one marble. It has two marbles.\r\nThe fourth bag contains the third plus one marble. It has three marbles.\r\n....\r\nThe 100th bag contains the 99th bag plus one marble. It has 99 marbles.\r\nThe 101st bag contains the 100th bag plus one marble. It has 100 marbles.\r\n\r\nIf nesting is not allowed, then an upper limit can be approximated by the formula for the sum of the first n whole numbers: \r\nT(n)=n(n+1)/2≤100; n(n+1)≤200\r\n13(14)=182; 14(15)=210\r\nThere can be no more than 13 differently \"weighted\" bags. ',NULL,0);
INSERT INTO comment VALUES (4414,159,1920,'Brian Smith','re: One Equation - equation in int and mod','2003-04-29 09:11:22',0,'It is possible to write ceil(x*y/3) using int and mod.\r\nceil(x*y/3) = int(x*y/3) + mod((mod(x*y,3))^2,3)\r\n\r\nSo the final formula would then be int(x*y/3) + mod((mod(x*y,3))^2,3) + mod((mod(x-y,3))^2,3) - 2\r\n\r\nI prefer my two part formula since it is easier to use in my opinion.',4405,0);
INSERT INTO comment VALUES (4415,783,775,'Cory Taylor','re: Two Possible Solutions','2003-04-29 09:20:40',0,'This was a neat trick. Upon personal inspection, I would suggest that the problem be re-ordered so the 3 and the omega are together and the 8 and the infinity are together. i.e., make it the limit of 8 as omega approaches 3, with the answer being infinity. It\'s not for any mathematical reason (obviously), simply looks better to me graphically that way (makes more sense).',4407,0);
INSERT INTO comment VALUES (4416,510,1920,'Brian Smith','Guesses for two and three','2003-04-29 09:23:14',0,'Im probably way off on these.\r\n\r\nThe second:a black hole. Any amount of matter can be thrown at a black hole and it will still suck up more\r\n\r\nThe third:the past. Events in the past have come and gone and will never return, only get further away.',NULL,0);
INSERT INTO comment VALUES (4417,780,2063,'e','Solution','2003-04-29 09:29:43',0,'13 bags\r\n1+2+3+4+6+7+8+9+10+11+12+13+14 = 100\r\n',NULL,0);
INSERT INTO comment VALUES (4418,780,1902,'Hank','re: Nesting Allowed?','2003-04-29 10:08:00',0,'if nesting is not allowed, there can still be a bag with zero, correct?\r\n\r\nMaking it 14.\r\n0 1 2 3 4 5 6 7 8 10 11 12 13 18\r\n',4413,0);
INSERT INTO comment VALUES (4419,510,1902,'Hank','More guesses','2003-04-29 10:55:07',1,'A man who is in the process of dying.\r\n\r\n1. Body (down)\r\n2. Mind (not dead yet)(the mind always searching, thirsting for knowledge, is never full)\r\n3. Soul (has left)',NULL,0);
INSERT INTO comment VALUES (4420,780,1626,'Gamer','re(2): Nesting Allowed?','2003-04-29 11:12:37',0,'...Put the marbles into bags... It depends on if you think you have to put at least 1 marble into a bag.\r\n\r\nNote: I thinkg \"the marbles\" in that quote refers to the 100 marbles, so that doesn\'t imply that you couldn\'t have a bag with 1.',4418,0);
INSERT INTO comment VALUES (4421,510,1626,'Gamer','Maybe...','2003-04-29 11:16:47',4,'Though I like your idea for mind (and that might be the answer), I take in \"eat\" as meaning used, and used up. For example, if you eat a cookie, nobody else can eat that cookie that you ate. I think that your knowing a fact doesn\'t stop someone else from knowing it as well.\r\n\r\nMy question would be are these three related? Or is it just problem compresion?',NULL,0);
INSERT INTO comment VALUES (4422,506,1626,'Gamer','re(2): well -- the computer language','2003-04-29 12:16:14',0,'I was going to learn that, but decided to put my effort towards other languages instead :)\r\n',4406,0);
INSERT INTO comment VALUES (4423,27,1626,'Gamer','I don\'t agree','2003-04-29 12:20:52',0,'If you are told what he was saying was true, than it is saying a contradiction is true, which is impossible. \r\n\r\nMy idea is that he is just lying. The exam can\'t be a suprise if it is a \"complete surprise\".\r\n\r\nSo he doesn\'t give the exam, and that\'s the answer. If he doesn\'t give the exam, there isn\'t going to be a \"suprise exam\".',NULL,0);
INSERT INTO comment VALUES (4424,28,1626,'Gamer','re: solution','2003-04-29 12:25:17',0,'I think that is the easiset way to solve that, but you can also think that based on Mr Brown\'s comment, exactly one must be sleeping, so it turns false somewhere, although it doesn\'t matter where.',240,0);
INSERT INTO comment VALUES (4425,780,2099,'christine','solution','2003-04-29 12:36:49',0,'14 bags\r\n0,1,2,3,4,5,6,7,8,9,10,11,12,22marbles\r\nor 13 is right if you cant have an empty one.',NULL,0);
INSERT INTO comment VALUES (4426,315,1126,'Bedhed','ahh, nice and easy for a change','2003-04-29 13:16:02',3,'easy...the man in the picture is the speaking man\'s son! (√x)²=x. Q.E.D.!',NULL,0);
INSERT INTO comment VALUES (4427,323,1126,'Bedhed','circ...umm...ference','2003-04-29 13:27:08',0,'well, looking at the date, we get 3/14, at 1:59. So i would guess that the day has something to do with pi, since π=3.14159...\r\npretty cool!',NULL,0);
INSERT INTO comment VALUES (4428,766,2100,'jack','answer','2003-04-29 16:53:36',3,'THEY ARE FISH!!! and there fish bowl fell over and cracked',NULL,0);
INSERT INTO comment VALUES (4429,501,2101,'Moe','Guessing the answer','2003-04-29 17:10:46',0,'Are they stars?',NULL,0);
INSERT INTO comment VALUES (4430,482,2101,'Moe','Another answer','2003-04-29 17:16:59',0,'It could be chicken, you throw away the feathers\r\nand that and cook the meat, then eat the meat and\r\nthrow away its insides',NULL,0);
INSERT INTO comment VALUES (4431,159,1253,'Brian Nowell','re(2): One Equation - equation in int and mod','2003-04-29 17:41:58',0,'I agree that the 2 part formula is simpler.\r\n\r\nI was being pedantic; Nick\'s query a) appeared to be asking for a single equation as a solution.\r\n\r\nAlso I am unaware of any scientific calculators having a \"ceil\" function therefore I raised \"Int-Mod\" issue.\r\n\r\nI have yet to acquaint myself with the \"Ceil to Int-mod\" translation.\r\n\r\nWhatever, I think that it is quite apparent that Nick should find joy in these respective solutions.',4414,0);
INSERT INTO comment VALUES (4432,510,979,'Ravi Raja','All Three are Related to each other','2003-04-29 23:38:23',0,'The first, second and the third things are all related to each other.',NULL,0);
INSERT INTO comment VALUES (4433,780,575,'not_so_einstein','Sum','2003-04-30 00:18:29',3,'I´ll use this srategy:\r\nThe 1st bag has 1 marble\r\nThe 2nd bag has 2\r\nThe 3rd bag has 3......\r\n\r\nuntil all 100 have been used.\r\nso we have an equation\r\n100=1+2+3+4..+n\r\n\r\nIt has been proved that sum 1+2+3..+n equals\r\n\r\nn(n+1)\r\n-------\r\n2\r\n\r\n->\r\n\r\n\r\n n(n+1)\r\n100= ------- /*2\r\n 2\r\n\r\n200=n(n+1)\r\n\r\nand then we have a quadratick equation:\r\nn²+n-200=0\r\nwhere a=1\r\nb=1\r\nand c=-200\r\n\r\n -1±√1²-4*1*(-200)\r\nn=--------------------------------\r\n 2*1\r\n\r\n\r\n=-1±√801\r\n --------------------\r\n 2\r\n\r\nn=27 or n=-2 (not right)\r\n\r\nAnswer=27 bags\r\n',NULL,0);
INSERT INTO comment VALUES (4434,780,575,'not_so_einstein','re: Sum','2003-04-30 00:24:37',0,'oopsie.....I noticed i did something wrong. The answer is 14 bags.',4433,0);
INSERT INTO comment VALUES (4435,768,1660,'Tim Axoy','Anyone?','2003-04-30 02:10:16',0,'Does anyone want to solve this one?\r\nIt is cool.',NULL,0);
INSERT INTO comment VALUES (4436,775,979,'Ravi Raja','This is Cheating','2003-04-30 04:47:53',0,'Tim, did you vote for your own problem using your other accounts ? \r\nI am saying this because just the problem has been submitted and it has been voted 5 without the posting of any comments.\r\nHow do you expect someone to vote for a problem without even trying it and that too \'5\', when the difficulty level of the problem is set to \'1\' !',NULL,0);
INSERT INTO comment VALUES (4437,775,979,'Ravi Raja','Solution','2003-04-30 05:03:30',3,'Case 1: Both Drew and Mohammad are Liars. Then Drew obviously cannot say: \"We are of the same type\". So, both of them are not Liars.\r\n\r\nCase 2: Both Drew and Mohammad are Truth Tellers.\r\nIn that case Mohammad cannot say: \" We are of different types\". So, both of them are not Truth Tellers.\r\n\r\nCase 3: Drew is a Truth Teller and Mohammad is a Liar. Then Mohammad cannot say: \"We are of different types\". So, this is also not a possibility.\r\n\r\nCase 4: Drew is a Liar and Mohammad is a Truth Teller. It is in this case only when Drew can say: \" We are of the same type\" and Mohammad can say: \" We are of different types\".\r\n\r\nSo, this is what each of them is:\r\nDrew: LIAR\r\nMohammad: Truth Teller\r\n',NULL,0);
INSERT INTO comment VALUES (4438,775,153,'TomM','Simple','2003-04-30 05:36:55',3,'If they are the same type, then they would give the same reponse. So they are of different types.\r\n\r\nIn that case, Mohammed, who makes a true statement is a Knight, and Drew, who makes a false statement, is a Liar.',NULL,0);
INSERT INTO comment VALUES (4439,504,979,'Ravi Raja','re: See the difference?','2003-04-30 05:56:05',0,'Okay DJ, I think I have mentioned this somewhere in my previous post that here the words True and False have their usual meanings. ',4402,0);
INSERT INTO comment VALUES (4440,775,1567,'Bryan','re: This is Cheating','2003-04-30 06:42:07',0,'Ravi, I\'m pretty sure this puzzle got three thumbs up plus plenty of general comments.',4436,0);
INSERT INTO comment VALUES (4441,510,2066,'David','Solution','2003-04-30 06:57:03',3,'the answer is a Stove, Fire, and Smoke',NULL,0);
INSERT INTO comment VALUES (4442,284,1920,'Brian Smith','Factorial fun','2003-04-30 07:35:15',0,'Each term in the sequence is the sum of two factorials\r\n2=0!+1! 3=1!+2! 8=2!+3! 30=3!+4! 144=4!+5!\r\n840=5!+6! 5760=6!+7! 45360=7!+8!\r\n\r\nThe first term would then be (-1)!+0! which is undefined since (-1)! is not defined.\r\n',NULL,0);
INSERT INTO comment VALUES (4443,227,1947,'Jon','politics','2003-04-30 07:35:24',0,'This question is quite easy if based out of the United States because it is quite likely one will wear a neck brace to court and therefore be laughed out of the court room. However, the following year he is likely to be elected president and given the sympathy of the nation for his troubled times. lol',NULL,0);
INSERT INTO comment VALUES (4444,768,1920,'Brian Smith','This sequence is super.....','2003-04-30 07:42:28',0,'This sequence is the sequence of superfactorials.\r\nsf(n)=n!*(n-1)!*(n-2)*..#3!*2!*1!\r\nsf(6)=6!*5!*4!*3!*2!*1!=24883200',NULL,0);
INSERT INTO comment VALUES (4445,511,1660,'Tim Axoy','No. God can...','2003-04-30 08:01:22',0,'No because God can carry anything.\r\n',NULL,0);
INSERT INTO comment VALUES (4446,511,1947,'Jon','idea','2003-04-30 08:04:46',1,'I think that an omnipotent God could indeed do such a feet. Reasons. A. An all power full god can do anything, therefore making it possible for him to do this. B. But this also allows the god to be able to pick up anything, hence it is a paradox. C. Loop hole. If the god were to create a stone he could not pick up, all he would have to do is make himself a normal human right after making an impossibly large stone. See, loop hole.',NULL,0);
INSERT INTO comment VALUES (4447,178,1947,'Jon','re: I beg to differ','2003-04-30 08:37:35',0,'In truth, this is accurate to an extent. Follow these scenarios using similar logic.\r\n\r\n1 pirate. (A) He takes all.
\r\n2 pirates. (a,b) B goes first and takes all. A doesn\'t have a neccesary majority to kill him off.
\r\n3 pirates. (a,b,c) C will offer A all of the coins just so A won\'t kill him of since B would have C killed anyways. A gets all the money here, or close to it depending on how brave C is.
\r\n4 pirates (a,b,c,d) D will offer B most the coins since B holds D\'s life. B will come out ahead here.\r\n5 pirates. (a,b,c,d,e) E will offer C and D half the coins a peice to save his life. Since neither has a more favorable position later on they will both except this. C has 250 and D has @50 leaving A, B, and E pennyless.',1736,0);
INSERT INTO comment VALUES (4448,511,2066,'David','re: idea','2003-04-30 08:58:44',0,'if he did make himself human, it wouldnt be a normal human, otherwise he would be stuck as a human, because a normal human cant change his/her form. He would still have an abnormal power to change himself back',4446,0);
INSERT INTO comment VALUES (4449,775,979,'Ravi Raja','re(2): This is Cheating','2003-04-30 09:25:14',0,'Bryan I am sorry if I have been talking about voting, but actually I meant Rating of this problem. Someone has rated this problem 5 even before a single comment had been posted for this problem. That is what I was trying to say and not what comments it received when it was in the queue.',4440,0);
INSERT INTO comment VALUES (4450,511,1,'levik','What they say','2003-04-30 10:02:54',0,'I believe the explanation given to this question by most religious authorities is that God would be able to create a stone that he cannot lift. And then he would be able to lift it.\r\n\r\nNot sure if there is a more logical \"official\" version.',NULL,0);
INSERT INTO comment VALUES (4451,511,1072,'Alan','What this proves','2003-04-30 10:22:11',3,'I am catholic so I DO believe in God. But the only reason this paradox was created was to prove that god is not a \"person\" or \"force\" that has an actual impact on the world. God doesn\'t have free will, god didn\'t create adam and eve (evolution took place) and god does not actually exist (as people perceive him to). I believe that God is used to describe a phase that brought about our existence. For, instance, god could merely be another term for \"big Bang\" or even something as general as \"Anything that exists, including nothing\"(Dependant on whether or not nothing exists(Hard to explain)) In other words, god does NOT have an impact on our world, he doesn\'t do things or make someone win or magically heal people.
in the end (since i know some catholics might be reading this) we have ask ourselves this. is it possible that the new testament was written as a book? Is it possible that Jesus was an extremely wise sage that fooled people into thiniing he healed and just wanted the world to become a better place in the future.
Our generation laughed at the concept of \"magic\" and \"spiritualism\" but is our belief in jesus still believing such things can exist?',NULL,0); INSERT INTO comment VALUES (4452,511,1626,'Gamer','My idea','2003-04-30 11:35:03',0,'Hmmm, I would say yes if infinity was greater than infinity, but if you expand the reflexive property to infinite numbers, I would say no.',NULL,0); INSERT INTO comment VALUES (4453,775,1626,'Gamer','Basic idea','2003-04-30 11:41:41',0,'The basic idea with same type, is:\r\n\r\nSame: Telling truth = They are truth, Lying = They are truth.\r\n\r\nDifferent: Telling truth = They are lying, Lying = They are lying.',NULL,0); INSERT INTO comment VALUES (4454,510,1626,'Gamer','re: Solution','2003-04-30 11:44:12',0,'Sounds good to me. I don\'t understand how a \"Stove\" is laying down, but if it makes sense to you, it is good :)',4441,0); INSERT INTO comment VALUES (4455,506,1794,'arbor','Two possible solutions?','2003-04-30 11:51:12',3,'The prime factors of 180 are 2,2,3,3,5 (their multiplication is 180). So we have 5 numbers, and we need to reduce them to 4. We know one of the guys studied for two figure number. So we have to use two of these numbers, to make a single 2 digit number.\r\n\r\nIt is either 5x2=10 OR 5x3=15\r\n\r\nSo possible solutions are\r\n\r\n10,3,3,2 (total of 18 years)\r\n15,3,2,2 (total of 22 years)\r\n\r\nChosing between the two needs some more information. The professor knows the answer, because he knows how long he has been teaching, but I do not really know.',NULL,0); INSERT INTO comment VALUES (4456,510,1126,'Bedhed','2 and 3','2003-04-30 12:13:11',2,'Something like an old riddle-\r\nthe second thing is fire, because everything that is fed to it never satiates its hunger;\r\nthe third item is smoke from the fire, because it rises and dissipates\r\nmaybe the first item is a match? or, as david suggested, a stove would be the most logical.',NULL,0); INSERT INTO comment VALUES (4457,504,1575,'DJ','re(2): See the difference?','2003-04-30 16:31:18',0,'Actually, Ravi, what you said was,\r\n\r\n\"Don\'t you think DJ that here, in this problem, the words True and False within quotes have the same meaning as we use it in general.\"\r\n\r\nAnd no, I think that saying something is \"True\" is entirely different than simply saying that it is True.',4439,0); INSERT INTO comment VALUES (4458,506,1575,'DJ','re(2): well -- the computer language','2003-04-30 16:36:30',0,'I was going to guess QBASIC, as the syntax resembles that of BASIC but without the line numbers, but I have never used it. And, honestly, I didn\'t know it was still in popular use. Thanks.',4406,0); INSERT INTO comment VALUES (4459,279,1575,'DJ','re(2): ehm..','2003-04-30 19:00:14',0,'Giving me credit on your page is not necessary, Brian, but I appreciate it. I am still iffy about the use of floor and ceil, I was under the impression that they are functions used by various computer languages rather than actual mathematical symbols like the radical sign (√). Seeing, however, that only three other people in fifty-some comments have shown qualms about the floor and ceil functions, I\'ll accept your solution (as if it were up to me anyway). It\'s obvious that coming up with the answers that you did took a lot of doing, and I didn\'t mean to sound like I was denigrating that effort.\r\n\r\nAny time a decimal is used can simply be replaced with \"+0\" instead of \".0\" at the expense of another operation (with the exception of one use of .2). I don\'t think it counts as an operation, but the decimal point is certainly a mathematical symbol. And subfactorial, while much less common that the factorial, I don\'t think is any less valid.\r\nWe all have our quirks, I guess. Too bad Raveen disappeared before clarifying the problem.\r\nI, though, am going to keep working on a so-called \"clean\" solution without rounding. If anyone thinks of anything to add, that\'s why I put it on a public notepad.',4352,0); INSERT INTO comment VALUES (4460,511,1575,'DJ','Read This','2003-04-30 19:17:08',1,'Alan, what kind of \"god\" do you believe in? Cause your \'belief\' sounds pretty piddly to me.\r\n\r\nI believe in the One God that created the heavens and the earth six thousand years ago, that put the stars in their place. The God that is still alive today, that has given me every good and perfect gift and He who still works in lives today. He created humans and all other life forms as they exist or existed; life did not \'evolve\' as post modern debunk evolutionary \'theory\' (as evolution does not even qualify as a scientific theory) has perpetuated and been force fed to every student in North America for the past century (a topic I will gladly debate with anyone).\r\n\r\nIt is impossible, first, to disprove God\'s existence, as you will be told by the many incredible minds who have set out to do just that, only to be convinced of God\'s reality.\r\n\r\nFurther, I don\'t think that it will be possible to prove that God does exist, in a formulaic mathematical or scientific approach, since such a proof would nullify the need for faith.\r\n\r\nA large topic of study for me this semester was examining in the contrived \'evidences\' of evolution, such as the 14 popularly supposed homonids (links between men and apes) that were discovered, each of which has been discredited, yet most of which still permeate current textbooks and resources (for lack of any better proof?). Further ovservations, such as the complete invalidity of the widely used C-14 dating, finds (anthropological and archaeological) that show that humans and dinosaurs lived at the same time, as well as rock layer formation and deposits that support the ideas of a single creation and a universal flood, back up the full literal story as told in the Bible, but are oft ignored, overlooked, or rationalized away. That is why there are still multi-million dollar rewards outstanding for anyone who can produce incorrigible evidence that evolution actually occured the way the textbooks claim. Why hasn\'t the reward been claimed? Because it didn\'t happen.\r\n\r\n[I hope to spur up a lot more debate on the subject]\r\n\r\n\r\n\r\nAnyway, back to the original question.\r\n\r\nIf you are talking about \"the omnipotent God,\" I think the gender of the pronouns is a non-issue. God has always been referred to as a masculine, from the original Greek and Hebrew of the Bible and in every translation hence. I am not sure why it should be ambiguous for the purpose of this problem. If the sentence read, \"an omnipotent god,\" then the pronouns to use might be a little more unclear. Further, the proper use in the English language (as any textbook, secular or otherwise, will tell you) is to capitalize God and all of His pronouns. So, without the \'blasphemy,\' the question should read, \r\n\r\n\"Can the omnipotent God create a stone which He Himself cannot carry?\"\r\n\r\nor alternatively,\r\n\"Can an omnipotent god create a stone which he/she himself/herself cannot carry?\"\r\n\r\nI will address the first question (the specific case).\r\n\r\nQuestions like this are designed to make people question their faith and wonder about the validity of statements such as \"God can do anything\" (how about, \"Can God make a mistake?\"). In any case, my direct answer to the question is yes. If the question were, \"can God create a stone which is too big for He Himself to carry?\" I would have a different response. I will address that problem in a minute (as I probably must, since I brought it up).\r\n\r\nThere are many things that God cannot do. God cannot \'make\' people do anything they don\'t want to. Similarly, God cannot cause people to sin. God cannot act injustly. God cannot lie, and He cannot go back on any of His promises. That does not mean that God is physically incapable of doing any of these things; obviously, if God wanted to come down to me in an audible voice and say, \"your shirt is green\" (it\'s really orange) I am sure He is quite capable of it. But the very nature of God, that is impossible for people to understand, will not let Him do anything below Himself. I apologize if that sounds cliché or contrived, but I have not even a base understanding of how God works, but I know what I mean by that and I hope it\'s clear enough. From that, anyway, God could create a stone that, if He carried it, would cause something else to happen, and situationally He would not be able to carry that particular stone because of some situation. An example escapes me, but in that way such a stone could be created, circumstantially (it wouldn\'t even have to be very big).\r\n\r\nConsider this. There is a stone, under the corner of someone\'s house that was just built by a contractor, that if He carried it somewhere, would make the house collapse. Suppose, then, if that were to happen, that the furious (ex-)homeowner would then go and strangle the contractor for his shoddy work. Does that mean that God could not carry that stone, because it would cause that man to sin (murder)? That said, I say no, because while the act of carrying that stone may have incited the man, he was not forced and we always still have free choice. A point which reminds me of the [well-known?] story of Job, who lost everything, his animals, his possessions, his family, yet did not blame God (note, that God did not cause Job\'s suffering either, but He allowed it). The point, I suppose, is the one I just stated; we always have the choice to do what we want to, and God cannot violate that. For which reason I cannot think of an example of a situation in which God would be unable to carry a stone, but I think something could be come up with.\r\n\r\n\r\nNow to ponder the other question, \"can God create a stone which is too big for He Himself to carry?\" that I posed before. Were God limited to three dimensions like we are, there still would not be anything too \'big\' for Him to physically carry. The earth is a pretty big rock (recall the little kids\' song, \"He\'s got the whole world in His hands\"). The God of time and space who commands galaxies and universes can most certainly handle anything bounded by the measly three dimensions we have to work with. He could, maybe, then go into the fourth dimension, time, and carry this infinitely huge stone through time. God could then create a stone that is permanent and go into the fifth dimension (whatever that is) and move it. However many dimensions God occupies, He could create a stone that completely encompasses everything, then go into another dimension and move the stone. Then you get into the ideas of what actually defines a stone (is it limited to three dimensions) and what constitutes \'carrying\' it. However, that may be most similar to what levik said, but since God exists outside of time, or once you get into the fourth dimension, are successive actions like that even valid? Food for thought, I guess.\r\n\r\n\r\n\r\nFinally, further response to Alan\'s comments. \"What this proves\" is not that god does not have an impact on the world. What a ridiculous statement to make, that a question so posed could \'prove\' anything about the existence, nature, or ablities of God. Natural secular as well as religious history will show that Jesus Christ not only lived, preached, and was killed, but that He rose from the dead. New miracles still occur and are documented every day, supernatural things that happen as a result of people praying to a living, caring God.\r\n\r\nAnd who\'s laughing at the spiritual or magic? I don\'t see David Copperfield being laughed of stage. Rather, people are astounded and amazed at his performances. I believe that his power comes from another very real, supernatural force (but that\'s an issue for another time). . .\r\n\r\nI know a number of Catholics who believe in the full truth of Jesus Christ (I\'m trying not to sound \'churchy,\' but it doesn\'t seem to be working), so to prevent stepping on any toes, I should refrain from any comments about the Catholic philosophy of dead rites and sacraments as opposed to a real relationship with Him. The Pharisees and Saducees in the Bible were \'doing\' all the right things, and Martha was busy running around trying to prepare a meal for Jesus. But look at Jesus\' reaction to them, compared to His reacion to Mary, who contented just to sit at His feet and spend time with Him. It\'s not about what you do. . That\'s all I will say about that.\r\n\r\nThe point is, God is not dead (rather, Nietche is dead. . .) and He is not inactive. I myself have seen too many instances of His hand to be explained away by coincidences. Moreover, I have seen my best friend completely cured of lukemia, leaving the doctors with no explanation than to credit it as a miracle to God. Broken bones fused, tumors and goiters disappearing. . . but of course you\'re not going to take my word for it. Nor should you. But you can ask my once-doubtful friends, completely atheistic or agnostic, who just asked for God to show them something to prove Himself to be real. And He is faithful. \r\n\r\n.\r\n\r\n.\r\n\r\n.\r\n\r\nI did not intend to be \'preachy\'; actually, I was a little [obviously?] upset about a few of the comments that had been made. As I wrote, though, I realized that there is nothing I can say to prove anything to anyone about God or His character or attributes. In even being on this site, I think, I label myself kind of an analytical science/math geek who in all likelihood won\'t believe anything without the backing of a mathematical proof or some fundamental theorem. I am assuming that most of the rest of you who visit here fall into the same category. I know, too, that the same God who has made Himself so real to me can do the same for each of you, if you let Him. I always love to share my personal story, because it is so amazing and just, real, to me, but I won\'t take the time here.\r\n[pause]\r\n[insert cheesy TV preacher line here]\r\nSo, whatever you\'re doing, at work, home, school, more than likely staring at a computer screen, I hope that I am making you think a little bit. More than that, though, since any words are so inadequate, I know that God is right there with you, and if you don\'t know Him, He is pulling on your heart. If there\'s even the slightest of chances that what I am saying here is true, don\'t you think it is worth it to see for yourself? Don\'t think that God can\'t show Himself wherever you are. I don\'t know what anyone expects to happen, and I don\'t know what God will do for you, but I know that those will probably be two different things. I also know that God will always have more for you than you expect, if you really are looking for Him. More than any formula or theory or paradox, God wants to know you. Just ask God to make Himself real to you, and He will. \r\n\r\nHopefully even after wading through all my weighty words (which still seem to be coming..) whoever reads this will get something out of it. I pray that He finds you. God bless.\r\n\r\n=)',4451,0); INSERT INTO comment VALUES (4461,494,979,'Ravi Raja','re(4): this is easy','2003-04-30 19:34:10',0,'Yes Michael, the are two ways I know to solve this problem and so all I can say that there are AT LEAST 2 ways to solve this problem. I do not know if there are more.',4321,0); INSERT INTO comment VALUES (4462,504,979,'Ravi Raja','re(3): See the difference?','2003-04-30 19:36:53',0,'Okay I am sorry then DJ. Now I say that the words True and False have their usual meanings and so now I believe you can solve the problem. ',4457,0); INSERT INTO comment VALUES (4463,504,979,'Ravi Raja','Please Make The Necessary Changes - Levik','2003-04-30 19:40:22',0,'Levik, can you please remove the QUOTES within which the two words True and False are written, so that people don\'t have problems in solving the problem. Then the words True and False will have their usual meanings or else everyone will start taking it with a dfferent meaning.',NULL,0); INSERT INTO comment VALUES (4464,511,2066,'David','re: Read This','2003-05-01 03:14:31',0,'Thank you very much for writing this. This kinda put into words what i woulda written had i the time. Thank you. ',4460,0); INSERT INTO comment VALUES (4465,511,1902,'Hank','re: Read This','2003-05-01 04:12:27',0,'1.) DJ, I didn\'t have enough time or patience to read your comment, I dont know where you got the time to write it.\r\n2.) Alan, sounds like you\'re saying God is dead (spoken like a true catholic)\r\n3.) The answer. God doesn\'t need to. If you believe either is true, then you believe in God. (God\'s way of tricking you into belief).\r\nOR (this just came to me) If he does the second, that proves that he did not create an unliftable stone. Meaning that God is wrong. God cannot be wrong.',4460,0); INSERT INTO comment VALUES (4466,778,1902,'Hank','Could be right','2003-05-01 04:16:30',1,'Similar to the solution from \'2 colors\':\r\nselect a point \'x\' then draw a circle around it with a radius of 1 meter.\r\nthere are an infinite number of points on the circle. one must be the same color.\r\n(or something like that)',NULL,0); INSERT INTO comment VALUES (4467,778,103,'friedlinguini','re: Could be right','2003-05-01 04:36:43',0,'Says who? Say the center point is red and that the circle is drawn in alternating bands of blue and green such that no blue point is exactly one meter from a green point (I don\'t know if this is possible, but that\'s not the point). The proof of this is going to be harder than the two-color variation.',4466,0); INSERT INTO comment VALUES (4468,778,979,'Ravi Raja','re(2): Could be right','2003-05-01 04:46:56',0,'Fried, I think Hank is correct since he is considering Infinite number of points lying on the circumference of the circle. Even if it consisted of alternating bands of blue and green then there must be at least one such pair of same colors which are unit distance apart and if in case the red color is there on the circumference, then the centre being red, there remains nothing to prove. I do not know if this reasoning of mine is correct.',4467,0); INSERT INTO comment VALUES (4469,778,1920,'Brian Smith','re: Could be right','2003-05-01 04:54:27',0,'Your reasoning is flawed. Assume the center is Red. The circle can consist of all Green and Blue points.',4466,0); INSERT INTO comment VALUES (4470,778,1301,'Charlie','re(3): Could be right','2003-05-01 05:24:13',0,'Specifically, if the center is red, the circumference could be alternating 60 degree arcs of blue and green, with the counter-clockwise-most point included (a closed endpoint) and the clockwise-most point excluded (an open endpoint). None of the points on the circumference 1-meter apart would be the same color and the center is a different color altogether.',4468,0); INSERT INTO comment VALUES (4471,778,979,'Ravi Raja','Two Or Three ?','2003-05-01 05:24:58',4,'Is that Mathematical Plane a Two-Dimensional Plane or a Three-Dimensional Plane ?',NULL,0); INSERT INTO comment VALUES (4472,778,979,'Ravi Raja','Two-Dimensional Plane','2003-05-01 05:25:28',3,'Suppose that the Mathematical Plane is a Two-Dimensional Plane, then we consider a CIRCLE of Unit radius. Then there are Infinitely many points lying on the circumference of the circle, all of which are at Unit distance from the centre of the circle. Suppose the centre of one color and there is AT LEAST one point on the circumference which is of the same color as that of the centre, then there is nothing left to prove. If suppose the circumference consists entirely of points of ther other two colors ONLY, then obviously there exists AT LEAST one pair of points on the circumference which will satisfy the given conditions. \r\nHence Proved.\r\n(I do not know whether this reasoning of mine is correct or not. If not then someone please do correct me).',NULL,0); INSERT INTO comment VALUES (4473,778,979,'Ravi Raja','Three-Dimensional Plane','2003-05-01 05:27:12',3,'Suppose that the Mathematical Plane is a Three-Dimensional Plane, then we consider a SPHERE of Unit radius. Then there are Infinitely many points lying on the circumference of the sphere, all of which are at Unit distance from the centre of the sphere. Suppose the centre of one color and there is AT LEAST one point on the circumference which is of the same color as that of the centre, then there is nothing left to prove. If suppose the circumference consists entirely of points of ther other two colors ONLY, then obviously there exists AT LEAST one pair of points on the circumference which will satisfy the given conditions. \r\nHence Proved.\r\n(I do not know whether this reasoning of mine is correct or not. If not then someone please do correct me).',NULL,0); INSERT INTO comment VALUES (4474,778,1301,'Charlie','re: Two-Dimensional Plane','2003-05-01 05:29:07',0,'Apparently you and I were posting at the same time. Again, consider 60-degree arcs along the circumference of alternating color. The endpoints of the arcs are 1 meter apart, and one of the endpoints of any arc is the opposite color as the other, since we always choose to include the endpoint as a specific (ie cw or ccw) end of each arc.',4472,0); INSERT INTO comment VALUES (4475,778,1902,'Hank','re(2): Could be right','2003-05-01 05:29:46',0,'Infinite is all encompassing.\r\nAssuming red is the center point.\r\nCan you prove that red is not on the circle? Or the the circle is only made up of green and blue? Keep in mind that there are an infinite number of point on the circle. (seriously, I am curious if this can be proved)',4469,0); INSERT INTO comment VALUES (4476,778,1301,'Charlie','re: Three-Dimensional Plane','2003-05-01 05:32:54',0,'In the three-dimensional case (which I don\'t think is actually the problem) your logic about the sphere is just as faulty as in the 2-d case, though in fact factually correct, you haven\'t proved it.\r\n\r\nIn the 3-D case, the best way is to expand upon the solution of the 2-d 2-color problem. Instead of a triangle, construct a regular tetrahedron with edges 1 meter long. Then as there are only 3 colors to go around, and there are 4 vertices to a tetrahedron, two vertices must be the same color, and since it\'s a regular tetrahedron the points are 1 meter apart.',4473,0); INSERT INTO comment VALUES (4477,778,1301,'Charlie','re(3): Could be right','2003-05-01 05:38:00',0,'One does not have to prove that red is not on the circle. The point is that we can\'t prove that red IS on the circle, and further we can\'t prove that if the circle is made up of two colors that there must be two of the same, within 1 meter along the circumference. Remember which side has the burden of proof.',4475,0); INSERT INTO comment VALUES (4478,778,103,'friedlinguini','re: Two Or Three ?','2003-05-01 06:02:43',0,'A plane is a two-dimensional space. A three-dimensional equivalent is called a hyperplane. I think we can safely assume that the problem refers to a two-dimensional plane.',4471,0); INSERT INTO comment VALUES (4479,510,2066,'David','','2003-05-01 06:14:56',0,'The stove I was talking about would be one of those old pot belly cast iron stoves. They\'re extremely heavy, so that would be pretty hard to \'get up\'. Plus they look like they\'re sitting down on little legs.',NULL,0); INSERT INTO comment VALUES (4480,511,1715,'Jonny Doe','re: Read This','2003-05-01 07:23:21',0,'I actually read your whole response and I feel sorry for your misguided belief. I think that the human evolution did happen and it has been proven again and again, but I never saw the proof for god’s existence. The only people who are trying to discredit the evolution theory are religious fanatics who know that if people stop believing in god, they will be out of a paycheck. And yes I believe that religion today is a business and a very profitable at that and a way of gaining power.\r\n
\r\nI am of Jewish decent but as you might guess I do not practice it. I see it daily as “Religious” people put a price tag on services the bible clearly show the to be as good deeds and only if you wish you can donate money to that person. Look at what is happening in the world the Muslims are using religion to justify suicide bombings and starting wars. And don’t get me started on Christianity just open the TV and put any channel that have those preachers all that I hear is send me your money and I will give you this book or artifact. Those shows sound to me like infomercials and not a religious ceremony as they suppose to be. Then you see them live in a multi million mansions driving expensive cars. Where do you think they get that money? Well I have a news flash; all that money that you are sending them that supposedly is going to charities is going into their pocket. And then when they are caught, they give that famous speech “I’m only human and I have sinned” and like magic every thing is forgotten and they are back in the business.\r\n
\r\nSo as you might have guessed I do not believe that an omnipotent god does exist and therefore that stone cannot exist and if an omnipotent god did exist then this riddle is a true paradox.\r\n
\r\nOn the bright side I did read the bible several times and I think that it is an excellent fictional/historical book that can teach us a lot of good things and if we all followed some of it’s teachings, the world would be a much better place to live. ',4460,0); INSERT INTO comment VALUES (4481,778,1686,'DuCk','Unproveable','2003-05-01 08:08:40',0,'I believe it is impossible to prove the existence in a plane. One would need three dimensions and a tetrahedron in order to prove it in 3 dimensions. But in the in the 2-D case, it is impossible...',NULL,0); INSERT INTO comment VALUES (4482,778,1301,'Charlie','Proof','2003-05-01 08:13:04',3,'Tesselate the plane with equilateral triangles of side length = 1 meter. \r\n\r\nLabel the three corners of one triangle R, G and B (as, if one were the same we\'d already have a match--we\'re trying to show we can\'t keep producing lacks of matches forever). This is the first triangle.\r\n\r\nIn the adjacent triangle that also includes the R-G side, label the remaining vertex B. This is the second triangle. In the triangle adjacent to the first triangle and sharing the R-B side, label the remaining vertex G, so as to avoid any matching colors at 1 meter so far. Finally in the triangle adjacent to the second triangle and sharing its R-B side, label the remaining vertex, G.\r\n\r\nThere are now 3 vertices labelled G that are at the vertices of an equilateral triangle whose sides are each sqrt(3) as they are at tips of back-to-back equilateral triangles whose side lengths are 1, and so each of those altitudes is sqrt(3)/2.\r\n\r\nDraw circles of radius 1 around each of these G vertices. They form a 3-lobed figure where the tips of the lobes are also sqrt(3) meters apart. As the points are all 1 meter from one G point or another, all points on this 3-lobed figure are R or B. \r\n\r\nIn particular consider the arcs on the counterclockwise side of the centerline of each lobe. If points are chosen equally far out on each of these arcs an equilateral triangle is formed. This equilateral triangle can be any size from zero-length sides, to the full sqrt(3)-length sides. Choose the one with sides of length 1 meter. As there are now only 2 colors to choose from, R and B, and 3 vertices to this triangle, two of them must have the same color.\r\n\r\n',NULL,0); INSERT INTO comment VALUES (4483,778,1920,'Brian Smith','Proof by contradiction','2003-05-01 08:37:44',3,'This is a proof by contradiction.\r\n\r\nLets assume the statement \"there exist two points on this plane, exactly one meter apart, that have the same color\" is false. Then every equilateral triangle with sides of 1 meter have three different colors at the verticies. Consider two adjacent triangles. The two triangles can be ABC and BCD and share side BC.\r\n\r\nPoints A, B, and C are all different and points B, C, and D are all different. The only way this happens is when A and D are the same color.\r\n\r\nConsider a second pair of triangles DEF and EFG with common side EF. Using the same argument as with points A, B, C and D, D is the same color as G. This means that A is the same color as G.\r\n\r\nBut points E, F, and G can be chosen such that the distance between A and G is 1 meter. A contradiction is formed, therefore the statement \"there exist two points on this plane, exactly one meter apart, that have the same color\" must be true.',NULL,0); INSERT INTO comment VALUES (4484,514,1920,'Brian Smith','Solution','2003-05-01 09:05:07',0,'Dang! I was going to submit a problem like this. Oh, well.\r\n\r\nI called the pumpkins A, B, C, D, and E. The smallest pair is A+B. The second smallest pair is A+C. The largest pair is D+E. The second largest pair is C+E. The sum of all ten pairs of weighings is 4*(A+B+C+D+E).\r\n\r\nThis gives us the following system of equations:\r\nA+B=16\r\nB+C=18\r\nC+E=26\r\nD+E=27\r\n4*(A+B+C+D+E)=216\r\n\r\nThis is easily solved. A=7, B=9, C=11, D=12, E=15.',NULL,0); INSERT INTO comment VALUES (4485,178,1575,'DJ','re: I beg to differ','2003-05-01 09:39:52',0,'While that would be true for a life scenario, and anyone would probably vote to kill the greedy old guy whether he offered them nothing or one coin, that is not the point in this problem. It is explicitly stated that each pirate will want to claim as many coins as he can without getting killed. Given that, as the problem states, the oldest pirate will walk away with nearly everything, as in the given solution.\r\n',1736,0); INSERT INTO comment VALUES (4486,514,1947,'Jon','my guess','2003-05-01 09:41:01',0,'7,9,11,12,15\r\nmostly you can see that the smallest must be greater than 5 and less than 8(It has to be less than 8 because if it were greater than 8, 16 would be impossible.) or it just wouldn\'t work. 5 and 6 are really easy to check to make sure don\'t work for the smallest. That leaves 7. building up from there is pretty simple. 7+9=16 7+11=18 9+11=20 7+12=19 9+12=21 11+12=23 7+15=22 9+15=24 11+15=26 12+15=27',NULL,0); INSERT INTO comment VALUES (4487,778,1301,'Charlie','re: Proof by contradiction','2003-05-01 10:08:13',0,'A lot simpler than mine; wish I\'d thought of that.',4483,0); INSERT INTO comment VALUES (4488,511,1575,'DJ','re(2): Read This','2003-05-01 11:10:13',0,'If you actually did read my whole response, you would have seen why there is no proof of God\'s existence. At least, not any that can be put onto paper.\r\n\r\nJonny, it\'s interesting how you say evolution \"has been proven again and again\" yet you only \"think\" that it happened. My first response to this is, was whatever proof you saw not good enough for you? My second question would be, what proof is there? Every time I pose the question, there are always people convinced that evolution is \'proven fact\' but never with anything to corroborate it. Simply put, there is no evidence.\r\n\r\nPeople like to be able to explain, understand, and control everything. We can do none of these regarding God, so we try explain Him away with fanciful theories and grab on to any little shred of potential evidence, even knowingly falsified or irrelevant shreds; meanwhile, the big picture and the majority of the evidence points in the opposite direction. Anyway, I\'m not going to try to prove God with evidence, because it can\'t be done. God created the world in its entirety and all life therein, six thousand years ago. But, if you have any evidence to the contrary, I should like to see it as nothing has ever been proven or even reasonably backed up.\r\n\r\nAs to your next statements, let me also say that I utterly cannot stand religion, the connotations of that word being a reliance on actions or rites to earn acceptance. If you had read my entire comment, I discussed [albeit briefly] the difference between dead religion and real relationship with God. The Bible is very clear; you can \'do\' all the right things and not be pleasing to God. He cares about the heart, and Biblical salvation is a gift that no one deserves. There are no steps or rituals or sacraments to earn God\'s approval. I think that, yes, a lot of TV preachers and other clergy are misguided or purposefully manipulative in order to gain wealth, popularity, or because they think they can earn \'brownie points\' with God to earn a better place in Heaven or something. Such religion is absolutely dead and I cannot stand it, in part because of the impression it gives people (obviously from your statements, Jonny) about Christians in general. Too often, people make judgements about the perfect God from the imperfect people He limits Himself to. The fact that Christians are normal people who make mistakes, who say things we don\'t mean, who do things we shouldn\'t, does not take away from the fact that God is perfect and infallible.\r\n\r\nI totally agree with you that religion today has become a business and a way to make money. That is nothing new, however; in Jesus\' time the Pharisees, the religious elite, were the most wealthy and apparently \'holy\' men of the era, yet Jesus rightfully called them hypocrites and vipers. Why? Because, as you said, they were in it only for money and appearances. Not so much is different in the world between now and then; our camels are faster and the toys are more expensive, if you will.\r\n\r\nI, however, do not subscribe to that religion. I do not call myself Baptist or Lutheran or any other particular label of Christianity (that is not to say, mind you, that every practicing church of such various denominations is a dead, religious one). I believe in the Bible as completely the Word of God, true in every word. Moreover, God is not dead, and the Bible is not merely an ancient rule book or a guide to \'good\' living. If that\'s what you think it all amounts to, then I feel sorry for your misguided beliefs.\r\n\r\nPenultimately, with regards again to the original question, whether or not you believe in God does not change whether or not the stone can exist. Despite what modern relativistic society would have you believe, there is such a thing as absolute truth. You can choose not to believe in gravity, but if you jump off the roof of your house, you can bet on hitting the ground shortly thereafter. You can even base your belief on observations of birds and helium balloons, and say that those prove that gravity is a farce. You could experiment further and find even more evidence, such as ice cubes in water and other things that show how \'nothing\' works the way the law of gravity says it should. But jump off the roof, and you\'re still hitting the ground. Perhaps that\'s a weak point, but you\'ll find that the more you examine specific cases like helium, you\'ll only serve to demonstrate further how gravity works. And if you set out to disprove God\'s existence, you\'ll end up with a lot of evidence that says the opposite of what you intended. Most of the supposed proof for evolution actually backs up Biblical creation, though you\'ll rarely see that publicized.\r\n\r\nHowever, I still maintain that God\'s existence cannot be proven, except to an individual person. The last few paragraphs of my previous comment (again, had you read the whole thing) are the summation of everything else I am trying to say. You cannot prove God, but you can experience Him. I don\'t know what specifically you will experience, but if you genuinely ask Him to make Himself real to you, He will. And I continue to pray that He does. God bless.\r\n\r\n=)',4480,0); INSERT INTO comment VALUES (4489,388,1919,'Lewis','i\'ve heard this one...','2003-05-01 11:14:15',0,'absolutely NOTHING.',NULL,0); INSERT INTO comment VALUES (4490,414,1919,'Lewis','answer','2003-05-01 11:18:22',3,'There is no l so you are saying \'noel\'. Ha',NULL,0); INSERT INTO comment VALUES (4491,514,1626,'Gamer','How to solve','2003-05-01 12:02:11',0,'Based on Brian\'s ideas, you just plug in A+B =16 and D+E = 26 into 4*(A+B+C+D+E)=216) to figure out C, then figure out B and E, then figure out A and D',4484,0); INSERT INTO comment VALUES (4492,775,2005,'Aamir Rashid','here is it','2003-05-01 12:12:48',3,'Drew: Liar\r\nMohammad: Knight',NULL,0); INSERT INTO comment VALUES (4493,775,1660,'Tim Axoy','Drew:Liar,Mohammad:Knight','2003-05-01 12:38:15',0,'Correct.',4492,0); INSERT INTO comment VALUES (4494,778,1575,'DJ','re: Proof by contradiction','2003-05-01 12:46:00',0,'Good job, Brian! I was trying to think of something similar to this, but you beat me to the punch.\r\n\r\nObviously, you can\'t have four distinct points equidistant from one another in a two-dimensional plane (I think someone mentioned a regular tetrahedron for a 3-D case).\r\n\r\nThe approach I was trying for involved a large set of equilateral triangles, squares, circles, soccer balls, trying to find a set of points at a unit distance from each other that would be impossible to give three colors without two adjacent points being the same. That approach, as DuCk prematurely ventured, may well be impossible without overlapping the shapes. What I can do (so as not to feel totally dumb) is refine Brian\'s answer geometrically.\r\n\r\nStart with an isoceles triangle with legs of length √3 and a base of unit length (or 1 meter, for this specific problem). Draw the perpendicular bisector of each leg, to a segment of unit length which is bisected by the leg. Both pairs of endpoints of these two segments form an equilateral triangle with the peak point of the large triangle and with its respective base point. Therefore, as Brian said, each set of endpoints needs to be a different color, as they are endpoints of a 1m segment, and each pair is comprised of the two colors that are different than the apex of the large isosceles triangle. Therefore, each segment forces its respective base point to be the same color as the apex. But, since the base of that triangle is of unit length, they cannot be the same color. So, somewhere in those 7 points are two that are 1 meter apart and have to be the same color.',4483,0); INSERT INTO comment VALUES (4495,778,1567,'Bryan','Elegant proof','2003-05-01 13:01:09',3,'Consider two points in cartesian space: A (0,0) and B (√3,0), where one unit equals 1m of distance. Points C (√3/2,1/2) and D (√3/2,-1/2) are each 1m from both A and B, and C and D are 1m from each other.
If A and B are different colors, both C and D will be the third color, and will satisfy the condition that two points 1m apart are the same color. To avoid the situation where two points √3m apart are different colors, for a given point, every point √3m from it would have to be the same color as the center point, in which case two points 1m apart on the resulting circle will satisfy the condition. ',NULL,0);
INSERT INTO comment VALUES (4496,511,1645,'luvya2003','re(3): Read This','2003-05-01 15:46:03',0,'I could not have said it better myself...',4488,0);
INSERT INTO comment VALUES (4497,511,2080,'Tristan','Beliefs','2003-05-01 20:33:40',1,'As stated before, this is a question of where the faith lies, in this peticular question, \"The\" is used to refer to as a single being who has power over all, a better way to word it would have been to use \"an\" so that it opens the doors a bit. I myself do not believe in any higher being, I\'m not saying it doesn\'t exist, but what isn\'t scientifically proven isn\'t good enough for my belief.\r\n\r\n To the question at hand:\r\n\r\n To us, an omni-potent god would be a being that is vastly superior to use in all ways, just as we are to an ant. A being with limitless power is an unreal thought, and everything has its limits (theoretically). We can create many things, but not carry all of them, although an ant might think we can. Simply put: \r\n\r\nIf he creates a rock that is too heavy for him to carry, then he can\'t carry it.',NULL,0);
INSERT INTO comment VALUES (4498,514,1686,'DuCk','answer only','2003-05-02 02:02:43',0,'7, 9, 11, 12, 15',NULL,0);
INSERT INTO comment VALUES (4499,351,1686,'DuCk','Solution and other words...','2003-05-02 02:40:52',0,'answer to the first question is the word contains the vowels (a,e,i,o,u&y) in order.\r\n\r\nas far as the second question is concerned, abstemiously qualifies. for the letters (a,e,i,o,u) in order we can also include arsenious. thanks....',NULL,0);
INSERT INTO comment VALUES (4500,750,1660,'Tim Axoy','Is this correct what I have?','2003-05-02 02:55:03',4,'10004000600040001?',NULL,0);
INSERT INTO comment VALUES (4501,750,1660,'Tim Axoy','I meant...','2003-05-02 02:55:44',0,'1004006004001.',4500,0);
INSERT INTO comment VALUES (4502,750,1920,'Brian Smith','Solution','2003-05-02 03:35:11',0,'Im guessing (f(n) + 1)^n = f(n+1)\r\n(1+1)^1=2 (2+1)^2=9 (9+1)^3=1000\r\nThen (1000+1)^4=1004006004001',NULL,0);
INSERT INTO comment VALUES (4503,750,979,'Ravi Raja','Solution','2003-05-02 04:18:50',3,'Since there is no number before 1, we take it as 0(zero) and follow the steps given below to obtain the remaining terms of the sequence.\r\n\r\nFirst Step: (0 + 1)^0 = 1\r\nSecond Step: (1 + 1)^1 = 2\r\nThird Step: (2 + 1)^2 = 9\r\nFourth Step: (9 + 1)^3 = 1000\r\nFifth Step: (1000 + 1)^4 = 1004006004001\r\n\r\nSo, the generl rule is given by the formula:\r\n\'N\'th Number = [(N - 1)st Number + 1]^(N - 1)',NULL,0);
INSERT INTO comment VALUES (4504,266,1920,'Brian Smith','Good one!','2003-05-02 04:39:43',0,'I\'ll have to give some of my friends this puzzle!',NULL,0);
INSERT INTO comment VALUES (4505,510,2118,'Chereese','Answer','2003-05-02 04:50:50',0,'I think that the 1st one is water. The 2cd is fire\r\nand the 3rd is air',NULL,0);
INSERT INTO comment VALUES (4506,388,2118,'Chereese','Answer (this was easy)','2003-05-02 04:59:24',0,'da answer is Nothing',NULL,0);
INSERT INTO comment VALUES (4507,766,2118,'Chereese','answer','2003-05-02 05:18:15',0,'They\'re goldfish and their aquarium got tipped over.',NULL,0);
INSERT INTO comment VALUES (4508,348,2118,'Chereese','easy','2003-05-02 05:22:01',0,'he is a snowman',NULL,0);
INSERT INTO comment VALUES (4509,977,1301,'Charlie','solution','2003-05-02 08:11:19',3,'A) For the fewest invocations of random(), start with two strings: one of zero length and the other of length containing the digits 1 to 9 where order doesn\'t matter.\r\n\r\nThen invoke random() 8 times starting with a parameter of 9, and ending with a parameter of 2. Each time, use its output to pick a character from the string that started full, and place it at the end of the string that started empty. After this there will be 1 character left in the originally-full string. Transfer that to the end of the almost-built string, which now has 9 digits and can be converted to a number by ordinary conversion processes.\r\n\r\nDECLARE FUNCTION randm& (n&)\r\nDEFLNG A-Z\r\nRANDOMIZE TIMER\r\n\r\nFOR trial = 1 TO 5\r\n source$ = \"123456789\"\r\n result$ = \"\"\r\n FOR i = 9 TO 2 STEP -1\r\n p = randm(i) \' random is a keyword in this language so using randm\r\n result$ = result$ + MID$(source$, p, 1)\r\n source$ = LEFT$(source$, p - 1) + MID$(source$, p + 1)\r\n NEXT\r\n result$ = result$ + source$\' now the last character\r\n n = VAL(result$)\r\n PRINT n\r\nNEXT trial\r\n\r\nEND\r\n\r\nFUNCTION randm (n)\r\n randm = INT(RND(1) * n + 1)\r\nEND FUNCTION\r\n\r\nOne run of the above (as it is set to give 5 examples) is:\r\n\r\n 786591324\r\n 281735694\r\n 928641357\r\n 478325619\r\n 784592316\r\n\r\nB) Oh, I\'ve already done that in A. Maybe you expected A to be to keep calling random() with a parameter of 1,000,000,000, until you get a result that was nine digits, all different and then stop. Or perhaps you had in mind calling random(9) as many times for each digit until it produced a digit different from any that you had previously. In any case the solution for B is my above solution for A.',NULL,0);
INSERT INTO comment VALUES (4510,977,1920,'Brian Smith','The goal of this problem....','2003-05-02 08:16:58',0,'I think the goal of this problem is to find a way to generate a random integer 1 to N when given a random integer generator which returns a value 1 to X.',NULL,0);
INSERT INTO comment VALUES (4511,977,1301,'Charlie','re: solution','2003-05-02 08:20:59',0,'Note that in the Basic computer language of my solution, strings are variable length, so as the letters are extracted from the source string, the string\'s total length decreases, with no padding with blanks. Also I meant to say \"length 9\" for the original length of the source string.',4509,0);
INSERT INTO comment VALUES (4512,977,1301,'Charlie','re: The goal of this problem....','2003-05-02 08:27:21',0,'No, Gamer specifically says he wants a random 9-digit number, so 1 through 99,999,999 are not acceptable outputs, and he wants every digit from 1 to 9 to appear exactly once in the output number, also far from random as zeros and repeated digits are disallowed. Only 9! = 362,880 numbers out of a billion satisfy this is about 1 in 2756, so it\'s highly selective rather than just any random number in the range.',4510,0);
INSERT INTO comment VALUES (4513,977,103,'friedlinguini','C++ solution','2003-05-02 10:28:52',3,'\r\nstruct MyRand {\r\n typedef std::vector<int>::difference_type DType;\r\n\r\n DType operator()(DType max) {\r\n return random(max) - 1;\r\n }\r\n};\r\n\r\nint foo() {\r\n std::vector<int> digits;\r\n\r\n for (int i = 1; i <= 9; ++i)\r\n digits.push_back(i);\r\n\r\n MyRand myRand;\r\n std::random_shuffle(digits.begin(), digits.end(), myRand);\r\n\r\n int result(0);\r\n\r\n for (int i = 0; i < 9; ++i)\r\n result = result * 10 + digits[i];\r\n\r\n return result;\r\n}\r\n=number) digits[count]=digits[count+1]\r\n}\r\n}\r\n\r\nfor (count=1;count<=9;count+=1){ cout << answer[count];}\r\n\r\n\r\nAll this is doing is creating a number 123456789, then picking a digit from that as the next digit. Then it takes out that digit and pushes everything down one, and replaces any old number spots with 0. Then it prints the number.\r\n\r\nFor example: (Using 5 digits)\r\n\r\nRandom(?) - Old:12345 New: \r\nRandom(5) 3 Old:12450 New: 3\r\nRandom(4) 1 Old:24500 New: 31\r\nRandom(3) 2 Old:25000 New: 314\r\nRandom(2) 2 Old:20000 New: 3145\r\nRandom(1) 1 Old:00000 New: 31452',NULL,0);
INSERT INTO comment VALUES (4517,750,1626,'Gamer','Zero powers?','2003-05-02 11:16:15',0,'I don\'t know if I am missing something, but I know that everything to the 0 power is 1, because when you take something divided by itself, it makes 1. But when you do the same thing to 0, you get undefined. So why does 0^0=1?',NULL,0);
INSERT INTO comment VALUES (4518,977,103,'friedlinguini','Yet another solution.','2003-05-02 11:21:38',3,'Start with digits 1-9 in a vector/array/list/string/whatever.\r\nLet d[n] denote the digit in the nth place.\r\nFor i from 1 to 8, swap d[i] with d[i + random(10-i) - 1]\r\nConvert digits to an actual number.\r\n\r\nIn C++ (borrowing a bit from Charlie\'s solution):\r\n\r\nstd::string digits(\"123456789\");\r\n\r\nfor (int i = 1; i <= 9; ++i)\r\n std::swap(digits[i - 1], d[i + random(10-i) - 2]);\r\n\r\nreturn boost::lexical_cast<int>(digits);\r\n \r\nStep 2: = 10 cents * 10 cents \r\n
\r\nStep 3: = 1/10 dollar * 1/10 dollar \r\n
\r\nStep 4: = 1/100 dollar = 1 cent \r\n
\r\nThe flaw lies in the Second step, where we are replacing 100 cents by 10 cents * 10 cents, which cannot be done, if the dimensions are taken into consideration. (As 100a cannot be written as 10a*10a). \r\nThat is it. ',NULL,0);
INSERT INTO comment VALUES (4552,483,2121,'Chaz','ANSWER','2003-05-03 04:14:22',0,'a= 15621 1246 9996, 7996 6396 5116 \r\nb= 3121 2496 1976 1596 1276 102',NULL,0);
INSERT INTO comment VALUES (4553,514,1301,'Charlie','re:','2003-05-03 04:17:06',0,'Aside from any requirement that all the weights be integers, your answer of 7.5, 8.5, 10.5, 11.5 and 15.5 adds up to 53.5. In the set of 10 weighings, each pumpkin was weighed 4 times (once in conjunction with each of the others), so if the total weight of the pumpkins were 53.5, the total of all 10 weighings would be 4 times that, or 214. But they actually add up to 216 pounds.\r\n\r\nI think there is sufficient algebra available to actually eliminate the need for the extra proviso that all the individual weights are integers. Look at the other solutions.',4548,0);
INSERT INTO comment VALUES (4554,788,153,'TomM','dimensional analysis','2003-05-03 04:17:16',3,'Your dimensional analysis is off.\r\n\r\nIf we were talking about inches, for example, 10 in * 10 in does not = 100 in, (linear), but 100 in² or 100 sq in (planar)\r\n\r\nlikewise, 100 ¢ does not equal 10 ¢ * 10 ¢, but 10 (with no dimensional units) * 10 ¢\r\n\r\nSo instead of $1 = 100¢ = 10¢ * 10¢ = ($1)/10 * ($1)/10 = 1¢,\r\n you get $1 = 100¢ = 10 * 10¢ = 10 * ($1)/10 = $1',NULL,0);
INSERT INTO comment VALUES (4555,506,1301,'Charlie','re(3): well -- the computer language','2003-05-03 04:43:16',0,'It probably is not still in popular use, as MicroSoft doesn\'t include it with today\'s systems, but it has its officionados, as it gets the work done. Actually QuickBasic is a bit different from QBASIC. QuickBasic was sold as a separate commercial package and could produce .EXE files if called upon to do so. QBASIC came later, using the same syntax, but was a purely interpretive language, and ran about 5 times slower, and was included with the later versions of DOS. Windows brought Visual Basic, which up through version 6.0 had quite similar syntax, minor variations being in using a format function instead of a using option on its print method, and a lack of a paint (floodfill) command in its graphics set, and lack of a DATA statement for internal initialization of arrays. I understand Visual Basic .net is quite different altogether.',4458,0);
INSERT INTO comment VALUES (4556,977,1626,'Gamer','re(3): Words too!','2003-05-03 05:01:47',0,'The reason I gave random as a given is because it can be done, and would just complicate the problem\'s idea :)\r\n\r\nHow to make a random number could be another problem.',4529,0);
INSERT INTO comment VALUES (4557,684,2121,'Chaz','Ive got the answer','2003-05-03 05:09:53',0,'OK, so the first guy has to say \"black\" for an even number of black hats or \"white\" for an odd number of blacks hats/ an even number of white hats. Then, based on what the first person said, if he sees an odd number of black hats after the guy said \"black\" he would realize that he must have a black hat on. Then, the next person could use what the last 2 said to realize what his hat was. If the first guy said black and the next guy said black, he could look in front to figure out what the people would be and stuff. \r\n\r\nOr they, being natives, could use their telepathy to tell eachother eachother what the answer is. Or they could TEAM UP AND KILL the MONSTER!',NULL,0);
INSERT INTO comment VALUES (4558,766,2121,'Chaz','re: Circumstancial','2003-05-03 05:14:06',0,'You are right. We should not even reply to these childish, illogical riddless that have about a million answers. They suck.',4377,0);
INSERT INTO comment VALUES (4559,496,2121,'Chaz','HERE','2003-05-03 05:51:58',0,'a is insane and applied\r\nb is sane and pure\r\nc is sane and applied\r\nd is insane and pure ',NULL,0);
INSERT INTO comment VALUES (4560,788,2121,'Chaz','E Z','2003-05-03 06:05:44',0,'When you multiplied the 10*10 and said it was equal to 1/10*1/10 AND 100 cents. That cannot be done because it would be like saying 2ax2a=4a, not 4a²',NULL,0);
INSERT INTO comment VALUES (4561,581,2121,'Chaz','Is it this Simple?','2003-05-03 07:42:22',0,'I think that it is because if he actually is against the death penalty, he would have joined the jury and said \"no\". Thats all I can gather from it.',NULL,0);
INSERT INTO comment VALUES (4562,581,2121,'Chaz','re: Since this is a logic puzzle--not the real world...','2003-05-03 07:45:14',0,'I was thinking the same thing. Nobody could just point out him being a liar just like that.',3228,0);
INSERT INTO comment VALUES (4563,581,2121,'Chaz','re: my thoghts and solution','2003-05-03 07:46:53',0,'He would not want to kill him. He probably would be a thinking person, who doesnt believe two wrongs make a right.',3263,0);
INSERT INTO comment VALUES (4564,218,2121,'Chaz','I got it','2003-05-03 07:51:03',0,'Weigh 8 bags at a time. If you find a number other than 80, take a bag off. Mark the bags you took off and BHnjskgrl BLAH ok i dont wanna explain it.',NULL,0);
INSERT INTO comment VALUES (4565,511,2121,'Chaz','I have the answer.','2003-05-03 08:08:19',0,'Yes. If the god wished to, he/she could. An omnipotent god could snuff out its own existence, and then come back into existence if it pleased.',NULL,0);
INSERT INTO comment VALUES (4566,511,2121,'Chaz','re: Beliefs','2003-05-03 08:09:50',0,'But the factor that you did not is OMNIPOTENT. Can do anything within anyhting if it wanted. It just matters it it wanted to or not.',4497,0);
INSERT INTO comment VALUES (4567,511,2121,'Chaz','re: read this','2003-05-03 08:17:54',0,'Ok the earth/ universe was NOT created 6000 years ago. This is completely disregarding logic in every sense. Everything we see is utterly disproving the notion of the earth/universe being 6000 years old, as is the earth being a flat plate. A small group people today still TRULY believe that the earth is flat, because they interpret the bible so literally that they are crazed. This is almost equivilent to psychosis, being unable to function in the REAL world, because of one\'s dillusions. I respect your beliefs, and I believe in the Christian God, too. But your belief of the world being 6000 years old may be due to you wanting the promise of eternal life SO badly, or just considering your beliefs SO much more \'true\' than everything else for some reason, just because you were raised with it. I am a Christian, but I still do check reality.\r\n\r\nGod Bless.',4460,0);
INSERT INTO comment VALUES (4568,504,2121,'Chaz','Got it','2003-05-03 08:24:14',0,'They are both in a \"neutral\" position, neither true or false.',NULL,0);
INSERT INTO comment VALUES (4569,672,2121,'Chaz','Solution','2003-05-03 08:28:58',0,'Matter cannot be destroyed. Its form can be changed though. So, the sword would slice the shield, but the shield maker would still have it, except changed.',NULL,0);
INSERT INTO comment VALUES (4570,476,2121,'Chaz','Solution','2003-05-03 08:32:16',0,'I would say:\r\n \"the following statement is false.\r\n \"the previous statement is true\"',NULL,0);
INSERT INTO comment VALUES (4571,263,2121,'Chaz','Brane world','2003-05-03 08:37:31',0,'Achilles and the tortoise are and a tenth dimension brane world. They pass through two intertwined wormholes. The tortoises wormhole is longer. :]',NULL,0);
INSERT INTO comment VALUES (4572,250,2121,'Chaz','Solution','2003-05-03 08:40:01',0,'You can assume that the man is truly lying about the lie. Therefore, it is as he said nothing to you.',NULL,0);
INSERT INTO comment VALUES (4573,227,2121,'Chaz','Solution','2003-05-03 08:45:04',0,'The student must win the case, and then not pay his teacher. Teacher therefore cannot charge the student again for the same thing, because that would be double jeopardy.',NULL,0);
INSERT INTO comment VALUES (4574,174,2121,'Chaz','Solution','2003-05-03 08:51:39',0,'Choose A. Then, by having a solution, it is solvable.',NULL,0);
INSERT INTO comment VALUES (4575,82,2121,'Chaz','Your paradox is flawed','2003-05-03 08:57:50',0,'It is flawed because it would take an infinite amount of time, even if it were stopped, to order each demon. Everything would be in suspended animation without noticing for an eternity.',NULL,0);
INSERT INTO comment VALUES (4576,82,2121,'Chaz','re: Who needs demons?','2003-05-03 08:58:50',0,'Prometheus GAVE them the fire. He did not have it. Besides men couldnt kill a titan.\r\n',4290,0);
INSERT INTO comment VALUES (4577,66,2121,'Chaz','Solution','2003-05-03 09:03:43',0,'Bill would not shave. If a near-infinite number of people came into the town and didnt shave, he would not have time to do so on a number of people, maybe himself.',NULL,0);
INSERT INTO comment VALUES (4578,31,2121,'Chaz','Solution','2003-05-03 09:05:51',0,'He will face the house.',NULL,0);
INSERT INTO comment VALUES (4579,27,2121,'Chaz','re: I don\'t agree','2003-05-03 09:08:45',0,'I wholeheartedly agree, gamer.',4423,0);
INSERT INTO comment VALUES (4580,687,2121,'Chaz','Solution','2003-05-03 09:14:13',0,'It will have absorbed some water, so slower than normal.',NULL,0);
INSERT INTO comment VALUES (4581,633,2121,'Chaz','Solution','2003-05-03 09:18:20',0,'Even from just looking at a piece of ice, you can see millions of air pockets trapped inside of it. The air will cause it to rise to the water\'s surface.',NULL,0);
INSERT INTO comment VALUES (4582,478,2121,'Chaz','Sol','2003-05-03 09:25:56',0,'The angular rotation of the earth has a small affect on the moons orbit. The gravity feild would be disrupted, slowly inching the moon away, decreasing is gravitational influence.',NULL,0);
INSERT INTO comment VALUES (4583,472,2121,'Chaz','','2003-05-03 09:28:43',0,'The pools level will decrease. it will do this because, though the cannon ball had weight, the boat is hollow and displaces more water due to its greater volume.',NULL,0);
INSERT INTO comment VALUES (4584,472,2121,'Chaz','re: depends on the density','2003-05-03 09:31:18',0,'The only factor that matters in this problem is volume.',3445,0);
INSERT INTO comment VALUES (4585,466,2121,'Chaz','Solution','2003-05-03 09:36:47',0,'Based on it being day/night, different parts DO get different amounts. But the tilt of the earth makes it so when the north gets sunlight, they get it indirectly, not a lesser amount.',NULL,0);
INSERT INTO comment VALUES (4586,394,2121,'Chaz','Solution','2003-05-03 09:57:33',0,'I noticed the \'Hot\' in the problem. I realized, that water is at ph 7 only under certain conditions, one of which is temperature. So, the jar conducted heat, and warmed the water in the jar so its properties changed slightly. There.',NULL,0);
INSERT INTO comment VALUES (4587,393,2121,'Chaz','Got it','2003-05-03 10:01:54',0,'The carbon from the AIR combined with the water. The jars obviously were not vacuum sealed.',NULL,0);
INSERT INTO comment VALUES (4588,355,2121,'Chaz','Strong forces','2003-05-03 10:08:46',0,'The forces that are \'Strong\' are magnetism and nuclear force. These two forces would cause the fly to come to a complete halt, and the be \'turned around\' for an immeasuribly small amount of time, before it goes SPLAT.',NULL,0);
INSERT INTO comment VALUES (4589,355,2121,'Chaz','re: Not a solution','2003-05-03 10:11:04',0,'your correct about that, but it doesnt matter who you distribute the velocity among.',2245,0);
INSERT INTO comment VALUES (4590,253,2121,'Chaz','SOLUTION','2003-05-03 10:13:43',0,'Molecules cant \'combust\'. Elementary particles, and their antiparticles can kind of combust, but not two molecules like those.',NULL,0);
INSERT INTO comment VALUES (4591,203,2121,'Chaz','Solution (to a flawed statement)','2003-05-03 10:17:50',0,'Black objects absorb radiant heat better. RADIANT. Not convection.',NULL,0);
INSERT INTO comment VALUES (4592,714,2121,'Chaz','I had to look at the solution :(','2003-05-03 10:30:05',0,'I had to. I would have never guesses it either.',NULL,0);
INSERT INTO comment VALUES (4593,510,2121,'Chaz','Ill try again','2003-05-03 10:33:37',0,'1= Star; doesnt really move, things move around it\r\n2= black hole\r\n3= after the black hole\'s mass becomes zero from emitting particles/antiparticles and disperses\r\n\r\nthis is a good one',NULL,0);
INSERT INTO comment VALUES (4594,500,2121,'Chaz','Possibly','2003-05-03 10:36:24',0,'Overthrowing the leader and siezing power for yourself',NULL,0);
INSERT INTO comment VALUES (4595,500,2121,'Chaz','another thought','2003-05-03 10:38:17',0,'Suicide is another heh kinda hard to punish a dead guy.',NULL,0);
INSERT INTO comment VALUES (4596,467,2121,'Chaz','I saw this on a cartoon :)','2003-05-03 10:41:27',0,'Man. In the dawn of his life, he crawls. For the most of it, he walks on 2 legs. As an old man he walks on two leg, and with a cane.\r\n\r\nOr a tap-dancing bear.',NULL,0);
INSERT INTO comment VALUES (4597,360,2121,'Chaz','the answer is..... ME!!!','2003-05-03 10:47:05',0,'I am greater than God (yah right)\r\nMore evil than the devil\r\nThe poor have me\r\nThe rich hot girls NEED me\r\nAnd I was eaten and I died :)\r\n\r\nBut seriously, the answer is NOTHING',NULL,0);
INSERT INTO comment VALUES (4598,315,2121,'Chaz','This was so ****ing easy','2003-05-03 10:49:27',0,'HIMSELF SELFY HIM HIM HIM !!! Himmy McSelfself',NULL,0);
INSERT INTO comment VALUES (4599,315,2121,'Chaz','WAIT.... there are 2 fathers!','2003-05-03 10:51:42',0,'Its his SON! this mans FATHER is MY FATHERS SON!!!',NULL,0);
INSERT INTO comment VALUES (4600,229,2121,'Chaz','Answer','2003-05-03 10:56:52',0,'Well, Edgar Allen Poe WROTE (writing desk) about the RAVEN, and people used to WRITE with quills, which ravens have.',NULL,0);
INSERT INTO comment VALUES (4601,780,2121,'Chaz','Possibly solution','2003-05-03 11:10:06',0,'If the bags could be as big as you wanted, you could place as many trash bags as you pleased inside other trashbags.',NULL,0);
INSERT INTO comment VALUES (4602,780,2121,'Chaz','If stacking isnt allowed....','2003-05-03 11:13:04',0,'Than it would be 13 yup big fat 13 start at 0. YES 0!',NULL,0);
INSERT INTO comment VALUES (4603,502,2121,'Chaz','SolUTioNN','2003-05-03 11:18:41',0,'HA a thousand thats SO WIERD! I never thought about that till I had to count!',NULL,0);
INSERT INTO comment VALUES (4604,511,1575,'DJ','re(2): read this','2003-05-03 12:18:36',0,'Just wondering how \"everything we see is utterly disproving\" that. Also wondering who still believes that the earth is flat, and where that would come from the Bible. I don\'t (surprisingly?) have time to comment further, but a little corroboration to such statements is always nice (since I don\'t think I suffer from any psychosis).',4567,0);
INSERT INTO comment VALUES (4605,788,1974,'Geoff','','2003-05-03 13:12:57',0,'Actually, the correct answer is that 10 cents * 10 cents does not equal 1/10 of a dollar.',NULL,0);
INSERT INTO comment VALUES (4606,977,1,'levik','re: C++ solution','2003-05-03 13:45:29',0,'Hmmm... Fried, I used to know some C++ way back when, but reading this took some effort. Looks like you\'re relying on some standard library functions here, (not sure what random_shuffle() does), which would probably be missing the point of the excercise.\r\n\r\nThis isn\'t a straight programming category after all.',4513,0);
INSERT INTO comment VALUES (4607,977,1,'levik','re(2): Words too!','2003-05-03 13:47:42',0,'Heh... I guess then ignore my other comment.\r\n\r\nI feel cool now that I didn\'t get that C++ joke... (Good thing you didn\'t joke in Java)',4515,0);
INSERT INTO comment VALUES (4608,775,1660,'Tim Axoy','This is NOT Cheating','2003-05-03 14:24:28',0,'It is a good problem,so I voted it 5.',4436,0);
INSERT INTO comment VALUES (4609,226,2121,'Chaz','(easy) Solution','2003-05-03 14:41:37',0,'There are 4 balls. 3 are red. Easy.',NULL,0);
INSERT INTO comment VALUES (4610,511,2121,'Chaz','re(3): read this','2003-05-03 14:45:39',0,'I meant that flat earthers are psycho. Flat earthers are just like people from the middle ages. I dont know where it says the earth is flat. I didnt mean for my comment to come off in that way, but you cannot hear voices online. Please excuse that last comment, and I apologize if I offended you. peace. Lets get back to the paradox problem.',4604,0);
INSERT INTO comment VALUES (4611,310,2121,'Chaz','Got it','2003-05-03 14:56:52',0,'If thats the keyboard, then I got it correct. V it is. \r\n\r\n QWERTY\r\n ASDFG\r\n ZXCV',NULL,0);
INSERT INTO comment VALUES (4612,690,2121,'Chaz','Solution','2003-05-03 15:09:44',0,'I assume that it would be the ice water, because the (convection/conduction) steam will remove the heat extremely affectively, because the heated water will move away, leaving the colder water to take its place.',NULL,0);
INSERT INTO comment VALUES (4613,783,2121,'Chaz','Derrrrr......','2003-05-03 15:18:29',0,'Ok im only 14 and this is just plain gibberish to me.',NULL,0);
INSERT INTO comment VALUES (4614,732,2121,'Chaz','soLOTION','2003-05-03 15:42:21',0,'Ok I dont feel like typing tonight so here it is:\r\nDREW LIES\r\nMOHAMMED NO LIES',NULL,0);
INSERT INTO comment VALUES (4615,432,2121,'Chaz','SOLUTION!!!!','2003-05-03 15:55:44',0,'Ha! Its ALAN! Because barry and carl contradict eachother, one must be the knight. So alan is DEFINETLY a liar. Assuming carl is the knight, barry would be a liar, and would have stolen the money. But allen would be left innocent, and so would carl. That makes 2 knights, which is not allowed. So, we must assume that barry is the knight. So carl is lying. So is allen, because there must be 2 liars. So allen LIES.',NULL,0);
INSERT INTO comment VALUES (4616,432,2121,'Chaz','re: Easy','2003-05-03 15:58:06',0,'So it WAS you mr Alan pants?',2885,0);
INSERT INTO comment VALUES (4617,788,2130,'ethan','duh!','2003-05-03 16:01:00',0,'duh! say Xs and Os are any sort of unit. \r\none X = one hundred O\'s. divide both sides of the equation by one hundred.\r\n1/100 X = one O.thats just what the problem says. 1 dollar = 100 cents. 1/100 dollar = 1 cent. the middle stuff is just to fool you.',NULL,0);
INSERT INTO comment VALUES (4618,432,2121,'Chaz','re(4): Easy','2003-05-03 16:07:12',0,'man it really is not that big of a deal! Who really cares?',2909,0);
INSERT INTO comment VALUES (4619,775,2130,'ethan','','2003-05-03 16:12:33',0,'Mohammad is a knight and drew is a liar.\r\nMohammad says,\"we\'re different and he is right.\"\r\nDrew says, \"we\'re the same but the liar is lying. it doesnt work any other way\r\n',NULL,0);
INSERT INTO comment VALUES (4620,231,1626,'Gamer','re(2): Need some math theory help over here','2003-05-03 16:44:52',0,'Another reason the problem excludes 2 and 5 is you can prove that the any number of 9s is NOT divisible by 2 or 5. Since n+1 is divisible by 2 and 5, n must not be.',3084,0);
INSERT INTO comment VALUES (4621,788,1626,'Gamer','re: E Z','2003-05-03 16:45:53',4,'Haven\'t I seen that before, like maybe in another post?',4560,0);
INSERT INTO comment VALUES (4622,775,1626,'Gamer','Note to levik!!!','2003-05-03 16:50:57',0,'You should make it so you can\'t vote on your own problem. ',4608,0);
INSERT INTO comment VALUES (4623,788,2080,'Tristan','kinda messed','2003-05-03 17:19:05',3,'to say 10 * 10 is equal to 10/100 * 10/100 just doesn\'t make sense, Any 8th grader with some eyes coulda picked that one out, thats just like saying 100 = 10/100 * 10/100, when in actuality 10/100 * 10/100 = 1/100. The problem lies in the coversion between \"10 cents * 10 cents\" --> \"1/10 dollar * 1/10 dollar\"',NULL,0);
INSERT INTO comment VALUES (4624,516,2131,'joe','how do you answer?','2003-05-03 22:23:24',0,'Bruce loves Ellen\r\nEllen loves Chad\r\nChad loves Mary\r\nMary loves David\r\nDavid loves Gloria\r\nGloria loves Arthur\r\nArthur loves Helen\r\nHelen loves Bruce',NULL,0);
INSERT INTO comment VALUES (4625,780,2131,'joe','','2003-05-03 22:38:24',0,'i think 14 too, including 0 of course',NULL,0);
INSERT INTO comment VALUES (4626,783,1919,'Lewis','re: Derrrrr......','2003-05-03 23:20:15',0,'Dont worry - you\'re not the only one. But i\'m only 13...',4613,0);
INSERT INTO comment VALUES (4627,683,1919,'Lewis','half a solution','2003-05-03 23:26:51',1,'Okay - the man thought \'gh\' made an \'f\' sound because of words like enouGH and touGH.\r\nErm... im not sure how the \'o\' is an \'i\' sound. \'Women\' perhaps?\r\nThe \'ti\' makes a \'sh\' sound from words like staTIon and motivaTIon. Therefore, \'ghoti\' could sound like \'fish\'.',NULL,0);
INSERT INTO comment VALUES (4628,397,1919,'Lewis','re: Another...','2003-05-03 23:32:43',0,'Iron is a two syllable word....',2623,0);
INSERT INTO comment VALUES (4629,397,1919,'Lewis','Yet Another','2003-05-03 23:39:06',3,'Vide(o)',NULL,0);
INSERT INTO comment VALUES (4630,174,2133,'abc','See for yourself','2003-05-04 01:32:15',0,'If anybody ever comes to the conclusion whether the problem is solvable or unsolvable, (s)he has solved the \'solvability\' of the problem. It is immaterial whether the nature of the solution is a or b, a solution has already come, and hence the problem is invariably solvable.',NULL,0);
INSERT INTO comment VALUES (4631,476,2133,'spinoza','solution','2003-05-04 01:38:09',0,'you may make any paradoxical statement like:\r\n\"i always lie\"',NULL,0);
INSERT INTO comment VALUES (4632,516,1301,'Charlie','solution','2003-05-04 05:14:49',3,'As there are no mutual loves, there are either 2 cycles with 4 people in each, or one full chain including all 8 people. For shorthand, I\'ll refer to people by their initials: A-D are men; E,M,G and H women (why couldn\'t Mary be called Florence, in the true puzzle tradition?)\r\n\r\nIf there are 2 cycles of 4, C and D are in one cycle because of statement (a), and that leaves A and B in the other. By (c) this would make A the man who loves M, and M would love B. By (b) B would then love E, completing this 4-cycle. That leaves G and H to fill out the 4-cycle with C and D. But that leaves (e) impossible to fulfill. Therefore there are not two cycles of 4, but rather one complete cycle of 8.\r\n\r\nLet\'s represent the cycle of love by two strings--one of men and one of women, such as the following:\r\nABCD\r\nEMGH\r\nwhere the above placement would indicate A loves E, who loves B, who loves M, who loves C, etc. In other words the letter representing the man who loves a particular woman is directly above that woman\'s letter, while the man loved by that woman is up and to the right of that woman\'s letter.\r\n\r\nWe can always start anywhere in the cycle so we might as well put A in the upper left.\r\n\r\nSince C loves the one who loves D, C and D have to appear directly in a row on the top row, which is therefore either ABCD or ACDB. Either way, as A loves the woman who loves the man who loves E, E must be the second letter in the lower string:\r\nACDB\r\n-E--\r\nor\r\nABCD\r\n-E--\r\n\r\nRule (c) then places M:\r\nACDB\r\nME--\r\nor\r\nABCD\r\n-EM-\r\n\r\nRules (d) and (e) prevent G and H from fitting into the ACDB scenario. Then rule (d) allows only the following placement in the ABCD scenario:\r\nABCD\r\nHEMG\r\n\r\nSo Arthur loves Helen, who loves Bruce, who loves Ellen, who loves Chad, who loves Mary, who loves David, who loves Gloria',NULL,0);
INSERT INTO comment VALUES (4633,7,1919,'Lewis','I think that...','2003-05-04 06:47:22',3,'Its a 50% chance that the second will say \'tails\' as well. The fact that the first one said tails doesn\'t affect the probability of the second one.',NULL,0);
INSERT INTO comment VALUES (4634,238,2121,'Chaz','Solution','2003-05-04 07:11:53',0,'Fill the big jug. Then pour all the water to the top of the smaller jug. Now you have 2 gallons in the (5) gal jug. So, now empty the 3 gal jug. Pour the water from the 5 into the 3. Fill the 5 again. Fill 3 with water from 5. 5 now has 4 gallons. Not too hard.',NULL,0);
INSERT INTO comment VALUES (4635,510,2121,'Chaz','AGAIN ill try','2003-05-04 07:18:00',0,'Ok they are all nothing heh heh ha ha HO HO OOGA BOOGA!',NULL,0);
INSERT INTO comment VALUES (4636,381,2121,'Chaz','Solution','2003-05-04 07:20:51',0,'Man on a horse, because the mayans thought that they were one creature when they came over.',NULL,0);
INSERT INTO comment VALUES (4637,381,2121,'Chaz','re: stupid solution','2003-05-04 07:21:57',0,'It isnt \'invalid\', it is a minor flaw. The feet could be the bottom of the leg if you want.',3193,0);
INSERT INTO comment VALUES (4638,379,2121,'Chaz','Solution','2003-05-04 07:24:37',0,'A stolen/fake item.',NULL,0);
INSERT INTO comment VALUES (4639,378,2121,'Chaz','Solution','2003-05-04 07:26:48',0,'A gravestone? Coffin?',NULL,0);
INSERT INTO comment VALUES (4640,377,2121,'Chaz','No chance','2003-05-04 07:30:36',0,'I just HAD to look at the solution. I would have never gotten it.',NULL,0);
INSERT INTO comment VALUES (4641,373,2121,'Chaz','Solution','2003-05-04 07:33:39',0,'Ok it has something to do with the words.... I know it does. Not really a solution here.',NULL,0);
INSERT INTO comment VALUES (4642,348,2121,'Chaz','At first. ..... .','2003-05-04 07:37:09',0,'At first I thought it was the man in the moon. Then I looked closer at the water parts and body parts and SUN! Sun! That gave it away. A SNOWMAN!',NULL,0);
INSERT INTO comment VALUES (4643,788,1626,'Gamer','re: kinda messed','2003-05-04 09:30:23',0,'That\'s not really a problem. 10 cents x 10 cents = 10/100 dollar x 10/100 dollar. This is because 1 cent = 1/100 dollar, so 10 cents = 10/100 dollar. Of course you can\'t really have cents² can you?',4623,0);
INSERT INTO comment VALUES (4644,516,2137,'Zach','Solution','2003-05-04 10:52:19',0,'Arthur loves Helen who loves Bruce who loves Ellen who loves Chad who loves Mary who loves David who loves Gloria who loves Arthur....a perfect circle! ',NULL,0);
INSERT INTO comment VALUES (4645,516,2138,'blabla','Solution','2003-05-04 12:02:56',0,'D loves G, G loves A, A loves H, H loves B, B loves E, E loves C, C loves M, and M loves D.',NULL,0);
INSERT INTO comment VALUES (4646,511,1072,'Alan','I enjoy a good debate','2003-05-04 12:45:34',0,'Please everyone who wishes to take place in this debate read a post in the forum. This debate regards the belief in god',NULL,0);
INSERT INTO comment VALUES (4647,788,2139,'Amy','Solution','2003-05-04 14:07:17',3,'It helps to look at the problem like this:\r\n\r\n1 dollar = 100 cents\r\n = 10 cents * 10 cents\r\n = 1/10 dollar * 1/10 dollar\r\n = 1/100 dollar\r\n = 1 cent\r\n\r\nWhatever you do to one side of the equation, you must also do to the other side. The terms dollars and cents are irrelevant. It\'s the math that counts! When going from \"10 cents * 10 cents\" to \"1/10 dollar * 1/10 dollar,\" you have divided one side of the equation by 100. (10/100 = 1/10) You must also divide the other side of the equation by 100. (1 dollar/100 = 1 cent) Thus, your final line would not read 1 dollar = 1 cent, but 1 cent = 1 cent.',NULL,0);
INSERT INTO comment VALUES (4648,977,2140,'daniel','Array Solution','2003-05-04 15:11:53',0,'Create an int array of size 9 indexed by 0 ... 8.\r\nUntil the array is empty perform the following steps:\r\n\r\n Make a call to random and store the result\r\n\r\n value = random(9);\r\n \r\n Access the element of the array corresponding to\r\n this value\r\n\r\n int_array[(value - 1)]\r\n\r\n As you use the values from the array replace them with a sentinel, such as -999. You could check to make sure they have not been used as follows:\r\n\r\n if(int_array[value - 1] != -999)\r\n <.. use to build random number ..>\r\n else\r\n <.. do not use. repeat process ..>\r\n\r\nRepeat this until the 9-digit random number is built.\r\n',NULL,0);
INSERT INTO comment VALUES (4649,780,2130,'ethan','it seems too ez. i dunno','2003-05-04 16:21:05',0,'13 bags.',NULL,0);
INSERT INTO comment VALUES (4650,511,2130,'ethan','re: What this proves','2003-05-04 16:32:13',0,'i am a conservative lutheran, and a son of a pastor. jesus was the real thing not some wise dude. the old testament prophecies say hundreds of things about him that actually happened. so if u call yourself a catholic, i dont see how u can question the fact that the new testament was just a book, if u have faith. oh, and by the way. where do u get that purgatory stuff? and limbo? it doesnt say anything about that in the bible.',4451,0);
INSERT INTO comment VALUES (4651,511,1626,'Gamer','re: I enjoy a good debate','2003-05-04 16:37:30',0,'Ummm this problem doesn\'t deal with the existance of one. It just says COULD IT CARRY..... See my comment on the chain.',4646,0);
INSERT INTO comment VALUES (4652,238,1919,'Lewis','solution','2003-05-04 20:38:57',3,'Fill the 3 and pour it into the 5.\r\nRefill the 3 and use that to fill the 5. You will have 1 gallon left in the 3 jug.\r\nDump the water in the five, and empty the 3 jug into the 5 jug.\r\nAdd another 3 gallons to the 1 gallon in the 5 jug, and then you have 4 gallons.',NULL,0);
INSERT INTO comment VALUES (4653,30,1919,'Lewis','perhaps...','2003-05-04 20:46:37',3,'Ask one of them what door the other would say leads to the way out. Which ever door he says, go out through the other one because both the liar and the knight are involved in the question, so the answer is definitely going to be a lie.',NULL,0);
INSERT INTO comment VALUES (4654,780,1982,'Adam','re: Sum','2003-05-04 22:12:27',0,'You forgot to divide your 27 by 2 !!\r\nOtherwise you\'d get 13 as TomM did.',4433,0);
INSERT INTO comment VALUES (4655,511,1575,'DJ','re(2): I enjoy a good debate','2003-05-04 22:52:42',0,'I don\'t see \"it\" anywhere in the problem; I see \"the omnipotent God,\" which is specific and depends on not only the existence of God, but His abilities, limitations; the very nature of God is being debated.',4651,0);
INSERT INTO comment VALUES (4656,516,2143,'Christen','is this it','2003-05-05 01:31:57',3,'Chad loves Helen\r\nArthur loves Mary\r\nBruce loves Ellen\r\nDavid loves Gloria\r\nEllen loves Arthur\r\nMary loves Bruce\r\nGloria loves Chad\r\nHelen loves David',NULL,0);
INSERT INTO comment VALUES (4657,788,1920,'Brian Smith','Solution','2003-05-05 03:42:41',0,'The first error is 100 cents cannot be expressed as 10 cents * 10 cents. The second error is 1/10 dollar * 1/10 dollar = 1/100 dollar. Cents and dollars can not be split into 2 factors like that.',NULL,0);
INSERT INTO comment VALUES (4658,514,1920,'Brian Smith','re:','2003-05-05 04:48:49',0,'In your list, you claim BC is lighter than AD. That is not always true. The only pairings which can always be identified are AB, AC, CE and DE.',4547,0);
INSERT INTO comment VALUES (4659,781,1575,'DJ','Multiple Solutions?','2003-05-05 10:08:46',1,'There are only three facts given in the problem:\r\nBob had traveled exactly one mile when his hat flew off,\r\nhe turned around exactly five minutes later,\r\nand he found the hat at the same spot (on the bank) he originated from.\r\nLet x be the full-throttle speed of Bob\'s boat (relative to the water) in miles/minute.\r\nLet y be the speed of the water downstream.\r\n\r\nWhen Bob first starts, he is going full throttle upstream. Thus, the speed of his boat is going against that of the river, and his speed relative to the shore is (x-y) miles per minute.\r\nHe traveled the first mile, then, in 1/(x-y) minutes, and he traveled 5(x-y) miles in the next 5 minutes.\r\n\r\nThe return trip was, of course, exactly the same distance along the shore as he has already come, or 1+5(x-y) miles upstream. The time it took him was the same as the time it took his hat to float downstream (which is moving at the same speed as the river) one mile, which would be 1/y minutes. Finally, his speed going downstream, with the current now, is (x+y)mi/min.\r\n\r\nSo, we have one equation with two unknowns, which means that unless I missed something in the problem, it can be solved, but with multiple solutions.\r\n\r\nThe equation is rate=distance/time, or:\r\nx+y = [1+5(x-y)]/[1/y]\r\nwhich becomes:\r\nx+y = y(1+5x-5y)\r\nx+y = y+5xy-5y²\r\nI don\'t know how to solve for a specific value of y, but to find one solution, just let y=1:\r\nx+(1) = 1 + 5x(1) -5(1²)\r\n5=4x\r\nx=5/4. Or, if the full-throttle speed of his boat is 5 miles/4 minutes, then the water is traveling at 1 mile/minute.\r\n\r\nDid I miss something?',NULL,0);
INSERT INTO comment VALUES (4660,781,1920,'Brian Smith','I remember this one','2003-05-05 10:18:10',0,'First define some variables:\r\nb=speed of Bob\'s boat in still water (miles/minute)\r\nr=speed of river (miles/minute)\r\nt=time Bob spent traveling downstream to get his hat back (minutes)\r\n\r\nThe distance Bob traveled upstream equals 5*(b-r)\r\nThe distance Bob traveled downstream equals t*(b+r)\r\nThe distance the hat traveled equals 1 or (t+5)*r\r\n\r\nTwo equations can be made: 5*(b-r) + 1 = t*(b+r) and (t+5)*r=1\r\n\r\nSolving for these equals t = 5 minutes and river speed r = 0.1 miles/minute. The speed of Bob\'s boat can be any speed.',NULL,0);
INSERT INTO comment VALUES (4661,781,1301,'Charlie','solution','2003-05-05 16:24:12',3,'Bob first loses his hat 1 mile upstream, at which time the hat remains stationary relative to the water. Bob continues to move in the water at a constant speed, first for 5 minutes away from the hat, and then for another 5 minutes towards the hat, as Bob\'s speed in the water is constant and the hat is not moving relative to the water. During this 10 minutes, the hat along with the water has moved 1 mile. One mile in 10 minutes is 6 miles per hour.',NULL,0);
INSERT INTO comment VALUES (4662,514,2148,'Jayaram Subramanian','The Correct Solution','2003-05-05 23:50:16',3,'The weights of the 5 pumpkins are 7,9,11,12 & 15 pounds',NULL,0);
INSERT INTO comment VALUES (4663,789,1301,'Charlie','solution','2003-05-06 03:12:53',3,'The centers of the circles (which are also points of intersection of two circles each) form an equilateral triangle. The area in question includes this triangle as well as adjacent areas bounded by arcs of circles.\r\n\r\nWe can also consider the area as three overlapping pie slices (sectors). Each pie slice is 1/6 of one of the full circle\'s, with area πr²/6. Three of these make πr²/2, but that counts the central equilateral triangle three times instead of one, so we have to subtract out twice the area of that triangle. The triangle\'s sides are r, and the altitude is ((√3)/2)r, so its area is r²(√3)/4, and twice its area is r²(√3)/2.\r\n\r\nSo the area sought is πr²/2 - r²(√3)/2. This is about .704770923 r².',NULL,0);
INSERT INTO comment VALUES (4664,516,2152,'w','The answer is......','2003-05-06 06:33:49',0,'david loves Gloria who loves arther who loves helen who loves bruce who loves ellen who loves chad who loves mary who loves DAVID ect. ect. and so on.',NULL,0);
INSERT INTO comment VALUES (4665,789,2151,'Fahim','solution','2003-05-06 06:54:05',3,'Each circle will pass through the center of the other two, when the three radii are equal.\r\nThe area between an arc (formed by the itersection of a line and a circle) and intersecting line is = .5*r²(theta - sin(theta))\r\nthe area of the equilateral triangle with side r is = .5*r²*sin(π/3) = √3r²/4\r\n\r\nSo, area of intersection is = (3/2)r²((π/3) - (√3/2) ) + (√3/4)r²\r\n= (π-√3)r²/2\r\n= 0.704770923r²',NULL,0);
INSERT INTO comment VALUES (4666,516,2153,'Randy Okum','My answer','2003-05-06 07:05:11',3,'Chad loves Mary loves David loves Gloria loves Arthor loves Helen Loves Bruce loves Ellen loves Chad',NULL,0);
INSERT INTO comment VALUES (4667,794,1920,'Brian Smith','Try this number','2003-05-06 07:58:44',0,'ZERO!\r\n\r\nThere is at least one person on the planet without a left hand.\r\n\r\nOtherwise 5^(5*10^9) = approx 10^(3.5*10^9)',NULL,0);
INSERT INTO comment VALUES (4668,781,1947,'Jon','hmmm.. got it','2003-05-06 08:01:46',0,'Speed of stream = Y\r\nSpeed of boat (without effect of stream) = X\r\ndistance boat goes in five minutes against stream = D = 5(x-y)\r\nNow set up an equation that writes total time for travel in terms of distance divided by rate for both hat and boat and set them equal.\r\n1 mile/Y = 5 min +(D+1 mile)/(X+Y) simplify it\r\n(X+Y)/Y= 5(X+Y) + (5(X-Y)+1)\r\n(X+Y)/Y= 5X+5Y+5X-5Y+1\r\n(X+Y)/Y= 10X+1\r\nX+Y=10XY+Y\r\nX=10XY\r\n1=10Y\r\n.1 miles/min = Y = 3/5 mph',NULL,0);
INSERT INTO comment VALUES (4669,794,1301,'Charlie','solution','2003-05-06 08:06:48',3,'The common log of 5 is about .6989700043360187. Multiply this by 5,000,000,000 to get 3494850021.680094, the common log of the answer. It shows that the answer has 3,494,850,022 digits (one more than the characteristic of the log), and that the first few are 47873... (based on the antilog of the mantissa).',NULL,0);
INSERT INTO comment VALUES (4670,794,1947,'Jon','re: Try this number','2003-05-06 08:06:56',0,'nicely done, I agree with both answers',4667,0);
INSERT INTO comment VALUES (4671,781,1920,'Brian Smith','re: solution','2003-05-06 08:12:18',0,'Very nice approach.',4661,0);
INSERT INTO comment VALUES (4672,788,1947,'Jon','another answer','2003-05-06 08:16:12',0,'you split the labels inapropriately.\r\n100 cents = 10 cents * 10 cents is false.\r\nreally 10 cents * 10 cents= 100 cents^2 which doesn\'t make sense. :) However, 10 cents * 10 cents = 1/10 dollars * 1/10 dollars is true because they both equal 100 cents^2 = 1/100 dollars^2 ( because of the squares you would have to multiply the 100 twice.)',NULL,0);
INSERT INTO comment VALUES (4673,511,1947,'Jon','re(3): I enjoy a good debate','2003-05-06 08:39:05',0,'For you who beleive in a God, any religion it doesn\'t much matter, this problem doesn\'t really question anything. If God wanted to do this he/she would. For anyone who doesn\'t really believe in a god the problem comes in only a way as this. God would then make himself able to carry it making this a paradox. For me, I think we are all kind of silly questioning the ability of something we can\'t possibly fathom. I personally am a christian, but I don\'t doubt that something like this was put here to teach someone a lesson. Very good thought question Ravi.',4655,0);
INSERT INTO comment VALUES (4674,794,1794,'arbor','re: solution','2003-05-06 09:06:41',0,'This is true if we expect the answer to be written as a base 10 number. However, the question is not complete in the sense it does not specify which base the result is expected to be in. E.g. if it is expected to be written as a base 5 number, it would be 5,000,000,001 digits.',4669,0);
INSERT INTO comment VALUES (4676,794,1,'levik','re(2): solution','2003-05-06 10:14:01',0,'While that is true, we can usually assume that base 10 is meant when nothing to the contrary is specified.',4674,0);
INSERT INTO comment VALUES (4677,794,1626,'Gamer','re(3): solution','2003-05-06 11:18:37',0,'There was another message set based on that...\r\n\r\nI agree with zero as the answer, but Charlie has a good idea :)',4676,0);
INSERT INTO comment VALUES (4678,790,775,'Cory Taylor','concept','2003-05-06 13:34:30',0,'This ones sure been waiting a long time...\r\n\r\nWhile what follows is no solution in itself, it is a method that could be used to find the solution.\r\n\r\nLatitude and Longtitude closely relate to the spherical coordinate system of locating points. While the cartesian (most common) system labels points with an x,y and z value which gives a unique 3 dimensional location, and cylindrical coordinates (an extension of polar coordinates) locate points with a planar angle from a reference line (generally the x-axis), a distance from the origin within that plane and the relative height to the point from the plane, spherical cooridinates locate points by the quantity of a first rotation (about a reference plane) between 0 and 360 (similar to longitude), a second rotation (perpendicularly away from the reference plane) between -90 and +90 (similar to latitude), and a distance from the origin (which would be the radius of the Earth). There are easily calculated formulas to transfer a known point from one coordinate system to another.\r\n\r\nUsing this infomation, and assuming a coordinate system that is convenient to the problem (i.e. the reference plane contains the equator, and the reference line goes through longitude 0 degrees), we can use the lat, lon and radius to create cartesian coordinates for any location on earth.\r\n\r\nNext we use the definition of vector dot product to calculate the absolute angle formed between these two surface points, and from there the distance of the great circle arc between them.\r\n\r\nThis is all math (and somewhat challenging but not prohibitively), and so far there is no need to make restrictive or error inducing guesses/assumptions.\r\n\r\nI\'m not certain how to proceed from here in a rigorous fashion, however, with a good map of the States (which I don\'t have), you could probably find the solution within a degree (still a lot of error) with 10 tries or so, and further narrow your result by performing more iterations until you\'ve the accuracy you require. Of course, there\'s most likely a better way to do it.',NULL,0);
INSERT INTO comment VALUES (4679,794,2029,'Jay Stone','re: Try this number','2003-05-06 15:38:45',0,'Brian is correct. Forget the \"log\" math. Any 2nd grader can do this. At least one person on earth will have zero fingers. Anything times zero is zero!',4667,0);
INSERT INTO comment VALUES (4680,790,775,'Cory Taylor','follow through guess','2003-05-06 15:54:45',0,'Is the following location in the U.S.?\r\n\r\nCircular (W. Longitude) 95d40\'\r\nZenith (Latitude) 39d00\'\r\n\r\nIf so, then that\'s my answer. This may not be in the states as there are two locations on Earth that will satisfy the distance requirements, I haven\'t found the other yet',NULL,0);
INSERT INTO comment VALUES (4681,790,1567,'Bryan','Solution','2003-05-06 18:17:26',3,'The sign is in Topeka, Kansas.
After a whole day with no comments on this puzzle, I decided to solve it. First I Googled \"spherical trigonometry\" to learn the first law of cosines for a spherical triangle:
(1) cos a = cos b cos c + sin b sin c cos A
where a, b, and c are the legs of a spherical triangle and A is the angle between b and c. Then, considering the geometry of this problem, I labeled the points of interest as T (Tokyo), L (London), N (north pole), and U (the mystery spot in the US).
For sperical triangle TNU, let a=side TU, b=side TN, and c=side UN. In this case, a=the arc corresponding to an arc length of 6182 miles, or 1.5615054 radians, and b=90 minus the north latitude of T, or 0.9482956 radians. Now we plug these values into (1), where c and A are the values to be found. Repeating this process for spherical triangle ULN, a=arc length for 4386 miles, or 1.1078555 radians and b=90-north lat of L, or 0.6719518 radians. Leg c for this triangle is the same as it was for the other one, and angle A for the two triangles adds up to the difference in longitude between L and T (on the far side of the earth; the US is obviously not between London and Tokyo the short way) which is 220.083333 degrees or 3.8411785 radians.
We now have two equations and two unknowns, but the sines and cosines made it too messy for me to solve algebraically, so I wrote a .vi in LabVIEW (it\'s all I have, so I used it) to solve numerically.
It turns out c=0.8892906, or 50 degrees 37.2 minutes from the north pole, i.e. 39 degrees 2.8 minutes north latitude. A=2.1741817, or 124 degrees 34.3 minutes east of Tokyo, which is to say 95 degrees 40.7 minutes west longitude. This puts us right in Topeka.
Now that I know spherical trig, I plan never to use it again! lol',NULL,0); INSERT INTO comment VALUES (4682,781,2144,'Ryan','re: Multiple Solutions?','2003-05-06 18:48:47',0,'If the river is going 1 mile per minute, the hat would travel downstream five miles in the five minutes before Bob turned around. However, since he was only 1 mile upstream from camp when this happened, the hat would already be 4 miles downstream past camp before Bob turned around..... ',4659,0); INSERT INTO comment VALUES (4683,781,2144,'Ryan','re: I remember this one','2003-05-06 18:57:16',0,'Hmmmm... doing some math, I have found that my answer of square root of 37 was obviously not correct... I guess I\'ll have to check my calculus. However, just to be anal, the boat speed does have to be faster than the current....',4660,0); INSERT INTO comment VALUES (4684,781,2144,'Ryan','re: hmmm.. got it','2003-05-06 18:58:16',0,'.1 miles/min = 6 mph, not 3/5 mph',4668,0); INSERT INTO comment VALUES (4685,778,2144,'Ryan','re: Elegant proof','2003-05-06 19:11:37',0,'\"If A and B are different colors\"..... true. However, A and B can be the same color, since the distance between them is ã3, not 1.',4495,0); INSERT INTO comment VALUES (4686,778,2144,'Ryan','re: Proof by contradiction','2003-05-06 19:25:56',0,'I disagree completely.\r\n\r\nA does not have to be the same color as G........ the conclusion you should have drawn is that E and F cannot be the same colors as B and C....\r\n\r\nLet me know.',4483,0); INSERT INTO comment VALUES (4687,788,2148,'Jayaram S','Easy Solution','2003-05-06 21:02:48',2,'Here\'s an easy way to understand the ERROR in the calculations:\r\n1 dollar = 100 cents = 10 coins * 10 cents = 10 coins * 1/10 dollar = 1 dollar\r\n\r\nHence the the FLAW in the original calculation was using CENTS for both the 10s',NULL,0); INSERT INTO comment VALUES (4688,781,2148,'Jayaram S','General Shortcut Formula','2003-05-07 00:14:54',3,'The general formula for solving these type of problems is :\r\n\r\nSpeed of the water = d / (2 * t) miles/minute\r\n\r\nWhere d = distance travelled by the hat\r\n t = time travelled upstream in minutes without noticing the fallen hat\r\n\r\nIn our present case, d = 1 mile, t = 5 minutes.\r\n\r\nHence Speed of the Water = 1 / (2 * 5) = 1/10 = 0.1 miles/minute or 0.1*60 = 6 miles per hour.',NULL,0); INSERT INTO comment VALUES (4689,39,450,'Paul Pereira','The solution...','2003-05-07 03:10:55',3,'The answer is one... one door will be left ajar after the 100 passes... The rational behind it is simple... Each door is closed by the time it\'s door number is the same as the number of passes... As the number of passes increase, some doors can no longer be toggled because their door number is too small to be divided... for instance the third door is opened on the first pass and closed on the third. It can no longer be opened after that... The eight door is opened on the first pass, closed on the second, opened on the fourth and closed on the eight... After that it is no longer opened... So if we follow this rule, the only door left opened after 100 passes is the first which is opened on the first pass and then never touched again... Happy solving!!',NULL,0); INSERT INTO comment VALUES (4690,778,1920,'Brian Smith','re(2): Proof by contradiction','2003-05-07 03:40:58',0,'Reread my proof AND read DJ\'s analysis of my proof. Note that my proof is a proof by contradiction.',4686,0); INSERT INTO comment VALUES (4691,513,1183,'fwaff','Ramblings of a confused mind','2003-05-07 04:13:53',1,'Hmmmm looks like another one for the grammar bods. Is the following two sentences or one? \r\n\r\nSo we correct the sentence by changing it to: \"This sentence does not contain Seven words\".\r\n\r\nIt starts with a capital letter and there is only one full stop (period), therefore one could take this to be a single sentence which includes the clause \"...this sentence does not contain seven words.\" in which case it is true. \r\n\r\nHowever, the colon followed by the opening speech marks could imply that \"This sentence does not contain seven letters\" is a (false) sentence in its own right.\r\n\r\nThis sentence does not contain 7 words. ',NULL,0); INSERT INTO comment VALUES (4692,513,1301,'Charlie','thoughts','2003-05-07 04:31:00',1,'The second sentence is not in fact a correction of the first--it is a completely different sentence. As such, it is talking about a different sentence. Therefore one is not a negation of the other, and therefore both can be false.',NULL,0); INSERT INTO comment VALUES (4693,513,1902,'Hank','more ramblings','2003-05-07 04:32:23',0,'I think that the puzzle is intented to make you think that they are speaking of the same sentence. If this were the case, then the second sentence would read:\r\n\"that sentence does not contain seven words\",\r\nwhich is true.',NULL,0); INSERT INTO comment VALUES (4694,513,1,'levik','re: thoughts','2003-05-07 05:55:11',0,'That\'s what I think... This doesn\'t seem to be a paradox at all - rather it\'s two false sentences, designed to look as though one is a negation of the other - but they are not.\r\n\r\n',4692,0); INSERT INTO comment VALUES (4695,513,1567,'Bryan','re: thoughts','2003-05-07 06:07:42',0,'Yeah! What he said!',4692,0); INSERT INTO comment VALUES (4696,778,1301,'Charlie','re(2): Proof by contradiction','2003-05-07 06:15:40',0,'In Brian Smiths solution E and F were in the same 1-m equilateral triangle with D and so could not be the same color as D or each other and so must be the same as B and C, which were also in a (different) 1-m equilateral triangle with D. Therefore G is the same color as D and that\'s the same color as A. Consider A and G opposite ends of two diamonds each composed of back-to-back eq. triangles, swivelling about pt D.',4686,0); INSERT INTO comment VALUES (4697,781,2164,'Nicole','My Guess (first time user)','2003-05-07 06:50:31',1,'Please don\'t laugh okay but I thought the answer might be...\r\n\r\nThe water wasn\'t travelling, Bob was.\r\n\r\n(It was under general so I\'m going under the ussumption that the answer doesn\'t have to me mathematical???)',NULL,0); INSERT INTO comment VALUES (4698,359,2144,'Ryan','Solution?','2003-05-07 07:00:44',0,'Hey, I don\'t see a solution to this problem using the criteria that you have to have no beads when you\'re done, so mine is as follows:\r\n\r\nstarting from 3/1/16/2/16/7, (44 beads), you can put 26 in your cup and end with 0, putting 18 in the opponents cup. The other 4 start between your cup and your opponents board.\r\n\r\nNote: following the rules of mancala, as provided in the link, you would just need 47 beads in one of your opponents first five cups from the left, and one bead in your cup of value (6- # of opponents cup with beads) from the left. Then you could simply take all of the 47, and your 1, but moving forward 1 square.\r\n\r\n(I\'m a big mancala fan)\r\n\r\n~Ryan',NULL,0); INSERT INTO comment VALUES (4699,65,2144,'Ryan','Clarified explanation (solution)','2003-05-07 07:22:41',0,'Let\'s look at it this way. When he shows you a side of the card (say red), it\'s either the front of the double red card, the back of the double red card, or the red side of the red/black card. You have a 1/3 chance.',NULL,0); INSERT INTO comment VALUES (4700,510,2165,'tally','my wrong answers','2003-05-07 07:55:41',0,'man, i thought for sure the first one was a chair... although i suppose that is too simple. since they were all related, i was thinking maybe a garbage disposal and a kitty cat, but i guess that is wrong ;o)',NULL,0); INSERT INTO comment VALUES (4701,510,2165,'tally','my wrong answers','2003-05-07 07:56:16',0,'man, i thought for sure the first one was a chair... although i suppose that is too simple. since they were all related, i was thinking maybe a garbage disposal (or a husband) and a kitty cat, but i guess that is wrong ;o)',NULL,0); INSERT INTO comment VALUES (4702,219,2144,'Ryan','Try this','2003-05-07 08:21:13',0,'The expected return would be infinite, if the \"house\" had an infinite amount of money. This is not the case. The fair price would be $1 (guaranteed) plus .5 dollars times the exponent of the house\'s money when the house\'s money is expressed as a power of 2. You can find it by using logs, but I\'m not up to date on those, and don\'t really feel like looking it up. So, unless the house can pay out $(2^199), the game is not fair.\r\n\r\nOf course, time becomes a factor based on the number of games played, so it would need to be computerized.... otherwise, I\'m not going to stand there for a few million coin flips.... but then I wouldn\'t play a \"fair game\" without infinite money either. ;-) Let me know what anyone thinks.',NULL,0); INSERT INTO comment VALUES (4703,786,1920,'Brian Smith','Off the top of my head....','2003-05-07 08:39:12',0,'Answer 1: 104010, 1050100, 10601000, 107010000...\r\n\r\nAnswer 2: 104040, 1050501, 10606060, 107070701...\r\n\r\nAnswer 3: 104030, 1050601, 10610040, 107151001...\r\nf(x)=10*f(x-1)+f(x-2)',NULL,0); INSERT INTO comment VALUES (4704,750,1920,'Brian Smith','The next next number','2003-05-07 08:45:44',0,'The next number is 1004006004001\r\nThe number after that is 1020191144865623440455270145683555422808365843606721760320032\r\n',NULL,0); INSERT INTO comment VALUES (4705,786,2166,'Chris','Solution?','2003-05-07 08:53:31',3,'The pattern seems to be:\r\n f(n)= 10*f(n-1) + f(n-2)\r\n\r\nTherefore the next two in the series are:\r\n 104,030 & 1,050,601.',NULL,0); INSERT INTO comment VALUES (4706,513,1626,'Gamer','re(2): thoughts','2003-05-07 11:19:27',0,'I see what Ravi means... That\'s why contractions were invented... This sentence doesn\'t contain seven words :D',4695,0); INSERT INTO comment VALUES (4707,786,2121,'Chaz','Think I got it','2003-05-07 11:31:29',0,'104030 and 1050601 I think.',NULL,0); INSERT INTO comment VALUES (4708,513,2129,'Sanjay','This is not That','2003-05-07 15:06:06',3,'The paradox seems to stem from the apparent contradiction between two statements about \'This sentence\' being both false, inspite of saying exactly opposite things. In other words, how can an entity both not have and not not have a property at the same time.\r\n\r\nHowever, the \'This\' in the first sentence and the \'This\' in the second sentence point to different things. The \'This\' in the first sentence refers to the first sentence, which is false. And the \'This\' in the second sentence refers to the second sentence, which is also false. \r\n\r\nSo all we have are two entities, one not possesing a property, and the other not possesing the exact opposite of that property. \r\n\r\nNothing paradoxical about that. It is entirely possibe for dogs to not have speech and for humans to not have \'no speech\'.\r\n\r\nI\'m having a tough time keeping a straight face here. Are you guys serious?\r\n\r\n',NULL,0); INSERT INTO comment VALUES (4709,778,2144,'Ryan','Try this proof','2003-05-07 15:46:43',0,'This one came to me and I tried to write it more clearly than some of the others had been written, since people are still talking about this one, even though it\'s solved. Let me know what you think.\r\n\r\nBegin proof:\r\n\r\nAssume no point is one meter from another point of that same color.\r\n\r\nRemember that every triangle has three vertices, and therefore interpret that every equilateral triangle on this plane must have one vertex of each color.\r\n\r\nUsing a Cartesian Plane, start at (0,0) and go right along the x-axis, draw three equalilateral triangles with sides of one meter.\r\n\r\nThe bases of the three triangles should be the following line segments: (0,0) to (0,1), (0,1) to (0,2), and (0,2) to (0,3).\r\n\r\nChose colors for these four points (0,0), (0,1), (0,2) and (0,3), and the three tops of the triangles, making sure each triangle has three different colored vertices.\r\n\r\nConclude: Points (0,0) and (0,3) have to be the same color.\r\n\r\nInterpret: Following this procedure, all points 3 meters from (0,0) must be the same color.\r\n\r\nGraphing all points three meters from (0,0) forms a large circle with radius 3 meters.\r\n\r\nChoose any point on the circumference of the large circle. Graph a circle with radius 1 meter around that chosen point. It will intersect the larger circle twice.\r\n\r\nInterpret: This can be done for each point on the large circle, so each point on the large circle is 1 meter away from two other points on the circle, all of the same color.\r\n\r\nConclude: There must exist more than zero points that are 1 meter away from a point of the same color on a plane with only three colors.\r\n\r\nNote: This is obviously true for any measure of distance.\r\nNote: One or two colors could have no points as described in the original problem (imagine a plane with one red point, one blue point, and the rest green), but a point of at least one of the three colors will have a point of the same color 1 meter away.\r\n\r\nEnd Proof.',NULL,0); INSERT INTO comment VALUES (4710,718,2130,'ethan','possible solution','2003-05-07 15:48:43',0,'2 to the -31 power, or 2^-31',NULL,0); INSERT INTO comment VALUES (4711,786,2173,'Mark','not sure','2003-05-07 17:45:02',4,'104020,1050301,10604020... so on, when the third number gets to 9, next cycle will start it from 1 again and the first number will be changed to 2 then goes the third cycle and so on... numbers between zeros are always 1 through 9. (Probably not that simple?)\r\n',NULL,0); INSERT INTO comment VALUES (4712,786,2173,'Mark','better solution!','2003-05-07 18:12:02',0,'sequence is n*10 plus the number before n, so let\'s try this. first number 1 times 10 plus number before one which does not exist so number after the first one is 10, then 10 time 10 plus the the number before 10, that equals 101, so next will be 101*10+10=1020, 1020*10+101=10301, next two are 104030, 1050601,...',NULL,0); INSERT INTO comment VALUES (4713,750,1301,'Charlie','re: The next next number','2003-05-07 18:34:37',0,'After\r\n?b 1020191144865623440455270145683555422808365843606721760320032\r\nOK\r\ncome\r\nc=(b+1)^6\r\nOK\r\n?c\r\n 1127429248894795788173112153077515559236798848673772146621525190034274748780569978724472375094324848586621734311950911723658856357231798723254621196087273362201760195419372037128638173776070766278919682010719613991733325415129613305551546383828612086670346491570584414219615617677596941938476199841381422548191953807947099289071776919729043092152301307326027969\r\nOK\r\nd=(c+1)^7\r\nOK\r\n?d\r\n 23153949552347568166717795312962564250383705732113626382789554460215386872937613235403897767461540445157693057226468440639260409646878456341811384683736197787747923154744577273414944889497155831235786471468348589361408643565777464983013224626301196322090093142811872979564912220044728721733361850993924648168926968208760284887252353214307415668293391452986790053811827750287531378711334520397115426004259829738482562344657311384867426292526135984870172215745862751946297641032969079411217626385101460083906637010482290723731479254880281618176695045042440909410420477395209722975156867638554634462508257189693069142130868884724051734268815856532474702964343668545499455547777105769428658609690305417143316072333098274085\r\n195503805974745950228785855595067795321875400881307162590802814070073203666617979221231117906766459178428881256926109612661864748967419734688411610723186714344901759739800952770118288211168833920167526458559141995695165203023822695958346319\r\n313035258540286499802132816910019979179992644345649674398424295778270538425742440556421119349720540346789342403883270593158223372719030697153309224911039502661777069116702727492354925543947162793563426934635328143524943619583084197576623922\r\n404110176968312576999136821195765546413737789189982726856456335921855727821884710707313335052162671170964082738216243361221893489126798663806995604324684568298736098973115466598958795755361735438896656766279276980314448336026892120959447811\r\n838854912810500011617562812941625730043354618144570940265536881869378855772213960453580061217249480783020696696035876840885085455956209338383778512118755580664646428255992630126345209701050258881976788123467307310998985151947632988381597367\r\n806672853474838986649042845667649801608814982542540167708579363602451863161832294514192152531639403295880691309595875681164480727071726554705231738742597247458209553813931935662611165964001830119731905727556936317212206622424252127264146933\r\n234948161201854478236961405574302312814187899058251977067504848738588174331649798382611086482077246914331377066594802464841290394989558271241643996632941804203459827599955712422941356309040737872828451117187502813562270458751133907018711043\r\n967199267017504597085403171838521775065040784082064520669301199732151002920195409516562242408410668898191011007165295405442804341411511565078632212859598635453773235461208390948925123544987633472769538618008863320897950809614941125093159180\r\n82295889905398334539255752084169893435906377853938549176175688844450070850156522000850535534188375036081267045662130000000\r\nOK',4704,0); INSERT INTO comment VALUES (4714,778,2144,'Ryan','Wait! I have something else!','2003-05-07 18:38:50',0,'According to the grammar, the painter colored \"all of the points\" \"one of three colors\".... that seems like it would imply they are all the same color, and that he had three to choose from. If it had said \"colored each of the points\" it would mean how we\'ve been discussing it. I am reminded of the same error in an old Eurythmics song \"If I had a dollar bill for all the things I\'ve done, there\'d be a mountain of money piled up to my chin\" (paraphrasing)\r\n\r\nLet me know what everyone thinks. Also, there aren\'t enough puzzles being newly posted here.... I think I\'ve solved most of these - is there some way to pick up the pace? I read that there are like 400 pending.\r\n\r\nLater.',NULL,0); INSERT INTO comment VALUES (4715,511,979,'Ravi Raja','re: No. God can...','2003-05-07 19:12:53',0,'If God can carry anything then this will mean that God cannot create Everything Tim. What do you say for that ?',4445,0); INSERT INTO comment VALUES (4716,511,979,'Ravi Raja','re: idea','2003-05-07 19:19:06',0,'But here the question of converting Himself into a human being does not arise at all Jon. What has been asked for are both related to the God only and no human beings. ',4446,0); INSERT INTO comment VALUES (4717,511,979,'Ravi Raja','re(2): idea','2003-05-07 19:23:04',0,'Its all the same David. Even if he is a human being with supenatural powers still both the tasks cannot be performed at the same time. I mean neither is possible.',4448,0); INSERT INTO comment VALUES (4718,511,979,'Ravi Raja','re: What they say','2003-05-07 19:26:00',0,'But Levik this does contradict the OMNIPOTENT characteristic of God. Does\'nt it ? ',4450,0); INSERT INTO comment VALUES (4719,511,979,'Ravi Raja','re: What this proves','2003-05-07 19:29:41',0,'I agree with some of your points Alan.',4451,0); INSERT INTO comment VALUES (4720,511,979,'Ravi Raja','re: My idea','2003-05-07 19:32:34',0,'Yes for what Gamer ? That the Omnipotent God CAN create such a stone ?',4452,0); INSERT INTO comment VALUES (4721,511,979,'Ravi Raja','re(2): Read This','2003-05-07 19:40:04',0,'Hank you said in your comment that: If he does the second, that proves that he did not create an unliftable stone. Meaning that God is wrong. God cannot be wrong. \r\nIn that case what is right? ',4465,0); INSERT INTO comment VALUES (4722,510,2173,'Mark','re: More guesses','2003-05-07 19:45:38',0,'good thinking\r\n',4419,0); INSERT INTO comment VALUES (4723,786,979,'Ravi Raja','Solution','2003-05-07 19:52:13',3,'First Step: The first number is 1, so we leave it as it is and since there is no number before that, we take it as 0. \r\n\r\nSecond Step: Multiply 1 (the first term) by 10 and add 0 to obtain the second term as 10.\r\n\r\nThird Step: Multiply 10 (the second term) by 10 and add 1 (the first term) to obtain the third term as 101.\r\n\r\nFourth Step: Multiply 101 (the third term) by 10 and add 10 (the second term) to obtain the fourth term as 1020.\r\n\r\nFifth Step: Multiply 1020 (the fourth term) by 10 and add 101 (the third term) to obtain the fifth term as 10301.\r\n\r\nSixth Step: Multiply 10301 (the fifth term) by 10 and add 1020 (the fourth term) to obtain the sixth term as 104030.\r\n\r\nSeventh Step: Multiply 104030 (the sixth term) by 10 and add 10301 (the fifth term) to obtain the seventh term as 1050601.\r\n\r\nSo, the general rule is given by:\r\n\r\n\'N\'th Term = 10 times (N-1)st Term added to (N-2)nd Term.',NULL,0); INSERT INTO comment VALUES (4724,513,2148,'Jayaram S','Suggestions','2003-05-07 20:40:24',1,'The corrected sentence to be TRUE could be:\r\n\r\nSuggestion 1: \"This sentence contains five words.\"\r\nSuggestion 2: \"The previous sentence does not contain seven words.\"\r\nSuggestion 3: \"That sentence does not contain seven words.\"\r\n\r\n',NULL,0); INSERT INTO comment VALUES (4725,781,2174,'Vinodhan Selvarajalu','re: solution','2003-05-07 21:12:18',0,'Surely this doesn\'t take into account the 1 mile the boat has to travel back to the campsite (the very same mile the hat travels) OVER AND ABOVE the ten minutes travel time...??',4661,0); INSERT INTO comment VALUES (4726,781,2174,'Vinodhan Selvarajalu','re: General Shortcut Formula','2003-05-07 21:16:07',0,'This has the same problem as Charlie\'s answer...the boat doesn\'t only travel for 10 minutes after the hat...have to also include the 1 mile the hat travelled, and how long the boat takes to cover that',4688,0); INSERT INTO comment VALUES (4727,483,2163,'sendil','re(2): i got it!','2003-05-07 21:21:30',0,'Hi Ravi\r\nI am new in here. Was just wondering if it is ok to use small code pieces to arrive at solutions;particualarly in cases like this where u have to solve hazaar eqn\'s.\r\nAround 12 lines of C-code generates 3121 and 15621.\r\nCheers',3785,0); INSERT INTO comment VALUES (4728,781,2148,'Jayaram S','re(2): General Shortcut Formula','2003-05-08 00:15:54',0,'While he is travellng upstream, remember he is travelling slower when compared to when he is travelling downstream. This can be mathematically wrtten as:\r\n\r\nRelative speed of the boat when travelling u/s = (boat speed - river speed)\r\nRelative speed of the boat when travelling d/s = (boat speed + river speed)\r\n\r\nHence he will cover more distance in 5 minutes travelling d/s compared to the same time travel along u/s. This accounts for the extra distance he covers.',4726,0); INSERT INTO comment VALUES (4729,781,2133,'spinoza','Solution','2003-05-08 00:56:08',0,'Since time difference is independent of frame of reference, in the f.o.r. of the river the hat is stationary while Bob is moving with a constant velocity.\r\nSo the time taken by Bob to recover his hat will be twice that taken for maximum separation with it. \r\nTotal time taken to recover the hat = 2 * 5mins.\r\n= 10 minutes\r\nAs the hat covers a distance of 1 mile in this time interval the river velocity will be .1 mile/min.',NULL,0); INSERT INTO comment VALUES (4730,62,2174,'Vinodhan Selvarajalu','Why 10 inches?','2003-05-08 01:04:09',0,'Just wondering why EVERYONE here assumes the chord is 10 inches when explaining their solutions? Is there something that leads them to that number??? I smell a rat...probably that other problem that\'s similar states a chord length of 10 and people are just transposing??\r\nWhatever...',NULL,0); INSERT INTO comment VALUES (4731,511,2174,'Vinodhan Selvarajalu','The \'Christian\' God','2003-05-08 01:52:47',0,'I find it interesting that this whole debate revolves around the argument of whether God exists as he is described in Christian literature. It is unfortunate that the only reference made is to a single book, namely the Bible. Christians believe so furtively that their take on things is definitive. I wonder; do you (the Christian preachers out there) believe that the rest of the world\'s religions are maybe just an indication that we all haven\'t accepted the \'one true faith\'? Do you perhaps honestly believe that other religious beliefs are \'inferior\' and that soon we will all \'see the light\'? What I am getting at is, by all means quote from the Bible, and relay the messages therein. But don\'t go around believing that one finitely sized book holds all the answers to the universe. Life and faith is about learning and growing in all respects. It should be a dynamic process not constrained by what was put down in paper a few thousand years ago and certainly not proven to be divine. You may challenge that by saying the Bible came from God himself. Can you prove it? It boils down to faith.And I challenge you to prove that one God didn\'t put all the major religious texts on this earth, just for us to be able to grow and learn from all of them and be able to discern the inherent good qualities of each, and in so doing strengthen ourselves instead of relying on a crutch he provided for us.\r\n\r\nAnd with regards to the paradox (just to justify my thoughts under this puzzle)perhaps consider this ( I certainly won\'t claim a definitive answer here). God could create an unliftable stone and then lift it, causing existence as we know it to end, only for it, and by association, him, to be recreated anew. To define \'uncarryable\'(?) is arbitrary-because we cannot claim to know what anything definitively means. \'Uncarryable\' could just mean that if it is carried, all bets are off and can\'t be explained by our (limited) perception of things...Is anything impossible?',NULL,0); INSERT INTO comment VALUES (4732,511,2174,'Vinodhan Selvarajalu','The \'Christian\' God','2003-05-08 01:52:58',3,'I find it interesting that this whole debate revolves around the argument of whether God exists as he is described in Christian literature. It is unfortunate that the only reference made is to a single book, namely the Bible. Christians believe so furtively that their take on things is definitive. I wonder; do you (the Christian preachers out there) believe that the rest of the world\'s religions are maybe just an indication that we all haven\'t accepted the \'one true faith\'? Do you perhaps honestly believe that other religious beliefs are \'inferior\' and that soon we will all \'see the light\'? What I am getting at is, by all means quote from the Bible, and relay the messages therein. But don\'t go around believing that one finitely sized book holds all the answers to the universe. Life and faith is about learning and growing in all respects. It should be a dynamic process not constrained by what was put down in paper a few thousand years ago and certainly not proven to be divine. You may challenge that by saying the Bible came from God himself. Can you prove it? It boils down to faith.And I challenge you to prove that one God didn\'t put all the major religious texts on this earth, just for us to be able to grow and learn from all of them and be able to discern the inherent good qualities of each, and in so doing strengthen ourselves instead of relying on a crutch he provided for us.\r\n\r\nAnd with regards to the paradox (just to justify my thoughts under this puzzle)perhaps consider this ( I certainly won\'t claim a definitive answer here). God could create an unliftable stone and then lift it, causing existence as we know it to end, only for it, and by association, him, to be recreated anew. To define \'uncarryable\'(?) is arbitrary-because we cannot claim to know what anything definitively means. \'Uncarryable\' could just mean that if it is carried, all bets are off and can\'t be explained by our (limited) perception of things...Is anything impossible?',NULL,0); INSERT INTO comment VALUES (4733,781,2174,'Vinodhan Selvarajalu','re(3): General Shortcut Formula','2003-05-08 02:44:58',0,'Yes thanks, I realise after reading all the comments that everyone has taken into account the relative speed of the boat. I read the question as saying he travels at the same speed regardless if he\'s going with the current or not:\"Assume that he travels the same speed the entire time\" . I still say its ambiguous at least (and at worst, poorly worded), but it makes more sense the \'your\' way.',4728,0); INSERT INTO comment VALUES (4734,469,979,'Ravi Raja','re(8): The solution','2003-05-08 04:43:29',0,'Exactly Gamer. You are correct and that I believe clears Charlie\'s doubts. It has been a lobg time since I have gone through these posts so I do not remember what Charlie was finding wrong in the posted solution, but I think it was this only, that how every one is in the same place as before.',4247,0); INSERT INTO comment VALUES (4735,469,979,'Ravi Raja','re(7): The solution','2003-05-08 04:48:07',0,'Yes Charlie. Now I agree with you but if you are considering that way where the narrator is an intermediary, then similarly, I think you can consider any one else too in place of the narrator. The situation would still remain the same. The entire thing can be reduced to a tw-person problem instead of the long chain of people.',4243,0); INSERT INTO comment VALUES (4736,469,979,'Ravi Raja','re(9): The solution','2003-05-08 04:51:51',0,'Yes Gamer. This does show that there were no losses and gains in the entire transaction as everyone got something or the other worth the same amount what he/she owed to the other. But this would not have been true unless a complete circle was formed. That is, the note was back to the narrator.',4248,0); INSERT INTO comment VALUES (4737,469,979,'Ravi Raja','re: umm','2003-05-08 04:53:57',0,'Tristan your reasoning is wrong. Just think over it again. I can also say that the author gained 100 ruppes instead of losing that amount. ',4533,0); INSERT INTO comment VALUES (4738,511,1902,'Hank','re(3): Read This','2003-05-08 05:09:29',0,'God is right. God is always right.\r\nIf God sets out to create an unliftable stone, then it will.\r\nIf God sets out to lift the heaviest stone, then it will.\r\nBut God will not contradict itself, by lifting a stone that it claimed unliftable.\r\n\r\nI guess, the answer to the question posed is yes.',4721,0); INSERT INTO comment VALUES (4739,231,1920,'Brian Smith','Here is my proof','2003-05-08 06:26:33',3,'The set {9, 99, 999, ...} can be expressed as {10^1 - 1, 10^2 - 1, 10^3 - 1, ...} \r\n\r\nChoose any number n coprime to 10 (stated by the problem) and consider the subset {10^1 - 1, 10^2 - 1, 10^3 - 1, ..., 10^(n+1) - 1}. \r\n\r\nThere are at most n unique remainders when the elements of the subset are divided by n. But because there are n+1 elements, there are at least two elements with the same remainder. \r\n\r\nLet 10^y - 1 and 10^x - 1 be two elements with the same remainder with y > x. Then ((10^y - 1) - (10^x - 1)) mod n = 0. \r\n\r\nLet d=y-x. (10^y - 1) - (10^x - 1) = 10^y - 10^x = 10^x * (10^(y-x) - 1) = 10^x * (10^d - 1) \r\n\r\nSince n is coprime to 10, n is a factor of 10^d - 1. \r\n\r\nThis proves there is some member of the set {9, 99, 999, ...} (the dth member) which has n as a factor.\r\n\r\nSince n+1 >= y and y > d, d will never be greater than n.\r\n\r\nThis proves that the number 10^d - 1 is one of the first n terms of the set {9, 99, 999, ...}.\n\nEdited on January 22, 2004, 1:14 pm',NULL,0); INSERT INTO comment VALUES (4740,515,1920,'Brian Smith','{P, r, o, o, f}','2003-05-08 06:55:32',1,'For any set with one element, that element is the least element\r\n\r\nFor any set with two elements, the smaller element is the least element.\r\n\r\nConsider set S {a, b, n1, n2, ... nx} with x+2 (x >= 1)elements. Let c be the smaller of a and b. A new and smaller set T with x+1 elements can be defined as {c, n1, n2, ...nx}. Since c is the smaller of a and b, the least element was not removed which implies the sets S and T have the same least element.\r\n\r\nFor any set R of k elements with k > 2, this argument can be applied k-2 times to create a set of two elements with the same least element as R.',NULL,0); INSERT INTO comment VALUES (4741,801,1947,'Jon','ideas','2003-05-08 07:12:39',3,'there must be some trick in how he laid them down. The first card determines the suit. assuming the cards having designs on the back that aren\'t symetrical, It can be place one of four directions. The remaining three can be used like a base four counting system. It would use four positions up, left, right, down, using the back of the card as a pointer. or I could be way off, but it might work.',NULL,0); INSERT INTO comment VALUES (4742,801,1,'levik','re: ideas','2003-05-08 07:22:46',2,'Hmmm... Usually the standard deck of cards will be completely symmetric, so you will be limited to only 2 positional variations per card: vertical or horizontal. That will give you 16 possible combinations.\r\n\r\nOne more thought - because you are seeing 4 of the 52 cards in the deck, they are eliminated, and there are only 48 possibilities left for card #5.\r\n\r\nProvided you agree on some scheme for enumerating the cards beforehand, your assistant would need to communicate a number between 1 and 48 to indicate what card #5 is.',4741,0); INSERT INTO comment VALUES (4743,801,1947,'Jon','solution corrected','2003-05-08 07:28:18',3,'you are rigt levik, but we only need 13 numbers in a binary counting system. there is another way to get the suit with how you hand the other magician the cards. For the first card, 1 finger and the thumb = hearts, 2 fingers an the thumb = spades and so on with the cards tilted up and down or sideways for a binary system four digits long that will get you 15 numbers. that works for every deck.',4742,0); INSERT INTO comment VALUES (4744,801,1920,'Brian Smith','How i would do it','2003-05-08 07:34:41',0,'Each card in the deck is assigned 1 to 52. Since the magician has 4 of the cards, there are only 48 possible other cards. The assistant hands the magician the cards in one of 24 permutation orders. With just the permutation, the magician can narrow down the card to one of two (48/24=2). The assistant can use his left or right hand when passing the cards to signal higher or lower of the two.',NULL,0); INSERT INTO comment VALUES (4745,801,1947,'Jon','re: How i would do it','2003-05-08 07:37:16',0,'the only problem with this is the audience chooses the cards at random. the magician would have to devise a plan to figure out a permutation midtrick, I can\'t think of one, but I am sure it is possible.\r\n',4744,0); INSERT INTO comment VALUES (4746,801,1920,'Brian Smith','re(2): How i would do it - How it works','2003-05-08 07:49:47',0,'It is a lot of mental math. \r\n\r\nThere are 24 permutations. In order of smallest to largest: 1234, 1243, 1324, 1342, 1423, 1432, 2134, 2143, 2314, 2341, 2413, 2431, 3124, 3142, 3214, 3241, 3412, 3421, 4123, 4132, 4213, 4231, 4312, 4321.\r\n\r\nEach of these are paired to 1 to 24. Example: 3412 is paired to 17. To communicate 17, the assistant would hand the magician the second highest then the highest then the smallest then the second smallest (3412).\r\n\r\nUsing a left hand would indicate add 24 and using the right would indicate add 0. \r\n\r\nAll together, this passes a number 1 to 48 to the magician. All the magician has to do is determine the nth card of the deck excluding the four cards he is holding.',4745,0); INSERT INTO comment VALUES (4747,801,1301,'Charlie','Solution: (I don\'t remember where I saw this but it was in the past year.)','2003-05-08 07:59:47',3,'With 5 cards, at least two must be in the same suit. The first card the assistant hands the magician will be one of these two cards and the one kept hidden will be the other (or one of the others, if more than one). The way to decide which, and the communication of the value depend on the following:\r\n\r\nConsider the Ace low and King high arranged around a 13-position circle, like a clockface except with 13 positions. Two cards from the same suit will have different positions on this imaginary circle. Choose to hand to the magician the one that is shorter to go counterclockwise from the other, which will be the card kept hidden. This way, the hidden card can be 1 to 6 clockwise positions from the one presented.\r\n\r\nThen the remaining three cards can be presented in one of 6 orders. You had to decide on a hierarchy of suits, say spades higher than clubs higher than hearts higher than diamonds, and within these suits, king is high and ace low. This way each of the remaining 3 cards to be presented to the magician can be evaluated as being the high, middle or low card of the set of three. If the order of presentation is LMH, then the hidden card\'s denomination is 1 position counterclockwise from that first presented; LHM means 2 positions; MLH, 3 positions; MHL, 4 positions; HLM, 5 positions; and HML, 6 positions. And of course the suit is the same as the first card presented.\r\n\r\nThis may have been in one of Ivars Peterson\'s MathLand (or is it MathTreks) sites for Science News.',NULL,0); INSERT INTO comment VALUES (4748,511,979,'Ravi Raja','re(4): Read This','2003-05-08 08:03:28',0,'Well then aren\'t you changing the definition of the word Omnipotent. If He can create such a thing then it is clear that He is not all Powerful and if He can lift such a stone, then clearly He cannot create everything. \r\n',4738,0); INSERT INTO comment VALUES (4749,750,1920,'Brian Smith','re(2): The next next number','2003-05-08 08:05:39',0,'How much spare time do you have?!',4713,0); INSERT INTO comment VALUES (4750,511,979,'Ravi Raja','re(4): Read This','2003-05-08 08:10:11',0,'I never said that God is wrong, but in this problem, I think God cannot be right too. Well whatever, the answer can never be Yes.',4738,0); INSERT INTO comment VALUES (4751,801,1902,'Hank','Hows dis?','2003-05-08 09:07:32',0,'The first card that the assistant hands the magician is the same suit as the hidden card (there are five cards so one must be the same)\r\n\r\nNow you\'ve narrowed down the feild to 13. Actually 12 because you know one that it definately isn\'t.\r\n\r\nthe remainig three cards can be used to determine the card ranking from 1 to 12 using four possible placements: Verticle and face up, horizontal and face up, vertical and face down, and horizontal and face down.',NULL,0); INSERT INTO comment VALUES (4752,801,1,'levik','re: Hows dis?','2003-05-08 09:17:59',0,'Now that i think about it, since it\'s supposed to be a \"magic\" trick, the assistant is probably not able to carefully lay out the cards - that would be too obvious.\r\n\r\nIt\'s probably OK to do something as non-obvious as passing the four cards (in one mini-deck) either all face up or face down - the audience will probably not see any meaning in that, but if the assistant lays out the four cards all in different manner it may be suspicious.',4751,0); INSERT INTO comment VALUES (4753,315,2180,'Cara','I finally get it!','2003-05-08 09:27:52',0,'I thought he was looking at a picture of a step brother, as in I have no full blood brothers and sisters, but the person in the picture, is his stepbrother, because they have the same father, yet are not true full blood brothers.\r\nBut I finally get it after seriously thinking about the solution after reading it. It\'s his son! \r\nThis is a good one.',NULL,0); INSERT INTO comment VALUES (4754,360,2180,'Cara','OMG! I know this without looking at the solution!','2003-05-08 09:34:41',3,'NOTHING!\r\nhahaha. I heard this one a long time ago, but couldn\'t remember what it was, and I was thinking, and finally it just hit me... I feel so smart. lol. :)',NULL,0); INSERT INTO comment VALUES (4755,502,2166,'Chris','And is for fractions','2003-05-08 09:34:54',0,'I believe the answer is \"one thousand.\" As for an explanation of why 101 is not correct:\r\n\r\nI was taught that the \"and\" in spoken numbers represents the decimal point. To say \"one hundred and one...\" is missing a place value.\r\n\r\nThe only way to complete the phrase correctly would be, for example, \"one hundred and one tenth,\" which of course is written 100.1\r\n\r\nSo we see that the word \"and\" never appears in the written or spoken representations of any cardinal numbers!',NULL,0); INSERT INTO comment VALUES (4756,501,2170,'Alex','Another possible solution','2003-05-08 09:48:57',0,'I was thinking knats. I\'ve never seen them in the day and you don\'t really fetch them at night but they come anyway.',NULL,0); INSERT INTO comment VALUES (4757,786,2180,'Cara','I had a cool theory','2003-05-08 09:58:53',1,'I just read Ravi Raja\'s solution and that is very smart. \r\nMy solution I came up with was more simple.\r\nWriting each number on a line I saw:\r\n1\r\n10\r\n101\r\n1020\r\n10301\r\n\r\nMy theory was that the first number stayed as a 1, the next one stayed a 0, the next line, always went up by 1 digit, the next line stayed as 0, the next line startd up again with 1, so my way to continue it was:\r\n\r\n104020\r\n1050301\r\n\r\nI still say it works. :) Even if it is less mathematical.',NULL,0); INSERT INTO comment VALUES (4758,786,1920,'Brian Smith','re: I had a cool theory','2003-05-08 10:02:17',0,'It certainly does work. Good job.',4757,0); INSERT INTO comment VALUES (4759,19,2180,'Cara','A long pondered question','2003-05-08 10:30:11',0,'I heard this riddle years ago, and the book I saw it in DIDN\'T print the answers. I never figured it out, but now I get it! I can\'t believe I never figured it out myself. It really is quite simple.',NULL,0); INSERT INTO comment VALUES (4760,304,2130,'ethan','easy','2003-05-08 10:51:19',3,'0%. any number whose digits\' sum is a multiple of three is divisible by three, making it not prime. 1+2+3+4+5+6+7+8+9=45, a multiple of three.',NULL,0); INSERT INTO comment VALUES (4761,469,2180,'Cara','Too easy','2003-05-08 11:04:13',0,'I thought this one was a little too easy.',NULL,0); INSERT INTO comment VALUES (4762,794,2182,'katey','Solution','2003-05-08 11:04:13',0,'Well assuming every person has 5 fingers on their left hand, you simply take 5,000,000,000 * 5 and the product is 25,000,000,000 . Pretty simple. If I got that, which I\'m positive is correct, and i\'m only a 7th grade level 1 math student, then there\'s no excuse for the rest of you! hehe :)',NULL,0); INSERT INTO comment VALUES (4763,801,2166,'Chris','re(3): How i would do it - How it works','2003-05-08 11:44:01',1,'I like the idea, Brian, but a couple of problems:\r\n\r\n1) What if the audience chooses two or more cards of the same value (i.e.: a pair of 3\'s)? I suppose the numbering of the deck could be absolute, such as 1 of clubs = 1,\r\n1 of diamonds = 2, 1 of hearts = 3 ...) this way if the 3h came before the 3d then he would know that to be high then low.\r\n\r\n2) The magician would have to mentally remove the 4 cards he is given from his numbering system, so that each time he does the trick the some of the cards will have different values (so if the audience chose 3c, 7d, 10s, Kh then the 5h becomes 19-1=18, the Qc becomes 45-3=42, etc. (assuming Aces low for ease of computation)).\r\n\r\n3) As you said, it would be a lot of mental math. While this works perfectly with pencil and paper and no audience, it becomes very difficult to do on stage as a magic effect. It runs the risk of either taking to much time to be effective, or worse, causes people to be suspicious of how the trick is really done.',4746,0); INSERT INTO comment VALUES (4764,515,103,'friedlinguini','re: {P, r, o, o, f}','2003-05-08 11:54:36',0,'The proof doesn\'t work.\r\n\r\nImagine that the problem referred to all integers rather than positive ones. Your proof does not use the fact that all the integers are positive. However, it is not the case that every set of integers has a least value. The set of even integers is one counterexample.',4740,0); INSERT INTO comment VALUES (4765,801,1626,'Gamer','Restrictions','2003-05-08 12:01:30',0,'Wouldn\'t the audience be suspicious if you handed the cards to the magician in a wierdo way? (like sideways or faceup or like that) I liked Bryan\'s solution.',NULL,0); INSERT INTO comment VALUES (4766,515,1626,'Gamer','re(2): {P, r, o, o, f}','2003-05-08 12:09:07',3,'I can find a counterexample. {2,2,3} doesn\'t have a least element, it has two equally least elements.\r\n\r\nIf you allow equally least elements, I can use the law of indirect reasoning.\r\n\r\n(Unless all elements are the same, in which all of them are equally least) Assume there wasn\'t a least element (or least elements). This means that each number has a number in that set that it is greater than. Eventually you will create a \"circle of greater thans\", and this can be proven as a contradiction by the transitive law of inequality. So this means there must be a least element (or least elements)\r\n\r\nIs that a good solution?',4764,0); INSERT INTO comment VALUES (4767,801,775,'Cory Taylor','my solution','2003-05-08 13:58:51',0,'people are making this too difficult - you\'re not trying to determine a card from the entire deck, you\'re trying to determine the easiest of five cards from the deck.\r\n\r\nSo yes, the first card can surely nail the suit of the target card, as the assistant will chose a card that has a duplicate suit to be guessed (or for repeat showings, a certain suit could mean the target card is a certain other suit to more easily camoflage the method).\r\nThis leaves only 12 cards to choose from, which can be narrowed down easily enough with the three remaining cards, with a number of methods, some of which presented before me....',NULL,0); INSERT INTO comment VALUES (4768,515,103,'friedlinguini','re(3): {P, r, o, o, f}','2003-05-08 14:14:54',0,'Sets, by definition, don\'t contain duplicates.\r\n\r\nMy argument against Brian Smith\'s answer also works against this one. The problem is that sets can be infinite in size.',4766,0); INSERT INTO comment VALUES (4769,7,2184,'mark hartman','My first answer','2003-05-08 19:27:02',0,'The answer is 1/3. The statement that at least one shows a tail reduces the original sample space of four outcomes to the following three: TH, HT, TT. Of these, only TT meets the second condition.',NULL,0); INSERT INTO comment VALUES (4770,513,1304,'Emon Hunte','What\'s so difficult','2003-05-08 19:44:44',3,'No one ever said that since the first statement is false the second one has to be true. This is a bunch of mumbo-jumbo trying to confuse the reader. The fact is the second one is in fact false as well. The sentence DOES have 7 words and therefore the statement is false. I could careless that a first statement even existed.\r\nAnd they say \"we correct the sentence\" which they don\'t. If they wanted to correct the sentence it would read \"This sentence obviously does contains seven words\".',NULL,0); INSERT INTO comment VALUES (4771,801,2186,'Steve','my solution','2003-05-08 20:22:05',0,'the first card is used to establish suit ebing that at least two of the cards have the same suit. after that the assistant hand the next card over either using two fingers opposite the thumb or one. One indicates the value of the card is A-7, two indicates 8-K. this process is repeated with the next card again roughly splitting the remaining 6 or 7 cards. the last card might be difficult in that the assistant may have to use all four fingers opposite thumb if the card is the seven.',NULL,0); INSERT INTO comment VALUES (4772,515,979,'Ravi Raja','re(2): {P, r, o, o, f}','2003-05-08 20:50:56',0,'Fried: How can you say that the set of even integers is a counterexample ?',4764,0); INSERT INTO comment VALUES (4773,515,979,'Ravi Raja','re(3): {P, r, o, o, f}','2003-05-08 20:55:03',0,'This is no counterexample Gamer. Just go through the definition of \"SET\" and then think if {2,2,3} is a SET or not.',4766,0); INSERT INTO comment VALUES (4774,515,979,'Ravi Raja','re(4): {P, r, o, o, f}','2003-05-08 21:00:54',0,'Yes Fried sets can be infinite in size and we know that the set of positive integers is an infinite set with 1 as its least element.',4768,0); INSERT INTO comment VALUES (4775,513,979,'Ravi Raja','re: This is not That','2003-05-08 21:05:37',0,'Sanjay: How can you say that the second statement is False?',4708,0); INSERT INTO comment VALUES (4776,513,979,'Ravi Raja','re: Suggestions','2003-05-08 21:11:23',0,'Yes Jayaram: \"That sentence does not contain seven words.\" is indeed true but what about the sentence : \r\n\"This sentence does not contain seven words.\" ?\r\n\r\n\r\n',4724,0); INSERT INTO comment VALUES (4777,483,2148,'Jayaram S','One-line Simple Solution','2003-05-08 21:37:23',0,'General Shortcut formula: (for Case (a) only:\r\n)\r\nAnswer = {n^(n+1) - (n-1)}, where n = number of people\r\n\r\nExample 1: n = 5\r\nAnswer = 5^6 - 4 = 15625 - 4 = 15621\r\n\r\nExample 2: n = 4\r\nAnswer = 4^5 - 3 = 1024 - 3 = 1021\r\n\r\nExample 3: n = 3\r\nAnswer = 3^4 - 2 = 81 - 2 = 79\r\n',NULL,0); INSERT INTO comment VALUES (4778,513,2148,'Jayaram S','re(2): Suggestions','2003-05-08 21:47:49',0,'Ravi, \"This sentence does not contain seven words\" will be obviously FALSE. My suggestions were if the second statement were to be TRUE.',4776,0); INSERT INTO comment VALUES (4779,451,2148,'Jayaram S','General Short Cut Formula','2003-05-08 23:47:15',3,'Let the number be n-1, n & n+1.\r\n\r\nThen, n = sqrt{(∑Q + 1) / 3) always.\r\n\r\nIn this case ∑Q = 74.\r\n\r\nHence n = sqrt{74 + 1) / 3) = sqrt (75/3) = sqrt(25) = ±5.\r\n\r\nHence the numbers are 4,5,6 OR -6,-5,-4',NULL,0); INSERT INTO comment VALUES (4780,515,103,'friedlinguini','re(3): {P, r, o, o, f}','2003-05-09 01:55:35',0,'It\'s a counterexample that invalidates Brian Smith\'s proof. His reasoning could apply just as easily apply to all integers as simply positive integers. However, the set of even integers is contained in this domain, but has no least element. Thus, the proof fails.',4772,0); INSERT INTO comment VALUES (4781,483,979,'Ravi Raja','re(3): i got it!','2003-05-09 04:10:10',0,'Sendil: Can you please write down the 12 lines of the C-Code using which you have solved the problem? Similar solution has been provided by some other user too, I mean using programming.\r\nSo it doesn\'t matter if you solve it using C-Code or hazaar equations. :)\r\n',4727,0); INSERT INTO comment VALUES (4782,483,979,'Ravi Raja','re: One-line Simple Solution','2003-05-09 04:18:08',0,'Okay Jayaram I can agree that the formula is correct but the question is how did you arrive at the formula. Please show the steps. ',4777,0); INSERT INTO comment VALUES (4783,469,979,'Ravi Raja','re: umm','2003-05-09 04:29:43',0,'I can also say Tristan that the person paid his plumber\'s bill using a fake 100 rupee note and so he gained 100 Rupees and did not lose that amount. ',4533,0); INSERT INTO comment VALUES (4784,469,979,'Ravi Raja','re: umm','2003-05-09 04:35:46',0,'tristan: If I say that the person who fopund the note paid his plumber that note instead of clearing his bill with a genuine one thus gaining 100 rupees and at the same time as the lady was supposed to pay him his 100 rupees cleared the debt with that counterfeit note so the author loses 100 rupees and therefore the net loss is 0 (zero). \r\nWell in my next comment I have shown that the author gained 100 rupees just the same way you say that he lost the same.\r\nRead and think what exactly is the case.',4533,0); INSERT INTO comment VALUES (4785,806,1301,'Charlie','Solution?','2003-05-09 04:40:45',3,'For part (a), the termite could start in the middle cube of the top face, then go to a neighboring cube on that face and proceed in a clockwise spiral, ending up at a corner cube on the top face. The termite then goes straight down to what was the second level from the top and spirals inward ending up at the center, at which point he goes down to the center of what had been the middle level. This level is done spiralling outward like the top, and the next level is again done spiralling inward like the second level from the top. The bottom is done spiralling outward from the center again.\r\n\r\nFor (b) we can only assume that eating the central internal cube last allows for the fact that that cube is going to be unsupported at a certain point in the progress of the eating, and therefore no longer in position.\r\n\r\nA way for the termite to proceed in this instance could be to spiral out along the top face as before, and then go down to a corner of the second level. This time instead of spiralling in to the center, go from left to right on one row of what was the second level, then right to left, left to right, right to left and finally left to right, ending up at the diagonally opposite corner of what originally was the second level from the top.\r\n\r\nThen proceed down to what was the middle level, at that corner, and spiral in, but don\'t consume the center. Instead go down to the next level at a position adjacent to the center cube. Go out toward the edge (away from the center) and then proceed clockwise around the outside. When the last cube on the outer edge is done, come back to the set surrounding the central cube of this originally 4th level and complete its consumption in a U-path, finishing on a cube that\'s diagonally adjacent to the center cube, so that now, on the 3rd and 4th levels the center cube is still intact. \r\n\r\nProceed down to the bottom level. Go away from the center again, which places you one unit away from a corner. Proceed to that near corner and then continue to proceed around the outer cubes of that level until again forced to go one in, and reverse direction around the central cube. What\'s left is a column of the center cubes of the mid to bottom levels. Eat upward so that the central cube of the large cube is last. At some point the column will probably topple, but keep eating anyway.',NULL,0); INSERT INTO comment VALUES (4786,513,979,'Ravi Raja','re(3): Suggestions','2003-05-09 04:42:47',0,'How can you say that: \"This sentence does not contain seven words\" is True when in the statement we are using the words \"DOES NOT\" ??',4778,0); INSERT INTO comment VALUES (4787,801,1947,'Jon','try this','2003-05-09 06:33:23',0,'what if the magician were to get all four cards face down and was just handed them with the face towards the audience. Is this trick still possible. My solution works, but it is really clumsy. Anyone else have any ideas?',NULL,0); INSERT INTO comment VALUES (4788,806,1947,'Jon','yummmm','2003-05-09 06:49:02',0,'If the work ate the first face by spiraling out, then eating down one square, then eating the rows of the next layer back and forth, crossing the layer and ending at an opposite corner. The worm could eat down one again and then eat a spiral around the third layer, also the original center layer, not eating the very center cube, instead stoppiong on one adjacent to it, eat down again, eat in a spiral fashion that did the revers of the previous layer, ending him at the corner of the layer, down one, a full spiral inside to the center, eat up the last to cubes straight up and end at the center cube in the center layer.',NULL,0); INSERT INTO comment VALUES (4789,794,1947,'Jon','re: Solution','2003-05-09 06:57:13',0,'thats not right, he isn\'t asking how many left hand fingers, he is asking how much is 5*5*5*....... or 5^5,000,000,000 which is alot more, but I don\'t think it is all that hard really, just look at brian smith\'s first answer, he was right and at least a couple o fus got the same thing, (which is 0, but we won\'t go there) :)',4762,0); INSERT INTO comment VALUES (4790,511,1947,'Jon','re(5): Read This','2003-05-09 07:00:11',0,'more blasphemy, :) this problem just affects everyone a little different, I think I am going to use it as a disscussion in the sunday school class I teach. thanks guys.',4750,0); INSERT INTO comment VALUES (4791,511,1947,'Jon','re: The \'Christian\' God','2003-05-09 07:02:19',0,'wow, you guys really are incredible thinkers, thank ummmm..... God this isn\'t a debate team, lol',4731,0); INSERT INTO comment VALUES (4792,827,1919,'Lewis','ok then.....','2003-05-09 08:56:48',4,'this makes absolutely no sense to me at all - anybody want to explain what { and ^ mean?!?',NULL,0); INSERT INTO comment VALUES (4793,827,1947,'Jon','re: ok then.....','2003-05-09 09:04:05',0,'{ is a symbol holding a set in, or in this case, a related dunch of numbers or functions. ^ means to the power of, 3^2=9. As for the attributes discription, umm........ give a few years and I might have the start of a guess.\r\nIt might have to do with the volumes, areas, and edge length of an eight sided figure or something, but thats just me pulling stuff out of the blue.',4792,0); INSERT INTO comment VALUES (4794,827,1920,'Brian Smith','First guess....','2003-05-09 09:17:38',0,'My first guess:\r\n{verticies on a cube, \r\n total length of edges on a cube of edge length n, \r\n total surface area of a cube of edge length n, \r\n area of a face of a cube of edge length n, \r\n length of an edge of a cube}',NULL,0); INSERT INTO comment VALUES (4795,390,1947,'Jon','another answer','2003-05-09 09:20:28',0,'coal seems the obvious cj=hoice, but what about a black and white photograph, starts off black, then turns red (due to the red light in most developing rooms while in use), and a grayish color when done.',NULL,0); INSERT INTO comment VALUES (4796,469,1947,'Jon','my previous solution...','2003-05-09 09:29:04',0,'I haven\'t rechecked this problem for a while, but Ravi in reponse to your question, here is the reason behind all profit. All of them start off in debt to someone else. Even if people owe them money, that can\'t be counted as tangible value because no one can for sure say that they are going to be payed back due to bankruptsy and such things. So each person then loses a 100 rupee debt that they could be forced to pay, because if they don\'t go bankrupt then the court could force the to pay it, and actually pay it with nothing. It wouldn\'t matter if the note was real, except then the person speaking would actually make 200 due to the true value of the rupee. Its just how you veiw the owing someone money thing, I never expect to get paid back if I give them money because it might not happen even to the most reliable people.',NULL,0); INSERT INTO comment VALUES (4797,827,1947,'Jon','re: First guess....','2003-05-09 09:39:52',0,'thats what I thought, but I couldn\'t figure out what 12n and 6n^2 were. You are right.',4794,0); INSERT INTO comment VALUES (4798,827,1626,'Gamer','Question about question','2003-05-09 09:52:26',4,'If two points are 0 apart from eachother, doesn\'t it mean they are the same point? If you used distance formula and it came out 0, it would mean they were the same point. So wouldn\'t the first set be {1, 0, 0, 0, 0} since all the verices are the same point?',NULL,0); INSERT INTO comment VALUES (4799,686,2130,'ethan','good one, gautam','2003-05-09 17:09:45',0,'He saw a group of crows, which is also called a murder.( and no, i didnt look at a different answer.)',NULL,0); INSERT INTO comment VALUES (4800,794,2189,'Michelle','That\'s something most ppl don\'t think about lolz','2003-05-09 18:04:47',0,'Hmm, brian smith is good . . . but if assuming everyone on earth had a left hand, i\'d say somewhere between 37184362478327425 and 46542345984347350. You\'re right, I have no idea what I\'m talking about.',NULL,0); INSERT INTO comment VALUES (4801,827,1253,'Brian Nowell','re: First guess....','2003-05-09 21:13:00',2,'Hey! This is a fine interpretation of the data given and certainly fits the generalisation, however this does not describe my scenario.\r\n\r\nYes, 8 are for vertices. \'n\' describes the \'order\' of the cube to which these attributes apply. In terms of edge length, \'n\' is actually n+2 units. ',4794,0); INSERT INTO comment VALUES (4802,789,1253,'Brian Nowell','Agreement','2003-05-09 21:26:53',0,'Solutions posed are quite explicit',NULL,0); INSERT INTO comment VALUES (4803,827,1919,'Lewis','re(2): ok then.....','2003-05-09 21:38:44',0,'hmm... I pretty much understand now. Thanks :)',4793,0); INSERT INTO comment VALUES (4804,26,2192,'O','re: inconsistent climber','2003-05-09 22:10:56',0,'I feel like the wording of this problem can change the answer based on the interpretation of the piece, \"same *point* during both days\". \r\n\r\nFirst, I believe that there is a general assumption that the climber used the same trail both days. With that assumption, then we move to the next variable in the question: (same point) If we believe that the phrase \"same point\" is a LOCATION, not time relevant, then the climber would be at the same location and the same altitude at any given point in each of the respective climbs. (Picture: draw a line and retrace it following it in reverse) At any point in the line it is on the exact spot of the first line drawn. \r\n\r\nHowever, if the phrase \"same point\" is in reference to TIME during each of the trips, then assuming that the climber is inconsistent we cannot pinpoint an exact spot in which the climber will be at the same altitude at the same time on each of the days. We would have to assume the the mountain climber was traveling at the same speed, CONSISTENT, traveling up and down the mountain. And, because the climber is not climbing at the same speed, it is not possible.',NULL,0); INSERT INTO comment VALUES (4805,26,2192,'O','regarding my previous posting','2003-05-09 22:15:57',0,'I retract my the second half of my comment. -My bad\r\n',NULL,0); INSERT INTO comment VALUES (4806,513,2193,'Berry','No Paradox Present','2003-05-10 02:28:02',0,'Both statements are false.\r\nThere is no reason why both must be true or both must be false; they are two separate sentences.',NULL,0); INSERT INTO comment VALUES (4807,672,2193,'Berry','Chaz, and What Could Happen','2003-05-10 02:36:08',0,'Chaz:\r\nYou are basically negating the entire existence of the word \'Destroy\'.\r\n\'Destruction\' can be the molecular separation of an object, not necessarily the elimination of its matter\'s existence.\r\n\r\nWhat could happen is that the blacksmith which forges swords kills the other blacksmith without even touching the shield; the blacksmith with the shield would not necessarily be able to block every attack, and I find it more likely that the sword would kill more effectively than the shield.',NULL,0); INSERT INTO comment VALUES (4808,431,2193,'Berry','Not Clear','2003-05-10 02:45:49',0,'\"on the left of\" could be misinterpreted for \"directly left of\".',NULL,0); INSERT INTO comment VALUES (4809,263,2193,'Berry','Old Stupid \'Paradox\'','2003-05-10 02:53:10',0,'There is nothing wrong with the situation.\r\n\r\nObviously, even though Achilles does have to keep moving, the time it takes him to do so after passing the first half is half the time it took to pass the previous half.\r\n\r\nLet the total distance be 10m, and the speed be 1m/s.\r\nTime taken = 5/1 + 2.5/1 + 1.25/1 + ... + 1/(1 * infinity)\r\nTime taken = 10 seconds\r\nIf you were to say Achilles needed to run an infinite amount of evenly spaced segments, the time that he would take to run each segment would be (1/infinity)/speed = speed/infinity = a finite value.',NULL,0); INSERT INTO comment VALUES (4810,263,2193,'Berry','re: re: Why is this a paradox?','2003-05-10 03:00:41',0,'Adam, it is not even a paradox mathematically.\r\nAs Chris used the term \'time frame\', there is no reason why Achilles could catch up with the Tortoise, as if his segments are spaced as shown (one half of the other), it takes him half as long to complete each segment as he took to complete the last segment.\r\n\r\nThe distance is finite. Let the distance be 1.\r\nSpeed = Distance / Time:\r\nSegment 1: 1 = (1/2) / (1/2)\r\nSegment 2: 1 = (1/4) / (1/4)\r\nSegment 3: 1 = (1/8) / (1/8)\r\nSegment 4: 1 = (1/16) / (1/16)\r\n...\r\nSegment n: 1 = (1/(2^n)) / (1/(2^n))\r\n\r\nHere, we can see that Achilles retains a constant speed.\r\nWe can consider the entire track as one segment, and as Time = Distance / Speed:\r\n\r\nTime = 1 / 1\r\n = 1\r\nThe time taken is finite.',3020,0); INSERT INTO comment VALUES (4811,786,2196,'Silly Jilly','Dunno','2003-05-10 05:31:13',4,'I dunno the answer.',NULL,0); INSERT INTO comment VALUES (4812,786,2196,'Silly Jilly','I think...','2003-05-10 05:38:39',0,'...104030,1050601.',NULL,0); INSERT INTO comment VALUES (4813,732,2196,'Silly Jilly','This might be it.','2003-05-10 05:49:15',3,'Drew cannot be a knight,because he would be lying.\r\nTherefore,Drew is a liar,and so they are not both liars,and so Mohammad is a knight.',NULL,0); INSERT INTO comment VALUES (4814,722,2193,'Berry','re: another solution','2003-05-10 05:55:51',0,'Jon, this simpler solution was actually the one I first devised in 1 minute.',4020,0); INSERT INTO comment VALUES (4815,344,2193,'Berry','My Original Helium Solution','2003-05-10 06:02:03',0,'My original idea that I came up with in 15 seconds was to put a helium balloon into the barrel.\r\n\r\nIf the barrel has a lid, the balloon can have enough upwards displacement force to counterbalance the weight of the lid, but no more.\r\nThis will make the total weight less.\r\n\r\nIf the barrel has no lid, the ballon can be stuck to the side of the barrel with tape or nailed by the balloon\'s inflated mouthpiece to the inner side of the barrel.\r\n',NULL,0); INSERT INTO comment VALUES (4816,513,2129,'Sanjay','re(2): This is not That','2003-05-10 06:14:59',0,'Because, dear Ravi, I can both read AND count.',4775,0); INSERT INTO comment VALUES (4817,518,1626,'Gamer','Solution','2003-05-10 06:47:58',3,'I got 36 miles per hour as the slow train\'s speed.\r\n\r\nIf point Z is where they meet when one is late then:\r\n\r\n\r\na) If the slow train leaves 5 minutes late, they meet more towards where the slow train was.\r\n\r\nSince the fast train has to make up the extra 2 miles from M to Z, the slow train has to be half that distance, or 1 mile from Z when the fast train passes M, Since the slow train is 3 miles from M when it is going 5 minutes late, it must go 3 miles in 1/12 hour, or 36 miles per hour.\r\n\r\n\r\nb) If the fast train leaves 5 minutes late, they meet more towards where the fast train was.\r\n\r\nUsing the same reasoning, the slow train makes up the extra 2 miles, so the fast train must be 4 miles from point Z when the slow train is at M. Since the fast train is 6 miles away when it leaves 5 minutes later, it travels 6 miles in 1/12 hour, or 72 miles per hour. This means the slow train moves half this fast, or 36 miles per hour.\r\n\r\nThese are the same solution, so there is only one solution: The slow train\'s speed is 36 miles per hour.',NULL,0); INSERT INTO comment VALUES (4818,518,2144,'Ryan','My thoughts','2003-05-10 07:04:56',0,'Okay. If the fast train is delayed, then it\'s five minutes from the meeting point when the slow on reaches it. The slow one will go 2 miles toward the fast one (away from point M) and the fast one will go 4 miles (twice as far, because it\'s going twice as fast) in the same time. That means the fast train was six miles from point M, and could cover that six miles in 5 more minutes. 6 miles in 5 minutes is 72mph, so the slow train is going 36.\r\n\r\nJust as a check, say the slow train was delayed. Fast train is at point M, and slow one is 5 minutes from there. Fast train advances 2 miles from point M while slow train advances 1 mile, so the slow train was 3 miles from point M. 3 miles in 5 minutes is 36mph, so the fast train is going 72mph.',NULL,0); INSERT INTO comment VALUES (4819,518,2129,'Sanjay','Slow Train Coming','2003-05-10 07:54:17',4,'Wonder if there is a unique solution (with the same data) if the two trains are moving in the same direction, i.e., if the slow train is pulling away from the fast train and the fast train is catching up on the slow train. \r\n\r\nHaven\'t worked it out yet, but just wondering.',NULL,0); INSERT INTO comment VALUES (4820,518,1947,'Jon','solution','2003-05-10 08:15:39',0,'a=2b\r\n5a=2\r\n10b=2\r\nb=5 mph\r\nthis is if the faster train left late\r\nthere has to be something wrong with my logic, but there is my answer\r\na=2b\r\n5b=2\r\nb= 0.4 mph\r\nthis is incase the slower train left late.',NULL,0); INSERT INTO comment VALUES (4821,827,1947,'Jon','re(2): First guess....','2003-05-10 08:19:55',0,'if n+2 is the edge length, then what does n^2 have to do with anything',4801,0); INSERT INTO comment VALUES (4822,518,1947,'Jon','re: solution','2003-05-10 08:27:46',0,'just forget I wrote that, I found my own reasoning gaps',4820,0); INSERT INTO comment VALUES (4823,518,2198,'Max','','2003-05-10 09:50:53',1,'The time difference of 5 min causes the two trains meet at 2 miles farther travelling at a relative speed of v+2v=3v\r\nThen 3v=2miles/5mins then v=8 miles per hour',NULL,0); INSERT INTO comment VALUES (4824,518,1567,'Bryan','What if it\'s not miles per hour?','2003-05-10 13:21:54',3,'Train A travels at x mph, and B travels at 2x. When they leave at the same time and travel for time t, they meet at point M.
If A leaves 1/12 hour (five minutes) late, then at time t, B is at point M and A is x/12 miles away. Since B travels twice as fast as A, they will meet at a point x/12 * 2/3 miles away, which is 2 miles.
2x/36=2
x=36 mph.
If, instead, B leaves 1/12 hour late, then at time t, A is at point M and B is 2x/12 miles away. Since A moves half as fast as B, they will meet 2x/12 * 1/3 miles\r\naway.
The math works out the same as before, so regardless of which train leaves five minutes late, the slow train travels 36 mph.
If miles per hour had not been specified, the answer in alternate units includes 78.795 microparsecs/millennium, or 96,768 furlongs/fortnight :)\r\n',NULL,0); INSERT INTO comment VALUES (4825,794,2199,'ashley','fingers','2003-05-10 13:22:17',0,'Now, unless I\"m wrong, the problem asks for fingers, so wouldn\'t the problem have something to do with 4 instead of 5? Most people (taking into account the one person who won\'t have any) have 4 fingers and 1 thumb therefore, 4 fingers',NULL,0); INSERT INTO comment VALUES (4826,518,1626,'Gamer','re:','2003-05-10 13:32:48',0,'The flaws I saw are:\r\n\r\nOne travels 2 miles farther, and one travels 2 miles less. So you can\'t use 2 miles for both, you need a -2 for one.\r\n\r\nAnd 5 minutes only applies to one. The other one doesn\'t leave 5 minutes late; it leaves on time...\r\n\r\nDid you check your answer?',4823,0); INSERT INTO comment VALUES (4827,518,1626,'Gamer','re: What if it\'s not miles per hour?','2003-05-10 13:34:01',0,':) That\'s fun!\r\n\r\nHow many miles are in a microparsec?',4824,0); INSERT INTO comment VALUES (4828,518,1567,'Bryan','re(2): What if it\'s not miles per hour?','2003-05-10 13:37:54',0,'I had it all worked out, but right now I don\'t have my notes with me. A parsec is approximately 3.26 lightyears, so ...
lol',4827,0);
INSERT INTO comment VALUES (4829,510,2199,'ashley','2 and 3','2003-05-10 13:43:49',0,'I\'m guessing the 2nd is a piggy bank and the third is the money you spend. But I have no clue as to the first one',NULL,0);
INSERT INTO comment VALUES (4830,513,2199,'ashley','possible solution to ponder','2003-05-10 13:55:45',0,'If you look closely at the first sentence it does in fact contain 7 words...\r\n\r\nThis (1) sentence (2) contains (3 and 4) seven (5) words (6 and 7). \r\n\r\nBeing a scrabble fan I know that contain is a word and contains is a different word...same arguement for word(s). So i feel the 1st statement is true. \r\n\r\nFollowing this same principle...the second sentence is TRUE. This(1) sentence (2) does (3) not(4) contain (5) seven(6) words (7 and 8) because in fact...it contains 8 words not 7.\r\n\r\njust a guess :)',NULL,0);
INSERT INTO comment VALUES (4831,518,2130,'ethan','answer','2003-05-10 14:08:14',0,'36mph. they cross at 2 miles from point m. Say the faster train was late. so in the time it took the slower train to go the two mile mark from the point m, the faster train traveled 4 miles to the 2 mile mark, making it six miles from point m. if it can travel 6 miles in the five minutes it was late, then it can travel 72 miles in an hour. so the slower train had to be 36 mph. it works when the slower train is late too, i checked.',NULL,0);
INSERT INTO comment VALUES (4832,794,2130,'ethan','what the answer should be if its not','2003-05-10 14:13:04',0,'zero. some people don\'t have a left hand, and anything times zero is zero',NULL,0);
INSERT INTO comment VALUES (4833,806,1304,'Emon Hunte','Logic?','2003-05-10 15:04:23',1,'Doesn\'t this belong in the math or shapes section of this site. Not really a logic problem now is it?',NULL,0);
INSERT INTO comment VALUES (4834,510,1304,'Emon Hunte','better solution then the solution.','2003-05-10 15:11:06',3,'What about when installing the stove it has to be picked up sometime to be moved. And why a stove? Wouldn\'t a fireplace make more sense! Cause a fireplace can be assemled but at that point it\'s just a pile of bricks not a fireplace. Only once errected does it become a fireplace. And then it never gets up! Yup Im changing the solution. Mine makes more sense. Fireplace, Fire, and Smoke.',NULL,0);
INSERT INTO comment VALUES (4835,500,1304,'Emon Hunte','Easy solution','2003-05-10 15:15:52',3,'It\'s suicide.',NULL,0);
INSERT INTO comment VALUES (4836,467,1304,'Emon Hunte','Stupid answer','2003-05-10 15:19:24',1,'What a dumb solution. In the riddle, it states morning, afternoon and evening. Not young age, middle aged, and old age. The answer should be over the course of one day not a lifetime!',NULL,0);
INSERT INTO comment VALUES (4837,315,1304,'Emon Hunte','omg easy','2003-05-10 15:20:34',3,'He\'s looking at HIMSELF!',NULL,0);
INSERT INTO comment VALUES (4838,315,1304,'Emon Hunte','The solution is wrong!','2003-05-10 15:30:11',3,'Using the word \"my\" is understood by most people as the guy looking at the picture. Considering its the guy looking at the picture saying it. Therefore he\'s talking about HIS FATHER! In turn he must be looking at a picture of himself! Your solution makes no sense. ',NULL,0);
INSERT INTO comment VALUES (4839,315,1304,'Emon Hunte','re: NOT Himself,selfish self,but his son,selfish son','2003-05-10 15:40:23',1,'Lets use the same names expect let add one and this would be John\'s Father call him Joe.\r\nLets now take your second line \"Jack\'s father is John\'s father\'s son. \r\nLet\'s now just take John father\'s son. \r\nWho is John\'s father? JOE! and who is joe\'s son? JOHN! \r\nIt is impossible for Joe to be a grandfather and a father to Jack! (barring sick stuff going on in the family).\r\nThe answer that the picture makes no sense no matter how you explain it because of that one line.\r\n\r\nOne more exercise here:\r\nLets change the word John\'s in that sentence to your (cause esentially he is talking about him)\r\nWho is Your father\'s son? If you have no brother\'s or sisters it\'s you!',3405,0);
INSERT INTO comment VALUES (4840,315,1304,'Emon Hunte','NEVERMIND I WAS WRONG!','2003-05-10 15:46:20',0,'lol disregard all my comments I finally get it!',NULL,0);
INSERT INTO comment VALUES (4841,229,1304,'Emon Hunte','re: same answer ........from me too','2003-05-10 15:49:22',0,'Writing desks come with inky quills? Poe wrote on ravens? Or just about a raven?',2604,0);
INSERT INTO comment VALUES (4842,360,1304,'Emon Hunte','I too knew it before looking at the solution','2003-05-10 15:50:54',0,'Nothing is greater then God\r\nNothing is more evil then the devil\r\nPoor people have nothing \r\nRich people have nothing \r\nand if you eat nothing you will die\r\n\r\nNOTHING',NULL,0);
INSERT INTO comment VALUES (4843,360,1304,'Emon Hunte','Ravi Raja version isn\'t totally right','2003-05-10 15:55:13',0,'Ravi, your first line \"what does a man love more then life\" isn\'t exactly true cause it\'s more then possible that a man can love a soulmate more then life itself. Also your last line \"what a man takes to the grave\" Well i\'m sure there are secrets the a person can take to there grave.',NULL,0);
INSERT INTO comment VALUES (4844,499,1304,'Emon Hunte','Im sure no one looked','2003-05-10 15:59:40',0,'Im sure no one looked at the solution! Yet almost everyone had Musicians as the answer. Yeah Right! My guess which makes sense is 4 men in a casino sitting at a blackjack table. None of the four men lose only the house.',NULL,0);
INSERT INTO comment VALUES (4845,827,1253,'Brian Nowell','Mmm! More clarity needed.','2003-05-10 17:33:47',0,'8 is the number of vertices, but also refers to something else. Consider the cube as being painted and the name I have given the puzzle. \r\n\r\nI believe that I saw the \"order 1\" example in a book by Martin Gardiner many years ago.',NULL,0);
INSERT INTO comment VALUES (4846,786,2201,'Brandon','How about...','2003-05-10 18:47:57',0,'104020, 1050301',NULL,0);
INSERT INTO comment VALUES (4847,472,2174,'Vinodhan Selvarajalu','re(2): depends on the density','2003-05-10 22:48:58',1,'Are you trying to say that if the boat were a smaller volume then the water level would be higher, because the boat would displace less water? This isn\'t true. The volume of water that is displaced by an object, such that it still floats, depends on what the mass of the object floating in it is. The displaced volume therefore depends on the floating mass, and the problem is actually one of mass (density) rather than volume. If the boat were made of a denser material, and yet was exactly the size and shape, it would displace more water (as long as it still stays afloat). So I think you can\'t correctly say that the solution lies in volume...and it is DEFINITELY not the only factor...it is about density at its core.',4584,0);
INSERT INTO comment VALUES (4848,356,2144,'Ryan','Correction?','2003-05-10 23:12:23',1,'I had heard this one before also, but in my version, the bet was \"I bet you\'ll move before I walk around you three times.\" .......after the man had walked around him twice, but before he had started the third time, the man threw his hands up in disgust..... \" It was something like that. Feel free to comment if that would be a better phrasing.',NULL,0);
INSERT INTO comment VALUES (4849,690,2174,'Vinodhan Selvarajalu','Definitely wrong','2003-05-10 23:34:19',0,'OK that solution posted up there is DEFINITELY wrong. I won\'t go into heat transfer principles or quote equations, which I could do, but just present simple logic and historical evidence. \r\n\r\nWe know that raising a liquid to above boiling requires more energy than simply raising its temperature. It is safe to assume the blade is of sufficient temperature to boil the water (ask any blacksmith/metallurgist/metal sculptor and he\'ll tell you its a lot hotter than 100 deg C that is required to mould metal-its more like 600 deg C depending on other factors). The latent heat of vaporisation for water, the property which defines the energy required for the liquid to change phase, is considerably larger than the energy required to heat oil to any temperature below its boiling point, and the boiling point for oils is in the range of over 300 deg C which means that oil will still be being raised degree by degree according to its specific heat capacity, well after the water would have boiled and in so doing created a mechanism to remove heat at a higher rate. The stuff about the creation of a layer around the blade might be plausible (though I\'ve never heard of such a consideration), but that layer will dissipate far sooner than it would take the oil to get to boiling. It would really be a transient condition if anything.\r\n\r\nAnyway you could argue many ways around what I said because I\'ve failed to give those numbers associated with eqch phenomenon, and I don\'t really have the inclination to go delve into heat transfer rates and specific heat capacities and so forth....BUT\r\n\r\nI know for a fact the solution is certainly wrong without any hesitation whatsoever, since in the process of making steel, water quenching is used to produce high martensite (brittle) steels because the faster a steel is cooled, the more martensite is formed. \r\n\r\nAnd one of the ways to cool down steels at reduced rates (thus making less brittle steels), used as a standard everywhere, and common knowledge for any mechanical engineer, is oil-quenching....\r\n\r\n(Air cooling is used to form even lower martensite steels)',NULL,0);
INSERT INTO comment VALUES (4850,786,1919,'Lewis','A Ha!','2003-05-11 00:06:23',3,'Okay, I got it.\r\nThe formula the the Nth term is :\r\n(10*(N-1)st term) + (N-2)nd term',NULL,0);
INSERT INTO comment VALUES (4851,40,2129,'Sanjay','Another 12 coin solution','2003-05-11 03:28:22',3,'Three piles A,B,C of 4 coins each. 1st weighing: A1,A2,A3,A4 (A) vs B1,B2,B3,B4 (B); 2nd weighing: A1,A2,A3,B4 (left) vs A4,C1,C2,C3 (right)\r\nIf A > B then: \r\nIf left > right, A1,A2, or A3 is heavier. 3rd weighing: A1 vs A2: if A1 > A2, A1 is heavier; if A1 = A2, A3 is heavier; if A1 < A2, A2 is heavier.\r\nIf left = right, B1,B2, or B3 is lighter. 3rd weighing: B1 vs B2: if B1 > B2, B2 is lighter; if B1 = B2, B3 is lighter; if B1 < B2, B1 is lighter.\r\nIf left < right, either A4 is heavier or B4 is lighter. 3rd weighing: A4 vs A1: if A4 > A1, A4 is heavier; if A4 = A1, B4 is lighter; A4 < A1 is impossible. \r\nIf A = B then:\r\nIf left > right, C1,C2, or C3 is lighter. 3rd weighing: C1 vs C2: if C1 > C2, C2 is lighter; if C1 = C2, C3 is lighter; if C1 < C2, C1 is lighter.\r\nIf left = right, C4 is either heavier or lighter. 3rd weighing: C4 vs C1 : if C4 > C1, C4 is heavier; C4 = C1 is impossible; if C4 < C1, C4 is lighter.\r\nIf left < right, C1,C2, or C3 is heavier. 3rd weighing C1 vs C2: if C1 > C2, C1 is heavier; if C1 = C2, C3 is heavier; if C1 < C2, C2 is heavier.\r\nIf A < B then:\r\nIf left > right, either A4 is lighter or B4 is heavier. 3rd weighing: A4 vs A1: A4 > A1 is impossible; if A4 = A1, B4 is heavier; if A4 < A1, A4 is lighter.\r\nIf left = right, B1,B2, or B3 is heavier. 3rd weighing: B1 vs B2: if B1 > B2, B1 is heavier; if B1 = B2, B3 is heavier; if B1 < B2, B2 is heavier.\r\nIf left < right, A1,A2, or A3 is lighter. 3rd weighing: A1 vs A2: if A1 > A2, A2 is lighter; if A1 = A2, A3 is lighter; if A1 < A2, A1 is lighter.',NULL,0);
INSERT INTO comment VALUES (4852,830,1301,'Charlie','thoughts and considerations','2003-05-11 05:27:04',1,'It would presumably have to consider a change in the freezing point of the water, by means of dissolved air or other considerations of the make up of the water, rather than having it cool off faster. Although initially a warmer tray of water would indeed lose heat faster, at some point it could only approach the temperature the initially cooler tray also achieved at that time. Once the warmer tray was essentially at the same temperature as the cooler tray, the only advantage that the warmer tray could have would be of composition, not a temperature difference.',NULL,0);
INSERT INTO comment VALUES (4853,786,1660,'Tim Axoy','Got it','2003-05-11 06:45:01',3,'That is correct.',4850,0);
INSERT INTO comment VALUES (4854,515,103,'friedlinguini','Proof by Contradiction','2003-05-11 07:03:35',3,'Let S denote a nonempty set of positive integers with no least element.\r\n\r\n1 is not an element of this set, since there is no positive integer less than 1, and therefore it would be a least value.\r\n\r\nAssume that all integers in the range [1, n] are not part of S. Then n+1 is not a member of S, because it would be a least element of S.\r\n\r\nBy induction, every positive integer is not a member of S. Since S consists only of positive integers, it is the empty set. However, it was given that S is not empty. Thus, by contradiction, every nonempty set of positive integers must have a least element.',NULL,0);
INSERT INTO comment VALUES (4855,830,1626,'Gamer','re: thoughts and considerations','2003-05-11 07:29:24',0,'Like Charlie said, I would have cold salt water (or another such thing) and hot distilled water. I think this might be forbid by the conditions of the problem though.',4852,0);
INSERT INTO comment VALUES (4856,510,1626,'Gamer','re: better solution then the solution.','2003-05-11 07:36:17',0,'Actually some could view a fireplace as being like a campfire, where if it was put ina nonflammable container of some kind it could be moved around...\r\n\r\nPlus fire doesn\'t eat everything, only things that melt at its temperature, or things that oxidize. Glass and other things would need a higher temperature.\r\n\r\nAnd if you were in a place with light gasses or lots of smoke, the smoke wouldn\'t rise or spread out.\r\n\r\nSo there are times when all three aren\'t true, but for the most part it is true.',4834,0);
INSERT INTO comment VALUES (4857,806,1626,'Gamer','re: Logic?','2003-05-11 07:38:00',0,'There isn\'t really any math to compute here, and a shape by definition is two dimentional. Using logic to prove there is a path may work.',4833,0);
INSERT INTO comment VALUES (4858,830,103,'friedlinguini','re(2): thoughts and considerations','2003-05-11 08:52:20',1,'It might not violate the conditions of the problem. Charlie referred to dissolved air, which might occur in an open container. It\'s not my specialty, but I would be willing to believe that hot water might dissolve more air from an open container than cold water.\r\n\r\nAnother possibility is that if both containers are open, some of the hot water might have evaporated, giving the freezer less work to do.\r\n\r\nIf it\'s a freezer with frost in it, hot water might melt some of the frost, which would otherwise act as an insulator between the container and the refrigeration coils.',4855,0);
INSERT INTO comment VALUES (4859,830,1072,'Alan','Just an idea','2003-05-11 10:28:11',2,'Have the hot mater in some sort of cheap plastic container that would expand when heated. When the hot water is put into this then the plastic would sort of melt allowing more hot water to have a larger surface area in contact with the air, thus making it coll faster(i think) the cold water would stay with very little of it exposed to the air.',NULL,0);
INSERT INTO comment VALUES (4860,513,1,'levik','Solution','2003-05-11 11:14:22',0,'Ravi - your submitted solution calls this a paradox, which it is most clearly not. (Both sentences are false, and sice they are DIFFERENT sentences, that doesn\'t cause a contradiction.)I think it\'s been explained pretty well here by others.\r\n\r\nSo, do you want to change the solution, or should I do it?',NULL,0);
INSERT INTO comment VALUES (4861,733,1660,'Tim Axoy','I do not recall...','2003-05-11 13:14:24',0,'I do not recall posting this.',4225,0);
INSERT INTO comment VALUES (4862,733,1660,'Tim Axoy','I do not recall...','2003-05-11 13:15:21',0,'Read I do not recall... saying I do not recall posting that.',4233,0);
INSERT INTO comment VALUES (4863,830,1575,'DJ','thinks and thunks','2003-05-11 13:45:38',1,'If both the cold and hot water are identical in composition, then the cold water will freeze faster due simply to the laws of heat transfer. Most people believe the opposite based on experience.\r\nWhen water is boiled until all the trapped air bubbles are released, it will freeze faster than cold water. Not because it\'s hot, but because of the different composition. Heating water promotes evaporation.\r\nSo, some of the mass is lost and there is actually less water to be cooled.\r\nSecond, during evaporation, the hottest molecules are released into the air first, actually lowering the temperature of the remaining water (that\'s why blowing on hot soup makes it cool off).\r\n\r\nThe folklore about hot water freezing faster probably started in the nineteenth century when water was carried in wooden buckets, which help retain the heat and increase evaporation. A modern experiment using wooden buckets showed hot water freezing 10% faster then a bucket of water at room temperature. (Bill McLain, \"Do Fish Drink Water?\")',NULL,0);
INSERT INTO comment VALUES (4864,348,2130,'ethan','an alternate solution','2003-05-11 14:06:10',1,'a water color painting of a man. he obviously has no life or breath. water had to be used to make him. sunlight will fade him and ultimately destroy him.',NULL,0);
INSERT INTO comment VALUES (4865,801,1575,'DJ','Lots of Little Somethings','2003-05-11 14:27:30',1,'Since there are five cards, and only four suits, there must be two cards with the same suit. So, have the assistant pick two cards with the same suit and keep the lower of the two. Always consider the ace to be low (or high, whatever) for convention. The other card would be laid down first. Now you know the suit, and you have at most 12 cards to work with, and at best, you already know what the hidden card is (if there happen to be a three and a deuce of the same suit in there). The remaining three cards are used to determine the value of the last card. Using a binary system, that only yields eight different possibilities. With a ternary system, there are 27 combinations of 3 bits. You only need, 12, or 13 to make the trick a little neater, so that gives room for some play. Actually, it would probably be most convenient to work out an arbitrary mechanism that would be inconspicuous to the audience and yet fast and obvious to the magician. \r\n.\r\n.\r\n..Ignore everything I just said, cause there are so many ways to do it that a comprehensive analytic solution is pretty much impossible.\r\n\r\nHere\'s what I would do (I am sitting here with a deck of cards, mulling over the easiest ways to put the cards down):\r\n\r\nThe first card is used to determine the suit. You could make it the lowest or highest of the flushed cards, but probably to have some sort of absolute method of determining the value only from the last three cards would be that much simpler. Or put down the card with the same suit last (just do it the same all the time). It doesn\'t matter, as long as you pick a convention and adhere to it.\r\nThe second card is used to determine the range. The simplest convention I came with is, hold on to the corner closest to the magician to indicate a \'high\' card, that is, 10-K. Hold the middle or side of the card to indicate 6-9, and the corner nearest yourself to indicate 2-5. Maybe, put all the cards down with your left hand instead of your right, if the card is an ace.\r\nAt this point, either you already know the hidden card (assuming that the \'suit\' card is laid first), or it is narrowed down to four cards. The remaining cards could be used in a binary system, say, hold the corner toward the magician for a \'1\' and the corner nearest you for a \'0\'.\r\n00 = 2, 6, or 10\r\n01 = 3, 7, or J\r\n10 = 4, 8, or Q\r\n11 = 5, 9, or K\r\nand if it\'s an ace you already know because of the aforementioned \'left-hand rule\'. That requires a little thought, but with a few minutes of practice for both people it can go very quickly and smoothly.\r\n\r\nPS: Sorry if I said anything redundant to the other comments; I haven\'t been around but I still wanted a chance for a fresh look at the problems. I\'ll check out the other comments now...',NULL,0);
INSERT INTO comment VALUES (4866,801,1575,'DJ','re: Lots of Little Somethings','2003-05-11 14:43:07',1,'(read the previous comment first)\r\nActually, on second thought, the \'suit\' card could also be used to give an indication of the value, with the way it is laid down. So, you then have four bits to work with, and a straight binary system is effective. Just let A-K represent binary values 1-13 (omit zero so that 2-10 are intuitive). Then use the corners method I described before, or anything else you want, to give each card a value of \'1\' or \'0\' by the way it is laid down.\r\nMaybe even by the way they are arranged; you could have them lined up horizontally with cards offset nearer to the assistant given a value of \'1\' and those nearer the magician a value of \'0\' (that would make it impossible to distinguish \'0000\' from \'1111\', but since we are not using 0 or 15, it does not matter). If you did that, the magician could be turned around or something while the assistant is laying down the cards, to alleviate suspicions of communication by the assistant.\r\n--A second look at the description in the problem says that the assistant hands the cards to the magician, in which case I default to my previous suggestion.\r\n\r\nAnyway, however you do it:\r\n0001 = A\r\n0010 = 2\r\n0011 = 3\r\n0100 = 4\r\n0101 = 5\r\n0110 = 6\r\n0111 = 7\r\n1000 = 8\r\n1001 = 9\r\n1010 = 10\r\n1011 = J\r\n1100 = Q\r\n1101 = K\r\n0000, 1110, 1111 = start sweating!\r\nAnd the suit of the hidden card is the same as the suit of the first (or the second, third, last, whatever the decision) card.',4865,0);
INSERT INTO comment VALUES (4867,801,1575,'DJ','Facedown','2003-05-11 15:44:23',0,'Okay, now I\'ve looked at everyone else\'s ideas..there were a lot of things suggested that I like that I didn\'t think of.\r\n\r\nThe 24-permutation thing by Brian is nifty, but man! You have to mentally take out the four cards, and sort out the remaining 48, as well as determine the relative values of the four you have, remembering them in order, and pick out the hidden card. As a couple people said, that\'s pretty intese.\r\n\r\nCharlie\'s suggestion with the \'clock\' is pretty cool, and it uses just the three cards to determine the value of the hidden one from the fourth. Pretty neat, and the giveaway card doesn\'t have to be the first card, though that is probably easiest since you are adding to/subtracting from that value. The only thing with this, as with Brian\'s, is that you have to remember the cards in order as they are handed to you. That\'s doable, with some practice. Also, cards with the same value could be troublesome, but ranking the suits works (I think the standard convention for that is ♠-♥-♣-◊ from high to low).\r\n\r\nI also liked the idea of the \'camouflage suit\' (I forget who said it) so that the giveaway is less obvious, but, what if all five cards are the same suit? You could make up some way to indicate that special exception, but that would be rather clumsy. Better might be just making the giveway card second or third instead of first, and therefore less consipicuous.\r\n\r\nFor Jon\'s last proposition, having the cards face down would obviously make the problem more difficult. My solution ignores everything but the suit of one card, but without that you have four times as much work to do. A ternary system with 4 bits yields 81 combinations, much more than are necessary. Three ternary bits and one binary bit gives 54 combinations, very close to what we want (heck, throw in two different jokers).\r\nHow about this:\r\nNumber the cards 1-52: A-K, Diamonds, Clubs, Hearts, Spades, again omitting zero for intuitivity (is that a word?).\r\nFor example; 1 = A◊, 2 = 2◊, 3 = 3◊, ... , 14 = A♣, all the way up to 52 = K♠.\r\n\r\nFor the first card, if the assistant is holding on the the corner/edge nearest you, do nothing (add 0), and for the corner nearest him, add 26.\r\nFor the second card, if he is holding the corner nearest you, add 0, the middle of the card, add 9, and the corner nearest himself, add 18.\r\nFor the third card, add 0 for the corner nearest you, 3 for the middle of the card, and 6 for the corner nearest him.\r\nFinally, the last card has similarly placed values of 0, 1, and 2.\r\nThis method can be used to determine any value between 0 and 53. Determining the hidden card from this number is relatively simple, especially if you think of the numbers in groups of 13. Determine the suit from its range:\r\n 1-13 = ◊\r\n14-26 = ♣\r\n27-39 = ♥\r\n40-52 = ♠\r\nThen just subtract the base (0, 13, 26, or 39) to get the value 1-13 that corresponds to A-K.\r\nThat whole process is a lot simpler than I made it sound. The hardest part, really, is for the assistant to quickly figure out the value of the card and convert it to this ternary-binary system mentally. That is still very much doable with a little practice (and remember, the assitant gets to choose the card, so he can pick a simpler one if that is possible).\r\nThe reason I am still saying to go by what corner or edge of the card is held, rather than the number of fingers, is because it is a heck of a lot easier to see where someone\'s thumb is on the top of the card than to try to count the number of fingers on the bottom (and being blocked by the thumb). Any way of distinguishing three methods, of course, will work.',NULL,0);
INSERT INTO comment VALUES (4868,518,2184,'mark hartman','my answer','2003-05-11 18:04:43',0,'Slow train is moving at 36 miles per hour; fast train at 72 miles per hour. If fast train leaves late, at the time the slow train arrives at M, the fast train has 72/12 = 6 miles yet to go. As the trains continue to proceed towards each other, the slow train goes 2 miles in the time that the fast train goes 4 miles. If the slow train leaves late, at the time the fast train arrives at point M, the slow train has 36/12 = 3 miles to go. The fast train goes 2 of the intervening miles, while the slow train goes one mile. Either way the trains meet 2 miles from M.\r\n',NULL,0);
INSERT INTO comment VALUES (4869,513,2148,'Jayaram S','re(4): Suggestions','2003-05-11 18:58:57',0,'Ravi,the second statement : \"This sentence does not contain seven words\" will be TRUE as long as the first word \"This\" is referring to the first statement: \"This sentence contains Seven words\". Merely adding DOES NOT does not neccesarily negate the first statement unless second statement is read always in context to the first statement. So independently read, second statement will be false with the existing choice of words.',4786,0);
INSERT INTO comment VALUES (4870,830,2144,'Ryan','Thoughts','2003-05-11 21:26:41',0,'A container that was spherical wouldn\'t freeze as quickly as a flat, thin container due to more surface area. Also, different insulating materials could be used. If one container was pressurized enough, it could prevent/slow the water from freezing. The contents of the water (salt, disolved gases, etc) could change freezing rates. However, if everything besides temperature is the same, the cold would freeze first. Just my thoughts, I\'m sure I left out some variables.',NULL,0);
INSERT INTO comment VALUES (4871,806,1253,'Brian Nowell','Reminds me of Konigsberg Puzzle','2003-05-11 22:26:27',0,'Won\'t reflect on Konigsberg (2 islands in river and 6 bridges, I think; islands are linked to each other, and each to each bank, and then the last bridge spans the river). The network of this scenario cannot be traced back to point \'X\' without covering previous ground. \r\n\r\nLet us convert the termite\'s cube into 27 connected locations within a plane. Hey, it\'s messy, but it can be done. From there look at the two aspects of the problem as posed.',NULL,0);
INSERT INTO comment VALUES (4872,518,2148,'Jayaram S','General Shortcut Formula','2003-05-11 23:46:29',3,'Given d = late distance (in miles), t = late time (in minutes),\r\n\r\n1. Late speed = (late distance / late time)..miles per min\r\n2. Slow Train speed = 1.5 * late speed \r\n3. Fast Train speed = 2 * Slow train speed\r\n---------------------------------------------------------------------------\r\nIn the given equation, d = 2 miles, t = 5 minutes,\r\n\r\n1. Late speed = 2/5 = 0.4 miles per min = 0.4*60 mph = 24 mph\r\n2. Slow Train speed = 1.5 * 24 = 36 mph\r\n3. Fast Train speed = 2 * 36 = 72 mph\r\n---------------------------------------------------------------------------\r\nI suggest the readers to derive the proof!',NULL,0);
INSERT INTO comment VALUES (4873,483,2148,'Jayaram S','re(2): One-line Simple Solution','2003-05-12 00:01:32',0,'Ravi, Instead of just giving the solutions the normal way, I try to derive some general shortcuts (as a habit) so that users can get a different flavour of the solution. In addition they can quickly work out solutions for different parameters of the problem. I suggest you take up the challenge of arriving at the formula as a NEW PROBLEM!!',4782,0);
INSERT INTO comment VALUES (4874,733,2196,'Silly Jilly','Hmmm...','2003-05-12 02:25:30',0,'Tim Axoy,it probably was not you who did that.',NULL,0);
INSERT INTO comment VALUES (4875,732,1660,'Tim Axoy','My new problem','2003-05-12 02:35:04',0,'My new problem,Drew and Mohammad come back,got posted.',NULL,0);
INSERT INTO comment VALUES (4876,439,1660,'Tim Axoy','Hard logic','2003-05-12 02:38:13',0,'You could do this by drawing all the 1024 possibilities and crossing out the ones it could not be.',NULL,0);
INSERT INTO comment VALUES (4877,519,1301,'Charlie','Excel Result','2003-05-12 03:47:07',3,'While I don\'t know how to do the problem, Excel\'s Solver gives 60 gallons of orange and 20 gallons of purple maximizing profit when disposal cost is $4 per gallon, and the profit is $1120. With disposal at $6 per gallon, Excel maximizes profit at 10 gallons of orange, 70 of purple and 50 of green, giving $1070 of profit.',NULL,0);
INSERT INTO comment VALUES (4878,513,979,'Ravi Raja','re(5): Suggestions','2003-05-12 04:20:19',0,'Yes Jayaram, \"This\" in the second statement refers to the second statement only and not to the first statement. In fact, the word \"This\" in each of the statements refers to that particular statement only and not to the previous or the next statement.',4869,0);
INSERT INTO comment VALUES (4879,519,1920,'Brian Smith','Linear maximization (Solution)','2003-05-12 05:09:37',3,'This problem is a linear maximization problem.\r\n\r\nFirst define some variables:\r\nLet a be the amount of red used to make purple.\r\nLet b be the amount of red used to make orange.\r\nLet c be the amount of yellow used to make orange.\r\nLet d be the amount of yellow used to make green.\r\nLet e be the amount of blue used to make green.\r\nLet f be the amount of blue used to make purple.\r\nLet k be the disposal cost per gallon ($4 or $6).\r\n\r\nNow create some equations:\r\na = f (equal parts red and blue)\r\nb = c (equal parts red and yellow)\r\nd = e (equal parts yellow and blue)\r\na + b <= 40 (amount of red)\r\nc + d <= 30 (amount of yellow)\r\ne + f <= 60 (amount of blue)\r\na,b,c,d,e,f >= 0 (all variables are non negative)\r\n\r\nNet profit is the amount of sales minus the amount of disposal. Net profit equation = 6*(a + f) + 20*(b + c) + 9*(d + e) - k*(130 - a - b - c - d - e - f)\r\n\r\nAfter some substitution a linear system of inequalities in 3 variables emerges:\r\n\r\na + b <= 40\r\nb + d <= 30\r\nd + a <= 60\r\na >= 0, b >= 0, d >= 0\r\n\r\nThe maximum net profit occurs at one of the verticies of the region defined by the inequalities. The verticies are (0,0,0), (0,0,30), (0,30,0), (40,0,0), (30, 0, 30), (40, 0, 20), (10, 30, 0), (35,5,25).\r\n\r\nIf the disposal cost is $4 then Net Profit = 20a + 48b + 26d - 520\r\nThis equation has a maximum value of $1120 with vertex (10, 30, 0).\r\n\r\nIf the disposal cost is $6 then Net Profit = 24a + 52b + 30d - 780\r\nThis equation has a maximum value $1070 with vertecies (10, 30, 0) and (35, 5, 25).\r\n\r\nWith a $4/gallon disposal cost, the most revenue $1120 will be made by making 20 gallons orange and 60 gallons green.\r\n\r\nWith a $6/gallon disposal cost, the most revenue $1070 will be made by making 20 gallons purple and 60 gallons orange or by making 70 gallons purple, 10 gallons orange and 50 gallons green.',NULL,0);
INSERT INTO comment VALUES (4880,513,979,'Ravi Raja','re: Solution','2003-05-12 05:31:55',0,'Levik: Everything has been explained in the solution that I have submitted and now I do not understand what changes I am supposed to make in it. So, please you make the necessary changes as required according to what you think is correct. \r\nThank You.',4860,0);
INSERT INTO comment VALUES (4881,439,1660,'Tim Axoy','On and on','2003-05-12 06:19:02',0,'TTTTTTTTTT,TTTTTTTTTL,TTTTTTTTLT,TTTTTTTTLL...',4876,0);
INSERT INTO comment VALUES (4882,805,1920,'Brian Smith','Next up is ...','2003-05-12 08:16:42',0,'Next up is 1854.\r\n\r\n 0*2+1=1\r\n 1*3-1=2\r\n 2*4+1=9\r\n 9*5-1=44\r\n 44*6+1=265\r\n265*7-1=1854',NULL,0);
INSERT INTO comment VALUES (4883,805,1686,'DuCk','quick guess at the next #...','2003-05-12 08:18:09',0,'My guess for the next # in the sequence would be 1,854. The only pattern i\'ve seen so far has been starting with 0 is mulitplying by 2 and adding 1, then for the next number multiplying by 3 and subtracting 1, then multiplying by 4 and adding 1, etc... As far as any significance is concerned, I\'m not sure. Shoot, I have to go to a meeting now. Hopefully, I can work on this more and have better reasoning later. ',NULL,0);
INSERT INTO comment VALUES (4884,805,1072,'Alan','Idea that works well','2003-05-12 10:38:19',2,'well 0+1x2=2
then 1+2x3=9,
then 2+9x4=44
then 9+44x5=265,
therefore 44+265x6=the next number. And if you were to follow this pattern in reverse it would go like this
-1+0x2=1
-2+(-1)x3=9 at which point the pattern alternates between positive and negative numbers.',NULL,0);
INSERT INTO comment VALUES (4885,805,1567,'Bryan','Solution','2003-05-12 11:35:25',3,'The next number in the series is 1854. The series is generated by
a(n)=n!*∑[(-1^x)/x!] for x=0 to n
What this series represents is the number of permutations of a set, such that none of the members of the permutation are in the same position as the members of the original set. To illustrate:
{A}: There are no permutations that meet the requirement (0 instances)
{A,B}: {B,A} (1 instance)
{A,B,C}: {B,C,A}, {C,A,B} (2 instances)
{A,B,C,D}: {B,A,D,C}, {B,C,D,A}, {B,D,A,C}, {C,A,D,B}, {C,D,A,B}, {C,D,B,A}, {D,A,B,C}, {D,C,A,B}, {D,C,B,A} (9 instances)
and so on.',NULL,0);
INSERT INTO comment VALUES (4886,519,1301,'Charlie','re: Linear maximization (Solution)','2003-05-12 16:10:58',0,'Something must be wrong. With $4 per gallon disposal, 20 gallons of orange and 60 of green would produce a selling price of $940, which, less the $200 disposal fee would net $740, plus it uses 40 gallons of yellow, which is more than we have.\r\n\r\nIt is the 60 gallons of orange and 20 of purple, listed for the $6/gallon disposal that\'s actually the maximum for the $4 disposal, and at $6/gallon disposal, the 60 orange/20 purple would net only $1020, which is less than the $1070 that is indeed the maximum for $6/gallon disposal with the said 70 purple, 10 orange and 50 green.',4879,0);
INSERT INTO comment VALUES (4887,515,1,'levik','re(4): {P, r, o, o, f}','2003-05-12 17:21:46',0,'Heh, made the same mistake as me. :)\r\n\r\nNow I feel less stupid.',4773,0);
INSERT INTO comment VALUES (4888,806,153,'TomM','re: Reminds me of Konigsberg Puzzle','2003-05-12 18:13:07',0,'In the classic bridge problem, the point was to use all of the bridges once and only once. Euler proved that it was impossible because there were more than two vertices (islands and banks)that were connected to an odd number of paths (bridges). \r\n\r\nWhat you propose is to consider the cube as a graph with 125 (not 27 -- it\'s 5³, not 3³) vertices and 300 paths. It can be done with graph theory, but it won\'t be as simple as the Konigsberg problem. Insted of all paths being traced, there will only be 124 of the 300 paths traced.',4871,0);
INSERT INTO comment VALUES (4889,806,153,'TomM','re(2): Logic?','2003-05-12 20:58:32',0,'If there were a category for graph theory that\'s where it would belong. I doubt that we\'ll ever have enough graph theory problems to justify a separate category, tho.\r\n\r\nOf the existing categories, I would suggest either General or Geometry.',4857,0);
INSERT INTO comment VALUES (4890,805,2163,'sendil','','2003-05-12 21:19:51',0,'Before I wonder at the significance, the sequnce itself is quite simple to complete.\r\n\r\nNth term= Sum of the previous 2 terms * n with the first 2 terms(oth term and 1st term) being 0 and 1.',NULL,0);
INSERT INTO comment VALUES (4891,805,2163,'sendil','re: Solution','2003-05-12 21:24:04',0,'Brilliant!!!',4885,0);
INSERT INTO comment VALUES (4892,806,1253,'Brian Nowell','re(2): Reminds me of Konigsberg Puzzle','2003-05-12 22:25:51',0,'Actually I misread the opening \'5x5x5 block\' stipulation; that would be painful to follow through with that may pathes!\r\n\r\nBut playing with a 3x3 model, using the ask of the author\'s 1a)stipulation, I can get the termite to finish at the centre cube of the opposite face.\r\n\r\nQuestion: Can I assume with a solution for this 3x3 case that a 5x5 automatically follows? \r\n\r\nBack to Konigsberg. How would a collary read? Could it be used to prove or disprove the b) possibility? I cannot perceive a solution from a centre faced cube of my model, but then I haven\'t started at a \'vertex\' or \'centre of edge\'.\r\n',4888,0);
INSERT INTO comment VALUES (4893,383,1660,'Tim Axoy','Snowman?','2003-05-13 03:02:48',4,'Snowman?',NULL,0);
INSERT INTO comment VALUES (4894,787,1902,'Hank','Solution','2003-05-13 03:08:27',3,'Question 1: A can answer Y or N\r\nQuestion 2: B can only answer N\r\nQuestion 3: Friend knows what each is after knowing whether they answered they same or differently.\r\n\r\nSolutions: If they answered differently A:Y, B:N, then A:Knight, B:Liar\r\nIf they answered the same A:N, B:N, then they are both knights.',NULL,0);
INSERT INTO comment VALUES (4895,511,1902,'Hank','re(5): Read This','2003-05-13 03:26:40',4,'If it is never \'yes\' then it must be \'no\'. But I disagree with that.\r\nI may still stick with \'yes\' because...\r\n\"Can the omnipotent God ________________ ?\" fill in the blank.\r\nMaybe the question posed would be like asking, \"Can God do better/more than God/himself?\"',4750,0);
INSERT INTO comment VALUES (4896,787,979,'Ravi Raja','Solution','2003-05-13 04:19:26',3,'We know that the answers given by A and B are in Yes-No form only. \r\n\r\nSo now, suppose that when Tim asked B if both of them were Liars, B answered No.Then either both A and B are Knights or A is a Liar and B is a Knight. \r\n\r\nIf now both of them are Knights, then even A answers No when Tim asks him if B is a Liar. So here he is getting both same answers (both No). \r\n\r\nNow, if A is a Liar and B is a Knight, then A answers Yes when Tim asks him if B is a Liar. So, in this case Tim gets two different answers (Yes from A and No from B).\r\n\r\nNext, let us assume that B answers Yes when he is asked if both of them are Liars. Then here we have only one combination and that is A is a Knight and B is a Liar and so A\'s answer will be Yes when Tim asks him if B is a Liar. So here once again Tim gets two same answers (both Yes). \r\n\r\nFrom the above arguments we see that the only two different answers that Tim can get from A and B is a Yes from A and a No from B and in that case, we see that A is a Liar and B is a Knight. \r\n\r\nBut we see that there are two cases when Tim gets same answers from both A and B (either both Yes or both No). \r\n\r\nIf both the answers are No, then both A and B are Knights.\r\nIf both the answers are Yes, then A is a Knight and B is a Liar. \r\n\r\nSuppose that when Tim\'s friend asked him (Tim) if both the answers were same and Tim replied Yes, then Tim\'s friend still wouldn\'t be able to determine what each of A and B were (for sure), since he would then be left out with two possibilities.\r\n\r\nBut since there is only one combination for two different answers, from which Tim\'s friend can easily determine what each of A and B are and actually does so, as the problem says: \"Timothy\'s friend hears his answer,and finally the friend has enough information to solve what A and B are\", so obviously Tim\'s answer was No, that is, the answers were not the same and therefore, we can conclude that:\r\n\r\nA is a KNIGHT \r\nB is a LIAR',NULL,0);
INSERT INTO comment VALUES (4897,787,1301,'Charlie','solution','2003-05-13 04:21:29',3,'The following table shows what the answers would be to questions 1 and 2 depending on the identities of the two inhabitants:\r\n\r\nA B 1 2\r\nKt L Y Y\r\nKt Kt N N\r\nL L N N\r\nL Kt Y N\r\n\r\nThere are three situations in which the two answers are the same, and only one in which they are different. So the friend must have made his conclusion based on the answers being different, and A is a liar and B a knight.\r\n',NULL,0);
INSERT INTO comment VALUES (4898,787,1301,'Charlie','re: Solution','2003-05-13 04:30:43',0,'You say \"So now, suppose that when Tim asked B if both of them were Liars, B answered No.Then either both A and B are Knights or A is a Liar and B is a Knight.\" But actually, if both are liars, B will also answer No, as he is a liar. So if both answers are No, then they are either both knights or both liars. You say correctly that If both answers are Yes then A is a knight and B a liar.\r\n\r\nYour final answer of A is a knight and B is a liar depends on that having different answers to the questions, yet you had (correctly) said that the answers in that instance are both Yes.\r\n\r\nThe unique non-same answer would be for A is Liar, B is Knight, where the answers are Y and N.',4896,0);
INSERT INTO comment VALUES (4899,741,872,'pleasance','better late than never','2003-05-13 05:13:39',0,'Apologies for not commenting sooner, haven\'t been around. Ravi, \"the other day\" was meant to imply sometime in the recent past, as others have said. It was put in specifically to make x=45 the only correct answer for Jim.',4178,0);
INSERT INTO comment VALUES (4900,515,2216,'val','proof','2003-05-13 05:15:48',3,'Let S be the set. Since S is non empty, it has at least one element, which we call x. Since S has positive integers only, then x is integer and x is larger than 0. Let T = S intersected with {1, 2, .., x}. T is finite (it has at most x elements) and is non-empty (it contains at least the element x); thus T has a least element. The least element of T is also the least element of S. qed.',NULL,0);
INSERT INTO comment VALUES (4901,827,1920,'Brian Smith','A Painted Cube','2003-05-13 07:11:22',1,'Consider a white cube of size n+2 divided into unit cubes. Paint the outer surface of the cube red.\r\n\r\nThere are 8 1x1x1 cubes which have 3 red faces.\r\nThere are 12n 1x1x1 cubes which have 2 red faces.\r\nThere are 6*n^2 1x1x1 cubes which have 1 red face.',NULL,0);
INSERT INTO comment VALUES (4902,807,1567,'Bryan','Solution','2003-05-13 07:29:23',3,'For all positive integers x, a string of 3^(2+x) 3\'s is divisible by 3*3*3*3. Since the set of positive integers is infinite, there are an infinite number of numbers n that meet the two requirements.',NULL,0);
INSERT INTO comment VALUES (4903,807,1920,'Brian Smith','Solution','2003-05-13 08:03:13',0,'(10^27-1)/3 is a number which fits the conditions of the problem. (10^27-1)/3 = 333333333333333333333333333 which is a multiple of 3*3*3*3.\r\n\r\nAn infinite sequence can be made using (10^(27*n)-1)/3',NULL,0);
INSERT INTO comment VALUES (4904,787,2129,'Sanjay','re: Solution','2003-05-13 11:33:36',0,'Hank, why do you say that B can only answer N to Question 2?\r\n\r\nIf A is a Knight and B is a liar, then B\'s answer to the question \"B, are you both liars?\" would be Y since they are both indeed NOT liars and B, a liar, would be telling the truth if he answers N.',4894,0);
INSERT INTO comment VALUES (4905,515,775,'Cory Taylor','vote','2003-05-13 11:40:47',0,'I think f.l.\'s solution is more clear than the posted solution (though it is certainly not \"better\", as a proof, if valid, is a proof)',NULL,0);
INSERT INTO comment VALUES (4906,787,2129,'Sanjay','Liars have to be True to themselves','2003-05-13 11:56:07',0,'Ravi, you say that \'So now, suppose that when Tim asked B if both of them were Liars, B answered No.Then either both A and B are Knights or A is a Liar and B is a Knight.\'\r\n\r\nYour inference is wrong because there is a third conclusion possible which you have missed out. That both A and B are Liars. \r\n\r\nB, being a liar, will not be true to himself if he answers Yes, because that would be the truth. He will therefore answer No.\r\n\r\n',4896,0);
INSERT INTO comment VALUES (4907,787,2129,'Sanjay','Liar\'s Knight at the Knight\'s Lair','2003-05-13 12:27:45',3,'\r\nIf Timothy tells his friend that the two answers were same, i.e. Timothy\'s answer is Yes, then his friend has three viable scenarios and therefore cannot be sure. These are:\r\n1. That the answers were Y,Y and that A is a Knight and B is a Liar.\r\n2. That the answers were N,N and that they are both Knights.\r\n3. That the answers were N,N and that they are both Liars.\r\n\r\nHowever, if Tomothy tells his friend that the two answers were not same, i.e. Timothy\'s answer is No, then his friend has only one viable scenario and therefore can be sure. This is:\r\n1. That the answers were Y,N and that A is a Liar and B is a Knight.\r\n\r\nSince upon hearing Timothy\'s answer his friend has enough information to solve what A and B are, Timothy must have answered No.\r\n\r\nHence,\r\nA is a Liar\r\nB is a Knight',NULL,0);
INSERT INTO comment VALUES (4908,787,1660,'Tim Axoy','Both wrong answers','2003-05-13 13:08:18',0,'Hank,here is my hint:Both of your answers are wrong.',4894,0);
INSERT INTO comment VALUES (4909,787,1660,'Tim Axoy','Charlie did it!!','2003-05-13 13:11:07',0,'Yes,Charlie!!',4897,0);
INSERT INTO comment VALUES (4910,807,1575,'DJ','Solution','2003-05-13 14:13:22',1,'Define 9[x] as being an integer composed of x 9s in a row (9[1]=9, 9[2]=99, etc). For any integer i, then, 9[2i]=9[i]*(9[i]+2).\r\nFor example:\r\n99=9*11\r\n9999=99*101\r\n999999=999*1001\r\nIf i is a multiple of 4, then the left-hand of that equation fits the parameters of this problem, or, n(i)=9[8i] for any integer i.\r\n\r\nPut more simply, any string of 9s where the number of digits is a multiple of 8 works. Since 8 has infinitely many multiples (or, since the set of integers is infinite), there are infinitely many integers that fit these parameters.',NULL,0);
INSERT INTO comment VALUES (4911,262,1626,'Gamer','re(2): From (a-x) to (z-x),part 2','2003-05-13 16:06:57',0,'If you still can\'t get it, write out the first 5 and the last 5 terms. ',3498,0);
INSERT INTO comment VALUES (4912,827,1253,'Brian Nowell','re: A Painted Cube','2003-05-13 18:54:18',0,'OK, but what of the significance of n^2?',4901,0);
INSERT INTO comment VALUES (4913,794,2184,'mark hartman','I\'ll take a stab at this','2003-05-13 19:04:51',0,'I estimate 10^3.5 billion; that is 1 followed by 3.5 billion zeroes.\r\n\r\nThe answer should be 5 raised to the 5 billionth power. But that is the same as 10 raised to the 5 billionth divided by 2 raised to the same exponent. Now 2^10 is approximately 1000 = 10^3, so the denominator is approximately 10^3^.5billion. So we have 10 ^5billion over 10^ 1.5 billion. Result 10 ^3.5 billion.',NULL,0);
INSERT INTO comment VALUES (4914,519,1183,'fwaff','re: Excel Result','2003-05-13 22:00:43',0,'Charlie: have a look at using the Simplex Method. Since you seem to be a fan of programming and algorithms it should be right up your street.\r\n\r\nBtw I got the same answer.',4877,0);
INSERT INTO comment VALUES (4915,830,1912,'Stewie','Changing Density','2003-05-13 23:26:41',0,'I always thought this problem had to do with the fact that the density of water changes at different temperature. At 4 degrees centigrade, water has a specific gravity of 1. It turns out that this falls off as the temperature decreases. So while you may have the same volume of cold water and hot water, they actually are different in mass. And from all those heat equations from chemistry, it is mass, not volume, that indicates how much energy is needed to heat/cool water. ',NULL,0);
INSERT INTO comment VALUES (4916,501,2174,'Vinodhan Selvarajalu','Possible?','2003-05-14 01:59:51',1,'What about Dreams? Doesn\'t apply to everyone but you usually forget your dreams when you wake up (or most of it) ...so it isn\'t stolen...And your dreams are said to come unbidden...ok I know it doesn\'t fit perfectly but it seems more poetic at the very least...!',NULL,0);
INSERT INTO comment VALUES (4917,520,1941,'shaun','Is this it?','2003-05-14 02:24:30',0,'King of Spades - Queen of Spades - Queen of Hearts',NULL,0);
INSERT INTO comment VALUES (4918,672,872,'pleasance','','2003-05-14 03:09:49',0,'I recall another version of this, I think it was by Martin Gardener. His question was something like \'What happens when an unstoppable force hits an immovable object?\'. After giving the canonical explanation that a universe which contains one cannot contain the other, he suggests the following:\r\nWhen an unstoppable force hits an immovable object, what transpires is an inconceivable event!',NULL,0);
INSERT INTO comment VALUES (4919,520,1301,'Charlie','re: Is this it?','2003-05-14 03:12:35',0,'Yes, that\'s certainly it.',4917,0);
INSERT INTO comment VALUES (4920,520,1902,'Hank','My initial reaction','2003-05-14 03:32:55',1,'K of spades, Q of spades, Q of hearts\r\n\r\nI\'m not sure if I completely understand the \'or two\' connotation, it seems like it is deliberately ambiguous.',NULL,0);
INSERT INTO comment VALUES (4921,787,1902,'Hank','re(2): Solution','2003-05-14 03:35:13',0,'yeah, yeah, yeah, I noticed that after I posted it. Next time I should try thinking more before I blurt it out.',4904,0);
INSERT INTO comment VALUES (4922,827,1920,'Brian Smith','re(2): A Painted Cube','2003-05-14 04:34:11',1,'Consider the n+2 size painted cube with all of the all white cubes removed. n^3 cubes are removed leaving a shell white on the inside and red on the outside. n^2 then refers to the number of cubes on one face which can be seen from the center of the hollowed out cube.',4912,0);
INSERT INTO comment VALUES (4923,807,1575,'DJ','re[fined]: Solution','2003-05-14 06:57:05',0,'On second thought, the digits don\'t even need to be 9s. Twos, threes, whatever, any string of like digits with 8i digits will work. 9s just occurred to me first.\r\nFor example:\r\n33333333=3333*10001\r\nAlso, the number of digits can be any multiple of 4, not just multiples of 8.\r\n555555555555=5555*100010001\r\n22222222222222222222=2222*10001000100010001\r\nand so on.\r\n\r\nWhat I said before is still true, but it does not have to be so specific. I don\'t know how to do a formal proof for the problem, but this is the general form of the/a solution.',4910,0);
INSERT INTO comment VALUES (4924,520,1575,'DJ','Yeah','2003-05-14 07:08:34',3,'The second clue implies two Queens immediately next to each other. The first clue (since there are only three cards) further shows that the King must be the leftmost card, followed by the two Queens.\r\nSimilarly, the last clue implies two Spades next to each other, and the third clue tells us that the Heart must be the rightmost card, with two Spades to the left.\r\n\r\nThe cards, from left to right, are:\r\nK♠ - Q♠ - Q♥\r\n\r\n(The \'or two\' in the first and third clues, I think, are because there really are two of the card named, and the ambiguous addition prevents making the clue way too obvious, or possibly incorrect from its omission. In the second and fourth clues, \'or two\' is added not out of necessity, but again to prevent the other two clues from being obvious.)',NULL,0);
INSERT INTO comment VALUES (4925,492,2166,'Chris','Possible Solution','2003-05-14 08:51:45',3,'I believe that the order is:\r\n\r\nPrancer\r\nCupid\r\nRudolph\r\nDasher\r\nBlitzen\r\nVixen\r\nComet\r\nDonner\r\nDancer',NULL,0);
INSERT INTO comment VALUES (4926,813,1301,'Charlie','solution for A; thoughts on B','2003-05-14 09:17:00',1,'Every weighing gives one of three results: the pans are balanced, the right pan is heavier, the left pan is heavier. As such it provides the equivalent of a base-3 digit, and so multiplies the number of possibilities covered by 3. So the solution to part A is N = 3^X.\r\n\r\nThe specific procedure for part A is to take one third of the set of coins and place it on the first pan, and another third on the second pan. If one side goes down, you know in which of these two pans the bad coin is located. If neither side goes down, the third that wasn\'t weighed has the bad coin. Continue as before with the set reduced to 1/3 its size.\r\n\r\nPart B presumably needs only one more bit of information and one additional weighing supplies even more than that (a base-3 digit rather than a base-2 digit). Based on information theory you could have N = [(X^3)/2], where the square brackets indicate the floor function, or truncated quotient. As to a specific general strategy for any X, I can\'t think of any.',NULL,0);
INSERT INTO comment VALUES (4927,813,1920,'Brian Smith','Weighing in on this one....','2003-05-14 09:21:22',0,'If it is known whether the fake is heavier or lighter, then in X weighings a fake coin can be found among N=3^X coins. \r\n\r\nAt each weighing, the coins are divided into 3 equal groups. Knowing whether the fake is heavier or lighter ahead of time is enough to determine which group the fake is in.\r\n\r\nIf the weight of the fake is not known, I will just guess N=(3^X-3)/2 based of the 1(N=0), 2(N=3), and 3(N=12) weighing cases.',NULL,0);
INSERT INTO comment VALUES (4928,813,2166,'Chris','Weighty Solution (maybe!)','2003-05-14 10:30:45',3,'For part A, I agree with Brian and Charlie about the equation being N = 3^X coins and with the procedure they described.
\r\nFor part B, however, I disagree. Actually, using Charlie\'s statement that an extra weighting will provide us with a little more information and the fact that we don\'t have to know how the coin is fake (light/heavy), I came up with:
\r\nN = 2^X coins maximum with X weightings.
\r\nThe procedure is as follows:\r\nDivide the coins into four groups which we will label A,B,C and D. First weigh group A against group B. Then weigh group B against group C. These two weightings will give one of four results (I will use <> for \'doesn\'t balance\'):
\r\nA=B=C: Then group D has the fake.\r\nA=B<>C: Then group C has the fake.\r\nA<>B=C: Then group A has the fake.\r\nA<>B<>C: Then group B has the fake.\r\n\r\nIn each case, repeat the process with the group indicated, discarding as real the three other groups. This will continue until the groups have only one coin each and one coin is indicated as the fake.',NULL,0);
INSERT INTO comment VALUES (4929,813,2166,'Chris','re: Weighty Solution (maybe!)','2003-05-14 10:48:06',0,'I realized two things after I posted:
\r\n1) The formula does not apply for X=1. One weighting would not give us enough information to detect a fake from any number of coins.
\r\n2) There may be numbers of coin for which the equation doe not seem to hold true. For example, 19 coins cannot be detected in 5 weightings as one might suspect. Remember that the equation gives a maximum number of coins for a given number of weightings.\r\nSince 19 is not divisible by 4, this will not be an efficient use of the scale, and therefore, not a maximum number. Indeed, one could detect a fake from 64 coins in as many weightings (six), due to symmetry. I hope this helps.',4928,0);
INSERT INTO comment VALUES (4930,813,1626,'Gamer','re(2): Weighty Solution (maybe!)','2003-05-14 12:22:35',0,'I don\'t think it would work for 3 weighings on B. You would only be able to use X if its divisible by 2.\r\n\r\nI would propose N=2^(2*floor(X/2))\r\n\r\nAnd the formula works for 0 too. If you couldn\'t use the scale at all, the most coins you could have was 1, and that\'s the fake coin! ',4929,0);
INSERT INTO comment VALUES (4931,807,1626,'Gamer','A problem with that','2003-05-14 12:24:45',0,'The problem there is 2222222 is not divisible by 2*2*2*2 or 16. You need the product of the 4 digits, not just the 4 digits in a row.',4923,0);
INSERT INTO comment VALUES (4932,827,1253,'Brian Nowell','re(3): A Painted Cube - Shame on me!','2003-05-14 18:54:31',0,'Before I came here this morning, I realised the error of my ways. I posted the 4th attribute as n^2 whan it should have been n^3 thus the 4th attributes should have been 0, 1, 8, 27 and 64 instead of 0, 1, 4, 9, 16.\r\n\r\nI am intrigued by the internal \'view\' of the shell of the cube. This solution actually identifies the n^3 attribute as all of internal cubes.\r\n\r\nApologies for my error.',4922,0);
INSERT INTO comment VALUES (4933,827,1253,'Brian Nowell','All addressed','2003-05-14 19:01:23',0,'All of the attributes have been identified although the generalisation was in error.\r\nThe intended generalisation should have read:\r\n{8, 12n, 6n^2, n^3, n}',NULL,0);
INSERT INTO comment VALUES (4934,511,979,'Ravi Raja','re(6): Read This','2003-05-14 20:37:29',0,'I am sorry Hank but the answer cannot be No also, if it is not Yes. In fact the question is the same as what you are looking for but just put in a different form. ',4895,0);
INSERT INTO comment VALUES (4935,807,1575,'DJ','Ooh..','2003-05-14 22:30:31',0,'I misread the problem.\r\n\r\nIt looked nice..',4931,0);
INSERT INTO comment VALUES (4936,813,1902,'Hank','re(3): Weighty Solution (maybe!)','2003-05-15 03:07:01',0,'A previous puzzle showed that you could find one fake coin (not knowing if it is heavier or lighter) out of 39 in 4 weighings. I would say that this is contrary to the equation in question.\r\nSorry to just pose a problem and offer no constructive thoughts, but I have yet to find the right path for this one.',4930,0);
INSERT INTO comment VALUES (4937,521,1941,'shaun','','2003-05-15 03:39:04',3,'9+1+6 = 16\r\n9+16 = 25\r\n9*16 = 144',NULL,0);
INSERT INTO comment VALUES (4938,43,1920,'Brian Smith','Really not that hard','2003-05-15 04:42:49',0,'The two numbers must be primes or powers of primes. Candidates: 2,3,4,5,7,8,9,11,13,16,17,19,23,25,27,29,31\r\n\r\nThe only consecutive pair is 16 and 17',NULL,0);
INSERT INTO comment VALUES (4939,520,2231,'Trevor Leitch','re: Yeah','2003-05-15 06:30:54',0,'But if the \"or two\" makes the clue ambiguous, why couldn\'t the following be an acceptable answer?\r\nK-spades, 2-(any suit), Q-hearts',4924,0);
INSERT INTO comment VALUES (4940,813,2166,'Chris','re(3): Weighty Solution (maybe!)','2003-05-15 06:43:16',0,'\r\nActually, it is quite simple to detect 1 out of 8 coins in 3 weighs.\r\n\r\nFirst divide the 8 coins into 4 pairs A,B,C,D.\r\n\r\nFollow the procedure from my first post to find which pair contains the fake (only 2 weighs used so far).\r\n\r\nLastly, use the third weigh to balance either of the coins in the \'fake pair\' against any of the six real coins.\r\n\r\nIf it balances, the untouched coin is the fake; if it doesn\'t, we know not only that it is the fake but whether it is light or heavy. \r\n\r\nBTW, if anyone can direct me to the problem Hank mentioned in which 39 coins can be detected in 4 weighs, I would greatly appreciate it.',4930,0);
INSERT INTO comment VALUES (4941,813,2166,'Chris','re(4): Weighty Solution (maybe!)','2003-05-15 06:53:29',0,'Oops, nevemind the last line of my last post, as I found the 39 coin problem. This does, however, put a damper on my solution, for now.',4940,0);
INSERT INTO comment VALUES (4942,521,2166,'Chris','Solution','2003-05-15 07:11:00',0,'The three-digit number is 916. As a check:\r\n\r\nA) 9 + 16 = 25 = 5^2\r\n\r\nB) 9 * 16 = 144 = 12^2\r\n\r\nC) 9 + 1 + 6 = 16 = 4^2',NULL,0);
INSERT INTO comment VALUES (4943,520,1575,'DJ','re(2): Yeah','2003-05-15 08:15:46',0,'Even though the \'or two\' makes it unclear whether there is one or two of the card, the problem does say \'immediately.\' So, if there is one, it is immediately next to the card named, or in the case of two, the neighboring card and the one directly after it.\r\n\r\nIt could be argued that there is only ever one card immediately to either side, regardless of that card\'s opposite neighbor, which is why omitting the \'or two\' only possibly would make the first and third clues incorrect.\r\nConsider this:\r\nIn the case of K♠-Q♠-Q♥, is \"there is one Queen immediately to the right of the King\" a true or false statement?\r\n\r\nBetter safe than sorry, and better to put down \'or two\' than have people arguing over how many Queens are considered to be immediately to the right of the K♠ (although, that would have made some interesting debate, I\'m sure).',4939,0);
INSERT INTO comment VALUES (4944,808,1567,'Bryan','No help here','2003-05-15 09:42:07',0,'I\'m not sure, but this might be one of those classic geometry problems with no solution.',NULL,0);
INSERT INTO comment VALUES (4945,808,1626,'Gamer','','2003-05-15 09:50:43',0,'I don\'t know of any leads, so I would agree with Bryan... I would think that since 5 and 104 are hard numbers to create.',NULL,0);
INSERT INTO comment VALUES (4946,521,1626,'Gamer','Do more','2003-05-15 10:18:28',4,'Explain how you got the number, and prove that there are or aren\'t any more three digit numbers. That is always a good idea for problems like this.',NULL,0);
INSERT INTO comment VALUES (4947,521,1301,'Charlie','solution','2003-05-15 11:25:51',3,'This program:\r\n\r\nFOR a = 1 TO 9\r\n FOR b = 0 TO 9\r\n FOR c = 0 TO 9\r\n t1 = a + 10 * b + c\r\n st1 = INT(SQR(t1) + .5)\r\n IF st1 * st1 = t1 THEN\r\n t2 = a * (10 * b + c)\r\n st2 = INT(SQR(t2) + .5)\r\n IF st2 * st2 = t2 THEN\r\n t3 = a + b + c\r\n st3 = INT(SQR(t3) + .5)\r\n IF st3 * st3 = t3 THEN\r\n PRINT a; b; c\r\n END IF\r\n END IF\r\n END IF\r\n NEXT\r\n NEXT\r\nNEXT \r\n\r\nProduces\r\n\r\n1 0 0\r\n 2 0 2\r\n 4 0 0\r\n 8 0 8\r\n 9 0 0\r\n 9 1 6\r\nso that if \"the number formed by the second and third digits\" is not allowed to have a leading zero, then 916 is the only solution.',NULL,0);
INSERT INTO comment VALUES (4948,521,1645,'luvya2003','another solution','2003-05-15 11:49:19',0,'Another possible solution is 808 because:
\r\na) 8+08= 16
\r\nb) 8*08= 64
\r\nc) 8+0+8= 16
',NULL,0);
INSERT INTO comment VALUES (4949,521,1626,'Gamer','re: solution (More confusing!)','2003-05-15 12:44:25',3,'Ok Charlie... You beat me to it, but I have a non-brute force solution.\r\n\r\nIf no leading zeroes are allowed (just like the condition in the post below), then this will work:\r\n\r\nFirst, think of the 3 digits as a,b,c, and the 3 square roots as x,y,z. All of these must be integers to be digits.\r\n\r\nThe three things we know are a+b+c=y^2, a+10b+c=x^2, a*(10b+c)=z^2.\r\n\r\nTaking the first two, using linear combination, it can be shown that 9b = y^2 - x^2. If y = w+x (since 9b is not negative positive, y must be greater than or equal to x, which means w is not negative), 9b = (w+x)^2 - x^2, which simplifies to 9b = 2wx + w^2.\r\n\r\nGiven the values 1 to 9 as possible values for w (10 to 18 would repeat):\r\n\r\n(x2 stands for x squared, y2 stands for y squared)\r\n\r\nW-X-y2--x2-B\r\n1-4-025-16-1\r\n2-8-100-64-4\r\n3-3-036-09-2\r\n4-7-121-49-8\r\n5-2-049-04-3\r\n6-6-036-36-12\r\n7-1-064-01-4\r\n8-5-169-25-16\r\n9-0-081-00-5\r\n\r\nYou can figure out x from w. Since 9b=(2x+w)w, (2x+w)w must be divisible by 9. Except for a number divisible by 3 (see below) there is only one x value for each w. (x can\'t be zero, or a,b,c = 0, or another disallowed value)\r\n\r\n(w+x)^2=y^2 is more than 27, no a,b,c all less than 10 will work. This means all but w=1 and w=3 (the only special case whose square isn\'t greater than 27) can be eliminated immediatley\r\n\r\nw=3 doesn\'t work because x=0 is disallowed, and if x=3, (3+3)^2 is greater than 27.\r\n\r\nSo w = 1, and x must equal 4. This means that y^2 = (1+4)^2, or 25, and x^2 = 16, and b = ((2(4)+1)1)/9, or 1.\r\n\r\n',4947,0);
INSERT INTO comment VALUES (4950,520,2231,'Trevor Leitch','re(3): Yeah','2003-05-15 12:56:54',0,'What I meant was, the \"or two\" could refer to a card of rank 2, not \"or two spaces to the right/left\". Thus, in the solution\r\nK-spades, 2-(any suit), Q-hearts,\r\nTo the right of the King there\'s a 2 (as in a \"Queen or two\"), to the left of the Heart there\'s a Spade (as in a \"Spade or two\"), etc',4943,0);
INSERT INTO comment VALUES (4951,521,1626,'Gamer','re(2): solution (More confusing!) Part 2','2003-05-15 13:01:28',3,'Now that we know a + 10 + c = 25, and a + 1 + c = 16, we can use the second equation to figure out what a and c are.\r\n\r\na(10+c)=z^2, and since you know that a + c = 15 (subracting constants from the above equations gives you this), you can substitute (15-c) for a.\r\n\r\nThis gives (15-c)(c+10)=z^2, and converting this into quadratic form gives -c^2 + 5c + (150- z^2) = 0\r\n\r\nPlugging -1 in for a, 5 for b and (150- z^2) for c in the quadratic formula, gives:\r\n\r\n1/2(5} ã (625-4(z^2)))=c\r\n\r\nThe only way c will be an integer is if the discriminant (d = (625-4(z^2))) is a perfect square. Since z has to be an integer, the only pairs that will work are (z=0, d=25) (z=10, d=15) and (z=12, d=7). Using a = 15-c once c is found gives (a,b,c) as (0,1,15) (5,1,10) and (9,1,6) because any any negative c would be disallowed.\r\n\r\nSince the first two sets aren\'t applicable for base 10 (although they do \"work\" when tested), the only one possible given our restrictions is (9,1,6) or the number 916.',4949,0);
INSERT INTO comment VALUES (4952,808,2130,'ethan','answer, i hope','2003-05-15 13:07:33',3,'First, with the compass, make a circle with radius r. Then make 5 marks on the cirumference of the circle, so that if any two consecutive marks would have a line drawn from them to the center of the circle, they would form a 72 degree angle. Next connect the five marks on the circumference.',NULL,0);
INSERT INTO comment VALUES (4953,808,2130,'ethan','my mistake','2003-05-15 13:12:10',0,'it just dawned on me, the compass probably doesn\'t measure angles. my mistake.',NULL,0);
INSERT INTO comment VALUES (4954,521,2227,'Mayer Kim','Solution','2003-05-15 13:21:35',3,'916...\r\n\r\na) 9 + 16 = 25\r\n √25 = 5\r\n\r\nb) 9 X 16 = 144\r\n √144 = 12\r\n\r\nc) 9 + 1 + 6 = 16\r\n √16 = 4',NULL,0);
INSERT INTO comment VALUES (4955,520,1575,'DJ','re(4): Yeah','2003-05-15 17:40:05',0,'Ooh..I like that. Even though \'two\' isn\'t capitalized and all the other named suits and ranks are, I don\'t see any reason why that wouldn\'t work.\r\n\r\nPerhaps a good problem would be impossible to solve, unless you made that play on words:\r\n\r\nImmediately to the right of a king there\'s a queen or two. \r\nImmediately to the left of a queen there\'s a king or two. \r\nImmediately to the left of a heart there\'s a spade or two. \r\nImmediately to the right of a spade there\'s a heart or two.\r\nImmediately to the left of a club there\'s a spade or two.\r\nImmediately to the right of a spade there\'s a club or two.\r\n\r\nThat set of clues cannot be solved straightforwardly. The answer must be something like K♠ - 2♣ - Q♥.\r\n\r\nGood point!',4950,0);
INSERT INTO comment VALUES (4956,808,979,'Ravi Raja','Solution','2003-05-15 19:16:22',3,'Given the line segment of length \'r\'. From one end of the line segment make an angle of 72 degrees with the compass. Then draw the straight line from that point such that the angle between the two lines (the given and the one that will be drawn) will be equal to 72 degrees. Then using the compass take the measure of the distance \'r\' from the given line and cut an arc which cuts the second line at a distance \'r\'. This is the second radius of the pentagon. Continuing the same procedure four more times, we will get six such straight lines such that when taken in pair, the angle between every two consecutive straight lines will be equal to 72 degrees and each straight line will be of length \'r\'. Now join all the end points of these straight lines and from the common point (from where the angles were measured and arcs of length \'r\' were cut off), draw a circle of radius \'r\'. We now get a circumcircle of radius \'r\' circumscribing a regular polygon. \r\n\r\n(I think I have not framed my answer properly but I hope everyone understands what I am trying to say. I mean my method. Actually the moment I thought of it I just posted everything out here).',NULL,0);
INSERT INTO comment VALUES (4957,521,1941,'shaun','re: another solution','2003-05-15 20:04:33',0,'It says in the question \"three different digits\". 8 and 8 look very similar to me ;-)',4948,0);
INSERT INTO comment VALUES (4958,521,1941,'shaun','re: Do more','2003-05-15 20:06:56',0,'I wrote all the possible sets of digits on a bit of paper and worked out which ones worked. Only 916 met all the criteria.',4946,0);
INSERT INTO comment VALUES (4959,520,2239,'Alpha Tiger','This problem is too easy !','2003-05-16 01:46:37',3,'King Heart\r\nQueen Spade\r\nQueen Spade',NULL,0);
INSERT INTO comment VALUES (4960,520,2239,'Alpha Tiger','re: This problem is too easy !','2003-05-16 01:48:25',0,'Excuse me it\'s\r\nKing Spade\r\nQueen Spade\r\nQueen Heart',4959,0);
INSERT INTO comment VALUES (4961,521,1686,'DuCk','Solution','2003-05-16 01:53:33',0,'916\r\n\r\n9+1+6=16=4²\r\n9*16=144=12²\r\n9+16=25=5²',NULL,0);
INSERT INTO comment VALUES (4962,21,2239,'Alpha Tiger','This game','2003-05-16 02:02:47',3,'I often seen this game ...\r\nMy solution :\r\nYou take 1, 2, 3 cards so it remains 4n cards (n is an integer). So if the opponent takes 1 card, you take 3 cards, if he takes 2, you take 2 ...\r\n\r\nAt the end it will remain 4 cards, the opponent won\'t be able to win.\r\n\r\nFor the decks :\r\n1:no\r\n2:no\r\n3:no\r\n4:yes\r\n\r\n(of course, if the opponent doesn\'t know the strategy, all the decks are good ...)',NULL,0);
INSERT INTO comment VALUES (4963,775,2239,'Alpha Tiger','Too easy ...','2003-05-16 02:06:54',3,'As Drew and Mohammad say different things, they are of different types, so Mohammad is a knight and Drew a liar ...',NULL,0);
INSERT INTO comment VALUES (4964,732,2239,'Alpha Tiger','Too easy ...','2003-05-16 02:09:39',3,'If Drew is a knight, as he says, he\'s a liar, so he does be a liar.\r\n\r\nAs he\'s a liar, Mohammad and Drew aren\'t both liars, so Mohammad is a knight.',NULL,0);
INSERT INTO comment VALUES (4965,813,872,'pleasance','another approach to problem B','2003-05-16 02:35:00',0,'For part A, everyone seems agreed that n=3^x is the maximum. For part B, you can definitely manage n=3^(x-1). That is, add one more weighing. I don\'t think this is the best possible, but it can definitely be done. \r\n\r\nFor example, with 9 coins, divide into 3 groups of 3. Weigh group A against B, if A heavier weigh A against C. You now know which threesome has the fake coin, and whether it\'s heavier or not, and one more wighing will solve it.',NULL,0);
INSERT INTO comment VALUES (4966,808,1301,'Charlie','re: Solution','2003-05-16 03:20:26',0,'A compass is not a protractor. It can\'t measure angles.',4956,0);
INSERT INTO comment VALUES (4967,808,979,'Ravi Raja','re(2): Solution','2003-05-16 04:32:39',0,'Well what I actually meant was that just how we draw a right angle, or 60 degrees or 45 degrees, or 30 degrees, etc. using a compass, just the similar way, we will be measuring or you can say cut off an angle of 72 degrees from a given point. That\'s whay I left a note Charlie at the end of the comment that I have posted regarding my way of explaining the solution. I knew that something or the other is there which the users might not be able to understand.',4966,0);
INSERT INTO comment VALUES (4968,829,2231,'Trevor Leitch','Solution','2003-05-16 04:47:28',3,'Before beginning, not the following:\r\n1) Each person makes four comments, which will be labeled as such: Ernesto\'s first comment is (E1), Gildenstern\'s last is (G4), etc.\r\n2) For each person, their first and third comments must both be true or both be false; there cannot be a situation where one is true and the other a lie. Similarly with their second and fourth comments.\r\n\r\nThus:\r\na) We know that Fontleroy is not a knight, because a knight would never call himself a knave. Thus, F1 - and by extension F3 - are lies.\r\nb) If Ernesto was a knight, then Gildenstern would also be a knight (via E2), but then Ernesto would have to be a knave (via G3). Thus, Ernesto cannot be a knight.\r\nc) Since Ernesto is not a knight, F4 is a lie, and thus so is F2. Therefore, Fontleroy is not a knight, and Gildenstern is not a liar.\r\nd) Also since Ernesto is not a knight, E1 is false and therefore so is E3. Thus, Fontleroy is not a liar - and since he\'s not a knight either (see c above), he must be a knave. Since F2 and F4 are lies, F1 and F3 must be the truth.\r\ne) Since Fontleroy is a knave, G1 must be true and therefore G3 as well. Thus, Ernesto must be a knave (via G3), and since E1 and E3 are false, E2 and E4 must be true. Gildenstern is therefore a knight (via E2), and G2 and G4 are true. \r\n\r\nFrom the above we know that: G2, F3 and E4 are all true. Thus, Gildenstern did not arrive first, nor did Fontleroy, and Gildenstern (the only knight and therefore most honest) did not arrive last. This means that only Ernesto could have come first, and the only place in which Gildenstern could have arrived is second. Finally, Fontleroy came last. If the innkeeper awards rooms to those individuals based on the order they arrived (rather than their honesty), the Ernesto gets the best room, the Gildenstern, and finally Fontleroy.',NULL,0);
INSERT INTO comment VALUES (4969,829,2231,'Trevor Leitch','re: Solution','2003-05-16 04:52:39',0,'Sorry, in my solution under part (a), ignore the last line (\"Thus, F1 - and by extension F3 - are lies\")... it makes no sense, just omit it.',4968,0);
INSERT INTO comment VALUES (4970,520,979,'Ravi Raja','re: My initial reaction','2003-05-16 04:53:44',0,'Hank: I believe that you are thinking that the \'two\' that I have mentioned in the problem refers to the \"Two Of Spades\' or something like that. Isn\'t it? But see carefully Hank, if it would have been so, the the statements would not have looked like what you are seeing, but they would have gone like this: \r\nImmediately to the right of the King there\'s a Queen or a Two. \r\nImmediately to the left of a Queen there\'s a Queen or a Two. \r\nImmediately to the left of a Heart there\'s a Spade or a Two. \r\nImmediately to the right of a Spade there\'s a Spade or a Two. \r\n',4920,0);
INSERT INTO comment VALUES (4971,520,979,'Ravi Raja','re(2): Yeah','2003-05-16 04:59:27',0,'Trevor: Read my comment \"re: My initial reaction\"',4939,0);
INSERT INTO comment VALUES (4972,520,979,'Ravi Raja','re(5): Yeah','2003-05-16 05:19:29',0,'DJ: please do check my comment \"re: My initial reaction\".',4955,0);
INSERT INTO comment VALUES (4973,520,979,'Ravi Raja','re: This problem is too easy !','2003-05-16 05:23:16',0,'Still you made a mistake while solving it Tiger.',4959,0);
INSERT INTO comment VALUES (4974,521,979,'Ravi Raja','re: Do more','2003-05-16 05:29:11',0,'Even I am looking for such a solution Gamer.',4946,0);
INSERT INTO comment VALUES (4975,521,979,'Ravi Raja','re(2): Do more','2003-05-16 05:29:31',0,'That is not the way to prove the uniqueness of such a number.',4958,0);
INSERT INTO comment VALUES (4976,521,979,'Ravi Raja','re: another solution','2003-05-16 05:32:43',0,'Luvya: Read the question properly. It asks you to find a three-digit number containing three DIFFERENT digits satisfying the given properties.\r\nSo your answer is not correct.\r\n',4948,0);
INSERT INTO comment VALUES (4977,521,979,'Ravi Raja','re(2): another solution','2003-05-16 05:33:33',0,'Yes indeed they are shaun. EvenI have commented for this answer of luvya.',4957,0);
INSERT INTO comment VALUES (4978,521,979,'Ravi Raja','re: solution','2003-05-16 05:36:00',0,'Nothing is mentioned about the leading zeros or such Charlie but the problem does ask for a three-digit number with three DIFFERENT digits. So, now you can say that 916 is the only solution.',4947,0);
INSERT INTO comment VALUES (4979,521,979,'Ravi Raja','re(3): solution (More confusing!) Part 2','2003-05-16 05:38:26',0,'1/2(5} ã (625-4(z^2)))=c \r\n\r\nWhat does all these characters mean Gamer ? Please Explain.',4951,0);
INSERT INTO comment VALUES (4980,829,1301,'Charlie','Same answer--different sequence of logic','2003-05-16 05:44:59',3,'Using Trevor Leitch\'s statement numbering system of E1 - F4:\r\n\r\nBy F1, F is not a knight by the same reasoning Trevor used.\r\n\r\nThen F2 is false, as F is either a knave who previously spoke the truth and is now lying or is a liar who is continuing to lie, so G is not a liar.\r\n\r\nSince F2 is false, so is F4, so E is not a knight.\r\n\r\nSo E1 is false, and therefore also E3, so F is not a liar.\r\n\r\nSince F is not a liar nor a knight he is a knave, so F1 is true and therefore also F3, so F did not arrive first.\r\n\r\nAs G1 agrees with true statement F1, it is also true, making G3 also true, so E is a knave.\r\n\r\nSince E is a knave and E1 is false, E2 is true, so G is a knight.\r\n\r\nSince G is a knight, G2 is true, and G did not arrive first.\r\n\r\nSince F did not arrive first and G did not arrive first, E must have arrived first.\r\n\r\nSince E2 is true E4 is true and the most honest (G, the only knight) did not arrive last. Since G did not arrive first, he arrived second.\r\n\r\nSince E arrived first, getting the best room; G arrived second, getting second best; F arrived last, getting the worst.\r\nAnd to recap, E and F are knaves and G is a knight.',4968,0);
INSERT INTO comment VALUES (4981,808,1567,'Bryan','re(3): Solution','2003-05-16 06:37:20',0,'Ravi, perhaps you are missing the point. With nothing but a compass for drawing circles and a straight edge for drawing lines, one can easily make a ninety or sixty degree angle and bisect them ad infinitum. But how does one create an angle of 72 degrees (or any angle that is not a multiple of 15, for that matter)? Only when you answer that will you fully answer the original question.',4967,0);
INSERT INTO comment VALUES (4982,521,1301,'Charlie','re(2): solution (More confusing!)','2003-05-16 08:03:20',0,'I start being lost when you say \r\na+b+c=y^2, a+10b+c=x^2\r\nand that these lead to\r\n 9b = y^2-x^2.\r\nPerhaps a typo in the interchange of x and y in one or the other of the lines, but not knowing which discourages me from reading further.',4949,0);
INSERT INTO comment VALUES (4983,524,2066,'David','Solution','2003-05-16 08:57:25',0,'The only possible answer would have to be \"eye\". It is the only word that can be read as one letter and be the same either direction',NULL,0);
INSERT INTO comment VALUES (4984,524,1626,'Gamer','re: Solution','2003-05-16 09:47:11',0,'This is one of the better versions of this puzzle I have seen around. Good job Ravi!',4983,0);
INSERT INTO comment VALUES (4985,521,1645,'luvya2003','re(2): another solution','2003-05-16 11:03:53',0,'I realized that they had to be three DIFFERENT digits as soon as I posted my solution. Once again, my impatience and haste has proved to my disadvantage. But since Shaun commented on this already, and I did read his comment before you even posted your reply, it wasn\'t really nescessary to point it out again.',4976,0);
INSERT INTO comment VALUES (4986,469,1645,'luvya2003','re(2): ???','2003-05-16 11:10:54',0,'\"NONE\" means just that... none. Or better put zero.',3437,0);
INSERT INTO comment VALUES (4987,765,2129,'Sanjay','General Solution','2003-05-16 13:16:12',3,'3 likely results per weighing; Left heavy (L), Right heavy (R), Balanced (B). Hence, 3^X likely results for X weighings.\r\n\r\nCreate X rows, 1 to X. For row n repeat \'L\',\'B\', &\'R\' 3^(n-1) times each, then repeat the pattern 3^(X-n) times. Full table for X=3:\r\n\r\nRow 1: L,B,R,L,B,R,L,B,R,L,B,R,L,B,R,L,B,R,L,B,R,L,B,R,L,B,R\r\nRow 2: L,L,L,B,B,B,R,R,R,L,L,L,B,B,B,R,R,R,L,L,L,B,B,B,R,R,R\r\nRow 3: L,L,L,L,L,L,L,L,L,B,B,B,B,B,B,B,B,B,R,R,R,R,R,R,R,R,R\r\n\r\nEach column is a possible result of X weighings. Weighing strategy:\r\n\r\nColumn 1 to (3^X-3)/2 represent coins with matching numbers. L,B,& R in row n tell us where coins go during nth weighing. L=Left; R=Right; B=Break (or stay out). A minor adjustment. First place coins as per table, then remove all known \'good\' coins from Left & add enough \'good\' coins to Right to make equal coins on both sides. There will always be enough \'good\' coins.\r\n\r\nFor X=3, 1st weighing: 1,4,7,10 on Left; 3,6,9,12 on Right; 2,5,8,11 on Break. If Left heavy, then 2,5,8,11 are \'good\'. So in the second weighing first put 1,2,3,10,11,12 on Left & 7,8,9 on Right, then remove 2 & 11 from Left & add one \'good\' coin to Right. So on. After X weighings, match results with one of the columns.\r\n\r\nIf match is in the first (3^X-3)/2 columns, \'fake\' coin is heavy & its number equals the matching column. If match is in the last (3^X-3)/2 columns, \'fake\' coin is light & its number equals 3^X+1 minus the matching column. Three central columns are always \'impossible\' results. (3^X-3)/2 is maximum \'solvable\' in X weighings.',NULL,0);
INSERT INTO comment VALUES (4988,524,2242,'hector','solution','2003-05-16 13:34:36',0,'the answer if EYE',NULL,0);
INSERT INTO comment VALUES (4989,524,2243,'J. Moore','Guessme Ten','2003-05-16 13:47:43',3,'Too easy - the word is eye.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (4990,521,1626,'Gamer','re(3): solution (More confusing!)','2003-05-16 14:54:46',1,'Oops... It looked fine in preview, but I didn\'t read my own post over.\r\n\r\nTo answer Charlie\'s question, I did make the mistake of mistyping x and y. The equations SHOULD read a+b+c=x^2, a+10b+c=y^2, a*(10b+c)=z^2.\r\n\r\nTo answer Ravi\'s question, I don\'t know how it got mangled in the set up, but those mean + or -, and square root.\r\n\r\nIf p means plus or minus, and s() means square root(), you can get:\r\n\r\n(5 p s(625-4(z^2) )))/ 2 out of that mess.\r\n\r\n\r\nI think √ or ã means square root and ± or } means plus or minus.',4982,0);
INSERT INTO comment VALUES (4991,521,1626,'Gamer','re(4): solution (More confusing!)','2003-05-16 14:56:38',0,'So in normal terms, you use (5±√(625-4(z^2))))/ 2',4990,0);
INSERT INTO comment VALUES (4992,520,1626,'Gamer','re(2): My initial reaction','2003-05-16 15:02:37',0,'But you are relying on capitalization to yield your meaning? When I read it, I thought of the OR as being logic, so I read it as Immediately to the right of the King, there\'s a \"Queen or two\", and since there is only 1 set, you would only need to capitalize the first leter of the set.\r\n\r\nI might have worded it as:\r\n\r\nImmediately to the right of the King there\'s at least one Queen. \r\nImmediately to the left of a Queen there\'s at least one Queen. \r\nImmediately to the left of a Heart there\'s at least one Spade. \r\nImmediately to the right of a Spade there\'s at least one Spade.',4970,0);
INSERT INTO comment VALUES (4993,732,1626,'Gamer','re: Too easy ... Of course!','2003-05-16 15:03:40',0,'Well duh! That is why this is only a 1 out of 5 difficulty, the easiest it can get.',4964,0);
INSERT INTO comment VALUES (4994,775,1626,'Gamer','re: Too easy ... That\'s good!','2003-05-16 15:05:39',0,'That is true, but only because same type and different type are complimentary events. But I think that\'s a quicker way to solve this for this special case.',4963,0);
INSERT INTO comment VALUES (4995,813,2129,'Sanjay','The answer to \'fakeness\'','2003-05-16 16:31:42',3,'\r\nA. N = 3^X\r\n\r\nAs everyone here has already said, each weighing has 3 possible results, so N weighings has 3^X possible results. Succesive trifurcation of the \'found out\' bunch does the trick. Each succesive weighing narrows the field by 2/3rds and it takes X weighings to reduce the possibility to 1 starting from 3^X.\r\n\r\nB. (3^X-3)/2 \r\n\r\nIf the the type of \'fakeness\' is not known then it doubles the information need and yields three less real possibilities than the theretical possibilities. This is because most known strategies involve some switching of coins from one side to the other. This leads to three \'impossible\' sequences where a result from a later weighing contradicts a result from an earlier weighing.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (4996,228,2130,'ethan','answer','2003-05-16 16:32:32',0,'1) Grammatically, \"is\" should be \"are\", because \"errors\" is plural.\r\n2)This is spelt wrong. \r\n3)There are only two errors.',NULL,0);
INSERT INTO comment VALUES (4997,524,153,'TomM','re: Solution','2003-05-16 17:16:05',0,'Although you are correct that the answer is \"eye,\" your reason is incorrect. \"Ewe\" also is pronounced the same as a letter, also is a palindrome, also is two letters, with one repeated for a total of three. Where it fails is in the color (I know of no blue sheep), and the \"I\'m double\" clue. ',4983,0);
INSERT INTO comment VALUES (4998,524,2148,'Jayaram S','Full Solution','2003-05-16 19:12:04',3,'The answer is definitely EYE.\r\n\r\nExplanation:\r\n1. Pronounced as one letter...(pronounced as \"I\")\r\n2. And written with three,....(\"EYE\" has 3 letters)\r\n3. Two letters there are......(two alphabets used are \"E\" & \"Y\") \r\n4. And two only in me....(Probably Ravi has 2 eyes)\r\n5. I\'m double, I\'m single..(Few have 2 eyes & few others only 1)\r\n6. I\'m black, blue, and gray..(That\'s true, we can see people with black or blue or gray and probably brown eyes)\r\n7. I\'m read from both ends\r\nAnd the same either way.....(That\'s obvious!)\r\nWhat am I? \r\n',NULL,0);
INSERT INTO comment VALUES (4999,524,1304,'Emon Hunte','eASiest guess me yet','2003-05-16 22:19:08',3,'To get that the answer in \"EYE\" is use to first two lines and go through the alphabet figuring out which letters also are pronounced as a word until you find the right one.',NULL,0);
INSERT INTO comment VALUES (5000,521,1575,'DJ','Hmm','2003-05-16 22:22:03',1,'Even though all three digits must be different, what about leading zeroes on the number itself? If those are valid, and if you consider zero to be a perfect square of itself, then 036 and 081 are also valid answers.',NULL,0);
INSERT INTO comment VALUES (5001,524,1575,'DJ','re: eASiest guess me yet','2003-05-16 22:26:11',0,'B, C, G, I, J, L, O, P, R, T, U, V, and Y all have similarly pronounced three-letter words (and a few other letters, but those words are rather uncommon).\r\nOf course, \'eye\' is still the only word that fits all the other clues.',4999,0);
INSERT INTO comment VALUES (5002,373,1575,'DJ','And..','2003-05-16 22:46:51',0,'Conveniently, whether you double the number of letters in ten, or take the number of letter in \'twice ten,\' twenty, you still get six. Just a point of interest.\r\n\r\nLooking back . . . man, was there seriously that much debate over a simple problem?',NULL,0);
INSERT INTO comment VALUES (5003,383,1575,'DJ','But..','2003-05-16 22:53:26',0,'Didn\'t you already do a snowman in guessme one?',NULL,0);
INSERT INTO comment VALUES (5004,520,1575,'DJ','re(6): Yeah','2003-05-16 23:16:34',0,'If you look at my previous response, you will see that I already noted the difference in capitalization, but that is more of an aesthetic difference than one that would definitively change the meaning of the word. Also, Ravi, I have found that your grammar (capitilazation, puncuation, etc) is often heavy-handed and yields something that is either incorrect or something you did not intend. Actually, none of the words \'king,\' \'queen,\' \'heart,\' or \'spade\' need be capitalized for this problem.\r\n\r\nSo, while it is probably obvious that you did not intend the \'or two\' to mean the possibility of the middle card being a deuce, merely not capitalizing the word in no way eliminates it.\r\nA wording such as Gamer suggested would still have the necessary ambiguity I mentioned in my first comment, but without the \'loophole\' Trevor noticed.',4972,0);
INSERT INTO comment VALUES (5005,524,2245,'Anu','','2003-05-16 23:20:33',0,'YOU',NULL,0);
INSERT INTO comment VALUES (5006,520,1575,'DJ','Ravi','2003-05-16 23:22:59',4,'and is it really necessary to make a reply to every single comment, even if only to bring attention a third time to a comment you left about a point I already mentioned(and you seemed to ignore), or a mistake someone made and immediately noticed and corrected?\r\n\r\nhaving submitted more problems than everyone else put together doesn\'t make you some sort of superior flooble guru',NULL,0);
INSERT INTO comment VALUES (5007,524,2246,'abhi','i cannot relate....','2003-05-16 23:45:02',0,'well.... I think the answer is EWE. But i cannot elate the answer with \'blue\'....',NULL,0);
INSERT INTO comment VALUES (5008,808,1575,'DJ','Clueless','2003-05-16 23:59:05',0,'I have been contemplating this for some time and cannot think of any good way to even begin constructing this problem. If it is solved, then from that regular pentagon is now a way also to create a 72° angle. And perhaps, by similar methods if they exist, the angles formed by other regular polygons, such as 40°.\r\n\r\nPerhaps the whole bit about r and the circumradius is overkill; simply constructing any regular pentagon or the required angle is going to be difficult, at least to come up with a method, and anything else is rather trivial.',NULL,0);
INSERT INTO comment VALUES (5009,808,1575,'DJ','Cheesy attempt','2003-05-17 00:05:36',0,'You can come pretty close to the angle by constructing a right angle, marking a distance on one side, and measuring three times that distance on the other side.\r\nThe bottom base angle is then invtan(3/1)=71.565°, relatively close to 72° but certainly not close enough.\r\nPerhaps another triangle/trig solution will allow an exact angle, but I haven\'t found one.',NULL,0);
INSERT INTO comment VALUES (5010,228,1575,'DJ','Here:','2003-05-17 00:16:14',0,'1. \'is\' should be \'are\' (or \'were\'?)\r\n2. \'thise\' should be \'this\'\r\n3. \'three\' should be \'four\'\r\n4. \'difficulty\' should not be 1 (a la Nick)',NULL,0);
INSERT INTO comment VALUES (5011,808,1575,'DJ','Der..','2003-05-17 00:48:25',0,'Of course, each angle in a regular polygon is [(5-2)180]/5=104°, not 360/5=72° as a few people suggested. An angle less than 90° doesn\'t make sense geometrically, of course, but I didn\'t even notice until just now.\r\n\r\nA similarly weak method to constructing a 104° angle as my previous attempt, might be a right triangle with legs of x and 4x. One of the base angles is then invtan(4/1)=75.963°, which is supplementary to 104.037° (found by extending the shorter leg and using the external angle). Again, this is relatively close to 104°, but not nearly close enough for a credible solution.\r\n\r\nI think that with insanely complex trig ratios, it would be possible to get very very close to the actual angle.\r\nFor example, tan 104°=--4.0107809335358447163457151294634..\r\nTo 5 places, that is -4.01078.\r\nSo, constructing a right angle, picking some arbitrary length, and adding that length 401078 times on one side and 10000 times on the other would give an external angle of\r\n180°-invtan(401078/10000)\r\n=180°-invtan(4.01078)\r\n=180°-75.999996869569406544894796255462°\r\n=-104.00000313043059345510520374454\r\n\r\nDoing this with increased precision, while not entirely physically feasible, would produce an angle as good or better than any you would come up with using a regular protractor.\r\n\r\nAgain, this will never be exact, so, there must be another route to look down...',NULL,0);
INSERT INTO comment VALUES (5012,524,979,'Ravi Raja','re:','2003-05-17 04:16:42',0,'Do you mean I am Black, BLUE, and Gray ??????',5005,0);
INSERT INTO comment VALUES (5013,520,979,'Ravi Raja','re: Ravi','2003-05-17 04:23:15',0,'DJ: Just stop talking like that OK! Just because I have submitted so many problems doesn\'t make me think as you have said, some sort of flooble guru or anything such and secondly, I read one comment at a time and reply to that comment (or you can say ask the submitter to correct it if it is wrong) and then move on to the next comment. Posting comments is not my hobby or anything such. So it would be better if you just stop talking like that to me.',5006,0);
INSERT INTO comment VALUES (5014,808,1767,'Fernando','A small hint','2003-05-17 06:29:37',0,'It\'s possible to construct it PERFECTLY!! A small hint is:\r\ncos72 = [-1 + √(5)]/4',NULL,0);
INSERT INTO comment VALUES (5015,523,1575,'DJ','Solution','2003-05-17 07:15:23',3,'Letters that can be made from straight line segments, and the number of segments, are as follows:\r\nA(3)\r\nE(4)\r\nF(3)\r\nH(3)\r\nI(1)(3?)\r\nK(3)\r\nL(2)\r\nM(4)\r\nN(3)\r\nT(2)\r\nV(2)\r\nW(4)\r\nX(2)\r\nY(3)(2?)\r\nZ(3)\r\nNumbers that can be made from these letters:\r\n5, 9, 10, 11, 12, 15, 19, 20, 25, 29, 50, 55, 59, 90...\r\nBut I doubt the number is higher than that. So, the number of segments in each of these numbers:\r\n5: 3+1+2+4 = 10\r\n9: 3+1+3+4 = 11\r\n10: 2+4+3 = 9\r\n11: 4+2+4+2+4+3 = 19\r\n12: 2+4+4+2+2+4 = 18\r\n15: 3+1+3+2+4+4+3 = 20\r\n19: 3+1+3+4+2+4+4+3 = 24\r\n20: 2+4+4+3+2+3 = 18\r\n25: (20)+(5) = 18+10 = 28\r\n29: (20)+(9) = 18+11 = 29\r\nBINGO\r\n\r\nTWENTY-NINE is comprised of 29 line segments (disregarding, as the problem states, the hyphen)',NULL,0);
INSERT INTO comment VALUES (5016,520,1575,'DJ','re(2): Ravi','2003-05-17 07:32:24',0,'Ravi, I don\'t, of course, mind that you have submitted so many problems (although, weighted or not, mine still take forever to be seen--that\'s besides the point). Many of the problems and many of the better problems on the site were yours, or submitted by you. All I\'m saying is, is it really necessary to leave Trevor and I each comments merely telling us to read what you wrote Hank? I don\'t get it. Moreover, and the really the reason I said anything at all, what good does it do anyone in saying that Alpha Tiger made a mistake? First, it wasn\'t a mistake in solving the problem, it was just a typo. Second, if you look at the timestamp, he(she?) corrected it in less then two minutes after posting the first comment. It\'s one thing to debate a point, it\'s quite another to have absolutely nothing constructive to say and point out and harp on other peoples\' simple mistakes. Just consider what you are saying to people before you post it.',5013,0);
INSERT INTO comment VALUES (5017,808,1575,'DJ','re: A small hint','2003-05-17 07:35:46',0,'Remember, we\'re not to find 72° or any supplement/complement. We need a 104° angle, or its supplement of 76°.\r\nEven still, i don\'t know how to find √5 with a ruler and compass.',5014,0);
INSERT INTO comment VALUES (5018,360,2249,'Kelley','solution','2003-05-17 07:55:12',0,'i\'ve heard this one a few times, so i know the answer is nothing.',NULL,0);
INSERT INTO comment VALUES (5019,808,1301,'Charlie','Solution','2003-05-17 09:08:11',3,'Start with a line. Erect a perpendicular to it. Set your compass to length r. Measure off this distance on one of the perpendicular lines, and twice this distance on the other. Connect the endpoints. You\'ve formed a right triangle with hypotenuse √5 in these units of r.\r\n\r\nUsing your unchanged compass mark off 1 unit (r length) from the hypotenuse, producing a line of length (√5)-1 in these units. Then bisect this remaining length, and bisect one of the two halves again, using the standard technique of erecting a perpendicular bisector. You now have a line segment of length ((√5)-1)/4 times r and a perpendicular to it at one end. At the other end place the compass point and draw a circle, which intersects the perpendicular line. Connect the center of the arc to this intersection point. At the center of the arc you will have created a 72-degree angle.\r\n\r\nYou have drawn a full circle of radius r around the 72-degree angle vertex as a center. \r\n\r\nNow fit the compass to the two points on the circle intersected by the two lines from the 72-degree angle and mark of four more of these 72-degree arcs (three more points actually). Connect the endpoints of the 72-degree arcs. The result is a regular pentagon with a circumradius of r.',NULL,0);
INSERT INTO comment VALUES (5020,521,1301,'Charlie','re: Hmm','2003-05-17 09:18:21',0,'When thinking of a \"three digit number\" I think of one that requires three digits rather than one that\'s made to be three digits arbitrarily. That\'s why in the computer program to find the solution I allowed the middle digit to be zero but not the first, as the number formed by the second and third digits was not specified to be necessarily a 2-digit number.',5000,0);
INSERT INTO comment VALUES (5021,765,1301,'Charlie','re: General Solution','2003-05-17 09:25:32',0,'This should be posted for Many Coins--One Fake.',4987,0);
INSERT INTO comment VALUES (5022,520,1626,'Gamer','re(3): Ravi','2003-05-17 12:18:01',0,'I think it would be more concise if you read all the comments before you posted, as sometimes you can agree/disagree with more people and it makes the ideas stronger... But I don\'t feel any problems with your method, so I don\'t mind.\r\n\r\nMake sure to keep an open mind as far as definitions go... We may not all follow the same standards of capitalization and so on, so disallowing a solution on capitalization or such may be questionable, just like disallowing singulars when using \"some\".',5016,0);
INSERT INTO comment VALUES (5023,315,2251,'matt','re: omg easy','2003-05-17 13:14:22',0,'look, \"this mans(his son) father(himself) is my father\'s(his dad) son\"\r\nhe is talking about his son. the key words begin with \"this man\". im sixteen, i understand it',4837,0);
INSERT INTO comment VALUES (5024,500,2251,'matt','the last chance','2003-05-17 13:19:54',0,'suicide',NULL,0);
INSERT INTO comment VALUES (5025,428,2251,'matt','ha','2003-05-17 13:52:29',0,'he was wearing a guiness shirt\r\n',NULL,0);
INSERT INTO comment VALUES (5026,829,979,'Ravi Raja','Please Someone Correct Me','2003-05-17 19:37:39',1,'If I am not mistaken, then we are assuming that each of the three men: Ernesto, Fontleroy and Gildenstern belong to different categories. That is, exactly one of them is a Knight, exactly one of them is a Knave and exactly one of them is a Liar.\r\n
\r\nLet us first assume that Ernesto is a Knight. But we see that Ernesto says in his second comment: \"Gildenstern is a Knight\". Ernesto being a Knight cannot Lie and therefore Gildenstern has to be a Knight. But again this is not possible, since each of the three belong to different categories. So our assumption that Ernesto is a Knight is wrong. Hence, Ernesto is not a Knight.\r\n
\r\nNow, let us suppose that Ernesto is a Knave. It is obvious that his first statement: \"I am a Knight\" is false, since if it were true, then he would have been a Knight and not a Knave (and in case if he were a Liar, still his statement had to be false). Therefore, his second statement must be True and his Third statement must be False, since he being a Knave, no two consecutive statements of his will be both True or both False, as according to the problem a knave\'s statements strictly alternates between truth and untruth. Then using this reasoning, we see that Gildendtern is a Knight and Fontleroy is NOT the Liar, which implies Fontleroy is either a Knight or a Knave, but according to our assumption, Ernesto is a Knave and his second statement being True, Gildenstern is a Knight, and since no two of the three belong to the same category, and Fontleroy cannot be the Liar, Fontleroy does not belong to any of the three categories. So once again we arrive at a contradiction, thus proving that Ernesto cannot be a Knave.\r\n
\r\nTill now we have proved that Ernesto can neither be a Knight nor a Knave. Therefore, Ernesto has to be a Liar. Now, consider the comments of Ernesto where he says: \"Gildenstern is a Knight\" and \"Fontleroy is the Liar\". Since Ernesto is a Liar, both his statements are false implying Gildenstern is a Knave and Fontleroy is a Knight. (Since if Fontleroy were a Knave, Gildenstern would be a Knight, contradictiong that Ernesto\'s statement is false). But we again arrive at a contradiction when we consider Fontleroy\'s statements: \"....I am only a Knave\", and \"Ernesto, you are a Knight\", since no Knight would say that about himself and a Liar (Ernesto). So once again we arrive at a contradiction, which means that our assumption that Ernesto is a Liar is wrong.\r\n
\r\nThus we see that Ernesto does not belong to either of the three categories: Knight, Knave and Liar. \r\n
\r\n(Now, I know that this is not possible and so I have made a mistake somewhere, but I am not able to find out where I am going wrong. Someone please help me with this).',NULL,0);
INSERT INTO comment VALUES (5027,520,979,'Ravi Raja','re(3): Ravi','2003-05-17 19:57:27',0,'DJ: I was just trying to correct their mistakes by showing them where they were going wrong. (This is to help them understand their mistakes and not to discourage them. In one problem of mine \'Around The World\', I have posted many such comments pointing out others\' mistakes but my intentions were not to discourage them, but make them understand the problem). I am not the kind of a person who likes to point out others\' mistakes. Secondly, you asked me to consider what I am saying to people before I post my comments. Did I say anything wrong to anyone that hurt his/her feelings or anything such. If that is so, then I apologise for that. I am really very sorry if I have said anything wrong to anyone. \r\nAnyway, thanks for all that. Even I would like people to point out where I am going wrong so that I can change myself, or you can say correct my mistakes. Next time if you feel I am going wrong anywhere, just feel fre to point it out and try to correct me.\r\nThanks again. ',5016,0);
INSERT INTO comment VALUES (5028,523,979,'Ravi Raja','Y : 3 Line Segments','2003-05-17 20:01:36',2,'To wrote Y we require 3 Line segments and not 2.',NULL,0);
INSERT INTO comment VALUES (5029,523,979,'Ravi Raja','re: Y : 3 Line Segments','2003-05-17 20:03:52',2,'To write Y we require 3 Line segments and not 2. \r\n',5028,0);
INSERT INTO comment VALUES (5030,313,2174,'Vinodhan Selvarajalu','re: Simple Simon met a Pieman who gave Simple Simon a problem called Sugar Cubes.','2003-05-18 00:46:49',0,'what???',4094,0);
INSERT INTO comment VALUES (5031,829,2129,'Sanjay','Flocking Together','2003-05-18 01:34:47',4,'Nowhere in the problem is it stated that the three young men belong to different dispositions. It only says that \'everyone was either a Knight or a knave or a Liar\', which does not preclude the possibility that all, or two out of the three were birds of the same feather. I wonder if this is deliberate or an oversight.',NULL,0);
INSERT INTO comment VALUES (5032,813,872,'pleasance','solution to B','2003-05-18 01:55:49',0,'OK, I think I\'ve finally cracked part B (type of \'fakeness\' unknown). I can manage up to:\r\n4 coins in 2 weighings\r\n13 coins in 3 weighings\r\n40 coins in 4 weighings.\r\nIt would appear that this generalises to \r\nn = 1 + 3 + 9 + ... 3^(x-1) coins in x weighings, or n = (3^x-1)/2.\r\n',NULL,0);
INSERT INTO comment VALUES (5033,829,1301,'Charlie','re: Please Someone Correct Me','2003-05-18 04:37:17',0,'The problem is in assuming that each of the three is a different category. If you look at the first two solutions posted you will see that that is proved not to be true, as two are of the same category, which those solutions prove.',5026,0);
INSERT INTO comment VALUES (5034,829,1301,'Charlie','re: Flocking Together','2003-05-18 04:38:27',0,'I\'m sure it\'s deliberate. See Ravi\'s comment and my reply. It\'s not intended that each must be different.',5031,0);
INSERT INTO comment VALUES (5035,813,1301,'Charlie','re: solution to B','2003-05-18 04:48:18',0,'I\'d be interested in seeing what the strategy is for any of these. I ask in light of Sanjay\'s comment to this and also to the 39 Coins problem, where he shows that not all information-theoretic possibilities are really possible. So I think there might be a flaw in what strategies you have found that allow more than n = (3^x-3)/2.',5032,0);
INSERT INTO comment VALUES (5036,829,1660,'Tim Axoy','K&L&K','2003-05-18 06:22:48',0,'True and false(T and F)
\r\nKnights:Always T
\r\nKnaves:Always F
\r\nLiars:Always F
\r\nCorrect?',NULL,0);
INSERT INTO comment VALUES (5037,516,2256,'Jackie','comment','2003-05-18 06:49:02',0,'I did this problem a few days ago (before I became a user.) I thought it was pretty easy to figure out by process of elimination. It was a fun problem. ',NULL,0);
INSERT INTO comment VALUES (5038,520,1575,'DJ','re(4): Ravi','2003-05-18 06:56:19',0,'I don\'t really feel like belaboring the point, but saying, \"still you made a mistake\" after someone corrects themself is not helping or even correcting anyone.',5027,0);
INSERT INTO comment VALUES (5039,834,2231,'Trevor Leitch','Solution?','2003-05-18 07:05:13',3,'This is very intuitive and not mathematical in the slightest, so please bear with me...\r\n\r\nI can\'t prove it, but I think the answer is that as first player you would want to limit each turn to removing cards within a denomination, and would lose if playing the game within suits instead.\r\n\r\nThe basic reasoning I have is that after a player\'s turn, he will win if the cards left on the table form some sort of \"symmetrical pairing\"... for instance, if there are two groups of three cards left, or two groups with one card and six groups with two each, etc. If this is the case, there must be an even number of piles left, and no matter what the other player does, one can use their own turn to restore this balance. Thus, as first player, if there are thirteen piles (as there would be with denominations), just remove one pile - the resulting spread (12 piles of four cards each) is symmetric, and the first player can mirror the second player\'s move until player 1 wins. However, if there are only four piles at the start (as there would be with suits), the spread is already symmetric, and the second player can mirror the first player until player 2 wins.\r\n\r\nRegarding the third possibility with some cards missing, I would say the first player should remove a card from the pile with 12 (i.e. remove one club), leaving a symmetric spread of 13, 13, 11, 11... this is again a winning situation.',NULL,0);
INSERT INTO comment VALUES (5040,829,2256,'Jackie','re: Please Someone Correct Me','2003-05-18 07:25:46',0,'From my understanding of the problem, I don\'t see that it says that the three must belong to distinct categories. in fact, it says, \"either...or.\" Hence, the solution posted by Trevor and Charlie stands correct. It is impossible for any of them to be complete liars.',5026,0);
INSERT INTO comment VALUES (5041,829,2196,'Silly Jilly','Correction!','2003-05-18 07:40:12',0,'Knaves:T and F',5036,0);
INSERT INTO comment VALUES (5042,432,1660,'Tim Axoy','Alan did not do it.','2003-05-18 07:57:19',0,'Alan,you did noot do it.',2885,0);
INSERT INTO comment VALUES (5043,518,2129,'Sanjay','re: General Shortcut Formula','2003-05-18 09:03:27',0,'This shortcut works only for the specific condition that the fast train is exactly twice as fast as the slow train.\r\n\r\nAn even more general solution for trains moving towards each other would be:\r\n\r\nLet\r\nd = late distance (miles), \r\nt = late time (hr), \r\nx = Slow Train speed (miles/hr), \r\nKx = Fast Train speed (miles/hr)\r\n\r\n1. Slow Train speed = x = ((1+K)/K)*(d/t) (miles/hr)\r\n2. Fast train speed = Kx = (1+K)*(d/t) (miles/hr',4872,0);
INSERT INTO comment VALUES (5044,813,2129,'Sanjay','re: solution to B','2003-05-18 10:12:28',0,'\r\n4 coins are \'unsolvable\' in 2 weighings because:\r\n\r\n4 coin \'solutions\' need eight pieces of info. So, any weighing strategy must lead to a decision tree with at least 8 terminal branches after two weighings.\r\n\r\nThe first weighing can either have one coin or two coins on each side\r\n\r\nScenario 1: (coin 1 vs coin 2)\r\n\r\nIf coin 1 > coin 2, then either coin 1 is \'fake\' and heavy or coin 2 is \'fake\' and light.\r\n\r\nTo determine the real \'fake\' between them, at least one of the two \'initial\' coins will have to be part of the second weighing. Also, just switching the coins from one side to the other will not do the trick, as won\'t just adding one \'standard\' coin on each side.\r\n\r\nSo we have to either weight one of the \'initial\' coins against a \'standard\' coin, or weigh both \'initial\' coins against both \'standard\' coins. In either case the two sides cannot be balanced. Hence this branch of the decision tree can at most have two sub-branches.\r\n\r\nIf coin 1 < coin 2, then similarly this branch can also yield at most two sub-branches after the second weghing.\r\n\r\nIf coin 1 = coin 2, then we can at most have three sub-branches from this branch after the second weighing.\r\n\r\nSo, we can have at most 2+2+3 = 7 sub-branches after two weighings. This is not enough.\r\n\r\nScenario 2: Coin 1 + Coin 2 vs Coin 3 + Coin 4\r\n\r\nClearly the two sides cannot be balanced. Hence after 1 weighing we have two branches. Each branch can lead to at most three sub-branches.\r\n\r\nSo we can have at most 3 + 3 = 6 sub-branches after two weighing. This is also not enough.\r\n\r\nWould love to see the \'solution\' for either X=2,N=4 or X=3,N=13',5032,0);
INSERT INTO comment VALUES (5045,834,1626,'Gamer','re: Solution?','2003-05-18 11:56:30',4,'Are you trying to take the last card, or not take the last card?\r\n\r\nThe largest problem with this is once you get down to 1 pile, your opponent can either take all the cards, or all the cards but one. ',5039,0);
INSERT INTO comment VALUES (5046,520,1626,'Gamer','re(5): Ravi','2003-05-18 12:00:12',0,'I agree with you Ravi, and most of my comments sound somewhat mean, but I am trying to be nice... :)',5038,0);
INSERT INTO comment VALUES (5047,518,1626,'Gamer','re(2): General Shortcut Formula','2003-05-18 12:03:08',4,'What is K?',5043,0);
INSERT INTO comment VALUES (5048,834,2231,'Trevor Leitch','re(2): Solution?','2003-05-18 13:35:49',0,'You are trying to take the last card. In my solution, if played properly, you will never leave a single pile for your opponent; rather, one will eventually be left for you (though most likely it will be a pile with only one card left in it).',5045,0);
INSERT INTO comment VALUES (5049,834,1626,'Gamer','re(3): Solution?','2003-05-18 15:48:13',0,'You are right... I misread your solution, not seeing you took 1 whole pile first.\r\n\r\nThe answer I read somewhere to the answer of this is pretty complicated, but I can\'t think of one outside Trevor\'s special case one (for example, what if there were 13, 10, 9, 6)\r\n\r\nDivide each into powers of two, then keep them so there is an even number of each power of two. For example, 13, 10, 9, 6 would be:\r\n\r\n13=84-1\r\n10=8-2-\r\n09=8--1\r\n06=-42-\r\n_______\r\n---3222\r\n\r\nSince there are 3 3s, take 8 from any pile. (For example, take 8 from 13 to leave 5)\r\n\r\n\r\nIf there were 9 6 3 1:\r\n\r\n9=8--1\r\n6=-42-\r\n3=--21\r\n1=---1\r\n______\r\n--1123\r\n\r\nSplit the 8 into 2 4s, then take a (4+1) or 5 from the 9 pile.\r\n\r\nEventually, this will get to a point where there is only 1 card or 1 pile left, then just take that pile. ',5048,0);
INSERT INTO comment VALUES (5050,189,1626,'Gamer','42 again','2003-05-18 15:57:33',1,'The number forty two is the answer to all questions.',NULL,0);
INSERT INTO comment VALUES (5051,523,1575,'DJ','re: Y : 3 Line Segments','2003-05-18 16:01:45',0,'When I print a capital \'Y,\' I only use two lines . Similarly, it is not uncommon to see someone cross the top and bottom of an \'I\' to make it three segments (although you didn\'t mention that, I considered both alternate cases and notated them in a like manner).\r\n\r\nFor most sans serif typefaces or handwritten block letters, though, \'Y\' is written with three segments and \'I\' with just one. If you look at my list, I have included both, but made it obvious which is probably more acceptable by putting a question mark with the other ones. Indeed, those are the numbers I used in my solution.\r\n\r\nI\'m not really sure what your point is, since [obviously] I counted 3 segments for \'Y.\' If you must leave a comment to everything, perhaps a good one for this problem would have been \"yes, that is right.\" ',5028,0);
INSERT INTO comment VALUES (5052,808,1567,'Bryan','re: A small hint','2003-05-18 17:58:45',0,'I would call that a huge hint! Once you have this piece of information, the problem is straight forward, as Charlie\'s solution demontrates. I spent days on this! Now that I know this trick, I can create angles of three degrees and its multiples. Thanks :P
Is there a list somewhere of integer-based formulae for the trig functions of other angles?',5014,0); INSERT INTO comment VALUES (5053,834,1575,'DJ','re: Solution?','2003-05-18 18:13:50',0,'That makes perfect sense; and for the given situations that seems to be ironclad.\r\nI was trying to work backwards, more or less. If there is only one card, or only cards in one pile, left, then just take it/them and win. If you leave the other person with two cards in different piles, they must take one of them and leave you with just one card. So, if you have one card in one pile and one in another, take all but one card to leave that same situation. Similarly, if you leave the other person with two cards each in two different piles, you can win no matter what they do. And so on...\r\nOnce you have that the piles have to be the same (in the case of two piles left) or symmetrical, then doing whatever you need to make it that way (or keep it that way) comes naturally. Seems too simple, but it will always work.\r\nI\'m not sure how you would manage it if the piles weren\'t symmetrical to begin with (I\'m still trying to figure out why/if Gamer\'s works).',5039,0); INSERT INTO comment VALUES (5054,67,2259,'calla tah-n','too easy!','2003-05-18 20:42:42',0,'if you take 3/3 it\'s 1 so 66/33 is two... so it takes twice the time: 6 minutes... duh',NULL,0); INSERT INTO comment VALUES (5055,185,2259,'calla tah-n','unrelated...','2003-05-18 21:28:00',0,'if you were to drive an electric car that used up one battery/mi driven... it would be very inefficient... unless the batteries were very small and cost less than gass that would get you an equal distance',NULL,0); INSERT INTO comment VALUES (5056,24,2259,'calla tah-n','i agree... stoopet!','2003-05-18 21:32:33',0,'velly velly dumb... luckilly for you, you almost confuuzzled me... but then the incorrect english just upset me...',NULL,0); INSERT INTO comment VALUES (5057,64,2259,'calla tah-n','fun','2003-05-18 21:37:48',0,'what a fun way of messing w/ your friends... talk about being ahead of the game...',NULL,0); INSERT INTO comment VALUES (5058,523,2259,'calla tah-n','confusing...','2003-05-18 21:46:37',0,'the answer should be 29... TWENTY NINE... but if the letter I is considered to be made of 3 parts... then the answer is not 29 and i\'ll have to keep looking... another answer could be TWENTY SIX if you wrote out the letter S in block, as the word twenty consists of 18 lines and then the word six of 8 lines',NULL,0); INSERT INTO comment VALUES (5059,50,2239,'Alpha Tiger','I\'ve already seen this problem','2003-05-19 01:03:26',3,'it\'s not 27+2 but 27-2=25, the price ...',NULL,0); INSERT INTO comment VALUES (5060,521,2239,'Alpha Tiger','The solution','2003-05-19 01:07:38',3,'916\r\n\r\nI made a program to search !...',NULL,0); INSERT INTO comment VALUES (5061,525,1660,'Tim Axoy','I know it!!!','2003-05-19 01:52:58',3,'Only 1.\r\nMe.\r\n',NULL,0); INSERT INTO comment VALUES (5062,525,1686,'DuCk','Solution','2003-05-19 01:53:02',3,'1 - you',NULL,0); INSERT INTO comment VALUES (5063,525,1575,'DJ','Well','2003-05-19 01:53:24',3,'\"While on my way to St. Ives\"\r\n\r\nSo, just one (you).',NULL,0); INSERT INTO comment VALUES (5064,525,1626,'Gamer','re: Well','2003-05-19 01:55:21',0,'I always heard this solution, but frequently there is someone ahead of me who is walking to the same place I am, I run ahead to talk with them... So someone I am talking with is going to the same place I am',5063,0); INSERT INTO comment VALUES (5065,813,872,'pleasance','re(2): solution to B','2003-05-19 03:18:05',0,'4 coins in 2 weighings is definitely possible. You don\'t need a tree with 8 terminal branches, because you don\'t necessarily have to know if the fake coin is heavier or lighter.\r\n\r\nLet\'s call the coins A,B,C,D.\r\n(1) weigh A - B\r\ncase I: they\'re even. In which case\r\n(2) weigh A - C.\r\nIf C is heavier or lighter, C is the fake.\r\nIf they\'re even, D is the fake.\r\ncase II: A is heavier than B (or lighter, doesn\'t matter).\r\n(2) weigh A - C.\r\nIf they\'re even, B is the fake.\r\nIf not, A is the fake. QED\r\n\r\n13 coins: divide them into groups A (4 coins) B (4 coins) and C (5 coins). \r\n(1) weigh all A coins - all B coins\r\ncase (1)I: they\'re even, therefore all A and B are \'true\'.\r\n(2) weigh 3 true coins - C1, C2, C3\r\ncase (2)I: they\'re not even - reduces to 3 coins, one weighing, but you KNOW if it\'s lighter or heavier (part A of riddle).\r\ncase (2)II: they\'re even - the fake is C4 or C5. Weigh C4 against a true coin.\r\n\r\ncase (1)II: A coins heavier than B coins (wlg):\r\n(2) weigh A1, A2, B1 - A3, A4, B2\r\nIf they\'re even - B3 or B4 is the fake, so (3) weigh B3 - true coin.\r\nIf left is heavier: A1 or A2 is heavy or B2 is light. So, (3) Weigh A1, B2 - 2 true coins. Left heavier - it\'s A1; right heavier - it\'s B2; even - it\'s A2. Similarly for right side heavier.\r\n\r\n40 coins is a bit long. But it starts with 13 coins v 13, and keeping 14 on the side.',5044,0); INSERT INTO comment VALUES (5066,525,1902,'Hank','Well...','2003-05-19 03:44:27',0,'Ok, i get and agree with \'one\'.\r\nHowever the question is: \"kits, cats, sacks, wives; how many were going to St. Ives?\" The question specifically addresses the subjects. In which case the answer would be \'zero\'.\r\n',NULL,0); INSERT INTO comment VALUES (5067,525,2239,'Alpha Tiger','The solution (hehe)','2003-05-19 04:20:52',3,'Only one, you.\r\nBecause the \"while\" explains that you seen the man only one time and that he wasn\'t following you (I mean he wasn\'t going to St Ives).',NULL,0); INSERT INTO comment VALUES (5068,813,1301,'Charlie','re(3): solution to B','2003-05-19 04:30:47',0,'Ahhh! This exploits the fact that the question never asked us to determine whether in fact the false coin is lighter or heavier, we can gain more information about which one it is, in greater number of coins.\r\n\r\nExcellent!',5065,0); INSERT INTO comment VALUES (5069,369,2196,'Silly Jilly','Puppies','2003-05-19 05:12:16',3,'Puppies that play with a kangaroo do not have a loud bark.',NULL,0); INSERT INTO comment VALUES (5070,154,2196,'Silly Jilly','Got it','2003-05-19 06:00:27',0,'92951522.',NULL,0); INSERT INTO comment VALUES (5071,813,872,'pleasance','re(4): solution to B','2003-05-19 06:49:49',0,'Yes, Charlie, and interestingly, it seems to me that in each of the cases it\'s only ONE COIN which is never weighed, that is, for n coins we distinguish between 2n-1 cases.',5068,0); INSERT INTO comment VALUES (5072,525,2262,'tony','thee answer','2003-05-19 06:54:19',0,'the answer is o none of them were going to saint ives statement was while on my way i met.',NULL,0); INSERT INTO comment VALUES (5073,813,2129,'Sanjay','re(3): solution to B - apologies','2003-05-19 09:00:57',0,'Please accept my apologies. You\'re right. This particular problem only requires us to identify the \'fake\' coin, not the type of \'fakeness\'.\r\n\r\nThe general solution I have provided is for the more difficult problem of not only identifying the \'fake\' coin but also identifying if the \'fake\' coin is heavier or lighter than the rest.\r\n\r\nI should\'ve been more careful while reading the problem. ',5065,0); INSERT INTO comment VALUES (5074,159,2256,'Jackie','re: Less than 21','2003-05-19 09:36:04',0,'to lucky: good job, you found a working pattern. as a far the solution... after tedious work I was able to calculate some equations (I\'ll get to that later) but yes, the minimum shaded squares for an 8x8 grid is indeed 20. \r\n\r\nAs far as a formula... I found something that works for any SQUARE grid, meaning 1x1, 2x2... 30x30...\r\nanyhow, the function I obtained is a piecewise function; more specifically, the relationship from x to y changes depending on the domain (x). \r\n\r\nHere are the intervals and their corresponding functions \r\n(x= side of square. ie: for and 8x8 grid, x=8):\r\n\r\nINTERVAL FUNCTION\r\n
[0,2] 3x-8\r\n[3,6] 5x-20\r\n[7,9] 7x-38\r\n[10,12] 9x-62\r\n[13,15] 11x-92\r\n\r\netc, etc... I could go on FOREVER! (If anyone would like a more in-depth description of how I obtained these relations, just let me know.)\r\n\r\nanyhow, so plug in 8 into f(x)= 5(x-4):\r\nf(8)= 5(8-4) = 20\r\n\r\nTry these equations for ANY square grid... they work!\r\n',834,0); INSERT INTO comment VALUES (5075,841,1301,'Charlie','Numerical Answers','2003-05-19 09:40:39',1,'The problem involves finding a probability distribution for the expanse taken up by a set of n random points on the circle. Each such probability distribution depends on a certain integration of the distribution on the preceding value, n-1.\r\n\r\nDaunted by the possibility of integrating this, I chose to integrate numerically. For a reasonable run time, 1/64 of a degree works as the interval for the numeric integration.\r\n\r\nWith n = 2, every separation from zero to 180 degrees is equally likely. From then on we need find the entire distribution from zero to 360 and see what fraction is below 180. Actually we could just integrate to 180, but finding the full distribution to 360 allows us to check our correctness to make sure our total probabilities add up to 1, or close enough to 1, based on the accuracy of our numerical integration.\r\n\r\nThe probability that n points will span the nominal value of the particular interval (of size 1/64 degree in the implementation) is equal to the probability of that span in the distribution for n-1 points multiplied by the probability that the next point would fall between the existing end points and so not increase the span, plus the total of the probabilities of any smaller span on the n-1 distribution multiplied by the probability that it would expand exactly (that is within 1/64 degree) to that span. \r\n\r\nFor a particular span, the probability that it would not change is span/360. The probability that a given smaller span would expand to a particular larger span, based on the interval of integration of 1/64 degree, is 2/64 for every new, larger span that lies between oldspan+1/64 and 180+oldspan/2 (the largest case, in which the new point is 180 degrees away from the midpoint of the old arc). (It\'s 2/64 rather than 1/64 as it could be on either side of the original span.) When trying to find the smallest previous span that could lead to the new span being calculated, the latter limit translates to lowest oldspan = 2 * newspan - 360. Of course the largest span that could expand to the new span would be just the new span minus the increment of 1/64.\r\n\r\nThe program to evaluate this is \r\n\r\nincr = 1 / 64\r\nDIM pr(360 / incr + 1)\r\nmultr = 2 * incr / 360\r\nn = 2\r\nFOR i = 0 TO 180 STEP incr\r\n ss = i / incr\r\n pr(ss) = 1 / (180 / incr)\r\nNEXT\r\nPRINT : PRINT n;\r\ntot = 0\r\nFOR i = 0 TO 360 STEP incr\r\n ss = i / incr\r\n tot = tot + pr(ss)\r\n IF i < 180 THEN tot2 = tot2 + pr(ss)\r\nNEXT\r\nPRINT tot, tot2 / tot\r\nDO\r\n n = n + 1\r\n FOR i = 360 TO 0 STEP -incr\r\n ss = i / incr\r\n pr(ss) = pr(ss) * i / 360\r\n lowv = 2 * i - 360: IF lowv < 0 THEN lowv = 0\r\n FOR j = lowv TO i - incr STEP incr\r\n ss2 = j / incr\r\n pr(ss) = pr(ss) + pr(ss2) * multr\r\n NEXT\r\n NEXT\r\n PRINT n;\r\n tot = 0: tot2 = 0\r\n FOR i = 0 TO 360 STEP incr\r\n ss = i / incr\r\n tot = tot + pr(ss)\r\n IF i < 180 THEN tot2 = tot2 + pr(ss)\r\n NEXT\r\n PRINT USING \\\"#.##### #.#####\\\"; tot; tot2 / tot\r\n \' DO: LOOP UNTIL INKEY$ > \"\"\r\nLOOP\r\n\r\nThe results from this program are\r\n 2 .9999816 .9999132 1\r\n 3 1.00013 0.74990 3/4\r\n 4 1.00010 0.49988 1/2\r\n 5 1.00008 0.31240 5/16\r\n 6 1.00006 0.18742 3/16\r\n 7 1.00004 0.10932 7/64\r\n 8 1.00001 0.06246 1/16\r\n 9 1.00000 0.03513 1/32 ?\r\n 10 0.99997 0.01951 ?\r\n\r\n\r\nThe total probability from zero to 360 is included as a check, and all are indeed close to 1. After the computed decimal fraction that are below 180 degrees, the rational approximations above were my estimates, rather than output. The numbers all looked like fractions with powers of 2 in the denominator. The question mark after 1/32 reflects the fact that, while in all the rest the numerical decimal fraction is slightly below what presumably is the rational fraction, .03513 is slightly above 1/32. I don\'t venture to guess about .01951.\r\n',NULL,0); INSERT INTO comment VALUES (5076,841,1301,'Charlie','re: Numerical Answers','2003-05-19 09:43:33',0,'In the post, where I say 2/64, that should be (2/64)/360, as specified in the program.',5075,0); INSERT INTO comment VALUES (5077,159,2256,'Jackie','re(2): Let me fix that!!','2003-05-19 09:46:56',0,'INTERVAL FUNCTION\r\n\r\n
[0,2] ZERO!\r\n[3,6] 3x-8\r\n[7,9] 5x-20\r\n[10,12] 7x-38 \r\n[13,15] 9x-62
\r\n\r\nThats better! NOW it works!\r\n',5074,0); INSERT INTO comment VALUES (5078,525,1902,'Hank','All possible solutions','2003-05-19 10:02:15',3,'Preface: First of all, more information is needed to determine whether they are traveling the same direction or opposite directions (either could be true dependant on the means of transportation [ie you are more likely to be traveling the same direction as another person on your train]) Second, I think the real question is can a woman carry nearly 400 felines? And is having so many cats in a sack humane?\r\n\r\nThese are the possibilities I came up with depending on interpretation: 0, 1, 2, 2802, 2800\r\n\r\n0: as I said before, the statement ends after the fifth line, then the question is: \'kits, cats, sacks, wives; how many were going to Saint Ives?\' assuming that you are traveling in different directions.\r\n1: assuming that you are traveling in different directions, then I\'m the only one going to St. Ives\r\n2: I met a man who was also going to St. Ives, he told me about his seven wives, etc. (but they were not joining him on his jorney)\r\n2802: me, the other man, his seven wives, all the sacks, cats and kits\r\n2800: assuming that everyone is headed the same direction, sticking to the actual question.',NULL,0); INSERT INTO comment VALUES (5079,841,1626,'Gamer','re(2): Numerical Answers','2003-05-19 10:11:34',0,'I am confused by the problem... (and didn\'t read Charlie\'s solution), does it mean \"What is the probability that none of the n points will reside on half of the circumference?\" (thinking that semicircle is exactly half a circle)\r\n\r\n',5076,0); INSERT INTO comment VALUES (5080,841,1567,'Bryan','Solution','2003-05-19 10:14:41',3,'Start by considering two points on the circle: one at zero degrees from some reference point and the other at 30 degrees. A third point will work (i.e. share some semicircle with the first two) if it falls between 0 and 180 degrees or between 210 and 360 degrees. There is only a 30 degree area in which the third point won’t work. In other words, for n=3 points, with one point at zero and a second point at Theta, the odds that the third point works is (2pi-Theta)/2pi, or 1 – Theta/2pi. Note that, for this equation to be valid, the first point must be selected such that the angle Theta to the second point is less than or equal to pi.Since Theta can have any value between zero and pi, the probability of the third point working (for all values of Theta) isP = 1/2pi * integral[1 – Theta/2pi] from 0 to 2pi
P = (2pi – pi)/2pi
P = 1/2
If we have a condition that works for n=3, again there will be an angle Theta that is less than or equal to pi that the three points fall within, and the odds of finding a fourth point that works is again 1 – Theta/2pi, or 1/2 for all values of Theta. Since a working set of 3 points was a prerequisite to finding a fourth point that works, the probability for n=4 is .5^2. From this logic, one sees that the probability for n points to work is
P = .5^(n-2)',NULL,0); INSERT INTO comment VALUES (5081,525,1626,'Gamer','re: All possible solutions','2003-05-19 10:16:35',1,'I don\'t want Ravi jumping on me for putting punctuation into a problem, so 0 may be an answer. But the way I heard it, the kits, cats, sacks, wives; \"All of these things included\" (as you might think only people who were actually moving would count otherwise), and in the version I heard, every other line rhymed.',5078,0); INSERT INTO comment VALUES (5082,525,1626,'Gamer','The version I heard','2003-05-19 10:18:27',2,'While on my way to the fair\r\n\r\nI met a man with a bear.\r\n\r\nEach bear had 7 cats,\r\n\r\nEach cat had 7 rats,\r\n\r\nEach rat had 7 mice,\r\n\r\nEach mouse had 7 lice,\r\n\r\nLice, mice, cats, rats, a man and a bear;\r\n\r\nHow many were going to the fair?',NULL,0); INSERT INTO comment VALUES (5083,841,1626,'Gamer','My idea as well','2003-05-19 12:10:27',2,'When you are putting points on a semicircle, you havea 1/2 chance of putting it on the semicircle, and a 1/2 chance of not. Other than the first point and the second point, this is the pattern that appears to me.',NULL,0); INSERT INTO comment VALUES (5084,521,1626,'Gamer','re: The solution','2003-05-19 12:16:42',0,'Compare your program with Charlie\'s... It\'s the 4th post from the bottom.',5060,0); INSERT INTO comment VALUES (5085,841,1567,'Bryan','re: Solution','2003-05-19 12:52:22',0,'It occurred to me after I posted that, since Theta is less than or equal to pi, the integral should be from 0 to pi as well, not from 0 to 2pi. Considering n=3, if the first two points are nearly 180 degrees apart, the third point needs to fall between them, the odds of which are 1/2, but if the first two points are nearly on top of each other, the third point can be almost anywhere, the odds of which approach 1/1. The average of these is 3/4 and, not coincidentally,
P = 1/pi * integral[1 - Theta/2pi] from 0 to pi
P = (pi - .75pi)/pi
P = .75
and the overall probability is
P = .75^(n-2)',5080,0);
INSERT INTO comment VALUES (5086,521,1626,'Gamer','re(2): solution (More mistakes!)','2003-05-19 13:36:12',0,'I made mistakes here... First x=3, w=3 also has x=3, w=6, and the B value for x=3, w=3 is 3. (Also, the other multiples of 3 and 9 for 3, 6, 9 were discarded because the y^2 value was too high)\r\n\r\nI can eliminate X=6,7,8,9 since X^2 is over 27 and x=5 because y^2 is over 108, and can also eliminate x=0 or 9 because 0 and 81 aren\'t allowed. Also, x=1 can be eliminated because that would mean at least one leading zero.\r\n\r\nThen the list would read:\r\n\r\nx-w-y2-x2-B\r\n2-5-49-04-3\r\n3-3-36-09-3 OR\r\n3-6-81-09-8\r\n4-1-25-16-1\r\n\r\nNote that with a + b + c = 4 (x=2), none of the combinations work. (220,310,130,211,121,112)\r\n\r\nWith x=3 (both ones) a+b = 6, and a+b=1, and like before none of the combinations work... so w must = 1',4949,0);
INSERT INTO comment VALUES (5087,841,1301,'Charlie','re(3): Numerical Answers','2003-05-19 15:40:22',0,'It means what is the probability that all some diameter can be placed on the circle such that all the points thus far lie on one side of the diameter. For example, points at theta = -20, 20 and 150 degrees all lie on a span of 170 degrees and therefore is ok. If, however they were at -40, 20 and 150 degrees, that would be a span of 190 degrees and so count as a non-occurrence of what is sought.',5079,0);
INSERT INTO comment VALUES (5088,841,1301,'Charlie','re: My idea as well','2003-05-19 15:44:21',0,'If the first point happens to be 0 degrees (or define 0 degrees as where the first point falls), and the second at say 30 degrees, then the third has to be between 0 and 180 or between 0 and -150. The only way for the test to fail if the first two were as stated would be for the third point to be between -150 and -180 (that is between 180 and 210, the same thing). So that particular case is not 1/2, but 30/360 = 1/12 of failing, or 11/12 of passing.',5083,0);
INSERT INTO comment VALUES (5089,841,1301,'Charlie','re(2): Solution','2003-05-19 16:15:15',0,'The derivation of the .75 probability depends on the probability distribution at the previous level (2 points) being uniform from 0 to pi. But the probabilities of the fourth point added are not going to be the result of a uniform distribution at level 3, but rather a distribution that favors the higher portion of the possible range, as spans can increase but never decrease. My numerical integration also shows that while 75% of cases had the first 3 points within a 180-degree span, 18.7% were within a 90-degree span and 56.2 % were a span between 90 degrees and 180 degrees. So multiplication by .75 from each stage to the next is not warranted.',5085,0);
INSERT INTO comment VALUES (5090,331,2130,'ethan','answer','2003-05-19 17:13:06',0,'lets say the rookie, who doesnt get to play much, has batted 2 for 8 against lefties, but 0 for 1 against righties. This gives him a .250 lefty avg, a .000 rightie avg, and a .222 overall avg.\r\n\r\nNow lets say the regular first baseman is 40 for 200 against lefties, but 150 for 400 against righties. this gives him a .200 avg against lefties, a .375 avg against lefties, and .317 avg overall. \r\n\r\nSo, in game one, the opposing team brings in a rightie reliever, and the rookie gets one at bat against him, which is a hit. Now his rightie avg is .500, which is better than the regular starting first baseman. That is how the situation could come about.\r\n\r\nBye the way, the Minnesota Twins are goin all the way this year.',NULL,0);
INSERT INTO comment VALUES (5091,841,1301,'Charlie','re: Numerical Answers','2003-05-19 17:59:22',0,'The algorithm I originally posted produces a distorted portion of the probability distribution above 180 degrees, but that below 180 degrees is unaffected so the probablities shown should still be accurate within the limitations of numerical integration.\r\n\r\nThe problem is exemplified by a span of 2 points spaced 170 degrees apart. The algorithm assumes an incremental probability that this would expand, with the third point, to, say, 250 by that third point being external to the original pair and 80 degrees from one of them. However, the distance between the original two is still 170, leaving an occupied span of 360 - 170 = 190 degrees. \r\n\r\nThis possibility of the new point flipping the occupied span to the opposite side again affects only the distribution within the part above 180 degrees, and not the probability of 180 or less versus 180 or more.',5075,0);
INSERT INTO comment VALUES (5092,525,1575,'DJ','re: The version I heard','2003-05-19 18:44:13',0,'I haven\'t heard that one; but I have seen different versions of the St. Ives problem before.\r\n\r\nIn reading this one, I didn\'t notice the penultimate line, which might imply only to count the kits, cats, sacks, and wives, in which case the answer would be zero. To be extremely pedantic about the English, though, a semicolon (;) separates a sentence into two independent (although usually related) clauses. For the last sentence of this puzzle, then, the first clause \"Kits, cats, sacks, wives\" is an incomplete fragment without a verb; the second clause \"How many were going to St. Ives?\" is separate, in which the subject of \'many\' could be ambiguous. A comma instead of the semicolon there would leave the first list as descriptors of the word \'many.\'\r\n\r\nHonestly, I was on my way out to work this morning and didn\'t notice that line, but an answer of one could be defended.',5082,0);
INSERT INTO comment VALUES (5093,525,2259,'calla tah-n','re: All possible solutions','2003-05-19 20:40:27',0,'solutions you missed: when it is said \"how many were going to Saint Ives\" it could be considered that this means living beings... therefore there are several other possible answers:\r\n2753 - all living beings, meaning everything \"going\" excluding the sacks\r\n9 - you, the man, his seven wives; meaning all human beings going\r\n\r\nin other words, this problem has many interpretations that could be taken in many ways, whether you were right with any answer depends on if you are an optimist or a pessimest.',5078,0);
INSERT INTO comment VALUES (5094,524,2239,'Alpha Tiger','Hehe','2003-05-19 22:10:15',3,'EYE\r\n\r\ntoo easy !',NULL,0);
INSERT INTO comment VALUES (5095,841,2163,'sendil','Am I correct in saying this','2003-05-20 01:06:32',0,'The first point can be placed anywhere in the circle,the second point as well, the farthest these two can be are on end points of a diameter.We then are in a position to define what is in the same semi-circle and what is not.\r\n\r\nIt is very clear that the next point onwards there is a 1/2 chance of it falling in the req semi-circle.\r\nSo are we looking at (1/2)^n-2 ????????',NULL,0);
INSERT INTO comment VALUES (5096,829,979,'Ravi Raja','re(2): Please Someone Correct Me','2003-05-20 01:28:27',0,'But have you gone through my proof Charlie? Just see what conclusion I am arriving at. Ernesto does not belong to any of the three categories (Knights, Knaves or Liars). How is that possible? That was what I wanted others to correct and not whether they belong to same or different categories.',5033,0);
INSERT INTO comment VALUES (5097,829,979,'Ravi Raja','re: K&L&K','2003-05-20 01:30:43',0,'No Tim. You\'re wrong.\r\nKnaves do not always Lie. \r\nIf their first statement is True, then their Second statement is False and if their first statement is False, then their Second statement is True. (That is, alternate True and False statements). \r\nSo, no two consecutive statements of a Knave is either both True or both False. ',5036,0);
INSERT INTO comment VALUES (5098,823,2129,'Sanjay','Solution','2003-05-20 02:43:38',3,'Assume that the coin is \'normal\'.\r\n\r\nEach flip produces 2 equi-probable outcomes; Heads or Tails. So three flips will produce 2^3 = 8 equi-probable sequences of outcomes.\r\n\r\nThese are:\r\n\r\n1. H H H All three Heads\r\n2. H H T Two Heads; One Tails\r\n3. H T H Two Heads; One Tails\r\n4. H T T One Heads; Two Tails\r\n5. T H H Two Heads; One Tails\r\n6. T H T One Heads; Two Tails \r\n7. T T H One Heads; Two Tails\r\n8. T T T All three Tails\r\n\r\nThese eight sequences are mutually exclusive and combinationally exhaustive. In exactly three (# 4,6,&7) out of these eight sequences, Heads appears exactly once. \r\n\r\nHence probability of getting exactly one Heads = 3/8 = 0.375',NULL,0);
INSERT INTO comment VALUES (5099,823,979,'Ravi Raja','Solution','2003-05-20 04:16:44',3,'The event space contains eight event points. They are: {H,H,H}, {H,H,T}, {H,T,H}, {T,H,H}, {T,T,H}, {T,H,T}, {H,T,T} and {T,T,T}. \r\nSo, the total number of outcomes is 8 and the number of favourable cases in which we are getting exactly one heads is 3. \r\nFrom the Classical definition of Probability, the probability of getting exactly one heads in flipping a coin three times is: 3/8.\r\n',NULL,0);
INSERT INTO comment VALUES (5100,841,1301,'Charlie','re: Am I correct in saying this','2003-05-20 04:53:19',0,'The second point might be less than 180 degrees from the first. Say it\'s 50 degrees away from the first. Then an entire span of 360 - 50 = 310 is OK to continue within one semicircle (the central 50 degrees plus 130 degrees on either side). So the probability depends on the whole probability distribution of the previous number of points, and after the third point plotted, the distribution is not even uniform.',5095,0);
INSERT INTO comment VALUES (5101,841,1567,'Bryan','re(3): Solution','2003-05-20 06:26:38',0,'Similar thoughts were going through my own mind last night, based on nothing more scientific than gut feelings. Ah well.',5089,0);
INSERT INTO comment VALUES (5102,829,1567,'Bryan','re: Please Someone Correct Me','2003-05-20 06:35:21',0,'Ravi, my advice to you is as follows: If you start with an assumption (in this case, that each of the three men is from a different category), and then find there is no solution that works, you must abandon that assumption and try something else. Wouldn\'t you agree?',5026,0);
INSERT INTO comment VALUES (5103,829,979,'Ravi Raja','re(2): Please Someone Correct Me','2003-05-20 09:44:16',0,'Okay Bryan. Suppose I had not written that statement and would have started working on it assuming that Ernesto belongs to one of the three categories (Knights, Knaves and Liars) then still I am arriving at the same result (read my entire proof of the problem) that Ernesto does not belong to any of the three groups. What do you have to say for that ?',5102,0);
INSERT INTO comment VALUES (5104,841,1301,'Charlie','Simulation','2003-05-20 10:03:08',0,'In a simulation of 1,000,000 trials, adding 11 points at random, one at a time, and noting at each number of points from 3 to 11 the span taken up, the following numbers appear:\r\n 3 187486 561980 749466 250534 0 1000000\r\n 4 62659 437033 499692 500308 0 1000000\r\n 5 19439 292777 312216 683941 3843 1000000\r\n 6 5880 181339 187219 787418 25363 1000000\r\n 7 1662 107769 109431 816731 73838 1000000\r\n 8 492 62104 62596 790008 147396 1000000\r\n 9 153 35259 35412 726006 238582 1000000\r\n 10 34 19706 19740 643549 336711 1000000\r\n 11 7 10834 10841 554994 434165 1000000\r\n\r\nThe middle column is the number, for the given number of points plotted so far, that are within 180 degrees. The two numbers before this are for the first and second quadrants (fitting within 90 degrees, fitting more than 90 less than 180). After the 180 figure come the 3rd and 4th quadrants and the final column has the total of 1,000,000 for a check.\r\n\r\nThe program simulating the random placement placed the first point always at 0 and everything else is relative to that:\r\n\r\nDIM span(11, 360)\r\nDIM pt(11)\r\nPRINT : PRINT : PRINT\r\nRANDOMIZE TIMER\r\nFOR trial = 1 TO 1000000\r\n ERASE pt\r\n pt(1) = 0\r\n pt(2) = RND(1) * 360\r\n FOR ptNo = 3 TO 11\r\n cPosn = RND(1) * 360\r\n ins = 0\r\n FOR i = 2 TO ptNo - 1\r\n IF pt(i) > cPosn THEN\r\n FOR j = i TO ptNo\r\n SWAP pt(j), cPosn\r\n NEXT\r\n ins = 1\r\n EXIT FOR\r\n END IF\r\n NEXT\r\n IF ins = 0 THEN pt(ptNo) = cPosn\r\n lgGap = 0\r\n FOR i = 2 TO ptNo\r\n IF pt(i) - pt(i - 1) > lgGap THEN lgGap = pt(i) - pt(i - 1)\r\n NEXT\r\n IF 360 - pt(ptNo) > lgGap THEN lgGap = 360 - pt(ptNo)\r\n lgSpan = 360 - lgGap\r\n span(ptNo, INT(lgSpan)) = span(ptNo, INT(lgSpan)) + 1\r\n NEXT\r\nNEXT trial\r\n\r\nFOR i = 3 TO 11\r\n tot = 0: subtot = 0: st2 = 0\r\n PRINT USING \"### \"; i;\r\n FOR j = 1 TO 360\r\n subtot = subtot + span(i, j - 1)\r\n \' j - 1 because of original truncation\r\n st2 = st2 + span(i, j - 1)\r\n tot = tot + span(i, j - 1)\r\n IF j / 90 = INT(j / 90) THEN\r\n PRINT USING \"#######\"; subtot;\r\n subtot = 0\r\n END IF\r\n IF j = 180 THEN\r\n PRINT USING \" ######## \"; st2;\r\n st2 = 0\r\n END IF\r\n NEXT\r\n PRINT USING \"##########\"; tot;\r\n tot = 0\r\n PRINT\r\nNEXT\r\n',NULL,0);
INSERT INTO comment VALUES (5105,841,1301,'Charlie','re: Simulation','2003-05-20 10:07:34',0,'Here\'s the table again--I hope it lines up better:\r\n\r\n 3 187486 561980 749466 250534 0 1000000\r\n 4 62659 437033 499692 500308 0 1000000\r\n 5 19439 292777 312216 683941 3843 1000000\r\n 6 5880 181339 187219 787418 25363 1000000\r\n 7 1662 107769 109431 816731 73838 1000000\r\n 8 492 62104 62596 790008 147396 1000000\r\n 9 153 35259 35412 726006 238582 1000000\r\n 10 34 19706 19740 643549 336711 1000000\r\n 11 7 10834 10841 554994 434165 1000000\r\n\r\n',5104,0);
INSERT INTO comment VALUES (5106,823,2130,'ethan','answer','2003-05-20 10:45:56',0,'here are the possible combinations.\r\nh=heads and t=tails\r\nhhh\r\nhht\r\nhth\r\nthh\r\ntth\r\ntht\r\nttt\r\nhtt\r\nOf those 8, there are 3 with one and only one heads. So the odds of getting heads only once is 3/8.',NULL,0);
INSERT INTO comment VALUES (5107,829,1301,'Charlie','re(3): Please Someone Correct Me','2003-05-20 11:06:33',0,'You say\r\nBut have you gone through my proof Charlie? Just see what conclusion I am arriving at. Ernesto does not belong to any of the three categories (Knights, Knaves or Liars). How is that possible? That was what I wanted others to correct and not whether they belong to same or different categories. \r\n\r\nBut it is not necessary to go through the proof. If one starts with contradictory premises, one can prove anything. The contradictory premises in this case are 1) All the people are different types and 2) The clues that are given, which contradict this. In fact, you have proved that they are not all different types because by starting with that assumption, you have come up with the impossibility that Ernesto is not any of the types. \r\n\r\nIt is always possible to prove an impossibility by starting out with contradictory premises. Again, looking at it the other way around, if an impossibility has been proved, one has demonstrated that at least one of the premises is wrong.',5096,0);
INSERT INTO comment VALUES (5108,718,1921,'Travis Taylor','Anything you can do I can do smaller','2003-05-20 11:12:56',1,'2^-(31!)\r\n\r\nbut .. 2^-((31!)!) is smaller .. \r\nbut .. 2^-(((31!)!)!) is smaller still .. \r\n\r\nand so on and so on .. ',NULL,0);
INSERT INTO comment VALUES (5109,718,1921,'Travis Taylor','re: Anything you can do I can do smaller','2003-05-20 11:14:24',0,'Disregard!\r\n\r\n.. I reread the problem .. ',5108,0);
INSERT INTO comment VALUES (5110,527,2130,'ethan','Solution','2003-05-20 11:24:23',3,'0=e\r\n1=n\r\n2=v\r\n3=s\r\n4=m\r\n5=a\r\n6=u\r\n7=p\r\n8=t\r\n9=r\r\n 4593\r\n MARS\r\n 20163\r\n VENUS\r\n 695163\r\n URANUS\r\n 358691\r\n SATURN\r\n---------\r\n 1078610\r\n NEPTUNE',NULL,0);
INSERT INTO comment VALUES (5111,524,2267,'Kim','solution','2003-05-20 14:51:22',0,'ewe',NULL,0);
INSERT INTO comment VALUES (5112,524,2267,'Kim','re: Solution','2003-05-20 14:56:50',0,'Although I\'m beginning to think it is \"I\", ewe can also be read both ways!',4983,0);
INSERT INTO comment VALUES (5113,823,2267,'Kim','solution','2003-05-20 15:12:29',0,'1/8',NULL,0);
INSERT INTO comment VALUES (5114,501,2267,'Kim','possible','2003-05-20 15:26:24',0,'stars?',NULL,0);
INSERT INTO comment VALUES (5115,686,2267,'Kim','guess','2003-05-20 15:34:14',0,'the police were already there\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (5116,527,2256,'Jackie','re: Solution','2003-05-20 16:24:25',0,'I actually obtained the same answer. I started with \"n\" because I figured it was most likely \"1\" because the digit could only have been carried over from the sum of the previous letters. From that point I was able to draw more relationships between letters, for instance, if s was even, then e must be odd, or vice versa.',5110,0);
INSERT INTO comment VALUES (5117,520,1575,'DJ','Solution?','2003-05-20 17:00:40',4,'How does the problem \'imply that there is just one possible answer\'? Simply in asking us to name the cards? Pretty weak if you ask me...\r\nObviously, since every statement ends in \'or two,\' the middle card could be a two of any suit. That doesn\'t preclude the possiblity.',NULL,0);
INSERT INTO comment VALUES (5118,829,1567,'Bryan','re(3): Please Someone Correct Me','2003-05-20 18:51:24',4,'To answer your question, Ravi, I would say you should reread your own proof. In several places, it says \"this is not possible, since each of the three belong to different categories\". Now remember, by the fact that your proof leaves no suitable category for Ernesto, you have proven this assumption is wrong. So why don\'t you drop that assumption and run through the problem a second time? Or, if you want to save the effort, try reading the excellent proofs by Trevor and Charlie, which show quite logically the category for each of the three men.',5103,0);
INSERT INTO comment VALUES (5119,518,2129,'Sanjay','re(3): General Shortcut Formula','2003-05-20 21:30:02',0,'K is a constant, representing the ratio of speeds of the two trains.\r\n\r\nK = (Fast Train speed)/(Slow Train speed)\r\n\r\nIt can be seen from the formula that K will never be less than 1',5047,0);
INSERT INTO comment VALUES (5120,227,2268,'David','just curious...','2003-05-20 21:32:15',0,'If the student truly saw a loophole, why wouldn\'t he/she have a different lawyer represent him/her. This way, the student will not have won his/her first case, rather the lawyer representing the student would have won.',NULL,0);
INSERT INTO comment VALUES (5121,518,2148,'Jayaram S','Good Thinking','2003-05-20 21:35:40',0,'Good line of thinking Sanjay!',5043,0);
INSERT INTO comment VALUES (5122,227,2268,'David','re: if I were his student','2003-05-20 21:35:47',0,'which states that they do not have to pay him UNTIL they have won their first case.\r\n\r\nIf both students were to sue each other, only one student would pay. Although, if in the future the student, who has lost the trial, wins an arguement, he/she would still have to abide by the contract and pay.',1760,0);
INSERT INTO comment VALUES (5123,227,2268,'David','re: just curious...','2003-05-20 21:40:50',0,'just to add on... \r\nIf the student won the case, the fee would be waived. If the student lost the case, he would not have to pay. In conclusion, neither would pay a fee.',5120,0);
INSERT INTO comment VALUES (5124,823,2129,'Sanjay','re: solution','2003-05-20 21:54:57',0,'Kim, could you explain your answer?',5113,0);
INSERT INTO comment VALUES (5125,814,2129,'Sanjay','Solution','2003-05-21 02:23:42',3,'There are 23 ways of putting + and - signs in the blanks, such that in the end it will all equal 1.\r\n\r\nexample 1: 0+1+2+3+4+5-6-7+8-9 = 1\r\nexample 2: 0-1-2-3-4-5+6-7+8+9 = 1 \r\n\r\nThere are 23 ways of putting + and - signs in the blanks, such that in the end it will all equal -1.\r\n\r\nexample 1: 0+1+2+3+4+5-6+7-8-9 = -1\r\nexample 2: 0-1-2-3-4-5+6+7-8+9 = -1\r\n \r\nThere is no way that we can make it add upto 0 or indeed to any even number because in the list of numbers are an odd number of odd numbers (1,3,5,7,&9), hence regardless of the placement of the signs, the full expression will always equal an odd number. ',NULL,0);
INSERT INTO comment VALUES (5126,814,2270,'peter','re: Solution','2003-05-21 03:00:21',0,'0+12+34-56-7+8+9=0',5125,0);
INSERT INTO comment VALUES (5127,841,1301,'Charlie','re(2): Simulation','2003-05-21 03:40:30',0,'Ok, this is the formatted table-- the middle column is the one applicable to the problem posed-- the ones on either side further break down the results into quadrants, and the last column the total number of trials:\r\n 3 187486 561980 749466 250534 0 1000000\r\n 4 62659 437033 499692 500308 0 1000000\r\n 5 19439 292777 312216 683941 3843 1000000\r\n 6 5880 181339 187219 787418 25363 1000000\r\n 7 1662 107769 109431 816731 73838 1000000\r\n 8 492 62104 62596 790008 147396 1000000\r\n 9 153 35259 35412 726006 238582 1000000\r\n 10 34 19706 19740 643549 336711 1000000\r\n 11 7 10834 10841 554994 434165 1000000\r\n',5105,0);
INSERT INTO comment VALUES (5128,829,979,'Ravi Raja','re(4): Please Someone Correct Me','2003-05-21 04:52:16',0,'Thanks Charlie. Actually I was confused. I am sorry for bothering everyone for such a stupid mistake of mine. ',5107,0);
INSERT INTO comment VALUES (5129,814,1567,'Bryan','Solution plus','2003-05-21 04:57:12',3,'0+1+2+3-4-5-6-7+8+9=1
0+12-3+4+5+6-7-8-9=0
0-1-2-3+4+5+6+7-8-9=-1
Obviously, if an expression can be made to equal a positive number, the same expression with all signs reversed will equal the negative of that number.
Carrying on:
0+12-3+4+5-6+7-8-9=2
0+1+2-3+4-5-6-7+8+9=3
0+12-3+4+5-6-7+8-9=4
0+1+2-3-4+5-6-7+8+9=5
0+12-3+4-5+6-7+8-9=6
0+1+2-3-4-5+6-7+8+9=7
0+12-3-4+5+6-7+8-9=8
0+1+2+3+4-5-6-7+8+9=9
0+12+3+4+5+6+7-8-9=10
I think a good question now would be: what is the first positive integer that cannot be achieved by adding + and - signs to the digits 0 through 9?\r\n',NULL,0);
INSERT INTO comment VALUES (5130,814,2166,'Chris','re: Solution plus','2003-05-21 08:58:39',0,'In response to Bryan\'s last line:\r\n\r\n>>I think a good question now would be: what is the first
>>positive integer that cannot be achieved by adding + and -
>>signs to the digits 0 through 9?\r\n\r\nthe answer is 46 if I understand the question correctly. The highest number possible is 45 with all numbers added. Remember that: S = n(n+1)/2 where S is the sum of the first n digits.\r\n\r\nBTW, I\'m wondering about the legality of combining two digits together as in this post and the previous.',5129,0);
INSERT INTO comment VALUES (5131,814,1567,'Bryan','re(2): Solution plus','2003-05-21 09:16:50',0,'In answer to your question, Chris, I say there is nothing \"illegal\" about combining two or more digits (e.g. 12). The problem says to put + and - signs in the blanks, but it does not say one has to put them in all the blanks, so why limit myself?
Now then, if we consider the possibility that multiple digits may be combined in the equation, obviously one can achieve numbers greater than 45. The question becomes: what is the first positive integer that cannot be achieved?',5130,0); INSERT INTO comment VALUES (5132,814,1301,'Charlie','re(3): Solution plus','2003-05-21 09:33:35',0,'While the rules say you can replace a space with + or - it doesn\'t say you can eliminate a space.\r\n\r\nHowever, once one does that, one can go up to 123,456,789 (commas inserted for clarity), with various gaps of course.',5131,0); INSERT INTO comment VALUES (5133,814,1626,'Gamer','Maybe','2003-05-21 09:57:29',0,'Does 1 2=3+4 look right? I don\'t think it does, but I think it\'s impossible for the expresion to equal 0 otherwise. Since the numbers alternate odd and even, it seems impossible for it not to make an even number (such as 0 or 2) without stacking the digits.\r\n',NULL,0); INSERT INTO comment VALUES (5134,851,1072,'Alan','Could it be?','2003-05-21 10:09:58',0,'Could these be digits that are all parts of pie',NULL,0); INSERT INTO comment VALUES (5135,524,2274,'MeGg','Solution','2003-05-21 11:52:23',0,'itz eye haha durr\r\n',NULL,0); INSERT INTO comment VALUES (5136,823,2274,'MeGg','HaHaHa','2003-05-21 11:56:59',0,'3/8 durr haha ',NULL,0); INSERT INTO comment VALUES (5137,851,1626,'Gamer','','2003-05-21 12:20:16',2,'Breaking up the sequence into groups of 4 gives:\r\n\r\n1914\r\n1918\r\n1939\r\n194_\r\n\r\nSeems as though they are dates, though I don\'t know what date it could be...',NULL,0); INSERT INTO comment VALUES (5138,851,1567,'Bryan','Solution','2003-05-21 12:35:08',0,'Looking at the numbers in groups of four we get 1914, 1918, 1939, and 194?. World War I ran from 1914 to 1918, and WWII ran from 1939 to 1945. Thus the last number in this sequence is 5.',NULL,0); INSERT INTO comment VALUES (5139,851,1626,'Gamer','re: Solution','2003-05-21 12:57:28',0,'Yes... I couldn\'t get what the dates meant, but I guess you did! (I have never been very good with history :D)',5138,0); INSERT INTO comment VALUES (5140,829,1660,'Tim Axoy','Find the bold spots.','2003-05-21 13:37:20',3,'Call Ernesto E,Fontleroy F,and Gildenstern G.\r\nFor any person P and any number N,let PN be P\'s Nth statement(Example:Fontleroy\'s second statement is F2).\r\nWe notice that for any knight-liar-knave person P and any number N1 and N2 both even or both odd,PN1 and PN2 are either both true or both false(Call this Fact 1).\r\n
\r\nA knight can never claim to be a knave like Fontleroy did in F1,so F is not a knight.\r\nF can be a knave that told the truth in F1 or a liar who always lies in all his statements.\r\nEither way,F2 and F4 are both false(You can check this).\r\nE is not a knight and G is not a liar.\r\n
\r\nE said he was a knight and he is not,so E1 is false.\r\nE3 must also be false by Fact 1 at the beginning,so F is not a liar.\r\n
\r\nSince F is neither a knight nor a liar,he is a knave.\r\n
\r\nTherefore,G told the truth in G1,and also G3 by Fact 1,so E is a knave.\r\nSince E1 is false and E is a knave,E2 is true,so G is a knight.\r\nWe have solved it.\r\n
\r\nE is a knave,F is a knave,and G is a knight.\r\n
\r\nP. S. Find all the bold spots.',NULL,0); INSERT INTO comment VALUES (5141,851,2184,'mark hartman','My answer:','2003-05-21 18:07:00',0,'I\'m going to go with 5. The series of numbers looks like dates associated with the World Wars: World War I from 1914 to 1918, and World War II from 1939 to 1945.\r\n\r\nJust a guess.\r\n',NULL,0); INSERT INTO comment VALUES (5142,851,1575,'DJ','and','2003-05-21 19:15:48',0,'I hope that question mark is the last number in the sequence altogether..',NULL,0); INSERT INTO comment VALUES (5143,841,1575,'DJ','re(3): Simulation','2003-05-21 19:23:55',0,'I found a simulation someone else had done, with 10000 samples per n, with the fraction of the time that all n points were within the same 180° arc. The table looked like this:\r\n n simulation \r\n 1 1.0000\r\n 2 1.0000\r\n 3 1.0000\r\n 4 0.8742\r\n 5 0.6862\r\n 6 0.4954\r\n 7 0.3365\r\n 8 0.2295\r\n 9 0.1508\r\n10 0.0889\r\nI didn\'t run that myself; that\'s just what I found. Anyway, it corresponds pretty well to the solution.',5127,0); INSERT INTO comment VALUES (5144,20,2259,'calla tah-n','easy! solution:','2003-05-21 20:05:06',0,'go from A to the midpoint of segment FD or segment DE and then go to point G.\r\nWhy? because if you were to unfold the cube and lay it flat the straight from A to G would either go through the midpoint of FD or DE, depending on how the cube was unfolded',NULL,0); INSERT INTO comment VALUES (5145,814,2129,'Sanjay','re(2): Solution','2003-05-21 22:12:17',0,'When it says \'You have to put in + and -signs in the blanks, ...\', I assume that you \'have to\' put in + and - signs in the blanks.\r\n\r\n\r\n',5126,0); INSERT INTO comment VALUES (5146,823,2239,'Alpha Tiger','Easy ...','2003-05-22 01:57:11',3,'1+1=3 hehe (er no it\'s not the problem ...)\r\n\r\nHHH\r\nHHT\r\nHTH\r\nTHH\r\nTTH\r\nTHT\r\nHTT\r\nTTT\r\n\r\nEr ... The probability is 3/8.',NULL,0); INSERT INTO comment VALUES (5147,810,2231,'Trevor Leitch','Solution','2003-05-22 02:48:20',3,'First off, I assume the question means that there were AT LEAST 2 people at the party who had shaken hands the same number of times, not EXACTLY 2 people... it is easy to think of a situation where more than two people had shaken hands the same number of times, e.g. a party of three people where everybody knew everybody else.\r\n\r\nSolution: At any given moment, there are n people at the party. Each person can know anywhere from 0 to (n-1) other people (since we assume that one cannot \"know oneself\", at least not shake one\'s own hand). Thus, for n different people there are n different numbers of handshakes one can possibly make (0, 1, 2, ... , n-1). However, it is impossible for there to be a person who knows (n-1) people AND a person who knows 0 people at a party; the first represents someone who knows everybody else, the second someone who knows nobody, and the two cannot coexist. Thus, there are only (n-1) possible different handshake counts a person at the party can have, and n people at the party; therefore, at least two people must have made the same number of handshakes (I think they called this pigeon-hole theory in college, but that could be wrong).',NULL,0); INSERT INTO comment VALUES (5148,15,2277,'steve','another approach','2003-05-22 03:09:30',0,'let x be the number WITHOUT the 2 at the end or the beginning. Then, if we append a 2 to the end, the value of this number is 10*x + 2. On the other hand, if a 2 is pre-appended to x, the value is 2*10^n + x, where n is the number of digits in x. The latter is double the former, 2*10^n + x = 2*(10*x + 2). Solving this, we get 2*10^n - 4 = 19*x. In other words, x is the quotient when a number of the form 199...996 is evenly divisible by 19. I obtained the solution by long division.\r\n\r\n',NULL,0); INSERT INTO comment VALUES (5149,814,2278,'Dave Neary','re: Solution','2003-05-22 03:28:29',3,'The solution is easier than that.\r\n\r\n0+1+...+9 = 45. We want to add +s and -s to make 1. Grouping all the +ed numbers and the -ed numbers together, we get \r\n(a1+b1+c1+...) - (a2+b2+...) = 1\r\nand\r\na1+b1+c1+...+a2+b2+... = 45.\r\n\r\nThe obvious solution to this is 23 - 22 = 1, 23 + 22 = 45 And in fact this is the only solution.\r\n\r\nSo to solve the problem we just need to take any subset of (0,1,...,9) which adds up to 22, minus them, and we\'re done.\r\n\r\nOne such group is 1,2,3,4,5,7 Another is 1,2,3,8,9, and so on.\r\n\r\nCheers,\r\nDave.',5125,0); INSERT INTO comment VALUES (5150,851,2278,'Dave Neary','re:','2003-05-22 03:33:03',0,'5\r\n\r\nYou could do with learning a little history. Assuming you were serious. Of course, you might have been joking :) \r\n\r\nDave.',5137,0); INSERT INTO comment VALUES (5151,810,1567,'Bryan','Solution','2003-05-22 04:43:20',3,'For n guests, the minimum number of people that one can shake hands with is zero, while the maximum number is n-1 (you aren’t shaking hands with yourself, after all). However, these two conditions are mutually exclusive, because if one person has shaken the hands of all of the n-1 other guests, another person cannot have shaken nobody’s hand, and vice versa. Therefore, for n guests, there are only n-1 possible number of handshakes, so at least two partiers must have the same number of handshakes.',NULL,0); INSERT INTO comment VALUES (5152,841,1301,'Charlie','re(4): Simulation','2003-05-22 05:25:35',0,'In all 10000 trials 3 random points all three fell within a 180° span? And with 4 points, 8742 out of 10000 fell within the span, when 5000 would have been expected? If 5000 are expected we\'d usually expect that number +/- 70 as the standard deviation, so even 3 std deviations would be 5210--nowhere near 8742.',5143,0); INSERT INTO comment VALUES (5153,814,2129,'Sanjay','re(2): Solution','2003-05-22 05:29:24',0,'Dave, I agree with you completely. All we have to do is to find subsets of (0,1,....,9) which add up to 22, and minus them. \r\n\r\nIt just so happens that there are 23 such subsets:\r\n\r\n{6,7,9},{5,8,9},{4,5,6,7},{3,5,6,8},{3,4,7,8},{3,4,6,9},{2,5,7,8},{2,5,6,9},{2,4,7,9},{2,3,8,9},{2,3,4,6,7},{2,3,4,5,8},{1,6,7,8},{1,5,7,9},{1,4,8,9},{1,3,5,6,7},{1,3,4,6,8},{1,3,4,5,9},{1,2,5,6,8},{1,2,4,7,8},{1,2,4,6,9},{1,2,3,7,9},{1,2,3,4,5,7}\r\n\r\nReversing the signs in any solution for +1 gives us a solution for -1.\r\n\r\nPS: Sorry to point it out Dave, but contrary to your suggestion {1,2,3,8,9} is not one such group. Obviously an oversight.',5149,0); INSERT INTO comment VALUES (5154,765,2129,'Sanjay','re: General Solution','2003-05-22 05:50:21',0,'I realize that since the problem only asks us to determine the identity of the \'fake\' coin and not the nature of its \'fakeness\' it will be possible to \'solve\' more than (3^X-3)/2 coins in X weighings. \r\n\r\nNot having to identify the nature of fakeness allows us to leave one coin out of the weighings altogether. Hence we can \'solve\' at least one more than (3^X-3)/2 coins in X weighings. However, I can\'t say for certain whether this is the maximum we can \'solve\'. ',4987,0); INSERT INTO comment VALUES (5155,814,1301,'Charlie','re: Solution plus','2003-05-22 06:52:24',0,'Following your allowing of the removal of spaces in addition to replacement of others by + or -, and to answer your question on the first positive integer that can\'t be produced in that manner, the answer is 211.\r\n\r\n 0 = 0- 1 - 2 + 34 + 56 - 78 - 9\r\n (32 others)\r\n 1 = 0- 1 - 2 - 3 - 4 - 5 + 6 - 7 + 8 + 9\r\n (68 others)\r\n 2 = 0- 1 + 2 - 34 + 5 + 6 + 7 + 8 + 9\r\n (28 others)\r\n 3 = 0- 1 - 2 - 3 - 4 - 5 - 6 + 7 + 8 + 9\r\n (58 others)\r\n 4 = 0- 1 - 2 + 34 - 5 + 67 - 89\r\n (25 others)\r\n 5 = 0- 1 - 2 - 3 + 4 - 5 + 6 + 7 + 8 - 9\r\n (60 others)\r\n 6 = 0- 1 - 2 + 34 + 5 - 6 - 7 - 8 - 9\r\n (35 others)\r\n 7 = 0- 1 - 2 - 3 - 4 - 5 - 67 + 89\r\n (55 others)\r\n 8 = 0- 1 - 2 - 34 - 5 + 67 - 8 - 9\r\n (25 others)\r\n 9 = 0- 1 - 2 - 3 - 4 + 5 + 6 + 7 - 8 + 9\r\n (67 others)\r\n 10 = 0- 1 - 2 + 34 - 5 - 6 + 7 - 8 - 9\r\n (28 others)\r\n 11 = 0- 1 - 2 - 3 - 4 + 5 + 6 - 7 + 8 + 9\r\n (58 others)\r\n 12 = 0- 1 - 2 - 3 - 45 - 6 + 78 - 9\r\n (37 others)\r\n 13 = 0- 1 - 2 - 3 - 4 + 5 - 6 + 7 + 8 + 9\r\n (53 others)\r\n 14 = 0- 1 - 2 + 34 - 5 - 6 - 7 - 8 + 9\r\n (38 others)\r\n 15 = 0- 1 - 2 - 3 - 4 - 5 + 6 + 7 + 8 + 9\r\n (62 others)\r\n 16 = 0- 1 - 2 - 3 - 4 - 56 - 7 + 89\r\n (25 others)\r\n 17 = 0- 1 - 2 - 3 - 4 + 5 - 67 + 89\r\n (55 others)\r\n 18 = 0- 1 - 2 - 34 + 5 + 67 - 8 - 9\r\n (33 others)\r\n 19 = 0- 1 - 2 - 3 + 4 + 5 + 6 - 7 + 8 + 9\r\n (56 others)\r\n 20 = 0- 1 - 2 + 34 + 5 - 6 + 7 - 8 - 9\r\n (37 others)\r\n 21 = 0- 1 - 2 - 3 - 4 - 56 + 78 + 9\r\n (58 others)\r\n 22 = 0- 1 - 2 - 3 - 4 + 56 - 7 - 8 - 9\r\n (35 others)\r\n 23 = 0- 1 - 2 - 3 + 4 - 5 + 6 + 7 + 8 + 9\r\n (58 others)\r\n 24 = 0- 1 - 2 - 3 - 45 + 6 + 78 - 9\r\n (49 others)\r\n 25 = 0- 1 - 2 - 3 - 4 + 5 + 6 + 7 + 8 + 9\r\n (48 others)\r\n 26 = 0- 1 - 2 - 34 - 5 + 67 - 8 + 9\r\n (38 others)\r\n 27 = 0- 1 - 2 - 3 + 45 - 6 - 7 - 8 + 9\r\n (64 others)\r\n 28 = 0- 1 - 2 + 3 - 4 + 56 - 7 - 8 - 9\r\n (39 others)\r\n 29 = 0- 1 - 2 - 3 + 4 - 56 + 78 + 9\r\n (53 others)\r\n 30 = 0- 1 - 2 - 3 - 4 - 56 + 7 + 89\r\n (50 others)\r\n 31 = 0- 1 - 2 - 34 + 5 - 6 + 78 - 9\r\n (44 others)\r\n 32 = 0- 1 - 2 + 34 + 5 + 6 + 7 - 8 - 9\r\n (44 others)\r\n 33 = 0- 1 - 2 - 3 - 45 + 67 + 8 + 9\r\n (55 others)\r\n 34 = 0- 1 - 2 - 34 - 5 - 6 - 7 + 89\r\n (30 others)\r\n 35 = 0- 1 - 2 - 3 - 4 - 5 + 67 - 8 - 9\r\n (48 others)\r\n 36 = 0- 1 - 2 - 3 - 4 + 56 + 7 - 8 - 9\r\n (50 others)\r\n 37 = 0- 1 - 2 - 3 - 45 + 6 - 7 + 89\r\n (50 others)\r\n 38 = 0- 1 - 2 - 3 - 4 + 56 - 7 + 8 - 9\r\n (43 others)\r\n 39 = 0- 1 - 2 - 3 - 45 - 6 + 7 + 89\r\n (54 others)\r\n 40 = 0- 1 - 2 - 3 - 4 + 56 - 7 - 8 + 9\r\n (46 others)\r\n 41 = 0- 1 - 2 - 3 + 45 - 6 + 7 - 8 + 9\r\n (42 others)\r\n 42 = 0- 1 - 2 - 3 - 45 + 6 + 78 + 9\r\n (51 others)\r\n 43 = 0- 1 - 2 - 3 + 4 - 5 + 67 - 8 - 9\r\n (43 others)\r\n 44 = 0- 1 - 2 - 3 + 4 + 56 + 7 - 8 - 9\r\n (43 others)\r\n 45 = 0- 1 - 2 - 3 - 4 + 5 + 67 - 8 - 9\r\n (67 others)\r\n 46 = 0- 1 - 2 - 3 + 4 + 56 - 7 + 8 - 9\r\n (44 others)\r\n 47 = 0- 1 - 2 + 3 + 45 - 6 + 7 - 8 + 9\r\n (41 others)\r\n 48 = 0- 1 - 2 - 3 - 4 - 5 - 6 + 78 - 9\r\n (50 others)\r\n 49 = 0- 1 - 2 - 34 + 5 - 6 + 78 + 9\r\n (37 others)\r\n 50 = 0- 1 - 2 + 3 + 4 + 56 + 7 - 8 - 9\r\n (44 others)\r\n 51 = 0- 1 - 2 - 3 - 4 - 5 + 67 + 8 - 9\r\n (53 others)\r\n 52 = 0- 1 - 2 - 3 - 4 + 56 + 7 + 8 - 9\r\n (37 others)\r\n 53 = 0- 1 - 2 - 3 - 4 - 5 + 67 - 8 + 9\r\n (49 others)\r\n 54 = 0- 1 - 2 - 3 - 4 + 56 + 7 - 8 + 9\r\n (50 others)\r\n 55 = 0- 1 - 2 - 3 + 45 + 6 - 7 + 8 + 9\r\n (41 others)\r\n 56 = 0- 1 - 2 - 3 - 4 + 56 - 7 + 8 + 9\r\n (35 others)\r\n 57 = 0- 1 - 2 - 3 + 45 - 6 + 7 + 8 + 9\r\n (42 others)\r\n 58 = 0- 1 - 2 - 3 - 4 + 5 - 6 + 78 - 9\r\n (47 others)\r\n 59 = 0- 1 - 2 - 3 + 4 - 5 + 67 + 8 - 9\r\n (41 others)\r\n 60 = 0- 1 - 2 - 3 - 4 - 5 + 6 + 78 - 9\r\n (49 others)\r\n 61 = 0- 1 - 2 - 3 - 4 - 5 - 6 - 7 + 89\r\n (40 others)\r\n 62 = 0- 1 - 2 - 3 + 4 + 56 + 7 - 8 + 9\r\n (36 others)\r\n 63 = 0- 1 - 2 - 3 - 4 + 5 + 67 - 8 + 9\r\n (55 others)\r\n 64 = 0- 1 - 2 - 3 + 4 + 56 - 7 + 8 + 9\r\n (35 others)\r\n 65 = 0- 1 - 2 + 3 + 4 - 5 + 67 + 8 - 9\r\n (38 others)\r\n 66 = 0- 1 - 2 - 3 - 4 - 5 - 6 + 78 + 9\r\n (46 others)\r\n 67 = 0- 1 - 2 + 3 - 4 - 5 - 6 - 7 + 89\r\n (44 others)\r\n 68 = 0- 1 - 2 - 3 + 4 - 5 + 6 + 78 - 9\r\n (39 others)\r\n 69 = 0- 1 - 2 - 3 - 4 - 5 + 67 + 8 + 9\r\n (45 others)\r\n 70 = 0- 1 - 2 - 3 - 4 + 5 + 6 + 78 - 9\r\n (28 others)\r\n 71 = 0- 1 - 2 - 3 - 4 + 5 - 6 - 7 + 89\r\n (38 others)\r\n 72 = 0- 1 - 2 + 3 - 4 - 5 - 6 + 78 + 9\r\n (42 others)\r\n 73 = 0- 1 - 2 - 3 - 4 - 5 + 6 - 7 + 89\r\n (38 others)\r\n 74 = 0- 1 - 2 - 3 + 4 - 5 - 6 + 78 + 9\r\n (33 others)\r\n 75 = 0- 1 - 2 - 3 - 4 - 5 - 6 + 7 + 89\r\n (38 others)\r\n 76 = 0- 1 - 2 - 3 - 4 + 5 - 6 + 78 + 9\r\n (38 others)\r\n 77 = 0- 1 - 2 - 3 + 4 - 5 + 67 + 8 + 9\r\n (35 others)\r\n 78 = 0- 1 - 2 - 3 - 4 - 5 + 6 + 78 + 9\r\n (37 others)\r\n 79 = 0- 1 - 2 - 3 - 4 + 5 + 67 + 8 + 9\r\n (34 others)\r\n 80 = 0- 1 - 2 + 3 + 4 - 5 - 6 + 78 + 9\r\n (27 others)\r\n 81 = 0- 1 - 2 - 3 + 4 - 5 + 6 - 7 + 89\r\n (49 others)\r\n 82 = 0- 1 - 2 + 3 - 4 + 5 - 6 + 78 + 9\r\n (31 others)\r\n 83 = 0- 1 - 2 - 3 - 4 + 5 + 6 - 7 + 89\r\n (35 others)\r\n 84 = 0- 1 - 2 - 3 + 4 + 5 - 6 + 78 + 9\r\n (37 others)\r\n 85 = 0- 1 - 2 - 3 - 4 + 5 - 6 + 7 + 89\r\n (32 others)\r\n 86 = 0- 1 - 2 - 3 + 4 - 5 + 6 + 78 + 9\r\n (28 others)\r\n 87 = 0- 1 - 2 - 3 - 4 - 5 + 6 + 7 + 89\r\n (34 others)\r\n 88 = 0- 1 - 2 - 3 - 4 + 5 + 6 + 78 + 9\r\n (22 others)\r\n 89 = 0- 1 - 2 - 3 + 45 + 67 - 8 - 9\r\n (35 others)\r\n 90 = 0- 1 - 2 + 3 + 4 + 5 - 6 + 78 + 9\r\n (34 others)\r\n 91 = 0- 1 - 2 - 3 + 4 + 5 + 6 - 7 + 89\r\n (37 others)\r\n 92 = 0- 1 - 2 + 3 + 4 - 5 + 6 + 78 + 9\r\n (33 others)\r\n 93 = 0- 1 - 2 - 3 + 4 + 5 - 6 + 7 + 89\r\n (33 others)\r\n 94 = 0- 1 - 2 + 3 - 4 + 5 + 6 + 78 + 9\r\n (27 others)\r\n 95 = 0- 1 - 2 - 3 + 4 - 5 + 6 + 7 + 89\r\n (26 others)\r\n 96 = 0- 1 - 2 - 3 + 4 + 5 + 6 + 78 + 9\r\n (29 others)\r\n 97 = 0- 1 - 2 - 3 - 4 + 5 + 6 + 7 + 89\r\n (27 others)\r\n 98 = 0- 1 + 2 + 3 - 4 + 5 + 6 + 78 + 9\r\n (23 others)\r\n 99 = 0- 1 - 2 + 3 + 4 + 5 - 6 + 7 + 89\r\n (41 others)\r\n 100 = 0- 1 + 2 - 3 + 4 + 5 + 6 + 78 + 9\r\n (22 others)\r\n 101 = 0- 1 - 2 - 34 + 56 - 7 + 89\r\n (27 others)\r\n 102 = 0- 1 - 2 - 3 + 45 - 6 + 78 - 9\r\n (26 others)\r\n 103 = 0- 1 - 2 + 3 - 4 + 5 + 6 + 7 + 89\r\n (22 others)\r\n 104 = 0- 1 - 2 + 34 + 5 + 67 - 8 + 9\r\n (24 others)\r\n 105 = 0- 1 - 2 - 3 - 45 + 67 + 89\r\n (23 others)\r\n 106 = 0- 1 - 2 - 34 + 56 + 78 + 9\r\n (24 others)\r\n 107 = 0- 1 - 2 - 3 + 45 + 67 - 8 + 9\r\n (27 others)\r\n 108 = 0- 1 - 2 + 3 + 45 - 6 + 78 - 9\r\n (33 others)\r\n 109 = 0- 1 - 23 + 45 + 6 - 7 + 89\r\n (18 others)\r\n 110 = 0- 1 - 2 + 34 - 5 + 67 + 8 + 9\r\n (23 others)\r\n 111 = 0- 1 - 2 + 3 - 45 + 67 + 89\r\n (24 others)\r\n 112 = 0- 1 - 2 + 34 + 5 - 6 - 7 + 89\r\n (20 others)\r\n 113 = 0- 1 - 2 + 3 + 45 + 67 - 8 + 9\r\n (21 others)\r\n 114 = 0- 1 - 2 - 3 + 45 + 6 + 78 - 9\r\n (25 others)\r\n 115 = 0- 1 - 2 - 3 - 4 + 56 + 78 - 9\r\n (16 others)\r\n 116 = 0- 1 - 2 + 34 - 5 - 6 + 7 + 89\r\n (24 others)\r\n 117 = 0- 1 - 2 + 34 + 5 - 6 + 78 + 9\r\n (34 others)\r\n 118 = 0- 1 - 23 + 4 + 56 - 7 + 89\r\n (20 others)\r\n 119 = 0- 1 - 2 + 34 - 5 + 6 + 78 + 9\r\n (14 others)\r\n 120 = 0- 1 - 2 - 3 + 45 - 6 + 78 + 9\r\n (27 others)\r\n 121 = 0- 1 - 2 + 3 - 4 + 56 + 78 - 9\r\n (15 others)\r\n 122 = 0+ 1 - 2 - 3 + 45 - 6 + 78 + 9\r\n (17 others)\r\n 123 = 0- 1 - 2 - 3 + 4 + 56 + 78 - 9\r\n (17 others)\r\n 124 = 0- 1 - 2 - 34 + 5 + 67 + 89\r\n (14 others)\r\n 125 = 0- 1 + 2 + 3 - 4 + 56 + 78 - 9\r\n (19 others)\r\n 126 = 0- 1 - 2 + 3 + 45 - 6 + 78 + 9\r\n (33 others)\r\n 127 = 0- 1 - 2 - 3 + 45 + 6 - 7 + 89\r\n (11 others)\r\n 128 = 0- 1 - 2 - 3 - 4 + 56 - 7 + 89\r\n (19 others)\r\n 129 = 0- 1 - 2 - 3 + 45 - 6 + 7 + 89\r\n (17 others)\r\n 130 = 0- 1 + 2 + 3 + 45 - 6 + 78 + 9\r\n (21 others)\r\n 131 = 0- 1 - 23 + 4 - 5 + 67 + 89\r\n (11 others)\r\n 132 = 0- 1 - 2 - 3 + 45 + 6 + 78 + 9\r\n (22 others)\r\n 133 = 0- 1 - 2 - 3 - 4 + 56 + 78 + 9\r\n (15 others)\r\n 134 = 0- 1 - 2 + 3 - 4 + 56 - 7 + 89\r\n (14 others)\r\n 135 = 0- 1 - 2 + 3 + 45 - 6 + 7 + 89\r\n (28 others)\r\n 136 = 0- 1 - 2 - 3 + 4 + 56 - 7 + 89\r\n (16 others)\r\n 137 = 0- 1 + 2 - 3 - 4 + 56 + 78 + 9\r\n (7 others)\r\n 138 = 0- 1 - 2 + 3 + 45 + 6 + 78 + 9\r\n (22 others)\r\n 139 = 0- 1 - 2 + 3 - 4 + 56 + 78 + 9\r\n (10 others)\r\n 140 = 0- 1 + 2 - 3 + 4 + 56 - 7 + 89\r\n (16 others)\r\n 141 = 0- 1 - 2 - 3 - 4 - 5 + 67 + 89\r\n (14 others)\r\n 142 = 0- 1 - 2 - 3 - 4 + 56 + 7 + 89\r\n (13 others)\r\n 143 = 0- 1 + 2 + 3 - 4 + 56 + 78 + 9\r\n (14 others)\r\n 144 = 0- 1 + 234 - 5 - 67 - 8 - 9\r\n (26 others)\r\n 145 = 0- 1 + 2 - 3 - 4 - 5 + 67 + 89\r\n (11 others)\r\n 146 = 0- 1 + 2 - 3 - 4 + 56 + 7 + 89\r\n (12 others)\r\n 147 = 0- 1 - 2 + 3 - 4 - 5 + 67 + 89\r\n (15 others)\r\n 148 = 0- 1 - 2 + 3 - 4 + 56 + 7 + 89\r\n (13 others)\r\n 149 = 0- 1 - 2 - 3 + 4 - 5 + 67 + 89\r\n (10 others)\r\n 150 = 0- 1 - 2 - 3 + 4 + 56 + 7 + 89\r\n (16 others)\r\n 151 = 0- 1 - 2 - 3 - 4 + 5 + 67 + 89\r\n (11 others)\r\n 152 = 0- 1 + 2 + 3 - 4 + 56 + 7 + 89\r\n (9 others)\r\n 153 = 0- 1 + 2 - 3 + 4 - 5 + 67 + 89\r\n (22 others)\r\n 154 = 0- 1 + 2 - 3 + 4 + 56 + 7 + 89\r\n (15 others)\r\n 155 = 0- 1 - 2 + 3 + 4 - 5 + 67 + 89\r\n (8 others)\r\n 156 = 0- 1 - 2 + 3 + 4 + 56 + 7 + 89\r\n (15 others)\r\n 157 = 0- 1 - 2 + 3 - 4 + 5 + 67 + 89\r\n (12 others)\r\n 158 = 0+ 1 - 2 + 3 + 4 + 56 + 7 + 89\r\n (7 others)\r\n 159 = 0- 1 - 2 - 3 + 4 + 5 + 67 + 89\r\n (13 others)\r\n 160 = 0- 1 + 2 + 3 + 4 + 56 + 7 + 89\r\n (4 others)\r\n 161 = 0- 1 + 2 + 3 - 4 + 5 + 67 + 89\r\n (5 others)\r\n 162 = 0- 1 + 234 - 5 - 67 - 8 + 9\r\n (19 others)\r\n 163 = 0- 1 + 2 - 3 + 4 + 5 + 67 + 89\r\n (7 others)\r\n 164 = 0- 1 + 23 + 4 + 56 - 7 + 89\r\n (10 others)\r\n 165 = 0- 1 - 2 + 3 + 4 + 5 + 67 + 89\r\n (10 others)\r\n 166 = 0+ 1 + 23 + 4 + 56 - 7 + 89\r\n (7 others)\r\n 167 = 0- 1 + 234 - 56 + 7 - 8 - 9\r\n (8 others)\r\n 168 = 0+ 123 - 45 - 6 + 7 + 89\r\n (5 others)\r\n 169 = 0- 1 - 2 + 34 + 56 - 7 + 89\r\n (9 others)\r\n 170 = 0- 1 + 23 - 4 + 56 + 7 + 89\r\n (5 others)\r\n 171 = 0- 1 + 234 - 56 - 7 - 8 + 9\r\n (18 others)\r\n 172 = 0- 1 + 234 + 5 - 67 - 8 + 9\r\n (10 others)\r\n 173 = 0- 1 + 2 + 34 + 56 - 7 + 89\r\n (5 others)\r\n 174 = 0- 1 - 2 + 34 + 56 + 78 + 9\r\n (7 others)\r\n 175 = 0- 1 + 234 + 5 + 6 - 78 + 9\r\n (4 others)\r\n 176 = 0+ 1 - 2 + 34 + 56 + 78 + 9\r\n (1 other)\r\n 177 = 0- 1 - 23 + 45 + 67 + 89\r\n (8 others)\r\n 178 = 0- 1 + 2 + 34 + 56 + 78 + 9\r\n (2 others)\r\n 179 = 0- 1 + 23 - 4 + 5 + 67 + 89\r\n (4 others)\r\n 180 = 0+ 1 + 2 + 34 + 56 + 78 + 9\r\n (13 others)\r\n 181 = 0+ 1 + 23 - 4 + 5 + 67 + 89\r\n (3 others)\r\n 182 = 0- 1 - 2 + 34 - 5 + 67 + 89\r\n (6 others)\r\n 183 = 0- 1 - 2 + 34 + 56 + 7 + 89\r\n (4 others)\r\n 184 = 0+ 1 - 2 + 34 - 5 + 67 + 89\r\n (5 others)\r\n 185 = 0- 1 + 234 - 56 + 7 - 8 + 9\r\n (8 others)\r\n 186 = 0- 1 - 2 + 345 - 67 - 89\r\n (4 others)\r\n 187 = 0- 1 + 2 + 34 + 56 + 7 + 89\r\n (6 others)\r\n 188 = 0- 1 + 234 + 5 - 67 + 8 + 9\r\n (6 others)\r\n 189 = 0+ 1 + 2 + 34 + 56 + 7 + 89\r\n (11 others)\r\n 190 = 0- 1 + 2 + 345 - 67 - 89\r\n (10 others)\r\n 191 = 0+ 123 + 4 + 56 + 7 - 8 + 9\r\n (1 other)\r\n 192 = 0- 1 - 2 + 34 + 5 + 67 + 89\r\n (5 others)\r\n 193 = 0- 1 + 234 + 56 - 7 - 89\r\n (2 others)\r\n 194 = 0+ 1 - 2 + 34 + 5 + 67 + 89\r\n (1 other)\r\n 195 = 0- 1 - 2 - 3 + 45 + 67 + 89\r\n (6 others)\r\n 196 = 0- 1 + 2 + 34 + 5 + 67 + 89\r\n 197 = 0+ 1 - 2 - 3 + 45 + 67 + 89\r\n (5 others)\r\n 198 = 0- 1 + 234 - 5 - 6 - 7 - 8 - 9\r\n (12 others)\r\n 199 = 0- 1 + 2 - 3 + 45 + 67 + 89\r\n (4 others)\r\n 200 = 0+ 1 + 234 - 5 - 6 - 7 - 8 - 9\r\n (5 others)\r\n 201 = 0- 1 - 2 + 3 + 45 + 67 + 89\r\n (5 others)\r\n 202 = 0- 1 + 234 + 56 - 78 - 9\r\n (2 others)\r\n 203 = 0+ 1 - 2 + 3 + 45 + 67 + 89\r\n (5 others)\r\n 204 = 0+ 1 + 234 + 56 - 78 - 9\r\n (3 others)\r\n 205 = 0- 1 + 2 + 3 + 45 + 67 + 89\r\n (2 others)\r\n 206 = 0- 1 + 234 - 5 + 67 - 89\r\n (2 others)\r\n 207 = 0- 1 + 234 + 56 + 7 - 89\r\n (10 others)\r\n 208 = 0- 1 + 234 + 5 - 6 - 7 - 8 - 9\r\n (6 others)\r\n 209 = 0+ 1 + 234 + 56 + 7 - 89\r\n (1 other)\r\n 210 = 0- 1 + 234 - 5 + 6 - 7 - 8 - 9\r\n (7 others)\r\nSkip 1 \r\n 212 = 0- 1 + 234 - 5 - 6 + 7 - 8 - 9\r\n (6 others)\r\n 213 = 0+ 123 + 4 + 5 - 6 + 78 + 9\r\n (1 other)\r\n 214 = 0- 1 + 234 - 5 - 6 - 7 + 8 - 9\r\n (4 others)\r\n 215 = 0+ 123 + 4 - 5 + 6 + 78 + 9\r\n (1 other)\r\n 216 = 0- 1 + 234 - 5 - 6 - 7 - 8 + 9\r\n (9 others)\r\n 217 = 0+ 123 - 4 + 5 + 6 + 78 + 9\r\n (1 other)\r\n 218 = 0+ 1 + 234 - 5 - 6 - 7 - 8 + 9\r\n (5 others)\r\nSkip 1 \r\n 220 = 0- 1 + 234 + 5 + 6 - 7 - 8 - 9\r\n (3 others)\r\nSkip 1 \r\n 222 = 0- 1 + 234 + 5 - 6 + 7 - 8 - 9\r\n (6 others)\r\n 223 = 0- 1 + 23 + 45 + 67 + 89\r\n 224 = 0- 1 + 234 - 5 + 6 + 7 - 8 - 9\r\n (5 others)\r\n 225 = 0+ 1 + 23 + 45 + 67 + 89\r\n (3 others)\r\n 226 = 0- 1 + 234 - 5 + 6 - 7 + 8 - 9\r\n (7 others)\r\nSkip 1 \r\n 228 = 0- 1 + 234 - 5 - 6 + 7 + 8 - 9\r\n (5 others)\r\nSkip 1 \r\n 230 = 0- 1 + 234 - 5 - 6 + 7 - 8 + 9\r\n',5129,0); INSERT INTO comment VALUES (5156,529,2280,'Alanna','archaelogical problem','2003-05-22 07:46:38',2,'think about the phrase \"coins dated 64 B.C.\".....',NULL,0); INSERT INTO comment VALUES (5157,529,2281,'Mae','coins','2003-05-22 08:05:44',0,'haha, good one :) back then, they wouldn\'t be dated B.C.',NULL,0); INSERT INTO comment VALUES (5158,525,2279,'Jason','','2003-05-22 09:41:22',3,'',NULL,0); INSERT INTO comment VALUES (5159,814,1567,'Bryan','re(2): Solution plus','2003-05-22 09:52:40',0,'Thanks, Charlie!\r\n\r\nI would have bet money that you would figure out the answer. lol',5155,0); INSERT INTO comment VALUES (5160,529,1626,'Gamer','re: coins','2003-05-22 09:55:02',4,'They wouldn\'t be BC, they would be BCE, or a big atheist support group would go up and storm the government and demand politically correct coins.\r\n\r\n(Note: \"gold coins dated 64 BC\" sometimes means \"gold coins that date back to 64 BC\" as an expression to me)\r\n\r\nI also talked to that archaelogist who found some coins with the writing \"George I\", should I believe him now?',5157,0); INSERT INTO comment VALUES (5161,529,1,'levik','re(2): coins','2003-05-22 10:04:10',0,'I also talked to that archaelogist who found some coins with the writing \"George I\", should I believe him now?\r\n\r\nActually a few monarchs were called \"The First\" even during their lifetimes. (No examples come to mind right now)\r\n\n\nEdited on August 25, 2003, 12:00 pm',5160,0); INSERT INTO comment VALUES (5162,529,1517,'jude','63','2003-05-22 10:42:04',0,'No, because numbers only went as high as 63 back then.\r\n\r\nHAHAHAHAHAHA',NULL,0); INSERT INTO comment VALUES (5163,272,2279,'redeemed277','Answer','2003-05-22 10:44:29',3,'Jack represents 9 and George represents 5. A little too easy I thought.',NULL,0); INSERT INTO comment VALUES (5164,529,1645,'luvya2003','solution','2003-05-22 11:00:14',0,'Before Christ was born, nobody knew when exactly He would be born, so there was no way specify what year it was B.C.',NULL,0); INSERT INTO comment VALUES (5165,814,1575,'DJ','re(3): Solution','2003-05-22 11:48:56',0,'Actually, there are 46 such subsets, since each one that you listed could also be relisted with 0 included.',5153,0); INSERT INTO comment VALUES (5166,841,1575,'DJ','re(5): Simulation','2003-05-22 11:57:25',0,'You\'re right...I was too lazy to write the program so I looked for one..the table that I found was one someone wrote to determine if n random points were all in the same hemisphere, not semicircle (obviously any three points are coplanar and can always be put into the same half of a sphere).\r\nIt was one in the morning, I wasn\'t paying attention...',5152,0); INSERT INTO comment VALUES (5167,249,2279,'redeemed277','Solution','2003-05-22 12:06:09',3,'The next line is : 1113213211. This is one of my favorites. ',NULL,0); INSERT INTO comment VALUES (5168,249,2279,'redeemed277','re: Is it?','2003-05-22 12:07:33',0,'I\'m afraid not. Sorry! : )',4090,0); INSERT INTO comment VALUES (5169,118,103,'friedlinguini','For Alan','2003-05-22 15:53:59',3,'Each couple is \'paired\' such that there was a total of 8 handshakes between them. Thus, one couple had 0 and 8, one had 1 and 7, etc. One of the couples must have had 4 and 4. Since every answer was different, Bill must not have asked one of the couple\'s members how many hands he or she shook. Since he asked everyone, including Alice, the only person that could have been left out was himself. Since he shook 4 hands, Alice did as well.',NULL,0); INSERT INTO comment VALUES (5170,529,2285,'vincent','how','2003-05-22 16:20:51',0,'i dont agree.\r\nhow do you carbon-date gold?',NULL,0); INSERT INTO comment VALUES (5171,529,1575,'DJ','re: how','2003-05-22 16:43:41',0,'I think the problem is referring to a stamped date on the coin itself. Carbon-dating is only used for living (or once-living) things, and it\'s not accurate anyway.',5170,0); INSERT INTO comment VALUES (5172,20,1575,'DJ','more..','2003-05-22 17:01:27',0,'The path does not have only to go through the midpoint of FD or DE. Any edge that does not include A or G is equivalent because they are opposite corners (the fact that you can\'t see them in the given diagram changes nothing). So, the shortest paths connect straight lines through CF, FD, DE, EB, and BX and CX (where X is the point on the \'far\' side of the cube, and not shown in the picture). Each of these points is √3/2 from both A and G.',NULL,0); INSERT INTO comment VALUES (5173,249,1575,'DJ','re(2): Is it?','2003-05-22 19:56:26',0,'isn\'t that the same thing you put? or did you post an incorrect solution as well..',5168,0); INSERT INTO comment VALUES (5174,529,2259,'calla tah-n','solution?','2003-05-22 20:12:51',3,'whell... this depends how picky you are being...\r\nthe solution should be no... as the people back at that time did not call it 64 B.C.\r\nBUT, the solution could also be yes... anyone could find a coin dated 64 B.C. - it would just be a fake, hmmm... wrong word... it would simply not be from 64 B.C.',NULL,0); INSERT INTO comment VALUES (5175,524,2259,'calla tah-n','too easy!!','2003-05-22 20:30:14',0,'the word EYE...\r\nthat was fun tho...',NULL,0); INSERT INTO comment VALUES (5176,139,2259,'calla tah-n','possible solution?','2003-05-22 20:53:54',0,'first split the group up into possible combinations:\r\n6 and 0\r\n5 and 1\r\n4 and 2\r\n3 and 3\r\nconsidering these combinations, it is not possible to get a combination with both numbers less than 3, so no matter what there will be at least 3 mutual friends or 3 mutual strangers',NULL,0); INSERT INTO comment VALUES (5177,139,2259,'calla tah-n','re: possible solution?','2003-05-22 20:59:50',0,'also... forgot to add this lah...\r\nif there are three groups...\r\nsay:\r\n2-2-2 or 1-2-3\r\nthen there will be three mutual strangers, in the second case possibly 3 mutual friends...\r\nif four groups (1-2-1-1) than there are 3 mutual strangers, person A does not know B, C, and D; person E will also not know persons B, C, and D\r\nif all are strangers then obviously by the above way they will be several sets of mutual strangers\r\nfor example: A and B: C,D,E\r\nA,C: B,D,E\r\nA,D: B,C,E... so on and so forth',5176,0); INSERT INTO comment VALUES (5178,145,2286,'imre bokor','If 25pc of the Square is shaded...','2003-05-22 21:28:11',0,'..what percentage of the square-side, is the radius?\r\nIn other words, if the side of the square is one metre, what is the radius of the circle, given that the circle covers 25 percent of the area of the square? (Answer to the nearest centimeter.)',NULL,0); INSERT INTO comment VALUES (5179,823,2286,'imre bokor','No solution yet? Nonsense!','2003-05-22 21:35:31',0,'Are there any problems on this site that actually do not have solutions yet? I like a challenge!',NULL,0); INSERT INTO comment VALUES (5180,529,872,'pleasance','no way!','2003-05-23 00:23:52',0,'clearly if the coin were for real, it would be marked as LXIV BC!',NULL,0); INSERT INTO comment VALUES (5181,525,2148,'Jayaram S','Most likely Answer','2003-05-23 00:41:46',1,'Only ONE (Ravi) was going to St. Ives. All other people he met on the way were perhaps returning back from St. Ives, when Ravi happened to meet them.',NULL,0); INSERT INTO comment VALUES (5182,840,1183,'fwaff','Say cheese!','2003-05-23 03:05:20',3,'A \'ton\' perchance?\r\n\r\nThis reminds me of the \"which cheese is made backwards?\" question.',NULL,0); INSERT INTO comment VALUES (5183,840,872,'pleasance','other solutions?','2003-05-23 03:37:09',0,'I\'m guessing \'ton\' is the correct answer. \r\n\r\nI wonder if we can come up with other solutions? How about \'iron\'? It\'s quite heavy, and backwards it spells \'nori\', the Japanese seaweed used to wrap sushi (definitely light-weight!).',NULL,0); INSERT INTO comment VALUES (5184,840,2238,'Ben lansdell','Solution','2003-05-23 03:48:18',3,'Hey, thankyou riddleplanet!\r\n\r\nton. a ton is heavy but spelt backwards its not. ',NULL,0); INSERT INTO comment VALUES (5185,841,1301,'Charlie','Web Research','2003-05-23 03:51:22',0,'A search for probability points semicircle yields a page (http://www.math.niu.edu/~rusin/known-math/98/hemisphere) asking about such problems in various dimensions, but including a statement about the two-dimensional case (actually 1-dimensional considered along the circumference):\r\n\r\n\"The case n = 0 yields the known probability that all k points lie on a semicircle: k/2^(k-1).\"\r\n\r\nIn fact the formula k/2^(k-1) fits with both the numerical integration solution as well as the simulation.\r\n\r\nOnly my estimate that the value .03513 for 9 points, which I took as 1/32, really should have been 9/256.\r\n\r\nThe .01951 for 10 points is close to the 10/512 theory predicts.',NULL,0); INSERT INTO comment VALUES (5186,840,979,'Ravi Raja','Solution','2003-05-23 04:00:53',3,'Forwards: T O N\r\nBackwards: N O T',NULL,0); INSERT INTO comment VALUES (5187,529,2281,'Mae','re(2): coins','2003-05-23 04:17:17',0,'The fact that the puzzle does word it to be \'dated 64 BC\', not \'dated back to 64 BC\' implies (to me at least ^__^) that on the coins were the date 64 BC. ',5160,0); INSERT INTO comment VALUES (5188,499,2272,'Clinton Heath','This must be the answer!','2003-05-23 04:49:31',3,'It was an all night pie eating contest! The \"jolly\" men, the \"money\" was the prize, the \"separate scores\" were how many pies each man ate, and they all \"made fair amounts\" because they all gained weight!',NULL,0); INSERT INTO comment VALUES (5189,529,1575,'DJ','re: solution?','2003-05-23 07:06:36',0,'Yeah, I like that..he very well could have found coins with that date on them, you just wouldn\'t believe that they were real.',5174,0); INSERT INTO comment VALUES (5190,823,2196,'Silly Jilly','I know it!','2003-05-23 09:37:12',3,'2/3.',NULL,0); INSERT INTO comment VALUES (5191,529,2289,'sammy','Answer.','2003-05-23 10:20:57',0,'They didn\'t have coins then so he is a big liar.',NULL,0); INSERT INTO comment VALUES (5192,394,2259,'calla tah-n','guess','2003-05-23 10:37:13',0,'does it have something to do with the temperature???',NULL,0); INSERT INTO comment VALUES (5193,250,2259,'calla tah-n','oldie!!!','2003-05-23 10:46:20',0,'this is one of the oldest paradoxes known to man. it\'s even in the Bible, though written slightly differently. another example of the same question is \"i am a liar, so it is just for me to say that all liars are liars\" but by saying this you must have lied about being a liar as the text states... but then you must be telling the truth as you are not a liar and it is not just for you to say you are a liar, so you are lying - therefore you are a liar...etc.',NULL,0); INSERT INTO comment VALUES (5194,263,2259,'calla tah-n','simple','2003-05-23 10:54:59',0,'say the distance between a and b is 80miles, and the distance between b and c is 40 miles, and the distance between c and d is 20 miles... etc.\r\nusing this the tortoise will forever be ahead of Achilles, until the limiting point, which in this case is just short of 160. If the finish point is beyond 160, then Achilles will win, therefore: if Achilles will never catch up with the tortoise, the finish must be within the limiting point.\r\nby the way// this uses the ratio of speed 1/2, this number can be substituted and the numbers changed accordingly, 1/2 is simply easier to show.',NULL,0); INSERT INTO comment VALUES (5195,263,2259,'calla tah-n','re: Why is this a paradox?','2003-05-23 10:58:06',0,'even thinking mathematically, it does not reach infinity. Infinity is a limitless number and using the solution \"simple\" shows that this does have a limiting point. So in reality, no matter how you put this problem, it is really not a paradox.',3020,0); INSERT INTO comment VALUES (5196,672,2259,'calla tah-n','skill?','2003-05-23 11:04:00',0,'when looked at, the problem might not contain enough information to say who wins. skill at using your object is also very important. this problem, with the amount of information it currently has, is unsolvable. it does make a good plot for writing a story though... imagine the possibilities...',NULL,0); INSERT INTO comment VALUES (5197,504,2259,'calla tah-n','re(2): Both false','2003-05-23 11:07:26',0,'hahaha... you guys are silly... its a classic paradox peoples!!! don\'t go ruining it!!!!',4389,0); INSERT INTO comment VALUES (5198,809,1517,'jude','hhmmmm...','2003-05-23 12:03:15',0,'I don\'t know HOW to prove it yet, but they are not prime numbers because they appear to be products of prime numbers....\r\n\r\n',NULL,0); INSERT INTO comment VALUES (5199,823,2196,'Silly Jilly','re: I know it!','2003-05-23 13:01:15',3,'I mean 3/8.',5190,0); INSERT INTO comment VALUES (5200,320,1660,'Tim Axoy','THE TWO BARBERS','2003-05-23 13:13:26',3,'Call the first one A and the second B.\r\n
\r\nA has hair all over the place because he gets more money while B does not get a lot of buisness.\r\n
\r\nA does nice haircuts on people like B,so B has a nice haircut while A does not since his hair got cut by the sloppy B.\r\n',NULL,0); INSERT INTO comment VALUES (5201,320,2196,'Silly Jilly','A is better!','2003-05-23 13:18:13',3,'We should denote the first and second barbers as A and B<b/> respectively.\r\n
\r\nA does better and cut B,so he has a better haircut.\r\n
\r\nB does worse and cut A,so he has a worse haircut.\r\n
\r\nObviously the better one,A,will get more buisness and hence more hair on the floor for those who came to him.',NULL,0); INSERT INTO comment VALUES (5202,809,1920,'Brian Smith','First observations','2003-05-23 14:21:20',0,'If the number of ones in a member of the sequence is composite, then the member itself is composite.\r\n\r\nExample: 100010001000100010001 has 6 ones and is composite (100010001)*(1000000000001)',NULL,0); INSERT INTO comment VALUES (5203,814,2129,'Sanjay','re(4): Solution','2003-05-23 14:28:47',0,'\r\nSince 0 is on the extreme left and we are required to put in + sign and - sign in the \'blanks\', we don\'t have the option of assigning a \'minus\' to 0. \r\n\r\nHence 0 must always remain in the complimentary (+ sign) subsets. The presence of 0 in any main (- sign) subset would render the subset \'unminussable\'. \r\n\r\nSo, there will be only 23 subsets.\r\n\r\nBut I take DJ\'s point. I should\'ve added the \'non-zero\' or \'minussability\' criteria while defining the subsets.',5165,0); INSERT INTO comment VALUES (5204,808,1920,'Brian Smith','If you really want a challenge ...','2003-05-23 15:13:01',0,'It is possible to make a 17-sided polygon using the ruler and compass. If that was too easy, try 257 sides.',NULL,0); INSERT INTO comment VALUES (5205,809,1626,'Gamer','re: First observations','2003-05-23 16:18:02',0,'Yes, and any number with a composite number of ones is composite, as you can multiply it like Brian did.\r\n\r\n',5202,0); INSERT INTO comment VALUES (5206,809,1575,'DJ','a twist, perhaps?','2003-05-23 20:23:11',3,'First some kind of sequential representation of the numbers might be in order. Each of these numbers can be expressed as:\r\n1 + 10^4 + 10^8 + ... + 10^4i\r\n\r\nFor any of these numbers, it can be said:\r\n10^(4i+4) -1 = (10^4 - 1)(1 + 10^4 + 10^8 + ... + 10^4i)\r\nfor example, if i=3:\r\n999999999999 = 9999 * 100010001\r\n(Remember the solution to the \"tetra-productial numbers\" problem\r\n\r\nSimilary, the same could be said for numbers of the form:\r\n1 + 10^2 + 10^4 + 10^6 + ... + 10^2i\r\nwhere:\r\n10^(2i+2) -1 = (10^2 - 1)(1 + 10^2 + 10^4 + ... + 10^2i)\r\nfor example:\r\n99999999 = 99 * 1010101\r\n\r\nFinally, we can say that:\r\n10^(4i+4) -1 = (10^(2i+2) -1)(10^(2i_2) +1)\r\nfor example, if i=2:\r\n99999999 = 9999 * 10001\r\n\r\nGoing back to the original equations, we have:\r\n10^(4i+4) -1 = (10^4 - 1)(1 + 10^4 + 10^8 + ... + 10^4i)\r\n10^(2i+2) -1 = (10^2 - 1)(1 + 10^2 + 10^4 + ... + 10^2i)\r\nbut since\r\n10^(4i+4) -1 = (10^(2i+2) -1)(10^(2i_2) +1)\r\nwe can say:\r\n10^(4i+4) -1 = (10^2 - 1)(1 + 10^2 + 10^4 + ... + 10^2i)(10^(2i_2) +1)\r\nand thus:\r\n(10^4 - 1)(1 + 10^4 + 10^8 + ... + 10^4i) = (10^2 - 1)(1 + 10^2 + 10^4 + ... + 10^2i)(10^(2i_2) +1)\r\n\r\n10^4-1 is, of course, always equal to 9999, and 10^2-1 is always 99. So, putting these onto the same side of the equations (9999/99=101):\r\n101(1 + 10^4 + 10^8 + ... + 10^4i) = (1 + 10^2 + 10^4 + ... + 10^2i)(10^(2i_2) +1)\r\n\r\nSince 101 is a prime number, one [or both] of the factors on the right-hand side of the equation must have 101 as a fator. If i>1, then for whichever number is divisible by 101, the quotient will exceed 1, meaning (1 + 10^4 + 10^8 + ... + 10^4i) is expressible as the product of two factors., each greater than 1. If k=1, we have the number 10^4 -1 = 10001, which is composite (73*137).',NULL,0); INSERT INTO comment VALUES (5207,809,1575,'DJ','re: a twist, perhaps? [TYPOS]','2003-05-23 20:24:46',0,'Anytime there is an underscore in my solution, as in 2i_2, it is supposed to be a plus sign [2i+2]',5206,0); INSERT INTO comment VALUES (5208,823,1660,'Tim Axoy','Good!','2003-05-24 03:29:12',0,'You solved it!',NULL,0); INSERT INTO comment VALUES (5209,823,1660,'Tim Axoy','re: No solution yet? Nonsense!','2003-05-24 03:29:59',0,'See the solution.',5179,0); INSERT INTO comment VALUES (5210,320,1660,'Tim Axoy','re: A is better!','2003-05-24 04:22:40',0,'Funny!',5201,0); INSERT INTO comment VALUES (5211,528,1301,'Charlie','solution','2003-05-24 04:59:16',3,'Let Old\'s age be L so as not to confuse with zero, and Young\'s age by Y.\r\n\r\nFirst, how long ago (t years) was Old 3x as old as Young?\r\n3(Y-t)=L-t\r\nwhich gives t = (3Y-L)/2 years ago,\r\nat which time Old was L - (3Y-L)/2\r\n\r\nYoung will be three times that when she is\r\n3(L-(3Y-L)/2)\r\nWhen Old was half that age he was\r\n3(L-(3Y-L)/2)/2\r\n\r\nAt that time, since the difference in their ages remains constant, Young was\r\n3(L-(3Y-L)/2)/2 - (L - Y)\r\n\r\nSince Old is now twice this he is\r\n3(L-(3Y-L)/2) - 2L + 2Y\r\nwhich equals\r\n5L/2 - 5Y/2\r\n\r\nThat\'s L = 5L/2 - 5Y/2, or 2L=5L-5Y but we also know that L+Y=48. Solving these simultaneously gives us Y = 18 and L = 30, that is, Young is 18 and Old is 30.\r\n',NULL,0); INSERT INTO comment VALUES (5212,809,979,'Ravi Raja','Part of the Solution - Hint','2003-05-24 05:21:04',1,'Firstly, we see that the number 10001 is not a Prime since it can be expressed as the product of the two numbers 73 and 137. That is, \r\n10001 = 73 * 137\r\nSimilarly, we have:\r\n1000100010001 = 73 * 13700000137\r\n........ and so on.\r\n\r\nTherefore, we can see that the numbers which contain \'2n\' number of 1\'s (Ones), where \'n\' is a Positive Integer is always divisible by 73 and therefore cannot be a Prime.\r\n\r\nSecondly, we know that the numbers the sum of whose digits is divisible by 3 (or is a multiple of 3) is divisible by 3. So all the numbers of the given sequence(of the given form) containing \'3n\' number of 1\'s (Ones), where \'n\' is a Positive Integer is obviously divisible by 3 and therefore not a prime.\r\n\r\nWhat we have obtained till now is that the numbers of the given form which contain \'2n\' and \'3n\' number of 1\'s (Ones), that is 2,3,4,6,8,9,10,12,14,15,16,18,20,........ number of Ones) can never be Primes. \r\n\r\nNow someone Please help me with the rest of the solution, that is to prove that the number with 5,7,11,13,17,19,........ number of Ones cannot be a Prime. ',NULL,0); INSERT INTO comment VALUES (5213,841,1301,'Charlie','The Solution & Generalization','2003-05-24 06:01:53',0,'The solution posted is ingenious (and amazingly simple). In fact for all arc lengths less than 180 degrees similar formulae hold, such as the probability that all the points will lie in the same quadrant, the formula is n/4^(n-1), as the occurrences of all within a given clockwise arc from each point are mutually exclusive.\r\n\r\nA more difficult generalization would be for arc lengths greater than 180 degrees. These are no longer mutually exclusive. For example if we seek the probability that all the points lie within a 270-degree arc (that is, the largest gap is at least 90 degrees), the events clockwise from a given point are not mutually exclusive as can be seen from three points separated by 120 degrees. All the points fit within a 270-degree arc going clockwise starting at any one of the points.\r\n\r\nSo what formula can fit the simulation results for 1,000,000 trials that come up as follows? (expressed as a fraction of the 1,000,000):\r\n3 1\r\n4 1\r\n5 .996157\r\n6 .974637\r\n7 .926162\r\n8 .852604\r\n9 .761418\r\n10 .663289\r\n11 .565835\r\n',NULL,0); INSERT INTO comment VALUES (5214,528,2184,'mark hartman','solution','2003-05-24 07:23:24',0,'Old is now 30, and Young is 18. \r\nTo see this, let: Ot = Old\'s age today\r\n Yt = Young\'s age today\r\n Ya = Young\'s age when Old was three times as old as Young\r\n Oa = Old\'s age when Young was Ya\r\nand d = difference in Old\'s and Young\'s ages. \r\n\r\n Then Ot + Yt = 48 \r\n Ot = Yt + d\r\n so Ot + (Ot - d) = 48 (I)\r\n The difference between Old\'s and Young\'s ages at all times is d, so the result of the convoluted statement is:\r\n Ot = 2 * (9/2 * Ya - d) \r\n Ot = 9*Ya - 2*d (II)\r\n\r\nNow Oa = Ya + d = 3* Ya, so Ya = d/2 \r\nSubstituting for Ya in (II) we get\r\n d = 2/5 * Ot\r\nSubstituting for Ot in (I),\r\n\r\n Ot + Ot - (2/5 * Ot) = 48\r\n Ot = 30\r\n Yt = 18\r\nand Ya = 6.\r\n\r\nThe convoluted statements says that 30 is twice the age Young was when Old was 27. At that time, Young was 15.',NULL,0); INSERT INTO comment VALUES (5215,823,1301,'Charlie','re: No solution yet? Nonsense!','2003-05-24 07:49:01',0,'There are some problems whose solution just says there\'s no solution, as such is impossible, such as Bascule\'s Book. Other times there are variations on a puzzle that are offered in the comments on a given puzzle, such as my latest comment on Don\'t Be a Square, where I propose a generalization for a 270-degree arc, which I have no idea how to solve.',5179,0); INSERT INTO comment VALUES (5216,528,2130,'ethan','answer','2003-05-24 11:33:14',0,'young is 27 and old is21',NULL,0); INSERT INTO comment VALUES (5217,823,1660,'Tim Axoy','Error','2003-05-24 12:08:23',0,'In the solution,I put HIS instead of YOUR.\r\n',NULL,0); INSERT INTO comment VALUES (5218,528,1575,'DJ','Solutions','2003-05-24 20:06:22',3,'Let A be the age of Old and B be the age of Young, and d is the difference in their ages at any given time.\r\n\r\nAt any given time, the age of Young can be expressed as the age of Old minus the difference.\r\n\r\nWhen Old is three times as old as Young (call this time x):\r\nAx=3Bx=3(Ax-d)\r\nAx=3Ax-3d\r\nAx=(3/2)d\r\n\r\nWhen Young will be three times that age (time y):\r\nBy=3Ax=(9/2)d\r\n\r\nAnd when Old is half of that age (time z):\r\nAz=(9/4)d\r\nAnd at that time:\r\nBz=Az-d=(9/4)d-d=(5/4)d\r\n\r\nAnd now, Old is twice that age:\r\nA=2Bz=(2)(5/4)d=(5/2)d\r\nand of course:\r\nB=A-d=(5/2)d-d=(3/2)d\r\n\r\nAnd we are given that A+B=48.\r\nSo:\r\n(5/2)d+(3/2)d=48\r\n4d=48\r\nd=12\r\nA=(5/2)d=30\r\nB=(3/2)d=18\r\n\r\nSo, Old is now 30.\r\n\r\nBut, to answer the question posed, \"How old is Old?\"... I think that whenever you say that with \"Old\" capitalized, you must mean how old is really really old. So, definitely not 30, or probably even 40. I would venture that someone is Old around 50, 60, or better. Someone is likely OLD when they are upwards of 70 or 80, but that\'s just my opinion (I\'m 20, but still a kid).\r\n\r\nFurther, I venture that they are both 24. All other times mentioned in the problem are 0.\r\nOld is twice as old (0) as Young was (0) when Old was half as old (0) as Young will be (0) when Young is three times as old (0) as Old was (0) when Old was three times as old (0) as Young (0).\r\n\r\n.. I suppose a couple of verb tenses don\'t quite fit. It seemed clever, anyway.',NULL,0); INSERT INTO comment VALUES (5219,732,2296,'Bob Jock','I solved it!','2003-05-25 03:41:02',3,'Drew is a liar and Mohammad is a knight.',NULL,0); INSERT INTO comment VALUES (5220,823,2296,'Bob Jock','Here it is!','2003-05-25 03:42:06',3,'3/8.',NULL,0); INSERT INTO comment VALUES (5221,775,2296,'Bob Jock','I did it!','2003-05-25 03:43:22',3,'Drew is a liar and Mohammad is a knight.',NULL,0); INSERT INTO comment VALUES (5222,809,1575,'DJ','re: a twist, perhaps?','2003-05-25 04:46:47',2,'My solution is complete, although my final explanation probably didn\'t make it very clear.\r\n\r\nSuppose you have the equation\r\nab=cd\r\nwhere you know the following:\r\na, b, c, and d are integers\r\nb is prime\r\nb is not equal to c or d\r\n\r\nThus, since b is prime it must be a factor of either c or d, giving an equation:\r\na=(c/b)d OR a=c(d/b)\r\n\r\nIn either case, since b is not equal to c or d, both terms on the right must evaluate to integers greater then 1, and we know that a cannot be prome.\r\n\r\nThis is the situation in my solution. I have derived the equation:\r\n101(1 + 10^4 + 10^8 + ... + 10^4i) = (1 + 10^2 + 10^4 + ... + 10^2i)(10^(2i_2) +1)\r\nIn which 101 is prime, and neither of the left-hand members is equal to 101 when i>1. Therefore, by the same reasoning described above, we know that all numbers of the form\r\n1 + 10^4 + 10^8 + ... + 10^4i\r\nare not prime (when i=1, the equation becomes 101(10001)=101(10001), which proves nothing, but 10001=73(137), so it is also not prime).',5206,0); INSERT INTO comment VALUES (5223,811,1301,'Charlie','solution','2003-05-25 05:26:17',3,'We must assume that ascending order means strictly ascending, that is, with no repeats, as repeats, such as in 2445, could be strung out indefinitely. Also, I\'ll assume we don\'t put a leading zero on any number, but we can adjust the answer for that possibility later.\r\n\r\nSince zeros are out in the first position, they are out everywhere as the digits are in ascending order. Each of the nine remaining digits can appear either zero or one time in the number, so this is just the task of finding the number subsets of nine things and then subtracting out those with zero or one element.\r\n\r\nThere are 2^9 subsets of nine things, or 512. There\'s one empty subset and nine with just one element (digit), leaving 502 subsets, each to be arranged in ascending sequence.\r\n\r\nSo there are 502 such numbers. If we allow a leading zero, any one of these can be preceded by a zero, bringing the total so far to 1004, but we can also precede a zero to the single-digit numbers, bringing that total to 1013.\r\n\r\nSo: without leading zeros, it\'s 502; with leading zeros it\'s 1013.',NULL,0); INSERT INTO comment VALUES (5224,528,1301,'Charlie','re: Solutions','2003-05-25 05:37:39',0,'In\r\n\"When Old is three times as old as Young (call this time x): \r\nAx=3Bx=3(Ax-d) \r\nAx=3Ax-3d \r\nAx=(3/2)d \"\r\nwhat is the purpose of multiplying by x? (in fact, what is x to represent? ... years past the present?, years past one of their births?, etc.)\r\n\r\nBut in any case, the claim that Ax = 3Bx is really a claim that A=3B as the x\'s cancel. But that\'s claiming that Old is today three times as old as B. If x represents time past the present, it should be (A+x) = 3(B+x) = 3(A-d+x). And by the wording of the problem, I\'m sure x would come out negative eventually to fit the tense.\r\n',5218,0); INSERT INTO comment VALUES (5225,811,2129,'Sanjay','re: solution','2003-05-25 07:17:08',0,'That is a stunning answer Charlie. The beauty is in the simplicity. \r\n\r\nThough, for sake for completion, I do think one must take a view on whether the problem, as stated, allows the legitimate use of leading zeros or not, rather than leave it at two optional answers.\r\n\r\nPersonally, I think leading zeros not only can, but must be used. So the answer, according to me, would be a definite \'1013\' and not a conditional \'502 or 1013\', depending on whether we want to consider leading zeros or not.\r\n\r\nI guess it boils down to whether, for example, we can consider 012 and 12 as different \'numbers\' or not. I believe they are different numbers (one is a two digit number and the other is a three digit number) with the same quantitative value rather than being the \'same\' number.',5223,0); INSERT INTO comment VALUES (5226,528,1575,'DJ','re(2): Solutions','2003-05-25 08:14:05',0,'Sorry, I didn\'t make my notation really clear. I meant for Ax to be a single subscripted variable meaning the value of A at time x. So, to answer your question, I\'m not multiplying by x (or y or z), those are just to make the distinction between the ages at different points in time.',5224,0); INSERT INTO comment VALUES (5227,809,1575,'DJ','re(2): a twist, perhaps?','2003-05-25 08:16:39',0,'\"neither of the left-hand members is equal to 101\" - I meant neither of the right-hand members (1 + 10^2 + 10^4 + ... + 10^2i) or (10^(2i+1) +1) is equal to 101 when i>1.\r\n',5222,0); INSERT INTO comment VALUES (5228,811,1301,'Charlie','re(2): solution','2003-05-25 10:27:16',0,'Of course if you prefer the inclusion of leading zeros, then the number could have been gotten directly with 2^10-1-10 = 1013, the subtraction being for the one zero-digit possibility and for the 10 single-digit possibilities.',5225,0); INSERT INTO comment VALUES (5229,524,2300,'Becky','Hmmmmm....','2003-05-25 14:51:29',0,'EYE maybe? ;)',NULL,0); INSERT INTO comment VALUES (5230,159,1253,'brianjn','re(3): Let me fix that!!','2003-05-25 20:26:17',1,'Haven\'t checked this but ... may I go to the interval column. The left element of each pair proceeds by 3; but the second goes sould probably begin with 3 (?) ... 2,6,9,12,15 ..... [2 to 6 = 4!!]\r\n\r\n',5077,0); INSERT INTO comment VALUES (5231,828,2231,'Trevor Leitch','Solution','2003-05-26 06:43:55',3,'The native is a knave.\r\n\r\nThere are three possible answers the native could give to the question:\r\n1) If he answers \"knight\", then the native could be a knight telling the truth, a knave telling a lie, or a liar telling a lie.\r\n2) If he answers \"knave\", then the native couldn\'t be a knight, but could be a knave telling the truth or a liar telling a lie.\r\n3) If he answers \"liar\", then the native couldn\'t be a knight or a liar, but could be a knave telling a lie.\r\n\r\nThus, since only one answer would enable you to figure out for sure the native\'s type, the native must have answered \"a liar\" and therefore is a knave. ',NULL,0); INSERT INTO comment VALUES (5232,811,1767,'Fernando','re(2): solution','2003-05-26 10:58:21',0,'Actually 012 = 12. They\'re considered (as far as I know) the same numbers. So the solution would be 502 numbers.\r\nSomething funny: In spanish there\'s a common saying: \"That thing matters less than a zero to the left\" meaning that a zero on the left of a number leaves it the same...',5225,0); INSERT INTO comment VALUES (5233,842,2256,'Jackie','a guess...','2003-05-26 11:55:51',1,'Just a guess...\r\n\r\nI think he broke something, maybe an expensive glass item, and didn\'t tell his mother. She wanted to find out which one of her children broke it, so she asked them to go clean her \"broken glass\" or they\'d get punished. But... she never specified what was broken or where. Therefore, when her son immediately went to go clean it, she says something to the likes of: \"so how did you know what was broken? you must have broken it and not told me. You are grounded!\" The boy stomped away, faced downcast, because he was busted and grounded.',NULL,0); INSERT INTO comment VALUES (5234,828,1919,'Lewis','solution','2003-05-26 11:59:18',3,'The native is a knave.\r\nIf he answered \'knight\' he could be a knight, or a liar or a knave telling a e.\r\nIf he answered \'liar\' he could only be a knave telling a lie\r\nand if he answered \'knave\' he could e a liar or a knave telling the truth\r\nso\r\nthe answer the native gave must have been \'liar\', meaning he could only be a knave.',NULL,0); INSERT INTO comment VALUES (5235,842,2307,'zineera','hmm..','2003-05-26 14:08:26',3,'well maybe the mother told them 2 do sumthing bad like curse at her, and the boy did so she grounded hiM??',NULL,0); INSERT INTO comment VALUES (5236,19,2307,'zineera','OH!','2003-05-26 14:10:43',0,'ohhhh you ask DOES BOB LIE?!',NULL,0); INSERT INTO comment VALUES (5237,717,2307,'zineera','ohh','2003-05-26 14:12:41',0,'ughhh i juss answered one like this....C lies definitely...A likes them and B doesnt!',NULL,0); INSERT INTO comment VALUES (5238,270,2307,'zineera','TRIPLETS!','2003-05-26 14:16:24',0,'there triplest or quadruplets or quintuplets or sumthin!',NULL,0); INSERT INTO comment VALUES (5239,152,2307,'zineera','EASY!!','2003-05-26 14:20:51',0,'well i think ive got it...carl was lookin away...into a MIRROR! lol',NULL,0); INSERT INTO comment VALUES (5240,152,2307,'zineera','simple','2003-05-26 14:21:14',3,'carl is looking into a mirror!',NULL,0); INSERT INTO comment VALUES (5241,356,2307,'zineera','simple','2003-05-26 14:24:03',3,'After the first man circled him twice he then stood and waited. Since he was allowed to walk around he could go to the bathroom, eat and do many other things as long as he didn\'t circle him the third time. Since the other man had to stand still he could not do these things. He then realized that the first man never would circle him a third time causing him to have to move in order to do normal day to day activities. ',NULL,0); INSERT INTO comment VALUES (5242,474,2307,'zineera','soo easy!>>matter of vocabulary!','2003-05-26 14:25:48',3,'Hazardous \r\nHorrendous \r\nStupendous \r\nTremendous ',NULL,0); INSERT INTO comment VALUES (5243,528,1626,'Gamer','How do you do these?','2003-05-26 16:47:20',4,'I always am so confused by the wording on these... How do you do them?',NULL,0); INSERT INTO comment VALUES (5244,528,153,'TomM','re: How do you do these?','2003-05-26 18:54:34',0,'You take each phrase and look at what it says separately.\r\n\r\n1) Old is twice as old as young was (L1=2(Y2)) [L1 =Old at time 1; Y2= Young at time 2] \r\n\r\n2) when Old was half as old as Young will be (L2 = (Y3)/2)) [Immediately after a \"when\" give the same time subscript as immediately before the when.]\r\n\r\n3) when Young is three times as old as Old was (Y3 = 3(L4))\r\n\r\n4) when Old was three times as old as young (L4 = 3(Y4))\r\n\r\nSo we have 5 equations: \r\n\r\nL1 + Y1 = 48\r\nL1=2(Y2)\r\nL2 = (Y3)/2\r\nY3 = 3(L4)\r\nL4 = 3(Y4)\r\n\r\nTo which we can add three more \r\nL1 - L4 = Y1 - Y4 \r\nL2 - L4 = Y2 - Y4\r\nL3 - L4 = Y3 - Y4\r\n\r\nsince Lx and Yx represent their respective ages at time x, and they both age at the same rate.\r\n\r\nSo now we have the problem of solving 8 equations for 8 variables, and it becomes simple algebra.\r\n\r\n\r\n\r\n',5243,0); INSERT INTO comment VALUES (5245,828,2148,'Jayaram S','Solution Plus','2003-05-26 19:06:40',3,'The native is a KNAVE.\r\n\r\nReason:\r\nThe only way we can figure out the type of native correctly is if the answer to the question is \"A LIAR\" and this answer could only be given by a KNAVE and none other.',NULL,0); INSERT INTO comment VALUES (5246,528,153,'TomM','Two Notes [re(2): How do you do these? ]','2003-05-26 19:10:37',0,'Two notes: \r\n\r\n1)Some of the earlier solvers used fewer equations and fewer variables, and used elapsed time as a variable. They actually pre-combined my last three equations with the \"main\" five and substituted. The approach is basically the same, but is harder to follow if like Gamer, you have trouble following the word-puzzle form.\r\n\r\n2) Lx and Yx in my next-to last sentence are the generic forms of the subscripted variables L1, L2, L3, L4, and Y1, Y2, Y3, and Y4.',5244,0); INSERT INTO comment VALUES (5247,529,2239,'Alpha Tiger','My thoughts','2003-05-27 00:01:15',3,'I don\'t believe him.\r\n_ At this time men wasn\'t thinking money.\r\n_ \"64 B.C.\" hasn\'t have been printed on the coin, it wasn\'t precise enough to print letters and at this time the letters weren\'t existing.\r\n_ The 14 Carbon is not enough precise to indicate the date.',NULL,0); INSERT INTO comment VALUES (5248,814,2239,'Alpha Tiger','Solution (it is easy)','2003-05-27 00:12:18',3,'0+1-2+3+4-5-6+7+8-9=1\r\n0-1+2-3-4+5+6-7-8+9=-1\r\n\r\nIt is impossible for 0 (because 0+1+2+3+4+5+6+7+8+9=45 that is odd (a-b is odd if a+b is odd and a-b is even if a+b is even so we can get an even number))',NULL,0); INSERT INTO comment VALUES (5249,840,2239,'Alpha Tiger','Hehe !','2003-05-27 00:14:45',3,'Forward TON is heavy\r\nBackward NOT is NOT (hehe)',NULL,0); INSERT INTO comment VALUES (5250,851,2239,'Alpha Tiger','Solution','2003-05-27 00:25:53',3,'5 because\r\n\r\n1,9,1,4\r\n First Worldwide War\r\n1,9,1,8\r\n\r\n1,9,3,9\r\n Second Worldwide War\r\n1,9,4,{5}',NULL,0); INSERT INTO comment VALUES (5251,842,872,'pleasance','solution','2003-05-27 00:50:41',0,'The only boy to obey was told by his mother \"I didn\'t say Simon Says!\"',NULL,0); INSERT INTO comment VALUES (5252,842,1253,'brianjn','re: solution','2003-05-27 01:15:24',0,'Like this! When you\'ve worked with young kids, you can appreciate the logic here, but \'spose this isn\'t the required solution. Pity!',5251,0); INSERT INTO comment VALUES (5253,840,2148,'Jayaram S','Alternative Answer','2003-05-27 01:37:01',1,'\r\nA Comet!',NULL,0); INSERT INTO comment VALUES (5254,530,1301,'Charlie','solution','2003-05-27 03:39:19',3,'For the last two digits to be divisible by 10 the number must end in zero. The third and second from the right must be divisible by 9, but the first digit must be even to accommodate the next pair\'s (to the left) being divisible by 8. The possibilities are\r\n270\r\n450\r\n630\r\n810\r\n\r\nPrepending digits to complete multiples of 8 gives\r\n3270\r\n2450\r\n6450\r\n1630\r\n9630\r\n4810\r\n\r\n(multiple-of-8 \'72\' left out as that involves repetition of the 7)\r\n\r\nPrepending a digit to make a multiple of 7, without producing a duplication of digits leaves\r\n63270\r\n91630\r\n49630\r\n\r\nThe next digit on the left must be the end of a multiple of 5 but can\'t be 0, to avoid repetition and so must be 5. 56 and 59 are not multiples of 6, so the rightmost 6 digits must be\r\n549630\r\n\r\nMultiples of 4 that don\'t repeat digits already present are 12, 72 and 28, giving us\r\n12549630\r\n72549630\r\n28549630\r\n\r\nFor the last one, beginning with 2, only 12 and 72 fit as multiples of 3, but the first digit of each is odd, preventing a multiple of 2 for the leftmost pair, so that last sequence is out.\r\n\r\nThat leaves\r\n12549630\r\n72549630\r\n\r\nThe only possible ways of fitting the remaining digits work out as\r\n7812549630\r\n1872549630\r\n\r\nthese last being the two answers.\r\n\r\n',NULL,0); INSERT INTO comment VALUES (5255,530,775,'Cory Taylor','re: solution','2003-05-27 06:38:24',0,'Precisely how I attacked the problem, with of course, the same result.\r\n\r\nI\'ve never seen the word \"prepend\" before, so I guess I\'ve even learned something in the solution!\r\n',5254,0); INSERT INTO comment VALUES (5256,530,153,'TomM','My solution','2003-05-27 07:51:13',3,'1) Digits 5 and 10 must be 5 and 0 respectively.\r\n\r\n2) Digits 2, 4, 6, and 8 are even\r\n2a) Digits 2 and and 6 are 4 and 8 in some order\r\n2b) Digits 4 and 8 are 2 and six in some order\r\n\r\n3) Digits 5 and 6 add to a multiple of three, so by 2a, digit 6 must be 4\r\n\r\nx8xe54xex0\r\n\r\n4) Digit 7 must be 2 or 9 and must be odd, so it is 9; \r\n\r\nx8xe549ex0\r\n\r\n5) Digit 8 must be 6 (96 is the only number between 90 and 99 divisible by 8); digit 4 then is 2\r\n\r\nx8x25496x0\r\n\r\n6) Digits 2 and 3 add up to a multiple of 3, so digit 3 must be 1 or 7; \r\n\r\nx8125496x0 or x8725496x0\r\n\r\n7) Digits 8 and 9 must add up to 9; Digit 9 is 3\r\n\r\n7812549630 or 1872549630\r\n\r\n\r\n',NULL,0); INSERT INTO comment VALUES (5257,817,2231,'Trevor Leitch','Solution?','2003-05-27 08:06:52',0,'The guest of honour\'s birthday is December 31. She is speaking at a New Year\'s Party (or a birthday party that has run late) after midnight, thus on January 1, just after her fifteenth birthday. Therefore, she was fourteen \"the day before yesterday\", is fifteen now, will be sixteen \"this year\", i.e. December 31 of the year she is speaking, and will be seventeen \"next year\".',NULL,0); INSERT INTO comment VALUES (5258,817,2272,'Clinton Heath','re: Solution?','2003-05-27 09:32:30',0,'That\'s the way I figured it.',5257,0); INSERT INTO comment VALUES (5259,828,1660,'Tim Axoy','You did it!','2003-05-27 11:26:28',3,'You did it!',NULL,0); INSERT INTO comment VALUES (5280,843,2272,'Clinton Heath','Solution','2003-05-28 09:26:47',0,'Each woman\'s measurements equal 93.\r\nOne of the runners-up had measurements of 36.5-22-34.5. The other had measurements of 37-23-33. (22=33*2/3)(23=34.5*2/3)',NULL,0); INSERT INTO comment VALUES (5261,817,1660,'Tim Axoy','NO WAY!','2003-05-27 11:34:24',0,'How?',NULL,0); INSERT INTO comment VALUES (5262,817,1660,'Tim Axoy','THERE IS A WAY!','2003-05-27 14:01:11',3,'Her birthday was December 31,and she said it on January 1.\r\nThe day before yesterday(December 30),she was indeed 14.\r\n
\r\nNow,she is 15,so this year on December 31 she will be 16.\r\n
\r\nTherefore,next year,she will be 17.',5261,0); INSERT INTO comment VALUES (5263,809,1660,'Tim Axoy','Infinite','2003-05-27 14:22:43',4,'This is an infinite sequence,so how can you prove it?\r\nIt goes on to ∞',NULL,0); INSERT INTO comment VALUES (5264,529,2190,'mike','he\'s a liar','2003-05-27 14:35:32',0,'the coin could not have been dated 64 B.C. because they did not designate years as bc or ad until much later. they couldn\'t have predicted the birth of christ!',NULL,0); INSERT INTO comment VALUES (5265,18,1575,'DJ','re: Pages','2003-05-27 16:00:25',0,'When asked how many pages are in a book, I look at the highest numbered page, instead of counting page by page every printed or blank leaf in the volume..',18,0); INSERT INTO comment VALUES (5266,527,1575,'DJ','just numbers..','2003-05-27 16:13:50',0,'does anyone know how to make a solution? just a minute, i\'ll do one myself..',NULL,0); INSERT INTO comment VALUES (5267,817,2319,'jovy',':)','2003-05-27 18:15:52',3,'because her birthday is on february 29th. ',NULL,0); INSERT INTO comment VALUES (5268,817,2148,'Jayaram S','re: Solution?','2003-05-27 20:08:52',1,'\r\nExcellent!\r\n\r\nAfter seeing the solutions of this sort for several other tricky problems, I have got a feeling that this site can offer solutions to anything! Keep it up friends!',5257,0); INSERT INTO comment VALUES (5269,344,1919,'Lewis','Easy','2003-05-27 22:46:41',3,'A HOLE!',NULL,0); INSERT INTO comment VALUES (5270,817,2322,'akshay','','2003-05-28 01:37:04',3,'Her birthday is on 31st december.She is talking on 1st january .Now day before yesterday is 30th december she was 14,then on 31st she will be 15.She is talking about this in january.Then this year she will 16 on 31st january.Then next year 17.',NULL,0); INSERT INTO comment VALUES (5271,532,1301,'Charlie','maybe?','2003-05-28 02:48:35',1,'They had no navels?',NULL,0); INSERT INTO comment VALUES (5272,532,1183,'fwaff','Solution','2003-05-28 02:49:19',3,'Assuming that this problem is based on Christianity then Adam and Eve were created by God rather than developing in a womb and being born. As a result Adam and Eve don\'t bear the scar where the umbilical cord was connected - ie they don\'t have belly buttons!\r\n\r\n\r\nOne thought I had from this problem is if we take the creation thing literally that we are all descendents of Adam and Eve. Then given that the Christian church forbids marriage and therefore procreation between siblings how did mankind survive beyond the second generation? Conversely, given that we have survived beyond that second generation (therefore inter-sibling procreation must have been allowed initially), at what point did the ban start?\r\n\r\nThis isn\'t meant to start up all the \'does God exist?\' discussion from previously, I\'m just curious as to the official explanation if anyone knows it.',NULL,0); INSERT INTO comment VALUES (5273,532,1660,'Tim Axoy','No belly buttons?','2003-05-28 03:00:35',0,'Really?',5272,0); INSERT INTO comment VALUES (5274,532,1715,'Jonny Doe','re: Solution','2003-05-28 03:15:37',0,'I think the ban started shortly after Jesus\'s \"death\".',5272,0); INSERT INTO comment VALUES (5275,532,2148,'Jayaram S','The Naked Solution','2003-05-28 03:29:09',3,'\r\nWhen a baby is born the umbilical chord is cut and it falls off, but it leaves a belly button. The couple he saw had NO BELLY BUTTON. The only humans never to be born from a womb were Adam and Eve. Hence he immediately knew they were indeed Adam and Eve. The real clue given in the problem itself is that all were naked!!\r\n',NULL,0); INSERT INTO comment VALUES (5276,532,775,'Cory Taylor','re: Solution','2003-05-28 06:28:57',0,'Similar to the question I had. How about the pre-marital sex issue. Obviously, since they were the first, there was no official (pastor, reverend, minister etc.) to marry them, nor any witnesses to make it legal, so how did they procreate without ending up in the bad place?',5272,0); INSERT INTO comment VALUES (5277,532,2066,'David','interesting...','2003-05-28 06:44:02',1,'We really cannot prove that Adam did or did not have a navel...',NULL,0); INSERT INTO comment VALUES (5278,532,2324,'mozart','re: interesting...','2003-05-28 07:30:17',0,'Adam and Eve are the only humans without parents. Thus, no umbilical cord.',5277,0); INSERT INTO comment VALUES (5279,68,1919,'Lewis','Absolutely, positively, fully easy!','2003-05-28 09:02:37',3,'Okay, with a subject of that I hope I get this this right.....\r\nTHEY ARE ALL IN ALPHABETICAL ORDER!!\r\nThank you.:)',NULL,0); INSERT INTO comment VALUES (5281,532,1301,'Charlie','re(2): Solution','2003-05-28 09:36:26',0,'According to Catholic teachings, anyway, it is the couple themselves who perform the marriage ceremony, and the priest is just a witness for the church.\r\n\r\nBesides, there wasn\'t much choice around, so they had to be devoted to each other.\r\n\r\nAlso there\'s the \"what God hath joined together\", so I guess God was the clergyman (or the clergyGod).',5276,0); INSERT INTO comment VALUES (5282,532,1301,'Charlie','re: No belly buttons?','2003-05-28 09:37:33',0,'Tim, please remember not to give away solutions in the title.',5273,0); INSERT INTO comment VALUES (5283,843,1567,'Bryan','Solution','2003-05-28 09:51:38',3,'The measurements of the two runners up are B1-W1-H1 and B2-W2-H2. It is given that W1=(2/3)*H2 and W2=(2/3)*H1. Since the tape is accurate only to a quarter inch, H1 and H2 must be multiples of 3/4”. The winner’s hips are 34”=136/4”. The only measurements that are multiples of 3/4” and are within one inch of this value are 135/4” (33 3/4”) and 138/4” (34 1/2”). Since we are not differentiating between the two runners up, let H1=135/4” and H2=138/4”. Then
W1=(2/3)*138/4=92/4=23” and
W2=(2/3)*135/4=90/4=22 1/2”.
Since B1+H1+W1=B2+W2+H2=36+23+34=93”
B1=93-23-33 3/4=36 1/4
B2=93-22 1/2-34 1/2=36
To sum up, the measurements of the two runners up are 36 1/4-23-33 3/4 and 36-22 1/2-34 1/2.',NULL,0);
INSERT INTO comment VALUES (5284,1,2184,'mark hartman','try this','2003-05-28 18:03:33',3,'Start both ends of the first rope and one end of the second rope burning at the same time ( = time zero). The first rope will take a half hour to burn. At that point, when the first rope is completely burned, start the second end of the second rope on fire. It will take 15 more minutes to complete the burning of the second rope. At the time the second rope is completely burned, 45 minutes will have elapsed.',NULL,0);
INSERT INTO comment VALUES (5285,104,2184,'mark hartman','an easy one','2003-05-28 18:18:07',0,'To answer this question, recognize how many losers there are. The number of matches has to be the same. The answer is X-1.',NULL,0);
INSERT INTO comment VALUES (5286,56,2316,'Warren Trotter','Einstein','2003-05-28 18:19:01',0,' This is a great problem. I think it is the classic logic problem attributed to Albert Einstein.',NULL,0);
INSERT INTO comment VALUES (5287,532,1183,'fwaff','re: interesting...','2003-05-28 21:34:00',0,'Neither can we prove that Adam ever existed or that there is a heaven. If it comes to it can you prove that you exist and that this isn\'t all just some delusional fantasy?',5277,0);
INSERT INTO comment VALUES (5288,533,2329,'Ricardo','wouldn\'t this be...','2003-05-29 02:27:16',1,'Isn\'t it n-1?\r\n\r\nWhen n=10 => n-1 = 9 => 9 / 10 = 0 and remainder 9.',NULL,0);
INSERT INTO comment VALUES (5289,533,2148,'Jayaram S','The Solution','2003-05-29 02:42:04',3,'Answer: 2519\r\n\r\nExplanation:\r\nLet\'s assume that the required number is N. \r\n\r\nThen the number (N+1) is given by:\r\n8x9x35 = 72x35 = 2520.\r\n\r\nHere \'8\' takes care of divisibility by 2, 4 & 8;\r\nand \'9\' takes care of divisibility by 3 & 9;\r\nand \'35\' takes care of divisibility by 5 & 7;\r\nand the combined product takes care of divisibility by 6 & 10;\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (5290,533,1575,'DJ','Solution','2003-05-29 07:48:24',3,'The answer will just be one less than the lowest common multiple of the numbers 2-10. To find that number, simply eliminate any common prime factors:\r\n2 3 4 5 6 7 8 9 10\r\n2, 3, 5, and 7 are prime and obviously must be factors of the solution:\r\n2 3 4 5 6 7 8 9 10\r\nAlso, we see that these numbers take care of 6 (2*3) and 10 (2*5):\r\n2 3 4 5 6 7 8 9 10\r\nThat leaves only 4, 8, and 9. The factor of 2 leaves 4 and 8 with 2 and 4, respectively, to take care of, or just another factor of 4 will be needed to cover both.\r\n2 3 4 5 6 7 8 9 10 (4)\r\nFinally, another factor of 3 is needed to make up for the 9:\r\n2 3 4 5 6 7 8 9 10 (4 3)\r\n\r\nAll in all, the lowest common factor of the numbers two through ten is the product of 2, 3, 3, 4, 5, and 7. This is 2520. One less than this is 2519, and should leave a remainder when divided by each number:\r\n2519/10 = 251+9/10\r\n2519/9 = 279+8/9\r\n2519/8 = 314+7/8\r\n2519/7 = 359+6/7\r\n2519/6 = 419+5/6\r\n2519/5 = 503+4/5\r\n2519/4 = 629+3/4\r\n2519/3 = 839+2/3\r\n2519/2 =1259+1/2',NULL,0);
INSERT INTO comment VALUES (5291,822,1575,'DJ','Solution','2003-05-29 09:16:33',3,'Ask, \"If I asked you if there were gold on this island, would you say yes?\"\r\nIf the native says yes, then there is gold. If the native says no, then there is no gold.',NULL,0);
INSERT INTO comment VALUES (5292,822,1575,'DJ','re: Solution','2003-05-29 09:21:22',1,'Oops, I intended to elaborate before submitting that.\r\n\r\nIf the native is a liar, then if you asked if there were gold, his answer would be opposite of the truth. Then, if you asked if he had said \'yes,\' his response would simply be the reverse of the first answer, and the response to the second question would be a truthful answer to \"Is there gold on the island?\"\r\n\r\nIf the native were a knight, then asking if there is any gold on the island will yield a truthful answer. Ask him, then, if he had just said yes, and his answer will be the same as the first one, again truthfully being an answer to \"Is there gold on the island?\"\r\n\r\nSo, if you ask \"If I asked if there were gold on this island, would you say yes?\" to either a knight or a liar, you will get the answer to whether or not there is gold or not.',5291,0);
INSERT INTO comment VALUES (5293,822,1919,'Lewis','A Different Solution','2003-05-29 09:27:29',3,'A different question you could ask is:\r\n\'Would a knight say that you would say there was gold on this island?\r\n\r\nIf he answers yes, then there is gold. If he answers no, then there isn\'t.',NULL,0);
INSERT INTO comment VALUES (5294,817,2331,'suga','solution...','2003-05-29 11:28:18',0,'she must be born on a leap year.',NULL,0);
INSERT INTO comment VALUES (5295,686,2331,'suga','guesses','2003-05-29 11:33:53',0,'because he was the one being murdered and a ghost can\'t go to the police OR because he had a hitman knock off an enemy. lol, now those are just guesses, dumb ones too!',NULL,0);
INSERT INTO comment VALUES (5296,822,1660,'Tim Axoy','P logic','2003-05-29 12:12:39',0,'The solution has propositional logic in it. ',NULL,0);
INSERT INTO comment VALUES (5297,532,2333,'piginablanket','adam and eve','2003-05-29 12:21:34',0,'they were wearing fig leaves or clothing',NULL,0);
INSERT INTO comment VALUES (5298,822,1626,'Gamer','Duplicate?','2003-05-29 14:35:44',4,'Isn\'t this a duplicate of 1 or 2 other problems?',NULL,0);
INSERT INTO comment VALUES (5299,822,1660,'Tim Axoy','re: Duplicate?','2003-05-29 15:18:15',0,'Which ones?',5298,0);
INSERT INTO comment VALUES (5300,822,1575,'DJ','re: Duplicate?','2003-05-29 15:26:15',0,'It seemed like it to me, too, but in looking at the other problems in the category it seems not. Must be that simple \"double negative\" L&K problems like this are everywhere, and just now is this one coming to this site.\r\n\r\nLewis\' solution is pretty much equivalent to mine, but the double negative becomes a quadruple negative. An interesting discuccion of this property can be found in TomM\'s Lost in the Catacombs problem.',5298,0);
INSERT INTO comment VALUES (5301,732,1660,'Tim Axoy','re: If you liked this','2003-05-29 15:44:04',0,'Drew and Mohammad come back is just like this one.',4224,0);
INSERT INTO comment VALUES (5302,843,1575,'DJ','re: Solution','2003-05-29 16:01:19',0,'Remember, the numbers differ by less than one inch',5280,0);
INSERT INTO comment VALUES (5303,822,1301,'Charlie','re: A Different Solution','2003-05-29 16:36:34',0,'The question \"Would a knight say that you would say there was gold on this island?\" is no different from saying \"Is there gold on this island?\". That is, if there is no gold on the island, a knight would say \"no\", but a liar would lie about what the knight would say and therefore would say \"yes\". If there was gold on the island a knight would say \"yes\" but the liar would lie about what the knight would say and say \"no\". Of course a knight would tell the truth about what a knight would say, and since you don\'t know if the native is a knight or a liar, you don\'t know whether there\'s gold on the island.\r\n\r\nA better version of this type would be \"Would the opposite kind of person say that there\'s gold on this island?\" Then if you get a yes then there is no gold on the island and if you get a no then there is gold on the island, as there would always be one level of untruth in the path of answers.',5293,0);
INSERT INTO comment VALUES (5304,822,1626,'Gamer','re(2): Duplicate?','2003-05-29 17:08:15',0,'There was one that was more complex (And we don\'t like simple problems do we?), that levik submitted, about not knowing the word for yes or no, and looking for a path.\r\n\r\nAnd besides, aren\'t many of Tim\'s puzzles, \"You don\'t know who is who, so ask a \"double negative\" question\"?',5300,0);
INSERT INTO comment VALUES (5305,822,1575,'DJ','re(2): A Different Solution','2003-05-29 17:59:05',0,'The point of these problems is how many times you negate the original question (if the person is a liar). In this case, the original question would be, \"Is there gold on this island?\" If you ask that question to a liar, he will answer oppositely, and a knight will answer truthfully, leaving you with no conclusion.\r\nIf you ask, as I first posed, \"Would you say that there is gold on this island?\" the person\'s answer to the first question (implicitly, \"Is there gold on this island?\") will be negated if the person is a liar, and then negated again (\"Would you say..\"), so that a liar is forced to give a truthful answer. A knight, of course, will give you the correct answer regardless. So, there needs to be an even number of questions implicitly asked.\r\n\r\nIn Lewis\'s solution, suppose, as you did, the person is a liar and there is gold on the island. Then, if asked, the person would say that there was no gold. If a knight were asked about this, he would say the same, that the person would say there is no gold. But if you ask the liar about the knight\'s response, he will lie about that and answer yes (..a knight would say that I would say that there is gold on this island). Again, for a knight, the answers to each intermediate question will be the same. This case poses four questions, and makes for a quadruple negative in the case of the liar. I think, Charlie, that you missed \"would a knight say that you would say...,\" thus making the solution messy, but valid.\r\n\r\nIn the version you suggested, \"Would the opposite kind of person say that there\'s gold on the island?\" is pretty much equivalent to \"Would you say that there\'s gold on the island?\" In the latter case, you might as well as \"Would the same kind of person say that there\'s gold on the island?\" in which any person of the same type, not necessarily the one you are talking to, would give the same answer. When you look at it that way, it\'s easy to see that the version you suggested is merely the opposite of the other, and that is why it yields the opposite answer. In either case, there are still only two questions being asked; in Lewis\'s solution, there are four.',5303,0);
INSERT INTO comment VALUES (5306,822,1575,'DJ','re(3): Duplicate?','2003-05-29 18:02:21',0,'I mentioned the problem I did because of the discussion in the comments. And actually, which problem of levik\'s are you referring to?',5304,0);
INSERT INTO comment VALUES (5307,532,1575,'DJ','re(2): interesting...','2003-05-29 18:09:10',0,'And for every Liars&Knights problem you can say that no one exists who always tells the truth (or always lies). You could also say for various problems that snow or rain will never fall at a perfectly constant rate, there is no such thing as a limitless water supply or a bottomless hole, the moon is not a perfect sphere and there is no way you could ever tie a rope around it.\r\n\r\nSince when do situations posed directly in the problem fall under scrutiny?',5287,0);
INSERT INTO comment VALUES (5308,817,2336,'kkkkk','The correct answer','2003-05-30 01:51:11',0,'She said this on January the 1st, when she\'s 15.\r\nHer birthday is December 31st.\r\nThe day before yesterday was before her 15th birthday, so she was 14.\r\nBy the last day of the year, she will be 16.\r\nBy the last day of the next year, she will be 17.',NULL,0);
INSERT INTO comment VALUES (5309,535,872,'pleasance','first try','2003-05-30 02:47:41',0,'It seems to me that 1 rupee each is the one and only way to distribute the money, given the conditions. \r\n\r\nLet\'s call the people (and the amounts) A, B, ... J. If C received more than A, then we have A \r\n(avb)<->c \r\nb<->(~c) \r\nNow,we find the truth and falsity of each. \r\na=true,b=false,c=true.',NULL,0);
INSERT INTO comment VALUES (5404,538,153,'TomM','re: perhaps','2003-06-02 16:17:57',0,'An arithmetic progression, specifically, is a sequence of the form: a, a+b, a+2b, a+3b, ...\r\n\r\nA sequence of the form a, ab, ab², ab³, ... (like your 1, 1², 1³, ...) is not an arithmetic progression, it is a geometric progression',5396,0);
INSERT INTO comment VALUES (5405,538,2239,'Alpha Tiger','Easy ...','2003-06-02 20:44:58',3,'As the product has to be prime, we must have 2 [1] and one prime number.\r\nSo we have -3 -1 1 and -1 1 3',NULL,0);
INSERT INTO comment VALUES (5406,538,2239,'Alpha Tiger','re: EASY!','2003-06-02 20:47:14',0,'Your solution isn\'t complete.\r\nWe can also have -3,-1 and 1 ...',5402,0);
INSERT INTO comment VALUES (5407,836,1626,'Gamer','Friends or not?','2003-06-03 02:08:47',0,'Are they friends of yours? Or is this a cutthroat auction? If they were friends of yours, have everyone bid up the line( 1 cent, 2 cents, 3 cents...) until it got time for your bid. Then get the dollar, and split it among everyone.',NULL,0);
INSERT INTO comment VALUES (5408,538,1626,'Gamer','re: Easy ...','2003-06-03 02:11:11',0,'Negative numbers are never prime (except -1 which is), because -x has 1, -1, x, -x.\r\n\r\nSo -1 x 1 x 3 gives -3, which is divisibly by 1, -1, 3, -3.',5405,0);
INSERT INTO comment VALUES (5409,836,1715,'Jonny Doe','Solution????','2003-06-03 03:27:07',3,'If my turn comes and no one bid a dollar yet, I would bid one dollar. Since we are bidding for a dollar hopefully no one will out bid me and therefore I would break even, paying a dollar for a dollar. If some one did bid a dollar already then that means that we have at least one bid and I don’t have to place a bid and therefore breaking even again.',NULL,0);
INSERT INTO comment VALUES (5410,824,2364,'milo','the answer','2003-06-03 03:27:13',0,'easy he was standing on block of ice and it melted',NULL,0);
INSERT INTO comment VALUES (5411,836,775,'Cory Taylor','re: Solution????','2003-06-03 04:13:13',0,'but this is not a winning strategy as described in the problem, this is a break even strategy. There is some way to maximize your *potential* cash inflow. That is the question\r\n\r\n',5409,0);
INSERT INTO comment VALUES (5412,836,1567,'Bryan','re: Solution????','2003-06-03 05:07:54',0,'Bidding one dollar for a buck at this auction is a disasterous tactic. Suppose the high bid before you was 90¢. Now that you bid a dollar, if the bidding stopped right now that person would be out the 90¢, since the first and second highest bidders have to pay. Knowing this, that person would probably outbid you, bidding perhaps $1.25, figuring it is better to win the buck and be out only 25¢ than it is to lose 90¢. Now you will lose your dollar, unless you outbid the other bidder, in which case this scenario gets worse and worse. As each of you outbids the other in an effort to minimize your loss, your money at stake (and potential loss) goes up and up, which is exactly what the auctioneer wanted in the first place. If you could collude with the other bidders to stop the bidding below 50¢ and split the buck, you could collectively make a profit. Obviously, this would be maximized if there were only one bid of 1¢ and the bidding stopped there. In all likelihood, however, someone in the group of bidders would forget the rules and outbid you, and as soon as the bidding gets above 50¢ it will most likely snowball to several dollars using the reasoning stated above. As Joshua (the WOPR) declared in War Games, AN INTERESTING GAME, PROFESSOR HOW ABOUT A NICE GAME OF CHESS?',5409,0);
INSERT INTO comment VALUES (5413,836,2129,'Sanjay','Bang for the Buck','2003-06-03 06:08:13',0,'Assuming that what is meant by \'everyone will want to do what is best for them\' is that every individual will seek to maximize their individual cash flow, and assuming that everyone posseses the skill to \'think forward and reason back\', the auction will never start because everyone\'s winning strategy is to stay out of the auction and break even.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (5414,836,775,'Cory Taylor','entrepreneurial answer','2003-06-03 06:14:32',0,'Reading carefully the wording of the question there are two comments to be made. First is that in the paragraph \"The catch?...\", the math doesn\'t add up correctly, so either its just been overlooked by Jonathan (more likely), or there is some trick to this(less likely). Second, the question is this: What would \"you\" do, assuming everybody was looking for only their own best interest. Now I\'m not a finalncial genius, so this\'ll be just the beginning of a conceptual solution, but how about coming up with some sort of bidders insurance, which you could sell to the bidders, that they would collect on if they were the second highest bidder, or some other catch. I\'m sure that some set of payment rules could be found that will always work in your favor. Also, there being a payout for the second highest bidder now will reduce the tendency of the bids to get out of hand as described by Bryan above...\r\nAs I mentioned that I\'m not a financial guru, I\'ll leave the details to another. Of course, this may not even be possible.\r\n\r\nPS, nice quote Bryan, impressive that you can get this correctly from a movire circa 1980. Matthew looks soooo young here - he\'s not even ready for his high school Ferris Bueller role yet!',5412,0);
INSERT INTO comment VALUES (5415,78,1919,'Lewis','Solution... I think','2003-06-03 06:26:20',3,'The man runs back 1/4 of the length of the tunnel and makes it out just in time. That means if he runs 1/4 of the distance the other way, the train will just be entering. This means that the man is 1/2 way through and the train is just entering.\r\nThe man gets out just as the train is about to catch him up. The train travelled twice as far as the man (the length of the tunnel as opposed to 1/2 of the length) in the same time, so it must have been travelling twice as fast.\r\nThe man was traveeling at 7 mph, so the train was going at 14 mph.',NULL,0);
INSERT INTO comment VALUES (5416,50,1919,'Lewis','ummmm..... I know','2003-06-03 06:35:38',3,'The hotel owner\'s profit was $30 - $5 = $25.\r\n\r\nThe farmer\'s each payed $9 dollars, so their total pay was $27.\r\n\r\nThe bell boy kept $2.\r\n\r\n$2 + $25 = $27 so all the money was there.\r\n\r\nThe mistake in the calculation was that it shouldn\'t be $27 + $2, but $27 - $2, which equals $25 (the hotel owner\'s profit).',NULL,0);
INSERT INTO comment VALUES (5417,828,1919,'Lewis','re: You did it!','2003-06-03 06:37:50',0,'Hooray for us!!',5259,0);
INSERT INTO comment VALUES (5418,538,2129,'Sanjay','re(2): Easy ...','2003-06-03 06:54:13',0,'Obviously we cannot have negative numbers as factors. Otherwise even 3 would not be a prime number since it would have two sets of factors 1,3 & -1,-3. \r\n\r\n',5408,0);
INSERT INTO comment VALUES (5419,538,2129,'Sanjay','One and Only','2003-06-03 07:00:49',0,'Going strictly by the definition of Arithmetic Progression provided in the problem 1,1,1 is a solution.\r\n\r\nx1=1,x2=1,x3=1\r\nx2-x1=0\r\nx3-x2=0\r\nSo, (x2-x1)=(x3-x2) \r\nTherefore 1,1,1 constitutes an Arithmetic Progression. Also, 1*1*1=1, which is a prime number.',NULL,0);
INSERT INTO comment VALUES (5420,28,1919,'Lewis','Solution','2003-06-03 07:02:07',3,'There are two possibilities :\r\n\r\nMr Brown could be asleep. If he was, he would be wrong in thinking Mrs Brown was asleep, so she would be awake. When she\'s awake, she is always correct, so she will think that Mr Brown is asleep. \r\n\r\n OR \r\n\r\nMr Brown could be awake. If that was the case, then Mrs Brown would be asleep, and would wrongly think that Mr Brown was asleep.\r\n\r\nEither way, Mrs Brown would be under the impression that Mr Brown was asleep.',NULL,0);
INSERT INTO comment VALUES (5421,29,1919,'Lewis','re: A puzzle about Drew','2003-06-03 07:06:18',0,'I have five liars and knights puzzles pending #=)',4240,0);
INSERT INTO comment VALUES (5422,836,1715,'Jonny Doe','re: Bang for the Buck','2003-06-03 07:32:50',0,'This is not an option since it states that there must be at least one bid.',5413,0);
INSERT INTO comment VALUES (5423,835,1301,'Charlie','solution','2003-06-03 08:20:48',3,'Certainly no more than 8 queens can be so placed, as each must be in its own row and own column. That in fact 8 can be so placed is demonstrated in a classic programming exercise to find such placements.\r\n\r\nThere are 12 basically different ways to arrange the 8 queens. Except for one such arrangment, there are 7 other trivial variations: 3 rotations (90, 180 and 270 degrees), a reflection and the rotations of the reflection. There is one basic arrangement that has only one rotation (90 degrees) for itself and one for its reflection, so the total, counting reflections and rotations, is 92, which is 11 x 8 + 1 x 4.\r\n\r\nI hope the following comes out ok using the html pre tag.\r\n Therefore, no one will bid and the dollar won\'t be \'won\' and everyone will break even.\r\n\r\n',5422,0);
INSERT INTO comment VALUES (5428,538,2129,'Sanjay','re(2): One and Only','2003-06-03 09:50:36',0,'If 1 is \'never\' a prime number then of course the 1,1,1 solution doesn\'t work. However, \'often excluded\' and \'almost always excluded\' still leave enough of a window for 1 to be considered a prime number \'sometimes\'.',5425,0);
INSERT INTO comment VALUES (5429,836,1919,'Lewis','re(3): Bang for the Buck','2003-06-03 09:59:39',3,'But somebody has got to bid for the dollar.\r\nOne way you could do this and still have everyone break even is by one person bidding $1. Nobody sane would bid any more than $1 for $1, so whoever bid would get there dollar back and everyone else will have all the money that they started with.',5427,0);
INSERT INTO comment VALUES (5430,836,775,'Cory Taylor','re(4): Bang for the Buck','2003-06-03 11:02:07',0,'how about bidding 99 cents then. The reasoning here follows from Lewis\' statement that if you bid $1 right away then nobody sane would outbid you. If the beginning bid were at .99, then also nobody would bid, because they do not improve their situation by outbidding you - they currently break even, and if they bid then they stand to AT MOST break even (but they could lose money as there is always the threat that you will outbid their bid of one dollar). However, this strategy only works if you are able to make the first bid at $.99',5429,0);
INSERT INTO comment VALUES (5431,836,1626,'Gamer','re(5): Bang for the Buck','2003-06-03 12:35:31',0,'I also disagree with Sanjay, as it states in the problem \"What would you do if you were at this auction, and there had to be at least one bid?\".\r\n\r\nI like the $1.00 and $.99 strategies... this one is beyond me...',5430,0);
INSERT INTO comment VALUES (5432,801,1171,'nikki','Face Up','2003-06-03 12:39:39',0,'I would just like to point out that the problem states that the assistant \"hands them to the magician one by one FACE UP.\" So solutions with the card facing down is not only a bit of a giveaway that something fishy is going on, but doesn\'t satisfy the problem statement either.\r\n\r\nLater!',NULL,0);
INSERT INTO comment VALUES (5433,538,1626,'Gamer','re(3): One and Only','2003-06-03 12:41:33',0,'I would say never can 1 be included as a prime number. First of all, if any problem wanted to include 1, just say \"non-composite\" instead of prime.\r\n\r\nIncluding the prime factorization argument, you could also state that a prime number has to have exactly 2 factors (which is the definition I heard, although it might not be right), and since 1 only has 1 factor, it isn\'t prime.\r\n\r\nI also would point out that in order to be in arithmetic progression, the sequence would need to progress (get larger or smaller). I don\'t know about this idea for this problem, because of the Note: definition given.\r\n\r\nI think this is an interesting solution though. If the progression arguement is thrown out, why not -1,-1,-1? -1 has two factors, -1 and 1, and is prime. (Are we saying also that 0 is not prime?)',5428,0);
INSERT INTO comment VALUES (5434,439,1660,'Tim Axoy','The k statements','2003-06-03 12:42:42',0,'Similarly,if there are k statements,then k-1 is the only true one.',NULL,0);
INSERT INTO comment VALUES (5435,836,1171,'nikki','Initial thought','2003-06-03 12:57:32',0,'This was just my initial thought, but I haven\'t reasoned it out yet, so I admit I am probably way off. What about bidding 50 cents right off? Here\'s why I thought of it:\r\n\r\nIf I were just watching people bid (1 cent, 5 cents, 23 cents! and so on) I would say to myself \"Self, if anyone bids 50, don\'t bid even 51 because then the auctioner will start to get a good deal.\" But this is more of a \"I want to make a profit AND not let anyone else make a profit\" which might not be everyones strategy.\r\n\r\nHowever, if everyone were like me then no one would want to bid 51 (even though they could make 49 cents on the deal, the auctioner would make a pretty penny), and I would get the dollar for 50 cents.\r\n\r\nLike I said, just a thought.\r\n\r\nLater!',NULL,0);
INSERT INTO comment VALUES (5436,824,2121,'Chaz','Another one','2003-06-03 13:29:12',0,'WOW it seems like kindergarten all over again! These \'how did they die\' things are so stupid. Ok here are a few possibilities: a ghost got him, he flew up and hung himself, he stood on his truck, he got a disease while he was playing with a knoose, he had a heart attack, some magic wizards did it, superheroes did it, (teleportation), he was a suicidal superhero/wizard, there is a hole in the ground, his truck came alive and did it to him, the desert sandman did it and disappeared..... use your imagination.',NULL,0);
INSERT INTO comment VALUES (5437,824,2121,'Chaz','Oh yah','2003-06-03 13:32:50',0,'oh yah and he had no pants and pissed on the ground.',NULL,0);
INSERT INTO comment VALUES (5438,532,2121,'Chaz','Easy','2003-06-03 13:40:13',0,'They wore nametags.',NULL,0);
INSERT INTO comment VALUES (5439,532,2121,'Chaz','Hmmm','2003-06-03 13:44:24',0,'Well, the bible says that everyone went to hell before Jesus came, so adam and eve shouldnt be in heavem. But the Bible says a lot of things that arent true, such as adam and eve.',NULL,0);
INSERT INTO comment VALUES (5440,824,2184,'mark hartman','a solid answer?','2003-06-03 16:31:56',0,'The man committed suicide by standing on a large block of ice. He hung himself as the ice melted below him.',NULL,0);
INSERT INTO comment VALUES (5441,836,1920,'Brian Smith','Thinking about making a profit','2003-06-03 16:37:28',0,'Some of my thoughts on positive expectation strategies.\r\n\r\nIf there is a positive expectation strategy, then it must apply to all bidders. If auctioneer sees a profit, then the net expectation is negative and if the auctioneer sees a loss, then the net expectation is positive.\r\n\r\nThis means the only way a positive expectation can be realized is if the average sum of the first and second place bids is less than $1.00.',NULL,0);
INSERT INTO comment VALUES (5442,836,2370,'Dave','quick question (and my thoughts)','2003-06-03 17:00:19',0,'Ok, my question is: Are we forced to bid? Because, if we are, I think the bidding will continously rise.\r\n\r\nHere\'s my reasoning. Logicaly, the bidding should rise up to $.99 without people giving it a second thought. However, there is still someone who has not made a bid and must, he will be forced to break even and bid a $1. However, mr. unlucky 99-cents would rather lose 1 cent then 99, so he will bid $1.01. Now, disappointed dollarboy would rather lose 2 cents than a buck, so he will bid $1.02, and so forth...',NULL,0);
INSERT INTO comment VALUES (5443,824,1920,'Brian Smith','Death Theory','2003-06-03 17:05:30',0,'I know about the standing on a block of ice solution, but I came up with something more creative\r\n\r\nThe room is large and has a sloping floor. The door is large enough to get the man\'s truck inside the room. The man ties the rope to the ceiling standing on his truck. He gets down and wedges a small ice block under the truck\'s front wheel and puts the truck into neutral. He climbs on top of the truck and waits for the ice wedge to melt. When it does, the truck rolls out of the room and he drops, thereby hanging himself.',NULL,0);
INSERT INTO comment VALUES (5444,836,2370,'Dave','continuing with my thought..','2003-06-03 17:25:10',0,'I think the \'winning\' strategy is if one person bids 1-cent, and no one else bids. ',5442,0);
INSERT INTO comment VALUES (5445,836,1919,'Lewis','re: continuing with my thought..','2003-06-03 21:36:43',0,'But if everyone wants to do what is best for them, they\'ll bid 2 cents and try to make a 98 cents profit rather than just break even. Then the person who bid 1 cent will bid more than 2 cents to try to make a profit rather than lose their 1 cent, and the bidding will just go up.\r\n\r\nIf the first person bid $1, anyone who bid over that would not be doing what is best for them because they would make a loss rather than break even. So, nobody would bid over $1.',5444,0);
INSERT INTO comment VALUES (5446,836,2129,'Sanjay','Bid Nothing?','2003-06-03 22:47:11',0,'The whole point of an auction is that each bidder acts in self-interest, often to the detriment of other bidders, and sometimes even to the detriment of the group of bidders as a whole. Therefore, I do not understand how a \'there must be at least one bid\' can be enforced if each bidder is allowed to bid or to not bid at any stage of the auction, including at the start. The only leverage that the person offering the dollar has is to withhold the dollar if no one bids. Many of the provided solutions are in the area of collective thinking and collective bidding strategies. But collective strategy flies in the face of \'everyone wanting to do what is best for them\'. If collective strategies are allowed then the 1 cent solution works for me. How about an opening bid of 0 cent and everyone agreeing to keep quiet?',NULL,0);
INSERT INTO comment VALUES (5447,824,2346,'me','hm','2003-06-03 23:31:28',0,'the block of ice theory is believable, but then its stated that theres 30 miles of sand in every direction, so wouldnt the ice have melted by the time he drove it back to the room? i dont even know the real solution, its just something i thought up of.',NULL,0);
INSERT INTO comment VALUES (5448,351,2346,'me','my guess','2003-06-03 23:56:32',0,'i think its because all the vowels, a,e,i,o n u are in the word.',NULL,0);
INSERT INTO comment VALUES (5449,351,2346,'me','re: my guess','2003-06-03 23:57:36',0,'and the only other word i can think of is onomatopoeia, only it has no u.',5448,0);
INSERT INTO comment VALUES (5450,359,2346,'me','actually..','2003-06-04 00:12:05',0,'there is a game similar to this one, but its called congkak, [pronounced chong-kahk] and its a traditional malay game. as fot the answer, i have no idea, i havent played congkak in a long time.',NULL,0);
INSERT INTO comment VALUES (5451,334,2346,'me','this is so bloody easy','2003-06-04 00:24:26',0,'the letter s. its in song but not tune, in star but not in moon, in sun but not in night, and in sight but not range.',NULL,0);
INSERT INTO comment VALUES (5452,865,1575,'DJ','er','2003-06-04 02:10:46',3,'Nope.',NULL,0);
INSERT INTO comment VALUES (5453,865,2357,'Ahmed','','2003-06-04 02:11:08',0,'no....because if i said yes..then yes is the answer for this question...and if i said no it will be untrue since the answer is to be said no and you ask about it that......',NULL,0);
INSERT INTO comment VALUES (5454,865,2357,'Ahmed','No solution','2003-06-04 02:14:39',0,'it may have no answer on this question cuz if i said no then u r searching about me saying ( NO ) \r\nthen it will be the answer and if i said yes..then how ( NO ) is the answer and i answered by ( YES )',NULL,0);
INSERT INTO comment VALUES (5455,865,1626,'Gamer','The way to go','2003-06-04 02:18:46',0,'The way to go with these problems is go with how DJ said.\r\n\r\nSo my answer is \"It is not\", or \"Probably not\".',NULL,0);
INSERT INTO comment VALUES (5456,15,1301,'Charlie','another method','2003-06-04 04:01:16',0,'This can be approached as a division problem, and thereby proceed from left to right, and it seems as easy as the multiplication approach:\r\n\r\n When the moisture-to-solids ratio is 50%/50%, each must weigh one pound, so the total weight of these dried out potatoes is 2 lbs.',NULL,0);
INSERT INTO comment VALUES (5465,836,1567,'Bryan','99¢ bid not safe','2003-06-04 10:35:12',0,'It is naive to think no one will bid $1 after a 99¢ bid just because they won\'t make any money at it. The world is full of people who feel deep down that they are better off if you are worse off, and they will bid $1 for no other reason than to hurt you, even if you are a complete stranger! We should use logic to solve this puzzle, which is not the same as assuming everyone at the auction acts logically.',5460,0);
INSERT INTO comment VALUES (5466,865,1575,'DJ','No buts about it','2003-06-04 11:05:46',0,'You could say \"Maybe\" as a truthful answer to any yes/no question, unless you take the literal meaning of the word, it \"may be,\" indicating that there is a chance that whatever is in question could be affirmed.\r\n \r\nObviously, \"no\" cannot be the answer, since it would contradict itself, so the answer must be negative. Something like \"nope\" or \"probably not\" would correctly answer the question in the problem without making a contradiction.\r\n\r\nAlso, for reasons stated above, I would say that \"maybe\" is an incorrect answer as well.',NULL,0);
INSERT INTO comment VALUES (5467,844,1575,'DJ','re(2): DJ or .?','2003-06-04 11:29:15',0,'Heh..I was editing my info and must have accidentally overwritten my name. I didn\'t post anything in the meantime and didn\'t notice the change until today (when one of my other problems went live). I don\'t know when it happened...',5461,0);
INSERT INTO comment VALUES (5468,865,2341,'Pickels','Awesome!!','2003-06-04 12:03:35',1,'I really love paradoxes. They make your brain work really hard.',NULL,0);
INSERT INTO comment VALUES (5469,836,2341,'Pickels','SOLUTION','2003-06-04 12:23:13',3,'Ok people, the question is how YOU would get the most money auctioning off the dollar, NOT other people. The way to get the most cash would be to wait for someone to bid 98 or 99 cents, then have a friend yell out a dollar, and the person who bid 99 cents would have to pay you. You\'d win 99 cents.',NULL,0);
INSERT INTO comment VALUES (5470,865,1575,'DJ','but..','2003-06-04 12:39:05',0,'This is a watery form of \"This statement is false.\" However, this particular problem limits itself to a single word, \"no,\" so any other wording of a negative answer is a valid correct response.\r\n\r\nIf, however, the problem said, \"Is the correct answer to this question a negative response?\", it might be more of a paradox.',NULL,0);
INSERT INTO comment VALUES (5471,836,1575,'DJ','Have some fun','2003-06-04 12:44:25',1,'The situation as posed in the problem is kind of funny, as the 95¢ bid came after the winning dollar bid, but I am assuming that was an oversight.\r\n\r\nI would probably, in a logical sense, bid a penny, or try to bid a dollar right off.\r\n\r\nOf course, it\'s still just a dollar, so there is room to have some fun; for instance, I might bid $1.01 after someone bid a dollar just to see what they would do. Or, I would start off with a five-dollar bid and try to convice everyone else that there is something special about the dollar bill, just to see if I can get two other people to pay, say, six and seven dollars in trying to get it.',NULL,0);
INSERT INTO comment VALUES (5472,836,1920,'Brian Smith','Its all about the first bid.','2003-06-04 14:16:05',0,'Just a thought: The only way to stop the vicious cycle of bidding higher and higher is to make an opening bid no one will challenge.',NULL,0);
INSERT INTO comment VALUES (5473,24,1575,'DJ','re(4): the solution posted is WRONG!!!!','2003-06-04 15:26:41',1,'I fail to see the distinction between proper English and so-called American English; they are one and the same if you ask me. You, however, are not talking about proper English, you are talking about spoken English. The correct way to write out a number, like the one above, would be \"twelve thousand one hundred eleven.\" That is also how it should be said aloud; the fact that most people add an \"and\" in no way changes what is \"proper\" or correct. 3.1 would usually be said aloud as \"three point one,\" but written down it should always read as \"three and one tenth.\" The \"and\" is always used to denote decimal or fractional parts of a number as a sum.\r\nPi to four decimal places, then, would be \"three and one thousand four hundred sixteen ten-thousandths.\" Not very simple to type, which is why you rarely see long decimals typed out in word form.\r\nI may add that I have never seen anything such as \"three point one\" typed out as such in any textbook or elsewhere.\r\n\r\nAs far as the number in the problem, I can live with \"eleven thousand eleven hundred\" (it is akin to numbers such as \"eleventy one\" to mean 111, etc). The \"and eleven,\" as implied, denotes a sum, as in \"two and thirty\" or \"four sccore and seven.\" So, the number stated is certainly not common or proper, but technically correct to mean 12111.',3662,0);
INSERT INTO comment VALUES (5474,836,1626,'Gamer','re: Bid Nothing?','2003-06-04 16:46:29',0,'Look in the problem. \"and there had to be at least one bid\"\r\n\r\nUnless you are saying there IS no strategy, saying that nobody will make a bid DIRECTLY contradicts what\'s in the problem. So someone has to make a bid, as the problem states.',5446,0);
INSERT INTO comment VALUES (5475,836,2370,'Dave','re: Its all about the first bid.','2003-06-04 16:59:24',0,'I agree with you and Lewis.\r\n\r\nThe first person should bid $1 and it should be over.',5472,0);
INSERT INTO comment VALUES (5476,351,1919,'Lewis','Special','2003-06-04 21:08:52',1,'The word contains all five vowels in alphabetical order.\r\nfAcEtIOUsly.\r\nThe closest to another word with this property I could think of was tEdIOUs, which doesn\'t have the A in.',NULL,0);
INSERT INTO comment VALUES (5477,836,2373,'ryan smith','Here\'s an idea','2003-06-05 00:00:00',0,'If there is a best bidding strategy it should be the same for each bidder. Also, we don\'t really know the rules of the auction, but they shouldn\'t matter as long as they fairly applied to all bidders.\r\n\r\nB = bid\r\nW = winnings\r\nL = loss\r\nP = chance of winning the auction\r\n\r\nW = 1 dollar - B\r\nL = B\r\n\r\nSo for any given instance of the auction,\r\n\r\nNet Profit, $ = P*W - (1-P)*L,\r\n = P*(1-B) - (1-P)*B\r\n\r\nThis applies to each bidder.\r\n\r\nTotal profit = Sum of $ for all auctions. Assuming a constant bidding stragegy, if we maximize $, we maximize Total profit.\r\n\r\nNow, let\'s assume that there is an optimum bid. When the auction opens there is no reason for the first bidder to bid anything but the optimum bid, since any bidder that follows with a higher bid is not playing by the best strategy (as I\'ve defined it above). Also, if the first bidder bids less than the optimim bid, they give that chance to the next bidder.\r\n\r\nNow look at the case with two bidders using the same bid, the optimum bid:\r\n\r\nP=0.5 (the bidder who goes first gets it)\r\n\r\nSo, $ = 0.5*(1-B) - (1-0.5)*B\r\n = 0.5 - 0.5*B - 0.5*B\r\n = 0.5 - B\r\n\r\n$ is a maximum when B is as small as possible. If the minimum bid is say 1 cent and the two bidders take turns bidding first, then each bidder wins an average of 48 cents per auction. If the optimum bid is 5 cents, each bidder earns an average of 45 cents per auction.\r\n\r\nNote, if the players have chosen two different optimum bids before the auction, the player with the higher optimum bid will always win the auction and the other player will always lose. The losing player must then increase his optimum bid until his profits are maximized (this should be at the other players bid, I think). If a bidding war gets started, both players should conclude that at a bids past 50 cents, they are losing in the long run (at 65, one round I win 35 cents, the next I lose 65 cents). If this happens, lower bids will seem more appealing.\r\n\r\nIn short, the bidders take turns getting a dollar for a penny.',NULL,0);
INSERT INTO comment VALUES (5478,865,2374,'John Tate','Confused','2003-06-05 02:46:24',4,'What is it?',NULL,0);
INSERT INTO comment VALUES (5479,732,2374,'John Tate','Answer','2003-06-05 02:47:32',3,'Drew=Liar\r\nMohammad=Knight',NULL,0);
INSERT INTO comment VALUES (5480,775,2374,'John Tate','Answer again','2003-06-05 02:48:41',3,'Drew=Liar\r\nMohammad=Knight',NULL,0);
INSERT INTO comment VALUES (5481,859,1301,'Charlie','solution?','2003-06-05 03:18:12',0,'Time?',NULL,0);
INSERT INTO comment VALUES (5482,844,1660,'Tim Axoy','re(2): DJ or .?','2003-06-05 03:20:16',0,'DJ,you changed your name to .!',5461,0);
INSERT INTO comment VALUES (5483,859,1660,'Tim Axoy','re: solution?','2003-06-05 03:25:30',0,'Not everything devours time.\r\nI know for sure I do not devour time.\r\nI understand what the second paragraph means.\r\nOver time,things get destroyed.',5481,0);
INSERT INTO comment VALUES (5484,859,1686,'DuCk','Solution','2003-06-05 03:57:34',3,'I believe the answer is Time...\r\n',NULL,0);
INSERT INTO comment VALUES (5485,859,1567,'Bryan','re(2): solution?','2003-06-05 04:47:56',0,'Tim, the first line says this thing all things devours, not devour. A verb ending in \"s\" applies to a singular noun, not a plural noun. In other words, the first line is really saying, \"This thing (time) devours all things,\" only the words are arranged in a more poetic syntax that was more common in the past than it is now and is more common to British authors than to Americans. Since \"The Hobbit\" was written by J.R.R. Tolkien (a Brit) in the 1930\'s, this makes sense.',5483,0);
INSERT INTO comment VALUES (5486,859,1301,'Charlie','re(2): solution?','2003-06-05 06:10:05',0,'\"Devours\" is a singular verb. Its subject must therefore be \"this thing\", rather than \"all things\". The word order has been changed poetically, but spelled out prosaically, it is saying \"This thing devours all things\", rather than \"All things devours this thing.\" In the latter the number of the subject does not match the number of the verb.',5483,0);
INSERT INTO comment VALUES (5487,24,1301,'Charlie','re(5): the solution posted is WRONG!!!!','2003-06-05 06:43:12',0,'You say you are \"not very grammar oriented\", and I agree.\r\n\r\nYou say \"and\" represents a decimal point. So \"Fourscore and seven\" is 80.7? (That was spoken by a well-known American in a famous speech.) \"Four and Twenty blackbirds\" is 4.20 blackbirds?\r\n\r\nYou say \"Brian Nowell- you just don\'t know what you\'re talking about\". Look toward yourself before you cast aspersions. \r\n\r\n\r\n',3792,0);
INSERT INTO comment VALUES (5488,846,775,'Cory Taylor','equation city','2003-06-05 08:14:42',0,'Defining some variables;\r\n s=snow depth at 6:00 am\r\n r=rate of snowfall (in per hours)\r\n t=time in hours (primary variable)\r\n v=linear velocity of plow\r\n k=proportional constant (likely unneccesary)\r\n\r\nUsing common formula for distance -> d=v*t\r\nAssume plow blade width is constant, therefore plow speed dependant only on snow height (this is questionable, as once the snow height rises to greater than the blade width the problem changes)\r\n\r\nCreating equations...\r\nHeight of snow at discreet time h(t)=s+rt\r\nv=k/h(t); v=k/(s+rt)\r\n\r\nand therefore\r\n\r\nd=∑[(kt)/(s+rt)], where the sum is an integral.\r\n\r\nNow the distance travelled in hour 2 is half that done in hour one so we have ;\r\n\r\n0.5*∑[(kt)/(s+rt)]{0 to 1}=∑[(kt)/(s+rt)]{1 to 2}\r\n\r\nLacking an integral table or the desire to solve this with my restricted memory, this is as far as I go. The answe should provide some relation between \'s\' and \'r\', which can then be used to determine the time when the snow began...\r\n\r\nOf course, calculus was never my strong point, so poke holes at will!',NULL,0);
INSERT INTO comment VALUES (5489,824,1919,'Lewis','re: hm','2003-06-05 09:27:30',0,'Maybe the block of ice was REALLY big at the start, and when he drove over the desert some of it melted, but not all of it. Hm..... Brian\'s answer is very elaborate and cool, but that relys on ice aswell....',5447,0);
INSERT INTO comment VALUES (5490,75,2376,'Jim C','And in more detail...','2003-06-05 09:33:32',0,'Ahhh, yes, the minute hand will pass the hour hand every one hour and 5 minutes, BUT, to get more specific, the hour hand is still moving even as the minute hand approaches, so it has moved another 5 minutes\' worth while the minute hand tries to reach it. 5 minutes = 1/12 hour, which translates to 1/12 of 5 minutes\' worth of distance for the minute hand--or 25 seconds. And of course, in THOSE 25 seconds, the hour hand has further retreated (ahhhh, what a futile attempt at escape) another 25 seconds\' worth. That translates to 1/144 hr, which is equivalent to 1/144 of the 5 minute period that the hour hand is moving in, which equals about 2 more seconds. So the minute hand crosses the hour hand once every 1 hr, 5 min, 27 sec. We could take this infinitely further (which is exactly what confused poor Mikey Boy), but any further iterations will result in fractions of a second, and this is an analog clock, so lets be sane! =0)',NULL,0);
INSERT INTO comment VALUES (5491,814,1301,'Charlie','re(2): Solution plus','2003-06-05 09:58:15',0,'The allowing of the deletion of a space, rather than only replacement by + or - makes this the equivalent of \"Plus and Minus\".',5155,0);
INSERT INTO comment VALUES (5492,380,1301,'Charlie','solution','2003-06-05 10:01:12',3,'As also posted against Add Down to One:\r\n0 = 0- 1 - 2 + 34 + 56 - 78 - 9 \r\n(32 others) \r\n1 = 0- 1 - 2 - 3 - 4 - 5 + 6 - 7 + 8 + 9 \r\n(68 others) \r\n2 = 0- 1 + 2 - 34 + 5 + 6 + 7 + 8 + 9 \r\n(28 others) \r\n3 = 0- 1 - 2 - 3 - 4 - 5 - 6 + 7 + 8 + 9 \r\n(58 others) \r\n4 = 0- 1 - 2 + 34 - 5 + 67 - 89 \r\n(25 others) \r\n5 = 0- 1 - 2 - 3 + 4 - 5 + 6 + 7 + 8 - 9 \r\n(60 others) \r\n6 = 0- 1 - 2 + 34 + 5 - 6 - 7 - 8 - 9 \r\n(35 others) \r\n7 = 0- 1 - 2 - 3 - 4 - 5 - 67 + 89 \r\n(55 others) \r\n8 = 0- 1 - 2 - 34 - 5 + 67 - 8 - 9 \r\n(25 others) \r\n9 = 0- 1 - 2 - 3 - 4 + 5 + 6 + 7 - 8 + 9 \r\n(67 others) \r\n10 = 0- 1 - 2 + 34 - 5 - 6 + 7 - 8 - 9 \r\n(28 others) \r\n11 = 0- 1 - 2 - 3 - 4 + 5 + 6 - 7 + 8 + 9 \r\n(58 others) \r\n12 = 0- 1 - 2 - 3 - 45 - 6 + 78 - 9 \r\n(37 others) \r\n13 = 0- 1 - 2 - 3 - 4 + 5 - 6 + 7 + 8 + 9 \r\n(53 others) \r\n14 = 0- 1 - 2 + 34 - 5 - 6 - 7 - 8 + 9 \r\n(38 others) \r\n15 = 0- 1 - 2 - 3 - 4 - 5 + 6 + 7 + 8 + 9 \r\n(62 others) \r\n16 = 0- 1 - 2 - 3 - 4 - 56 - 7 + 89 \r\n(25 others) \r\n17 = 0- 1 - 2 - 3 - 4 + 5 - 67 + 89 \r\n(55 others) \r\n18 = 0- 1 - 2 - 34 + 5 + 67 - 8 - 9 \r\n(33 others) \r\n19 = 0- 1 - 2 - 3 + 4 + 5 + 6 - 7 + 8 + 9 \r\n(56 others) \r\n20 = 0- 1 - 2 + 34 + 5 - 6 + 7 - 8 - 9 \r\n(37 others) \r\n21 = 0- 1 - 2 - 3 - 4 - 56 + 78 + 9 \r\n(58 others) \r\n22 = 0- 1 - 2 - 3 - 4 + 56 - 7 - 8 - 9 \r\n(35 others) \r\n23 = 0- 1 - 2 - 3 + 4 - 5 + 6 + 7 + 8 + 9 \r\n(58 others) \r\n24 = 0- 1 - 2 - 3 - 45 + 6 + 78 - 9 \r\n(49 others) \r\n25 = 0- 1 - 2 - 3 - 4 + 5 + 6 + 7 + 8 + 9 \r\n(48 others) \r\n26 = 0- 1 - 2 - 34 - 5 + 67 - 8 + 9 \r\n(38 others) \r\n27 = 0- 1 - 2 - 3 + 45 - 6 - 7 - 8 + 9 \r\n(64 others) \r\n28 = 0- 1 - 2 + 3 - 4 + 56 - 7 - 8 - 9 \r\n(39 others) \r\n29 = 0- 1 - 2 - 3 + 4 - 56 + 78 + 9 \r\n(53 others) \r\n30 = 0- 1 - 2 - 3 - 4 - 56 + 7 + 89 \r\n(50 others) \r\n31 = 0- 1 - 2 - 34 + 5 - 6 + 78 - 9 \r\n(44 others) \r\n32 = 0- 1 - 2 + 34 + 5 + 6 + 7 - 8 - 9 \r\n(44 others) \r\n33 = 0- 1 - 2 - 3 - 45 + 67 + 8 + 9 \r\n(55 others) \r\n34 = 0- 1 - 2 - 34 - 5 - 6 - 7 + 89 \r\n(30 others) \r\n35 = 0- 1 - 2 - 3 - 4 - 5 + 67 - 8 - 9 \r\n(48 others) \r\n36 = 0- 1 - 2 - 3 - 4 + 56 + 7 - 8 - 9 \r\n(50 others) \r\n37 = 0- 1 - 2 - 3 - 45 + 6 - 7 + 89 \r\n(50 others) \r\n38 = 0- 1 - 2 - 3 - 4 + 56 - 7 + 8 - 9 \r\n(43 others) \r\n39 = 0- 1 - 2 - 3 - 45 - 6 + 7 + 89 \r\n(54 others) \r\n40 = 0- 1 - 2 - 3 - 4 + 56 - 7 - 8 + 9 \r\n(46 others) \r\n41 = 0- 1 - 2 - 3 + 45 - 6 + 7 - 8 + 9 \r\n(42 others) \r\n42 = 0- 1 - 2 - 3 - 45 + 6 + 78 + 9 \r\n(51 others) \r\n43 = 0- 1 - 2 - 3 + 4 - 5 + 67 - 8 - 9 \r\n(43 others) \r\n44 = 0- 1 - 2 - 3 + 4 + 56 + 7 - 8 - 9 \r\n(43 others) \r\n45 = 0- 1 - 2 - 3 - 4 + 5 + 67 - 8 - 9 \r\n(67 others) \r\n46 = 0- 1 - 2 - 3 + 4 + 56 - 7 + 8 - 9 \r\n(44 others) \r\n47 = 0- 1 - 2 + 3 + 45 - 6 + 7 - 8 + 9 \r\n(41 others) \r\n48 = 0- 1 - 2 - 3 - 4 - 5 - 6 + 78 - 9 \r\n(50 others) \r\n49 = 0- 1 - 2 - 34 + 5 - 6 + 78 + 9 \r\n(37 others) \r\n50 = 0- 1 - 2 + 3 + 4 + 56 + 7 - 8 - 9 \r\n(44 others) \r\n51 = 0- 1 - 2 - 3 - 4 - 5 + 67 + 8 - 9 \r\n(53 others) \r\n52 = 0- 1 - 2 - 3 - 4 + 56 + 7 + 8 - 9 \r\n(37 others) \r\n53 = 0- 1 - 2 - 3 - 4 - 5 + 67 - 8 + 9 \r\n(49 others) \r\n54 = 0- 1 - 2 - 3 - 4 + 56 + 7 - 8 + 9 \r\n(50 others) \r\n55 = 0- 1 - 2 - 3 + 45 + 6 - 7 + 8 + 9 \r\n(41 others) \r\n56 = 0- 1 - 2 - 3 - 4 + 56 - 7 + 8 + 9 \r\n(35 others) \r\n57 = 0- 1 - 2 - 3 + 45 - 6 + 7 + 8 + 9 \r\n(42 others) \r\n58 = 0- 1 - 2 - 3 - 4 + 5 - 6 + 78 - 9 \r\n(47 others) \r\n59 = 0- 1 - 2 - 3 + 4 - 5 + 67 + 8 - 9 \r\n(41 others) \r\n60 = 0- 1 - 2 - 3 - 4 - 5 + 6 + 78 - 9 \r\n(49 others) \r\n61 = 0- 1 - 2 - 3 - 4 - 5 - 6 - 7 + 89 \r\n(40 others) \r\n62 = 0- 1 - 2 - 3 + 4 + 56 + 7 - 8 + 9 \r\n(36 others) \r\n63 = 0- 1 - 2 - 3 - 4 + 5 + 67 - 8 + 9 \r\n(55 others) \r\n64 = 0- 1 - 2 - 3 + 4 + 56 - 7 + 8 + 9 \r\n(35 others) \r\n65 = 0- 1 - 2 + 3 + 4 - 5 + 67 + 8 - 9 \r\n(38 others) \r\n66 = 0- 1 - 2 - 3 - 4 - 5 - 6 + 78 + 9 \r\n(46 others) \r\n67 = 0- 1 - 2 + 3 - 4 - 5 - 6 - 7 + 89 \r\n(44 others) \r\n68 = 0- 1 - 2 - 3 + 4 - 5 + 6 + 78 - 9 \r\n(39 others) \r\n69 = 0- 1 - 2 - 3 - 4 - 5 + 67 + 8 + 9 \r\n(45 others) \r\n70 = 0- 1 - 2 - 3 - 4 + 5 + 6 + 78 - 9 \r\n(28 others) \r\n71 = 0- 1 - 2 - 3 - 4 + 5 - 6 - 7 + 89 \r\n(38 others) \r\n72 = 0- 1 - 2 + 3 - 4 - 5 - 6 + 78 + 9 \r\n(42 others) \r\n73 = 0- 1 - 2 - 3 - 4 - 5 + 6 - 7 + 89 \r\n(38 others) \r\n74 = 0- 1 - 2 - 3 + 4 - 5 - 6 + 78 + 9 \r\n(33 others) \r\n75 = 0- 1 - 2 - 3 - 4 - 5 - 6 + 7 + 89 \r\n(38 others) \r\n76 = 0- 1 - 2 - 3 - 4 + 5 - 6 + 78 + 9 \r\n(38 others) \r\n77 = 0- 1 - 2 - 3 + 4 - 5 + 67 + 8 + 9 \r\n(35 others) \r\n78 = 0- 1 - 2 - 3 - 4 - 5 + 6 + 78 + 9 \r\n(37 others) \r\n79 = 0- 1 - 2 - 3 - 4 + 5 + 67 + 8 + 9 \r\n(34 others) \r\n80 = 0- 1 - 2 + 3 + 4 - 5 - 6 + 78 + 9 \r\n(27 others) \r\n81 = 0- 1 - 2 - 3 + 4 - 5 + 6 - 7 + 89 \r\n(49 others) \r\n82 = 0- 1 - 2 + 3 - 4 + 5 - 6 + 78 + 9 \r\n(31 others) \r\n83 = 0- 1 - 2 - 3 - 4 + 5 + 6 - 7 + 89 \r\n(35 others) \r\n84 = 0- 1 - 2 - 3 + 4 + 5 - 6 + 78 + 9 \r\n(37 others) \r\n85 = 0- 1 - 2 - 3 - 4 + 5 - 6 + 7 + 89 \r\n(32 others) \r\n86 = 0- 1 - 2 - 3 + 4 - 5 + 6 + 78 + 9 \r\n(28 others) \r\n87 = 0- 1 - 2 - 3 - 4 - 5 + 6 + 7 + 89 \r\n(34 others) \r\n88 = 0- 1 - 2 - 3 - 4 + 5 + 6 + 78 + 9 \r\n(22 others) \r\n89 = 0- 1 - 2 - 3 + 45 + 67 - 8 - 9 \r\n(35 others) \r\n90 = 0- 1 - 2 + 3 + 4 + 5 - 6 + 78 + 9 \r\n(34 others) \r\n91 = 0- 1 - 2 - 3 + 4 + 5 + 6 - 7 + 89 \r\n(37 others) \r\n92 = 0- 1 - 2 + 3 + 4 - 5 + 6 + 78 + 9 \r\n(33 others) \r\n93 = 0- 1 - 2 - 3 + 4 + 5 - 6 + 7 + 89 \r\n(33 others) \r\n94 = 0- 1 - 2 + 3 - 4 + 5 + 6 + 78 + 9 \r\n(27 others) \r\n95 = 0- 1 - 2 - 3 + 4 - 5 + 6 + 7 + 89 \r\n(26 others) \r\n96 = 0- 1 - 2 - 3 + 4 + 5 + 6 + 78 + 9 \r\n(29 others) \r\n97 = 0- 1 - 2 - 3 - 4 + 5 + 6 + 7 + 89 \r\n(27 others) \r\n98 = 0- 1 + 2 + 3 - 4 + 5 + 6 + 78 + 9 \r\n(23 others) \r\n99 = 0- 1 - 2 + 3 + 4 + 5 - 6 + 7 + 89 \r\n(41 others) \r\n100 = 0- 1 + 2 - 3 + 4 + 5 + 6 + 78 + 9 \r\n(22 others) \r\n101 = 0- 1 - 2 - 34 + 56 - 7 + 89 \r\n(27 others) \r\n102 = 0- 1 - 2 - 3 + 45 - 6 + 78 - 9 \r\n(26 others) \r\n103 = 0- 1 - 2 + 3 - 4 + 5 + 6 + 7 + 89 \r\n(22 others) \r\n104 = 0- 1 - 2 + 34 + 5 + 67 - 8 + 9 \r\n(24 others) \r\n105 = 0- 1 - 2 - 3 - 45 + 67 + 89 \r\n(23 others) \r\n106 = 0- 1 - 2 - 34 + 56 + 78 + 9 \r\n(24 others) \r\n107 = 0- 1 - 2 - 3 + 45 + 67 - 8 + 9 \r\n(27 others) \r\n108 = 0- 1 - 2 + 3 + 45 - 6 + 78 - 9 \r\n(33 others) \r\n109 = 0- 1 - 23 + 45 + 6 - 7 + 89 \r\n(18 others) \r\n110 = 0- 1 - 2 + 34 - 5 + 67 + 8 + 9 \r\n(23 others) \r\n111 = 0- 1 - 2 + 3 - 45 + 67 + 89 \r\n(24 others) \r\n112 = 0- 1 - 2 + 34 + 5 - 6 - 7 + 89 \r\n(20 others) \r\n113 = 0- 1 - 2 + 3 + 45 + 67 - 8 + 9 \r\n(21 others) \r\n114 = 0- 1 - 2 - 3 + 45 + 6 + 78 - 9 \r\n(25 others) \r\n115 = 0- 1 - 2 - 3 - 4 + 56 + 78 - 9 \r\n(16 others) \r\n116 = 0- 1 - 2 + 34 - 5 - 6 + 7 + 89 \r\n(24 others) \r\n117 = 0- 1 - 2 + 34 + 5 - 6 + 78 + 9 \r\n(34 others) \r\n118 = 0- 1 - 23 + 4 + 56 - 7 + 89 \r\n(20 others) \r\n119 = 0- 1 - 2 + 34 - 5 + 6 + 78 + 9 \r\n(14 others) \r\n120 = 0- 1 - 2 - 3 + 45 - 6 + 78 + 9 \r\n(27 others) \r\n121 = 0- 1 - 2 + 3 - 4 + 56 + 78 - 9 \r\n(15 others) \r\n122 = 0+ 1 - 2 - 3 + 45 - 6 + 78 + 9 \r\n(17 others) \r\n123 = 0- 1 - 2 - 3 + 4 + 56 + 78 - 9 \r\n(17 others) \r\n124 = 0- 1 - 2 - 34 + 5 + 67 + 89 \r\n(14 others) \r\n125 = 0- 1 + 2 + 3 - 4 + 56 + 78 - 9 \r\n(19 others) \r\n126 = 0- 1 - 2 + 3 + 45 - 6 + 78 + 9 \r\n(33 others) \r\n127 = 0- 1 - 2 - 3 + 45 + 6 - 7 + 89 \r\n(11 others) \r\n128 = 0- 1 - 2 - 3 - 4 + 56 - 7 + 89 \r\n(19 others) \r\n129 = 0- 1 - 2 - 3 + 45 - 6 + 7 + 89 \r\n(17 others) \r\n130 = 0- 1 + 2 + 3 + 45 - 6 + 78 + 9 \r\n(21 others) \r\n131 = 0- 1 - 23 + 4 - 5 + 67 + 89 \r\n(11 others) \r\n132 = 0- 1 - 2 - 3 + 45 + 6 + 78 + 9 \r\n(22 others) \r\n133 = 0- 1 - 2 - 3 - 4 + 56 + 78 + 9 \r\n(15 others) \r\n134 = 0- 1 - 2 + 3 - 4 + 56 - 7 + 89 \r\n(14 others) \r\n135 = 0- 1 - 2 + 3 + 45 - 6 + 7 + 89 \r\n(28 others) \r\n136 = 0- 1 - 2 - 3 + 4 + 56 - 7 + 89 \r\n(16 others) \r\n137 = 0- 1 + 2 - 3 - 4 + 56 + 78 + 9 \r\n(7 others) \r\n138 = 0- 1 - 2 + 3 + 45 + 6 + 78 + 9 \r\n(22 others) \r\n139 = 0- 1 - 2 + 3 - 4 + 56 + 78 + 9 \r\n(10 others) \r\n140 = 0- 1 + 2 - 3 + 4 + 56 - 7 + 89 \r\n(16 others) \r\n141 = 0- 1 - 2 - 3 - 4 - 5 + 67 + 89 \r\n(14 others) \r\n142 = 0- 1 - 2 - 3 - 4 + 56 + 7 + 89 \r\n(13 others) \r\n143 = 0- 1 + 2 + 3 - 4 + 56 + 78 + 9 \r\n(14 others) \r\n144 = 0- 1 + 234 - 5 - 67 - 8 - 9 \r\n(26 others) \r\n145 = 0- 1 + 2 - 3 - 4 - 5 + 67 + 89 \r\n(11 others) \r\n146 = 0- 1 + 2 - 3 - 4 + 56 + 7 + 89 \r\n(12 others) \r\n147 = 0- 1 - 2 + 3 - 4 - 5 + 67 + 89 \r\n(15 others) \r\n148 = 0- 1 - 2 + 3 - 4 + 56 + 7 + 89 \r\n(13 others) \r\n149 = 0- 1 - 2 - 3 + 4 - 5 + 67 + 89 \r\n(10 others) \r\n150 = 0- 1 - 2 - 3 + 4 + 56 + 7 + 89 \r\n(16 others) \r\n151 = 0- 1 - 2 - 3 - 4 + 5 + 67 + 89 \r\n(11 others) \r\n152 = 0- 1 + 2 + 3 - 4 + 56 + 7 + 89 \r\n(9 others) \r\n153 = 0- 1 + 2 - 3 + 4 - 5 + 67 + 89 \r\n(22 others) \r\n154 = 0- 1 + 2 - 3 + 4 + 56 + 7 + 89 \r\n(15 others) \r\n155 = 0- 1 - 2 + 3 + 4 - 5 + 67 + 89 \r\n(8 others) \r\n156 = 0- 1 - 2 + 3 + 4 + 56 + 7 + 89 \r\n(15 others) \r\n157 = 0- 1 - 2 + 3 - 4 + 5 + 67 + 89 \r\n(12 others) \r\n158 = 0+ 1 - 2 + 3 + 4 + 56 + 7 + 89 \r\n(7 others) \r\n159 = 0- 1 - 2 - 3 + 4 + 5 + 67 + 89 \r\n(13 others) \r\n160 = 0- 1 + 2 + 3 + 4 + 56 + 7 + 89 \r\n(4 others) \r\n161 = 0- 1 + 2 + 3 - 4 + 5 + 67 + 89 \r\n(5 others) \r\n162 = 0- 1 + 234 - 5 - 67 - 8 + 9 \r\n(19 others) \r\n163 = 0- 1 + 2 - 3 + 4 + 5 + 67 + 89 \r\n(7 others) \r\n164 = 0- 1 + 23 + 4 + 56 - 7 + 89 \r\n(10 others) \r\n165 = 0- 1 - 2 + 3 + 4 + 5 + 67 + 89 \r\n(10 others) \r\n166 = 0+ 1 + 23 + 4 + 56 - 7 + 89 \r\n(7 others) \r\n167 = 0- 1 + 234 - 56 + 7 - 8 - 9 \r\n(8 others) \r\n168 = 0+ 123 - 45 - 6 + 7 + 89 \r\n(5 others) \r\n169 = 0- 1 - 2 + 34 + 56 - 7 + 89 \r\n(9 others) \r\n170 = 0- 1 + 23 - 4 + 56 + 7 + 89 \r\n(5 others) \r\n171 = 0- 1 + 234 - 56 - 7 - 8 + 9 \r\n(18 others) \r\n172 = 0- 1 + 234 + 5 - 67 - 8 + 9 \r\n(10 others) \r\n173 = 0- 1 + 2 + 34 + 56 - 7 + 89 \r\n(5 others) \r\n174 = 0- 1 - 2 + 34 + 56 + 78 + 9 \r\n(7 others) \r\n175 = 0- 1 + 234 + 5 + 6 - 78 + 9 \r\n(4 others) \r\n176 = 0+ 1 - 2 + 34 + 56 + 78 + 9 \r\n(1 other) \r\n177 = 0- 1 - 23 + 45 + 67 + 89 \r\n(8 others) \r\n178 = 0- 1 + 2 + 34 + 56 + 78 + 9 \r\n(2 others) \r\n179 = 0- 1 + 23 - 4 + 5 + 67 + 89 \r\n(4 others) \r\n180 = 0+ 1 + 2 + 34 + 56 + 78 + 9 \r\n(13 others) \r\n181 = 0+ 1 + 23 - 4 + 5 + 67 + 89 \r\n(3 others) \r\n182 = 0- 1 - 2 + 34 - 5 + 67 + 89 \r\n(6 others) \r\n183 = 0- 1 - 2 + 34 + 56 + 7 + 89 \r\n(4 others) \r\n184 = 0+ 1 - 2 + 34 - 5 + 67 + 89 \r\n(5 others) \r\n185 = 0- 1 + 234 - 56 + 7 - 8 + 9 \r\n(8 others) \r\n186 = 0- 1 - 2 + 345 - 67 - 89 \r\n(4 others) \r\n187 = 0- 1 + 2 + 34 + 56 + 7 + 89 \r\n(6 others) \r\n188 = 0- 1 + 234 + 5 - 67 + 8 + 9 \r\n(6 others) \r\n189 = 0+ 1 + 2 + 34 + 56 + 7 + 89 \r\n(11 others) \r\n190 = 0- 1 + 2 + 345 - 67 - 89 \r\n(10 others) \r\n191 = 0+ 123 + 4 + 56 + 7 - 8 + 9 \r\n(1 other) \r\n192 = 0- 1 - 2 + 34 + 5 + 67 + 89 \r\n(5 others) \r\n193 = 0- 1 + 234 + 56 - 7 - 89 \r\n(2 others) \r\n194 = 0+ 1 - 2 + 34 + 5 + 67 + 89 \r\n(1 other) \r\n195 = 0- 1 - 2 - 3 + 45 + 67 + 89 \r\n(6 others) \r\n196 = 0- 1 + 2 + 34 + 5 + 67 + 89 \r\n197 = 0+ 1 - 2 - 3 + 45 + 67 + 89 \r\n(5 others) \r\n198 = 0- 1 + 234 - 5 - 6 - 7 - 8 - 9 \r\n(12 others) \r\n199 = 0- 1 + 2 - 3 + 45 + 67 + 89 \r\n(4 others) \r\n200 = 0+ 1 + 234 - 5 - 6 - 7 - 8 - 9 \r\n(5 others) \r\n201 = 0- 1 - 2 + 3 + 45 + 67 + 89 \r\n(5 others) \r\n202 = 0- 1 + 234 + 56 - 78 - 9 \r\n(2 others) \r\n203 = 0+ 1 - 2 + 3 + 45 + 67 + 89 \r\n(5 others) \r\n204 = 0+ 1 + 234 + 56 - 78 - 9 \r\n(3 others) \r\n205 = 0- 1 + 2 + 3 + 45 + 67 + 89 \r\n(2 others) \r\n206 = 0- 1 + 234 - 5 + 67 - 89 \r\n(2 others) \r\n207 = 0- 1 + 234 + 56 + 7 - 89 \r\n(10 others) \r\n208 = 0- 1 + 234 + 5 - 6 - 7 - 8 - 9 \r\n(6 others) \r\n209 = 0+ 1 + 234 + 56 + 7 - 89 \r\n(1 other) \r\n210 = 0- 1 + 234 - 5 + 6 - 7 - 8 - 9 \r\n(7 others) \r\nSkip 1 \r\n212 = 0- 1 + 234 - 5 - 6 + 7 - 8 - 9 \r\n(6 others) \r\n213 = 0+ 123 + 4 + 5 - 6 + 78 + 9 \r\n(1 other) \r\n214 = 0- 1 + 234 - 5 - 6 - 7 + 8 - 9 \r\n(4 others) \r\n215 = 0+ 123 + 4 - 5 + 6 + 78 + 9 \r\n(1 other) \r\n216 = 0- 1 + 234 - 5 - 6 - 7 - 8 + 9 \r\n(9 others) \r\n217 = 0+ 123 - 4 + 5 + 6 + 78 + 9 \r\n(1 other) \r\n218 = 0+ 1 + 234 - 5 - 6 - 7 - 8 + 9 \r\n(5 others) \r\nSkip 1 \r\n220 = 0- 1 + 234 + 5 + 6 - 7 - 8 - 9 \r\n(3 others) \r\nSkip 1 \r\n222 = 0- 1 + 234 + 5 - 6 + 7 - 8 - 9 \r\n(6 others) \r\n223 = 0- 1 + 23 + 45 + 67 + 89 \r\n224 = 0- 1 + 234 - 5 + 6 + 7 - 8 - 9 \r\n(5 others) \r\n225 = 0+ 1 + 23 + 45 + 67 + 89 \r\n(3 others) \r\n226 = 0- 1 + 234 - 5 + 6 - 7 + 8 - 9 \r\n(7 others) \r\nSkip 1 \r\n228 = 0- 1 + 234 - 5 - 6 + 7 + 8 - 9 \r\n(5 others) \r\nSkip 1 \r\n230 = 0- 1 + 234 - 5 - 6 + 7 - 8 + 9 \r\n... etc.',NULL,0);
INSERT INTO comment VALUES (5493,380,1301,'Charlie','re: solution','2003-06-05 10:14:26',0,'The program for finding these is as follows. (Of course after this, the output file had to be sorted and then run through another program summarizing duplicate totals with (## others).):\r\nDECLARE SUB setIt (noOps#, thisOp#)\r\nDEFDBL A-Z\r\nDIM SHARED s$\r\nDIM SHARED posn(9)\r\nDIM SHARED t$(9)\r\n\r\nOPEN \"tendig.txt\" FOR OUTPUT AS #1\r\ns$ = \"0123456789\"\r\n\r\nFOR noOps = 1 TO 9\r\n setIt noOps, 1\r\nNEXT\r\nCLOSE\r\nEND\r\n\r\nSUB setIt (noOps, thisOp)\r\n IF thisOp = 1 THEN strt = 2: ELSE strt = posn(thisOp - 1) + 1\r\n ending = 10 - noOps + thisOp\r\n FOR posit = strt TO ending\r\n posn(thisOp) = posit\r\n t$(thisOp) = \"+\"\r\n GOSUB tryIt\r\n t$(thisOp) = \"-\"\r\n GOSUB tryIt\r\n NEXT\r\n EXIT SUB\r\n\r\ntryIt:\r\n IF thisOp = noOps THEN\r\n tot = VAL(LEFT$(s$, posn(1) - 1))\r\n PRINT #1, LEFT$(s$, posn(1) - 1);\r\n FOR j = 2 TO noOps\r\n v = VAL(MID$(s$, posn(j - 1), posn(j) - posn(j - 1)))\r\n IF t$(j - 1) = \"+\" THEN tot = tot + v: ELSE tot = tot - v\r\n PRINT #1, t$(j - 1); v;\r\n NEXT\r\n v = VAL(MID$(s$, posn(noOps)))\r\n IF t$(noOps) = \"+\" THEN tot = tot + v: ELSE tot = tot - v\r\n PRINT #1, t$(noOps); v; \"=\"; tot\r\n ELSE\r\n setIt noOps, thisOp + 1\r\n END IF\r\n RETURN\r\nEND SUB\r\n\r\n',5492,0);
INSERT INTO comment VALUES (5494,846,1301,'Charlie','If my math is right...','2003-06-05 10:33:03',3,'We can assume that the snow piles up at 1 unit per hour, as it\'s arbitrary what units are being used. We need to find a c (number of hours before the beginning of plowing) such that\r\n\r\n∫{0 to 1}(a/(x+c))dx = 2∫{1 to 2}(a/(x+c))dx\r\n\r\na/(x+c) = a(x+c)^-1, so the integral involves the natural log function, and we get\r\n\r\na [ln(x+c)]{0 to 1} = 2a [ln(x+c)]{1 to 2}\r\n\r\nln(1+c) - ln(c) = 2 ln(2+c) + ln(c)\r\n\r\nTaking antilog:\r\n\r\n(1+c)³ = c (2+c)²\r\n\r\nc³ + 3c² + 3c + 1 = c³ + 4c² + 4c\r\n\r\n0 = c² + c - 1\r\n\r\nc = (-1 ±√(1+4))/2 = -1/2 ±√(5/4)\r\n\r\nThe lower solution is negative and thus spurious. The upper solutin is .6180339887498949, which is the reciprocal of the golden ratio, aka phi or tau depending on the text.\r\n\r\nSubtracting from 6 and converting to h:m:s gives us 5:22:55.0776... but that\'s already too accurate for the start of a snowfall.',NULL,0);
INSERT INTO comment VALUES (5495,846,1567,'Bryan','Solution','2003-06-05 10:53:20',3,'Same as Charlie\'s, with more explanation... Let S be the constant rate of snowfall, and say snow began falling at time t=0. The height H of the snow at any time t is H=S*t Let R be the constant rate of snow removal by plowing, and say the plow moves at a speed of dL/dt. Then R = H*dL/dt The length L that the plow travels in a given time is simply the integral of dL over that time period. If plowing begins at time t=T, we know the plow travels twice as far during the first hour (from T to T+1 hour) as it does in the second hour (T+1 hour to T+2 hours). Therefore, ∫ [R/(S*t)]*dt from T to T+1 = 2*∫ [R/(S*t)]*dt from T+1 to T+2 Since plowing begins a positive number of minutes after snowfall begins, T>0, and therefore only the positive root makes sense. As T occurs at 6:00 a.m. , t=0 must have been 37 minutes earlier, or in other words, the snow began falling at 5:23 a.m.',NULL,0);
INSERT INTO comment VALUES (5496,824,2121,'Chaz','re(2): hm','2003-06-05 11:16:19',0,'He probably had a refrigerator or a cooler, but we assume that he could have a block of us when he got there.',5489,0);
INSERT INTO comment VALUES (5497,865,2121,'Chaz','Answer','2003-06-05 11:26:09',0,'I like getting around paradoxes, so I had to think of something:\r\n\r\nThe answer is yes. This is because yes would be yes to the answer being no, not actually being the answer to the question, but putting no in the place of the answer.',NULL,0);
INSERT INTO comment VALUES (5498,513,2121,'Chaz','Answer','2003-06-05 11:31:47',0,'Ok. You conclude it by ignoring what the second sentence says, and by just assuming that the latter sentence is the first+1.',NULL,0);
INSERT INTO comment VALUES (5499,511,2121,'Chaz','Simple, really','2003-06-05 11:46:23',0,'Ok ill explain why the answer is no. Lets say a man could lift 200 pounds. He comes across a stone that weighs 200 lbs, and he, of course, can lift it. Now, we can all agree that God can lift an \"infinite\" amount of mass. When God creates a boulder that ways an infinite amount of mass, he will be able to lift it if he pleases, because the limit of mass he can hold is infinite, which matches the weight of any stone he will create.',NULL,0);
INSERT INTO comment VALUES (5500,817,2121,'Chaz','','2003-06-05 11:59:02',0,'Got it!\r\n\r\nOk, so lets she says this on lets say january 1st. Her birthday was december 31st. Two days ago, she was 14. Then, she turned 15 on the 31st. A year from now, she would turn 16 on the same year, and then the year exactly a year from now (but at the end) she will be 17.',NULL,0);
INSERT INTO comment VALUES (5501,859,1626,'Gamer','re(3): solution?','2003-06-05 12:35:13',0,'Time is singular... Time slows down, rather than time slow down.\r\n\r\nI would agree with Tim\'s solution... It doesn\'t seem perfect, but somewhat works.',5486,0);
INSERT INTO comment VALUES (5502,859,1626,'Gamer','re(4): solution? (correction)','2003-06-05 12:36:29',0,'I mean the Time solution (which as I read isn\'t Tim\'s solution)...\r\n\r\nI don\'t understand how time could gnaw iron... Maybe it\'s just personification or something...',5501,0);
INSERT INTO comment VALUES (5503,846,2231,'Trevor Leitch','re: Solution','2003-06-05 13:23:51',0,'This can\'t be right. No unionised snow-plower would be out on the road working within forty minutes of the first snowflake. This problem should be under \"Paradoxes\"...',5495,0);
INSERT INTO comment VALUES (5504,846,1920,'Brian Smith','re: Solution','2003-06-05 13:32:42',0,'Nicely done.',5495,0);
INSERT INTO comment VALUES (5505,836,1920,'Brian Smith','re: Here\'s an idea','2003-06-05 13:39:15',0,'I thought of the same thing at first but then I saw a problem.\r\n\r\nIf a bidder makes an opening bid of any amount less than a dollar then other bidders can jump in with a bid which still earns a profit or at least break even. And then the bidding war begins. There is no guarantee that the bidders will be cooperative and not try to outbid any bid under a dollar.',5477,0);
INSERT INTO comment VALUES (5506,24,1626,'Gamer','re(6): the solution posted is WRONG!!!!','2003-06-05 15:42:42',0,'When you are strictly speaking math talk, yes and means decimal point. You aren\'t really supposed to have that and in there...\r\n\r\nBut some people put it in there anyway... It\'s like alot. It\'s not an actual word, but people use it so it is becoming one.\r\n\r\nAnd as I have said before, you shouldn\'t pick at puzzles like this... You know what the author means hopefully.',5487,0);
INSERT INTO comment VALUES (5507,24,1301,'Charlie','re(7): the solution posted is WRONG!!!!','2003-06-05 16:14:26',0,'I\'m still trying to figure out where people get the idea that \"and\" means decimal point. I\'ve seen examples given in this discussion where \"and\" is used in conjunction with a fraction, such as two and three tenths, but it the \"ths\" at the end of ten that makes the fraction, not the \"and\". The only mathematical meaning assigned to \"and\" by the Random House dictionary (handy because it is on the computer), is 2. added to; plus:, and indeed two and three tenths is indeed two plus three tenths, as one hundred and five is one hundred plus five, which is 105, and \"fourscore and seven\" is fourscore plus seven, which is 87, and \"four and twenty blackbirds\" is 24 blackbirds. \"And\" in no way, by itself, performs any function as a decimal point. I\'d be interested in seeing any reference which defines \"and\" by itself to represent such.',5506,0);
INSERT INTO comment VALUES (5508,859,2341,'Pickels','Hmmmm..........','2003-06-05 16:24:54',1,'Well, like many of you said, the answer \"time\" seems right, even though it doesn\'t really fit. Maybe it\'s some other answer, but time does seem to work.',NULL,0);
INSERT INTO comment VALUES (5509,24,1301,'Charlie','re(8): the solution posted is WRONG!!!!','2003-06-05 16:27:38',0,'In fact, I just looked up a table of numeration in Merriam Webster\'s Collegiate Dictionary, tenth edition, page 798, and, after \"one hundred\", comes \"one hundred and one or one hundred one\" (their italics). Such locutions would be impossibly ambiguous if \"one hundred and one\" could mean 100.1. The same appears under \"number\" on page 1549 of Webster\'s Third International dictionary.\r\n\r\nThe locution does not even seem to be given any colloquial or other pejorative notation. And nowhere is there evidence of a meaning of \"decimal point\" for the word \"and\".',5507,0);
INSERT INTO comment VALUES (5510,535,2341,'Pickels','re(2): None','2003-06-05 16:28:22',0,'Finding out the answer is really unnecessary. All you have to do is just run a scan through all the patterns and see if they fit. It\'s a lot more fun when you have to make your mind flexible and cope with new answers and solutions.',5338,0);
INSERT INTO comment VALUES (5511,836,2373,'ryan smith','re(2): Here\'s an idea','2003-06-05 16:41:32',0,'Hey, fellow Smith!\r\n\r\nAfter a few hair-raising auctions (assuming we can play more than once), all players should realize:\r\n\r\nA higher bid means both less profit and more loss (depending on the outcome of the bidding),\r\n\r\nA lower bid means both more profit and less loss (again, depending on the outcome),\r\n\r\nand,\r\n\r\nthat the outcome is effectively random.\r\n\r\nI can\'t prove this, but unless you can get into the minds of the other players, you really have no way of influencing the outcome of the auction. For example, consider the type of auction where the bidders write a single bid on a piece of paper. That guy could be bidding low, and the other guy could be bidding high. Who knows? Even in a open auction, where bidders yell out their bids and bidding wars occur, how can we know when the other guy will stop?\r\n\r\nSo, I think that the tendancy will be for lower bids in the long run.\r\n\r\nAlso, people were talking about bidding a dollar and breaking even just to spite the other guy. Seriously, if the other guy faces losing 90 cents, why wouldn\'t he bid $1.10 to win the auction and reduce his loss to 10 cents. Actually, any bidding war supports the argument that the outcome is random. He bids $1.10 and now you face losing $1.00, so you bid $1.20 (cut your loss to 20 cents). This goes up and up until the difference between winning and losing is negelgible. Finally, you pay $8000 for $1, and he\'s out $7999 for losing. Where does the bidding eventually stop? Who knows? Random outcome.\r\n\r\n',5505,0);
INSERT INTO comment VALUES (5512,836,2373,'ryan smith','re(3): Here\'s an idea','2003-06-05 16:44:24',0,'(continued from last post, I\'m such a windbag)\r\n\r\nMaybe a good strategy would be to bid randomly (below a dollar of course). Thus, you could not be drawn into suicidal bidding wars and would probably even win a few rounds. Bidding randomly would also mess up other bidders\' \"strategies\". They would be puzzled (Geez, last time he dropped out at 40 cents, but this time he\'s all the way at 75 cents).\r\n\r\nFor random bidding with many other players (N),\r\n\r\nAverage winnings for bids, B, are:\r\n\r\n$ = Pwin * B - Plose * B\r\n\r\nand with a random outcome, your chances of winning and losing (second place) are the same (1/N):\r\n\r\n$ = (1/N)*B - (1/N)*B\r\n\r\nIt looks like random bidding is a break even strategy, but I think it may be profitable as, on average, I suspect that your winning bids will be higher than your losing bids.',5511,0);
INSERT INTO comment VALUES (5513,836,1920,'Brian Smith','re(4): Here\'s an idea','2003-06-05 17:03:07',0,'You do make some good points. If there is a strategy better than breaking even, it would have to be randomly based. I\'ll think about it more tomorrow.',5512,0);
INSERT INTO comment VALUES (5514,846,2184,'mark hartman','let it snow, let it snow','2003-06-05 19:18:13',0,'The snow started at 5:30 AM. Since the plow covered twice as much distance in the first hour, we can infer that the average snow depth in the second hour is twice as deep as in the first hour.\r\n\r\nSo if we let d = depth of snow at 6:00 AM, and r = rate of snow fall per hour, then the depth of the snow after at 7:00 AM is d+r, and the depth of the snow at 8:00 AM is d+2*r.\r\nAverage snow depth between 6:00 AM and 7:00 AM is then\r\n(d+d+r)/2\r\nAverage snow depth between 7:00 AM and 8:00 AM is\r\n(d+r+d+2*r)/2.\r\n\r\nOur equation then is:\r\n2*(d+d+r)/2 = (d+r+d+2*r)/2\r\n\r\nSolving we get d = r/2.\r\n\r\nWe conclude that snow had fallen for one half hour before the plow started at 6:00 AM.\r\n',NULL,0);
INSERT INTO comment VALUES (5515,846,2184,'mark hartman','re: let it snow, let it snow','2003-06-05 19:37:58',0,'Wow, you calculus guys are working too hard! Even though my solution is alot easier, I think I\'m going to stick by mine. Maybe sometime when I have a couple hours to kill, I work through your solution...and either agree with it or try to refute it.\r\nExcellent problem!',5514,0);
INSERT INTO comment VALUES (5516,846,2238,'cheeZ','re: let is snow, let it snow','2003-06-05 20:50:18',0,'Yeah, I got the same answer as you mark. 5:30 am.\r\nOnly through a more graphical method that would obviously require graphs to explain. So I wont here.\r\n\r\nWeird how calculus and other methods dont agree. I wonder which ones right. \r\n\r\n\r\n\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (5517,40,2346,'me','this is easy..','2003-06-05 22:59:02',0,'first, divide the 10 coins into 2 piles with 5 coins each. weigh these piles against each other. the pile with the heavier coin will naturally weigh more. take this pile and divide it into 2 more piles of coins, each containing 2 coins. you will have 1 extra coin; put this aside. weigh the 2 new piles of coins against each other. if either one is heavier, weigh both coins against each other to find out the heavier coin. if both piles weigh the same, that means the 1 coin you have put aside is the heavier coin. as for the open problem, you can have more coins, as long as they are an even number.',NULL,0);
INSERT INTO comment VALUES (5518,40,2346,'me','re: this is easy..','2003-06-05 23:05:41',0,'wops, i made a mistake, its 11 not 10 coins.. anyway its about the same solution... divide the coins into piles of 5, leaving 1 out. weigh the 2 piles against each other, if one is heavier, it contains the odd coin. if both weigh the same, the coin you left out is the odd one. lets say the odd coin is in a pile. divide this one into piles of 2 and leave 1 out once again. weight them; if one is heavier, weigh 1 coin against the other. if both weigh the same, the coin you left out is the odd one. as for the open problem, im not sure..',5517,0);
INSERT INTO comment VALUES (5519,765,2346,'me','soooo simple','2003-06-05 23:11:41',0,'divide the coins into piles of 15, leaving 1 out. weigh the piles against each other; if one is heavier, it contains the odd coin. if they weigh the same, the coin you left out is the odd one. if not, take the heavier pile and divide it into piles of 7, leaving 1 out again. repeat the process another 2 times and you will get your odd coin. ',NULL,0);
INSERT INTO comment VALUES (5520,765,2346,'me','re: soooo simple','2003-06-05 23:15:47',0,'oops its wrong, doesnt work out.. bleh',5519,0);
INSERT INTO comment VALUES (5521,846,1575,'DJ','re: let it snow, let it snow','2003-06-06 02:21:19',0,'That would work if the plow moved at a constant rate for each hour, based on the average depth of the snow for that hour. Since, however, both are constantly changing, the calculus is required.',5514,0);
INSERT INTO comment VALUES (5522,836,2382,'blink','','2003-06-06 02:48:17',0,'why would anyone even bid?',NULL,0);
INSERT INTO comment VALUES (5523,865,1575,'DJ','re: Answer','2003-06-06 02:50:59',0,'what? i didn\'t follow something there..',5497,0);
INSERT INTO comment VALUES (5524,540,1575,'DJ','Hmm..','2003-06-06 02:53:43',1,'Teeth, I believe.\r\n\r\nAlso, is this from Lord of the Rings as well? It sounds familiar from somewhere or other..',NULL,0);
INSERT INTO comment VALUES (5525,540,1301,'Charlie','The number','2003-06-06 05:06:33',4,'Why is this 30 rather than 32. In the voting, friedlinguini said he had an idea of why, and I\'m curious.',NULL,0);
INSERT INTO comment VALUES (5526,540,1301,'Charlie','re: The number','2003-06-06 05:08:13',0,'I\'d think extraction of wisdom teeth would bring it down to 28 rather than 32. I\'ve seen children\'s versions where the number is 20, for the 20 deciduous teeth.',5525,0);
INSERT INTO comment VALUES (5527,836,1626,'Gamer','re:','2003-06-06 05:57:33',0,'Because they have to... \"What would you do if you were at this auction, and there had to be at least one bid?\"',5522,0);
INSERT INTO comment VALUES (5528,836,1626,'Gamer','End the bidding wars!','2003-06-06 06:00:54',0,'Here\'s my strategy for how to end a bidding war: Just bid twice as much as the last person who bid, minus one dollar.\r\n\r\nFor example, if the last person bid 2 dollars, you bid 3 dollars. Now, the person could either pass and keep at 2 dollars, or bid 3.01 (or higher) and be out over 2 dollars.\r\n\r\nAnother example is if the last bid was 3, you could bid 5. The last bidder could be out 3, or 3 plus however much higher he goes (which is greater than 0, and thus more expensive)\r\n\r\nI am still in favor of making a first bid of one dollar.',NULL,0);
INSERT INTO comment VALUES (5529,311,2256,'Jackie','re: Easier solution?','2003-06-06 06:27:18',0,'That\'s exactly how I figured it out. I think it is an easier solution.',4217,0);
INSERT INTO comment VALUES (5530,848,1301,'Charlie','solution','2003-06-06 09:02:59',3,'One way, in 5 steps, is\r\nLONE\r\nLOVE\r\nROVE\r\nROLE\r\nROLF\r\nWOLF\r\n\r\nIf you don\'t like rolfing, there\'s\r\n\r\nLONE\r\nLORE\r\nLORD\r\nWORD\r\nWOLD\r\nWOLF\r\n\r\nA wold is an elevated tract of open country.\r\n',NULL,0);
INSERT INTO comment VALUES (5531,848,1567,'Bryan','Out and about','2003-06-06 10:46:06',3,'LONE A Gond is a member of a Dravidian people of central India (I just happened to know that--yeah, right).',NULL,0);
INSERT INTO comment VALUES (5532,836,1919,'Lewis','re:','2003-06-06 12:16:13',0,'Because the problem states there has to be at least one bid, and because people are greedy and want to make money.',5522,0);
INSERT INTO comment VALUES (5533,848,1626,'Gamer','re: Out and about','2003-06-06 13:31:42',0,'The trick in these (in my opinion) is to do them without \"wierd\" words like gond and wold... (If you have to explain the word, it\'s probably wierd)\r\n\r\nLONE\r\nBONE\r\nBOND\r\nBOLD\r\nGOLD\r\nGOLF\r\nWOLF\r\n\r\nTrying to use the most common words (like LONE BONE BOND BOLD instead of LONE HONE HOLD BOLD) is good in my opinion.',5531,0);
INSERT INTO comment VALUES (5534,40,2129,'Sanjay','re(2): this is easy..','2003-06-06 14:16:37',0,'How do you conclude that the heavier pile contains the odd coin? The problem only states that one of the eleven coins has a different weight (lighter or heavier). ',5518,0);
INSERT INTO comment VALUES (5535,24,1626,'Gamer','re(9): the solution posted is WRONG!!!!','2003-06-06 15:49:53',0,'I don\'t agree with you that and isn\'t used for decimal points...\r\n\r\nWhich sounds better: 20.2 twenty two tenths... Is this 20.2 or 2.2 (22/10)\r\n\r\nOr twenty and two tenths?\r\n\r\nI have always heard that you are supposed to not put the and before the decimal point, but this is \"technical math talk\", which doesn\'t come into the question in my opinion. I don\'t really like to follow this rule, but it sounds wierd to say: One million and two hundred and thirty four thousand and five hundred and sixty seven and eighty nine hundredths... What??? (It\'s 1,234,567.89)',5509,0);
INSERT INTO comment VALUES (5536,848,1575,'DJ','re(2): Out and about','2003-06-06 16:06:19',0,'Yeah, perhaps I should have said common instead of \"true\" English words (either way, proper nouns like \"Gond\" are not valid).\r\n\r\nTo me, \"BONE\" and \"HONE\" are equivalent, no point in pedantry over which words are more common than other common words.',5533,0);
INSERT INTO comment VALUES (5537,540,2341,'Pickels','Hmmm......','2003-06-06 17:07:41',1,'Yeah, I think teeth is right. It does seem to make the most sense.',NULL,0);
INSERT INTO comment VALUES (5538,540,2341,'Pickels','forgot something','2003-06-06 17:08:53',1,'One thing everyone up to now was the \"red hill\". Maybe the tounge, or gums?',NULL,0);
INSERT INTO comment VALUES (5539,859,1253,'brianjn','More natural?','2003-06-06 20:06:47',0,'I am wondering if Nature is more what Tolkien was thinking.\r\n\r\nTime is an abstract whereas Nature might be considered to be a .. somewhat, more, concrete thing. ',NULL,0);
INSERT INTO comment VALUES (5540,848,2184,'mark hartman','A soln in six steps; anybody do better?','2003-06-06 20:39:46',0,'L O N E\r\nB O N E\r\nB O N D\r\nB O L D\r\nG O L D\r\nG O L F\r\nW O L F',NULL,0);
INSERT INTO comment VALUES (5541,836,1919,'Lewis','re: End the bidding wars!','2003-06-06 22:49:04',3,'If, for whatever reason, you decide not to bid 1 dollar as the first bid, and get caught in a bidding war, the best way to stop it is simply to stop bidding.\r\nIn Gamers\' comment he said \'if the last person bid 2 dollars, you bid 3 dollars. Now, the person could either pass and keep at 2 dollars, or bid 3.01 (or higher) and be out over 2 dollars.\' If the highest bid was 2 dollars , you couldn\'t have bid more than 1 dollar 99 cents, meaning you could lose a maximum of 1 dollar 99 cents.\r\n\r\nIf you bid 3 dollars, you will lose 2. The only thing bidding higher would acheive is slightly increasing your loss and stopping the other bidder getting the dollar.\r\n\r\n',5528,0);
INSERT INTO comment VALUES (5542,445,1919,'Lewis','Gone Bananas','2003-06-06 23:50:39',3,'One of the statements is true, and its not possible for statements 3 and 4 to both be false, so one is true.\r\n\r\nThat means statements 1 & 2 are both false, so C had grapes.\r\n\r\nThat means statement 3 is true, and statement 4 is false, so B had apples.\r\n\r\nThat leaves A, who had bananas.',NULL,0);
INSERT INTO comment VALUES (5543,836,153,'TomM','Solution','2003-06-07 00:49:00',3,'OK.\r\n\r\nFirst, the puzzle posits that everyone thinks logically (and knows all the others do, too). This does not match the real world, but is common in puzzles, just as Knights and Liars are not real world figures.\r\n\r\nSecond, everyone wishes to maximize their winnings and minimize their losses. They will bid as low as possible, and will not bid if a bidding war is inevitable.(But see the third point.)\r\n\r\nThird, there has to be at least one bid.\r\n\r\nNotice that no matter how low he bids, the first bidder is out money if a second bid is the last bid. Even if no one else makes the third bid, he has to (to recoup his losses) and the bidding war begins. \r\n\r\nSince each of the others know this, they will not make the second bid. (See my second point, above.)\r\n\r\nSo the winning strategy is to make the first bid. And since no one will outbid you, make that bid as low as possible: 1 cent.',NULL,0);
INSERT INTO comment VALUES (5544,848,1660,'Tim Axoy','Four steps','2003-06-07 02:51:48',0,'LONE,LOVE,WOVE,WOLE,WOLF(WOLE SOYINKA IS A PHILOSOPHER I READ ABOUT).\r\n',NULL,0);
INSERT INTO comment VALUES (5545,848,1626,'Gamer','re: Four steps','2003-06-07 03:08:19',0,'Sorry, but WOLE isn\'t a word, it\'s a name. So that doesn\'t work.',5544,0);
INSERT INTO comment VALUES (5546,905,2341,'Pickels','Woah!','2003-06-07 04:52:06',0,'This problem is insane!',NULL,0);
INSERT INTO comment VALUES (5547,905,1301,'Charlie','Brute force method.','2003-06-07 06:12:31',0,'For this problem the brute force method is the only way I know. \r\n\r\nThe following program goes through all the possibilities (the only simplifying logic being that the possible answer to 1 determines questions 2 and 4 as well). A through D are represented by 1 through 4 respectively.\r\n\r\nCLS\r\nFOR q1 = 1 TO 4\r\n q2 = q1 MOD 4 + 1\r\n SELECT CASE q2\r\n CASE 1\r\n q4 = 4\r\n CASE 2\r\n q4 = 3\r\n CASE 3\r\n q4 = 1\r\n CASE 4\r\n q4 = 2\r\n END SELECT\r\n FOR q3 = 1 TO 4\r\n FOR q5 = 1 TO 4\r\n FOR q6 = 1 TO 4\r\n FOR q7 = 1 TO 4\r\n FOR q8 = 1 TO 4\r\n q(1) = q1\r\n q(2) = q2\r\n q(3) = q3\r\n q(4) = q4\r\n q(5) = q5\r\n q(6) = q6\r\n q(7) = q7\r\n q(8) = q8\r\n \'eval q3\r\n leastC = 0\r\n FOR i = 1 TO 8\r\n IF q(i) = 3 THEN leastC = i: EXIT FOR\r\n NEXT\r\n IF q3 = 1 AND leastC = 4 OR q3 = 2 AND leastC = 2 OR q3 = 3 AND leastC = 3 OR q3 = 4 AND leastC = 1 THEN\r\n ctB = 0\r\n FOR i = 1 TO 8\r\n IF q(i) = 2 THEN ctB = ctB + 1\r\n NEXT\r\n IF ctB = q4 THEN\r\n ctCB = 0\r\n FOR i = 2 TO 8 STEP 2\r\n IF q(i) = 2 OR q(i) = 3 THEN ctCB = ctCB + 1\r\n NEXT\r\n IF q5 = 1 AND ctCB = 1 OR q5 = 2 AND ctCB = 3 OR q5 = 3 AND ctCB = 0 OR q5 = 4 AND ctCB = 2 THEN\r\n lastA = 0\r\n FOR i = 1 TO 8\r\n IF q(i) = 1 THEN lastA = i\r\n NEXT\r\n IF lastA = 6 AND q6 = 1 OR lastA = 7 AND q6 = 2 OR lastA = 5 AND q6 = 3 OR lastA = 8 AND q6 = 4 THEN\r\n ctDD = 0\r\n FOR i = 2 TO 8\r\n IF q(i - 1) = 4 AND q(i) = 4 THEN ctDD = ctDD + 1\r\n NEXT\r\n IF 1 = 1 THEN\r\n \' IF q7 = 1 AND ctDD = 2 OR q7 = 2 AND ctDD = 0 OR q7 = 3 AND ctDD = 1 OR q7 = 4 AND ctDD = 3 THEN\r\n REDIM ctA(4)\r\n FOR i = 1 TO 8\r\n ctA(q(i)) = ctA(q(i)) + 1\r\n NEXT\r\n ctr3 = 0\r\n FOR i = 1 TO 4\r\n IF ctA(i) = 3 THEN the3 = i: ctr3 = ctr3 + 1\r\n NEXT\r\n IF ctr3 = 1 THEN\r\n IF q8 = 1 AND the3 = 3 OR q8 = 2 AND the3 = 4 OR q8 = 3 AND the3 = 2 OR q8 = 4 AND the3 = 1 THEN\r\n FOR i = 1 TO 8\r\n PRINT i, MID$(\"ABCD\", q(i), 1)\r\n NEXT\r\n END IF\r\n END IF\r\n END IF\r\n END IF\r\n END IF\r\n END IF\r\n END IF\r\n NEXT\r\n NEXT\r\n NEXT\r\n NEXT\r\n NEXT\r\nNEXT\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (5548,905,1301,'Charlie','re: Brute force method.--solution','2003-06-07 06:14:34',3,'Running the posted program produces a solution:\r\n\r\n 1 C\r\n 2 D\r\n 3 D\r\n 4 B\r\n 5 D\r\n 6 A\r\n 7 C\r\n 8 B',5547,0);
INSERT INTO comment VALUES (5549,848,1301,'Charlie','re(3): Out and about','2003-06-07 06:24:51',0,'I would imagine that ROLF is in a gray area of commonness. I didn\'t think it needed an explanation, but it is a more uncommon variant of RALPH in the sense of vomiting.',5536,0);
INSERT INTO comment VALUES (5550,836,2373,'ryan smith','re: Solution','2003-06-07 06:29:12',3,'This is all fine, however, can we expect the other bidders to be so thoughtful? Although I agree with your logic, I think that there is a bid that guarantees a win and takes into account human nature.\r\n\r\nBid first, bid 99 cents, because...\r\n\r\nbidders naturally want to change positions as follows:\r\n\r\nneutral --> win\r\nwin --> bigger win (impossible in this scenario)\r\nloss --> neutral\r\nbig loss --> small loss.\r\n\r\nSo, IF YOU GET TO BID FIRST, bidding 99 cents makes all other possible bids neutral --> loss. Sure, someone could bid $1.00 in what appears to be neutral --> neutral, but they\'d be risking at least $1.00 for zero chance of profit, so this is really neutral --> loss.\r\n\r\nIf you don\'t get to bid first, don\'t bid. Don\'t force the previous bidder to reduce his loss as this will lead to a bidding war.\r\n\r\nAny bid less than 99 cents runs the risk of some wiseguy changing from a neutral/loss --> win. While it would be nice to get the dollar for less than 99 cents, bidding less than 99 cents cannot guarantee that you will be the winner.\r\n\r\nAny bid over $1.00 is insane, it guarantees a loss (and probably a big one as many others have pointed out).\r\n\r\nFinally, not bidding is not a winning strategy.\r\n\r\nAppologies for my silly notation, poor spleeing, and use of CAPS.',5543,0);
INSERT INTO comment VALUES (5551,848,2388,'mitali','steps','2003-06-07 06:42:13',3,'LONE\r\nline\r\nwine\r\nwind\r\nwild\r\nwold\r\nWOLF',NULL,0);
INSERT INTO comment VALUES (5552,24,1301,'Charlie','re(10): the solution posted is WRONG!!!!','2003-06-07 06:49:12',0,'I agree that \"and\" has a very good use in separating a number from its fractional part as in \"twenty and two tenths\".\r\n\r\nBut in the above it is the word \"tenths\" that actually produces the fraction; the \"and\" is merely synonymous with \"plus\". If it were merely \"twenty and two\" it would be 22. I NEVER said one should say \"twenty two tenths\" for 20.2; what I did say was that the word \"tenths\" is necessary within \"twenty and two tenths\" to make it mean 20.2 rather than 22. \"AND\" MEANS PLUS and nothing more.\r\n\r\nI also never advocated saying \"one million and two hundred and thirty four thousand and five hundred and sixty seven and eighty nine hundredths\". All I said was that IF someone said this, it is indeed, as you seem to agree, 1,234,567.89, rather than a continued fraction that I wouldn\'t know how to disassemble, but would be something like 1,000,000 + 200/1000 + 34,000/100,000/1000 ... (the extra thousand on the end for being a fraction within a larger fraction).\r\n\r\nAnother common usage for \"and\" in numeration is just after \"hundred\" before the tens and units position numerations. This is a very common usage, recognized by the dictionaries cited. \r\n\r\nluvya\'s comment, which started the title of this thread, was that the solution is wrong, not that the locution in the puzzle itself was wrong. Given the locution in the question, 4037 is the correct solution.\r\n\r\nBeyond that, the puzzle is certainly an odd locution that one would never use in real life, not because of the \"and\" but rather for the \"eleven thousand\" in conjunction with the \"eleven hundred\". This obviously was the gimmick to mislead and the whole idea of the puzzle. But given what was said in the puzzle, there\'s no indication that a fraction would be possible in the meaning of the dividend.',5535,0);
INSERT INTO comment VALUES (5553,905,1626,'Gamer','What a good problem!','2003-06-07 07:15:52',0,'I think this problem looks cool... I am in the process of creating a \"quiz\" problem but it\'s not like this... :)',NULL,0);
INSERT INTO comment VALUES (5554,836,153,'TomM','re(2): Solution','2003-06-07 07:29:54',0,'I agree that first bid wins, unless someone makes a second bid. and \"in the real world\" to ensure against the second bid you must bid $.99. \r\n\r\nBut in \"Puzzleland,\" everyone realizes that any second bid results in a bidding war, so no one will outbid even $.01. Like I said, \"Puzzleland\" is inhabited by ideally logical people like Knights and Liars. ',5550,0);
INSERT INTO comment VALUES (5555,905,1575,'DJ','Solution','2003-06-07 07:50:40',1,'I don\'t know how to logically approach this, other than to make some random assumption and continue from there until the possibility of a valid set of answers is eliminated, or until a solution is found.\r\n\r\nArbitrarily choosing \'A\' as the answer to the first question, it then follows that 2 is \r\n\'B,\' and from there, 4 is \'C.\'\r\n\r\nThe answer to 3 could be \'A\' or \'C,\' independent of any other question.\r\n\r\nWe also know that, if this is a valid solution, there are 3 answers for \'B\' altogether.\r\nSince question 8 stipulates that only one letter correctly answers three questions, we have that \'B\' must be that letter, and the answer to #8 is \'C.\'\r\n\r\nMoving on to question five, we have to count the even-numbered questions with \'B\' or \'C\' as their answer. Since the possible choices are 0, 1, 2, or 3, and we already have three (in 2-B, 4-C, 8-C), we know that the answer to #5 must be \'B.\"\r\nFurther, the answer to six cannot be \'B\' or \'C;\' it must be \'A\' or \'D.\'\r\n\r\nGiven that, the last question for which \'A\' is the answer must be #6, the problem we are looking at, or #8, which we already have as \'B.\' Thus, this answer must be \'A.\'\r\nThe answer to the remaining question, seven, cannot be \'A.\' Given the assumption we have already made in questions four and eight, there must be exactly three \'B\' answers. Only two are selected thus far, and the answer to #7 is \'B.\'\r\nThis makes sense, since not only are there not two consecutive Ds, there is not a single \'D\' in this entire set of solutions.\r\n\r\nFinally, number three can be either \'A\' or \'C.\' Since, however, question eight specifies that no letter other than \'B\' is the answer to exactly three questions, and we have (so far) one \'A\' and two Cs, the remaining answer must be A.\r\n\r\nFrom this, the (rather, a possible) set of answers looks like:\r\n1. A\r\n2. B\r\n3. A\r\n4. C\r\n5. B\r\n6. A\r\n7. B\r\n8. C\r\n\r\nI stopped upon finding this, due to a lack of time. I\'ll continue verifying or eliminating other possibilities later..',NULL,0);
INSERT INTO comment VALUES (5556,836,1919,'Lewis','re(3): Solution','2003-06-07 07:51:51',1,'But in \'Puzzleland\' the other people will also know that. If you bid 1 cent, they might bid 2 cents because, using the same logic that you used, they\'ll think that you wouldn\'t bid any higher at the risk of a bidding war. \r\nI still think the best strategy is to bid $1 on the first bid.',5554,0);
INSERT INTO comment VALUES (5557,905,1575,'DJ','re: Solution','2003-06-07 07:52:25',0,'Whoops, I just noticed that I still ended up with three As, so scratch that...I\'ll still follow up later.',5555,0);
INSERT INTO comment VALUES (5558,848,1575,'DJ','','2003-06-07 08:02:29',0,'Perhaps I shouldn\'t put how many steps it took me, because it seems people will make up words, or find obscure ones, to try to fit it in. None of these problems (I know there\'s only one, but I have a series of them) use any words most people will not have heard before.',NULL,0);
INSERT INTO comment VALUES (5559,10,1919,'Lewis','ummmm','2003-06-07 08:04:18',3,'I think its 17 minutes. Here are the steps:\r\n\r\nA + B goes across - 2 Minutes\r\nA comes back - 1 minute.\r\nC + D goes across - 10 minutes.\r\nB comes back - 2 minutes.\r\nA + B goes across - 2 minutes.\r\n\r\nObviously the flashlight just travels with the people who come back.',NULL,0);
INSERT INTO comment VALUES (5560,824,1919,'Lewis','re(3): hm','2003-06-07 08:11:06',1,'It says Apart from the truck he came with, there\'s only 30 miles of sand to every direction of the room. I suppose it doesn\'t actually say \'there is nothing in the truck\', so perhaps he could have brought a cooler with him and left it in the truck.\r\n\r\nBTW by \'block of us\' did you mean \'block of ice\'?\r\n\r\n',5496,0);
INSERT INTO comment VALUES (5561,905,1567,'Bryan','Hint','2003-06-07 08:16:24',0,'Sure, a computer can root out the answer, but this can be solved logically as well. By looking at the nature of the first four questions, one of them should appear to be the best starting point, i.e. start with assumptions for that question and logic will quickly rule out several options.',NULL,0);
INSERT INTO comment VALUES (5562,836,153,'TomM','re(4): Solution','2003-06-07 09:21:30',0,'No, because once the second person bids, the first person loses money unless someone else bids, so if no one else bids, he will bid. Consider: \r\nA) He bids 1¢. If there are no other bids, he gains 99¢\r\nB) Bidder 2 bids 2¢. Bidder 1 will lose 1¢, so...\r\nC) He bids 3¢ and stands to gain 97¢. \r\n\r\nBut then by the same reasoning, ...\r\nD) Bidder 2 bids 4¢, and so on. The bidding war has begun.\r\n\r\nA second bid does not \"risk\" a bidding war, it guarantees one!\r\n\r\nSince everyone can think it through, they all realize that \r\nthe best position is to be the first to bid, and the second best, if they are too slow for the best, is not to bid. If there can be only one bid, it might as well be for the least permissible amount.\r\n\r\n\r\n',5556,0);
INSERT INTO comment VALUES (5563,905,1301,'Charlie','re: Hint','2003-06-07 09:23:15',0,'The first four immediatly rule out 1. B and its consequent 2. C, 3. B and 4. A as 4A would be contradicted by already having two B\'s. But for 1-4 the possibilities still are \r\nABAC, ABCC, CDDB and DACD. The DACD is quickly ruled out by the requirement that all the rest be B\'s including 5 calling for more B\'s and C\'s than can be accommodated.\r\n\r\nI guess it\'s trial and error from there.',5561,0);
INSERT INTO comment VALUES (5564,848,1626,'Gamer','re(4): Out and about','2003-06-07 12:24:50',4,'I think Rolf is more of a \"added word\" to english... It sounds more like a \"Meow\" or \"Ruff\" word, which is used, but still not really a word.\r\n\r\nBut if it does count as a word (which it could, if you counted added words), it isn\'t the \"commonest word\" solution in my opinion.',5549,0);
INSERT INTO comment VALUES (5565,859,2259,'calla tah-n','solution','2003-06-07 13:53:40',0,'time of course... all things die over time',NULL,0);
INSERT INTO comment VALUES (5566,865,2259,'calla tah-n','nyce','2003-06-07 13:55:25',0,'good variation of a common paradox... fun fun',NULL,0);
INSERT INTO comment VALUES (5567,24,1626,'Gamer','re(11): the solution posted is WRONG!!!!','2003-06-07 17:39:27',0,'I\'m not saying it shouldn\'t be used that way, and cultural sources (like dictionaries and other people) would agree with me. But the current definition (by math dudes, as I have heard) disallows and from being used in that type of usage.',5552,0);
INSERT INTO comment VALUES (5568,836,2373,'ryan smith','re(5): Solution','2003-06-07 19:03:19',0,'Since we cannot forcast the outcome of a bidding war or at what level it will stop, why shouldn\'t a bidder make the second bid? Bidding may stop at 10 cents, it may stop at $8000.\r\n\r\nConsider two bidders. If both make bids, the chance of each winning is 50%. Sure, in reality this chance depends on a lot of factors, but here in puzzleland I think we can agree that it\'s near 50/50. Most important, the bid level at which the auction ends is irrelevant to this 50/50 probability.\r\n\r\nIf each bidder \"wants to do what is best for them\", they will be bound to act by this probability as they cannot foresee the outcome of the auction. They will surely risk 2 cents, or even 10 cents, for the dollar. At a 50% chance of winning, a bid of 10 cents risks 5 cents for 45 cents. That is, I have a 50% chance of winning with a bid of 10 cents (0.5*90 cent profit), and I have a 50% chance of losing with the same bid (loss = 0.5*10 cents). So, making a bid of 10 cents, on average, I will earn 40 cents per auction - a very good profit.\r\n\r\nThe logic for making the first bid is the same as the logic for making a second bid.\r\n\r\nHowever, since neither a bidding war nor a sucessful low bid can be guaranteed, the best first bid is 99 cents. A first bid of 99 cents makes a second bid impossible.\r\n\r\n',5562,0);
INSERT INTO comment VALUES (5569,905,1575,'DJ','Solution','2003-06-08 00:47:42',3,'C D D B D A C B\r\n\r\nFinishing what I started earlier, the answer to 1 cannot be \'A\' since we end up with more than one answer with exactly three choices, defying problem 8.\r\n\r\nFirst, something I failed to do earlier, I will make a few observations. One of the first four answers must be a \'C\' (from clue 3). Similarly, one of questions 5-8 must be answered with an \'A\' (6). There is only one letter which is the correct answer to exactly three questions.\r\n\r\nAssume, then, that the answer to 1 is \'B.\'\r\nB _ _ _ _ _ _ _\r\nFrom this, the answer to 2 is \'C.\'\r\nB C _ _ _ _ _ _\r\nGiven that, number two is the first answer of \'C\' and number 3 is \'B.\'\r\nB C B _ _ _ _ _\r\nAlso, from number two, four must be \'A.\'\r\nB C B A _ _ _ _\r\nThat means that only one question has an answer of \'B.\' Since we already have two Bs, this entire train of thought is disproved.\r\n The problem asks, \'On what kind of surface would a square wheel function the same as a round wheel?\'. Meaning, find a surface on which both a square wheel and a round wheel would bahave the same way. It does not say that the square wheel\'s behaviour on this surface should be the same as a round wheel\'s behaviour on a flat surface. Nor does it say anything about rolling; smoothly or otherwise. All the comments have either assumed one or the other of these (non) requirements, or failed to furnish adequate proof. The official solution does not provide any answer either. It merely comments on the comments, without taking any position. In my opinion the answer should be: A frictionless surface. In the absence of any traction, both types of wheels will slide, rather than roll; and fairly smoothly at that. ',NULL,0);
INSERT INTO comment VALUES (5587,540,2080,'Tristan','hmmm. . .','2003-06-08 16:27:02',0,'Yea, this is familiar to a \"Teeth\" riddle, as stated before. When I heard it before it was \"chomp\" and \"stomp\", not \"champ\" and \"stamp\" but there is always a variation. We might all just be retarded and way off too.',NULL,0);
INSERT INTO comment VALUES (5588,836,775,'Cory Taylor','collude','2003-06-08 18:15:22',0,'Is that a word?\r\n\r\nHow about this - create a short term company between yourself and one other bidder. One of you bids a penny, and the other of you bids two pennies. If I were to see a situation like this as a non-bidder, I\'d definitely back out as I\'sd assume that these two jokers wer e going to run a prolonged bidding war. Of course, the first bidder then does not outbid his partner, and the company ends up making a 0.97 profit, which of course they could share...',NULL,0);
INSERT INTO comment VALUES (5589,848,2373,'ryan smith','Seven Step Solution!!!','2003-06-08 20:38:29',1,'LONE\r\nLORE\r\nCORE\r\nCORP (like a company!)\r\nGORP (ever been hiking?)\r\nGORF (classic 80\'s video game, played it?)\r\nWORF (from star trek, of course)\r\nWOLF (ta da!)',NULL,0);
INSERT INTO comment VALUES (5590,859,2373,'ryan smith','Solution','2003-06-08 22:10:57',3,'I read the Hobbit too long ago to remember this riddle, but what about...\r\n\r\nwater.\r\n\r\nIt fits the \"devour\" a bit better.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (5591,860,1575,'DJ','Straight from the source','2003-06-09 00:01:49',3,'\"Easy!\" said Bilbo. \"Mountain, I suppose.\"',NULL,0);
INSERT INTO comment VALUES (5592,848,1567,'Bryan','LONE to WOLF in three steps!','2003-06-09 05:17:34',0,'LONE LONF - a short, forceful exhalation through the nose, typically in response to a joke told in English by a native French speaker -- considered slang. I\'m kidding, of course! I agree with those who said before that these problems are meant to be solved with common words (or with humor; ryan smith\'s solution is my favorite). My apologies for searching the dictionary. It\'s an addiction of mine.',NULL,0);
INSERT INTO comment VALUES (5593,905,2256,'Jackie','easier solution','2003-06-09 05:46:53',0,'I solved this problem in less than 15 minutes using simple logic. An obvious starting point would be to test Question 3, then using each hypothetical answer to check if the answers to questions 1-4 are logical. then from that point you can easily eliminate certain possibilties. My answers were: \r\n1. c\r\n2. d\r\n3. d\r\n4. b\r\n5. d\r\n6. a\r\n7. c\r\n8. b',5578,0);
INSERT INTO comment VALUES (5594,892,1567,'Bryan','t1v2d3x4x5k1q2n3i4','2003-06-09 07:41:50',0,'g1q2x3v4,g1q2u3m1c2u3k4j5w1c2o3y4j5y6p1h2p1p2h3!\r\n',NULL,0);
INSERT INTO comment VALUES (5595,892,1919,'Lewis','re: t1v2d3x4x5k1q2n3i4 HELP','2003-06-09 08:18:52',4,'What on Earth does that mean?!',5594,0);
INSERT INTO comment VALUES (5596,892,103,'friedlinguini','re(2): t1v2d3x4x5k1q2n3i4 HELP (hint)','2003-06-09 08:34:44',2,'I think you meant to say:\r\n\r\nx1j2d3x4p1p2f1c2u3x4m5e1q2h3w4u1j2d3x4n1g2d3r4?!',5595,0);
INSERT INTO comment VALUES (5597,860,2379,'Dark','','2003-06-09 08:48:27',3,'Past, present, future of a line of blood- family tree, yet greater, since family tree only knows past.\r\nIt can continue on until eternity, but can never grow as it is set by destiny.\r\nRoots start from beginning of time, no one knows.',NULL,0);
INSERT INTO comment VALUES (5598,892,1567,'Bryan','re: t1v2d3x4x5k1q2n3i4 HELP','2003-06-09 08:50:08',2,'Have you ever seen the results of a poll, with A% giving one answer, B% giving another answer, and C% giving a third answer, and A, B, and C add to more than 100%? How is that possible? The simple answer is it isn\'t, but rounding creates strange answers in statistics. My comment is kind of like that. The joke as I originally read it was: One plus one equals three for large values of one. It doesn\'t make a lot of sense, but it always had a certain appear for me. Now hold on while I translate this using Gamer\'s code! (just kidding!) What I should have answered in the first place is t1e2k3s4t5r6i1q2x3w4j5s1q2f3o4 Since Grandma is 45 years older than Dad, she can\'t be in her 20s or 30s. Nor can she be in her 50s, because then Dad couldn\'t even have a double digit age, leave alone sire a son of his own. (53-45=8 and 52-45=7). So she must be in her 70s. Since Grandma is in her 70s, Dad can\'t be in his 50s. Nor can he be in his 30s, because then Grandma\'s age would be overstated, and she would mind terribly. (35+45=80 and 37+45=82). So he must be in his 20s. Since the digits in their ages reverse, they must be 27 and 72. Moreover, once we have removed the impossible, what remains, upon taking 27 from 72, however improbable, must be 45. No need to even check. Eliminatory my dear. What son?',NULL,0);
INSERT INTO comment VALUES (5622,836,2129,'Sanjay','Dollars and Sense','2003-06-09 15:33:57',0,'A good strategy must cover all scenarios. Hence, I think the full strategy should read as follows: If someone has already made an opening bid, and the bid is anything less than a dollar, then you should stay out of the bidding and watch me get very very rich. Enjoy the entertainment. Its free. At least for you. If someone has already made an opening bid, and the bid is exactly a dollar, then it will be a very short auction. No one will make any money, including me, and everyone will wonder what the fuss was about. If, by the time you gather your wits, no one has yet made an opening bid and there is an uncomfortable silence around you, you should bid a dollar and put everyone out of their misery, because otherwise no one will get to go home since there just has to be at least one bid. (Hey, I didn\'t make the rules). Someone has to do the dirty job. So why not you? Think about it. It makes cents.',NULL,0);
INSERT INTO comment VALUES (5623,845,1920,'Brian Smith','Category Placement?','2003-06-09 15:56:35',0,'Why is this in algorithms? I thought this category was for problems which require computer programs to solve?',NULL,0);
INSERT INTO comment VALUES (5624,860,2341,'Pickels','Hmmm....','2003-06-09 16:35:41',1,'Well, I really don\'t think it\'s a mountain, as mountains have no roots. A family tree isn\'t very likely either, seeing as no one person is taller than the tallest tree. Maybe if they all stood on each others shoulders...no. Well, just remember before you put an answer, make sure it actually works. That way, you don\'t look really stupid, like a lot of people do.',NULL,0);
INSERT INTO comment VALUES (5625,824,2411,'Amy','How About This One','2003-06-09 18:06:45',0,'Since the whole ice thing in the desert is far fetched, how about.....\r\nThe man uses the truck: standing on the inside of the door. When he is ready he reaches down to let the truck drive out of the building (it never said that the truck wasn\'t rigged). The truck only has a little gas in it so it dosen\'t go far and the water could be from the ac in the truck while he was getting in position!!!',NULL,0);
INSERT INTO comment VALUES (5626,499,2411,'Amy','my thoughts','2003-06-09 19:49:19',1,'I thought that they may be betting at a race track of any sort(horses or dogs etc.) since there is a scoring system of sorts. They\'d be betting against the house and therefore not loose money to eachother. Some other games such as blackjack or whatever could fit as well but then there are not many \"scores\" in those types of games.',NULL,0);
INSERT INTO comment VALUES (5627,859,2411,'Amy','Alternative Solution','2003-06-09 20:24:47',1,'I think the answer is wind...(air or whatever other term you want to use). All living things \"devour\" air since all would die without it (including trees and flowers). Also it causes (and the things in it ie: dust, particles, moisture) cause damage to iron and steel over time. Strong winds can kill and destroy especially in tornado form. Lastly it erodes mountains. It fits all criteria. \r\nWater could also fit.',NULL,0);
INSERT INTO comment VALUES (5628,836,2373,'ryan smith','re: Dollars and Sense','2003-06-09 21:48:21',0,'Great!\r\n\r\nHave you considered an opening bid of 99 cents (I feel like a salesman)?\r\n\r\nWould you bid $1.00 against an initial bid of 99 cents?\r\n\r\nThus, I challenge all fans of this problem:\r\n\r\nI hereby bid 99 cents for that dollar. If anyone would like to bid against me (by say, bidding $1.00) please explain the logic in doing so.\r\n\r\nI\'m waiting...',5622,0);
INSERT INTO comment VALUES (5629,102,2415,'hemalatha','answer','2003-06-10 01:07:56',0,'The first one was Carl.The middle one was Bill and the last one was Abe',NULL,0);
INSERT INTO comment VALUES (5630,848,2415,'hemalatha','solution','2003-06-10 01:33:05',0,'lone\r\ngone \r\ngole\r\ngold\r\ngolf\r\nwolf',NULL,0);
INSERT INTO comment VALUES (5631,541,2231,'Trevor Leitch','Maybe...','2003-06-10 02:34:39',3,'The sun, looking from the sky at it\'s reflection in a green pond? I assume green ponds exist, in Bermuda we only have blue ocean...',NULL,0);
INSERT INTO comment VALUES (5632,541,2341,'Pickels','Code?','2003-06-10 05:21:24',1,'Just the way the whole message is written, I kinda think there\'s some code hidden in it. I mean, with all the capital letters and weird errors in grammer, I think there\'s some other message. But I\'m still lost.',NULL,0);
INSERT INTO comment VALUES (5633,892,2341,'Pickels','re(2): s1g2: t1q2o3y4y5o6v7v8','2003-06-10 05:27:23',4,'What on Earth does that mean? How do you guys come up with this stuff?',5608,0);
INSERT INTO comment VALUES (5634,892,1919,'Lewis','re(3): s1g2: t1q2o3y4y5o6v7v8','2003-06-10 06:13:29',3,'s1g2d3h4n1a2t1q2o3y4y5o6v7v8!\r\n\r\n(Read my solution)',5633,0);
INSERT INTO comment VALUES (5635,836,1919,'Lewis','re(2): Dollars and Sense','2003-06-10 06:21:56',1,'Hello - I am the auctioneer\'s friend.\r\n\r\nI\'m bidding $1 to try to make you lose as much money as possible.\r\n\r\nWhatever money I lose my friend (the auctioneer) pays me back, and splits the profit. Therefore, I would like a bidding war.\r\n(You get the picture).\r\n\r\nBut then again, there\'s no guarantee that this won\'t happen with an opening bid of $1 either...',5628,0);
INSERT INTO comment VALUES (5636,541,1626,'Gamer','re: Code?','2003-06-10 06:32:07',0,'Yes... Maybe something along the lines of \"Yes, sir\"...\r\n\r\nIt\'s not totally written wierd, so I wouldn\'t rule out suggestions like the sun, supposing it\'s in the sky.',5632,0);
INSERT INTO comment VALUES (5637,806,2378,'Nich','simple','2003-06-10 08:02:59',3,'easy just spiral out on the botom block then when all squares are done spiral in the second layer the out on the third and so one until you are at the top and all the squares are gone',NULL,0);
INSERT INTO comment VALUES (5638,434,2378,'Nich','re: I believe it to be...','2003-06-10 08:06:40',3,'you are stupid it is obviosly 1. Just take a ball from the box labled BW if it is black label the box BB if white label WW then just switch the other two around because they are both wrong and the only other option is to switch them',2891,0);
INSERT INTO comment VALUES (5639,848,1301,'Charlie','re: solution','2003-06-10 08:10:53',0,'But \"gole\" is not a word ... certainly not a common word.',5630,0);
INSERT INTO comment VALUES (5640,176,2378,'Nich','to easy','2003-06-10 08:12:57',3,'obviosly they are at a police academy and the thugs are police dressed up the and guns are fake or laser ',NULL,0);
INSERT INTO comment VALUES (5641,917,1301,'Charlie','solution (assuming...)','2003-06-10 09:52:36',3,'If the statement \"only 4 of us are knights\" means that exactly 4 are knights then the following logic applies:\r\n\r\nC and D cannot both be knights as A can be only a knight or a liar--not both.\r\n\r\nBut if E stole it, they\'d both be knights, so E did not steal it.\r\n\r\nE is a knight since he truthfully says he did not steal it.\r\n\r\nSo C did not steal it based on Eddy\'s word. I also take it that \"only 4 of us are knights\" means that exactly 4 are knights, so exactly 2 are liars.\r\n\r\nIf D were a liar and actually took it, then so would A and C be liars as they name someone else, and that\'s too many liars. So D is a knight and D did not steal it.\r\n\r\nC is in fact a liar as he claims E stole it. So A and D are not both knights, though D is one, so A is a liar, not a knight. So F did not steal it.\r\n\r\nSince only A and C are liars, B and F are also knights, so B did not steal it and A did not steal it.\r\n\r\nThis rules out all the witnesses as being the thief, none of A through F stole the wallet.\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (5642,124,2378,'Nich','easy','2003-06-10 10:12:16',3,'arley is giving the better deal',NULL,0);
INSERT INTO comment VALUES (5643,917,1919,'Lewis','Solution','2003-06-10 10:15:14',3,'Calvin says \'Allan and Dwayne are both knights\', but then his next statement disagrees with Allan\'s statement, so Calvin is a liar. This means Eddy did not steal it.\r\n\r\nEddy said he did not steal it, so he is a knight. This means that there are only four knights, and Calvin did not steal it.\r\n\r\nBarry says \'Calvin is a liar\' so he too is a knight. That means neither he nor Allan stole it.\r\n\r\nThis means that the person who stole it is either Fred or Dwayne. Fred said that Barry did not steal it, which is true, so he is a knight. That means that Fred really is deaf, so Allan is a liar.\r\n\r\nAllan said that Fred stole it, which was a lie. Because there are four knights, that leaves Dwayne to be a knight, so Allan stole it.\r\n\r\nSo...\r\nAllan = Liar + Thief\r\nBarry = Knight\r\nCalvin = Liar\r\nDwayne = Knight\r\nEddy = Knight\r\nFred = Knight',NULL,0);
INSERT INTO comment VALUES (5644,917,1919,'Lewis','re: Solution (whoops, done it wrong)','2003-06-10 10:18:48',0,'Oops, my last solution was wrong.\r\n\r\nI missed Barry\'s statement that Allan definitely didn\'t steal it, so that means that.... nobody stole it?? Is that right??',5643,0);
INSERT INTO comment VALUES (5645,124,1919,'Lewis','REALLY easy','2003-06-10 10:22:10',3,'Arley takes away five coins per 67 days, and Bentley takes away five every 57 days. That means Bentley pays the same but takes away more for upkeep, so Arley offers the best deal.',NULL,0);
INSERT INTO comment VALUES (5646,836,2129,'Sanjay','re(2): Dollars and Sense','2003-06-10 10:42:59',0,'I wouldn\'t bid $1.00 against an opening bid of $0.99. I have said that already. In fact I wouldn\'t bid against any opening bid. But, that doesn\'t mean that no one else will. If you claim that no one will bid $1.00 against your opening bid of $0.99, because they would know that you would stand to lose less by outbidding them and this would in turn neccessitate their outbidding you etc .. then the same logic can be extended to argue that no one will bid $0.99 against your opening bid of $0.98, because they would know that you would have to outbid them etc .., all the way down to no one will outbid an opening bid of $0.01. The point is this. We can argue, either that everyone is a perfect logician, hence no one outbids anyone, because everyone knows that a second bid invariably starts a bidding war, or that there are a few imperfect logicians in the crowd, hence a second bid will be made against any opening bid below $1.00. We cannot argue that a crowd of some perfect and some imperfect logicians, somehow transforms itself into a crowd of all perfect logicians as soon as the \'magical\' opening bid of $0.99 is made. The problem states that \'everyone will want to do what is best for them\'. But, wanting to do something does not always make one capable of doing it. So, while everyone can reasonably calculate their immediate gains or losses from their bidding or passing, there will be at least some who will fail to figure out the long term impact of their bidding or passing, in terms of its likelihood of starting or preventing a bidding war. The \'winning\' strategy must therefore render any further bidding disadvantageous, \'in the moment\'. This can only be guaranteed by an opening bid of $1.00. ',5628,0);
INSERT INTO comment VALUES (5647,917,1715,'Jonny Doe','Error','2003-06-10 10:49:53',0,'I think that there is an error in the answers/statements.',NULL,0);
INSERT INTO comment VALUES (5648,917,103,'friedlinguini','re: solution (assuming...)','2003-06-10 11:46:23',3,'I get the same result. Here\'s my reasoning:\r\n\r\nAssume F stole it. This implies that A is a knight. If A is a knight, D is a liar. If D is a liar, then he stole it, which contradicts the assumption.\r\n\r\nThis means F didn\'t steal it. This implies that A is a liar. If A is a liar, then C is a liar and D is a knight. If C is a liar, then B is a knight.\r\n\r\nThere are two possibilities at this point for E. Assume E is a liar. If he is, then he stole it. Unfortunately, this contradicts the notion that C is a liar.\r\n\r\nNow assume E is a knight. Then F must be the fourth knight. We now have the only consistent arrangement of knights and liars. To recap:\r\n\r\nA - liar\r\nB - knight\r\nC - liar\r\nD - knight\r\nE - knight\r\nF - knight\r\n\r\nNow, let\'s figure out who the thief is:\r\n\r\nB\'s statement eliminates A. F\'s statement eliminates B. E\'s statement eliminates C. D\'s statement eliminates D.\r\nE\'s statement eliminates E. A\'s statement (a lie) eliminates F. This eliminates all possibilities for the thief.',5641,0);
INSERT INTO comment VALUES (5649,917,2166,'Chris','I know, I know!','2003-06-10 12:12:27',1,'Oliver Stone wrote the question using Jon as an alias. Therefore, the correct answer is that there is a huge government cover-up and all six of them are innocent. The actual thief is the man standing on the grassy knoll behind you who got away while you were questioning six decoys. :)',NULL,0);
INSERT INTO comment VALUES (5650,917,775,'Cory Taylor','hmm.','2003-06-10 12:28:10',0,'1) Assume that Allan is a knight, then Fred hears well and stole the wallet. Since Fred claims to be deaf then he is a liar - but he claims that Barry didn\'t steal the wallet, which means he did. The contradictions shows us that Allan is a liar, Fred is a knight, and Fred and Barry are innocent.\r\n2) Dwayne remarks that Allan is a liar (which is true, so his second statement proves his innocence.\r\n3) Calvins statement that BOTH Allan and Dwayne are knihts is a lie, proving that Eddy is innocent.\r\n4) With two confirmed liars, there can be at most 4 knights, so the only/exactly controversy in Eddys comment is moot.\r\n5) We previously know that Eddy is innocent (as Calvin is a liar), so his comment to that effect proves him to be a knight. This leads to the conclusion that Calvin in innocent, and to complete the group with 4 knights Barry must also be a knight. This eliminates our final suspect Allan.\r\n\r\nIn summary, using each characters first initial, and k=knight l=liar, we have the following;\r\nA,l proves F innocent\r\nB,k proves B and A innocent\r\nC,l proves E innocent\r\nD,k proves D innocent\r\nE,k proves C innocent\r\nF,k confirms B innocent\r\n\r\nWhat does this mean? Well there is no one person responsible among them for the theft. Could be you\'ve lost it or left it at home, could be someone else, or maybe there is a possible solution where the members have cooperatively stolen your wallet. Haven\'t checked this out yet, but to explain my thinking...\r\nre-assuming that Fred is a knight, his second comment could be construed as true if Barry AND Mr. X. stole the wallet.\r\n\r\nI\'m not sure this will produce a solution either, but if this isn\'t the idea, I\'ve nothing else to go on.\r\n',NULL,0);
INSERT INTO comment VALUES (5651,917,1575,'DJ','liar!','2003-06-10 14:14:56',1,'Some notation: knights, liars, and \r\nSo lets examine the statements pretaining to who stole the wallet. Is safe to assume that since knights always tell the truth, they will alway know the truth before speaking but this is not true with a liar.\r\n \r\nThe knights always say \"I know ...\" while liars just say \"... stole it\" which implies that they might know the truth or not and just pointing fingers. When Calvin accuses Eddy of stealling the wallet, Eddy says that he did not steal the wallet and since he is a knight we know this is true. When Allan accuses Fred, Fred is not denying it.\r\n \r\nSo I know it is far fetched but I think FRED STOLE THE WALLET.',NULL,0);
INSERT INTO comment VALUES (5673,917,1919,'Lewis','re: Fred??','2003-06-11 07:18:14',1,'Allan is a liar, so everything he says has to be a lie. So Fred definitely did not steal the wallet.\r\nYou said knights only speak if they know the truth - perhaps liars only speak if they know what they\'re saying is incorrect.\r\n',5672,0);
INSERT INTO comment VALUES (5674,900,1567,'Bryan','Great puzzle!','2003-06-11 08:01:59',3,'From the clues given, the letters on top of the dice are P,I,N,T,A,G,E,F,R,M,L,C,H,O,Y,W. There are 16 different letters, so no letter appears twice in the 4x4 grid. To solve this puzzle, we will arrange the letters so that all the words can be formed, then flip or rotate as necessary to get C&O in a horizontal line with W in the upper lefthand corner. PINT runs across the board. Every word with A in it is constructed such that the other letters must be on the same side of PINT that A is. This accounts for every letter except for W, so all the letters must be on one side of PINT, so we will begin by writing PINT across the bottom of the 4x4 grid. x x x x FAINT tells us A is adjacent to I, and FRAGMENT requires E adjacent to N, so AGE must run left to right in the second row from the bottom. Also, from FRAGMENT, PALACE, and FAINT we know F, R, and L are adjacent to A. This requires there be a blank space to the left of A, so the layout must look like x x x x From PALACE, C is adjacent to A and E, so it must be above G. From ARCHLY, R is adjacent to A and C and is therefore above A. Since L is either left of A or left and above A, ARCHLY requires H above R, L left of R (leaving F left of A), and Y in the upper left corner. Y H x x CHORAL requires O above C, FRAGMENT requires M right of C, leaving W in the upper right corner. Y H O W Rotating this arrangement CCW puts W in the upper lefthand corner, and it puts C and O in a horizontal line. Therefore, correct arrangement is W M E T Father A is 70 For 1.5*Sb to be a multiple of 5, all ages could be zero, which is not possible, or all ages could be multiplied by the same integer factor, which would make the Fathers too old to have fathered.',NULL,0);
INSERT INTO comment VALUES (5676,919,1919,'Lewis','re: Most realistic solution','2003-06-11 10:33:20',0,'Good point. I should have put in the problem that they all had to be below 100.\r\n\r\nBy the way, you are 100% correct.',5675,0);
INSERT INTO comment VALUES (5677,860,2426,'Will H','Answer','2003-06-11 10:45:19',0,'A mountain',NULL,0);
INSERT INTO comment VALUES (5678,900,2376,'Jim C','Its about time','2003-06-11 11:09:27',3,'It took me all day (off and on, of course--gotta make a living), and I danced around it for hours. I finally used excel to track all my trials just so I coould see the one step I KEPT forgetting grrrr.\r\n\r\nAnyway, the solution lies on three key points, that Pint and Age are straight lines, that CO is a horizontal connection (so it could also be OC) And that the C MUST be placed between the A and G adjacent to \'AGE.\' (because of the need to spell \'Palace\'). Then, looking at all of the listed words, we determine that the A must be surrounded with G,L,R,I,C,F,P in some order. What this tells us is that the A can\'t be on an edge because there wouldn\'t be enough squares; Which through investigation also tells us that \'PINT\' can\'t be diagonal because that would force the A onto an edge (the A and P have to connect for \'Palace.\'). So we basically have the following starting block\r\n\r\nP I N T or P I N T\r\n A G E A G E \r\n C O C\r\n O\r\ndepending on which way it is rotated (BTW, we know \'AGE and \'PINT\' have to be adjacent because of \'PALACE\' and \'COMET\'. We also know that the M has to be in contact with both the O and the E, and that the O,M,H,Y can\'t be in contact with the A (because we\'ve already used up our one \"useless\" contact with the A on the N. After that its very simple trial and error, rotating the starting configuration. Since \'PINT\' can only fit on two edges (either forward or backward) we only have four possible starting points and the rest is easy (unless, like me you KEEP forgetting one arrangement--the CORRECT one).\r\n\r\nW M E T\r\nO C G N\r\nH R A I\r\nY L F P',NULL,0);
INSERT INTO comment VALUES (5679,900,2376,'Jim C','re: Great puzzle!','2003-06-11 11:17:14',0,'I agree, Bry, this was an awesome puzzle. And thanks, DJ for making it with 16 individual letters. Had there been any repeats I think I might have had to hunt you down and kill you. =0)',5674,0);
INSERT INTO comment VALUES (5680,917,2432,'Bob','Eliminate','2003-06-11 16:37:28',0,'Assuming only ONE person stole the wallet:\r\n\r\nBarry and Eddy MUST be telling the truth when they each say two different people did not steal it. (If they were lying, that would mean TWO people stole it.) Therefore, Allan and Barry did NOT steal it (per Barry), and Eddy and Calvin did not steal it (per Eddy.) \r\n\r\nThat leaves only Fred and Dwayne. \r\n\r\nFred said Barry did not steal it (which we know is true), so it must also be true that Fred is deaf. \r\n\r\nThat makes Allan a liar...and that means Fred did NOT steal it. \r\n\r\nOnly Dwayne is left. Dwayne stole the wallet.',NULL,0);
INSERT INTO comment VALUES (5681,917,1301,'Charlie','re: Eliminate','2003-06-11 16:53:37',0,'But as you say, Allan is a liar. Dwayne also says as much, so Dwayne always tells the truth. And Dwayne said he did not steal the wallet; therefore he didn\'t steal the wallet.',5680,0);
INSERT INTO comment VALUES (5682,65,2433,'molly','','2003-06-11 17:53:58',0,'what a crap problem',NULL,0);
INSERT INTO comment VALUES (5683,848,1183,'fwaff','re(2): solution','2003-06-12 00:59:11',0,'\'Gole\' is a late nineteenth century British military term for a group of horsemen in the middle of a battlefield.\r\n',5639,0);
INSERT INTO comment VALUES (5684,861,1941,'shaun','maybe','2003-06-12 03:02:39',1,'Maybe a fish',NULL,0);
INSERT INTO comment VALUES (5685,919,2357,'Ahmed','Too easy','2003-06-12 03:58:40',0,'let A\' is the age of son A\r\nand B\' is the age of son B\r\n\r\ntherefore,\r\n A=2(B-A\')\r\nagain,\r\n A\'=(1+1/2)B\'=3/2 B\'\r\n\r\nsince, all the ages are multiles of five\r\n\r\ntherefore,\r\n B\' as a age must be a number divisble by 5 and by 2.......also A\' must be a number divisble by 5 and 3.....\r\n i.e. B\'={10,20,30,40,50,.......}\r\n A\'={15,30,45,60,75,.......}\r\n\r\nnow we must use the last data to get the truely age of A, this data is that....\r\n \r\n B=2A\' at B\"=2B\' \r\n\r\ntherefore,\r\n B={30,60,90,120,......}\r\nalso B\"={20,40,60,80,..}\r\n\r\n as B=2A\'=2*3/2B\"=3B\"\r\n \r\n now it is obivous that the age of Father B is 60 yrs and the age of B\"( B\" is the double of the age of B\' as to use B=2A\') is 20 also the age of A\' is 30 yrs old\r\n\r\nnow it is too easy to know that Father A has \r\n A=2(B-A\')=2(60-30)=60 yrs \r\nfinally, Father A has 60 yrs old\r\n \r\n \r\n ',NULL,0);
INSERT INTO comment VALUES (5686,919,1941,'shaun','re: Too easy','2003-06-12 04:13:52',0,'Yeah, so easy you got it wrong.',5685,0);
INSERT INTO comment VALUES (5687,919,2357,'Ahmed','','2003-06-12 05:04:15',0,'yes it \'s so easy.......but this mistake i\'ve made is my misunderstanding to the sentence of Father B is .....etc..but i\'m insisted it\'s too easy....and if u see my solution is wrong please u can tell me what is the mistake in it...',NULL,0);
INSERT INTO comment VALUES (5688,917,2434,'rob','sollution...','2003-06-12 05:05:47',0,'Walking the tree of posibility\r\n\r\nAssume Allan speads truth:\r\nImplies Fred is thief and Fred lies\r\nWhen fred lies, it means that barry is the thief. There is only one thief, so Allan lies!\r\n\r\nAllan lies:\r\nFred is not thief and fred speaks the truth\r\nFred speaks thruth = Barry is not thief\r\nBarry is not thief, so barry speaks the truth\r\nBarry speaks truth = Allan is not thief and Calvin lies\r\nCalvin lies = Eddie is not thief\r\nDwayne: \"Allan is a liar\" which is true as we have seen, so dwayne speaks truth\r\ndwayne speaks truth = Dwayne is not thief\r\nNow we have : Fred, Barry, Allan, Eddie, Dwayne are not thief\r\nSo Calvin is the thief',NULL,0);
INSERT INTO comment VALUES (5689,917,1715,'Jonny Doe','re: sollution...','2003-06-12 06:14:41',0,'You forgot one important piece of the puzzle. Is Eddy a knight or a liar? If you check your logic you will find that Eddy is a knight and he said that Celvin is not the thief.',5688,0);
INSERT INTO comment VALUES (5690,861,1645,'luvya2003','solution','2003-06-12 06:18:52',3,'A fish',NULL,0);
INSERT INTO comment VALUES (5691,917,1183,'fwaff','Solution and inane ramblings','2003-06-12 06:54:10',3,'It has been shown by numerous people already that on the basis that the six men are either knights or liars then none of them stole the wallet.\r\n\r\nIn answer to the question of who stole the wallet, my guess is that it\'s the same evil pixies that take pairs of socks from my drawer and replace them with random odd socks that presumably come from the socks they\'ve stolen from other people\'s drawers. \r\n\r\nI think this problem is great because the answer is so unexpected. It made an amusing change to spend time solving it, for the answer to be \'who knows?. Nice one Jon :-)',NULL,0);
INSERT INTO comment VALUES (5692,919,1919,'Lewis','re:','2003-06-12 07:44:10',0,'The sentence \'father b is....\' basically means that when Son B is double the age that he currently is, Father B will be twice the age of Son A.\r\n\r\nThis means that FB = 2(SA + SB).',5687,0);
INSERT INTO comment VALUES (5693,441,2376,'Jim C','re(4): Already not the latest... another solution','2003-06-12 08:06:11',0,'The fact is, the two-flower solution is a classic case of lateral thinking. We remove all assumptions and find a different solution from the norm. BUT, in this case (as in many other puzzles, unfortunately), in order to come up with 2 as the answer we must operate on the basis that the riddler intentionally set out to deceive. The language and the context imply that there are, in fact roses, tulips, and daisies. And that leads us to the \'common\' answer of three. It was fun figuring out that the answer could be 2, but to be honest that was the first thing that came to mind. I had to do the processing to figure out one of each as the solution. Basically, this puzzle comes down to this: Aren\'t \"all\" and \"none\" diametrically opposed? Of course, when it comes to these problems, its all or nothing anyway, right =0)',3007,0);
INSERT INTO comment VALUES (5694,925,1301,'Charlie','solution','2003-06-12 08:58:01',3,'If the word were CAT, DRY or RUN, the person with the C or the U, or the two with D and Y would have announced he knew the word right away, as there is only one of each of these letters in all the words.\r\n\r\nIf the word were NET, the logician with the T would, after the first round, know that the word was not CAT, and so must be NET as there are only 2 A\'s, and announce such on round 2. Likewise, if the word were MAN, the logician with the A would also know that the word isn\'t CAT, and announce MAN on round 2.\r\n\r\nNow everyone knows that the word must be MEN, as any other word would have been guessed in round 1 or round 2.\r\n\r\n or MAN, the logicians, knowing about what was said in the first paragraph here, ',NULL,0);
INSERT INTO comment VALUES (5695,925,1919,'Lewis','Solution','2003-06-12 09:24:56',3,'If one of the logicians had the letter C, D or U they would know that the words are CAT it it was C, DRY if it was D or RUN if it was U. Therefore, when they all said no first time that meant neither had any of those three letters.\r\n\r\nOf the remaining three words, if either had a T or a A they would know that the word was NET if they had a T or MAN if they had a A. The second time they answered no meant none of them had either of these two letters.\r\n\r\nThat leaves one word - MEN. Obviously, when they all said yes they all knew they had MEN because it was the only word left.',NULL,0);
INSERT INTO comment VALUES (5696,523,2376,'Jim C','re(2): Y : 3 Line Segments','2003-06-12 10:35:00',0,'I\'m sorry, Ravi. I love your puzzles, but in this case DJ is right. Looking at his solution made it obvious that he counted the Y as three segments (and beat me to the punch with the solution!). I don\'t understand the point to your comment, unless it was to confirm that he had made the right choice.',5051,0);
INSERT INTO comment VALUES (5697,925,1575,'DJ','Solution','2003-06-12 11:47:29',3,'MEN\r\n\r\nI am assuming that the men can see the list of possible words, or else the problem does not make sense. Also, I assume they can hear everyone\'s answers for the previous questions..\r\n\r\nIf any of the men had a C, D, Y, or U, they would know right away since each of those letters appears in only one word.\r\nSince no one guesses it right away, they know that the word is not CAT, DRY, or RUN.\r\n\r\nThe remaining words are, then, NET, MEN, or MAN.\r\nAt this point, a logician with a T or an A will know right away what the word is after the first answer, since they each appear in only one of the remaining words.\r\n\r\nSince no one guessed it the second time around, none of them had either T or A, and the word is not NET or MAN.\r\nTherefore, the three letters are E, M, and N, spelling MEN.',NULL,0);
INSERT INTO comment VALUES (5698,861,1575,'DJ','direct quote','2003-06-12 12:52:01',3,'\"Fish! Fish!\" he cried. \"It is fish!\"',NULL,0);
INSERT INTO comment VALUES (5699,836,2129,'Sanjay','re(4): Dollars and Sense','2003-06-12 13:42:18',0,'The \'99c\' solution relies on a dynamically shifting logical capability on the part of the potential second bidder. If he can think only one step ahead, then: The person making the second bid of $1.00 against an opening bid of 99c will figure that he will \'win\' the dollar on auction but will \'neither gain nor lose financially\', and not that he is \'bound to either win $1.00 or win NOTHING\'. Likewise, the person making the second bid of 99c against an opening bid of 98c will reason that he will \'win\' the dollar on auction and \'will make 1 cent\' and not that he \'may make 1 cent\'. Hence, he will make the bid. If he can think several steps ahead, then: The person making the second bid of $1.00 against an opening bid of 99c will figure that he is \'bound to lose $1.00\', and not that he is \'bound to either lose $1.00 or win NOTHING\'. Likewise, the person making the second bid of 99c against an opening bid of 98c will figure that he is \'bound to lose 99 cents\', rather than reason that he \'may make 1 cent\'. In any event: For an opening bid of 99c to be a \'winning\' strategy and an opening bid of 98c to not, the potential second bidder should be able to think ahead at least two steps when the opening bid is 99c, but only one step when the opening bid is 98c. This cannot be guaranteed. Hence, an opening bid of 99c is not a reliable winning strategy. On the other hand, an opening bid of $1.00 is more \'idiot proof\'.\r\n\r\n\r\n\r\n ',5654,0);
INSERT INTO comment VALUES (5700,836,2129,'Sanjay','re(4): Dollars and Sense','2003-06-12 13:51:57',0,'You\'re right. A second bid of $2.00 (or more) against an opening bid of $1.00 will certainly ensure that there is no bidding war. But I can\'t think of even one earthly reason why anyone would make that bid when there is a perfectly workable strategy in place.',5654,0);
INSERT INTO comment VALUES (5701,836,2373,'ryan smith','re(5): Dollars and Sense','2003-06-12 15:52:38',0,'Okay, so where we differ is in how far a bidder can see/guess the future.\r\n\r\nI understand your logic, and I\'m sure you understand mine. I can\'t argue against the first bid of $1.00 being a solution. I don\'t think it\'s a very good one, however, as it risks exactly what it returns (nevermind that, the problem forces a first bid). I take \"what\'s best for them\" to mean a player will not unnecessarily risk money (why risk what you already have?).\r\n\r\nThere is one -earthly- reason (maybe not according to formal logic) to make a bid of $2 against $1. If I bid 99c following my strategy and someone figures he can spite me and break even by bidding $1, then I bid $2 (losing 99c and $1 is about the same to me). I do this to demonstrate to all bidders the risk of bidding $1 against 99c. In successive auctions, very few people would consider bidding $1 against 99c. As long as there are a lot of auctions, I can win back my loss and more. Yes, it\'s a stretch considering the scope of the problem, but I can\'t come up with a counter stategy to beat it.\r\n\r\nAnyway, we must agree to disagree, as any solution relies on psychology after all. Have you considered what happens if the auction is blind (a maximum of one bid per bidder, written on a scrap of paper and handed to the auctioneer)?',5700,0);
INSERT INTO comment VALUES (5702,914,2231,'Trevor Leitch','Solution','2003-06-13 02:54:57',3,'Because after you find it, you stop looking for it.\r\n',NULL,0);
INSERT INTO comment VALUES (5703,329,1575,'DJ','re: Hmm..','2003-06-13 03:21:11',1,'By the months going in order, JASON is July, August, September, October, November. DJ is December, January, FM is February, March, and AM is April, May. The next month, in order, is June. July is certainly not a common girl\'s name (or would you argue that \'Pepper\' is a girl\'s name because it appears in the musical as well?).\r\n\r\nAnyway, the solution makes no sense no matter how you look at it.',4038,0);
INSERT INTO comment VALUES (5704,381,2376,'Jim C','re: stupid solution','2003-06-13 04:34:23',0,'Oh, C\'mon! Hooves are a type of foot. Are we also going to say that dogs don\'t have feet, they have paws? Fine, how about if he rdes an elephant? We are a multi-cultural group, after all.',3193,0);
INSERT INTO comment VALUES (5705,524,2376,'Jim C','Baa Baa Black Sheep','2003-06-13 04:39:29',0,'I suppose it could also be a ewe (U). Hey, I have a blue wool shirt! Isn\'t that proof? =0)',NULL,0);
INSERT INTO comment VALUES (5706,914,1567,'Bryan','un-solution','2003-06-13 04:48:44',2,'Because I\'m cursed? Seriously, if something in my house is in a cabinet with 5 doors, regardless of what order I try, it seems it\'s always behind the fifth door! Imps must move my things for this to happen so regularly.',NULL,0);
INSERT INTO comment VALUES (5707,520,2376,'Jim C','re: My solution is different','2003-06-13 05:02:38',0,'The only problem with this solution is that a 2 of diamonds or a 2 of clubs would also fit. As Ravi explained, we can\'t get a definitive answer with a 2 in the middle, thus the K, Q, Q.',5356,0);
INSERT INTO comment VALUES (5708,914,103,'friedlinguini','Solution','2003-06-13 05:44:24',3,'It\'s those blasted underwear gnomes.',NULL,0);
INSERT INTO comment VALUES (5709,914,1626,'Gamer','re: Solution','2003-06-13 05:54:26',0,'It\'s probably because the item moves around from an opened drawer/place to an unopened drawer/place. The things are alive and you just don\'t know it. :)\r\n\r\nI actually heard this problem from someone when I complained about a problem similar to Bryan\'s.',5708,0);
INSERT INTO comment VALUES (5710,836,1626,'Gamer','re(6): Dollars and Sense','2003-06-13 05:58:05',0,'You could submit that last problem idea as a problem. In other words, you all have to pay what you put on the paper, but only the highest bidder gets the money (1 dollar or any other amount)',5701,0);
INSERT INTO comment VALUES (5711,441,775,'Cory Taylor','re(5): Already not the latest... another solution','2003-06-13 07:38:25',0,'Actually, from what I remember from structured logic, all and none are not diametrically opposed. As an example, if I have no elephants (which is quite correct by the way), then it is correct for me to say that \"all my elephants are sleeping\". It would not, however, be correct to say that \"some of my elephants are sleeping\", as \"some\" requires at least one.',5693,0);
INSERT INTO comment VALUES (5712,537,2436,'Chris','','2003-06-13 12:10:10',0,'Dark.',NULL,0);
INSERT INTO comment VALUES (5713,925,1171,'nikki','Solution','2003-06-13 14:28:43',3,'I haven\'t read the other posted solutions, so maybe mine is just a boring repeat.\r\n\r\nThe word is MEN.\r\n\r\nAfter the first time they all answer, we know none of the logicians have C, D, Y or U. There is only one word that has one of those letters in them, so if one of them had C, D, Y or U then they would know the word on the first cycle.\r\n\r\nBefore they all answer the second time, everyone knows that noone knew the word yet, so they rule out Cat, Dry, and Run. Following the same idea, after they answer we know none of the logicians have T or A because now there is only one word that has one of those letters in them (after removing the previously mentioned words).\r\n\r\nSo at the beginning of the third cycle, the logicians have already removed Net and Man from the list, so the only word left is MEN so now they can all say yes at the same time.\r\n\r\nQuestion: How is the \"they all answer at once and need 3 tries to know the word\" concept any different than if they each answered individually and the result was \"Logician A: No, Logician B: No, Logician A: Yes\"? It\'s the same idea.',NULL,0);
INSERT INTO comment VALUES (5714,537,2441,'Amy','','2003-06-13 16:16:37',0,'air?',NULL,0);
INSERT INTO comment VALUES (5715,537,2341,'Pickels','Solution?','2003-06-13 16:28:54',1,'Well, as for the first two comments, you can see dark and can smell and feel air. I\'m guessing the answer is quite simply, death.',NULL,0);
INSERT INTO comment VALUES (5716,914,2341,'Pickels','re(2): Solution','2003-06-13 16:37:03',1,'Just for a second, lets get back to the problem, and away from underwear gnomes. The question is just asking for a logical answer, not your life stories. Anyway, the problem with the problem is the word always. Some answers, like 14,000 meters under the sea, are good for some things, like looking for fire, which cannnot possibly be under the sea. However, if looking for fish, you can find lots under the sea. I really don\'t think there is one place where you would never look for something.',5709,0);
INSERT INTO comment VALUES (5717,537,1626,'Gamer','re: Solution?','2003-06-13 16:43:35',0,'I like those three answers (particularly death, that\'s good!), but I had though of work. Once your body works too hard, it dies... When you work, you aren\'t happy (more of a disgruntled work than a profession work), and it fills empty holes.',5715,0);
INSERT INTO comment VALUES (5718,914,2163,'sendil','solution','2003-06-13 19:09:36',0,'When you are looking for something and find it,you will stop looking.\r\nThat makes the place you found your article the last place. This can be the first place second and so on.\r\n',NULL,0);
INSERT INTO comment VALUES (5788,902,1301,'Charlie','re: solution','2003-06-15 05:28:15',3,'As pointed out by Trevor and DJ, I had made an algebraic or arithmetic error in my previous analysis of a couple of cases.\r\n\r\nTo correct my previous handling of the case where Stefanie lost 1/3 of her money in Final Jeopardy:\r\n\r\nIf Stef had lost 1/3 in Final, she would have gone from 6000 to 4000. If x is the amount the 2nd place finisher started with, then the first place finisher started Final Jeopardy with 7000-x. \r\n\r\nThis has two subcases: The first place winner was the one to have doubled his money or the 2nd place winner was the one to have doubled his money.\r\n\r\nIn the latter case, (7000-x+2000) - 2x = 3000, or 3x = 6000, or x = 2000, meaning the 2nd place finisher had 4000 dollars at the end, the same as the 3rd place finisher, which would mean they were really tied for 2nd/3rd place with no way to distinguish them, so this is no good.\r\n\r\nIn the former case, 2(7000-x) - (x+2000) = 3000, or 3x = 9000, or x=3000. Then the winner had 4000 going into Final and 8000 after final; the 2nd place finisher 3000 going in, 5000 after; and Stefanie at 6000 going in and 4000 after. Ben was the winner, having doubled his money in Final; the 2nd place finisher was McNabb and Stef was from Summerset. Since the winner was not Hardy, and neither was 2nd place McNabb, third place was Stefanie Hardy (aha!, yes she is indeed better off named Stefanie than Laurel) from Summerset. That leaves Smith in first place, that is Ben Smith, who must be from Peyton Park, leaving Thoreau Falls to 2nd place finisher Jay McNabb.\r\n\r\nSummary of this solution:\r\nBen Smith from Peyton Park, 4000 to 8000\r\nJay McNabb from Thoreau Falls, 3000 to 5000\r\nStefanie Hardy from Summerset, 6000 to 4000\r\n\r\nThis is in addition to the solution I had already found:\r\nBen Smith from Peyton Park: 3875 to 7750 \r\nJay Hardy of Summerset: 7125 to 4750 \r\nStefanie McNabb of Thoreau Falls: 2000 to 4000 \r\n\r\nThis should be the complete set (2 solutions) as I don\'t think I made any mistakes in the cases of the first place winner having been the one to lose 1/3 in Final Jeopardy, which does not work out in either of its subcases (2nd place double or 3rd place double).\r\n\r\n',5776,0);
INSERT INTO comment VALUES (5787,914,2453,'Suzanne','Solution','2003-06-15 04:20:57',0,'You clearly stop lookin once you have found what you want! so it would be the last place you would look. You would not keep looking for the fun of it.',NULL,0);
INSERT INTO comment VALUES (5786,496,2449,'Gt Vegita','hmm','2003-06-14 18:01:34',0,'A is insane, because no one denied it, and he said he was\r\nB is pure, because he said he was, even though C said B was applied, it was a lie, because C himself admitted to being applied\r\nC is insane, because he wouldn\'t have said he was applied if he was, he would\'ve said he was something else, because applied mathematicians lie about their beliefs. by misconceiving what he is, this makes him insane.\r\nD is insane, beacuase B is pure\r\n......? let\'s check the solution....\r\n',NULL,0);
INSERT INTO comment VALUES (5785,529,2449,'Gt Vegita','re: My thoughts','2003-06-14 17:16:43',0,'actually, carbon 14 dating, as you reversely put it (14 carbon, is quite precise. (sorry, reading all of these after I posted)',5247,0);
INSERT INTO comment VALUES (5739,914,2443,'stephy','','2003-06-13 19:42:42',0,'Your brain is straing to remember.Thous its in the last place you look because its the last place you had it.',NULL,0);
INSERT INTO comment VALUES (5742,836,2443,'stephy','','2003-06-13 19:45:26',0,'the first bid should be for .50 that way it makes a 1.00 and no one looses....',NULL,0);
INSERT INTO comment VALUES (5784,529,2449,'Gt Vegita','Well, that wasn\'t so intelligent','2003-06-14 17:13:32',0,'If you don\'t mind I\'m going to disprove the ill thought solution you\'ve provided us. While this question may have seemed intelligent from the get go, your solution isn\'t logical. I WOULD believe the archaeologist, and not because you didn\'t. By uncovering the coin, you also uncover the dirt and soil around it, soil contains carbon. A sample of the soil drudged from the same basic area of the coin, can be carbon tested, to reveal an age that is exact larger than 80% of the time. Counting back, then, from this day, the amount of years the carbon was dating back to, could easily reveal a date of 64 B.C., regardless of Jesus being born back then or not, because we are in modern day, when such calendars already exist.',NULL,0);
INSERT INTO comment VALUES (5783,914,1575,'DJ','Hm','2003-06-14 15:00:39',1,'Invariably, if I\'m looking for something, I will not find it until I am trying to find something else. At that point, I have the first thing I was looking for, but not the last, so I keep looking. Therefore, I never find anything in the last place I look, because there is always more looking to do.',NULL,0);
INSERT INTO comment VALUES (5782,902,1575,'DJ','re: solution','2003-06-14 14:35:35',1,'If Stefanie had been the one from Summerset and lost 1/3 of her winnings in the final round, she would have had $6000 and the other two would have added up to $7000, not $5000.\r\n\r\n...So, I\'m trying to figure out why your solution (which, by the way, is different than mine) still seems to work. The way I solved it, it was a unique solution with all other possibilities eliminated, but by some fluke you made an arithmetic error and found an alternate solution, it seems. Can anyone else see a problem with this, cuase I can\'t...',5776,0);
INSERT INTO comment VALUES (5781,902,2231,'Trevor Leitch','re: solution','2003-06-14 14:21:46',3,'You\'ve made an algebraic mistake, I think. If Stef was the one who lost 1/3 going into the final, she went in with $6000; thus, the winner and second place finisher together had $7000, not $5000. Therefore, at least one other possible answer is the following:\r\n\r\nBen Smith, from Peyton Park, going from $4000 to $8000\r\nJay McNabb, from Thoreau Falls, going from $3000 to $5000\r\nStefanie Hardy, from Summerset, going from $6000 to $4000\r\n\r\nThe existence of your solution as well shows that there are multiple solutions to this problem.\r\n',5776,0);
INSERT INTO comment VALUES (5753,320,2259,'calla tah-n','way too easy!','2003-06-13 20:51:10',0,'b/c the uneven haired barber had to be the one to cut the nice haired barbers hair... so therefore the better barber is the messy haired one... the dirt everywhere part - that wasn\'t in the version i\'ve heard',NULL,0);
INSERT INTO comment VALUES (5754,537,2259,'calla tah-n','solution','2003-06-13 20:57:38',0,'the dark... bad timing.. but tis a nice try by gollum... ;-)',NULL,0);
INSERT INTO comment VALUES (5755,537,2259,'calla tah-n','re(2): Solution?','2003-06-13 21:01:50',0,'um... how would death or work lie behind stars?... i understand death being under hills... but only one of those answers works... dark... which is what the book says in the least... ',5717,0);
INSERT INTO comment VALUES (5756,537,2259,'calla tah-n','re: hehe answer rated PG-13','2003-06-13 21:03:32',0,'i don\'t remember... what was the real answer to that... that isn\'t... whell... pg-13',5724,0);
INSERT INTO comment VALUES (5757,914,2259,'calla tah-n','solution','2003-06-13 21:08:13',3,'if you find the thing you are looking for... you won\'t go looking still... so even if it is in the first place you happen to look... it will be the last place you look for that item.',NULL,0);
INSERT INTO comment VALUES (5758,861,2259,'calla tah-n','solution','2003-06-13 21:18:06',0,'a fish... doesn\'t breathe... usually aren\'t warm... have to \"drink\" water to get oxygen... has scales all over but they don\'t clink',NULL,0);
INSERT INTO comment VALUES (5759,919,2259,'calla tah-n','one of many solutions','2003-06-13 21:25:19',0,'father a = 70\r\nfather b = 50\r\nson a = 15\r\nson b = 10...\r\nthere are many more though... such as:\r\nfather a = 140\r\nfather b = 100\r\nson a = 30\r\nson b = 20...\r\nand so on progressing with son b\'s age by 10s... these answers, though, don\'t make much sense in today\'s world',NULL,0);
INSERT INTO comment VALUES (5760,860,2259,'calla tah-n','a questioning solution','2003-06-13 21:36:51',0,'the solution is a mountain... but does a mountain never grow?... what if you were to add more and more dirt to the top of it?... would that be considered growing?',NULL,0);
INSERT INTO comment VALUES (5761,315,2259,'calla tah-n','answer plus comment','2003-06-13 21:47:16',2,'his son is the obvious answer...\r\npeepoles... plz don\'t post the \"answer\" in your titles... they can be wrong sometimes!... plus it takes all the fun away!',NULL,0);
INSERT INTO comment VALUES (5762,360,2259,'calla tah-n','re(2): too easy','2003-06-13 21:53:28',0,'really?... this is the first time i\'ve heard this one... and it seemed wrong to say anything else but nothing',2292,0);
INSERT INTO comment VALUES (5763,467,2259,'calla tah-n','re: Oldie','2003-06-13 21:56:37',0,'i agree with silvis... i knew the answer was a person before even seeing the question... it is a very famous riddle',3618,0);
INSERT INTO comment VALUES (5764,467,2259,'calla tah-n','re: Stupid answer','2003-06-13 21:59:04',0,'i\'m not sure if you meant to not understand... but the time of day or the position of the sun is a common simile used to describe a time in a person\'s life... for example: just as the sun is setting represents the coming to the end of life for a person',4836,0);
INSERT INTO comment VALUES (5765,532,2259,'calla tah-n','re(2): their son','2003-06-13 22:08:31',0,'this question really depends on how you believe people go to heaven... there is faiths in which everyone goes to heaven at once, and the dead remain dead in a state of rest, so it could be their son that was killed',5392,0);
INSERT INTO comment VALUES (5766,532,2259,'calla tah-n','another thought...','2003-06-13 22:10:57',0,'God could have thought about giving Adam and Eve belly buttons and made them with belly buttons, so all man could look the same... just sayin... thats all',NULL,0);
INSERT INTO comment VALUES (5767,817,2259,'calla tah-n','random thought','2003-06-13 22:15:57',0,'what if the girl was confused and didn\'t know what the words day and year meant and confused them... she was 16 and one day from her birthday, two \"days\" ago, meaning years, she was 14, and the next \"year\", meaning day, she will be 17...\r\nbut this is just a silly thought... you never know... it could happen',NULL,0);
INSERT INTO comment VALUES (5768,840,2259,'calla tah-n','different possibility?','2003-06-13 22:21:10',0,'pushing a big object up a hill is heavy work, back down is not heavy work... haha... otherwise the best answer is not... seeing as how this is in the riddle section',NULL,0);
INSERT INTO comment VALUES (5769,510,2259,'calla tah-n','re: better solution then the solution.','2003-06-13 22:24:33',1,'whelll... you could have a portable fireplace and a stove made of stones... so either way... you have a problem with the solution',4834,0);
INSERT INTO comment VALUES (5770,501,2259,'calla tah-n','???','2003-06-13 22:31:20',1,'i dunno... sounds like stars... i\'ll look at the solution now...',NULL,0);
INSERT INTO comment VALUES (5771,702,2259,'calla tah-n','re: I know I SWEAR','2003-06-13 22:37:42',0,'um... somebody is obviously a democrat here... hahahahaha... ish alll good... whateva... do how you plz',4528,0);
INSERT INTO comment VALUES (5772,482,2259,'calla tah-n','re(2): Isn\'t the range of possible answers quite large?','2003-06-13 22:40:32',0,'okay... not only a democrat who openly speaks out against being republican... but also a sexist... what is this???... ',4530,0);
INSERT INTO comment VALUES (5773,537,2231,'Trevor Leitch','re: hehe answer rated PG-13','2003-06-13 23:31:41',0,'A last name.\r\nAt least, I hope that\'s what you\'re thinking of...',5724,0);
INSERT INTO comment VALUES (5774,439,1919,'Lewis','Easy','2003-06-14 00:39:50',3,'All of the statements disagree, so only one can be true. This means that statement 9 must be true, because if 1 is true 9 are false.\r\n\r\nIf the word exactly is removed 10 can\'t be true, because that would be a contradiction. That means statement 1 is definitely true.\r\n\r\nThat also means statement 9 can\'t be true, because that will also be a contradiction. Using this logic we can tell that statements 6,7,8,9 & 10 are all false, so 1,2,3,4 & 5 are true.',NULL,0);
INSERT INTO comment VALUES (5775,537,1301,'Charlie','another answer','2003-06-14 02:27:58',0,'The answer \"time\" fits this riddle as well as it does one of the previous Hobbit riddles.',NULL,0);
INSERT INTO comment VALUES (5776,902,1301,'Charlie','solution','2003-06-14 04:51:34',3,'If Stef, in last place, had been the one to lose 1/3 in Final, then, if x is the amount the 2nd place finisher went into Final with, the winner went in with 5000-x. If the winner was the one to have doubled in Final, then 2(5000-x)-(x+2000)=3000 or 3x=10,000 - 5000, but the right hand side is not divisible by 3. On the other hand if the 2nd finisher were the one to double in Final, 5000-x+2000 - 2x = 3000, or 3x=4000, with the same problem. So Stef, the last finisher, is not the one to lose 1/3 in Final Jeopardy.\r\n\r\nSo Stef went from 2000 to 4000 in Final Jeopardy, and since Stef is not Ben, this counts as the \"adding 2000\" rather than the \"doubling\", so she is Stefanie McNabb. \r\n\r\nAgain, let x be the amount the 2nd place finisher had going into Final Jeopardy. The first place finisher then must have had 11,000 - x going in.\r\n\r\nIf the second place finisher were the one to have doubled in Final, and the first place finisher had lost 1/3, then 2(11000-x)/3-2x = 3000, or x=1625. Twice this would still be less than Stef\'s last place finish, so this is no good.\r\n\r\nSo the first place finisher was the one to have doubled his money in Final Jeopardy. This works out as 2(11000-x)-2x/3=3000, or 8x=57000, or x=7125.\r\n\r\nSo the first place went from 3875 to 7750, doubling his money and so was Ben.\r\nThe second place went from 7125 to 4750, and was from Summerset.\r\nLast place was Stefanie McNabb, who went from 2000 to 4000.\r\n\r\nSince the winner was not Hardy, he was Ben Smith, leaving the second place to Jay Hardy.\r\n\r\nSince Smith came from neither Thoreau Falls nor from Summerset, he came from Peyton Park, leaving Thoreau Falls for the last place finisher, Stefanie.\r\n\r\nSummary:\r\nBen Smith from Peyton Park: 3875 to 7750\r\nJay Hardy of Summerset: 7125 to 4750\r\nStefanie McNabb of Thoreau Falls: 2000 to 4000',NULL,0);
INSERT INTO comment VALUES (5777,914,2426,'Will H','Answer','2003-06-14 10:13:59',0,'The explanation is that once you find something, you stop looking for it. Therefore, the place you find it is the last place you look.',NULL,0);
INSERT INTO comment VALUES (5778,537,2426,'Will H','Answer','2003-06-14 10:16:44',0,'Darkness\r\nLooks like your submission got through first...',NULL,0);
INSERT INTO comment VALUES (5779,860,2426,'Will H','Answer','2003-06-14 10:17:31',0,'A mountain',NULL,0);
INSERT INTO comment VALUES (5780,861,2426,'Will H','Answer','2003-06-14 10:19:22',0,'A fish\r\nLooks like your submission got through first...',NULL,0);
INSERT INTO comment VALUES (5789,901,1301,'Charlie','One Possibility','2003-06-15 05:42:52',3,'I don\'t know if there are other sets, but 2 cents and 3 1/2 cents works, as 2 x (3 1/2) + 3 x 2 = 13 cents and 4 x (3 1/2) = 14 cents.\r\n\r\nI don\'t know of any sets that avoid the fractional cent.',NULL,0);
INSERT INTO comment VALUES (5790,901,1575,'DJ','re: One Possibility','2003-06-15 07:03:32',2,'There are any number of sets of coins that can be made with fractional parts, for instance ¼¢, 12¢, and 13¼¢.\r\n\r\nThere is, however, one solution with all coins in integer denominations.',5789,0);
INSERT INTO comment VALUES (5791,901,2231,'Trevor Leitch','Solution','2003-06-15 09:59:11',3,'The coin values are 2 cents and 5 cents.\r\n\r\nThe fewest coins needed to make 13 is five: 5,2,2,2,2\r\nThe fewest coins needed to make 14 is four: 5,5,2,2\r\n\r\nI haven\'t a clue which country has only these denominations of coin.',NULL,0);
INSERT INTO comment VALUES (5792,902,1575,'DJ','re(2): solution','2003-06-15 15:03:03',0,'Trevor must have posted that while I was writing my response; I didn\'t see it before.\r\n\r\nAnd yes, that explanation is pretty much equivalent to the one I have.\r\n\r\nEven knowing the result, however, I cannot find any [algebraically correct] reasoning that would lead to the solution you previously found, although it works and fits all the clues.\r\n\r\nAnyone with any ideas?',5788,0);
INSERT INTO comment VALUES (5793,902,1301,'Charlie','re(3): solution','2003-06-15 16:33:05',0,'When you say \"Even knowing the result, however, I cannot find any [algebraically correct] reasoning that would lead to the solution you previously found, although it works and fits all the clues,\" I assume you mean to avoid the enumeration of cases. That is, the six possible permutations of which place finisher 1-3 could be matched against the three Final Jeopardy outcomes: doubling, adding 2000 and losing 1/3.\r\n\r\nSince there are only six, each could be handled separately, and the solution originally presented was the result of assuming the 1st place doubled; the 2nd place lost 1/3 and the 3rd place added 2000.\r\n\r\nThat resulted in, 3rd place adding 2000 to 2000 to get the 4000 she was said to have ended up with, and if x is the amount the 2nd place finisher had going into double jeopardy, he had 2x/3 after Final, and as Stefanie went into Final with 2000, 11000 was left between 1st and 2nd, meaning 1st went in with 11000-x, and since he doubled, came out with 22000-2x. As the final difference between first and second was 3000, then\r\n22000-2x - 2x/3 = 3000\r\n66000-6x -2x = 9000\r\n8x = 57000\r\nx=7125\r\n\r\nThis is the algebraically correct reasoning. Unfortunately I had applied incorrect numbers to the other valid case, 1st place doubled, second place gained 2000 and third place lost 1/3, thereby making me think the case was invalid.\r\n\r\nSo, yes, if you are referring to using algebra to avoid breaking the problem down into six cases, I don\'t see a way. But what a present above is certainly valid algebra for the case you are wondering about.\r\n',5792,0);
INSERT INTO comment VALUES (5794,902,1575,'DJ','OOH!!','2003-06-15 21:39:14',1,'When I originally wrote this problem, there was a statement in the opening paragraph that said that the trio\'s winnings totaled $17000, with no two having the same sum. During the voting, which I think those with access might recall, someone mentioned that that tidbit might be better suited as one of the clues, rather than in the introduction. I made the change, but either I messed it up somehow and only deleted the sentence, there was a problem with some part of the code I appended that made it not show up, or the submission form somehow truncated the problem when I submitted the change (such errors are very rare, but I have seen it happen a few times).\r\n\r\nAnyway, I thought that the problem had only one possible solution; now I know why that is not the case. I finally realized, when I was going over the solution I have saved, what piece was missing. I shall have to be more careful when editing future problems. Good thing, Charlie, that you came upon the discrepancy when you did, or it may never have been noticed.\r\n\r\nI have left the solution as I originally had it, and added to the end.',NULL,0);
INSERT INTO comment VALUES (5795,922,1183,'fwaff','Possible solution?','2003-06-16 03:09:46',3,'Given the usual caveats about it being a genuinely random number with each of the values 1,2,...100 having equal chance (1%), then the answer is 7 using the methodology of halving the valid range.\r\n\r\nWith each guess the best one can hope to achieve is to halve the range of valid numbers, so the first guess is always 50 - after which the worst case is that there are 50 possibilities (ie the number is in the range 51-100). After the second guess there are at most 25 possibilities. Etc, etc until the seventh guess when the range is only 1 number.\r\n\r\nAs an aside, using this methodology seven guesses can pick a number from up to 127 options.',NULL,0);
INSERT INTO comment VALUES (5796,901,1715,'Jonny Doe','Country','2003-06-16 03:35:45',3,'The country is Englang and the proper name is Pence and not cents.',NULL,0);
INSERT INTO comment VALUES (5797,901,1183,'fwaff','re: Country','2003-06-16 03:40:53',0,'No it isn\'t - we have 1p coins along with 2p, 5p, 10p, 20p, 50p, £1 and £2 in common circulation.',5796,0);
INSERT INTO comment VALUES (5798,922,1626,'Gamer','re: Possible solution?','2003-06-16 05:57:42',0,'If you also get the \"equal\" choice, I only seem to get 6 choices each time. Just split the set each time. For example for 17:\r\n\r\n50 Lower\r\n25 Lower\r\n12 Higher\r\n18 Lower\r\n15 Higher\r\n16 Higher\r\n\r\nOr for \r\n\r\n50 Higher\r\n75 Higher\r\n87 Higher\r\n93 Higher\r\n97 Higher\r\n99 Lower\r\n\r\nAfter 0 guesses, 100 numbers remain\r\nAfter 1 guess, 50 numbers remain (49 on the other side)\r\nAfter 2 guesses, 25 numbers remain (24 on the other side)\r\nAfter 3 guesses, 12 numbers remain (12 on each side plus one in the middle)\r\nAfter 4 guesses, 6 numbers remain (5 on the other side)\r\nAfter 5 guesses, 3 numbers remain (2 on the other side)\r\nAfter 6 guesses, 1 number remains (1 on the other side, and the one you guessed)\r\n\r\n\"On the other side\" means 1-49 if you guessed 50, because there are 49 numbers there.',5795,0);
INSERT INTO comment VALUES (5799,922,1575,'DJ','re(2): Possible solution?','2003-06-16 06:29:30',0,'In both of the examples you know what the number is, but you never guessed it. I think the seventh guess would have to be where you actually guess 17, 98, or whatever the number is (if it takes that many to find it).',5798,0);
INSERT INTO comment VALUES (5800,836,1919,'Lewis','re: No Subject','2003-06-16 07:23:52',1,'If everybody wants to do what\'s best for them, somebody will bid .51 to make a .49 profit rather than break even, unless he can tell that will cause a bidding war.',5742,0);
INSERT INTO comment VALUES (5801,922,575,'not_so_einstein','My way','2003-06-16 07:31:26',0,'I like to use this:\r\n\r\nI ask if it´s 50.\r\nIf it is greater than 50, I ask if it´s 75.\r\nIf it is less 50, I ask if it´s 25\r\n\r\nand so on, I hope you got the point. Always add or take half out.\r\n\r\nThis will take about..........7 guesses',NULL,0);
INSERT INTO comment VALUES (5802,922,2129,'Sanjay','Some Halve it, some don\'t','2003-06-16 09:46:30',0,'This is a standard case for a binary search. Each successive guess is at the half-way mark (or the closest to it) of the range that is still \'in play\'. e.g. at the start the entire range 1-100 is \'in play\'. You guess 50 and lets say you are told that the number is higher than 50. Now, the range 1-50 is ruled out and the range 51-100 is still \'in play\'. And so on... The minimum number of guesses within which you are sure to guess the number correctly is 7.',NULL,0);
INSERT INTO comment VALUES (5803,901,1715,'Jonny Doe','re(2): Country','2003-06-16 10:19:32',0,'If you look at Trevor\'s solution you will see that the combinations are 5+2+2+2+2 and 5+5+2+2 and as far as I know England is using 2p & 5p in circulation.',5797,0);
INSERT INTO comment VALUES (5804,542,1902,'Hank','This works...','2003-06-16 11:00:21',1,'I\'m not sure what the question is, but this is my reply:\r\n\r\nA boy (two legs) sat on a three-legged stool (three legs) watching his fish (no legs) laying on a table that was supported by one leg in the center (one leg) when his cat (four legs) snatch the fish from where he lay.',NULL,0);
INSERT INTO comment VALUES (5805,542,2231,'Trevor Leitch','re: This works...','2003-06-16 12:40:57',0,'If the aim is to concoct a situation which vaguely matches the description, the sky (and one\'s imagination) is the limit.\r\n\r\nHere\'s mine: a snake is hitching a ride on a wading flamingo, while a trained circus bear is resting nearby on the back of an amputee tortoise; unbeknownst to all of them, a crawling baby is making the rounds stealing their food.\r\n\r\nI hope there\'s an actual question here that we\'re missing.',5804,0);
INSERT INTO comment VALUES (5806,901,2231,'Trevor Leitch','re(3): Country','2003-06-16 12:45:35',0,'My solution also requires that there are no 1 cent or 10 cent coins in circulation, eliminating the possibility that it\'s England.',5803,0);
INSERT INTO comment VALUES (5807,542,1626,'Gamer','re(2): This works...','2003-06-16 15:23:29',0,'Yes, but would that ever happen? I think the goal is to find the most likely event.',5805,0);
INSERT INTO comment VALUES (5808,901,2341,'Pickels','Maybe...','2003-06-16 16:05:34',1,'Maybe the country is the United States of America. For the first one, 13 cents, you need two nickels and three pennies, which is five coins. I\'m not sure about the other one.',NULL,0);
INSERT INTO comment VALUES (5809,542,2341,'Pickels','re(3): This works...','2003-06-16 16:24:58',1,'The answer will proably just be something similar to either of the first two answers, unless there is some hidden meaning in between the words. I can\'t find one though.',5807,0);
INSERT INTO comment VALUES (5810,845,2456,'joy','solution','2003-06-16 17:21:54',0,'22',NULL,0);
INSERT INTO comment VALUES (5811,201,2456,'joy','','2003-06-16 17:49:12',0,'ok i have a few problems with some of the comments posted.... first of all which north pole are we talking abou here- the magnetice north pole or the geographic north pole? Because that definitely makes a difference because the magnetic north pole which is true north actually moves.\r\nAlso i wouold like to point out that i noticed that all these comments seem to be well thought out mathmatically, but no one seems to use mathmatical convention. For instance numerous times you have used an irrational number in your answer. i belive the proper way of writing 1/sqrt2 would be sqrt2/2.\r\n',NULL,0);
INSERT INTO comment VALUES (5812,96,2456,'joy','solution','2003-06-16 17:57:41',0,'this one is easy... 4sqrt3\r\nit is all simple geometry, you dont even need trig\r\nconect the vertices to the center of the circle giving you 3 smaller iso triangles adn then draw an altitude to the center of the circle for one of them and you have a simple 30-60-90 right triangle which makes it quite easy to solve for the hypotenues which is also the radius.',NULL,0);
INSERT INTO comment VALUES (5813,901,153,'TomM','re: Maybe...','2003-06-16 18:12:58',0,'But you can make 13 cents with 3 pennies and a dime (1+1+1+10), which is only four coins. And 14 cents takes a minimum of 5 coins: 4 pennies and a dime (1+1+1+1+10).\r\n\r\n\r\n\r\n',5808,0);
INSERT INTO comment VALUES (5814,260,2456,'joy','solution','2003-06-16 18:24:31',0,'this one was no problem\r\ncalling the first small circle circle 1 with a diameter of AB, the 2nd small circle circle 2 with a diameter of BC, the 3rd small circle circle 3 with a diameter CD, the 4th small circle circle 4 with diameter DE and the large circle circle 5 with a diameter AE\r\nwe want to prove that- circumfrence1+circumfrence2+circumfrence3+ circumfrence4= circumfrence5\r\n\r\n1) AB+BC+CD+DE=AE - because the whole =\'s the sum of its parts\r\n\r\n2) Circumfrence1=piAB \r\n Circumfrence2=piBC \r\n Circumfrence3=piCD Circumfrence4=piDE \r\nCircumfrence5=piAE\r\nbecause the equation for the circumfrence of a circle is C=pi(d)\r\n\r\n3) pi(AB+BC+CD+DE)=piAE you can multiply both sides of the equation in step1 by any varible without changing the value of the equation\r\n\r\n4)piAB+piBC=piCD+piDE=piAE this is simple multiplying\r\n\r\n5)circumfrence1+circumfrence2+circumfrence3+ circumfrence4= circumference5\r\nthis is just simple substitution\r\n',NULL,0);
INSERT INTO comment VALUES (5815,901,153,'TomM','re(3): Country','2003-06-16 19:50:28',0,'England won\'t work because of the other small coins: 13 can be done in 4 coins in several ways: 1+1+1+10; 1+2+5+5 (it can even be done in three coins: 1+2+10.); 14 can be done in three coins: 2+2+10.\r\n\r\nNot only does the country need a \"2\" and a \"5\" coin, but they can be the only denominations under 15',5803,0);
INSERT INTO comment VALUES (5816,542,1183,'fwaff','Random thoughts','2003-06-16 23:14:16',1,'The title (leg bye) is a term used in cricket...\r\n\r\nTwo legs sat near on three legs - this could refer to one of the wickets (two bails resting on three stumps).\r\n\r\nFour legs got some - this could refer to the two batsmen getting some runs.\r\n\r\nNo legs lay on one leg - hmmm this has me stumped',NULL,0);
INSERT INTO comment VALUES (5817,542,872,'pleasance','solution','2003-06-17 02:44:54',0,'I think the sought after solution is something like Hank\'s answer. A man (two legs) is sitting on a stool (three legs), eating fish (no legs) on a table (one leg), and gives the leftovers to the dog or cat (four legs). \r\n\r\nThen again, Trevor\'s bears and flamingos are far more amusing.',NULL,0);
INSERT INTO comment VALUES (5818,542,158,'Ender','This is YAHR (Yet Another Hobbit Riddle)','2003-06-17 02:57:17',3,'The solution given in the book is what pleasance wrote, with the cat getting the bones.',NULL,0);
INSERT INTO comment VALUES (5819,543,1715,'Jonny Doe','How about ...?','2003-06-17 03:04:48',0,'Egg',NULL,0);
INSERT INTO comment VALUES (5820,914,1732,'Helen','Not always','2003-06-17 03:44:34',0,'This assumes that you find the object at all',NULL,0);
INSERT INTO comment VALUES (5821,542,1626,'Gamer','Hypenation?','2003-06-17 07:12:41',4,'Why are some \"legs\" words seperate words and some have them hypenated?',NULL,0);
INSERT INTO comment VALUES (5822,914,2460,'gabi','solution','2003-06-17 09:40:10',0,' You may not have looked for it in the last place . It was probably the first place that you looked . after a while you got frustrated . and the last place you looked (which you had already looked at) you found it!',NULL,0);
INSERT INTO comment VALUES (5823,903,1902,'Hank','sOLUTION','2003-06-17 10:15:27',3,'c,u,r,h,k,o\r\na,l,d,w,t,m\r\nv,f,p,g,z,i\r\ne,b,y,h,n,s\r\n\r\nMy logic: I made four columns. Wrote the word using one letter from each column:\r\n\r\nC A V E\r\n L F (because C, E are already used)\r\nU D P\r\nR\r\n B\r\n W G\r\nH Z Y\r\nK T I H\r\nO N\r\n M\r\n S\r\n\r\nit is a fix as you go method.',NULL,0);
INSERT INTO comment VALUES (5824,903,1715,'Jonny Doe','Correct Solution','2003-06-17 10:36:27',0,'Dice 1 - F G I P V Z\r\nDice 2 - C H J O R U\r\nDice 3 - A D L M T W\r\nDice 4 - B E K N S Y',NULL,0);
INSERT INTO comment VALUES (5825,903,2129,'Sanjay','re: sOLUTION','2003-06-17 10:41:05',0,'You have h appearing twice; in cube 1 and in cube 4. You have j not appearing at all, when the problem clearly specifies that j needs to be there, even though it does not form part of any of the clue words.',5823,0);
INSERT INTO comment VALUES (5826,903,2129,'Sanjay','Solution','2003-06-17 10:49:53',3,'B,E,K,N,S,Y\r\nA,D,L,M,T,W\r\nC,H,J,O,R,U\r\nF,G,I,P,V,Z',NULL,0);
INSERT INTO comment VALUES (5827,836,2129,'Sanjay','re:','2003-06-17 11:09:59',0,'Further to Lewis\'s comment (which I agree with), if the the first bidder can count on no further bids forthcoming on account of everyone knowing that a second bid will start a bidding war, then the first bidder is better off bidding $0.01 rather than $0.50. By the way, even assuming that no one else bids, how does the first bid of $0.50 \'make\' a $1.00?',5742,0);
INSERT INTO comment VALUES (5828,305,1919,'Lewis','answer','2003-06-17 11:23:23',3,'Ben owes one drink and is owed four.\r\nGlen owes two drinks and is owed one.\r\nRhen owes three drinks and is owed two.\r\nSven owes four drinks and is owed three.\r\n\r\nTherefore, everybody owes one more drink than they are owed, except Ben who is owed three, so Glen, Rhen and Sven each buy one drink which they give to Ben.',NULL,0);
INSERT INTO comment VALUES (5829,914,2129,'Sanjay','Looking, with tongue firmly in cheek.','2003-06-17 12:18:11',0,'I can understand why whenever Gamer is looking for something, it is always in the last place he looks for it, because after he finds it he stops looking for it. That seems logical to me. What I can\'t understand is why it is always in the last place he looks. Unless Gamer only ever looked for one thing and went blind after he found what he was looking for, and just could not look anymore. Or maybe, after he found what he was looking for, he got married and stopped looking altogether. But then, words like \'Whenever\' and \'always\', though perhaps technically corect, would be inappropriate. ',NULL,0);
INSERT INTO comment VALUES (5830,903,1626,'Gamer','re: Solution','2003-06-17 12:26:14',4,'How did you come upon these solutions? I am curious to see if there are ways other than my own.',5826,0);
INSERT INTO comment VALUES (5831,903,1575,'DJ','re(2): Solution','2003-06-17 16:38:09',0,'I agree...I just see lists of letters, and no solutions.',5830,0);
INSERT INTO comment VALUES (5832,543,1575,'DJ','..said Gollum','2003-06-17 16:49:12',0,'\"Eggses!\" he hissed. \"Eggses, it is!\"',NULL,0);
INSERT INTO comment VALUES (5833,903,1301,'Charlie','solution','2003-06-17 16:56:24',3,'V and Y appear on the same cubes as S and P (from VARY and RASP)\r\nK and H appear on the same cubes as R and E (from KITH and TIRE)\r\nH and Z appear on the same cubes as R and V (from HAZY and VARY)\r\nG and W appear on the same cubes as T and I (from GREW and TIRE)\r\nF and E appear on the same cubes as V and Y (from FARE and VARY)\r\n\r\nBut V and E can\'t appear on the same cube (from CAVE), so F and V share a cube while E and Y share a cube. Then, since Y can\'t share a cube with H (from HAZY), both E and Y must share a cube with K (see second line above) while R shares a cube with H. Then, as P can\'t appear on the same cube as E, and from the first line above, taking E, Y and K together, E, Y and K appear with S, while V shares a cube with P. And since E goes with Y, F must go along with V (and its attendant P), per the fifth line above\r\n\r\nSo far we have \r\nHR\r\nEYKS\r\nFVP\r\nAnd none of these can be combined as each has at least one letter in the same word as a letter in any of the other lines.\r\n\r\nFrom DUPE and POEM, O and M appear on the same cubes as D and U. But M and U can\'t share a cube (from SMUG) so M shares with D and O shares with U.\r\n\r\nFrom CLEF and FLUB, C and E appear on the same cubes as B and U, but E is already tied to Y, K and S, and O us already tied to U. Since, because of DUPE, E can\'t appear on the same cube as U, E (and Y, K and S) must be on the same cube as B, while C is tied to U (together with O).\r\n\r\nSo now we have \r\nBEYKS and\r\nCOU\r\n\r\nFrom FARE and CLEF, C (with its previously determined O and U) and L appear on the same two cubes as A and R (with its previously determined H). As C can\'t appear on the same cube as A (from CAVE), C, O and U share with R and H, while A shares with L.\r\n\r\nSo far we have\r\nCOURH\r\nBEYKS\r\nFVP\r\nMD\r\n\r\nA and L will fit only on one of the last two, but from CLEF, L can\'t share a cube with F, so the last line must be \r\nMDAL\r\n\r\nOne or the other of M and D share words with each of the other lines, so these are four separate cubes.\r\n\r\nA and L will fit only on one of the last two, but from CLEF, L can\'t share a cube with F, so the last line must be \r\nMDAL\r\n\r\nSMUG has all its letters accounted for except G, which must go on the cube with F, V and P.\r\n\r\nTIRE\'s R and E have already been placed. Its I can\'t go with L (from LOIN) and so must go with F, V and P, while T goes with M, D, A and L.\r\n\r\nSo far it\'s\r\nCOURH\r\nBEYKS\r\nFVPI\r\nMDALT\r\n\r\nSMUG can fit only by putting G with FVPI, and then GREW forces W with MDALT. The LOIN puts the N with BEYKS and HAZY puts the Z with FVPIG, leaving COURH as the only one with room to hold the J.\r\n\r\nSummary:\r\nCOURHJ\r\nBEYKSN\r\nFVPIGZ\r\nMDALTW\r\n',NULL,0);
INSERT INTO comment VALUES (5834,922,1575,'DJ','The Trick (Full Solution)','2003-06-17 17:24:10',3,'You can find the number with six guesses.\r\n\r\nLet us work backwards; given a certain number of guesses, determine the maximum range of numbers from which you can determine a single number.\r\n\r\nIf you have one guess, then you of course know what the answer is without having guessed at all. However, you will still require one guess to guess the correct answer.\r\n Since we only have cards with numbers 2,3,7 and 8, the probably of picking a \'perfect square\' is zero.',NULL,0);
INSERT INTO comment VALUES (5875,929,2129,'Sanjay','re(3): Solution','2003-06-19 10:50:35',0,'Aren\'t we forgetting the zero? Possible digits in the ones column of any number are 0-9. Therefore, the digit in the ones column of any perfect square will be the last digit in the squares of 0-9. 0*0=0 These happen to be 0,1,4,5,6 and 9.',5866,0);
INSERT INTO comment VALUES (5876,903,2482,'ann','solution','2003-06-19 11:02:39',0,'I am sorry, I put it in the comments section. My solution is: fvizpg ; altmdw ;rchouj ;eyknbs.Is this correct?',NULL,0);
INSERT INTO comment VALUES (5877,363,1919,'Lewis','Solution','2003-06-19 11:03:07',3,'For the first logician to know the word, his letter must have been either H, R, P, D, V, because each letter is only used once. From this, the other two logicians must have know that the word was either Hoe, Oar, Pad or Vat.\r\n\r\nFor the second logician to know the word, hemust have had and E, T or P/D (whichever the first didn\'t have). This means that the word was either HOE, PAD or VAT.\r\n\r\nOut of them, the third logician must have the middle letter of whatever the word is, because the first two logicians had the other two. Because he knew the word, this means that he must have had an O and the word was HOE.',NULL,0);
INSERT INTO comment VALUES (5878,921,158,'Ender','My thoughts','2003-06-19 11:05:23',0,'I would not take the bet. If he manages to drink it under the stated conditions, I\'m out 15 dollars (10 for the drink, 5 for the bet). But my guess is that he\'ll just remove the piece of glass and down the drink, playing me 5 dollars for my 10 dollar drink. ',NULL,0);
INSERT INTO comment VALUES (5879,903,1919,'Lewis','re: solution','2003-06-19 11:05:29',0,'Yes it is ann. :)',5876,0);
INSERT INTO comment VALUES (5880,921,1919,'Lewis','I Think....','2003-06-19 11:56:25',3,'...the important thing is that the wager is five dollars, but the drink is worth ten.\r\n\r\nI cannot see any way that the man could drink the, er.. drink without touching the glass, but he could just drink it normally and give you the five dollars. That means that he would have payed five dollars for a ten dollar drink, an obvious profit, so the bet should definitely not be taken.',NULL,0);
INSERT INTO comment VALUES (5881,488,2474,'riddler','Hard','2003-06-19 11:59:39',0,'This was hard. How were we supposed to figure this out?³<>≥∞±',NULL,0);
INSERT INTO comment VALUES (5882,921,1626,'Gamer','A different opinion','2003-06-19 12:08:41',0,'I finally figured this one out without looking at the solution! Like I had said in the queue, I think anything the shady guy does is considered trickery, so you will win the bet automatically.\r\n\r\nIn any case, I would take the bet. I would never want to drink any alcohol, for fear of being busted for drinking under 21. (Look at the first part, \"YOU are in a disreputable bar\") Since I must have been insane or otherwise influenced to order the drink, I would take the bet to get 5 dollars back.',5880,0);
INSERT INTO comment VALUES (5883,543,2474,'riddler','SO EASY','2003-06-19 12:17:42',1,'The answer is egg. Anyone who read the Hobbit would know this.∑π∞≥≤><³²√',NULL,0);
INSERT INTO comment VALUES (5884,861,2474,'riddler','This Riddle was easy','2003-06-19 12:20:08',0,'This is one of the easiest riddles in The Hobbit. It was fish.±',NULL,0);
INSERT INTO comment VALUES (5885,922,2474,'riddler','So hard','2003-06-19 12:21:28',0,'How are we supposed to figure this out? it\'s so hard√',NULL,0);
INSERT INTO comment VALUES (5886,533,2474,'riddler','Was this supposed to be easy?','2003-06-19 12:25:46',0,'this brainteaser was so hard≤≥',NULL,0);
INSERT INTO comment VALUES (5887,903,2129,'Sanjay','re(2): Solution (Method)','2003-06-19 14:16:57',0,'23 letters appear in clue words. J is stipulated. This eliminates Q & X. From FARE, we know that the three most frequent letters {E,R,A} must be on seperate cubes. Assign E to cube 1. Eliminate {A,C,D,F,G,I,L,M,O,P,R,T,U,V,W} since they all share a word with E, leaving 5 of {B,H,J,K,N,S,Y,Z} as contenders for cube 1. From HAZY, since A stands eliminated, 1 of {H,Y,Z} is a contender. Hence 4 of {B,J,K,N,S} are contenders. Assign R to cube 2. Eliminate {A,F,G,I,P,S,T,V,W,Y}, leaving 5 of {B,C,D,H,J,K,L,M,N,O,U,Z} as contenders for cube 2. From FLUB, since F stands eliminated, 1 of {B,L,U} is a contender; from HAZY, since {A,Y} stand eliminated, 1 of {H,Z} is a contender; from POEM, since {P,E} stand eliminated, 1 of {O,M} is a contender. Hence 2 of {C,D,J,K,N} are contenders. Assign A to cube 3. Eliminate {C,F,H,P,S,V,Y,Z}, leaving 5 of {B,D,G,I,J,K,L,M,N,O,T,U,W} as contenders for cube 3. From FLUB, GREW, LOIN and POEM we get 1 each of {B,U},{G,W},{I,K} and {M.O} as contenders, leaving 1 of {D,J,N} as contender. Finally, {F,P,V} occupy cube 4, the only cube left for them to occupy, eliminating {B,C,D,L,M,O,S,U,Y) and leaving 3 of {G,H,I,J,K,N,T,W,Z} as contenders for cube 4. From GREW and KITH we get 1 each from (G,W} and {H,I,K,T} as contenders, leaving 1 of (J,N,Z} as contender. Here on, through an iteration of letters occupying the only cube left to occupy, in turn eliminating other letters from certain cubes, in turn those letters occupying the only cube left to occupy and so on, all other letters fall into place. ',5830,0);
INSERT INTO comment VALUES (5888,929,1626,'Gamer','re(4): Solution','2003-06-19 15:35:49',0,'Yes. you have a point there, but still, there isn\'t a 0 card in the deck so it doesn\'t matter :) Good observation!',5875,0);
INSERT INTO comment VALUES (5889,922,1575,'DJ','re: Is this right?','2003-06-19 16:53:58',1,'Even if you know the number after 6 guesses with a binary system, you \"trying to guess [Jon\'s] favorite number,\" as stated in the introduction. Therefore, it will take an extra guess, and the fewest number you can do it in is seven.\r\n\r\nThe problem states, \"You can guess anything you like and I will tell you whether my number is higher or lower then (sic) your guess.\"\r\nRegarding the range, let\'s use the example you suggested. I guess that the number is between 82 and 90. Jon does not then have to say, \"That\'s it!\" Similarly, he will not say \"Both,\" as the number is neither higher nor lower than my guess (not both). I am guessing a range, not two values.\r\n\r\nRather, he will say if it is higher or lower, or if the number is indeed in that range, he will either say nothing or say that the number is not higher or lower than my guess.\r\n\r\nThus, I think that it will work as I described, and you can find (and guess) the number with six guesses.\r\n\r\nA final minor point, I don\'t think that every problem in which the solution is not obvious is required to be categorized under \'Tricks.\"',5868,0);
INSERT INTO comment VALUES (5890,921,2184,'mark hartman','Drinking bet','2003-06-19 18:07:10',0,'I wouldn\'t take the bet; for if I do, the slinky guy merely removes the flat piece of glass and drinks my drink, and then pays me off $5 for losing the bet. He gains a ten dollar drink, for which he only pays five.',NULL,0);
INSERT INTO comment VALUES (5891,929,2184,'mark hartman','squares?','2003-06-19 18:13:59',0,'Probability is zero. No squares end in the digits 2,3,7, or 8.',NULL,0);
INSERT INTO comment VALUES (5892,921,2485,'lucidogg','i\'d say','2003-06-19 18:16:30',3,'i would take the bet. as soon as he touches the glass, he has lost and you can take your drink and the 5 dollars. as long as you don\'t stand there and let him drink away, you come out alright that way.',NULL,0);
INSERT INTO comment VALUES (5893,254,2184,'mark hartman','bumpy ride?','2003-06-19 18:21:19',0,'The curve described by the surface would bea series of arches, the length of each arch coincides with one side of the square. The corners of the square wheels would hit the surface at the bottom between each set of arches. I believe the name for this curve is a hypocycloid?',NULL,0);
INSERT INTO comment VALUES (5894,903,2456,'joy','','2003-06-19 19:07:15',0,'i thougth that this one was easy.... i just wrote out the alphebet 4 times and picked a word to start with and asigned one cube to each of the letters in that word and then just started crossing out letters that could eb eliminated and circling letters when they were only left on one cube and the answer fell into place quite nicely',NULL,0);
INSERT INTO comment VALUES (5895,900,2456,'joy','','2003-06-19 20:46:05',0,'this one is a great one. It took me a while. i like to use the elimination method. It takes a while, but it works eventually. I put all 16 letters in each square and just kept crossing out letters until they fell into place, not a whole of strategy, just alot of thinking :)',NULL,0);
INSERT INTO comment VALUES (5896,932,2436,'Chris','Let me think...','2003-06-20 03:58:44',0,'Electric trains do not blow smoke. Unless, of course, they are on fire...',NULL,0);
INSERT INTO comment VALUES (5897,543,2436,'Chris','delicious gold!','2003-06-20 04:15:58',0,'eggsies!',NULL,0);
INSERT INTO comment VALUES (5898,921,2436,'Chris','not likely','2003-06-20 04:21:19',0,'Avoid this bet. The particularly slinky character will end up paying 5 bucks for a ten dollar drink, and you will be out both five dollars and a good stiff drink.\r\nBetter yet, spend five of ten on a bottle of good rum, two of ten on some coca cola, and the remaining three of ten on DVDs, and get good and drunk in the privacy and security of your oun home!',NULL,0);
INSERT INTO comment VALUES (5899,542,2436,'Chris','re: copycat','2003-06-20 04:34:34',0,'Tolkien riddles rule. Especially when you tell them to those who haven\'t read The Hobbit...',5861,0);
INSERT INTO comment VALUES (5900,932,1686,'DuCk','Solution','2003-06-20 05:16:15',3,'Ah, this is an oldie. It saddens me to say that electric trains don\'t blow smoke. ;)',NULL,0);
INSERT INTO comment VALUES (5901,903,1919,'Lewis','re:','2003-06-20 08:17:02',4,'Well, what answer did you get? Were you actually correct?',5894,0);
INSERT INTO comment VALUES (5902,908,1301,'Charlie','re: Solution (After all that)','2003-06-20 08:55:20',0,'The problem with combining all pairs of ways of getting 50 cents is that some pairs add up to the same number of quarters, dimes and nickels as a completely different pair.\r\n\r\nFor example (0 q 0 d 10 n) combined with (0 q 5 d 0 n) gives 0 q 5 d 10 n, but so does (0 q 1 d 8 n) & (0 q 4 d 2 n), as well as (0 q 2 d 6 n) & (0 q 3 d 4 n). If this one way of changing a dollar (5 dimes and 10 nickels) could be counted three times under different arrangements, then it could be counted 3003 times for all its permutations (15!/(5!10!)). Counting all the permutations of all the ways would produce 27,517 arrangements.',5845,0);
INSERT INTO comment VALUES (5903,932,2489,'nellie','Old Smokie','2003-06-20 09:09:36',0,'No smoke without fire, but if smoke then it would go North at 31 km/h.',NULL,0);
INSERT INTO comment VALUES (6015,965,1575,'DJ','First Thoughts','2003-06-25 10:31:38',2,'I haven\'t finished solving this yet, but my first observation is that all the statements but one refer to who is first.\r\n\r\nCicero\'s second statement, \"Balthazar did not arrive second,\" must be true or false.\r\nIf it\'s false, then B is second, the other clues will determine who was first, and we know who was third by elimination.\r\n\r\nIf that statement is true, B can be first or third. If it means B is first, however, there are no other clues that will help us determine who is second or third in what order.\r\nTherefore, in order to be able to solve the problem, the truth of that statement must imply that B is third.\r\n\r\nEither way, I think that in order to have a concrete solution, B cannot be first, or we will not know which of the other two came earlier.',NULL,0);
INSERT INTO comment VALUES (5905,921,2490,'qw','solution','2003-06-20 09:20:37',0,'yes take it. when he touches the glass and attempts to drink it and you win the $5, you smack him right on the gr0in and grab it and then pull off his pants and lift up his shirt, then pour the drink in his gr0in and suck it.',NULL,0);
INSERT INTO comment VALUES (6780,577,2898,'dorkdork','Done !!','2003-07-29 11:13:21',0,'\"That, that is, is that that is not, is not. Is that it ? That is it.\" ',NULL,0);
INSERT INTO comment VALUES (6781,577,2898,'dorkdork','re: Done !!','2003-07-29 11:18:07',0,'\"That, that is, is. That, that is not, is not. Is that it ? That is it. ',6780,0);
INSERT INTO comment VALUES (5907,467,2490,'qw','B0N3R','2003-06-20 09:24:56',0,'BONER',NULL,0);
INSERT INTO comment VALUES (5908,865,2490,'qw','BON3R?','2003-06-20 09:29:10',0,'BONER?',NULL,0);
INSERT INTO comment VALUES (5909,743,2490,'qw','49.2929… %.','2003-06-20 09:31:48',0,'49.2929… %.',NULL,0);
INSERT INTO comment VALUES (5910,532,2490,'qw','belly button','2003-06-20 09:33:04',0,'belly button needed f0e s3hx',NULL,0);
INSERT INTO comment VALUES (5911,686,2490,'qw','murder of crows?','2003-06-20 09:34:38',0,'B0Ne',NULL,0);
INSERT INTO comment VALUES (5912,911,1626,'Gamer','Speedy idea','2003-06-20 09:52:36',1,'A few of the things I noted was every other term (for a while) has either a previous line with / \\ around it, or with a - after it.',NULL,0);
INSERT INTO comment VALUES (5913,911,1919,'Lewis','My guess','2003-06-20 10:25:11',1,'I think the next terms would be:\r\n//-\\\\--\r\n////-\\\\\\\\\r\n//-\\\\---\r\n/-\\/-\\/-\\/-\\\r\nIs this right??',NULL,0);
INSERT INTO comment VALUES (5914,366,1919,'Lewis','Solution','2003-06-20 10:33:58',3,'Two people\'s statements agree - A & B\' first statements and B & C\'s second statements.\r\nIf A\'s first statement is true, then B\'s first statement is also true, meaning B & C did not do it because of their second statements. That would also make C\'s first statement was true, so he did not do it because of his second statement, meaning D did it.\r\n\r\nIf A\'s first statement is false, then he did it, but that would mean that both of B\'s statements are false, so that\'s not possible.\r\n\r\nSo the robber is D and everybody\'s first statement is the true one.',NULL,0);
INSERT INTO comment VALUES (5915,932,2491,'grace','','2003-06-20 11:20:28',0,'electric trainz hav no smoke. lyke, dat wuz sho hard 2 figure out!',NULL,0);
INSERT INTO comment VALUES (5916,921,2341,'Pickels','re: solution','2003-06-20 17:59:44',0,'Ok...listen, whoever you are, qw, u are sick and perverted. No one would do that. Everyone here is trying to solve a puzzle, and you just start firing off sick remarks like that. Just leave.',5905,0);
INSERT INTO comment VALUES (5917,932,2341,'Pickels','We got it','2003-06-20 18:03:29',1,'Please, people, when one person has said the answer, don\'t repeat it 5 or 6 times. It is really annoying. The answer is obvious, even more so after someone said it. Copying him just makes you look stupid.',NULL,0);
INSERT INTO comment VALUES (5918,835,2494,'Gary Butler','I don\'t get it.','2003-06-20 20:07:46',0,'\"so that no two queens can attack each other?\"\r\n\r\nDoes this mean they can not attack on the first move? If they can move into possision there can be only 1 queen. What am I missing?',NULL,0);
INSERT INTO comment VALUES (5919,911,1919,'Lewis','Another thought','2003-06-20 22:20:17',1,'It looks to me that there are two separarte sequences in this - The odd terms being one sequence and the even terms being the other.',NULL,0);
INSERT INTO comment VALUES (5920,932,1919,'Lewis','re: We got it','2003-06-21 00:22:41',0,'People can post the answers whenever they want. Just because the answer is there doesn\'t mean they have to look at it and not work it out themselves. Anyway if its so annoying why not just don\'t take any notice of any comments saying \'solution\' or something?',5917,0);
INSERT INTO comment VALUES (5921,836,1919,'Lewis','If you know each other....','2003-06-21 00:27:14',1,'The problem doesn\'t say that you can\'t talk to people beforehand, so why not start a pretend bidding war with someone?\r\n\r\nYou could start bidding at 1 cent and each bid up 1 cent to something small like 10 cents. I\'m not sure whether the other people in the crowd would be logical enough to foresee the bidding war, but if they do bid you could just stop bidding and only lose 10 cents, but if you win you and your friend would get a profit of 81 cents between you.',NULL,0);
INSERT INTO comment VALUES (5922,689,1919,'Lewis','Simple Solution','2003-06-21 01:04:19',3,'The second die has 3 red and 3 blue faces.\r\n\r\nThis is because whatever colour the first die shows, there is a 50-50 chance that the second will show the same colour.',NULL,0);
INSERT INTO comment VALUES (5923,732,1919,'Lewis','re: Answer','2003-06-21 01:06:35',4,'Tim - why do you keep solving your own problems under a different alias?!',5479,0);
INSERT INTO comment VALUES (5924,823,1919,'Lewis','Solution','2003-06-21 02:03:55',3,'There are eight different possible outcomes :\r\n\r\nHHH\r\nHHT\r\nHTH\r\nHTT\r\nTTT\r\nTTH\r\nTHT\r\nTHH\r\n\r\n(H = heads, T = tails).\r\n\r\nOf thes eight, 3 contain exactly one head, so the probability is 3/8',NULL,0);
INSERT INTO comment VALUES (5925,865,2271,'mullen','hmmmm!!!!','2003-06-21 03:11:11',0,'well that\'s a head killer but i\'d have to say yes.....wait imean no........wait deffinatly yes......or is it no!',NULL,0);
INSERT INTO comment VALUES (5926,826,2271,'mullen','huh?','2003-06-21 03:15:31',0,'okay i\'m not a genius by any stretch but can i say HUH????????????? you lost me on Let\'s',NULL,0);
INSERT INTO comment VALUES (5927,513,2271,'mullen','well','2003-06-21 03:20:56',0,'no we can\'t say that because, ignoring what the words infer, the sentence does contain seven words, it could be corrected by saying \r\nNOW this sentence DEFFINATELY contains seven words.\r\neasy',NULL,0);
INSERT INTO comment VALUES (5928,27,2271,'mullen','i must agree to disagree','2003-06-21 03:28:59',0,'we as can eliminate the days one by one by saying this, but the only one which will be true could be that if it came to the end of thursday and the teacher hasn\'t given them an exam then they will expect one on friday, but when you eliminate thursday then wednesday as possible exam days you can re open friday and thursday and so on as the class will have discounted these as days and thus won\'t be expecting them',NULL,0);
INSERT INTO comment VALUES (5929,511,2271,'mullen','it depends','2003-06-21 03:36:52',0,'this paradox depends on the aim of making the stone that they can\'t lift the yes because they were powerfull enough to do it. ',NULL,0);
INSERT INTO comment VALUES (5930,932,2496,'anoop','re: Old Smokie','2003-06-21 05:37:56',0,'In case it has a smoke - for waht ever reason - , I think the speed would be 53.75 km/h and angle would 69.06 from south',5903,0);
INSERT INTO comment VALUES (5931,932,2489,'nellie','re(2): Old Smokie','2003-06-21 07:29:54',0,'Perhaps it\'s more difficult than I thought. I thought that once emitted the smoke would itself have no momentum, but simply become part of the air mass within the prevailing wind, going North at 31 km/h.\r\nThe smoke trail across the sky would however remain in a NW/SE line.\r\nThe smoke is more like a boat sitting in a cross tide rather than sailing against a tide.\r\nIf I\'m wrong please explain your thinking.\r\n',5930,0);
INSERT INTO comment VALUES (5932,924,1575,'DJ','A start','2003-06-21 08:05:20',2,'It might help to rewrite this as a set of equations, such as:\r\n* + % = $\r\n3$ = 2@ + 2% + *\r\n@ = ! + *\r\nThen, you just have to determine which of (4! + 2@) and (2$ + % + *) is larger.',NULL,0);
INSERT INTO comment VALUES (5933,911,1575,'DJ','Hint #1','2003-06-21 08:06:31',2,'Hint: Maybe it\'ll go easier if you replace - with 0, and the / and \\ with ( and ). If the hoober-goober cannot create such a stone, by definition it is not omnipotent. If, on the other hand, it cannot lift the stone, then again by definition it is not omnipotent. What this proves is that nothing can be literally omnipotent, because literal omnipotence conveys the ability to do things that cannot be done or, for that matter, the inability to do things that can be done. This is a question about the meaning of omnipotence, not the existence of God.\r\n',NULL,0);
INSERT INTO comment VALUES (5973,936,2129,'Sanjay','Balancing Act','2003-06-23 12:51:32',3,' (1) Exactly eight weights wil be required to balance the weight of the item. (2) These also happen to be the fewest number of weights that can be used to balance the weight of the item. This is so because it will always be possible to iteratively replace any pair of similar weights with a single higher weight till such time that not more than one of each weight remains. There\'s a more efficient method possible, but this involves being allowed to use both pans rather than only one pan to place the weights, and I\'m not sure if the problem permits it. You can balance the pans with the use of four weights by placing a 1024 lb weight on one pan and the item along with 16, 4, & 1 lb weights on the other pan. \r\n ',NULL,0);
INSERT INTO comment VALUES (5974,511,2528,'Sam','heh...','2003-06-23 14:52:13',0,'way to rip off george carlin man reeeeeeal original',NULL,0);
INSERT INTO comment VALUES (5975,672,2528,'Sam','somewhat of an answer','2003-06-23 15:00:18',3,'well you clearly stated that the shields cannot be DESTROYED, and so if the blacksmith who makes the swords cuts through one of the \"indestructible\" shields, it is not necessarily destroyed, but broken. yet being the skilled blacksmith that he is, he can mend his shield, but after being sliced and diced by the sword. therefore i predict the swordsmith will triumph.',NULL,0);
INSERT INTO comment VALUES (5976,936,2529,'Roger','Binary','2003-06-23 15:11:09',0,'(1)\r\nThe answer is easily solved by converting 1003 into a binary number. That number is:\r\n\r\n1111101011\r\n\r\nThere are 8 1\'s, corresponding to:\r\n512, 256, 128, 64, 32, 8, 2, 1. The answer is 8.\r\n\r\n(2)\r\nThis answer is only different from the answer to (1) when some of the eight weights can be \"combined\" to equal a new available weight. Since this is not possible, the answer is the same as (1): 8.',NULL,0);
INSERT INTO comment VALUES (5977,937,2528,'Sam','pfff','2003-06-23 15:17:59',0,'an ear',NULL,0);
INSERT INTO comment VALUES (5978,921,2528,'Sam','re: easy to solve','2003-06-23 15:20:11',0,'yes you do pay 10 bucks for your drink, but if you do happen to win the bet, your net loss would only be 5 bucks. then again, if you lose the bet, youre down $15.',5949,0);
INSERT INTO comment VALUES (5979,37,153,'TomM','re: but','2003-06-23 15:58:33',0,'That\'s not a \"scratch.\" That\'s stripping the entire board!',5953,0);
INSERT INTO comment VALUES (5980,924,1839,'Rajeev','solution','2003-06-23 21:39:11',0,'%$*$ > !@!!@!\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (5981,929,1839,'Rajeev','Zero','2003-06-23 21:44:07',0,'the number cannot be perfect square as no perfect square has 2, 3, 7, 8 as a last digit',NULL,0);
INSERT INTO comment VALUES (5982,936,1183,'fwaff','re: Balancing Act - outside the box','2003-06-23 21:44:42',3,'It\'s possible to go further than Sanjay\'s more efficient solution and balance the item with only one of the 2^n weights..... move the balance\'s fulcrum.\r\n\r\nFor simplicity if one takes the 2^0 (1lb) weight and constructs the balance such that the 2^0lb weight is 1003 times further from the fulcrum than the 1003lb item then the balance is errr... balanced. Clearly this principle works for any of the 2^n weights, provided the balance is constructed correctly.',5973,0);
INSERT INTO comment VALUES (5983,279,2536,'Peter','','2003-06-23 23:26:52',1,'Here\'s what I\'ve got;\r\n\r\n1= -2-0+0+3\r\n2= 2*(-2-0+0+3)\r\n3= 2*(-2-0+0+3)-2-0+0+3\r\n4= 2²*(-2-0+0+3)\r\n5= 2²*(-2-0+0+3)-2-0+0+3\r\n\r\nJust to check: can this do??\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (5984,937,1253,'brianjn','Mmm! Up tempo!','2003-06-24 01:47:17',0,'Yes, we have the ear being referenced, but .. we have more!\r\n\r\nThere are five components, if that be the right choice of word, here of:\r\n\"The Middle ear.\" ',NULL,0);
INSERT INTO comment VALUES (5985,96,2436,'Chris','Law of signs','2003-06-24 02:10:04',3,'Basicly, I used the law of signs:\r\n(sin 120/6 cm) = (sin 30/x) => x=(6 sin 30/sin120)\r\nx is aproximatly 3.46 cm, and just so happens to be the radius. d = 2r => d = 2(3.46 cm), about 6.92 cm.',NULL,0);
INSERT INTO comment VALUES (5986,936,1567,'Bryan','re(2): Balancing Act - outside the box','2003-06-24 04:41:50',3,'fwaff\'s solution gives the least number of weights needed if the balance is modified. If the balance is not modified, the answer is four. Place the 1024 lbs weight on the scale opposite the 1003-lbs item, and put 1, 4, and 16 lbs on the same side as the item. Presto! The weight of the item is balanced.',5982,0);
INSERT INTO comment VALUES (5987,911,158,'Ender','Solution','2003-06-24 04:46:17',3,'From hint 2 the pattern -, /-\\, //-\\\\, ///-\\\\\\ = 1, 2, 4, 8 became obvious, so I could see that it most likely used exponents. With hint 3 to confirm the bases, it fell into place.\r\n\r\nHow to read numbers:\r\nEach - is a column entry. The number of \"/\\\"\'s surrounding the dash is the value of the column (- is 0, /-\\ is 1, //-\\\\ is 2, etc)\r\nEach column is a prime, starting with the rightmost being 2, the lowest prime.\r\nThe entry in the column is the exponent for that prime (e.g, a 0 in the 2\'s column means 2^0 = 1).\r\nEach column is ultimately multiplied to get the result.\r\n\r\nThus the given sequence would be read:\r\n0: (2^0) = 1\r\n1: (2^1) = 2\r\n1,0: (3^1)*(2^0) = 3\r\n2: (2^2) = 4\r\n1,0,0: (5^1)*(3^0)*(2^0) = 5\r\n1,1: (3^1)*(2^1) = 6\r\n1,0,0,0: (7^1)*(5^0)*(3^0)*(2^0) = 7\r\n3: (2^3) = 8\r\n2,0: (3^2)*(2^0) = 9\r\n1,0,1: (5^1)*(3^0)*(2^1) = 10\r\n\r\nSo the next few terms are:\r\n/-\\----\r\n/-\\//-\\\\\r\n/-\\-----\r\n/-\\--/-\\\r\n/-\\/-\\-\r\n////-\\\\\\\\\r\n',NULL,0);
INSERT INTO comment VALUES (5988,957,1626,'Gamer','My notes','2003-06-24 09:35:37',2,'I haven\'t found a solution that isn\'t more than a little over 1/3... The only solution I found was a 4/4 grid.\r\n\r\nKLLK\r\nLLKL\r\nLKLL\r\nKLLK\r\n\r\nThe two rules to remember when creating where liars and knights could be (in order to fulfil the \"Opposite\" condition) are:\r\n\r\nKnights must be around all liars\r\nLiars must be not be around all knights\r\n\r\nOne possible solution for an \"at least 1/3 must be knights\" would be to take any sized grid (not divisible by 3) and repeat KLLKLLKLL so on going across first then down. (to do divisible by 3, just repeat when starting a new row)\r\n\r\nI don\'t know how to \"improve\" this to 37% though',NULL,0);
INSERT INTO comment VALUES (5989,306,1626,'Gamer','re(2): perplexed','2003-06-24 09:38:31',0,'I think the last paragraph would be better phrased \"Many don\'t believe that\", but I still think it maes sense in this problem.',3210,0);
INSERT INTO comment VALUES (5990,911,1567,'Bryan','re: Solution','2003-06-24 10:06:52',0,'Ender, even after reading your solution, it took me a few minutes to noodle it out. Very well done!',5987,0);
INSERT INTO comment VALUES (5991,957,1575,'DJ','First Glance','2003-06-24 10:49:45',1,'A first look at the setup of the problem, with each person in rows and columns forming a perfect square, would indicate that, for two people A and B, if A is next to B, B is next to A.\r\nSuppose A is a knight. For him to say that B is of the opposite persuasion (a liar), B must indeed be a liar since A always tells the truth.\r\nFor B to say that A is of the opposite persuasion (a knight), however, A must be a liar, so that B will untruthfully say that he is a knight.\r\nFrom this, it seems to be impossible, since each knight must be surrounded by all liars, and each liar must be surrounded by all liars, therefore there can be no knights in the arrangement.\r\n\r\nThat was my first impression.\r\n\r\nSince the problem states, however, that each person will say that all adjacent persons are of the opposite persuasion, then a liar surrounded by, say, all knights and one liar, or anything but all knights, will be able to say that he is surrounded by knights and still be lying.\r\n\r\nTherefore, any arrangement in which no two knights are next to each other, and each liar is next to at least one other liar, will work.\r\n\r\nSince we need at least 100 people, the smallest could be 10x10. Of these 100 people, at least 37 must be knights.\r\n\r\nI would guess that knights should be placed on every third diagonal, so as to fit as many as possible with none adjacent to each other. There are two distinct ways to do this:\r\n o o o o o The problem quickly becomes one of getting other checkers to level 2, then sideways so they get under the checker advanced to level 3. And the higher we go, the further sideways they have to go. If I saw how to get to level 4, I suspect I could determine how to get beyond it, or if it is impossible.',5996,0);
INSERT INTO comment VALUES (6002,957,1567,'Bryan','re: Solution?','2003-06-24 16:15:43',0,'You are definitely on the right track, but the answer is less than 98.',5995,0);
INSERT INTO comment VALUES (6003,936,1183,'fwaff','re(3): Balancing Act - outside the box','2003-06-24 22:16:56',3,'I think that the wording of the question is suitably vague such that any of the three answers given so far are correct for a given interpretation....\r\n\r\nIf any type of balance can be used then the answer is one. I used to work in a butchers where the balance used was of a type where the balance weight slid along the balance lever which effectively moves the fulcrum and the weight was read from the balance lever depending on the equilibrium position.\r\n\r\nIf one assumes a traditional pan balance and are allowed to put weights in either pan then the answer is four.\r\n\r\nIf one assumes a traditional pan balance and interprets \'balance the weight\' to mean exactly balance the weight, no more, no less, then the answer is eight.\r\n\r\nI\'m curious to see which interpretation luvya had in mind when composing the problem.',5986,0);
INSERT INTO comment VALUES (6004,958,1183,'fwaff','A solution + challenge for Charlie','2003-06-25 02:04:11',3,'One set of missing letters gives Reese Witherspoon.\r\n\r\nI\'m sure Charlie can write a program to come up with some alternatives.',NULL,0);
INSERT INTO comment VALUES (6005,911,1626,'Gamer','re(2): Solution','2003-06-25 02:18:06',0,'Seems so easy now! :)',5990,0);
INSERT INTO comment VALUES (6006,958,2129,'Sanjay','Solution','2003-06-25 03:11:35',3,'STRAY SEWER The number of moves will at most be one less than the number of checkers in the starting set-up, since each move eliminates one checker and at least one checker has to survive in the end. Since the arrangement needed for level 4 has 20 checkers, one will need 19 moves to reach level 4.',6029,0);
INSERT INTO comment VALUES (6071,958,2569,'yaman','solution','2003-06-27 10:37:16',0,'reese witherspoon---COME ON',NULL,0);
INSERT INTO comment VALUES (6072,912,1567,'Bryan','Impossible?','2003-06-27 11:39:56',4,'I still don\'t see how to get to level 4, let alone level 5. In order to go higher, more and more checkers are needed, and since they may only be placed on the first two rows, they stretch out over a wide area. The checkers on the edges ultimately need to jump toward the middle so they can meet and work together towards reaching higher levels. But whenever I set up lots of checkers and start jumping, the resulting checkers end up with an empty space between them, i.e. they can\'t jump each other. If anyone can shed some light on this problem, I would appreciate it. Right now this puzzle seems impossible as stated.',NULL,0);
INSERT INTO comment VALUES (6073,916,1626,'Gamer','Solution','2003-06-28 05:01:27',3,'I think this solution is right:\r\n\r\nABCHTU\r\nDEKLQY\r\nFGIMNW\r\nOPRSVZ',NULL,0);
INSERT INTO comment VALUES (6074,554,1626,'Gamer','The easy way','2003-06-28 06:35:06',0,'I like the 101000 repeating sequnece... I think that could be argued as the right answer.',6065,0);
INSERT INTO comment VALUES (6075,85,1919,'Lewis','Solution','2003-06-28 22:39:22',3,'Obviously, from the problem each man cannot have the color tie of his name.\r\n\r\nThe man with a green tie replies to Mr Yellow, so Mr Yellow must have the brown tie.\r\n\r\nThis leaves Mr. Green with the yellow tie and Mr Brown with the green tie.',NULL,0);
INSERT INTO comment VALUES (6076,958,2581,'becca','Legally Blonde!','2003-06-28 23:23:19',3,'STRAY\r\nCHEAT\r\nQUEEN\r\nMESSY\r\nSTEAM\r\n\r\nSEWER\r\nSPINE\r\nTOTEM\r\nASHES\r\nSPEED\r\nHURRY\r\nJESUS\r\nZIPPY\r\nSCOLD\r\nGOODS\r\nFUNNY\r\n\r\nThus. . .Reese Witherspoon\r\n',NULL,0);
INSERT INTO comment VALUES (6077,929,2581,'becca','can\'t be. . .','2003-06-28 23:31:35',0,'it says that if you take four cards off the top. therefore it has to be a four digit number and not the squares between 0 and 100. so i really don\'t see how 0 is the solution.',NULL,0);
INSERT INTO comment VALUES (6078,554,2581,'becca','solution','2003-06-28 23:58:58',0,'i have no idea if it\'s right, but here\'s what i think. . .\r\n\r\nsince it\'s asking for the next 5 digits, i tried breaking it up into 5 digit parts with the second number becoming the first of the next number. thus, you get:\r\n10101-01010-10100-01000-10001-00010-00101-01010-10100-01000-10001-00010-00101-01010-10100-01000\r\n\r\nso i think the next sequence is 10001. . .i could be wrong, but you never know.',NULL,0);
INSERT INTO comment VALUES (6079,929,2129,'Sanjay','re: can\'t be. . .','2003-06-29 02:31:41',0,'Of course, if you take four cards off the top it has to yield a four digit number. The question however is, what is the probablilty of this four digit number being a perfect square. And the answer to that question is zero. I have no idea what you are refering to when you say \'...and not the squares between 0 and 100\' ',6077,0);
INSERT INTO comment VALUES (6080,946,1626,'Gamer','Common solution','2003-06-29 03:27:23',3,'Most solutions are variations on this theme:\r\n\r\nPick up one of the papers and tear it up in anger. Then apologize and note that it must have been \"LIFE\" because the one that says \"DEATH\" is left.',NULL,0);
INSERT INTO comment VALUES (6081,916,1301,'Charlie','re: Solution','2003-06-29 03:58:43',0,'I agree with Gamer\'s answer. It\'s rather difficult to reconstruct in a posting the scribblings on paper that lead to the conclusion, but one starts by noting that I and P are on the same two cubes as O and G (from CLIP and CLOG), and various other such pairs of letters from pairs of words. This includes such things as M and R being on the same two cubes as F and Z (from FAZE and MARE). Then when FURL shows that F and R can\'t be on the same cube F must share a cube with M and Z with R. You then have the beginnings of the four separate cubes:\r\nFM...\r\nRZ...\r\nU...\r\nL...\r\n(based on the word FURL).\r\n\r\nOnce letters are tied to others, their individual prohibitions and ties apply to each other, similarly to the original Letter Cubes\r\n',6073,0);
INSERT INTO comment VALUES (6082,946,2129,'Sanjay','re: Common solution','2003-06-29 07:25:53',0,'...better still, eat the paper. Otherwise they can put the torn pieces back together to determine what you picked. Then again, since this is a country of strange laws and since they seem to be so determined to kill you, they\'ll probably throw a law at you that says that eating or tearing the paper invites automatic execution by a firing squad.',6080,0);
INSERT INTO comment VALUES (6083,946,1626,'Gamer','re(2): Common solution','2003-06-29 07:52:45',0,'That is a good idea, but they probably put some sort of poison on the paper (besides, who knows where it\'s been), so I choose tearing up the paper... ;D',6082,0);
INSERT INTO comment VALUES (6084,946,2571,'Rob','re(3): Common solution','2003-06-29 20:10:24',1,'I don\'t think anyone would poison paper for just that emergency. Just to be safe though, you should probably try and throw it out a window, or burn it with the match book you cleverly had in your shoe.',6083,0);
INSERT INTO comment VALUES (6085,918,2075,'Matt','','2003-06-30 02:20:42',0,'70',NULL,0);
INSERT INTO comment VALUES (6086,918,1626,'Gamer','Difficulty change','2003-06-30 02:47:45',3,'I think this got off the queue without its difficulty changed. I think it should be 2/5.\r\n\r\nThe way I prove how to get the number of squares in a board is like this:\r\n\r\nFor a 24x24 square on a 24x24 board, there is 1 bottom right square such that this will work.\r\n\r\nFor a 23x23 square on a 24x24 board, there are 4 bottom right squares on the 24x24 board that could be the bottom right square of the 23x23, without the top and left edges of the 23x23 square running off the board.\r\n\r\nThis would continue on, so the number of squares on a n-by-n board is the sum of n² down to 1².\r\n\r\nThe sum of 24² down to 1² is 4900, and the square root of this is 70, so 70 is the answer.',NULL,0);
INSERT INTO comment VALUES (6087,918,1301,'Charlie','solution','2003-06-30 03:20:17',3,'There can be squares that start at the full size of the 24x24 board, 23x23, 22x22, etc. down to 1x1. There\'s only one 24x24 square--that\'s the whole thing. With a 23x23 square, the upper left corner can be placed at any of 2x2 intersections (including the top left of the original board). A 22x22 square can be placed in 3x3 positions, etc.\r\n\r\nThese add up as shown in the following table:\r\n Seriously, the words \"runshine\" and \"mathways\" lead me to believe this is a verse where every word has had one letter altered, resulting in the verse we see in this puzzle (and these two words would of course be \"sunshine\" and \"pathways\"). Perhaps if I stick with it I can make sense of the verse this way, but after ten minutes I can\'t even figure out the title!',NULL,0);
INSERT INTO comment VALUES (6142,511,2592,'ben young','Numbers 23:19','2003-07-02 05:30:17',0,'I\'m REALLY coming in late, but hopefully I will be heard anyhow.\r\n\r\nAlthough I believe that God is omnipotent, I also believe that there are certain things that He cannot do. In Numbers, it basically says that God is incapable of lying, or in other words, incapable of contradicting Himself. \r\n\r\nThe primary thing to consider is that God preordained everything from the beginning. He had an intricate plan, far too complex for us to fathom, before He ever said, \"Let there be...\". And since God is incapable of contradicting His own words and His own plan, He cannot (and will not) create a stone that He cannot lift. If it isn\'t part of His predetermined design, then He is not able to do it, because then He would contradict Himself, which is fundamentally impossible. Let us not forget that we are referring to the same person who \"created\" time and space. Talk about blowing your mind!',NULL,0);
INSERT INTO comment VALUES (6143,483,1626,'Gamer','re(3): One-line Simple Solution','2003-07-02 06:04:44',0,'You can submit it as well... Is it on its way now?',4873,0);
INSERT INTO comment VALUES (6144,971,103,'friedlinguini','re(2): Solution','2003-07-02 06:24:48',0,'It\'s because I messed up in the fourth term of each of the factors. I also switched the comparison operators. The corrected (again!) result is:\r\n\r\nreturn (By*Cx - Ay*Cx + Ax*Cy - Bx*Cy + Ay*Bx - Ax*By) *\r\n (By*Dx - Ay*Dx + Ax*Dy - Bx*Dy + Ay*Bx - Ax*By) <= 0\r\n && (Dy*Ax - Cy*Ax + Cx*Ay - Dx*Ay + Cy*Dx - Cx*Dy) *\r\n (Dy*Bx - Cy*Bx + Cx*By - Dx*By + Cy*Dx - Cx*Dy) <= 0; \r\n\r\nThis gives the expected result.',6140,0);
INSERT INTO comment VALUES (6145,973,1072,'Alan','Yes gamer','2003-07-02 06:26:49',0,'Yes Gamer I guess you are right. There was one answer I was hoping everyone would see but instead everyone managed to come up with other answers as well.',NULL,0);
INSERT INTO comment VALUES (6146,974,122,'Happy','Sled Shiver Sally','2003-07-02 06:54:13',3,'The answer is C. The title pretty much gives it away.\r\n\r\nHere are the lyrics to \"Red River Valley\":\r\n\r\nFrom this valley they say you are going\r\nWe will miss your bright eyes and sweet smile\r\nFor they say you are taking the sunshine\r\nThat has brightened our path for a while\r\n',NULL,0);
INSERT INTO comment VALUES (6147,974,1626,'Gamer','re: Sled Shiver Sally','2003-07-02 07:23:13',2,':) Yes, it is a rhyming... I hope all of you liked it! :)\r\n\r\nI had a problem rhyming sunshine and pathways... (I had heard \"pathways\" instead of \"path for\" when I wrote this)\r\n\r\nI hope the title didn\'t make it too obvious!',6146,0);
INSERT INTO comment VALUES (6148,969,2592,'ben young','The freaks come out at knight','2003-07-02 07:45:03',0,'D and E are your bank robbers.\r\n\r\nThis is a good puzzle.',NULL,0);
INSERT INTO comment VALUES (6149,971,2592,'ben young','fairly easy','2003-07-02 07:59:24',0,'I would calculate the slope of each line using the coordinates. If the slopes of the two lines are equal, then they are parallel. If not, then they intersect.',NULL,0);
INSERT INTO comment VALUES (6150,946,2599,'amy','avoiding death','2003-07-02 08:04:48',0,'tell them about a strange law that they just made up..the law about not being able to die because its a strange law..in a foreign country..they wouldnt know..:D',NULL,0);
INSERT INTO comment VALUES (6151,971,1301,'Charlie','re: fairly easy','2003-07-02 08:24:21',0,'Even if they are not parallel, since they are segments rather than full lines, either might end before reaching the point of intersection of the whole line.',6149,0);
INSERT INTO comment VALUES (6152,969,2599,'amy','i think','2003-07-02 08:25:14',0,'i think its bill and eddy :p',NULL,0);
INSERT INTO comment VALUES (6153,946,2129,'Sanjay','re: My Solution','2003-07-02 08:39:38',0,'If you ask them to pick and they tear up, burn, or eat the paper that they pick, you\'re dead.',6118,0);
INSERT INTO comment VALUES (6154,986,103,'friedlinguini','Cheesy solution','2003-07-02 08:47:59',0,'The C++ standard library strikes again!\r\n\r\nvoid shuffle(std::string& input)\r\n{\r\n std::next_permutation(input.begin(), input.end());\r\n}',NULL,0);
INSERT INTO comment VALUES (6155,946,2129,'Sanjay','re(2): Common solution','2003-07-02 09:08:41',0,'That\'s an excellent question. You should try and take a quick peek at what\'s written on the paper before deciding whether to keep it or to get rid of it. If it says LIFE, then keep it and show it to the authorities. If it says DEATH, then get rid of it and go, \'oops\'. If the guy was truthful and both papers say DEATH, then you are saved. If the probability of his telling the truth or telling a lie is 50:50; if the probability of his telling a lie and writing LIFE on both paper and the probability of his telling a lie and not switching any paper is 50:50; if the probability of your picking \'this\' paper or \'that\' is 50:50, then you will be saved 7 out of 8 times (or 87.5% of the times) following this strategy. I wonder if there is a strategy that delivers a 100% success rate. ',6117,0);
INSERT INTO comment VALUES (6156,554,2601,'Kevin Steele','I Think I Got It','2003-07-02 11:15:02',0,'I believe the next 5 digits are 10101. This makes the sequence symetric. Print it out, look at it in a mirror, and the sequence will be the same.',NULL,0);
INSERT INTO comment VALUES (6157,971,1171,'nikki','No Code, just theory','2003-07-02 13:41:53',0,'\r\nI don\'t have any code or anything, but the basic idea is this:\r\n\r\nUsing the points given, find the Slope of each line - call them mAB and mCD. You\'d need a check to see if |mAB| = |mCD| but that\'s a trivial case.\r\n\r\nNext using the points given, and the all-purpose Line Equation y = m*x + b, find bAB and bCD.\r\n\r\nFor the moment, treat the two segments as lines and find the X coordinate of the \"intersection point\". This is easily done by substituting for y and solving for x: x\' = (bAB - bCD)/(mCD - mAB)\r\n\r\nNext you have to check to see if this intersection point exists on BOTH segments. This is easily done by checking to see if Ax <= x\' <= Bx, and Cx <= x\' <= Dx (note: those <= signs could be >= signs if Ax>=Bx or Cx>=Dx but you can easily check which cases you are dealing with first)\r\n\r\nUsing x\' solve for y\' and repeat the segment-check with Ay, By, Cy and Dy.\r\n\r\nAt first I thought the x\' check was all that was needed, but then I considered a vertical segment and another segment that passes over it such that if you only extended the vertical segment there would be an intersection. In this case x\' = Ax = Bx, and would satisfy Cx <= x\' <= Dx, so you would come to a false conclusion. That\'s why you need to check y\' too.\r\n\r\nIf the format of my answer isn\'t \"valid\" for the Algorithms section, I apologize and please let me know so I don\'t do it again.\r\n\r\nLater!',NULL,0);
INSERT INTO comment VALUES (6158,946,2603,'Esem','Oh, Its not that hard!','2003-07-02 14:29:16',0,'The person only has to pick up a paper, read it and swallow it! The authorities will check the other paper out, and it will have \"DEATH\" written on it so it will be \"obvious\" that the paper the person swallowed had \"LIFE\" on it. PERSON SAVED!!',NULL,0);
INSERT INTO comment VALUES (6159,946,2599,'amy','re: Oh, Its not that hard!','2003-07-02 16:16:10',0,'lol..i think thats a good idea',6158,0);
INSERT INTO comment VALUES (6160,971,1183,'fwaff','re: No Code, just theory','2003-07-02 23:20:57',1,'The dictionary definition of an algorithm is that it is a process or set of rules for performing a calculation. What you\'ve given is exactly that - ie a process for performing a calculation that gives the required solution. Just because it\'s less formal than some of the previous answers doesn\'t mean it\'s less valid.\r\n\r\nFor what it\'s worth, I used exactly the same method as you - to be honest I didn\'t even understand half of what Charlie and fried were describing!\r\n\r\nHappy floobling :-)',6157,0);
INSERT INTO comment VALUES (6161,975,1183,'fwaff','Close but no cigar','2003-07-03 02:18:40',1,'1/81 is equal to 0.0123456790123456790.... hmmmm now where did I leave those 8s??',NULL,0);
INSERT INTO comment VALUES (6162,975,1626,'Gamer','re: Close but no cigar','2003-07-03 02:53:51',0,'Good idea... If you add 10/denominator to the answer (numerator/denominator), it does equal 1/81.',6161,0);
INSERT INTO comment VALUES (6163,975,1301,'Charlie','solution','2003-07-03 02:57:15',3,'Any decimal fraction which begins repeating right after the decimal point is the repeated set of digits treated as an integer over an integer formed from as many 9\'s as are in the repetition period. So .01234567890123456789... is 123456789/9999999999 (that\'s 10 9\'s in the denominator as the period is 10). The two numbers have 9 as their highest common factor and so the fraction reduces to 13717421/1111111111, where the numerator and denominator are relatively prime.',NULL,0);
INSERT INTO comment VALUES (6164,975,1626,'Gamer','re: solution','2003-07-03 03:06:28',2,'Charlie is right :) And 13717421x81=1111111101, ten less than 1111111111.',6163,0);
INSERT INTO comment VALUES (6165,986,1626,'Gamer','Not really','2003-07-03 03:08:17',2,'No offense, but that\'s not an algrorithm, that\'s programming. If I said \"Create a permutarion\" as my answer (or some such thing), I would have to say what a permutation is.',NULL,0);
INSERT INTO comment VALUES (6166,971,1301,'Charlie','re: No Code, just theory','2003-07-03 03:15:44',0,'Indeed descriptions in English are just as valid as descriptions in computer language.\r\n\r\nHowever I find a problem with\r\n\"Using the points given, find the Slope of each line - call them mAB and mCD. You\'d need a check to see if |mAB| = |mCD| but that\'s a trivial case.\"\r\n\r\nI don\'t see the use of the absolute value indications. If one has slope 2 and the other has slope -2, it\'s the ordinary case of seeing where they intersect.\r\n\r\nAlso even if the slopes are themselves the same, the lines could be either parallel or the same line. If parallel they don\'t intersect. If they are the same line, you have to check if the endpoint of either is located between the two endpoints of the other. If so, there\'s an extended intersection (in the set theory definition of intersection, as they share not only 1 but many points).\r\n\r\nLikewise your solution considers one of the lines\' being vertical, but there is the possibility that both are vertical, with the same considerations as other lines with the same slope.\r\n\r\nYour solution, with the addition of the above, are basically what the code in Algebraic Solution did. And specifying it in English is fine.\r\n',6157,0);
INSERT INTO comment VALUES (6167,986,103,'friedlinguini','re: Not really','2003-07-03 05:15:31',0,'I know. I was just being silly again. I almost know an answer to this one, except that it requires that the characters start off being sorted. It could be shoehorned into place by storing the original string somewhere, but I don\'t think that\'s what Charlie had in mind.',6165,0);
INSERT INTO comment VALUES (6168,986,251,'Cheradenine','two ways','2003-07-03 05:54:01',3,'here\'s one subroutine in loose code\r\n\r\nlist perms(list[n])\r\n{\r\nstate int i = 0\r\n\r\nelement e = list[ (i/(n-1)!) % n ]\r\nlist remainder = list[n] - e\r\n\r\nif(remainder empty) {\r\ni = i + 1 \r\nreturn e\r\n}\r\nelse {\r\nreturn e + perms(remainder)\r\n}\r\n}\r\n\r\nofcourse a subroutine with state is an example of imperative programming trash. try for example Haskell:\r\n\r\nperms x = [ a:y | a <- x; y <- perms (x // [a]) ]\r\n\r\nfor something much neater',NULL,0);
INSERT INTO comment VALUES (6169,449,1626,'Gamer','The easy way','2003-07-03 05:56:27',3,'The way to think about this is the amount of money spent by the 2 rupee stamps and the 1 rupee stamps must be a multiple of 5 (so the rest of the money can be used for 5 rupee stamps).\r\n\r\nThen, the amount of money spent must be a multiple of 8 (2+(6x1))\r\n\r\nThe only mutliple of 5 and 8 under 75 is 40.\r\n\r\n40/8 is 5, so he got 5 2-rupee stamps, 6x5 or 30 1-rupee stamps and (75-40)/5 or 7 5-rupee stamps',NULL,0);
INSERT INTO comment VALUES (6170,986,103,'friedlinguini','re: two ways','2003-07-03 06:00:48',0,'Problem is that there is supposed to be one call per permutation. I also infer from the fact that the modified string is used as an input into the function that there is no state information stored anywhere other than in the string. I\'d asked Charlie for clarification on that while the problem was pending, but it never happened. :-(>',6168,0);
INSERT INTO comment VALUES (6171,986,251,'Cheradenine','re(2): two ways','2003-07-03 06:06:21',0,'the first code i posted does yield one permutation per call, the list return is composed of characters (or whatever..)\r\n\r\non the other hand i assumed the call was made with the same string each time.. hmm',6170,0);
INSERT INTO comment VALUES (6172,924,2376,'Jim C','*!$@# puzzle!','2003-07-03 07:05:50',3,'I LOVE tug-o-wars! They\'re so raw, yaknow. Oh! Anyway, here goes.\r\n\r\nIf we change everything to equations (with the plus sign understood), we get:\r\n$ = *%\r\n$$$=@@%%*\r\nso $$ = %@@\r\n@ = !*\r\n\r\nNow we need to get both sides in terms that can be compared.\r\n\r\n!!!!@@----%*$$\r\n\r\nThe right side is the same strength as $$$ \r\n($$+(%*)), and we can then substitute the $$$ equivalent on the right:\r\n\r\n!!!!@@----%%@@*\r\nwhich then can be simplified\r\n!!!!----%%*\r\n\r\nWell, this doesn\'t seem to be going anywhere. EXCEPT, maybe we can get something more workable if we visit the original examples.\r\n\r\n$$ = %@@, and $ = %*, so\r\n%%** = %@@\r\n%** = @@\r\n%** = !*!*\r\nand so % = !!\r\n\r\ngetting back to the \'pitted\' battle (I\'m thinking chocolate pudding in there, but that\'s a personal issue =0),\r\n\r\n(!!)(!!)----%%*\r\nsubstitute on the left\r\n%%----%%*\r\nAnd the weiner is: Team Righty!\r\nNote: I actually came up with the % = !! by stopping at our stopping point above, taking another approach, and ending up with \r\n!!!!!!----%%%*, but once I got there and saw the equivalency, I decided it was neater to prove it \"mathematically.\"\r\n',NULL,0);
INSERT INTO comment VALUES (6173,924,2376,'Jim C','re: solution','2003-07-03 07:33:42',1,'MAthematically, this works, but why must we assume that * and % are equal? Couldn\'t they be say, * = 70 and % = 30?\r\n\r\nIf so, then we can figure out that @ = 85 and ! = 15.\r\nIt still works, since 230 < 300, but number substitution isn\'t a valid proof, because we haven\'t demonstrated that our solution works for all number sets. In fact, your solution brings up an interesting point. If we continually make the % higher, we get closer and closer to equality. For instance, if % = 99, we get 299 , 300, and if we use 99.9 for % we get 299.9 < 300. This seems to indicate that as * approaches 0, (where % would then equal $ and @ = ! = $/2), the sides approach equality. You could argue that since someone on a side must have some mass or strength, and so a value can never reach zero, that this equality is an impossibility, and I would agree--except for maybe my daughter =-)',6025,0);
INSERT INTO comment VALUES (6174,924,2376,'Jim C','re: Yaman\'s solution','2003-07-03 07:35:14',0,'Wow! Nice job, Ya! That\'s the simplest I\'ve seen yet.',6052,0);
INSERT INTO comment VALUES (6175,986,1626,'Gamer','Hmmm','2003-07-03 08:36:38',2,'The last line gave me an idea. Instead of taking the letters out entirely, just switch them in turn. Swtich the last (n-1) letters until they form every permutation, then switch the letter that precedes the last (n-1) letters with the first one in the last (n-1) letters (designated by __ in the below example), then start over\r\n\r\nSo it would look like this:\r\n\r\nFor 1:\r\n\r\nA (You can\'t switch one letter, so A will always be A)\r\n\r\nA Back to beginning\r\n\r\nNote how once the 1-set is done (each time after the first one) the first letter switches with the second letter\r\n\r\nFor 2:\r\n\r\nAB- First 1 set\r\n\r\nBA_ Second 1-set\r\n\r\nAB_ Back to beginning\r\n\r\nThis 2-set is used in the 2+1 or 3-set. Again, after each 2-set is completed, the first letter switches with the second.\r\n\r\nABC- First 2-set\r\nACB- First 2-set\r\n\r\nCAB_ Second 2-set\r\nCBA- Second 2-set\r\n\r\nBCA_ Third 2-set\r\nBAC- Third 2-set\r\n\r\nABC_ Back to beginning (not printed)\r\n\r\nOn a 4 letter scale, that 3-set would be used 4 times. So it would be a recursive way to generate strings.\r\n',NULL,0);
INSERT INTO comment VALUES (6176,983,2572,'derek','solution','2003-07-03 09:09:58',3,'S\r\n\r\nfirst letter of each word in the question',NULL,0);
INSERT INTO comment VALUES (6177,986,1301,'Charlie','re(2): two ways','2003-07-03 09:13:19',0,'fl, you\'re correct--there\'s no state information stored anywhere except in the string; so multiple areas of a program could call the subroutine on their respective strings without interfering with each other.\r\n\r\nI had not seen any notes the first time I looked and saw the problem in the queue, and then the next time I looked it was posted, so I didn\'t see anyone\'s comments pre-posting.',6170,0);
INSERT INTO comment VALUES (6178,908,2572,'derek','re: Challenge','2003-07-03 10:24:19',1,'this may be purely coincidence, but:\r\n\r\n2 50c = $1\r\n4 25c = $1\r\n10 10c = $1\r\n20 5c = $1\r\n\r\n2 * 4 * 10 * 20 = 1600\r\nsqrt(1600) = 40\r\n\r\n',6028,0);
INSERT INTO comment VALUES (6179,986,103,'friedlinguini','Solution','2003-07-03 12:37:23',3,'I think it\'s easier to think of this problem in terms of numbers, rather than characters. It\'s really the same thing--you just think of every character as a digit in a base-(size of character set) number system.\r\n\r\nSuppose it wasn\'t permutations. Suppose you were given a 4-digit number, and told to walk through every 4-digit number until you came back to your starting point. Each iteration doesn\'t have to yield a permutation of the original number, and leading zeros are allowed. The most straightforward way would be to just keep adding 1 to the input until you reached the highest value, 9999, and then loop back to the smallest value, 0000, and keep going. This gives you every result.\r\n\r\nThink about how ordinary counting works. You start at the rightmost digit that you can increase (i.e., the rightmost digit that isn\'t 9) and you increase it by the smallest amount possible (add 1 to it). Then you set all the digits to the right of that digit to the smallest number available. In this case, it\'s all zeros. Everything to the left of the digit you increased is unaffected.\r\n\r\nThat\'s approximately the approach we\'ll look for in finding permutations. Find the rightmost digit that you can increase, and increase it by the smallest amount possible. Set the digits to the right of that digit to the smallest value possible. If we get to a number we can\'t increase, loop around and rearrange the digits to the smallest one possible.\r\n\r\nGiven an input number, start walking through its digits, starting from the right. In order for us to increase a digit without affecting the digits to its left, we\'ll have to find a digit A such that some digit to the right of it is larger than A. Note that all the digits to the right of A must be in descending order. Otherwise, our search would have stopped before we got to A. So really all you have to do is start at the rightmost digit and work your way to the left until the digit you\'re looking at is smaller than the one to the right of it. This is the digit you will be increasing.\r\n\r\nNext, we have to figure out what we\'ll be increasing it to. We want the smallest digit that is still larger than A. Again, the digits to the right of A are in descending order, so all we have to do is start searching from the right side of the number for a digit larger than A. The first one we find will be the one we want to use. We\'ll call it B. To increase the digit at A\'s position, swap A and B.\r\n\r\nRemember that all digits to the right of B\'s former position were smaller than A. Also, since B is larger than A, and all the digits that were between A and B were in descending order, all digits that were between A and B were larger than A. That means that after we swap A and B, A will be in a sequence of digits that is still in descending order. Specifically, all the digits after B will be in descending order after the swap.\r\n\r\nThe last step is to make all the digits to the right of B represent the smallest number possible. That means the most significant digit must be as small as possible, the one to the right of it must be the smallest digit of those remaining, and so on. In other words, those digits must be in ascending order. Since they are already in descending order, all we have to do is reverse the sequence.\r\n\r\nSubstitute characters for digits, and that pretty much does it. Here\'s the C++ code:\r\n\r\nvoid perm(std::string& val)\r\n{\r\n int aPos = val.size() - 2;\r\n\r\n while (aPos >= 0)\r\n {\r\n if (val[aPos] < val[aPos + 1])\r\n break;\r\n\r\n --aPos;\r\n }\r\n\r\n if (aPos < 0)\r\n {\r\n // characters are in descending order\r\n std::reverse(val.begin(), val.end());\r\n return;\r\n }\r\n\r\n int bPos = val.size() - 1;\r\n\r\n while (val[bPos] < val[aPos])\r\n --bPos;\r\n\r\n std::swap(val[aPos], val[bPos]);\r\n std::reverse(val.begin() + aPos + 1, val.end());\r\n}\r\n\r\n\r\n (1/4)x^2 = 196 ..>\r\n\r\n x^2 = 784 ..>\r\n\r\n x = 28 or x = -28 ',NULL,0);
INSERT INTO comment VALUES (6208,971,1301,'Charlie','re(3): Solution','2003-07-04 06:02:41',0,'When the fl solution is applied to points that are all colinear, each of the four parenthetical factors is zero, satisfying the equality portion of the <= and therefore reporting an intersection, even if the segments are on disjoint portions of the line they share.\r\n\r\nThis can be verified using 1,1,2,2,3,3,4,4 as Ax,Ay,Bx,By,Cx,Cy,Dx,Dy or 1,5,2,3,3,1,4,-1.',6144,0);
INSERT INTO comment VALUES (6209,987,1183,'fwaff','8-step solution','2003-07-04 07:20:43',3,'buzz\r\nfuzz\r\nfuze\r\nfaze\r\ndaze\r\ndare\r\ndore\r\nwore\r\nword',NULL,0);
INSERT INTO comment VALUES (6210,987,1183,'fwaff','D\'oh... 7 step solution','2003-07-04 07:27:09',3,'buzz\r\nfuzz\r\nfuze\r\nfaze\r\nfare\r\nfore\r\nwore\r\nword',NULL,0);
INSERT INTO comment VALUES (6211,987,1301,'Charlie','More solutions in that number','2003-07-04 08:03:58',3,'I\'d say the solution is 7. (So I don\'t put it in the header.)\r\n\r\nBut if the solution is the actual list of words, fwaff\'s list can be modified by replacing fore and wore with ware and ward, or just replacing fore with ware or wore with ford:\r\nAfter buzz come:\r\n\r\nfuzz\r\nfuze\r\nfaze\r\nfare\r\nfore\r\nford\r\nword\r\n-------\r\nfuzz\r\nfuze\r\nfaze\r\nfare\r\nware\r\nward\r\nword\r\n-------\r\nfuzz\r\nfuze\r\nfaze\r\nfare\r\nware\r\nwore\r\nword\r\n',NULL,0);
INSERT INTO comment VALUES (6212,66,2490,'qw','solution','2003-07-04 08:16:00',0,'Bill could just shave off his c0ck and eat it?',NULL,0);
INSERT INTO comment VALUES (6213,974,1919,'Lewis','re(2): Easy','2003-07-04 11:13:57',4,'Do you pronounce while with one syllable?',6203,0);
INSERT INTO comment VALUES (6214,968,2609,'mathemagician','Love those transcendentals!','2003-07-04 13:32:00',0,'Nice problem, especially the second part. I\'ve always liked working with the transcendental functions. \r\n\r\ne^iπ = cos π + isin π = = -1 ;\r\n\r\nHence, ln(-1) = ln(e^iπ) = iπ ;\r\n\r\nThus, f(-1) = ln(-1)/ SQRT(-1) = πi/ i = π',NULL,0);
INSERT INTO comment VALUES (6215,166,153,'TomM','An interesting e-mail','2003-07-04 14:41:56',0,'I recently recieved the following message in my e-mail:\r\n\r\n> Dear TomM,\r\n> \r\n> I was interrested in your solution to the problem of\r\n> the pyramid of balls. As it happens, I was recently\r\n> considering this issue and came up with the same\r\n> soution. However I suspect that there is possibly\r\n> another aspect to this worthy of consideration. If\r\n> we look at triangular numbers alone, i.e. the\r\n> solution to how many balls \"y\" would make up a\r\n> triangle of \"x\" sides then the equation is :\r\n> \r\n> \r\n> y = x * (x + 1)/2\r\n> \r\n> \r\n> If we extend this to the third dimension i.e. how\r\n> many balls make up a triangular pyramid of \"x\" sides\r\n> then the sulution is :\r\n> \r\n> y = x * (x + 1)/2 * (x + 2)/3\r\n> \r\n> (or as you note : x * (x + 1) * (x + 2)/6)\r\n> \r\n> One could be pedantic and suggest that the first\r\n> term in the equation (i.e. the intial x) is actually\r\n> (x + 0)/1giving a formula for the pyramid of :\r\n> \r\n> y = (x + 0)/1 * (x + 1)/2 * (x + 2)/3\r\n> \r\n> It is interresting therefore to speculate on a\r\n> general formula for the number of balls contained in\r\n> an \"n\" dimensional \"triangular-type object\"\r\n> (whatever that would look like) with the general\r\n> formula :\r\n> \r\n> y = (x + 0)/1 * (x + 1)/2 * (x + 2)/3 * ....... (x +\r\n> n - 1)/n\r\n> \r\n> Regards,\r\n> \r\n> Jim G.\r\n\r\nHere is my reply:\r\n\r\nAn interesting idea. It\'s hard to visualze four or more dimensions, so it\'s had to be sure, but it looks like the relationship holds. \r\n\r\nIf we call the function which gives the value y for n dimensions Tn(x), \r\nthen T1(x) = x = (x+0)/1!\r\nT2(x) = x(x+1)/2 = (x+0)(x+1)/2!\r\nT3(x) = x(x+1)(x+2)/6 = (x+0)(x+1)(x+2)/3!\r\n...\r\nTn(x) = x(x+1)(x+2)...(x+n-1)/n!\r\n\r\nIf we let X = x+n-1, the numerator becomes (X)(X-1)(X-2)...(X-n+1) = X!/(X-n)!\r\n\r\nSo Tn(x) = X!/(X-n)!(n!) = C(X,n) where C is the \"combinatorial\" operator more usually designated by placing the two arguments vertically between a set of parenthases(very hard to accurately type in an e-mail*)\r\n\r\nSo Tn(x) = C((x+n-1),n)\r\n\r\n*or in a message box',NULL,0);
INSERT INTO comment VALUES (6216,975,1626,'Gamer','re: Another Solution','2003-07-04 16:27:52',1,'That\'s a good proof of why the 99999 thing works imho... Good job! :)',6201,0);
INSERT INTO comment VALUES (6217,248,1919,'Lewis','Solution! Really!','2003-07-04 21:31:36',3,'Well, the problem states \'365 days a year\'.\r\nIf you have a leap year there will be 366 days that year, so it will have to close for one day, hence needing the locks.\r\n\r\nIf you say that a year is 365 1/4 days long, then it will still need to close for six hours a year.',NULL,0);
INSERT INTO comment VALUES (6218,974,1919,'Lewis','re: First guess (Title)','2003-07-04 23:10:41',1,'I think the title must be \'Red River Valley\' but I don\'t know how the song goes.',6141,0);
INSERT INTO comment VALUES (6219,987,2231,'Trevor Leitch','re: More solutions in that number','2003-07-04 23:27:17',0,'While it\'s at the discretion of DJ to confirm the suitability of any words, I would like to challenge the use of \"fuze\" in an answer. The word only appears in the OED as an archaic spelling of \"fuse\", and was last seen used in a trade journal in 1895. \r\n',6211,0);
INSERT INTO comment VALUES (6220,975,2609,'mathemagician','re(2): Another Solution','2003-07-04 23:41:16',0,'Thanks Gamer. This was a really cute problem. ',6216,0);
INSERT INTO comment VALUES (6221,919,2609,'mathemagician','','2003-07-05 01:13:39',0,'',NULL,0);
INSERT INTO comment VALUES (6222,919,2609,'mathemagician','Algebraic Solution','2003-07-05 01:34:59',3,'Here\'s the solution I meant to post previously.\r\n\r\nLet x = age of Son B ,\r\n\r\nthen 1.5 x = age of Son A .\r\n\r\nNow, Son B will be double his present age x years from now, at which time Son A will be 2.5 x years old.\r\n\r\nHence, the current age of Father B = 2(2.5 x) = 5x\r\n\r\nIt follows then that the age of Father A is :\r\n\r\n2( 5x - 1.5 x) = 7x \r\n\r\nIn summary, the current ages are:\r\n\r\nSon B = x\r\n\r\nSon A = 1.5 x\r\n\r\nFather B = 5x\r\n\r\nFather A = 7x\r\n\r\nSince all of the ages are multiples of five , then x must be a multiple of 10 ( i.e., x = 10, 20, 30, ...) . But, unless these fathers and sons lived during the time of Abraham and Noah, the only realistic solution occurs when x = 10.\r\n\r\nTherefore, the ages are as follows:\r\n\r\nSB = 10\r\n\r\nSA = 15\r\n\r\nFB = 50\r\n\r\nFA = 70',NULL,0);
INSERT INTO comment VALUES (6223,561,2231,'Trevor Leitch','Solution','2003-07-05 05:18:12',3,'In order to find out how much time the clock gains or loses, we need to find out how frequently the hands of a properly running clock meet.\r\n\r\nAssume that the hands are together at a given time. An hour later, the minute hand will be in the same position, and the hour hand will be 30 degrees ahead. Assume x minutes pass from that time, and define the functions m(x) and h(x) as the position of the minute and hour hand x minutes later, given as degrees from where the minute hand is at x=0:\r\n\r\nm(x) = 6x\r\nh(x) = 30 + (x/60)*30 = 30 + x/2\r\n\r\nWhen the hands meet, m(x) = h(x); thus, 6x = 30 + x/2, and x=60/11 (i.e. 5 minutes and 27.27272727... seconds). Thus, on a properly running clock the hands meet about every 65 minutes and 27 seconds; the clock in the question is therefore gaining about 27 seconds every 65 minutes, or about 25 seconds per hour.',NULL,0);
INSERT INTO comment VALUES (6224,971,103,'friedlinguini','re(4): Solution','2003-07-05 06:18:58',0,'Oh well. Scrap that solution, then.',6208,0);
INSERT INTO comment VALUES (6225,561,2129,'Sanjay','tick tock','2003-07-05 08:37:48',3,'In a normal watch: If hour hand and minute hand start together: Now, (360+x)/360 = x/30 Therefore, time elapsed between hour hand and minute hand meetings Since, in the watch in question, the two hands meet every 65 minutes instead, it must be gaining 27.2727.. sec in every 1 hr & 5 min, Any \'two card 21\' hand is called a Blackjack, even if it is not a winning hand (i.e when the dealer also has a Blackjack). Since the question asks, \'what are the odds that you will be dealt Blackjack ...\', and not, \'what are the odds that you will be dealt Blackjack and win..\' the correct answer is 4.83% and not 4.65%',NULL,0);
INSERT INTO comment VALUES (6227,400,2129,'Sanjay','re: Change the official solution','2003-07-05 09:30:47',0,'As a matter of fact, if we want to get all technical here, since the question asks for \'odds\' and not \'probability\' the corrcet answer should be: Odds are slightly different from probability, in that if the probability of occurance of an outcome is, lets say, 1/5 (or 20%), this translates to odds of 1 to 4 for the outcome, and to odds of 4 to 1 against the outcome. In other words, in this example, it means that the outcome is 4 times more likely to \'not occur\', than to \'occur\'.',6226,0);
INSERT INTO comment VALUES (6228,248,1301,'Charlie','In addition','2003-07-05 09:37:27',0,'In addition to all the reasons posted thus far, perhaps the store has several entrances and sometimes due to staffing reasons, only one is kept open, and on some of these occasions it is one and other occasions another.',NULL,0);
INSERT INTO comment VALUES (6229,561,2609,'mathemagician','Another Question!','2003-07-05 11:53:42',4,'\r\nSuppose that at precisely noon on July 1, you set the watch to show the correct time . If you don\'t reset the watch again, when will the watch again show the CORRECT time?',NULL,0);
INSERT INTO comment VALUES (6230,561,1301,'Charlie','re: Another Question!','2003-07-05 13:29:34',0,'The hands move at 144/143 times as fast as a perfectly accurate watch, so after 143 12-hour periods the watch will have traveled through 144 12-hour cycles. After 72.5 days this will take place, or the midnight at the end of September 10, beginning of September 11.',6229,0);
INSERT INTO comment VALUES (6231,543,2490,'qw','mmm','2003-07-05 15:13:17',0,'mmm.. i know this cuz i eat them every day! gr0ins!',NULL,0);
INSERT INTO comment VALUES (6232,842,2490,'qw','simon sez','2003-07-05 15:19:52',0,'they are playing simon says but then the kid that lost got mad and went around biting everyone\'s gr0ins off inclusing his mom\'s',NULL,0);
INSERT INTO comment VALUES (6233,983,1016,'...','SLOVED','2003-07-05 21:40:42',0,'W T N L I T, THE NEXT LETTER MUST BE EITHER M, Z, F, E, K, Y, OR X',NULL,0);
INSERT INTO comment VALUES (6234,976,1919,'Lewis','Solution','2003-07-06 04:45:24',3,'To divide the number by 10 and get the starting number, the number and its reverse needs to end with a 0. This means that the first and last numbers could be 1 & 9, 2 & 8, 3 & 7 and 4 & 6, but not 5 and 5 because the digits need to be different.\r\n\r\nOne solution (i dont know if there\'s more or not) is 1089 because 1089 + 9801 equals 10890, which is ten times 1089, the original number.',NULL,0);
INSERT INTO comment VALUES (6235,449,1919,'Lewis','Solution','2003-07-06 04:49:14',3,'For every two rupee stamp there has to be 6 rupees worth of 1 rupee stamps, making a total of 8 rupees. To be able to fill the rest with 5 rupee stamps you need to have a multiple of 5 of these. With eight you can make forty.\r\n\r\nSo the amount of stamps are:\r\n5 lots of 2 rupee stamps\r\n30 lots of 1 rupee stamps\r\nand\r\n7 lots of 5 rupee stamps.',NULL,0);
INSERT INTO comment VALUES (6236,976,1301,'Charlie','re: Solution','2003-07-06 06:07:14',0,'The uniqueness of that solution is verified by the following program. It also shows that there are no solutions even with digits allowed to be repeated.\r\n\r\n What if commas, full-stops and spaces are also part of the clue?',6259,0);
INSERT INTO comment VALUES (6264,971,1171,'nikki','re(2): No Code, just theory','2003-07-07 13:04:14',0,'\r\nGood points! As you could probably tell from my writing, I pretty much skipped over the parallel segments, trying to get to the details of the rest of the algorithm. I definitely didn\'t think those cases out. Thank you! =)\r\n\r\nHmmm, ok, here\'s a second try at the parallel segments part:\r\n\r\nSince we have to worry about vertical segments (I\'m pretty sure we shouldn\'t divide by zero in a program) we shouldn\'t go straight for the slopes mAB and mCD. First look at delta_x_AB and delta_x_CD. By checking to see if either of the delta_x\'s = 0, we can determine if we are dealing with one, two or no vertical segments.\r\n\r\nIf we are dealing with ONE vertical segment (keeping track of if it is AB or CD that is vertical - but for simplicity let\'s say it is AB for the explanation) we know what the x-coordinate of the \"intersection\" is. In this example it would be Ax (or Bx since they are equal). We find the line equation for CD: y = mCD*x + bCD. Using x\'=Ax, solve for y\'. Now follow the same check I had in my last posting for seeing if that \"intersection\" point exists on both segments.\r\n\r\nIf we are dealing with TWO vertical segments we know they are parallel. To find out if they are the same line, simply see if Ax = Cx. If they are not equal, then the segments do not intersect and you are done. If they are equal, you need to see if the segments overlap. Assuming Cy <= Dy (if not, then just flip all the inequalities):\r\n\r\n-------------------------------------------------------------\r\nIf (Cy <= Ay <= Dy) OR (Cy <= By <= Dy) then the segments overlap. Else, they don\'t and there is no intersection.\r\n-------------------------------------------------------------\r\n\r\nI\'m running out of room! Please see \"re(2): No Code, just theory Part 2\" for the rest =)\r\n',6166,0);
INSERT INTO comment VALUES (6265,971,1171,'nikki','re(2): No Code, just theory Part 2','2003-07-07 13:08:33',0,'Ok, when I left off last I was using the following if statment to determine if two vertical segments (that I had already determined existed on the same line) overlapped at all:\r\n\r\n-------------------------------------------------------------\r\nIf (Cy <= Ay <= Dy) OR (Cy <= By <= Dy) then the segments overlap. Else, they don\'t and there is no intersection.\r\n-------------------------------------------------------------\r\n\r\nI am pretty sure that statement covers if the two segments touch endpoints, if the segments overlap a little, or if one segment is a subset of the other.\r\n\r\nAnd finally, if we are dealing with NO vertical segments then we can check to see if mAB = mCD (since we know we aren\'t dealing with an infinite slope). If they are not equal, then go into the check I explained in my very first posting \"No Code, just theory\".\r\n\r\nIf they are equal, we next have to see if the two segments exist on the same line (this is very similar to the two vertical segments portion in \"re(2): No Code, just theory\"). We do this by solving for bAB and bCD in the two line equations, and checking to see if they are equal. If they are not equal, then the two segments do not exist on the same line, so there is no intersection. If they are equal then we have to check if the two segments overlap at all. Since the two segments have the same line equation, we only need to check either x-coordinates or y-coordinates (not both). The equation in the \"box\" up there can be used again to determine if the segments overlap at all.\r\n\r\nWow! I hope that covers it. I can\'t believe I thought the parallel line cases were trivial! Shame on me =)\r\n\r\nThanks Charlie!',6166,0);
INSERT INTO comment VALUES (6266,988,2640,'heather','','2003-07-07 16:09:49',3,'√²²THis site ANd problem SUCKS!!!∑∞≥',NULL,0);
INSERT INTO comment VALUES (6267,987,1575,'DJ','re(5): More solutions in that number','2003-07-07 16:49:22',0,'Sorry, fwaff\'s first solution had eight steps, which I had hurriedly looked at. So, yes, the other offered solutions do have seven steps.\r\n\r\nAll the dictionaries I have consulted, including two version of Webster\'s and the American Heritage, either list \'fuze\' only under \'fuse,\' or as a variant thereof, without its own defintion. In any case, you will recall that dictionary entries were found for \'wold,\' \'gond,\' \'wole,\' \'rolf,\' \'gole,\' etc, none of which were much liked. To me, \'fuze\' is an archaic variant that falls under the same category.\r\n\r\nAdmittedly, however, while I did not explicitly exclude slang terms, \'futz\' and \'putz\' (which are in my solution) could perhaps be deemed questionable as well. I was merely trying to find combinations that would require using words that maybe are not used daily, but are common enough that everyone should know and recognize.\r\n\r\nI\'ll put up both my intended solution and the shorter one(s). In the future, I\'ll have to be more careful.',6256,0);
INSERT INTO comment VALUES (6268,988,2571,'Rob','re:','2003-07-07 17:36:15',1,'Why do you say that heather? This site doesn\'t suck. I think it\'s pretty fun. Anyway, if you hate it so much, why did you bother signing up in the first place?\r\n As to the problem, I think it\'s insanely confusing. A few thoughts though:\r\n1. The first two times # appears, it\'s in front of an s. Maybe something?\r\n2. Maybe it\'s the number of times each one shows up.\r\n# shows up 6 times $ shows up 6 times @ shows up 12 times % 6 times * 3 times...wait, each of these is a multiple of 3, 3 once, 6 three times, and 12 once. Coincidence?\r\n Good luck with the problem!\r\n',6266,0);
INSERT INTO comment VALUES (6269,988,1575,'DJ','Quasi-Hints','2003-07-07 18:03:37',2,'Just clarifying some [hopefully useful] observations:\r\n\r\nThere are five symbols that stand out: #$@*%.\r\n\r\nThese occur between letters; they do not replace letters.\r\n\r\nThe number of times that each symbol occurs are:\r\n@=12, $=7, %=6, #=6, *=3.\r\n\r\nThe total is 34 symbols (maybe the hidden message contains 34 letters).',NULL,0);
INSERT INTO comment VALUES (6270,971,1253,'brianjn','Points on an ellipse','2003-07-07 19:56:42',4,'I note that if a pair of lines are to intersect, then there endpoints must lie on the \'circumference\' of an ellipse. \r\n\r\nWithout wanting to know the exact point of intersection, is there a property of ellipses (and circles) that can be employed here?\r\n\r\nLevi is only asking \"How would you determine if the two line segments intersect? \", nothing else seems to be required.',NULL,0);
INSERT INTO comment VALUES (6271,988,1919,'Lewis','Stumped','2003-07-07 21:28:33',4,'OK, I have no clue what this one is.\r\n\r\nDJ - does the title have the same rule/method of encryption, or is it just random symbols placed in the words?',NULL,0);
INSERT INTO comment VALUES (6272,987,1183,'fwaff','re(6): More solutions in that number','2003-07-07 22:23:22',0,'I\'ve never heard the words putz or futz before! The (common) slang route I had in mind included jizz and razz.\r\n\r\nIf \'common\' is defined as \'known by everybody\' then given the variety of people on the site the likelihood is that \'common word solutions\' will be elementary which takes away much of the challenge (and fun) of the problem. It also takes away the educational element of learning new words from other people\'s solutions. I think it\'s better to exclude slang rather than trying to exclude uncommon words.\r\n\r\nAs a suggestion for future problems of this type how about a caveat at the end along the lines of \"All words must be included in the xxxxx online dictionary, www.xxxxx.com\". Provided the chosen dictionary is a modern abridged one then this should at least eliminate archaic usages. This is how word games such as Scrabble overcome the problem.',6267,0);
INSERT INTO comment VALUES (6273,988,158,'Ender','re: Quasi-Hints','2003-07-08 03:10:42',0,'Interesting order for the frequency of symbols. I wonder if the number of pen strokes to write the symbols might be significant.\r\n@ = 1 stroke\r\n$ = 2\r\n% = 3\r\n# = 4\r\n* = 5 (at least with some fonts - or 3, or 6)\r\n',6269,0);
INSERT INTO comment VALUES (6274,988,1575,'DJ','re: Stumped','2003-07-08 04:11:53',0,'The title uses the same method of encryption. Actually, after you solve the puzzle, you should find that the title is easy.',6271,0);
INSERT INTO comment VALUES (6275,990,2572,'derek','solution?','2003-07-08 04:45:01',3,'Neither team had any runs at the end of 9 innings. The game went into extra innings and another pitcher was subbed in. He let up run(s) and his team lost.',NULL,0);
INSERT INTO comment VALUES (6276,990,1567,'Bryan','Perhaps','2003-07-08 04:48:33',3,'Maybe another pitcher on the team started the game, gave up some early runs and no outs, and this pitcher replaced him in the first inning and pitched (for himself) a perfect game. But by then it was too late; the other team already had enough runs to win. Or, the other team kept the pitcher\'s team scoreless through nine innings as well, then won the game in extra innings after this pitcher had been replaced by a relief pitcher.',NULL,0);
INSERT INTO comment VALUES (6277,988,2572,'derek','solution','2003-07-08 05:16:10',3,'The hint gives away the encryption. He says the decrypting of the title is \"easy\". I\'ll explain.\r\n\r\nThere are only 5 symbols used: @, #, $, %, * (in order which they appear on the number-row of a keyboard)\r\n\r\nNow, consider the number of letters before each symbol, and treat it as an ordered pair (4, $), etc.\r\n\r\nIt should be noted, in addition, that there are a minimum of 0 and a maximum of 4 letters between symbols.\r\n\r\nIf we treat the symbols in order they appear on the keyboard, we could do the following: (0, @) = A, (1, @) = B, ..., (0, #) = F, ..., (0, $) = K, ..., (0, %) = P, (0, *) = U\r\n\r\nThe title has the resulting ordered pairs:\r\n(4, @), (0, @), (3, %), (4, *)\r\nor\r\nE A S Y\r\n\r\nApply this to the problem, and you get the following message:\r\n\r\nI never met a huckleberry pie I didn\'t like.\r\n',NULL,0);
INSERT INTO comment VALUES (6278,990,2376,'Jim C','The Perfect Loss?','2003-07-08 07:11:24',3,'I betcha he hates his bullpen after that one! So the game went extra innings after a scoreless 9 and they lost, right? \r\n\r\nOr maybe this game was played on \"Opposite Day?\" and the team with the least runs wins? =0)',NULL,0);
INSERT INTO comment VALUES (6279,990,2376,'Jim C','re: Perhaps','2003-07-08 07:12:39',0,'Perfect, Bry!\r\nI forgot about the \"Came in in the first inning\" statement.',6276,0);
INSERT INTO comment VALUES (6280,937,2376,'Jim C','Huh?','2003-07-08 07:14:11',0,'I Can\'t \'EAR ya!',NULL,0);
INSERT INTO comment VALUES (6281,990,2648,'reed','','2003-07-08 08:19:11',0,'The game went into extra innings and the pitcher was relieved at the end of nine innings ',NULL,0);
INSERT INTO comment VALUES (6282,990,2649,'Yoda','My solution','2003-07-08 08:33:57',0,'Haven\'t read any comments yet, so I don\'t know if any of you have the same solution as me, but I\'m saying that the other team had a shutout through 9 as well, so they played extra innings. This pitcher only pitched 9 innings, so he was pulled, and the other team won in extra innings (by scoring more runs in 10th, 11th inning, etc.).',NULL,0);
INSERT INTO comment VALUES (6283,990,2650,'Al','Solution','2003-07-08 08:39:01',0,'He is a relief pitcher......he came in the game down a couple of runs already w/out any outs in the first inning and pitched a perfect 9 innings of baseball.',NULL,0);
INSERT INTO comment VALUES (6284,971,1301,'Charlie','re: Points on an ellipse','2003-07-08 08:44:37',0,'If AB extends from (-4,1) to (4,1) and CD extends from (-4,-1) to (4,-1), all the endpoints lie on the \'circumference\' of an ellipse. In fact I think an ellipse can be constructed using any four points.\r\n\r\nAlso, what is one to do if the four points given all lie on one line? The algorithm is required to say either yes or no. If point C is between A and B or D is between A and B, then the line segments share points and can be said to intersect, while if line AB is disjoint from line CD, they do not.\r\n\r\nAs a geometric solution, there is still my original proposal that ACBD forms a non-concave quadrilateral (either convex, or having a 180-degree angle or two).',6270,0);
INSERT INTO comment VALUES (6285,988,1919,'Lewis','re(2): Stumped','2003-07-08 09:49:33',0,'Ha - good little hint there DJ - very subtle. I didn\'t even notice it until I read Derek\'s solution.',6274,0);
INSERT INTO comment VALUES (6286,990,2651,'Laurie','Solution','2003-07-08 09:53:58',3,'The pitcher comes in, pitches a perfect game, but the other team doesn\'t allow any runs either. In the 10th inning, they put a relief pitcher in, but the other team scores a run and wins.',NULL,0);
INSERT INTO comment VALUES (6287,976,2652,'kevin','answer','2003-07-08 10:06:03',0,'1089',NULL,0);
INSERT INTO comment VALUES (6288,994,1919,'Lewis','Solution','2003-07-08 11:07:34',3,'Barry was at the bar and he went to the church afterwords.\r\n\r\nNone of the statements were completely true, and the only combination of person and place that wasn\'t said was \'Barry went to the church.\'\r\n\r\nThe six statements that are half true are the four that said \'Barry went....\' and the two that said \'....to the church\'.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (6289,140,1919,'Lewis','Solution','2003-07-08 11:14:40',3,'X/Y = X\r\n\r\nWith this Y would equal one.',NULL,0);
INSERT INTO comment VALUES (6290,990,775,'Cory Taylor','another way','2003-07-08 14:30:18',0,'so we\'ve come up with the ideas that the pitcher did not start the game and that the game went to extra innings. There is yet another way, where the pitcher was in fact the starter and the game ends in 9 innings where this can happen. Any takers???',NULL,0);
INSERT INTO comment VALUES (6291,990,2571,'Rob','re: another way','2003-07-08 15:41:40',0,'It might be little league baseball, where after nine innings, if it\'s a tie, special rules state that they have some sort of home run derby for the tie breaker, and they\'re team lost that. ',6290,0);
INSERT INTO comment VALUES (6292,994,1575,'DJ','Alternate Approach','2003-07-08 18:17:29',3,'Since only six \'parts\' of the statements are true, and each person\'s name is mentioned four times (once in each line), the \'true place\' must occur twice.\r\n\r\nThe bank is mentioned three times, home four, the store three, and the church only twice. Therefore, \'went to the church\' must be the true half.\r\n\r\nLarry and Harry are each paired with the church in given statements, so it must have been Barry that went to the church and the bar (an odd combination) while the other two brothers stayed home.',NULL,0);
INSERT INTO comment VALUES (6293,988,2571,'Rob','re: solution','2003-07-08 18:18:34',4,'Hey derek, could you explain your method a little more? I\'m still pretty confused.',6277,0);
INSERT INTO comment VALUES (6294,990,1575,'DJ','Hmm','2003-07-08 18:20:38',0,'I had thought of the two things other people mentioned, either he relieved someone in the first inning or the game was lost by another pitcher in extra innings. Any other possibilities escape me...',6290,0);
INSERT INTO comment VALUES (6295,990,2130,'ethan','solution','2003-07-08 18:39:07',0,'neither team scored for the first 9 innings, bringing the game into extra innings, when a reliever came in and allowed the winning run.',NULL,0);
INSERT INTO comment VALUES (6296,990,1183,'fwaff','re: another way - solution?','2003-07-08 22:12:32',1,'How about if the pitcher was temporarily relieved during the game whilst receiving treatment to an injury. If the relief pitcher conceded runs and the opposing team didn\'t then Mr Perfect starts the game, loses and it only lasts 9 innings.\r\n\r\nPlease note: being an island monkey I know nothing about baseball so my answer may be complete nonsense.',6290,0);
INSERT INTO comment VALUES (6297,140,1183,'fwaff','re: Solution','2003-07-09 00:19:33',0,'Unless X=0, then Y can have any value (with the possible exception of zero).',6289,0);
INSERT INTO comment VALUES (6298,988,2572,'derek','re(2): solution','2003-07-09 03:22:31',3,'Which part do you understand the least? I\'ll try to re-explain.\r\n\r\nThere are 5 symbols in this puzzle (in order they appear in the number row of the keyboard): @, #, $, %, *\r\n\r\nThere are always 0-4 letters preceding a symbol. We can write the number of preceding letters and the symbol as an ordered pair: (0, @), etc.\r\n\r\nFor example, in the title \"Can Y@@ou D%ecry*pt This?\"\r\nWe have 4 letters (Can Y) preceding @, so you get (4, @). Then 0 letters before the next @, so (0, @). Continuing, you get (3, %) and (4, *).\r\n\r\nThe following are all the ordered pairs in the encrypted message:\r\n(3, #) (3, $) (4, @) (1, *) (4, @) (2, %) (2, $) (4, @) (4, %) (0, @) (2, #) (0, *) (2, @) (0, $) (1, $) (4, @) (1, @) (4, @) (2, %) (2, %) (4, *) (0, %) (3, #) (4, @) (3, #) (3, @) (3, #) (3, @) (3, $) (4, %) (1, $) (3, #) (1, $) (4, @)\r\n\r\nNow, you\'ll notice that there were 5 symbols, and that the numbers in the ordered pairs range from 0-4. This gives 25 possible combinations (which turn out to be 25 distinct letters). The most common ordered pair is (4, @), so this is most likely E.\r\n\r\nThis can be confirmed after reading the hint, where it states that you will find the decryption of the title \"easy\". So, we can logically choose to assign:\r\n(0, @) = A\r\n(1, @) = B\r\n(2, @) = C\r\n(3, @) = D\r\n(4, @) = E\r\n(0, #) = F\r\n(1, #) = G\r\n\r\n...and so on throughout the alphabet (using the symbols in the order they appear on the keyboard).\r\n\r\nAny additional questions, let me know!',6293,0);
INSERT INTO comment VALUES (6299,990,1301,'Charlie','re(2): another way - solution?','2003-07-09 03:47:24',0,'I think once a player is substituted for, he can\'t come back in the game.',6296,0);
INSERT INTO comment VALUES (6300,566,2659,'Nick Hastings','Quenched','2003-07-09 05:01:50',3,'Farmer fills 6 gallon bucket and pours into 11 gallon bucket, then repeats until 11 gallon bucket is full, thus leaving 1 gallon in the 6 gallon bucket. He then fills the other 6 gallon bucket using the water he already has in the 11 gallon bucket, thus leaving 5 gallons in the 11 gallon bucket and the remaining 6 gallon bucket full. He then empties the 5 gallons in the 11 gallon bucket and pours the 6 gallon bucket back in. He then refills the second 6 gallon bucket and pours that in the 11 gallon, until the 11 gallon is full, thus leaving 1 gallon in both the 6 gallon buckets. He then empties the 11 gallon bucket completely, pours in the single gallon from both the 6 gallon buckets to give two gallons, then fills one of the now empty six gallon buckets and adds it to the 11 gallon bucket, thus leaving 8 gallons. Phew!',NULL,0);
INSERT INTO comment VALUES (6301,566,2659,'Nick Hastings','The solution','2003-07-09 05:58:39',0,'Pour first 6 gallon into 11 gallon. Pour in second 6 gallon. Leaves 1 gallon in second 6 gallon. Empty 11 gallon. Fill other 6 gallon and pour into 11 gallon. Repeat, leaving 11 gallon full and 1 gallon in both 6 gallon buckets. Empty 11 gallon. Pour both 1 gallons from the 6 gallon buckets into 11 gallon. Fill one 6 gallon and add to 11 gallon, thereby leaving 8 gallons. This is surely the answer.',NULL,0);
INSERT INTO comment VALUES (6302,566,103,'friedlinguini','re: The solution','2003-07-09 06:09:06',0,'It is an answer. Still, does it minimize water wastage? This solution wastes 22 gallons by my count.',6301,0);
INSERT INTO comment VALUES (6303,566,1183,'fwaff','re: Quenched - less waste','2003-07-09 06:18:16',3,'Following this through I make it that you wasted 16 gallons: 5 gallons the first time the 11 gallon bucket is emptied and all 11 gallons the second time it\'s emptied. This can be reduced to only wasting 10 gallons. For simplicity I\'ll represent each step with four numbers showing the total in each bucket and the amount wasted so far as follows:\r\n\r\n6G1;6G2;11G;waste\r\n\r\n0;0;0;0\r\n6;0;0;0 - fill 6G1\r\n0;0;6;0 - empty 6G1 into 11G\r\n6;0;6;0 - refill 6G1\r\n1;0;11;0 - fill 11G from 6G1 leaving 1gall in 6G1\r\n1;6;5;0 - fill 6G2 from 11G leaving 5gall in 11G\r\n1;6;0;5 - waste contents of 11G\r\n1;0;6;5 - empty 6G2 back into 11G\r\n1;6;6;5 - refill 6G2\r\n1;1;11;5 - fill 11G from 6G2 leaving 1gall in 6G2\r\n2;0;11;5 - transfer contents of 6G2 to 6G1\r\n2;6;5;5 - fill 6G2 from 11G\r\n2;6;0;10 - waste contents of 11G\r\n0;0;8;10 - pour contents of 6G1 and 6G2 into 11G\r\n\r\nHey presto, 8 gallons in the 11 gallon bucket and only 10 gallons wasted.',6300,0);
INSERT INTO comment VALUES (6304,990,2662,'Chris','re: solution','2003-07-09 07:19:34',0,'Or perhaps this pitcher was a reliever. The first pitcher to come into the game gave up, say a home run, but with no outs. Then the reliever came in and struck out 27 straight. There was already a run scored for the other team, but not on his record.',6295,0);
INSERT INTO comment VALUES (6305,969,1919,'Lewis','Solution','2003-07-09 08:55:28',3,'Bill has to be a liar. He said that Alex and Carl were both guilty - if this was true then Carl\'s first statement would be a lie, so he would be a liar, and because of his second statement that would also make Bill guilty.\r\n\r\nWe now know that Eddy is guilty, although one out of Alex and Carl can still be guilty.\r\n\r\nBecause we know Eddy is guilty we know that Carl is a knight, because of his 1st statement. That menas Bill is not guilty.\r\n\r\nDave is a liar. If he was a knight, there would have to be three guilty people. Obviously, in his 1st statement they can\'t both be guilty, so neither Alex nor Bill is guilty (but we already new about Bill).\r\n\r\nThe second robber is either Carl or Dave. Since neither Alex nor Bill is guilty, Dave is a liar. This means that Dave is guilty.\r\n\r\nThe status of each person is:\r\n\r\nAlex: Knight - Innocent\r\nBill: Liar - Innocent\r\nCarl: Knight - Innocent\r\nDave: Liar - Guilty\r\nEddy: Liar - Guilty',NULL,0);
INSERT INTO comment VALUES (6306,1015,2572,'derek','solution','2003-07-09 09:16:12',3,'stop looking at the numbers upside down :P\r\n\r\nits actually 88, 89, 90, 91 if you flip \'em right-side up',NULL,0);
INSERT INTO comment VALUES (6307,140,1919,'Lewis','re(2): Solution','2003-07-09 11:16:29',3,'No it can\'t, because if Y = 7 then X/7 wouldn\'t still be X. It would have to be X/1 to equal X',6297,0);
INSERT INTO comment VALUES (6308,990,775,'Cory Taylor','another hint on the third method','2003-07-09 12:57:47',0,'Has to do with how the pitcher recorded the outs...',NULL,0);
INSERT INTO comment VALUES (6309,566,2665,'sami','i think i figured it out...this made me thirsty!','2003-07-09 14:46:36',0,'first the farmer should fill the eleven gallon bucket till it\'s full. then empty that out into one of the six gallon buckets till that one is full. there will be five gallons left in the eleven gallon bucket. so then, you would pour out the water from the six gallon bucket into the other six gallon bucket until it is half full. then the five gallons in the eleven gallon bucket plus one of the half full six gallon buckets equals six, assuming that you discard the water from one of the six gallon buckets.',NULL,0);
INSERT INTO comment VALUES (6310,566,2665,'sami','re: i think i figured it out...this made me thirsty!','2003-07-09 14:48:54',0,'i made a mistake...instead of the five gallons in the eleven gallon bucket plus the half full six gallon bucket equalling six, they would equal eight, assuming you discard the water from the other six gallon bucket. but if the farmer were smart, he\'d save it for later. hehe!',6309,0);
INSERT INTO comment VALUES (6311,990,2667,'Viet','i got it ! i think','2003-07-09 15:27:41',0,'itz tied up to the 9th inning and they went into the tenth inning where the other team score a run.',NULL,0);
INSERT INTO comment VALUES (6312,566,2667,'Viet','proove me wrong!!','2003-07-09 16:19:25',0,' aight the nigga pour the 11 gal full then he pour from the 11 to the 6 making the 11 5. okai he then pour the 6 gal to the other 6 gal so them two would be equal amount as eachother. so the 6 gal each has 3 the nigga then pour one of the 3 gal onto the 11 which had 5 gal in it making it 8 gallon ther ya go.',NULL,0);
INSERT INTO comment VALUES (6313,566,1919,'Lewis','re: proove me wrong!!','2003-07-09 20:39:34',1,'His buckets are unmarked, so he cannot share the 6 gallons equally into the two buckets.',6312,0);
INSERT INTO comment VALUES (6314,1015,1732,'Helen','I suppose really...','2003-07-10 02:52:42',4,'87 would be a bit of a givaway cos that can\'t be turned upside down. I wonder what the longest possible sequence of upside down consecutive numbers is!',NULL,0);
INSERT INTO comment VALUES (6315,1014,1732,'Helen','I think I\'ve got it','2003-07-10 03:37:40',3,'You change the letter on your calender For example: going from Saturday to sunday, you go from s to s so no change, And going from june to july is J to J so no change. All the other months and days need a letter change!',NULL,0);
INSERT INTO comment VALUES (6316,980,2669,'Abby','re(2): Solution','2003-07-10 04:09:57',0,'Jimmy is a Knight and Johnny is a Knave.',6248,0);
INSERT INTO comment VALUES (6317,1014,1301,'Charlie','re: I think I\'ve got it','2003-07-10 04:11:58',0,'If that\'s the solution then the problem is poorly worded, as Saturday is the earlier (in succession) of the two no-change days while July is the later of the two no-change months.',6315,0);
INSERT INTO comment VALUES (6318,1014,1575,'DJ','Eh','2003-07-10 04:26:11',0,'I was thinking of the way each is pronounced. Every day of the week except for Saturday has a trochaic foot, that is, two syllables with the first one stressed. August is the same way (as is April), but July has the accent on the second syllable. That\'s probably not right, because I have no idea what \"you do\" in those cases..',NULL,0);
INSERT INTO comment VALUES (6319,1014,1567,'Bryan','This makes sense','2003-07-10 05:18:50',3,'Use the letter \"a\". The name of each weekday contains one \"a\", except Saturday, which has two! And while \"August\" starts with \"a\", it doesn\'t appear at all in \"July\".',NULL,0);
INSERT INTO comment VALUES (6320,1014,1919,'Lewis','re: Eh','2003-07-10 06:09:55',0,'Thats quite good - I never actually thought of that.\r\n\r\nIf that was the case then what \'you do\' could be stress first syllable, but that isn\'t the right answer. ',6318,0);
INSERT INTO comment VALUES (6321,1015,1183,'fwaff','re: I suppose really...','2003-07-10 06:27:21',1,'Re the longest sequence....\r\n\r\nIt depends on what font you\'re using. With most fonts the only \'invertible\' numbers are 0,1,6,8,9 - in which case the longest sequence is four: *8, *9, *0, *1 because the preceding number (*7) and following number (*2) contain non-invertible numbers (7 & 2 resp.).\r\n\r\nHowever, if you consider how numbers appear on a calculator then 2 and 5 are also invertible - which increase the longest sequence to 5: *8, *9, *0, *1, *2 as both *7 and *3 are non-invertible.',6314,0);
INSERT INTO comment VALUES (6322,566,1183,'fwaff','re(2): prove me wrong!!','2003-07-10 06:38:35',0,'The question also states that the farmer has ONLY 3 unmarked buckets, this presumably precludes using some sort of balance which could be used to share the water by weight between the two (identical?) 6 gallon buckets.\r\n\r\nOn this basis both Sami and Viet\'s solutions are invalid.',6313,0);
INSERT INTO comment VALUES (6323,140,1919,'Lewis','re(3): Solution','2003-07-10 07:13:12',0,'Actually, I see what you mean. I did get it wrong :0(',6307,0);
INSERT INTO comment VALUES (6324,1016,1183,'fwaff','First steps....','2003-07-10 08:00:37',1,'Each number has a 1/2 chance of being divisible by 2, so there is a 1/4 chance of them both being divisible by 2.\r\n\r\nSimilarly there\'s a 1/9 chance of both being divisible by 3, a 1/16 chance of both being divisible by 4, etc etc etc.\r\n\r\nSo my first though was along the lines of...\r\n\r\n1 - (1/4 + 1/9 + 1/16 +...+ 1/n^2 +.....)\r\n\r\nBut this has duplication. For example if both numbers are divisible by 2 and divisible by 3, then they must both be divisible by 6 - which perhaps means that the 1/36 element shouldn\'t be included. This would give a solution of...\r\n\r\n1 - (1/4 + 1/9 + 1/25 + 1/49 +...+ 1/n^2 +...) for all prime n\r\n\r\nI have absolutely no idea though as to the value of this sum! ',NULL,0);
INSERT INTO comment VALUES (6325,1016,103,'friedlinguini','re: First steps....','2003-07-10 08:20:52',1,'Except that you don\'t add the probabilities. The probability of A or B occuring is 1 - the probability of neither occuring. If A and B are independent (and I think they are for this problem), P(A or B) = 1 - (1 - P(A)) x (1 - P(B)). This gives the even more complicated formula of:\r\n\r\n1 - (1 - 1/4) x (1 - 1/9) x (1 - 1/25) ... (1 - 1/n²)... for all prime n.',6324,0);
INSERT INTO comment VALUES (6326,1016,1301,'Charlie','solution','2003-07-10 08:24:24',3,'First a caveat: The method by which you randomize the numbers is going to affect the probability. If each of the two random numbers is drawn from a uniform distribution of integers from 1 to 10, then the probability would be 63% as 63 out of the 100 equally possible pairings would be relatively prime. If drawn from a uniform distribution from 1 to 100, the probability would be 60.87% as 6087 of the possible 10000 pairings would be relatively prime. If the two numbers were each the result of a toss of two dice, 784 of the 1296 ways of the dice falling would result in relative primeness, or 60.49...%.\r\n\r\nBut if we assume that what is meant is to find what the probability approaches if the two numbers are drawn from a uniform distribution from 1 to n, as n increases without limit, then the following logic applies:\r\n\r\nThe probability that the two numbers would both be even (divisible by 2) is (1/2)^2 so the probability that they are not both divisible by 2 is 1- (1/2)^2. This is independent of the probability that they are divisible by 3. The probability that they are not divisible by 3 is 1 - (1/3)^2. This is repeated for each prime divisor, as the probability of divisibility by different primes is independent, and divisibility by primes is all that counts. So we need (1-(1/2)^2)*(1-(1/3)^2)*(1-(1/5)^2)*(1-(1/7)^2)*(1-(1/11)^2)*....\r\n\r\nBy the time the 10th prime, 29, is considered, the probability is down to .612344.... By the hundredth prime, 541, it is down to .6080819.... By the thousandth prime, 7919, .607929.... By the 10,000th prime, 104,729, it\'s .6079275.... By the 100,000th prime, 1,299,709, it\'s .6079271....\r\n\r\nBy the millionth prime, 15,485,863, it is still characterized by .6079271..., so I\'ll leave it at that.\r\n\r\nBy the way the program for the above:\r\nlist\r\n 5 T=1\r\n 6 P=1\r\n 10 for I=1 to 1000000\r\n 15 P=nxtprm(P)\r\n 20 T=T*(1-1/(P*P))\r\n 30 if I/10000=int(I/10000) or I<11 then print I,P,T\r\n 40 next\r\nOK',NULL,0);
INSERT INTO comment VALUES (6327,1016,1301,'Charlie','re(2): First steps....','2003-07-10 08:30:26',0,'Rather than\r\n1 - (1 - 1/4) x (1 - 1/9) x (1 - 1/25) ... (1 - 1/n²)... for all prime n,\r\n\r\nthe subtracting of probability of non-rel-prime from 1 has already been done within each parentheses to give rel-prime (for the particular prime) so the final product is the answer without subtraction from 1.\r\n',6325,0);
INSERT INTO comment VALUES (6328,990,2670,'saad','Solution','2003-07-10 08:43:10',0,'he may have given up wild pitches and the cather may have given up passed balls, which are not errors, allowing the batter to strike out and advance to base at the same time...maybe the batters just kept advancing via these or they were stealing the bases.',NULL,0);
INSERT INTO comment VALUES (6329,566,1919,'Lewis','re(3): prove me wrong!!','2003-07-10 09:39:13',3,'I guess we did \'prove him/her wrong!!\'.\r\n\r\nBy the way, here\'s my solution.\r\n\r\nFill both 6\'s and pour into the 11. There\'ll be 1 left in one of the 6\'s.\r\nEmpty the eleven into the six and discard the remaining 5. Pour 6 back into eleven. Fill the empty 6 and pour into 11. Add remaining 1 to other 1.\r\nFill empty six with water from 11, and get rid of remaining 5. Put the six and two into the 11, and then the farmer has 8 gallons. This method wastes 10 gallons, but I don\'t think there\'s a better way.',6322,0);
INSERT INTO comment VALUES (6330,1014,2671,'bruce','solution?','2003-07-10 10:14:04',0,'write the letter A',NULL,0);
INSERT INTO comment VALUES (6331,1014,2376,'Jim C','re: solution?','2003-07-10 10:18:46',0,'Ah Hah! That was the first thing I came up with, except that I then said, \"Duh, Saturday has an A in it!\" But you\'re right, you don\'t have the letter A ONCE in saturday, you have it twice.\r\n\r\nThanks, Bruce',6330,0);
INSERT INTO comment VALUES (6332,994,2667,'Viet','just a guess','2003-07-10 11:13:23',0,'aight if them ppl was at the bar then how would they know who gone where. so they was proberbly all drunk. barry was metion that he went home twice starange someone solve this!!!!',NULL,0);
INSERT INTO comment VALUES (6333,990,775,'Cory Taylor','re: Solution','2003-07-10 11:40:16',0,'Bingo on the third method. A wild pitch is not classed as an error, thereby allowing a batter to strike out, however advance to first base on the play. From here, though the baserunner would be required to steal bases all the way home, as this rule only applies with first base open (otherwise the defending team could essentially eliminate any batter on first base by purposely causing this situation and then turning the double play (similar to the reasoning for the infield fly rule).',6328,0);
INSERT INTO comment VALUES (6334,994,1919,'Lewis','re: just a guess','2003-07-10 11:41:00',0,'Me and DJ (or is it DJ and I?) already have solved it! Look at the comments!',6332,0);
INSERT INTO comment VALUES (6335,988,2571,'Rob','re(3): solution','2003-07-10 13:56:59',0,'Thanks derek. I was just confused on how you assigned the ordered pairs to different letters, but I think I have it now. Thanks again!',6298,0);
INSERT INTO comment VALUES (6336,937,2672,'Stephanie','a solution from ur sis, Stephanie','2003-07-10 14:23:05',0,'is the human ear',NULL,0);
INSERT INTO comment VALUES (6337,937,2672,'Stephanie','re: my solution here','2003-07-10 14:23:44',0,'no\r\n',6194,0);
INSERT INTO comment VALUES (6338,1015,2673,'erica','solution','2003-07-10 16:41:05',3,'he was looking at them upside down :-)',NULL,0);
INSERT INTO comment VALUES (6339,980,2673,'erica','solution','2003-07-10 17:06:24',0,'It is most logical to say that Johnny is telling the truth, therefore he is a knight. He says that Jimmy is not a knight and that Jimmy is a knave.\r\nJimmy says that he is a knave (the truth) and that Johnny is a knave (lie). Therefore, Jimmy is a knave.',NULL,0);
INSERT INTO comment VALUES (6340,994,2667,'Viet','re(2): just a guess','2003-07-10 17:29:23',0,'then why they still mark it as no solution they should update this so it b easier to know and by the way wat them light bulb for?',6334,0);
INSERT INTO comment VALUES (6341,994,2674,'mike','no way','2003-07-10 17:36:28',0,'there is no solution. It is completely impossible, with the information given to determine which tripet was at the bar. even if one of the four friend was not lying, they were still giving bad information. they where not telling which triplet went to the bar. furthermore if half of the things are half true meanig 6 are 1/2 true and 3 of those truths where names and the other 3 places it would still be impossible to intelligently match those up correctly. so either the answer is that there is no answer and this is a trick question or you recited this question incorrectly and may god have mercy on your soul.',NULL,0);
INSERT INTO comment VALUES (6342,994,2674,'mike','revoke','2003-07-10 18:01:43',0,'after reviewing the problem i revoke my earlier statemeant\r\n',NULL,0);
INSERT INTO comment VALUES (6343,26,2545,'rajesh','how about this?','2003-07-10 20:51:00',0,'Now if both the days were superimposed i.e., if when the climber climbs up another him starts descending down the same trail then they HAVE to cross each other at some point of time to reach their destinations.The altitude at which they do is the required altitude.',NULL,0);
INSERT INTO comment VALUES (6344,26,2545,'rajesh','kela!','2003-07-10 20:53:01',0,'hey!i saw the solution after i posted my comment,I swear!!!!!',NULL,0);
INSERT INTO comment VALUES (6345,994,1919,'Lewis','re(3): just a guess','2003-07-10 21:21:42',0,'Well when a user solves a puzzle they can only post it as a comment. When it says \'No Solution Yet\' that means that the author\'s official solution has not yet been posted. This normally gets posted after a few days, unless the author is a Journeyman or above when they can post it when they like\r\n\r\nBy the way, the light bulbs by the comments tell people that the comment contains a solution, so anyone trying to solve the problem themselves won\'t accidently look at them.',6340,0);
INSERT INTO comment VALUES (6346,566,1183,'fwaff','re(4): prove me wrong!!','2003-07-10 21:23:29',0,'Yep, same as me. I guess it\'s up to Ravi now to prove us both wrong.',6329,0);
INSERT INTO comment VALUES (6347,566,2545,'rajesh','just a thought....','2003-07-10 21:36:16',0,'The contents of one of the 6 litre buckets could be exactly divided into half if it was cylindrical or even cuboidal(like some buckets are).this could be achieved by pouring out water till the water level just reveals the bottom edge(in case of a cuboid-along one of the longest diagonals).\r\nthis is because the diagonal divides the volume of the bucket in half.',NULL,0);
INSERT INTO comment VALUES (6348,1015,1839,'Rajeev','opposite direction','2003-07-10 22:24:13',0,'cause he is coming from opposite direction',NULL,0);
INSERT INTO comment VALUES (6349,50,2376,'Jim C','Oldie But Goodie','2003-07-11 05:53:26',3,'I love this problem, and even though I\'ve seen it before it STILL took me about 3 minutes to come up with the solution.\r\n\r\nThe problem with this problem =0) is that the logic of the question is incorrect.\r\n\r\nThe three farmers did pay $27, or 9 apiece, and the bellboy did keep $2. But the error is the assumption that these two values should be totaled. What we have to remember is that the bellboy didn\'t take the $2 from the manager, but rather from the men! The men paid $27, but the rate was only $25, which is where the bellboy gets his $2. $25 + $2 = $27, which is what was paid.\r\n\r\nNow, on a separate note, do you think the farmers tipped the bellboy? I hope they stole the towles or something for that extra two bucks! =0)',NULL,0);
INSERT INTO comment VALUES (6350,1017,1575,'DJ','No clue','2003-07-11 06:05:50',0,'Hm..the differences between terms are:\r\n1, 1, 2, 1, 3, 1, 5, 3, 6, 1, 9, 1\r\nThat doesn\'t look like anything to me, except the number of consecutive terms might be noteworthy. Nothing else comes to mind, either..',NULL,0);
INSERT INTO comment VALUES (6351,1017,2667,'Viet','somethin','2003-07-11 06:36:54',0,'does it goes something like \r\n1+2=3\r\n2+3=5\r\n1+5=6\r\n1+3+5=9\r\n2+3+5=10\r\n1+3+5+6=15 i unnno what the sequence go by',NULL,0);
INSERT INTO comment VALUES (6352,1017,2685,'tiffany','solution','2003-07-11 08:24:29',0,'I think it might be 37,38',NULL,0);
INSERT INTO comment VALUES (6353,66,2686,'Bill','Think outside the box... (solution)','2003-07-11 08:57:28',0,'Upon making this decision, Bill had better move out of town. Upon extricating himself from the set, he can then commute back each day and do his work on the remaining residents.',NULL,0);
INSERT INTO comment VALUES (6354,847,2667,'Viet','','2003-07-11 09:06:56',0,'still 100 pound',NULL,0);
INSERT INTO comment VALUES (6355,82,2686,'Bill','Kill the demons!','2003-07-11 09:09:05',0,'Regardless of how snappy the demons are, it takes a bit of time for a person to die, during which time an infinite number of demons would have stuck their titan-stickers into Prometheus-the-pincushion. So the gods need merely use their godly powers to determine the latest instant of remaining fleeting life in Prometheus, and kill all of the demons that \'killed\' him before that.',NULL,0);
INSERT INTO comment VALUES (6356,865,2674,'mike','your all wrong','2003-07-11 09:48:05',0,'no and yes arent the only possible answers. the answer is : it is not. i nevr said yes meaning that the answer was no but i never said no, literally, to mean it wasyes.',NULL,0);
INSERT INTO comment VALUES (6357,924,2681,'helena','','2003-07-11 09:50:22',0,'',NULL,0);
INSERT INTO comment VALUES (6358,1015,2681,'helena','solution','2003-07-11 09:56:36',0,'He was looking at it upside down. It was in consecutive order.',NULL,0);
INSERT INTO comment VALUES (6359,581,2667,'Viet','okai yea....','2003-07-11 10:22:42',0,'he is a murderer himself so saying that make him a hypocrite',NULL,0);
INSERT INTO comment VALUES (6360,424,2667,'Viet','my solution','2003-07-11 10:35:56',0,'Man C Women 2 1 Cat 2 Dog\r\nMan A Women 1 1 Cat\r\nMan B Women 3 1 Cat 1 Dog',NULL,0);
INSERT INTO comment VALUES (6361,424,2667,'Viet','re: my solution','2003-07-11 10:37:28',0,'wait Man B has no cat he hates it my fault',6360,0);
INSERT INTO comment VALUES (6362,349,2667,'Viet','no','2003-07-11 10:43:58',0,'then how does the first person qussing know the coolor of there hat',NULL,0);
INSERT INTO comment VALUES (6363,90,2667,'Viet','this one is the easiest of all i think','2003-07-11 10:57:04',3,'kerry is not terry twin terry must be a twin to another bother of his',NULL,0);
INSERT INTO comment VALUES (6364,1017,2681,'helena','i was almost there- somebody help me!!!','2003-07-11 11:01:30',0,'1,2,3,5,6,9,10,15,18,24,25,34,35\r\n \r\n We start off with 1,(x)and go(skip no spaces) to 2(2x)and then immediatelt to 3(3x).Then from 3(y)we skip one space and jump to 6(2y)and then immediately to 9(3y).Then from 5(z)we skip two spaces and jump to 10 (2z)and then go immediately to 15(3z).Then from 6(a)we skip 3 spaces and jump to 18(2a)then immediately to 24(3a). \r\nI have found a pattern up to here but cant seem to figure out the rest. Where do 25,34, and 35 come in? will someone help me?',NULL,0);
INSERT INTO comment VALUES (6365,1031,2572,'derek','solution','2003-07-11 11:05:28',3,'$1.20, $1.25, $1.50, $3.16',NULL,0);
INSERT INTO comment VALUES (6366,1031,103,'friedlinguini','Talk about a well-timed problem (nt)...','2003-07-11 12:17:38',0,' ',NULL,0);
INSERT INTO comment VALUES (6367,294,2674,'mike','duh','2003-07-11 13:29:31',0,'the probability is of course one(1). The average isnt one and the only possible number isnt one but according to probability rules there is a 1 in 9 chance that you will label any given jar correctly. 1/9 probability times the 9 jars = 1 ',NULL,0);
INSERT INTO comment VALUES (6368,1031,2674,'mike','ah ha','2003-07-11 13:34:08',3,' $1.25 1.25 x 1.20 x 1.50 x 3.16= $7.11\r\n $1.20\r\n $1.50\r\n +$3.16= \r\n________\r\n$7.11',NULL,0);
INSERT INTO comment VALUES (6369,836,2674,'mike','ok','2003-07-11 13:39:49',1,'all you need to do is bid 95 cents and no one would be dumb enough to bid a dollar since they would win nothing',NULL,0);
INSERT INTO comment VALUES (6370,990,2080,'Tristan','re(2): Solution','2003-07-11 13:39:50',0,'nice try, but no run was recorded during his time on the mound.',6333,0);
INSERT INTO comment VALUES (6371,1031,1171,'nikki','Ok, but how?','2003-07-11 13:40:42',0,'\r\nI saw the solution that some of you found, but I\'m curious about your method. Was it trial and error, or did you have some plan? I tried some plans, and they didn\'t work out, so I\'m curious about how others approached this problem.\r\n\r\nLater!',NULL,0);
INSERT INTO comment VALUES (6372,566,2080,'Tristan','re: just a thought....','2003-07-11 13:57:24',0,'the shapes are undefined, it could be a 6 gallon cylinder and a 6 gallon cube.',6347,0);
INSERT INTO comment VALUES (6373,1017,2674,'mike','thoughts','2003-07-11 13:58:01',1,'i think there are two comletely different patterns with similar or same formulas as to their creation. what they are, i havent figured out yet.\r\n',NULL,0);
INSERT INTO comment VALUES (6374,1014,2674,'mike','re(2): I think I\'ve got it','2003-07-11 14:06:46',0,'but if that is the solution than why would it be not in july that you would change the day. and once in august? It doesnt add up.',6317,0);
INSERT INTO comment VALUES (6375,1014,2674,'mike','re(2): I think I\'ve got it','2003-07-11 14:06:53',0,'but if that is the solution than why would it be not in july that you would change the day. and once in august? It doesnt add up.',6317,0);
INSERT INTO comment VALUES (6376,990,2674,'mike','easy','2003-07-11 16:48:14',3,'the game went into overtime and the team loss sometime after the 10th inning. a similar thing happened to a former red sox pitcher who lost a no-hitter on walks, errors and hit batsmen.',NULL,0);
INSERT INTO comment VALUES (6377,1031,2674,'mike','re: Ok, but how?','2003-07-11 16:53:37',0,'it was really just trial and error for me. i usually dont use that method but i couldnt find a formula. and it took a while. it was kind of a lucky situation ',6371,0);
INSERT INTO comment VALUES (6378,566,2674,'mike','i got this one easy-full solution','2003-07-11 17:06:43',3,'first he would fill the 6 gallon bucket and pour its contents into the 11 gallon bucket.than he would fill the 6 gallon bucket again and pour its contents into the 11 gallon bucket. since there are only 11 gallons to be held, one gallon of water would be left in the 6 gallon bucket. he would than empty the 11 gallon bucket and repeat the same steps with the remaining 6 gallon bucket.he would than combine the leftover 2 gallons into 11 gallon bucket. He would than fill the 6 gallon bucket with water and empty that into the 11 gallon bucket that already has 2 gallons of water to make 8 gallons. It is also possible to do this with only two buckets but thats another story.',NULL,0);
INSERT INTO comment VALUES (6379,980,2674,'mike','i guess','2003-07-11 17:10:07',3,'both are knaves',NULL,0);
INSERT INTO comment VALUES (6380,1017,1575,'DJ','Solution','2003-07-11 18:06:13',3,'Assign each term a numerical value, starting with 1 as term one. Each term is then found by adding the previous term to the term in the place of that terms highest factor. For example, term eight is found by adding term seven to term four (four is eight\'s greatest factor). If the term number is prime, add term one (which is of course just one).\r\nObserve:\r\n\r\nTerm Highest Factor Value\r\n1 1\r\n2 prime -> 1 1+1 = 2\r\n3 prime -> 1 1+2 = 3\r\n4 2 -> 2 2+3 = 5\r\n5 prime -> 1 1+5 = 6\r\n6 3 -> 3 3+6 = 9\r\n7 prime -> 1 1+9 = 10\r\n8 4 -> 5 5+10 = 15\r\n9 3 -> 3 3+15 = 18\r\n10 5 -> 6 6+18 = 24\r\n11 prime -> 1 1+24 = 25\r\n12 6 -> 9 9+25 = 34\r\n13 prime -> 1 1+34 = 35\r\n...\r\n14 7 -> 10 10+35 = 45\r\n15 5 -> 6 6+45 = 51\r\n16 8 -> 15 15+51 = 66\r\n\r\nTherefore, the next two terms in the sequence are 45 and 51.',NULL,0);
INSERT INTO comment VALUES (6381,836,1919,'Lewis','re: ok','2003-07-11 22:08:33',1,'The problem with that is that people are allowed to bid 96 cents, so if you bid 95 cents you will be starting a \'bidding war\'.',6369,0);
INSERT INTO comment VALUES (6382,146,1919,'Lewis','Solution','2003-07-11 22:11:28',3,'This is easy - you like square numbers.\r\n\r\n2500 = 50^2\r\n576 = 24^2\r\n169 = 13^2',NULL,0);
INSERT INTO comment VALUES (6383,140,1919,'Lewis','Proper Solution','2003-07-11 22:16:13',3,'Erk... would this work.\r\n\r\nX/Y = 0.\r\n\r\nNo number can be divided to zero, so X must be 0.',NULL,0);
INSERT INTO comment VALUES (6384,228,1919,'Lewis','More of a Paradox than a Riddle','2003-07-12 01:21:50',3,'This problem should definitely be a paradox because:\r\n\r\nError 1 - \'is\' instead of \'are\'.\r\nError 2 - \'thise\' instead of \'this\'.\r\nError 3 - there isn\'t a third error.\r\n\r\nBut obviously, error 3 contradicts itself, creating a paradox style cycle.',NULL,0);
INSERT INTO comment VALUES (6385,1015,575,'not_so_einstein','Solution','2003-07-12 02:19:26',3,'The numbers were upside-down. 16 upside-down is 91 etc.\r\nNote: I haven´t looked at the other answers!',NULL,0);
INSERT INTO comment VALUES (6386,1031,2682,'exoticorn','a way to the solution','2003-07-12 03:19:39',3,'let\'s use cents instead of dollars, so that the four numbers result in 711 when added and 711000000 when multiplied.\r\n\r\nthe prime factors of the latter are:\r\n2*2*2*2*2*2 * 3*3 * 5*5*5*5*5*5 * 79 = 711\r\n\r\nthe least significant digit of the four numbers are ...1 when added and ...0 when multiplied. The only combinations for which this works are (at least i think they are the only ones):\r\n0 0 0 1 and 0 0 5 6\r\n\r\nThe only number ending in 1 that can be build from the prime factors is 711 (3*3*79), which is obviously too big.\r\n\r\nThe only numbers ending in 6 are 6 (2*3) and 316 (2*2*79).\r\n6 isn\'t possible as well, because the sum of the remaining 3 numbers will always be bigger than 765.\r\n\r\nTherefore 316 is one of the four numbers need to be 316.\r\n\r\nThe remaining prime factors are now:\r\n2*2*2*2 * 3*3 * 5*5*5*5*5*5\r\n\r\nWe know that one of the remaining numbers needs to end with a 5, the possible numbers are:\r\n15 (5*3), 25 (5*5), 75 (5*5*3) which are all too small (the sum would exceed 711)\r\n125 (5*5*5), 225 (5*5*3*3) both seem to be possible on first glance\r\n375 (5*5*5*3) and bigger ones which are obviously too big.\r\n\r\nLet\'s assume we would pick 225, now the sum of the two missing numbers needs to be 711-316-225 = 170, while the product needs to be 711000000/316/225 = 10000.\r\nThe biggest product you can get from two numbers whose sum is 170 is (170/2)^2 = 7225 which is smaller than 10000, so 225 is out as well.\r\n\r\nThis means that we have 125 and 316 as the first two solutions, so the sum of the last two numbers needs to be 270. The product needs to be 18000.\r\nThis is pretty simple math:\r\n\r\nx * (270 - x) = 18000\r\n270x - x^2 = 18000\r\nx^2 - 270x + 18000 = 0\r\nx(1, 2) = 270/2 +- sqrt((270/2)^2 - 18000)\r\nx1 = 150, x2 = 120\r\n\r\nso the solution is (as others have found before):\r\n120, 125, 150, 316',NULL,0);
INSERT INTO comment VALUES (6387,251,2674,'mike','hmmmm','2003-07-12 05:04:01',3,'i dont think they where all boys. I think there where 3 boys 3 girls and 1 hermaphrodite.',NULL,0);
INSERT INTO comment VALUES (6388,279,1575,'DJ','re:','2003-07-12 06:10:19',0,'i\'m not sure if you\'re kidding, but.. no. the first one you have is fine, of course, but each equation should contain exactly one two, two zeroes, and one three, in that order.',5983,0);
INSERT INTO comment VALUES (6389,67,2667,'Viet','yea easy','2003-07-12 06:29:55',3,'3 min',NULL,0);
INSERT INTO comment VALUES (6390,67,2667,'Viet','re: yea easy','2003-07-12 06:33:18',0,'itz twice the rat so 6 min',6389,0);
INSERT INTO comment VALUES (6391,1031,1301,'Charlie','re: a way to the solution','2003-07-12 06:43:37',0,'It\'s an impressive solution!\r\n\r\nA couple of questions, though, on narrowing down the choices...\r\n\r\nWhen you list\r\n0 0 0 1 and 0 0 5 6 \r\nas the only two possible sets of ending digits, how were\r\n0 1 5 5 and 5 5 5 6\r\neliminated?\r\n\r\nAlso, in \"The only numbers ending in 6 are 6 (2*3) and 316 (2*2*79),\" how was 36 (2*2*3*3) eliminated? ... also 576 (2*2*2*2*2*2*3*3) and 16(2*2*2*2)?\r\n\r\n',6386,0);
INSERT INTO comment VALUES (6392,1008,783,'Ahmed','','2003-07-12 06:54:05',0,'Niether nor',NULL,0);
INSERT INTO comment VALUES (6393,1014,2667,'Viet','could b','2003-07-12 06:55:08',1,'sunday through friday come before saturday everyday since saturday is the last day of the week and july come before august only once a month',NULL,0);
INSERT INTO comment VALUES (6394,1008,1575,'DJ','Possible Solution','2003-07-12 06:57:44',1,'I think that since George, Helen, and Steve each have two \'e\'s in their names, and they are drinking coffee, Elizabeth would also be drinking coffee. Bert, Karen, and Dave each have one e, so perhaps they should be drinking tea instead of soda?\r\n\r\nMaybe, though, Elizabeth is drinking lemonade or apple juice.',NULL,0);
INSERT INTO comment VALUES (6395,1008,2667,'Viet','re: Possible Solution','2003-07-12 07:07:30',2,'or bert should be bart and your soulution would be rite but elizabeth have bott E and A so she drink both\r\n\r\nmaybe so maybe not...',6394,0);
INSERT INTO comment VALUES (6396,1008,1575,'DJ','re(2): Possible Solution','2003-07-12 07:10:58',0,'i never said anything about a, just about the number of times e is in the name (Elizabeth has two)..',6395,0);
INSERT INTO comment VALUES (6397,1017,783,'Ahmed','i agree','2003-07-12 07:49:59',0,'i really really agree with the answer posted by DJ\r\nbut there are something wrong in his solution...concerned by the second wanted next number in the sequence...which is he said to be\r\n(51) i think it must be 54 .....\r\nbecause the previous term was 45\r\nand the highest factor is 9 not 5\r\nso i think the next two numbers in this sequence are 45...54....and thank u DJ ',NULL,0);
INSERT INTO comment VALUES (6398,1008,1626,'Gamer','Another solution?','2003-07-12 08:18:06',2,'When I saw this I thought \"double letters in the first names, and no double letters in the second names\", so Elizabeth has coffee.',NULL,0);
INSERT INTO comment VALUES (6399,976,1626,'Gamer','re: Non-algorithmic solution','2003-07-12 08:28:02',0,'I agree with what you said TomM, and this goes for Four Digit Number as well. I think my solution is like yours, (except more \"pictures\" and less words)\r\n\r\nShould the solution be released for this problem? ',6240,0);
INSERT INTO comment VALUES (6400,566,1626,'Gamer','thoughts','2003-07-12 08:36:14',1,'mike, I think your solution is the same as fwaff\'s.\r\n\r\nI also think that unless the problem states that you can \"split\" the container equally, you can\'t do it.',NULL,0);
INSERT INTO comment VALUES (6401,1017,1575,'DJ','re: i agree','2003-07-12 09:15:22',0,'You\'re right.. a 2 am oversight on my part',6397,0);
INSERT INTO comment VALUES (6402,980,2690,'Paul Spykerman','Answer','2003-07-12 09:54:13',0,'Jimmy is a knave\r\nJophnny is a kinght\r\n\r\nLogic:\r\n1) Jimmy truthed.--> Said, I am a knave.--> means he is a knave.\r\n3) Jimmy lied.--> Johnny is a knave.--> means that Johnny isn\'t a knave.\r\n\r\n2) Johnny truthed.--> Jimmy is not a knight.- Correct.\r\n4) Jimmy is not a knave--> correct.',NULL,0);
INSERT INTO comment VALUES (6403,847,2690,'Paul Spykerman','Answer','2003-07-12 10:15:34',0,'At first, the potatoe stuff is 1 pound (1% times 100 pounds) and the water is 99 pounds (99% times 100 pounds). At 98% water, the potatoe stuff is 2% weight, which is 1 pound, making the 98% weight (water) weight 49 pounds. Therefore, the combined wieght is 50 pounds.\r\n\r\nWhen the water content is 50%, both weight the same, so since the potatoe stuff is 1 pound, so is the water. Therefore, the total weight is two pounds.',NULL,0);
INSERT INTO comment VALUES (6404,1008,1919,'Lewis','Solution','2003-07-12 10:45:58',3,'Funnily enough I went on riddlenut.com a few hours ago for the first time, and I saw this exact problem.\r\n\r\nThe solution is (apparently) Coffee because the coffee-drinkers have two \'e\'s, although this isn\'t exactly logic. My names Lewis but that doesn\'t mean I drink soda....',NULL,0);
INSERT INTO comment VALUES (6405,912,1626,'Gamer','re: Impossible?','2003-07-12 11:02:15',1,'Yes, I would think it would be impossible too... It seems like you could get checkers to level 2 easily, and even get to level 3. But no distribution of checkers (that I have found) makes it possible to put a checker (through jumps) 2 spaces to the left of the furthest left checker. ',6072,0);
INSERT INTO comment VALUES (6406,1017,1575,'DJ','re(2): i agree [i don\'t]','2003-07-12 11:35:33',1,'No, never mind, that\'s not right.\r\n\r\nEach term is found by taking the term that is in the place of the greatest factor of the term number, not of the value itself. That 5, then, is the greatest factor of 15 (for the 15th term), not of its value of 45 (which, you are correct, would be 9, but that\'s not what we\'re looking at).\r\n\r\nTherefore, my original solution stands.',6401,0);
INSERT INTO comment VALUES (6407,1008,2674,'mike','re: Solution','2003-07-12 16:06:28',1,'thats what i was thinking. I think this problem contradicts the means of logical thinking. I don\'t think it would be logical to find how many \'e\'s are in somebodies name to figure out what they are drinking, do you? My name also has one \'e\' in it but i drink both beverages.\r\n ',6404,0);
INSERT INTO comment VALUES (6408,1008,2571,'Rob','re(2): Solution','2003-07-12 18:13:20',1,'What Chaz means is, within the boundaries of these seven people, two e\'s drink coffee. The only setback is, soda has an a, but only two of the soda drinkers have an a. This leaves Bert drinkless. You could try the o in soda, people who don\'t have o\'s, and that would make Bert, Karen, Dave, and Elizabeth soda drinkers, but that would also mean Helen and Steve also would. This destroys the confines of the problem. Only one solution remains, and that is that while if you have two e\'s, you drink coffee, but if you don\'t, then you drink soda. Not many names have two e\'s, so the coffee company must be losing money like heck.',6407,0);
INSERT INTO comment VALUES (6409,1008,2184,'mark hartman','Coffee or soda?','2003-07-12 22:30:02',0,'Elizabeth would be drinking coffee. People with 2 e\'s drink coffee. The others drink soda.',NULL,0);
INSERT INTO comment VALUES (6410,496,1919,'Lewis','Solution','2003-07-13 00:13:27',3,'A says the is insane. He could either be insane and applied, or sane and applied.\r\nB says he is pure. He could be Pure and Sane or Applied and Sane.\r\nC says he is applied. He could be Pure and Insane, or Applied and Insane.\r\nD says he is sane. He could be Sane and Pure or Insane and Pure.\r\n\r\nSo far we know:\r\nA = Applied\r\nB = Sane\r\nC = Insane\r\nD = Pure\r\n\r\nD says C is sane, which we know is incorrect. Since we know D is pure, he must be insane.\r\nB correctly says D is insane. He is sane so he must also be pure.\r\nC says B is applied, which is also incorrect. C is insane, so he must be pure.\r\nA says C is pure - which is correct. Seeing as A is applied he must be insane.\r\n\r\nSo we get:\r\n\r\nA = Applied & Insane\r\nB = Sane & Pure\r\nC = Insane & Pure\r\nD = Pure & Insane\r\n',NULL,0);
INSERT INTO comment VALUES (6411,360,1919,'Lewis','Solution','2003-07-13 00:18:21',3,'The answer is.....Nothing.\r\n\r\nI don\'t mean there\'s no answer, the answer is literally, well, nothing. Ahem.\r\n\r\nBTW, isn\'t \'Knowledge\' spelt wrong in the title?',NULL,0);
INSERT INTO comment VALUES (6412,1031,2682,'exoticorn','re(2): a way to the solution','2003-07-13 01:57:49',0,'Hm.. yes, you are right, I overlooked a few things that still need to be dealt with.\r\n\r\n0 1 5 5: The same argument as with 0 0 0 1: 711 is too big\r\n5 5 5 6: Since I only used 5 and 6 to find two numbers of the solution, this set works just as well.\r\n\r\nThe numbers ending in 6: I wasn\'t looking hard enough outside the range of 75 - 319, because it is simple to show that all numbers of the solution have to be in that range:\r\nFor any number x in the solution, the following must be true:\r\n((711-x)/3)^3 > 711000000/x\r\nOtherwise the product of the remaining numbers can never be big enough. This is quite simple. (711-x) is the remaining sum for the 3 other numbers. This is divided by 3, and the result multiplied 3 times, as this will give the largest possible product for the given sum. The result is then compared to 711000000/x which is the target product for the last 3 numbers.\r\nI won\'t solve this inequation now, it is simpler to just try out for which range of numbers it holds true.\r\n\r\nThanks for finding the holes in my solution so that I could try to fill them ;)',6391,0);
INSERT INTO comment VALUES (6413,1008,2700,'claire','the answer','2003-07-13 02:05:27',0,'elizabeth was drinking coffee. she has two e\'s in her name like everyone else drinking coffee.',NULL,0);
INSERT INTO comment VALUES (6414,1032,1575,'DJ','Wild Guess','2003-07-13 08:46:50',3,'KG and QN, maybe?\r\n\r\nThey are abbreviations of the chess pieces by value:\r\nPawN, BishoP, KnighT, RooK...',NULL,0);
INSERT INTO comment VALUES (6415,1032,2703,'Mike Grunfield','','2003-07-13 09:12:04',0,'I think your on the right track Wild Guess but I would suggest \"QN, KG\" instead since it appears the peices are being sorted first by chessic value then alphabetical name (ie: PN (value = 1), BP (value =3), KT (value = 3), RK (value = 5), QN (value = 9), KG (value = priceless) ',NULL,0);
INSERT INTO comment VALUES (6416,1008,2703,'Mr. Spock','Illogical','2003-07-13 09:23:40',0,'I don\'t think it\'s logical to assume just because Elizabeth has two e\'s in her same she is drinking coffee. So I think the actual answer is \"possibly\" (raises eyebrow)',NULL,0);
INSERT INTO comment VALUES (6417,1008,2703,'Mr. Spock','Illogical','2003-07-13 09:30:56',0,'Please forgive my misspelling of the word name in my previous posting, although perfectly logical my human side makes occasional spelling errors.',NULL,0);
INSERT INTO comment VALUES (6418,1032,1626,'Gamer','re:','2003-07-13 10:57:12',0,'Yes, I would say DJ\'s idea is right, but flipped... QN, then KG',6415,0);
INSERT INTO comment VALUES (6419,1032,2571,'Rob','Other thoughts','2003-07-13 18:02:11',1,'I\'d go with your theory, but in chess a knight\'s abbreviation is N, not K. So here\'s what I think. The first two pairs, PN and BP, both have something in common. They each have a P. Also, N and B are right next to each other on the keyboard, N being directly to the left of P. Then look at KT and RK. Both have K\'s, and T is next to R. Is would help if the next pair was shown, and you only had to figure out one of the pairs, but you just have to guess.',NULL,0);
INSERT INTO comment VALUES (6420,1016,1575,'DJ','Solution','2003-07-13 20:54:54',3,'The greatest common divisor of two integers m and n can be interpreted as the number of lattice points in the plane which lie on the straight line connecting the vectors (0,0) and (m, n), excluding (m, n) itself.\r\n\r\nTherefore, any lattice point (m, n) that is \'visible\' from the origin, that is, no other lattice points lie on the line connecting the (0,0) vector and its own, means that the selected values of m and n have no greatest common factor; they are relatively prime.\r\n\r\nTherefore, we need to find the fraction of all lattice points that are visible from the origin. This is found by using the Riemann zeta function, to represent which let\'s use Ç(z).\r\n\r\n1/[Ç(2)] is the fraction of Cartesian coordinate pairs visible from the origin, and is thus the fraction we are looking for.This evaluates to 1/(π²/6), or 6/π².\r\n\r\n6/π² is approximately 0.60788555894594382, which is about the same value Charlie found experimentally.\r\n\r\nIn general, the probability that n randomly selected integers lack a common divisor is [Ç(n)]^(-1).\r\nThe probability that n random integers lack a pth power common divisor is [Ç(np)]^(-1).\r\n\r\nFor more about the Riemann zeta function, look <a href=http://mathworld.wolfram.com/RiemannZetaFunction.html>here.',NULL,0);
INSERT INTO comment VALUES (6421,1032,2709,'Chris','i m gonna have to say...','2003-07-13 21:00:21',3,'ND, SN... i say this cuz of their position on the keyboard... am i right? cuz from P, left one down one is K, and left one down one is N... and for the other letters... N left one down one (imagine going back to the top of the board) would be T, and left one down one of T is D... and S is left of D just like B is left of N and R is left of T... so i would have to say ND, SN...',NULL,0);
INSERT INTO comment VALUES (6422,1008,2710,'Richie','But but but...','2003-07-13 22:52:30',1,'this is a bit of an illogical one.. If steve is referred to as \"ste\" by his friends, does it mean he can only drink soda in their presence?',NULL,0);
INSERT INTO comment VALUES (6423,983,2710,'Richie','Hehe... reminds me of my local','2003-07-13 23:08:19',0,'Reminds me of a sign we have in the bar I frequent... the sign states: IITYWYBMAD?\r\nWhen someone notices it, the simple reply of \"If I tell you, will you buy me a drink?\" is usually enough to get alcohol gratis ;)\r\nSometimes though, they get really pissed off.... :/',NULL,0);
INSERT INTO comment VALUES (6424,1008,1732,'Helen','logical statement','2003-07-14 00:22:12',0,'Elizabeth is drinking coffee = TRUE,\r\nELSE Elizabath is not drinking coffee\r\n',NULL,0);
INSERT INTO comment VALUES (6425,1008,1732,'Helen','re: But but but...','2003-07-14 00:25:08',0,'If ste can only drink soda infront of his friends, so can \'Lizzie\' and \'Hel\'. :-Q',6422,0);
INSERT INTO comment VALUES (6426,976,2592,'ben young','solution','2003-07-14 03:03:59',0,'1089+9801=10890/10=1089',NULL,0);
INSERT INTO comment VALUES (6427,1016,1301,'Charlie','re: Solution','2003-07-14 03:08:54',0,'But 6/π² is 0.6079271018540279 to the accuracy given, closer in fact to the product calculation I did than the 0.60788555894594382 you quote.',6420,0);
INSERT INTO comment VALUES (6428,1032,2572,'derek','re: Other thoughts','2003-07-14 03:17:02',0,'While this is indeed the case, I think it\'s more coincidental than anything. I agree with the previous solutions regarding the chess pieces. The title is \"A Word Sequence\", so I doubt they are just pairs of letters that are positioned in a certain way on the keyboard.',6419,0);
INSERT INTO comment VALUES (6429,1015,2708,'Kyph','Solution','2003-07-14 03:42:29',0,'He\'s looking at the numbers in the wrong way. If he had gone around and looked at the numbers from the other side, he would\'ve seen 91, 90, 89, and 88.',NULL,0);
INSERT INTO comment VALUES (6430,1033,2682,'exoticorn','I cheated...','2003-07-14 04:01:09',3,'...and used Google.\r\nBut then I\'m not from the US and don\'t know the full initials of the former US presidents. In fact, I\'m not even used to middle names, so the letters didn\'t look much like initials to me, although I am aware that they are common in the US.',NULL,0);
INSERT INTO comment VALUES (6431,1033,2572,'derek','solution','2003-07-14 04:03:19',3,'LBJ, JFK\r\n\r\npresidents\r\ngeorge h. w. bush\r\nronald w. reagan\r\njames e. carter\r\ngerald r. ford\r\nrichard m. nixon\r\nlyndon b. johnson\r\njohn f. kennedy',NULL,0);
INSERT INTO comment VALUES (6432,1033,2710,'Richie','a wee bit biased','2003-07-14 04:58:24',1,'Yea, \'tis a bit biased in favour (or should that be favor? lol) of our american counterparts.\r\n\r\nIf it were to be a list of british prime ministers, I think they too would struggle.\r\n\r\nR.',NULL,0);
INSERT INTO comment VALUES (6433,1008,2710,'Richie','re(2): But but but...','2003-07-14 05:03:58',1,'But I presume \'Kaz\' isn\'t allowed a drink with her friends, irrelevant of how thirsty she is? :s\r\n\r\nR.',6425,0);
INSERT INTO comment VALUES (6434,483,2681,'helena','wierd','2003-07-14 05:19:10',0,'These guys are really dumb because all of the guys except the last one who divided the coconuts knew that there were more to start than there were now and none of them would accept the coconuts happily unless the first guy who went knew for sure that he went first.',NULL,0);
INSERT INTO comment VALUES (6435,1016,1575,'DJ','re(2): Solution','2003-07-14 05:43:21',0,'Sorry, that must have just been a calculator error on my part...',6427,0);
INSERT INTO comment VALUES (6436,1033,1732,'Helen','re: a wee bit biased','2003-07-14 05:48:36',0,'I second that!\r\n\r\nLets see how good the americans are\r\n\r\nWC, MT, JM, TB....',6432,0);
INSERT INTO comment VALUES (6437,1033,1921,'Travis Taylor','re(2): a wee bit biased','2003-07-14 06:00:56',0,'Winston Churchill, Margaret Thatcher, (I\'m still racking my brain for JM, and for integrity\'s sake, I\'m not looking it up) and Tony Blair\r\n\r\n',6436,0);
INSERT INTO comment VALUES (6438,1033,1645,'luvya2003','re: a wee bit biased','2003-07-14 06:09:21',0,'Actually i wasn\'t being biased at all. When this problem first entered the voting queue, i had a much wider range of presisdents, but using that many gave the problem away (as the voters reminded). So I ended cutting a few off the beginning and end. :!',6432,0);
INSERT INTO comment VALUES (6439,995,2708,'Kyph','The Cheap Solution','2003-07-14 06:37:02',0,'I guess I can cheat and say 1 + 1 + 1 + 1 is such a geometric series, as well as 1 + (9 times), but I doubt that\'s what you want.\r\n\r\nVery interesting problem. I\'ve got to spend my lunch thinking about this.',NULL,0);
INSERT INTO comment VALUES (6440,957,1567,'Bryan','re: Please post more about Solution','2003-07-14 06:40:30',2,'Ender, sorry to keep you waiting. Yes, a picture helps immensely with this puzzle. Unfortunately, a 50x50 grid is a little unwieldy in this format, so I will explain with a 10x10 grid.\r\n\r\nOne early solution posted was to repeat a pattern such as:\r\n\r\nl...\r\n.l.l\r\n..l.\r\n.l.l\r\n\r\nwhere a period (“.”) represents a liar, while an “l” represents a knight. This is almost correct, but if you look at a 10x10 grid of this you get:\r\n\r\nl...l...l.\r\n.l.l.l.l.l\r\n..l...l...\r\n.l.l.l.l.l\r\nl...l...l.\r\n.l.l.l.l.l\r\n..l...l...\r\n.l.l.l.l.l\r\nl...l...l.\r\n.l.l.l.l.l\r\n\r\nObviously, there are a few liars on the bottom and right-hand edges that are surrounded by knights, which violates the requirements of this problem. Instead, lets start with a pure checkerboard pattern:\r\n\r\nl.l.l.l.l.\r\n.l.l.l.l.l\r\nl.l.l.l.l.\r\n.l.l.l.l.l\r\nl.l.l.l.l.\r\n.l.l.l.l.l\r\nl.l.l.l.l.\r\n.l.l.l.l.l\r\nl.l.l.l.l.\r\n.l.l.l.l.l\r\n\r\nIf you count the diagonals of l’s that travel from the upper right corner to the lower left, there are ten of them (or n diagonals for an nxn grid), each with an odd number of l’s. To generate a pattern where no liar is completely surrounded by knights, we will change every other diagonal of l’s, removing every other l, always starting by removing an l from the edge of the grid. The resulting pattern looks like:\r\n\r\nl...l...l.\r\n.l.l.l.l..\r\n..l...l.l.\r\n.l.l.l...l\r\nl...l.l.l.\r\n.l.l...l..\r\n..l.l.l.l.\r\n.l...l...l\r\nl.l.l.l.l.\r\n...l...l..\r\n\r\nThus from the initial n²/2 l’s of a pure checkerboard, we subtract one fourth of them (n²/8) when we subtract every other l from every other diagonal, and we subtract an addition n/4 l’s when we force the altered diagonals to start and end with a liar (“.”). The n/4 may not be obvious at first blush, but try this with grids of 14x14 etc. and this term is confirmed.\r\n\r\nSorry I didn’t submit a diagram with the original solution.\r\n',6121,0);
INSERT INTO comment VALUES (6441,995,1575,'DJ','Starters','2003-07-14 06:43:22',1,'The sum of the first n terms of a geometric series is:\r\n\r\nSn = t1(1-r^n)/(1-r)\r\n\r\nwhere t1 is the first term and r is the common ratio (and not 0).\r\n\r\nSince this problem specifies that t1=1, we need to find a solution for\r\n\r\nSn = (1-r^n)/(1-r) = x²\r\n\r\nwhere x, r, and n are all integers.\r\n\r\nI haven\'t time to complete it now (back to work!), but that is where I think we need to start.',NULL,0);
INSERT INTO comment VALUES (6442,544,2667,'Viet','','2003-07-14 06:43:28',3,'a charcoal',NULL,0);
INSERT INTO comment VALUES (6443,174,2667,'Viet','','2003-07-14 06:45:38',0,'if you choose and answer itz solveable so A',NULL,0);
INSERT INTO comment VALUES (6444,995,2708,'Kyph','Solution','2003-07-14 06:46:14',0,'Well, I tried this one, and it worked.\r\n\r\n1 + 3 + 9 + 27 + 81 = 121 = 11²',NULL,0);
INSERT INTO comment VALUES (6445,995,2682,'exoticorn','2 solutions','2003-07-14 06:48:05',3,'1 + 3 + 9 + 27 + 81 = 121 = 11^2\r\n1 + 7 + 49 + 343 = 400 = 20^2',NULL,0);
INSERT INTO comment VALUES (6446,995,1567,'Bryan','Halfway there','2003-07-14 06:51:51',2,'From simple observation, I found a geometric factor of 3 to work with five terms:\r\n\r\n1+3+9+27+81=121=11²\r\n',NULL,0);
INSERT INTO comment VALUES (6447,995,2682,'exoticorn','after some quick programming...','2003-07-14 06:58:54',0,'If my program works correctly, my two solutions are the only ones resulting in a square smaller than 10,000,000, so it seems they are the only ones.\r\nMaybe someone can find a proof that those are indeed the only solutions.',NULL,0);
INSERT INTO comment VALUES (6448,922,2667,'Viet','hopefully this site is so confusing','2003-07-14 07:03:04',0,'7 times keep on guessing the middle number like 50 then if lower 25 and so on',NULL,0);
INSERT INTO comment VALUES (6449,334,2667,'Viet','','2003-07-14 07:10:11',0,'light?',NULL,0);
INSERT INTO comment VALUES (6450,202,2667,'Viet','i got it.....','2003-07-14 07:21:55',3,'the son go down first 90-75 =15 ao it okai\r\nthe son then hop on to the other basket and take the wieght out making it 90 then the daughter goes down 105-90=15 so itz okai\r\nthen the daughter use the wieght and herself to get in the basket making it 180 the queen is 195 so 180-195=15 so itz safe',NULL,0);
INSERT INTO comment VALUES (6451,61,2681,'helena','another possible solution','2003-07-14 08:24:52',0,'he left his origin on saturday\r\n',NULL,0);
INSERT INTO comment VALUES (6452,990,2713,'matt Tortorice','w/out reading everyone\'s responses','2003-07-14 09:24:58',0,'It doesn\'t say the pitcher started the game, it says he came in, \"in the first inning.\" Which could be after the previous pitcher gave up any number of runs.',NULL,0);
INSERT INTO comment VALUES (6453,921,2713,'matt Tortorice','No, never take a bet where you have no chance of coming out ahead','2003-07-14 09:31:42',0,'Not to mention it doesn\'t say anything about whether there may be a hole in either glass.',NULL,0);
INSERT INTO comment VALUES (6454,1033,1626,'Gamer','re(2): a wee bit biased','2003-07-14 11:34:07',1,'I think what they mean is using American presidents, rather than something from another place (such as prime ministers)',6438,0);
INSERT INTO comment VALUES (6455,980,2716,'Federico Kereki','Solution?','2003-07-14 15:10:41',0,'I\'d say Johnny is a Knight and Jimmy is a Knave (first sentence, true; second sentence, false).',NULL,0);
INSERT INTO comment VALUES (6456,1008,2716,'Federico Kereki','','2003-07-14 15:17:13',1,'I\'d suggest Elizabeth should drink coffee, because there are two \'E\'s in her name. \r\n\r\nMaybe the others (who only have ONE \'E\') are having Coke, Pepsi, or Sprite! ;-)',NULL,0);
INSERT INTO comment VALUES (6457,977,2716,'Federico Kereki','Solution','2003-07-14 15:35:14',3,'for i = 9 down to 1, \r\n set array[i] to i\r\nfor i = 9 down to 1, \r\n swap array[i] with array[random(i)]\r\n',NULL,0);
INSERT INTO comment VALUES (6458,970,2716,'Federico Kereki','A binary solution','2003-07-14 15:49:01',3,'Use RAND5() to generate a binary number like this:\r\n\r\nBINARY(): \r\n repeat \r\n let B = RAND5()\r\n until B<5\r\n if B=1 or 2, return 0; else, return 1\r\n\r\nThis BINARY() function does, on the average, 5/4ths calls to RAND5().\r\n\r\nYou can construct the desired function as\r\n\r\nRANDOM_1_TO_7():\r\n return BINARY() + 2*BINARY() + 4*BINARY()\r\n\r\nwhich requires three calls to BINARY(), and thus 15/4ths calls to RAND5().\r\n',NULL,0);
INSERT INTO comment VALUES (6459,65,1626,'Gamer','re: Clarified explanation (solution)','2003-07-14 17:08:00',0,'The arguement I would say is either side of the red/black card is fine. If it\'s the front of the red black card you can with with it and if it\'s the back you can also win.',4699,0);
INSERT INTO comment VALUES (6460,995,1575,'DJ','Programming Solution','2003-07-14 18:10:12',3,'Earlier, I quoted the rule for the sum of a number of terms in a geometric sequence, which I had hoped would lead to a \'clean\' (not brute-force) method of solving the problem:\r\n\r\nSn = (1-r^n)/(1-r)\r\n\r\nI could not come up with anything, so I wrote the following small javascript program to find the solutions:\r\n\r\nvar rlim=10\r\nvar nlim=10\r\nfor (r=2; r<=rlim; r++) {\r\n for (n=3; n<=nlim; n++) {\r\n test=Math.sqrt((Math.pow(r,n)-1)/(r-1));\r\n if (test==Math.round(test)) {\r\n document.write(\"r=\" + r + \", n=\" + n);\r\n document.write(\", root=\" + test + \"<br>\");\r\n }\r\n }\r\n}\r\n\r\nThe program will use values of the geometric ratio from 2 to rlim, and check the sum of the first 3 up to nlim terms.\r\n\r\nThe first time, I set both parameters to 10, and came up with:\r\n\r\nr=3, n=5, root=11\r\nr=7, n=4, root=20\r\n\r\nThese correspond to the series:\r\n\r\n1+3+9+27+81 = 121 = 11²\r\n1+7+49+343 = 400 = 20²\r\n\r\nThen, I set both to 100, and came up with more solutions than I will bother posting.\r\n\r\nSetting rlim to 15 and nlim to 30 yields:\r\n\r\nr=3, n=5, root=11\r\nr=7, n=4, root=20\r\nr=11, n=30, root=1320961856712237\r\nr=13, n=28, root=1136622658092180\r\nr=13, n=29, root=4098151274605530\r\nr=13, n=30, root=14776094555198342\r\nr=14, n=29, root=11531474452649720\r\nr=14, n=30, root=43146826566151816\r\nr=15, n=28, root=7802137664603434\r\nr=15, n=29, root=30217549239826724\r\nr=15, n=30, root=117032064969051500\r\n\r\nFrom this, I garner that there are an infinite number of solutions, or at least an exorbitant number, but the lowest two are the only ones with a reasulting square that is less than a million or so.\r\n\r\nLastly, I decided to try to find the least number of terms required for each ratio. I rewrote the program as follows:\r\n\r\nvar rlim=100\r\nfor (r=2; r<=rlim; r++) {\r\n found=0;\r\n for (n=3; found==0; n++) {\r\n test=Math.sqrt((Math.pow(r,n)-1)/(r-1));\r\n if (test==Math.round(test)) {\r\n document.write(\"r=\" + r + \", n=\" + n);\r\n document.write(\", root=\" + test + \"<br>\");\r\n found=1;\r\n }\r\n }\r\n}\r\n\r\nThis program will take the sums of each ratio, starting with 2, and go on the the next as soon as a solution is found. Here are the first 50 terms:\r\n\r\nr=2, n=54, root=134217728\r\nr=3, n=5, root=11\r\nr=4, n=51, root=1300077228592327\r\nr=5, n=46, root=5960464477539062\r\nr=6, n=40, root=1635083761698081\r\nr=7, n=4, root=20\r\nr=8, n=35, root=2407275258974741\r\nr=9, n=34, root=5896274135457212\r\nr=10, n=33, root=10540925533894598\r\nr=11, n=30, root=1320961856712237\r\nr=12, n=31, root=16092109205777158\r\nr=13, n=28, root=1136622658092180\r\nr=14, n=29, root=11531474452649720\r\nr=15, n=28, root=7802137664603434\r\nr=16, n=27, root=4651297694611162\r\nr=17, n=26, root=2476144508226484\r\nr=18, n=25, root=1190369670978259\r\nr=19, n=25, root=2273964913345265\r\nr=20, n=24, root=939686845933821\r\nr=21, n=26, root=34541073727069636\r\nr=22, n=24, root=2805191553125691\r\nr=23, n=22, root=203139722937865\r\nr=24, n=23, root=1554409213026084\r\nr=25, n=24, root=12166747166629524\r\nr=26, n=23, root=3743031632151674\r\nr=27, n=24, root=29435979779422724\r\nr=28, n=23, root=8445696647005056\r\nr=29, n=22, root=2305679622019467\r\nr=30, n=23, root=18017537321387356\r\nr=31, n=22, root=4638931982669926\r\nr=32, n=23, root=36605294376580070\r\nr=33, n=22, root=8934666562827252\r\nr=34, n=22, root=12218309374749672\r\nr=35, n=22, root=16558043886178964\r\nr=36, n=20, root=618003572316160\r\nr=37, n=21, root=4874912807386812\r\nr=38, n=21, root=6362486918825504\r\nr=39, n=22, root=51501381505130264\r\nr=40, n=21, root=10619341945791228\r\nr=41, n=21, root=13589406813041232\r\nr=42, n=20, root=2667478794465129\r\nr=43, n=20, root=3334724118586259\r\nr=44, n=20, root=4147558659928599\r\nr=45, n=20, root=5133325454093174\r\nr=46, n=21, root=42889499254061090\r\nr=47, n=19, root=1131229532544889\r\nr=48, n=20, root=9470293632463196\r\nr=49, n=20, root=11517021606544148\r\nr=50, n=20, root=13950892857142858\r\n\r\nThe number of terms needed to add to find a square pretty steadily decreases as the base ratio increases.\r\nClose to 100, it takes about 17 terms to find a perfect square sum;\r\naround 1000, 12;\r\naround 10000, 9;\r\naround 100000, 8;\r\naround a million, 6;\r\n10 million, 6;\r\naround 100 million, 5 (although exactly 100000000 is a local minimum of 4);\r\nand there is not a series of three terms to be found with a ratio anywhere less than 1000000000000.',NULL,0);
INSERT INTO comment VALUES (6461,1033,1183,'fwaff','re(3): a wee bit biased','2003-07-14 21:28:53',0,'Hmmm... the (British) problem would have been more difficult had it not missed out several between Sir Winston and Maggie the milk-snatcher. Also Tony Blair\'s initials are AB (or even ACLB) rather than TB.',6437,0);
INSERT INTO comment VALUES (6462,566,1183,'fwaff','re: thoughts','2003-07-14 21:35:38',0,'Mike\'s is similar, but more wasteful. I reuse 6 galls from the 11gall bucket on each of the two \'1 gallon loops\', thereby only wasting 10 in total rather than 22.',6400,0);
INSERT INTO comment VALUES (6463,995,2682,'exoticorn','re: Programming Solution','2003-07-14 22:41:33',0,'Unfortunately, it appears that your program suffers from precision problems. Since Math.sqrt and Math.pow are most likely floating point operations, their precission is limited.\r\nYour first two \"big\" solutions are:\r\n\r\nr=11, n=30, root=1320961856712237\r\nr=13, n=28, root=1136622658092180\r\n<\\tt>\r\n\r\nBut the sum of the first series is:\r\n1744940226888640731855880375380\r\nWhile the square of your root is:\r\n1744940226888640555371025544169\r\n\r\nThe sum of your second series is:\r\n1291911066888533017939127925460\r\nWhile the square is:\r\n1291911066888532717237377152400\r\n\r\nSo it still looks like there are no further solutions after the first two, but of course such things need to be proved mathematically.',6460,0);
INSERT INTO comment VALUES (6464,1033,1732,'Helen','re(4): a wee bit biased','2003-07-14 22:47:58',0,'OK I hang my head in shame! I don\'t actually know who was prime minister after Whinston Churchill, and I forgot that it was Anthony Blair rather than Tony. We could have done a similar puzzle with monarchs of countries etc.',6461,0);
INSERT INTO comment VALUES (6465,567,2682,'exoticorn','solution','2003-07-15 02:11:47',3,'A table showing who was expecting who to win:\r\n\r\nA: P..S\r\nB: .QRS\r\nC: PQ..\r\n\r\nIt is easy to see that the only contestant who wasn\'t expected to win by two people is R, so B made the correct statement.',NULL,0);
INSERT INTO comment VALUES (6466,567,1732,'Helen','the answer','2003-07-15 02:47:06',0,'B is correct because if A or c are correct, P is expected to win and lose. Therefore R wins.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (6467,567,1732,'Helen','just being pedantic...','2003-07-15 02:51:02',0,'if P or S wins, then A, B and C could all have made correct statements, because B and C only said they were CONFIDENT. You can have false confidence in something.',NULL,0);
INSERT INTO comment VALUES (6468,830,2722,'Jack Putz','Doubt this is the expected solution, but it works','2003-07-15 04:00:02',0,'Imagine the two samples of water are held in rigid containers, completely covered, and filled to 100% capacity.\r\n\r\nNow if your cold sample was at 4 degrees C, it would not be able to freeze because it cannot expand in the rigid container. \r\n\r\nThe hot sample would be able to freeze because, if it were hot enough, will be able to cool down (become more dense), then freeze (expand again).\r\n\r\nAgain... doubt that the expected solution deals with pressure in this way, but it works\r\n',NULL,0);
INSERT INTO comment VALUES (6469,478,2722,'Jack Putz','simple','2003-07-15 04:10:01',0,'if the premise behind the question is correct (that the Earth\'s rotation is slowing down because of tidal bulges), then its quite simple. As said, the energy is dissipated as heat. Likewise, the Angular momentum is transfered to the individual particles along with the heat (momentum and energy are not separate concepts, but are linked)',NULL,0);
INSERT INTO comment VALUES (6470,633,2722,'Jack Putz','re: Answer???','2003-07-15 04:25:23',0,'i think its because you\'re an idiot',3509,0);
INSERT INTO comment VALUES (6471,633,2722,'Jack Putz','re: Solution','2003-07-15 04:26:52',0,'please refer to my answer to Chris\'s comment',4581,0);
INSERT INTO comment VALUES (6472,567,2708,'Kyph','Solution','2003-07-15 04:50:10',0,'If P won, then A and C are right.\r\nIf Q won, then B and C are right.\r\nIf S won, then A and B are right.\r\nSo R won, and B is the only one that was right.',NULL,0);
INSERT INTO comment VALUES (6473,990,2670,'saad','re(3): Solution','2003-07-15 04:58:14',0,'yes, but does the word \"recorded\" mean that it wasnt recorded into THE PITCHER\'S stats or the scoreboard in the stadium? because the ERA is still 0.00 because a wildpitch is not an error, if his ERA is still 0.00, then no it wasnt recorded into his stats but was only recorded in the scoreboard and for the sake of the game, meaning who was going to win or lose...it is that if he came into the first inning due to injury to the starter...also, i think this pitcher might be the relief pitcher, the starter gave up runs and was taken out of the game, which is the most likely.',6370,0);
INSERT INTO comment VALUES (6474,860,2670,'saad','?','2003-07-15 04:59:33',0,'Heaven? (assuming what people think of it as, up in the sky, and hell is down under) i dont know just a wild guess...',NULL,0);
INSERT INTO comment VALUES (6475,537,2670,'saad','?','2003-07-15 05:01:08',0,'death',NULL,0);
INSERT INTO comment VALUES (6476,537,2670,'saad','re: Solution?','2003-07-15 05:03:02',0,'i agree, you can \"see\" darkness (if your eyes are wide open and there is no light and its dark, you therefore see darkness) , i had the same answer as you, which was death.',5715,0);
INSERT INTO comment VALUES (6477,360,2670,'saad','good one','2003-07-15 05:04:51',0,'it may have been easy for some, but it was a good one nonetheless.',NULL,0);
INSERT INTO comment VALUES (6478,567,1575,'DJ','Well','2003-07-15 05:26:46',0,'If P or S won, then A is correct, and B and C were lying about how confident they were.\r\n\r\nIf Q or R won, then A was wrong, and of B and C, one was telling the truth and the other was lying.\r\n\r\nA statement of confidence can be true or false regardless of the actual result of the contest.',NULL,0);
INSERT INTO comment VALUES (6479,995,1575,'DJ','re(2): Programming Solution','2003-07-15 05:41:05',0,'You\'re right; I wrote the program quickly, expecting to find relatively small, workable numbers, then failed to consider the precision involved since all the numbers are integers.\r\n\r\nI rewrote the program as follows to show the entire expansion and its sum, as well as the square of the located root for comparison. I used rlim==1 and nlim=30, so as to only show the first two \'accepted\' solutions and the lowest \'big\' solution found previously:\r\n\r\nfunction display(r, n, root) {\r\n var sum=0;\r\n for (a=0; a<=n-1; a++) {\r\n term=Math.pow(r,a);\r\n document.write(term);\r\n if (a<n-1)\r\n document.write(\" + \");\r\n sum+=term;\r\n }\r\n var square=root*root;\r\n document.write(\" = \" + sum + \"<br>\" + root + \"² = \"\r\n document.write(square + \"<br><br>\");\r\n}\r\n\r\nvar rlim=11\r\nvar nlim=30\r\nfor (r=2; r<=rlim; r++) { \r\n for (n=3; n<=nlim; n++) { \r\n test=Math.sqrt((Math.pow(r,n)-1)/(r-1)); \r\n if (test)==(Math.round(test)) { \r\n display(r,n,test);\r\n } \r\n } \r\n} \r\n\r\nThis yielded:\r\n\r\n1 + 3 + 9 + 27 + 81 = 121\r\n11² = 121\r\n\r\n1 + 7 + 49 + 343 = 400\r\n20² = 400\r\n\r\n1 + 11 + 121 + 1331 + 14641 + 161051 + 1771561 + 19487171 + 214358881 + 2357947691 + 25937424601 + 285311670611 + 3138428376721 + 34522712143931 + 379749833583241 + 4177248169415651 + 45949729863572160 + 505447028499293760 + 5559917313492231000 + 61159090448414550000 + 672749994932560100000 + 7.400249944258161e+21 + 8.140274938683976e+22 + 8.954302432552373e+23 + 9.84973267580761e+24 + 1.0834705943388372e+26 + 1.191817653772721e+27 + 1.310999419149993e+28 + 1.4420993610649922e+29 + 1.5863092971714916e+30 = 1.7449402268886408e+30\r\n1320961856712237² = 1.7449402268886406e+30\r\n\r\nSo indeed, the default precision of 16 places in javascript should account for the insane number of solutions the first program found, as well as the steady decline in the number of terms.\r\n\r\nI don\'t know how to prove that those two soltions are unique, but it is certainly shown that they are the only sets of \'workable\' numbers that work.\r\n\r\nI really shouldn\'t tackle problems like this at 2am...',6463,0);
INSERT INTO comment VALUES (6480,567,2681,'helena','maybe','2003-07-15 06:38:54',0,'c made the correct statement and R won\r\n',NULL,0);
INSERT INTO comment VALUES (6481,543,2670,'saad','what about...?','2003-07-15 07:23:35',0,'...your head or skull?',NULL,0);
INSERT INTO comment VALUES (6482,1033,2724,'PRIVATE','','2003-07-15 07:35:40',0,'I GOT IT.... SUDDENLY IT BECAME OBVIOUS.. I DON\'T KNOW IF I SHOULD GIVE THE ANSWER HERE, BUT HERES A HINT. IT STARTS IN 1989, AND GOES BACK TO 1961\r\n\r\n-PEACE OUT!!',NULL,0);
INSERT INTO comment VALUES (6483,393,2722,'Jack Putz','Solution','2003-07-15 08:15:54',0,'The solution is a little off. The reaction \"HCO3(-) --> 2H + CO3(2-)\" is actually negligible when you factor in Equilibrium constants and the like.\r\n\r\nBut yes... The basic idea to the solution is correct as far as Carbonic Acid being the reason',NULL,0);
INSERT INTO comment VALUES (6484,1025,2572,'derek','solution','2003-07-15 08:24:11',3,'9, 81\r\n\r\nsquare each individual number and sum them \r\n9^2=81\r\n8^2=64, 1^2=1, 64+1=65\r\n6^2=36, 5^2=25, 36+25=61\r\n\r\n...\r\n\r\n145, 42, 20, 4\r\n\r\nthe next 1 digit number will be 4',NULL,0);
INSERT INTO comment VALUES (6485,1025,1301,'Charlie','Phenomenon','2003-07-15 09:35:21',1,'Regardless of what number you start with, using the procedure from the solution, you will eventually get into either a continuous repetition of 1, or a cycle consisting of the numbers 4 16 37 58 89 145 42 20, beginning at some number within this cycle.\r\n\r\nStarting with one of: 1, 7, 10, 13, 19, 23, 28, 31, 32 ... eventually (quickly actually) leads to the repetition of 1\'s. Other numbers smaller than 31 lead to the cycle that includes 4. I don\'t see a particular pattern of what leads to the 1\'s and what leads to the 4-etc.-cycle.',NULL,0);
INSERT INTO comment VALUES (6486,567,2725,'J K','solution','2003-07-15 10:47:05',0,'B made the correct statement and R won.\r\n\r\nIf P won, A would be true, B would be false, and C would be true.\r\nIf Q won, A would be false, B would be true, and C would be true.\r\nIf R won, A would be false, B would be true, and C would be false.\r\nIf S won, A would be true, B would be true, and C would be false.\r\n\r\nTherefore, R won because there was only one true statement.\r\n\r\nJennifer,16,CT',NULL,0);
INSERT INTO comment VALUES (6487,566,2730,'Pok Teh','alternative solution','2003-07-15 23:55:52',0,'this solution is very similar to lewis\' with only a slight difference..\r\n\r\nfill both 6G -> 0-6-6\r\nfill 11G from both 6G -> 11-1-0\r\nfill empty 6G from 11G -> 5-1-6\r\nempty 11G -> 0-1-6\r\nfill 11G from both 6G -> 7-0-0\r\nfill 6G -> 7-6-0\r\nfill 11G from 6G -> 11-2-0\r\nfill empty 6G from 11G -> 5-2-6\r\nempty 11G -> 0-2-6\r\nfill 11G -> 8-0-0',NULL,0);
INSERT INTO comment VALUES (6488,568,2731,'Venisha Nair','hmmm...','2003-07-16 01:59:06',0,'ok... first you heat up the bottle or a flame so the air within it expands. As a result of that, the cork should pop out on its own. Then you turn the bottle upside down. The coin will then fall out. (assuming gravity exist) ((haha... ok. lousy joke!)) I did not take out the cork. Neither did i break the bottle. :) ',NULL,0);
INSERT INTO comment VALUES (6489,568,2682,'exoticorn','maybe...','2003-07-16 02:09:15',3,'...you can simply try to push the cork IN, leaving the neck unobstructed without taking the cork out ;)',NULL,0);
INSERT INTO comment VALUES (6490,568,1732,'Helen','solutions','2003-07-16 03:00:15',3,'Push the cork into the bottle and tip the coin out.\r\n\r\nOr if the cork is big enough, drill a hole in it and tip the coin through the hole.\r\n\r\nFailing that, ring scottie and ask him to \'beam it up\', LOL!',NULL,0);
INSERT INTO comment VALUES (6491,567,2732,'gary','solution','2003-07-16 03:29:32',0,'r wins the race and b was correct. all other winners have at least two people who would be telling the truth.',NULL,0);
INSERT INTO comment VALUES (6492,905,2733,'angela','^-^','2003-07-16 03:44:37',0,'wow...cant believe how fast i did this (in bout 5 mins?) when i first read the questions i was like \"what the...\" \r\nthen i just decided to pick a random answer and go from there...as it happened to turn out i got the same solution as DJ, except my ques. 3 answer was c) *^^*',NULL,0);
INSERT INTO comment VALUES (6493,568,2667,'Viet','my lil sister told me this lolz','2003-07-16 04:36:50',0,'imagine the coin outside like you just did with the coin and cork above',NULL,0);
INSERT INTO comment VALUES (6494,984,2674,'mike','solution','2003-07-16 08:32:58',3,'Father-41\r\nMother-40\r\nSon-20\r\nDaughter-12\r\nGrandmother-54',NULL,0);
INSERT INTO comment VALUES (6495,984,2674,'mike','solution','2003-07-16 08:33:09',3,'Father-41\r\nMother-40\r\nSon-20\r\nDaughter-12\r\nGrandmother-54',NULL,0);
INSERT INTO comment VALUES (6496,984,1301,'Charlie','Solution','2003-07-16 08:54:39',3,'If the ages are: father, F; mother, M; daughter, D; son, S; grandmother, G, then:\r\n\r\n1. This was M-D years ago so G-(M-D)=2(F-(M-D)) or G=2F-M+D\r\n\r\n2. F+1=2(S+1) or F = 2S+1\r\n\r\n3. S-D/3=2(2D/3) or S=5D/3\r\n\r\n4. This was M-(2D-10) years ago so G-(M-(2D-10))=2(2D-10) or G = 2D+M-10\r\n\r\nand from 1 & 4: M=(2F-D+10)/2\r\n\r\nFrom 3, D must be a multiple of 3 and from the last equation, from 1&4, D must be even, thus D must be a multiple of 6. Using the possible values for D we get a table of the other values:\r\n Consider a situation where the ages are not all the same, say ages of 43, 44, and 45. The [products of these ages is 1892, 1935, and, 1980. Not only do these values not meet the requirements of the puzzle, but subtracting each of those numbers from any given year gives too large a disparity in ages, which when you multiply them together gives products that are even further apart. In other words, it seems the three partygoers must be the same age for this to work.',NULL,0);
INSERT INTO comment VALUES (6581,1021,1301,'Charlie','solution','2003-07-21 12:10:19',3,'It would seem that all three must be age 44 at the party and have been born in 1936. That would mean the party took place in the latter part of 1980, after all have had their birthdays, or in the early part of 1981, before any had a birthday. So 1981 is the latest year in which this could happen.',NULL,0);
INSERT INTO comment VALUES (6582,573,1626,'Gamer','re: solution','2003-07-21 17:15:33',2,'This is a good idea, but it says \"all three of the surgeons are needed to operate on the cook\", which I think means they have to actually do it.\r\n\r\nThere are actully only 3 people who need glove/gloves, but 4 glove surfaces. So unless a surgeon operates with only one hand, there isn\'t any possibility other than a \"trick\" answer like sterilizing the gloves on the campfire in my opinion.',6579,0);
INSERT INTO comment VALUES (6583,1021,2571,'Rob','Solution','2003-07-21 17:19:53',3,'The earliest year it could\'ve been is the year 6. The age of all three people is two. They were all born in the year 4.',NULL,0);
INSERT INTO comment VALUES (6584,571,2790,'SumoJim','','2003-07-21 19:48:20',3,'Put one tray in full of water. Close the door. There is no specification in the question about how much ice must be made.\r\n\r\nCould just fill one of the cube holes with water.',NULL,0);
INSERT INTO comment VALUES (6585,498,1919,'Lewis','I Think....','2003-07-21 20:54:22',3,'Is it to do with describing the previous numbers?\r\n\r\n11 is one 1 so far. 31 is three 1\'s so far. 4113 is four 1\'s and one 3 etc.',NULL,0);
INSERT INTO comment VALUES (6586,569,1919,'Lewis','Depends','2003-07-21 20:56:45',3,'The only solution I can think of is you send the object in the box with a lock. Your friend then fits another lock and sends it back. You remove your lock, send it back again then the friend can take his lock off and open it. I don\'t know whether we can assume the friend has his own locks, though.',NULL,0);
INSERT INTO comment VALUES (6587,179,2775,'tyler','Similar Problem','2003-07-21 22:35:11',0,'What get\'s larger the more you take away.\r\n\r\nA HOLE.',NULL,0);
INSERT INTO comment VALUES (6588,177,2775,'tyler','Not enough detail','2003-07-21 22:37:03',0,'It didn\'t talk about how deep or wide the hole was. If the ball was wedged in... no amount of water would make it float out.',NULL,0);
INSERT INTO comment VALUES (6589,278,2775,'tyler','Hmmm','2003-07-21 22:38:22',0,'Simple yet effective solution. Despite having no meaning what so ever.',NULL,0);
INSERT INTO comment VALUES (6590,90,2775,'tyler','Why international waters????','2003-07-21 22:50:10',0,'Do they have to be in international waters??? Can\'t it just be that Kerry was born at 11:59 PM on Feb 28... then Terry was born at 12:01 AM on March 1st... and this particular puzzle takes place in a leap year... thereby separating their birthdays by 2 days.',NULL,0);
INSERT INTO comment VALUES (6591,569,2373,'ryan smith','re(3): solution','2003-07-21 22:58:28',0,'That\'s all fine and dandy, but I think that you are assuming that the box would arrive safely before the key. Countering this assumption, I would suggest that a box interceptor forge a receipt or impersonate your friend on the telephone to convince you to send the first key after he has intercepted the box.\r\n\r\nSuch a solution and counter attack are out of scope, I think.\r\n\r\nI like your first solution better.',6548,0);
INSERT INTO comment VALUES (6592,569,2373,'ryan smith','Smarty Pants Solution','2003-07-21 23:06:30',1,'Send the object in a brown paper bag. That way no one will want to steal it.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (6593,520,2775,'tyler','re: My solution is different','2003-07-21 23:10:25',0,'I GOT THE SAME ANSWER YOU DID! I THINK IT MEETS ALL THE CRITERIA!!!',5356,0);
INSERT INTO comment VALUES (6594,520,2775,'tyler','Oh... Jim C you are correct','2003-07-21 23:11:53',0,'U R COrrect',NULL,0);
INSERT INTO comment VALUES (6595,903,2731,'Venisha Nair','ok','2003-07-22 01:49:41',0,'Haha... i think i got it. \r\nthe first cube has the letters urchoj\r\nthe second cube eybkns\r\nthe third fivpgz\r\nand finally dtalwm\r\n\r\nI think! :) ',NULL,0);
INSERT INTO comment VALUES (6596,1010,2731,'Venisha','','2003-07-22 01:59:17',0,'you are the heart! ',NULL,0);
INSERT INTO comment VALUES (6597,1010,1732,'Helen','my answer','2003-07-22 02:49:07',3,'Its the Soul. \r\n\r\n',NULL,0);
INSERT INTO comment VALUES (6598,1018,2792,'Thomas','My first shot','2003-07-22 04:55:39',0,'I believe the sets are of the form {N,N+X,N+(N*N/X)} such that (N*N/X) is an integer.',NULL,0);
INSERT INTO comment VALUES (6599,1018,2592,'ben young','guess','2003-07-22 05:00:14',0,'it appears as if there are an infinite set of integers, satisfied by the following equations:\r\n\r\nB = A * 2, A>0\r\nC = B\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (6600,1010,1919,'Lewis','Answer','2003-07-22 07:13:11',3,'Its the soul.\r\n\r\nObviously it can\'t be seen, felt or touched.\r\nEveryone has one, although somebody don\'t believe they exist.\r\nThere\'s soul music.',NULL,0);
INSERT INTO comment VALUES (6601,1021,158,'Ender','Longer solution','2003-07-22 07:27:07',3,'If x is the current year, a is the birth year of person 1, b is the birth year of person 2, and c is the birth year of person 3, then we are trying to find:\r\n(x-a)*(x-b)=c\r\n(x-b)*(x-c)=a\r\n(x-c)*(x-a)=b\r\n\r\nWe can pick two and simplify them:\r\n(x-b)*(x-c)=a => (x-b)=a/(x-c)\r\n(x-a)*(x-b)=c => (x-b)=c/(x-a)\r\na(x-a)=(x-c)c => (a-c)x=(a-c)(a+c)\r\n\r\nSo solutions can be at a-c=0 and x=a+c. x=a+c leads to a solution where two of the people are 1 year old, and the other was born in year 1. Unless we allow for a 2000 year old person, that most likely won\'t be the best answer. The other solution is a=c; in other words, person 1 is the same age as person 2. By similar reasoning it can be shown person 3 must also be the same age.\r\n\r\nNow we have an easier problem: (x-a)*(x-a)=a => x^2-2a+(a^2-a)=0\r\nThe roots of this are x = a +/- sqrt(a). Or in other words, the year of the party is the birth year plus the square root of the birth year. But the year of the party is also equal to the birth year plus the age of the person. So the birth year must be a square number, and the age of the people must be the square root of that year.\r\n\r\nSo what is the numeric solution? The closest squares around 2003 are: 43^2 = 1849, 44^2 = 1936, 45^2 = 2025, so those are the birth years that will work. The party years would be 1849+43=1892, 1936+44=1980, and 2025+45=2070. So as the others said, 1980 is the most recent party year.\r\n\r\nThat being said, if the three people were being absurdly precise, and said they were 44 1/4 years old, the party could have been sometime around April 2002. But while 4 year olds might say their ages like that, I don\'t know many 44 years olds that would.\r\n',NULL,0);
INSERT INTO comment VALUES (6602,1018,1921,'Travis Taylor','','2003-07-22 07:52:22',0,'I don\'t think this is every set, but if A = n, B = n+1 and C = n(n+1) then 1/A = 1/B + 1/C ',NULL,0);
INSERT INTO comment VALUES (6603,1010,2794,'Ryan','answer','2003-07-22 08:18:20',0,'soul',NULL,0);
INSERT INTO comment VALUES (6604,349,1919,'Lewis','Solution','2003-07-22 09:27:31',3,'Everyone says the colour of the person to their left\'s hat. Once everybody knows their colour, they can use their second guess to say their own colour.',NULL,0);
INSERT INTO comment VALUES (6605,1037,1301,'Charlie','solution','2003-07-22 12:40:52',3,'The best numbers to have on your card are those that are more likely to have a way of being formed from numbers that come up as the dice totals. The probability of being able to form a given number is proportional to the number of ways the two dice can fall that can be used to form that number.\r\n\r\nThe number of ways that the dice can fall to produce given numbers is:\r\n If the bike actually was worth $40, he came out even; with the bike in his possession, and $40 down. Now, a little question... why is this problem in the \"LOGIC\" section?',NULL,0);
INSERT INTO comment VALUES (6723,1038,1919,'Lewis','re(3): Answer','2003-07-26 22:17:59',1,'I look at the question more like \'did Mike gain or did Mike lose money?\' where the answer would be \'neither - he broke even\'.',6721,0);
INSERT INTO comment VALUES (6724,48,2716,'Federico Kereki','Simple solution','2003-07-27 05:11:05',3,'Half the pregnant women will have boys (and keep on getting pregnant) and half will have girls (and stop)... but the key point is that there were the same quantity of boys and girls. Those women who keep on will repeat the average (50% boys, and 50% girls), and thus the ratio will always be 1:1.\r\n',NULL,0);
INSERT INTO comment VALUES (6725,577,2716,'Federico Kereki','A couple of obvious solutions...','2003-07-27 05:21:48',1,'\"That that is is that that\" is not \"is not is that it that is it\".\r\n\"That that is is that that is not\" is not \"is that it that is it\".\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (6726,577,1301,'Charlie','How about...','2003-07-27 06:36:15',3,'That that is is. That that is not is not. Is that it? That is it.',NULL,0);
INSERT INTO comment VALUES (6727,577,2716,'Federico Kereki','re: How about...','2003-07-27 06:58:54',0,'I\'d add a couple more commas, but this solution looks better than mine!\r\n\r\nThat that is, is. \r\nThat that is not, is not. \r\nIs that it? \r\nThat is it. ',6726,0);
INSERT INTO comment VALUES (6728,1022,2489,'nellie','re: Solution to half the problem','2003-07-27 07:00:21',0,'I think you and I are answering a different question to the others. We have taken the least likely total as basis to the question. The way others are addressing the problem is to ask whether it is more likely to get a lower total (15) before a higher total (14 + 6).\r\n\r\nI just haven\'t a clue about Charlie\'s probabilities. ',6707,0);
INSERT INTO comment VALUES (6729,569,2489,'nellie','disappointment','2003-07-27 07:08:11',0,'I was disappointed with the answer which introduces new facts of the friend having locks of his own. An equally valid answer would have been to use a security delivery service. The question becomes one of imagination rather than the logical evaluation of the given facts.\r\n\r\nBut I enjoyed tackling the question albeit I failed to solve it.\r\n',NULL,0);
INSERT INTO comment VALUES (6730,577,2703,'Mr. Spock','re(2): How about...','2003-07-27 08:29:49',0,'That\'s what I came up with, it\'s certainly gramatically and logically correct.',6727,0);
INSERT INTO comment VALUES (6731,1038,2703,'Mr. Spock','re(2): Answer','2003-07-27 08:37:13',0,'The questions asks \"did Mike gain or lose money on the transactions?\" not \"what did mike do?\" Since he neither gained or lost, no is the simplest correct answer unless you respond with a single negation symbol. Why overly complicate the answer. ',6719,0);
INSERT INTO comment VALUES (6732,348,2880,'Lynne','Perhaps...','2003-07-27 12:21:02',3,'The Mississippi River?',NULL,0);
INSERT INTO comment VALUES (6733,400,2881,'perucho','Another way of looking at it','2003-07-27 13:35:48',0,'How about this?: Black Jack... You against the dealer right? You get dealt first, then the dealer, then you again. You need a figure and an ace to BJ. Two ways of getting it: a) The figure and then the ace = 16/52*((4-(4/51))/50) b)The ace first and then the figure = 4/52*((16-(16/51))/50)... Add... = 4.827% probability or 1 in 20.71775 odds?',NULL,0);
INSERT INTO comment VALUES (6734,406,2881,'perucho','How about this?','2003-07-27 13:56:24',0,'There are 1000 peanuts in a bag. So that they are all individual peanuts, single chambered peanuts have to be picked every time. The supply of the different types of peanuts is unlimited therefore the odds stay the same. Peanuts are picked individualy (ie. a quadruple chambered group has 4 chances of being picked). This takes us to 1 quadruple group (1*4=4 peanuts), 2 triple (2*3=6 peanuts), 4 double (4*2=8 peanuts) and 8 singles. 26 peanuts in all. Chances that you pick a single are then 8/26. Chances that you do this 1000 times in a row is (8/26)^1000 because the odds don\'t change and in order for them to be all single chambered you have to make 1000 picks. What do you guys think?',NULL,0);
INSERT INTO comment VALUES (6735,577,1575,'DJ','Perhaps','2003-07-27 16:27:18',1,'If the intent of the problem was to make four sentences, perhaps it would have been better to give \"that that is is that that is not is not is that it that is it\" and say, puncuate and capitalize (as in \"Had Had\"). The way the problem is stated, punctuation alone will not make it coherent without also capitalizing the initial letters of the other three sentences.',NULL,0);
INSERT INTO comment VALUES (6736,1038,1575,'DJ','re(4): Answer','2003-07-27 18:23:46',0,'I understand, of course, how you\'re looking at the problem, and the answer you gave is the way most people would have stated it. The way the problem is worded, though, \'no\' does indeed correctly answer the question, and there is not really any basis for saying Spock\'s answer is invalid.',6723,0);
INSERT INTO comment VALUES (6737,1010,2889,'dianne','cannot be felt seen or touched','2003-07-27 19:05:20',0,'my suggestion is - Mood',NULL,0);
INSERT INTO comment VALUES (6738,577,2891,'Shauna','Could this be it?','2003-07-27 22:01:40',0,'That, that is, is that. That is not. Is not, Is that it? That is it.',NULL,0);
INSERT INTO comment VALUES (6739,1027,1919,'Lewis','Solution','2003-07-28 02:03:22',3,'Send 20, 21, 23 and 27 across with both lights. Send 20 back with both lights for a total time of 47 minutes.\r\n\r\nSend 29, 31, 34 and 37 across with both lights and send 21 back with both lights for a total time of 105 minutes.\r\n\r\nNow just send 20, 21, 41 and 43 across with both lights. Now everybody is across in 148 minutes.',NULL,0);
INSERT INTO comment VALUES (6740,1027,2231,'Trevor Leitch','re: Solution','2003-07-28 03:29:35',3,'If their seargent is interested in the team getting across the bridge as fast as possible, a quicker solution puts more work on the fittest member:\r\n\r\nSend 20, 37, 41 and 43 across with both lights. Send 20 back with both lights for a total time of 63 minutes. \r\n\r\nSend 20, 29, 31 and 34 across with both lights. Send 20 back with both lights for a total time of 117 minutes. \r\n\r\nNow just send 20, 21, 23 and 27 across with both lights. Everybody is across in only 144 minutes. ',6739,0);
INSERT INTO comment VALUES (6741,1027,2867,'suyarajan','SOLN','2003-07-28 04:18:21',3,'\r\n\r\n * Send 20, 21, 23 and 27 across with\r\n both lights. Send 20 back with both\r\n lights for a total time of 47 minutes. \r\n\r\n * Send 43,41,37, and 34 across with\r\n both lights. Send 21 back with both\r\n lights for a total time of 111 minutes.\r\n\r\n\r\n * Now just send 20, 21, 27 and 29\r\n across with both lights. Everybody is\r\n across in only 140 minutes. ',NULL,0);
INSERT INTO comment VALUES (6742,540,2892,'Eric','I hate you','2003-07-28 04:33:53',0,'And your puzzle',NULL,0);
INSERT INTO comment VALUES (6743,577,2667,'Viet','maybe','2003-07-28 06:33:19',3,'that ! -pointing at something\r\nthis is? -not agreeing at wat he pointing at\r\nis that? -asking again\r\nthat is not. -answer to the question before\r\nis not? -questioning the answer\r\nis that it? -asking if its it again\r\nthat is it -finnally answering it is it\r\n\r\nawww damn i confise myself o well ill post it anyway',NULL,0);
INSERT INTO comment VALUES (6744,1038,2667,'Viet','comment','2003-07-28 06:53:41',0,'this kid is dumb buying the bike back 10 dollor more than he sold it.',NULL,0);
INSERT INTO comment VALUES (6745,577,1575,'DJ','Discussion','2003-07-28 07:47:10',1,'Or, maybe we are just missing the first line of the conversation:\r\n\r\n\"What words are capitalized?\"\r\n\"\'That,\' that is.\"\r\n\"is \'that\'?\"\r\n\"\'that\' is not.\"\r\n\"Is \'No\'?\"\r\n\"\'tis.\"\r\n\"that it?\"\r\n\"that is it.\"',NULL,0);
INSERT INTO comment VALUES (6746,1027,1183,'fwaff','re: SOLN','2003-07-28 08:05:48',3,'Almost - you\'ve sent 27 across twice and forgotten about 31. Revising your solution gives:\r\n\r\n*Send 20, 21, 23 and 27 across with both lights. Send 20 back with both lights for a total time of 47 minutes. \r\n\r\n* Send 43,41,37, and 34 across with both lights. Send 21 back with both lights for a total time of 111 minutes. \r\n\r\n* Now just send 20, 21, 29 and 31 across with both lights. Everybody is across in only 142 minutes. \r\n',6741,0);
INSERT INTO comment VALUES (6747,1027,2839,'Andrew Mitchell','Solution','2003-07-28 09:00:32',3,'for convenience designate each person by the time it takes them to cross\r\n\r\ntime | Action\r\n00 | 20,43 and 37,41 set out\r\n41 | 37, 41 arrive\r\n43 | 20,43 arrive 20 returns w/ both lights\r\n63 | 20 arrives w/lights 20,34 and 29,31 set out\r\n94 | 29,31 arrive\r\n97 | 20,34 arrive; 20 returns w/both lights\r\n117 | 20 arrives w/lights 20,27 and 21,23 set out\r\n140 | 21,23 arrive\r\n144 | 20,27 arrive, all are across',NULL,0);
INSERT INTO comment VALUES (6748,577,2839,'Andrew Mitchell','Solution','2003-07-28 09:20:17',3,'That, that is, is. That, that is not, is not.\r\nIs that it? That is is.',NULL,0);
INSERT INTO comment VALUES (6749,1027,2667,'Viet','re: SOLN','2003-07-28 09:41:34',0,'You send 27 over twice and 31 was left out making 144 still the shortest time',6741,0);
INSERT INTO comment VALUES (6750,1040,2572,'derek','solution','2003-07-28 10:33:47',3,'I\'m not sure how the 1st 2 numbers fit in, but:\r\n\r\n8 = 2² + 4\r\n13 = 3² + 4\r\n20 = 4² + 4\r\n29 = 5² + 4\r\n40 = 6² + 4\r\n53 = 7² + 4\r\n',NULL,0);
INSERT INTO comment VALUES (6751,1040,1919,'Lewis','re: solution','2003-07-28 10:36:24',1,'That\'s good, but not anything to do with the answer I\'m looking for.',6750,0);
INSERT INTO comment VALUES (6752,1010,2897,'Laura','I differ on my answer....','2003-07-28 11:19:53',3,'.....I believe it is rhythm',NULL,0);
INSERT INTO comment VALUES (6753,1010,2898,'gina','without a doubt...','2003-07-28 12:40:43',0,'a thought.',NULL,0);
INSERT INTO comment VALUES (6754,1026,2899,'Brian Wainscott','re(3): solution (plus one)','2003-07-28 13:35:23',0,'Sorry, I just couldn\'t let this go....how about 83 bags?\r\n\r\nSet one aside. Split the rest into two groups A and B. Take one from each of A and two from each of B. Total weight should be 1476. If it is, the one you set aside is light. Else it is light by 41 or 82 grams. So now you are down to at most 41 bags. Split the rest into 3 groups a, b ,c. Take one from each of a, two from each of b, three from each of c (a and b have 14 each, c has 13). Total weight should be 12 grams*(14+28+39)=950 grams. You can immediately determine which group is light. Then use the 1, 2, 3, 4, .... trick for that set. Since each set has less than 15, you are fine.\r\n ',6720,0);
INSERT INTO comment VALUES (6755,1040,1301,'Charlie','re: solution','2003-07-28 15:13:36',0,'What\'s wrong with this is that 4 is not equal to 1²+4 and 2 is not equal to 0²+4.',6750,0);
INSERT INTO comment VALUES (6756,1026,1301,'Charlie','','2003-07-28 15:49:36',0,'',6754,0);
INSERT INTO comment VALUES (6757,1026,1301,'Charlie','re(4): solution (plus one)--Even More','2003-07-28 15:50:13',0,'Start with 125 bags.\r\n\r\nAt the beginning, set aside 45 instead of just one. Split the remaining 84 into two groups A and B, with 45 in group A and 40 in group B. Again take one from each of A and two from each of B. The total weight should be 1500. If it is, one of the 45 you set aside is light, otherwise you can tell if one of group A or one of group B is light by whether the weighing is light by 1 or 2. In the case of A you also have 45 from which still to determine the fake; in the case of B, 40.\r\n\r\nIn either case, as before, split the 45 or 40 into 3 groups a,b,c. Again take 1 from each of a, 2 from each of b and 3 from each of c. There\'ll be at most 15 in each group, and again you can immediately determine which group is light. With 15 you can still use the 1,2,3,...,15 trick, and you are done.',6754,0);
INSERT INTO comment VALUES (6758,1026,1301,'Charlie','re(5): solution (plus one)--Even More','2003-07-28 15:53:01',3,'Sorry: make that:\r\n\r\nStart with 130 bags. \r\n\r\nAt the beginning, set aside 45 instead of just one. Split the remaining 85 into two groups A and B, with 45 in group A and 40 in group B. Again take one from each of A and two from each of B. The total weight should be 1500. If it is, one of the 45 you set aside is light, otherwise you can tell if one of group A or one of group B is light by whether the weighing is light by 1 or 2. In the case of A you also have 45 from which still to determine the fake; in the case of B, 40. \r\n\r\nIn either case, as before, split the 45 or 40 into 3 groups a,b,c. Again take 1 from each of a, 2 from each of b and 3 from each of c. There\'ll be at most 15 in each group, and again you can immediately determine which group is light. With 15 you can still use the 1,2,3,...,15 trick, and you are done. \r\n',6757,0);
INSERT INTO comment VALUES (6759,1040,1919,'Lewis','A little hint','2003-07-28 21:40:32',2,'This is just to make sure you don\'t waste time trying the wrong thing.\r\n\r\nThis sequence wasn\'t made with a formula.',NULL,0);
INSERT INTO comment VALUES (6760,983,1919,'Lewis','re: Hehe... reminds me of my local','2003-07-28 22:46:32',0,'I saw one on holiday that had something likt YCHCYOEFTBSTY, which is \'your curiosity has cost you one euro for the bar staff thank you\'',6423,0);
INSERT INTO comment VALUES (6761,1040,2907,'ohad','solution','2003-07-29 02:39:16',0,'could the following numbers be 41 and 57?',NULL,0);
INSERT INTO comment VALUES (6762,1040,1301,'Charlie','re: solution','2003-07-29 02:49:48',0,'That\'s your proposed answer, but what is the solution? ..., i.e., the logic that got you there.',6761,0);
INSERT INTO comment VALUES (6763,1040,1919,'Lewis','re: solution','2003-07-29 03:15:43',1,'There are, but how did you come to your answer?',6761,0);
INSERT INTO comment VALUES (6764,1040,2907,'ohad','answer','2003-07-29 03:35:15',0,'every two numbers add up to a number that is related to the next number.\r\nin the biginning third number - sum = 2. then forth number - sum =1. then fifth number - sum = -1. as you can see the solutions to these equations is :2,1,-1,-4 that means the difference between each solution is growing in 1 numver each time. that means the next \"solutions\" are -8 and then -13.\r\n20+29-8=41..... 29+41-13=57\r\nand thats my answer...',NULL,0);
INSERT INTO comment VALUES (6765,1050,1183,'fwaff','A possible solution','2003-07-29 03:40:11',3,'The best I can do without resorting to rare words is five steps for each of the changes...\r\n\r\nsoft\r\nsort\r\ntort\r\ntart\r\nhart\r\nhard\r\nhare\r\ncare\r\ncase\r\nease\r\neasy',NULL,0);
INSERT INTO comment VALUES (6766,1050,2839,'Andrew Mitchell','Solution and Alternative','2003-07-29 04:13:35',0,'SOFT\r\n----\r\nSORT\r\nFORT\r\nFORE\r\nFARE\r\nHARE\r\n----\r\nHARD\r\n----\r\nHARE\r\nBARE\r\nBASE\r\nEASE\r\n----\r\nEASY\r\n\r\nor, if you don\'t mind slang\r\n\r\nSOFT\r\n----\r\nSORT\r\nFORT\r\nFART\r\nHART\r\n----\r\nHARD\r\n----\r\nHARE\r\nBARE\r\nBASE\r\nEASE\r\n----\r\nEASY\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (6767,1040,1919,'Lewis','re: answer (hint)','2003-07-29 06:40:39',2,'Your answers are indeed correct, but the method you used to get the answers is not what I was looking for. You\'re close with adding the last two numbers. Just three more points to be made.\r\n',6764,0);
INSERT INTO comment VALUES (6768,1026,2899,'Brian Wainscott','re(6): solution (plus one)--Still more','2003-07-29 06:42:48',0,'Good ideas! Here are some more:\r\n\r\nStart with 153 bags.\r\n\r\nStart by setting aside 68 bags. Take the other 85 and split them as you said. The only difficulty is if these 85 are OK and the 68 are light.\r\n\r\nIf the 68 are light, set aside 15. Of the remaining 53, split them into sets A, B, C, D with 15 each of A, B, C and 8 in set D. Take one each from A, two each from B, three each from C, and four each from D. Total weight should be 1464 (at most). If A is light, the total would be 15 grams low, B 30, C 45, and D 32. You can then do the 1,2,3,... trick with the proper remaining pile (A,B,C,D or the one set aside, each of which have at most 15 coins in them).\r\n\r\nBummer though -- since we can get 68 bags in two weighings, it is too bad we can\'t put 136 in the first A,B pairing instead of only 85. Also, I\'d really like to be able to use those last 36 grams in ABCD weighing above, but don\'t see how at the moment....',6758,0);
INSERT INTO comment VALUES (6769,1012,2898,'gina','looking at every angle?!#%$&&**.','2003-07-29 08:04:03',0,'because, Adam was created by God, had no mother and married Eve.',NULL,0);
INSERT INTO comment VALUES (6770,228,2898,'dorkdork','maybe?????','2003-07-29 08:15:44',0,'is (are),thise (this),three (two).',NULL,0);
INSERT INTO comment VALUES (6771,543,2898,'dorkdork','could be, could be not.','2003-07-29 08:20:03',0,'the minds eye.',NULL,0);
INSERT INTO comment VALUES (6772,360,2898,'dorkdork','duhhh!','2003-07-29 08:23:52',0,'NOTHING\' duhhhhh!',NULL,0);
INSERT INTO comment VALUES (6773,315,2898,'dorkdork','keep\'n kin closely~','2003-07-29 08:29:04',0,'his son.',NULL,0);
INSERT INTO comment VALUES (6774,859,2898,'dorkdork','???','2003-07-29 08:30:59',0,'time',NULL,0);
INSERT INTO comment VALUES (6775,467,2898,'dorkdork','!~*&%^$#@?\":?','2003-07-29 08:33:38',0,'man.',NULL,0);
INSERT INTO comment VALUES (6776,525,2898,'dorkdork','possibly...','2003-07-29 08:39:17',0,'106.',NULL,0);
INSERT INTO comment VALUES (6777,540,2898,'dorkdork','well, I.. ummmmm?','2003-07-29 08:45:33',0,'teeth.',NULL,0);
INSERT INTO comment VALUES (6778,1026,2899,'Brian Wainscott','My best so far','2003-07-29 09:12:23',3,'169\r\n\r\nDivide the coins into piles A=71, B=71, C=27 coins. Set aside A. Take one coin each from B, two coins each from C, and weigh these. The total is either 1500 (in which case A is light), 1499 (B is light), or 1498 (C is light).\r\n\r\nSuppose A is light (B is handled the same way). Create 5 piles a, b, c, d each with 16 bags, and e with 7. Set aside a, take 1 each from b, 2 each from c, 3 each from d, and 4 each from e. If the total weight is 1488, then a is light. If b is light the total is 1487, c gives 1486, d 1485, and e gives 1484.\r\n\r\nSet e is easy: the 1,2,3,...,7 trick works fine. For the others, set aside one bag and use the 1,2,3,....,15 trick on the other 15. If the total is 1440 then the bag set aside is light.\r\n\r\nIf the original set C was light, it is easy. Since it only has 27 bags you can just do the 1,2,3 trick on half of them, then on the other half. ',6768,0);
INSERT INTO comment VALUES (6779,1040,2667,'Viet','re: answer','2003-07-29 09:35:36',0,'somebody explain this better for me i still don\'t understand -2 -1 1 4 how and where does -8 and -13 pop up\r\nthe difference isn\'t 1 each is it?',6764,0);
INSERT INTO comment VALUES (6782,390,2898,'dorkdork','either or..','2003-07-29 11:23:01',0,'an electric oven burner; Or... coal.',NULL,0);
INSERT INTO comment VALUES (6783,334,2898,'dorkdork','I wonder ?...','2003-07-29 11:28:14',0,'Life.',NULL,0);
INSERT INTO comment VALUES (6784,544,2898,'dorkdork','simply simple !!!','2003-07-29 11:33:27',0,'a match stick.',NULL,0);
INSERT INTO comment VALUES (6785,532,2898,'dorkdork','hypethetically guess\'n.','2003-07-29 11:40:39',0,'He knew because Adam & Eve were the oldest ones there.? ',NULL,0);
INSERT INTO comment VALUES (6786,541,2898,'dorkdork','not quite surrrr.','2003-07-29 11:49:08',0,'cause and effect... ?.',NULL,0);
INSERT INTO comment VALUES (6787,817,2898,'dorkdork',' ? ~~~~~','2003-07-29 11:54:15',0,'it isn\'t , she lied.',NULL,0);
INSERT INTO comment VALUES (6788,482,2898,'dorkdork','doughno','2003-07-29 11:58:35',0,'a boiled egg?.',NULL,0);
INSERT INTO comment VALUES (6789,510,2898,'dorkdork','clueless','2003-07-29 12:20:25',0,'the 1st one- ? 2nd- ? 3rd-?',NULL,0);
INSERT INTO comment VALUES (6790,511,2898,'dorkdork','NO.','2003-07-29 12:22:33',0,'no.',NULL,0);
INSERT INTO comment VALUES (6791,476,2898,'dorkdork','weird \'','2003-07-29 12:26:52',0,'\"Humans are an intelligent species.\"',NULL,0);
INSERT INTO comment VALUES (6792,174,2898,'dorkdork','??????','2003-07-29 12:31:40',0,'B.problems are unsolved situations. situations are solveable.',NULL,0);
INSERT INTO comment VALUES (6793,250,2898,'dorkdork','helloooo.','2003-07-29 12:33:55',0,'he\'s telling the truth even if he\'s lying about it. ',NULL,0);
INSERT INTO comment VALUES (6794,488,2898,'dorkdork','Doknotnoah.','2003-07-29 12:41:14',0,'a poem or nonsence',NULL,0);
INSERT INTO comment VALUES (6795,429,2898,'dorkdork','perfect timing','2003-07-29 12:44:01',0,'he left early, didnt drink enough to die.',NULL,0);
INSERT INTO comment VALUES (6796,1040,1575,'DJ','Explanation','2003-07-29 12:56:08',3,'This is just to clarify ohad\'s solution, since it\'s not exactly clear, but I think it was what Lewis was looking for..\r\n\r\nFirst, consider a function:\r\nf(n+1) = f(n) - n\r\nWhere f(0)=2, this gives the sequence:\r\n2, 2, 1, -1, -4, -8, -13\r\n\r\nNow, consider a sequence, for which S0=2, and\r\nSn+1 = Sn + Sn-1 + f(n)\r\n\r\nNow, we have:\r\n If one clock gains 10 seconds per hour, it will gain one minute in 6 hours, one hour in 6*60=360 hours, and 6 hours in 6*360=2160 hours, or 90 days. Now, the clocks are synchronized in January, and will agree again in May, and the intervening time is 90 days. The only way this can be true is if this occurs in a non-leap year and the clocks are synchronized on January 31, since 28 days in February + 31 days in March + 30 days in April = 89 days, leaving May 1st as the 90th day. Joe tells us the clocks will align again on Moe\'s 47th B-day. If Moe was born in 1933, he would turn 47 in 1980, which is a leapyear, which does not work for this scenario. Therefore Moe was born in 1932 and Joe was born in \'33, making Moe older.',NULL,0);
INSERT INTO comment VALUES (6860,1045,2899,'Brian Wainscott','Same answer, different reason','2003-08-01 10:26:05',3,'I got 1806 also, but I figured each number was multiplied by the next prime:\r\n\r\n1*2=2\r\n2*3=6\r\n6*7=42\r\n42*43=1806\r\n1806*1811=3270666\r\n\r\nBut I like DJ\'s answer better. No point in making things unnecessarily complicated. Primality is just the first thing that occured to me....',NULL,0);
INSERT INTO comment VALUES (6861,1043,1919,'Lewis','re: **:**','2003-08-01 10:27:06',0,'Jeremy - thats very good that you can solve this - but please don\'t give away the answer in your subjects. Thank you.',6857,0);
INSERT INTO comment VALUES (6862,1045,2899,'Brian Wainscott','re: Same answer, different reason: Correction','2003-08-01 10:27:50',0,'I meant to say Andrew\'s solution. It is numerically equivalent to DJ\'s, of course, but simpler.',6860,0);
INSERT INTO comment VALUES (6863,780,2792,'Thomas','First cut at solution','2003-08-01 10:47:26',0,'Answer: 27. Put 1, 2, 3 ... 13 in the first 13 bags. Then put bag 11 plus 3 marbles in bag 14, bag 13 plus 2 in 15, and bag 12 plus 4 in 16. Then combine bags as follows: 8&9 in 17, 2&16 in 18, 7&14 in 21, and 15,3&1 in 19. At this point the bag count is 20. Continue combining bags: 5&17 in 22, 6&18 in 24, 4&21 in 25, and 10&19 in 29. Total now is 24. Finally 22&24 in 46, 25&29 in 54, and 46&54 in 100.',NULL,0);
INSERT INTO comment VALUES (6864,1038,2950,'ray lavko','answer','2003-08-01 11:44:23',0,'i agree, he is even',NULL,0);
INSERT INTO comment VALUES (6865,67,1919,'Lewis','Solution','2003-08-01 12:37:47',3,'Three fat cats eat three fat rats in 3 minutes. We can assume each cat eats one rat each, so each cat takes 3 minutes to eat a rat.\r\n\r\nWhen thirty three cats eat sixty six rats, each cat needs to eat 2 rats. Since i rat took 3 minutes, this will take 6 minutes.',NULL,0);
INSERT INTO comment VALUES (6866,578,2951,'Jim Breaux','Solution','2003-08-01 13:05:07',0,'As I interpreted the instructions, the 8 words cannot be made by skipping over letters. HITMAN appears to fit the bill.\r\n\r\nHITMAN:\r\nHi\r\nHit\r\nIt\r\nI\r\nMa\r\nA\r\nAn\r\nMan',NULL,0);
INSERT INTO comment VALUES (6867,575,2921,'Salem D','I\'M CONFUSED','2003-08-01 13:45:31',0,'I got the following\r\n\r\n 9142\r\n 8117\r\n ----\r\n 17259 \r\nwhich would mean s=9, o=1, m=4, e=2,g=8, d=7,i=1,a=5\r\nand the equation works, but it is different than your answer. What did I do wrong?\r\nAlso if o=7 how does e=5 ? ',NULL,0);
INSERT INTO comment VALUES (6868,576,1626,'Gamer','Hmmmm','2003-08-01 13:48:07',4,'I really love getting 4 of the exact same solution, but it\'s kind of redundant.',NULL,0);
INSERT INTO comment VALUES (6869,575,2921,'Salem D','nevermind','2003-08-01 13:51:30',0,'I was blinded for a moment.\r\nI now see my mistake.\r\n',NULL,0);
INSERT INTO comment VALUES (6870,1045,1301,'Charlie','More solutions from the on-line handbook of integer sequences','2003-08-01 15:07:53',3,'Aside from a few more obscure sequences and the ones mentioned already, this also shows up as:\r\n\r\n1,2,6,42,618,15018,533418,25935018,1651637418\r\nSum_{k=1...n} (k!)^2.\r\nExample: a(3)=0!*0!+1!*1!+2!*2!=6.\r\n\r\n1,2,6,42,62,102,107,157,232,249,350,384,473,547,637,731,790,920,1005,1031,1042,1063,1109\r\na(n+1)=a(n) + sum of squares of digits of a(n).\r\nExample: After 1063, since 1^2 + 0^2 + 6^2 + 3^2 = 46 we get 1063+46 = 1109.\r\n\r\n1,2,6,42,26,48,92,96,132,20,6,42,26,48,92,96,132,20,6,42,26\r\nStart with 1; add the digits of the previous term and the squares of the digits of the previous term.\r\n\r\n1,2,6,42,21,27,405,2304,88263,88263,861993,6100974,80207226\r\nFactorial numbers written backwards.\r\nFor example, 5! = 120, backwards it\'s 021, then drop the now leading zero.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (6871,228,2953,'Frank K','the REAL answer :)','2003-08-01 15:32:29',0,'There are three errors in the riddle:\r\n1. S/V disagreement\r\n2. \"thise\" is incorrect\r\n3. \"errors\" in riddle counts as the third! :)\r\n\r\nMy son came up with this answer.',NULL,0);
INSERT INTO comment VALUES (6872,830,2955,'banerd','literary solution','2003-08-01 16:29:29',0,'I\'m a literary person, so my solution is a play on words.\r\n\r\nNote the exact phrasing: the water in the hot container would freeze before the water in the cold container.\r\n\r\nMore specifically, \"hot CONTAINER\" and \"cold CONTAINER\"\r\n\r\nThus, you could put boiling water in a cold container and near-frozen water in a warmed container and still satisfy the exact wording of the problem.',NULL,0);
INSERT INTO comment VALUES (6873,633,2955,'banerd','answer','2003-08-01 16:39:42',0,'I\'m not sure whether this is real or something invented in the desperation of a chem final, but when water freezes, the molecules, due to the interaction of the 120-degree bond angles, forms hexagons, with enpty space in between. That\'s also believed to be the reason mature snowflakes always have six arms.\r\n\r\n.O.O\r\nO...O\r\n.O.O\r\n\r\nIgnore the little periods. I couldn\'t get the flooble thing to accept multiple continguous spaces.',NULL,0);
INSERT INTO comment VALUES (6874,1041,1301,'Charlie','Is it this simple or am I misinterpreting the rules?','2003-08-02 05:17:49',3,'Since the judge was not a knave and he contradicted himself, he must be a liar, so neither Bert nor Coby won.\r\n\r\nCoby\'s first statement was that a certain person (Dave) won, so his second statement would also have to be about stating a certain person won. Only statements a, b and e do this. Coby couldn\'t have made statement a as then he\'d be agreeing with himself, which is not allowed for a knave. That leaves b and e. Either one would be a lie as neither he (Coby) nor Bert won. Thus his first statement (Dave won) would have to be true.\r\n\r\nTherefore Dave won.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (6875,1041,1919,'Lewis','re: Is it this simple or am I misinterpreting the rules?','2003-08-02 07:43:04',0,'You are correct. It is indeed that simple. The rest is there as a distraction (obviously didn\'t work that well :)',6874,0);
INSERT INTO comment VALUES (6876,1041,1301,'Charlie','re(2): Is it this simple or am I misinterpreting the rules?','2003-08-02 09:21:51',0,'Actually it did somewhat, as I made up a grid and started Xing out bad combinations. Only after I started filling in the implications of the empty (non-xed) squares, which I started with Coby, did I realize this pair was the key.',6875,0);
INSERT INTO comment VALUES (6877,1038,2703,'Mr. Spock','re: answer','2003-08-02 09:24:45',0,'Now that we agree he is even we can all agree the answer is \"no.\"',6864,0);
INSERT INTO comment VALUES (6878,1041,1567,'Bryan','I disagree ...','2003-08-02 13:53:44',2,'So far there is a solution that Dave won, but assume the racers finish A, B, D, E, and C, and that each made the following second statement: Alex: Dave won. In this scenario, each person makes one true statement and one false statement. Therefore, A could also be the winner, given the statements.',NULL,0);
INSERT INTO comment VALUES (6879,1041,2899,'Brian Wainscott','re: I disagree ...','2003-08-02 15:51:04',0,'I don\'t think this matches the indicated assumption. Coby answers the first question \"Dave won\". According to the assumption, his second statement must therefore be a statement about who won. \"I didn\'t win\" would have to have been matched with someone who, in their first answer, gave information about their own position.\r\n\r\nI think it works if Alex = c, Bert = a, Coby = e, Dave = b and Ed = d. The type of statements then match, and as Charlie said, Dave won the race.',6878,0);
INSERT INTO comment VALUES (6880,576,2898,'dorkdork','got it!','2003-08-02 16:13:41',0,'there isnt any.',NULL,0);
INSERT INTO comment VALUES (6881,1041,1567,'Bryan','re(2): I disagree ...','2003-08-02 18:18:08',0,'I really didn\'t understand the statement about the assumption the first time I read it, but thanks to your comment, it makes sense now. I have a natural tendency not to make such assumptions when solving puzzles, and I guess that\'s why it made no sense at first.',6879,0);
INSERT INTO comment VALUES (6882,1038,2898,'dorkdork','yah ? I think.','2003-08-02 21:31:38',0,'yes, his profit was $10.00.',NULL,0);
INSERT INTO comment VALUES (6883,337,2898,'dorkdork','certainly!!','2003-08-02 21:44:00',0,'90,520,000 seconds in one year.',NULL,0);
INSERT INTO comment VALUES (6884,783,2898,'dorkdork','?','2003-08-02 21:53:27',0,'how can there be a limit within any part of infinity? unless alpha=begining, and omegaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa..............etc. ',NULL,0);
INSERT INTO comment VALUES (6885,788,2898,'dorkdork','Never ~ !!~','2003-08-02 22:03:48',0,'yes,where did the( =10 cents) have anything to do with that equasion? 1 dollar=100 cents=[10 cents] Wrong!',NULL,0);
INSERT INTO comment VALUES (6886,307,2898,'dorkdork','iseeit.','2003-08-02 22:09:49',0,'pie =10000....whatever(3.14etc.). Not pi=E 100...ect. ',NULL,0);
INSERT INTO comment VALUES (6887,274,2898,'dorkdork','watup!@#%^$','2003-08-02 22:19:13',0,'harold drew another line shorter than the kings line,his line was the same as the kings except his was shorter.',NULL,0);
INSERT INTO comment VALUES (6888,1063,2898,'dorkdork','maybe itz...','2003-08-02 22:27:35',0,'moe',NULL,0);
INSERT INTO comment VALUES (6889,988,2898,'dorkdork','no problem.','2003-08-02 22:34:23',0,'sure; ( Thi#s%)',NULL,0);
INSERT INTO comment VALUES (6890,314,2898,'dorkdork','not sure for sure','2003-08-02 23:08:00',0,'22.',NULL,0);
INSERT INTO comment VALUES (6891,20,2898,'dorkdork','?>*&%!@#$.','2003-08-02 23:22:58',0,'c and d',NULL,0);
INSERT INTO comment VALUES (6892,578,2898,'dorkdork','thinkin\'....','2003-08-02 23:37:15',0,'the alphabet.',NULL,0);
INSERT INTO comment VALUES (6893,909,2898,'dorkdork','guess\'n i think.','2003-08-02 23:46:37',0,'0.',NULL,0);
INSERT INTO comment VALUES (6894,1038,2973,'eva','i think..','2003-08-03 00:30:30',0,'I think Mike lost $10',NULL,0);
INSERT INTO comment VALUES (6895,578,1626,'Gamer','Hmmm','2003-08-03 03:57:31',0,'Note that I is a capitalized word. It would look silly to have hatpIn as a spelling... And is ha i word or just an interjection?\r\n\r\nI don\'t know if the idea is to use common letters or less common letters.',NULL,0);
INSERT INTO comment VALUES (6896,7,1301,'Charlie','re: People! Get a clue!','2003-08-03 07:10:11',0,'The \"I\" who tells is a person. That person has choices. Just because it is not a third person doesn\'t change the fact that the person, the narrator, had to choose what to report in the case of a split outcome.',6021,0);
INSERT INTO comment VALUES (6897,579,1575,'DJ','Hmm','2003-08-03 07:15:58',0,'It appears that it\'s not geometric, and nothing is multiplied to get each subsequent term, unless it\'s multiplied then added or subtracted:\r\n1×1+1=2\r\n2×1+2=4 or 2×2+0=4\r\n4×2+5=13 or 4×3+1=13\r\n13×2+5=31\r\n.. okay, no pattern that I can see ..\r\n\r\nLooking at the differences:\r\n1+1=2, 2+2=4, 4+9=13, 13+18=31, 31+73=112...\r\nStill no help. For a second it looked like each term just added a perfect square, but that\'s not it.\r\nThe other thought I had was that it\'s the ascending sequence of numbers whose digits add up to 4 (4, 13, 22, 31, 40, 103, 112, 121, 130, 211..) but then I realized that it was missing some terms, besides the fact that the first two terms don\'t even fit.',NULL,0);
INSERT INTO comment VALUES (6898,579,2703,'Mr. Spock','Solution','2003-08-03 07:39:53',0,'Having an anthropological background will help you with this answer. How you ask? Observing in the sequence all digits are 1-4 is suggestive, this seems to indicate to me a hand (base 5) numbering system. Converting to base 10 yields the sequence 1,2,4,8,16,32.. or obviously 2^n-1 so the next term in base 10 is 2^6 = 64, converting back to base 5 gives the answer, 224.',NULL,0);
INSERT INTO comment VALUES (6899,1041,2703,'Mr. Spock','Noodle bake','2003-08-03 07:49:50',0,'Dave won, but how do we know the framer of the question is not a knave?',NULL,0);
INSERT INTO comment VALUES (6900,1038,2703,'Mr. Spock','re: i think..','2003-08-03 08:00:40',0,'I disagree, don\'t listen to Greenspan, there is no assumption of deflation in the problem. Don\'t be like Kolby Bryant, try to understand that the answer is \"no\".',6894,0);
INSERT INTO comment VALUES (6901,579,2974,'Terri','wow....I dunno','2003-08-03 08:13:47',0,'I\'m not really sure, this one\'s a toughie, is it 224?',NULL,0);
INSERT INTO comment VALUES (6902,579,2974,'Terri','re: Solution','2003-08-03 08:15:02',0,'Hey I got the same answer as you, but i did it a totally different way...',6898,0);
INSERT INTO comment VALUES (6903,578,1575,'DJ','re: Hmmm','2003-08-03 08:26:40',0,'Are you saying \'I\' shouldn\'t count as a word? I\'m not sure of your point...\r\n\r\nAnd \'ha\' is a word, and in interjection .. interjections are one of the eight parts of speech.\r\n\r\nAnd did you mean common letters or common words? If you meant words, do you mean to suggest we should try to use less common words than more common ones? Again, I\'m not sure of your point..',6895,0);
INSERT INTO comment VALUES (6904,574,2974,'Terri','This was one of the easier ones','2003-08-03 08:38:29',0,'I think its: Mr. North took the south.\r\nMr. South took the west\r\nMr. East took the north \r\nMr. West took the east\r\nYep ( if I\'m right) that one was pretty easy',NULL,0);
INSERT INTO comment VALUES (6905,579,1919,'Lewis','re: wow....I dunno','2003-08-03 09:02:51',0,'How did you get to your answer? For all we know you could have just copied the same answer that people got.',6901,0);
INSERT INTO comment VALUES (6906,1041,1919,'Lewis','re: Noodle bake','2003-08-03 09:05:06',1,'Good point, but sadly I am not a knave. Just to prove it I shall say it in alternating statements.\r\n\r\nI am not a knave.\r\n\r\nI am not a knave. :p',6899,0);
INSERT INTO comment VALUES (6907,579,2974,'Terri','re(2): wow....I dunno','2003-08-03 09:19:58',0,'Well I saw that the numers only ranged from 1-4. and after the 3\'s I saw it started over with 3 1\'s so I assumed next it\'d be 3 2\'s and 112 ended in a 2 so the next number would be 224\r\nand u didn\'t have to be so rude anout it',6905,0);
INSERT INTO comment VALUES (6908,579,2978,'Freddy Grants','The solution','2003-08-03 14:02:48',0,'I believe the next number in the sequence would be 274. When I looked at the problem the only definate pattern i realized was... 1+1squared+2(1squared)+3squared+2(3squared)+9squared+2(9squared). When you follow this formula you can derive that the number after 112 will be 274.',NULL,0);
INSERT INTO comment VALUES (6909,777,2979,'Monica','','2003-08-03 14:08:52',0,'Well...I was under the impression that we were working with a single plane....a Plane is another name for a line....A Line having infinite number of points in between and also having definite points at the beginning and end... If we are working with only 2 colors...then obviously we would have two of the same color. What i don\'t understand is the part about the meter. How long is the plane initially? Maybe its me and I missed something.',NULL,0);
INSERT INTO comment VALUES (6910,1041,1575,'DJ','re(2): Noodle bake','2003-08-03 16:39:08',1,'We also know, now, that Lewis is not a liar, since he said \"I shall say it in alternating statements,\" and then he did. Therefore, Lewis is a Knight, or maybe even just a normal person (gasp!).',6906,0);
INSERT INTO comment VALUES (6911,1010,2981,'Melanie','my answer','2003-08-03 19:21:56',0,'You are a Soul. That one was easy!',NULL,0);
INSERT INTO comment VALUES (6912,1038,2981,'Melanie','re: answer','2003-08-03 19:46:24',0,'I\'m probably wrong but I think that Mike \"Broke Even\" ',NULL,0);
INSERT INTO comment VALUES (6913,579,1919,'Lewis','re(3): wow....I dunno','2003-08-03 22:22:03',0,'I wasn\'t being rude about it, I was just stating my opinion. Now you said how you got your answer I know you didn\'t just copy it.',6907,0);
INSERT INTO comment VALUES (6914,1041,1919,'Lewis','re(3): Noodle bake','2003-08-03 22:26:45',0,'Wow, I was in my very own Liars and Knights puzzle! :0)',6910,0);
INSERT INTO comment VALUES (6915,1051,1301,'Charlie','Is it...','2003-08-04 02:45:33',0,'a cowbird?',NULL,0);
INSERT INTO comment VALUES (6916,578,1626,'Gamer','re(2): Hmmm','2003-08-04 03:19:38',0,'But then Er is an interjection as well... Like used when you don\'t know a word. Anyway, anything can be an interjection... I could go from HARD to EASY saying interjections.\r\n\r\nWhat I am saying is i isn\'t a word, or not a proper word. It would need to be capitalized in the word anyway to count. Only I would count, and the word is in lower case.',6903,0);
INSERT INTO comment VALUES (6917,1051,2840,'Becky','could it be....','2003-08-04 03:47:51',0,'my guess is a manatee',NULL,0);
INSERT INTO comment VALUES (6918,579,1575,'DJ','re: Solution','2003-08-04 03:55:30',0,'I can\'t believe I didn\'t catch that.. good job. =)',6898,0);
INSERT INTO comment VALUES (6919,1051,2912,'Talon5000','re: could it be....','2003-08-04 03:56:42',0,'maybe it\'s a flying manatee (sea cow)',6917,0);
INSERT INTO comment VALUES (6920,578,2912,'Talon5000','re(3): Hmmm','2003-08-04 04:09:05',0,'that\'s dumb...when you do word problems like this you always count i as a word. and, you will find ha in the dictionary, and ouch, and wow, as interjections, but not er. you can make up a word that is anything.\r\ni can go from hard to easy saying verbs:\r\nhard\r\neard \"i wanted to eard you when i found out.\"\r\neary \"when did she eary last time?\"\r\neasy\r\n\r\nmaking up a word doesn\'t mean you can use it, but that doesn\'t mean all of the same part of speech can\'t work.',6916,0);
INSERT INTO comment VALUES (6921,1038,2983,'Daniel','he gains','2003-08-04 04:16:38',3,'I believe he gains 20$ off this. he lost 40 dollars in the transactions, but the original cost of the bike was 20. therefore he has a 40 dollar bike, yet he only paid 20. HE GAINS $20!',NULL,0);
INSERT INTO comment VALUES (6922,466,2722,'Jack Putz','Reason','2003-08-04 05:23:33',0,'Different Lattitudes do get different ammounts of sunlight (in hours). If the world were a perfect sphere, this would not be the case. the world is not a perfect sphere, but bulges at the equator.',NULL,0);
INSERT INTO comment VALUES (6923,1051,2839,'Andrew Mitchell','re(2): could it be....','2003-08-04 06:22:24',0,'Flying is not a problem as a manatee when swimming would be \"off the ground\" but the back end of a manatee is not round unless you count that the letter \"e\" is roundish...',6919,0);
INSERT INTO comment VALUES (6924,1051,2839,'Andrew Mitchell','A little gross...','2003-08-04 06:25:44',0,'A side of beef?\r\nsince it is skinned it would be neiether white nor black (rather pinkish red)\r\nThe \"round\" comment could be referring to the cut of meat\r\nand a dress side of beef hangs from a hook so it is off the ground',NULL,0);
INSERT INTO comment VALUES (6925,1064,1626,'Gamer','Queue problems','2003-08-04 06:36:11',4,'Wasn\'t the solution to this in the solution queue 2 days before now? ',NULL,0);
INSERT INTO comment VALUES (6926,1051,1626,'Gamer','re: A little gross...','2003-08-04 06:38:00',0,'I just realized \"stay off the ground\" doesn\'t mean it needs to fly. When it\'s swimming around it\'s off the ground, and on the water instead.',6924,0);
INSERT INTO comment VALUES (6927,1038,1626,'Gamer','re: he gains','2003-08-04 06:43:21',0,'You are counting the original cost of the bike twice. He gets -20 + (30-40) + (50-60) or -40 for the 40 dollar bike. ',6921,0);
INSERT INTO comment VALUES (6928,1064,1575,'DJ','re: Queue problems','2003-08-04 06:45:22',0,'Yeah, I messed up the date stamp somehow, and levik just fixed it, so if you saw the answer..don\'t say anything.',6925,0);
INSERT INTO comment VALUES (6929,1064,2899,'Brian Wainscott','Picky of me....','2003-08-04 06:59:21',1,'I know, but if n=0 there are in infinite number of such sequences:\r\n\r\n-1 + 0 + 1 = 0\r\n-2 + -1 + 0 + 1 + 2 = 0\r\netc.\r\n\r\n(a) specifically states a POSITIVE integer, but the first sentence of the puzzle is in fact false.\r\n\r\nAll I have for (a) so far is some ugly quadratic equations.....',NULL,0);
INSERT INTO comment VALUES (6930,1051,2985,'Vic','Its a...','2003-08-04 06:59:45',0,'Its a female walrus. Or an airplane.',NULL,0);
INSERT INTO comment VALUES (6931,1064,2899,'Brian Wainscott','re: Picky of me....leads to solution?','2003-08-04 07:21:23',3,'(a) requires n to be positive, but not all the terms of the sequence. So I\'d say the longest sequence has 2n terms:\r\n\r\n-(n-1) + -(n-2) + ... + 0 + 1 +...+(n-1)+n\r\n\r\n(eg, for n=4 you have -3 + -2 + -1 + 0 + 1 + 2 + 3 + 4)\r\n\r\nfor (b), the first term is -(n-1) and the last term is n.\r\n\r\nI\'ll have to think a bit about the proof that this is the longest such sequence, but it sounds right....',6929,0);
INSERT INTO comment VALUES (6932,428,2988,'bob','possible explanation','2003-08-04 08:31:32',0,'The bar only serves Guinness or Worthington and the barmaid served the last of the Worthington to the first stranger.',NULL,0);
INSERT INTO comment VALUES (6933,903,1919,'Lewis','Solution','2003-08-04 08:35:26',3,'My method of working it out was as follows. Start with C,A,V & E on cubes 1 to 4 respectively. Then you find another word, like CLEF. We know the position of the C & E, but not the L and F, which are either on the A cube or V cube. Now we need to find a word with either a V or A and either a L or F. The word FARE contains a F and an A, so they cannot be on the same cube. So we have C on cube 1, A & L on cube 2, V and F on cube 3 and E on cube 4. \r\n\r\nRepeating this method we get: S,G ON 3,4\r\n\r\nCube 1:C,U,R,H,O,X\r\nCube 2:A,L,D,T,M,W\r\nCube 3:V,F,P,I,Z,G\r\nCube 4:E,B,Y,K,N,S\r\n\r\nLetters that aren\'t used are X and Q.',NULL,0);
INSERT INTO comment VALUES (6934,903,1919,'Lewis','re: Solution','2003-08-04 08:37:15',3,'The last letter on cube 1 should be \'J\', becuase as I said, X isn\'t used, and from the start it says \'including J\'.',6933,0);
INSERT INTO comment VALUES (6935,343,2988,'bob','re: yes/no','2003-08-04 08:42:53',0,'I agree but your solution doesn\'t address the \"in the side of the mountain\" part of the riddle. For that, I figured the mountain was an avalanche of snow that covered the front of the cabin (door) and the part sticking out had no other way to get in so they froze to death.',2202,0);
INSERT INTO comment VALUES (6936,1038,1919,'Lewis','re: he gains','2003-08-04 09:28:25',3,'You saidhe lost 40 dollars and got a 20 dollar bike, gaining 20 dollars. But if you pay 40 dollars for a 20 dollar bike, thats losing money. Also, the bike is worth 40 dollars, as it says at the end. He paid 40 dollars for a 40 dollar bike, therefore broke even. HE BROKE EVEN!',6921,0);
INSERT INTO comment VALUES (6937,1038,1919,'Lewis','re: The money','2003-08-04 09:29:57',1,'Thats actually a very good point. Although that is probably not the answer Jon was looking for, from the way it is worded that is, strictly speaking, correct.',6833,0);
INSERT INTO comment VALUES (6938,1064,2716,'Federico Kereki','Some hints','2003-08-04 10:00:49',2,'If a number can be factored as p times q, and p is odd, then\r\n\r\nn = (q-(p-1)/2) + ... + (q-1) + q + (q+1) + ... + (q+(p-1)/2)\r\n\r\nShould the first term be negative, the first terms would cancel each other (as in 5=-1+0+1+2+3) and you would have\r\n\r\nn = (-q+(p+1)/2) + ... + (q-1) + q + (q+1) + ... + (q+(p-1)/2)\r\n\r\nThe longest sequence could be the largest odd factor of n.\r\n\r\nThe last term would the the largest value of (q+(p-1)/2), as seen above.\r\n\r\nAs a remark, you can deduce which numbers do *not* allow such a sequence...\r\n\r\nPS. If p is odd and q is even, you can also write\r\n\r\nn = (p-q+1)/2 + .... (p-1)/2 + (p+1)/2 + ... + (p+q-1)/2\r\n\r\nSome of the negative terms (if present) could cancel out some positive terms. The length of this sequence is q, and the maximum term, (p+q-1)/2.',NULL,0);
INSERT INTO comment VALUES (6939,1038,2989,'Andre','basic','2003-08-04 12:21:24',3,' -20.00\r\n +30.00\r\n _______\r\n +10.00\r\n -40.00\r\n _______\r\n -30.00\r\n +50.00\r\n _______\r\n +20.00\r\n -60.00\r\n _______\r\n -40.00\r\n\r\nIt looks as if Mike lost 40.00 but you must count the initial 20.00 Mike paid for the bike. So Mike lost money in deciding to keep the bike, but he\'d have lost at least 20.00 (the same 20.00 he paid for the bike originally and WOULDN\'T HAVE the bike) had he not decided to keep it.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (6940,1051,2990,'Hayley','Fix','2003-08-04 13:05:05',0,'The riddle is not possiable to solve. There are a number of different objects it could be, but none can be certain.',NULL,0);
INSERT INTO comment VALUES (6941,1064,1626,'Gamer','re: Some hints','2003-08-04 15:36:13',0,'This is all fine and such, but I can say a prime number like 5 does have more than 1 number that could be in its group. Maybe I just misread your post.',6938,0);
INSERT INTO comment VALUES (6942,1038,2992,'Chan Wah','re: basic','2003-08-04 15:37:58',0,'I don\'t understand how he would lose at least 20 if he had not kept the bike. The original 20 was already included in your calculation. The way I see it, he is down by 40 but the bike is currently worth 40 so he\'s even.',6939,0);
INSERT INTO comment VALUES (6943,912,2992,'Chan Wah','re: Impossible?','2003-08-04 16:08:06',0,'Agreed',6072,0);
INSERT INTO comment VALUES (6944,1051,2992,'Chan Wah','More grosss','2003-08-04 16:35:13',0,'A calf in the middle of being born?',NULL,0);
INSERT INTO comment VALUES (6945,1064,2995,'H','My solution','2003-08-04 16:43:28',3,'Assuming that the sequence does not restrict itself to just positive integers, my solutions are:\r\nA) the number of terms will be 2n, if the series extends from -(n-1) to n\r\nb) the bounds will thus be -(n-1) and n\r\n\r\nExample: if the integer is 587, the sequence will be -586+(-585)+(-584)...+587',NULL,0);
INSERT INTO comment VALUES (6946,1038,2989,'Andre','re(2): basic, not so basic','2003-08-04 16:51:43',0,'You are right\r\nI miscalculated!\r\nHowever, even though he\'s even he has lost 20.00 because he originally got a deal when he bought a bike valued at 40.00 for half price.',6942,0);
INSERT INTO comment VALUES (6947,44,1919,'Lewis','Solution','2003-08-04 23:16:51',3,'If a wife knew of no unfaithfull-ness, then becuase there was at least one husband, she would know it was hers. The fact that no shots were fired on the first night meant everyone knew of at least one.\r\n\r\nOn the second night if someone knew of only one, but there was definitely more than one because of what happened the previous night, she would know that her husband was unfaithful. The fact that no gunshots were heard meant that everyone knew of at least two.\r\n\r\nThis would continue all the way through to the fortieth night. On that night, anyone who knew of 39 unfaithful husbands would know theirs was unfaithful, so I think 40 men were shot.',NULL,0);
INSERT INTO comment VALUES (6948,134,1919,'Lewis','Step-by-Step Solution','2003-08-04 23:24:51',3,'When he goes across first time he cannot take the grain as the chicken will be alone with the dog, and he cannot take the dog as the chicken will be with the grain. Therefore, he must take the chicken.\r\n\r\nWhen he comes back he can take either the dog or the grain. But when he takes it across he must bring the chicken back, otherwise there will be a bad combination whichever one he takes.\r\n\r\nNow he takes whichever one out of the dog and grain that he didn\'t take on the second trip across. Now all he needs to do is go back and get the chicken.\r\n\r\nThis is a classic puzzle and is one of my favourite logic puzzles of all time.',NULL,0);
INSERT INTO comment VALUES (6949,1059,1575,'DJ','Perhaps','2003-08-05 02:07:52',1,'All of the words can be paired with the word \'ball\' to make a word or expression:\r\nblackball, cornball, eight ball, gutterball, hairball, medicine ball, tea ball.\r\nI had never heard of a tea ball before, but I looked it up and it exists, so, that\'s one possible answer. I can\'t think of anything else..\r\n\r\nair, fly, foot, screw, spit ..',NULL,0);
INSERT INTO comment VALUES (6950,1059,2840,'Becky','ummm','2003-08-05 02:36:46',0,'they all precede the word ball',NULL,0);
INSERT INTO comment VALUES (6951,1059,2839,'Andrew Mitchell','Solution','2003-08-05 03:24:08',3,'All can be combined with \"ball\" to make a common expression\r\nblack ball - to vote against someone\r\ncorn ball - hackneyed\r\neight ball - a pool ball\r\ngutter ball - bowling expression\r\nhair ball - cat owners know\r\nmedicine ball - old fashioned excercise equipment\r\ntea ball - a tool for brewing loose tea',NULL,0);
INSERT INTO comment VALUES (6952,1059,1919,'Lewis','Solution','2003-08-05 04:02:13',3,'All of the words go with the word \'ball\'.\r\nBlackball\r\nCornball\r\nEightball\r\nGutterball etc.',NULL,0);
INSERT INTO comment VALUES (6953,1059,2997,'danielle','re: Solution','2003-08-05 05:22:23',0,'r u fuckin kiddin me?',6952,0);
INSERT INTO comment VALUES (6954,1059,2997,'danielle','re: Solution','2003-08-05 05:23:34',0,'no j/k ur right\r\nlol',6952,0);
INSERT INTO comment VALUES (6955,1038,1626,'Gamer','re(2): The money','2003-08-05 08:28:32',0,'You can\'t really interpret the instructions that way, because it says to include the worth of the bike, which isn\'t done in that solution.',6937,0);
INSERT INTO comment VALUES (6956,1066,1626,'Gamer','First ideas','2003-08-05 12:07:08',2,'By multiplying each side by a²b²c² and subtracting a²c² from each side, then factoring, you can get a²(b²-c²) = b²c²\r\n\r\nFrom this you can see that the difference of two perfect squares has to be a factor of their product.',NULL,0);
INSERT INTO comment VALUES (6957,579,3000,'V','','2003-08-05 12:26:44',0,'The answer is got is 274. \r\n\r\nMethod: To get each number multiply the previous number by 2 then add an additional number on top of those. For the first two numbers you add 0, the next two you add 5 then the last two you add 50.\r\n\r\nThats how I got it anyway ^_^. How old are people on this? I\'m 14.',NULL,0);
INSERT INTO comment VALUES (6958,1066,1626,'Gamer','One solution','2003-08-05 12:47:06',3,'Here is my solution: a = 15, b = 20, c = 12. It seems like the sum 47 would be the smallest, but I haven\'t found a proof yet.',NULL,0);
INSERT INTO comment VALUES (6959,1066,1626,'Gamer','I have a proof now! :)','2003-08-05 13:22:11',3,'\r\nThe idea in solving this one is to multiply each side by a²b²c² and factor and divide by c² to get a² + b² = (ab/c)²\r\n\r\nSince the left side is a perfect square, the right side must be a perfect square. So a and b must be the lesser two from a Pythagorean triple.\r\n\r\nThe smallest pythagorean triple where all of the values are over 0 but integers is 3, 4, 5.\r\n\r\nPutting x3 and x4 (allowing for mutliples of this sequence) in for a and b gives c²(x²5²)=x²3²x²4²\r\n\r\nDividing out x² gives (5*c)² = (3*4*x)²\r\n\r\nThe least possible value for x is 5 (if c is 12), so a=3(5) b=4(5) and c is 12. So 1/(15²) + 1/(20²) = 1/(12²), and so a = 15, b = 20, c = 12 is the lowest solution, and 15 + 20 + 12 = 47 is the lowest value for a + b + c',NULL,0);
INSERT INTO comment VALUES (6960,579,2978,'Freddy Grants','re: no subject(V)','2003-08-05 14:20:54',0,'Well I got the same answer as you. Except I had a different approach, I added 1^2 to the first number(1), then I added 2(1^2) to the sum of 1+1^2, then I multiplied the base of the previous square by 3 making it 3^2, then added that to the sum of 1+1^2+2(1^2) then I added 2(3^2) to that sum. I continued this process, coming to an answer of 274. Basically its (1)+1^2=(2)+2(1^2)=(4)+(3^2)=(13)+2(3^2)=(31)+(9^2)=(112)+2(9^2)=(274),if you wanted to continue the sequence it would be (274)+(27^2)=(1003)+2(27^2)=(2461) so on and so on. The only problem with your approach, I\'m not totally sure if you would know what number to add by after multiplying 274 by 2. And I\'m 16.',6957,0);
INSERT INTO comment VALUES (6961,1066,3005,'Mathcop','re: I have a proof now! :)','2003-08-05 16:26:22',4,'Nice solve Gamer. I kind of figured it was going to begin with a pythagorean triple, but I didn\'t get much past 3,4,5. LOL.\r\n\r\nI have been out of the math game for a few years and I\'m afraid my brain has atrophied. I have to get it in gear again. I\'m afraid I\'m going to sound dumb, but I\'m just going to jump right in. May I ask some possibly obvious questions ...\r\n\r\nYou state, \"Since the left side is a perfect square, the right side must be a perfect square\". How do we know this? Are you referring to a² + b²? How do we know it is a perfect square? And how do we know that means that the right side must also be one?\r\n\r\nI have one or two more questions, but I don\'t think I will display all of my ignorance in one post! And perhaps your response will clear up the rest for me.',6959,0);
INSERT INTO comment VALUES (6962,1066,1626,'Gamer','','2003-08-05 16:57:23',2,'There are usually people who have the same question but feel too silly to ask. I don\'t know what the problem is unless you tell me! :)\r\n\r\nI actually thought I wrote why and didn\'t. Sorry about that...\r\n\r\n(I think you mean a² + b² = (ab/c)²) We can conclude that (ab/c)² is an integer because the left side has to be an integer. I was thinking the only thing that could be squared and become an integer is the square root of something (which would be irrational) or another integer. Based on (ab/c) is an integer, (ab/c)² must be a perfect square, and this means the left side (a² + b²) is a perfect square as well.',NULL,0);
INSERT INTO comment VALUES (6963,1051,2898,'dorkdork','jus ges\'n ~','2003-08-05 19:28:49',0,'walrus- sea cow',NULL,0);
INSERT INTO comment VALUES (6964,1059,2898,'dorkdork','? ~ ?','2003-08-05 19:34:57',0,'nothing.',NULL,0);
INSERT INTO comment VALUES (6965,633,2898,'dorkdork','my hypothesis.','2003-08-05 19:45:30',0,'this procedure - (frozen water), contains oxygen as an element. When frozen, the other elements combine, thus allowing the oxygen element to expand, making the entire frozen object to become light enough to float.',NULL,0);
INSERT INTO comment VALUES (6966,1066,1575,'DJ','A start?','2003-08-05 22:21:24',1,'If the sides of a right triangle are 1/a, 1/b, and 1/c, then the Pythagorean equation becomes 1/a² + 1/b² = 1/c².\r\n\r\nIn the recent problem, Reciprocal Equations #2, we found all the sets of positive integers a, b, and c for which 1/a + 1/b = 1/c. For this problem, we need to find such a case where a, b, and c are all perfect squares.\r\n\r\nIn the other problem, the given solution was that for a given value of a and some number x, b=a+x, and c=a²/x + a. I don\'t know how to solve this directly, but it looks like a good place to start..\r\n',NULL,0);
INSERT INTO comment VALUES (6967,1066,979,'Ravi Raja','re: A start?','2003-08-05 22:44:33',2,'The equation that you have got, that is, c=a²/x + a, gives you a third degree equation in a and may be using Cardan\'s method might help or may be using that makes it more complicated ? I haven\'t tried that yet, because I am thinking of some different method to solve this problem. It was just a suggestion. if anyone knows that method, he/she can give it a try.',6966,0);
INSERT INTO comment VALUES (6968,1062,1919,'Lewis','Solution','2003-08-06 00:31:51',3,'To get the Nth term you multiply the (N-1)st term by (N+1).\r\n\r\n3=1*3\r\n12=3*4\r\n60=12*5\r\n360=60*6\r\n2520=360*7\r\n\r\nSo the next two numbers are going to be:\r\n20160=2520*8\r\n181440=20160*9',NULL,0);
INSERT INTO comment VALUES (6969,1045,1919,'Lewis','Solution','2003-08-06 01:22:06',3,'To get the Nth term you square the (N-1)st term and then add the (N-1)st term.\r\n\r\n2=1^2+1\r\n6=2^2+2\r\n42=6^2+6\r\n\r\nSo the next number will be:\r\n\r\n1806, which is 42^2+42',NULL,0);
INSERT INTO comment VALUES (6970,1062,2918,'Jay','','2003-08-06 02:32:29',0,'20160',NULL,0);
INSERT INTO comment VALUES (6971,504,3009,'sam','classic','2003-08-06 03:11:30',0,'It\'s a classic self-referential strange loop paradox, as espoused by Goedel, same as the sentence: \'This sentence is false.\' Neither sentence is true nor false, in the same way a Moebius strip only has one side.',NULL,0);
INSERT INTO comment VALUES (6972,1066,1626,'Gamer','My Idea','2003-08-06 03:46:24',0,'I tried lots of fancy stuff (like a²/c² - a²/b² = 1) but it didn\'t seem to help me as much as my simple equation.\r\n\r\nYou can read the lower posts if you want to learn more :)',NULL,0);
INSERT INTO comment VALUES (6973,1062,1171,'nikki','Previous numbers','2003-08-06 04:42:45',3,'The pattern is that the division of consecutive elements (k+1)/k results in consecutive numbers, starting with 3.\r\n\r\n 3/1=3\r\n12/3=4\r\n60/12=5\r\n360/60=6\r\n2520/360=7\r\nso\r\nX/2520=8 => X = 2520*8 = 20160\r\n\r\nThe next question in my mind is, what are the previous numbers in the sequence? 1/2 and 1/2 =) I don\'t think there can be a finite number before those, because then you would have\r\nY = 0.5/0\r\n\r\nLater!\r\n',NULL,0);
INSERT INTO comment VALUES (6974,1062,3013,'Murugappan','','2003-08-06 11:53:28',3,'The Solution is 20160.',NULL,0);
INSERT INTO comment VALUES (6975,1062,2978,'Freddy Grants','Solution','2003-08-06 12:43:43',0,'Well this sequence was fairly easy. All you do is multiply the first number in the sequence (1) by 3, You take that product (3) and multiply by 4, You take that product (12) and multiply it by 5. When you continue this pattern you would have to multiply 2520 by 8 giving you 20160 and you would multiply that by 9 giving you 181440 you could continue this on and on, but I want to spend some time on other problems :).',NULL,0);
INSERT INTO comment VALUES (6976,707,2839,'Andrew Mitchell','BRUTAL','2003-08-06 13:25:26',0,'Yehaaa! I ahve not checked anyone elses solutions but here is what I came up with, I\'m darn certain...\r\n\r\n5B Albert Loomis, Zookeeper 60 yrs\r\n4A Edgar James, Pastry Chef 24 yrs\r\n3E Dan Masse, Nurse 72 yrs\r\n2C Calvin Nash, Banker 36 yrs\r\n1D Blake Knight, Electrician 84 yrs\r\n\r\nI dig these type of puzzles',NULL,0);
INSERT INTO comment VALUES (6977,414,2898,'dorkdork','///~~??','2003-08-06 14:19:27',0,'everything',NULL,0);
INSERT INTO comment VALUES (6978,1051,3018,'may keg','Not to sure','2003-08-06 14:19:37',0,'But, is it a \'Cowboy riding a horse?\"',NULL,0);
INSERT INTO comment VALUES (6979,1051,2667,'Viet','how bout','2003-08-06 14:21:44',0,'a hamburger about to be eat i unno wat leg letz say it our hand holding the round bun and itz not on the ground hahaha',NULL,0);
INSERT INTO comment VALUES (6980,421,2898,'dorkdork','humdinger?!~','2003-08-06 14:27:30',0,'because one size fits all?',NULL,0);
INSERT INTO comment VALUES (6981,343,2898,'dorkdork','humdedoo','2003-08-06 14:35:06',0,'they must have fallen.',NULL,0);
INSERT INTO comment VALUES (6982,329,2898,'dorkdork',' no know.','2003-08-06 14:44:24',0,'dawn',NULL,0);
INSERT INTO comment VALUES (6983,278,2898,'dorkdork','do no know','2003-08-06 14:50:00',0,'send one kid home.',NULL,0);
INSERT INTO comment VALUES (6984,299,2898,'dorkdork','~~~~','2003-08-06 14:58:32',0,'calendar.',NULL,0);
INSERT INTO comment VALUES (6985,1058,1919,'Lewis','Some Ramblings','2003-08-06 16:05:34',1,'Hmm.. this is a tricky one.\r\n\r\nBecause two genuine coins weigh the same as one light and one heavy, I don\'t think there\'s a way to get a 100% success rate. Obviously, I could be wrong....\r\n\r\nMy best success rate so far is about 50%... pretty pathetic if you consider picking a coin at random will give you a 40% chance...\r\n\r\nI\'m pretty sure there\'s a better way though. Obviously, I could be wrong....Ooh, Deja Vu!\r\n',NULL,0);
INSERT INTO comment VALUES (6986,469,1919,'Lewis','re: umm','2003-08-06 16:44:13',3,'But the author used the note to pay off the plumber\'s bill, gaining 100 rupees (not dollars!) THEN lost the other 100 rupees, as you said, therefore breaking even like everyone else in the problem.',4533,0);
INSERT INTO comment VALUES (6987,1038,1919,'Lewis','re(3): The money','2003-08-06 17:31:54',0,'Ahh... for some reason I didn\'t see that last sentence...',6955,0);
INSERT INTO comment VALUES (6988,826,3024,'Stuart','Simpler solution','2003-08-06 21:28:54',4,'Isn\'t it simpler to say that just because 1 particular group of k dogs are all the same colour doesn\'t mean all groups of k dogs are the same colour. Assuming it\'s true is assuming that the statement you are trying to prove is true. You can\'t prove something by assuming it\'s true. It\'s false logic.',NULL,0);
INSERT INTO comment VALUES (6989,826,3024,'Stuart','Furthermore','2003-08-06 21:33:58',1,'The proof assumes that k dogs in a group must all be the same colour. Where is the proof of this statement? This would be true if all dogs are the same colour but that is what is being proven (supposedly).',NULL,0);
INSERT INTO comment VALUES (6990,511,3024,'Stuart','Nonsense','2003-08-06 23:14:04',1,'There\'s a difference between \"not wanting to\" and \"not being able to\". If god doesn\'t want to lift the rock because it would contradict his omnipotence that doesn\'t mean he can\'t lift the rock.\r\n\r\nI don\'t believe in god. That doesn\'t mean \"he\" doesn\'t exist, it just means I see no reason to believe in god. Blind faith is nothing but wishful thinking. What\'s wrong with proof denying faith? More important than the existence of god is \"his\" nature. Just because god created everything including us (assuming this is true) doesn\'t mean \"he\" is omnipotent (what if god created a being more powerful than him?). It doesn\'t mean he is omniscient either. What makes god omniscient? What makes something a sin? Why? My view of god is that \"he\" is arrogant and narrow minded because \"he\" will not tolerate being challenged. It\'s \"his\" way or no way. \"He\" doesn\'t even give good reasons for \"his rules\". Why should we always do what god wants us to do? Sounds selfish to me. Non-believers supposedly go to hell but why? Just because they don\'t believe in god. Isn\'t that exercising their free will given to them by god. If god wants us to believe in \"him\" and worship him (self-indulgence? conceit?) why doesn\'t \"he\" just prove to us that he exists? What is so important about faith.\r\n\r\nOne of the main reasons for my non-belief is that I don\'t believe in fundamental truths. Nothing can ever be proved beyond a shadow of a doubt whether scientific, moral, or otherwise. Morality is a matter of opinion and scientific \"facts\" can always (potentially) be disproved no matter how old the \"facts\" are. Of course, this belief is paradoxical. That\'s why it\'s a belief. Some might say I\'m contradicting myself. I don\'t believe in god because there\'s no proof, but I believe there are no fundamental truths despite no proof. I can\'t prove it because there are no fundamental truths. Of course, there has to be fundamental truths as far as science is concerned but what I mean is that no-one will ever know what they are. As for morals, whether or not god exists, and whatever \"his\" views and opinions are (if he exists), there is no such thing as right and wrong except in the minds of the individual.',NULL,0);
INSERT INTO comment VALUES (6991,1058,2373,'ryan smith','~50%','2003-08-07 01:05:53',0,'Weighing one coin against two others in two separate weighings, I calcualted about a 50% chance over all of picking a fake by picking a coin out of the weighed 3 or unweighed 7 depending on the weighing results.\r\n\r\nSimilar to Lewis I guess. I\'m not going to show my work, since there is reams of it. Weighing more than one coin at a time scares the dickens out of me.',NULL,0);
INSERT INTO comment VALUES (6992,1066,979,'Ravi Raja','My Idea','2003-08-07 01:51:26',1,'We all know that the three pythagorean triplets are expressed in the form: n, (n²-1)/2 and (n²+1)/2, where \'n\' is a positive odd integer and the number (n²+1)/2 being the greatest, is the hypotenuse. \r\nSo the three sides I know can be expressed in the above form when it is given that the three sides are integral but I do not know in which form am I supposed to express the lengths of the sides of a right triangle if they are fractional as in the given problem.\r\nThis was just a hint (may be a useless one) but may be someone can get to some result using the fact.',NULL,0);
INSERT INTO comment VALUES (6993,587,693,'Jun','My 2 cents worth','2003-08-07 08:45:18',0,'if you empty all of the wine in one barrel of half filled wine to another barrel of half filled wine you\'ll get 8 fully filled barrels, 5 half filled barrels and 8 empty barrels. repeat this step, you\'ll get 9 fully filled barrels, 3 half filled barrels and 9 empty barrels. thus the 3 men can split these barrels among themselves equally.\r\n\r\ni figured that you can\'t use another method of pouring half of the wine in a fully filled barrel to an empty to make the number of fully filled barrles 6, half filled barrels 9 and empty barrels 6, since it was mentioned that no measuring devices was available though this method would be much easier.',NULL,0);
INSERT INTO comment VALUES (6994,587,2839,'Andrew Mitchell','Solution','2003-08-07 08:51:18',3,'poor the contents of one of the hlf full barrels into another half full barrel , do this a second time.\r\nNOw you have 9 full barrells, 3 half full barrels, and 9 empties.\r\neach son gets 3 full 1 half and 3 empty',NULL,0);
INSERT INTO comment VALUES (6995,587,1575,'DJ','Solution','2003-08-07 10:56:09',3,'The only thing you can do with the barrels is pour them. So, if you take one of the full barrels, and one of the half-barrels, and pour them down the drain, each son gets two full, two half-full, and three empty barrels.\r\nProblem solved!',NULL,0);
INSERT INTO comment VALUES (6996,587,1626,'Gamer','Another Solution','2003-08-07 12:14:48',3,'What I would do is give two sons 3 full, 1 half full, and 3 empty barrels, and give the other son 1 full, 5 half full and 1 empty. Pour the contents of 2 of the half full barrels into 2 other half full barrels. This way each son has the most wine possible, and only one son has to do anything! :)',NULL,0);
INSERT INTO comment VALUES (6997,1066,1626,'Gamer','re: My Idea','2003-08-07 13:10:24',0,'Another interesting pythagorean triplet is 20, 21, 29. This means 1/609 squared plus 1/580 squared equals 1/420 squared.',6992,0);
INSERT INTO comment VALUES (6998,587,1919,'Lewis','Solution','2003-08-07 13:38:09',3,'Pour two half-filled barrels into two other half-filled barrels. This makes\r\n7+2=9 full barrels.\r\n7-4=3 half-full barrels\r\n2+2=9 empty barrels.\r\n\r\nNow each son gets 3 full barrels, 1 half-full barrel and 3 empty barrels.',NULL,0);
INSERT INTO comment VALUES (6999,587,2978,'Freddy Grants','solution','2003-08-07 13:46:16',0,'The easiest way you can distribute an equal amount of full, half full, and empty barrels, is take two half full barrels and pour each into another 2 other half full barrels. Once this is done, there will be 9 full barrels, 3 half full barrels, and 9 empty barrels, since all these numbers are equally divisible by three that means the barrels can be distributed equally.',NULL,0);
INSERT INTO comment VALUES (7000,718,3032,'gregada','re: possible solution','2003-08-07 14:53:16',0,'that\'s the one i came up with as well... do you know if it is correct?',4710,0);
INSERT INTO comment VALUES (7001,279,3032,'gregada','using functions??','2003-08-07 15:12:02',0,'since when are functions being treated as symbols?? allowing floors, ceilings, and the rest makes the problem a bit too easy... don\'t you think?',6388,0);
INSERT INTO comment VALUES (7002,1044,1575,'DJ','Simple Method','2003-08-07 15:27:26',3,'The formula for the nth triangle number is\r\nT(n)=[n(n+1)]/2.\r\nSo, a method that relies largely on inspection would be:\r\nSuppose you are given the integer T. Take the square root of twice T, then the \'floor\' of that value (round down to the next highest integer). That should be your n, if T is indeed a triangle number.\r\nn = _√(2T)_\r\nThen just check; multiply n by n+1, take half of that sum, and it should be your original number. If it is, then T is the nth triangle number; if not, then T is not a triangle number at all.\r\n\r\nI\'m sure other, cleaner methods will be found, but that simple method presented itself, and it doesn\'t violate the rules of the problem.',NULL,0);
INSERT INTO comment VALUES (7003,279,3032,'gregada','re: using functions?? -- here is an easy way...','2003-08-07 15:29:13',0,'here is a way to get to 15 without doing anything highly questionable... i will do to 150 when i have time.\r\n\r\n1=-2+0+0+3\r\n2=2+0*0*3\r\n3=2*0*0+3\r\n4=2^0+0+3\r\n5=2+0+0+3\r\n6=2*(0+0+3)\r\n7=2+0!+0!+3\r\n8=2+0+0+3!\r\n9=2+0!+0+3!\r\n10=2+0!+0!+3!\r\n11=(2+0!)!-0!+3!\r\n12=2*(0+0+3!)\r\n13=20-0!-3!\r\n14=20-0-3!\r\n15=20+0!-3!\r\n',7001,0);
INSERT INTO comment VALUES (7004,1058,1919,'Lewis','Wow...This is Hard','2003-08-07 15:45:47',0,'I know I said 50% was rather pathetic, but I think thats the best I can do. I\'ll continue to look into this one.\r\n',NULL,0);
INSERT INTO comment VALUES (7005,1044,2899,'Brian Wainscott','re: Simple Method','2003-08-07 16:48:37',0,'In the last line of your post you say \"I\'m sure other, cleaner methods will be found\"\r\n\r\nI am not so sure. This is the same method that immediately occured to me and really, it is about as simple as one could expect.\r\n\r\nBut I confess I did have to look up \"Triangle number\" just to be sure it meant what I inferred from Lewis\' brief description.',7002,0);
INSERT INTO comment VALUES (7006,1044,3036,'LynetteVivian','','2003-08-07 17:53:57',0,'take the rand. pos. int. that you were given, and multiply it by eight\r\nthen add one to this\r\n\r\nif the result is both odd and a perfect square, then \r\nthe rand.pos. nbr your were given is a triangle number\r\n\r\n1 is a triangle nbr because 1 + 8(1) = 9 (result is both odd and square)\r\n\r\n3 is a triangle nbr because 1 + 8(3) = 25 (result is both odd and square)\r\n\r\n28 is a triangle nbr because 1 + 8(28) = 225 (result is both odd and square)',NULL,0);
INSERT INTO comment VALUES (7007,1044,1626,'Gamer','Another simple method','2003-08-07 18:32:32',3,'Any time you multiply a number by 2 (or a multiple of two) it will be even by definition, then when you add 1, (since 1/2 isn\'t an integer) it will be odd.\r\n\r\nWhen you solve 1/2n² + 1/2n - T = 0 using the quadratic formula, you get (√(8T+1)-1)/2 to find what order number the triangle number is. This method doesn\'t need any testing too. If you know perfect squares it can even be performed mentally! :)',7006,0);
INSERT INTO comment VALUES (7008,1044,3036,'LynetteVivian','','2003-08-07 20:36:17',0,'I worded my previous post very poorly. Sorry.\r\nYes, I understand that 2n is even and that 2n+1 is odd when n is an int.\r\nIt is because of this that you\'ll see only the odd squares and never the evens coming up. Which is what I was trying so clumsily to point out.\r\n\r\n\r\nTake the rand. pos. int. that you were given, and multiply it by eight; \r\nthen add one to this. If the result is a perfect square, then \r\nthe rand.pos. int. your were given is a triangle number.\r\n\r\nNote - this perfect square will only be odd - you\'ll never have an even here.\r\nYou have 3^2 but not 4^2; you have 5^2 but not 6^2; you have 7^2 but not 8^2 & so on.\r\n\r\n1 is a tri nbr because 1 + 8(1) = 9 = 3^2\r\n3 is a tri nbr because 1 + 8(3) = 25 = 5^2\r\n6 is a tri nbr because 1 + 8(6) = 49 = 7^2\r\n10 is a tri nbr because 1 + 8(10) = 81 = 9^2\r\n15 is a tri nbr because 1 + 8(15) = 121 = 11^2\r\n21 is a tri nbr because 1 + 8(21) = 169 = 13^2\r\n28 is a tri nbr because 1 + 8(28) = 225 = 15^2\r\n',NULL,0);
INSERT INTO comment VALUES (7009,1044,1575,'DJ','Simpler Derivation','2003-08-07 21:25:56',3,'Starting from the equation for the nth triangle number:\r\n\r\nT = [n(n+1)]/2\r\n2T = n² + n\r\n4T = 2n² + 2n\r\n8T = 4n² + 4n\r\n8T + 1 = 4n² + 4n + 1\r\n8T + 1 = (2n + 1)²\r\n\r\nSo, if you are given an integer T, (8T + 1) is a perfect square iff T is a triangular number. Further, that result is the square of (2n + 1), such that T is the nth Triangle number.',NULL,0);
INSERT INTO comment VALUES (7010,1051,3043,'Angel','i think...','2003-08-08 02:39:29',0,'i think its a seal',NULL,0);
INSERT INTO comment VALUES (7011,1051,2840,'Becky','','2003-08-08 08:07:35',0,'you a crazy, funny person',NULL,0);
INSERT INTO comment VALUES (7012,1060,1575,'DJ','Guess?','2003-08-08 08:23:23',1,'My guess is that all the words are still valid words when you switch the first and last letters:\r\nlain, gnus, repel, wines, riffed, satchel, dignifies.\r\nI don\'t know if that\'s the intended answer; it could be mere coincidence..',NULL,0);
INSERT INTO comment VALUES (7013,1066,979,'Ravi Raja','re(2): My Idea','2003-08-08 10:20:47',0,'I do not know if that relation which you have suggested holds or not and I haven\'t checked it out yet but by giving an example you cannot give all possible solutions to the given problem. What I was trying to ask others was that if anyone could find out a general result using the given fact. Anyway, your solution might also work (not verified) but we are looking for the general result and not just one or two examples. ',6997,0);
INSERT INTO comment VALUES (7014,1060,1301,'Charlie','re: Guess?--Other words like this and a probability problem','2003-08-08 11:25:38',0,'In the following list, less common words are not shown, but the words with switched letters (first and last letter) might be less common, so the reverse might not be listed.\r\n\r\nStatistics-wise, 580 out of 74,780 of the more common words had this property or about 1 in 129. It would be an even smaller fraction if the check on the reverse word required more common words also, but even with a probability of 1/129, the probability of getting 7 such words would be about 1 in 600 trillion (American trillion).\r\n\r\naims, air, are, ate, atoms, aunt, bad, bag, ban, bard, bas, bat, bed, ben, bibs, bid, big, bin, blurs, bog, boy, bra, brad, brag, bro, bud, bun, bur, bus, but, cam, cap, cod, combat, cor, curia, dab, dabbler, dafter, dagger, dairy, dais, dallier, dam, damper, danger, danker, dapper, darer, darken, darn, dashes, dater, dates, daub, deal, dear, dearer, deb, debater, decanter, deceiver, declaimer, decliner, decoder, decomposer, deduces, deem, deep, deer, defer, deferrer, defiler, definer, deflower, degrader, del, delayer, deliver, demander, denouncer, dens, dent, deoxidizer, depolarizer, deposer, deprogrammer, desensitizer, designer, deviser, dew, dicer, dicker, diet, differ, dig, digger, dignifies, dim, dimmer, dingles, dipper, dispel, diver, doc, dodder, dog, doles, dolt, don, doom, door, doper, dos, doser, dot, dotter, douses, dowel, dower, drab, drag, drop, dub, dubber, duds, dues, duffel, duffer, duo, dup, duster, dwindles, eager, eat, eats, eel, ekes, emits, eons, epics, era, eruct, eta, fain, fir, flea, foal, fool, fret, furs, gab, gad, gal, gam, gar, gas, gel, gem, get, gins, glans, gnus, gob, god, got, grab, grad, grip, grit, gum, guns, gut, had, hangs, hap, hasp, hate, hay, hep, hey, hits, hon, hoop, hoots, hop, hops, host, hugs, jar, kames, keel, keep, khans, kind, king, lab, lad, lag, lain, lair, lap, lapper, lascar, latches, later, lead, leaf, leap, led, lee, leek, leer, lees, leg, leper, let, lever, liar, lied, lilt, lily, lisped, lit, loaf, loin, loom, loop, loot, lop, lowed, lower, luffed, lug, mad, mag, magus, man, map, mar, mat, mates, may, meat, meed, meet, meg, meter, mid, mod, mon, mood, moor, moot, mop, morn, mot, mug, nab, nag, nail, nap, napper, narc, nard, naris, nary, neap, neb, net, new, news, nib, nil, nip, nit, nitric, nod, noh, nom, norm, nos, not, now, nub, nuns, nut, oat, ohm, ohms, oils, oink, orb, ova, pad, pal, pales, pals, pan, par, part, pas, pat, paw, pay, peal, pear, peek, peen, per, pig, pin, pis, pit, plums, pol, pooh, pool, pot, pour, pow, prig, prod, pus, put, racked, racket, rafted, rag, rages, ragged, rail, rakes, rallied, rallies, ram, rammed, ranged, ranges, ranked, rap, rapped, rascal, rat, rated, ravages, ravel, raves, raw, ray, read, real, reap, reared, rebated, recanted, recedes, received, reclaimed, reclined, recomposed, rectos, reduces, reed, reel, ref, referred, refiled, refined, reflowed, reflowered, reformed, regraded, relayed, relighted, relived, remanded, rennet, renounced, rep, repel, reposed, reserved, resigned, retailed, retained, retested, revel, reveres, revised, rheas, rial, ribbed, riced, riddled, riel, riffed, rigged, rim, rimmed, ringed, ringlet, ripped, rived, rives, robbed, robes, rocked, rod, rood, room, roped, rot, rotted, roused, rout, routes, rowed, rub, rubbed, rubes, rues, ruffed, russet, rusted, sabin, sachem, sachet, saddled, sag, sager, saggier, said, saint, sallied, sandier, sap, sat, satchel, sate, sated, saver, saw, seal, sealer, seat, seceder, sector, seder, seduced, seducer, seed, seep, seer, send, sent, serried, seven, severer, sewn, sexed, shank, shear, ship, shout, shut, sic, signified, silly, silo, silt, simpler, sinew, sing, singed, singled, sink, sip, sit, six, slang, slump, smite, snug, soak, sob, sober, sod, sold, soled, son, sonnet, sooth, soph, sort, sought, soused, sow, sown, spice, sub, sued, suer, suffer, suit, sum, sun, sung, sup, surf, swat, swindled, tab, tacker, tag, tam, tamer, tao, tap, tar, taw, team, teas, teed, teem, tel, ten, tend, tennis, tens, testes, thaw, this, thus, tied, till, tiller, tin, tingler, tingles, tip, tippler, toad, tog, told, tom, ton, too, tool, top, totem, toughs, tour, tow, town, trap, trig, truce, tub, tug, tuna, twos, vat, wad, wan, war, was, way, wed, wet, what, whet, wines, won, yak, yam, yap, yarn, yaw, yob. ',7012,0);
INSERT INTO comment VALUES (7015,980,2839,'Andrew Mitchell','solution','2003-08-08 12:22:33',3,'Jimmy = knave\r\nJohnny = knight',NULL,0);
INSERT INTO comment VALUES (7016,1060,1301,'Charlie','re(2): Guess?--Other words like this and a probability problem','2003-08-08 13:57:48',0,'Actually using a consistent word list, the fraction of the 74780 \"more common\" words that have the switched values also on the more-common list comes out to 376/74780, or about 1 in 199, making the probability of all 7 being accidentally of this type less than 1 in 10^16.\r\n\r\nbad, dab, bed, deb, cod, doc, brad, drab, bud, dub, are, era, ate, eta, bag, gab, bog, gob, dog, god, brag, grab, drag, grad, gal, lag, deal, lead, del, led, eel, lee, keel, leek, gel, leg, dispel, lisped, foal, loaf, dowel, lowed, duffel, luffed, dam, mad, gam, mag, deem, meed, gem, meg, dim, mid, doom, mood, gum, mug, ban, nab, lain, nail, darn, nard, ben, neb, bin, nib, don, nod, hon, noh, mon, nom, morn, norm, bun, nub, bro, orb, lap, pal, nap, pan, leap, peal, keep, peek, nip, pin, lop, pol, hoop, pooh, loop, pool, grip, prig, drop, prod, dafter, rafted, gar, rag, dagger, ragged, lair, rail, dallier, rallied, mar, ram, danger, ranged, danker, ranked, par, rap, dapper, rapped, lascar, rascal, dater, rated, dear, read, pear, reap, dearer, reared, debater, rebated, decanter, recanted, deceiver, received, declaimer, reclaimed, decliner, reclined, decomposer, recomposed, deer, reed, leer, reel, deferrer, referred, defiler, refiled, definer, refined, deflower, reflowed, degrader, regraded, delayer, relayed, deliver, relived, demander, remanded, denouncer, renounced, per, rep, leper, repel, deposer, reposed, designer, resigned, lever, revel, deviser, revised, liar, rial, dicer, riced, differ, riffed, digger, rigged, dimmer, rimmed, dipper, ripped, diver, rived, door, rood, moor, room, doper, roped, dotter, rotted, dower, rowed, bur, rub, dubber, rubbed, duffer, ruffed, duster, rusted, gas, sag, rages, sager, dais, said, pas, sap, latches, satchel, eats, sate, dates, sated, raves, saver, recedes, seceder, rectos, sector, deduces, seduced, reduces, seducer, dens, send, reveres, severer, news, sewn, khans, shank, rheas, shear, dignifies, signified, oils, silo, gins, sing, dingles, singled, pis, sip, glans, slang, plums, slump, emits, smite, gnus, snug, robes, sober, dos, sod, doles, soled, nos, son, hoots, sooth, hops, soph, douses, soused, epics, spice, bus, sub, dues, sued, rues, suer, guns, sung, pus, sup, furs, surf, dwindles, swindled, bat, tab, racket, tacker, mat, tam, oat, tao, pat, tap, rat, tar, meat, team, seat, teas, meet, teem, let, tel, net, ten, dent, tend, sent, tens, shut, thus, diet, tied, lilt, till, nit, tin, ringlet, tingler, pit, tip, got, tog, dolt, told, mot, tom, not, ton, loot, tool, pot, top, sought, toughs, rout, tour, grit, trig, eruct, truce, but, tub, gut, tug, aunt, tuna, raw, war, saw, was, dew, wed, thaw, what, sinew, wines, now, won, may, yam, pay, yap, nary, yarn, way, yaw, boy, yob.',7014,0);
INSERT INTO comment VALUES (7017,586,2572,'derek','solution','2003-08-08 14:34:40',3,'sequence = *4, +4, /4, -4, repeat\r\n\r\nnext = 12, 3, -1, -4, 0, 0, -4, ...',NULL,0);
INSERT INTO comment VALUES (7018,586,1919,'Lewis','Solution','2003-08-08 14:41:25',3,'I\'m not sure if this is the actual rule, bet it goes:\r\n*4, +4, divide by 4, -4.\r\nSo, the next numbers will be:\r\n\r\n12 (8+4)\r\n3 (12/4)\r\n-1 (3-4)',NULL,0);
INSERT INTO comment VALUES (7019,732,2839,'Andrew Mitchell','solution','2003-08-08 15:02:59',3,'drew = liar\r\nmohammed = truth teller',NULL,0);
INSERT INTO comment VALUES (7020,524,2839,'FatBoy','solution','2003-08-08 15:33:33',0,'eye',NULL,0);
INSERT INTO comment VALUES (7021,431,2839,'FatBoy','','2003-08-08 15:37:15',3,'10 diamonds\r\nKing hearts\r\n8 spades',NULL,0);
INSERT INTO comment VALUES (7022,775,2839,'FatBoy','solution','2003-08-08 15:41:33',3,'drew = liar\r\nmoh\'d = knight',NULL,0);
INSERT INTO comment VALUES (7023,633,3051,'Bruce','dorkdork','2003-08-08 18:10:52',0,'Are you kidding me? DO YOU EVEN KNOW WHAT ICE IS? FROZEN WATER. WATER, YOU JACKASS. This means that the molecules are still intact. I hope you drown in the bath tub so you can figure out what water is.',NULL,0);
INSERT INTO comment VALUES (7024,586,2722,'Jack Putz','12','2003-08-08 18:35:08',0,'12',NULL,0);
INSERT INTO comment VALUES (7025,586,2722,'Jack Putz','12','2003-08-08 18:35:10',0,'12',NULL,0);
INSERT INTO comment VALUES (7026,99,2995,'H','re: bigger than Nicks the sequel','2003-08-08 18:38:28',0,'That would actually make the number smaller, as -3e2 would be .1^-300 as opposed to Nick\'s solution of .1^-2000',3743,0);
INSERT INTO comment VALUES (7027,586,1627,'deborah','re: Solution','2003-08-08 19:11:57',0,'I agee this is exactly the solution I came up with.\r\n\r\nDeb',7018,0);
INSERT INTO comment VALUES (7028,586,3052,'Richard Hopkins','good starter problem','2003-08-08 21:02:56',0,'Answer is 12, the sequence is x4, +4, /4, -4.. took approximately a minute and a half to figure out..',NULL,0);
INSERT INTO comment VALUES (7029,586,3013,'Murugappan','Solution','2003-08-09 04:47:42',3,'The solution is 12.\r\nThe Sequence is like x,4x,4x+4,(4x+4)/4,((4x+4)/4)-4,4(((4x+4)/4)-4)...\r\n\r\nso 5\r\n 5*4=20\r\n 20+4=24\r\n 24/4=6\r\n 6-4=2\r\n 2*4=8\r\n 8+4=12 is the Solution.',NULL,0);
INSERT INTO comment VALUES (7030,1074,1919,'Lewis','Solution','2003-08-09 08:27:24',3,'The number of times the digit 0 appears in this puzzle is 1.\r\nThe number of times the digit 1 appears in this puzzle is 7.\r\nThe number of times the digit 2 appears in this puzzle is 3.\r\nThe number of times the digit 3 appears in this puzzle is 2.\r\nThe number of times the digit 4 appears in this puzzle is 1.\r\nThe number of times the digit 5 appears in this puzzle is 1.\r\nThe number of times the digit 6 appears in this puzzle is 1.\r\nThe number of times the digit 7 appears in this puzzle is 2.\r\nThe number of times the digit 8 appears in this puzzle is 1.\r\nThe number of times the digit 9 appears in this puzzle is 1.',NULL,0);
INSERT INTO comment VALUES (7031,1074,1919,'Lewis','re: Solution','2003-08-09 09:06:58',0,'The second bit got put on AFTER I posted that solution. It\'s a bit tricky...',7030,0);
INSERT INTO comment VALUES (7032,1074,1626,'Gamer','re: Solution','2003-08-09 09:17:20',0,'This solution is easily derived if you know the solution for self-descriptor is 6210001000. You need to add 1 to all of them and shift all the numbers down a blank.\r\n\r\n6210001000\r\n7321112111\r\n1732111211',7030,0);
INSERT INTO comment VALUES (7033,865,3058,'nav','solution','2003-08-09 10:11:01',0,'this is what i think.\r\nthe so called \"question \" contains a referrence\r\nto itself and so is not complete and so cannot have any answer. what im sayin is, the word \'question\' in the given \"question\" can be substituted with \'is no the correct answer to this question?\'.and in order to get the absolute or complete meaning of this question the word \"question\" has to be eliminated which we find is not possible.another eg of this kind is \r\nTHIS STATEMENT IS FALSE. because of the self refference this statement is neither true nor false.it is incomplete.',NULL,0);
INSERT INTO comment VALUES (7034,476,3058,'nav','say \"u r gonna eject me into space\"','2003-08-09 10:28:21',0,'think!',NULL,0);
INSERT INTO comment VALUES (7035,250,3058,'nav','solution','2003-08-09 10:42:11',0,'let\'s say he is lying.\r\nso the statement \"everything i(ie he) say to you is a lie\" is a lie.the opposite of this must me the truth.consider the most general opposite of this statement.it is \"not everything i say to you is a lie\". this allows the possibility that this particular statement is a lie and solves the paradox {this type of paradox is known as loop hole paradox. a much tougher one is\"i am lying\"}',NULL,0);
INSERT INTO comment VALUES (7036,587,2489,'nellie','','2003-08-09 12:55:01',0,'Are we all missing something in the question? Puzzles from this author generally demand more.',NULL,0);
INSERT INTO comment VALUES (7037,586,2703,'Mr. Spock','Solution','2003-08-09 13:58:01',0,'Agreed answer is 12, Recursive formula for all n> 1: If Mod(n,4)=0 then t(n)=t(n-1)/4; If Mod(n-1,4)=0 then t(n)=t(n-1)-4; If Mod(n-2,4)=0 then t(n)=t(n-1)*4; If Mod(n-3,4)=0 then t(n)=t(n-1)+4. ',NULL,0);
INSERT INTO comment VALUES (7038,1060,2703,'Mr. Spock','re: Guess?','2003-08-09 14:22:27',0,'Hmmmm, this is true and statistically very coincidental, I think maybe you have hit it. ',7012,0);
INSERT INTO comment VALUES (7039,1074,1575,'DJ','Half done..','2003-08-09 14:27:14',1,'That\'s good, but how would you do it with only one 7?',NULL,0);
INSERT INTO comment VALUES (7040,1074,2703,'Mr. Spock','Answer','2003-08-09 14:46:52',0,'Computationally, There are only two possible answers for the first condition, the first is: 1;7;3;2;1;1;1;2;1;1 it also satisifes condition 2, the second is fairly simplistic 1 1;11;2;1;1;1;1;1;1;1 but obviously doesn\'t satisify the first conidition.',NULL,0);
INSERT INTO comment VALUES (7041,1074,2703,'Mr. Spock','re: Answer(corrected)','2003-08-09 14:51:08',0,'Ok, it says the digit 7 must appear only once in the completed statements not must appear ONLY ONCE in the completed parts of the statements, the second answer provided 1;11;2;1;1;1;1;1;1;1 is therefore the correct one sheesh.',7040,0);
INSERT INTO comment VALUES (7042,567,3061,'joseph','easy','2003-08-09 14:57:33',3,'the answer is b',NULL,0);
INSERT INTO comment VALUES (7043,587,3063,'gill','Solution?','2003-08-09 17:40:57',1,'Call each son A B and C (original yeh)> Give each son 2 of the full barrels. give each son 2 of the half barrels and give each son 2 of the empty barrels. you are left with 1 full, 1 half and 1 empty barrel. Pour half of your full barrel into the empty one and then divide between A B and C, each getting half a barrel. sorry if this is wrong, just found this site while drunk..quite like it',NULL,0);
INSERT INTO comment VALUES (7044,586,1626,'Gamer','re: Solution','2003-08-09 20:01:35',1,'Simplifying that shows the actual behavior of the sequence.\r\n\r\nx, 4x, 4x+4, x+1, x-3, 4x-12, 4x-8, x-2, x-6, 4x-24, 4x-20, x-5,\r\n\r\nTaking every fourth term:\r\n\r\nx, x-3, x-6,\r\n4x, 4x-12, 4x-24,\r\n4x+4, 4x-8, 4x-20,\r\nx+1, x-2, x-5,\r\n\r\nEvery x term gets less by 3, and every 4x term gets less by 4(3) or 12.',7029,0);
INSERT INTO comment VALUES (7045,427,2951,'Jim Breaux','Smart Chap??','2003-08-10 00:55:50',0,'If the waiter is such a \"smart chap\", why does he present a bill to someone who has not eaten anything. I have another solution that might also work:\r\n\r\nI ought to owe over 1.80. (Over = O+FOUR)\r\n\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (7046,20,2130,'ethan','Solution','2003-08-10 12:54:36',3,'To solve this, it is easiest to think of part of the cube on a plane. Take faces FDAC and GEDF. Think of them as flattened on a plane. Since the shortest distance between any two points is a straight line, draw the line from A to G. Now, put them back on the cube. The line the fly should follow should go from A to a point that bisects segment FD, and then to G.',NULL,0);
INSERT INTO comment VALUES (7047,587,3070,'supriya','guessing','2003-08-10 15:09:28',0,'divide 2 full barrels among each son. suppose the remaining full barrel is given to the first son then to balance the quantity of wine give 2 half barrels to each of the other 2 sons. the remaining 3 barrels are given one to each son. the quantity of wine is the same with all of them except the no of barrels. so give 3 empty barrels to the first son and 2 each to the remaining sons. so each has the same no of barrels and wine',NULL,0);
INSERT INTO comment VALUES (7048,1101,2703,'Mr. Spock','Toughie','2003-08-10 16:24:51',0,'Hmmmmm, this doesn\'t have anything to do with Starkey Corners Maine does it?',NULL,0);
INSERT INTO comment VALUES (7049,587,1626,'Gamer','re: guessing','2003-08-10 21:41:09',0,'\"However, the wine and barrels must be split so that each son has the same number of full barrels, the same number of half-full barrels, and the same number of empty barrels.\" which means you need some pouring involved instead of just dividing them involved.',7047,0);
INSERT INTO comment VALUES (7050,128,3072,'Ryan','one thing I\'m confused about','2003-08-10 23:59:37',0,'Sorry it\'s several months later, but I just read the problem.\r\nIn this part:\r\n\"Are you sitting between two Knights?\", to which Richard smiled and gave the same reply as he had previously. \r\n\r\nDoesn\'t that imply that if he said \"yes\" to the odd-number query, then he would also say \"yes\" to this one, and vice-versa?',NULL,0);
INSERT INTO comment VALUES (7051,1010,2130,'ethan','Solution','2003-08-11 00:02:32',0,'I am saying a soul.',NULL,0);
INSERT INTO comment VALUES (7052,569,3073,'Kelly','just a guess','2003-08-11 00:13:35',0,'Send the key, in an envelope, through the mail.',NULL,0);
INSERT INTO comment VALUES (7053,1044,3074,'Adam Sisco','Quadratic','2003-08-11 02:40:29',3,'Let us call a proposed triangular number x.\r\n\r\nFrom the triangular number formula, we assume x is a triangular number:\r\n\r\nx = (n^2 + n)/2\r\n\r\nMultiply booth sides by 2:\r\n\r\n2x = n^2 + n\r\n0 = n^2 + n – 2x\r\n\r\nThis can be broken down into a quadratic equation with\r\n\r\na = 1 , b = 1 , c = -2x\r\n\r\nBy using the quadratic formula:\r\n\r\nn = (-1±(1+8x)^0.5)/2\r\n\r\nIn order to prove that x is a triangular number, it must be substituted into the above equation with a positive integer resulting for n.',NULL,0);
INSERT INTO comment VALUES (7054,1101,1575,'DJ','Tricky indeed','2003-08-11 04:15:44',0,'Umm.. I have no clue, so I\'m just going to start stating the obvious (sometimes when I do that, something helpful to the solution pops out at me).\r\n\r\nFirst, only the letters A and E are used, and every digit except six. The letters are not to the left, right, top, or bottom of either a number or a letter every time; that appears to be random, or at least not useful. They are arranged in a 7×5 grid, with the following frequencies:\r\n The expected loss therefore would be 677.6 British billion pounds.\r\n',7057,0);
INSERT INTO comment VALUES (7060,1101,3032,'gregada','re: Tricky indeed','2003-08-11 11:37:08',0,'Something I noticed:\r\n\r\nAssigning A=1 and E=5, column sums are:\r\n\r\n17 29 20 18 9 25 14\r\n\r\nThese numbers transfer back to following letters:\r\n\r\nQ C T R I Y N\r\n\r\nYou can see 5 out of 6 letters that are in the word \'Tricky\' here. What i think is going on is that the title itself is coded. Will post as soon as I can proof it.',7054,0);
INSERT INTO comment VALUES (7061,1101,3032,'gregada','Got it!!','2003-08-11 11:44:34',0,'Continuing with the logic of the previous post:\r\n\r\nNow adding rows, you get:\r\n\r\n28\r\n29\r\n30 (count 0 as 10)\r\n24\r\n33\r\n\r\nwhich transfers into \r\n\r\nc\r\nd\r\ne\r\nx\r\ng\r\n\r\nonce again you have 3 out of 4 letters needed for \'code\' and have two remaining. now let\'s see what\'s left to do:\r\n\r\nwe need to combine q and n to get k to complete tricky and we need to combine x and g to get o to complete code.\r\n\r\nq=17, n=14 q-n=3 n-3=11 11=k so we got k\r\ng=33, x=24 g-x=9 x-9=15 15=o so we got o\r\n\r\nso column sums contain word tricky and row sums contain word code.',7060,0);
INSERT INTO comment VALUES (7062,1101,1567,'Bryan','re: Got it!!','2003-08-11 11:58:22',2,'Very creative, gregada, but that ain\'t it. I think Charlie was on the right track...',7061,0);
INSERT INTO comment VALUES (7063,587,3077,'steve','the easy solution','2003-08-11 12:26:01',0,'you don\'t need to pour any of them into another, all you have to do is give 3 full barrels, 1 half full, and 3 empty barrels to 2 of the sons. The other son gets 1 full, 5 half full, and 1 empty barrel. This way all the sons get a total of 3 1/2 barrels of wine, and 7 barrels',NULL,0);
INSERT INTO comment VALUES (7064,1101,1626,'Gamer','Ideas','2003-08-11 12:27:53',0,'I don\'t see the answer here. One idea I had was converting base 16 numbers to base 10, (like across or down) but wouldn\'t that be like a really big number?\r\n\r\nIf I converted the numbers to letters, it would look like:\r\n\r\nO O G C B E A\r\nD I B D K H K\r\nD O B D C ? D\r\nD K B D K H D\r\nD I G C B D D\r\n\r\nThat clearly doesn\'t make any sense, at least to me. Another thing I noticed was that the last and first colum were 4s at the end. Also, the middle three rows are repetetive: 72227, 34443, 2A3A2 are reflected as not reflected.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (7065,1103,1626,'Gamer','code versus using it?','2003-08-11 12:33:39',0,'I am unsure if invoking the code is as important as knowing the code.\r\n\r\nAnyway, I think of knowing how to work the safe as not having to do with the code. I think by \"not having a clue what the code is\" means they know how to work the safe (as it doesn\'t say they don\'t know the clockwise/counterclockwise, but it does about the code), so I would agree with Charlie\'s answer.',NULL,0);
INSERT INTO comment VALUES (7066,1058,2899,'Brian Wainscott','re: ~50%','2003-08-11 13:31:50',3,'Good strategy, but I get over 82% this way unless I am doing something seriously wrong.\r\n\r\nI get lost in all the combinations, so I wrote a program. Here are my results:\r\n\r\nI arrange the coins in a row, and number them 1-10. Each coin is either \"+\", \"-\" or \"0\" (two each of +/-, six 0). There are 1260 distinct arrangements (10! permutations, but 4*6! of each are indistinguishable). Of these 1260 cases, I put together a matrix of weighings: weigh coin 1 against 2, then 1 against 3. There are 9 possible outcomes: (left,left), (left,even), etc,\r\nwhere \"left\" means the first of the two is heavy, \"even\" they balance, \"right\" the second of the two is heavy.\r\n\r\nOf the 1260 combinations, I get the following weight matrix (number of combinations that give each result):\r\n\r\nleft,left = 217\r\nleft,even = 133\r\nleft,right= 42\r\neven,left = 133\r\neven,even = 210\r\neven,right= 133\r\nright,left = 42\r\nright,even = 133\r\nright,right= 217\r\n\r\nIn each of the nine cases, I also counted the number of times each of the 10 coins was phony. For example, in the (left,left) weighing, 196 times out of 217 the first coin is phony. (since it is heavier both times, there are very few cases where it is real and both the second and third coins are light).\r\n\r\nSo I computed probabilities as follows:\r\n\r\nFor each of the 9 cases, always pick the coin which has the highest number of cases of being phony. Add these up over all 9 possibilities, and divide by the number of combinations. This will compute, over all combinations, the number of times I can guess a phony coin. The best coin to pick in each of the 9 cases (along with the number of times it is phony) are:\r\n\r\nleft,left = coin 1 (196/217)\r\nleft,even = coin 2 (112/133)\r\nleft,right= coin 2 or 3 (42/42)\r\neven,left = coin 3 (112/133)\r\neven,even = coin 3 or higher (120/210)\r\neven,right= coin 3 (112/133)\r\nright,left = coin 2 or 3 (42/42)\r\nright,even = coin 2 (112/133)\r\nright,right= coin 1 (196/217)\r\n\r\nIn total, I compute that a phony coin can be found 1044 times out of 1260, or 82.85%\r\n\r\nThis seems quite high to me (much better than I was able to do weighing 4 vs 4 or 3 vs 3 or 2 vs 2).\r\n\r\nIn the case of having 1 known good coin, you can weigh it against 1 then 2. 2/3 of the time one of these two will be bad, and you are sure to be right. The other third of the time, pick one of the remaining 8 and you have a 50% chance. Total chance then becomes 5/6, or 83.3%\r\n\r\nIf I did everything right, this really isn\'t much better, which is surprising.\r\n\r\nDoes this all sound right? I\'ll be happy to email my code (in C) to anyone who wants to check it out. It is a bit sloppy, but pretty short.',6991,0);
INSERT INTO comment VALUES (7067,1101,1301,'Charlie','re(2): Got it!!','2003-08-11 13:50:51',0,'If I was on the right track with the hexadecimal logic, then, to all non-programmers: A is 10 and E is 14. How this fits to the puzzle, I don\'t know.',7062,0);
INSERT INTO comment VALUES (7068,37,3032,'gregada','re(2): Proof at last (I think)','2003-08-11 14:32:34',0,'I don\'t think 15 is correct. Even forgetting about the width objection, imagine a line from one corner of the board to a diagonally opposite one. It will affect all eight squares on the diagonal and also 7 intersections, where it will affect two more squares... so the total number of venners needed would be 8+2*7=22.',297,0);
INSERT INTO comment VALUES (7069,1073,1567,'Bryan','With apologies to Mother Goose','2003-08-11 15:14:46',3,'Jack did pour from sixteen to four The first piece of glass held 4 times the last If he hits his first shot, he can try to make the second shot, which will put the game into overtime and give his team an opportunity to win, OR he can miss the shot and hope his team gets the rebound and makes a basket in the remaining 1.7 seconds of the game. Since the odds are in favor of the opposing team getting the rebound (since they are given better rebounding position by the rules of the game), the shooter will elect to try his best on the second shot as well, which he will miss 20% of the time. Odds of making one shot so far is .8*.2=16% 20% of the time the shooter will miss the first shot. In this scenario, hitting the second free throw will not help win the game – they will most likely not get the ball back in the final 1.7 seconds, and the opposing team will win by one point. The only winning strategy here is to deliberately miss the second shot, and hope his team can rebound and make a shot in the remaining 1.7 seconds to tie the game and force overtime (or kick it out for a 3-pointer, to win in regulation). Therefore the odds of missing the first free throw and then making the second one is 0%. The total odds of making only one free throw, given the player’s desire to win the game, is 16%.',7135,0);
INSERT INTO comment VALUES (7137,1110,2130,'ethan','Solution','2003-08-15 12:41:06',3,'The odds of him making one are 80%. The odds of him missing one are 20%. 20% x 80%=.2 x .8=.16=16%\r\nThe odds of him missing one are 16%.',NULL,0);
INSERT INTO comment VALUES (7138,1110,1919,'Lewis','re: Solution','2003-08-15 12:50:52',0,'Just nitpicking. The last line should read \"The odds of him missing one and scoring one are 16%\".\r\n\r\nBTW, why\'s this is games?',7137,0);
INSERT INTO comment VALUES (7139,600,2130,'ethan','Solution','2003-08-15 12:56:40',3,'He sold the box of 29 balls. Of the ones he has left, 18, 7, and 5 are red, and 14 and 16 are blue, or vice versa.',NULL,0);
INSERT INTO comment VALUES (7140,1115,1626,'Gamer','The Mechanical Revolution','2003-08-15 14:18:10',3,'I think the answer here would be half of the LCM of 35, 27, 84, and 34, or 2 * 3 * 3 * 3 * 5 * 7 * 17, or 32,130. The stripes would be on the opposite side of the gear than they were originally.',NULL,0);
INSERT INTO comment VALUES (7141,1115,1567,'Bryan','re: The Mechanical Revolution','2003-08-15 14:28:59',0,'No, this answer is way too high.',7140,0);
INSERT INTO comment VALUES (7142,1115,1301,'Charlie','re: The Mechanical Revolution','2003-08-15 14:49:10',3,'32,130 is the number of teeth that have to be advanced. Since the problem called for the number of revolutions of the 35-tooth wheel, this has to be divided by 35, giving 918.',7140,0);
INSERT INTO comment VALUES (7143,1110,1575,'DJ','re(2): Solution','2003-08-15 18:23:11',0,'The 16%, as ethan found it, is a wrong explanation, only accounting for one of the cases, making only the first short or the second shot, not both (see Brian Wainscott\'s comment). As Bryan realized, he will only try to make the second shot if he has made the first one anyway, so that answer is close to the actual answer by coincidence (there is one more very minor consideration that I made).\r\n\r\nPutting \'Games\' as the category served as a hint that this is not just a straightforward probability problem. Also, many people got the same answer by leaving some considerations out, as Bryan did by the correct method, so maybe I was playing \'games\' with their heads?',7138,0);
INSERT INTO comment VALUES (7144,1110,2899,'Brian Wainscott','re(4): Simple','2003-08-15 18:40:11',0,'I stand corrected. As DJ pointed out, I took this as a pure probability problem, and didn\'t consider all the conditions on the problem.\r\n',7136,0);
INSERT INTO comment VALUES (7145,1115,2716,'Federico Kereki','A correction','2003-08-15 22:13:09',1,'Though the answer works out to the same, it should be noted that the lines on gears C and D would be vertical even after only half a revolution, so the total number of teeth to advance would be calculated as the LCM of 35, 27, 42 and 17.',NULL,0);
INSERT INTO comment VALUES (7146,1094,2716,'Federico Kereki','re: arrrggghhhh','2003-08-15 22:16:27',1,'I doubt a woman could be fertile for 60 years...',7120,0);
INSERT INTO comment VALUES (7147,718,3116,'Sergio Martins','Possible solution','2003-08-15 23:48:22',3,'√(2^-31*e)',NULL,0);
INSERT INTO comment VALUES (7148,1110,3109,'Roger','how to win','2003-08-16 05:05:40',0,'yes the probabilty of him getting only one is 16%\r\ngetting both is 64%\r\ngetting neither is 4%\r\nbut logically he is trying to win the game so his options are \r\na) make both and get into overtime 64% chance to tie\r\nb) getting the first and intentionally missing the second in hopes of rebounding for a two point taking the win - 80% chance of getting the first shot, and then he intentionally misses therefor only getting one of the two shots. Hopefully they rebound it then and win the game.\r\nc) if he misses the first, he has to try for the second shot and still hope for a rebound. then his odds are 16% between both shots or 80% on the second shot.\r\n\r\nregardless of how he shoots, his team must get the rebound and make a shot inorder to pull off a win, unless they can manage to steal the ball from a team that will probably hold it close to their body when they rebound it. Once they do get the ball they will have nearly no time to put the ball up in the air and win.\r\n\r\nI suspect that the game is rather hopeless, but miracles have happened.\r\n\r\nAlso the shooter can miss the first and bounce the ball off the backboard to the three point line where one of his players would be ready to recieve it and shoot a 3-pointer to win the game. That would require either a hit and intentional miss 80% or two intentional misses 100% (unless you you assume that even in two intentional misses there is the 20% chance of making it which would mean that two intentional misses still have a 4% chance of making it)',NULL,0);
INSERT INTO comment VALUES (7149,1111,3122,'Gert','could it be','2003-08-16 09:35:06',1,' PASSER\r\n. PASSRE\r\n. PSASRE\r\n. SPASRE\r\n. SPASER\r\n SPARSE',NULL,0);
INSERT INTO comment VALUES (7150,1121,3122,'Gert','ummm','2003-08-16 10:32:41',1,'Benny : Knave\r\nLenny : Knave',NULL,0);
INSERT INTO comment VALUES (7151,1121,3123,'Omphie','HmMm','2003-08-16 10:48:10',0,'Benny- Knave\r\nLenny- Liar',NULL,0);
INSERT INTO comment VALUES (7152,1121,2703,'Mr. Spock','Couple of Knaves','2003-08-16 11:30:54',0,'Most apparent is that Lenny\'s statement precludes him from being a knight, which in turn precludesBenny from being a knight by his first statement, so we\'re dealing with knaves and liars only. Assume Lenny is a liar, this means since Benny\'s second statement is true, he must be a knave and therefore his first statement would have to be true. However this yields a contradiction because Benny states he is of the same type as Lenny, a liar. Thus it must be that Lenny is a knave, which means Benny\'s second statement is false, if Benny were a liar then it would be a contradiction because his first statement would be true, therefore Benny is a knave also.',NULL,0);
INSERT INTO comment VALUES (7153,1121,1626,'Gamer','re: ummm','2003-08-16 11:34:35',3,'Disregarding the comment on the bottom, there are three solutions for Benny and Lenny: Knave, Knave; Liar, Knave; and Knave, Liar. The comment at the bottom says that you will know what Benny is when you know what lenny is. If Lenny was a knave, you wouldn\'t know what Benny was. So Lenny must be a liar, and Benny must be a knave.',7150,0);
INSERT INTO comment VALUES (7154,1121,2703,'Mr. Spock','re(2): ummm','2003-08-16 11:42:25',0,'Oops, switched a false with a true in my explanation, you are correct there seem to be 3 possible solutions actually. ',7153,0);
INSERT INTO comment VALUES (7155,1111,1301,'Charlie','re: could it be','2003-08-16 11:59:26',0,'The last step, going from SPASER to SPARSE, is not a swap of two adjacent letters, but rather, a swap of one letter with an adjacent pair of letters.',7149,0);
INSERT INTO comment VALUES (7156,1121,1919,'Lewis','re(3): ummm','2003-08-16 13:03:44',0,'There are three possible combinations of what Benny and Lenny could be, as Gamer said, but from the last clue (A knight then tells me what Lenny is. From this I was able to work out what they were) there can only be one solution.',7154,0);
INSERT INTO comment VALUES (7157,775,3026,'Drew Skau','I Always Lie','2003-08-16 18:39:47',0,'I always lie, so am I lying or telling the truth?',NULL,0);
INSERT INTO comment VALUES (7158,1121,1575,'DJ','Full Solution','2003-08-16 20:06:19',3,'Benny - Knave; Lenny - Liar\r\n\r\nThe first thing I notice is that Lenny can\'t be a knight, since he calls himself a knave. Also, Benny can\'t be a knight, because then he would be claiming that both men are liars.\r\n\r\nSince Lenny made only one statement, we can\'t tell if he is a liar or knave from that alone; he could easily be either. So, we have to look at Benny\'s statements.\r\n\r\nIf Benny is a liar, his first statement must be false, so Lenny is not of the same type, and Lenny is a knave.\r\nBenny\'s second statement would also be false, leading us to the same conclusion (he\'s a knave). So, one possibility is that Benny is a liar, and Lenny is a knave (whose statement is true).\r\n\r\nIf Benny is a knave, and his first statement is true, then Lenny must be of the same type and is also a liar. Then, Benny\'s second statement is false, and Lenny is not a knave, which again agrees with itself. So another possibility is that Benny is a knave (whose first statement is true and second statement is false) and Lenny is also a knave (whose only statement is true).\r\n\r\nLastly, Benny could be a knave who is lying at first and then telling the truth. If that is the case, then his first statement implies that Lenny cannot also be a knave; he must be a liar. Similarly, Benny\'s second statement (which must be true) agrees that Lenny is a liar. If Lenny is a liar, of course, his only statement is indeed false. So, a third possibility is that Benny is a knave (whose first statement is false and second statement is true) and Lenny is a liar.\r\n\r\nIn sum, there are three possibilities from the statements alone:\r\nBenny - Liar; Lenny - Knave\r\nBenny - Knave; Lenny - Knave\r\nBenny - Knave; Lenny - Liar\r\n\r\nIf then, a knight reveals Lenny\'s type, and it is possible to work out what both are, Lenny must be a Liar (if he were a knave, there are still two possibilities) and Benny is a Knave. Incidentally, Benny\'s first statement is false and his second is true.',NULL,0);
INSERT INTO comment VALUES (7159,1121,3127,'lesa','solution','2003-08-16 21:46:08',0,'they are both knaves',NULL,0);
INSERT INTO comment VALUES (7160,1038,3127,'lesa','solution','2003-08-16 21:53:41',0,'he comes out even. he has spent $40, but the bike is worth $40.',NULL,0);
INSERT INTO comment VALUES (7161,567,3127,'lesa','solution','2003-08-16 22:24:00',0,'r wins. if p won, statements 1 & 3 are both correct. if q won, statements 2 & 3 are both correct. if s won, statements 1 & 2 are both correct.',NULL,0);
INSERT INTO comment VALUES (7162,1008,3127,'lesa','solution','2003-08-16 22:27:57',0,'soda, because her name begins with a letter from the first half of the alphabet',NULL,0);
INSERT INTO comment VALUES (7163,916,3127,'lesa','solution','2003-08-16 22:50:12',0,'cube #1 = A B C H U T\r\ncube #2 = O P R S V Z\r\ncube #3 = F G I M N W\r\ncube #4 = D E K L Q Y',NULL,0);
INSERT INTO comment VALUES (7164,1038,3129,'Maura','Solution','2003-08-16 22:51:39',3,'Neither. He ended up spending $40 but it was worth $40. So he got his moneys worth.',NULL,0);
INSERT INTO comment VALUES (7165,600,3127,'lesa','SOLUTION','2003-08-16 22:57:32',0,'THE BOX WITH 29 BALLS',NULL,0);
INSERT INTO comment VALUES (7166,1094,3129,'Maura','Solution','2003-08-16 22:59:42',3,'The twins are 9 years old and the other brother is 7.',NULL,0);
INSERT INTO comment VALUES (7167,775,1626,'Gamer','re: I Always Lie','2003-08-16 23:13:09',0,'Lying... you just don\'t always lie; you lie some of the time.',7157,0);
INSERT INTO comment VALUES (7168,1112,1301,'Charlie','solution','2003-08-17 11:16:21',3,'From CHAD and GOAD we know that C and H share the same two cubes as G and O. From HOAR we see the O and the H must be on different cubes, so H and G share a cube as do C and O.\r\n\r\nFrom CHAD and HOAR, we know C and D share 2 cubes with O and R. Since we know that C shares with O, it follows that D shares with R.\r\n\r\nFrom GOAD and GROW, we see A,D share with R,W, and since D shares with R, A shares with W.\r\n\r\nFrom JUMP and MUCK, we see J,P share with C (along with its O) and K. OPTS tells us that O (and its accompanying C) can\'t share with P, so P shares with K and J shares with C and O.\r\n\r\nThen, using the word OPTS to give starting identities to the four cubes we have:\r\nJCO\r\nPK\r\nT\r\nS\r\n\r\nUsing the words to indicate which letters can\'t appear with which others, we can produce a grid, and using the letters that we just found must go with each other to copy information from one row and column to another to fill in blanks, we get a grid like:\r\n or Now, consider a point equidistant from the two red points. Either it is also red, meeting our condition, or it is blue. If it is blue, we can consider the other point X that is equidistant from the two red points: If the male sailor told the truth, both the male soldier and the female sailor would be liars, but this cannot be, so the male sailor is a liar. \r\n The male soldier says that the male sailor is a truth teller, so he also lies; both males lie, and thus both females tell the truth.\r\n Since the male sailor lies, the male soldier isn\'t Lee, so he is Loren, and the male sailor is thus Lee.\r\n Since the female soldier is truthful, the female sailor isn\'t Terry; she is Tracy and the female soldier is thus Terry.\r\n A sailor is in Hawaii; since Tracy is in Afghanistan, Lee is in Hawaii. As Loren isn\'t in Texas, he must be in Kuwait, and Lee is in Texas.\r\n',NULL,0);
INSERT INTO comment VALUES (7588,567,2716,'Federico Kereki','Short solution','2003-09-01 21:04:52',3,'If P won, A and C would have been right.\r\nIf Q won, B and C would have been right.\r\nIf S won, A and B would have been right.\r\n\r\nSo, R won, and B was correct.',NULL,0);
INSERT INTO comment VALUES (7589,1200,1575,'DJ','Ig2e (I give)','2003-09-02 00:25:15',1,' I agree with fwaff\'s math on this, which showed that the player has a slight mathematical advantage over the house, winning an average of $0.0309 per game over the long haul. Statistically speaking, however, winning and losing comes in streaks, and for the player to win overall, she needs to bring a big enough bankroll to outlast a losing streak of potentially infinite length. Generally, players don\'t bring a big enough bankroll to do this, or in any case their bankroll is substantially smaller than the house\'s, so it is the house that has the advantage. Sure, some players will make some dough, but most will leave a losing streak when their bankroll (or nerves) runs out, and the house should still turn a profit.',7971,0);
INSERT INTO comment VALUES (7975,1232,3372,'Sam','re(2): Solution','2003-09-18 11:42:21',0,'Huh? I\'m not sure what you mean by \"Statistically speaking, winning and losing comes in streaks.\" The first rule of statistics is that each trial is completely independent from what came before. Now, since the advantage over the house in this case isn\'t huge, you are right that for any one person coming to the stall with just a few bucks, they may well lose, but the chance of them winning is greater. Put it another way: Over the course of the day the house will have lost money. Therefore on average the players must have won money, even if each one only came with a couple of bucks.',7974,0);
INSERT INTO comment VALUES (7976,1160,3372,'Sam','re(2): Just a thought','2003-09-18 11:43:35',0,'Oh sheesh, I miss-read the puzzle. I thought it seemed strange! Thanks.',7966,0);
INSERT INTO comment VALUES (7977,1341,3172,'SilverKnight','re: finally','2003-09-18 12:09:49',0,'Cory,\r\n\r\nIf you\'re happy with my response... Great! But your message indicates an underlying dissatisfaction with the resolution.\r\n________________\r\n\r\n\"...the math is irrelevant here.\"\r\nNo. It is relevant. Which is why if one misapplies concepts (as you have done), one might be led to erroneous results.\r\n_________________\r\n\r\n\"...it is the interpretation of the problem itself from where the paradox is derived...\"\r\nActually, there is no paradox, in the mathematical sense (even if Levik chose to place the problem in that category). There is a paradox if one doesn\'t understand what the problem is really asking, generally due to a lack of understanding of the concepts with which the problem deals (infinities).\r\n_______________\r\n\r\n\"I have chosen... to ignore different constraints.\"\r\nYou have chosen to ignore constraints, but not conststraints imposed by the problem. You have chosen to ignore constraints imposed by the logic describing infinities. I have not ignored any constraints.\r\n______________\r\n\r\n\"I don\'t agree that I can\'t create an infinite sum by infinitly adding a constant term. This is a basic tenet of calculus\"\r\nNo. Calculus (well Riemann Sums anyway) does not add an infinite number of items. It deals with the limit of a summation as a variable approaches infinity (or zero depending on which variable you are looking at). This is an important distinction. (By, the way, ∑9 as n goes from 1 to infinity approaches infinity, no argument here.... it just doesn\'t apply to the problem at hand.)\r\n_______________\r\n\r\n\"...this aleph null is defined as the smallest infinity - what heppens[sic] to this if you take away one?\"\r\nYou question results from a misunderstanding of infinity. Aleph Null is not an integer. It describes a set ONTO which and FROM which I can provide a mapping from/to other sets. It is equivalent to the set of integers, or the set of positive even integers, or the set of prime numbers. There is no infinite set for which I cannot provide a mapping onto Aleph Null (for if there were, it would be an infinite set smaller than Aleph Null). And I am not going to include a proof here.\r\nAleph One, which is equivalent to the set containing the real numbers is larger and while there exists a mapping of the Aleph One set (e.g., real numbers) ONTO an Aleph Null set (the integers), there does not exist the reverse. Therefore Aleph One is larger than Aleph Null.\r\n______________________\r\n\r\nI encourage you to take the initiative and learn more about the subject.\r\n\r\n --- SK',7972,0);
INSERT INTO comment VALUES (7978,1160,1220,'abc','re(3): Solution','2003-09-18 13:00:21',0,'Yeah, I\'m sure you are right. That\'s good cause in this case I would have solved it as well! ;) \r\n\r\nRegarding the slab:\r\nI thought that it\'s all one slab on the sidewalk in a straight line. It simply means he doesn\'t walk zig-zag. ',7956,0);
INSERT INTO comment VALUES (7979,1231,3196,'Dan','WRONG, Gamer !!!!!!!!','2003-09-18 13:12:50',0,'Gamer, here are your words: \"\"There once was a horse who had great fame. What do you think was the horse\'s name.\" I am surprised that someone as clever as you could be so obtuse !!!!! \"What do you think\" could not possibly be the horse\'s name, because no horse by that name ever \"had great fame\" !!!! I checked on the Internet, and the only horse by that name is the one in this flooble thread. I assure you most solemnly that it takes a heckuva lot more than being mentioned on the flooble website, to constitute \"great fame.\" Also, the fact that there is no question mark after \"What do you think was the horses name\" is a total red herring. It is quite common in English and other languages to have questions without question marks. There is not a single question mark in the entire Bible !! (The Bible was written before the question mark was invented). \"Why anyone would go out in this weather is beyond me....\" is clearly a question, although there is no question mark. No, here is the REAL ANSWER: Mr. ED the Talking Horse....because the question was not \"What WAS the horse\'s name\"; the question was \"What do you THINK was the horse\'s name.\" Since I THINK that Mr. Ed is the horse\'s name, then Mr. Ed is the correct answer. QED \n\nEdited on September 18, 2003, 2:05 pm',NULL,0);
INSERT INTO comment VALUES (7980,1232,1220,'abc','rough solution','2003-09-18 13:15:49',0,'I\'m not very good at probability myself. I didn\'t make any more calculations than fwaff.\r\n\r\nfwaff is right, that the chance to succeed is about 34% (0.3439). \r\nThis means that I win every third game, statistically speaking.\r\nLosing two games costs 2$. I pay for the third game and lose another 1$. I should win this one and get 3$ in return.\r\nAfter all there\'s no gain and no loss. You spend 3$ on average and win them back in the third game resulting in a balance.\r\n\r\nAssuming that probability is cheating me I would probably lose money on the long run. 8) ',NULL,0);
INSERT INTO comment VALUES (7981,1332,3430,'pat','words in common','2003-09-18 13:25:37',0,'more like this...less aha (aha is a palidrome)',NULL,0);
INSERT INTO comment VALUES (7982,1205,2899,'Brian Wainscott','re: Got it - but you gotta be fast!!!','2003-09-18 13:42:17',0,'Norfolk:\r\n\r\nHow close are you going to get? Since 25 minutes = 5/12 of an hour, and 5/12 has an infinite, non-repeating decimal expansion base 2 (decimal? Anybody know the proper term for this?), I don\'t think you are ever going to get EXACTLY 25 minutes.',7973,0);
INSERT INTO comment VALUES (7983,1205,2899,'Brian Wainscott','re: Closer and closer','2003-09-18 13:44:30',0,'Great! I like it -- much cleaner than the mess I was working with. But can anyone figure out how to do something like this and keep it to a finite amount of time? The problem seems to be that the small bits of the hour are always at the tail end of an hour\'s worth of clock doubling....',7929,0);
INSERT INTO comment VALUES (7984,1205,1920,'Brian Smith','re(2): Closer and closer','2003-09-18 14:31:49',0,'Well, if it is possible to measure 25 min in a finite time, I would expect there to be an infinite number of timers used and an infinite number of steps.',7983,0);
INSERT INTO comment VALUES (7985,1231,1920,'Brian Smith','re: WRONG, Gamer !!!!!!!!','2003-09-18 15:08:21',0,'I think you\'re taking this problem TOO seriously.',7979,0);
INSERT INTO comment VALUES (7986,1232,1301,'Charlie','re(3): Solution','2003-09-18 15:13:23',0,'The figures previously given in this comment were erroneous, based on a programming error.\r\n\r\n\n\nEdited on September 18, 2003, 4:51 pm',7975,0);
INSERT INTO comment VALUES (7996,1232,1301,'Charlie','re(5): Solution','2003-09-18 16:52:51',0,'You\'re right of course; I just noticed that myself. I retracted the comment, and am working on a new one.',7995,0);
INSERT INTO comment VALUES (7997,1232,1301,'Charlie','Corrected Simulation Results','2003-09-18 17:25:04',0,'Backing up Bryan\'s comments on needing to be able to ride out losing streaks, a simulation shows that, for example, if the player starts with a bankroll of $10 and a goal of playing until that has grown to $100, in 100,000 simulations of this situation, the player got to the $100 only 28% of the time, having lost the whole $10 72% of the time. It took an average of about 1400 plays to win when she did so, and 243 plays to lose when that happened.\r\n\r\nWhen greedier, and going for $1000, she still lost about the same percentage of the time, but took on average about 343 plays to lose, and about 30,000 plays to win.\r\n\r\nAnd when starting out with a measly $1, trying to leave with $100, she won not much more than 3% of the time (but of course gaining $100) and took an average of about 24 plays for a loss or 1400 plays for a win.\r\n\r\nSo, yes, losing streaks are statistically \"inevitable\" (or rather, merely likely), and the house has the \"advantage\" of a bigger bankroll against an individual, though with these odds not against the public at large.\r\n\r\nThe results (first line in each pair showing initial bankroll and goal; second line showing the number of trials, number of wins, number of losses, average number of plays for a win, and average number of plays for a loss) of several trials are:\r\n\r\n My calculator tells me that last year was the first year after 1961 to read the same rightside up and upside down, and that the next year in which this will happen is 2112.',NULL,0);
INSERT INTO comment VALUES (8129,624,3430,'pat','bad addition','2003-09-23 12:59:59',0,'mid 20th century ok i\'ll take 1961(even though 1950 is accurate) but add 4000 years to either doesn\'t add up and is too misleading. logic is good but ad hoc logic is dangerous. :)',NULL,0);
INSERT INTO comment VALUES (8130,1163,1920,'Brian Smith','Self Printing Program in BASIC','2003-09-23 13:36:54',0,'105 A$=CHR$(32)+CHR$(68)+CHR$(65)+CHR$(84)+CHR$(65)+CHR$(32)+CHR$(34)\r\n110 B$=CHR$(32)\r\n115 C$=CHR$(34)\r\n120 FOR I=100 TO 200 STEP 100\r\n125 FOR J=5 TO 75 STEP 5\r\n130 READ D$\r\n135 L$=MID$(STR$(I+J),2)\r\n140 IF I=100 THEN 155\r\n145 PRINT L$+A$+D$+C$\r\n150 GOTO 160\r\n155 PRINT L$+B$+D$\r\n160 NEXT J\r\n165 RESTORE\r\n170 NEXT I\r\n175 END\r\n205 DATA \"A$=CHR$(32)+CHR$(68)+CHR$(65)+CHR$(84)+CHR$(65)+CHR$(32)+CHR$(34)\"\r\n210 DATA \"B$=CHR$(32)\"\r\n215 DATA \"C$=CHR$(34)\"\r\n220 DATA \"FOR I=100 TO 200 STEP 100\"\r\n225 DATA \"FOR J=5 TO 75 STEP 5\"\r\n230 DATA \"READ D$\"\r\n235 DATA \"L$=MID$(STR$(I+J),2)\"\r\n240 DATA \"IF I=100 THEN 155\"\r\n245 DATA \"PRINT L$+A$+D$+C$\"\r\n250 DATA \"GOTO 160\"\r\n255 DATA \"PRINT L$+B$+D$\"\r\n260 DATA \"NEXT J\"\r\n265 DATA \"RESTORE\"\r\n270 DATA \"NEXT I\"\r\n275 DATA \"END\"',NULL,0);
INSERT INTO comment VALUES (8131,1163,1920,'Brian Smith','re: Self Printing Program in BASIC','2003-09-23 13:38:07',0,'This is my own program.\r\n\r\nUnfortuneatly the comment posting split up lines 105 and 205.\n\nEdited on September 23, 2003, 1:38 pm',8130,0);
INSERT INTO comment VALUES (8132,1166,3172,'SilverKnight','Solution - I think','2003-09-23 14:05:27',3,'Hmmm... I\'m not sure I am clear on what DJ is asking, but I think I understand it.\r\n\r\nIf so, we find that\r\n\r\nWhere:\r\nx is the long side,\r\ny is the short side, and\r\ntheta is the interior angle between the long side and the diagonal.\r\n\r\nx * tan(theta) = y, and\r\nx * sin (90-theta) = y\r\n\r\nsubtract one equation from the other:\r\nx * ( tan(theta) - sin(90-theta) ) = 0\r\n\r\ndivide by x, and we see that this is independent of the lengths of x and y (as it should be):\r\ntan(theta) - sin (90-theta) = 0\r\n\r\nsolving numerically, we find theta equals\r\n0.666243 radians\r\n\r\nThis means that since y/x = tan (theta) = .786157,\r\ny/x = .786157\r\nand x/y = 1.27201',NULL,0);
INSERT INTO comment VALUES (8133,1163,3172,'SilverKnight','re: Self Printing Program in BASIC','2003-09-23 14:10:25',0,'WOW!!!! DATA/READ/RESTORE.... it\'s been SOOOO long since I\'ve seen this stuff.... brings back memories of coding 20 years ago... how old are you!?! :-) And are you still using this?\r\n\r\n --- SK',8130,0);
INSERT INTO comment VALUES (8134,1163,1920,'Brian Smith','re(2): Self Printing Program in BASIC','2003-09-23 14:27:23',0,'Since you asked, I am 23. BASIC is the first programming language I learned. I still use a version of BASIC called UBASIC for high precision arithmetic (built in 2000 digit capabilities!).',8133,0);
INSERT INTO comment VALUES (8135,1166,1920,'Brian Smith','','2003-09-23 15:13:33',3,'Let the rectangle\'s corners be A, B, C, and D. Assume the fold unites corners A and C. The fold creates a line EF. Let E be on AB and F be on CD. From the folding, AF and FC are congruent. Let the center of the rectangle be G. AC is perpendictular to EF and the lines intersect at G. G also bisects AC and EF.\r\n\r\nSince AD is the shorter side, let AD=1 and AB=x (and EF=x). Let DF=a. Then FC=x-a (and AF=x-a), FG=x/2, and AG=(sqrt(1+x^2))/2. \r\n\r\nADF is a right triangle, then AD^2+DF^2=AF^2: 1 + a^2 = (x-a)^2. AFG is also a right triangle, then AF^2=FG^2+AG^2: (x-a)^2 = (1+x^2)/4 + x^2/4\r\n\r\nSolving the pair of equations yeilds x=1.27202, hence the ratio of the sides is 1.27202',NULL,0);
INSERT INTO comment VALUES (8136,1166,1920,'Brian Smith','\'No Comment\' should be \'Solution\'','2003-09-23 15:14:54',0,'\'No Comment\' should be \'Solution\'',8135,0);
INSERT INTO comment VALUES (8137,624,1626,'Gamer','re: bad addition','2003-09-23 16:26:03',0,'Of course I never write those wierd things that the font shows. It would look so wierd. In addition, I never write 5s or 2s the way that the calculator shows them, I write them as 5 and 2.\r\n\r\nFurthermore, I would assume a 1 upside down would still look like a 1, but I think the problem should be rephrased to say around 4000 years',8129,0);
INSERT INTO comment VALUES (8138,1164,3593,'b','hard','2003-09-23 16:51:32',0,'this is hard',NULL,0);
INSERT INTO comment VALUES (8139,1164,3593,'b','o=0','2003-09-23 16:52:03',0,'o=0\r\n',NULL,0);
INSERT INTO comment VALUES (8140,1164,3593,'b','Help!','2003-09-23 16:52:29',0,'Help!!!!',NULL,0);
INSERT INTO comment VALUES (8141,1279,3593,'b','Solution','2003-09-23 16:55:34',0,'tEn, nIne, sEven, sIx, fIve, fOur, tHree, tWo\r\n\r\nanswer = N\r\n oNe',NULL,0);
INSERT INTO comment VALUES (8142,1279,3594,'Bry','solution','2003-09-23 19:15:04',3,'It is the second letter of each word counting down from ten\r\n\r\ntEn, nIne, eIght etc.\r\n\r\ntherefore the answer is N',NULL,0);
INSERT INTO comment VALUES (8143,1032,3594,'Bry','Solution','2003-09-23 19:17:42',3,'it is the first and last letter of the chess pieces in order from weakest to strongest\r\n\r\nPawN, BishoP, KnighT etc.\r\n\r\nQN, KG',NULL,0);
INSERT INTO comment VALUES (8144,983,3594,'Bry','Solution','2003-09-23 19:19:38',3,'first letter:\r\n\r\nWhat\'s The Next Letter In This Sequence\r\n\r\n? = S',NULL,0);
INSERT INTO comment VALUES (8145,1332,2707,'Gordon Steel','At Least One Characteristic in Common','2003-09-23 19:50:39',0,'The seven words selected have at least one attribute in common. None of these words is an anagram for another English word. That is, one can not take the letters from any of these words and using the same letters but in different sequence construct a viable English word. Gordon S.',NULL,0);
INSERT INTO comment VALUES (8146,1025,3594,'Bry','solution','2003-09-23 20:27:18',3,' The whole sequence is 9, 81, 65, 61, 37, 58, 89, 145, 42, 20, 4, ...\r\n\r\nThe sequence is found by taking the square of each digit, and adding them together. 4 squared is 16, 1 squared is 1, 6 squared is 36, added together they are 37.\r\n\r\nSo, the number the sequence starts out with is 9.\r\n\r\nThe next single digit number in the sequence is the eleventh term, which is 4.\r\n',NULL,0);
INSERT INTO comment VALUES (8147,1210,3594,'Bry','Solution??','2003-09-23 20:40:28',4,'Warritire\r\nIt just seems like the right answer\r\n\r\nwar = second line third word\r\nit = first line third word',NULL,0);
INSERT INTO comment VALUES (8148,1266,3594,'Bry','guess','2003-09-23 20:49:03',1,'60, 65, 80, 90',NULL,0);
INSERT INTO comment VALUES (8149,1164,3594,'Bry','HINT! HINT! HINT!','2003-09-23 20:52:37',2,'It is not based on a base ten system.\r\n\r\n?????????? base 5 ?????????????',NULL,0);
INSERT INTO comment VALUES (8150,1164,3594,'Bry','Hint','2003-09-23 20:53:39',2,'k = 1, 2, 3\r\nt = 3, 6, 9',NULL,0);
INSERT INTO comment VALUES (8151,1266,1301,'Charlie','solution','2003-09-23 20:55:22',3,'If w is the first integer and a is the difference, then the first three terms are \r\nw, w+a, w+2a.\r\n\r\nIn order for the last three terms to be in geometric sequence, the ratio of the last (4th) term to the 3rd must be the same as that of the 3rd to the 2nd:\r\n\r\n(w+2a)/(w+a)\r\n\r\nso the last term must be\r\n\r\n(w+2a)^2/(w+a)\r\n\r\nso that the difference between the last term and the first will be\r\n\r\n(w+2a)^2/(w+a) - w\r\n\r\nwhich must be set to 30. After that is done we can multiply both sides by (w+a), giving\r\n\r\n(w+2a)^2 - w^2 - wa = 30 (w+a)\r\nw^2+4wa+4a^2-w^2-wa = 30w + 30a\r\nw(3a-30) = -4a^2 + 30a\r\nw = (4a^2 - 30a)/(30-3a)\r\n\r\nThe only positive integral value for a which gives a positive integral value for w is 9, which gives w=18, so the sequence is\r\n\r\n18, 27, 36, 48',NULL,0);
INSERT INTO comment VALUES (8152,1266,1301,'Charlie','re: guess','2003-09-23 20:58:51',0,'For the first three terms to be in arithmetic sequence would require the difference between the first two terms to be the same as the difference between the second and third terms, which is not the case here.\r\n\r\nFor the last three terms to be in geometric sequence the ratio of the last term to the next to last would have to be the same as that between the next to last and the one before it, which is also not the case in 60, 65, 80, 90.',8148,0);
INSERT INTO comment VALUES (8153,1160,3594,'Bry','??solution??','2003-09-23 21:06:44',0,'95 inche slabs',NULL,0);
INSERT INTO comment VALUES (8154,544,3594,'Bry','Solution','2003-09-23 21:08:23',3,'match',NULL,0);
INSERT INTO comment VALUES (8155,1231,3595,'elton','the solution to this problem','2003-09-23 21:08:59',0,'The name of the horse is a little strange and long. So the name of the horse is [WHAT DO YOU THINK]. I know its simple but dont feel ashaimed now because after all it was a trick problem.',NULL,0);
INSERT INTO comment VALUES (8156,824,3594,'Bry','Solution','2003-09-23 21:09:42',3,'He stood on a block of ice',NULL,0);
INSERT INTO comment VALUES (8157,840,3594,'Bry','Solution','2003-09-23 21:11:38',3,'A Ton',NULL,0);
INSERT INTO comment VALUES (8158,1163,3594,'Bry','Java','2003-09-23 21:16:06',0,'Public class print{\r\n public static void main(String[] args) {\r\n system.out.println (DIRECTORY/print.class);\r\n }\r\n}',NULL,0);
INSERT INTO comment VALUES (8159,1231,3594,'Bry','ANSWER','2003-09-23 21:18:26',3,'SeaBiscuit',NULL,0);
INSERT INTO comment VALUES (8160,624,3594,'Bry','re: solution','2003-09-23 21:21:52',0,'6009-1961=4048',8126,0);
INSERT INTO comment VALUES (8161,1107,3595,'elton','My nic name is TheSolutionMan','2003-09-23 21:22:26',0,'It will take 80 days if 20 cows graze on it.\r\n',NULL,0);
INSERT INTO comment VALUES (8162,1164,1626,'Gamer','OK','2003-09-23 22:09:29',0,'That\'s all great and such, but I think all the Ts are supposed to equal the same amount. :)\r\n\r\nIt\'s not based on base 5 or 10, as you will see in the numerous full solutions below ;)',NULL,0);
INSERT INTO comment VALUES (8163,624,1220,'abc','re(2): solution','2003-09-24 07:15:12',0,'That\'s correct. 8)',8160,0);
INSERT INTO comment VALUES (8164,1163,1920,'Brian Smith','re: Java','2003-09-24 09:14:46',0,'Your algorithm has a problem. The \"print.class\" file is a bytecode file. It does not contain the source code.',8158,0);
INSERT INTO comment VALUES (8165,625,3275,'retiarius','Solution','2003-09-24 09:52:27',0,'The line joining the centre of one of the large spheres with the small sphere forms a hypotenuse of length R + r with the other two sides of length R and R - r. Therefore:\r\n\r\nR^2 + (R - r)^2 = (R + r)^2\r\n2R^2 + r^2 - 2Rr = R^2 + r^2 + 2Rr\r\nR^2 = 4Rr\r\nr = R/4 = 25\r\ndiameter = 50\r\n',NULL,0);
INSERT INTO comment VALUES (8166,625,1301,'Charlie','solution','2003-09-24 09:55:32',3,'Consider the vertical plane containing the centers of the two spheres, and the center of the small sphere, at its tightest point in the passage.\r\n\r\nThe spheres will have circular cross sections. Construct a square with a corner at the center of one of the larger spheres and another where the two larger spheres touch. It will also have corners on the floor, where the smaller circle touches it, and also directly under the center chosen for the first corner.\r\n\r\nThis square then includes 1/4 of one of the larger circles and 1/2 of the smaller circle.\r\n\r\nDraw a line from the corner that\'s at the center of a large circle, to the center of the smaller circle. This is on an edge of the square. The top edge of the square is 100 cm., and the center of the smaller circle is r cm above the floor, where r is the radius of the smaller circle. This leaves 100-r as the portion of the side of the square that also forms part of a newly formed right triangle whose hypotenuse we just drew.\r\n\r\nThe length of this hypotenuse is just the total of the two radii, 100+r. Using the Pythagorean Theorem, 100^2+(100-r)^2 = (100+r)^2. Then\r\n\r\n2(100^2) - 200r + r^2 = 100^2 + 200r + r^2\r\n\r\n400r = 100^2\r\n\r\nr = 25\r\n\r\nso the diameter is 50 cm.',NULL,0);
INSERT INTO comment VALUES (8167,1166,3546,'RoyCook','Solution','2003-09-24 10:43:15',3,'Let a be the short side and b the longer. Then the triangle formed by a, b and the diagonal is similar to that formed by b, half the diagonal, and half the crease. So we have:\r\n\r\na/b = (1/2b)/(√(a^2 + b^2))\r\n\r\nwhich gives a = b * √((√5 - 1)/2)\r\n\r\nor\r\n\r\nb = a * √(2/(√5 - 1))',NULL,0);
INSERT INTO comment VALUES (8168,1163,3594,'Bry','re(2): Java','2003-09-24 10:46:39',0,'public class print {\r\n public static void main(string[] args) {\r\n system.out.println(DIRECTORY/print.java);\r\n }\r\n}\r\n\r\nyou were right, I messed up',8164,0);
INSERT INTO comment VALUES (8169,1163,3594,'Bry','Real solution(JAVA)','2003-09-24 10:47:14',3,'public class print {\r\n public static void main(string[] args) {\r\n system.out.println(DIRECTORY/print.java);\r\n }\r\n}',NULL,0);
INSERT INTO comment VALUES (8170,1163,1920,'Brian Smith','re: Real solution(JAVA) - another problem','2003-09-24 11:31:08',0,'You have a new problem. It is possible to make a .class file and run it without the .java file being present. Your algorithm is now dependant on an external file.',8169,0);
INSERT INTO comment VALUES (8171,622,3430,'pat','dj is too smart','2003-09-24 13:18:25',0,'dj,,,, you\'re too smart.... ',NULL,0);
INSERT INTO comment VALUES (8172,611,3602,'Andrew','Deduction','2003-09-24 13:48:39',0,'Two gentlemen have their own coat. That leaves two coats to distribute among the other two men. Since each man has one and only one item of his own, C and D cannot each have their own coat--they have received another item of their own (hat and gloves, respectively). Hence, C has D\'s coat and D has C\'s coat.\r\n\r\nEach man must have one item each from the other four gentlemen. We have already assigned a couple items to C and D. C cannot have his own cane, nor D\'s cane; likewise, D cannot have either C or D\'s cane. C and D together have the canes belonging to A and B. Therefore, A and B together must have the canes belonging to C and D. Since A does not have C\'s cane (as stated in the problem description), A must have D\'s cane; B has C\'s cane.\r\n\r\nNow that we have assigned a couple items to A and B, we can try to figure out whose hats and gloves they have. A has one of his own items, plus one of D\'s. Meanwhile, C\'s hat has already been placed. Therefore, A must have B\'s hat. Now with one item from A, B, and D, we know that A must have C\'s gloves.\r\n\r\nLikewise, we have already figured out a couple of the items that B walked out of the restaurant with. He has one of his own items (coat) plus one from C (cane); the other two items must come from A and D. D\'s gloves have been assigned already; B must have A\'s gloves, and his final item (hat) comes from D.\r\n\r\nWe have now placed three of the hats: C has his own, while A has B\'s hat and B has D\'s hat. The last hat (A\'s) goes to D. Likewise, we have placed three of the gloves. C must have the remaining pair of gloves from B.\r\n\r\nThe last two items are A\'s and B\'s canes. Each gentleman has one item from each of the others; we\'ve already placed C with items from B, C, and D. C must have A\'s cane. Finally, D must have B\'s cane.\r\n\r\nA: A\'s coat, B\'s hat, C\'s gloves, D\'s cane\r\nB: B D A C\r\nC: D C B A\r\nD: C A D B\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (8173,1367,3546,'RoyCook','An Idea','2003-09-24 13:49:20',0,'I have what I think is a start on the right track, but I got stuck and thought I would just share it:\r\n\r\nFact 1: Basically, we can use the strip of paper to give us a unit measure (just fold it in half and the fold will give you a segment of length one). \r\n\r\nFact 2: Once we have the fold in the paper, this allows us to construct right angles, since the fold will be at a right angle to the two parallel sides of the strip.\r\n\r\nFact 3: Once we have a unit length, we can also constuct lenghths 1/2, 1/4, etc. of a unit by folding the paper repeatedly in the other direction (in principle as many times as we want, in practice only about 7 times, but either way it is okay, since the construction below only requires us to fold it twice).\r\n\r\nFirst, construct a right triangle with base 1 and height 1/2. The hypotenuse will then be √5/4. Now, mark off 1/4 unit on the hypotenuse, giving us a segment of length (√5 -1)/4. Now, Draw a line perpendicular to the segment of length (√5 - 1)/4 passing through one of the endpoints. Now use the strip of paper to construct a right triangle with the line of length (√5 - 1)/4 as base and unit length as hypotenuse. This triangle will have angles of 72 and 18 degrees.\r\n\r\nSince a pentagon has five interior angles of 108 (180-72) degrees, I cannot help but feel like I am on the right track here, but I could not get it any farther. The problem is that I cannot find a way to modify the construction above so that I can construct 72 (or 108) degree angles at an arbitrary point.\r\n\r\nAny ideas?',NULL,0);
INSERT INTO comment VALUES (8174,1163,1920,'Brian Smith','Self Printing Program in Java','2003-09-24 14:19:11',0,'This is the same idea as my BASIC program. Half of the program is data echoing the other half.\r\n\r\npublic class selfprint { public static void main(string[] args) {\r\nString[] data = new String[13];\r\nchar quote=34, endline=\';\';\r\nString front = Character.toString(\'d\')+\'a\'+\'t\'+\'a\'+\'[\';\r\nString middle = Character.toString(\']\')+\'=\'+quote;\r\nString back = Character.toString(quote)+endline;\r\ndata[0]=\"public class selfprint { public static void main(string[] args) {\";\r\ndata[1]=\"String[] data = new String[13];\";\r\ndata[2]=\"char quote=34, endline=\';\';\";\r\ndata[3]=\"String front = Character.toString(\'d\')+\'a\'+\'t\'+\'a\'+\'[\';\";\r\ndata[4]=\"String middle = Character.toString(\']\')+\'=\'+quote;\";\r\ndata[5]=\"String back = Character.toString(quote)+endline;\";\r\ndata[6]=\"for (int i = 0; i<26; i++) {\\\";\r\ndata[7]=\\\"if (i<7) {\\\";\r\ndata[8]=\\\"System.out.println(data[i]);\\\";\r\ndata[9]=\\\"} else if (i>20) {\";\r\ndata[10]=\"System.out.println(data[i-14]);\";\r\ndata[11]=\"} else {\";\r\ndata[12]=\"System.out.println(front+(i-7)+middle+data[i-7]+back);\";\r\ndata[13]=\"} } } }\";\r\nfor (int i = 0; i<28; i++) {\r\nif (i<7) {\r\nSystem.out.println(data[i]);\r\n} else if (i>20) {\r\nSystem.out.println(data[i-14]);\r\n} else {\r\nSystem.out.println(front+(i-7)+middle+data[i-7]+back);\r\n} } } }',NULL,0);
INSERT INTO comment VALUES (8175,1354,1920,'Brian Smith','Initial thoughts','2003-09-24 14:20:57',0,'File I/O looks necessary. This most likely would benefit from recursion.',NULL,0);
INSERT INTO comment VALUES (8176,1354,3172,'SilverKnight','solution','2003-09-24 14:52:49',3,'(I will appreciate if Levik will ensure that the PRE-codes are being used here.) \r\n\r\nHere\'s some C++/Pseudo code that I think is easy to follow... feel free to ask questions.\r\n\r\nI\'ll take for granted that we have the trivial function and class:\r\n\r\nFindAdjacentWords(GivenWord) bolt, bond, card, gnus, idle, peal, rain, salt, spit \"goniums\" does not appear in any dictionary I own (although \"gonio-\" is a prefix meaning \"angle\"). Not really a complaint, since it was looking at the possibilities of this word that helped me solve the puzzle.',NULL,0);
INSERT INTO comment VALUES (8299,1171,3430,'pat','odd problem','2003-10-01 13:09:40',0,'all words should be real... and this is real odd',NULL,0);
INSERT INTO comment VALUES (8300,1171,1575,'DJ','re: Not only do they all have 7 letters, but...','2003-10-01 13:14:49',0,'Yeah, I found these words by using the word search at wordles.com (here), which usually has a pretty conservative, acceptable listing of common English words, so I didn\'t question the results.\r\n\r\nNow that you mention it, I couldn\'t find the definition directly either, but a gonium is another word for a single reproductive cell, like a gamete.',8298,0);
INSERT INTO comment VALUES (8301,1171,1301,'Charlie','re(2): Not only do they all have 7 letters, but...','2003-10-01 14:30:33',0,'Yes, my dictionary lists the plural of gonium as gonia, like millennia.',8300,0);
INSERT INTO comment VALUES (8302,1171,1920,'Brian Smith','re(2): Not only do they all have 7 letters, but...','2003-10-01 14:37:37',0,'In my dictionary, gonium is a suffix.',8300,0);
INSERT INTO comment VALUES (8303,1166,2707,'Gordon Steel','Solution Futher Clarified','2003-10-01 14:53:04',0,'Designate a rectangle as ABCD where AC and BD are the diagonals. Designate the width of the rectangle as W and the length as L. Bring corner A into coincidence with corner C, creating a crease of XY where X lies on line AB and Y on line CD. AX must equal CX (since the length is a constant). We can also prove that XC = AX = CY = AY by virtue of being similar triangles. Thus diagonal AC is perpendicular to and bisects XY at a point we may label Z. Since triangles AZX and ABC are similar, we know that XZ/BC = AZ/AB. And, since XY = 2XZ, we can rewrite this as 2 x (AZ) x (BC)/AB. But this is the same as (W/L) x Square root of (L squared + Y squared). Gordon S. \r\n',NULL,0);
INSERT INTO comment VALUES (8304,1416,2899,'Brian Wainscott','re(2): Solution','2003-10-01 15:14:57',0,'Since what A said would happen did in fact not happen, it seemed clear to me that A must be a liar.\r\n\r\nI guess I\'m reading the question as if A\'s statement were: \"B will say I am lying.\" If in fact A is being more general, as in \"If you asked B, he would tell you I am a liar\" and B replied \"that is true\", then you probably have to go through cases.\r\n\r\nSo in the end, I guess I can\'t disagree with you -- I just read the problem slightly differently.\r\n\r\nI think the wording is just a bit ambiguous. \"I lie\" could mean either \"I am lying\" or \"I tell lies\" I took it the first way, and it may indeed be meant in the second.',8297,0);
INSERT INTO comment VALUES (8305,1416,3172,'SilverKnight','re(3): Solution','2003-10-01 15:57:18',0,'aaahhhh... I see what you\'re saying.\r\n\r\nI don\'t think that\'s what was meant (referring to the particular instance of this statement). But I agree... there is an ambiguity in the meaning.',8304,0);
INSERT INTO comment VALUES (8306,27,3670,'Bruno','You guys are forgetting something...','2003-10-01 17:03:26',2,'You guys are forgetting the fact that we can eliminate Friday only due to the fact that the teacher hasn´t applied the test on the other days. If we eliminate Friday by this process and we want to eliminate Thursday the same way, we must now include Friday back in the days that the test is possible. \r\n\r\nI stand firm to being a paradox only if the test was to be applied on Friday:\r\n\r\nThe teacher hasn´t applied the test until Thursday. All the students assume he won´t apply it tomorrow since they all know he HAS to apply it tomorrow, thus not being a surprise. Since everyone knows it won´t be tomorrow, the teacher may then apply it on Friday. This is ONLY valid for Friday - making this a paradox.\r\n\r\nSuppose the teacher comes and applies the test on Monday. Why can´t he apply it? Of course he can, because the elimination of Friday was ONLY DUE TO THE FACT THAT HE DIDN´T APPLY IT UNTIL THURSDAY. It would still be a surprise to some students.\r\n\r\nAnd, finally, if the teacher comes on the first day of class and says: \"This year, I will give you a surprise test.\" If we were to use this elimination process for all the days of the year, never would a teacher be able to apply a surprise test - in other words, surprise tests wouldn´t exist.\r\n\r\nHope this clears it up a bit. :)',NULL,0);
INSERT INTO comment VALUES (8307,1277,1171,'nikki','Solution','2003-10-01 17:18:45',3,'I\'d write out the table if I could, but here\'s what I deduced. Hopefully I didn\'t make any errors:\r\n\r\nAzdam went with Forgam, who wore\r\nwhite suspenders\r\nblue tie\r\ngreen shirt\r\n\r\nBastam went with Holdram, who wore\r\nblue suspenders\r\nwhite tie\r\nred shirt\r\n\r\nCagram went with Golkam, who wore\r\ngreen suspenders\r\nred tie\r\nwhite shirt\r\n\r\nDartam went with Epotram, who wore\r\nred suspenders\r\ngreen tie\r\nblue shirt\r\n\r\nLater!',NULL,0);
INSERT INTO comment VALUES (8308,27,3172,'SilverKnight','re: You guys are forgetting something...','2003-10-01 18:02:46',0,'You wrote, \"If we eliminate Friday by this process and we want to eliminate Thursday the same way, we must now include Friday back in the days that the test is possible.\"\r\n\r\nNo, Bruno, we must not include Friday back in the possible days. We have already eliminated it. And we are now examining Thursday. This is an example of the notion of recursivity.\r\n\r\nSince I don\'t wish to repeat myself, please look here or here for the explanation of your preference.\r\n\r\nThe paradox comes from the \"fact\" that we\'ve eliminated all the possible days, and therefore we don\'t expect it on any day, and when it occur we are surprised.\r\n\r\nHope this clears it up for ya. :)',8306,0);
INSERT INTO comment VALUES (8309,1229,3558,'Tristan','re(4): solution - I see','2003-10-01 18:54:19',0,'I stand completely corrected. Good job catching what I didn\'t. I apparently didn\'t think of the extra five pounds being included. Brian is also correct.',8295,0);
INSERT INTO comment VALUES (8310,27,1626,'Gamer','re(2): You guys are forgetting something...','2003-10-01 20:17:07',0,'First of all, to address your issue of \"What if he did it on Monday\", he lied then. The Assuming we are given to do and the problem are in contradiction.\r\n\r\nI understand what you are saying. We can\'t eliminate Friday if TODAY is Wednesday Evening because there is still Thursday and Friday, and we don\'t know what day.\r\n\r\nIf it was Wednesday Evening, the students could think \"The test must be tommorrow if the professor isn\'t lying. If he doesn\'t give it tommorrow, there is no way he could give it without lying, so he can\'t give it tommorrow.\"\r\n\r\nDoes this make sense, and did I interpret what you said properly? I am hoping to address your problem more closely instead of just repeating what has been said by others.\r\n',8308,0);
INSERT INTO comment VALUES (8311,86,3558,'Tristan','alternate proof','2003-10-01 21:10:08',3,'No one seems to have thought of this proof:\r\n\r\nAny two different numbers have more different numbers inbetween them. Can you think of a number that\'s inbetween 3.9999... and 4? I don\'t think so. Therefore, 3.999... and 4 are the same number.',NULL,0);
INSERT INTO comment VALUES (8312,1277,3660,'ratsnstuff','Possible solution','2003-10-02 05:11:17',0,'Fisrtly, what gives with the weird names...? Anyway, this is what I came up with.\r\n\r\nForgam >> Azdan \r\nWhite susp.\r\nBlue tie\r\nGreen shirt\r\n\r\nGolkram/Golkam >> Cagram\r\nGreen susp.\r\nRed tie\r\nWhite shirt\r\n\r\nEpotram >> Dartam\r\nRed susp.\r\nGreen tie\r\nBlue shirt\r\n\r\nHoldram >> Bastam\r\nBlue susp.\r\nWhite tie\r\nRed shirt\r\n',NULL,0);
INSERT INTO comment VALUES (8313,1416,3660,'ratsnstuff','Short discussion','2003-10-02 05:25:05',0,'This is straight binary, with only two digits, and can be solved with brute force. \r\nSay if a person is a knight, his value is 0 and a liar\'s value would be 1. Thus, all possible combinations are:\r\n\r\nA B\r\n0 0 A would know B is a knight and would not\r\n make the first statement. FALSE\r\n0 1 The first statement is possible, but the\r\n second is not. FALSE\r\n1 0 The first statement would be true, but\r\n would not be spoken by a liar. FALSE\r\n1 1 \"B would say I lie\": B is a liar and would\r\n say otherwise, thus making the first\r\n statement a lie and possible. \"That is true\"\r\n refering to the first statement, would\r\n be a lie. Thus for the case of both A and B\r\n being liars, these statements are possible.\r\n\r\nSo without any further ado, I would say that A and B are both liars...',NULL,0);
INSERT INTO comment VALUES (8314,1151,3660,'ratsnstuff','re: SOLUTION?','2003-10-02 06:36:52',3,'Well gee, OK. Here goes: This is how I went about this problem. (Sorry for this VERY lengthy discussion)\r\n\r\nFirst, I drew the shelves, numbered from one to six (top to bottom then left to right). Each shelf has three characteristics. A first name, a surname and a toy. So I divided each shelf in three parts (kinda like this):\r\n\r\n-------------------------------\r\n| 1 : : | 4 : : | \r\n| : : | : : | \r\n| : : | : : |\r\n-------------------------------\r\n| 2 : : | 5 : : |\r\n| : : | : : |\r\n| : : | : : |\r\n-------------------------------\r\n| 3 : : | 6 : : |\r\n| : : | : : |\r\n| : : | : : |\r\n-------------------------------\r\n\r\nRight, now comes the fun part. I used the first column for the name, next the surname and lastly the toy. Every clue gives you a few possibilities. These should ALL be written down in thhe shelves.\r\n\r\nClue 1:\r\n**Kevin\'s surname is NOT Baker**. Kevin and the Baker kid is on the top shelves (1 and 4). The Lorenz kid can at this stage be either on shelf 2 or 5, because we don\'t know if Mark may be the Baker kid. Thus write in Kevin in both the top shelf names and Baker in the top surnames. Write Lorenz in shelf 2 and 5 surnames. \r\n\r\nClue 2:\r\n**Holly\'s surname is NOT Collins**. Collins is in a shelf on the right and lower than Holly. This would mean that Collins is in 5 or 6 (write it in there) and Holly would be in one of the four higher shelves (yep, write it down now). The picture book is on the left in either 2 or 3.\r\n\r\nClue 3:\r\nForbes and Crayons are in even numbered shelves. ie. in 2, 4 or 6. **Forbes does NOT own Crayons**.\r\n\r\nClue 4:\r\n**Darren does NOT own blocks**. Daren and the Blocks are both in the four higher shelves (1,2,4 and 5). Fire eng. is in the four lower shelves (2,3,5 and 6). Write all of these in the right spots as you are going along...\r\n\r\nClue 5: \r\nThis is the best clue. We know that the Teddy is on one of the middle shelves. The McKenna kid sits at the bottom and Monica is at the top and her surname is Baker!!\r\n\r\nNow we need to slowly digest all the above info.\r\nWe can start by noting that the top two kids have the names Monica and Kevin. Thus, we can cross out Holly and Daren.\r\n\r\nFrom clue 2: Holly has a higher shelf... That means she MUST be in either 2 or 5. which means that the Collins kid must be in the bottom right shelf: \" to the right of the one containing the picture book\" We also KNOW that the picture book is in the bottom left. Encircle the picture book in the bottom left and also Collins in the bottom right. Cross out the picture book in 2. Also the other surnames in 6. We now also know that the fire engine is in 6: From clue 4: \"Darrens toy... above the fire eng.\" Since Kevin and monica is top most, Daren must be in 2 or 5. The fire engine must be in the bottom and to the right, since the picture book is to the left... (encircle the fire eng. in 6 and cross out the crayons. Also get rid of the fire engine everywhere else)\r\n\r\nFrom clue 5: We see that the McKenna child is at the bottom (must be 3, because Collins is in 6). Meaning that the Teddy IS in 2 and Monica is in 1. Thus Baker is also in 1 (Monica Baker) And Kevin is in 4.\r\n\r\nFrom clue 1: \"Lorenz has a shelf with higher number than Mark\'s\" That can only be shelf 5. And Mark must be in either 2 or 3.\r\n\r\nBack to clue 4: Darren IS in either 2 or 5 (because he sits above the fire truck in 6) therefore the blocks and the Teddy are neigbours. So the blocks are in 5 and Darren is in 2.\r\n\r\nClue 3: The even numbers. The crayons must be in shelf 4 because 2 and 6 are occupied by the teddy and the fire eng. And since the crayons don\'t belong to the Forbes kid, he MUST be in 2.\r\n\r\nLets just recap what we know for sure.\r\n1. Monica Baker\r\n2. Darren Forbes, Teddy\r\n3. McKenna, Picture Book\r\n4. Kevin , Crayons\r\n5. Lorenz, Blocks\r\n6. Collins, Fire eng.\r\n\r\nClue 2: Holly has a higher shelf than Collins. Thus it must be 5, because Darren is in 2. \r\n\r\nClue 1: Lorenz has a higher number than Mark. Lorenz is in 5. The only lower number stil needing a name is 3, thus Mark is in three. \r\n\r\nNow we still need a first name in 6, a surname in 4 and a toy in 1. These are all given in the first two paragraphs: Janet, Farrel and Puzzle.\r\n\r\nThus, to summarise the solution:\r\n1. Monica Baker, Puzzle\r\n2. Darren Forbes, Teddy\r\n3. Mark McKenna, Picture Book\r\n4. Kevin Farrel, Crayons\r\n5. Holly Lorenz, Blocks\r\n6. Janet Collins, Fire Engine\r\n\r\nHope this covers it. Let me know if anything is amis. ',8293,0);
INSERT INTO comment VALUES (8315,1267,3660,'ratsnstuff','Possible solution','2003-10-02 07:19:39',0,'Amery, Brant and Fredo are liars. And Cuthbert, Derek, and Everard are knights.\r\n\r\nI basically gave it a trial and error run, by first assuming that Brant is a knight (because he pointed to two more knights). I then evaluated all the statements leading from there. He says that Everard and Fredo are knights. But they contradict eachother, so they can not both be knights, thus making Brant a liar. I then went to the next iteration in assuming that Cuthbert is a knight (because he already correctly states that Brant is a liar). C says that E is a knight, which in turn turn says that C and D are knights. So far so good. D says that A and B are liars (we know B is). A says that that C is a liar (which is false according to our assumption), making it a lie in this case. As for F saying D is a liar and A is a knight, makes him a liar. \r\n\r\nThus, A, B and F are liars. And C, D, and E are knights.',NULL,0);
INSERT INTO comment VALUES (8316,86,1626,'Gamer','re: alternate proof','2003-10-02 07:22:12',0,'I would like to say that 3.999... is the number directly BEOFRE 4, but isn\'t actually 4. Any two numbers that are directly together don\'t have any numbers between them. We don\'t normally think of this because any sensible numbers aren\'t directly together.\r\n\r\nThink of it this way, modelled with a discrete set of numbers (the integers) 5 and 6 are the closest possible numbers to each other. There isn\'t an integer in between them, so they must be the same number? I don\'t think that makes sense, and I don\'t think your argument is true either.',8311,0);
INSERT INTO comment VALUES (8317,1216,1301,'Charlie','solution','2003-10-02 09:23:29',3,'First let\'s figure when the centers of the cars will pass the point where their (the centers) paths cross. It\'s assumed that the incident takes place in America, where people drive on the right side of the road, and that Bill, in his car, does not react in any way to the impending potential problem, while George\'s only reaction is in applying the brakes (neither swerves). We\'ll further assume that the left side of the car is on the center line of each respective road, as we are not told how much distance to allow or how wide the road is or in what lane; at least it\'s better than assuming driving down the center of the road altogether. The width of the highway is not given so it\'s assumed that the distance to the intersection is the distance to the intersecting roadway center line.\r\n\r\nFor this center-point calculation, Bill\'s car must travel 150-3.5 feet (to allow for the half car-width that George\'s car is on Bill\'s side of the center line of George\'s road) at 30 ft/s, or 4.883 seconds.\r\n\r\nGeorge\'s center has 125+3.5 feet to get to the car-center intersection point. To find the time to get there, recognize that the average speed for any duration of time from the application of the brakes is 100-15t ft/s, so the time is found via\r\n(100-15t)t = 128.5\r\n15t^2-100t+128.5=0\r\nt=10/3 +/- 1.595 sec\r\n\r\nThe higher number of seconds would be if the negative acceleration continued after the car came to a stop, and started going backward into the intersection again, so the lesser time is what\'s sought, or 1.738 seconds. So George\'s car does pass the intersection before Bill\'s; but is is soon enough to avoid a collision?\r\n\r\nGeorge\'s car must clear (travel) a total of 125 + 7 + 13/2 feet to account for the full width of Bill\'s car and the back half of itself. That\'s 138.5 feet.\r\n\r\n(100-15t)t = 138.5\r\n15t^2-100t+138.5=0\r\nt=10/3 +/- 1.370 sec\r\n\r\nso the time is 1.963 seconds, by which time Bill\'s car has traveled 1.963 x 30 = 58.89 feet, bringing its front 150-58.89-7 feet back from the path of the right side of George\'s car, which is still a safe margin even if George is in a right lane or somewhat further to the right of the centerline than we allowed for.',NULL,0);
INSERT INTO comment VALUES (8318,1216,2839,'FatBoy','okay, here goes','2003-10-02 09:25:22',3,'The distance between the front of Bills car adn the potential location of the right side of georges car is 140 ft (distance to intersection - 1/2 length of car - 1/2 width of car)\r\n\r\ntime to potential impact \r\nt=d/v=140/30=4.67secs\r\n\r\nlocation of the rear of George\'s car at potential time of impact\r\n\r\nd = vt +1/2 at^2\r\n = (100 * 4.67)+ 1/2 (-30)(4.67)2\r\n = 140\r\n\r\ndistance rear of george\'s car must travel to clear bill\'s car =\r\ndistance to intersection + length of car = \r\n125 + 13 = 138 ft\r\n\r\ngeorge should just clear bill by 2 ft\r\nwhew',NULL,0);
INSERT INTO comment VALUES (8319,1216,2839,'FatBoy','re: solution','2003-10-02 09:27:31',0,'Curse you Charlie!!!\r\nnot ony did you successfuly solve teh problem whil I was typing my answer,\r\nyou answered it better than me.\r\nfie on you!\r\na pox on your house!!\r\n\r\n',8317,0);
INSERT INTO comment VALUES (8320,1216,1301,'Charlie','re: okay, here goes','2003-10-02 09:43:34',0,'Sorry FatBoy. (But I am getting better, though: I didn\'t work on the problem until after it was posted live.)\r\n\r\nThe problem with your solution, though, is at time t=4.67 seconds, the acceleration given would have George\'s car already going backward into the intersection a second time, and that\'s the only reason it looks so close.\r\n',8318,0);
INSERT INTO comment VALUES (8321,1216,3707,'David','Solution','2003-10-02 11:27:37',3,'Bill is travelling at 30 fps and is 150 ft from the intersection, so he takes 5 seconds to get there.\r\nGeorge is travelling at (100-30t) fps, where t is the time, so he travels a distance of (100t-15t*t) (by integral calculus). So in 5 seconds George travels 125 feet, which is exactly his distance to the intersection. \r\nSo there is a collision. The size of the cars is irrelevant - it\'s a direct hit.',NULL,0);
INSERT INTO comment VALUES (8322,1216,1183,'fwaff','re: Solution','2003-10-02 12:59:23',0,'Except that George\'s car came to a halt after 3.33 seconds, a second or two after he slid through the junction. Unless of course he instantaneously slammed it in reverse and accelerated backwards at 30f/s/s. \r\n\r\nI guess this just proves that integral calculus and driving make a deadly combination!',8321,0);
INSERT INTO comment VALUES (8323,1216,3172,'SilverKnight','re: Solution','2003-10-02 13:00:45',2,'No David.\r\n\r\nAs Charlie has already pointed out (and as I\'m guessing that DJ was trying to show by proposing the problem), you are simply blindly applying the equations.\r\n\r\nThe equation shows a CONSTANT -30 ft/sec/sec. But that\'s not what happens. When the car finally stops... the brakes don\'t \"push\" the car backwards... The car will stop in less than 5 seconds (past the intersection). If the car then continued with a -30 ft/sec/sec acceleration, it would back up into the intersection and collide. But it doesn\'t.\r\n\r\nSo, Charlie was correct in that there is no collision.',8321,0);
INSERT INTO comment VALUES (8324,86,3172,'SilverKnight','re(2): alternate proof','2003-10-02 13:06:38',0,'Wow! Gamer I\'m surprised to see you write this. I also don\'t like Tristan\'s \"proof\". I don\'t think it\'s at all rigorous.... (just because I can\'t come up with a number between the two doesn\'t mean there isn\'t one). To continue with that proof, Tristan must PROVE that there is no number between the two.\r\n\r\nHowever, .3999... (repeating) *IS* equal to 4.\r\n\r\nIn fact, it is just another way of describing the same number in our chosen notation. And the proof of this has already been posted.\r\n\r\n--- SK',8316,0);
INSERT INTO comment VALUES (8325,1216,2839,'FatBoy','Hey guys!!','2003-10-02 13:12:35',4,'I see where I sreced up with the whole decerating until you\'re going backwards thing.\r\nBut (even taking that into account) why did I (using standard kinematics) come up with with different answer than Charlie did using Calc?\r\nI checked my work and can\'t find any obvious error (other than the kind of sloppy rounding I always use) and frankly I never liked calc enough to summon the will to look figure out charli\'s answer.',NULL,0);
INSERT INTO comment VALUES (8326,1416,2839,'FatBoy','please ignore','2003-10-02 13:24:50',3,'If they were both knights then B would could not say that A would lie and A could not say that he would say it so they are not both knights\r\n\r\nIf A were a lier and B were a Knight then A\'s statement would be true so that arrangement is not possible either\r\n\r\nIf A were a KNight and Be were a liar than B saying A had told the truth would indicate that A had really lied so this is not possible\r\n\r\nIF they BOTH were liars, however, A could Say that B would say he is a liar because he knows that be would not say that b/c it is true. But B could say that what a said was true because a is a liar too so what he said is false',NULL,0);
INSERT INTO comment VALUES (8327,1216,3172,'SilverKnight','re: Hey guys!!','2003-10-02 13:56:27',0,'FatBoy,\r\n\r\nFirst, I think you are comparing the time when George comes back to intersection (in reverse, rather than the first time he goes through).\r\n\r\nAnd second, Charlie is taking into account the notion that the center of the car is not travelling down the center of the road... which I think is a little extreme and not what DJ intended.\r\n\r\nEither way, this will explain the difference.\r\n\r\nBut in the spirit of this site, I think you should actually read the previous posts and endeavor to understand what he (Charlie) said, and if necessary summon the will to learn/grow. That can be fun too.\r\n\r\n--- SK',8325,0);
INSERT INTO comment VALUES (8328,1216,2839,'FatBoy','re(2): Hey guys!!','2003-10-02 14:12:45',0,'Your point is taken',8327,0);
INSERT INTO comment VALUES (8329,1216,1301,'Charlie','re: Hey guys!!','2003-10-02 14:25:02',0,'The problem was in using a constant negative acceleration for 4.67 seconds, rather than switching to zero acceleration at time =3.33 seconds as pointed out by fwaff\'s comment. That is the time (I\'m assuming fwaff did the math) at which George\'s car came to a complete stop past the intersection. To plug 4.67 seconds into the original non-changing acceleration of -30 is to allow that the car then started to back up into the intersection. Presumable he would not do that. And even if he did, that would not be a near miss, but rather as he was going backward, would be entering the intersection (albeit from the opposite direction) and causing a collision.',8325,0);
INSERT INTO comment VALUES (8330,1216,2839,'FatBoy','oops, made myself look dumber than I really am','2003-10-02 14:26:06',0,'My original question should have said \"why did I get a different answer than DAVID? Not Charlie.\r\nTaking SKs advice I have reevaluated and saw that the reason I got a different result than David was that David was assuming 5 seconds to impact point while I was assuming 4.67\r\nSorry all but I felt I\'d made an idiot of myself and had to show that I really am somewhat brighter than I appear',8328,0);
INSERT INTO comment VALUES (8331,1432,1301,'Charlie','For starters','2003-10-02 15:45:16',2,'As each new wall must go to a previously isolated point (vertex), and there are (x-1)(y-1) such isolated vertices, the maximum number of walls that can be so placed is (x-1)(y-1).\r\n\r\nAt each stage, when less than this many have been placed, at least some must be adjacent to points that are already the endpoints of an existing wall, so those are eligible for building a new wall. This continues until all (x-1)(y-1) are no longer isolated, so there\'s no way that this maximum will be unreachable.',NULL,0);
INSERT INTO comment VALUES (8332,1216,1171,'nikki','Just to be complete...','2003-10-02 16:15:00',0,'\r\nI know it\'s been discussed a lot, and the fact that George comes to a stop at 3.33 seconds has been pointed out. But it\'s been bugging me that the rest of the problem didn\'t get formally solved, so here it is.\r\n\r\nTo find out how long it takes George to stop:\r\nV = 0 = 100ft/s + (-30ft/s/s)*T\r\nT = 10/3 seconds = 3.3333 seconds\r\n\r\nNow, let\'s see how far the center of George\'s car travelled from when he hit the brakes and when he stopped:\r\nDg = 100ft/s * 10/3s + 0.5*(-30ft/s/s)*(10/3s)^2\r\nDg = 166.666 ft\r\n\r\nAnd let\'s see how far the center of Bill\'s car travelled during this time:\r\nDb = 30ft/s * 10/3s\r\nDb = 100ft\r\n\r\nSo at the moment George stopped, he has already passed through the intersection, and the back end of his car is 35.16ft from the center of the intersection. Bill hasn\'t gone through the intersection yet, and the front end of his car is 43.5ft from the center of the intersection.\r\n\r\nBoth of these numbers show that there is enough clearance for these 13x7 cars to avoid a collision.',NULL,0);
INSERT INTO comment VALUES (8333,1277,1626,'Gamer','Explanation?','2003-10-02 17:15:09',4,'Without using a diagram, I was able to explain it... Does anyone have an explanation for this one?',NULL,0);
INSERT INTO comment VALUES (8334,86,3558,'Tristan','re(3): alternate proof','2003-10-02 17:39:00',0,'I believe Tom already addressed this in one of his replies. He said that no matter how small a number you add to 3.99999... you will not get inbetween 3.9999... and 4, but go above four. \r\n\r\nUnlike the example gamer gave, this isn\'t just a set of integers from which there is no number inbetween. This is ALL numbers. There are plenty of numbers inbetween 1 and 2 if you think of the complete set of numbers.\r\n\r\nI admit my proof isn\'t rigorous, but I believe that should be enough proof for most people. If you, SK, think you can improve it, go ahead (or not).',8324,0);
INSERT INTO comment VALUES (8335,86,3172,'SilverKnight','re(4): alternate proof','2003-10-02 18:28:42',0,'Tristan, you wrote:\r\nNo one seems to have thought of this proof...\r\nNow you write:\r\nTom already addressed this in one of his replies.\r\n\r\nSo either:\r\n Another three: |√10 - 3|, all raised to the power 1 There are lots of possibilities along these lines. Also, you could just raise one of the bits of the expression to the power 1 by using the numeral 1 and the carat symbol ^.\r\n\r\nCombining these ideas gives lots of possibilities.',NULL,0);
INSERT INTO comment VALUES (8423,637,1171,'nikki','Thanks guys =)','2003-10-07 11:22:55',0,'I just wanted to say thanks for your compliments. They were really nice =)\r\n\r\nLater!',NULL,0);
INSERT INTO comment VALUES (8424,1449,2231,'Trevor Leitch','Solution','2003-10-07 11:47:15',3,'Brazil won gold, Argentina the silver, and Chile the bronze.\r\n\r\nSince there are only three teams and three positions, there are six possible outcomes. If ABC means Argentina won gold, Brazil won silver and Chile the bronze, then these are:\r\n\r\nABC\r\nACB\r\nBAC\r\nBCA\r\nCAB\r\nCBA\r\n\r\nFrom the first reporter\'s statement we can eliminate ABC, CAB and CBA (neither Brazil won gold nor Chile won silver) and BCA (both Brazil won gold and Chile won silver). This leaves ACB and BAC. \r\nWe don\'t know how the second reporter\'s sentence ended... it might have been \"Chile won silver, but not both\" or \"Chile won gold, but not both.\" Had it been the former, the third reporter would have been unable to distinguish between options ACB and BAC. Since we were told he could reason the final order, the sentence must have ended \"Chile won gold, but not both\". This eliminates ACB (neither Argentina won silver nor Chile won gold) so the only possible answer is BAC.',NULL,0);
INSERT INTO comment VALUES (8425,1449,3172,'SilverKnight','solution','2003-10-07 11:48:34',3,'The second statement must be one of the two following:\r\n(2a) \"Either Argentine won silver, or Chile won bronze\" --or--\r\n(2b) \"Either Argentine won silver, or Chile won gold\"\r\n\r\nThere are only 6 possibilities:\r\nA B C (ruled out by statement 1 & 2b)\r\nA C B (ruled out by statement 2a & 2b)\r\nB A C (ruled out by statement 2a)\r\nB C A (ruled out by statement 1, 2a, 2b)\r\nC A B (ruled out by statement 1, 2b)\r\nC B A (ruled out by statement 1, 2a)\r\n\r\nIf it had been 2a, then there is no solution (all are ruled out), so it must have been 2b.\r\n\r\nWhich means:\r\nBrazil won Gold\r\nArgentine won Silver, and\r\nChile won Bronze\r\n\r\nOkay... I was hurried through this... I hope further analysis supports mine.',NULL,0);
INSERT INTO comment VALUES (8426,1449,3172,'SilverKnight','re: Solution','2003-10-07 11:55:36',0,'Trevor,\r\n\r\nI assume you meant Chile won bronze (not silver) in your answer.\r\n\r\nThe only disagreement I have with your analysis, is that you wrote:\r\nHad it been the former, the third reporter would have been unable to distinguish between options ACB and BAC.\r\n\r\nAssuming that you mean the former is: \"Either Argentine won Silver or Chile won Bronze, but not both\".\r\n\r\nThen BOTH of these are ruled out... Again, you wrote both are possible and can\'t be distinguished.\r\n\r\nThe rest of your analysis holds.\r\n\r\n--- SK',8424,0);
INSERT INTO comment VALUES (8427,1449,3224,'Lee','re:solution','2003-10-07 12:05:13',0,'I agree with Trevor. SilverKnight doesn\'t entertain the possibility of the sentence finishing \"...or Chile won silver\".\r\nIf the sentence finishes this way then BAC ACB both hold and the press reporter can\'t deduce the order.\r\nTherefore the sentence must have finished \"...or Chile won Gold\" and the order is\r\nBrazil\r\nArgentine\r\nChile',NULL,0);
INSERT INTO comment VALUES (8428,1449,3172,'SilverKnight','re(2):solution','2003-10-07 12:10:56',0,'uh... Lee... No.\r\n\r\nPoint (1):\r\nThen it would be similarly started to say \"Either Argentine won silver, or Chile won silver, but not both\"... which is ridiculous, and Trevor *DID* complete it with \"but not both\".\r\n\r\nPoint (2):\r\nFurther, if what you\'re suggesting is the case, then Trevor didn\'t entertain the possibility that the sentence was \"Either Argentine won silver, or Chile won Bronze\" at all.\r\n\r\nEither way, the analysis fails.\r\n\r\n--- SK\n\nEdited on October 7, 2003, 12:11 pm',8427,0);
INSERT INTO comment VALUES (8429,1449,3224,'Lee','re(3):solution','2003-10-07 12:48:00',0,'SilverKnight,\r\nIf the characters in logic puzzles aren\'t allowed to say odd things there would be a few less logic puzzles.\r\nIf sports reporters aren\'t allowed to say odd things the would be no sports reporters.\r\nMy method was to assume the reporter could finish with \"Gold\", \"Silver\" or \"Bronze\".\r\nNo consistent order can be found if the reporter says \"Bronze\" and no unique order if \"Silver\" so it must have finished \"Gold\" (and the order follows)\r\nThat\'s why I agree with Trevor - I concede he didn\'t entertain \"Bronze\" as a possibility, but I thought that was because, with \"Bronze\", the podium positions so obviously contradict. I feel I skimmed through his post since we used the similar approaches and our answers matched',NULL,0);
INSERT INTO comment VALUES (8430,1449,3172,'SilverKnight','re(4):solution','2003-10-07 13:08:22',0,'Lee,\r\n\r\nAs you say, no consistent order can be found if the reporters says anything but \"Gold\". But for one to assert this statement, one must show WHY no other statement will work.\r\n\r\nAnd, therefore, the solution must entertain the notion of \"Bronze\", or it remains incomplete.\r\n\r\nAgain, I think Trevor meant Bronze when he wrote Silver. But if he meant Silver, then he ignored Bronze. If meant Bronze, then he erred in the logic, but came up with the correct result anyway.\r\n\r\nAs for what your method is... I have no idea... you have yet to post it. You merely (1) said you accounted for Bronze, Silver, and Gold, (2) agreed with someone who did NOT account for Bronze (or did and erred in logic) and (3) disagreed with someone who DID account for Bronze.\r\n\r\nCheers!',8429,0);
INSERT INTO comment VALUES (8431,1449,1301,'Charlie','re(5):solution','2003-10-07 13:36:17',0,'The second reporter could have said:\r\n\r\n1) \"Either Argentina won silver, or Chile won Gold\" (possibly, but not necessarily, adding \"but not both\").\r\n\r\n2) \"Either Argentina won silver, or Chile won Silver\" (making any reference to \"but not both\" unnecessary and redundant).\r\n\r\nor \r\n\r\n3) \"Either Argentina won silver, or Chile won Bronze\" (possibly, but not necessarily, adding \"but not both\").\r\n\r\nSince we already know that Chile did not win gold, either version of (1) implies the order BAC for Gold, Silver and Bronze.\r\n\r\nIf the statement had been (2), then the more-hearing listener would still not have been able to determine the outcome, but in fact he did, so we know that statement (2) was not made, not because it is a ridiculous thing to say, but because it wouldn\'t have determined the order.\r\n\r\nIf statement (3) had been the case, then the version with \"but not both\" would have left an impossible situation, that is, inconsistent with what we already know, so that didn\'t happen. The version without the \"but not both\" is consistent and again points to the order being BAC.\r\n\r\nSo we know the order is BAC, but don\'t know how the second announcer continued what he was saying.',8430,0);
INSERT INTO comment VALUES (8432,1449,3172,'SilverKnight','re(6):solution','2003-10-07 13:51:21',0,'Agreed,\r\n\r\nThe \"but not both\" is necessary in the case of (2), because otherwise it is incorrect for Federico to have written \"similarly\" in the problem. He would have just written \"the radio reporter started to say...\".\r\n\r\nGiven that the \"but not both\" is in the statement, \r\n\"Argentina won silver, or Chile won silver\" does not need to be addressed. If one wishes to address it ANYWAY, then your logic holds, and it doesn\'t uniquely identify the outcome.\r\n\r\nSTILL... as Charlie also contends... the solution must still address bronze.\r\n\r\nIn any case, the English statements above have an implied \"exclusive or\" in it. And the \"but not both\" (provided you don\'t say the non-sensical silver/silver) is exclusive or. Either/OR *is* exclusive or.\r\n\r\nTherefore, logically, we do know, that the second announcer said Gold. (The statement of the problem implies that he continues with \"but not both\" at the end... but it is redundant.)',8431,0);
INSERT INTO comment VALUES (8433,1449,2716,'Federico Kereki','re(7):solution','2003-10-07 14:05:43',0,'I agree with the solution. As to the \"but not both\", I included it to make sure that \"Either A or B\" was understood as (\"A and not B\" or \"not A and B\"). \r\n\r\nFor me, the \"but not both\" was unnecessary, but in at least one of Smullyan\'s books, he used the \"either/or\" construction meaning \"A or B\"... \r\n\r\nAs it was correctly noticed, the \"similarly\" implied that the second reporter would have ended his sentence with \"but not both\".\r\n\r\n',8432,0);
INSERT INTO comment VALUES (8434,1449,1301,'Charlie','re(8):solution','2003-10-07 14:33:07',0,'You say \"the \'similarly\' implied that the second reporter would have ended his sentence with \'but not both\',\" but it was \"similarly started to say\", not \"similarly said\".\r\n\r\nI would agree with Smullyan that \"either ... or ...\" can mean \"A or B\", and would find a difference in meaning by adding \"but not both\".\r\n\r\nBut even with either view allowed, the answer to the puzzle is still the same, Brazil, Argentina, Chile.',8433,0);
INSERT INTO comment VALUES (8435,1436,1920,'Brian Smith','A few thoughts..','2003-10-07 14:53:33',0,'There are at least 52 Thursdays in a year, every month has at least 4 Thursdays. Then, there are at least 4 (52 - 12 * 4) Thursdays which occur as the 5th Thursday of a month.\n\nEdited on October 7, 2003, 2:54 pm',NULL,0);
INSERT INTO comment VALUES (8436,1449,3224,'Lee','nothing new','2003-10-07 14:57:53',0,'The possible podium positions are thus\r\nABC\r\nACB\r\nBAC\r\nBCA\r\nCBA\r\nCAB\r\nReporter 1 says either Brazil for gold or Chile for silver hence,\r\nB__ (Brazil in the top spot - B is the 1st letter) or,\r\n_C_ (Chile with Silver - C is the 2nd letter) \r\n\r\nbut not both. \r\nI would guess that the numbers represented are maybe the counting numbers, where the last bit is on a mod 4 scale (+0, +1, -2, -1) or something, but still nothing is apparent yet. Maybe this arrangement will help someone else figure it out..',8457,0);
INSERT INTO comment VALUES (8469,377,3766,'Drew','Solution','2003-10-08 23:57:58',3,'Ok anyone who knows their Roman numerals and biblical lore knows this one.\r\nYou got D = 500 in a position much like a bookend: D . . . D\r\nThen you have the reverse of the first clue where 5 = V.\r\nAnd finally you have the first letter, A, and first number, 1, producing both the A and I in DAVID or a Teryaki sauce brand. I\'ll leave it to you.',NULL,0);
INSERT INTO comment VALUES (8470,100,3766,'Drew','Yes or No Question','2003-10-09 00:03:57',0,'This is a yes or know question oonly, people.\r\nAll you must do is pic a random number with digits including all in 1-9, say 381654729, and test it:\r\n3+8+1+6+5+4+7+2+9=45\r\n45~9? Yes, 49 is divisible by 5, thus proving that you could arrange the digits 1-9 in any order so that: \r\nThe number formed by the first two digits is divisible by 2. \r\nThe number formed by the first three digits is divisible by 3. \r\nThe number formed by the first four digits is divisible by 4 \r\nand so on up to nine digits...\r\n',NULL,0);
INSERT INTO comment VALUES (8471,990,3766,'Drew','Uhhh . . . whatever','2003-10-09 00:09:57',0,'Pitcher comes in middle of 1st inning as a relief (I before E?) where the starter pitched hits and other team scores. The problem needs to be a lot more specific.',NULL,0);
INSERT INTO comment VALUES (8472,7,3766,'Drew','Actual Soluion','2003-10-09 00:14:58',0,'The problem actually CAN\'T be restated as \r\n\r\n\"When two coins are tossed, what is the probability that they both show tails, given that at least one is showing tails?\"\r\n\r\nGivin the fact that a coin most frequently has two sides, the probability of one of them doing ALMOST ANYTHING is 1:2. Yeesh.',NULL,0);
INSERT INTO comment VALUES (8473,16,3766,'Drew','Unlimited options','2003-10-09 00:22:03',0,'You could go on and on speculating that it is indeed NO.\r\n1. They have all died.\r\n2. All but one have died.\r\n3. All but two have died.\r\n4. All but three have died.\r\n . . .\r\n567. They all turned brown in an insane chameleon orgy.\r\n . . . \r\n4060. They all contracted smallpox . . . \r\n\r\nHave I gone too far? Oh well, the answer is NO.',NULL,0);
INSERT INTO comment VALUES (8474,643,3172,'SilverKnight','re(3): solution - different manner of looking at this','2003-10-09 02:23:10',0,'I\'m familiar with Baye\'s theorem... it wasn\'t clear to me how you applied it... I musta been tired. :-)\r\n\r\nAnd yup, it exactly corresponds to the leaves. Thanks!',8464,0);
INSERT INTO comment VALUES (8475,638,3796,'amber','solution','2003-10-09 02:44:54',0,'the answer is 45\r\n\r\nhere is how it is solved\r\n\r\nthe first marker he sees is 16. the second is 61\r\n\r\n61-16=45\r\n\r\nthe third marker he see is 106.\r\n\r\n106-61=45\r\n\r\n45mph is the answer',NULL,0);
INSERT INTO comment VALUES (8476,1317,3660,'ratsnstuff','re(3): First Stabs','2003-10-09 04:00:20',0,'I have replaced your symbols with A,B,C and D. Mapped like this:\r\n\r\nA: /\\\\\r\nB: /-\\\\\r\nC: \\\\-/\r\nD: \\\\/\r\n\r\nThus the series will look like this. \r\n\r\n1 A \r\n2 B \r\n3 A C \r\n4 A - D \r\n5 B A A\r\n6 A C B B\r\n7 A - C - C\r\n8 B D D D D\r\n9 D - D D D A\r\n\r\nI am wondering about the dash on its own though. Could it also be a symbol? Or might it be an operator? If it is a symbol, where does it fit in the ABCD order? \r\n',8468,0);
INSERT INTO comment VALUES (8477,1449,3660,'ratsnstuff','re: Of course one thing is assumed.','2003-10-09 04:08:57',0,'Well, the question does state that the reporter IS able to deduce the order. The only assumption that I make about that is to assume that he did actually deduce it correctly (even if he had to make assumptions like the one you are mentioning). \r\n\r\nThis is why, in my opinion, restricting it to those three countries is not necessarily an assumption. The question should maybe state whether the reporter got it right or not...',8443,0);
INSERT INTO comment VALUES (8478,643,2839,'FatBoy','re(2): I have not read Charlie\'s post yet','2003-10-09 07:33:47',0,'This looks like another case of me not really grasping the ground rules (and I do not want ot start another \"marbles bonanza\"- style circus) I just had always been taught that nothing that happens after an event can effect the likelyhood of that event. (once the coin is tossed it stays tossed)\r\nAnyway, I see what you are saying andthat I was laboring under some misconceptions again.\r\n',8452,0);
INSERT INTO comment VALUES (8479,84,3660,'ratsnstuff','re(3): No! You cannot! You cannot overtake the last person! No,no,no!','2003-10-09 08:09:45',0,'Would you have a position if you were not in the race?',6824,0);
INSERT INTO comment VALUES (8480,643,1183,'fwaff','re(3): I have not read Charlie\'s post yet','2003-10-09 08:52:48',0,'Ahhh, well there\'s your problem. If you\'ve got a misconception then you don\'t end up with anything to add to the hospital nursery no matter how much labour you go through.',8478,0);
INSERT INTO comment VALUES (8481,82,3799,'vlad','','2003-10-09 09:13:10',0,'If we pick any moment in time, there would be infinite number of demons before and finite number of demons after, therefore all demons killed him except finite number of them...\r\n\r\nOr, my favourite: this kind of problem is the proof that there is no infinity in practise, only in theory, because noone proved that infinity exists in practise, and that is taken for granted...',NULL,0);
INSERT INTO comment VALUES (8482,1315,1920,'Brian Smith','re: Aha!','2003-10-09 09:48:46',0,'That must be the correct answer. It fits so nicely.',8466,0);
INSERT INTO comment VALUES (8483,31,3799,'vlad','Backwards','2003-10-09 09:51:43',0,'Let\'s go backwards and assume that bee is facing something and the time is up. If it can change its direction in no time then it can change its direction twice in no time so there is no solution, as the bee turns and turns infinite number of times in no time :). ',NULL,0);
INSERT INTO comment VALUES (8484,924,3660,'ratsnstuff','Cool!!','2003-10-09 10:06:44',0,'For the first three matches I will replace the rope with equals:\r\n\r\n*% = $ [1]\r\n@ = !* [2] \r\n\r\n$$$ = @@%%* [3]\r\nfrom eq 1.\r\n$$ = @@% [4]\r\nfrom eq 2.\r\n$$ = @!*% [5]\r\nthus\r\n$ = @! = !!* [6]\r\nand\r\n@! = *% [7]\r\n\r\nLeft side of last contest:\r\n!@!!@!\r\n=$$!!\r\n\r\nRight side\r\n%$*$\r\n=$$$\r\n=$$!!* \r\n\r\nThus the right side will win (that is the side on the right :)',NULL,0);
INSERT INTO comment VALUES (8485,250,3799,'vlad','','2003-10-09 10:12:41',0,'Ok, by now I think we agreed that this is a lie. But what about \"I am lying (now).\"?\r\n\r\nThis is also a lie, because only one lie is needed for a sentence to be a lie, while all parts of sentence must be true if it is truth.\r\nSo if someone is lying and telling the truth at the same time, I guess it is a lie.',NULL,0);
INSERT INTO comment VALUES (8486,1450,3546,'RoyCook','Solution','2003-10-09 10:17:24',3,'Combinatorially, there are six possibilities (listing gold first and bronze last): (1) DSF The first, fully heard sentence rules out (1), (2), and (6). The second sentence must be one of: Demark won bronze, and/or France won gold. The first of these does not allow us to distinguish between (3) and (5), the third does not allow us to distinguish between (3) and (4), so it follows that the press reporter must have heard the third sentence, which can only be true if the order is as in (3), i.e. Spain wins Gold, France Silver, and Denmark Bronze.',NULL,0);
INSERT INTO comment VALUES (8487,263,3799,'vlad','Math?','2003-10-09 10:26:37',0,'It looks like mathematical and intuitive solutions don\'t agree.\r\nBut think again.\r\nInfinity was not defined with math, it was defined intuitively as \'infinity\'.\r\n\r\nSo the solution is this: in the universe where infinity exists, in that infiniti paralell lines do cross, and Achilles never reaches the turtle.\r\n\r\nDown with infinity!!!',NULL,0);
INSERT INTO comment VALUES (8488,672,3799,'vlad','','2003-10-09 10:40:09',0,'The shield \'heals\' itself so the sword will slice through it an the shield will not be destroyed...\r\nWord play :)',NULL,0);
INSERT INTO comment VALUES (8489,643,3172,'SilverKnight','re(3): I have not read Charlie\'s post yet','2003-10-09 11:21:29',0,'FatBoy,\r\n\r\nDon\'t misunderstand the problem.\r\n\r\nEven with the problem as stated. For any given birth, the likelihood that a girl is added to the nursery versus a boy being added is 50% (our assumption for the calculation).\r\n\r\nWhether or not we select a baby at random, after the fact, doesn\'t change that likelihood.\r\n____________\r\n\r\nA different example that may help this is... what if we selected a baby at random 10000 times (with replacement) afterwards.\r\n\r\nAssuming there are fewer than, say, 20 babies in the nursery, we will likely come up with a VERY close approximation to the actual ratio of babies in the nursery. If we further know there had been only 2 boys in there initially, we could almost definitively (with a high degree of accuracy) state whether the last baby added had been a third boy or another girl!\r\n\r\nIt still doesn\'t change the fact that, independently, the likelihood of adding a boy versus adding a girl is 50/50.\r\n\r\nIn other words, doing random sampling afterwards, tells us something about what happened earlier.',8478,0);
INSERT INTO comment VALUES (8490,168,3546,'RoyCook','re: Other Solution','2003-10-09 11:30:44',0,'Actually, the Arabic book will not work. The problem is as follows: English speakers, upon glancing at the book, would indeed be surprised, at first, to find the epilogue, for example, in the pages at the far left (when one is holding the book with the spine away from them). Nevertheless, the epilogue is still at the end of the book and is after the foreword, since in an Arabic book the beginning is on the right, and the end is on the left. Lewis was understanding \"end\", \"beginning\", etc, to mean those bits of a book where the actual beginning and end occur in English language texts, whereas the proper understanding is that the end of a book is just whatever part of the book contains the end material such as the epilogue, index, bibliography, etc.\r\n\r\nBy the way, strictly speaking this riddle is ill-formed. Many dictionaries will in fact contain a foreword, and this foreword will occur at the very beginning of the book, and any dictionary will contain an end, which of course will occur at the end. In a dictionary, the entry for \"end\" is not in the end, however, and the entry for \"foreword\" occurs (almost certainly) after the foreword. Note the use of quotations to distinguish between talking about, for example, the foreword of a book and the word \"foreword\" (the latter contains 8 letters, the former most likely contains much more than 8 letters). \r\n\r\nI admit, however, that such pickiness ruins the charm of the riddle. ',4047,0);
INSERT INTO comment VALUES (8491,1166,3546,'RoyCook','Corrected computation','2003-10-09 11:46:34',0,'Although I still think my general reasoning was right, I now get:\r\n\r\n√((√5 + 1)/2)\r\n\r\nas the final answer. (In other words, I think that I screwed up the computation before!)',NULL,0);
INSERT INTO comment VALUES (8492,643,2839,'FatBoy','re(4): I have not read Charlie\'s post yet','2003-10-09 12:36:20',0,'I understand, I don\'t object, I get it.\r\nI\'m on board, I support and fully agree with the solution by Charlie.\r\nThanks for your help.',8489,0);
INSERT INTO comment VALUES (8493,1220,1567,'Bryan','Sez me ...','2003-10-09 14:49:53',3,'2/3. To draw a chord with a pencil, you put the pencil point somewhere on the circle, then draw a line to any other point on the circle. Orient a polar coordinate system such that the origin is at the center of the circle and the first point of the chord is at zero degrees. Then the second point of the chord can be anywhere from 0 to 360 degrees, exclusive. A chord exactly as long as the circle\'d radius will intersect the circle at +/- 60 degrees. Chords with their second point within this sector will be shorter than the radius, while chords with their second point outside this sector will be longer than the radius. since the area outside the sector from -60 to +60 degrees is 2/3 of the circle, the odds are 2/3.',NULL,0);
INSERT INTO comment VALUES (8494,813,3804,'geoffrey','my solution','2003-10-09 14:53:17',0,'A: N=(2^(x+1))-1\r\nB: N=2x-1\r\n\r\nA and B are two completely different problems.\r\nYou must find the most efficient way of weighing.',NULL,0);
INSERT INTO comment VALUES (8495,1220,885,'np_rt','Solution (I Think)','2003-10-09 15:00:05',0,'We only need to consider at most half of the circle since the other half will not affect the solution due to symmetry. But we could break it up to consider the half-chord only instead of the full chord.\r\n\r\nIt\'s hard to do it without a picture. Draw one radius of the circle. We need to consider how far down this radius where the half-chord is r/2. Draw a radius to the point where this cord meets the circle and you\'d get a right triangle with hypotenus r and one leg r/2. The other leg is length √(3)*r/2.\r\n\r\nIf you \"travel\" less than √(3)*r/2 down the radius, then the semi-chord will be longer than r/2, which means the chord will be longer than r. Hence the probability is (√(3)*r/2)/r = √(3)/2.',NULL,0);
INSERT INTO comment VALUES (8496,1220,1301,'Charlie','Both right, but...','2003-10-09 15:32:00',0,'Bryan and np_rt both give the correct solution for their respective ways of choosing a random chord.\r\n\r\nHowever, I\'d have to go with np_rt\'s solution as that of the more \"natural\" way of randomly drawing a chord.\r\n\r\nImagine a flat universe on a 2-D plane. Then imagine it being criss-crossed with either micrometeoroids or by cosmic rays or whatever at random locations. A circle could be intersected by any of these rays. Let the first one be the random chord that we\'re talking about. It\'s coming from some direction or other, and will cross a perpendicular diameter (and radius) of the circle at some random point uniformly distributed along that radius, the way np_rt posits. And, his derivation being correct, makes his solution the \"more correct\" one, IMHO. You can\'t get more natural, or more random, than where a cosmic ray will hit.\r\n\r\nBryan\'s depends on a person choosing two points on a circle and then making a chord to connect them. There\'s no natural analog to this method of choice of points, so I\'d call it less random.',NULL,0);
INSERT INTO comment VALUES (8497,1220,3546,'RoyCook','Another solution','2003-10-09 15:36:28',3,'Take an arbitrary point on the circle. Then the problem is equivalent to asking: if we pick another point on the circle randomly, what is the probability that the line from the original point to the randomly chosen point is longer than the radius? If we divide the circle into six equal arcs (each determined by a 60 degree angle situated at the centre of the circle) such that two of the arcs meet at the original point, then the line in question will be less than the length of the radius if and only if the randomly chosen point lies on one of the two arcs which have the original point as one of their endpoints. Thus, the probability in question reduces to asking what the probability is that a point chosen randomly from one of six different regions of equal measure will not fall into one of two particular such regions. The answer is 4/6, or 2/3.\n\nEdited on October 9, 2003, 3:37 pm',NULL,0);
INSERT INTO comment VALUES (8498,1450,3806,'Matthew','Solution','2003-10-09 15:40:18',0,'Roy is right, but he made a mistake in his text, he meant to say that the tv report must have said the second sentence, it was a typo on his part, but the logic is correct, it is the only sentence that leaves only one possible solution',NULL,0);
INSERT INTO comment VALUES (8499,1220,3546,'RoyCook','re: Both right, but...','2003-10-09 15:54:03',0,'I am not sure that I agree with Charlie\'s idea that the \"randomness\" of a particular method depends on their being some natural analogue of it (in fact, i would have suspected the opposite, in general). Nevertheless, he does have a point.\r\n\r\nImagine that we have a circular disk in 2-D space. then the answer given by myself and Bryan (fair enough- he got it first) corresponds to something like: Given that we know cosmic ray X passed through point Y, but we know nothing about the angle of impact of the ray on the edge of the circle (and think that the angle of impact is random), what is the probability that the chord is greater in length than the radius. np_rt\'s answer corresponds to something like: Given that we know cosmic ray X passed through point Y on the diameter of the circle which is at a right angle to cosmic ray X, and we know nothing about where point Y is located on this diameter (and think that the location of Y on the diameter is random), what is the probability that the resulting chord is longer than the radius. In other words, the different answers depend on different intepretations of what is random, either the angle at which the ray hits, or the point on the orthogonal diameter which it hits.',8496,0);
INSERT INTO comment VALUES (8500,1151,3805,'Markus','Solution','2003-10-09 15:56:54',3,'Clue 5 gives us one column: Monica, Teddy bear & McKenna. Clue 1 gives us the top row: Kevin & Baker. Since Monica can\'t be Kevin, she must be Baker.\r\n\r\nClue 2 gives us another row. Above this row is Holly, so it can\'t be the top row. We already have both first names in the top row, so Holly must be in the middle row and Collins and the picture book must be in the bottom row. Since we already have McKenna in the bottom row, he must have the picture book and is in #3 (Collins is to the right).\r\n\r\nClue 4 gives us another row: not the bottom one (the fire engine is below) and not the top one (we already have both first names in the top row). Darren is not Holly, so Holly has the set of blocks and Collins the Fire Engine.\r\n\r\nClue 3 specifies even numbered boxes for a surname and a toy. Since box 6 already has both, it must be #2 and #4. #2 already has a toy so it is Forbes and #4 is the box of crayons.\r\n\r\nClue 1 specifies Lorenz in the middle row, only #5 has no surname. Mark has a smaller number, only #3 has no first name.\r\n\r\nFrom the text above the clues we get the missing first name (Janet), toy (puzzle), and surname (Farell: Francis Farell ... to care for her own child).\r\nSo our result is (hopefully):\r\n\r\n#1 Monica Baker, puzzle\r\n#2 Darren Forbes, teddy bear\r\n#3 Mark McKenna, picture book\r\n#4 Kevin Farell, box of crayons\r\n#5 Holly Lorenz, set of blocks\r\n#6 Janet Collins, fire engine\r\n',NULL,0);
INSERT INTO comment VALUES (8501,7,3546,'RoyCook','re: Actual Soluion','2003-10-09 16:07:00',0,'Actually, Drew, you are confusing two questions. The probability that both coins are showing tails, given that one of them is (but nothing is specified regarding which one) is in fact 1/3. The probability that both coins are showing tails, given that a particular specified one (say the one on the left) is, however is 1/2. To illustrate the difference, imagine I throw a penny and a dime. You are given very different information (and should arrive at very different probabilities) depending on whether I tell you that \"either the penny or the dime is tails\" versus my telling you that \"the dime is tails\".',8472,0);
INSERT INTO comment VALUES (8502,1220,2899,'Brian Wainscott','re(2): Both right, but...','2003-10-09 16:47:14',0,'I agree with RoyCook. Bryan takes \"random\" to mean the endpoints are uniformly distributed around the circle. np_rt has the chords uniformly distributed along the bisecting diameter. These are most definitely NOT the same, particularly near the ends of the diameter.\r\n\r\nI think Bryan\'s choice of \"random\" is much more natural, and probably what DJ had in mind.\n\nEdited on October 9, 2003, 4:47 pm',8499,0);
INSERT INTO comment VALUES (8503,1170,3735,'Nick Hobson','By power series','2003-10-09 17:08:14',3,'The power series for e^x is 1 + x + x²/2! + x³/3! + ...\r\nSo we have e^x > 1 + x, for x > 0. (1)\r\n\r\nNow set x = π/e - 1.\r\nThen, by (1), e^(π/e - 1) > π/e.\r\nMultiply by e: e^(π/e) > π.\r\nRaise to the power e: e^π > π^e.',NULL,0);
INSERT INTO comment VALUES (8504,1216,3807,'Robin Routledge','Shorter solution','2003-10-09 17:12:05',0,'At constant speed, Bill reaches the intersection in 5 seconds\r\nGeorge\'s motion is governed by the equation\r\ns=ut+at*t/2\r\n125 = 100t - 15t*t\r\nThis simplifies to\r\n3t*t -20t + 25 = 0\r\n(3t-5)(t-5) = 0\r\nAt first the two positive solutions worried me. Then I realised that if the car continues to decelerate the speed will eventually become negative & the car will reverse. That happens after 5 seconds. The solution that interests us is t=5/3 seconds. This is when George reaches the junction, well before Bill. Consequently there is no collision.',NULL,0);
INSERT INTO comment VALUES (8505,1220,3804,'geoffrey','answer a ? with a ?','2003-10-09 17:16:55',0,'What is the probability that a randomly drawn chord will be the exact same length as the radius of the circle?\r\n\r\nThat said, I think the answer that DJ is looking for is 2/3 as others have figured.\r\n\r\nmy way of explaining:\r\n\r\n>6 equilateral triangles can fit inside a circle.\r\n (a picture does help)\r\n\r\n>Take any two of these triangles that are next to each other. \r\n\r\n>The triangles share 2 points: the center of the circle and a point you can defined as the arbitrary starting point of the chord.\r\n\r\n>The other two points of the triangles- the most distant points- define 1/3 the circumference of the circle.\r\n\r\n>If a chord is drawn from the arbitrary starting point to a point within this area it will be shorter than the radius.\r\n\r\n>You can see how this is true because the two sides of the triangles which are chords themselves are the same lenth as the radius.\r\n\r\n>Therefore, a chord drawn from the starting point to the other 2/3rds of the circle will be longer than the radius.',NULL,0);
INSERT INTO comment VALUES (8506,1205,3806,'Matthew','Solution','2003-10-09 17:22:33',0,'the correct answer to this puzzle is no, you cannot time exactly 25 minutes since you ate limites to only fractions with denominations in powers of 2, and 25, is 5/12, which does not have a power of two for a deniminator using an infinite number of timers it is possible to refine your time closer and closer and get increasingly more acurate, but as you are cutting the value in half each time, after a point the variance will be so little as to be insignificant, but it is an exponetial equation that approaches, but never reaches the 25 minute mark.',NULL,0);
INSERT INTO comment VALUES (8507,638,3807,'DrBob','Solution','2003-10-09 17:25:07',0,'If the speed is s; the two digits a,b\r\nThe first number is 10a+b\r\nThe second is 10b+a\r\nThe third is 100a+b\r\n\r\nFrom the first 2: s = 9b-9a ... Eqn 1\r\nFrom the second & third: s = 99a-9b ... Eqn 2\r\n\r\nAdding: 2s = 90a so s = 45a\r\n\r\nEquating eqns 1 & 2\r\n99a-9b = 9b-9a so 108a = 18b i.e. 6a = b\r\nSince a & b are < 10, a=1, b=6\r\n\r\nSo s = 45',NULL,0);
INSERT INTO comment VALUES (8508,1220,3172,'SilverKnight','re: answer a ? with a ?','2003-10-09 17:56:35',0,'I think DJ was even cleverer (is that a word?)... and that he asked the problem KNOWING that to answer it, one must make an assumption about how the random number is determined.\r\n\r\n(I think so, because I submitted a problem doing exactly that :-)... hopefully, it will come get posted in the next year or so.... :-)',8505,0);
INSERT INTO comment VALUES (8509,1220,1575,'DJ','You never know..','2003-10-09 17:58:38',1,'Bryan\'s idea is to pick a point on the perimeter, and then consider the distribution in question to be chords originating from that point to any other point. Then, since the analysis will be the same for any given point on the perimeter, and every chord in the circle will be equally represented (exactly twice) in such an analysis of every point, that is sufficient. That makes sense.\r\nHowever, the analysis also depends on the assumption that any given range of angles gives an equal probability of random selection. That is to say, you need to assume the the chance of getting between 0¡Æ and 10¡Æ is the same as the chance of getting between 80¡Æ and 90¡Æ. How can you prove that this is true? I\'m not saying it\'s right or wrong, but you need to support that part of the analysis.\r\n\r\nNow, consider this: the perpendicular bisector of any chord will be a diameter of the circle. So, take a single diameter of the circle, and move along its length. At each \'point,\' draw the chord perpendicular to the diameter at this point. The chords thus formed will be unique; there is only one specific diameter and distance that will form any given chord. When this chord is exactly equal in length to the radius, you are at a point on the diameter (√3)r/2 from the center. Farther than this from the center, the chord will be shorter than the radius; closer to the center, you will draw a chord that is longer than the radius.\r\nAt this point, np_rt said (in effect) that the probability is the ratio of points closer to the center to the total number of points on the whole diameter (which, if we assume even distribution of points along the diameter, is the ratio of these lengths). That ratio then becomes (2(√3)r/2)/2r, or just (√3)/2. Since it is a safe assumption that the distribution of points along the diameter is uniform, and such an analysis for every diameter of the circle would cover every possible chord exactly once, it could follor that this ratio is also the probability that any chord in the entire circle is longer than the radius.\r\n\r\nHere\'s another way to look at it:\r\nEach chord has a unique midpoint within the area of the circle. Thus, you could actually select any random point, draw the chord that has that point as its midpoint, and let that be your random chord. Then, assuming uniform distribution of points over the area of the circle, the ratio of longer chords (than the radius) to shorter ones will be the ratio of the areas of two circles. The \'top\' part of this ratio will be the area of the circle, concentric to the original one, whose radius is small enough that any point within the circle will yield a chord whose length is greater than the radius. The radius of this circle is already determined; it is (√3)r/2. The \'bottom\' of the ratio is, of course, the entire original circle. The ratio of the areas of two circles is the square of the ratio of their radii; thus this ratio is ((√3)/2)² = 3/4.\r\nThis means that, if you pick a random point in the circle, there is a 75% chance it will be less than (√3)r/2 from the center, and thus is the unique perpendicular bisector of a chord which is longer than the radius of the circle.\r\n\r\nThese all seem like fairly sound analyses, yet they come up with completely different answers.\r\n\r\nSo, what\'s the right answer?\n\nEdited on October 9, 2003, 6:00 pm',NULL,0);
INSERT INTO comment VALUES (8510,1220,3172,'SilverKnight','re: You never know..','2003-10-09 18:12:47',0,'based on DJ\'s comment, I think my last comment is correct.',8509,0);
INSERT INTO comment VALUES (8511,1315,1626,'Gamer','re(2): Aha!','2003-10-09 18:17:27',0,'It is... :) I hope you all liked this problem.',8482,0);
INSERT INTO comment VALUES (8512,1317,1626,'Gamer','Closer ;)','2003-10-09 18:34:25',2,'To DJ, Each row is read left to right, so the only thing important about the last part each is what has already been said. The rows are the important part... the columns aren\'t important like they were in Line Drive. Also, the rows don\'t need to be spaced out or used with a \"pre\" because the spacing doesn\'t matter, only the characters.\r\n\r\nOnce you know how many there are, you will know how to convert them. :)',NULL,0);
INSERT INTO comment VALUES (8513,1220,3558,'Tristan','No solution','2003-10-09 18:38:29',0,'If we\'re supposed to prove it, the puzzle is impossible. To prove something, we can\'t assume anything. We don\'t have enough information. Of course, this being probability, I might be wrong on this.',NULL,0);
INSERT INTO comment VALUES (8514,643,3809,'e','','2003-10-09 19:00:47',0,'I\'m guessing 50%, because nothing in problem effects the liklihood/sex of the baby added. Kind of like, if you flip a coin 3 times, and it turns up heads, what\'s the probability that the 4th flip will also be heads -> 50%.',NULL,0);
INSERT INTO comment VALUES (8515,1450,3809,'e','possible answer','2003-10-09 19:04:33',0,'Denmark won bronze, Spain won gold and France won silver..?',NULL,0);
INSERT INTO comment VALUES (8516,1341,3809,'e','newbie guessing - and I haven\'t read comments so my apologies if you\'ve already covered this','2003-10-09 19:21:14',0,'An infinite number of marbles are still in the container, because how can you subtract from infinite? ',NULL,0);
INSERT INTO comment VALUES (8517,511,3558,'Tristan','Logic','2003-10-09 19:30:01',0,'I\'m completely disregarding anything about God and treating this as logic.\r\n\r\nTo change this sentence, can an omnipotent someone defy logic? Well, that someone being omnipotent, I\'d say yes. In fact, being omnipotent in the first place defies logic. It\'s like asking if 1=2 if you can divide by 0. Not to say omnipotence doesn\'t exist.',NULL,0);
INSERT INTO comment VALUES (8518,488,3766,'Drew','Hmmmm','2003-10-09 20:06:49',0,'Well lets speculate:\r\nSIR? What is that supposed to be? It doesn\'t seem like this riddle is adressing anyone in paritcular so why SIR?\r\nA RHYME EXCELLING? Could this word possibly rhyme with one of the words in the riddle? It makes sense that the answer would rhyme with the I in WHAT AM I?\r\nMystic force? Seemingly no relation.\r\nMagic spelling? OK, so it is a word that is spelled curiously. Big whoop.\r\nCelestial sprites? Elucidate? What a load of garbage! This is definentily a filler of some sort.\r\nStriving? Maybe everything it states has little relationship to other clues. That or it could be composed of entirely different elements (not literally) like a play on words. Or, this being the worst scenario, everything it had said was completely bogus and we have to turn to other clues for evidence.\r\nIf so, how about patterns? None.\r\nHmm, capitol letters? SICAW, no. WACIS, no.\r\nBlimey, math! Ok letter-number substituion, no.\r\n\r\nOMG!\r\n\r\nNumber of letters in a word, BINGO! 3,14159 . . . where the , is a .! Wow, pi. It actually works! Man, someone give me a cookie for all that!\r\nIt works because the unrelated striving stuff is refering to a repeating irrational decimal.\r\n\r\nA red-rated difficulty all mine! I have triumphed!',NULL,0);
INSERT INTO comment VALUES (8519,243,3766,'Drew','duh','2003-10-09 20:12:44',0,'They equal one because they are opposing ratios.\r\n\r\nWorks for every real number. Easy.',NULL,0);
INSERT INTO comment VALUES (8520,243,3172,'SilverKnight','re: duh','2003-10-09 21:17:38',4,'I\'ve never heard that term.... what\'s an \"opposing ratio\" ?',8519,0);
INSERT INTO comment VALUES (8521,488,3810,'John','Solution','2003-10-09 21:40:06',0,'This is actually technically not a riddle...\r\nThat is a rhyme that was designed to remember the value of pi (3.14...) The amount of letters in each word represents the different values of pi (Sir [3], I [1] bear [4] a [1] rhyme [5]...)\r\n\r\nIt even keeps going for all the 31 first numbers in pi:\r\n\r\nSir, I bear a rhyme excelling \r\nIn mystic force, and magic spelling \r\nCelestial sprites elucidate \r\nAll my own striving can\'t relate \r\nOr locate they who can cogitate \r\nAnd so finally terminate. Finis.',NULL,0);
INSERT INTO comment VALUES (8522,1220,2716,'Federico Kereki','A needed fact','2003-10-09 22:01:41',1,'I think you need to explain how the chord was \"randomly drawn\" first, before calculating any probabilities.\r\n\r\nIn any case, I arrived to the answer 2/3 by two different ways:\r\n\r\nstarting with a point, just take another in the circunference\r\n\r\nstarting with a point, draw a line at a random angle, and thus determine the other point.\r\n\r\nOf course, by \"randomly\" I here mean \"with a uniform distribution\" -- but that isn\'t necessary, you know...',NULL,0);
INSERT INTO comment VALUES (8523,1220,3351,'Eric','keep it simple, ...','2003-10-09 22:52:33',1,' It is indeed significant that we establish the method by which our chord is randomly drawn. I can see how this was abstracted by both of our solutions, and would like to offer another avenue of consideration.\r\n\r\n Let us consider a regular n-gon (since probability is so much more concrete in the discrete world), and the set of line segments joining verticies of it. Let me then ask \"what is the probability that a randomly chosen line segment is longer than the \"radius\" of the n-gon(distance from center of polygon to a vertex). This problem is easy to define and percieve. For example: In a regular hexagon there are 15 unique line segments 9 of which are longer then the \"radius\" giving a probability of 3/5. Furthermore in a regular 60-agon there are 59(60)/2 = 1770 unique line segments 39(60)/2 = 1170 of which are longer than the radius giving a probability of 1170/1770 = 39/59.\r\n\r\n If we take the limit as n approches ∞ and extrapolate this method of randomly choosing a line segment in an ∞-gon, we see that our line segment becomes a chord, our n-gon becomes a circle, and our probability is indeed 2/3.\r\n\r\n Should we use similar logic with regard to the \"random point on a perpendicular bisector\" method, we\'d have to construct some kind of index of points along the perpendicular bisector, which frankly, is a construction not warranted by the problem.',8522,0);
INSERT INTO comment VALUES (8524,1317,2561,'Aaron','base 5?','2003-10-10 01:49:16',0,'i thought of just changing each ~symbol~ to a number, and then read each row as a number in base 5, if you count the - as 0, /\\\\ as 1, /-\\\\ as 2, \\\\-/ as 3, and \\\\/ as 4, you get\r\n1, 2, 13, 104, 211, 1322, 10303, 24444, 404441, which is 1, 2, 8, 29, 56, 312, 703, 1874, 13121 in decimal.\r\ndon\'t see much there, though, it was just an idea.',NULL,0);
INSERT INTO comment VALUES (8525,1450,3660,'ratsnstuff','re: Solution','2003-10-10 01:53:51',0,'I must say I was quite stuck till I read your first sentence. I stoped reading and was able to solve the rest myself. Thanks. \r\n\r\nHere is how I did it in the end:\r\n\r\nD S F\r\n-------\r\nG S B$ \r\nG B S$ \r\nS G B # \r\nS B G # \r\nB G S #* \r\nB S G * \r\n\r\nFrom the first statement we see that all \r\ncombinations allowing Denmark silver or\r\nSpain gold could be true. These are marked \r\nwith #. Similarly, the second statement will \r\nnominate three possibilities, starting with \r\nDenmark getting Bronze. (Marked with *)\r\n\r\nBecause the reporter was able to deduce the\r\noutcome the second statement must have been\r\n\"...France silver\" or \"...France bronze\", \r\nmarked with $ so that we only have the one\r\noverlap: Spain gold, France silver, \r\nDenmark bronze.\n\nEdited on October 10, 2003, 2:00 am',8486,0);
INSERT INTO comment VALUES (8526,1220,2561,'Aaron','i think','2003-10-10 02:03:43',0,'i think the problem\'s a good one, but rather than finding the actual probability, the difficulty is in finding a truly random way of picking a chord. i don\'t think that selecting a single point on the circumference and then picking any other point is as good a method, because if you draw the chords on a circle, and draw the lines to evenly spaced points on the circumference, the chords you draw that way are ~scrunched~ at the bottom and ~spread out~ at the top. On the other hand, if you draw lines from a single point at evenly spaced angles, they are distributed differently. what you guys were saying about picking a point and then another point is actually equivalent to picking an angle, not a point, because you were considering the points to be evenly distributed by the angle they form, rather than arclength.\r\ni\'m not sure that makes sense, but i\'m pretty sure they are two different analyses.\r\nalso, nobody has commented on the thing dj added, about picking a random point, which would work because each point in the circle maps 1:1 directly to a single chord -- every point except for the center. there are an infinit number of diameters, and of course the midpoint of each is the center of the circle. however, since the center makes up for only as much of the ratio as any other point, that would seem to imply that the actual probability is even greater than 3/4. then again, the center is part of both the inside and outside circles, so if the center actually should count greater than the other points, perhaps the probability is less (if a<b and c>0, (a+c)/(b+c)>a/b ).\r\ni find this whole discussion very fascinating, although i don\'t think i\'m explaining my thoughts very well. i look forward to seeing what everyone else has to say.',NULL,0);
INSERT INTO comment VALUES (8527,1220,3807,'DrBob','Solution','2003-10-10 03:31:11',3,'Without loss of generality, choose any point on the circumference of the circle as the starting poinrt for the chord (Q), Draw a chord equal to the length of the radius from this point in each direction - these join the circumference at points P & R. Any chord from Q that joins the circumference on the larger arc PQ of the circle is longer than the radius; any that joins the circumference on the smaller arc PQ is equal to or shorter than the radius. We know that we can draw exactly 6 consecutive arcs equal to the length of the radius around the circumference of the circle; the smaller arc, PQ, comprises 2 of them. Hence the probability of choosing a point on that arc is 1/3. Thw probability of choosing another point on the circumference, giving a chord longer than the radius, is thus 2/3',NULL,0);
INSERT INTO comment VALUES (8528,1229,3807,'DrBob','re: solution','2003-10-10 04:30:14',0,'You\'ve missed a bracket in 2^27-1; it should be 2^26; giving 67,108,864\r\nThe conclusion is the same, though',8263,0);
INSERT INTO comment VALUES (8529,1229,3807,'DrBob','re: solution','2003-10-10 04:35:24',0,'Ignore my last comment. You, of course, are referring to the total given over 27 years which is the figure you give (though, in my defence, not the figure you say you are giving). ',8263,0);
INSERT INTO comment VALUES (8530,1242,3275,'retiarius','Solution','2003-10-10 08:00:44',0,'Let AB = x\r\nAF = FE = x\r\nBC = CD = 2x\r\nED = x\r\nA = 3x^2\r\nP = 8x\r\n3x^2 - 8x - 60 = 0\r\n(3x + 10) (x - 6) = 0\r\nx = 6\r\nAC = (6^2 + 12 ^2)^½ = 180^½ = 6 x 5^½ = 13.42\r\n',NULL,0);
INSERT INTO comment VALUES (8531,1242,3801,'Callum','A different angle','2003-10-10 08:01:31',0,'this was easy as we have been doing triganometry at school these past weeks.\r\nthe answer is a-c=26.828.\r\ni got this because the preimeter is 8ab or 8af etc\r\nand the area is (af x ba)+(ed x cd). if i put this in to a ratio it would equal area:perimeter 3:8. i then use the information to work out a-p=60.\r\nso if 3-8 had to equal 60 i would have to times the area and perimeter -12. this gave me the equation -36+96=60 which is equal on each side.\r\ni then used the phyphagourous (pardon my spelling) to find A to C. this worked out like\r\n12² + 24² =720 when i squared rooted it ,it came to 26.828.\r\nthank you and now i can be a student',NULL,0);
INSERT INTO comment VALUES (8532,1220,1301,'Charlie','Faith or Reason--no one will come to a final conclusion.','2003-10-10 08:59:06',0,'No one is going to come to a conclusion as to the \"best\" way of randomizing a chord.\r\n\r\nIn support of (√3)/2, the following comes from mathworld:\r\nThe latter interpretation is more satisfactory in the sense that the result remains the same for a rotated circle, a slightly smaller circle inscribed in the first, or for a circle of the same size but with its center slightly offset. Jaynes (1983) shows that the interpretation of \"random\" as a continuous uniform distribution over the radius is the only one possessing all these three invariances. \r\n\r\nIn addition to the cosmic ray argument presented in my previous post, I\'d also give an example of a plane that is criss-crossed with random lines. A circle is then placed upon the plane and is intersected by a number of lines. The expected proportion that would form chords longer than the radius would be the (√3)/2. Those pre-existing random lines would be just like the random cosmic rays.\r\n\r\nBy the way, most random number generators are pseudo-random, actually being deterministic. But radiation, detected by a geiger counter, actually is random, so those cosmic rays do really hit randomly, having originated in quantum events.\r\n\r\nAs Aaron has pointed out, by taking two random points on the circumference, you are overcrowding chords that are at nearby endpoints, and overseparating them at far reaches.\r\n\r\nWhile Federico Kereki claims that 2/3 is reached two ways, actually, choosing two points at random on the circumference is not really different from choosing a central angle--they are really the same thing, so of course the probability is the same.\r\n\r\nI, however, do not understand DJ\'s objection to Bryan\'s answer:\r\n\"However, the analysis also depends on the assumption that any given range of angles gives an equal probability of random selection. That is to say, you need to assume the the chance of getting between 0 deg and 10 deg is the same as the chance of getting between 80deg and 90deg. How can you prove that this is true?\"\r\n\r\nWell, one can\'t prove that one\'s selection method is true. One just decides on a selection method. In this particular case someone has chosen a uniform distribution of angles (arclengths) from which to select a chord.',NULL,0);
INSERT INTO comment VALUES (8533,1242,1575,'DJ','simply put','2003-10-10 09:20:37',3,'Let x be the length AB, AF, etc.\r\nThen, the perimeter P = 8x, and the area of the figure A = 3x².\r\nA - P = 60\r\n3x² - 8x = 60\r\n3x² - 8x - 60 = 0\r\n(3x + 10)(x - 6) = 0\r\nx = 6, -10.\r\nObviously, the distance in question must be positive, so x= 60.\r\n\r\nThen, AC is the hypotenuse of a right triangle with legs 6 and 12.\r\nThus, AC² = 6² + 12²\r\nAC = √180\r\nAC = 6√5\r\nAC ~= 13.4164',NULL,0);
INSERT INTO comment VALUES (8534,1242,1575,'DJ','re: A different angle','2003-10-10 09:31:00',2,'First, when you came up with a negative value for the length, that should have been a sign that something is wrong.\r\nThe problem with your anaysis is, the ratio of A to P is not simply 3/8, it is 3/8 times whatever ab is (or af, de, etc). Then, you would have to \"times the area and perimeter\" 6, instead of -12, to get the equation 104-48=60, which is equal on each side (in essence, you were trying to solve 3x-8x=60 instead of 3x²-8x=60, which is why you got a negative answer). Once you have the right value for x, the Pythagorean theorem gives AC²=6²+12²=180, so AC is about 13.416.',8531,0);
INSERT INTO comment VALUES (8535,1317,1575,'DJ','re: base 5?','2003-10-10 09:37:11',0,'I was thinking of a number system in another base (although I was thinking base 4), which is why I had put the rows of \'symbols\' right-aligned. That way, the values in each column would carry the same \'weight,\' just as right-aligning normal decimal values would put all the ones into a column, the tens places into a column, etc. Gamer\'s comment seemed to indicate that my last arrangement wouldn\'t be helpful, so I\'m guessing that some base-n number system isn\'t the answer.\r\nAlso, I would hope the symbols have more meaning than straight substitution for digits.\r\nIn any case, I don\'t see a pattern in the numbers you have listed, and I would be disappointed if that\'s all there was to the solution..',8524,0);
INSERT INTO comment VALUES (8536,1112,2839,'FatBoy','please ignore','2003-10-10 10:15:12',3,'First off: by inspection Q and Z are not used\r\n\r\nGOAD and GROW indicate that A,D are on same cubes as R,W but HOAR tells us that A and R are not on same cube so D is with R and A is with W \r\nGOAD and HOAR indicate that G,D are on same cubes as H,R and since D is with R then G is with H\r\nCHAD and HOAR indicate that C,D are on same cubes as O,R and since D is with R then C is with O\r\n\r\nCHAD indicates that C, H, A and D must be on different cubes so we now know the following about the four cubes (I through IV for convenience)\r\n\r\nI contains A,W\r\nII contains G,H\r\nIII contains C,O\r\nIV contains D,R\r\n\r\nStarting with cube III if we eliminate from the alphabet the two unused letters (Q,Z), the six letters we know are on other cubes and all the letters that share words on the list with C or O we are left with seven possible letters (including C and O which we know are on the cube) they are:\r\nC,E,J,N,O,V,X\r\nBut since V is in both NAVY and VIBE we can eliminate it because its presence would rule out N and E leaving us with less than six. So cube III is labeled C,E,J,N,O and X.\r\n\r\nConsider OPTS and TURN since O and N are both on cube III this tells us that P,S are on same cubes as U,R. but JUMP has both U and P so P is with R (on cube IV) and S is with U. AXIS tells us that S can’t be with A so S,U must be on cube III\r\n\r\nNow in the word AXIS A is on I, S is on II, X is on III\r\nWhich means I must be on IV (oops confusing nomenclature).\r\n\r\nThis leaves us with the following info on the cubes\r\nI A,W\r\nII G,H,S,U\r\nIII C,E,J,N,O,X\r\nIV D,R,P,I\r\n\r\nNow look at cube I eliminating the two non-used letters, the 14 we now know are on other cubes and all the letters that share words on the list with A and W leaves us only six possible letters: A,W,B,L,M,T\r\n\r\nIn BOUY B is on I, U is on II and O is on III\r\nSo Y is on IV\r\n\r\nSimilarly in MUCK M is on I, U is on II and C is on III so K is on IV. This make six for IV (D,R,P,I,Y,K)\r\n\r\nWhich leave only F and V to fill the empty two sides of II\r\n\r\nThus the final cubes are as follows\r\n\r\nI A,W,B,L,M,T\r\nII G,H,S,U,F,V\r\nIII C,E,J,N,O,X\r\nIV D,R,P,I,Y,K \r\n',NULL,0);
INSERT INTO comment VALUES (8537,1112,2839,'FatBoy','please ignore','2003-10-10 10:15:20',3,'First off: by inspection Q and Z are not used\r\n\r\nGOAD and GROW indicate that A,D are on same cubes as R,W but HOAR tells us that A and R are not on same cube so D is with R and A is with W \r\nGOAD and HOAR indicate that G,D are on same cubes as H,R and since D is with R then G is with H\r\nCHAD and HOAR indicate that C,D are on same cubes as O,R and since D is with R then C is with O\r\n\r\nCHAD indicates that C, H, A and D must be on different cubes so we now know the following about the four cubes (I through IV for convenience)\r\n\r\nI contains A,W\r\nII contains G,H\r\nIII contains C,O\r\nIV contains D,R\r\n\r\nStarting with cube III if we eliminate from the alphabet the two unused letters (Q,Z), the six letters we know are on other cubes and all the letters that share words on the list with C or O we are left with seven possible letters (including C and O which we know are on the cube) they are:\r\nC,E,J,N,O,V,X\r\nBut since V is in both NAVY and VIBE we can eliminate it because its presence would rule out N and E leaving us with less than six. So cube III is labeled C,E,J,N,O and X.\r\n\r\nConsider OPTS and TURN since O and N are both on cube III this tells us that P,S are on same cubes as U,R. but JUMP has both U and P so P is with R (on cube IV) and S is with U. AXIS tells us that S can’t be with A so S,U must be on cube III\r\n\r\nNow in the word AXIS A is on I, S is on II, X is on III\r\nWhich means I must be on IV (oops confusing nomenclature).\r\n\r\nThis leaves us with the following info on the cubes\r\nI A,W\r\nII G,H,S,U\r\nIII C,E,J,N,O,X\r\nIV D,R,P,I\r\n\r\nNow look at cube I eliminating the two non-used letters, the 14 we now know are on other cubes and all the letters that share words on the list with A and W leaves us only six possible letters: A,W,B,L,M,T\r\n\r\nIn BOUY B is on I, U is on II and O is on III\r\nSo Y is on IV\r\n\r\nSimilarly in MUCK M is on I, U is on II and C is on III so K is on IV. This make six for IV (D,R,P,I,Y,K)\r\n\r\nWhich leave only F and V to fill the empty two sides of II\r\n\r\nThus the final cubes are as follows\r\n\r\nI A,W,B,L,M,T\r\nII G,H,S,U,F,V\r\nIII C,E,J,N,O,X\r\nIV D,R,P,I,Y,K \r\n',NULL,0);
INSERT INTO comment VALUES (8538,1220,1567,'Bryan','An elegant solution','2003-10-10 11:04:39',0,'I think what we need to do here is move this puzzle from the \"Geometry\" category to the \"Paradoxes\" category :P',NULL,0);
INSERT INTO comment VALUES (8539,1112,3172,'SilverKnight','re: please ignore','2003-10-10 11:14:07',4,'FatBoy,\r\n\r\nI think you may have answered this before, but I can\'t recall the reason, and can\'t seem to find it....\r\n\r\nWhy is it that you litter all these problems with your solutions, ignoring people\'s previous posts?\r\n\r\nI completely understand going through earlier problems, and solving them, on your own, without reading other people\'s solutions. But why post for everyone to see?\r\n\r\nIt clutters up the comment lists and generally doesn\'t add anything for anyone other than you (although I fail to see what it adds for you).\r\n\r\nMight you simply solve the problem... on your own, in ink. And then compare for yourself (without our having to see it)?\r\n\r\n--- SK',8537,0);
INSERT INTO comment VALUES (8540,1317,3778,'Hipnox','re(2): base 5?','2003-10-10 11:58:52',0,' Gamer said in his firts post we should to convert symbols, so we don\'t need to do it, but is it a way to solve it. \r\nThe problem is that we don\'t know what convert. In other words we dont know if each / \\ or - is a number or a group of / \\ or - is a number.',8535,0);
INSERT INTO comment VALUES (8541,1112,2839,'FatBoy','re(2): please ignore','2003-10-10 12:35:31',0,'Silver Knight,\r\n\r\nWho died and made you the “comment cop” of Flooble?\r\n\r\nAt first it was kind of funny but now its just pathetic.\r\n\r\nI clearly label my posts (when I see other solutions posted) “please ignore.” I do this to that you (you specifically as you are the only one ever to have complained) will know that I am just solving the puzzle and not be tempted to open and read a posting that will “not add anything” to the general discussion.\r\n\r\nFor pity’s sake! this puzzle is two months old, the official solution has been posted. I can not believe that you went to the trouble to go to a puzzle that you KNEW had been solved, read a posting labeled “please ignore” that you knew (or should have known since you seem reasonably bright) would contain nothing more than a solution, just to be irritated.\r\n\r\nBACK OFF\r\n\r\nIf my postings are bothering the management of Flooble, I am sure that Levik will let me know and I will gladly stop. If my postings are irritating a reasonable number of Flooble users, they are welcome to post a message to that effect either here or in the forums and I will stop. Until that time, I will continue to enjoy Flooble in my (I believe) harmless way.\r\n\r\nAs for you (if you would like a bit of advice, if you see a posting labeled “please ignore” ignore it like everyone else. If you choose not to ignore it, that’s fine too. Read it, sneer at it, tell all your friends what an obvious moron I am, post a sneering condescending criticism if you want (It’s a pretty open minded site and most people figure you should be able to post what you want) but give me a break. I am not going to stop enjoying this excellent site until either the management or my fellow users give me reason to.\r\n',8539,0);
INSERT INTO comment VALUES (8542,1112,3172,'SilverKnight','re(3): please ignore','2003-10-10 13:23:30',0,'Um... er... uh...\r\n\r\nI didn\'t go back two months... I often check the \"new comments\" as you obviously did, too.\r\n\r\nTo answer your questions:\r\nNo one died (as far as I know), and I\'m not a cop... I merely asked you why you do this (and you conveniently didn\'t answer ;-) ).\r\n\r\nAnd if you choose to scan the forums, I\'m sure you\'ll find I\'m not the only one with this sentiment.\r\n\r\nInterestingly, \"At first it was kind of funny but now it\'s kinda pathetic\" is what I thought, when I saw you doing something that so clearly cried out for attention.\r\n\r\nSo, I\'ll ask for a second time today (just for giggles): since it obviously clutters up posts (particularly when we are scanning archives or checking new comments... what is it that you get out of it that you couldn\'t also get by writing down your solution in ink and checking without posting to the site?\r\n\r\nCheers!',8541,0);
INSERT INTO comment VALUES (8543,1319,3172,'SilverKnight','cheesy solution...','2003-10-10 14:52:40',3,'... but it demonstrates the fact.\r\n\r\nIf you perform the long division of 1001 by 7, you find 143.\r\n\r\nIf you perform the long division of 1002001 by 7, you find 143143.\r\n\r\nIf you perform the long division of 1002002001 by 7, you find 143143143.\r\n\r\nIn short, if you look at the mechanism of doing the long division (go ahead and actually carry out the long division steps), you find that the insertion of every extra \'200\' in the middle, just repeats exactly the same steps as the previous \'200\'.\r\n\r\nHere\'s the cycle:\r\nNamely you have a remainder of 2, drop the new 2 down (22), and 7 goes into 22 3 times with a remainder of 1. Drop the the 0 down (10), and 7 goes into 10 1 time with a remainder of 3. Drop the 0 down (30), and 7 goes into 30 4 times with a remainder of 2, bringing us back to the beginning of the cycle.\r\n\r\nThis continues until you end with the final \'1\' instead of a 2. With the final \'1\', you have (21) and the process ends with a 3.\r\n\r\nClearly, since this is always divisible by 7, the number is composite.\r\n\r\nI look forward to seeing someone\'s more formal solution.\n\nEdited on October 10, 2003, 2:54 pm',NULL,0);
INSERT INTO comment VALUES (8544,1319,3735,'Nick Hobson','Divisibility','2003-10-10 15:20:14',3,'Each number is divisible by 11.\r\n\r\nTo see why, recall the divisibility test for 11: the sum of the even power decimal digits minus the sum of the odd power digits must itself be divisible by 11.\r\n\r\nExample: 3828.\r\nEven digits - odd digits = 16 - 5 = 11.\r\nHence 3828 is divisible by 11.\r\n\r\nApplying this test to the numbers above, notice that, since the double zeroes occupy an odd and an even position, they can be removed without affecting divisibility by 11. So we obtain:\r\n\r\n121,\r\n1221,\r\n12221,\r\n122221.\r\n\r\nNow it is a simple matter to confirm that the first two numbers are divisible by 11. It follows that the other numbers in the series are divisible by 11, since they can be constructed by inserting a number of double twos (one even and one odd digit, again) into one of 121 or 1221.\r\n\r\n\r\nYou can also show that each number is divisible by 1001 by setting x = 1000 in the identity:\r\n\r\n(1 + x)(1 + x + ... + x^n) = 1 + 2x + ... + 2x^n + x^(n+1).',NULL,0);
INSERT INTO comment VALUES (8545,1319,1920,'Brian Smith','A solution','2003-10-10 15:22:26',0,'The first term is a multiple of 1001 (1002001 = 1001*1001). The nth term of the sequence can be expressed as a recursion: t(n) = 1000*t(n-1)+1001. t(n) is a multiple of 1001 if and only if t(n-1) also is a multiple of 1001. Since t(1) is a multiple of 1001 then t(2) is a multiple of 1001. Since t(2) is a multiple of 1001 then t(3) is a multiple of 1001. Etc...',NULL,0);
INSERT INTO comment VALUES (8546,1319,1626,'Gamer','re: A solution','2003-10-10 15:57:28',0,'This was something cool I thought up, but it was better suited for a morning problem because its \"All are divisible by 1001\" solution is so easy. :) ',8545,0);
INSERT INTO comment VALUES (8547,638,3735,'Nick Hobson','Divisibility','2003-10-10 16:20:38',3,'Milestones 1 and 2 tell us:\r\n(a) the speed is a multiple of 9; and\r\n(b) the speed is less than 90.\r\n\r\nMilestones 1 and 3 tell us:\r\n(c) the speed is a multiple of 5.\r\n\r\nPutting these results together, the speed is a multiple of 45 and is less than 90.\r\n\r\nHence the speed is 45 m.p.h.',NULL,0);
INSERT INTO comment VALUES (8548,638,3172,'SilverKnight','re: Divisibility','2003-10-10 16:29:47',0,'Nick,\r\n\r\nWhile your points are true, it may not be obvious WHY it\'s true. You might want to show why Milestones 1 and 3 imply (c)... and why the Milestones 1 and 2 imply (a) and (b).\r\n\r\nOtherwise... it is roughly equivalent to saying...\r\nMilestones 1, 2, and 3 tell us the speed is 45 mph.\r\n\r\nTrue.... but not all that explanatory.',8547,0);
INSERT INTO comment VALUES (8549,1319,3172,'SilverKnight','re: Divisibility','2003-10-10 16:33:58',0,'ooohhhh I\'m in such a nitpicking mood today...\r\n\r\nSimilar to your \"Formula None Racer\" problem... I suggest that you demonstrate why the divisibility test, you refer to, works. Or at least provide a reference to it on the web (I saw plenty of those).',8544,0);
INSERT INTO comment VALUES (8550,638,3735,'Nick Hobson','re(2): Divisibility','2003-10-10 16:40:52',1,'Yes, I could have posted a fuller explanation. In fact, I did just that earlier this evening for another puzzle based on divisibility rules.\r\n\r\nIn this case, a number of previous posts had already explained the relevant divisibility rules. So I decided to present a shorthand solution that showed how to derive the speed without deriving the milestones.',8548,0);
INSERT INTO comment VALUES (8551,638,3172,'SilverKnight','re(3): Divisibility','2003-10-10 16:49:34',0,'That makes sense... but please reference (preferably through a hyperlink) the previous work/comment on which you are basing your conclusions (unless you are replying to that very comment, of course).',8550,0);
INSERT INTO comment VALUES (8552,1319,1626,'Gamer','re(2): Divisibility','2003-10-10 17:02:44',0,'When you do the multiplication of 1001 times 1001, 1001001, so on, you will see this: [deleted] Edited on March 1, 2004, 2:06 pm',NULL,1);
INSERT INTO comment VALUES (12336,1526,5858,'slsl','A switch solution - maybe not the optimal one...','2004-03-01 14:18:40',0,'a3b2, e3d2, d2b4, b2d4, d4e3, a1b2, b2c1, e1c3, c3a1, b4c3, c1a3, e3c1, c3d4, a3b4, b4e1, c1d2, d4b2, b2a3, d2e3\r\n\r\nSorry for the crude layout. I double-checked it, and I think that this is the way to switch the places of black and white figures. I\'m not sure if it\'s the only way (the symetric doesn\'t count ;) ), and if it\'s the optimal solution to the problem. Anyone?',NULL,0);
INSERT INTO comment VALUES (12337,1651,5285,'Ady TZIDON','it is either or','2004-03-01 15:37:28',3,'It is either SRQ , RQS or QSR. -OTHERWISE CONTRADICTION\r\nSince R is recognized the solution is unique,if the Romanian spoke first then RQS, if 2nd SRQ, if 3rd QSR.',NULL,0);
INSERT INTO comment VALUES (8564,1317,1626,'Gamer','re(2): base 5?','2003-10-10 21:55:32',0,'I never said your arrangement wouldn\'t be useful, I only said it wouldn\'t be more useful. What Hipnox has done is more useful, yet it doesn\'t require pre tags or any such things.\r\n\r\nNote to Hipnox: Your numbers aren\'t correct... a \\\\/ is not a 4; it is another number instead.',8535,0);
INSERT INTO comment VALUES (8565,1220,3820,'Joseph ODonnell','Introductory Solution','2003-10-11 08:20:45',3,'My brother thinks this may be to solution to the geometical problem which you presented. He has asked that I post it on your web site to entertain comments.\r\n\r\nPlease share my solution on the site. I\'d be \r\ninterested to know what they think.\r\n\r\nBasically, the probability is SQRT(3)/2.\r\n\r\nThe reason is that the length of chords vary from \r\n0 (really a line tangent to the circle) to 2r, the diameter. If you start at the tangent line and draw chords perpendicular to a radius line, the chords will be less than zero until you hit some point on the radius, between the edge of the circle and the center. After that, your chords will be greater than the radius as you approach the center where the length of the chord equals the diameter. \r\n\r\nThe proportion of the distance from the center of \r\nthe circle to the point where a chord drawn perpendicular to the radius line is the same length as the radius, divided by the length of the radius, is the probability that a chord drawn \r\nperpendicular to the radius line is longer than \r\nthe radius.\r\n\r\nSince an infinite number of radii can be drawn \r\nfor a circle, we can assume an infinite number of chords that are perpendicular to each radius line. We also know that you cannot draw a chord in a circle that is not perpendicular to a radius line. For each radius line the proportions will stay the same, so the overall probability will\r\nlikewise remain the same.\r\n\r\nThus our problem is to find the point on a single \r\nradius line where a chord drawn perpendicular to the radius is equal to the radius. \r\n\r\n1. We draw a chord equal to the radius of the \r\ncircle and draw two radii, one from each end of the chord to the center of the circle. This forms an equilateral triangle, all sides being equal. So the angles at each corner of the triangle are 60 degrees, again by definition.\r\n\r\n2. We now draw a radius from the center of the \r\ncircle perpendicular to the chord. This line will bisect the chord and divide our equilateral triangle into two right triangles.\r\n\r\n3. Each right triangle is a 30-60-90 degree right triangle with hypotenuse = r and the short leg = r/2. By the definition of a 30-60-90 triangle, the long leg equals r * SQRT(3)/2.\r\n\r\n4. The proportion between the distance from the \r\ncenter of the circle to the point where the radius line bisects the chord and the radius of the circle is our probability. So we divide ...\r\n\r\n r * SQRT(3)/2 SQRT(3)\r\n --------------- = -------- = SQRT(3)/2\r\n r 2\r\n\r\nQED',NULL,0);
INSERT INTO comment VALUES (8566,648,1626,'Gamer','A recursive solution','2003-10-11 08:59:20',3,'I read that each number for n gift people followed a pattern: \r\n(1)Let the given number x between 100 and 1000 be represented by the 3 digits abc (which means x = 100a + 10b + c).\r\n(2)Mentally calculate the number 2x. Since x ranges from 101 to 999, 2x ranges from 202 to 1998 and hence has a minimum of 3 and a maximum of 4 digits. let the number 2x be represented by the 4 digits ABCD where the leading digit A = 0 if 2x is a 3-digit number. (this means 2x = 1000A + 100B + 10C + D where A = 0 if 2x has only 3 digits.)\r\n(3)Juxtapose x with 2x on its right to come up with the 7-digit number\r\n<x><2x> = <abc><ABCD> = abcABCD.\r\n(4)Mentally divide this number by 6 and you get the answer from left to right. Multiplying the given 3-digit number mentally by 2, juxtaposing the given number on its right with twice the number (after adding a leading 0 if twice the number has only 3 digits), and dividing the resultant 7-digit number by 6 mentally can all be done under 10 seconds. For instance,\r\n(a)1667*101 = 101<0202>/6 = 1010202/6 = 168367;\r\n(b)1667*674 = 674<1348>/6 = 6741348/6 = 1123558; and \r\n(c)1667*999 = 999<1998>/6 = 9991998/6 = 1665333. \r\nHere is the basis for this method.\r\n1667 = 10002/6.\r\nSo, 1667*x = 1/6*(10002x) = 1/6*(10000x+2x)\r\nSince 202 ≤ 2x ≤ 1998, 2x has a minimum of 3 and a maximum of 4 digits, represented by the digits ABCD. 10000x has the number x followed by 4 zeroes at the end. so, it is a piece of cake to add 10000x to 2x to get the number 10002x. In terms of digits,\r\n10000x = abc0000 (since x has the digits abc),\r\n2x = 000ABCD, and \r\n10002x = abcABCD\r\nHence abcABCD divided by 6 is equal to 10002x/6 or 1667x, which is the answer we are looking for. ',NULL,0);
INSERT INTO comment VALUES (8599,1451,1183,'fwaff','Solution','2003-10-13 08:44:15',3,'Assuming that an \"either...or...\" statement precludes both events from being true, then the announcer\'s statement leaves the following possibilities:\r\n\r\nGIH (Greece won gold; Italy won Silver; Holland won bronze)\r\nHGI (Holland won gold; Greece won Silver; Italy won bronze)\r\nHIG (Holland won gold; Italy won Silver; Greece won bronze)\r\n\r\nWe are told that the Italian reporter cannot deduce the other teams\' places despite knowing Italy\'s position. This means that either GIH or HIG must be true, since HGI cannot be true.\r\n\r\nSimilarly, we are told that the Dutch reporter cannot deduce the other teams\' places despite knowing Holland\'s position. This means that either HGI or HIG must be true, since GIH cannot be true.\r\n\r\nTherefore it must be HIG that is true.\r\n\r\nSo Holland won gold, Italy won Silver and Greece won bronze.\r\n\r\nIf my original assumption regarding \"either...or...\" statements is invalid, then the announcer\'s statement permits that GHI is true. However, it is then the only one of the four possibilities where Holland win silver, therefore the Dutch reporter could deduce the other positions if he knew Holland finished second. ie the Dutch reporter\'s remark prevents GHI from being true and therefore the answer is unchanged.',NULL,0);
INSERT INTO comment VALUES (8600,824,3802,'Sheets','re: easy? or did I miss a bit?','2003-10-13 08:48:43',0,'What if the ice melted b4 reaching.....he was surrounded by sand',5382,0);
INSERT INTO comment VALUES (8601,921,3802,'Sheets','','2003-10-13 08:56:46',0,'Yep accept the bet and when he goes for yr drink grab his fiver + drink....gulp it down and pocket the money.....SIMPLE',NULL,0);
INSERT INTO comment VALUES (8602,573,3802,'Sheets','Erm....','2003-10-13 09:09:59',1,'Thers a number of solutions to this????',NULL,0);
INSERT INTO comment VALUES (8603,1220,1920,'Brian Smith','re: An elegant solution','2003-10-13 09:46:13',0,'This problem is a variation of \"Bertrand\'s Paradox\". There are three ways of generating random chords, all of which give different probabilities.',8538,0);
INSERT INTO comment VALUES (8604,686,3840,'Hal9000','Solution','2003-10-13 09:57:18',0,'Are you sure it isn\'t because he was the killer, his name is Clem Kadiddlehopper, perhaps excessive childhood ridicule drove him to it.',NULL,0);
INSERT INTO comment VALUES (8605,1219,3840,'Hal9000','Pshaw','2003-10-13 10:12:18',0,'While I am still working on the answer I resent the implication Shannon Jones is an obscure golfer. Shannon Jones from New South Wales is the Champion of the Power Play Charters Pro Am. Listen and learn his humble words of victory, \"The Power Play Charters Pro Am Tournament is a prestigious and challenging event and I am honoured to win amongst such strong competition,” Kindly retract your discourteous comments, we should look to Mr. Jones for his sagacious tutelage if nothing else.\r\n',NULL,0);
INSERT INTO comment VALUES (8606,1451,872,'pleasance','re: Solution','2003-10-13 11:09:26',0,'I Agree with fwaff for the \'xor\' case (either ... or, but not both), but not for the other case. If both can be true, the announcer leaves us with 4 possibilities:\r\nGIH\r\nHGI\r\nHIG\r\nGHI\r\nThe Italian reporter\'s comment then adds no information at all, since there are two possibilities of Italy being silver, and two of Italy\'s being bronze, i.e., in any case he could not have deduced all the positions.\r\nThe Dutch reporter\'s comments leave us with HGI or HIG, with no way to deduce the right answer.\r\n\r\nI therefore deduce that \'xor\' was intended! So the solution is HIG (Holland gold, Italy silver, Greece bronze).\n\nEdited on October 13, 2003, 11:10 am',8599,0);
INSERT INTO comment VALUES (8607,1219,3430,'pat','shoot the bogie man','2003-10-13 11:24:46',0,'too broadly putt',NULL,0);
INSERT INTO comment VALUES (8608,1219,3856,'Petio Petev','Solution','2003-10-13 11:58:26',0,'Looking at the numbers it happened that no ideia came to my head. Then I looked at the title of the problem and... voilla! Those are the number of ways to make N points in american football.\r\nThat means the answer we are searching for is 5.',NULL,0);
INSERT INTO comment VALUES (8609,1423,3224,'Lee','none','2003-10-13 12:26:47',0,'mohan,\r\nI think we all see your method for multiplying by 10002 (push the original digits up 4 places (x10000) and tack on 2x the number)and that it is straight-forward. What I, for one, can\'t figure is how dividing a 7 digit number, that you\'ve only just derived (and therefore hanging around nervously in your short term memory) by 6 is easy.\r\nOn paper it is easy but in your head?\r\ne.g. 6741348/6 = \r\n\"okay, six into six goes once ..\"1\"\r\nsix into seven goes once with 1 remainder..\"1\"\r\nsix into fourteen goes twice with 2 remainder..\"2\"\r\nsix into twenty-one goes thrice with 3 remainder..\"3\"\r\nsix into thirty-three goes five times with 3 remainder..\"5\"\r\nsix into thirty-four goes five times with 4 remainder..\"5\"\r\nsix into forty-eight goes eight times exactly..\"8\"\"\r\n\r\nPossibly, but I don\'t think my mind could cope.\r\nAlso the original question is how the poster, nellie, does it. As s/he claims not to fully understand how they do it, it seems unlikely that they go through this memorable long-division procedure. I feel it\'s along the lines of what Charlie and Gamer have considered and has more to do with \'patching\' numbers together than doing a conventional approach \r\nJust my 2p',NULL,0);
INSERT INTO comment VALUES (8610,1242,3546,'RoyCook','re: simple','2003-10-13 12:55:06',0,'Triangle acd is NOT equilateral!',8573,0);
INSERT INTO comment VALUES (8611,1451,3858,'Amy','solution','2003-10-13 13:00:51',3,'1. Greece\r\n2. Italy\r\n3. Holland',NULL,0);
INSERT INTO comment VALUES (8612,1319,3546,'RoyCook','re: Simple solution, with no words!','2003-10-13 13:11:46',0,'Unfortunately, your simple solution without words does not seem to me to be a solution at all, at least not without some words to explain it. Lets call a number a 1-2 number if it begins with 1, ends with 1, has any number of 2\'s in the middle, and \'adjacent\' 1\'s and 2\'s are always separated by two 0\'s. Let us call a number a 1-1 number if it is the result of replacing every 2 in a 1-2 number with a 1. Then your computation indicates in a schematic way that, given any 1-1 number, if we multiply it by 1001, we get a 1-2 number. What is required by the problem, however, is (something like) a demonstration that, given any 1-2 number, it is the multiple of a 1-1 number and 1001.\r\n\r\nTo see the difference, compare the idea of proving that the sum of any two primes greater than 2 is an even number greater than 4 (easy), versus the idea of proving that every even number greater than 4 is the sum of two primes greater than 2 (still not proven, by anyone!). \r\n\r\nOf course, one can easily adapt your computation to a correct solution, but, unfortunately for your subject heading, such an adaptation requires some words.',8569,0);
INSERT INTO comment VALUES (8613,1319,3546,'RoyCook','re: Simple solution, with no words!','2003-10-13 13:12:52',0,'Unfortunately, your simple solution without words does not seem to me to be a solution at all, at least not without some words to explain it. Lets call a number a 1-2 number if it begins with 1, ends with 1, has any number of 2\'s in the middle, and \'adjacent\' 1\'s and 2\'s are always separated by two 0\'s. Let us call a number a 1-1 number if it is the result of replacing every 2 in a 1-2 number with a 1. Then your computation indicates in a schematic way that, given any 1-1 number, if we multiply it by 1001, we get a 1-2 number. What is required by the problem, however, is (something like) a demonstration that, given any 1-2 number, it is the multiple of a 1-1 number and 1001.\r\n\r\nTo see the difference, compare the idea of proving that the sum of any two primes greater than 2 is an even number greater than 4 (easy), versus the idea of proving that every even number greater than 4 is the sum of two primes greater than 2 (still not proven, by anyone!). \r\n\r\nOf course, one can easily adapt your computation to a correct solution, but, unfortunately for your subject heading, such an adaptation requires some words.',8569,0);
INSERT INTO comment VALUES (8614,1451,3859,'Isaac','Solution...Really','2003-10-13 13:40:38',3,'While these people are all posting new ideas, I\'m going to have to say I agree with Amy\'s post.\r\n\r\nBoth reporters heard this, and if either one was in first, they\'d know that Greece wasn\'t. And they wouldn\'t be able to say that they didn\'t know where either one was\r\n\r\nItaly knows its position. It doesn\'t know Greece\'s. Italy can\'t have gold.\r\n\r\nHolland knows its position, it doesn\'t know Greece\'s or Italy\'s. It can\'t be first either.\r\n\r\nGreece can either be in first, or Holland can be better than Italy, right? Well, since both don\'t know for sure where Greece stands, neither one can have the Gold, meaning Greece does.\r\n\r\nAnd if Greece has the gold, Holland can\'t be better than Italy.\r\n\r\nThe order is as Amy stated. Greece, Italy, Holland for the Gold, Silver, and Bronze, respectively.',NULL,0);
INSERT INTO comment VALUES (8615,1451,3807,'DrBob','I\'m with fwaff on this','2003-10-13 14:23:44',0,'Holland could not have come third. If it did, then Holland was not better than Italy, & so Greece must have gold. The Dutch reporter would then have deduced the order Greece, Italy, Holland (unless of course he wasn\'t all that bright).\r\nItaly could not have won; because then Holland was not better than Italy, and so Greece must have won (I\'m assuming there were no ties). If Italy was last, Holland was better than Italy, and so Greece did not win gold - this would allow the Italian reporter to deduce the order Holland, Greece, Italy. So Italy must have been second (the reporter then wouldn\'t know who was above and below).\r\nIf Holland is not last, & not second (because Italy is) it must have wone gold.\r\nThis gives the order: Holland, Italy, Greece.',NULL,0);
INSERT INTO comment VALUES (8616,1220,1301,'Charlie','re(2): An elegant solution','2003-10-13 15:01:42',0,'There are probably even more than 3 ways of generating random chords. The most popular have already been mentioned: a random arc length (or central angle) uniformly distributed; a uniformly distributed choice of one point within the circle to serve as a center point of the chord; a line chosen in a uniform distribution of parallel lines intersecting the circle (along a radius or diameter). Another way would be a uniform distribution of angles measured from a point on the circumference. In fact a uniform angular distribution could be made about any point, from the center out to infinity, the latter case being the parallel line case. You could choose random points on two parallel lines on either side of the circle and have them intersect the circle in two resulting points, etc. They would result in different probabilities.',8603,0);
INSERT INTO comment VALUES (8617,1451,1171,'nikki','re: Solution...Really','2003-10-13 15:20:24',0,'\"Both reporters heard this, and if either one was in first, they\'d know that Greece wasn\'t. And they wouldn\'t be able to say that they didn\'t know where either one was\"\r\n\r\nI disagree. If either Italy or Holland won gold, then one of the reporters would know Greece did not win gold - that I agree with. However, let\'s say Holland won gold. Since the Dutch reporter would know Greece did not win gold, he/she would know that the \"Holland was better than Italy\" part must be true. Well, Italy could win either Silver or Bronze and still satisfy this condition. So the Dutch reporter could still say \"hmmm, I don\'t know what places the other two countries got.\"\r\n\r\nSo it is not necessarily true that Greece had to win Gold.\n\nEdited on October 13, 2003, 3:22 pm',8614,0);
INSERT INTO comment VALUES (8618,649,2231,'Trevor Leitch','Solution','2003-10-13 15:25:11',3,'5/8\r\n\r\nThe probability that the second marble drawn is black is an expected value; it\'s equal to Pr(bag 1 was selected)Pr(a black marble will be drawn from bag 1) plus Pr(bag 2 was selected)Pr(a black marble will be drawn from bag 2).\r\n\r\nLet f(x)= Pr(bag x was selected) and g(x)= Pr(a black marble will be drawn from bag x). Then:\r\ng(1)=.75\r\ng(2)=.25\r\n\r\nNow, f(x) is also equal to [Pr(bag x would be selected AND a black marble drawn)/ Pr(a black marble would be drawn)]. The top part of this equation is (.5)(g(x)), and the bottom is ∑(.5)(g(x)) for all values of x. Thus:\r\n∑(.5)(g(x)) = (.5)(.75) + (.5)(.25) = .5\r\n(.5)(g(1)) = (.5)(.75) = .375\r\n(.5)(g(2)) = (.5)(.25) = .125\r\nf(1) = (.375)/(.5) = .75\r\nf(2) = (.125)/(.5) = .25\r\n\r\nThe final probability is given by ∑f(x)g(x) for all values of x, or simply f(1)g(1) + f(2)g(2). Thus:\r\nPr(second marble is black) = (.75)(.75) + (.25)(.25) = 9/16 + 1/16 = 10/16 = 5/8.\r\n\r\nSorry this was so long, but I didn\'t want to skip over any steps...\r\n(Whew...)',NULL,0);
INSERT INTO comment VALUES (8619,649,1171,'nikki','Could be wrong','2003-10-13 15:47:36',1,'I\'m not great at probability problems, so I won\'t be surprised if I am wrong. When I was reading Trevor\'s solution, I got all confused - so even though my answer is different, I\'m definitely not trying to say Trevor is wrong.\r\n\r\nThat said, I think the answer is 5/16. I kind of read the problem as \"given these bags, what is the probability that two black marbles will be pulled in a row?\" Already I could be wrong by thinking about it this way.\r\n\r\nI saw the answer to this problem as \"1/2*(probability of pulling two from Bag 1) + 1/2*(probability of pulling two from Bag 2)\" So I calculated 1/2*3/4*3/4 + 1/2*1/4*1/4 = 9/32 + 1/32 = 5/16.\r\n\r\nMy version of the problem ignores that we know for certain that a black marble was pulled the first time. But then would that make my calculations 1/2*1*3/4 + 1/2*1*1/4 = 3/8 + 1/8 = 1/2? That doesn\'t make sense to me either.\r\n\r\nPlease be nice when you tell me what I did wrong =) Thanx!',NULL,0);
INSERT INTO comment VALUES (8620,649,1575,'DJ','Solution','2003-10-13 15:55:18',3,'5/8\r\n\r\nTo me, the simplest approach would be to contruct a probability tree diagram. Let A be the event that you chose the bag with three black marbles, and B is the event that you chose the bag with three white marbles.\r\n Thus, the sum of the numbers of the n-th row works out to be (n-1)n+1 plus n(n+1)-1, times n, which is n cubed.',NULL,0);
INSERT INTO comment VALUES (8675,10,1920,'Brian Smith','re: Not that long - Too slow','2003-10-15 09:44:25',0,'There is a faster method which takes 17 minutes.',8667,0);
INSERT INTO comment VALUES (8676,1458,1171,'nikki','Possible?','2003-10-15 09:48:02',3,'Well, the fact that (1) this is a cigarette, (2) it was specifically pointed out that it is standing on its butt, and (3) the question was worded \"How can you make it DROP\" instead of \"fall over\" for example, here is my guess:\r\n\r\nGet out your handy dandy magnifying glass, hope there is enough sunlight available, and use it burn the tip of the cigarette. Then the end of it will \"drop\" as it burns down.\r\n\r\nI don\'t think you can just light a match or a lighter and hold it near the end of the cigarette because then you are using the warm gas to heat it up.\r\n\r\nPhotons aren\'t exactly a solid, liquid or gas, right? I think this is a possible solution.\r\n\r\nLater!',NULL,0);
INSERT INTO comment VALUES (8677,1458,3660,'ratsnstuff','re: Possible?','2003-10-15 10:09:11',0,'Is a flame gas? Or is it plasma? If not, what is plasma? \r\n\r\nLets assume a flame is plasma. Then you could also take out your trusty ZIPPO (tm probably) and light it. In terms of the ciggy falling over or dropping... You want to destabilise it, so light it on one side near the butt. Think that should work.',8676,0);
INSERT INTO comment VALUES (8678,1218,3196,'Dan','Answer','2003-10-15 10:35:35',0,'CUBE 1: A B J T U Y\r\nCUBE 2: E H L M N Z\r\nCUBE 3: D F G K O R\r\nCUBE 4: C I P S V W ',NULL,0);
INSERT INTO comment VALUES (8679,1242,3878,'sean','re(2): simply put','2003-10-15 11:54:57',0,'sorry should finish 125sqrt=11.180339...',8661,0);
INSERT INTO comment VALUES (8680,1220,1575,'DJ','re(2): Different Approach (Continued)','2003-10-15 12:17:35',0,'It doesn\'t matter if you have 180 chords or 1800 chords, the number is still finite; we need to examine the entire infinite set of possible chords. As it turns out, as the number of chords approaches infinity, the probability approaches 2/3 (66.66...%).\r\n\r\nThe problem with this is assuming that the distribution of angles from a single point on the circumference is the same distribution of chords over the entire circle. In other words, you are assuming the same number of chords between 1° and 5° as between 76° and 80°, but how do you know that this is true for the entire infinite set of possible chords.\r\nAs Aaron pointed out, the chords closer to 0° and 180° are \'scrunched\' together, while the chords around 90° are more spread out. That would seem to imply a different distrubution to accurately represent the entire range of possible chords.',8630,0);
INSERT INTO comment VALUES (8681,1458,1567,'Bryan','re(2): Possible?','2003-10-15 12:39:39',0,'Uh, let\'s not assume a flame is plasma, since it is not (it\'s just hot gas in the process of oxidizing). I think nikki has the right idea. Certain lasers could accomplish this task as well.',8677,0);
INSERT INTO comment VALUES (8682,1458,1171,'nikki','re(2): Possible?','2003-10-15 12:58:49',0,'\"In terms of the ciggy falling over or dropping... You want to destabilise it, so light it on one side near the butt.\"\r\n\r\nBut the butt doesn\'t burn, so that wouldn\'t make it topple over, would it?\r\n\r\nEnh, I think we all get the idea =)',8677,0);
INSERT INTO comment VALUES (8683,1423,2489,'nellie','gamer\'s reply','2003-10-15 13:23:50',0,'Hi - I am unfamiliar with the site processes. Are they set out somewhere?\r\n\r\nOthers have made attempts at solutions, and I have enjoyed watching their thought processes.\r\nI am uncertain whether they will have seen my solution. How do they see this?\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (8684,1458,3818,'A','re(3): Possible?','2003-10-15 15:06:02',0,'cigarettes are made to burn; why not light it up?',8682,0);
INSERT INTO comment VALUES (8685,1322,3172,'SilverKnight','solution','2003-10-15 15:38:08',3,'Proper order: A < B < C\r\nLikelihood of winning: 91/162\r\n____________________\r\n\r\nProof:\r\n\r\nLet\'s call the first prize A, the second prize B, and the third prize C.\r\n\r\nAssumption: each prize is equally likely to fall anywhere within its range\r\n\r\nA:\r\n1 - 0500-1000\r\n2 - 1000-1500\r\n3 - 1500-2000\r\nB:\r\n4 - 1000-1500\r\n5 - 1500-2000\r\n6 - 2000-2500\r\nC:\r\n7 - 1500-2000\r\n8 - 2000-2500\r\n9 - 2500-3000\r\n\r\nThere are 3x3x3=27 equally likely regions that these could fall in, and we can describe each region as an ordered triplet. These regions can be divided up into 4 groups of size 10, 10, 6, and 1.\r\n\r\nThe first group consists of those 10 regions that unambiguously guarantee a win (+10).\r\n{1, 4, 7} {1, 4, 8} {1, 4, 9} {1, 5, 8} {1, 5, 9}\r\n{1, 6, 9} {2, 5, 8} {2, 5, 9} {2, 6, 9} {3, 6, 9}\r\n\r\nThe second group consists of those ten regions where A is DEFINITELY less than B and C \r\n\r\n-or- where C is DEFINITELY greater than A or B. In these regions the other \r\n\r\ntwo will be in the proper order 1/2 of the time for a win (10/2 = +5):\r\n{1, 5, 7} {1, 6, 8} {2, 4, 7} {2, 4, 8} {2, 4, 9}\r\n{2, 5, 7} {2, 6, 8} {3, 5, 8} {3, 5, 9} {3, 6, 8}\r\n\r\nThe third group consists of those six regions that unambiguously guarantee a loss (+0).\r\n{1, 6, 7} {2, 6, 7} {3, 4, 7} {3, 4, 8} {3, 4, 9} {3, 6, 7}\r\n\r\nAnd the final group consists of the one region where A, B, and C all fall within 1500-2000. It is equally likely that we have them any of the six possible orders: \r\n\r\nABC, ACB, BAC, BCA, CAB, CBA, but only ABC will give a win (+1/6):\r\n{3, 5, 7}\r\n\r\nSo, totalling up, we have: 10 + 5 + 1/6 = 91/6\r\n\r\nPutting this over the 27 possible regions we have:\r\n(91/6) / 27 = 91/162\r\n\r\nSince this is greater than 50%, any other possibility is less than 50%. Therefore this has the greatest likelihood to occur.\n\nEdited on October 15, 2003, 3:42 pm',NULL,0);
INSERT INTO comment VALUES (8686,1322,1575,'DJ','Full Solution','2003-10-15 16:24:49',3,'You should put the prizes in the order they are presented with a chance of winning of 91/162 (around 56.17%).\r\n\r\nTo achieve this, I put the prices into ranges of $500, like so:\r\n Since AB and (AB-1) are relatively prime to each other, 1/(AB-1) must be a non-repeating fraction, so AB-1 must divide 100, which allows just a few values.\r\n Running through those values, AB=26 solves the problem.',8890,0);
INSERT INTO comment VALUES (8897,1475,3977,'Bill','Possibility','2003-10-24 11:59:50',0,'He flew, not crossing any land borders. US does not control the pacific ocean.',NULL,0);
INSERT INTO comment VALUES (8898,1475,3430,'pat','interesting','2003-10-24 12:25:30',0,'west east south north... sometimes are the same...',NULL,0);
INSERT INTO comment VALUES (8899,1324,3172,'SilverKnight','I know I\'m reaching...','2003-10-24 16:15:17',1,'(1)\r\n... but if we\'re allowed to work in four dimensions, this becomes trivial.\r\n_____\r\n\r\n(2)\r\nI read the problem to indicate the larger cube must be 3x3x3. But if the larger cube is allowed to be 2x2x2, for example, then we can shuffle the cubes near each other, and leave 13 on one side, 13 (including the larger cube) on the other side... and one cube in the middle.... then removing that one cube solves the riddle.',NULL,0);
INSERT INTO comment VALUES (8900,1324,1171,'nikki','Slow solution','2003-10-24 16:20:51',1,'First, I assume the 27 small cubes will need to be the same size, but not necessarily identical.\r\n\r\nWhat if I had 26 wooden cubes, 1 inch on a side, and 1 cube of ice, 1 inch on a side? Then I could place 9 wooden cubes on a table, 8 wooden cubes plus the ice cube on the next layer (with the ice in the middle), and 9 more wooden cubes on top of that.\r\n\r\nThen I just sit and wait. Since the cubes are not perfect, there will be some gaps between them and the water can come dribbling out onto the table. You only said I couldn\'t move or change the OUTER cubes.\r\n\r\nHmmmm, but then the top cube would fall down on its own. Does that violate the problem?\r\n\r\nIsn\'t there something you can do to a sugar cube to make it mostly gone, but the outer surfaces of the structure are still there. That would allow the top cube to be supported while MOST of the middle cube was removed.\r\n\r\nMy only last thought is a variation on the ice cube. If the ice cube were made around a wire frame that would stay behind and support the top cube after the melting occurred. Of course, this still means that only MOST of the cube was removed.\r\n\r\nI wonder if I\'m even close to the right track =)\r\n\r\nLater!\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (8901,1324,3172,'SilverKnight','re: Slow solution','2003-10-24 16:26:46',0,'oh no... not another ice melting problem!!!!\r\n\r\nj/k :-)',8900,0);
INSERT INTO comment VALUES (8902,1324,1626,'Gamer','Hints:','2003-10-24 16:56:22',2,'My first request would be anyone who knew the answer to this while it was still in the queue not to post it. :)\r\n\r\nSecond of all, I will say that all the small cubes mentioned in the beginning of this problem are equivalent, but not equivalent to the cube in the middle you take away',8901,0);
INSERT INTO comment VALUES (8903,1324,3172,'SilverKnight','re: Hints:','2003-10-24 17:00:27',0,'Gamer, if your comment was directed at me, and the answer is... the middle cube is ice... well... I didn\'t \"give it away\"... Nikki already suggested that in the second comment.\r\n\r\nBut, more than that, I am still a student. I don\'t have access to the queue, so I couldn\'t possibly have seen the answer. (Even if I did, I wouldn\'t dream of revealing the solution if I had prior access to it.)',8902,0);
INSERT INTO comment VALUES (8904,656,1626,'Gamer','Ideas','2003-10-24 17:02:25',0,'Check out the differences between the terms.\r\n\r\n1 2 6 12 6 12 12\r\n\r\nIt does one time with 1 and 2 seperated, then with them together. Then it does two 12s, so I would propose 54 56\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (8905,1463,1626,'Gamer','Hint:','2003-10-24 17:04:37',0,'I have looked at the solution, and this is not really satisfying in my opinion.\r\n\r\nThe hint I will give is the sequence is the sum of two other sequences. One of those sequences is kind of every other type.',NULL,0);
INSERT INTO comment VALUES (8906,1324,3558,'Tristan','the middle cube','2003-10-24 17:15:18',1,'Define \"the cube in the middle.\" The middle of the larger cube? The middle of the top 9 cubes? Is the middle cube the larger cube? This probably isn\'t the solution, but it IS in tricks, so you can never be too sure.\r\n\r\nI didn\'t really understand what SK was talking about... 13 cubes on each side? What does that mean?\r\n\r\nWell, assuming the middle cube is what everyone naturally assumes it is, this creates a problem. How can you remove the cube without letting the one above it fall? You could use glue beforehand, put the cube on an angle, or something like that. \r\n\r\nMaybe I\'m just over-analyzing this problem. It\'s probably something clever, and I\'ll later say \"Why didn\'t I think of that?\"',NULL,0);
INSERT INTO comment VALUES (8907,1324,3172,'SilverKnight','re: the middle cube','2003-10-24 17:22:02',0,'well... the problem didn\'t say that the \'middle top\' must remain in position... if the center cube melts away (and all the other cubes are porous, or allow water to go between/through them), then I suppose this would be an answer to the problem.... letting the \'top middle\' slide down to the center of the 3x3x3 cube.\r\n____________________\r\n\r\nWhat I meant to say earlier (to answer your question), was you have 13 cubes on the left side of the table (in a jumble), and 5 cubes plus a 2x2x2 \'larger cube\' on the right side of the table, and 1 little cube in the center (in the middle of the 27 cubes) of the table... 13 + 5 + 8 + 1 = 27 cubes.\r\n\r\nNow, take the \"middle\" cube away, and you have 26 cubes remaining on the table.\r\n\r\n(As I said... I know I\'m reaching)',8906,0);
INSERT INTO comment VALUES (8908,1324,1626,'Gamer','re(2): the middle cube','2003-10-24 17:41:13',0,'I don\'t understand how you could create this scenario if you didn\'t move or change any parts of the larger cube.',8907,0);
INSERT INTO comment VALUES (8909,1324,3558,'Tristan','re(2): the middle cube','2003-10-24 17:42:37',0,'The problem indeed does not say the middle top cube must remain in position. It does, however, state that we may not \"in any way do anything that would move or change them.\"\r\nMelting the ice cube causes the top middle cube to move, though you might say that the ice cube is really melting on its own. Thanks for explaining your comment.',8907,0);
INSERT INTO comment VALUES (8910,1324,3172,'SilverKnight','re(3): the middle cube','2003-10-24 18:20:34',0,'Gamer, I don\'t understand what you don\'t understand.\r\n\r\n13 cubes on your left\r\n13 cubes on your right (including 2x2x2 cube and 5 lone cubes)\r\none cube in the middle\r\n\r\ntake the middle one away',8908,0);
INSERT INTO comment VALUES (8911,1324,1112,'Greg','one solution, probably not the right one','2003-10-24 19:14:25',0,'\"Start with 27 small cubes.\" Suppose these small cubes are all wirefram cubes that are designed to be collapsable. \r\netc...\r\n\r\nperform the little trick of calculus of differences (or any little trick you know) to determine the equation that generates this sequence.\r\n\r\nIf you do so, you\'ll find out that the equation is:\r\nx = (n² + n + 2) / 2 ',NULL,0);
INSERT INTO comment VALUES (8967,660,3172,'SilverKnight','re: full solution','2003-10-27 15:23:19',0,'Hey Charlie... I put a <P> right after the </PRE>...\r\n\r\nand it didn\'t work!!!! *sigh* someone please tell me how to get the pre to work...',8966,0);
INSERT INTO comment VALUES (8968,660,1301,'Charlie','re(2): full solution','2003-10-27 15:26:49',0,'When I said a paragraph I didn\'t mean actually coding the bracketed p. Just typing a return. One short line, then two carriage returns and then some typing that\'s more extensive. Works for me. I don\'t know if the bracketed p would mess it up, but if that\'s what you\'re typing, perhaps it does.\r\n\r\nHave you tried lower case? that\'s what works for me.\r\n\n\nEdited on October 27, 2003, 3:28 pm',8967,0);
INSERT INTO comment VALUES (8969,660,3172,'SilverKnight','re(3): full solution','2003-10-27 15:39:14',0,'I think that the site only lets Journeymen and Scholars use the pre tag.... Levik... would you confirm?',8968,0);
INSERT INTO comment VALUES (8970,660,1301,'Charlie','re(4): full solution','2003-10-27 15:48:39',0,'Looking at the HTML tags thread in the Reference forum I see that pre is for apprentices and above.',8969,0);
INSERT INTO comment VALUES (8971,660,3172,'SilverKnight','re(5): full solution','2003-10-27 15:50:58',0,'I feel so worthless.... (But thanks for finding that! I obviously missed it.)',8970,0);
INSERT INTO comment VALUES (8972,1358,4050,'winston','# sons = 0','2003-10-27 16:25:28',0,'right?',NULL,0);
INSERT INTO comment VALUES (8973,1358,1626,'Gamer','re: # sons = ?','2003-10-27 16:58:08',0,'If posting a solution, don\'t give it away in the subject!\r\n\r\nright?',8972,0);
INSERT INTO comment VALUES (8974,655,3558,'Tristan','re: Solution','2003-10-27 18:41:16',0,'Also, you\'re not allowed to subtract, though some might assume that you can if they don\'t read the problem carefully.',8946,0);
INSERT INTO comment VALUES (8975,660,4055,'S','re: full solution','2003-10-27 20:47:32',0,'One small nitpick:\r\n\r\nAlthough I agree with your solution (and it is well explained), it is only valid for a 2-Dimensional pizza. If it is 3-dimensional, it can be sliced through the centre three times so that for n=3, x=8.',8966,0);
INSERT INTO comment VALUES (8976,1357,3386,'Victor Zapana','re: idea','2003-10-27 21:32:23',0,'that would make sense.\r\nIf look at that way using factor sequences, all the answers are true. Heck every sequence that starts with any positive number will become 2 no matter what, cept 1.',NULL,0);
INSERT INTO comment VALUES (8977,1475,3386,'Victor Zapana','re: Solution','2003-10-27 21:35:54',0,'hmm didnt no Alaksa is also most eastern poin in usa, thought Maine was.. heh the things u find out on these posts lol',8954,0);
INSERT INTO comment VALUES (8978,660,3172,'SilverKnight','re(2): full solution','2003-10-27 21:41:16',0,'perhaps... but in a previous life I was a software engineer and we eat only flat food (so it can slide under the door).',8975,0);
INSERT INTO comment VALUES (8979,1227,3172,'SilverKnight','if we are allowed...','2003-10-28 08:59:56',1,'... to include balks... then I suppose the pitcher could continue to do that, getting two \'batters\' on bases and then throw one pitch to a third batter, and hopefully get a triple play. Thereby getting 3 outs and having thrown only one pitch for the inning.\r\n\r\nSo, doing that for nine innings, would mean nine pitches. Perhaps there\'s another rule that would allow one to have fewer.\r\n\r\nBTW, the fewest number of pitches recorded in a major league game is 58, and here are those details.',NULL,0);
INSERT INTO comment VALUES (8980,1324,3136,'Popstar Dave','Nice...','2003-10-28 09:10:39',0,'Gamer,\r\nNice, question. I\'m impressed. But the solution that I thought was best of them all was Helen\'s CAD program one. It seems that everything is getting easier with computers these days.',NULL,0);
INSERT INTO comment VALUES (8981,1227,4060,'daniel trosdahl','re:','2003-10-28 09:31:08',0,'I believed the correct answer is 25. A balk does not put runners on base. It only moves runners up one base who are already on base.\r\n\r\nHere\'s the break down. A visiting pitcher throws one pitch to each batter he faces and each batter is putout. This happens for all batters save one who hits a homerun off of him. The home pitcher shuts out the visiting team. Thereby not needing to play the bottom of the ninth inning. \r\n\r\nSo the visiting pitcher faces only 25 batters.',NULL,0);
INSERT INTO comment VALUES (8982,1227,3172,'SilverKnight','re(2):','2003-10-28 09:36:03',0,'I thought a balk counts as a ball (on the count). So... 4 balks would be four balls, and the pitcher would walk the batter.\r\n\r\nI\'m no expert on this rule (or baseball in general), so I\'ll defer to someone else\'s expertise.\r\n\r\n--- SK',8981,0);
INSERT INTO comment VALUES (8983,1227,4060,'daniel trosdahl','re: SilverKnight','2003-10-28 09:48:06',0,'That logic won\'t work. A balk is only called when a runner is on base. So let\'s propose the pitcher hits the batter. Now he proceeds to balk 3 times. Even if a balk counted as a ball without a pitch(I don\'t believe this is true but I would have to check) the runner would move up three bases and score. So there would be no way to create a double play\r\nfrom that.\r\n\r\nIt\'s a novel angle on this problem however.',8982,0);
INSERT INTO comment VALUES (8984,1227,3172,'SilverKnight','re(2): SilverKnight','2003-10-28 10:48:19',0,'Are you sure about two following two points?\r\n \r\nO X \r\nX O \r\nthen flip the bottom right off making it. \r\nO O \r\nO X \r\nthen flip the top left again. \r\nX X \r\nX X \r\nOh yeah, after thinking it a bit more this \"can\'t\" happen because x is not in the center for there is no center in a y by y square if y is even. \r\nhmm.. so the only grids that have centers that work are 1x1 and 3x3 my bad :P\n\nEdited on November 2, 2003, 5:18 pm',9162,0);
INSERT INTO comment VALUES (9164,1344,1301,'Charlie','Brute Force','2003-11-02 18:01:31',3,'The following arrangements of flipped switches (1 = flipped, 0 = not flipped) will turn off the center light while keeping or returning off the other lights:\r\n \r\n{x|x=perfect square} (this is because of what jill said) \r\n{y|y not < 0} (the convo doesn\'t really set limits to y) \r\nx-y= perfect square (according to what jill said, this has to be even) \r\nin addition because (x - y) must be not less than 0 (everyone can understand why this must be), x must be greater than y \r\nbecause x > y, x cannot be 0 also, because if x is 0, then there is no possible y, with the y cannot be negative restraint., thus x cannot be 0 either. \r\nWell the least number y could be is 0 here because x is already a perfect square (now is abbreviated as PS)and a PS - 0 = PS and PS + 0 = PS, PS > 0. This then means the smallest perfect square that is higher than y (0) would be 1. so x=1 and y=0. \r\nHOWEVER, ravi also said they both had collections, which can make you believe that x > 0 and y > 0 \r\nso now, you can assume x-y=0, because if both cant be zero, they can be the same exact number, and if they are the same exact number, jack can give jill everything he got and still end up with an even square, 0. This would then infer x=y. \r\nso the smallest even number higher than 0 is 1, so x=1 and y=1. \r\nto be continued. gotta do sum things. comment and criticize this as much as u want.\r\n',9201,0);
INSERT INTO comment VALUES (9208,663,3386,'Victor Zapana','part 2 of the mayhem of my previous post','2003-11-03 19:20:53',0,'(note: read part 1 first) now lets consider that all of these numbers are perfect squares and when ravi says even squares he meant perfect squares that is a multiple of 2. \r\n(for my third scenario assume that collections can equal 0)this would then make the following restrictions: \r\n{x|x=perfect square & even & integral} (infered by Jill) \r\n{y|y=non-negative and integral} (must be integral for both x and y because of the reason stated in part 1) \r\nx+y = perfect square, integral. \r\nx-y = perfect square, integral, and not less than 0. this then leads you to conclude that x > y \r\nx > 0 (reasons stated in part 1) \r\nwith the following restraints, x = 4 (the smallest perfect square > 0) and y = 0 \r\nnow like scenario 2 in part 1, we must now assume that collections does mean x and y are both more than 0. so like in part 1 we can also assume than x-y = 0, so x=y. \r\nso, with these restraints, x= 4 and y= 4\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (9209,1234,3136,'Popstar Dave','re: Solution','2003-11-03 19:22:41',0,'Good work, C... Must be a bit easier if you\'re from the US. No wonder I couldn\'t work it out, sitting all the way over here in Australia!',9199,0);
INSERT INTO comment VALUES (9210,105,3136,'Popstar Dave','4 straws!','2003-11-03 20:19:00',0,'This is easy, they each grab a straw and start sucking down the beer!',NULL,0);
INSERT INTO comment VALUES (9211,1234,1301,'Charlie','re(2): Solution','2003-11-03 20:30:23',0,'Yes they are all U.S. airport codes.\r\n\r\nAustralia would have\r\nADO ANDAMOOKA Australia\r\nARM ARMIDALE Australia\r\nASP ALICE SPRINGS Australia\r\nBEE BEAGLE BAY Australia\r\nBOX BORROLOOLA Australia\r\nBUY BUNBURY Australia\r\nCOB COOLIBAH Australia\r\nCOY COOLAWANYAH Australia\r\nCRY CARLTON HILL Australia\r\nCUD CALOUNDRA Australia\r\nFLY FINLEY Australia\r\nGET GERALDTON Australia\r\nGOO GOONDIWINDI Australia\r\nHAT HEATHLANDS Australia\r\nHID HORN ISLAND Australia\r\nHIP HEADINGLY Australia\r\nHIS HAYMAN ISLAND Australia\r\nHUB HUMBERT RIVER Australia\r\nJAB JABIRU Australia\r\nLEA LEARMONTH Australia\r\nLIB LIMBUNYA Australia\r\nMET MORETON Australia\r\nMHO MT. HOUSE Australia\r\nMOO MOOMBA Australia\r\nNUB NUMBULWAR Australia\r\nODD OODNADATTA Australia\r\nPEA PENNESHAW Australia\r\nPEP PEPPIMENARTI Australia\r\nPER PERTH Australia\r\nPUG PORT AUGUSTA PAGAS Australia\r\nRAM RAMINGINING Australia\r\nSIX SINGLETON Australia\r\nTAN TANGALOOMA BRISBANE Australia\r\nWAN WAVERNEY Australia\r\nWIN WINTON Australia\r\nWIT WITTENOOM GORGE Australia\r\nWON WONDOOLA Australia',9209,0);
INSERT INTO comment VALUES (9212,1234,1301,'Charlie','re(3): Solution','2003-11-03 20:33:51',0,'I see the site still has FLU, though Queens got rid of that a while back, as too close to LGA.',9204,0);
INSERT INTO comment VALUES (9213,663,1301,'Charlie','re: Fuller Solution','2003-11-03 22:09:37',0,'More solutions in order of the number that Jack started out with can be gotten just by trying out the squares in sequence and within each square subtracting and adding up to the number available in Jack\'s possession. In tabular form showing x-y, x, x+y and y:\r\n \r\nA) Depressing (It\'s depressing that a bull would swallowed a bomb.) \r\nand \r\nB) Helpful (It\'ll be helpful to blow up a bull that\'s so stupid that he would swallow a bomb) \r\nYou can see that I\'m not much of a bull fan.\n\nEdited on November 4, 2003, 10:46 am',9222,0);
INSERT INTO comment VALUES (9224,1343,3372,'Sam','re: solution','2003-11-04 10:47:02',0,'Ha! My family and I used to play this exact game. The \"Bull game\" is rather like pictionary, only the picture must include a bull in it, and the word must be pun of the sort above. Noble would then be signified either by a bull with a line through it, or just a blank page. Anyone guess what a simple drawing of a bull would mean?\r\n\r\nApologies, it was just funny to see such a blast from the past. :)',9222,0);
INSERT INTO comment VALUES (9225,1343,3136,'Popstar Dave','re: solution','2003-11-04 11:49:35',0,'Hehehe... smooth.\r\nI was trying to work out how I\'d feel in each of those situations. Then thinking \"Hmmm... this really isn\'t much of a problem. More of an opinion piece, but I like the sybolism he\'s used!\"',9222,0);
INSERT INTO comment VALUES (9226,532,2839,'FatBoy','re: a dissenting view','2003-11-04 12:08:49',0,'HOLY COW!!!\r\nI took Sarah\'s advice and I may have found a clue as to the independent purpose pre-dating the umbilical cord. \r\n\r\nI\'m not sure what it means but inside my navel is a yellow sign that says \"property of AT&T. Before digging call Miss Utility!!\"\n\nEdited on November 4, 2003, 12:10 pm',9202,0);
INSERT INTO comment VALUES (9227,1227,4060,'daniel trosdahl','re: Solution ?','2003-11-04 13:01:47',0,'That will work for two instances, then the umpire will go to the mound and tell him to knock it off. If he does it again he will get ejected. The correct answer is 25. There are no loopholes.',9136,0);
INSERT INTO comment VALUES (9228,643,4175,'Robert Bell','Bayes Theorem','2003-11-04 13:17:44',0,'What we want is prob(Girl added(G)|Boy was picked(X))?\r\n\r\nDefine:\r\nNumber of babies after the addition = N\r\nGirl added = G\r\nBoy added = B\r\nBoy Picked = X\r\n \r\nProb(G|X) = Prob(G intersect X)/ {Prob(G intersect X) + Prob(B intersect X)}\r\n\r\n = (2/N) / (2/N + 3/N) = 2/5 = .40',NULL,0);
INSERT INTO comment VALUES (9229,1479,4119,'Maria','Close','2003-11-04 14:05:50',0,'I do not think there is something else to say: Lee is right. But I would have liked the answer to be: Ursula Andress. A beautiful actress that shared the big screen with four of them.',NULL,0);
INSERT INTO comment VALUES (9230,1227,4176,'Joe C','Easy prob','2003-11-04 14:44:44',0,'To get the complete game a pitcher has to pitch 7 innings\r\n7 times 3 is 21\r\nor it might be 6 innings and be 18',NULL,0);
INSERT INTO comment VALUES (9231,1489,4055,'S','Solution','2003-11-04 15:33:36',3,'The father is 60 years old.\r\nThe son is 35 years old.\r\nThe grandson is 5 years old.\r\n \r\nGreen Shirt= $50 \r\nRed Shirt= $40 \r\nBlue Shirt= $30 \r\nYellow Shirt= $20 \r\nOrange Shirt= $10 \r\nCarol spent $70, buying a red and blue shirt. \r\nDiane spend $80, buring a green and blue shirt. \r\nEmily spent $60, buying a red and yellow shirt. \r\nAlice spent $70, buying a green and yellow shirt. \r\nBettey spent $60, buying a red and yellow shirt. \r\nThe orange shirt is unpopular. No one bought it. lol.',NULL,0);
INSERT INTO comment VALUES (9298,1345,3386,'Victor Zapana','re: Solution with no proof lol','2003-11-06 20:08:10',0,'woops my bad i noticed a flaw in my solution so dun pay attention to it lol',9297,0);
INSERT INTO comment VALUES (9299,1345,4201,'morgan','Solution with no proof','2003-11-06 20:19:28',0,'well no two girls can have the same color shirt\r\nso \r\nAlice green\r\nbetty red\r\ncarol blue\r\ndiane orange\r\nemily yellow\r\n\r\nthe money spent\r\nAlice 10$\r\nbetty 30$\r\ncarol 40$\r\ndiane 50$\r\nemily 20$',NULL,0);
INSERT INTO comment VALUES (9300,1345,3558,'Tristan','re: Solution with no proof','2003-11-06 20:24:54',0,'Each girl bought two shirts.',9299,0);
INSERT INTO comment VALUES (9301,1345,3386,'Victor Zapana','re(2): Solution with no proof','2003-11-06 20:42:31',0,'also the problem also states: Alice went with Carol to pick out the same color shirt to buy, noting that it didn\'t cost 20 dollars like last week.',9300,0);
INSERT INTO comment VALUES (9302,1345,3386,'Victor Zapana','Possible Impossibility','2003-11-06 21:24:03',0,'hm... based by my intesive \"read between the lines\" analysis... Betty and either Emily or Alice must have the same shirts. so the solution is impossible. probably im wrong coz gamers previous post infers there is an answer.. hu nos?',NULL,0);
INSERT INTO comment VALUES (9303,1345,4203,'Jun','Solution (maybe)','2003-11-06 22:38:24',0,'Shirt Costs:\r\nGreen - $10\r\nRed - $20\r\nBlue - $30\r\nYellow - $40\r\nOrange - $50\r\n\r\nWhat the girls spent and how they spent it:\r\nDiane - $90 = orange + yellow\r\nCarol - $70 = blue + yellow\r\nBetty - $70 = red + orange\r\nAlice - $50 = yellow + green\r\nEmily - $50 = red + blue\r\n\r\nIf this is right and anyone cares, then I\'ll post a proof. It was done in shorthand and as a series of short notes, so it\'d take a while to rewrite properly.',NULL,0);
INSERT INTO comment VALUES (9304,1345,3386,'Victor Zapana','re: Solution (maybe)','2003-11-06 22:42:09',0,'n/m\n\nEdited on November 6, 2003, 10:44 pm',9303,0);
INSERT INTO comment VALUES (9305,1345,3386,'Victor Zapana','re: Possible Impossibility','2003-11-06 22:45:45',0,'blah. read number 4 wrong... i was wondering why it seemed impossible.. i think jun is right but cant be sure right now.. just sped red through it.',9302,0);
INSERT INTO comment VALUES (9306,1345,4203,'Jun','re(2): Solution (maybe)','2003-11-06 22:46:19',0,'Actually I think the only thing stated about what Alice and Emily had in common was that they did _not_ buy an orange shirt. Statement 4 said that it was Alice and _Carol_ who had a shirt in common. I misread that the first time through too.',9304,0);
INSERT INTO comment VALUES (9307,658,4059,'Saso','re(4): Waste a test','2003-11-07 03:37:59',0,'I do not want to argue. However, in my opinion when you have a method A which can distinguish a poisoned glass in 7 tests in 98,45% of cases and in 8 tests in rest 1,55% of cases and you have a method B, which will do the same in 8 tests 99,2% of time, I wouldn\'t call choosing method B as \"minimizing the maximum possible\". Perhaps I just have a different perception of words not being a native English speaker.',9285,0);
INSERT INTO comment VALUES (9308,1458,3136,'Popstar Dave','Getting \'round the wording.','2003-11-07 04:34:41',0,'So you can\'t \"ask\" another person to do it. Could you persuade another person to do it, without directly asking them? \r\n\r\nSorry, I\'m just being a smart-arse!',NULL,0);
INSERT INTO comment VALUES (9309,1344,1626,'Gamer','re: well one way','2003-11-07 07:10:13',0,'But unfortunately, doing so would trigger the lights around it because there is only one switch connecting to this light. Furthermore, if you took away its power source you wouldn\'t be using switches to do it as the problem suggests.',9274,0);
INSERT INTO comment VALUES (9310,658,3172,'SilverKnight','re(5): Waste a test','2003-11-07 09:00:16',0,'Saso, I agree with your last statement! In BOTH of your cases (method A and method B), the maximum possible is 8 tests.\r\n\r\nThe point of the problem, though, is ... given that we know that exactly one glass is poisoned, the MAXIMUM for 128 glasses is seven tests (assuming you use the appropriate algorithm).\r\n\r\nAs soon as I have more than 128 glasses (and no more than 256), then the maximum becomes eight tests.\r\n\r\nBut if, as the problem suggests, a detective FIRST selects a single glass at random, then we are diverging from the optimal method.\r\n\r\nThe point here is that it doesn\'t change the maximum if we have only 129 glasses, because if we don\'t find the poison in the first glass, then we can continue with 7 tests to find it (maintaining 8 total checks).\r\n\r\nIf we have 130 glasses, and we don\'t find the poison in the first glass, it is possible (even if improbable) that the next 7 tests will only bring us to TWO candidates, and a ninth test will be required to find the suspect glass.\r\n____________________\r\n\r\nI also do not wish to argue, but, as I hope you\'ll agree, it is important that language be used precisely, particularly in problem statements (such as on Flooble).\r\n\r\nNevertheless, misunderstandings and ambiguities occur, and you can find several problems on this site where it ended up causing multiple possible solutions (varied from the intended singular solution).\r\n\r\n--- SK',9307,0);
INSERT INTO comment VALUES (9311,1496,4189,'John','re(3): W00t','2003-11-07 09:21:59',0,'That\'s making an assumption. If that is true, then the foreign currency they were holding lost that value instantaneously the day the exchange rate changed, NOT as a result of Charlie\'s transactions. \r\n\r\nThey break even on Charlie\'s transactions, which is what the problem is asking.',9295,0);
INSERT INTO comment VALUES (9312,1235,3136,'Popstar Dave','First guess at a solution','2003-11-07 10:07:22',1,'I\'ve only had a quick look at this, but I\'ve got a strategy where he can say it up to (and including) the 5th. \r\nIt goes a bit like this:\r\n1st: Shot 1 duck (30th Jul shot 0, 25th shot 2)\r\n2nd: Shot 1 duck (31st Jul shot 0, 26th shot 2)\r\n3rd: Shot 2 ducks (1st shot 1, 27th shot 3)\r\n4th: Shot 2 ducks (2nd shot 1, 28th shot 3)\r\n5th: Shot 3 ducks (3rd shot 2, 29th shot 4)\r\n\r\nOn the 6th he cant say it as he can\'t shoot less than the 0 ducks he shot on the 30th.',NULL,0);
INSERT INTO comment VALUES (9313,1235,1301,'Charlie','solution','2003-11-07 10:20:42',3,'If on July 30 he had shot 7 ducks and on July 31, 1 duck, then on the 1st thru 6th of August he could have shot 8, 2, 9, 4, 10 and 6 ducks respectively, so he could do this for 6 days.',NULL,0);
INSERT INTO comment VALUES (9314,1235,3136,'Popstar Dave','re: solution','2003-11-07 10:36:26',0,'Good call on the alternation. I thought there might be a way to get that extra day!\r\n\r\nGood old Günnstefen, one more day to tell Hans Weißmüller (his cook) about his hunting sucesses!',9313,0);
INSERT INTO comment VALUES (9315,1235,4189,'John','','2003-11-07 10:38:41',0,'My initial instincts say that at most he could say this truthfully for 14 days. On the 14th day, he can not have shot fewer than a week ago, since we know he has been shooting progressively more and more ducks in every two-day period. Day 14 is the first day that we KNOW he has shot more on the seventh weekday than the first.',NULL,0);
INSERT INTO comment VALUES (9316,1235,4189,'John','bah','2003-11-07 10:48:28',0,'Well, that\'s what I get for posting before I check my answer. I can\'t make it work out at 14.\r\n\r\nMy new best theory is that he can say it for EIGHT (8) days.\r\nDay1 6 ducks\r\nDay2 1 ducks\r\nDay3 7 ducks\r\nDay4 2 ducks\r\nDay5 8 ducks\r\nDay6 3 ducks\r\nDay7 9 ducks\r\nDay8 4 ducks\r\n',9315,0);
INSERT INTO comment VALUES (9317,1235,1920,'Brian Smith','Solution','2003-11-07 11:05:15',0,'Denote the Baron\'s sequence of ducks as d1, d2, d3, d4, d5, d6, d7, d8, and d9.\r\n\r\nEight days is possible.\r\n\"I shot more ducks than two days ago\" means d8>d6>d4>d2 and d7>d5>d3>d1.\r\n\"But fewer than a week ago\" forces d1 to d8 to satisfy the following inequality:\r\nd7>d5>d3>d1>d8>d6>d4>d2\r\n\r\nNine days is impossible. The quote from the problem requires d2>d9>d7, but the inequality for eight days has d7>d2.\r\n\r\nThe answer to the problem is eight days.',NULL,0);
INSERT INTO comment VALUES (9318,1235,1301,'Charlie','re: Solution','2003-11-07 11:23:44',0,'Regarding\r\n\r\n\"I shot more ducks than two days ago\" means d8>d6>d4>d2 and d7>d5>d3>d1. \r\n\"But fewer than a week ago\" forces d1 to d8 to satisfy the following inequality: \r\nd7>d5>d3>d1>d8>d6>d4>d2 \r\n\r\nBut d2 has to be greater than d0 (not mentioned but must be existing) while d7 must be less than d0 (so we can\'t ignore it on the assumption that he wasn\'t hunting then). So d6 is the last day it would work.',9317,0);
INSERT INTO comment VALUES (9319,1235,4206,'Eric','solution','2003-11-07 14:26:50',0,'I began the problem by drawing 8 boxes in a row. The last box I labeled \"a\" as the first day, August 1st 2000, then proceeded to label day \"b\" the third box from the end (\"two days ago\"), while \"c\" was used to label the first box (\"a week ago\"). I continued adding boxes to the end, continuing the alphabetical labeling and wrote down each inequality (last week > present day > two days before) that resulted. Then as I added days to the end, I wrote down the combined inequalities that resulted, all with respect to \"a\", the first day. On the 7th day, these were my results: \r\n\r\n[c,g,h] > [a] > [b,m,i,d,e,n,k,g]\r\n\r\nSeeing that this was the first day that a letter appeared on both sides of the inequality (the letter \"g\"), I reasoned that one cannot reach the 7th day without creating an inconsitency. Therefore, the baron may say the phrase until and including August 6th, 2000. ',NULL,0);
INSERT INTO comment VALUES (9320,1424,3172,'SilverKnight','solution','2003-11-07 15:13:58',3,'I found only 420\r\nwith the following program:\r\n\r\n#include <iostream.h>\r\n\r\nint main(int argc, char* argv[])\r\n{\r\n int a, b, c;\r\n\r\n for (a=1; a<10; a++)\r\n {\r\n for (b=0; b<10; b++)\r\n {\r\n for (c=0; c<10; c++)\r\n {\r\n if ( (a!=b) && (a!=c) && (b!=c) )\r\n {\r\n if ( ((a*a) + (b*b) + (c*c)) == (10*b + c) )\r\n {\r\n if ( ( ((10*b+c)*(10*b+c)) + (a*a + a)) == (100*a + 10*b + c) )\r\n cout << a << b << c << endl;\r\n }\r\n }\r\n }\r\n }\r\n }\r\n \r\n return 0;\r\n}\r\n',NULL,0);
INSERT INTO comment VALUES (9321,1345,1301,'Charlie','21 solutions?--brute force','2003-11-07 15:43:05',3,'This program:\r\n\r\nDECLARE SUB varyGirl (which!)\r\nDECLARE SUB permute (a$)\r\nCLS\r\nDIM SHARED colr$, gs$(2, 5), total(5)\r\ncolr$ = \"rgbyo\"\r\nOPEN \"shirts.txt\" FOR OUTPUT AS #2\r\nFOR costs = 1 TO 120\r\n varyGirl 1\r\n permute colr$\r\nNEXT\r\n\r\nCLOSE\r\n\r\nSUB permute (a$)\r\nDEFINT A-Z\r\n x$ = \"\"\r\n FOR i = LEN(a$) TO 1 STEP -1\r\n l$ = x$\r\n x$ = MID$(a$, i, 1)\r\n IF x$ < l$ THEN EXIT FOR\r\n NEXT\r\n\r\n IF i = 0 THEN\r\n FOR j = 1 TO LEN(a$) \\ 2\r\n x$ = MID$(a$, j, 1)\r\n MID$(a$, j, 1) = MID$(a$, LEN(a$) - j + 1, 1)\r\n MID$(a$, LEN(a$) - j + 1, 1) = x$\r\n NEXT\r\n ELSE\r\n FOR j = LEN(a$) TO i + 1 STEP -1\r\n IF MID$(a$, j, 1) > x$ THEN EXIT FOR\r\n NEXT\r\n MID$(a$, i, 1) = MID$(a$, j, 1)\r\n MID$(a$, j, 1) = x$\r\n FOR j = 1 TO (LEN(a$) - i) \\ 2\r\n x$ = MID$(a$, i + j, 1)\r\n MID$(a$, i + j, 1) = MID$(a$, LEN(a$) - j + 1, 1)\r\n MID$(a$, LEN(a$) - j + 1, 1) = x$\r\n NEXT\r\n END IF\r\nEND SUB\r\n\r\nDEFSNG A-Z\r\nSUB varyGirl (which)\r\n DIM t(5)\r\n FOR shirt1 = 1 TO 4\r\n gs$(1, which) = MID$(colr$, shirt1, 1)\r\n FOR shirt2 = shirt1 + 1 TO 5\r\n gs$(2, which) = MID$(colr$, shirt2, 1)\r\n total(which) = shirt1 + shirt2\r\n SELECT CASE which\r\n CASE 1\r\n IF gs$(1, which) = \"o\" OR gs$(2, which) = \"o\" THEN GOTO notThis\r\n CASE 2\r\n IF gs$(1, which) <> \"r\" AND gs$(2, which) <> \"r\" THEN GOTO notThis\r\n CASE 3\r\n IF gs$(1, which) <> \"b\" AND gs$(2, which) <> \"b\" THEN GOTO notThis\r\n IF gs$(1, which) = \"b\" AND shirt1 = 1 OR gs$(2, which) = \"b\" AND shirt2 = 1 THEN GOTO notThis\r\n IF gs$(1, which) = \"g\" OR gs$(2, which) = \"g\" THEN GOTO notThis\r\n IF gs$(1, which) <> gs$(1, 1) AND gs$(1, which) <> gs$(2, 1) AND gs$(2, which) <> gs$(1, 1) AND gs$(2, which) <> gs$(2, 1) THEN GOTO notThis\r\n IF gs$(1, which) = gs$(1, 1) OR gs$(1, which) = gs$(2, 1) THEN\r\n IF shirt1 = 2 THEN GOTO notThis\r\n ELSE\r\n IF shirt2 = 2 THEN GOTO notThis\r\n END IF\r\n IF shirt1 <> 4 AND shirt2 <> 4 THEN GOTO notThis\r\n CASE 5\r\n IF gs$(1, which) = \"o\" OR gs$(2, which) = \"o\" THEN GOTO notThis\r\n END SELECT\r\n FOR j = 1 TO which - 1\r\n IF gs$(1, j) = gs$(1, which) AND gs$(2, j) = gs$(2, which) THEN GOTO notThis\r\n NEXT\r\n IF which < 5 THEN\r\n varyGirl which + 1\r\n ELSE\r\n GOSUB evaluate\r\n END IF\r\nnotThis:\r\n NEXT\r\n NEXT\r\n EXIT SUB\r\n\r\nevaluate:\r\n IF total(4) > total(1) AND total(4) > total(2) AND total(4) > total(3) AND total(4) > total(5) THEN\r\n t(1) = total(1): t(2) = total(2): t(3) = total(3): t(4) = total(5)\r\n DO\r\n fl = 0\r\n FOR i = 1 TO 3\r\n IF t(i) > t(i + 1) THEN SWAP t(i), t(i + 1): fl = 1\r\n NEXT\r\n LOOP UNTIL fl = 0\r\n gs1$ = gs$(1, 1) + gs$(1, 2) + gs$(1, 3) + gs$(1, 4) + gs$(1, 5)\r\n gs2$ = gs$(2, 1) + gs$(2, 2) + gs$(2, 3) + gs$(2, 4) + gs$(2, 5)\r\n IF t(3) = t(4) AND t(1) = t(2) THEN\r\n IF gs$(1, 4) <> gs$(1, 5) AND gs$(1, 4) <> gs$(2, 5) AND gs$(2, 4) <> gs$(1, 5) AND gs$(2, 4) <> gs$(2, 5) THEN\r\n PRINT #2,\r\n PRINT #2, colr$\r\n PRINT #2, gs1$\r\n PRINT #2, gs2$\r\n FOR g = 1 TO 5\r\n PRINT #2, 10 * total(g);\r\n NEXT\r\n PRINT #2,\r\n END IF\r\n END IF\r\n END IF\r\n RETURN\r\nEND SUB\r\n\r\nseems to produce 21 solutions:\r\n \r\nE then must be 8. \r\nalso just as a heads up, \r\n13333A + 1330B + 100C - 320D - 3332E = 0 \r\n13333A + 1330B + 100C = 320D + 3332E \r\n26666 + 1330B + 100C = 320D + 26656 \r\n1330B + 100C + 10= 320D \r\n133B + 10C + 1 = 32D \r\nAccording to this, B must be odd, so it\'s probably 1.\r\n\r\nEdited on November 9, 2003, 8:57 am\r\n\r\nEdited on November 9, 2003, 8:58 am\r\n\r\nEdited on November 9, 2003, 9:01 am\r\n\r\nEdited on November 9, 2003, 9:09 am\r\n\r\nEdited on November 9, 2003, 9:12 am\r\n\r\nEdited on November 9, 2003, 9:14 am\r\n\r\nEdited on November 9, 2003, 9:15 am\n\nEdited on November 9, 2003, 9:18 am',NULL,0);
INSERT INTO comment VALUES (9354,666,3705,'zaphod','Full solution','2003-11-09 10:23:24',0,'As Victor points out, A has to be 2 and E has to be 8. This, by substitution, yields\r\n133B+10C-32D+1=0\r\nSince the result begins with an 8, no carry goes through the 4th digit mutliplication, so whatever is carried from the 3rd digit, 4B must be less than 10. Therefore B is either 0, 1 or 2. However, 10C-32D is even, forcing 133B (and B) to be odd. So B=1 and the equation becomes\r\n16D-5C=67\r\nThe product\'s second digit is 1, so 4D has to end in an 8 (3 is carried over by 4E=32). This means that D is either 2 or 7. Substituting D with 2, C becomes -7 which is impossible. Therefore D=7 and C=9, which completes the proof.\r\nI agree with Victor\'s second post, only adding that NO other 5-digit number has this property, as my proof shows ;)',NULL,0);
INSERT INTO comment VALUES (9353,666,3386,'Victor Zapana','solution based on my thoughts','2003-11-09 09:17:41',3,'A = 2, B = 1, C = 9, D = 7, E = 8. \r\n21978 x 4 = 87912',NULL,0);
INSERT INTO comment VALUES (9355,666,3196,'Dan','I need some digitalis !!!!','2003-11-09 13:02:28',0,'(Since the integers must be unique, we can discount the obvious trivial solution, A=B=C=D=E=0)\r\n\r\nIn the base 10 number system:\r\n \r\n(E +10D +100C +1000B+ 10000A) *4 = A + 10B + 100C + 1000D + 10000E\r\n\r\n39999A + 3990B + 300C - 960D - 9996E = 0\r\n\r\nNow all I need is a handy dandy computer program or spreadsheet to give me the 0-to-many unique solutions. \r\n\r\n\n\nEdited on November 9, 2003, 1:04 pm',NULL,0);
INSERT INTO comment VALUES (9356,1235,1626,'Gamer','re: Ducks Unlimited','2003-11-09 13:50:49',0,'This belongs in the tricks comments and not here. :)',9349,0);
INSERT INTO comment VALUES (9357,1458,4224,'John Pile','Ruminate','2003-11-09 14:56:17',3,'Leave it alone. If another customer doesn\'t swipe it before closing, a barmaid will take care of it... without asking.',NULL,0);
INSERT INTO comment VALUES (9358,1491,3840,'Hal9000','Solution','2003-11-09 15:19:02',0,'One way is to buy a rectangular box of dimensions 6\' x 7/4\' and place the fishing pole diagonally inside it. Of course in actuality the pole must have some width so lets make the box 6\'x6\' to ensure it fits and annoy the bus driver.',NULL,0);
INSERT INTO comment VALUES (9359,666,3558,'Tristan','re: a thought','2003-11-09 17:37:38',1,'Your assumption that A cannot be 0 needs a better reason! A number 0???? * 4 indeed can equal a five digit number! There is a better reason that A cannot equal 0. Assume that A=0. The first integer multiplied by 4 must therefore be equal to a multiple of 10. Knowing our multiplication, the first integer must be a multiple of 5. E must therefore either be 0 or 5. We already know that E cannot be 0, and no 4 digit number *4 can equal 5????. Therefore, A must not be 0.',9352,0);
INSERT INTO comment VALUES (9360,666,1626,'Gamer','re(2): a thought','2003-11-09 18:35:52',0,'You aren\'t really supposed to include leading zeroes in a number. That\'s enough reason for me.',9359,0);
INSERT INTO comment VALUES (9361,1475,4235,'casper','everyones answers thus far','2003-11-09 20:52:12',0,'what i haven\'t heard anyone mention yet is what about Puerto Rico and the U.S. Virgin Islands which are all under U.S. Control.',NULL,0);
INSERT INTO comment VALUES (9362,666,3623,'jaypee','','2003-11-09 21:03:31',3,'full solution by jaypee\r\n\r\nif you\'re multiplying by 4 A must be an even number\r\n\r\nso If A = 2 then E = 3 or 8\r\n\r\nif A = 4 then E = 1 or 6\r\n\r\nif A = 6 then E = 4 or 9\r\n\r\nif A = 8 then E = 2 or 7\r\n\r\nthe possibilities for ABCDE are\r\n\r\n2_ _ _3\r\n2_ _ _8\r\n4_ _ _1\r\n4_ _ _6\r\n6_ _ _4\r\n6_ _ _9\r\n8_ _ _2\r\n8_ _ _7\r\n\r\nbut A must be less than E so that narrows the possibilities down to\r\n\r\n2_ _ _3\r\n2_ _ _8\r\n4_ _ _6\r\n6_ _ _9\r\n\r\nfor 2_ _ _3 A = 2 but E would have to equal 8\r\n\r\nso 2_ _ _8 is a possibility\r\n\r\nfor 4_ _ _6 A = 4 but E would have to equal either 1 or 2\r\n\r\nfor 6_ _ _9 A = 6 but E would have to equal either 2 or 3\r\n\r\nso the only possibility is 2_ _ _8\r\n\r\nregardless if D is even or odd B would always be odd because if you multiply by 4 any digit it will always come out even but if you add 3 to that the result will always be odd so B will be either\r\n1, 3, 5, 7 or 9\r\n\r\nnow the sum of the middle three digits must equal 8 by elimination of 9\'s\r\nfor example: the the number 349 3 + 4 + 9 = 7\r\n\r\nif B = 1 and D = 7 then C = 9\r\nif B = 3 and D = 5 then C = 9\r\nif B = 5 and D = 3 then C = 9\r\nif B = 7 and D = 1 then C = 9\r\nif B = 7 and D = 6 then C = 4\r\nif B = 9 and D = 4 then C = 4 which is not possible\r\n\r\nif B = 7, D = 6 and C = 4 in the number ABCDE\r\nthen C in the number EDCBA is equal to 8 but C must be equal in both numbers so the only possible number for C is 9\r\n\r\nso far we have 2_9_8\r\n\r\nso by eliminating 9 as a possible value for B\r\nwe now have 1, 3, 5 and 7 for possible value for B\r\n\r\nthe possible combinations are:\r\n\r\nB = 1 and D = 7\r\nB = 3 and D = 5\r\nB = 5 and D = 3\r\nB = 7 and D = 1\r\nthe only combination that will work is B = 1 and D = 7\r\n\r\nso your number is 21978 for ABCDE\r\n\r\nEdited on November 9, 2003, 9:09 pm\r\n\r\nEdited on November 9, 2003, 9:15 pm\r\n\r\nEdited on November 9, 2003, 9:17 pm\n\nEdited on November 9, 2003, 9:21 pm',NULL,0);
INSERT INTO comment VALUES (9363,544,4235,'casper','answer','2003-11-09 21:07:23',0,'you are a match',NULL,0);
INSERT INTO comment VALUES (9364,937,4235,'casper','answer','2003-11-09 21:10:07',0,'you are an ear ',NULL,0);
INSERT INTO comment VALUES (9365,990,4235,'casper','answer','2003-11-09 21:14:57',0,'his team didnt score either and the lost it in over time ',NULL,0);
INSERT INTO comment VALUES (9366,1010,4235,'casper','answer','2003-11-09 21:19:18',0,'soul',NULL,0);
INSERT INTO comment VALUES (9367,666,4236,'Jim Butt','Concur','2003-11-09 21:31:10',0,'Brute force shows this in Excel, too. Next problem.',NULL,0);
INSERT INTO comment VALUES (9368,649,4224,'PhatFingers','Figuring out loud.','2003-11-09 23:29:35',0,'Bag A has marbles bbbw, bag B has bwww.\r\nThe odds of the 1st black marble being drawn from bag A was 3:4 (3 ways of drawing a black marble from A, 4 ways of drawing a black marble from the whole set of A+B).\r\n\r\nThe odds of drawing a second black marble from bag A are 3:4 times 3:4, or 9:16.\r\nThe odds of drawing a second black marble from bag B are 1:4 times 1:4, or 1:16.\r\n\r\nOdds of drawing a second black marble from either bag are the sum of the odds for the two bags, or 10:16, which can be reduced to 5:8. Yup.',NULL,0);
INSERT INTO comment VALUES (9369,248,4235,'casper','in response to the answer','2003-11-10 00:24:10',0,'i had a girlfriend that managed a 7-11 and the reason for the locks is this. if only 1 person works the midnight shift then yhe doors are locked for saftey reasons ans the person is to clean the store until the manager or second employee gets there. it,s a saftey policy. ',NULL,0);
INSERT INTO comment VALUES (9370,1488,3196,'Dan','re: solution','2003-11-10 00:38:34',0,'All correct except 5, which is \"Variety is the spice of life\". \r\n \r\nHere are some more of these. I\'ll supply the answers too, lest I be accused of going outside channels to post a new puzzle.\r\n \r\n6. All that coruscates with resplendence will not assay auriferous. (All that glitters is not gold.)\r\n \r\n7. Sorting on the part of mendicants must be interdicted. (Beggars can\'t be choosers).\r\n \r\n8. Male cadavers are incapable of rendering any testimony. (Dead men tell no tales.)\r\n \r\n9. The temperature of the aqueous content of an unremittingly ogled saucepan does not reach 212 degrees Fahrenheit. (A watched pot doesn\'t boil)\r\n \r\n10. Neophite\'s serendipity. (Beginner\'s luck)\r\n \r\n11. A revolving lithic conglomerate accumulates no congeries of a miniscule, verdant bryophyte. (A rolling stone gathers no moss)\r\n \r\n12. Pulchritude possesses solely cutaneous profundity. (Beauty is only skin deep)\r\n \r\n13. Freedom from incrustations of grime is contiguous to rectitude. (Cleanliness is next to godliness).\r\n \r\n14. It is fruitless to become lachrymose of precipitately departed lactile fluid. (Don\'t cry over spilt milk).\r\n \r\n15. Eschew the implement of correction and vitiate the scion. (Spare the rod and spoil the child).\r\n \r\n16. The stylus is more potent than the rapier. (The pen is mightier than the sword).\r\n \r\n17. It is fruitless to attempt to indoctrinate a superannuated canine with innovative maneuvers. (You can\'t try to teach an old dog new tricks)\r\n \r\n18. Surveillance should precede saltation. (Look before you leap)\r\n \r\n19. Scintillate, scintillate, diminutive asteroid. (Twinkle,twinkle, little star). \r\n\r\n20. The person presenting the ultimate cachinnation possesses thereby the optimal cachinnation. (He who laughs last, laughs best).\r\n \r\n21. Exclusive dedication to necessitous chores without interludes of hedonistic diversion renders Jack a hebetudinous fellow. (All work and no play makes Jack a dull boy). \r\n \r\n22. Individuals who make their abodes in vitreous edifices would be advised to refrain from catapulting petrious projectiles. (People who live in glass houses should not throw stones).\r\n \r\n23. Where there are visible vapors having their provenance in ignited carbonaceous materials, there is conflagration. (Where there\'s smoke, there\'s fire).\r\n \r\n24. Abstention from any aleatory undertakings precludes a potential escalation of a lucrative nature. (Nothing ventured, nothing gained.) \r\n \r\n25. Missiles of ligneous and of nonmetallic mineral consistency have the potential to fracture my osseous structure, but malicious appellations are eternally innocuous. (Sticks and stones may break my bones, but words will never hurt me.) \r\n \r\n26. Desist from enumerating your fowl prior to their emergence from the prenatal ovoid structure. (Don\'t count your chickens before they hatch). \r\n \r\n27. Disposition to inquiry deprived the feline of its vital state. (Curiosity killed the cat).\r\n \r\n28. It is practicible to entice an Equus Caballus to a reservoir of liquid hydrogen oxide, but coercing him to imbibe is insuperable. (You can lead a horse to water, but you can\'t make him drink.)\r\n \r\n29. Upon the non-presence of the Felis Catus the Mus Musculi proceed to engage in sportive capers. (When the cats away the mice will play.)\r\n \r\n30. A buffoon and his accumulation of legal tender are expeditiously disunited, (A fool and his money are easlily parted.)\r\n \r\n31. Exigency is the matriarch of ingenious contrivance. (Neccessity is the mother of invention).\r\n \r\n32. Probity gratifies reflexively. (Honesty is its own reward.)\r\n \r\n33. Promiscuity, controlled substances, and annepestic tempo. (Sex, drugs, and roll \'n\' roll). \r\n',9277,0);
INSERT INTO comment VALUES (9371,1229,4235,'casper','i think i have the right answer','2003-11-10 02:51:53',0,'if i understand the questions correctly, the grandfather gave16,384on the 15th birthday and the grand mother gave 10,837. Now as far as the second part the answer is the grandfather w/ 268,435,395. after all the question was who gave the most after the 27 yrs. if you add all that the grandfather gave over the entire 27 yrs. you get 268,435,395. where as the grandmother only gave 88,756,884.',NULL,0);
INSERT INTO comment VALUES (9372,1236,3136,'Popstar Dave','Solution','2003-11-10 07:08:00',3,'As the chamber is spun after every turn the probability of a shot being fired on any turn is (1/6) the probability of a miss is (5/6).\r\n\r\nPlayer 1 could lose on the first turn. This has a probability of (1/6). \r\n\r\nIf not, they could lose by missing on the first turn, then the second player also misses, then the first player loses on their second turn. This has a probability of (5/6)²(1/6). \r\n\r\nIf this still doesn\'t happen then they could lose by both players missing on their first two turns then player one loses on their third turn. This has a probability of (5/6)^4(1/6). \r\n\r\nAs this pattern continues indefinately, the probability of player one losing is the total of the infinite series:\r\n(1/6) + (5/6)^2(1/6) + (5/6)^4(1/6) + ... + (5/6)^n(1/6)\r\n\r\nThis equates to 6/11 or a 54.545% chance of the first player losing.',NULL,0);
INSERT INTO comment VALUES (9373,1236,4082,'wonshot','solution','2003-11-10 10:25:44',0,'The probability that the first man will lose is 54/99. To get this answer you must sum an infinite series. The first term is 1/6, the probability that he will lose on the first round. The next term will be (5/6)*(5/6)*(1/6), the probability that he will not lose on his first shot times the probability that his opponent will not lose on his first shot times the probablity that he will lose on his second shot.\r\nContinuing in this way, his overall chances of losing are 1/6 + (5/6)^2*(1/6) + (5/6)^4*(1/6) + . . . + (5/6)^(n-1)*(1/6) = 54/99.\r\nHe has a slightly greater chance of losing than his opponent as he must take his chances first. This assumes that one man must lose and that they do not quit after one round.',NULL,0);
INSERT INTO comment VALUES (9374,1236,4082,'wonshot','re: Solution','2003-11-10 10:28:12',0,'popstar dave you beat me and reduced your fraction.',9372,0);
INSERT INTO comment VALUES (9375,1236,3224,'Lee','solution','2003-11-10 10:29:36',0,'Round 1\r\nThe first shooter has a 1/6 chance of losing (or 6/36)\r\nThe second has a 5/6 chance of getting the gun, then a 1/6 chance of losing (or 5/36)\r\nSo the first shooter in the round is 6/5 times more likely to lose.\r\nThis follows in any round - since a round without the gun going off can be viewed as one event, like a coin toss, and can be ignored for future probabilities.\r\nSince the first shooter has 6 chances to lose for every 5 chances the second shooter has, it follows the probability the first man will lose is 6/11',NULL,0);
INSERT INTO comment VALUES (9376,1236,4082,'wonshot','re: solution','2003-11-10 10:32:29',0,'I like that explanation of how 6/11 isn\'t just an arbitrary percentage.',9375,0);
INSERT INTO comment VALUES (9377,1236,3224,'Lee','completeness','2003-11-10 11:45:12',0,'In general if p is the probability associated with the gun going off then\r\nShooter 1 has p probability of shooting himself in the round\r\nShooter 2 has (1-p)p probability of shooting himself in the round.\r\nThe first man is therefore always p/(1-p)p (cancelling gives) 1/(1-p)more likely to \'lose\'.\r\nProbability first man will lose is given by\r\n1/ (1-p)+1\r\nAnd for the second man;\r\n(1-p) / (1-p)+1\r\nSo in general the probability that the first man will lose is 1/ (2-p)\r\n',NULL,0);
INSERT INTO comment VALUES (9378,1236,2716,'Federico Kereki','An easy solution','2003-11-10 12:46:22',3,'The chance of the second player dying is 5/6 the odds of the first player dying -- if the first player survives the shot (5/6 probability) then the second player becomes the first player.\r\n\r\nAs the probabilities must sum 1, the first player\'s probability is 6/11 and the second\'s 5/11, which are in the correct ratio. \n\nEdited on November 10, 2003, 1:36 pm',NULL,0);
INSERT INTO comment VALUES (9379,1491,250,'Nick Reed','Or...','2003-11-10 13:57:48',0,'...he could have bought some fishing line. Thread it up through the eyes of the rod and create a loop of line along its length that extends back down to the handle again. Most fishing rods are designed to bend to some extent, so by keeping the loop of line held taut, and the rod bent over, it could be considered shorter now as a result.',NULL,0);
INSERT INTO comment VALUES (9380,1350,3172,'SilverKnight','solution','2003-11-10 14:53:22',3,'As Lee pointed out in his \"completeness\" comment for a previous problem, the total probability must equal one.\r\n\r\nAnd since person B is essentially the first player, B has the first and best chance of winning (of 1/6).\r\n\r\nSo... the others following are 5/6 as likely of winning as the previous player.\r\n\r\nSo, call B\'s chance x. Then C\'s chance is 5/6x and A\'s chance is 25/36x.... and this must total one.\r\n\r\nSo we set it up:\r\nx + 5/6x + 25/36x = 1\r\n\r\nand x = 36/91\r\n\r\ntherefore,\r\nB\'s chance is 36/91\r\nC\'s chance is 30/91, and\r\nA\'s chance is 25/91\n\nEdited on November 10, 2003, 2:54 pm',NULL,0);
INSERT INTO comment VALUES (9381,1350,775,'Cory Taylor','re: solution','2003-11-10 14:59:43',0,'An interesting method, cetainly easier than attempting the full series simplification...\r\nIt\'s very impressive that you can solve this so quickly (within 10 minutes of the posting). You must have some sort of alert to new problems being posted!!',9380,0);
INSERT INTO comment VALUES (9382,1350,3172,'SilverKnight','re(2): solution','2003-11-10 15:05:35',0,'Thanks Cory...\r\n\r\nI will direct you (and others) to a previous forum comment of mine.\r\n\r\n--- SK',9381,0);
INSERT INTO comment VALUES (9383,1236,3196,'Dan','A footnote to this problem','2003-11-10 15:59:16',0,'Had DJ stated that \"the chamber is NOT spun after every turn\" (as in that infamous scene in the movie \"Malcolm X\"), then the odds change. (And you\'d have to have a hole in your head to play it this way!) The decreasing likelihood of getting to succeeding turns is offset by the fewer and fewer possible empty chambers..... \r\n\r\n1st turn: 1/6 for 1st guy to lose, same as before\r\n2nd turn: (5/6)*(1/5) = 1/6 for 2nd guy to lose\r\n3rd turn: (4/6)*(1/4) = 1/6 for 1st guy to lose\r\n4rth turn: (3/6)*(1/3) = 1/6 for 2nd guy to lose\r\n5th turn: (2/6)*(1/2) = 1/6 for 1st guy to lose\r\n6th turn: 2nd guy loses if it gets this far\r\n \r\nFirst guy\'s chance of losing in this game is 1/2. \r\n\n\nEdited on November 10, 2003, 11:53 pm',NULL,0);
INSERT INTO comment VALUES (9384,1236,3136,'Popstar Dave','re: A footnote to this problem','2003-11-10 18:50:30',1,'If the chamber\'s not spun after every turn \"you\'d have to have a hole in your head to play it this way\"?!!?!!\r\n\r\nAre you trying to tell my that it\'s perfectly fine to play, as long as the chamber is spun after each turn?\r\n\r\nI don\'t like the idea of people shooting themselves, so here\'s my version of the problem:\r\n\r\nTwo men are trying to find a gold coin in a container that contains the gold coin and five other coins of the same weight, shape and size (i.e. indistinguishable by touch)\r\nThey take turns reaching into the container without looking and drawing out a random coin. If they draw a coin that isn\'t gold they return it to the box and the turn passes to the other player.\r\n\r\nWhat is the probability that the first man will get the gold coin?\r\n\r\nThere we go, no dead people! \r\nAs another flavor, you added info just because it wasnt sed it cant happen in the question. So... who\'s not to say that there were already broken eggs to be able to be sold? Who\'s not to say that someone wanted 0.0000000000000000000000001 of an egg + half of that? Just by assuming what\'s not sed in the question can lead to too many possibilities. So, instead of trying to find a terribly hard way, just find the easy way. The answer is clear- 7.\n\nEdited on November 11, 2003, 7:27 pm',9421,0);
INSERT INTO comment VALUES (9430,574,4270,'Chelsea','wow.','2003-11-11 21:32:40',3,'wow that was easy. mr north took south road, mr south took west road, mr east took north road and mr west took east road.',NULL,0);
INSERT INTO comment VALUES (9431,1491,4270,'Chelsea','uhh...','2003-11-11 21:42:20',0,'I say he bought another fishing pole that was 6feet.',NULL,0);
INSERT INTO comment VALUES (9432,1428,3196,'Dan','Spare the rod, spoil the magician','2003-11-12 02:39:32',3,'Every number between 1 and 31 (inclusive) can be uniquely represented as a sum of one or more of the following powers of 2 (where the symbol ^ means \"raised to the power of\"):\r\n\r\n2^0 = 1 \r\n2^1 = 2 \r\n2^2 = 4 \r\n2^3 = 8 \r\n2^4 = 16 \r\n\r\nFor example, 7 = (2^2) + (2^1) + (2^0) \r\nand 21 = (2^4) + (2^2) + (2^0) \r\n\r\nSo let\'s call the five rods A B C D E. Write each of the numbers 1-31 on them as follows:\r\n\r\nWrite the number on A if, when it is represented as a sum of those powers of 2, the sum does **NOT** include 2^0 \r\nWrite it on B if the sum does **NOT** include 2^1\r\nWrite it on C if the sum does **NOT** include 2^2\r\nWrite it on D if the sum does **NOT** include 2^3\r\nWrite it on E if the sum does **NOT** include 2^4 \r\n \r\n (For example, 18 = 2^4 + 2^1, and since this sum does not contain 2^0, 2^2 or 2^3, we would write 18 on A, C and D)\r\n \r\nFinally, write 31 on **ALL** the rods. \r\n \r\nWrite these numbers on these rods in this exact physical sequence from the tops of the rods: \r\n\r\nA = {2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,31} \r\nB = {1,4,5,8,9,12,13,16,17,20,21,24,25,28,29,31} \r\nC = {3,2,1,5,8,9,10,11,16,18,19,24,25,26,27,31} \r\nD = {4,2,3,1,5,6,7,16,17,18,19,20,21,22,23,31} \r\nE = {5,2,3,4,1,6,7,8,9,10,11,12,13,14,15,31} \r\n\r\nThen if the person shows the magician the numbers 2,1,3,4,5, the magician will instantly know that the person had picked 31, the only number on all the rods. If the person only shows him 3, he will know that the person has picked a number which is only on the rod that does not include numbers with representative sums that contain 2^2 -- so the number is (2^0) + (2^1) + (2^3) + (2^4) = 27. If he shows him 3 and 5, the magician will know that the picked number\'s representative sum does not contain 2^2 or 2^4 -- hence it must be (2^0) + (2^1) + (2^3) = 11. \r\n\r\netc. \r\n\n\nEdited on November 12, 2003, 7:47 pm',NULL,0);
INSERT INTO comment VALUES (9461,1458,4296,'Stephen Buck','Maybe!?','2003-11-12 20:05:05',0,'You could get a large radio(Boom Box) set it next to the cigarette and crank up the volume. The sound waves would surly know it over.',NULL,0);
INSERT INTO comment VALUES (9433,1428,3196,'Dan','re: The top number?','2003-11-12 02:58:35',0,'Charlie, you wrote: \"If the person tells you it\'s on no rods, it\'s 31, as the total is zero to be subtracted from 31.\"\r\n \r\nThis solution fails because the problem strongly implied that no number can be omitted from the rods, since the problem stated that \"Then you ask people to pick a number and show you only the top number of whatever rods it is on.\" They don\'t apparently have the option of not showing at least one top number. The fact that Lewis highlighted the phrase \"only the top number\" indicates that this was probably a tricky aspect of the puzzle. The \"top\" number has to be \"the number physically at the top of the rod\", not \"the number of greatest magnitude on the rod.\" But what do I know? I\'m the guy who answered the \"Egg-celent Question\" puzzle with that \"The yoke is on the previous posters\" solution. I still have egg on my face over that one. \r\n\n\nEdited on November 12, 2003, 3:04 am',9413,0);
INSERT INTO comment VALUES (9434,1428,4277,'Nelson','Why so complicated?','2003-11-12 03:22:57',0,'If the top number of each rod is the following\r\nA-1 B-2 C-4 D-8 E-16 then the solution would be the following:\r\nA 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31\r\nB 2 3 6 7 10 11 14 15 18 19 22 23 26 27 30 31\r\nC 4 5 6 7 12 13 14 15 20 21 22 23 28 29 30 31\r\nD 8 9 10 11 12 13 14 15 24 25 26 27 28 29 30 31\r\nE 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31\r\n\r\nIf a someone picks the number 27 then they would show A B D E and you would see 16 8 2 1 and you just add 16+8+2+1=27 and you say 27. ',NULL,0);
INSERT INTO comment VALUES (9435,27,4275,'Brainteaser','That cannot be.','2003-11-12 03:34:54',0,'I remember seeing this problem before and the solution was that the professor gives the exam IMMEDIATE after he tells them that he will give a surprise exam, since by the same logic as mentioned in The Solution, it cannot be on any of those days in the next week nor any other day BUT the current day.',NULL,0);
INSERT INTO comment VALUES (9436,658,4279,'Mark Longhurst','Solution','2003-11-12 03:47:14',0,'There must have been 129 glasses.\r\n\r\nRemoving 1 (the random test at the start) leaves 128, which divides by 2 all the way down to 1. Therefore half the sample can be tested (starting with 64) and, if no poison is found that half can be discarded. If poison IS found in that half, the other half are discarded. Then you test half the remaining glasses, again discarding the half with no poison. keep halving the sample until you are down to the last 2, then test 1.',NULL,0);
INSERT INTO comment VALUES (9437,817,4280,'Trevor','Remember!Remember the 31st of December?','2003-11-12 06:29:52',0,'She was born on the 31st of December, Therefore \"the day before yesterday\" was the 30th of December!!',NULL,0);
INSERT INTO comment VALUES (9438,1493,4098,'lovejoy','solution','2003-11-12 07:31:49',0,'It nwas a game of chess',NULL,0);
INSERT INTO comment VALUES (9439,1472,4265,'Yevgen','re: Solution? (& extensions of the problem)','2003-11-12 08:39:23',0,'I came up with exactly the same solution, i.e. given the distance to travel r (0<=r<=1) the probability of staying in the square is P = (r^2-4r)/pi+1\r\n\r\nAnother interesting problem is to calculate the probability of staying within the square when distance r is randomly chosen from an interval [r0,r1] where 0<=r0<=r1<=1 (Answer 1 at the bottom of the message)\r\n\r\nYet another extension of the problem is to calculate the probability of staying within the square for any r > 0. Obviously for r >= 2^(1/2) P=0 so we only have to consider 1<=r<=2^(1/2). (Answer 2 at the bottom)\r\n\r\nThe probability of staying within the square when r is randomly chosen from an interval [r0;r1] where 0<=r0<=r1 can be calculated for any specific case of r0 and r1 using the formulae from the above problems, but general formula is a bit messy.\r\n\r\nAnyone to offer a solution for a rectangle with one unit side and the other side of s where s > 1?\r\n\r\n\r\n\r\n\r\n\r\nAnswer1:\r\n\r\nP=((r1^2+r1r0+r0^2)/3 - 2(r1+r0))/pi+1\r\n\r\nAnswer2:\r\n\r\nP=[4(r^2-1)^(1/2)-r^2-2-4arctg(-1/(r^2-1)^(1/2))]/pi-1',9266,0);
INSERT INTO comment VALUES (9440,1493,3196,'Dan','Not so fast !!','2003-11-12 08:46:31',0,'This riddle is diabolically devious. Without even reading any other post(s), I know that they all say that it refers to a chess game. It does not. The riddle states that there were \"30 men with ladies two.\" A chess game has 2 ladies (the queens), only 26 men (2 kings, 4 bishops, 4 knights, 16 pawns), and 4 non-gendered rooks (castles). And if all the pieces are referred to as chessmen, then there are 32 men, not 30. \"Dressed quite formal, black and white\" - of course no one \"dresses\" chess pieces. They are made of wood or plastic, and painted various colors. And \"movement turned to nasty fight\" - chess games are enjoyable, never nasty. \r\n \r\nThe riddle actually refers to the Rule of the Thirty Tyrants in Athens, who were oligarchs put in place by the Spartan general Lysander after the defeat of Athens by Sparta in the Peloponnesian War. These 30 men ruled over Athens in 404-403 B.C. As it was customary for the Greek historians to refer to their cities in the feminine case, Athens and Sparta are the two \"ladies\" of the riddle. These men dressed in Greek togas, which were an austere black-and-white in Classical Greece. And the rule of the Thirty Tyrants was a \"nasty fight\" indeed against the freedom-loving Athenians, culminating in their violent overthrow by the exiled Athenian general Thrasybulus. One tragic aftereffect of their rule was Athens\' execution of Socrates in 399 B.C. He was wrongly suspected of being a quisling during their rule, when in fact he had been a courageous conscientious objector. \n\nEdited on November 12, 2003, 8:59 am',NULL,0);
INSERT INTO comment VALUES (9441,1493,4059,'Saso','re: Not so fast !!','2003-11-12 08:57:04',0,'I came to the same solution as lovejoy but reading yours Dan, I am in great doubt :)',9440,0);
INSERT INTO comment VALUES (9442,1493,3136,'Popstar Dave','re(2): Not so fast !!','2003-11-12 09:06:11',1,'Dan, \r\nI think you\'ve got a little too much time on your hands!',9441,0);
INSERT INTO comment VALUES (9443,1493,4170,'Alex Layman','Getting a life','2003-11-12 11:55:20',0,'I think that we need to agree to send Dan a life. \"The nasty fight\" refers to the taking and killing of your opponents pieces, not to some obscure Greek battle. ',NULL,0);
INSERT INTO comment VALUES (9444,1493,2839,'FatBoy','with apologies to the Popstar','2003-11-12 12:40:49',0,'Hmmmmmm, a little rewrite might get around Dan\'s concerns (although I rather like his answer), With Apologies to Popstar Dave (and to anyone who finds my abuse of the urban venacular offensive), how about this version: \r\nSandi: \" I could not find a pattern...or maybe there wasn\'t one??\" \r\nI think possibly you are expecting this puzzle to be deeper than it really is. In this case, I believe you\'ll find that, instead, it\'s just perhaps a little easier than one would normally expect... ;)',9542,0);
INSERT INTO comment VALUES (9545,1051,4351,'Dennis','Its a ...','2003-11-16 20:42:49',0,'Its a manitee they are called sea cows and only have two front legs and a flat beaver like tail',NULL,0);
INSERT INTO comment VALUES (9546,670,3558,'Tristan','re: a little more straightforward','2003-11-16 20:52:59',0,'If you take out the first and last 24 1s, you\'d be left with 1? with 24 zeros afterwards. I suppose that means 10^24 is divisible by 13. Yes, it is...',9520,0);
INSERT INTO comment VALUES (9547,672,4351,'Dennis','Gareth and Vlad Unrelated to topic','2003-11-16 20:53:04',0,'DO you two Play Ultima online?',NULL,0);
INSERT INTO comment VALUES (9548,1475,4356,'Blah','Clue?','2003-11-17 07:32:47',0,'I wonder if it involves travelling across sea rather than land... Hawaii -> Alaska etc etc...? I dunno.',NULL,0);
INSERT INTO comment VALUES (9549,1447,4356,'Blah','THE SOLUTION!!!','2003-11-17 07:42:00',0,'The sentence \"A Secret Message\" is merged in with the phrase \"Take the money to the swinging bridge the other side of town.\"\r\n\r\nQuite easy, really.',NULL,0);
INSERT INTO comment VALUES (9550,1351,4356,'Blah','Easy','2003-11-17 07:50:51',0,'\"It may look fine when YOU YOU read it over hastily... it\'s NOT NOT to hard to spot...\" some words are repeated very cunningly.',NULL,0);
INSERT INTO comment VALUES (9551,1220,1301,'Charlie','re: A revised solution:','2003-11-17 08:20:40',0,'This is valid only if the method used to randomize the chord was indeed to choose its midpoint. Other methods of randomization produce the other answers. There isn\'t just one answer.',9533,0);
INSERT INTO comment VALUES (9552,1382,3372,'Sam','Partial Solution','2003-11-17 09:07:31',1,'You would have to break links 4 and 11 to pay him one a day:\r\n\r\nOOO U OOOOOO U OOOOOOOOOOOO\r\n\r\nGive him a broken one, then another broken one, then take them back and give him the three, then a broken one, then another broken one, then take them back and give him the six, and so on so forth.\r\n\r\nThe rest of the puzzle to follow sometime in the future...',NULL,0);
INSERT INTO comment VALUES (9553,1382,1183,'fwaff','Most of the rest of the solution','2003-11-17 09:57:00',3,'Following on from Sam\'s correct solution to the first part of the problem...\r\n\r\nWith 3 breaks we have enough pieces to pay the person in days 1-3 using the broken links. Then we need a 4-link piece to pay him on day 4 (taking back the broken links).\r\nOn days 5-7 we again pay him using the broken links until day 8 when we need an 8-link piece to pay him (taking back the 3 broken links and the 4-link piece).\r\nThis is repeated which takes us to day 16 when we need a 16-link piece (taking back the 3 broken links, the 8-link and the 4-link).\r\nRepeating again takes us through to day 32 when we need a 32-link piece.\r\nRepeating again takes us through to day 63 when we run out of chain.\r\nSo the pieces in the 3 broken link chain are: 32 links, 1st broken link, 16 links, 2nd broken link, 8 links, 3rd broken link, 4 links.\r\n----------------------------------------------\r\nTaking this to a general case with x broken links we would have a chain made up of:\r\n(x+1)links, 1st broken link, 2(x+1)links, 2nd broken link, 4(x+1)links, 3rd broken link, ... , xth broken link, (2^x)(x+1)links\r\n\r\nUnfortunately this is as far as I go since my sum theory is sufficiently distant that I can\'t remember how to simplify the equation to give a neat solution as to the total number of links.\r\n',NULL,0);
INSERT INTO comment VALUES (9554,1382,1183,'fwaff','The last little bit...','2003-11-17 10:10:52',3,'Following a quick trawl of tinternet I\'ve found the formula for the sum of the geometric series at the end of my previous post. The total number of links is:\r\n\r\n(x+1)((2^(x+1)) - 1) + x\r\n\r\nwhich can be simplified to:\r\n\r\n(2^(x+1))(x+1) - 1\r\n\r\nAs a check, putting x=2 into this gives 23 and x=3 gives 63 which are consistent with the rest of the answer.',9553,0);
INSERT INTO comment VALUES (9555,1382,4055,'S','Comment to Levik','2003-11-17 10:45:11',0,'Just a comment: It appears this problem refers to another problem, that holds helpful information required to understand this puzzle. It would be great to have either the rules for chain payment restated or have a reference to the original puzzle.\r\n\r\nS\n\nEdited on November 17, 2003, 10:47 am',NULL,0);
INSERT INTO comment VALUES (9556,1447,2839,'FatBoy','re(2): I am confused','2003-11-17 10:47:50',0,'Dan,\r\nI know where you are coming from with the Brad Pitt thing, it happens to me all the time. Its only really embarassing when its Jennifer Anniston. Thank goodness my wife is a patient woman.',9542,0);
INSERT INTO comment VALUES (9557,1220,4323,'Benjamin J. Ladd','You\'re right!','2003-11-17 10:56:19',2,'I wish I would have read the other comments more closely before posting my solution. I\'m really amazed at this paradox.\r\n\r\nWell, I created a simple program in QBasic that creates two absolutely random points on a circle of radius 10 and calculated how many times out of 100000 that the length of the chord is greater than the radius. I was surprised. Unless my algorithm is off (which I don\'t believe it is), the computer returned a value of 63.2 (and I ran multiple tests). I randomized the random number generator with the computer\'s timer before getting any value for the points to ensure absolute randomness and calculated values for 100,000 iterations. This method seems the closest to the cosmic ray method and I really can\'t see the values that I got for this approaching 66.66 even though they are close. If I had more time, I think I\'d make a program that works for a single fixed point and the second point totally random, and see how close they compare.',NULL,0);
INSERT INTO comment VALUES (9558,674,1686,'DuCk','a starting shot...','2003-11-17 13:48:03',0,'Well, I\'m first noting that x is maximized when either y or z is 0. It doesn\'t matter which one is 0 due to the structure of the equations as they both lead to the same two variable equations with interchangable y and z. Solving these two two-variable equations yields an answer of x maximized at x = 5-√2 = 3.5857\r\n\r\nThis might make sense or I could just be talking out of my butt....',NULL,0);
INSERT INTO comment VALUES (9559,674,1301,'Charlie','re: a starting shot...','2003-11-17 14:15:32',0,'xy+yz+zx=3 is a hyperboloid of two sheets that intersects the plane x+y+z=5 in a circle, but its center lies along an axis of x=y=z and is therefore diagonal to all the axes. Thus you can\'t take one of the variables as zero.\r\n\r\nA good way to visualize this is to use David Parker\'s DPGraph software, which is a lot cheaper than Mathematica, but produces 3-D graphs of things like this, including both surfaces. \r\n\r\nSee www.davidparker.com.',9558,0);
INSERT INTO comment VALUES (9560,1383,1626,'Gamer','Don\'t comment on this yet!','2003-11-17 14:50:58',2,'Unfortunately due to my mistake this got posted due to a mistake in typing in a comment rather than it should actually posting it.\r\n\r\nSo I would prefer if everyone didn\'t write on this yet!',NULL,0);
INSERT INTO comment VALUES (9561,674,3172,'SilverKnight','re: a starting shot...','2003-11-17 15:11:35',2,'My thoughts are to multiply the first equation by 3, the second equation by 5, and set them equal to each other (they\'re both equal to 15).\r\n\r\nThen solve for X, and find the gradient.\r\n\r\nSolve for the gradient =0...\r\n\r\nI did some \"back of the napkin\" calculations... and I find that max x = 13/3, while y = z = 1/3.\r\n\r\nI, admittedly did the problem quick and dirty... I hope someone will do this on his own and verify this work.\r\n\r\n--- SK',9558,0);
INSERT INTO comment VALUES (9562,674,1301,'Charlie','solution','2003-11-17 15:31:51',3,'(Corrected per SilverKnight\'s comment (#8)):\r\n\r\nSubstituting z=5-x-y into xy+yz+xz=3 gives\r\nxy+y(5-x-y)+x(5-x-y)=3 \r\n\r\nwhich can be simplified to \r\n-y²+(5-x)y+5x-x²-3=0\r\n\r\nConsidered as an equation to be solved for y, but without actually solving, we get a discriminant of 13+10x-3x² This must be positive in order for there to be a real solution for y.\r\n\r\nThe bounds of where this is positive are those two points where it is zero. So, setting that discriminant to zero, we get \r\n\r\nx=(10±√256)/6 = (10±16)/6\r\nor x = 13/3 or -1\r\n\r\nBetween these two values of x, the discriminant is positive, so y has a real value (as well as z).\r\n\r\nSo in answer to the question, the largest value that x can have is 13/3.\n\nEdited on November 18, 2003, 9:12 am',NULL,0);
INSERT INTO comment VALUES (9563,1383,3172,'SilverKnight','re: Don\'t comment on this yet!','2003-11-17 15:53:39',4,'Methinks you should allow people to post (since you\'ve already \"spilled the beans\" so to speak).\r\n\r\nAny scholar want to grant permission for people to post?',9560,0);
INSERT INTO comment VALUES (9564,1220,1301,'Charlie','re: You\'re right!','2003-11-17 15:58:59',0,'Perhaps you could post your program. If the method of randomization is to choose two random points on the circle, or one fixed point and one random point, then the probability should indeed be 2/3. The following program simulates the negative value, that the chord length is less than the radius and comes out with a probability close to 33%:\r\nRANDOMIZE TIMER\r\n\r\nFOR i = 1 TO 100000\r\n pt1 = RND(1)\r\n pt2 = RND(1)\r\n dist = ABS(pt1 - pt2)\r\n IF dist < 1 / 6 OR dist > 5 / 6 THEN hit = hit + 1\r\n ct = ct + 1\r\nNEXT\r\np = hit / ct\r\nq = 1 - p\r\nPRINT USING \"#.##### \"; p; SQR(ct * p * q) / ct\r\n\r\nA run produced:\r\n0.33283 0.00149\r\nindicating that indeed about 1/3 of the time the two points were within 60 degrees (1/6 of the full circle) of each other. The second number is the std error of the mean of the probability.\r\n\r\nIn fact, if the number of iterations is raised to 1,000,000, I get:\r\n\r\n0.33354 0.00047\r\n\r\nNote, if posting a program, leading spaces should each be converted to (I use a program to do this.)',9557,0);
INSERT INTO comment VALUES (9565,674,3172,'SilverKnight','re: solution','2003-11-17 15:59:29',4,'Charlie,\r\n\r\nI may VERY WELL need sleep (I\'m kinda tired), but doesn\'t x=5 require imaginary numbers (when the problem says that x, y, and z are all real).\r\n\r\n--- SK',9562,0);
INSERT INTO comment VALUES (9566,1220,1301,'Charlie','re(2): You\'re right!','2003-11-17 16:11:15',0,'In the case of the random chords being chosen by taking a random point within the circle and using that as the midpoint of the chord, the following program simulates that:\r\n\r\nRANDOMIZE TIMER\r\ncritDist = SQR(3) / 2\r\nFOR i = 1 TO 100000\r\n x = 2 * RND(1) - 1\r\n y = 2 * RND(1) - 1\r\n dist = SQR(x * x + y * y)\r\n IF dist < 1 THEN\r\n \r\n IF dist < critDist THEN hit = hit + 1\r\n ct = ct + 1\r\n END IF\r\nNEXT\r\np = hit / ct\r\nq = 1 - p\r\nPRINT USING \"####### \"; hit; ct;\r\nPRINT USING \"#.##### \"; p; SQR(ct * p * q) / ct\r\n\r\nIn this case the positive case is reported (prob of chord length greater than radius). It is reported as\r\n 58866 78570 0.74922 0.00155\r\nwith the first two numbers signifying 58866 hits out of 78570 tries (as in some cases the random points were not even in the circle and thus not counted). The probability does match the 3/4 you had specified in a prior post.',9564,0);
INSERT INTO comment VALUES (9567,1383,3386,'Victor Zapana','ahh...','2003-11-17 16:44:28',0,'come on Gamer... even I got the answer to this. Can\'t you just let us post comments on this. It\'s already posted. Probably half the people come to flooble already saw this.. so... come on.. lol',NULL,0);
INSERT INTO comment VALUES (9568,1383,1626,'Gamer','re: ahh...','2003-11-17 16:48:01',0,'If you can get permission, go for it. I think you should likely ask Ravi that mostly, as it was his problem that got bumped. :)',9567,0);
INSERT INTO comment VALUES (9569,1383,3386,'Victor Zapana','re(2): ahh...','2003-11-17 16:51:41',0,'fine... (PUBLIC ANNOUNCEMENT to RAVI): Can I have permission to answer this? (lol)',9568,0);
INSERT INTO comment VALUES (9570,674,1626,'Gamer','re: solution','2003-11-17 16:54:52',4,'I agree with SK. If your substituted equation is right, then I get 5y + y(5-5-y) + 5(5-5-y)=3\r\n\r\nThis substitutes to 5y-(y^2)-5y=3, or y^2=-3, which requires an imaginary value for 3.',9562,0);
INSERT INTO comment VALUES (9571,1383,3386,'Victor Zapana','hm...','2003-11-17 16:56:02',0,'actually ... hm.... mebe i dun have an answer... technically u dun give the answer to the guesser\'s last question... sry fr the semi-commenting of the problem b4 permission\r\n\r\nEdited on November 17, 2003, 4:56 pm\n\nEdited on November 17, 2003, 4:57 pm',NULL,0);
INSERT INTO comment VALUES (9572,674,1626,'Gamer','Also this way to think about it.','2003-11-17 16:57:38',4,'If x = 5, y = -z. This means yz is negative (assuming y and z are real), and since yx = -zx, 3 = something negative. This is a contradiction, so it doesn\'t work.\r\n\r\nI can\'t find a flaw yet in Charlie\'s solution; is this just extraneous solutions again?',NULL,0);
INSERT INTO comment VALUES (9573,1383,3172,'SilverKnight','re: hm...','2003-11-17 16:59:33',0,'Victor,\r\n\r\nNot to be disagreeable.... but the fact that the guesser *did* find the correct combination, after the \'divisible question\' was answered.... means that this riddle *can* be determined exactly.\r\n\r\nI\'m curious as to how you went about solving it, though.... :-)\r\n\r\nI would brute force it.\r\n\r\n--- SK',9571,0);
INSERT INTO comment VALUES (9574,1383,3386,'Victor Zapana','re(2): hm...','2003-11-17 17:08:35',0,'hmm.. well i guess and checked, not sure if it is \"brute force\" lol. I achieved an answer if the answer to the guesser\'s question was \"yes.\" I can\'t yet find one if it is \"no.\"',9573,0);
INSERT INTO comment VALUES (9575,674,3172,'SilverKnight','re: solution - corrected, I think','2003-11-17 17:17:00',3,'It\'s a good thought, and Charlie made an algebraic mistake (I think).\r\n\r\nIt *can* be simplified to -y² + (5-x)y + 5x - x² - 3 = 0 (He forgot the -3).\r\n\r\nContinue with this... find the descriminant, and I think you\'ll find the bounds to be 5/3 ± 8/3. And the higher of the two is 13/3, which agrees with what I wrote earlier.\r\n\r\n--- SK\n\nEdited on November 17, 2003, 5:18 pm',9562,0);
INSERT INTO comment VALUES (9576,1383,3172,'SilverKnight','re(3): hm...','2003-11-17 17:20:01',0,'lol...\r\n\r\nwell... if I *had* to guess... I would say there are THREE solutions if the answer is \"no\", but only ONE solution if the answer is \"yes\", and therefore the answer must have ben yes (since the guesser identified the combination after hearing the answer to the question).\r\n\r\n:-)',9574,0);
INSERT INTO comment VALUES (9577,1383,3386,'Victor Zapana','re(4): hm...','2003-11-17 17:21:57',0,'hm... nice \"guessing.\" lol. well if it is indeed yes, then i do have an answer yay. lol',9576,0);
INSERT INTO comment VALUES (9578,1383,3386,'Victor Zapana','re(5): hm...','2003-11-17 17:25:54',0,'hm wait. wudnt the number of solution then add up to 5? coz (5)C(1)= 5. (You already know 3 numbers, so u gotta find that last number from the 5 remaining numbers.) mebe im missing sumthing here....',9577,0);
INSERT INTO comment VALUES (9579,360,3386,'Victor Zapana','hmm...','2003-11-17 17:31:56',0,'My thoughts... Who here who have posted the answer knew the answer from previous tellings of it? Hm... I guess all of yas did, and so did I. So, to say it was easy is quite biased, for uve already read it. Really, would you have guessed \"Nothing\" immediately after reading this? Come on... This would be a pretty hard question if you didn\'t know the riddle previously, for you would probably think to urself that answer can\'t be nothing, it\'s gotta be something.',NULL,0);
INSERT INTO comment VALUES (9580,370,4361,'Johana','','2003-11-17 18:18:49',0,';\r\n',NULL,0);
INSERT INTO comment VALUES (9581,1383,4367,'Jeff','What do I do','2003-11-17 21:07:25',0,'If I think I know the answer?',NULL,0);
INSERT INTO comment VALUES (9582,1458,4351,'Dennis','solution?','2003-11-17 23:03:25',0,'simply blow it over',NULL,0);
INSERT INTO comment VALUES (9583,674,4374,'Richard','re(2): solution - corrected, I think','2003-11-18 00:40:16',0,'I confirm that x=13/3 is the solution. In addition to being the high end boundary for any of the variables such that the others don\'t go complex, it is also the ``calculus\" answer that you obtain by solving for x as a function of y, setting the derivative wrt y equal to 0, and solving for y. You get y=1/3 or 3, of which the 1/3 gives x=13/3, z=1/3 or x=1/3, z=13/3 and the 3 gives x=3, z=-1 or x=-1, z=3.',9575,0);
INSERT INTO comment VALUES (9584,1383,3224,'Lee','desperate','2003-11-18 02:44:04',0,'I\'m stuck. Royally. None of my 3 \'possibles\' are divisible by 7. It sounds like I\'ve found the three that SK guesses won\'t divide cleanly, whikst neglecting to find the possible.\r\nI normally like these.\r\nCan anyone point me?\r\n ',NULL,0);
INSERT INTO comment VALUES (9585,1383,3196,'Dan','Here is a corrected version of the original problem.','2003-11-18 04:20:44',3,'(OH OH, Gamer, I just noticed your warning to everyone not to post...)\r\n\r\nThe matrix, reloaded:\r\nReplace \"Is the number divisible by 7?\", by \"Is the number divisible by 5?\"\r\n\r\nThe combination is 7825\r\n \r\nExplanation:\r\n\r\n1235 (one of the guesses) has exactly one of its digits both correct in value and correct in position, vis-a-vis the true combination, Therefore, in the true combination, pos1=1 or pos2=2 or pos3=3 or pos4=5.\r\n \r\nIf pos1=1, then pos2=(3 or 5) or pos3=(2 or 5), \r\nor pos4=(2 or 3), since 1235 also has a digit correct in value but wrong in position. The only number like this that is consistent with the other two guesses is 1763.\r\n\r\nSimilarly, if pos2=2, then pos1=(3 or 5) or \r\nor pos3={1 or 5} or pos4={1 or 3}. I found no number like this that is consistent with the other two guesses.\r\n\r\nIf pos3=3, then pos1={2 or 5} or pos2={1 or 5} or pos4={1 or 2}, 7831 is the only number like this which is consistent with the other two guesses.\r\n\r\nLastly, if pos4=5, then pos1={2 or 3} or pos2={1 or 3} or pos3={1 or 2}. 7825 is the only number like this that is in keeping with the other two guesses. \r\n \r\nSo the potential combinations are: \r\n1763, 7831, and 7825.\r\n \r\nAnd when the guesser was told that the combination was indeed divisible by 5, he knew that the combination must be 7825. \r\n\r\n:-)\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\n\nEdited on November 18, 2003, 6:19 am',NULL,0);
INSERT INTO comment VALUES (9586,674,3275,'retiarius','another solution','2003-11-18 07:39:35',0,'x + y + z = 5\r\nx^2 + y^2 + z^2 + 2xy + 2yz + 2zx = 25\r\n2xy + 2yz + 2zx = 6\r\nx^2 + y^2 + z^2 = 19\r\nx max = √19\r\n\r\nsorry, something wrong.\r\n\n\nEdited on November 18, 2003, 7:54 am',NULL,0);
INSERT INTO comment VALUES (9587,1383,3172,'SilverKnight','Solution - the original problem is fine as it is!','2003-11-18 08:19:40',3,'The answer is 2765. And I am very impressed by the guesser, who apparently did this in his head.\r\n\r\nIf one executes the following program (which determines which numbers satisfy the problem\'s criteria):\r\n\r\n\r\n#include \"stdafx.h\"\r\n#include <iostream.h>\r\n\r\nint CheckDiff(int i, int j)\r\n{\r\n int numInRightPlace=0;\r\n int numInWrongPlace=0;\r\n\r\n if ( (i%10) == (j%10) )\r\n numInRightPlace ++;\r\n if ( ((i%100)/10) == ((j%100)/10) )\r\n numInRightPlace ++;\r\n if ( ((i%1000)/100) == ((j%1000)/100) )\r\n numInRightPlace ++;\r\n if ( (i/1000) == (j/1000) )\r\n numInRightPlace ++;\r\n\r\n if ( (i%10) == ((j%100)/10) )\r\n numInWrongPlace ++;\r\n if ( (i%10) == ((j%1000)/100) )\r\n numInWrongPlace ++;\r\n if ( (i%10) == (j/1000) )\r\n numInWrongPlace ++;\r\n\r\n if ( ((i%100)/10) == (j%10) )\r\n numInWrongPlace ++;\r\n if ( ((i%100)/10) == ((j%1000)/100) )\r\n numInWrongPlace ++;\r\n if ( ((i%100)/10) == (j/1000) )\r\n numInWrongPlace ++;\r\n\r\n if ( ((i%1000)/100) == (j%10) )\r\n numInWrongPlace ++;\r\n if ( ((i%1000)/100) == ((j%100)/10) )\r\n numInWrongPlace ++;\r\n if ( ((i%1000)/100) == (j/1000) )\r\n numInWrongPlace ++;\r\n\r\n if ( (i/1000) == (j%10) )\r\n numInWrongPlace ++;\r\n if ( (i/1000) == ((j%100)/10) )\r\n numInWrongPlace ++;\r\n if ( (i/1000) == ((j%1000)/100) )\r\n numInWrongPlace ++;\r\n\r\n if (numInRightPlace==1 && numInWrongPlace==1)\r\n return (1);\r\n else\r\n return (0);\r\n}\r\n \r\n\r\n\r\nint main(int argc, char* argv[])\r\n{\r\n int w, x, y, z;\r\n\r\n int check1 = 1235;\r\n int check2 = 4721;\r\n int check3 = 3862;\r\n\r\n for (w = 1; w<9; w++)\r\n for (x = 1; x<9; x++)\r\n for (y = 1; y<9; y++)\r\n for (z = 1; z<9; z++)\r\n if ( (w!=x) && (w!=y) && (w!=z) && (x!=y) && (x!=z) && (y!=z) )\r\n {\r\n int num = w*1000+x*100+y*10+z;\r\n if ( CheckDiff(check1, num) &&\r\n CheckDiff(check2, num) &&\r\n CheckDiff(check3,num) )\r\n cout << num << \\\" mod 7 = \\\" << num%7 << endl;\r\n }\r\n\r\n return 0;\r\n}\r\n2765\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (9588,1383,1301,'Charlie','In Basic','2003-11-18 09:40:19',3,'DECLARE SUB check (str1$, str2$, bl!, wh!)\r\nPRINT\r\nFOR n = 1234 TO 8765\r\n n$ = LTRIM$(STR$(n))\r\n check n$, \"1235\", black, white\r\n IF black = 1 AND white = 1 THEN\r\n check n$, \"4721\", black, white\r\n IF black = 1 AND white = 1 THEN\r\n check n$, \"3862\", black, white\r\n IF black = 1 AND white = 1 THEN\r\n good = 1\r\n FOR i = 1 TO LEN(n$)\r\n IF MID$(n$, i, 1) < \\\\\"1\\\\\" OR MID$(n$, i, 1) > \"8\" THEN\r\n good = 0: EXIT FOR\r\n END IF\r\n IF INSTR(MID$(n$, i + 1), MID$(n$, i, 1)) THEN\r\n good = 0: EXIT FOR\r\n END IF\r\n NEXT\r\n IF good THEN\r\n PRINT n$, n MOD 7\r\n END IF\r\n END IF\r\n END IF\r\n END IF\r\nNEXT\r\n\r\nSUB check (str1$, str2$, bl, wh)\r\n s1$ = str1$: s2$ = str2$\r\n bl = 0: wh = 0\r\n FOR i = 1 TO LEN(s1$)\r\n IF MID$(s1$, i, 1) = MID$(s2$, i, 1) THEN\r\n bl = bl + 1\r\n END IF\r\n NEXT\r\n FOR i = 1 TO LEN(s1$)\r\n ix = INSTR(s2$, MID$(s1$, i, 1))\r\n IF ix > 0 THEN\r\n wh = wh + 1\r\n s2$ = LEFT$(s2$, ix - 1) + MID$(s2$, ix + 1)\r\n END IF\r\n NEXT\r\n wh = wh - bl\r\nEND SUB\r\n\r\nwith results:\r\n1763 6\r\n2765 0\r\n7825 6\r\n7831 5\r\n\r\nwith 2765 uniquely divisible by 7.\r\n\r\n(The terminology black and white comes from MasterMind, which uses black and white pegs to indicate such matches.)\n\nEdited on November 18, 2003, 9:42 am',9587,0);
INSERT INTO comment VALUES (9590,1383,3172,'SilverKnight','re: Dear Silver Kinght and Charlie,,,,,','2003-11-18 11:36:47',0,'Dan,\r\n\r\nI\'m not really sure this is the right forum for this discussion....\r\n\r\nAnyway, I love the game of chess... but I don\'t play that well, so I don\'t think I\'d provide much challenge for you. Perhaps Charlie would.\r\n\r\nI certainly can\'t hold a candle to Kasparov.\r\n\r\nBut to answer your question: yes, I agree that it\'s very impressive that you didn\'t break a sweat in either of the two games you referenced. It\'s even more impressive that you chose to tell everyone about it.',9589,0);
INSERT INTO comment VALUES (9589,1383,3196,'Dan','Dear Silver Kinght and Charlie,,,,,','2003-11-18 11:19:12',0,'We are really going to have to play some chess !! (This is no bull...) I am quite the Internet chess player. On my favorite website, my rating approaches that of Gary Kasparov. I win about 98% of my games. Two of my recent victims were a guy who had tied for 2nd place in the 2nd World Open in 1986 (I dispatched him in 26 moves), and another who had tied for 2nd in the 2002 Joseph Ileto Memorial Open. And you know what? I didn\'t break a sweat in either of these games. Pretty impressive, don\'t you agree? ',NULL,0);
INSERT INTO comment VALUES (9591,1383,3196,'Dan','re(2): Dear Silver Kinght and Charlie,,,,,','2003-11-18 11:47:12',0,'Sorry, my subtle humor escaped you. I am only that good because I use a computer to defeat my human opponents, as you two did to solve this puzzle. (I also out-bench-pressed Arnold Schwarzenegger once, by using a forklift). No offense. I\'m just having a little fun at your expense. ',9590,0);
INSERT INTO comment VALUES (9592,1383,3172,'SilverKnight','re(3): Dear Silver Kinght and Charlie,,,,,','2003-11-18 11:52:10',0,'Interestingly, I \"held my tongue\" on my last message... I was gonna say... \"I\'m sure you don\'t use one, but a lot of people use Fritz or some other computer program to win on those internet sites\".... heheh...\r\n\r\nSeriously, though, do you really use a program to beat others? And if so, why?\r\n_____________________\r\n\r\nAs to Charlie and my use of programs.... We both \'brute forced\' the solution. But it\'s not like we pretended to do otherwise.... we both posted our code, acknowledging the use of the \'puter (unlike some people who play chess online).\r\n______________\r\n\r\nOne must admit, it virtually guarantees we don\'t miss one of the valid combinations.',9591,0);
INSERT INTO comment VALUES (9593,1383,1183,'fwaff','Logical (brute force) solution, no programs','2003-11-18 11:57:59',3,'From the first guess then the combination contains one of the following pairs of numbers; (1,2) (1,3) (1,5) (2,3) (2,5) (3,5)\r\n\r\nFour of these pairs can be ruled out as follows:\r\n\r\nIf (1,2) is in the combination, then guess 1 rules out 3&5, guess 2 rules out 4&7 and guess 3 permits only one of either 6 or 8. This only gives three digits in the combination, so (1,2) is not a valid pair.\r\n\r\nIf (2,3) is in the combination, then guess 1 rules out 1&5, guess 3 rules out 6&8, guess 2 permits only one of either 4 or 7. This only gives three digits in the combination, so (2,3) is not a valid pair.\r\n\r\nIf (1,5) is in the combination then guess 1 rules out 2&3, thus guess 2 gives one of either 4 or 7 and guess 3 gives that both 6&8 must be in the combination. This gives 5 digits in the combination, so (1,5) is not a valid pair.\r\n\r\nIf (3,5) is in the combination, then guess 1 rules out 1&2, thus guess 2 gives that both 4&7 must be in the combination and guess 3 gives that one of either 6 or 8 must be in the combination.. This gives 5 digits in the combination, so (3,5) is not a valid pair.\r\n\r\nThis leaves us with (1,3) and (2,5) as the only valid pairs. In the first guess for each of these pairs one of the digits is in the correct place and the other is in the wrong place. Going through the possibilities gives:\r\n\r\nAssume 1 is in the correct place and 3 is in the wrong place:\r\nGuess 2 shows that the 2nd digit must be 7 Therefore the 4th digit must be 3\r\nGuess 3 shows that the 3rd digit must be 6\r\nThis gives combination 1763 (which is not divisible by 7)\r\n\r\nAssume 3 is in the correct place and 1 is in the wrong place:\r\nGuess 3 shows that the 2nd digit must be 8\r\nTherefore the 4th digit is 1\r\nGuess 2 then shows that the 1st digit is 7\r\nThis gives combination 7831 (which is not divisible by 7)\r\n\r\nAssume 2 is in the correct place and 5 is in the wrong place:\r\nGuess 2 shows that the 1st digit must be 4, therefore the 3rd digit must be 5\r\nHowever, guess 3 shows that the 3rd digit must be 6\r\nTherefore there are no valid combinations for this possibility.\r\n\r\nAssume 5 is in the correct place and 2 is in the wrong place, this gives either 2xx5 or xx25.\r\nTaking the xx25 possibility first:\r\nGuess 3 shows that the 2nd digit must be 8\r\nGuess 2 then shows that the 1st digit must be 7\r\nThis gives combination 7825 (which is not divisible by 7)\r\nNow taking the 2xx5 possibility:\r\nGuess 2 shows that the 2nd digit is 7\r\nGuess 3 shows that the 3rd digit is 6\r\nThis gives combination 2765 (which is divisible by 7)\r\n\r\nSo there are 3 combinations not divisible by 7 and a single combination that is divisible by 7. Therefore since the guesser was able to correctly determine the combination then the combination must be 2765.\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (9594,1383,3172,'SilverKnight','re: Logical (brute force) solution, no programs','2003-11-18 12:03:04',0,'very well described...',9593,0);
INSERT INTO comment VALUES (9595,1383,3196,'Dan','re(4): Dear Silver Kinght and Charlie,,,,,','2003-11-18 12:16:24',0,'Silver Knight writes: \"Seriously, though, do you really use a program to beat others? And if so, why?\"\r\n \r\n:-) \r\n',9592,0);
INSERT INTO comment VALUES (9596,1383,3172,'SilverKnight','re(5): Dear Silver Kinght and Charlie,,,,,','2003-11-18 12:21:16',0,'I take it that you do (use a program to play chess)... or you have.... and you aren\'t the first.\r\n\r\n;-)',9595,0);
INSERT INTO comment VALUES (9597,1383,3196,'Dan','Not to belabor this, but.....','2003-11-18 12:53:18',0,'(1) As a brainteaser, this puzzle was a worthy entry, as fwaff demonstrated in his insightful solution.\r\n \r\n(2) But as a computer programming assignment, it is not worthy of the attention of an intoductory programming class in junior high school.',NULL,0);
INSERT INTO comment VALUES (9598,1383,3172,'SilverKnight','re: Not to belabor this, but.....','2003-11-18 13:01:18',0,'Dan,\r\n\r\nAs fwaff pointed out, he limited the solution and \'brute forced\' it as well. Kudos to him for doing it a different way, and not relying on a program.\r\n\r\nI sincerely wish you had not missed the only number that fit the criteria that was also divisible by seven (namely 2765).\r\n\r\nIf you had found it, it would have saved us\r\n(1) your desire to change the problem,\r\n(2) your ranting about computer programs, and\r\n(3) apparent dismissal of the solution(s) that solved the problem correctly before you did, which seems to be what is driving your comments\r\n\r\nCheers!',9597,0);
INSERT INTO comment VALUES (9599,1447,3430,'pat','internalies','2003-11-18 13:07:54',0,'usuually your stuff is pretty good:) ',NULL,0);
INSERT INTO comment VALUES (9600,1383,1301,'Charlie','re(3): Dear Silver Kinght and Charlie,,,,,','2003-11-18 13:24:48',0,'Perhaps there would be interesting portions of your chess-playing source code that you could share by posting portions of the chess-playing problem, with source-code solution, in the Algorithms category.',9591,0);
INSERT INTO comment VALUES (9601,1240,3172,'SilverKnight','solution','2003-11-18 14:54:09',3,'Shea (I suppose there are other working combinations...)\r\n\r\n(all the combinations can prefix \'-ther\' to form words).\r\n\r\ngather\r\nslither\r\nsmother\r\nwither\r\nbother\r\nlather\r\nfeather\r\n',NULL,0);
INSERT INTO comment VALUES (9602,1240,1626,'Gamer','re: solution','2003-11-18 15:09:09',0,'I didn\'t say this in the queue, but be careful with names. I can say Toge is a name (and it actually might be) but there may be other combinations',9601,0);
INSERT INTO comment VALUES (9603,1240,1567,'Bryan','One Hot Minute!','2003-11-18 15:14:28',3,'All the combinations of letters have the consonants first and the vowels last (a rather obvious property, but they all share it). One man\'s name that fits this rule is Flea, bassist for the Red Hot Chili Peppers.',NULL,0);
INSERT INTO comment VALUES (9604,1220,4323,'Benjamin J. Ladd','Program:','2003-11-18 15:38:31',0,'I\'ll post the program (second method using one fixed point and one random point) as soon as I get it put on this computer. The results were surprising! The average of 4 trials at 10,000 iterations of random chords produced not 66.66% as expected, but...\r\n\r\n...75.00125\r\n\r\nWhich would seem to show that the method used to arrive at 66% (namely the choosing of a second random point on a circle in relation to a fixed point) is faulty somehow (I take it that it\'s because the point spreads are different from a fixed point). But I\'m altogether happy about that! If that is the case, and 75% can be reached by both methods, then this problem isn\'t a paradox and it does have a real solution regardless of the method taken. I\'m pretty sure I was wrong when I wrote my first program and after I find the error, I\'ll go ahead and post both programs.\r\n\r\nNow--I\'m only wondering why your program gave you 66%?',NULL,0);
INSERT INTO comment VALUES (9605,1364,4383,'sim wi','Solution','2003-11-18 15:44:01',0,'Jeswin = knight = Grot\r\nParker = knave = Cloysta\r\nCrasbo = liar = Blarg',NULL,0);
INSERT INTO comment VALUES (9606,1240,1301,'Charlie','thoughts','2003-11-18 16:08:24',0,'I had always thought of Shea as a surname, but I guess you can name a boy anything. A Google search on Shea shows about 5 individuals, a stadium and a theater as examples of a last name before the use as a first name occurs. A girl\'s name would be Inga.',NULL,0);
INSERT INTO comment VALUES (9607,1240,3196,'Dan','Visting hours are over.......','2003-11-18 17:23:55',3,'Of course the answer is that since Ga, Sli, Smo, Wi, Bo, La and Fea are figures of Norse mythology, the man is Thor Heyerdahl. (The puzzle is called \"Norse Code\"). But if I dared to give that answer, Charlie and Silver Knight would accuse me of using a computer search !! Therefore...\r\n\r\nI also recognized smo and bo as medical acronyms, so I called my sister, a psychiatric nurse in Vermont, and she instantly identified all these well known medical acronyms:\r\n\r\nga = Gastric Analysis \r\nsli = Sodium Lauryl Ishethionate \r\nsmo = Second Medical Opinion \r\nwi = Wave Injector (used to separate gases in medical research) \r\nbo = Body Odor \r\nla = Laser Annealing \r\nfea = Front End Analysis (used more frequently by psychiatrists than by proctologists) \r\n\r\nAnd so we also have a very familiar acronym used by hospital emt\'s and paramedics:\r\n\r\n ford = Found On Road Dead\r\n \r\nSo the man\'s name is Harrison Ford. Like those letter combo\'s, his name is also a medical acronym.\r\n \r\n:-)\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\n\nEdited on November 18, 2003, 9:04 pm',NULL,0);
INSERT INTO comment VALUES (9609,674,1626,'Gamer','re: another solution','2003-11-18 18:13:10',0,'Solving the second equation for that X gives\r\n\r\n√(19)(y+z) + yz = 3, but since y + z = 5-√(19), you can replace that.\r\n\r\n25 - 5√(19) +yz = 3\r\n22 - 5√(19) + yz = 0\r\n\r\nThis ends up with yz equalling negative; don\'t know if that\'s a problem though',9586,0);
INSERT INTO comment VALUES (9608,1341,4385,'Andy','solution','2003-11-18 17:50:17',0,'In the math of infinity(ies), in this case the infinity that corresponds to the number of integers that exist (Aleph-0), the answer in both cases is still infinity. It holds true (simplified) that infinity + infinity = infinity. More technically, to show that the number of marbles in the container is infinite, you (must?) show a 1 to 1 mapping between the marbles and the positive integers. The marbles in the container (as long as they are not ALL removed at each interval) can be assigned sequential integer numbers, creating this mapping. \r\nSo, putting ANY number of marbles in the container an infinite number of times results in a container with an infinite number of marbles in it.',NULL,0);
INSERT INTO comment VALUES (9610,674,3558,'Tristan','re: another solution','2003-11-18 18:15:22',0,'√(x²+y²+z²) does not equal x+y+z',9586,0);
INSERT INTO comment VALUES (9611,1240,3196,'Dan','Hint...it says NORSE code.','2003-11-18 20:22:57',2,'\"Visiting hours are over\" was the first attempted solution that recognized that.......',NULL,0);
INSERT INTO comment VALUES (9612,1383,3386,'Victor Zapana','wow...','2003-11-18 20:28:42',0,'hmm.. im the only one who guessed and check i see.. (i cudnt say this b4 coz i was sick.. poor me) u were impressed sk? lol',NULL,0);
INSERT INTO comment VALUES (9613,674,1301,'Charlie','re(2): another solution','2003-11-18 21:00:40',0,'At the maximum x, y is negative while z is positive.',9609,0);
INSERT INTO comment VALUES (9614,674,3172,'SilverKnight','re(3): another solution','2003-11-18 21:02:31',0,'As mentioned earlier, at the maximum, y and z are both = 1/3. Is there another solution?',9613,0);
INSERT INTO comment VALUES (9615,674,3351,'Eric','shaving the sphere','2003-11-18 21:24:48',0,' No, the correct solution is 13/3. This was best alluded to before visually by the intersection of the hyperboloid xy + xz + yz = 3 and the plane x + y + z = 5. It becomes much easier to see in examining the intersection of the plane x + y + z = 5 and the sphere x^2 + y^2 + z^2 = 19. \r\n\r\nIn this case we can clearly see that the solution set to both equations is the circle centered at 5/3,5/3,5/3 with radius √(19 - 25/3) = √32/3. Of course, this exists in the plane with the points 5,0,0 0,5,0 and 0,0,5. If we wish to maximize x we simply need to choose the point on the circle closest to 5,0,0. With some help from pythagorus we see that point is (13/3,1/3,1/3).',9614,0);
INSERT INTO comment VALUES (9616,674,1301,'Charlie','re(4): another solution','2003-11-18 21:28:07',0,'Whoops. Not doing so good today. I was looking at a \"3-D\" graph and misjudged the maximum by eye.',9614,0);
INSERT INTO comment VALUES (9617,674,3172,'SilverKnight','re: shaving the sphere','2003-11-18 21:32:14',0,'Um... like, uh... yeah... like that\'s what I said.',9615,0);
INSERT INTO comment VALUES (9618,674,4374,'Richard','Solution by Lagrange Multipliers','2003-11-18 23:22:18',3,'Let f(x,y,z)=x, g(x,y,z)=x+y+z-5, h(x,y,z)=xy+yz+zx-3. Then subject to the constraints g=0 and h=0, f is stationary for any real x,y,z,L,M that satisfy g=h=0 and grad(f)=Lgrad(g)+Mgrad(h) (L and M are the Lagrange multipliers, see, e.g. the Dover book \"Advanced Calculus of Several Variables\" by C.H. Edwards, Jr.) The gradient equation evaluates to the 3 scalar equations 1=L +M(y+z), 0=L+M(x+z), 0=L+M(x+y) and the last two of these imply y=z. Writing y for z in g=0 gives x=5-2y and putting this into h=0 and also writing y for z then gives 3y^2-10y+3=0 so that y=1/3 or 3. Hence x=13/3,y=z=1/3 or x=-1,y=z=3. These correspond respectively to the maximum and the minimum attained by x on the intersection curve of g=0 and h=0.',NULL,0);
INSERT INTO comment VALUES (9619,670,4374,'Richard','re: a little more straightforward','2003-11-19 00:10:42',0,'That 111111 is divisible by 13 is an excellent observation. So the 50-digit number is the sum of multiples of 111111, i.e. multiples of 13, plus (10*x+1)*10^24 where x is the unknown digit. If 10*x+1 is a multiple of 13, we have a solution. Now 91=13*7. so we can use x=9. Also 10^24 is congruent to 1 mod 13 (10^4 is congruent to 3), so any multiplier of 10^24 must be congruent to 0 mod 13, so I think that 9 has to be the only possible value for x.',9520,0);
INSERT INTO comment VALUES (9620,1458,4070,'Tim','A few possible solutions','2003-11-19 00:13:32',0,'Solution 1: Hit your fist against the table. This does not actually touch the cigarette with any object other than the table itself... which I will assume is not off limits. This results in vibrations which will knock the cigarette over.\r\n\r\nSolution 2: Throw a rock in east india over and over until you disrupt a birds flight, which then causes a ripple in the space-time fabric (general relativity) that careens its way to the cigarette, disturbing the table\'s ability to hold the cigarette upright (like throwing a pebble in the water).',NULL,0);
INSERT INTO comment VALUES (9621,1351,4070,'Tim','Solution','2003-11-19 00:20:41',0,'The third sentance should read: It\'s not too hard to spot, and may surprise you if you are trying to read this over AND over quickly without being as observant a reader as you really should be and not paying much attention.\r\n\r\nThe origional text says: \"read this over over\", and \"should be and and\".... the and is on the wrong line/ in the wrong place depending on how you look at it',NULL,0);
INSERT INTO comment VALUES (9622,1351,4070,'Tim','Oops... Real solution','2003-11-19 00:22:37',3,'The last word of every line is the same as the first word of the next line.',NULL,0);
INSERT INTO comment VALUES (9623,1447,4070,'Tim','Solution','2003-11-19 00:43:23',3,'Take the money to the swinging bridge the other side of town. If you fill in the blanks, you get \"a secret message\"',NULL,0);
INSERT INTO comment VALUES (9624,670,4374,'Richard','re(2): a little more straightforward','2003-11-19 01:59:52',3,'10^24 is not divisible by 13 by unique factorization into primes as 10^24 factors uniquely as 2^24 * 5^24 and the prime 13 does not appear. The 50-digit number written out in normal number (arabic) notation looks like\r\n111111 111111 111111 111111 x1 111111 111111 111111 111111\r\nwhere I have put in spaces to make the blocks of 6 ones stand out. Thus the number is the sum of multiples of 111111, which is divisble by 13, and x1*10^24. Thus to make the whole thing divisible by 13, x1*10^24 must also be divisible by 13. Since 10^24 certainly is not divisible by 13, x1 must be. The only two-digit number ending in 1 that is divisble by 13 is 91=13*7, so x=9 is the unique solution.',9546,0);
INSERT INTO comment VALUES (9625,1240,1183,'fwaff','re: Hint...it says NORSE code.','2003-11-19 06:21:52',3,'Another solution using the \'Norse Code\' hint is Inga. This uses the same logic as the Shea and Toge solutions, ie all the words can be extended by adding \'ther\'.\r\n\r\nTo be honest none of the names I\'ve seen in any of the solutions so far could be thought of as common, so perhaps we\'re all barking up the wrong fjord.',9611,0);
INSERT INTO comment VALUES (9626,671,1183,'fwaff','Solution','2003-11-19 09:38:00',3,'Let x = 10a + b and assume x is the correct number\r\nLet y = 10b + a then y is the incorrect transposed number\r\nLet z be the sum of the other nine numbers\r\n\r\nSo we have....\r\n\r\n(z + x)/10 + 1.8 = (z + y)/10\r\nz + x + 18 = z + y\r\nx + 18 = y\r\n\r\nre-writing this in terms of a & b gives\r\n\r\n10a + b + 18 = 10b + a\r\n9b - 9a = 18\r\nb - a = 2\r\n',NULL,0);
INSERT INTO comment VALUES (9627,671,4381,'ben','solution','2003-11-19 09:46:11',0,'(s9 +10a +b)/10= (s9+10b+a)/10 - 1.8\r\n\r\ns9 + 10a + b = s9 + 10b + a - 18\r\n\r\n10a - a =10b - b - 18\r\n\r\n9a = 9b - 18\r\n a = b -2\r\n2 = b - a',NULL,0);
INSERT INTO comment VALUES (9628,1341,775,'Cory Taylor','re: solution','2003-11-19 09:51:18',0,'wait wait wait. wouldn\'t that then fall back to near the beginning of the comment list when I said that the paradox comes from our imposed nomenclature rather than the actual situation itself?\r\nI\'ve felt so alone over here till now :)',9608,0);
INSERT INTO comment VALUES (9629,1383,4381,'ben','','2003-11-19 09:53:11',0,'the only combinations which work for the first part are:\r\n7831\r\n1763\r\n7825\r\n2765\r\n\r\nThe only one of thes that is divisible by 7 is 2765. As he knew which of the combinations was correct it must have been this one.\r\n',NULL,0);
INSERT INTO comment VALUES (9630,671,4385,'Andy','Layman\'s analysis of a solution','2003-11-19 11:11:43',0,'If the mean is off by 1.8, and it is the mean of 10 numbers, then the transposed number is off by 18 (10 x 1.8 = 18). So, find any two digit number that, when the digits are reversed, is 18 more than it was before. (13, 24, 35, 46, ...). Looking at these, b-a = 2.',NULL,0);
INSERT INTO comment VALUES (9631,1240,2839,'FatBoy','oh, I hate to beat a dead horse....','2003-11-19 11:53:19',0,'While SK has recognized a pattern and Shea certainly fits it, DJ went out of his way in the problem to specify a \"common\" name. I\'m not sure that Shea really fits that bill. \r\nwell many of the numbers that signify letters are multiples of 3. mebe they\'re consonants? \r\n420 is very common in this message. possibly it is a vowel, or a common consonant? \r\nmany are multiples of 10, mebe that helps? \r\nit probably doesn\'t involve the factors of the numbers... \r\nhmm.. some random observations...',NULL,0);
INSERT INTO comment VALUES (9669,1505,3386,'Victor Zapana','nm on my first thoughts','2003-11-20 11:19:35',0,'hmm gus.. enlighten us.. i assume ur post title means ANSWER, but i dun get the key.. please explain how you optain these numbers and change them into letters.',NULL,0);
INSERT INTO comment VALUES (9670,1451,4406,'r','nice','2003-11-20 11:21:17',0,'cool prob',NULL,0);
INSERT INTO comment VALUES (9671,65,4385,'Andy','A-priori probability','2003-11-20 11:22:59',0,'Understanding the deception here is akin to understanding a-priori probability. Before a card is drawn you have a 1 in 3 chance of winning. No matter which card is drawn you will still play the game. Even though you have new information after the draw (one of the cards cannot be the visible one), you are not making any decisions based on this new information, therefore you cannot change your previous odds of winning.',NULL,0);
INSERT INTO comment VALUES (9672,1505,4360,'Gus','re: nm on my first thoughts','2003-11-20 11:31:47',0,'Hi Victor, I used a similar logic to the one that E. A. Poe used in one of his famous tales. That is, to see which numbers appears more times un the text and associate it to the most common letters in english and then to try to find some patterns and associate them to common words. \r\n\r\nI really did not follow this rule strictly, but surely it helps a lot.\r\n\r\n72-240-272-30 / 420-72-90-380 / 72-30-156-272-380!!\r\n',9669,0);
INSERT INTO comment VALUES (9673,1505,3172,'SilverKnight','210-240-420 / 420-240-240 / 72-2-342-20','2003-11-20 12:00:01',3,'uh... or, er... something like that...',NULL,0);
INSERT INTO comment VALUES (9674,1474,3196,'Dan','re(2): I think I\'ve got it. (No computer program used).','2003-11-20 12:10:43',0,'Dear SilverKnight:\r\n\r\nI stand by my analysis, sir.\r\n\r\n(1) The Merriam Webster online dictionary contains the following two entries: \"three of a kind\" - \"three cards of the same rank in one hand; see POKER\"; and \"full house\" - a poker hand containing three of a kind and a pair — see POKER\". Any casual poker player instantly recognizes the term \"three of a kind\" and understands it in that sense - a five card poker hand (3 matching cards, 2 unmatching), different from a full house( 3 matching cards, 2 matching cards\".\r\n(2) In your example, the following cards are drawn: Ace Ace 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 Jack Jack Queen Queen King King. After the first four cards in this sequence are drawn, it is no longer possible to draw a \"3 of a kind\" in the poker sense. As soon as you draw another Ace, you now have 3 Aces and two 2\'s, since the 3rd and 4rth cards drawn were 2\'s -- you have a full house, not \"3 of a kind\". \r\n\r\n\r\n:-)\n\nEdited on November 20, 2003, 12:16 pm',9665,0);
INSERT INTO comment VALUES (9675,1505,3922,'Paul','Solution, if you want help...','2003-11-20 12:18:09',0,'Several things to notice: the number 2 shows up by its self. Meaning either an \"I\" or an \"A\". most likely an \"A\". And there are few 3 letter words that come up often in codes: \"THE\" \"AND\" \"ITS\". So we can rule out \"AND\" for the second word because the \"A\" is already used. \r\nWhen looking at just these two parts we can show that the middle section looks like this:\r\nT_, _E, _ _, _ _T, T_, _E, THAT, _ _, THE, _ _ E_T_ _ _ . \r\n\r\nLooking at the spaces available I found it ovious what this quote should be, because not to many letters can go after \"T\" to make a 2 letter word (A and E already taken). With the numbers found in the second quote, and the end of the quote starts with a squiggle (normally meaning someone said/wrote it) I was able to create enough of word to crack the code. ',NULL,0);
INSERT INTO comment VALUES (9676,1474,3224,'Lee','','2003-11-20 12:20:34',0,'Dan,\r\nHow can you claim \"Three of a kind\" is exclusively a poker term? \r\nMan1: I\'ve got a luverrly matching set of two coconuts\r\nMan2: You mean a pair?\r\nMan1: Pardon?\r\nMan2: You\'ll have to excuse me, it\'s poker jargon. \r\n\r\nInternet search? Pop \'three of a kind\' into g00gle and wake me up when you find the poker sites.\r\n\r\nThis gets me;\r\n\"....Therefore the puzzle can be clarified as follows: \"...You then shuffle them and begin to draw out cards until you have three that match and two that do not match, as for example 3 jacks, an ace and a queen. What is the most likely number of cards drawn when this happens?\"\r\n\r\nLet\'s see. I draw 5 card hands until I get 3 that match and 2 that don\'t.\r\nThe most likely number of cards drawn when this happens?\"\r\nIs it.......no, it can\'t be....is it 5?\r\n\r\nYour argument\'s about 3 times bigger than its diameter.\r\nI hope I see a neat computer-free answer but since a calculator (does this count as a computer?) comes in handy just working out 1 case, I feel a computer is required.\r\nCan anyone figure out the distribution???????\r\nI could go to jail and never justify the time to do this by hand',NULL,0);
INSERT INTO comment VALUES (9677,1474,3224,'Lee','My house is full of pears!','2003-11-20 12:24:58',0,'I was going to use that title last time but I forgot.\r\nI can\'t see me using the phrase anywhere else so it might as well go here.\r\nIt was topical and funny when I thought of it.\r\nHonest.',NULL,0);
INSERT INTO comment VALUES (9678,1505,3922,'Paul','Code Revealed..','2003-11-20 12:27:19',3,'As for what each letter is. The difference between each letter and the number represented by that number follows a pattern. A (2) and B (6). There is a difference of 4. The difference between B (6) and C (12) is 6. This pattern of adding 2 to the difference shows up all the way to Z (702) which is 52 more than Y (650) which is 50 more than X...etc...',NULL,0);
INSERT INTO comment VALUES (9679,1474,3172,'SilverKnight','re(3): I think I\'ve got it. (No computer program used).','2003-11-20 12:40:27',4,'Dan,\r\n\r\nYou wrote:\r\n\"You can only achieve a true \'three of a kind\' hand by drawing between 5 and 14 cards.\"\r\n\r\nSo, why do you have a probability of getting the \"3 of a kind\" on the 15th card (of 0.0000002468)?',9674,0);
INSERT INTO comment VALUES (9680,1474,3196,'Dan','re:','2003-11-20 12:42:53',0,'OK, wiseguy...it isn\'t just pears your house is full of... But seriously, I know that my answer, 5, goes against intuition, but if \"3-of-a-kind\" is interpreted as a poker hand, as it should be, then when more than 5 cards are drawn, the odds of \"2 pairs\" overwhelm the odds of a true poker \"3-of-a-kind\". Btw...since you don\'t like puzzles that tempt the less ambitious among us to run crying to their programs and spreadsheets, here are 2 excellent puzzles you can try that don\'t require computers: \"If a square has perimeter of length 32 inches, what is the length of one of its sides?\" and \"What are the fewest steps required to put a bag of M&Ms in alphabetic sequence?\" Don\'t laugh; after that \"An Egg-Celent Question\" entry, I am half expecting to see puzzles like these on this website... :-) \r\n\r\n\n\nEdited on November 20, 2003, 12:45 pm',9676,0);
INSERT INTO comment VALUES (9681,1474,3172,'SilverKnight','re(2):','2003-11-20 12:54:35',0,'Holy dismissive people batman!\r\n\r\nDan... chill out...\r\n\r\n(1) I (and others) don\'t think the intent here is to make a 3 of five hand.\r\n(2) You are welcome to attempt to solve the problem as if that was the intent.\r\n(3) The problem, as you are interpreting it, is a much easier problem than interpreting it the way most of us are interpreting it.\r\n\r\nso, I suggest you solve the same problem that we are solving (and preferably do it without a computer).',9680,0);
INSERT INTO comment VALUES (9682,1474,3224,'Lee','re(2):','2003-11-20 13:42:26',0,'As soon as 4 cards are drawn (and making 2 pairs possible) the\r\n\"the odds of \"2 pairs\" overwhelm the odds of a true poker \"3-of-a-kind\". \r\nThis is a facet of two pairs always being easier to make\r\nSometimes problems get posted that the poster doesn\'t know the solution to - or knows a way of doing it (using computers) but finds the problem of potential interest to others. I\'d love to see the problem solved in a \"Wow, that\'s a neat way of thinking\" kinda way but if it isn\'t my nose retains all its epidermis. Sometimes a computer assisted answer generates interest or pointers to \'solve\' the puzzle without one - and this can only be a good thing.\r\n',9680,0);
INSERT INTO comment VALUES (9683,1474,3172,'SilverKnight','Dan - yet another problem with your analysis','2003-11-20 14:30:39',1,'Dan,\r\n\r\nAgain, you can stand by your previous analysis or anything else you want.\r\n\r\nTo be very clear: I think the intent of this problem is to have THREE CARDS of the same rank (ignoring poker hands).\r\n\r\nBut I decided to follow your analysis on the assumption that the intent was a \"poker hand\".\r\n\r\nI assumed that your analysis of combinatorial probability was correct (and I didn\'t previously check your figures). It is not correct.\r\n_________________________\r\n\r\n(1)\r\nYou wrote:\r\n\"There are 52*51*50*49*48=311875200 ways to draw the first 5 cards, of which there are (4*3*2)*(48*44)*(5*4*3*2*1)=2880*(48*44)=6082560 ways to get 3 aces and 2 nonmatching cards. Odds=0.0195031859\"\r\n\r\nThis is definitely wrong.\r\n\r\nThe proper analysis of the likelihood of getting 3 Aces and 2 non-matching OTHER cards is:\r\n\r\nTotal combinations (not permutations) of getting ANY 5 cards is:\r\n52!/(47! * 5!) which is 52*51*50*49*58/(5*4*3*2*1)\r\nwhich is 2,598,960\r\nSo far, this is similar to what you did, except you were working with permutations not combinations (so you didn\'t divide by 5!).\r\n\r\nTo continue, to identify the number of combinations that have Three Aces and two non-matching cards:\r\n4*3*2*48*44/(3! * 2!) = 4*24*44 = 4224\r\n\r\nTherefore, the likelihood of getting three aces is:\r\n4224/2598960 = .001625265\r\n(This is less than one tenth of the figure you came up with.)\r\n\r\nBy symmetry, multiply this by 13 (not just aces) and you get:\r\n~.02112845 is the probability of being dealt a three of a kind poker hand (not including a full house).\r\n\r\nThis is definitely not equal to what you came up with.\r\n\r\nI will allow you to extend this logic, if you wish, to 6 cards, 7 cards, etc.\r\n_________________________\r\n\r\n(2)\r\nYou wrote:\r\nYou can only achieve a true \"three of a kind\" hand by drawing between 5 and 14 cards.\r\n\r\nYou still haven\'t addressed why you have a probability for getting this on the 15th draw:\r\n\"(15 draws) = 0.0000002468\"\r\n\r\nThis is inconsistent.',9656,0);
INSERT INTO comment VALUES (9684,670,4408,'Kirk','A similar problem but perhaps a bit trickier','2003-11-20 14:53:01',0,'Hi.\r\nI\'m new here, so please forgive me for posting this if I\'m not supposed to, but I like this kind of problem. The technique to the problem is handy to remember in maths challenges...\r\nThe problem is this:\r\n\r\nA student realises that a certain 12-digit number is exactly divisible by 11. His mate comes along and drops ink over the 8th digit. The student can now only read 11 of the 12 digits and cannot remember what the \"inked\" digit was. Can you work it out? The number now reads:\r\n5643879x2841. (Where \'x\' is the number blotted out with ink)\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (9685,670,1301,'Charlie','re: A similar problem but perhaps a bit trickier','2003-11-20 14:59:49',0,'One way is to find that 564387902841 leaves a remainder of 4 when divided by 11, while 10000 leaves a remainder of 1. So we need to add (11-4) = 7 times 10000, by placing a 7 in that x position (the 10,000\'s position) in which we had tentatively placed a zero.',9684,0);
INSERT INTO comment VALUES (9686,1252,3172,'SilverKnight','please clarify','2003-11-20 15:09:31',1,'I don\'t understand what \"a circle that is perfectly inscribed in a rectangle\" means.\r\n\r\nDoes this mean it is completely inside the rectangle , is tangent to three of the sides, and has diameter equal to the shorter of the rectangle\'s two sides?\r\n\r\nAlso, what does \"A smaller rectangle is placed on top of the first one\" mean? What is the \"edge of the circle\"?\r\n\r\nA picture would really help!\r\n\r\n--- SK',NULL,0);
INSERT INTO comment VALUES (9687,1252,4082,'wonshot','solution','2003-11-20 15:16:34',0,'Firstly, since the circle is inscribed in a rectangle the rectangle is a square.\r\n\r\nAssume the circle is of radius 1.\r\n\r\nThe coordinates of the corner of the smaller rectangle is ((1-2h),(1-h)) where h is the height of the smaller rectangle.\r\n\r\nUsing the equation of a unit circle, x^2 + y^2 = 1, and putting in the above coordinates we get the equation (1-2h)^2 + (1-h)^2 = 1.\r\n\r\nThis simplifies to 5h^2 - 6h + 1 = 0,\r\nwhich is the same as (5h-1)(h-1) = 0. \r\nTherefore, h=(1/5),1 but h cannot =1. \r\n\r\nSo the height of the rectangle is 1/5 the radius, and the length is 2/5 the radius. We can therefore fit 10 of these inside the larger rectangle heightwise, and 5 lenghtwise. Which means that we can fit 50 of the smaller rectangles inside of the larger rectangle, regardless of the size of the circle.\r\n\r\n50 smaller rectangles fit in the larger rectangle.',NULL,0);
INSERT INTO comment VALUES (9688,1474,4410,'Chris','Just a thought..','2003-11-20 15:30:51',0,'I may be thinking about this all wrong.. but hear me out.\r\n\r\nIf u have a deck of cards and u draw out one card at a time. according to odds, wouldnt the most likely situation be that if u drew out 13 cards, the cards that you would have would be 2-A?\r\n\r\nI mean the probability of pairing up is less likely than getting a card in which there are four others rather than three..\r\n\r\nUsing this (absurd) logic, wouldnt that mean that the likelyhood of getting a three of a kind would most likely come exactly between 26(number of cards drawn before u can no longer not have a pair) and 39(the number of cards drawn before u can no longer have 3 of a kind)\r\n\r\n...i know this is very wrong, and i know its wrong because it was too easy to think of.. but according to what i said, the average number of cards would be (39-26) / 2 = 6.5 + 26 = 32.5\r\n\r\nCould someone explain how this is incorrect. even though im almost positive it is.',NULL,0);
INSERT INTO comment VALUES (9689,1224,4411,'Elias','solution?','2003-11-20 15:33:05',3,'I*m pretty sure that a solution is: A = 0, B = 0, C = 0, D = 0 and E = 0 :)\r\n',NULL,0);
INSERT INTO comment VALUES (9690,1474,3172,'SilverKnight','re: Just a thought..','2003-11-20 15:34:57',0,'Well, Chris, one obvious problem with your thought (and I mentioned it earlier here--the first comment for this problem) is that, once you get your 27th card, you MUST have three of a kind of SOMETHING.\r\n\r\nYou\'ll never need to take the 28th card.',9688,0);
INSERT INTO comment VALUES (9691,1252,3351,'Eric','sdrawkcabbackwards?','2003-11-20 15:35:46',0,'\r\n\n\nEdited on November 20, 2003, 3:39 pm',9687,0);
INSERT INTO comment VALUES (9692,1474,3196,'Dan','Some responses for SilverKnight,,,,','2003-11-20 15:37:26',0,'SilverKnight, you wrote:\r\n\"...to follow your analysis on the assumption that the intent was a \'poker hand\'. \r\n(1) [Dan] wrote: \r\n\'There are 52*51*50*49*48=311875200 ways to draw the first 5 cards, of which there are (4*3*2)*(48*44)*(5*4*3*2*1)=2880*(48*44)=6082560 ways to get 3 aces and 2 nonmatching cards. Odds=0.0195031859\' This is definitely wrong.\r\n[The correct formula is]\r\n52!/(47! * 5!) [for all the 5 card combinations in a deck of 52]\"\r\nThat you formula is incorrect, Silver Knight, is easily seen by applying it to the case of 2 cards. I think we can agree that there are 52*51 = 2652 possibilites for 2 cards out of 52. But applying your formula: \r\n52!/(50! * 2!) = (52*51)*2 = 5304. Can you really come up with that many different 2-card hands in a deck of 52 ?\r\nWell, SilverKnight, if I am holding 5 cards of a 52 card dack, lets call them A,B,C,D,and E, then there are 52 possibilities for A. For each of these, there are 51 possibilities for B. 52*51= 2652. For each of these 2652 possibilities for A and B, there are 50 possibilities for C. 2652*50= 132600. For each of these 132600 possibilities for A, B and C, there are 49 possibilities for D. 132600*49 = 6497400. For each of these 6497400 posibilities for A,B,C,and D, there are 48 possibilities for E. 6497400*48 = 311875200.\r\n(2) You wrote: \r\n\"[Dan] wrote: \r\n\'you can only achieve a true \"three of a kind\" hand by drawing between 5 and 14 cards.\'\r\nYou still haven\'t addressed why you have a probability for getting this on the 15th draw: \r\n\'(15 draws) = 0.0000002468\' This is inconsistent.\"\r\nNot inconsistent at all. The explanation for that small figure is that, by the time we get to 15 cards, it is astronomically unlikely that we haven\'t bumped into a \"2 pairs\" situation by now. When I said that a poker \"3-of-a-kind\" could only be achieved between 5 and 14 cards, you misconstrued me to mean that it was a certainty within 5 and 14 cards. That is incorrect. It is only possible within 5 and 14 cards, but may not occur at all. If I were to say \"The only way I could knock out Mike Tyson in a 15 round bout, is between rounds 1 and 15\". That would hardly mean I am certain of knocking him out within those rounds. My actual chances of knocking out Mike Tyson with 15 rounds are only about 4 in 10. \r\n(3) Lastly, I have taken up your good-natured\r\nchallenge to solve the problem given your interpretation, rather than the poker rules one. I will be posting it in a few minutes.\r\n:-) \r\n',NULL,0);
INSERT INTO comment VALUES (9693,1252,1301,'Charlie','Another possibility--being picky.','2003-11-20 15:45:07',0,'The problem states that \"one corner is on the edge of the circle\" but not that \"only one corner is on the edge of the circle\". If two corners are on the edge of the circle they lie at the ends of the diameter that connects opposite sides of the square, that is at the points of tangency. As the smaller rectangle then also has two vertices that coincide with two vertices of the square, it takes up half the square, and two such rectangles fill the square.\r\n\r\nThis corresponds to the other solution of the quadratic.',NULL,0);
INSERT INTO comment VALUES (9694,1474,3172,'SilverKnight','re: Some responses for SilverKnight,,,,','2003-11-20 15:50:13',0,'Dan, please go back and read my post AGAIN.\r\n\r\n(1)\r\nYou wrote that:\r\n52!/(50! * 2!) = (52*51)*2 = 5304\r\nNo, this is incorrect.\r\n52!/(50! * 2!) = (52*51)/2 = 1326\r\n\r\nAnd yes, Dan, I *do* think I can come up with that many different 2-card hands in a deck of 52.\r\n\r\n(2)\r\nPlease forgive me for taking what you wrote LITERALLY. I simply thought that when you used the word \'only\' that you meant \'only\'. Silly me.\r\n\r\n(3)\r\nDid you take into account (I\'m betting that you didn\'t...) the notion that you could get a straight or flush before you get your three of a kind? (The only reason I bring it up, is because you discounted getting a full house, in a previous post.)\r\n\r\n--- SK',9692,0);
INSERT INTO comment VALUES (9695,1252,4082,'wonshot','re: sdrawkcabbackwards?','2003-11-20 15:50:16',0,'-------------------\r\n| /-----\\|____| \r\n| / \\ |\r\n| / \\ |\r\n| / \\ |\r\n| / \\ |\r\n|/ \\|\r\n-------------------\r\n\r\nBad, rough, picture of the top half of what I believe to be the picture to be. Circle inside a rectangle touching a smaller rectangle. Let me know what you think.',9691,0);
INSERT INTO comment VALUES (9696,1252,4082,'wonshot','re(2): sdrawkcabbackwards?','2003-11-20 16:05:31',0,'sorry picture didn\'t come out\r\n',9695,0);
INSERT INTO comment VALUES (9697,599,4412,'krdmt5_000','this is easy','2003-11-20 16:24:57',3,'You start with a full 12 liter jug. you fill the 8 liter jug to the brim with the 12 liter jug. then you fill the 5 liter jug with the water in the 8 liter jug.\r\n\r\nyou now have...4 liters in the 12 liter jug...3 liters in the 8 liter jug...and 5 liters in the 5 liter jug.\r\n\r\nnow you place the water in the 5 liter jug in the 12 liter jug. and then you place the 8 liter jug, now filled with 3 liters, next to the empty 5 liter jug. then using the water level in the 8 liter jug as a mark for the 5 liter jug, fill the 5 liter jug to 3 liters and empty the 5 liter jug into the 8 liter jug\r\n\r\nyou now have...6 liters in the 12 liter jug...6 liters in the 8 liter jug... and 0 liters in the 5 liter jug\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (9698,1252,4317,'C.B.','','2003-11-20 16:54:08',3,'2\r\nThe larger is a square (the only rectangle one can inscribe a circle in). One corner of the smaller rectangle matches the lower left corner of the square. The opposite corner is at the point where the circle touches the square, halfway up the square\'s height. Its length is then twice its height, and one more can fit in the square right above it.',NULL,0);
INSERT INTO comment VALUES (9699,1474,3196,'Dan','Additional clarifications for SilverKnight','2003-11-20 16:58:08',0,'SilverKnight wrote: \"(1) [Dan] wrote that: \r\n52!/(50! * 2!) = (52*51)*2 = 5304 \r\nNo, this is incorrect. \r\n52!/(50! * 2!) = (52*51)/2 = 1326 \r\nAnd yes, Dan, I *do* think I can come up with that many different 2-card hands in a deck of 52.\"\r\n \r\nSilverKnight, you divided by 2! to elimiate duplicates, and I didn\'t. We\'re both correct. \r\nTo demontrate this, consider a 6-card deck: \r\nAh, Ad, Ac, Ks, Kh, Kd. (i.e Ace of hearts, Ace of diamonds, etc.) If you draw 2 cards, what are your chances of drawing 2 aces ? All the ways to draw 2 consecutive cards from such a deck are:\r\n(Ah,Ad), (Ah,Ac), (Ah,Ks), (Ah,Kh), (Ah,Kd),\r\n(Ad,Ah), (Ad,Ac), (Ad,Ks), (Ad,Kh), (Ad,Kd),\r\n(Ac,Ah), (Ac,Ad), (Ac,Ks), (Ac,Kh), (Ac,Kd),\r\n(Ks,Ah), (Ks,Ad), (Ks,Ac), (Ks,Kh), (Ks,Kd),\r\n(Kh,Ah), (Kh,Ad), (Kh,Ac), (Kh,Ks), (Kh,Kd),\r\n(Kd,Ah), (Kd,Ad), (Kd,Ac), (Kd,Ks), Kd,Kh)\r\n30 total possibilities, with 6 ace pairs. Odds are 1 in 5. But if you now insist on dividing by 2!, they become:\r\n(Ah,Ad), (Ah,Ac), (Ah,Ks), (Ah,Kh), (Ah,Kd),\r\n(Ad,Ac), (Ad,Ks), (Ad,Kh), (Ad,Kd),\r\n(Ac,Ks), (Ac,Kh), (Ac,Kd), (Ks,Kh), (Ks,Kd),\r\n(Kh,Kd).\r\n15 total possibilites, 3 ace pairs. Same result - 1 in 5. The elimination of duplicate ace pairs is counterbalanced by the elimination of all duplicates. The division by 2! buys you nothing.\r\n \r\nSilverKnight wrote: \r\n\"(2) Please forgive me for taking what you wrote LITERALLY. I simply thought that when you used the word \'only\' that you meant \'only\'. Silly me.\"\r\n \r\nI still cannot fathom what point you are trying to make here, SilverKnight. If I were to say, correctly, that \"It will only be possible for me to win the Nobel Prize in Chemistry within the next 30 years\" I really WOULD mean only. And I would not be implying that I was certain to win it. This is Logic 101, sir. \r\n \r\nSilverKnight wrote:\r\n\"(3) Did you take into account (I\'m betting that you didn\'t...) the notion that you could get a straight or flush before you get your three of a kind?\"\r\n \r\nSmart bet, SilverKnight. Of course I didn\'t,\r\nbecause straights and flushes are completely irrrelevant to the problem at hand. A straight would mean that there were no matches at all, as would a flush. For a match, the two cards MUST be of equal \"face value\" (2 aces, 2 jacks etc) AND of different suit. Neither a straight nor a flush have any two cards that meet both those requirements.\r\n:-)\n\nEdited on November 20, 2003, 5:01 pm',NULL,0);
INSERT INTO comment VALUES (9700,670,4408,'Kirk','re(2): A similar problem but perhaps a bit trickier','2003-11-20 17:13:45',0,'Hmmm..the right answer, but I didn\'t understand the method!!! The method I like *only* works when dividing numbers by 11 and is a method one should learn!\r\nIf a number is divisible by 11, then, after putting -+-+-+ etc between its digits, the result should be a multiple of 11, whether positive or negative or 0, i.e. -22, -11, 0, 11, 22 are common answers. E.g. 132 IS divisible by 11, as 1-3+2=0. 1342 IS divisible by 11 as 1-3+4-2=0 but 6543 is not as 6-5+4-3 does not equal 0 or 11 or the other \"multiples\" of 11.\r\n\r\nSo, in this question, calling the unknown number \'x\', we have:\r\n\r\n5-6+4-3+8-7+9-x+2-8+4-1. This evaluates to 7-x. Now this must equal one of the multiples of 11.\r\n7-x = -11 ....gives x=18\r\n7-x = 0 ....gives x=7\r\n7-x = 11 ...gives x= -4\r\n\r\nAs \'x\' is a single digit from 0 to 9, you can see the solution we require is x=7. Obviously, you could work out all the others, i.e. 7-x=-22 and 7-x=-33 but that would be pointless, as you can tell \'x\' is getting smaller and smaller!! So, x=7 is the required solution. \r\n\r\nNice answer by you though, Charlie!\r\nRemember that rule for division by 11, putting -+-+ in, very hand for maths challenges I\'ve found!\r\n\r\nRegards,\r\nKirk\r\nP.s It *only* works on 11s though, perhaps your method works on any number!',9685,0);
INSERT INTO comment VALUES (9701,670,4408,'Kirk','re(3): A similar problem but perhaps a bit trickier','2003-11-20 17:17:18',0,'Of course, I meant \'x\' is getting bigger and bigger if we take 7-x=-22 and 7-x=-33 etc. My argument still applies though, but I apologise for the error! Oh, and \"hand\" should read \"handy\"!\r\nKirk',9700,0);
INSERT INTO comment VALUES (9702,670,4374,'Richard','re: A similar problem but perhaps a bit trickier','2003-11-20 17:47:15',0,'Since 10 is -1 mod 11, we can calculate the alternating sum of the digits and easily find that x=7. A similar method, employing the values of 10^n mod 13, can be used on the original problem, but it would be laborious due to the large number of digits.',9684,0);
INSERT INTO comment VALUES (9703,1474,3196,'Dan','A non-poker solution (computer program not used)','2003-11-20 18:03:41',3,'SilverKight wrote: \"The problem, as you are interpreting it, is a much easier problem than interpreting it the way most of us are interpreting it. so, I suggest you solve the same problem that we are solving (and preferably do it without a computer).\"\r\n \r\nFair enough. Here is the solution according to which \"3-of-a-kind\" just means \"there are now three matching cards for the first time after n cards (n >= 3) have been drawn\". This is for the 52-card deck only. Later I will edit this post for the 104-card case. I will just add that this version of the problem is immensely easier than the poker-rules version. So easy, in fact, that it is really not worthy to be on the flooble/perplexus website. :0)\r\n\r\nThere are 52*51*50=132600 ways to draw the first 3 cards from a 52 card deck. (SilverKnight says you need to divide by 3! to eliminate the duplicates. But as I conclusively demonstrated in \"Some additional clarificatioins for SilverKnight\", this is like \"improving\" an equation by dividing both sides by 1. You get the same result either way.) If these 3 cards are all aces, then there are 4*3*2=24 possibilities for these cards (e.g. spades/clubs/diamonds, hearts/clubs/spades...). So the odds of getting 3 aces in 3 draws are: 24/132600 = 0.0001809955\r\n\r\nThere are 52*51*50*49=6497400 ways to draw the first 4 cards from a deck of 52. If the 4rth card is an ace, there are 2+1=3 places 3 aces can be situated in 4 cards. For each of these, there are 48 possibilities for the non-ace. 24*3*48 = 3456 4-card draws containing 3 aces. The odds of this are 0.0005319051.\r\n\r\nThere are 52*51*50*49*48=311875200 ways to draw the first 5 cards from a 52 card deck. If the 5rth card is an ace, there are 3+2+1=6 places for the aces cards to be located among the 5 drawn cards. For each of these, there are 48*47 =2256 possibilities for the two non-aces. 24*5*2256 = 270720 5-card draws containing 3 aces. The odds of this are: 0.0008680395\r\n\r\nSimilarly, the odds...\r\nFor 6 cards: 0.0016991412\r\nFor 7 cards: 0.002493305\r\nFor 8 cards: 0.1097054206 \r\nFor 9 cards: 0.2001292825\r\nFor 10 cards: 0.2513251454\r\nFor 11 cards: 0.3066765168\r\nFor 12 cards: 0.3656847354\r\nFor 13 cards: 0.4278511405\r\nFor 14 cards: 0.4926770708\r\nFor 15 cards: 0.5596638655\r\nFor 16 cards: 0.6283128636\r\nFor 17 cards: 0.698125404\r\nFor 18 cards: 0.7686028257\r\n\r\nLooking at this data, it is my judgment that when we have 3 matching cards, in all probability we will have drawn 15 cards.\r\n \r\n:-)\r\n\r\n\r\n\r\nEdited on November 20, 2003, 6:06 pm\n\nEdited on November 20, 2003, 6:09 pm',NULL,0);
INSERT INTO comment VALUES (9704,1474,3172,'SilverKnight','re: Additional clarifications for SilverKnight','2003-11-20 18:21:34',0,'No, Dan... I hate arguing what should be obvious .... but you MULTIPLIED by (5!). There is no \"this is the same\" about it....\r\n\r\n(1)\r\nI\'ll quote you AGAIN:\r\n\"There are 52*51*50*49*48=311875200 ways to draw the first 5 cards, of which there are (4*3*2)*(48*44)*(5*4*3*2*1)=2880*(48*44)=6082560 ways to get 3 aces and 2 nonmatching cards. Odds=0.0195031859\"\r\n\r\nif you want all PERMUTATIONS of 3 aces and 2 OTHER non-matching-rank cards... then the number should be:\r\n(4*3*2) * 48 * 44.\r\nIf you want all COMBINATIONS of 3 aces and 2 OTHER non-matching-rank cards... then the number should be (as I said):\r\n(4*3*2) * 48 * 44 / 3! / 2!\r\n\r\nYou did NEITHER of these, as can be seen from the quote above.\r\n\r\nWhat\'s more, the odds you calculated are wrong. As I mentioned in my earlier post the odds that you tried to calculate (odds of 3 Aces and two non-matching cards in a 5 card poker hand) is .001625265. You wrote that it is 0.0195031859. These are not equal. They are not \"one way of looking at it... and another way of looking at it\".\r\n\r\nI tire of your attempt at justifying the wrong answer.\r\n\r\n(2)\r\nPlease go back and read my post AGAIN. I agree that what you wrote does not imply that you WILL get 3 of a kind. What you wrote DOES imply that *IF* you get 3 of a kind, it will occur on the 5th to 14th card. And this is incorrect.\r\n\r\n(3) Straights and Flushes have EXACTLY as much bearing on this problem as fullhouses.... Because, otherwise, I can choose WHICH five cards I wish... and get A, A, 1, 1, 2, 2, ... K, K, and wait until I get my 27th card (say an 8) before getting my 3 of a kind. And then I\'ll choose three 8\'s, a 9, and a 4, and I have my three of a kind, but I couldn\'t get my three of a kind before the 27th card.\r\n\r\nYou can\'t have it both ways, Dan. If you take into account Full Houses, then you should also take into account straights and flushes.\n\nEdited on November 20, 2003, 6:23 pm',9699,0);
INSERT INTO comment VALUES (9705,1252,3136,'Popstar Dave','What it looks like...','2003-11-20 18:26:44',2,'Ok, here\'s a link to a rendering of what I believe this problem should look like.\r\n\r\nRight here.\r\n\r\nI don\'t have a solution yet... but just wait.',NULL,0);
INSERT INTO comment VALUES (9706,1252,3386,'Victor Zapana','stupid question, or is it?','2003-11-20 18:49:43',0,'do they want how many will fit if the circle is still in there (thus not overlap circle also) or without circle>',NULL,0);
INSERT INTO comment VALUES (9707,686,4413,'Tiana','re: What a retarded name','2003-11-20 18:49:55',0,'He\'s not real buddy. fix your sentence. It\'s not didnt it\'s didn\'t. ',4526,0);
INSERT INTO comment VALUES (9708,1252,3136,'Popstar Dave','re: What it looks like...','2003-11-20 18:56:17',3,'OK, I said that I had a solution in the works... and it turned out exactly the same as wonshot\'s here.\r\n50 smaller rectangles can fit inside the larger one...',9705,0);
INSERT INTO comment VALUES (9709,1252,3172,'SilverKnight','re(2): What it looks like...','2003-11-20 18:59:50',3,'Dave.... I will work with what you drew.... since that makes sense to me too.... Thanks for your effort.\r\n\r\nIt seems to me the answer is 50.',9708,0);
INSERT INTO comment VALUES (9710,1252,3386,'Victor Zapana','solution','2003-11-20 19:07:17',0,'Well based on pd\'s picture lets make a unit circle, and a unit square on the origin. The point where the corner of the small rectangle to a point on the circle is point ((1-2x),(1-x)). To find the point, make a quadratic formula adapted from x^2+y^2= 1: (1-2x)^2 + (1-x)^2 = 1 \r\n1 - 4x + 4x^2 + 1 - 2x + x^2 = 1 \r\n5x^2 - 6x + 2 = 1 \r\n5x^2 - 6x + 1 = 0 \r\nUsing the quadratic formula, you get roots 1 and .2. 1 cant be a root so x = 0.2. \r\nThus the corner is (0.6 , 0.8). \r\nEventually, you get that the 4 corners of the small rectangle is (1,1), (0.6,1), (1,0.8), (0.6, 0.8). You find that it is a 0.4 x 0.2 rectangle. Thus, 5 rectangles can fit the length of the large square, and 10 rectangles can fit the width of the large square. 5 x 10= 50. \r\n50',NULL,0);
INSERT INTO comment VALUES (9711,1252,3386,'Victor Zapana','hm..','2003-11-20 19:08:12',0,'lol after looking at the other posts i see others got to the same conclusion as my solution.. oh well lol.',NULL,0);
INSERT INTO comment VALUES (9712,670,3558,'Tristan','re(6): a little more straightforward','2003-11-20 19:31:37',0,'Wait, your right. I guess I was thinking about it all wrong. Without thinking, I must have tried to find a digit where the big number is 13^ a certain integer. I was confusing myself.',9652,0);
INSERT INTO comment VALUES (9713,658,4417,'don','binary search doesnt work','2003-11-20 19:38:29',0,'Unfortunately, the binary search technique would not work in this case. A binary search can ONLY be used when the data set has been sorted first. If you do not sort the data first, then you have no way of knowing whether or not the item you are looking for is in one subset or the other. Since the poison can be in any glass, then the data isn\'t sorted, it is random.',NULL,0);
INSERT INTO comment VALUES (9714,658,4417,'don','','2003-11-20 19:44:30',0,'the correct answer is that there is not enough information to answer this question.',NULL,0);
INSERT INTO comment VALUES (9715,1474,3558,'Tristan','thoughts','2003-11-20 20:01:35',0,'First of all, I think this problem is a little beyond me, but I interpreted the problem to mean the probability of getting a three of a kind(non-poker) on drawing on a particular card. That means that you don\'t include the probability of already having drawn a three of a kind. Having a list of probabilities for each card makes it simple to calculate both anyway.\r\n\r\nSecond of all, to Dan,\r\nYou and other people have probably already told you this, but you take these puzzles too literally (or not literally enough, depending on how you look at it). I\'m absolutely sure that yours was not the intended answer, and I think you know that, but pursue it anyway. Do you know how hard it is to write a puzzle that is free from problems that could be exploited by people like you? It takes very, careful phrasing.\r\n\r\nNot that there\'s anything wrong with what you\'re doing, but the intended solution is what we\'re looking for, or a better one. By better, I mean things like a shorter proof.',NULL,0);
INSERT INTO comment VALUES (9716,1505,3558,'Tristan','re: Code Revealed..','2003-11-20 20:07:30',3,'The sequence you\'re describing is x²+x.\r\n\r\nThis comment is labeled as a solution so it doesn\'t do any spoiling.\n\nEdited on November 20, 2003, 8:11 pm',9678,0);
INSERT INTO comment VALUES (9717,1252,3558,'Tristan','2 solutions','2003-11-20 20:22:08',3,'Combining what has already been said, there are 2 solutions: 2, and 50. This is taken from C.B.\'s and wonshot\'s comments. Why are there two solutions? Because there are two ways this smaller rectangle can be. Its corner can touch the circle edge close to it, or it can touch the further edge of the circle where it is tangent to the rectangle.',NULL,0);
INSERT INTO comment VALUES (9718,670,4374,'Richard','re: solution','2003-11-20 20:35:49',0,'Your observation about the powers of 10 mod 13 leads to the conclusion that replacing the powers of 10 by their mod 13 equivalents gives 4*0+10*x+1+4*0 as a mod 13 representation of the 50-digit number since 1+10+9+12+3+4=39 is divisble by 13. Now 10*x+1 is divisble by 13 if x=9, and one may readily check by brute force that 91 is the only two-digit number that ends in 1 and is divisible by 13. Hence x=9 uniquely renders the 50-digit number divisble by 13 as desired.',9513,0);
INSERT INTO comment VALUES (9719,1474,3196,'Dan','When you\'re right, you\'re right, SilverKnight...','2003-11-20 20:41:35',1,'This post is only with respect to the \"Three of a Kind\" brain teaser as interpreted according to poker rules. (Most people disagree with that interpretation).\r\n \r\n(01) SK: No, Dan... I hate arguing what should be obvious .... but you MULTIPLIED by (5!). There is no \'this is the same\' about it....\r\n \r\nDan: I went haywire when I did that. I believe it would be unethical for me to go back now and correct the original post, so I will either put a heading comment in it, or post a corrected version of it. \r\n\r\nLet me break this out. The 52*51*50*49*48=51979200 part is correct if duplicates are not eliminated. 4*3*2 reflects all the ways that three aces can be ordered vis-a-vis each other in a hand of five: (spades - clubs - diamonds), (spades, clubs, hearts), (spades-diamonds-clubs), etc. There really are 4*3*2 = 24 such possibilities. So far, so good. Now each of these orderings will have 2 other cards that are not aces and don\'t match each other. If you remove all the aces, you\'re left with 48 cards. If you consider such a card (let\'s say, a jack), then the other non-ace among the 5 cards can be neither an ace nor a jack, for this to be a \"3 of a kind\" in the poker sense. There are only 44 cards in a deck of 52 that are neither aces nor jacks. That\'s where the 48*44= 2112 came from. Where I went wrong here is to multiply by (5!) in a misguided attempt to factor in permutations, since I had aleady considered ace permutations vis-a-vis each other with that 4*3*2 business. What I should have done is considered all the ways 3 aces \r\nof a particual ordering with respect to each other (e.g. Hearts-Clubs-Diamonds = HCD), can lie among 5 cards. There are ten possibilies: \r\n(HCD--), (HC-D-), (HC--D), (H-CD-), (H-C-D), \r\n(H--CD), (-HCD-), (-HC-D), (-H-CD), (--HCD) \r\nSo all the 3-ace combinations in a true poker hand of 5 have to be: \r\n(4*3*2)*(48*46)*(10) = 529920.\r\nAnd the odds are 529920/51979200=0.0101948472\r\nThis is a different value than either of us has given so far. I defy anyone to find a flaw in that reasoning.\r\n\r\n(02) SK: I tire of your attempt at justifying the wrong answer.\r\nDan: Yeah, life is rough, isn\'t it? It\'s really unfair that you have to suffer so. Maybe Hollywood will turn your life into a movie. I see the role of \"SilverKnight\" in the movie as being played by John Ritter, Robert Stack, Bob Hope, Art Carney, Gregory Peck or Charles Bronson...\r\n\r\n(03)SK: What you wrote DOES imply that *IF* you get 3 of a kind, it will occur on the 5th to 14th card. And this is incorrect. Straights and Flushes have EXACTLY as much bearing on this problem as fullhouses.... Because, otherwise, I can choose WHICH five cards I wish... and get A, A, 1, 1, 2, 2, ... K, K, and wait until I get my 27th card (say an 8) before getting my 3 of a kind. And then I\'ll choose three 8\'s, a 9, and a 4, and I have my three of a kind, but I couldn\'t get my three of a kind before the 27th card.\r\n \r\nDan: This is an interpretation of the puzzle that I hadn\'t considered. I was just ass-uming that, as soon as you got A A 2 2 3 you now had \"two pairs\", and it was too late to get a \"three-of-a-kind.\" Interesting..... If this is your interpretatiopn of the poker-verion of the puzzle, then you\'re right in regarding it as being as dumb as a box of hair.\r\n\r\n:-) \r\n\r\n\r\n\r\n\r\nEdited on November 20, 2003, 9:06 pm\n\nEdited on November 20, 2003, 9:11 pm',NULL,0);
INSERT INTO comment VALUES (9720,1475,4323,'Benjamin J. Ladd','Guam?','2003-11-20 21:52:09',4,'Do you count Guam as a point in the U.S.?',NULL,0);
INSERT INTO comment VALUES (9721,1474,3172,'SilverKnight','One flaw in your reasoning...','2003-11-20 21:57:52',1,'Dan,\r\n\r\nI think you\'re just throwin\' these up in the air for me to slam down like a volleyball....\r\n\r\nYou wrote:\r\n\"Let me break this out. The 52*51*50*49*48=51979200 part is correct if duplicates are not eliminated.\" ... \"I defy anyone to find a flaw in that reasoning.\"\r\n\r\nWell... according to my calculations...\r\n\r\n\r\n52*51*50*49* 8 = 51979200\r\n\r\nso... I if we replace the 8 with a 48... \r\nwe get 311,875,200\r\n\r\nThen, you suggested we multiply:\r\n(4*3*2)*(48*46)*(10) = 529920\r\nBut I wonder... if we replace the 46 with a 44:\r\nwe get 506,880\r\n\r\nNow 506880/311875200 = .0016252655\r\n\r\nHmmm.... that number sure looks familiar... wait... I saw it somewhere.... yes! I remember now... it was in a couple of my earlier comments.\r\n',9719,0);
INSERT INTO comment VALUES (9722,1474,1301,'Charlie','re: A non-poker solution (computer program not used)','2003-11-20 22:36:38',0,'In the dialog manner,\r\n\r\nDan:\r\nThere are 52*51*50=132600 ways to draw the first 3 cards from a 52 card deck. (SilverKnight says you need to divide by 3! to eliminate the duplicates. But as I conclusively demonstrated in \"Some additional clarificatioins for SilverKnight\", this is like \"improving\" an equation by dividing both sides by 1. You get the same result either way.) If these 3 cards are all aces, then there are 4*3*2=24 possibilities for these cards (e.g. spades/clubs/diamonds, hearts/clubs/spades...). So the odds of getting 3 aces in 3 draws are: 24/132600 = 0.0001809955 \r\n\r\nThere are 52*51*50*49=6497400 ways to draw the first 4 cards from a deck of 52. If the 4rth card is an ace, there are 2+1=3 places 3 aces can be situated in 4 cards. For each of these, there are 48 possibilities for the non-ace. 24*3*48 = 3456 4-card draws containing 3 aces. The odds of this are 0.0005319051. \r\n\r\nCharlie:\r\nSo far so good, so long as we are going to multiply by 13 to get the probability of any three of a kind, not just three aces.\r\n\r\nDan:\r\nThere are 52*51*50*49*48=311875200 ways to draw the first 5 cards from a 52 card deck. If the 5rth card is an ace, there are 3+2+1=6 places for the aces cards to be located among the 5 drawn cards. For each of these, there are 48*47 =2256 possibilities for the two non-aces. 24*5*2256 = 270720 5-card draws containing 3 aces. The odds of this are: 0.0008680395 \r\n\r\nCharlie:\r\nConceptually, with that 13x caveat, this is still good; however there\'s a bookkeeping mistake: the 6 ways of placing the other 2 aces among the previous 4 cards is carried down into the final multiplication as a 5 rather than a 6. It should indeed be 6, as 2C4, or 4*3/2. I don\'t know how it was derived as 3+2+1, but that\'s beside the point. \r\n\r\nOnce that correction is made, as with the previously defined numbers, once they\'re multiplied by 13 and by 1,000,000 they agree within the expected statistical variations with the simulation results.\r\n\r\nDan:\r\nSimilarly, the odds... \r\n\r\nCharlie:\r\nJust when they easy ones go by the wayside, the description ends. Six is the first time we come to the situation where the numbers other than the newly completed triplet also themselves could contain a triplet and must be excluded from the consideration that this was the first triplet. It\'s irrelevant when considering ace-only triplets, but kills the possibility of merely multiplying by 13 to get the probability of any triplet first being completed at the given stage. Since the others were capable of being multiplied by 13 to get the latter probability, the numbers are not even proportional to the given probabilities.\r\n\r\nI also note that the probabilities for the cases of 3, 4 and 5 were individual probabilities of completing the first (ace) triplet at that number, rather than a cumulative probability. The numbers you post are monotonically increasing and add up to more than 1; are these intended as cumulative probabilities, by adding the \"similar\" calculations? At what point to you switch over from individual to cumulative probabilities?\r\n\r\nThe procedure you describe, correct for finding what is the probability of completing a set of 3 aces first at draw n, can be stated mathematically as \r\n\r\n(C(n-1,2)*24/(52!/(52-n)!)) (48!/(48-n+3)!)\r\n\r\nwhich can be verified for the first few from the following table generated with that formula:\r\n 3 0.000180995\r\n 4 0.000531905\r\n 5 0.001041647\r\n 6 0.001699141\r\n 7 0.002493305\r\n 8 0.003413058\r\n 9 0.004447317\r\n 10 0.005585003\r\n 11 0.006815034\r\n 12 0.008126327\r\n 13 0.009507803\r\n 14 0.010948379\r\n 15 0.012436975\r\n 16 0.013962508\r\n 17 0.015513898\r\n 18 0.017080063\r\nThe values for 3 and 4 agree with yours. The value for 5 is 6/5 what you give, consistent with your mistakenly bringing down 5 instead of 6 as a factor. The values for 6 and 7 agree with your table. Then your table goes off into something only you know how was calculated--not \"similarly\" to the other calculations. You haven\'t told us at all how these were arrived at.',9703,0);
INSERT INTO comment VALUES (9723,1474,1301,'Charlie','re(2): A non-poker solution (computer program not used)','2003-11-20 22:43:55',0,'By the way, the remaining figures on your table can\'t even be the cumulative version of the numbers you calculate, that is, of the prob of completing an ace triplet by that number. That comes out to the last column of the following table:\r\n 3 0.000180995 0.000180995\r\n 4 0.000531905 0.000712901\r\n 5 0.001041647 0.001754548\r\n 6 0.001699141 0.003453689\r\n 7 0.002493305 0.005946994\r\n 8 0.003413058 0.009360052\r\n 9 0.004447317 0.013807369\r\n 10 0.005585003 0.019392372\r\n 11 0.006815034 0.026207406\r\n 12 0.008126327 0.034333733\r\n 13 0.009507803 0.043841537\r\n 14 0.010948379 0.054789916\r\n 15 0.012436975 0.067226891\r\n 16 0.013962508 0.081189399\r\n 17 0.015513898 0.096703297\r\n 18 0.017080063 0.113783359\r\n 19 0.018649922 0.132433281\r\n 20 0.020212393 0.152645674\r\n 21 0.021756395 0.174402069\r\n 22 0.023270847 0.197672915\r\n 23 0.024744667 0.222417582\r\n 24 0.026166774 0.248584357\r\n 25 0.027526087 0.276110444\r\n 26 0.028811525 0.304921969\r\n 27 0.030012005 0.334933974\r\n 28 0.031116447 0.366050420\r\n 29 0.032113769 0.398164189\r\n 30 0.032992889 0.431157078\r\n 31 0.033742728 0.464899806\r\n 32 0.034352202 0.499252008\r\n 33 0.034810232 0.534062240\r\n 34 0.035105735 0.569167975\r\n 35 0.035227630 0.604395604\r\n 36 0.035164835 0.639560440\r\n 37 0.034906270 0.674466710\r\n 38 0.034440853 0.708907563\r\n 39 0.033757503 0.742665066\r\n 40 0.032845138 0.775510204\r\n\r\nAnd certainly there\'s no hope of multiplying these by 13 and getting anything that resembles a probability.\r\n',9722,0);
INSERT INTO comment VALUES (9724,1474,1301,'Charlie','re(3): A non-poker solution (computer program not used)','2003-11-20 22:48:04',0,'Also, by the way, the cumulative prob of completing 3 aces does come out to 1 by the time you get to 52:\r\n41 0.031692677 0.807202881\r\n42 0.030289039 0.837491920\r\n43 0.028623142 0.866115061\r\n44 0.026683904 0.892798966\r\n45 0.024460246 0.917259211\r\n46 0.021941084 0.939200296\r\n47 0.019115338 0.958315634\r\n48 0.015971927 0.974287561\r\n49 0.012499769 0.986787330\r\n50 0.008687783 0.995475113\r\n51 0.004524887 1.000000000\r\n\r\nBut how to do for 3 of any value card?',9723,0);
INSERT INTO comment VALUES (9741,651,4374,'Richard','We are in a field','2003-11-21 14:32:16',0,'The integers mod p are a field for any prime p, so we can add, subtract, multiply and divide (except by 0) at will. Also, any polynomial equation of degree n has at most n solutions. Multiplying the nonzero elements together, we must get a number that is -1 mod p, because an even number of these elements are not self-reciprocal and therefore the reciprocals pair up, while the self-reciprocal element(s) are p-1 (congruent to -1) and 1 (since the equation x^2=1 has only these 2 solutions).',NULL,0);
INSERT INTO comment VALUES (9742,1474,1301,'Charlie','Analytic Solution:Computer aided for computations','2003-11-21 15:58:44',3,'At any given number, n, of cards having been drawn, the situation that the first triplet has been completed just at that step entails that, among the first n-1 cards drawn, there were exactly 2 of that denomination. Of the remaining 12 denominations there could have been zero through [(n-3)/2] pairs, where the square brackets indicate the floor function (greatest integer not exceeding the contents). Call the number of pairs p (excluding the previous pair of the denomination whose triplet was just completed).\r\n\r\nThe number of singlets (one of a kind) drawn then must be n-3-2p. The total of pairs and singlets must be less than or equal to 12, so don\'t count terms which use larger values for these.\r\n\r\nThere are 13 choices for which of the denominations is represented by the newly formed triplet. But there are also 4 possible choices of which card is the triplet completion card, and C(3,2) ways of choosing the first 2 of the triplet.\r\n\r\nFor each of these, there are C(12,p) ways of choosing which denominations are present in pairs, and, since each pair can be any of C(4,2)=6 choices from the original deck, the C(12,p) is to be multiplied by 6^p.\r\n\r\nFor each of the choices so far, the s singlets can be each of the 4 from the original deck, so we multiply the product so far by 4^s. And there are C(12-p,s) of them, that factors in also.\r\n\r\nThe total of the [(n-3)/2] terms thus calculated must then be divided by the total combinations of 52 cards taken n at a time.\r\n\r\nFor two decks the 52 becomes 104. Also, in the above, there are 8 ways of choosing the triplet-completion card for a given denomination and C(7,2) ways of choosing the first 2 of the triplet, and C(4,2)=6 becomes C(8,2)=28, SO that 6^p becomes 28^p.\r\n\r\nA program that calculates the above is:\r\nDECLARE FUNCTION combi# (x#, y#)\r\nDECLARE FUNCTION lxf# (x#)\r\nDEFDBL A-Z\r\nDIM SHARED twopi\r\nDIM cum(28)\r\ntwopi = ATN(1) * 8\r\ndecks = 1\r\npairBase = combi(4 * decks, 2)\r\ntotCards = 52 * decks\r\nPRINT\r\nFOR n = 3 TO 28\r\n tot = 0\r\n FOR p = 0 TO INT((n - 3) / 2)\r\n s = n - 3 - 2 * p\r\n IF p + s <= 12 AND s >= 0 THEN\r\n term = 13 * 4 * decks * combi(4 * decks - 1, 2) * combi(12, p) * pairBase ^ p * (4 * decks) ^ s * combi(12 - p, s)\r\n tot = tot + term\r\n END IF\r\n NEXT\r\n tot = tot / (combi(totCards - 1, n - 1) * totCards)\r\n cumTot = cumTot + tot\r\n cum(n) = cumTot\r\n PRINT USING \"## ####### #.####### #.#######\"; n; tot * 1000000; tot; cumTot\r\nNEXT\r\n\r\ntot = 0\r\nFOR i = 1 TO 27\r\n IF cum(i) > .5 AND med = 0 THEN\r\n med = i - 1 + (.5 - cum(i - 1)) / (cum(i) - cum(i - 1))\r\n PRINT \"Median is\"; med\r\n END IF\r\n tot = tot + i * (cum(i) - cum(i - 1))\r\nNEXT\r\nPRINT \"Mean is\"; tot\r\n\r\n FUNCTION combi (x, y)\r\n lg = lxf(x) - lxf(y) - lxf(x - y)\r\n combi = INT(EXP(lg) + .5)\r\n END FUNCTION\r\n\r\nFUNCTION lxf (x)\r\n IF x < 171 THEN\r\n fact = 1\r\n IF x > 1 THEN\r\n FOR i = 2 TO x\r\n fact = fact * i\r\n NEXT\r\n END IF\r\n lo = LOG(fact)\r\n ELSE\r\n lo = LOG(x) * (x + .5)\r\n lo = lo + (-x + 1 / (12 * x) - 1 / (360 * x * x * x) + 1 / (1260 * x * x * x * x * x))\r\n lo = lo + LOG(twopi) / 2\r\n END IF\r\n lxf = lo\r\nEND FUNCTION\r\n\r\nIt produces\r\n \r\n88 69 91 16 \r\n61 86 18 99 \r\n19 98 66 81 \r\nthey all add to 264, and its a \"topsy-turvy\" square.\n\nEdited on November 21, 2003, 9:02 pm',NULL,0);
INSERT INTO comment VALUES (9748,1506,3386,'Victor Zapana','re: solution','2003-11-21 17:56:58',0,'so the answer is yes. heh',9747,0);
INSERT INTO comment VALUES (9749,1383,3529,'Senthil Kumar','Solution','2003-11-21 18:04:05',3,'1) 1235\r\n2) 4721\r\n3) 3862\r\n\r\nWe know that 2 digits are in the magic number from (1). So it could be either \r\na) 1&2 \r\nb) 1&3\r\nc) 1&5\r\nd) 2&3\r\ne) 2&5 \r\nf) 3&5.\r\n\r\na, c, d and f are not possible, because u will end up with a 5 digit number.\r\n\r\nSo only 1&3, 2&5 are possible. This will give you the following possilbe numbers:\r\n7831\r\n1763\r\n4825\r\n2765\r\n\r\nThere is no ambiguity if the number is divisible by 7, which 2765. So the magic number is 2765.\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (9750,1506,3172,'SilverKnight','re: solution - very nice','2003-11-21 18:14:49',0,'very nice Victor....\r\n\r\nI would be interested in the thought process that you used to find the solution, if you\'d care to share it with us. :-)',9747,0);
INSERT INTO comment VALUES (9751,1447,4112,'Sniper59','re(3): I am confused','2003-11-21 20:33:46',0,'That\'s not necessarily true. In cryptography, it\'s often the custom to only include necessary information. The more ciphertext available to a codebreaker, the easier it usually is to decipher it. While this is not exactly a difficult cipher to break (I found the \"take the money ...\" part by simply looking at it), just because a word was omitted does not necessarily imply that it was done by accident. ',9544,0);
INSERT INTO comment VALUES (9752,1259,4438,'marta','possible answer','2003-11-21 20:49:16',0,'Maurice lives #137- babysitter\r\nZack lives #139- Walk dogs\r\nRaquel lives #141- gardening\r\nAngelica lices #143- house cleaning',NULL,0);
INSERT INTO comment VALUES (9753,1506,3386,'Victor Zapana','re(2): solution - very nice','2003-11-21 21:00:07',0,'hmm.. i cant really explain it lol its like... i guess a couple of numbers... i kinda figured it would be 2-digit numbers all around coz it cant be 1-digit ands for higher, i just thought it would be simpler than that lol. so basically its a lot of luck and guess & check. oh yeah.. i thought that probably each row,column, and diagonal had like 1, 6, 8, 9 once, so i looked for a number that end in the ones digit 4. eventually i got to that... lol\n\nEdited on November 21, 2003, 9:03 pm',9750,0);
INSERT INTO comment VALUES (9730,1474,1768,'Lorne Hrynkiw','Comments on poker hand solutions','2003-11-21 05:40:13',0,'The only justification for rejecting the maximum count of 27 is that it results in a full house; and a full house beats three of a kind(3oK). The two pair can be ignored because 3oK beats two pair. I agree that a count of five is the lowest count that can produce 3oK but disagree on 14 being the maximum. Consider drawing the cards 2 thru king and three aces, thats 15 by my count. Also consider that a straight beats 3oK thus run lengths can be a maximum of 4. As an example 2-5, 7-10, QK, and three aces for a count of 13. Flushes can be ignored - well yes the first 5 cards can be the same suit - when considering ranges since we cannot guarantee a flush with fewer than 14 cards.\r\n\r\nOverall I\'m not a big fan of the poker hand requirement and am studying the wording in the hope of finding inspiration. ',9725,0);
INSERT INTO comment VALUES (9731,1228,3224,'Lee','re: A simpler formula','2003-11-21 07:16:18',0,'Love it.',9420,0);
INSERT INTO comment VALUES (9732,1475,4430,'Eberhard','Solution-','2003-11-21 10:54:08',0,'The solution to this problem is simple, but you need to know a bit more geography than you can pick up most maps. The key to this is that Alaska satisfies three criteria northern, western, and eastern most points. If you look at a good map of Alaska you will see that the Alaskan archipelago extends past the 180 degree mark separating east and west longitude, meaning it exists in both the eastern and western hemispheres simultaneously. Second international law dictates that a country controls the waters 3 miles out from any land they control. This is important because it means that you are not leaving US controlled territory as you travel island to island. From there it is a simple matter of traveling to Hawaii, the southernmost point. ',NULL,0);
INSERT INTO comment VALUES (9733,1259,4431,'walt','possible answer','2003-11-21 11:04:01',0,'zach-139, walk the dogs\r\nraquel-143,house cleaning\r\nangelica-141,babysitting\r\nmaurice-141,gardening\r\n',NULL,0);
INSERT INTO comment VALUES (9734,1259,4432,'Brian Affourtit','my guess','2003-11-21 11:08:20',0,'Raquel, 137, Housecleaning\r\nZack, 139, Walk Dogs\r\nAngelica, 141, Babysitting\r\nMaurice, 143, Gardening',NULL,0);
INSERT INTO comment VALUES (9735,1259,4432,'Brian Affourtit','re: possible answer','2003-11-21 11:09:07',0,'Either Angelica or Maurice lives at #141.\r\n\r\nnot both.',9733,0);
INSERT INTO comment VALUES (9736,1259,3172,'SilverKnight','solution','2003-11-21 11:57:19',3,'Angela - 141 - Gardening\r\nMaurice - 139 - Babysitting\r\nRaquel - 143 - Housecleaning\r\nZach - 137 - Walk his dogs',NULL,0);
INSERT INTO comment VALUES (9737,1259,4082,'wonshot','Solution','2003-11-21 12:05:38',0,'Assume: House Numbers are #137, #139, #141, #143\r\nAll on same side of the street and #143 is last, no skipping or half numbers.\r\n\r\nAssume: Zach and Maurice are male.\r\nAssume: Angelica and Heidi are female.\r\n\r\nZach: Walk dogs lives at #137\r\nAngelica: Babysitter lives at #139\r\nMaurice: Gardener lives at #141\r\nRaquek: Housecleaner lives at #143',NULL,0);
INSERT INTO comment VALUES (9738,1259,2231,'Trevor Leitch','re: my guess','2003-11-21 12:31:25',0,'Two things wrong with Brian\'s solution:\r\n\r\n1) The person who lives in 143 is NOT the person who hired Heidi to garden (statement #5)\r\n2) Raquel lives 2 houses EAST of the person who needed a babysitter (statement #3); since 143 is the easternmost (statement #5), your solution has Raquel living WEST of that person',9734,0);
INSERT INTO comment VALUES (9739,1259,4082,'wonshot','re: Solution (oops) + reason (SK\'s right)','2003-11-21 12:34:06',0,'Zach had dogs walked #1\r\n\r\nRaquel lives 2 houses east of babysitter #3\r\n therefore, Raquel lives at 141 or 143, but can\'t live\r\n at 141 because of #2.\r\n Also, babysitter lives at 139.\r\nRaquel lives at 143.\r\n\r\nMale lives at 139, therefore Zach or Maurice, but 139 is the babysitter and since zach has his dogs walked, Maurice lives at 139\r\n\r\nMaurice lives at 139 and needs a babysitter.\r\n\r\nAngelica lives at 141 because Maurice doesn\'t.\r\nZach must live at 137.\r\n\r\nGardener does not live in 143, therefore Raquel isn\'t gardener but the housecleaner, and Angel is therefore in need of a gardener.\r\n\r\nOverall, SK was right\r\nZach lives at 137 needs Dogs walked\r\nMaurice lives at 139 needs babies sat\r\nAngelica lives at 141 needs Garden tended\r\nRaquel lives at 143 needs house cleaned.\r\n',9737,0);
INSERT INTO comment VALUES (9740,690,4430,'Eberhard','flash point','2003-11-21 12:48:19',0,'Just another thought about why this is an incorrect answer -- while in may cases it is very high, oil does have a flash point and will catch fire- crude oil for example ranges between 100 and 200 degrees, if the steel is hot enough to boil water, which has far lower specific heat value and will therfore absorb less energy, before rasing temperature, the threat of igniting the oil is very real. Any chemist ot blacksmith would cringe at the thought of placing super-heated steel into oil.',NULL,0);
INSERT INTO comment VALUES (9754,1506,3386,'Victor Zapana','re(3): solution - very nice','2003-11-21 21:01:39',0,'oh yeah one other thing. why i called it a topsy-turvy square. my math teacher in like 9th grade used to give us like magic square extra credit. but he kept on saying that there was special squares that can be upside down and rightside up and he called them topsy-turvy. so there heh',9753,0);
INSERT INTO comment VALUES (9755,1259,4439,'max','correct answer','2003-11-21 21:15:06',3,'143 Raquel, Housecleaning\r\n141 Angelica, Gardening\r\n139 Maurice, Babysitting\r\n137 Zach, Dog walking',NULL,0);
INSERT INTO comment VALUES (9756,651,4374,'Richard','re: full solution','2003-11-21 21:38:31',0,'The first Wikipedia proff and the others to which you give the link are essentially the same as I gave in my previous comment. It is due to Gauss, according to Uspensky and Heaslit\'s Elementary Number Theory (a gem, but out of print). For someone with scant experience with number theory and congruences, this would be a very difficult problem, in my opinion.\r\n\r\n~Richard ',8713,0);
INSERT INTO comment VALUES (9757,1345,3127,'lesa','correct solution','2003-11-22 00:44:27',0,'Yello shirt = $10\r\nRed shirt = $20\r\nOrange shirt = $30\r\nBlue shirt = $40\r\nGreen shirt = $50\r\n\r\nDiane = Orange(30) & Green(50) $80\r\nAlice = Yellow(10) & Green(50) $60\r\nEmily = Red(20) & Blue(40) $60\r\nBetty = Red(20) & Orange(30) $50\r\nCarol = Yellow(10) & Blue(40) $50\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (9758,1235,4300,'Minion123','maybe?','2003-11-22 02:08:40',0,'till the ducks migrate',NULL,0);
INSERT INTO comment VALUES (9759,1505,4374,'Richard','re(2): Code Revealed..','2003-11-22 04:13:29',0,'The code c then represents letter number -1/2+sqrt(m+1/4) with a=1,b=2, etc. then. This appears to equal the integer part of sqrt(c). floor(sqrt(2))=1,...,floor(sqrt(702))=26. Can anybody verify the ... ?',9716,0);
INSERT INTO comment VALUES (9760,1505,4374,'Richard','','2003-11-22 12:40:01',0,'',9759,0);
INSERT INTO comment VALUES (9761,1504,3351,'Eric','first thoughts','2003-11-22 12:41:16',0,' My first line of thought would be to construct two quadrilaterals within our unit circle. Let us call them AOBR1 and AOBR2 where points A and B are as described above, point O is the origin of the circle and points R1 and R2 are the two points of reflection that our light rays are bouncing off with R1 at the top of the circle and R2 at the bottom. Now note that angle AR1O = OR1B and AR2O = OR2B.\r\nSolving the top quadrilateral first, and introducing some variables(say x and y), let us define the following angles:\r\nAOB = 60\r\nAR1O = OR1B = x\r\nAOR1 = y\r\nR1OB = 60-y\r\nR1AO = 180-x-y\r\nR1BO = 120+y-x\r\nBy the law of sines on both triangles OAR1 and OR1B we see that sin x = .35sin(180-x-y) = .6sin(120+y-x).\r\nAlso by the law of cosines we see that the distance AB is √.2725.\r\n\r\nI hope this helps\n\nEdited on November 22, 2003, 12:46 pm',NULL,0);
INSERT INTO comment VALUES (9762,1505,4374,'Richard','correction','2003-11-22 12:46:36',0,'m should be c in my expression -1/2+sqrt(m+1/4). I can show algebraically that sqrt(c) minus this is between 0 and 1. Setting my TI-30X calculator on FIX 0, the integer part of the square root is automatically displayed and I easily get BREAK THE CODE for the first three words.\r\n\r\nMy previous comment timed out or something and didn\'t register -- this takes its place.',9760,0);
INSERT INTO comment VALUES (9763,670,4374,'Richard','correction','2003-11-22 12:54:55',0,'(10^n)%11=(-1)^n should have been (10^n)%11=((-1)^n)%m since by remainder I mean least nonnegative remainder as is usual in long division. Notice that this does NOT give negatives (quotient or remainder) for the negative of a positive integer: 12=5*2+2 but -12=5*(-3)+3 so that 12%5=2 but (-12)%5=3.',9746,0);
INSERT INTO comment VALUES (9764,1505,4450,'drew','re: correction(solution)','2003-11-22 14:11:31',0,'you are a friggen idiot.lol\r\nwhat you put may work but it is much simpler.\r\nthe awnser is x²+x where x is the number of the letter in the alphebet. by getting 3 letters i personally guessed that 2 was A 6 was B and e was 30\r\ni guesed these using most common two letter words and that 2 stands by itself\r\nwhen you put these into functions you get\r\nf(1)=2\r\nf(2)=6\r\nf(5)=30\r\nso plug these into the function\r\nf(x)=ax²+bx+c\r\nwhen you solve this function you find out that A=1, B=1, and C = 0.',9762,0);
INSERT INTO comment VALUES (9765,1506,1626,'Gamer','Another way to do this:','2003-11-22 14:16:55',0,'Since 1s and 8s look the same when flipped and 6s and 9s switch, if you have one of each number in the ones place and in the tens place it would work.\r\n\r\nUsing the grids of ABCD magic squares, you can construct one of these.\r\n\r\nABCD Simply using reflections and rotations on this grid will give\r\nDCBA another grid of the same type. Just replace A through D with \r\nBADC a number 1, 6, 8, 9 and it should work. Then put the two grids\r\nCDAB together with one digit equalling the tens place and the other\r\ngrid equalling the ones place, and you have a magic square created.\r\nOther places can be added in the same way. :)\r\n\r\nMaybe someone could devise a program that creates these this way? :)',NULL,0);
INSERT INTO comment VALUES (9766,1505,4450,'drew','re(2): 72-4-182-156-30-420 (correction)','2003-11-22 14:26:28',0,'90/2-56-342-30-30',9667,0);
INSERT INTO comment VALUES (9767,1504,4450,'drew','help?','2003-11-22 14:34:59',0,'yah i am still in Algebra two anyone wanna help me with this?',NULL,0);
INSERT INTO comment VALUES (9768,1505,4374,'Richard','re(2): correction(solution)','2003-11-22 14:38:14',0,'Right you are except for the idiot part. If x²+x=c then\r\n x=-1/2+sqrt(c+1/4) but since c is an integer it can be shown that x=floor(sqrt(c)) (integer part of the square root). For c=30(e) x=5, then. All you have to do is pick the biggest integer x such that x² does not exceed c in order to decode.',9764,0);
INSERT INTO comment VALUES (9769,1497,4450,'drew','?????','2003-11-22 14:48:10',0,'isnt there a therom that prooves that?',NULL,0);
INSERT INTO comment VALUES (9770,1505,4374,'Richard','re(3): 72-4-182-156-30-420 (correction)','2003-11-22 14:51:20',0,'One objective should be to find a simple way to decode. That encoding is via x^2+x was revealed way back in an earlier comment. On a calculator, it is easy to encode using x(x+1), but decoding is even simpler if you use the integer part of the square root of the coded letter as I have suggested.',9766,0);
INSERT INTO comment VALUES (9771,670,4408,'Kirk','re: correction','2003-11-22 18:39:12',0,'Of course, why didn\'t I think of that!? :-s\r\nThanks for your effort of typing in everything you know about modulus numbers...but, nope, unfortunately I cannot start to use them to solve puzzles as I still haven\'t the foggiest idea what you\'re going on about! I was OK until you starting putting equations in. Stating what % meant, I was averagely happy with - but then you started using equations, it didn\'t make any sense! To you or experts, maybe - but to a complete beginner these things take time - so, I\'d advise you not to give up your day job! Hopefully it isn\'t a teacher! \r\n I understand that teaching over the internet is difficult at the best of times, but seriously...am I supposed to understand (10^n)%11=((-1)^n)%m?????? And no, we don\'t do ANY of that now! GCSE mathematics is very simple. A-level mathematics and Further Mathematics are trickier and involve differentiation, integration and numerous functions...including hyperbolic and inverse hyperbolic functions and their derivatives (this bit *only* features on the Further Mathematics course)\r\n\r\nBack to your explanation...just a handy teaching hint...read back over your previous message - in the viewpoint of a person who knows *nothing* about modulo....can you see that half-way through, you shoot *too* quickly into multiple equations that would confuse any poor soul? I think I speak for the majority of youngsters...if not all - but I\'m sure there\'s some university students out there thinking how silly I am - but, not knowing as much means I can spot a good teacher a mile off - which is why I want to become a mathematics teacher, as I know where problems lie, and how to explain things thoroughly - thoroughly enough that they understand what is going on step by step. If part one of something is a bit \'cloudy\', then extending that even further is even mroe cloudy, e.g. a student may not remember that \"2a\" means \"2 x a\" but infacts thinks it\'s \"a x a\". When you talk about \"2a x 2a = 4aa\" (or \"4 a^2\" or \"4 a squared\") - it will confuse him beyond belief, even though it seems simple to him. Just that *one* part of an equation, and it confuses him. Going on to show him the, almost simple Quadratic formula would make the student faint!\r\nSee where I\'m coming from? Sorry that you tried so hard yet I didn\'t understand, I feel quite bad now as you\'ve tried hard to explain things and I still haven\'t understood...but never mind, I\'ll save you the effort of teaching me now...unless you\'re preapred to explain in FULL...or of course if you have MSN messenger, where you could explain in full and I can question parts as we go along! For now, I\'ll leave you, and prepare for my television recordings in under 2 weeks time - and, yes, it does involve some maths, but only mental arithmetic! :-)',9763,0);
INSERT INTO comment VALUES (9772,670,4408,'Kirk','re(4): solution','2003-11-22 18:49:19',0,'I don\'t want to knock you Richard....but you typed this:\r\n\r\nwe have a=m*(a/m) + a%m=m*q+r. It is quite easy to show that (a+b)%m= (a%m+b%m)%m and (ab)%m= ((a%m)*(b%m))%m, which means we can remainder first before adding or multiplying without affecting the remainder of the result. It is this that makes casting out nines work as a checksum. Since (10^n)%9=1, 176923%9 =(1+7+6+9+2+3)%9=1. The same idea can be applied to digit problems using any value for m, although m=9 is the nicest for decimals, and m=11 is second nicest (since (10^n)%11=(-1)^n). \r\n\r\nNow...read that over. That does not make *any* sense at all!! You\'re telling me, when you typed it, you thought it would make sense to a normal 17 year old!? E.g. the first equation... a=m*(a/m)...I can understand that, as the \'m\'s cancel and so you are left with \'a\', but wait...you\'ve mysteriously added on a%m...and that is equal to m*q + r. What the heck is \'q\' and \'r\'? \r\n Also...you said \"It is this that makes casting out nines work as a checksum\". It is *what*? Here is an example...sdfffggggg...it is that that makes eggs lay placebo generating coefficients of friction. It makes no sense!!! PLUS....what is \"casting\" out nines??? What is a \"checksum\"! If you\'re going to explain yourself, Richard, please do it properly!',9746,0);
INSERT INTO comment VALUES (9773,670,4374,'Richard','','2003-11-22 21:31:34',0,'',9772,0);
INSERT INTO comment VALUES (9774,670,4374,'Richard','re(5): solution','2003-11-22 21:34:28',0,'Sorry to not be able to explain \"mod m\" to your satisfaction. My correction needs a correction too -- that first: \r\n (10^n)%11=((-1)^n))%m\r\nshould have been\r\n (10^n)%11=((-1)^n))%11 ,\r\nthat is m=11 here and I should have just used 11 instead of m. Thus 1000 and -1 are congruent mod 11 since\r\n 1000%11=10, and -1%11=10 as -1=-1*11+10.\r\nNotice that the remainder is always nonnegative and less than the modulus -- this is what remainder means.\r\n\r\nAs to a=m*(a/m)+a%m=q*m+r, the point is that here / indicates integer division as would be performed (at least for positive numbers) on integer variables in a computer program. a/m is an integer, not a fraction. It is the quotient when you divide a by m. You should have been able to discern this from the q*m +r. \r\nAs for the rest, the idea is simply that remaindering can be mixed in with adding, subtracting and multiplying (we will avoid dividing, so as not to get into something a little more complicated). The reason we would want to mix remaindering in with addition, subtraction and multiplication is to keep the number sizes small. Consider the problem of deciding what (10^24)%13 is. Instead of doing the whole long division of 1000000000000000000000000 by 13, we can, for example, do ((10000%13)^6)%13 and get the same answer: 10000%13=3, 3^6=729, 729%13=1, and hence\r\n (10^24)%13=1. Since a decimal number n with digit string abcd equals a*10^3+b*10^2+c*10^1+d*10^0, n%13 is congruent mod 13 to n\'=a*12+b*6+c*10+d because we can remainder the powers of 10 in advance. Then if we want n%13 we can calculate n\'%13 instead and get the same answer. For the modulus 9, n%9=(a+b+c+d)%9, and for the modulus 11, n%11=(a*10+b+c*10+d)%11=(-a+b-c+d)%11.\r\n\r\nYou should be able to give a proof that\r\n (a+b)%m=((a%m)+(b%m))%m.\r\n\r\nIn closing, here is a reliable maxim (in my opinion): \"Mathematics is learned, not taught.\"\r\n\r\n\r\n\r\n',9772,0);
INSERT INTO comment VALUES (9775,1504,4450,'drew','my first thoughts','2003-11-22 22:31:29',0,'I am assuming that the light beam intersets the circle then bounces off the circle in 90 degrees. You can then draw a right triangle with the hypotinuse at the .2725 side. From here i dont know where to go.',NULL,0);
INSERT INTO comment VALUES (9776,1505,4450,'drew','re(4): 72-4-182-156-30-420 (correction)','2003-11-22 22:40:12',0,'another way to decode which is easy is to put into y1 on your graphing calculator y1=1-x and y2=-(number)/x then find where the y\'s are equal to each other and then find out which letter is equal to that letter of the alphebet.',9770,0);
INSERT INTO comment VALUES (9777,1505,4450,'drew','program','2003-11-22 22:41:03',0,'for whoever posts these crypto phrases i have created a program using Java that encodes phrases into numbers, does anyone want this.',NULL,0);
INSERT INTO comment VALUES (9778,625,3182,'Antonio','Solution','2003-11-22 23:31:49',3,'Considering an angle Theta with it\'s vertex in the center of any of the two larger spheres and it\'s aperture from the vertex to the floor and from the vertex to the center of the small sphere in the mentioned gap between spheres. By drawing an isoceles triangle from the three centers of each circle, and relating Theta to the new isoceles triangle, it gives out the relation 4*R ²=2*(R+X)²*(1-cos[180-2*(90-Theta)]), where X is the radius to be calculated. By makeing another triangle with sides R, R+X, √(R²+X²) and Theta between R and R+X, we get the relation Theta=ArcCos[((R+X)²-X²)/(2*R*(R+X))], so we finally get the transient equation: 1=((2*R²)/(R+X)²)+Cos[180-2*[90-ArcCos[((R+X)²-X²)/(2*R*(R+X))]]], solving this equation for X, it gives X=25cm, so the diameter of the sphere in the gap between spheres is 50cm',NULL,0);
INSERT INTO comment VALUES (9779,1259,4453,'muzo','answer','2003-11-23 00:35:25',0,'R-143-hk\r\nA-141-g\r\nM-139-bs\r\nZ-137-wd',NULL,0);
INSERT INTO comment VALUES (9780,1504,3136,'Popstar Dave','re: my first thoughts (clarification regarding reflection properties)','2003-11-23 01:16:22',2,'The angle of reflection here can be found using the standard reflection property, angle of incidence equals angle of reflection. These angles are based around a tangent to the circle at the point of reflection. This can also be found by measuring aroung a radius to the point of reflection. The angle between where the light hits the reflection point and the radius will be the same as the angle that the light travels out on the other side of the radius. \r\nJust thought this might help...\r\n\r\n',9775,0);
INSERT INTO comment VALUES (9781,621,3182,'Antonio','Solution','2003-11-23 02:00:28',3,'Drawing a line from the center of the greater sphere to the center of the smaller sphere gives a distance X+R, where X is the radius to be obtained and R is 100cm. Makeing a right triangle of sides R-X and R-X gives out an hypotenuse of √2*(R-X), therefore √2*(R-X)=X+R. X=R*(√2-1)/(√2+1)=17.1572875253cm. The Diameter of the largest sphere between the gap is 34.3145750506cm. ',NULL,0);
INSERT INTO comment VALUES (9782,670,3172,'SilverKnight','re(6): solution','2003-11-23 02:11:44',0,'Richard,\r\n\r\nWith all due respect, I must agree with Kirk. And, half the reason (IMHO) of posting to flooble is to explain (in a USEFUL way) one\'s thought processs to others who might read it.\r\n\r\nSome of your earlier comments make little sense to me... (particularly this one) and I am familiar with modular arithmetic.\r\n\r\nI (and many other common submitters), generally, endeavor to write solutions/comments that include much detail--perhaps more detail than some require, but enough to help those, who are not so familiar with the subject matter, to understand the related thought processes and relationships and perhaps understand the issue better.\r\n\r\nWhen one submits a solution, it should be more than an answer. It should be, if at all possible, a straightforward method/algorithm of how to come by the answer. Failing that, one might provide hyperlinks that readers could follow to learn more about the solution or subject matter.\n\nEdited on November 23, 2003, 2:12 am',9774,0);
INSERT INTO comment VALUES (9783,1504,3172,'SilverKnight','solution (solved numerically)','2003-11-23 04:47:38',3,'I\'m ashamed to admit that I have forgotten much of my vector calculus as well as much of my polar coordinate education.\r\n\r\nThis shouldn\'t be such a difficult problem for me.\r\n\r\nAnyway, I set up a bunch of relationships and then solved it numerically (that basically means I set up a bunch of constraints, and let some variable, theta, change until the constraints settled into an appropriate range... usually zero).\r\n\r\nThat being said, this is a very unsatisfactory post for me.\r\n_______________________________________\r\n\r\nAssuming that I did all my calculations correctly, and I look forward to someone verifying this work... preferably analytically.\r\n\r\nThe numerical results I found were to aim for the points on the circle where from the origin\'s perspective the radian measure would be 83.43201955 degrees, and -85.75353466 degrees.\r\nThese correspond to aiming at points:\r\n(0.11438199,0.993436843) and (0.074046968,-.997254755)\r\n\r\nBy the way, this makes a reflection angle of 18.50560563 degrees, and 9.049321949 degrees respectively. (The reflection angle, as Popstar Dave already mentioned, is measured as the angle between the ray of light and line segment along the radius of the circle at the point of reflection)\r\n_______________________________________\r\n\r\nBut that\'s not what Antonio asked.\r\n\r\nAntonio asked what direction it should point from point A\'s perspective.\r\n\r\nTo aim at the first point, A should point at 64.92641392 degrees (off the horizontal, so aimed up and to the right.)\r\n(This is roughly the angle a \'/\' makes. :-)\r\n\r\nTo aim at the second point, A should point at -76.70421272 degrees (off the horizontal which means down and to the right... mostly down... :-)\r\n\r\nPlease advise if this isn\'t clear. And apologies for not providing an analytic solution.',NULL,0);
INSERT INTO comment VALUES (9784,676,4450,'drew','arithmetic progression?','2003-11-23 11:37:20',0,'whats arithmetic progreston?\r\n',NULL,0);
INSERT INTO comment VALUES (9785,290,4450,'drew','sort of solution','2003-11-23 11:40:53',0,'I derived that pi=tan(180/infinity)infinity\r\nsince you cant find infinity then that prooves that pi is irrational.',NULL,0);
INSERT INTO comment VALUES (9786,676,3558,'Tristan','re: arithmetic progression?','2003-11-23 11:46:07',0,'An arithmetic progression is where a certain number is added to each number to get the next number. For example, 3,4,5,6,7 is an arithmetic progression, or 2,7,12,17.',9784,0);
INSERT INTO comment VALUES (9787,1504,1301,'Charlie','re: solution (solved numerically) -- verified','2003-11-23 12:07:20',0,'The following program verifies SilverKnight\'s solution. As it only verifies a found solution, it would be interesting to see AgN\'s program that actually iterates to the solution.\r\n\r\nDECLARE SUB rect2pol (x#, y#, r#, theta#)\r\nDECLARE FUNCTION norm# (x#)\r\nDECLARE SUB pol2rect (r#, theta#, x#, y#)\r\nDEFDBL A-Z\r\nDIM SHARED pi, dr\r\npi = ATN(1) * 4\r\ndr = pi / 180\r\n\r\nCLS\r\ndir(1) = 83.43201955000001#\r\ndir(2) = -85.75353466#\r\n\r\nFOR d = 1 TO 2\r\n dir = dir(d)\r\n pol2rect 1, dir, x, y\r\n PRINT \"x=\"; x; \"y=\"; y\r\n pol2rect .35, 130, Ax, Ay\r\n pol2rect .6, 70, Bx, By\r\n rect2pol x - Ax, y - Ay, dist, dirA\r\n PRINT \"Aim direction=\"; dirA\r\n incidence = dir - dirA\r\n rect2pol x - Bx, y - By, dist, dirB\r\n reflection = dirB - dir\r\n PRINT norm(incidence), norm(reflection)\r\n PRINT \"--\"\r\nNEXT\r\n\r\nFUNCTION norm (x)\r\n n = x\r\n DO UNTIL n > -180\r\n n = n + 360\r\n LOOP\r\n DO UNTIL n <= 180\r\n n = n - 360\r\n LOOP\r\n norm = n\r\nEND FUNCTION\r\n\r\nSUB pol2rect (r, theta, x, y)\r\n x = r * COS(theta * dr)\r\n y = r * SIN(theta * dr)\r\nEND SUB\r\n\r\nSUB rect2pol (x, y, r, theta)\r\n r = SQR(x * x + y * y)\r\n IF x = 0 THEN\r\n theta = 90 * SGN(y)\r\n ELSE\r\n theta = ATN(y / x) / dr\r\n END IF\r\n IF x < 0 THEN theta = theta + 180\r\nEND SUB\r\n\r\nwith the results:\r\nx= .114381989608504 y= .993436842709792\r\nAim direction= 64.92641431087746\r\n 18.50560523912254 18.5056072763774\r\n--\r\nx= .0740469682395594 y=-.997254755062381\r\nAim direction=-76.70421283029224\r\n-9.049321829707765 -9.049322178724935\r\n--',9783,0);
INSERT INTO comment VALUES (9788,676,3351,'Eric','re(2): arithmetic progression?','2003-11-23 12:17:11',0,'Just to get things started let us call the mid-length side of our triangle \'s\', the short side \'s-p\' and the long side \'s+p\'. Then the perimeter is of course 3s and the area of the triangle is 3/5*(area of eqilateral = s2?3/4). The height of our triangle when side \'s\' is laid flat on the bottom is then s3?3/10. I am guessing we can solve for s and p with a little pythagorean algebra. Have Fun!\n\nEdited on November 23, 2003, 7:13 pm',9786,0);
INSERT INTO comment VALUES (9789,676,3558,'Tristan','Starters','2003-11-23 12:22:33',1,'Call the three sides x-y, x, and x+y.\r\n\r\nUsing Heron\'s formula, the area of the triangle is:\r\n√((3x/2)(3x/2-x+y)(3x/2-x)(3x/2-x-y))=\r\n√((3x²/4)(x²/4-y²))=\r\n√(3x^4/16-3x²y²/4)\r\n\r\nThe area of the equilateral triangle is:\r\nx²√3/4\r\n\r\nPutting this together:\r\nx²√3/4=(3/5)*√(3x^4/16-3x²y²/4)\r\n5x²√3/12=√(3x^4/16-3x²y²/4)\r\n75x^4/144=3x^4/16-3x²y²/4\r\n48x^4/144+3x²y²/4=0\r\nx²(x²/3+3y²/4)=0\r\nSo, either x=0(obviously not forming a triangle), or x²/3+3y²/4=0\r\n\r\nWould anyone like to check my work or finish it?',NULL,0);
INSERT INTO comment VALUES (9790,670,4374,'Richard','re(7): solution','2003-11-23 12:24:27',0,'SilverKnight:\r\nYour opinion carries weight with me as you appear to be the star solver on this site. None of the hyperlinks I could find on \"mod m\" are suitable to pass on here. The books I could find aren\'t either. Perhaps you know of a hyperlink or book that is suitable. I know that I am done trying to explain the concept to novices. For the more advanced, I highly recommend a gander at the first sections of Gauss\' Disquistiones Arithmeticae in the Clarke translation.\r\n~Richard',9782,0);
INSERT INTO comment VALUES (9791,676,3558,'Tristan','re: Starters- self correction','2003-11-23 12:36:11',3,'Oh, I just realized I made an obvious mistake. I put 3/5 on the wrong side of the equation!\r\n\r\nBack to \"Putting this together:\"\r\n(3/5)*x²√3/4=√(3x^4/16-3x²y²/4)\r\n3x²√3/20=√;(3x^4/16-3x²y²/4)\r\n27x^4/400=3x^4/16-3x²y²/4\r\n0=48x^4/400-3x²y²/4\r\n0=3x²(x²/25-y²/4)\r\n0=3x²(x/5+y/2)(x/5-y/2)\r\nSo x=0, or x/5±y/2=0\r\nx/5=±y/2\r\nx=±5y/2\r\n\r\nI doesn\'t make a difference whether y is positive or negative, so just call it positive. The ratio is:\r\n5y/2+y:5y/2:5y/2-y\r\n7y:5y:3y\r\n7:5:3\r\n\r\nThe ratio is 7:5:3',9789,0);
INSERT INTO comment VALUES (9792,676,4374,'Richard','re: Starters','2003-11-23 12:40:57',0,'x²/3+3y²/4=0? No real x,y>0 can satisfy this since both its terms are nonegative. ',9789,0);
INSERT INTO comment VALUES (9793,676,4450,'drew','re(3): arithmetic progression?','2003-11-23 12:59:17',0,'i dont think it is a right triangle so i dont think we can use the pyythagorean therom n where does it say right triangle',9788,0);
INSERT INTO comment VALUES (9794,676,4374,'Richard','re(2): Starters- self correction','2003-11-23 13:05:52',0,'I get the same.',9791,0);
INSERT INTO comment VALUES (9795,290,4450,'drew','for anyone wondering how i derived tan(180/infinity)infinity','2003-11-23 13:09:10',0,'The perimeter of an octagon is represented by all of the eight sides of an octagon added together. let 1/2 a side of the octagon = x. we are going to set the radious(i am forgetting my geometry) or apothom i think equal to 1. We now draw a triangle using the apothom one side and then drawn a line to the intersect fo two sides. The inner angle of this triangle will be set equal to A. therefor the tan(a)=x/1. angle a equals 1/2(360/n) where n is the number of sides. tan(180/n)=x 2(pi)r=perimiter of circle 2*x*n=perimeter of octagon 2*tan(180/n)*n=2(pi)*r r=1 in out octagon divide by 2 tan(180/n)*n=pi where the number of sides is equal to infinity ie the larger n is the closer to pi you will get.',NULL,0);
INSERT INTO comment VALUES (9796,676,4450,'drew','re(3): Starters- self correction','2003-11-23 13:14:15',0,'after looking at other commments i understand now. i am sstill in algebra II so we havent learned about herons formula. but now that i have tried it i derive the same thing.',9794,0);
INSERT INTO comment VALUES (9797,676,3840,'Hal9000','Starter','2003-11-23 14:19:48',0,'Without loss of generality let us label the smallest side of the triangle a, the second smallest/largest side a+r, and the largest side (a+2r). Then the perimeter is 3*(a+r), and the corresponding equilateral triangle has sides of s=(a+r) and thus area of √3s²/4 = √3(a+r)²/4.',NULL,0);
INSERT INTO comment VALUES (9798,676,4374,'Richard','re(4): Starters- self correction','2003-11-23 15:19:54',0,'This one would be nearly impossible to solve without Heron\'s formula, I think, because the perimeter, the sides, and the area need to be related by some formula in order to get the result. For the record, Heron\'s formula for the area of a triangle with sides a,b,c is\r\n\r\n A=sqrt(s*(s-a)*(s-b)*(s-c))\r\n\r\nwhere s=(a+b+c)/2 (the semiperimeter).\r\n\r\nAn equilateral triangle of side 1 has area (sqrt(3)/2)*1/2 by height*base/2. By Heron, the same area is\r\n sqrt(3/2*1/2*1/2*1/2), so the formula checks for equilateral triangles. ',9796,0);
INSERT INTO comment VALUES (9799,1504,1301,'Charlie','Solution of one case described','2003-11-23 20:27:25',0,'Comment previously posted for wrong problem, removed.\n\nEdited on November 23, 2003, 10:27 pm',NULL,0);
INSERT INTO comment VALUES (9804,1458,4459,'phillip elliott','cigarette bar bet','2003-11-23 22:52:26',0,'would you define drop? do you mean fall over?',NULL,0);
INSERT INTO comment VALUES (9805,1458,4459,'phillip elliott','re: Another answer that works','2003-11-23 22:54:59',0,'my thought was that you are applying gas although afire to the cig.',9641,0);
INSERT INTO comment VALUES (9806,1504,1301,'Charlie','A Basic language numerical solution','2003-11-23 23:03:32',3,'The following program iterates to the same solutions SilverKnight found with Excel\'s solver:\r\n\r\nDECLARE SUB rect2pol (x#, y#, r#, theta#)\r\nDECLARE FUNCTION norm# (x#)\r\nDECLARE SUB pol2rect (r#, theta#, x#, y#)\r\nDEFDBL A-Z\r\nDIM SHARED pi, dr\r\npi = ATN(1) * 4\r\ndr = pi / 180\r\n\r\nCLS\r\n\r\ndir = 90\r\ndir(1) = dir\r\nGOSUB evalu\r\ndiff(1) = norm(reflection - incidence)\r\ndir = 88\r\ndir(2) = dir\r\nGOSUB evalu\r\ndiff(2) = norm(reflection - incidence)\r\nDO\r\n slope = (diff(2) - diff(1)) / (dir(2) - dir(1))\r\n amt = -diff(1) / slope\r\n dir(3) = dir(1) + amt\r\n dir = dir(3): GOSUB evalu: diff(3) = norm(reflection - incidence)\r\n dir(1) = dir(2): diff(1) = diff(2)\r\n dir(2) = dir(3): diff(2) = diff(3)\r\nLOOP UNTIL ABS(amt / dir(1)) < 1E-14 OR diff(1) = 0\r\n PRINT \\\"Aim direction=\\\"; dirA\r\n\r\ndir = 270\r\ndir(1) = dir\r\nGOSUB evalu\r\ndiff(1) = norm(reflection - incidence)\r\ndir = 272\r\ndir(2) = dir\r\nGOSUB evalu\r\ndiff(2) = norm(reflection - incidence)\r\nDO\r\n slope = (diff(2) - diff(1)) / (dir(2) - dir(1))\r\n amt = -diff(1) / slope\r\n dir(3) = dir(1) + amt\r\n dir = dir(3): GOSUB evalu: diff(3) = norm(reflection - incidence)\r\n dir(1) = dir(2): diff(1) = diff(2)\r\n dir(2) = dir(3): diff(2) = diff(3)\r\nLOOP UNTIL ABS(amt / dir(1)) < 1E-14 OR diff(1) = 0\r\n PRINT \\\"Aim direction=\\\"; dirA\r\n\r\nEND\r\n\r\nevalu:\r\n pol2rect 1, dir, x, y\r\n\' PRINT \\\"x=\\\"; x; \\\"y=\\\"; y\r\n pol2rect .35, 130, Ax, Ay\r\n pol2rect .6, 70, Bx, By\r\n rect2pol x - Ax, y - Ay, dist, dirA\r\n\' PRINT \\\"Aim direction=\\\"; dirA\r\n incidence = dir - dirA\r\n rect2pol x - Bx, y - By, dist, dirB\r\n reflection = dirB - dir\r\n\' PRINT norm(incidence), norm(reflection)\r\n\' PRINT \\\"--\\\"\r\nRETURN\r\n\r\nFUNCTION norm (x)\r\n n = x\r\n DO UNTIL n > -180\r\n n = n + 360\r\n LOOP\r\n DO UNTIL n <= 180\r\n n = n - 360\r\n LOOP\r\n norm = n\r\nEND FUNCTION\r\n\r\nSUB pol2rect (r, theta, x, y)\r\n x = r * COS(theta * dr)\r\n y = r * SIN(theta * dr)\r\nEND SUB\r\n\r\nSUB rect2pol (x, y, r, theta)\r\n r = SQR(x * x + y * y)\r\n IF x = 0 THEN\r\n theta = 90 * SGN(y)\r\n ELSE\r\n theta = ATN(y / x) / dr\r\n END IF\r\n IF x < 0 THEN theta = theta + 180\r\nEND SUB\r\n\r\nwhich finds\r\nAim direction= 64.92641251550131\r\nAim direction=-76.70421326480458',NULL,0);
INSERT INTO comment VALUES (9807,1458,4459,'phillip elliott','cigarette bar bet','2003-11-23 23:03:46',0,'if you use a heat source such as a high intensity light to set the cig. aflame then it would burn,but is this enough to make it drop? define drop.',NULL,0);
INSERT INTO comment VALUES (9808,1252,1253,'brianjn','Rectangles','2003-11-23 23:06:08',1,'In thinking rectangles, not squares, if the inscribed circle had its centre at the intersection of the diagonals of a rectangle whose length was 3 times the diameter of the circle, then 6 smaller rectangles, as defined, would cover the larger one; the width of the smaller rectangle would be the radius of the circle.\r\n\r\nConsidering Tristan\'s \'2 solutions\', two rectangles with a width of the diameter of the circle would cover a rectangle of length 4 times the circle\'s diameter.\r\n\r\nI am wondering if further cases of this type exist, including a mix of horizontal and vertical rectangles.',NULL,0);
INSERT INTO comment VALUES (9809,1458,4459,'phillip elliott','re: haha got it','2003-11-24 00:21:51',0,'your stll using air',9457,0);
INSERT INTO comment VALUES (9810,1458,4459,'phillip elliott','re: Maybe!?','2003-11-24 00:23:23',0,'air is sound waves not yet',9461,0);
INSERT INTO comment VALUES (9811,1458,4459,'phillip elliott','re: Bet this is it','2003-11-24 00:26:03',0,'my thought exactly who says no answer yet?',9456,0);
INSERT INTO comment VALUES (9812,1351,4459,'phillip elliott','re: Bet this is it','2003-11-24 00:39:37',0,'repetative words at the end of statments',NULL,0);
INSERT INTO comment VALUES (9813,84,4459,'phillip elliott','race answer','2003-11-24 00:54:53',0,'it was not a person that was last',NULL,0);
INSERT INTO comment VALUES (9814,1493,4459,'phillip elliott','riddle?','2003-11-24 01:00:03',0,'chess game',NULL,0);
INSERT INTO comment VALUES (9800,1504,3172,'SilverKnight','re: Solution of one case described','2003-11-23 20:29:22',4,'Didja ever get that feelin\' that you posted a comment to the wrong problem? :-)',9799,0);
INSERT INTO comment VALUES (9801,1504,3172,'SilverKnight','re(2): solution (solved numerically) -- verified','2003-11-23 21:18:05',0,'Charlie, to address your query about the program I used... I used a very valuable tool in these problems.... Excel\'s solver :-)\r\n___________________________\r\n\r\nNot so easy to post an Excel spreadsheet here, but perhaps it will be useful if I explain some relationships (and each of you can reproduce this in your own Excel worksheets).\r\n\r\n(all angular measures below are in degrees, which is kinda annoying since Excel\'s functions are all in radians)\r\n\r\nAx = .35 * cos (130) ~ -0.22497566\r\nAy = .35 * sin (130) ~ 0.268115566\r\nBx = .60 * cos (70) ~ .20521209\r\nBy = .60 * cos (70) ~ .56381557\r\n\r\nNow, let\'s imagine a point P that moves around the circle. This can be described, classically, as:\r\nPx = cos (theta)\r\nPy = sin (theta)\r\nwhere theta is the angular measure of the point where 0 degrees is at (1,0), 90 degrees at (0,1), 180 degrees at (-1,0), etc...\r\n\r\nThen the angle, theta2, (you gotta remember your trigonometry) from point A to point P is given by:\r\n\r\ntheta2 = atan[ ( sin(theta) - .35*sin(130) ) / ( cos(theta) - .35*cos(130) ) ]\r\n\r\nBut that angle is wider than what we\'re after... so we need to SUBTRACT the angle of point P (from the origin\'s perspective (90-theta).\r\n\r\nThis will give us the \'angle of incidence\' from the point A as a function of the location of point P.\r\n_________________________\r\n\r\nNow we do a similar thing with Point B.\r\n\r\nthe angle to point P from Point B is given by:\r\ntheta3 = atan[ ( sin(theta) - .6*sin(70) ) / (cos(theta) - .6 *cos(130) ) ]\r\nbut, again we need to subtract that from the angle of P so we have the angle of incidence (on the other side of the radial line to point P).\r\n_________________________\r\n\r\nNow, I \'moved point P\' along the circle, until theta2 = theta 3. (I used solver to move P until the difference (theta2 - theta3) equalled zero.)\r\n\r\nThen, I performed a similar process to identify the point P on \'the other side\' of the circle.\r\n_________________________\r\n\r\nWhew... all that said, I\'d still like to see someone\'s analytic solution.',9787,0);
INSERT INTO comment VALUES (9802,1227,4459,'phillip elliott','re: Strike 2???','2003-11-23 22:20:00',0,'that\'s very good \r\nthey need to define their terms \r\nwhat do you mean by pitches and what do they mean by complete game?',9087,0);
INSERT INTO comment VALUES (9803,1474,1301,'Charlie','Solution Described for One Case','2003-11-23 22:25:55',0,'The following is an example of the calculation involved for a particular value of n, in the 1-deck case. We\'ll do the case of n=16--completion of the first triplet at the 16th draw.\r\n\r\nThere are 52 possible choices for the triplet-completing card. Then that must be multiplied by the number of combinations of cards that could precede that card and still have that card be the first completion of a triplet. The computation of those combinations of the first 15 without a triplet follows:\r\n\r\nIn the case of n=16, of the first 15 cards drawn are two of the same denomination as the 16th. As there are three others of that denomination in the deck, there are C(3,2)=3 possible ways of choosing these two cards.\r\n\r\nThat leaves 13 cards still to be accounted for, but only 12 denominations to choose from, so there must be at least one pair; that is, the number of pairs, p, cannot be zero. \r\n\r\nIf there is 1 pair, there are 12 choices for the denomination of the pair. As there are C(4,2)=6 possible pairs of individual cards of this denomination, we must also multiply by 6. In this case there is no choice for which singlets we use--we have to use all the 11 remaining denominations. (This is equivalent to C(11,11)=1 way of doing it.) There are 4 choices (of suit) for each of the 11 singlets as well so we have to multiply by 4^11=4194304.\r\n\r\nThen the next term:\r\nIf there are 2 pairs, there are C(12,2)=66 choices for the denomination of the pair. As there are C(4,2)=6 possible pairs of individual cards of each of these denominations, we must also multiply by 6^2=36. Now there is a choice for which 9 singlets we use out of the remaining 10 denominatins--C(10,9)=10. There are 4 choices (of suit) for each of the 9 singlets as well so we have to multiply by 4^9=262144.\r\n\r\nThen the next term:\r\nIf there are 3 pairs, there are C(12,3)=220 choices for the denomination of the pair. As there are still C(4,2)=6 possible pairs of individual cards of each of these denominations, we must also multiply by 6^3=216. Now there is a choice for which 7 singlets we use out of the remaining 9 denominatins--C(9,7)=36. There are 4 choices (of suit) for each of the 7 singlets as well so we have to multiply by 4^7=16384.\r\n\r\nThen the next term:\r\nIf there are 4 pairs, there are C(12,4)=495 choices for the denomination of the pair. As there are still 6 possible pairs of individual cards of each of these denominations, we must also multiply by 6^4=1296. Now there is a choice for which 5 singlets we use out of the remaining 8 denominatins--C(8,5)=56. There are 4 choices (of suit) for each of the 5 singlets as well so we have to multiply by 4^5=1024.\r\n\r\nThen the next term:\r\nIf there are 5 pairs, there are C(12,5)=792 choices for the denomination of the pair. As there are still 6 possible pairs of individual cards of each of these denominations, we must also multiply by 6^5=7776. Now there is a choice for which 3 singlets we use out of the remaining 7 denominatins--C(7,3)=35. There are 4 choices (of suit) for each of the 3 singlets as well so we have to multiply by 4^3=64.\r\n\r\nThen the next term:\r\nIf there are 6 pairs, there are C(12,6)=924 choices for the denomination of the pair. As there are still 6 possible pairs of individual cards of each of these denominations, we must also multiply by 6^6=46656. Now there is a choice for which singlet we use out of the remaining 6 denominatins--C(6,1)=6. There are 4 choices (of suit) for each of the 3 singlets as well so we have to multiply by 4^1=4.\r\n\r\nSo the terms are added together and the sum muliplied by that 52.\r\n\r\nThe terms as described above are 905969664, 18685624320, 84085309440, 110361968640, 41385738240 and 3103930368, adding up to 258528540672. We have to multiply this by 52, and then divide by 52 times the total number of combinations that the first 15 cards chosen from 15 could have. Note that the 52\'s in the numerator and denominator actually cancel. C(51,15)=3188675231420. Doing the division comes up with the 0.0810771 that\'s shown in the table for the row labeled 16 in the analytic solution.\r\n\r\nIn the program, the 52 possible choices for the triplet-completing card are distributed over the individual terms we just summed, but it doesn\'t make any difference if the sum is multiplied by 52 or each individual term is. Also, the factor of 52 is included both in the dividend and the divisor. It could have been left out.',NULL,0);
INSERT INTO comment VALUES (9815,532,4459,'phillip elliott','a e','2003-11-24 01:03:03',0,'no belly buttons',NULL,0);
INSERT INTO comment VALUES (9816,1475,4459,'phillip elliott','vacation','2003-11-24 01:10:43',0,'alaska is eastern/western/northern/ of the u.s. hawaii is the southern most\r\n',NULL,0);
INSERT INTO comment VALUES (9817,1504,3182,'Antonio','The objective of the problem','2003-11-24 02:17:51',2,'Well, my original problem ment to calculate the angle formed between the reflected beams, but with flooble\'s re-wording is transcribed as \"use an angular measure paralleling the Theta coordinate it would have if directed from the origin\", that refeers to the aperture between the center of the surrounding circle, the point of reflection and point A. So, calculate 2*Theta or the angle between reflected beams.\n\nEdited on November 24, 2003, 2:21 am',NULL,0);
INSERT INTO comment VALUES (9818,1504,3172,'SilverKnight','re: The objective of the problem','2003-11-24 02:50:12',0,'Well, I\'m happy to say that I (also) did report the angular measure of the reflected angle in my earlier comment... which (assuming I did it correctly) should satisfy what you were looking for.',9817,0);
INSERT INTO comment VALUES (9819,1264,1183,'fwaff','Logical solution without a grid','2003-11-24 08:52:05',3,'For simplicity I\'ve refered to the pictures as P1,...P4 and the clues as C1,...,C5\r\n\r\nSTEP 1\r\nC5 means that either P1 or P2 must show surfing, but C2 has P2 as either hang-gliding or motorcycling. \r\nTherefore P1 must depict surfing. Which in turn means that P3 is a watercolour (from C5).\r\n\r\nSTEP 2\r\nP4 must be the windmill scene - since P1 is surfing, P2 is hang-glinding or motorcycling and C3 tells us that the windmill wasn\'t done in watercolour (and STEP 1 told us that P3 is watercolour).\r\n\r\nSTEP 3\r\nC1 says that P1 is not in oils, C5 says that the surfing pic (which we know is P1 from STEP 1) is not acrylic and STEP 1 told us that P3 is the watercolour - therefore P1 must be in tempera paints.\r\n\r\nSTEP 4\r\nSTEP 2 showed that P4 is the windmill and C3 says that the windmill is either acrylic or tempera. STEP 3 just showed that P1 is in tempera. Therefore P4 must be in acrylic. This also means that P2 must be in oils as it is the only medium left.\r\n\r\nSTEP 5\r\nSTEP 3 showed that P1 is in tempera and C4 says that the tempera painting and the hang-glider are in different rows, therefore either P3 or P4 must depict hang-gliding. STEP 2 showed that P4 is the windmill, therefore P3 portays hang-gliding. This also means that P2 must depict motorcycling.\r\n\r\nSo in summary we have:\r\nP1: Surfing in tempera paints\r\nP2: Motorcycling in oils (sounds dangerous!)\r\nP3: Hang-gliding in watercolour\r\nP4: Windmill in acrylics.',NULL,0);
INSERT INTO comment VALUES (9820,1264,3372,'Sam','Rats...','2003-11-24 09:29:24',0,'I always come too late to post the solution. Wretched fwaff...',NULL,0);
INSERT INTO comment VALUES (9821,1264,4450,'drew','(solution)','2003-11-24 12:47:13',0,'picture 1 is surfing with tempra paints,\r\npicture 2 is motor cycle with oils,\r\npicture 3 is hang gliding with water color,\r\npicture 4 is windmill with acrylics.',NULL,0);
INSERT INTO comment VALUES (9822,1504,3182,'Antonio','re(2): The objective of the problem','2003-11-24 12:52:46',0,'Well SilverKnight, the angle measurements you calculated earlier in your solution and obtain the angular measurement (in degrees) between beam rays in the reflection, not from the origin nor from point A, I hope your calculations are correct.',9818,0);
INSERT INTO comment VALUES (9823,1504,3172,'SilverKnight','re(3): The objective of the problem','2003-11-24 13:25:09',0,'Well... I *think* I did it correctly... and I believe that Charlie verified/confirmed my calculations, but....\r\n\r\nI reserve the right to be wrong--in this problem and ALL future ones! :-)',9822,0);
INSERT INTO comment VALUES (9824,1264,4450,'drew','re: Rats...','2003-11-24 14:14:28',0,'i just realized that the same thing happened to me!!\r\n=(',9820,0);
INSERT INTO comment VALUES (9825,1504,1301,'Charlie','re(4): The objective of the problem','2003-11-24 14:21:34',0,'SilverKnight\'s original solution included \"this makes a reflection angle of 18.50560563 degrees, and 9.049321949 degrees respectively.\" What Antonio apparently wants is twice each of these, that is, the angle between the incident and reflected rays, rather than the angle between either and the normal to the mirror surface.',9823,0);
INSERT INTO comment VALUES (9826,1504,3182,'Antonio','re(5): The objective of the problem','2003-11-24 15:10:31',0,'Your calculations are correct SilverKnight, using Charlie´s results. Please, post your final transcient equations and then the final results, I think is fair to also post the final equations of the whole problem, where the angle to be obtained is the only variable in the whole equation. For example: Theta*Sin(Theta)+Theta²*Cos(Theta)=.2 (This is a transcient equation)',9825,0);
INSERT INTO comment VALUES (9827,1508,3172,'SilverKnight','wow... don\'t everyone jump in at once....','2003-11-24 16:14:30',0,':-)\r\n\r\nPerhaps I should have marked the difficulty higher...',NULL,0);
INSERT INTO comment VALUES (9828,1508,2899,'Brian Wainscott','Seems simple enough','2003-11-24 16:39:58',0,'Call the given element N.\r\n\r\nWe are going to have to reset the \"next\" pointer of the element that points to N, and the only way to find it is to start at the top. So I don\'t see that we have any choice.....\r\n\r\nPresuming H is a pointer to the head of the list (SK has to have given us at least this much, since he indicates the list is not circular), I\'d do two things:\r\n\r\none (with beautiful indenting removed because I don\'t know how this system works):\r\n\r\n if(H==N)\r\n H=N->next;\r\n else {\r\n K=H;\r\n while(K->next != N)\r\n K=K->next;\r\n K->next = N->next;\r\n }\r\n\r\ntwo:\r\n question who would singly link such a long list\r\n',NULL,0);
INSERT INTO comment VALUES (9829,1508,3172,'SilverKnight','re: Seems simple enough','2003-11-24 16:45:08',0,'You\'ve (inaccurately) assumed that I give you H, a pointer to the head of the list.\r\n\r\nThe problem requires that you are given ONLY a pointer to a particular node, the node that is to be deleted.\r\n\r\n--- SK',9828,0);
INSERT INTO comment VALUES (9830,1508,3386,'Victor Zapana','me very confused','2003-11-24 16:58:25',0,'can u explain this problem to those who are computer-language illiterate?',NULL,0);
INSERT INTO comment VALUES (9831,1508,3172,'SilverKnight','re: me very confused','2003-11-24 17:27:19',0,'I could, but introduction to computer algorithms and data structures are generally one or two college-level courses.\r\n\r\nIf you are interested in the problem, I will suggest that you purchase any decent college text on data structures or do a lot of research online.\r\n\r\nHere is a link to get you started.\r\n\r\n- SK',9830,0);
INSERT INTO comment VALUES (9832,1240,3430,'pat','thunder','2003-11-24 17:54:30',0,'could we be confusing the god of thunder with someone else?',NULL,0);
INSERT INTO comment VALUES (9833,1508,2899,'Brian Wainscott','re(2): Seems simple enough','2003-11-24 18:13:58',0,'Hum...tricky....I suspect there is something you are not telling me, or are asuming that I am not, or vice versa.\r\n\r\nIs the list contiguous in memory (ie, consists of constant sized elements taken from a single array, but linked in some different order)?\r\n\r\nI\'m assuming the elements are separately allocated, and so have no particular ordering/location in memory.\r\n\r\nAssuming you don\'t intend to search all of allocated memory, I don\'t see how you can possibly resurrect the parent of the current element without a pointer to somthing above it. I will think on this, and look forward to the solution....\r\n',9829,0);
INSERT INTO comment VALUES (9834,1508,1626,'Gamer','','2003-11-24 18:45:45',0,'I think problems that are based for only a few computer literate people aren\'t as usable as other problems. :)\r\n\r\nThat may be why nobody jumped in?',NULL,0);
INSERT INTO comment VALUES (9835,1508,3558,'Tristan','re: -Exactly!','2003-11-24 18:57:41',0,'Exactly! I\'m not the most computer literate, so I feel reluctant to jump in or judge an algorithm puzzle. All I can say about this puzzle is that the first solution probably involves that which the second question forbids.',9834,0);
INSERT INTO comment VALUES (9836,1508,4450,'drew','way over my head!','2003-11-24 20:34:44',0,'I must be in too low of a level to understand what is going on so i wont even try. It sounds easy but i havent got a clue what an algorithum is. I will read up on this and try to understand the question but i doubt i will do much.',NULL,0);
INSERT INTO comment VALUES (9837,977,4450,'drew','anyone wanna see if i got the right idea?','2003-11-24 21:18:45',0,'yah i am going to do this in java.\r\ni would create an array for every random number that has been picked(up to nine). then i would have it check through the arrey to see if the number has been picked already then create another random int.',NULL,0);
INSERT INTO comment VALUES (9838,330,4476,'Adriane','That is not what the first sentence says','2003-11-25 01:05:24',0,'the first sentence says that donna is the daughter of donnetta not the mother',NULL,0);
INSERT INTO comment VALUES (9839,678,4059,'Saso','solution','2003-11-25 09:18:32',3,'After first 5 attempts, there are 26 allowed possibilities of survival or death of a fly. 16 of them include 3 deaths (quota filled). For these 16 possibilities, next attempt will be successful. For rest 10 possibilities, next attempt will be successful with 50% rate.\r\n\r\nSo the probability of survival for 6th fly is: P= (10.1+16*0.5)/26=9/13=cca 69,23%',NULL,0);
INSERT INTO comment VALUES (9840,678,3172,'SilverKnight','solution','2003-11-25 09:19:08',3,'Given that the spider has not yet reached his quota, the fly will have a 50% chance of getting through... but we don\'t know whether or not the spider has reached his quota from the first 5 flies...\r\n\r\nSo, there are several possibilities that the spider could have reached his quota within the first 5 flies:\r\n(let C = caught, and N = not caught)\r\n\r\nHere they are, along with the likelihood of them occuring:\r\n\r\nCCC = 1/8 = 4/32\r\nCCNC = 1/16 = 2/32\r\nCCNNC = 1/32\r\nCNCC = 1/16 = 2/32\r\nCNCNC = 1/32\r\nCNNCC = 1/32\r\nNCCC = 1/16 = 2/32\r\nNCNCC = 1/32\r\nNCCNC = 1/32\r\nNNCCC = 1/32\r\n\r\nThese are ALL the possibilities (I think) of the spider having caught his fill for the day.\r\n\r\nNow, if we total this up, we show there is a 1/2 chance that the spider has already caught his fill.\r\n\r\nIf he has, then he won\'t attempt capturing the fly.... and if he hasn\'t, there is a 50% chance he\'ll capture the fly...\r\n\r\nThe question asked... what\'s the probability the fly will make it... so\r\n1/2 * 50% + 1/2 * 100% = 3/4',NULL,0);
INSERT INTO comment VALUES (9841,678,4059,'Saso','just a little correction in my text','2003-11-25 09:23:40',0,'Sorry for one mistake in text of my solution - 10 possibilities of initial 26 include three deaths, so in these ten cases the 6th fly will definitely escape. But the result is correct.',NULL,0);
INSERT INTO comment VALUES (9842,678,4059,'Saso','well, I was wrong - corrected solution','2003-11-25 09:45:18',3,'Well, I was wrong in my first solution in the assumption, that all 26 allowed possibilities after first 5 attempts have the same probability - they dont. 10 possibilities, where 3 flies are eaten have a probability of 50% of happening and rest 16 possibilities have probability of 50% as well. \r\n\r\nSo correct solution is: 0,5*1+0,5*0.5=75%. Sorry for confusion.',NULL,0);
INSERT INTO comment VALUES (9843,678,3172,'SilverKnight','re: just a little correction in my text','2003-11-25 09:46:00',0,'Saso, I believe you made a mistake in your calculation... 26 cases does NOT mean 26 equally likely cases.... and you interpreted them as equally likely.\r\n\r\n--- SK',9841,0);
INSERT INTO comment VALUES (9844,678,1301,'Charlie','simpler computation','2003-11-25 09:58:41',3,'Out of the 2^5=32 combinations of surviving flies among the first 5, in 5C3=10 have 3 been eaten, in 5C4=5 have 4 been eaten and in 5C5=1 have 5 been eaten. So the spider is satisfied 16/32 = 1/2 of the time and the new fly is safe.\r\n\r\nAlso in half the remaining cases (when the spider is not yet satiated), the fly also escapes, so he escapes 3/4 of the time, that is, with 3/4 probability.',NULL,0);
INSERT INTO comment VALUES (9845,678,3172,'SilverKnight','re: simpler computation','2003-11-25 10:10:59',0,'Charlie... I thought of that when I first looked at the problem.... but it is misleading.\r\n\r\nThough your calculation \'works out\', the spider NEVER eats 5 or 4 flies in the first 5 flies. Once he\'s eaten the first 3, he stops capturing them.\r\n\r\nIf you want to use combinatorial mathematics (and I purposefully, avoided the combination function for ease of understanding), you should total up the likelihood of getting 3 eaten if the THIRD fly is eaten, the likelihood of getting 3 eaten if the FOURTH fly is eaten, and the likelihood of getting eaten if the FIFTH fly is eaten....\r\n\r\nThis would correspond to:\r\n\r\n1/8 chance:\r\nCCC\r\n\r\n1/16 chance (each):\r\nCCNC\r\nCNCC\r\nNCCC\r\n\r\n1/32 chance (each):\r\nCCNNC\r\nCNCNC\r\nCNNCC\r\nNCCNC\r\nNCNCC\r\nNNCCC\r\n\r\ntotal: 1/2\r\n_____________\r\n\r\nAll the 16 remaining possibilities don\'t have 3 flies eaten (and all have 1/32 chance of occuring)\r\nNNNNN\r\nNNNNC\r\nNNNCN\r\nNNCNN\r\nNCNNN\r\nCNNNN\r\nCNNNC\r\nCNNCN\r\nCNCNN\r\nCCNNN\r\nNCNNC\r\nNCNCN\r\nNCCNN\r\nNNCNC\r\nNNCCN\r\nNNNCC\r\ntotal: 1/2\r\n',9844,0);
INSERT INTO comment VALUES (9846,678,1301,'Charlie','re(2): simpler computation','2003-11-25 10:36:38',0,'You are right of course that the spider would never actually eat another fly after having eaten 3. However, the spider\'s satiety is filled anyway, and for the purposes of the probabilities for fly #6, it\'s \"as if\" he had, and makes it less worrisome about missing cases.\r\n\r\nIn other words, consider the cases to be combinations that either were eaten or would have been eaten except for having been given the satiety reprieve.\n\nEdited on November 25, 2003, 10:38 am',9845,0);
INSERT INTO comment VALUES (9847,678,1102,'Robin Gatter','re(3): simpler computation','2003-11-25 12:13:45',0,'Actually Charlie you were almost correct originally. If you look at the problem in terms of how many flies have made it past the spider rather than calculating how many have been eaten, you find 5C3=10 cases that have 3 have escaped, 5C4=5 that 4 have escaped and 5C5=1 that all 5 have escaped. These are the only cases in which the spider is still hungry, i.e. 16/32 = 1/2 of the time.',9846,0);
INSERT INTO comment VALUES (9848,1508,836,'Rushi','questions','2003-11-25 12:18:42',0,'I\'ve got two questions:\r\n\r\n1. Can you not overload the -> operator and get it to point at the next element instead? I suppose you would have issues with the next pointer of the previous node getting pointed to a null pointer in the case of the last element\r\n\r\n2. Can you do the following (if the nodes are the same size):\r\n\r\n //Say you have the address to node N\r\n //Get the pointer to the next node\r\n Node * next = N->getNext() ;\r\n //overwrite the current node with the next node\r\n memcpy(N, next, sizeof(N)) ;\r\n //remove the next pointer from the next node\r\n next->setNext(0) ;\r\n //delete the next node (which has now been copied to the original address)\r\n delete next ;\r\n\r\n',9836,0);
INSERT INTO comment VALUES (9849,540,4483,'Bluewolfe','they are','2003-11-25 12:35:33',0,'teeth and gums!\r\nI knew this ! I did NOT see that answer...I swear!',NULL,0);
INSERT INTO comment VALUES (9850,1508,3172,'SilverKnight','re: questions - well done','2003-11-25 13:04:39',0,'1. No.\r\n2. Yes... :-) (Though I think it could be described differently, and this satisfies both elements of the problem, in constant time.)',9848,0);
INSERT INTO comment VALUES (9851,1268,2716,'Federico Kereki','Short solution?','2003-11-25 13:23:15',4,'If Z=ln(X), then X^Y = e^(Y.Z). As Y.Z can have a zero imaginary part, therefore X^Y can be real... or am I missing something?',NULL,0);
INSERT INTO comment VALUES (9852,1268,2716,'Federico Kereki','Further elaboration','2003-11-25 13:23:55',1,'Some bits of notation. Let R\\P be polar notation for R(cos(P)+i.sen(P)). Let ^ denote exponentiation.\r\n By definition, X^Y = e^(Y.ln(X)). If the imaginary part of Y.ln(X) is zero, the result is real.\r\n Let X=R\\P; then ln(X)=ln(R)+i.P. Also, let Y=R\'\\P\' = R\'(cos(P\')+i.sen(P\')). The imaginary part of Y.ln(X) is then R\'(ln(R).sen(P\')+P.cos(P\'))=0.\r\n If we don\'t allow R\'=0, we could take\r\nP=-1/cos(P\'), ln(R)=1/sen(P\'), and we would have the sought result.\r\n Did I miss anything? Opinions?',NULL,0);
INSERT INTO comment VALUES (9853,1268,3172,'SilverKnight','example of said case','2003-11-25 13:32:36',3,'restatement of problem:\r\n\r\nIf we let x = a ^ b\r\nwhere a and b are complex numbers, then prove that x can be real (or show an example where X is real)\r\n______________________\r\n\r\nif a = b = i (the imaginary square root of -1), then\r\n\r\nx = (√-1) ^ (√-1)\r\nx = e ^ [ ln( (√-1) ^ (√-1) ) ]\r\nx = e ^ [ (√-1) * ln (√-1) ]\r\nx = e ^ [ (√-1) * (π/2) * (√-1) ], since ln (√-1) = (π/2) * (√-1)\r\nx = e ^ [ -(π/2) ]\r\n\r\nwhich is real (though irrational).',NULL,0);
INSERT INTO comment VALUES (9854,1268,1301,'Charlie','solution','2003-11-25 13:56:11',3,'We seek x^y=r where x and y are complex and r is real.\r\n\r\nThis corresponds to x=r^(1/y), where a real is raised to a complex power to get the x value that we need. I don\'t have a proof that a real to a complex power would be complex, but it certainly seems plausible.\r\n\r\nTrying a few numbers in a calculator that handles complex numbers (I used UBASIC in immediate mode as such a calculator), we can find examples such as:\r\n\r\nr=10\r\nOK\r\nx=r^(1/(1+#i))\r\nOK\r\n?x\r\n 1.2880188077230996985-2.8880802535510616817#i\r\nOK\r\n?x^(1+#i)\r\n 9.9999999999999999917-0.000000000000000001#i\r\nOK\r\n\r\nHere the symbol #i represents i. The final result shows a tiny imaginary part due to internal rounding errors.\r\n\r\nAnalytically:\r\nLet x be 1+i\r\n\r\nLet y be log(√2) - (π/4)i\r\n\r\nTo raise a number to a power using logarithms, use log(x^y)=y log(x). I will be using natural logs here and use the mathematical notation log, rather than engineering notation ln.\r\n\r\n(1+i) = √2 e^iπ/4\r\nso\r\nlog(1+i)= log(√2) + (π/4)i\r\n(which is why we chose its complex conjugate for y)\r\n\r\nso y log(x) = log(x^y) is\r\nlog(x^y) = (log(√2) + (π/4)i) (log(√2) - (π/4)i)\r\n = (log(√2))^2 - (iπ/4)^2 = (log(√2))^2 + (π^2)/16\r\n\r\nThis number is a real number. Raising e to this power (taking its natural antilogarithm) will give a real number which is x^y.\r\n',NULL,0);
INSERT INTO comment VALUES (9855,865,2376,'Jim C','IN other words....','2003-11-25 15:42:22',0,'Nope, Uh-uh, No Way. Absolutely not! Are you kidding me? probably not, not likely, I don\'t think so!',NULL,0);
INSERT INTO comment VALUES (9856,865,2376,'Jim C','re(2): er','2003-11-25 15:46:13',0,'Actually, maybe was my first thought, but it doesn\'t work. If the answer were \"maybe,\" then it would not be \"no.\" So then the answer is no, and we\'re stuck in the same loop.',5462,0);
INSERT INTO comment VALUES (9857,678,4412,'krdmt5_000','Solution to a strange question','2003-11-25 16:18:30',3,'The 6th fly has a 50% of Survival like the other 5 flies that pass through. the answer is right there in the question...idiots',NULL,0);
INSERT INTO comment VALUES (9858,678,4412,'krdmt5_000','re: Solution to a strange question','2003-11-25 16:23:48',0,'No...stupid now time for some pointless java script≥≤∞±π∑π∑π√³<²<>≤≥<>³²³',9857,0);
INSERT INTO comment VALUES (9859,1268,4374,'Richard','solution','2003-11-25 18:53:12',3,'log=(log to base e).\r\nlog(x^y)=ylogx.\r\nx^y=e^(ylogx).\r\nLet y=i, x=e^(it) with t real and not a multiple of pi so that x is not real. Then\r\nx^y=e^(i(it))=e^(-t)=real.\n\nEdited on November 25, 2003, 10:05 pm',NULL,0);
INSERT INTO comment VALUES (9860,1268,3558,'Tristan','re: example of said case','2003-11-25 19:02:43',0,'I know that ln(i)=(π/2)*i, but you need to prove it. I know it\'s true because it comes from the fact that e^(iπ)=-1, but then you\'d need to prove that too. If you didn\'t need to prove it, then you could just say that e^(iπ)=-1 as your example...\r\n\r\nSince it needs to be proven, I suppose I should ask you to, but then I\'d get a long calculus proof I wouldn\'t understand... So I\'m happy with your proof! Ah... such is the world of complex numbers!',9853,0);
INSERT INTO comment VALUES (9861,1505,4488,'Venkateswarlu Sama','Found the Answer','2003-11-25 19:21:10',4,'The Phrase is \r\n\"Break the code to reveal a famous phrase and its author: To be or not to be that is the question.\r\n~ William Shakespeare\"\r\n',NULL,0);
INSERT INTO comment VALUES (9862,1264,4489,'ben','(solution) hello','2003-11-25 19:25:21',0,'1 Surfing Tempera\r\n2 Oil Motorcycle\r\n3 Watercolor Hang Gliding\r\n4 Acrylics Windmill\r\n\r\nLong time listener, first time caller',NULL,0);
INSERT INTO comment VALUES (9863,1268,3172,'SilverKnight','re(2): example of said case','2003-11-25 20:15:05',0,'Tristan, you\'ve made a very good point.\r\n\r\nIt\'s always sort of a question about where does one stop \'proving\' one\'s rules/postulates... and this one, I can understand, is somewhat confusing.\r\n\r\nI don\'t think this is the appropriate forum for the proof of it, suffice it to say that it comes from the power series expansion of the irrational number, e, as well as the series expansion of both sin() and cos().\r\n\r\nThis link may be a good start if you would like to learn more about this subject.\r\n\r\nHope it helps.\r\n\r\n-SK',9860,0);
INSERT INTO comment VALUES (9864,1264,4490,'SHARON','I HAVE IT','2003-11-25 20:46:26',3,'# 1 = SURFING, TEMPERA\r\n# 2 = MOTORCYCLE, OIL\r\n# 3 = HANGGLIDER, WATERCOLOR\r\n# 4 = WINDMILL, ACRYLIC',NULL,0);
INSERT INTO comment VALUES (9865,1268,4374,'Richard','re(3): example of said case','2003-11-25 22:56:42',0,'I think that the problem itself is assuming that the solver knows what x^y means for complex x and y. Anybody who knows that must also know that i=e^(i*pi/2) and that log() and e^() are inverses. A good reference text is Marsden and Hoffman, \"Basic Complex Analysis\", 2nd Ed., pp 27-44, for those who want to study up. This is not pre-university material, except perhaps for the gifted.',9863,0);
INSERT INTO comment VALUES (9866,1264,4494,'David','A Solution Hurrah!','2003-11-26 06:12:58',0,'#1 = Surfing, Tempera\r\n#2 = Motorcycle, Oils\r\n#3 = Windmill, Watercolour\r\n#4 = Gliding, Acrylics\r\n\r\nThis seems to me to work also. Can anyone see something wrong with this?? PLEASE LET ME KNOW\r\nDoes the definition of rows mean in the horizontal or vertical or both?? I thought the vertical lines were called colums. But if its rows as in vertical and horizontal then \'Art\'s hang gliding picture and the one done in tempera paints are in different rows\' must mean they should be diagonally to eachother. This is why i think this is correct!\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (9867,1268,1301,'Charlie','What\'s a complex number?','2003-11-26 08:11:21',0,'A complex number is said to have the form a+bi. One solution here uses a number in which a is zero, making the number purely imaginary. If b were zero it would be purely real. Is the purely imaginary number considered complex, even though the purely real number is not?',NULL,0);
INSERT INTO comment VALUES (9868,1478,4495,'J','solution','2003-11-26 08:37:15',0,'1st- Ben Jones\'s Fruit cake\r\n2nd- James Best\'s Chocolate cake\r\n3rd- Nigel Stevens\'s Spnge Cake\r\n4th- Vicky Andrews\'s cheese cake',NULL,0);
INSERT INTO comment VALUES (9869,1478,2716,'Federico Kereki','Reasoned solution','2003-11-26 09:27:42',3,'From #1, James Best and Vicky were either 1st and 3rd, or 2nd and 4th; since from #2 the 3rd was a boy, then James Best was 2nd (with a chocolate cake, from #4) and Vicky was 4th.\r\n From #2, Ben was 1st with his fruit cake, and his last name was Jones (from #4).\r\n \r\nAs the sponge cake was in the top three (from #3) it must have been 3rd, since we already know about the other two places. The cheese cake must have been 4th, since it\'s the only possibility that remains.\r\n \r\nThe 3rd must be a boy (from #3) so he\'s Nigel Stevens, and thus the 4th is Vicky Andrews.\r\n',NULL,0);
INSERT INTO comment VALUES (9870,195,2716,'Federico Kereki','Win, starting anywhere','2003-11-26 11:29:49',3,'There\'s no need to play the center first; you can actually start anywhere. Then, whenever the other player makes his move, play symmetrically, and if that can\'t be done, play the center.',NULL,0);
INSERT INTO comment VALUES (9871,195,3172,'SilverKnight','re: Win, starting anywhere','2003-11-26 11:34:43',0,'I beg to differ. It is not so clear cut, because if you (the 1st player) allow the 2nd player to play the center, he can INSTEAD play a coin the is NOT centered, but covers the exact center of a circular table.\r\n\r\nThen it is not possible for you to play either symmetrically or the center.\r\n____________\r\n\r\nBest (easiest) bet is to play the center and then continue symmetrically.',9870,0);
INSERT INTO comment VALUES (9872,678,2272,'Clinton Heath','Solution','2003-11-26 12:24:57',3,'This didn\'t seem like a hard question, then I saw the disparity of the replies and gave it a second look. Since each individual fly has a 50% chance of survival, then the possibilities are that all survived (1/25) that one was eaten (5/25 that is A or B or C or D or E) that two were eaten (10/25 that is A and one of the other 4, or B and one of the other 3, or C and one of the other 2, or D & E) or that three were eaten (9/25 that is A B and one of the other three, A C and one of the other two, A D E, B C and one of the remaining two, or C D E). So in 16 of the 25 cases, he has a 50% chance of survival, or 16/25*.5 which equals 32%',NULL,0);
INSERT INTO comment VALUES (9873,7,4430,'Eberhard','Solution Using Real Prob/Stats','2003-11-26 12:50:30',0,'Well, this subject seems to have been covered multiple times in multiple ways- but the real answer and why are as follows: The first know that each toss is concidered a seperate event by probability (known as independence)- meaning that the probability of either coin showing a particular side is always one half 1/2. Second know that when trying to determine if both will be the same side the probabilities are multiplied, i.e. 1/4 (this can be thought of as an ordered sequence). \r\n\r\nSo-\r\nBased on the information given in this question, the answer is 1/2 even though it seems like it should be 1/4. This is ONLY because we know that the one coin is tails, meaning that we must apply the principle of independece to determine the probability of the second be tails. \r\n\r\nIn order to simplify this- think of it this way-\r\n\r\nI have two coins I filp them both and ask you to guess what they are-\r\n\r\n1) I tell you one is tails and ask you to guess the other- where you clearly have a 1/2 chance of guessing correctly- this is the same as our problem\r\n\r\n2) I tell you neither and ask you to guess both where your chances would be 1/2 * 1/2 = 1/4\r\n\r\nHope this clear up the confusion- I will post the more complicated math behind this if requested',NULL,0);
INSERT INTO comment VALUES (9874,1478,3529,'Senthil Kumar','Solution','2003-11-26 12:52:24',3,'1. Ben Jones Fruit\r\n2. James Best Chocolate\r\n3. Nigel Stevens Sponge\r\n4. Vicky Andrews Cheese',NULL,0);
INSERT INTO comment VALUES (9875,7,3172,'SilverKnight','re: Solution Using Real Prob/Stats','2003-11-26 12:57:24',0,'The answer is not 1/2, nor does it seem to be 1/4 (at least not to me).\r\n\r\nIt is quite evident that you did not read the posted solution.\r\n\r\nBut, please, post the more complicated math behind this.\r\n\r\nI look forward to reading how you more fully justify your answer.',9873,0);
INSERT INTO comment VALUES (9876,678,3224,'Lee','none','2003-11-26 13:53:19',0,'5 flies have made the attempt. Since survival/non-survival is equally likely, either\r\na)Survivors are in the \'majority\' (3 or more) and the spider is still hungry \r\nor\r\nb)The non-survivors are in the majority - the spider is full and a safe passage for the 6th fly is assured.\r\nSo half the time the 6th fly is safe and half the time he has a 50% survival rate\r\np=.5 + .5*.5\r\np=.75 (or 75%)',NULL,0);
INSERT INTO comment VALUES (9877,1239,4425,'Sam','question','2003-11-26 13:57:17',0,'Do we have to use the exsisting letters in our solution?\r\n',9497,0);
INSERT INTO comment VALUES (9878,1264,3224,'Lee','re: A Solution Hurrah! - why it\'s wrong','2003-11-26 14:04:02',0,'Clue 3 says\r\n\"The painting of Art next to a windmill is done either in acrylics or tempera paints. \"\r\nYou\'ve got \r\n#3 = Windmill, Watercolour ',9866,0);
INSERT INTO comment VALUES (9879,672,4425,'Sam','1=1 and 2=2','2003-11-26 14:31:15',0,'Assuming that both these statements are correct, one of two possibilities could happen:\r\n\r\n1.both break....because of their equal strength, they destrtoy each other the same instant.\r\n\r\n2.Neither break....because they have equal strength, they repel each other\r\n\r\nAgain...this is assuming that both of the \'smiths\' statements are true. Chances are they say that there wares are the mightiest in order to attract customers\r\n\r\nthis was written by the newbie sam.....just so you know ',NULL,0);
INSERT INTO comment VALUES (9880,263,4425,'Sam','what if?','2003-11-26 14:40:26',0,'the tortoise took his time to get to point a then changed his speed by revealing the super powered rocket boosters enabling him to match achilles\' speed\r\n\r\n...once again...newbie sam',NULL,0);
INSERT INTO comment VALUES (9881,672,3172,'SilverKnight','re: 1=1 and 2=2','2003-11-26 14:42:09',4,'Sam... why don\'t you change your name to Sam2 or SamToo, or something like that...?\r\n\r\nI relate to Sam (the original), because I have this, yet unfounded, fear that some evil critter will come on and call himself SilverKnight! *gasp*',9879,0);
INSERT INTO comment VALUES (9882,1510,4450,'drew','yay i am the first to post a solution','2003-11-26 14:59:22',0,'i derived the quation x/(y-z)=y/x\r\nwhere y is the long side and x is the short side\r\nand z==x \r\nthen pluged in numbers and vwala\r\ni got 1.618033\r\nis that right?',NULL,0);
INSERT INTO comment VALUES (9883,1268,4197,'luminita','solution','2003-11-26 15:09:01',3,'yes, it is possible:\r\ni^i=e^(-pi/2)\r\n\r\nProof:\r\nif a=0 and b=1, the complex number is z=i\r\ni = cos(pi/2) + i in(pi/2)= e^(i(pi/2))\r\ni^i = e^(i(pi/2))^i= e^(-pi/2) which is a real number',NULL,0);
INSERT INTO comment VALUES (9884,1510,1626,'Gamer','A way to solve this','2003-11-26 16:20:12',3,'The idea here is that from a rectangle dimensions x by y, y-x is to x as x is to y, by the proportion given information.\r\n\r\n(y-x)/x = x/y, which equals y/x - 1 = x/y. In other words, the ratio is equal to 1 more than its reciprocal. ',NULL,0);
INSERT INTO comment VALUES (9885,1268,3558,'Tristan','re(3): example of said case','2003-11-26 18:13:58',0,'Actually, the link did help somewhat. I already had the mild idea that it was proven that way. But then you\'d need to prove that e^n=n^0/0!+n^1/1!+n^2/2!... You don\'t actually need to though, I think that what is done is enough, let\'s just assume that it\'s given. Though, Charlie brings up a good point; this solution might be considered invalid anyway.\r\n\r\nI like complex numbers, they make everything more open-minded, and they\'re so cool! I happen to have submitted a complex puzzle too. There\'s a simple calculator program that calculates quadratic roots, but only the real ones. That program annoys me so much because someone wasted their time making so it wouldn\'t show complex roots! It\'s like they don\'t like complex numbers or something!',9863,0);
INSERT INTO comment VALUES (9886,678,4510,'Ed Lunn','spider and fly','2003-11-26 18:19:49',0,'Solution : 3 out of 4',NULL,0);
INSERT INTO comment VALUES (9887,1268,4374,'Richard','re: solution','2003-11-26 19:00:29',0,'Your solution is much better than mine because you avoid using the logarithm function. For your solution, we do have to believe e^(it)=cos(t)+i*sin(t) for real t and that the law of exponents (a^b)^c=a^(b*c) extends from the real numbers to the complex numbers (or, in other words, not very much). You have really scaled the problem down to essentials. Excellent!',9883,0);
INSERT INTO comment VALUES (9888,1268,3558,'Tristan','re(2): solution','2003-11-26 19:31:01',0,'But (a^b)^c=a^(b*c) doesn\'t extend to complex numbers! ...Or at least not always...',9887,0);
INSERT INTO comment VALUES (9889,672,1626,'Gamer','(about name changes)','2003-11-26 20:52:45',0,'I don\'t think he needs to. There hasn\'t been any change disallowing people to be called the same thing when I had mentioned this, so I don\'t think it\'s important that people can impersonate others.',9881,0);
INSERT INTO comment VALUES (9890,672,3172,'SilverKnight','re: (about name changes)','2003-11-26 23:00:40',0,'Noone said anyone NEEDS to. And it\'s not important... not until someone acts malicious about it....\r\n\r\nNevertheless, Sam2 felt the need/desire below to make a point that he\'s the \"newbie Sam\"... and he did it again here.\r\n\r\nWhile, he is obviously thoughtful and courteous, the next person may not be.... It\'s only a matter of time.',9889,0);
INSERT INTO comment VALUES (9891,1478,4513,'paige','Solution','2003-11-26 23:11:13',0,'James Best- 2nd place- chocolate cake\r\nBen Jones- 1st place- fruit cake\r\nVicky Andrews- 4th place- cheese cake\r\nNigel Stevens - 3rd place- sponge cake',NULL,0);
INSERT INTO comment VALUES (9892,1510,1253,'brianjn','Donald in MathMagicLand','2003-11-26 23:16:09',0,'Back in the late 50\'s our primary school had a visiting projectionist. One 16mm film was my subject title. It has been screened on Disneyland on occasions too. It showed many examples of the employment of this ratio. I note that it has even been employed by many of the old masters, like Da Vinci, in creating the balance of what appears on their respective canvases.',NULL,0);
INSERT INTO comment VALUES (9893,1268,4374,'Richard','re(3): solution','2003-11-26 23:20:02',0,'Example?',9888,0);
INSERT INTO comment VALUES (9894,1259,4513,'paige','Solution','2003-11-26 23:22:42',3,'Zach- 137- walk dogs\r\nAngelica- 141- gardening\r\nMaurice- 139- babysitting\r\nRaquel- 143- house keeping',NULL,0);
INSERT INTO comment VALUES (9895,1428,4513,'paige','Solution','2003-11-26 23:29:34',3,'The numbers on the rods should be 4,5,6,7,8',NULL,0);
INSERT INTO comment VALUES (9896,1497,1253,'brianjn','Theorem - Drew','2003-11-26 23:51:46',0,'Drew, there is a theorem which states something to the effect that if the diagonal of a circle forms one side of a triangle, and the third vertex lies on the circumference of the circle, then the triangle is right-angled.\r\n\r\nProve this theorem, quote the corollary, and I believe you have the solution which Antonio requires',NULL,0);
INSERT INTO comment VALUES (9897,1268,4374,'Richard','re: What\'s a complex number?','2003-11-27 00:32:18',0,'Yes. This is tradition. If you want to be super clear you say b is not 0 in a+bi, like in the note that is part of the problem statement.',9867,0);
INSERT INTO comment VALUES (9898,1008,4515,'Zuninga!','Eh?','2003-11-27 01:03:30',0,'George, Helen, and Steve are drinking coffee. Bert, Karen, and Dave are drinking soda. Using my (il)logic, Elizabeth is drinking nothing because she\'s not even mentioned.\r\n\r\nIf she was smart, she\'d be drinking hot chocolate. MmmmMMmmMmMmMMM...',NULL,0);
INSERT INTO comment VALUES (9899,1510,4515,'Zuninga!','Da answer','2003-11-27 01:07:58',0,'1.618034, about.',NULL,0);
INSERT INTO comment VALUES (9900,1478,4515,'Zuninga!','here it is','2003-11-27 01:22:24',3,'Ben Jones(fruitcake), James Best(chocolate cake), Nigel Stevens(sponge cake), Vicky Andrews (cheesecake)\r\n\r\nHOW!??!?!?! Simple!\r\n\r\nJames Best beat Vicky by two places. Cool. But Ben\'s fruitcake beat Stevens, who was in third. This makes Ben(fruitcake) either first or second. He cannot be second because James Best has to be two places ahead of Vicky, and if James Best is first, he will be two places ahead of Stevens in third place. Ben(fruitcake) is first place, and James Best is in second. The chocolate cake came in second place, so James Best made the chocolate cake. Also, Stevens\' first name must be Nigel, as it\'s the last male name unaccounted for and it was stated that Mrs. Stevens had a son. This makes Vicky Andrews the unlucky last place finisher.\r\n\r\nJones\' mother\'s son took first. Established is that Ben(fruitcake) is in first, therefore his name is Ben Jones.\r\n\r\nSo, we have Ben Jones(fruitcake), James Best(chocolate cake), Nigel Stevens, and Vicky Andrews. The Sponge cake was said to come in the top three, so Nigel must have made it. That means Vicky made the cheesecake. Thus,\r\n\r\nBen Jones(fruitcake), James Best(chocolate cake), Nigel Stevens(sponge cake), Vicky Andrews (cheesecake).\r\n\r\nTa da.\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (9901,1510,3275,'retiarius','Golden Section - an interesting number','2003-11-27 02:29:23',0,'Try this on your calculator:\r\n\r\n(√5 - 1) / 2\r\n\r\nNow take the reciprocal\r\n\r\nNow square the result\r\n',NULL,0);
INSERT INTO comment VALUES (9902,1510,1626,'Gamer','re: Golden Section - an interesting number','2003-11-27 07:50:33',0,'To continue with my answer (because nobody else did) the equation can be multiplied by y/x by both sides, and 1 can be subtracted from both sides to give:\r\n\r\n(y/x)² - (y/x) -1 = 0; and since this is quadratic, solving with the quadratic formula gives: (1±√(5))/2\r\n\r\nThis makes sense because if you multiply (√(5) -1)/2 by (√(5)+1)/(√(5)+1) it will stay equal (you are multiplying by 1), but you will get (5-1)/(2(√(5)+1)) or 4/(2(√(5)+))), or 2/(√(5)+1)',9901,0);
INSERT INTO comment VALUES (9903,265,3430,'pat','names','2003-11-27 08:29:11',0,'look at it another way,.. what if John\'s last name was \"Had\" or worse his middle name was \"Had\" or worse yet Jane\'s middle name and last names were \"Jane While\" I see a series of colons, quotation marks and all the other murky ilk of grammar. :)',NULL,0);
INSERT INTO comment VALUES (9904,86,1626,'Gamer','re: more thoughts','2003-11-27 10:48:28',0,'As 1/x goes on, it approaches 0. Does this mean 1/ some number equals 0? I think the key word there is approaches, not is. It can only exist in an infinite state, and we have already ruled that out. (In other words, this only works when you plug in infinity for x, and you can\'t do that.)\r\n\r\nYour trying to use the converse of that postulatee. Sure 4 and 4 don\'t have any numbers in between them, but just because numbers don\'t have any space between them, doesn\'t mean that they are the same number; it\'s the other way around. \r\n\r\nAbout dividing by 0 or infinity, you can\'t find a number that satisfies that. When I graph x/0, I think, what number times 0 equals the certain x I have chosen? I actually find no answer. So for x = any number, it won\'t appear. Maybe I am wrong by some super-math secrets or something, but the way I am thinking it is true.\r\n\r\nI have no problem with being wrong, but I don\'t see a way to do it yet. :)',9538,0);
INSERT INTO comment VALUES (9905,86,1626,'Gamer','re(3): Ideas','2003-11-27 10:49:48',0,'Anyway SK I am sure you know what I mean. The fact that you choose to try and knock me down based on a small issue that you know doesn\'t come into the question is your problem.',9532,0);
INSERT INTO comment VALUES (9906,1509,3386,'Victor Zapana','solution','2003-11-27 11:11:39',3,'Valentines Day is 2/14/96, in that year. \r\nEach day, he will go up a net value of 1 foot. So, he would go up in 30 days, on 3/14/96. \r\nThis is WRONG, for he will be go up 3 feet. If he is already out he can\'t slip back. \r\nOn the 27th day, the snail would be at the 30 feet point, but he isn\'t out yet, so he\'ll still sleep and fall down 2 feet. Thus on the 28th day, he\'ll be out. \r\nThus, the date is 27 days after 2/14, for 2/14 is also a day he goes up 3 feet and falls down 2. Remember, 1996 is a LEAP year, so in 15 days, it\'s 2/29, and there\'s 12 extra days left, so the answer is March 12, 1996.',NULL,0);
INSERT INTO comment VALUES (9907,1509,3372,'Sam','Solution','2003-11-27 11:13:02',3,'He climbs an average of 1 foot a day for 27 days until he is 27 feet up, and on the 28th day climbs 3 feet and gets out. Valentine\'s Day is on the 14th of Febuary, and Febuary in \'96 had 29 days, so Herb got out March the 13th.',NULL,0);
INSERT INTO comment VALUES (9908,1509,3372,'Sam','re: solution','2003-11-27 11:15:01',0,'Ga, you slipped that in while I was typing, and also realized that we have to include Valentine\'s day itself. Silly me. Yes, March 12, not 13th',9906,0);
INSERT INTO comment VALUES (9909,1509,3386,'Victor Zapana','re(2): solution','2003-11-27 11:15:28',0,'heh sry sam lol',9908,0);
INSERT INTO comment VALUES (9910,86,3386,'Victor Zapana','solution is wrong','2003-11-27 11:29:41',0,'hmm.. well 3.999... x 10 would equal 39.9999...9, and now has an end, for u moved everything number is moved one place to the left, thus ending infinity. thus 3.999...9 - 3.999... does not equal 36, but 36.00000...1.',NULL,0);
INSERT INTO comment VALUES (9911,1509,4507,'Penny','Comments','2003-11-27 11:40:26',1,'This one, SilverKnight, and your other puzzle, Golden Ratio, have been on the Internet since forever. Can\'t you think of anything original? I\'d be willing to bet that whenever you go to the mind reader, you always get half price. ',NULL,0);
INSERT INTO comment VALUES (9912,86,3172,'SilverKnight','re(4): Ideas','2003-11-27 12:28:58',0,'Gamer,\r\n\r\nI didn\'t (try to) knock you down. The point is 3.9 (bar over the 9) exists, because our nomenclature allows it to exist, and we have the facilities/rules to deal with it.\r\n\r\nThere is a proof that shows why this does equal 4.\r\n\r\nJust like .5 (bar over the 5), DOES equal 5/9. Similar proof.\r\n\r\nNothing personal... just seems like a pointless argument.',9905,0);
INSERT INTO comment VALUES (9913,1509,4521,'supriya','solution','2003-11-27 13:22:15',3,'on the 27th day herb climbs 3 feet up that is 30 feet and is out of the well. so herb gets out on march 12th',NULL,0);
INSERT INTO comment VALUES (9914,1509,3558,'Tristan','re: Comments','2003-11-27 13:43:25',0,'To come to SilverKnight\'s defense, there is nothing wrong with posting a non-original puzzle. Besides that, he did post an original puzzle here. If all the puzzles had to be original, then we\'d miss out on a lot of great puzzles!',9911,0);
INSERT INTO comment VALUES (9915,1268,3558,'Tristan','re(4): solution','2003-11-27 13:52:19',0,'Ok, we all know e^(iπ)=-1, right?\r\nSo, e^(2iπ)=1\r\ne^(2iπ*i)=1^i\r\ne^(-2π)=(1^0)^i\r\ne^(-2π)=1^0=1\r\nSo, e^(-2π)=1\r\n\r\nYeah, that last equation is obviously incorrect. This little paradox comes from the fact that that law of exponents doesn\'t work with complex numbers with magnitude greater than e^π... or something like that. There\'s some calculus reason behind it, but I don\'t really understand it.\r\n\r\nEdited on November 27, 2003, 1:54 pm\n\nEdited on November 27, 2003, 1:56 pm',9893,0);
INSERT INTO comment VALUES (9916,1396,4507,'Penny','Solution','2003-11-27 14:52:48',0,'The following apportionment is consistent with A being a Knave, B a Liar, and C a Knight.\r\n\r\nA wants ketchup,mustard,onions and lettuce. B wants onions,relish,tomato andlettuce. C wants mustard,tomato,cheese and lettuce.\r\n\r\nExplanation:\r\nA: I want ketchup, mustard, onions, lettuce, relish. (LIE) \r\nB: A wants tomato too (LIE), and he doesn\'t want mustard (LIE). I want ketchup, tomato, cheese, lettuce.(LIE)\r\nC: B doesn\'t want ketchup (TRUTH), and he doesn\'t want mustard (TRUTH). A doesn\'t want relish (TRUTH). I want mustard, tomato, cheese, lettuce (TRUTH).\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (9917,1396,4507,'Penny','re: Solution','2003-11-27 15:07:33',0,'That solution is incorrect. If A is a Knave, then either\r\nA wants ketchup, doesn\'t want mustard, wants onions, doesn\'t want lettuce, and wants relish..... OR \r\nA doesn\'t ketchup, wants mustard, doesn\'t want onions, wants lettuce, and doesn\'t want relish.\r\n \r\nBack to the drawing board.....\r\n',9916,0);
INSERT INTO comment VALUES (9918,1268,4374,'Richard','re(5): solution','2003-11-27 18:58:30',0,'Your example is great. It shows what happens if one doesn\'t carefully define what z^c is for complex z and c. So let\'s take a stab at defining things and see what happens then.\r\n\r\nLet x,y,r,t be real, z=x+iy, and let n be an integer. Denote pi by P.\r\n\r\nAssume we know e^(it)=cos(t)+i*sin(t), e^z=(e^x)(e^iy), and e^z is never 0. We should perhaps write exp(z) instead of e^z, since it will turn out that this e^z is a specially designated one of the possible values that (2.718...)^z could be defined to have. When we write e^z below we always mean the one we just defined here.\r\n\r\nOne can easily show that e^(z+z\')=(e^z)(e^z\')and e^(z+i2nP)=e^z.\r\n\r\nIf equation e^z=z\' has a solution z, then z+i2nP is also a solution for any n. Each such solution is a logarithm of z\'. To have a well-defined logarithm function, we need a rule to pick out just one solution. We will do that like this:\r\n\r\nDefine the function Log by Log(z)=log(r)+it, where z=r*e^(it), log is the ordinary real logarithm to the base e, r>0, and the angle t is chosen to satisfy -P < t <= P.\r\n\r\nLog is then defined for all nonzero complex numbers. We have e^(Log(z))=e^(log(r)+it)=r*e^(it)=z.\r\n\r\nNow define z^c=e^(c*Log(z)). (This definition makes (2.718...)^c =e^c because of the way Log is defined.) Then (z^c)^c\'=(e^(c*Log(z)))^c\'=e^(c\'*Log(e^(c*Log(z)))=e^(c\'c*Log(z))=z^(c\'c). \r\n\r\nRestricting the imaginary part of the complex log to some other half open interval of length 2P will also give (z^c)^c\'=z^(c\'c) with the similar definition of z^c, but z^c may then have a different value. The angle assigned to z is what makes the difference. The angle of 1 may be taken to be any one of the values 2nP so that 1^i can be defined to have any of the values e^(i*2inP)=e^(-2nP). This does not mean that e^0=e^(-2P)=e^(-4P) etc.\r\n\r\n\n\nEdited on November 29, 2003, 8:01 pm',9915,0);
INSERT INTO comment VALUES (9919,1478,4527,'Tiffany','solution','2003-11-27 22:10:03',3,'1st - Fruit - Ben Jones\r\n2nd - Chocolate - James Best\r\n3rd - Sponge - Nigel Stevens\r\n4th - Cheese - Vicky Andrews',NULL,0);
INSERT INTO comment VALUES (9920,1396,3386,'Victor Zapana','thoughts','2003-11-27 23:16:24',0,'A must be a knave. \r\nB can\'t be a liar.If B is telling the truth, then A is a knave, and wants ketchup, onions, relish, and something else. B then wats ketchup, tomato, cheese, and lettuce. \r\nC can\'t be a liar. \n\nEdited on November 27, 2003, 11:18 pm',NULL,0);
INSERT INTO comment VALUES (9921,1396,3386,'Victor Zapana','solution','2003-11-27 23:23:30',0,'im not sure if this is right but sumone plz prove or disprove me. A is a knave, B is a knight, and C is a knave \r\nA wants ketchup, onions, relish, and tomato. \r\nB wants ketchup, tomato, cheese, and lettuce. \r\nC wants tomato, lettuce, onions, and relish.\n\nEdited on November 27, 2003, 11:24 pm',NULL,0);
INSERT INTO comment VALUES (9922,1396,4507,'Penny','re: solution','2003-11-28 00:14:23',0,'I don\'t think that your solution is correct, because you have C (a Knave) making back-to-back false statements: \r\n\r\nC: B doesn\'t want ketchup(false), and he doesn\'t want mustard(true). A doesn\'t want relish(false). I want mustard(false), tomato(true), cheese(false), lettuce(true).\r\n \r\nKnaves have to alternate truth-telling with lying. They can\'t do it back-to-back.\r\n',9921,0);
INSERT INTO comment VALUES (9923,678,4178,'Prab','Solution?','2003-11-28 00:30:00',0,'Let A denote the event that the sixth fly survives and B denote the event that the spider has already had his quota of 3 flies filled from the first five flies. Let C denote the complementary event for B, i.e., that the spider still needs one or more flies for his quota. \r\nWe need to find P(A).\r\nP(A)=P(A and B) + P(A and C)\r\n =P(A|B).P(B)+P(A|C).P(C)\r\nWe are told that P(A|C) = (1/2). We assume that \r\nP(A|B) is 1 since the spider is already satiated; ignoring the possibility that the spider could very well kill \'for pleasure\' even if it is already full.\r\nP(C)=P(spider caught 0,1,or 2 flies out of first 5)= (1+5+10)/32=1/2.\r\nP(B)= 1-P(C)=1/2\r\nSo P(A)=1.(1/2)+(1/2).(1/2)=(3/4)',NULL,0);
INSERT INTO comment VALUES (9924,1396,1301,'Charlie','A consistent set','2003-11-28 00:47:02',1,'This set is similar to Victor Zapana\'s list: A is a knave, B is a knight, and C is a knave.\r\n\r\nA wants ketchup, onions, relish, and tomato. \r\n\r\nB wants ketchup, tomato, cheese, and lettuce. \r\n\r\nbut\r\nC wants mustard, cheese, and two of the following: relish, ketchup and onions.\r\n\r\nThere\'s no way to determin, in this scenario, which two of that set of three that C wants.\r\n\r\nAnd I can\'t guarantee there aren\'t other solutions altogether.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (9925,86,3558,'Tristan','re: solution is wrong','2003-11-28 00:49:17',0,'If moving every nine to the left ended infinity (talk of oxymorons!), where do you think it would end it at? Is there some special finite number that is equal to ∞-1?\r\n\r\nWhat\'s infinity-1? Infinity! If everything moves over to the left, it does not end infinity, because infinity by definition never ends, no matter how much you subtract or add. Also, 36.00000...1 would have infinite 0\'s, making so there is actually no 1 that would ever appear in the number. So, 36.0000...1 is equal to 36 anyway.',9910,0);
INSERT INTO comment VALUES (9926,1509,4530,'Benjamin','','2003-11-28 01:09:49',0,'march 12 i think...',NULL,0);
INSERT INTO comment VALUES (9927,643,4529,'Ben','re: It really does seem too easy.','2003-11-28 01:14:00',0,'In some regards, people are incredible probability measurers...for example, we all know that \'e\' is a more commonly used letter than \'x\'...how many of you had to count to check?\r\nBut unfortunately, Bayes\' Theorem just isn\'t something we\'re good at. It\'s not intuitive. Anyone who answered 1/2 for this problem should look up a good website about it and read. Seriously, it\'s fun stuff. Or read this (a bash you over the head it\'s so simple problem):\r\n\r\nSuppose there is an empty nursery. A baby is added to it. Later on we select a baby at random from the room (there\'s only one in there to choose) - and voila, we picked a boy. Now, what was the probability that the baby we added was a boy?...\r\n\r\nI hope nobody answers 50%. Before we peaked, the probability may have been even, but now we have new information. Bayes\' Theorem is a way of understanding the implications of this new information for less trivial examples.\r\n\r\nA really famous example of how people get themselves into trouble with this is the Monty Hall problem: On a game show, there are 3 doors, A, B, and C. Behind one is a new car. The contestant picks a door, say he picks A. Then the host opens one of the other doors that is empty, say B is empty. \r\nWe all know the contestant had a 1 in 3 chance of being right to begin with. Could this new information have changed things? Could Bayes be involved? (sort of, but there are several ways to think about good ol\' Monty).\r\n\r\nIf anyone is still reading, another interesting problem people have is extrapolating probabilities. I mean, we\'re good at subconsciously counting that \'e\' is more common than \'x\', but do a lousy job forming theoretical probabilities when you can\'t really count. I\'m floundering while trying to describe this example I once heard, so maybe I better just give the example (simplified):\r\n\r\nJanet was a very bright girl, but she never cared much for school. She thought there was too much wrong with the world so she dropped out and joined a group that organizes rallies to save the forests. What probability would you assign to Janet having since done the following: \r\nA) become a librarian.\r\nB) learned to play acoustic guitar.\r\nC) become a bank teller.\r\nD) climbed to head of the forest-rally organization.\r\nE) become a kindergarten teacher.\r\nF) gotten married and raised a large family.\r\nG) become a bank teller, even though she continues to fight for the forests in her spare time.\r\nH) fought off a drug addiction.\r\n\r\nI\'ll explain after a few responses =DDD Oh, and hope I\'m not repeating too much stuff already out there...first time here. But fun fun fun!\r\n\r\nAnd, Charlie - you\'re my hero.',9386,0);
INSERT INTO comment VALUES (9928,1396,1301,'Charlie','re: A consistent set--confirmation -- 3 Solutions','2003-11-28 01:39:27',3,'The following are the possibilities, each set listing, for each of the buddies, the initials of the four condiments he wanted, plus the number of true odd-numbered statements he made and the number of true even-numbered statements he made:\r\n\r\nkort 3 0\r\nktcl 3 3\r\nkmoc 0 3\r\n\r\nkort 3 0\r\nktcl 3 3\r\nkmrc 0 3\r\n\r\nkort 3 0\r\nktcl 3 3\r\nmorc 0 3\r\n\r\nIn each instance A and C were knaves and B a knight. In each instance A had ketchup, onions, relish and tomato, while B had ketchup, tomato, cheese and lettuce. C does indeed have mustard and cheese in each instance, but could have any pair out of relish, ketchup and onions.\r\n\r\nThe program to find this is:\r\nDECLARE FUNCTION present! (person!, condi$)\r\nDECLARE SUB vary (person!)\r\nDIM SHARED list$\r\nlist$ = \"kmortcl\"\r\nDIM SHARED st$(3), p1(3), p2(3)\r\n\r\nvary 1\r\n\r\nFUNCTION present (person, condi$)\r\n IF INSTR(st$(person), condi$) > 0 THEN present = 1: ELSE present = 0\r\nEND FUNCTION\r\n\r\nSUB vary (person)\r\n st$(person) = SPACE$(4)\r\n FOR i = 1 TO 4\r\n MID$(st$(person), 1, 1) = MID$(list$, i, 1)\r\n FOR j = i + 1 TO 5\r\n MID$(st$(person), 2, 1) = MID$(list$, j, 1)\r\n FOR k = j + 1 TO 6\r\n MID$(st$(person), 3, 1) = MID$(list$, k, 1)\r\n FOR l = k + 1 TO 7\r\n MID$(st$(person), 4, 1) = MID$(list$, l, 1)\r\n IF person = 1 THEN\r\n p1 = present(person, \"k\") + present(person, \"o\") + present(person, \"r\")\r\n p2 = present(person, \"m\") + present(person, \"l\")\r\n IF p1 <> 0 AND p1 <> 3 OR p2 <> 0 AND p2 <> 2 THEN GOTO notThis\r\n p1(1) = p1: p2(1) = p2\r\n END IF\r\n IF person = 2 THEN\r\n p1 = present(1, \"t\") + present(person, \"k\") + present(person, \"c\")\r\n p2 = 1 - present(1, \"m\") + present(person, \"t\") + present(person, \"l\")\r\n IF p1 <> 0 AND p1 <> 3 OR p2 <> 0 AND p2 <> 3 THEN GOTO notThis\r\n p1(2) = p1: p2(2) = p2\r\n END IF\r\n IF person = 3 THEN\r\n p1 = 1 - present(2, \"k\") + 1 - present(1, \"r\") + present(person, \"t\") + present(person, \"l\")\r\n p2 = 1 - present(2, \"m\") + present(person, \"m\") + present(person, \"c\")\r\n IF p1 <> 0 AND p1 <> 4 OR p2 <> 0 AND p2 <> 3 THEN GOTO notThis\r\n p1(3) = p1: p2(3) = p2\r\n END IF\r\n IF person < 3 THEN\r\n vary person + 1\r\n ELSE\r\n FOR p = 1 TO 3\r\n PRINT st$(p), p1(p), p2(p)\r\n NEXT\r\n PRINT\r\n END IF\r\n\r\nnotThis:\r\n NEXT\r\n NEXT\r\n NEXT\r\n NEXT\r\nEND SUB\r\n\r\n\r\n',9924,0);
INSERT INTO comment VALUES (9929,1224,1253,'brianjn','re: solution?','2003-11-28 02:19:00',0,'Impetuous. How many times do we find a solution to a problem, whether concrete or abstract only to find that a perception, measurement, or misreading of the data leaves us embarrassed?\r\n\r\nIn this case we have been told that each letter represents a unique digit.',9689,0);
INSERT INTO comment VALUES (9930,1396,4507,'Penny','This is more like it','2003-11-28 02:32:32',3,'It seems that there is more than one valid solution to thsi puzzle. One of them is:\r\n\r\nA (Knave) wants ketchup,onions,relish,tomato. \r\nB (Knight) wants ketchup,tomato,cheese,lettuce.\r\nC (Knave) wants mustard,cheese,ketchup,onions.\r\n\r\nThen their three statements are:\r\nA: \"I want ketchup(TRUE), mustard(FALSE), onions(TRUE), lettuce(FALSE), relish(TRUE).\"\r\nB: \"A wants tomato too(TRUE), and he doesn\'t want mustard(TRUE). I want ketchup(TRUE), tomato(TRUE), cheese(TRUE), lettuce(TRUE).\"\r\nC: \"B doesn\'t want ketchup(FALSE), and he doesn\'t want mustard(TRUE). A doesn\'t want relish(FALSE). I want mustard(TRUE), tomato(FALSE), cheese(TRUE), lettuce(FALSE).\"\r\n',NULL,0);
INSERT INTO comment VALUES (9931,1509,1183,'fwaff','re(2): Comments','2003-11-28 03:21:42',0,'That one\'s not exactly orginal either, I remember it from a lateral thinking book I was given as a child (about 20 years ago). But as you say, just cos it\'s old/non-original doesn\'t mean it\'s not interesting or challenging. \r\n\r\nI think this snails puzzle is a great one for teaching children to think through to the end of a problem. It\'s really easy to work out that the snail effectively climbs 1 foot per day, but then many leap to the (incorrect) solution that therefore it must take 30 days to climb 30 feet. And then SK\'s added the twist of starting on Valentine\'s day in a leap year to introduce the chance of another error, which is variation on the problem that I\'ve not seen before.',9914,0);
INSERT INTO comment VALUES (9932,1396,4507,'Penny','Is that for here or to go?','2003-11-28 06:43:02',0,'I don\'t relish having to point this out, but in addition to:\r\n\r\nA (Knave) wants ketchup,onions,relish,tomato. \r\nB (Knight) wants ketchup,tomato,cheese,lettuce. \r\nC (Knave) wants mustard,cheese,ketchup,onions. \r\n\r\nThere are at least two more valid solutions, by changing \r\nC\'s order to:\r\n \r\n\"C (Knave) wants mustard,cheese,ketchup,relish\",\r\n\"C (Knave) wants mustard, cheese, onions, relish\" \r\n\r\nIdeally there should only have been one valid solution. This pickle fails to cut the mustard in that respect. But otherwise I\'d say it\'s the best thing since sliced bread!',9930,0);
INSERT INTO comment VALUES (9933,86,3386,'Victor Zapana','re(2): solution is wrong','2003-11-28 08:39:33',0,'infinity never ends yes but if u infinity-1, then that has an end meaning it is finite \r\nIn addition, theoretically, 3.99999... needs a 0.000...1 to equal 4. this might be slightly flawed coz 9\'s go on forever and the 0.000...1 has an end, but still, i dont see how one number can equal another one. its like the 2 = 1 proof\n\nEdited on November 28, 2003, 8:41 am',9925,0);
INSERT INTO comment VALUES (9934,1509,3386,'Victor Zapana','re(3): Comments','2003-11-28 08:54:17',0,'i agree with fwaff many old problems are great. i especially like the \"nothing\" riddle. it was a real stumper for me the first time i read it. and besides not all people know of these riddles. so its absolutely fine to put these kinds of riddles up.',9931,0);
INSERT INTO comment VALUES (9935,1478,4537,'etsy','solution','2003-11-28 11:04:06',0,'name last name position type of cake\r\njames best #2 chocolate\r\nben jones #1 fruit\r\nvicky andrews #4 cheese\r\nnigel stevens #3 sponge\r\n',NULL,0);
INSERT INTO comment VALUES (9936,1396,1626,'Gamer','Change:','2003-11-28 11:11:34',0,'Unfortunately, I made a change to this without thinking about the problem. I had written that the 3 didn\'t want the same toppings when I had written this all out, and I had apparently thought that meant 3 toppings as a group, when in fact they don\'t want any of the 3 toppings.\r\n\r\nIn other words, if A wants ketchup and B wants ketchup, C can\'t want ketchup',NULL,0);
INSERT INTO comment VALUES (9937,1270,3224,'Lee','solution','2003-11-28 13:01:09',3,'Feeder.......House..........Bird............Food\r\nAllison..........6...........Thrush.........Birdseed\r\nBrewer........10...........Robin..........Suet\r\nChandler.......2...........Blackbird......Toast\r\nDennis.........4...........Sparrow........Bread\r\nEmery..........8...........Cardinal.......Crumbs\r\n\r\nDon\'t knock the layout if you please.\r\n',NULL,0);
INSERT INTO comment VALUES (9938,86,3558,'Tristan','re(3): solution is wrong','2003-11-28 14:39:56',0,'Again, I say that infinity-1 is infinite by definition. If it were finite, what number do you think it would be? .000...1, with infinite 0\'s does not have an end. If it ends, where do you think it would end? This is not a case where one number is equal to another one, they are the same number written differently. Like SK said, that\'s just how our number system\'s nomenclature goes.',9933,0);
INSERT INTO comment VALUES (9939,1509,4541,'fraser','hmmm...','2003-11-28 15:25:53',0,'march 12, me thinks',NULL,0);
INSERT INTO comment VALUES (9940,676,4542,'Katie','got it','2003-11-28 15:30:33',0,'area of triange with sides x-y,x,x+y:\r\n(3/16x^4-12/16x^2*y^2)^(1/2)\r\narea of equallateral triangle with side x:\r\n(3/16x^4)^(1/2)\r\n\r\n(3x^4-12x^2*y^2)^(1/2)=3/5(3x^4)^(1/2)\r\n3x^4-12x^2*y^2=27/25*x^4\r\nx^2-4y^2=9/25*x^2\r\ny^2=4/25*x^2\r\ny=2/5*x\r\n\r\nThe ratio of the sides with x=5 is 3:5:7',NULL,0);
INSERT INTO comment VALUES (9941,865,4541,'Fraze','no','2003-11-28 15:38:46',0,'no',NULL,0);
INSERT INTO comment VALUES (9942,1270,4507,'Penny','This is deja vu all over again','2003-11-28 15:38:59',4,'Isn\'t this a rehash of that hamburger puzzle? When I showed this one to my boyfriend Sylvester, he remarked that puzzles like this are childishly easy. You just draw a few tables, eliminate possibilites, etc. No real insight or higher intelligence is required. Sylvester remembered that one year, on his birthday, which was also the birthday of his grandfather Garfield, he and Garfield were celebrating that joyous double occasion by working on a puzzle similar to this one. As they were solving it with ease, Sylvester suddenly observed that not only had he (Sylvester) just turned as old as the last two digits of the year he (Sylvester) was born in, but he (Sylvester) was also a prime number of years old. Also, each of the two digits making up Sylvester\'s age on that occasion was also a prime number. Garfield thought for a second, turned to Sylvester, and said that all these things were also true for him (Garfield) at that time! What year did this occur, and how old had Sylvester and Garfield just turned?',NULL,0);
INSERT INTO comment VALUES (9943,672,4541,'Fraze','hmm','2003-11-28 15:44:41',0,'that is actually could not possibly happen\r\nSo I suppose if this did happenthere would be like a glitch in the universe or something',NULL,0);
INSERT INTO comment VALUES (9944,511,4541,'Fraze','answer','2003-11-28 16:05:50',0,'no.\r\nBecause if he can lift everything something unliftable is impossible and cannot exist',NULL,0);
INSERT INTO comment VALUES (9945,1270,2839,'FatBoy','re: This is deja vu all over again','2003-11-28 16:47:41',0,'Hey Penny,\r\nWelcome to Flooble. You seem like a very smart person and I bet you will be come a vary valuable member of the Flooble community. \r\nDamn, stop smacking Penny around. I feel bad for her :P\n\nEdited on November 30, 2003, 11:28 am',9991,0);
INSERT INTO comment VALUES (9996,1513,3558,'Tristan','Explain...','2003-11-30 12:34:54',4,'Not to be rude (like some people are), but neither of your explanations were very easy to understand for me. \r\n\r\nIs (2^(p-1))*(2^p-1) the definition of perfect numbers, or does it just succeed in finding many perfect numbers? It seems like an unnecessarily complex equation if it\'s defining it rather than finding it. Also, if it was defining it, than it would be simple to prove that there are no odd perfect numbers.\r\n\r\nBut then, even if there were more perfect numbers besides the ones that are found by that equation, it isn\'t necessarily relevant to the sequence. The sequence could be the following: all perfect numbers, perfect numbers found by the equation, or the outputs of the equation when p is prime. BTW, no one said directly that p had to be prime, which further confused me.\r\n\r\nIf I\'m missing something obvious, maybe that something wasn\'t as obvious as you thought.',NULL,0);
INSERT INTO comment VALUES (9997,1513,4507,'Penny','re: Explain...','2003-11-30 13:34:10',2,'Certainly, Tristan, and, like you, I am appalled at the nasty rude insults that Lamer and SenileKnight...ah, I mean, Gamer and SilverKnight... have leveled at me in this thread. People who don\'t have enough maturity to avoid petty personal attacks should not be on such a fine website as this. If either of them were to say these things to my face, and my boyfriend Sylvester were present, they would immediately be going down faster than a house of cards on a greased banana peel in a typhoon. But if you seek clarification about perfect numbers, your best bet is to check out any or all of the following fine texts on the subject. \r\n\r\nDickson, L.E.: _History of the Theory of Numbers_, 1, Chelsea, \r\nreprint, 1952. \r\n\r\nNankar, M.L.: \"History of perfect numbers,\" Ganita Bharati 1, \r\nno. 1-2 (1979), 7-8. \r\n\r\nHagis, P.: \"A Lower Bound for the set of odd Perfect Prime Numbers\", \r\nMath. Comp. 27, (1973), 951-953. \r\n\r\nRiele, H.J.J. \"Perfect Numbers and Aliquot Sequences\" in H.W. Lenstra \r\nand R. Tijdeman (eds.): _Computational Methods in Number Theory_, \r\nVol. 154, Amsterdam, 1982, pp. 141-157. \r\n\r\nRiesel, H. _Prime Numbers and Computer Methods for Factorisation_, \r\nBirkhauser, 1985. \r\n ',9996,0);
INSERT INTO comment VALUES (9998,1513,4507,'Penny','re: In fact... (another solution)','2003-11-30 14:22:03',0,'Interesting.... \n\nEdited on November 30, 2003, 3:05 pm',9993,0);
INSERT INTO comment VALUES (10000,1513,4507,'Penny','re: In fact... (another solution)','2003-11-30 15:08:54',0,'You\'re saying that SilverKnights\'s \"Flawless Sequence\" is as flawed as Gamer\'s original version of \"Burger Buddies\" --neither has a unique solution. As my boyfriend Sylvester noted, this proves again the wisdom of the old saying \"Feeble minds think alike\". \n\nEdited on November 30, 2003, 3:11 pm',9993,0);
INSERT INTO comment VALUES (9999,1513,4300,'Minion123','re(2): In fact... (another solution)','2003-11-30 14:55:52',0,'Please Penny just answer the problem, show how you got that answer, and stop talking about your boyfriend. ',9998,0);
INSERT INTO comment VALUES (10001,1513,4507,'Penny','re(3): In fact... (another solution)','2003-11-30 15:17:01',0,'Well, Minion123, I do not claim to be smarter than Euclid. (No doubt SilverKnight thinks he is, though. SilverKnight has delusions of adequacy...) I did indeed \"cut and paste the formula and plug in the numbers...blah blah blah\", which is exactly what every good engineer does when he builds anything. I wouldn\'t want to drive a car, cross a bridge, or fly on a plane that had been constructed in any other manner. Would you? \r\n\r\n\n\nEdited on November 30, 2003, 3:24 pm',9999,0);
INSERT INTO comment VALUES (10002,1513,1301,'Charlie','re: Explain...','2003-11-30 15:22:37',0,'The definition of a perfect number is that it is a number which is equal to the sum of all the numbers that divide exactly into it, including 1, but excluding itself. Thus 6 is a perfect number because 6 is divisible by 1, 2 and 3, and the total of those numbers is also 6. As mentioned, the fact that it is divisible by itself, 6, does not add to the total.\r\n\r\nLikewise 28 is divisible by 1, 2, 4, 7 and 14, which add up to 28.\r\n\r\nThat\'s how the definition works.\r\n\r\nIt turns out that all the even perfect numbers are given by\r\n(2^(p-1))*(2^p-1) where p is a prime and 2^p-1 is also prime (this form is called a Mersenne prime). It is believed, but not proved, that there are no odd perfect numbers, so that this list, via Mersenne primes, will find any perfect number at all (is in 1-to-1 correspondence with the perfect numbers).\r\n\r\nThe alternative solution that I posted previously, uses the mere formula (2^(p-1))*(2^p-1) considering only p as prime without requiring 2^p-1 to be prime. This results in numbers, such as 2096128, showing up on the alternative sequence while not being perfect.',9996,0);
INSERT INTO comment VALUES (10003,1513,1301,'Charlie','re(2): Explain...','2003-11-30 15:26:44',0,'Why did you choose not to explain, in response to a post which asked for an explanation? Why, when a simple answer is wanted, do you point to a whole history of perfect numbers? The simple answer does fit within a comment. This is a puzzle site, not a mathematics seminar.',9997,0);
INSERT INTO comment VALUES (10004,1513,4300,'Minion123','re(4): In fact... (another solution)','2003-11-30 15:28:24',0,'I can\'t drive yet, I haven\'t been on many bridges, and I hate going on planes. \n\nEdited on November 30, 2003, 3:30 pm',10001,0);
INSERT INTO comment VALUES (10005,1513,3386,'Victor Zapana','re(4): In fact... (another solution)','2003-11-30 15:50:30',0,'Penny darling, because you have tried to post problems up in your posts, here\'s some of mine: \r\nWho says you are a good \"engineer\", as you proclaim in your metaphor? Not just anyone can copy and paste and be a \"good engineer.\" \r\nWho says you have a boyfriend, Penny? Chances are you are making this up, projecting your opinions through a nonexistent entity. \r\nWho says your have the right to criticism and hinder others problems? Sk\'s problems are perfectly fine. Gamer\'s problems are perfectly fine. Criticizing others\' problems because you can\'t get yours posted up is a silly excuse. \r\nWhy are you slandering back at Silverknight and Gamer? \"Lamer?\" \"Senileknight?\" heh heh heh no. I agree two wrongs don\'t make a right, but neither does three. \r\nCan\'t you understand requests? When people ask you to explain, then copy and paste garbage and bibliographies. This proves that you CAN\'T explain. We don\'t need a Dr. Math posting from you. \n\nEdited on November 30, 2003, 4:02 pm',10001,0);
INSERT INTO comment VALUES (10006,1513,1626,'Gamer','About attacks','2003-11-30 15:54:58',0,'I indeed commend your effort of calling me Lamer, as few have found out as I have that\'s a great name! :) \r\n\r\nHowever, if you deplore personal attacks, you should look no further than yourself. I was certainly disapproving of this act of yours. Please correct me if I am taking these out of context.\r\n\r\n\"I\'d be willing to bet that whenever you go to the mind reader, you always get half price\" (on Lovelorn Snail)\r\n\r\nBack to the drawing board, dude. You\'re in serious need of some hamburger helper !! (Less bad, but still from Burger Buddies)\r\n\r\npuzzles like this are childishly easy. You just draw a few tables, eliminate possibilites, etc. No real insight or higher intelligence is required. (from Feed the birds)\r\n\r\nAnd a kind synonym for SK\'s posting is UNORIGINAL.\r\n\r\nI hate to contend with unarmed opponents\r\n\r\nBesides deflate your massive ego? \"Flawless Series\" collapsed faster under my laser-like scrutiny than any other lame conundrum in the history of the brainteaser\r\n\r\nSilverKnight, I bet I could have you and Gamer working feverishly for at least 48 hours if I handed you pieces of paper that had \"turn over\" written on both sides. \r\n\r\nYou also have all the originality and creativity of a fax machine. Let\'s see...\"Golden Ratio\" - that\'s been around since Ancient Egypt... \"Lovelorn Snail\" -- that one was old when Reagan was in diapers.... \"Relativistic bullet\" -- Einstein beat you to the punch in the 1930s.... and now \"perfect numbers\" -- the ancient Greek, Euclid, \"anticipated\" you on that one. Can\'t you come up with anything new, SilverKnight? Is it asking too much for you to use your brain for something more than keeping your hat in place? \r\n\r\nFeeble minds think alike\r\n\r\nNo doubt SilverKnight thinks he is, though. SilverKnight has delusions of adequacy...) \r\n\r\n(All during this thread)\r\n\r\nAll I was doing was defending myself, and I am sorry that I sunk to your level if I have made that many insults towards you. I know that I definitely wouldn\'t have any personal attacks I should ignore if you would stop giving them to us.\r\n\r\nPlease stop mentioning your boyfriend. We don\'t need to know any more. ',NULL,0);
INSERT INTO comment VALUES (10007,1509,4575,'Angel','perhaps a solution','2003-11-30 16:04:16',0,'I`d like to bit on 13th March 1996, if Herb is able to live that long.\r\nGood luck to all of you! ;)',NULL,0);
INSERT INTO comment VALUES (10008,1513,4507,'Penny','re: About attacks','2003-11-30 16:12:29',0,'LMFAO !!! Great stuff !! You only missed one: \"If either of them were to say these things to my face, and my boyfriend Sylvester were present, they would immediately be going down faster than a house of cards on a greased banana peel in a typhoon.\"\r\n \r\nThey say that the great German philosopher Schiller was once reproached for insulting someone in very clever and creative terms. He replied \"Aber wurde es nicht schon ausgedruckt?\" \r\n \r\n:-)',10006,0);
INSERT INTO comment VALUES (10009,1513,153,'TomM','deja vu','2003-11-30 16:12:57',0,'I remember two other occassions when a newbie poster who felt that this site needed someone to \"stir things up\" upset some of the old-timers so much that levik was asked to ban them. But a little patience was all that was needed for Gamer and especially Silver Knight to settle down and become valued members on this site.\r\n\r\nOn the other hand, I also remember Tim Axoy who only kept acting worse, and finally did need to be banned. But, then again, Tim was only 9 years old and didn\'t really fit in here anyway. ',NULL,0);
INSERT INTO comment VALUES (10010,1513,4507,'Penny','re: deja vu','2003-11-30 16:23:38',0,'So SilverKnight and Gamer are suffering what they themselves used to dish out? Well, as they say in the San Francisco bath-houses - \"turn around is fair play\". \r\n\r\nBut who says SilverKnight and Gamer \"settled down\"? They still wield a mighty insult here and there. They aren\'t in my forensic league, however, just as Woody Allen isn\'t quite ready to step into the boxing ring with Mike Tyson. \n\nEdited on November 30, 2003, 4:24 pm',10009,0);
INSERT INTO comment VALUES (10011,1513,3840,'Hal9000','Real Answer','2003-11-30 16:37:32',0,'Obviously t(n) = (3359/3)n³ -6495n² +(35008/3)x-6288.',NULL,0);
INSERT INTO comment VALUES (10012,1513,1626,'Gamer','re(2): deja vu','2003-11-30 16:37:57',0,'I am about as potent as a bomb I guess. If there\'s a big explosion of insulting, I will just blow up! :) I will try to work on that. :)\r\n\r\nI don\'t think the proper response is to be proud of your insults! Maybe you should work on that! :)',10010,0);
INSERT INTO comment VALUES (10013,1513,3840,'Hal9000','re: Real Answer','2003-11-30 16:38:13',0,'where x=n of course.',10011,0);
INSERT INTO comment VALUES (10014,1517,4064,'rerun141','solution','2003-11-30 16:42:13',3,'signs with numbers on them, a digit for 10 cents!:) ',NULL,0);
INSERT INTO comment VALUES (10015,1513,3840,'Hal9000','Perfect Shmerfect','2003-11-30 16:43:07',0,'I don\'t buy into this perfect number mumbo jumbo, t(n) = (3359/3)n³ -6495n² +(35008/3)n-6288. ',NULL,0);
INSERT INTO comment VALUES (10016,1513,3840,'Hal9000','','2003-11-30 16:47:54',0,'The next three numbers are 29642, 71756, 141188 because t(n) = (3359/3)n³ -6495n² +(35008/3)n-6288.',NULL,0);
INSERT INTO comment VALUES (10017,1517,3840,'Hal9000','re: solution','2003-11-30 17:20:07',0,'He\'s selling numbers and all I can gather is the digits 0,1,5 each cost 10 cents. \r\n\r\n\"Mathematics is free from contradiction but apparently no longer free\" - Hal9000',10014,0);
INSERT INTO comment VALUES (10018,1513,1301,'Charlie','re: Real Answer','2003-11-30 17:48:38',0,'The only problem with this is that a cubic can be fit to any 4 points, and a 4th degree polynomial to any 5 points, etc., so such curve fitting is not usually considered an answer to such a puzzle.',10011,0);
INSERT INTO comment VALUES (10019,1513,3840,'Hal9000','re(2): Real Answer','2003-11-30 18:02:18',0,'Indeed, however I cannot be faulted for establishing such a pattern based on the limited amount of terms in the sequence given. While I concede your point that such curve fitting is not usually considered an answer to such a puzzle, I will validate it by saying 4 terms is not usually considered a question for such a puzzle. A flawed question deserves a flawed answer.',10018,0);
INSERT INTO comment VALUES (10020,1513,4507,'Penny','The original post in this thread.....','2003-11-30 18:05:41',0,'Had it not been for my original post, Gamer would still be searching for the answer by translating the numbers into Roman Numerals, and Hal9000 would be looking for patterns in the Periodic Table of Chemical Elements. Victor Zapana would be trying to find cities whose rank, in terms of population size, are 6, 28, 496, and 8128, and Tristan would be trying to translate those numbers into international airport codes. Charlie\'s computer program would be in an infinite loop. So don\'t be mad at little Penny, with my cut-past-plug-in-the-numbers. I saved you countless wasted hours barking up fruitless trees. I didn\'t just go off and leave you Penny-less. \r\n \r\n(Besides, my clever insults, worthy of David Letterman on his best night, were amusing even to the \"butts\" of the jokes.) \r\n\r\n\r\n\n\nEdited on November 30, 2003, 6:15 pm',9969,0);
INSERT INTO comment VALUES (10021,1513,4064,'rerun141','re: The original post in this thread.....','2003-11-30 18:28:28',0,'Are you so self absorbed you haven\'t realised that hal and charlie came up with there own solutions?? and it was charlie who finally explained what a perfect number really was.',10020,0);
INSERT INTO comment VALUES (10022,1513,3840,'Hal9000','Patterns in the Periodic Table of Elements','2003-11-30 18:29:30',0,'The periodic table is an layout of all identified elements in order of growing atomic number. The rationale of why the elements are positioned as they are in the periodic table is firstly to show them all, with their widely diverse physical and chemical properties, into a logical pattern. If sodium is placed beneath lithium and not next door to fluorine, and potassium is placed beneath sodium to begin another row - and so on - it is found that the vertical lines of elements are chemically similar. These vertical lines are called GROUPS. Horizontal lines of elements on the table are called periods. The set of D-BLOCK ELEMENTS, sometimes called \"transition metals\", occur between Groups 2 and 13; these are chemically similar to each other. Some Groups exhibit striking similarity between their elements, such as Group 1, and in other Groups the elements are less similar to each other, such as Group 4, but each Group does has a common set of characteristics. The periodic table is also divided into blocks. The s-block elements have valence configuration s1 or s2. The p-block elements have valence configuration s2p1 to s2p6. The d-block elements have valence configurations in which d-subshells are being filled. Hydrogen occupies a unique position at the top of the periodic table. Unfortunately it does not fit naturally into any Group. All the members of a Group have the same valence configuration but different principal quantum numbers. The number of valence electrons equals the Group number. The period number equals the principal quantum number of the valence shell. Chemically, elements in the same block exhibit the same general characteristics. This is most apparent for the s-block elements which are all metals with low electronegativity. The p-block elements are more varied with some metals such as aluminium on the left and non-metals on the right. Between them, indicating the gradual change in character going across the periodic table, are the metalloids (or semi-metals), which lie roughly in a diagonal line from silicon to tellurium. The d-block elements are often called the transition metals, but some of them, such as zinc, do not fit this description well. They are usually considered together as differences between Groups are much less apparent in this block. Periodicity is the name given to regularly-occurring similarities in physical and chemical properties of the elements. Periodicity reflects the periodic repetition of similar electron configurations. Very many properties of the elements show periodicity. The most obvious of these is the continuing change from metal on the left to non-metal on the right. This is reflected in the graph of melting points for the first 20 elements. For each period the melting point rises from Group 1 to Group 14, then falls to the lowest value at Group 18. If the d-block elements are also included periodicity can be seen between rows of these elements, but as periodicity becomes less apparent with increasing atomic number this is less obvious than for the s- and p-block elements. Variation of first ionisation energy with atomic number also shows striking periodicity. The relative position of each Group in relation to the others follows the same pattern in each period. Periodicity is also seen for atomic radius and can be summarised by indicating the main trends. Some chemical properties of the elements also follow trends and can be summarised in the same way. These include bonding, oxidising properties, acid-base properties of the oxides and electronegativity.\r\n ',NULL,0);
INSERT INTO comment VALUES (10023,1513,1626,'Gamer','re: The original post in this thread.....','2003-11-30 18:37:56',0,'Hey! A psychopath is more dangerous than just an innocent kid (like Tim Axoy) right? Time for some action? I mean now she has dragged everyone into it, and despite everyone\'s knowledge of perfect numbers, she continues to insult us. The reason I call her a psychopath (yes, I do have a reason) is because she persists on calling people insults despite some warning, and she took delight when I pointed out all her insults.\r\n\r\nThat\'s all I am saying about her if it continues.',10020,0);
INSERT INTO comment VALUES (10024,1513,4300,'Minion123','Let it be','2003-11-30 18:56:26',3,'Here are some words of wisdom from the Beatles for everyone. Just let it be. ',NULL,0);
INSERT INTO comment VALUES (10025,1513,3386,'Victor Zapana','Re: Let it be','2003-11-30 18:59:44',0,'Damn right',NULL,0);
INSERT INTO comment VALUES (10026,1517,4507,'Penny','A Penny-wise solution','2003-11-30 19:36:44',3,'\"... a sign advertising: 1 for 10 cents, 15 for 20 cents and 110 for 30 cents. What is he selling?\"\r\n \r\nCopies of Gamer\'s autobiography? \r\n\r\nJust kidding !!! The real answer came to me at once, from the fact that there was a \"steep\" price (all of 10 cents!!) for the first one, then a rapid decline for subsequent increments. He is selling copies on his copying machine !! Every hardware store seems to have one. It makes economic sense that one copy should have a minimum fee, 10 cents -- to offset the cost in power usage, etc., to initialize the copier, and then to copy the document once to a virtual image, because these are the two really significant steps in the process. But when you make more copies, you are invoking the relatively simplistic step of imposing a virtual image on blank paper. So it makes sense that the price will decline for multiple copies. Thus it would cost $11, and rightly so, if you made 110 copies by making one copy each day for 110 days, because you would be causing the machine to go through the initialization process and the virtual image creation process 110 times. But if you made all 110 copies at once, then the initialization would occur just once, the document in question would be \"imaged\" just once, and thanks to such concepts as buffering, the copying of the virtual image to paper would be performed with such rapid speed thereafter that the cost of subsequent copying would decline dramatically. In economic theory, this is known as \"the law of diminishing returns.\" It\'s also known as \"buying in bulk\". True, there would be the cost of the sheets of paper on which the virtual image is imposed, but the production of paper is also affected by the \"diminishing returns\" concept. Imagine how absurd it would be if the sign had read: \"1 copy for 10 cents, 15 copies for $1.50, and 110 copies for $11.00\". I know I sure wouldn\'t go there if I needed to make more than just a few copies !!! \r\n\r\n\r\n\r\n\r\n\r\n\n\nEdited on November 30, 2003, 8:53 pm',NULL,0);
INSERT INTO comment VALUES (10027,1517,4064,'rerun141','re: A Penny-wise solution','2003-11-30 19:54:25',0,'AHHHH! of course, selling copies! Why didn\'t we think of that!\r\nI hope there was as much sarcasm in your post as there was in this one...',10026,0);
INSERT INTO comment VALUES (10028,1517,4507,'Penny','re(2): A Penny-wise solution','2003-11-30 20:19:54',1,'Sarcasm ? Oh I don\'t know, rerun141...I\'d say my solution was a bit more insightful than yours. Someone once said \"Karate is the martial art of the brave, and sarcasm that of the timid.\" ',10027,0);
INSERT INTO comment VALUES (10029,1517,4064,'rerun141','re(3): A Penny-wise solution','2003-11-30 20:28:43',0,'well, im not kooking for another 40 posts of back and forth insults so i\'ll commend your creativity, hope this is the last post with no relation to the problem, and wait 2 weeks for the real solution. ',10028,0);
INSERT INTO comment VALUES (10030,1517,1072,'Alan','','2003-11-30 20:54:52',0,'Hmmm Penny who wrote those autobiographys of gamer you were talking about? Was it you? If so I understand the pricing. Just kidding But I decided to throw in some sarcasm of my own.\r\nAnyways Instead of saying they\'re selling signs how about they\'re selling the service of paining letters on things. Lets assume it was quite some time ago when 10 cents could be considered reasonable.',NULL,0);
INSERT INTO comment VALUES (10031,1517,4507,'Penny','re:','2003-11-30 21:12:20',0,'Alan: \"Hmmm Penny who wrote those autobiographys of gamer you were talking about?\"\r\n \r\nI believe Gamer is the only person who could write an autobiography of Gamer. By the way, Alan, maybe you can help me out. \r\n\r\nI just bought a bottle of \"One-A-Day Multiple Vitamins\", but it doesn\'t say on the bottle how many of them I should take each day. When I called the pharmacy and asked this question, the pharmacist hung up on me.\r\n \r\nDo you have any ideas about the optimal daily dosage of \"One-A-Day Multiple Vitamins\" ?\r\n\r\nI sure hope they don\'t kick me off this website. I would really miss all you brilliant people !!!!!\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\n\nEdited on November 30, 2003, 9:36 pm',10030,0);
INSERT INTO comment VALUES (10032,1517,1626,'Gamer','Ideas:','2003-11-30 21:49:38',0,'As long as you don\'t insult lots of people at once *COUGH COUGH* then you should be fine. I would be careful with sarcasm and insults too. They are always a problem. (Remember that others joke sometimes too, so don\'t get mad if Alan asks who wrote the autobiography, it\'s likely not an actual question.)\r\n\r\nPersonally I think that\'s a pretty good solution, but the real time for you to shine is in tricks, where anything goes. :)',NULL,0);
INSERT INTO comment VALUES (10033,1517,4507,'Penny','re: Ideas:','2003-11-30 23:09:52',0,'Thank you, Gamer, that was very big of you, to praise a solution that contained a joke at your expense (\"Copies of Gamer\'s autobiography?\") As my boyfriend Sylvester and I were sitting around, admiring your magnanimity, there was a sudden knock on the door. (The only reason I mention this anecdote, is to impress you with my puzzle-solving bona fides. I am not trying to post a new puzzle). When we opened the door, in walked our four new Indian friends: Montu, Bantu, Chantu and Pintu. (They are Microsoft engineers). They each have pets. Montu said: \"If Pintu and I each have a dog, then exactly one of Bantu and Chantu has a dog.\" Bantu said: \"If Chantu and I each have a cat, then exactly one of Montu and Pintu has a dog.\" Chantu said: \"If Montu and I each have a dog, then exactly one of Bantu and Pintu has a cat.\" Pintu said: \"If Bantu and I each have a cat, then exactly one of Bantu and I has a dog.\" Sylvester suddenly turned and said to me: \"I know that only one of our Indian friends is telling the truth.\" When I heard that, I instantly identified the truth-teller. Not bad, eh ?\n\nEdited on November 30, 2003, 11:17 pm',10032,0);
INSERT INTO comment VALUES (10034,1517,4300,'Minion123','re(2): Ideas:','2003-11-30 23:20:39',0,'My girlfriend Sylvia and I were wondering if friends of yours regulary walk in and talk to you about their personal life in the format of a puzzle without saying hello first.',10033,0);
INSERT INTO comment VALUES (10035,1513,3172,'SilverKnight','re(3): Real Answer','2003-12-01 00:23:08',0,'I hate to admit it... but (unless I\'ve missed a correct posting) only Hal9000 has actually answered the question.\r\n\r\nIt\'s not a flawed question (no matter how many terms we specify, we can always create a function that runs through the points). And it\'s not a flawed answer (IMHO), except that it doesn\'t take into account the title.\r\n\r\nNot only did Hal9000 specify \"the next three numbers\", but he provided understanding and an explanation for it.\r\n________________________\r\n\r\nI hope someone will find ANOTHER solution that takes the title into account. (And Penny, I see that you\'ve resigned yourself to doing no more than \"plugging numbers into a formula\". I\'m sorry that you\'ve given up so easily.)',10019,0);
INSERT INTO comment VALUES (10036,1396,4582,'Devon','solution','2003-12-01 01:34:30',0,'A is a knave and wants ketchup, onions, relish and tomato\r\n\r\nB is a knight and wants ketchup, tomato, lettuce and cheese\r\n\r\nC is a knave and wants mustard, cheese, onion and relish',NULL,0);
INSERT INTO comment VALUES (10037,1513,4507,'Penny','re(4): Real Answer','2003-12-01 04:20:39',1,'As the very first reply to this problem pointed out, \"flawless\" is a synonym for \"perfect\". As the first four \"perfect numbers\" are 6, 28, 496, 8128, it would have been exceedingly malicious if \"perfect numbers\" were meant to be a red herring in this puzzle !! \r\n\r\nHere are some interesting facts about perfect numbers. (What follows is what SilverKnight calls \"mindless cut-and-paste\", but it could also be called \"mindful research and scholarship\")...\r\n\r\nAn alternate way to define a perfect number is: a positive integer that is equal to the sum of all its positive dividers, except itself. (6=1+2+3, 28=1+2+4+7+14, etc). As pointed out in the original reply, these numbers are of the form [2^(n-1)][(2^n)-1)], where (2^n)-1 is a prime number (a \"Mersenne prime\").\r\n\r\nTheorem One: k is an even perfect number if and only if it is of form [2^(n-1)][(2^n)-1)] and (2^n)-1 is prime.\r\n\r\nTheorem Two: If 2^n-1 is prime, then so is n.\r\n\r\nSo the search for Mersennes is also the search for even perfect numbers!\r\n \r\nThe perfect numbers listed in this puzzle (6, 28, 496, 8128) all end with either the digit 6 or the digit 8--this is also very easy to prove (but no, they do not continue to alternate 6, 8, 6, 8,...). If you like that digit pattern, look at the first four perfect numbers in binary: 110 11100 111110000 1111111000000 \r\n\r\n(The binary digit pattern is a consequence of Theorem One.) It is not known whether or not there is an odd perfect number, but if there is one it is big! This is probably the oldest unsolved problem in all of mathematics. \r\n\r\nWhen checking to see if a Mersenne number is prime, first look for any small divisors. The following theorem of Euler and Fermat is very useful in this regard.\r\n\r\nTheorem Three: Let p and q be primes. \r\nIf q divides M(subscript p) = 2^p-1, then q = (+/-)1 (mod 8) and q = 2kp + 1 for some integer k.\r\n\r\nTheorem Four. Let p = 3 (mod 4) be prime. 2p+1 is also prime if and only if 2p+1 divides M(subscript p) \r\n\r\nTheorem Five. If you sum the digits of any even perfect number (except 6), then sum the digits of the resulting number, and repeat this process until you get a single digit, that digit will be one.\r\n\r\nMersenne primes (and therefore even perfect numbers) are found using the Lucas-Lehmer Test: For p odd, the Mersenne number 2^p-1 is prime if and only if 2^p-1 divides S(p-1) where S(n+1) = S(n)^2-2, and S(1) = 4. \r\n\r\nThe theory for this test was initiated by Lucas in the late 1870\'s and then made into this simple test about 1930 by Lehmer. The sequence S(n) is computed modulo 2^p-1 to save time. This test is ideal for binary computers because the division by 2^p-1 (in binary) can be done using rotation and addition only. \r\n\r\nIn 1811 Peter Barlow wrote in his text Theory of Numbers that 2^30(2^31-1) \"is the greatest [perfect number] that will be discovered; for as they are merely curious, without being useful, it is not likely that any person will attempt to find one beyond it.\" I wonder what he would have made of the first attempts to climb Mount Everest, to run faster miles, or to jump a longer broad jump--other tasks that are curious but not useful. Obviously no one in the late 1800\'s had any idea of the power of modern computers. What might we know about the machines of 50 years from now?\r\n\r\nAfter the 23rd Mersenne prime was found at the University of Illinois, the mathematics department was so proud that the chair of their department, Dr. Bateman, had their postage meter changed to stamp \"2^11213-1 is prime\" on each envelope. This was used until the four color theorem was proved in 1976.\r\n\r\nThe 25th and 26th Mersenne primes were found by high-school students Laura Nickel and LaLandon Curt Noll who, though they had little understanding of the mathematics involved, used Lucas\' simple test on the local university\'s mainframe (CSUH\'s CDC 174) to find the next two primes. Their discovery of the first prime made the national television news and the front page of the New York Times. They went their separate ways after finding the first prime, but Noll kept the program running to find the second--so Noll claims complete ownership. Noll searched later, and though he never found another Mersenne prime, he is one of a team that holds the record for the largest non-Mersenne prime. He currently works for Silicon Graphics. \r\n\r\nSlowinski, who works for Cray computers, has written a version of the Lucas test that he has convinced many Cray labs around the world to run in their spare time (time that would be lost otherwise). He had to delay announcing one of his prime records until he got permission to begin looking for it. Slowinski\'s search for record primes is \"not so organized as you would suppose\" (his words), as he does not search systematically. \r\n\r\nEnter George Woltman, an excellent programmer and organizer. Starting in late 1995 he gathered up the disparate databases and combined them into one. Then he placed this database, and a free, highly optimized program for search for Mersennes onto the web. This began GIMPS (the Great Internet Mersenne Prime Search) which: has now found the largest known Mersennes, has scanned all of the regions left unexplored between the previous record primes, combines the efforts of dozens of experts and thousands of amateurs, and which offers free software for most computer platforms. \r\n\r\nIn late 1997 Scott Kurowski (and others) established PrimeNet to automate the selection of ranges and reporting of results for GIMPS, now almost anyone can join this search! \r\n\r\nConjectures and unsolved problems:\r\n\r\nIs there an odd perfect number? We know that all even perfect numbers are a Mersenne prime times a power of two, but what about odd perfect numbers? If there is one, then it is a perfect square times an odd power of a single prime; it is divisible by at least eight primes and has at least 37 prime factors (not necessarily distinct); it has at least 300 decimal digits; and it has a prime divisor greater than 10^20.\r\n \r\nAre there infinitely many Mersenne primes? Equivalently we could ask: Are there infinitely many even perfect numbers? The answer is probably yes (because the harmonic series diverges). \r\n\r\nAre there infinitely many Mersenne composites? Euler showed: If k>1 and p=4k+3 is prime, then 2p+1 is prime if and only if 2^p = 1 (mod 2p+1). So if p=4k+3 and 2p+1 are prime then the Mersenne number 2^p-1 is composite (and it seems reasonable to conjecture that there are infinitely many primes pairs such p, 2p+1).\r\n \r\nThe New Mersenne Conjecture: Bateman, Selfridge and Wagstaff have conjectured the following. Let p be any odd natural number. If two of the following conditions hold, then so does the third: 1. p = 2^k+/-1 or p=4^k+/-3; \r\n2. 2^p-1 is a prime (obviously a Mersenne prime); \r\n3. (2^p+1)/3 is a prime. Notice how this conjecture is related to the theorem in the previous conjecture. This conjecture has been verified for all primes p<=100,000.\r\n \r\nIs every Mersenne number square free? This falls more in the category of an open question (to which we do not know the answer), rather than a conjecture (which we guess is true). It is easy to show that if the square of a prime p divides a Mersenne, then p is a \"Wieferich prime\", and these are rare! Only two are known below 4,000,000,000,000 and neither of these squared divide a Mersenne. \r\n\r\nLet C(subscript 0) = 2, then let C(sub 1) = 2^[C(sub 0)]-1, C(sub 2) = 2^[C(sub 1)]-1, \r\nC(sub 3) = 2^[C(sub 2)]-1, ... Are these all prime? According to Dickson Catalan responded in 1876 to Lucas\' stating 2^127-1 (C(sub 4)) is prime with this sequence. These numbers grow very quickly: C(sub 0)=2 (prime), C(sub 1)=3 (prime), C(sub 2)=7 (prime), \r\nC(sub3)=127 (prime), C(sub 4)=170141183460469231731687303715884105727 (prime)...It seems very unlikely that C(sub 4) (or many of the larger terms) would be prime, so this is no doubt another example of Guy\'s strong law of small numbers. Notice that if there is even one composite term in this sequences, then by theorem one all of the following terms are composite. (Landon Curt Noll has used his program calc to verify that C(sub 5) has no prime divisors below 5*10^50). \r\n\r\nAre there more double-Mersenne primes? Another common early misconception was that if n=M(sub p) is prime, \r\nthen so is M(sub m); lets call this number MM(sub p) (a \"double-Mersenne\"). Indeed each of the first four such numbers are prime: \r\nMM(sub 2) = 2^3-1 = 7; MM(sub 3) = 2^7-1 = 127; MM(sub 3) = 2^31-1 = 2147483647;\r\nMM(sub 7) = 2^127-1 = 170141183460469231731687303715884105727. However, the next four (MM(sub 13) MM(sub 17) MM(sub 19) and MM(sub 31)) all have known factors--so are composite. Are there any more primes in this sequence? Probably not, but it remains an open question. Tony Forbes is leadinga project to search for a factor of the next term: MM(sub 61); you might want to join and help! Notice the Catalan sequence is a subsequence of this one. \r\n \r\n \r\n\r\n\r\n\r\n\n\nEdited on December 1, 2003, 4:22 am',10035,0);
INSERT INTO comment VALUES (10038,1517,1183,'fwaff','re: A Penny-wise solution','2003-12-01 04:22:36',0,'My pet goat Doris and I were sat in the jacuzzi sipping Tizer and thoroughly enjoying your intriguing lateral thinking solution to the old house number problem, unfortunately we were interrupted by a nun enquiring as to the whereabouts of the soap. However, that is a subject for another problem and I should digress no further.\r\n\r\nFrom reading your many insightful posts I notice that you enjoy deliberately including errata within your comments to test whether us mentally challenged flooblers will notice them. Therefore I hereby include the correct explanations for the economic theories that you cited incorrectly. \r\n\r\nThe law of diminishing returns is a principle used to explain the fact that in most situations the relative benefit received diminishes with increasing investment.\r\n\r\nBuying in bulk is term used to mean purchasing power, whereby discounts are demanded (and often given) on the basis of increased quantities.\r\n\r\nThe unit-cost reductions you describe for the photocopying business are a simple outcome of high-volume batch-process manufacturing. Basically, the greater the batch-quantity, then the lower the set-up cost per unit. When combined with stock considerations (ie the cost of workinging capital) then this leads to a calculation of economic batch quantity.\r\n\r\nDo I win the speedboat for spotting the deliberate flaw?\r\n\r\nPlease pass on my regards to Sylvester. I do hope that the ointment is working.',10026,0);
INSERT INTO comment VALUES (10039,1513,3172,'SilverKnight','re(5): Real Answer','2003-12-01 04:44:54',0,'Penny, really... an impressive display of copying and pasting. I applaud your bleeding-edge abilities in the field of \'cutandpastology\'. We would most certainly walk on any bridge you cutandpasted, and you\'ve really outdone yourself with your attempt to \'solve by voluminous submission\'.\r\n\r\nI admit it. I am amused by your desire to do anything and everything except actually understand this problem. But I encourage you (and all flooblers) to actually submit a solution (preferably less than 3+ pages long). (Think.... less is more).',10037,0);
INSERT INTO comment VALUES (10040,1517,4507,'Penny','re(2): A Penny-wise solution','2003-12-01 05:00:56',0,'fwaff: \"My pet goat Doris and I were sat [sic] in the jacuzzi sipping Tizer and thoroughly enjoying your intriguing lateral thinking solution....From reading your many insightful posts...deliberately including errata within your comments to test whether us mentally challenged flooblers will notice them....The law of diminishing returns is a principle used to explain the fact that in most situations the relative benefit received diminishes with increasing investment. Buying in bulk is term used to mean purchasing power, whereby discounts are demanded (and often given) on the basis of increased quantities...\"\r\n \r\nYou give me too much credit, fwaff. Those were not deliberate errors. Since I was using the terms loosely, they were not errors at all. \r\n\r\n\"Diminishing returns\" is a term applied to all manner of subjects, from sexual intercourse to alien abductions. Legendary sportscaster Vin Scully once said \"Moving the infielders back when power hitters approach the plate can suffer from the law of diminishing returns.\" So if a term is being used loosely, it cannot accurately be called an error. If I had said, for example, \"I need to get up at sunrise tomorrow\", would you have protested my \"erratum\" of supposing that the sun actually rises, when in fact the earth rotates on its axis?\r\n \r\nIf I really wanted to insert a deliberate error, I might have asked \"Who wrote so-and-so\'s autobiography?\" This would be a form of auto-errata-cism. (I am still laughing about that one!!) \r\n\r\nfwaff: \"Do I win the speedboat for spotting the deliberate flaw?\" \r\n \r\nNo, there is only one way to win the speedboat: come up with a better answer to \"What\'s for sale?\" than my \"Penny-wise Solution\". I\'m not holding my breath until SilverKnight does so. Previous posters have made such lame attempts as suggesting that the hardware store is selling numbers, numerals on signs, or the services of painting such numerals on signs. LOL !! You\'ll have to be a lot smarter than that !!!!! \r\n\r\nfwaff:\"Please pass on my regards to Sylvester. I do hope that the ointment is working.\"\r\n \r\nDon\'t pick on my boyfriend Sylvester. He\'s been having a \r\nrough time lately. His doctor has him on a combined therapy of Viagra (under the brandname \"Fix-A-Flat\") and Metamucil. The poor guy doesn\'t know whether he\'s coming or going these days !!!! \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\n\nEdited on December 1, 2003, 6:07 am',10038,0);
INSERT INTO comment VALUES (10041,1513,4507,'Penny','re(6): Real Answer','2003-12-01 05:44:48',0,'Dear SillyKnight:\r\n\r\nLess is more...But in your case, less is definitely less.\r\n\r\nAt the risk of arousing you, sir, from what is obviously a profound state of catatonia, the post you refer to did not claim to be a \"solution\" of any kind. It stated up front that it was an attempt to share interesting facts about perfect numbers and Mersenne primes, and anyone who was not interested in reading them could simply have bypassed that post. There was no need to make an insulting and insipid response, but you just had to do that, didn\'t you? Your problem is that you have mastered the art of using a keyboard, but you have not yet mastered the arts of intelligent discourse and civilized communication. I would estimate your age as 15, at most.\r\n \r\nAnd another thing...Don\'t you dare criticize me for cutting and pasting, when you have no compunction about using a computer program to help solve these puzzles. Which is more artificial? \r\n\r\nHave a nice day. \r\n\r\n\n\nEdited on December 1, 2003, 5:52 am',10039,0);
INSERT INTO comment VALUES (10042,1517,1183,'fwaff','re(3): A Penny-wise solution','2003-12-01 05:48:27',0,'Please accept my most humble apologies for falsely accusing you of error. It was when you stated, \"In economic theory, this is known as \"the law of diminishing returns.\" \", that made me think that you were applying this \'law\' to the specific case of economic theory. How foolish of me not to realise that this could equally have meant that you were referring to alien abductions, a subject which we should probe no further.\r\n\r\nAs you have proved your superior intellectual capacity beyond any shadow of doubt, may I wish you and the mighty Sly (if I may be so familiar) glad tidings for your speedboat trips. I hope that his medical regime doesn\'t present you with too stiff a problem.',10040,0);
INSERT INTO comment VALUES (10043,1513,3172,'SilverKnight','re(7): Real Answer','2003-12-01 05:57:03',0,'Penny... you remind me of Dan... ;-) a recent visitor to the site, who, like you, did everything he could to avoid the issue at hand... changing subjects and backpeddling to try and save face.\r\n\r\nHe, like you, was irked when he fell short of what he claimed to be able to do.\r\n\r\nYou used the \"full solution\" icon below (but go ahead and change it to hint or thought...).\r\n\r\nYou wrote: \"Flawless Series\" collapsed faster under my laser-like scrutiny than any other lame conundrum in the history of the brainteaser\r\n\r\nAnd yet you still haven\'t once answered the problem.\r\n\r\nAt the risk of sounding repetitive... \r\n\r\n I encourage you (and all flooblers) to actually submit a solution (preferably less than 3+ pages long). (Think.... less is more).\r\n____________________________\r\n\r\nI suggest that you either demonstrate WHY that formula might work, or better yet, show the answer (and how you got it) without relying on Mersene primes. But, *sigh*, again [now a fourth time], I doubt Penny will be up to the task.',10041,0);
INSERT INTO comment VALUES (10044,1513,4507,'Penny','re(8): Real Answer','2003-12-01 06:03:37',0,'Dearest SK:\r\n\r\nI believe your problem stated \"What are the next three numbers in this sequence? 6, 28, 496, 8128, ... ? Please explain how you determined these three numbers.\"\r\n\r\nMy response, in the first reply on this thread, identified the formula for Mersenne primes and \"perfect numbers\" and so BY IMPLICATION supplied not only the next three numbers, but the explanation of how they were determined. I did not explicitly state these numbers, but since I had given the formula, that would only be a problem in the mind of a stupid person. So SK, would else is on your mind (if you\'ll forgive the overstatement)?\r\n \r\n(btw, it\'s Mersenne, not Mersene, Einstein.) \n\nEdited on December 1, 2003, 6:23 am',10043,0);
INSERT INTO comment VALUES (10045,1513,3172,'SilverKnight','re(9): Real Answer','2003-12-01 06:36:57',0,'Well... I see that it took you 20 minutes to change your previous response (which was simply:)\r\n\r\n\" It\'s Mersenne, not Mersene, Einstein. \"\r\n\r\nTo what it is now...\r\n__________________________________\r\n\r\nAnd now, you\'re back peddling and trying to state that you\'ve answered it again.\r\n\r\nI\'ve already addressed your issue of Mersenne primes and your continued lack of providing any insight except one of copy-and-paste. I am tired of rehashing the same thing.\r\n\r\nSo, no, stating a formula that you found on the internet is not demonstrating understanding of anything... I\'m sorry to disappoint you.\r\n\r\nPerhaps if you could explain the connection, it might help.\r\n__________________________________\r\n\r\nAnd, at least you limited it to just me this time.... and no mention of your boyfriend... and no submission of new problems....\r\n\r\nI\'m disappointed in you.',10044,0);
INSERT INTO comment VALUES (10046,1513,4507,'Penny','That\'s it, SilverKinght','2003-12-01 06:53:01',4,'SK, you pathetic little hypocrite....\r\n\r\nYour solution to \"The powers that be\" was clearly copy/pasted from the Internet, since it contains symbols (the check mark and the symbol for pi) not found on computer keyboards. Where in that post do you demonstrate the slightest understanding of the formulas?\r\n\n\nEdited on December 1, 2003, 6:54 am',NULL,0);
INSERT INTO comment VALUES (10047,1513,3172,'SilverKnight','That\'s right, Penny!','2003-12-01 06:58:23',0,'Penny:\r\n\"Your solution to \"The powers that be\" was clearly copy/pasted from the Internet, since it contains symbols (the check mark and the symbol for pi) not found on computer keyboards.\"\r\n\r\nπ √\r\n\r\nThese symbols?!? LOL! You\'re right... I couldn\'t POSSIBLY have generated these symbols without cut and paste.... You\'ve caught me!\r\n\r\nSame with these: x² & x³\r\n\r\nP.S. I wonder what those buttons right above the PREVIEW and POST buttons do....',NULL,0);
INSERT INTO comment VALUES (10048,1513,4507,'Penny','re: That\'s right, Penny!','2003-12-01 07:01:08',0,'And where in \"an example of said case\" in \"the powers that be\" do you demonstrate any understanding of your formulas?',10047,0);
INSERT INTO comment VALUES (10049,1513,3172,'SilverKnight','Penny - please stop changing previous posts','2003-12-01 07:01:57',0,'Penny,\r\n\r\nAs you continue to change previous posts, I\'m beginning to be forced to actually copyandpaste from YOUR postings into my postings... because you seem to change them later.\r\n\r\nPlease try to minimize your changing what you\'ve previously written, because it is becoming quite an inconvenience for me to have to quote you (not to mention making my comments longer).\r\n\r\nThank you in advance, for your consideration.',NULL,0);
INSERT INTO comment VALUES (10050,1513,4507,'Penny','','2003-12-01 07:13:41',0,'SK pontificates: \"So, no, stating a formula...is not demonstrating understanding of anything... I\'m sorry to disappoint you.\"\r\n \r\nThen please, where in the first \"example of said case\" (which you offered as the \"full solution\" to \"The Powers That Be\") do you do anything but state one equation after another? btw...I can\'t wait to see your brilliant solution to \"What\'s for sale?\" Feel free to copy/paste \"A Penny-wise Solution\" if you can\'t come up with anything original.... \n\nEdited on December 1, 2003, 7:15 am',NULL,0);
INSERT INTO comment VALUES (10051,1517,4507,'Penny','I can\'t wait to read SilverKnight\'s defnitive solution','2003-12-01 07:19:43',0,'(this page intentionally left blank)',NULL,0);
INSERT INTO comment VALUES (10052,1513,3172,'SilverKnight','Penny... having trouble staying on task?','2003-12-01 07:27:16',0,'It\'s impressive how consistently you change the subject when the truth stares at you in the face:\r\n\r\nPenny... you remind me of Dan... ;-) a recent visitor to the site, who, like you, did everything he could to avoid the issue at hand... changing subjects and backpeddling to try and save face.\r\n\r\nHe, like you, was irked when he fell short of what he claimed to be able to do.\r\n\r\nAnd yet you still haven\'t once answered the problem.\r\n\r\nI suggest that you either demonstrate WHY that formula might work, or better yet, show the answer (and how you got it) without relying on Mersene primes. But, *sigh*, again [now a FIFTH time], I doubt Penny will be up to the task.',NULL,0);
INSERT INTO comment VALUES (10053,1513,4507,'Penny','SilverKnight...there\'s nothing impressive about you','2003-12-01 07:32:06',0,'Does this ring a bell? If you read it enough times, perhaps you\'ll try to answer it....\r\n \r\n\"SK pontificates: \"So, no, stating a formula...is not demonstrating understanding of anything... I\'m sorry to disappoint you.\" \r\n\r\nThen please, where in the first \"example of said case\" (which you offered as the \"full solution\" to \"The Powers That Be\") do you do anything but state one equation after another? btw...I can\'t wait to see your brilliant solution to \"What\'s for sale?\" Feel free to copy/paste \"A Penny-wise Solution\" if you can\'t come up with anything original.... \r\n\r\n',10052,0);
INSERT INTO comment VALUES (10054,1513,3172,'SilverKnight','re: Penny... having trouble staying on task?','2003-12-01 07:44:41',0,'tsk tsk tsk... please stay on task. Flawless series?',10052,0);
INSERT INTO comment VALUES (10055,1513,3172,'SilverKnight','Penny... I\'ve had enough of this','2003-12-01 07:51:55',0,'So, you may continue to get the \'last word\'... and you can continue to avoid answering the problem, and insulting me (and perhaps others)...\r\n\r\nBut I no longer have the desire (or time) to continue this silliness. I hope you have a wonderful time, continuing the thread.',10054,0);
INSERT INTO comment VALUES (10056,1517,4589,'Kim Splawn','','2003-12-01 09:32:34',0,'He is selling signs.',NULL,0);
INSERT INTO comment VALUES (10057,1511,3172,'SilverKnight','re(3): My stilborn dream','2003-12-01 09:33:45',0,'Yes :-)\r\n\r\nBut I wanted the guy shooting a gun... and a bullet travelling at 1%c would be one impressive bullet (and gun) ! :-)',9968,0);
INSERT INTO comment VALUES (10058,1389,3372,'Sam','Some thoughs','2003-12-01 10:34:58',0,'Well, don\'t have time to do it, so here is what I\'ve been working on.\r\n\r\nEvery work is an even number of digits, so I assume each letter corresponds to a two-ddigit number.\r\n18241218\'37 probably ends in \'s, making S:37. Simply adding 16 to each letters natural number doesn\'t work though.\r\n12 is on it\'s own often, making 12 either A or I. It\'s on it\'s own several times, implying that the numbers are fixed, and don\'t change through the message.\r\nWords that end in double letters are\r\n16343737, 22233535 and 19233535. Letters commonly doubled up at the end are LL, SS and (less often) TT. 37 is already S, so 35 may well be L. \r\nFrom those words, 34 and 23 should be vowels.\r\n19233535 could possibly be WELL, since it is quite common for a sentence to start with \"Well, blah blah..\" (last sentence). That would make W:19 and E:23.\r\n\r\nOk, must dash, will see if this has been solved when I get back.\r\n\n\nEdited on December 1, 2003, 10:52 am',NULL,0);
INSERT INTO comment VALUES (10059,197,4206,'Eric','yep','2003-12-01 11:09:14',0,'The duffer copied the moves of both players, thus assuring that either both games result in a draw, or a win lose situation.\r\n\r\nIf the competent chess players insist that the duffer always be the first person to play, and assuming that their experience will lead them to victory, then that should suffice to guarantee that the duffer loses both games. ',NULL,0);
INSERT INTO comment VALUES (10060,442,4206,'Eric','yep','2003-12-01 11:31:16',0,'Grandma is 72 years old.',NULL,0);
INSERT INTO comment VALUES (10061,1389,3372,'Sam','Solution','2003-12-01 11:37:14',3,'Or rather, the next line...:\r\n\r\n2423353536 3617232712183627, 173523123723 14343823 1623 262816222327 9\r\n\r\nBy the way \"Q\" doesn\'t look like it could fit into your pattern. It looks like you jumped over it and went o,p,r,s. Good thing it was never needed...',NULL,0);
INSERT INTO comment VALUES (10062,1517,1575,'DJ','','2003-12-01 12:23:45',3,'The sign is obviously referring to a computerized vending machine near the door, selling base-ten logarithms in bunches of ten for ten cents each.\r\n\r\nIf you want one bunch of ten, you pay ten cents for it (log(10)=1 × 10 is 10¢).\r\nIf you want fifteen bunches of ten, you pay twenty cents (log(150=2.176 × 10 is 21.7¢) but since the vending machine only takes dimes, you can just give it 20¢).\r\nSimilarly, you can buy 110 ten bunches of ten (the base-ten logarithm of 1100 is 3.041, at ten cents each, but 30.4¢ to the machine is just three dimes).\r\n\r\nThe problem arises when you want to buy 316 of these little bundles of joy, and the simplistic mechanism inside the machine computes log(3160) in two different ways as 3.49 and 3.50 and doesn\'t know whether to charge you three dimes or four.',NULL,0);
INSERT INTO comment VALUES (10063,1508,1575,'DJ','Passed by','2003-12-01 13:21:46',3,'I was gone for a week and a half, and it\'s sad that I missed this problem being posted; I was looking forward to it when I saw it in the queue.\r\n\r\nMy first thoughts were the same as Brian\'s; you need a pointer to the head of the list, and would need to traverse the list until you the node after the current node is the one you want to delete. Then, you change the next-node pointer to the one after, and delete the one you want to. That can be done is fixed space, but not in constant time (it will be O(n)). That\'s the normally cited approach to deleting a node in a singly-linked list.\r\n\r\nAfter SK\'s comments suggested that you don\'t have a pointer to the head of the list, the problem changes. Because it is singly linked, you access the previous node, but you need to change the pointer of that node to the one after it. That got me thinking, and actually the process is more efficient if you don\'t use the head of the list anyway.\r\n\r\nYou will not actually have to delete the node you are pointing to, but you will delete the value of the node you are pointing to. I\'m assuming that\'s what SK was intending here; because otherwise the problem is indeed impossible. You just assign the current node the value and the next-node pointer from the one following it, and the delete that node from memory.\r\n\r\nHere\'s a short function that takes a pointer (iterator) to an element of a singly-linked list and effectively deletes it (although that actual node is not deleted):\r\n\r\n Let\'s consider the continued fraction n=0.abcde...z2abcde...z2... It follows that n/10+0.2 = 0.2abcde...z2abcde...z2... = 2n as stated, and we get n=2/19=0.105263157894736842.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (10202,1235,1575,'DJ','re: Ducks Unlimited','2003-12-04 09:58:16',0,'You are correct, the word \'consecutive\' is never used in the puzzle. However, it does say that he made the statement every day starting on August first, and that he is never lying. Therefore, it is necessary that all the days being considered are consecutive, even if that word is not used.',9349,0);
INSERT INTO comment VALUES (10203,1310,1301,'Charlie','solution','2003-12-04 10:57:38',3,'Proof that three straight cuts cannot cut a circle into seven pieces with equal area:\r\n\r\nIn fact, each of the 3 straight line (chords) would have to cut the circle in a 3:4 ratio. If we take the radius of the cake as being our unit of measure, the smaller area cut off would have to be π*3/7.\r\n\r\nThe area of the smaller piece is the area of the sector that would be produced by connecting the endpoints of the chord and the center, minus the area of the triangle formed by the endpoints and the center of the circle. If the angle at the center subtending the chord is called α, the area of the smaller cut off piece is A = α/2 - sin(α/2)*cos(α/2) when measured in radians. This is the same as (α-sin(α))/2, which is to be set equal to π*3/7, so α-sin(α) = π*6/7.\r\n\r\nUsing Excel\'s solver, this happens when α = 2.916221 radians, or 167.0871582 degrees, and the chord is cos(α/2) = 0.112447 units from the center.\r\n\r\nAs each of the outer \"sort of normal cake-slice-shaped\" pieces must be the same size, by symmetry the chords must be placed at 120-degree intervals. That leaves the center piece an equilateral triangle with the center 0.112447 units from each base. That triangle then has a base of .389529 and a height of .337342 for an area of .065702, which, out of a total circle area of π, is only 0.020913725 or 1/47.81548878 of the circle\'s total area.\r\n\r\nSo seven equal pieces is impossible. There are various ways of getting six.\r\n\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (10204,1404,2839,'FatBoy','re(2): 1 last question for gamer','2003-12-04 11:28:47',0,'D\'oh...\r\nokay, hand me the pointy hat',10199,0);
INSERT INTO comment VALUES (10205,1310,3623,'jaypee','possible solution','2003-12-04 11:31:32',0,'one cut can go all the way through the cake so as to form a diameter. the other two cuts only go to the center so as to form two radii. this will equally divide the cake into eight pieces.',NULL,0);
INSERT INTO comment VALUES (10206,697,4638,'Jim','the answer is','2003-12-04 12:02:37',0,'Mr. Y lives in 13 and Mr. X lives in 23',NULL,0);
INSERT INTO comment VALUES (10207,1310,3172,'SilverKnight','re: possible solution','2003-12-04 12:28:37',0,'won\'t that only divide it into 4 pieces?',10205,0);
INSERT INTO comment VALUES (10208,697,3172,'SilverKnight','re: the answer is','2003-12-04 12:30:07',0,'I think you reversed them.\r\n13 = 2² + 3²',10206,0);
INSERT INTO comment VALUES (10209,1310,1920,'Brian Smith','An idea','2003-12-04 12:45:38',0,'Since we are cutting a three dimensional cake, why not make a cut at an angle.',NULL,0);
INSERT INTO comment VALUES (10210,1310,4430,'Eberhard','re: solution','2003-12-04 13:24:12',0,'Great post- The only thing that makes this solution possible is that it is not a circle but rather a cylinder and the solution has already been stated, it is interesting to note however that if we were cutting a concave substance after the first cut (like a doughnut) it would be possible to get 12 equal pieces with only three cuts. ',10203,0);
INSERT INTO comment VALUES (10211,1310,3172,'SilverKnight','re(2): solution','2003-12-04 14:21:23',0,'Eberhard,\r\n\r\nI\'m having trouble visualizing how to cut 12 equal pieces from a donut with only three cuts. Could you please describe this?\r\n\r\n(Or are you suggesting that you have three cuts AFTER a first cut, for a total of four cuts?)\r\n\r\n- SK',10210,0);
INSERT INTO comment VALUES (10212,1404,1626,'Gamer','re: 1 last question for gamer','2003-12-04 16:22:20',0,'I originally had a plan for the words to be 4 and 6 in a pattern, but that didn\'t work too well. So I just took whatever words I could find. Hogtie isn\'t a word according to some sources (it\'s hog tie) and midrib isn\'t a common word either, but gt and dr are wierdo combos.\r\n\r\nThe reason they all end with a 5 letter word is each line has an odd number of letters.',10192,0);
INSERT INTO comment VALUES (10213,1499,4507,'Penny','Solution','2003-12-04 16:25:37',0,'This is a well known problem in three dimensional geometry that I worked out in about 5 minutes. I leave the details as an exercise for the reader. ',NULL,0);
INSERT INTO comment VALUES (10214,678,4505,'Bob Genisot','re(2): simpler computation','2003-12-04 16:31:08',0,'Thus, by the time the 6th fly passes by, the spider has a probability of 0.5 of being \"hungry\", so the 6th fly will be eaten with a prob. of (0.5)(0.5) = 0.25. The probability the 6th fly will survive is 1 - 0.25 = 0.75.',9845,0);
INSERT INTO comment VALUES (10215,1499,1301,'Charlie','solution','2003-12-04 16:31:53',3,'First figure the distance from the center of one pentagon to the center of the next. To do this, consider the net of arcs connecting the centers as the spherical projection of the edges of a regular icosahedron, a solid having 20 triangular faces. Consider one spherical triangle face. The arc length of one side is the arc length between pentagons. Each corner angle of this triangle is 72 degrees, as five fit together to completely surround the vertex.\r\n\r\nThen we use the law of cosines for spherical triangle, for angles:\r\n\r\ncos 72 = -cos²72 + sin²72 cos S,\r\nwhere S is the side length sought.\r\n\r\nThis solves to S=63.424948... degrees or 1.10714871779... radians, or in this instance 6.6428923... inches.\r\n\r\nIf x is the arc length of one side of each pentagon, then 2x is the arc length between tips of adjacent pentagons, as the latter is subtended by two separate chords each the same length as that subtending the side of the pentagon.\r\n\r\nIf we take a pentagon and divide it into 5 isosceles triangles, and then divide each isosceles triangle into two right triangles, we get the side of one of those right triangles opposite its 36-degree angle as x/2 degrees. The hypotenuse, which runs from the center of the pentagon to a vertex, is (S - 2x) / 2, whether measured in degrees or radians. Algebraically this equals S/2 - x. \r\n\r\nUsing the spherical law of sines, sin(S/2-x)/sin(90) = sin(x/2)/sin(36), using degree measure.\r\n\r\nUsing Excel\'s solver, using the radian equivalent, x comes out to be about 0.298135 radians, which equates to 1.7888... inches given the 6-inch radius of the ball.',NULL,0);
INSERT INTO comment VALUES (10216,1499,3172,'SilverKnight','re: solution','2003-12-04 16:49:07',0,'Charlie,\r\n\r\nWhile it\'s true that \"five fit together to completely surround a vertex\", each triangle is an equilateral triangle and therefore has three 60-degree interior angles.\r\n\r\nIf we project the vertex in question down (towards the center of the ball) until it reaches the plane containing the pentagon in question (centered on that vertex), then indeed the triangles are no longer equilateral and they have one angle of 72-degrees (and two angles of 54-degrees).\r\n\r\nBut now we\'re not talking about 72 degrees from the center of the ball, but rather from the center of that pentagon.\r\n\r\nAm I misunderstanding what you wrote?\r\n\r\n- SK',10215,0);
INSERT INTO comment VALUES (10217,678,3172,'SilverKnight','re(3): simpler computation','2003-12-04 16:55:15',0,'While this is true, you haven\'t demonstrated WHY \"by the time the 6th fly passes by, the spider has a probability of 0.5 of being \'hungry\'\". (Unless you\'re relying on the calculations of previous comment-posters.',10214,0);
INSERT INTO comment VALUES (10218,1508,2899,'Brian Wainscott','re: Passed by','2003-12-04 17:05:40',0,'OK, I get it. Of course there are problems if there are other references to your object, and this won\'t work for the last element in the list (which was specifically excluded, I know), so I don\'t know how often this might be useful in general programming practice, but I\'ll remember it just in case. I\'ve always used doubly linked lists for this, but perhaps I could have used this trick in some cases.\r\n\r\nCertainly I didn\'t think of it -- Good job Rushi, DJ and David. ',10063,0);
INSERT INTO comment VALUES (10219,1508,3172,'SilverKnight','re(2): Passed by','2003-12-04 17:24:27',0,'For what it\'s worth, if I saw a programmer (who worked for me) do this, I would fire him! :-)\r\n\r\nYou\'ve already pointed out several potential problems with doing such things. Setting aside the maintenance issues (the next programmer would be scratching his head wondering what to make of the code and hopefully the comments), it\'d be much better to use container classes which take care of the implementation.\r\n\r\nLet\'s leave this as a \"flooble problem\" and do NOT tell your employer that flooble suggested you do such things! :-)',10218,0);
INSERT INTO comment VALUES (10220,1499,3172,'SilverKnight','re(2): solution','2003-12-04 17:53:38',0,'Ahhhh.... I did misunderstand what you wrote.\r\n\r\nYou are analyzing the arc length of the side of \"one spherical triangular face\"--not, as I suggested, one of 5 equilateral triangles.\r\n\r\nYour calculation looks correct to me.\r\n\r\n- SK',10216,0);
INSERT INTO comment VALUES (10221,1517,4610,'plextor','re(3): Answer is obvious','2003-12-04 18:36:50',0,'Exactly ! DJ understands the concept ...\r\n\r\nSimplicity is king and the answer is what it is :-)',10124,0);
INSERT INTO comment VALUES (10222,625,4646,'nathan','Solution','2003-12-04 22:06:11',3,'Since the distances between the radiuses of all three circles forms an isoceles triangle, with angle of CIRCLE-circle-CIRCLE of 90 degrees, we know that the other two angles are 45 degrees.Now knowing all three angles, and the hypotenuse (200 cm), we can use the \"Sine Law\" to define the space between the center of any of the big circles to the small circle which fits in between the two big circles. The Sine Law is (SinA/a)=(SinB/b). Where the center of the big circle is A, and the center of the little circle is B, their opposing sides are evidently a and b. Subbing values in, we know that Sin45/a=Sin90/200.\r\nThis comes out with an a-value of 141.4213562. To get the RADIUS of the little circle, we must subtract the RADIUS of the big circle, 100cm, which comes out to 41.42135624. Since, however, the question asks for the diameter of the little circle, we must double the radius, which gives a diameter of 82.84271247cm. Quite simple...I\'m only 16 years old.',NULL,0);
INSERT INTO comment VALUES (10223,625,3172,'SilverKnight','re: Solution','2003-12-04 22:39:58',0,'umm....\r\n\r\nmust..... fight... urge... to make... not-so-witty... remark. \r\n\r\nI want KARMA POINTS!!!!',10222,0);
INSERT INTO comment VALUES (10224,1517,4648,'Matthew','Solution Idea','2003-12-04 22:46:15',0,'Maybe he\'s selling those number shaped birthday candles at 10 cents a digit. I think the price is about right for that.',NULL,0);
INSERT INTO comment VALUES (10225,1270,4648,'Matthew','re: & my solution','2003-12-04 23:17:26',0,'I got the same solution.',10081,0);
INSERT INTO comment VALUES (10226,355,4627,'donnmike','','2003-12-04 23:55:44',0,'i\'m no physics expert, but it seems to me that the problem lies in treating the two objects, car and fly, as both points and objects of mass. they can\'t be both. if we are talking about two points colliding then at the instant they collide they will share a constant speed, not passing through any other speeds to get there (fly will never pass through 0 km/h). but if we are talking about two objects of mass then the atomic repulsive forces between the two objects will cause the fly to decelarate before it collides with the car (the fly will never actually collide with the car), so the fly passes through 0 km/h but it does this as it is still approaching the car (talking nano distances here) so there is always some distance between the two which decreases until the point that the fly has reached the same speed as the car.',NULL,0);
INSERT INTO comment VALUES (10227,1517,4652,'Gary','Solution...','2003-12-05 09:49:40',3,'Numerals to be displayed on the house. 1 for 10 cents; 1 and 5 for 20 cents; 1, 1, and 0 for 30 cents.',NULL,0);
INSERT INTO comment VALUES (10228,1509,4653,'elisa','answer i think','2003-12-05 09:51:58',0,'Herb got out on March the 14th 1996',NULL,0);
INSERT INTO comment VALUES (10229,1310,1920,'Brian Smith','re(3): solution','2003-12-05 09:56:49',0,'I have seen a diagram illustrating how to cut a torus (doughnut) into 12 pieces, but the pieces were no where near equal in volume.',10211,0);
INSERT INTO comment VALUES (10230,1310,3623,'jaypee','re(2): possible solution','2003-12-05 10:02:08',0,'I was taking into account the two cuts already made in the cake, dividing it into four equal pieces.Then by making three additional cuts in the cake as I described it would divide the cake into eight pieces.\r\nfor the pieces to be equal the three additional cuts would have to be bisecting the right angles created by the first two cuts. But if you are talking about ONLY three cuts then my thinking is incorrect. ',10207,0);
INSERT INTO comment VALUES (10231,1515,3386,'Victor Zapana','Thoughts that will possibly end with a solution.','2003-12-05 11:20:47',3,'Well.. obviously the area will be 100π square meters, so the circular area that the horse may have is 50π square meters. hmm so the radius is √50 of the circle that\'s half the corral. that reduces to 5√2. and i believe that\'s the answer',NULL,0);
INSERT INTO comment VALUES (10232,1515,2839,'FatBoy','re: Thoughts that will possibly end with a solution.','2003-12-05 11:25:41',0,'Victor,\r\nAren\'t you assuming that the horses grzing area will be a circle. THis can\'t be if he\'s tied to a fence post in a round corral.\r\nIf I\'m misnderstanding what you are saying, then forgive me.',10231,0);
INSERT INTO comment VALUES (10233,1515,1301,'Charlie','solution','2003-12-05 11:25:56',3,'The area to be reached by the horse is the intersection of the contents of two circles. For simplicity of calculations, let\'s consider the radius of the corral to be 1 unit; then we can scale up by a factor of 10 meters later. We need to find the radius of the second circle so that the area of intersection is 1/2 the area of the whole first circle (the corral).\r\n\r\nCall the radius of the second circle r, which is to be found.\r\n\r\nForm a triangle with vertices at the center of the corral, the center of the second circle (the hitching point), and one of the two points of intersection of the two circles. Call the angle at the center of the corral θ and that at the hitching point α. By the law of sines, since we have taken the corral\'s radius to be 1, r/sin θ = 1/sin α, or r=sin θ/sin α. But by the fact that the side of the triangle with length r is a chord of the corral\'s circle, θ = 2 arcsin(r/2). Going back to r=sin θ/sin α, we get α = arcsin(sin θ / r).\r\n\r\nThe area of intersection is the sum of the sectors of the two circles demarcated by the intersection points of the two circles minus the area where they overlap, which is two triangular areas -- the same triangle mentioned in the above paragraph, and the symetrically opposite one. We can take an altitude of one of them as sin α (which is the same as sin θ), and the base as r. As there are two of them, their combined area is r sin θ.\r\n\r\nSo the area of overlap is r²α + θ - r sin θ when angles are measured in radians\r\n\r\nWe want this to come out to pi/2.\r\n\r\nUsing Excel, allocate a cell for r, say A2, then cells for θ (B2), α (C2), the area in D2 and the area divided by pi in E2:\r\nB2: =2*ASIN(A2/2)\r\nC2: =ASIN(SIN(B2)/A2)\r\nD2: =A2*A2*C2+B2-A2*SIN(C2)\r\nE2: =D2/PI()\r\n\r\nThen use solver to make E2 = .5 by changing cell A2.\r\n\r\nThe result is 1.158728483, which, when scaled up by a factor of 10 meters, is 11.58728483\r\n\r\nThe result is checked by using a simulation with this value:\r\nDO\r\n x = 2 * RND(1) - 1\r\n y = 2 * RND(1) - 1\r\n IF x * x + y * y < 1 THEN\r\n ct1 = ct1 + 1\r\n IF (x - 1) * (x - 1) + y * y < 1.158728 * 1.158728 THEN ct2 = ct2 + 1\r\n PRINT ct2 / ct1\r\n END IF\r\nLOOP\r\n\r\nand the ratio does indeed hover around .5.\r\n',NULL,0);
INSERT INTO comment VALUES (10234,1515,4507,'Penny','Solution','2003-12-05 11:26:11',3,'This problem has been around forever, sir. This website seems to be experiencing originality deficits. The ratio of the length of the horse\'s rope to the radius of the corral is 1.15872847. \r\n\r\nThe horse\'s rope should be 11.5872847 meters long.\r\n\r\nAnyone requiring an explanation, is probably someone who, before he starts his car in the morning, first finds a large rock and then re-invents the wheel. But here is the explanation from the Dr. Math website:\r\n\r\nDraw a circle with radius r (the corral). \r\n\r\nNow take a point C on the circumference and with a slightly larger radius R draw an arc of a circle to cut the first circle in points A and B. Join AC and BC. \r\n\r\nLet O be the centre of the first circle of radius r. Let angle OCA = x (radians). This will also be equal to angle OCB. \r\n\r\nThe area we require is made up of a sector of a circle radius R with angle 2x at the centre, C, of this circle, plus two small segments of the first circle of radius r cut off by the chords AC and BC. \r\n\r\nThe area of the sector of circle R is (1/2)R^2*2x = R^2*x \r\n\r\nThe area of the two segments \r\n\r\n= 2[(1/2)r^2(pi-2x) - (1/2)r^2sin(pi-2x)]\r\n= r^2[pi - 2x - sin(2x)] \r\n\r\nWe also have R = 2rcos(x) so R^2*x = 4r^2*x*cos^2(x) \r\nWe add the two elements of area and equate to (1/2)pi*r^2 \r\n\r\n4r^2*x*cos^2(x) + r^2[pi-2x-sin(2x)] = (1/2)pi*r^2 divide out r^2 \r\n4x*cos^2(x) + pi - 2x - sin(2x) = (1/2)pi \r\n\r\n4x*cos^2(x) + (1/2)pi - 2x - sin(2x) = 0 \r\n\r\nWe must solve this for x and we can then find R/r from R/r = 2cos(x)\r\n \r\nNewton-Raphson is a suitable method for solving this equation, using a starting value for x at about 0.7 radians. \r\n\r\nThe solution I get is x = 0.95284786466 and from this cos(x) = 0.579364236509 \r\n\r\nand so finally R/r = 2cos(x) = 1.15872847\r\n\n\nEdited on December 5, 2003, 11:56 am',NULL,0);
INSERT INTO comment VALUES (10235,1515,3224,'Lee','finding a solution the easy way.','2003-12-05 12:52:18',0,'Penny\'s method was slick, but I managed to find an even easier way to solve the problem than searching the internet (or clicking \'favorites\' ->\'Dr Math) finding the relevant problem - copy-pasting into flooble and tacking on some snide barb - \'cos that would\'ve taken ages!\r\nI just copy-pasted Penny\'s.\r\n\r\nThe horse\'s rope should be 11.5872847 meters long. \r\n\r\nAnyone requiring an explanation, is probably someone who, before he starts his car in the morning, first finds a large rock and then re-invents the wheel. But here is the explanation from the Dr. Math website: \r\n\r\nDraw a circle with radius r (the corral). \r\n\r\nNow take a point C on the circumference and with a slightly larger radius R draw an arc of a circle to cut the first circle in points A and B. Join AC and BC. \r\n\r\nLet O be the centre of the first circle of radius r. Let angle OCA = x (radians). This will also be equal to angle OCB. \r\n\r\nThe area we require is made up of a sector of a circle radius R with angle 2x at the centre, C, of this circle, plus two small segments of the first circle of radius r cut off by the chords AC and BC. \r\n\r\nThe area of the sector of circle R is (1/2)R^2*2x = R^2*x \r\n\r\nThe area of the two segments \r\n\r\n= 2[(1/2)r^2(pi-2x) - (1/2)r^2sin(pi-2x)] \r\n= r^2[pi - 2x - sin(2x)] \r\n\r\nWe also have R = 2rcos(x) so R^2*x = 4r^2*x*cos^2(x) \r\nWe add the two elements of area and equate to (1/2)pi*r^2 \r\n\r\n4r^2*x*cos^2(x) + r^2[pi-2x-sin(2x)] = (1/2)pi*r^2 divide out r^2 \r\n4x*cos^2(x) + pi - 2x - sin(2x) = (1/2)pi \r\n\r\n4x*cos^2(x) + (1/2)pi - 2x - sin(2x) = 0 \r\n\r\nWe must solve this for x and we can then find R/r from R/r = 2cos(x) \r\n\r\nNewton-Raphson is a suitable method for solving this equation, using a starting value for x at about 0.7 radians. \r\n\r\nThe solution I get is x = 0.95284786466 and from this cos(x) = 0.579364236509 \r\n\r\nand so finally R/r = 2cos(x) = 1.15872847 \r\n',NULL,0);
INSERT INTO comment VALUES (10236,1517,1575,'DJ','re: Solution Idea','2003-12-05 13:05:08',0,'Maybe, but then 110 would only cost 27 cents (with the 10% senior citizens\' discount, of course)..',10224,0);
INSERT INTO comment VALUES (10237,1515,4507,'Penny','re: finding a solution the easy way.','2003-12-05 13:29:25',0,'LMAO !!!!!!!!!!!!!!!!!!!!!!!!!!!!',10235,0);
INSERT INTO comment VALUES (10238,1311,3386,'Victor Zapana','really really stumped...','2003-12-05 17:28:11',0,'... I am.',NULL,0);
INSERT INTO comment VALUES (10239,1311,3558,'Tristan','hmm...','2003-12-05 18:25:35',1,'If there\'s 270 characters in both the code and the message, and it\'s not a simple substitution cipher, then exactly what is it?',NULL,0);
INSERT INTO comment VALUES (10240,1508,2899,'Brian Wainscott','re(3): Passed by (off topic....)','2003-12-05 19:16:10',0,'Container classes? You lucky dog.....\r\n\r\nI get to write in Python on rare occasions, and get to do some real work in C, but 95-98% of my work is in (gasp) FORTRAN. Not even Fortran90, but the 77 variety!',10219,0);
INSERT INTO comment VALUES (10241,1311,2716,'Federico Kereki','re: hmm...','2003-12-05 20:40:37',1,'It can either be a complex (i.e., not \"simple\") substitution cipher, or a transposition cipher... or then again, it may be anything else! ;-)',10239,0);
INSERT INTO comment VALUES (10242,1311,3386,'Victor Zapana','re(2): hmm...','2003-12-05 21:20:44',0,'hmm also mebe some pairs of letters may symbolize a letter , coz it seys that there might need to be extra characters added to the end to make 270.',10241,0);
INSERT INTO comment VALUES (10243,1311,4507,'Penny','Solution?','2003-12-05 22:24:35',3,'DJ wrote: \"Both the original plain text message and the encrypted message contain 270 characters...You might be able to guess the full text after determining only the first three words.\" \r\n \r\nThose were huge hints. Very few passages in English literature are uniquely identified by their first three words, and even fewer of those contain 270 characters. Allthough I haven\'t yet figured out the cipher, I definitely plan to...\r\n\r\nDJ miscounted. The passage which I suspect is the one encoded, when deciphered, actually contains 269 characters:\r\n \r\n\"We, the people of the United States, in order to form a more perfect Union, establish justice, insure domestic tranquility, provide for the common defense, promote the general welfare, and secure the blessings of liberty to ourselves and our posterity, do ordain and establish this Constitution for the United States of America.\" \r\n',NULL,0);
INSERT INTO comment VALUES (10244,1311,3372,'Sam','Some Thoughts','2003-12-05 22:36:40',0,'It\'s not a simple substitution, but that obviously doesn\'t mean that there can\'t be a system for substituting. Letters could be changed based on their position in each five letter word, for instance. Moving position 1 by 1 up or down, 2 by 2 up or down and so on generates nothing, however. Might still be a possible path to follow, though.\r\n\r\nThere are either the same or less numbers in the encrypted version. This means that we won\'t be grouping chunks of encryption to make single letters. Specifically, the five letter \"words\" aren\'t going to be letters.\r\n\r\nThe title could just be a title, but my guess is that it\'s the puzzle key (it is just too perfectly five groups of five). I tried setting up a substitution like this:\r\n\r\nKey : PGKKW XIMAF TNEGA NFYGZ TMUIV\r\nTxt : WATAE TXLAL PDIBI MGTBU YBTMM\r\n\r\nBut couldn\'t get anything usful out of it.\r\n\r\nThen I randomly tried\r\n\r\nKey : PPPPP GGGGG KKKKK KKKKK WWWWW\r\nTxt : WATAE TXLAL PDIBI MGTBU YBTMM\r\n\r\nand got\r\n\r\n___ : GODOA CDEFE EGBIB BDIIJ BUCJJ\r\n\r\nWhich is still meaningless, but now contains a surprising number of vowels, far more than would be expected were it random. This might mean that I\'m heading in the right direction, but quite possibly it\'s just chance. Will have to see if the trend continues with the rest of the text.\r\n\r\nLook forward to seeing if anyone else is coming up with anything.\r\n\r\nPS- How do I get a monospaced font? Using <font> tags doesn\'t seem to work.',NULL,0);
INSERT INTO comment VALUES (10245,1311,4507,'Penny','re: Solution?','2003-12-05 22:46:57',0,'We can figure out the passage from the first three words? Then it must begin in one of the following ways:\r\n\r\n\"We the people..\" (My candidiate, since it is 269 characters - DJ miscounted when he said 270)\r\n\"In the beginning...\"\r\n\"Call me Ishmael...\"\r\n\"On your mark...\"\r\n\"Space, the final...\"\r\n\"Long, long ago...\"\r\n\"I pledge allegiance...\"\r\n\"Ashes to Ashes...\"\r\n\"Four score and...\"\r\n\"One small step...\"\r\n\"Good Morning Vietnam!\"',10243,0);
INSERT INTO comment VALUES (10246,1311,1301,'Charlie','re: Some Thoughts','2003-12-06 00:44:10',0,'How do I get a monospaced font? Using <font> tags doesn\'t seem to work. \r\n\r\nUse <tt> and </tt>.\r\n\r\nOnce reaching a certain level in flooble, you can start using <pre>. I don\'t recall which level.\r\n\r\nWith <tt>:\r\n\r\nKey : PPPPP GGGGG KKKKK KKKKK WWWWW \r\nTxt : WATAE TXLAL PDIBI MGTBU YBTMM \r\n',10244,0);
INSERT INTO comment VALUES (10247,1382,4627,'donnmike','not sufficient information','2003-12-06 02:22:32',0,'there is not sufficient information given in the problem to solve it. we are not told that we can take back pieces of the chain from the person, and because the chain pieces have monetary value we must assume that we cannot take the pieces back. also, it should read \"pay this person the equivalent of one each day\" because the way it is currently worded would mean one link.',NULL,0);
INSERT INTO comment VALUES (10248,1311,3372,'Sam','re: Some Thoughts','2003-12-06 09:29:54',0,'(Thanks for the tip, Charlie)\r\n\r\nWell, I got no further with my attempt. It seems that the high number of vowels was just a coincidence. I feel that this shouldn\'t be too difficult, yet I\'m very stuck. I keep finding new ways of generating long strings of gibberish.\r\n\r\nAny tips, DJ? Was I heading in the right direction with the title? I might have to throw in the towel soon without a little push... :)\n\nEdited on December 6, 2003, 9:31 am',10244,0);
INSERT INTO comment VALUES (10249,1310,3623,'jaypee','re(3): possible solution','2003-12-06 09:55:10',0,'If you\'re using only three cuts in the cake the greatest number of pieces that can be created with equal volume would be 6. One cut would be through the center of the cake, forming a diameter. The other two cuts would be made perpendicular to the first cut, creating two chords to the circle. One chord would be on one side of the center at a distance \"x\" from the center and the other chord would be on the other side at a distance \"x\" from the center. This would create two equal chords. The question is what is distance \"x\" so that the three cuts create six pieces of equal volume? That I haven\'t determined yet.',10230,0);
INSERT INTO comment VALUES (10250,698,4670,'Eduardo Guerrero','Easy!','2003-12-06 11:00:14',3,'1 and 1 does the job!',NULL,0);
INSERT INTO comment VALUES (10251,1310,3623,'jaypee','another possible solution','2003-12-06 11:06:15',1,'Another way of cutting the cake is as follows:\r\nSince a cake has height make one cut cutting the height in half. Then make the other two cuts as described in the second paragraph of the posted problem. This will divide up the cake into 8 eqaual pieces, though the bottom pieces will not have a lot of icing on them.',NULL,0);
INSERT INTO comment VALUES (10252,698,2716,'Federico Kereki','The second solution?','2003-12-06 11:10:42',3,'Apart from all trivial N,N solutions, 6 and 10 also works out. \r\nPS, you don\'t have to have any knowledge other than SAS postulate, 30-60-90 triangle, and how to make 2 constructions. you don\'t fancy trig stuff.\r\n\r\nEdited on December 18, 2003, 5:28 pm\n\nEdited on December 18, 2003, 5:30 pm',NULL,0);
INSERT INTO comment VALUES (10598,1509,4858,'Anne','solution','2003-12-18 18:33:26',3,'never because bythe time it\'s the end of Feb. Herb will be dead or he waits till a animal or human will pick him up.',NULL,0);
INSERT INTO comment VALUES (10599,1475,4858,'Anne','I know it','2003-12-18 18:39:15',3,'he used aship to cross the ocean or something',NULL,0);
INSERT INTO comment VALUES (10600,1509,3172,'SilverKnight','re: solution','2003-12-18 18:58:52',0,'lol... you should write for Hallmark!',10598,0);
INSERT INTO comment VALUES (10601,1545,2716,'Federico Kereki','re: Racing around','2003-12-18 21:12:07',3,'This is the best solution, because it works with lists any size. The order is O(N), and you can simplify the code to\r\n\r\nlet P = first node; if P=NULL, exit\r\nlet Q = NEXT(P); if Q=NULL, exit\r\nloop\r\n P = NEXT(P)\r\n Q = NEXT(Q); if Q=NULL, exit\r\n Q = NEXT(Q); if Q=NULL, exit\r\nuntil P=Q \r\n\r\ndoing away with R and a test. It should be understood that if the code exits from the middle, it means that the list actually ends; if the code finishes at the bottom, a loop was found.',10591,0);
INSERT INTO comment VALUES (10602,1547,4859,'nick','nice one','2003-12-18 21:52:33',0,'has to be \"slinky\" \r\nlol it would be funny if thats it...iv never sloved a riddle in my life...probably because iv never tried one',NULL,0);
INSERT INTO comment VALUES (10603,1545,1301,'Charlie','re(2): Racing around','2003-12-18 22:26:40',4,'\"This is the best solution, because it works with lists any size.\"\r\n\r\nIs there a list size that my algorithm will not handle?',10601,0);
INSERT INTO comment VALUES (10604,1543,1575,'DJ','Solution','2003-12-18 22:43:01',3,'The problem is that we are assuming that \"statement\" S is, indeed, a statement (in fact it is, but only because the antecedent of the statement is already true; \"God exists\" was a poor choice here).\r\n\r\nOn the other hand:\r\n T: If statement T is true, then 1 + 1 = 3.\r\nIs not a statement, because it can be neither true nor false.\r\nThe next line, \"Logically, S must be true or false,\" is not necessarily true for every statement of this form.\r\n\r\nA more appropriate title for this riddle may be \"Proof of Anything That is Already True.\"\r\n\r\nFinally, a statement is not an arrangment of words, but a logical idea. So, something like:\r\n U: Statement U contains five words.\r\nIs meaningless, because\r\n U: There are five words in statement U.\r\nIs the same statement, although it is worded differently (they are the same statement, but not the same sentence).',NULL,0);
INSERT INTO comment VALUES (10605,1543,3558,'Tristan','re(2): Partial disproof','2003-12-18 22:51:38',0,'I understood well the note Sam left at the end, but I thougtht that maybe the antecedent could be false as well as the statement if the antecedent is sometimes true. I guess your right; that\'s not how it works. I think that it is how it works, however, when the statement is not in \"if...then...\" form, but in the \"when..., ...\" form. Of course, I may be wrong here too.',10577,0);
INSERT INTO comment VALUES (10606,723,4850,'Rachel','re(2): a solution?','2003-12-19 01:26:06',0,'Oh. opps. Yes. ;)',10587,0);
INSERT INTO comment VALUES (10607,723,4830,'Jils','re: the simplified answer','2003-12-19 08:43:52',0,'Your answer comes to 6.22 - I tried drawing this and it just isn\'t big enough... 6.8 however works.',10597,0);
INSERT INTO comment VALUES (10608,1547,4830,'Jils','re: nice one','2003-12-19 09:09:05',0,'Funny enough, I was thinking it might be spring.. bed springs helping you get out of bed in the morning ...',10602,0);
INSERT INTO comment VALUES (10609,1336,4064,'rerun141','the possible combos','2003-12-19 10:47:38',1,'the seven possible values of p,q, and r are\r\n16, 50, 33\r\n22, 18, 59\r\n34, 10, 67\r\n44, 46, 64\r\n48, 72, 15\r\n98, 28, 27\r\n98, 32, 21\r\n\r\nfound by the basic program\r\ncls\r\nfor p = 10 to 99\r\nfor q = 10 to 99\r\nfor r = 10 to 99\r\ns = p ^ 3 + q ^ 3 + r ^ 3\r\nt = p * 10000 + q * 100 + r\r\nif s = t then print p, q, r\r\nnext r\r\nnext q\r\nnext p\r\nend ',NULL,0);
INSERT INTO comment VALUES (10610,1336,4064,'rerun141','SOLUTION','2003-12-19 11:05:16',3,'see my previous post for p, q, and r possibilities\r\nsince p is 2m tiwce, 2m=98 aand m = 49\r\nn2 = 9 so n must be 59\r\na/2 must be 22, a = 44\r\nc/4 must be 18, c = 72\r\nb then must be 48 and 2(h+j)/4/44=15\r\n\r\nto recap the lines of the table\r\nline 1 = 44, 46, 64\r\nline 2 = 22, 18, 59\r\nline 3 = 48, 72, 15\r\nline 4 = 16, 50, 33\r\nline 5 = 98, 28, 27\r\nline 6 = 98, 32, 21\r\nunused possibility = 34, 10, 67\r\nthe table:\r\n4 4 7 2\r\n8 3 7 6\r\n4 1 7 5\r\n6 4 4 9\r\n\r\n\n\nEdited on December 19, 2003, 11:09 am',NULL,0);
INSERT INTO comment VALUES (10611,1336,3172,'SilverKnight','re: SOLUTION','2003-12-19 11:14:32',0,'... almost like cheating :-)\r\n\r\nbut clever use of the repeated number in list (98), and kudos for solving the problem!',10610,0);
INSERT INTO comment VALUES (10612,1545,2716,'Federico Kereki','re(3): Racing around','2003-12-19 11:50:31',0,'Right you are; sorry! I should have added \"...and it seems to be the speediest possible.\" Now, a question of mine: How did you figure it took me eight minutes?',10759,0);
INSERT INTO comment VALUES (10762,1440,4197,'luminita','another solution','2003-12-28 14:56:43',3,'both solutions are correct (Zaphod and Larry).\r\nNow I give the 3-rd one which is based on formula of the sum of the first n squared numbers:\r\n1² + 2² +....+ n² = n(n+1)(2n+1)/6\r\nThe sequence may be expressed as:\r\n(1² + 2² + ... + x² + (x+1)² + ... + 2x²) -\r\n2(1² + 2² + ... + x²) =\r\n2x(2x+1)(4x+1)/6 - 2x(x+1)(2x+1)/6 =\r\nx²(2x+1)\r\nQED\r\nThe last one is elementary:\r\nx²(2x+1) = x²(x+1)-x^4.\r\n',NULL,0);
INSERT INTO comment VALUES (10763,726,4507,'Penny','Solution (No program used - not even my faulty calculator)','2003-12-28 15:23:53',3,'NOSIER + ASTRAL = 725613\r\nT=1 N=2 S=3 A=4 L=5 E=6 I=7 R=8 O=9\r\n293768 + 431845 = 725613\r\n\r\n725613=INLETS\r\n\r\nExplanation:\r\n\r\nL+R results in 3. Nonzero distinct possibilities for (L,R) are (1,2), (2,1), (4,9), (9,4), (5,8), (8,5), (7,6), (6,7).\r\n\r\nSuppose (L,R)=(5,8)\r\n100000(A+N) + 10000(O+S) + 1000(S+T) + 100(I+8) + 10(A+E) + 13 = 725613\r\nA+E=10\r\nThe possibilities for (A,E) are:\r\n(1,9),(3,7),(4,6),(6,4)\r\n \r\nCase 1: (A,E)=(1,9). Then I=7.\r\n100000(1+N) + 10000(O+S) + 1000(S+T) + 1613 = 725613\r\nS+T=14 This does not allow any values of (S,T) different than 1,5,8,9\r\nSo Case 1 is ruled out.\r\n \r\nCase 2: (A,E)=(3,7)\r\n100000(3+N) + 10000(O+S) + 1000(S+T) + 100(I+8) + 113 = 725613\r\nthen I=7, which is wrong since E=7\r\nSo Case 2 is wrong.\r\n \r\nCase 3: (AE)=(4,6) (Then again I=7)\r\n100000(4+N) + 10000(O+S) + 1000(S+T) + 1613 = 725613\r\nThen (S,T)=(1,3),(3,1)\r\n\r\nCase 3a: (S,T)=(1,3)\r\n100000(4+N) + 10000(O+1) + 5613 = 725613\r\nO=1, which is disallowed since S=1\r\nSo Case 3a is ruled out.\r\n \r\nCase 3b: (S,T)=(3,1) (Then O=9)\r\n100000(4+N) + 125613 = 725613\r\nN=2\r\nThis case works.\r\n\n\nEdited on December 28, 2003, 3:25 pm',NULL,0);
INSERT INTO comment VALUES (10764,726,4507,'Penny','re(3): Solution','2003-12-28 15:34:41',0,'e.g.: \"Now, a question of mine: How did you figure it took me eight minutes?\"\r\n \r\nCharlie must have known the time the problem was posted. It must have been around 9:26. He subtracted that from 9:34, the time you posted your solution. \r\n',10761,0);
INSERT INTO comment VALUES (10765,726,1301,'Charlie','re(4): Solution','2003-12-28 16:01:05',0,'Yes, that\'s how.',10764,0);
INSERT INTO comment VALUES (10766,1240,4970,'Jack the Reaper','','2003-12-28 16:22:21',0,'Standing on the shoulders of you giants, I figured out the solution. The words DJ is looking for aren\'t gather, slither, smother, bother, lather, and feather; they are gathered, slithered, smothered, bothered, lathered, and feathered. Each of the combinations prefix \"thered.\" The answer, therefore, is Eric, as in Eric the Red.',NULL,0);
INSERT INTO comment VALUES (10767,726,1626,'Gamer','re: Solution (No program used - not even my faulty calculator)','2003-12-28 17:17:32',0,'You are using trial and error to solve this Penny, and you only listed about 1 possibility for L+R=3. So you basically just did the SAME thing as a program, only lots slower and less efficiently.',10763,0);
INSERT INTO comment VALUES (10768,726,1575,'DJ','','2003-12-28 17:39:42',3,'First, since there are no zeroes and all digits are distinct, O + S cannot be 2. Thus, O + S is either 11 or 12, but there is a carry digit in either case. So, N + A = 6.\r\n\r\nSimilarly, E + A cannot be 1; either E + A = 10 or E + A = 11.\r\n\r\nSuppose E + A = 11. Then, R + L = 3 (with no carry digit), so R and L are 1 and 2 in some order. Also, I + R = 5 (there is a carried 1 into that column, and I cannot be big enough to make the column total 15). Additionally, if E + A = 11, and N + A = 6, then N + 5 = E. So, N cannot be 5 or 6 (that would make E 10 or 11). Also, N is not 1 or 2 (R and L are). If N = 3, then A = 3 (N + A = 6), and if N = 4, A = 2, but again either L or R is 2. Therefore, the assumption that E + A = 11 must be false.\r\n\r\nSo, E + A = 10, and there is a carry digit from the ones column, so R + L = 13.\r\n\r\nSince N + A = 6 and E + A = 10, N + 4 = E. So, N cannot be 6 (E would be 10). If N = 3, then A = 3, which is not possible; N (or A) cannot be 3). If N = 1, then A = 5, but if N = 1, E = 5, which is also not possible.\r\nSo, there are three valid possibilities so far for N, A, and E:\r\nN = 2, A = 4, E = 6;\r\nN = 4, A = 2, E = 8; or\r\nN = 5, A = 1, E = 9.\r\n\r\nSince R + L = 13, R and L must be (in some order) 4 and 9, 5 and 8, or 6 and 7. However, each of the possibilities for N, A, E includes a 4 or a 9, so R and L must be 5 and 8 or 6 and 7.\r\n\r\nTherefore, the smallest value R can take is 5, but since there is a carry digit into the I + R = 6 column, and I cannot be zero, I + R must equal 15 (not 5). R cannot be 5 (I would have to be 10).\r\n\r\nSince R + I = 15 and R + L = 13, L + 2 = I.\r\nTherefore, there are three sets of possible values for R, L, and I:\r\nR = 6, L = 7, I = 9;\r\nR = 7, L = 6, I = 8; or\r\nR = 8, L = 5, I = 7.\r\n\r\nComparing the sets of values for N, A, E with the possibilities for R, L, I, we can pair them up.\r\nIf E = 6, R or L cannot be six, so the first set for N, A, E is only possible with the third group of R, L, I.\r\nSimilarly, if E = 8, neither I nor R can be 8, so the second N, A, E is only possible with the first R, L, I.\r\nFinally, if N = 5, L cannot be 5, and if E = 9, I is not 9, so the third N, A, E matches the second R, L, I.\r\n\r\nThere are three possibilities, namely:\r\nN = 2, A = 4, E = 6, R = 8, L = 5, I = 7;\r\nN = 4, A = 2, E = 8, R = 6, L = 7. I = 9; or\r\nN = 5, A = 1, E = 9, R = 7, L = 6, I = 8.\r\n\r\nThere are three variables left to look at (S, T, O), and two possibilities for the sums of the remaining columns. Either S + T = 4, O + S = 12, and T + 8 = O, or S + T = 14, O + S = 11, and O + 3 = T.\r\n\r\nIf, in the first case, T + 8 = O, the only possible values are T = 1 and O = 9, with S = 3.\r\nWe need to look at the above three cases for the other six letters to see if there is one in which those values have not yet been assigned, and we find that the first set fits.\r\nSo, one possible set of values is:\r\nN = 2, A = 4, E = 6, R = 8, L = 5, I = 7, T = 1, O = 9, S = 3.\r\nGiven these values, 725613 becomes INLETS, which is indeed a word.\r\n\r\nJust to be thorough, check the second case above, wherein S + T = 14, O + S = 11, and O + 3 = T. The greatest O can be is 6, but since 6 is already represented in each of the above possibilities for the other six letters, O can\'t be six. If O is 5, T is 8, but all of the choices above have a letter for 5 or 8 already as well. Similarly, 4 and 7, 3 and 6, or 2 and 5 are not possible either. If O = 1 and T = 4, S would have to be 10 (to make O + S = 11); so we see that there are no remaining possibilities for the value of O.\r\n\r\nThus, the unique solution is as follows:\r\nT = 1\r\nN = 2\r\nS = 3\r\nA = 4\r\nL = 5\r\nE = 6\r\nI = 7\r\nR = 8\r\nO = 9\r\nand the word in question is INLETS.',NULL,0);
INSERT INTO comment VALUES (10769,726,693,'Jun','Solution','2003-12-28 18:45:50',0,'INLETS\r\n\r\nI just hope that the solution provides a good explanation cos I solved this by trial and error, though I took me like 5 minutes... Guess I got lucky.',NULL,0);
INSERT INTO comment VALUES (10770,1491,1626,'Gamer','re(3): solution is wrong','2003-12-28 20:02:41',0,'No, because then anythink the bus driver was wearing wouldn\'t count, or any of his organs; they are things too. He couldn\'t take his backbone in. You have to interperet it to mean nothing 6 on the dimensions. Think of it subjectively; if something is in tricks you can pull this; if it\'s not you can\'t.',10735,0);
INSERT INTO comment VALUES (10771,726,4670,'e.g.','re(5): Solution','2003-12-28 20:05:57',0,'OK, so that shows that Charlie is a special kind of user, right? That almost makes me feel like the hero in that old TV show, where the alien invaders could be recognized because they couldn\'t move their little fingers or something like that! :-)',10765,0);
INSERT INTO comment VALUES (10772,726,4507,'Penny','re(2): Solution (No program used - not even my faulty calculator)','2003-12-28 20:19:39',0,'Gamer: \"You are using trial and error to solve this Penny, and you only listed about 1 possibility for L+R=3. So you basically just did the SAME thing as a program, only lots slower and less efficiently.\"\r\n \r\nDon\'t be silly, Gamer. I copy/pasted my solution from the Dr. Math website.\r\n\r\n(Just kidding)\r\n \r\nSeriously though, the use of computer programs to solve real-life problems makes sense, but their use to solve made-up problems does seem a little goofy to me. It\'s like heaping up a big barrier of rocks, and then going to the hardware store and bringing back a long ladder to get over the rocks. Pretty silly. But that\'s just my opinion. I could be wrong. \r\n \r\n\n\nEdited on December 28, 2003, 9:47 pm',10767,0);
INSERT INTO comment VALUES (10773,726,1626,'Gamer','re(3): Solution (No program used - not even my faulty calculator)','2003-12-28 22:13:03',0,'But not if we want experience climbing ladders. :) We don\'t even need to cross that barrier of rocks if it would be boring or too hard to do anyway.',10772,0);
INSERT INTO comment VALUES (10774,726,1575,'DJ','re(4): Solution (No program used - not even my faulty calculator)','2003-12-28 22:16:08',0,'Or, you could go heap up a big pile of rocks, and say, \"I don\'t feel like using the ladder; I\'ll just crawl over...\"',10773,0);
INSERT INTO comment VALUES (10775,1491,4627,'donnmike','re(4): solution is wrong','2003-12-29 02:38:47',0,'What does the bus driver\'s clothes have to do with anything? We are talking about what this kid cannot bring with him onto the bus. And because his organs are a part of him, he is not taking them with him, they ARE him. And the bus driver did not explicitly state he couldn\'t take anything of length dimensions greater than 6\'. Besides, length, height, and width aren\'t specific measurements and it all depends on how something is oriented. I could orient the diagonal of a box so that it could be considered the length.\r\n\r\nAnd if we are to assume that the rule given by the bus driver does not have to be followed, and that the kid only gets away with bringing the rod onto the bus because he is concealing it, then we could also assume that the bus driver realizes that he could have something longer than 6\' in the box and inspect it.\r\n\r\nit\'s just a bad problem, even for a trick.',10770,0);
INSERT INTO comment VALUES (10776,543,4978,'susan','i got it i got it','2003-12-29 02:54:17',3,'eggs',NULL,0);
INSERT INTO comment VALUES (10777,1334,2444,'dr pyser','re(2): is 4 not ok ??','2003-12-29 05:18:18',0,'i\'m a n00b, so i dunno if the solution\'s here or not, but afaik you arrange three touching pennies in a triangle and then put the fourth on top so that it covers all three right?',10746,0);
INSERT INTO comment VALUES (10778,1361,1301,'Charlie','solution--computer used','2003-12-29 10:42:54',3,'By rule 1, a 7 has to be over a 5 or a 5 over a 3.\r\n\r\nThe pairs satisfying rule 3 could be 2,4 or 7,9.\r\n\r\nBy rule 4, either 8 is above 4 or 5 above 1.\r\n\r\nThe pairs satisfying rule 5 are 1,2 or 8,9.\r\n\r\nThe following program looks for such, as well as most of rule 2:\r\n\r\nDECLARE SUB permute (a$)\r\nCLS\r\ns$ = \"123456789\"\r\nFOR i = 1 TO 362880\r\n bad = 1\r\n ix = INSTR(s$, \"7\")\r\n IF ix < 7 THEN IF MID$(s$, ix + 3, 1) = \\\"5\\\" THEN bad = 0\r\n ix = INSTR(s$, \\\"5\\\")\r\n IF ix < 7 THEN IF MID$(s$, ix + 3, 1) = \\\"3\\\" THEN bad = 0\r\n IF bad THEN GOTO notThis\r\n\r\n bad = 1\r\n ix = INSTR(s$, \\\"8\\\")\r\n IF ix < 7 THEN IF MID$(s$, ix + 3, 1) = \\\"4\\\" THEN bad = 0\r\n ix = INSTR(s$, \\\"5\\\")\r\n IF ix < 7 THEN IF MID$(s$, ix + 3, 1) = \\\"1\\\" THEN bad = 0\r\n IF bad THEN GOTO notThis\r\n\r\n bad = 1\r\n ix = INSTR(s$, \\\"2\\\")\r\n IF ix MOD 3 THEN IF MID$(s$, ix + 1, 1) = \\\"4\\\" THEN bad = 0\r\n ix = INSTR(s$, \\\"7\\\")\r\n IF ix MOD 3 THEN IF MID$(s$, ix + 1, 1) = \\\"9\\\" THEN bad = 0\r\n IF bad THEN GOTO notThis\r\n\r\n bad = 1\r\n ix = INSTR(s$, \\\"1\\\")\r\n IF ix MOD 3 THEN IF MID$(s$, ix + 1, 1) = \\\"2\\\" THEN bad = 0\r\n ix = INSTR(s$, \\\"8\\\")\r\n IF ix MOD 3 THEN IF MID$(s$, ix + 1, 1) = \\\"9\\\" THEN bad = 0\r\n IF bad THEN GOTO notThis\r\n\r\nsqCt = 0\r\n FOR col = 1 TO 3\r\n t(col) = 0\r\n FOR row = 1 TO 3\r\n t(col) = t(col) + VAL(MID$(s$, (row - 1) * 3 + col, 1))\r\n NEXT\r\n sqrt = INT(SQR(t(col)) + .5)\r\n IF sqrt * sqrt = t(col) THEN sqCt = sqCt + 1: sq(sqCt) = t(col)\r\n NEXT\r\n IF sqCt < 2 THEN GOTO notThis\r\n IF sq(1) <> sq(2) THEN GOTO notThis\r\n p1 = VAL(MID$(s$, 1, 1)) + VAL(MID$(s$, 9, 1))\r\n p2 = VAL(MID$(s$, 3, 1)) + VAL(MID$(s$, 7, 1))\r\n IF p1 <> p2 THEN GOTO notThis\r\n\r\n\r\n PRINT MID$(s$, 1, 3)\r\n PRINT MID$(s$, 4, 3)\r\n PRINT MID$(s$, 7, 3)\r\n PRINT\r\nnotThis:\r\n permute s$\r\nNEXT\r\n\r\nSUB permute (a$)\r\nDEFINT A-Z\r\n x$ = \"\"\r\n FOR i = LEN(a$) TO 1 STEP -1\r\n l$ = x$\r\n x$ = MID$(a$, i, 1)\r\n IF x$ < l$ THEN EXIT FOR\r\n NEXT\r\n\r\n IF i = 0 THEN\r\n FOR j = 1 TO LEN(a$) \\ 2\r\n x$ = MID$(a$, j, 1)\r\n MID$(a$, j, 1) = MID$(a$, LEN(a$) - j + 1, 1)\r\n MID$(a$, LEN(a$) - j + 1, 1) = x$\r\n NEXT\r\n ELSE\r\n FOR j = LEN(a$) TO i + 1 STEP -1\r\n IF MID$(a$, j, 1) > x$ THEN EXIT FOR\r\n NEXT\r\n MID$(a$, i, 1) = MID$(a$, j, 1)\r\n MID$(a$, j, 1) = x$\r\n FOR j = 1 TO (LEN(a$) - i) \\ 2\r\n x$ = MID$(a$, i + j, 1)\r\n MID$(a$, i + j, 1) = MID$(a$, LEN(a$) - j + 1, 1)\r\n MID$(a$, LEN(a$) - j + 1, 1) = x$\r\n NEXT\r\n END IF\r\nEND SUB\r\n\r\nand finds\r\n\r\n789\r\n524\r\n163\r\n\r\n897\r\n635\r\n241\r\n\r\nThe first does not satisfy the perfect square condition of the sums of opposite corners, so the latter is the solution.\r\n',NULL,0);
INSERT INTO comment VALUES (10779,1361,3224,'Lee','solution (no computer used)','2003-12-29 13:00:26',3,'Some things should be easily deducible.\r\n\r\n1) There is a 5 above a 3 OR a 7 above a 5 (herein denoted by [5/3] OR [7/5])\r\n2) Opposite corners total 9\r\nThe column totals are 13, 16, 16 (not necessarily in that order)\r\n3) There is a 2 left of a 4 OR 7 left of a 9 (herein denoted by (2,4) OR (7,9))\r\n4) There is [5/1] OR [8/4]\r\n5) There is (1,2) OR (8,9)\r\n\r\n(Restraining my amateur notation for the first part)\r\nConsider the number 5 in a column totaling 16, \r\n\r\nIf the 5 is above the 3 then the remaining number in that column must be an 8. Since the 8 can’t then be above a 4 then 5 must be above 1 (by rule 4) which is a contradiction.\r\n\r\nIf the 7 is above the 5 then the remaining number in that column must be a 4. Since there is no 8 in the column 8 can’t then be above a 4 and again, by rule 4, 5 must be above 1 which is another contradiction.\r\n\r\nSo the 5 is in a column totaling 13.\r\n\r\nClearly the 5 can’t be above the 3 since this would require another 5 in the column, so 7 is above the 5 and the other number in the column is a 1.\r\n\r\nOptions\r\n[1/7/5]\r\n[7,5,1]\r\n\r\nIf [1/7/5] is the extreme left or right column the other side must be [4/x/8] and this column must total 16. x = 4 is a contradiction to our remit - that you can’t duplicate a number.\r\nIf [1/7/5] is in the middle column there is no room for a (8,9) combination and (1,2) must be true. The 2 in the top-right position would require a 7 bottom-left that’s already spoken for.\r\n\r\nSo, [7/5/1] appears in the solution.\r\nAgain if this were the middle column there is no room for the (8,9) and (1,2) must be true – requiring the extra 7 in the 2’s opposite corner.\r\nSo [7/5/1] appears as the extreme right or left column with the opposing left or right column being [8/6/2] (since opposite corners sum to 9 and this column must sum to 16).\r\n[7/5/1] as the left column and the right column as [8/6/2] means (1,2) can’t be true so there must be an (8,9) combination – a contradiction with the 8 to the extreme right of the grid.\r\nSo [7/5/1] must be the extreme right column.\r\nThe rest fills itself.\r\nAnswer;\r\n897\r\n635\r\n241\r\n',NULL,0);
INSERT INTO comment VALUES (10780,1361,4507,'Penny','Solution (no program needed)','2003-12-29 13:55:49',3,'This one requires neither a program nor time-consuming deductive thought. If you focus at first on conditions 1,3,4 and 5, there are basically 8 conditions in four mutually exclusive pairs. Call them s,t,u,v,w,x,y,z. \r\n\r\n(s) 5/3 or (t) 7/5; \r\n(u) 24 or (v) 79; \r\n(w) 8/4 or (x) 5/1; \r\n(y) 12 or (z) 89; \r\n\r\nThere are 2^4=16 groups of possible combinations. So you just evaluate each possible matrix until you get one that meets rule 2. This is actually possible to do fairly quickly, so brain-straining ratiocination is uncalled for. \r\n\r\n(s u w y) 5/3 24 8/4 12 It is impossible to satisfy this combination in a 3x3 matrix.\r\n\r\n(s u w z) 5/3 24 8/4 89, with 1,6,7 unaccounted for. \r\nThe only possible pattern is:\r\n?89\r\n245\r\n??3\r\nFails rule 2.\r\n\r\netc. etc..... until we get to: \r\n\r\n(t u x z) 7/5 24 5/1 89 with 3,6 unaccountted for. There are 12 possible patterns here:\r\n \r\n724 789 7?? 7?? 724 789\r\n589 524 524 589 5?? 5??\r\n1?? 1?? 189 124 189 124\r\n\r\n247 897 ??7 ??7 247 897\r\n895 245 245 895 ??5 ??5\r\n?11 ??1 891 241 891 241\r\n\r\nOnly the last one can possibly satisfy rule 2. We are down to two possibilities:\r\n\r\n897 897\r\n365 635\r\n241 241\r\n\r\nOnly the second one meets both stipulations of rule 2.\r\n\r\nThe answer is:\r\n \r\n897\r\n635\r\n241 \r\n\r\n\r\n\n\nEdited on December 29, 2003, 2:01 pm',NULL,0);
INSERT INTO comment VALUES (10781,1334,1301,'Charlie','re(3): is 4 not ok ??','2003-12-29 14:11:05',0,'But then the fourth is not lying flat on the table.',10777,0);
INSERT INTO comment VALUES (10782,1361,4982,'Dan Blume','Solution (no program required)','2003-12-29 15:54:09',0,'From 1: Columns of\r\n 3 5 7\r\n | | |\r\n 1 3 5\r\n\r\nFrom 4: Columns of\r\n 5 8\r\n | |\r\n 1 4\r\n\r\nOnly possiblity is column:\r\n 7\r\n 5\r\n 1\r\n\r\nFrom 2 we have corner sums of 9 since all other squares are impossible for two locations. From this we find that 9 cannot be in a corner.\r\n\r\nFrom Rule 3 we have the choice of row:\r\n2 - 4\r\n or\r\n7 - 9\r\n\r\nIf the column (7,5,1) is in center position then from Rule 3 :2-4 is not possible (requires split) and 7-9 puts 9 in a corner where it cannot go. Therefore column (7,5,1) is not in center position.\r\n\r\nFrom Rule 5 we have rows:\r\n 1 - 2\r\n or\r\n 8 - 9\r\n\r\nIf column (7,5,1) is the left column, then to meet Rule 2, the right column is (8, x, 2). Neither possibility (1-2, 8-9) for Rule 5 will fit.\r\n\r\nTherefore column (7,5,1) is the right column.\r\nUsing Rule 2 and drawing the 3x3 square: \r\n 8 x 7\r\n x x 5\r\n 2 x 1\r\n\r\nRule 5 gives (cube next to number 1 higher)\r\n 8 9 7\r\n x x 5\r\n 2 x 1\r\n\r\nRule 3 (prime next to non-prime 2 higher) gives\r\n 8 9 7\r\n x x 5\r\n 2 4 1\r\nand to meet the remaining requirement of Rule 2, the first two columns must total 16.\r\n 8 9 7\r\n 6 3 5\r\n 2 4 1\r\n \r\n',NULL,0);
INSERT INTO comment VALUES (10783,469,2256,'Jackie','re(2): The solution is incorrect.','2003-12-29 17:10:22',0,'Even if it cost the counterfeiter zero dollars to produce the note (which is doubtful) there is still the opportunity cost of producing the note. Also, if the person who lost the note was not the counterfeiter, then the person who did make the note - and subsequentally traded with it - had a net gain of 100 rupees minus the production and opportunity costs of making the note. Also, if the aforementioned premise is true, and the person who lost the note in the park had not yet had a chance to trade with it, then he lost 100 rupees.',10655,0);
INSERT INTO comment VALUES (10784,1509,4984,'ebeth','lovelorn snail','2003-12-29 17:32:01',0,'march 27 or 28',NULL,0);
INSERT INTO comment VALUES (10785,1551,4925,'Jeff','Lacking data','2003-12-29 19:43:34',0,'It seems to me there is insufficient data to derive just one correct solution. For example, the second encryption could be sending a total of 676 symbols to a pair of upper-case latin characters. As such, it is viable to say that:\r\n\r\nW -> WE\r\nh -> IU\r\no -> TI\r\nI -> BS\r\ns -> TB\r\nN -> ZW\r\ne -> JE\r\na -> PB\r\nr -> GN\r\nb -> SF\r\ny -> UK\r\n? -> HR\r\n\r\nAs such, the second plaintext is: WhoIsNearby? which I can answer: my boss at work.\r\n\r\n--Graatz',NULL,0);
INSERT INTO comment VALUES (10786,1442,4925,'Jeff','hmmm','2003-12-29 20:39:08',0,'Personally, I don\'t think I\'ve met anyone that thinks either pronounciation is okay for any word. Thus my conclusion is that the wife is a very agreeable person that doesn\'t like to make waves. The husband also seems very dull-witted to think that the second day of the week, according to us in the States, would have anything to do with the question at hand. Rather than to correct her husband (which would make waves) the wife induldges him and says \"Either way sounds fine, dear\" and be on her merry way.\r\n\r\n--Graatz',NULL,0);
INSERT INTO comment VALUES (10787,1341,4925,'Jeff','Integer infinity','2003-12-29 20:56:56',1,'Theoretical mathematics tells us that two sets are the same size iff there exists a one-to-one & onto function between the two. The size of the set of integers is deemed aluph null (spelling?). This is also the same size as the set of even integers (since n -> 2n is a valid one-to-one onto function). However, for example, the number of rational numbers is not aluph null since it takes 2 integers to produce all of the rationals. By this reasoning, every set in the puzzle contains aluph null marbles.',NULL,0);
INSERT INTO comment VALUES (10788,1334,2444,'dr pyser','re(4): is 4 not ok ??','2003-12-30 02:17:18',0,'as i said, i\'m n00b, i only realised that afterwards :D',10781,0);
INSERT INTO comment VALUES (10789,1441,4507,'Penny','Solution (no computer program used)','2003-12-30 04:54:21',3,'The number in parentheses after each group of 3 Schoolgirls signifies the room they\'re in.\r\n\r\nDay 1: ABC(1), DEF(2); GHI(3); JKL(4); MNO(5);\r\nDay 2: ADG(6); BEH(7); CLO(8); JNI(9); MKF(10);\r\nDay 3: DHO(1); AJM(2); BNK(3); CFI(4); GEL(5);\r\nDay 4: AEN(4); DKI(5); BFO(6); CGJ(7); MHL(9);\r\nDay 5: GNF(1); BLI(2); CDM(3); AHK(8); JEO(10);\r\nDay 6: MEI(1); GKO(2); AFL(3); CNH(6); BDJ(8);\r\nDay 7: BGM(4); JHF(5); AOI(7); CEK(9); DNL(10);\r\n',NULL,0);
INSERT INTO comment VALUES (10790,574,4162,'rohit','Finally got one','2003-12-30 05:53:27',0,'Finally found one that was easy : Mr. East takes the north road, Mr. West takes the east road, Mr. North takes the south road and Mr. South takes the West road.',NULL,0);
INSERT INTO comment VALUES (10791,1441,1301,'Charlie','re: Solution (no computer program used)','2003-12-30 10:22:35',0,'What was the manner of solution? Are there other solutions? Can it be done with fewer than 10 tables? (Yes, those are separate tables, not separate rooms.)',10789,0);
INSERT INTO comment VALUES (10792,1441,1301,'Charlie','solution--computer used','2003-12-30 10:56:46',3,'If the members are arranged in a circle, if each member were one vertex of a triangle, they\'d be arranged in 5 triangles. The problem is to get all triangles to differ each day.\r\n\r\nFrom looking at Internet treatments of the 15-schoolgirl problem, we see the idea is to arrange 14 members around the outside of the circle, with one at the center. That way, each of the seven days, the entire structure of triangles can be advanced by two units.\r\n\r\nSo that each person is paired with a given other person only once in the week, each of the sides (chords of the circle, so to speak) that a given person will see in a given direction (say clockwise) must be a different length (different number of persons over). As the motion of the whole set of triangles is by 2 units each day, the vertices are odd and even parity. A chord of even length will connect points of the same parity; a chord of odd length will connect points of opposite parity. The chords of even length will connect to a given point twice: once as length 2n and once as length 14-2n, coming from the other side. The chords of odd length will cover both even and odd parity points.\r\n\r\nThat means we need two sets of even-length chords--to cover the even and odd parity points. The following program accomplishes this by switching from even to odd beginning points past a chord length of 7. (The chord length is not the strict geometric consideration, but only a counting in the clockwise direction of how many over the chord shifts, even up to 13, which is really 1 counterclockwise). There are 13 chords placed, all of different \"size\". That\'s 26 endpoints--enough for each point except for 2 to be at the ends of two chords, as it should be in a triangle. The two vertices that remain with one chord each connecting them are then tied to the center point.\r\n\r\nChecks are made to assure that no quadrilaterals, etc. are formed, just triangles. When a set is found, letters are assigned, making the first triangle ABC, etc. The triangle set is then rotated by adding 2*day to each position, mod 4, and the results presented. There are 84 sets that are found. I haven\'t checked yet whether any are trivially related (just a difference in the order of the days, or people within groups).\r\n\r\nIn assigning the tables, I just assign the next one that\'s not used that day and that none of the people in the group have used that week. I don\'t know if this is optimal, but it finds some of the 84 solutions to the first part of the problem are capable of being done with only 9 tables; some require 10 and others 11. Perhaps with some optimization, all could be done in at most 10; I don\'t know.\r\n\r\nHere are the first four results out of the 84:\r\n\r\n \r\nMore stuff (Edited in later): B CANNOT be a knight for, he makes a statement that C is a knight. C can\'t be a knight, coz B is a knight. \r\n \r\nMore stuff (Edited in later): Based on what I did, A is most like not the knight.\r\n\r\n\r\n\n\nEdited on January 1, 2004, 12:07 pm',NULL,0);
INSERT INTO comment VALUES (10836,1443,3386,'Victor Zapana','answer.','2004-01-01 12:11:41',0,'Based on my thoughts, and some lucky guesses, I have found that A is the liar, B is the rebel, C is the knave, and D is the knight. Also, D is 1st place, C is 2nd, B is 3rd, and A is last.\n\nEdited on January 1, 2004, 12:12 pm',NULL,0);
INSERT INTO comment VALUES (10837,1443,3386,'Victor Zapana','re: answer (Some justification)','2004-01-01 12:20:10',0,'A is a liar, so: \r\nB is not a liar.\r\nC did not win the race.\r\nA was not 2nd. \r\nThis give us _ _ _ _, C not 1st, and A not 2nd. \r\nB is a rebel, so: \r\nC is not a knight. (He gave a false statement) \r\nB is not last. (He gave another false statement)\r\nC is 2nd. (He gave a true statement) \r\nThis gives us _ C _ _, and A not 2nd (duh... 2 ppl cant be the same place). \r\nC is a knave, so: \r\nD is not a knave. (He gave a false statement.) \r\nA did not win the race. (He gave a true statement.) \r\nB did not come in last place. (He gave a false statement.) \r\nThis gives us _ C _ _, A not 1st, B not last. \r\nD is a knight, so: \r\nB is a rebel.\r\nC is 2nd. \r\nB is 3rd. \r\nThis gives us _ C B _, A not 1st. This then makes _ C B A. Becuase the remaining letter is D, then the order must be: \r\nD C B A.\r\n\r\nEdited on January 1, 2004, 12:21 pm\n\nEdited on January 1, 2004, 12:21 pm',10836,0);
INSERT INTO comment VALUES (10838,1443,1301,'Charlie','re(2): answer (Some justification)','2004-01-01 14:02:30',0,'C\'s second statement is that A did win the race, not that he did not win the race. Then C\'s being a knave, with his first and last statements being false, the truth of C\'s middle statement makes A the first place winner, not D.',10837,0);
INSERT INTO comment VALUES (10839,1443,3386,'Victor Zapana','re(3): answer (Some justification)','2004-01-01 16:17:13',0,'woops. my bad. Thanks Charlie. So, the answer for order is A C B D.',10838,0);
INSERT INTO comment VALUES (10840,730,5004,'John Miller','Solution','2004-01-01 18:09:33',0,'The first, last, and only digit has to be \"1\". 1, when continualy raised to a positive, full power, i.e. 1, 3, 7, etc. will continue to remain 1.',NULL,0);
INSERT INTO comment VALUES (10841,1443,5012,'LeeAnna','The answer: I believe that A is first','2004-01-02 02:14:21',0,'D Knight, A Liar, B rebel, C Knave and A is first, C Second, B third, and D fourth. A has to be first because C is the knave, the first line of C is false implies the second line of C is true. Hence, A won the race.',NULL,0);
INSERT INTO comment VALUES (10842,731,4374,'Richard','Solution','2004-01-02 10:51:26',3,'2^n is congruent only to 2, 4, or 1 mod 7, so 2^n+1 is congruent only to 3, 5, or 2 mod 7. Hence there are 0 positive integers n such that 2^n + 1 (or 2^(n+1) for that matter) is divisible by 7.',NULL,0);
INSERT INTO comment VALUES (10843,1493,5009,'Eduardo Pensado','how many men and ladies?','2004-01-02 11:26:07',0,'In a chess match, there are 32 total pieces, so unless you are eliminating the kings or queens, there can\'t be 30 men and ladies too.',NULL,0);
INSERT INTO comment VALUES (10844,1409,5011,'Katie','solution','2004-01-02 12:17:32',1,'if it has to be a number like 6/7 or 5/6 or somthing like that you could have 89 questions and you would have to get 88 of them right to have a 99% and for and 89% you could have 9 questions and have to get 8 right\r\nthats all i have so ar',NULL,0);
INSERT INTO comment VALUES (10845,1509,5011,'Katie','The Solution','2004-01-02 12:35:15',0,'it took 10 days if once he got out he fell back in by two feet so he got out on Febuary 24th if he didn\'t slip back in when he got out then he got out on Febuary 23rd',NULL,0);
INSERT INTO comment VALUES (10846,1509,5011,'Katie','i think maybe this is it','2004-01-02 13:02:02',0,'march 16th',NULL,0);
INSERT INTO comment VALUES (10847,1493,153,'TomM','re: how many men and ladies?','2004-01-02 13:18:26',0,'It\'s not \"ladies, too\" (which would mean that the ladies are included in the count of thirty), but rather \"ladies two\" (Thirty men and two ladies, for a total of 32).',10843,0);
INSERT INTO comment VALUES (10848,1555,4064,'rerun141','solution','2004-01-02 14:48:46',3,'CLS\r\nA=123\r\nB=456\r\nPRINT a,b\r\nA=A+B\r\nB=A-B\r\nA=A-B\r\nPRINT A,B\r\nEND\n\nEdited on January 2, 2004, 3:47 pm',NULL,0);
INSERT INTO comment VALUES (10849,1443,4982,'Dan Blume','','2004-01-02 15:08:01',0,'',NULL,0);
INSERT INTO comment VALUES (10850,1554,5018,'Dave County','5 questions or less','2004-01-02 15:18:27',3,'Q1. Am I blindfolded? (If Yes, at least 1 knight, if No at least 1 liar)\r\nQ2. Is the person next to you a liar? (If Q1=Yes & Q2= No then there are 2 knights; if Q1=No & Q2 = No then 2 liars; else 1 of each)\r\nQ3 A. Are you Bert? (Ask this if both are liars or knights - then its solved.)\r\nQ3 B. Is Bert a liar? (If Q3=Yes, then Bert is speaking. If No, Alex is speaking.)\r\nQ4. Did you answer the previous question? (now we have a table with Q3 & Q4 answers. If both Q3 & Q4 are No or if both are Yes, then Bert is a liar. Otherwise Bert is a knight.)\r\nQ5. Is Bert a liar? (this repeats a question, but it also lets you know who is talking. And so its solved.)',NULL,0);
INSERT INTO comment VALUES (10851,1555,4906,'stan','Nice!','2004-01-02 16:04:54',0,'I was stumped by this one!',NULL,0);
INSERT INTO comment VALUES (10852,1555,1626,'Gamer','re: solution','2004-01-02 16:10:22',0,'I was thinking you couldn\'t use math or sophisticated programming. This is a good solution though :)',10848,0);
INSERT INTO comment VALUES (10853,1551,1920,'Brian Smith','Hints','2004-01-02 16:16:46',0,'Each number in the first encrypted question represents a whole word.\r\n\r\nThe second encrypted question is broken up into five words by: WEIUT IBS TBZWJE PBGNS FUKHR?',NULL,0);
INSERT INTO comment VALUES (10854,137,4718,'Jack Squat','Solution in 6 variables','2004-01-02 16:19:28',3,'Here was my disgusting solution. The intuitive route is so much better. In fact stop reading this post.\r\n\r\nd = distance from airport to house\r\ngt = go-time for friend to leave house\r\nat = normal arrival time of airplane\r\ncarsp = car speed\r\nwd = walking distance\r\nwt = walking time\r\n\r\ncarsp = 2*d/(12:00-gt) (distance over time)\r\ncarsp = 2(d-wd)/(11:40-gt)\r\n\r\nat + d/carsp = 12:00 \r\n(at-1) + wt + (d-wd)/carsp = 11:40\r\n\r\n<Why are you still reading this?>\r\n\r\nNow substitute carsp from the first two equations into the second two and you end up with another 2:\r\n\r\n(1) at + (12:00-gt)/2 = 12:00\r\n(2) at-1 + wt + (11:40-gt)/2 = 11:40\r\n\r\nTake the 1 from equation (2) over to the other side.\r\n\r\nat + wt + (11:40-gt)/2 = 12:40\r\n\r\n<You can\'t be enjoying this>\r\n\r\nNow add and subtract twenty minutes in the bracket:\r\n\r\nat + wt + (11:40-gt+20mins-20mins)/2 = 12:40\r\nwhich equals:\r\nat + wt + (12:00-gt)/2 + 20mins/2 = 12:40\r\n\r\nTake the 20mins/2 or 10mins to the other side:\r\n\r\nat + wt + (12:00-gt)/2 = 12:50\r\n\r\nLooking at equation (1), we can see wt = 50 mins. \r\n\r\n<You are sick>',NULL,0);
INSERT INTO comment VALUES (10855,731,4982,'Dan Blume','Brute force','2004-01-02 16:44:11',3,'Zero.\r\n\r\nThe remainder of the (2^n+1)/7 follows the pattern 2,3,5,2,3,5. This will never reach zero to create a solution. If you take one of the remainders, subtract 1, double it, and add 1, then the next number in the series appears. Thus there are zero solutions for this problem.',NULL,0);
INSERT INTO comment VALUES (10856,1443,4982,'Dan Blume','Solution','2004-01-02 16:59:58',3,'A 1st liar\r\nB 3rd rebel\r\nC 2nd knave\r\nD 4th knight\r\n\r\nStart with who is the knight.\r\n\r\nB is not the knight due to statement B1. True or False, B is not the knight.\r\n\r\nC is not the knight. If C is the knight, D is the knave. Statement D3 must be False since it does not agree with C3. So D1 must also be False. This means that B must be the liar, and statement B1 is False. So C is not the knight.\r\n\r\nA is not the knight. If A is the knight, B is the liar, and either C or D is the knave. If C is the knave, then C1 is False, making C2 True. However, C2 is False since it disagrees with A2. Then C is not the knave. If D is the knave, then D1 conflicts with A1 and must be False. Then D2 must be True, but it disagrees with A2. Then D is not the knave and thus A is not the knight.\r\n\r\nD is the knight.\r\nThis leads to:\r\nB is the rebel, C is 2nd, B is 3rd.\r\nA\'s statements become F,F,F - A is the liar\r\nB\'s statements are F,F,T - B is the rebel\r\nC\'s statements are F,X,F - C is the knave and C2 is True\r\nFilling in the matrix\r\nA 1st liar\r\nB 3rd rebel\r\nC 2nd knave\r\nD 4th knight',NULL,0);
INSERT INTO comment VALUES (10857,1555,1301,'Charlie','other solutions','2004-01-02 17:03:48',3,'Since this looks like it was written in GWBASIC (aka BASICA), you could use\r\n\r\nSWAP A,B\r\n\r\nbut that\'s cheating, and also internally probably uses a temporary variable.\r\n\r\nThe classic method is\r\n\r\nA = A XOR B\r\nB = A XOR B\r\nA = A XOR B\r\n\r\nThis works in integers in Basic, but rerun141\'s answer allows floating point numbers with fractions also. In languages like C or C++, the XOR could be done on a byte-by-byte basis, avoiding loss of precision in non-integral floating-point numbers, and working with equal-sized strings as well.',NULL,0);
INSERT INTO comment VALUES (10858,1547,4778,'chic','re: Life can\'t be all Beer and Skittles','2004-01-02 20:15:43',1,'beer and skittles???? i would almost think that you would like that crap. besides that, ofcourse life can\'t be a bowl of cherries all the time. but, you have to endure the sour to enjoy the sweet. and by the way try a tid bit of simplicity. it feels good on. sometimes you are looking for something so hard and you try to read into every little thing you miss out on the obvious. also, when you are down and out just remember you gotta S-M-I-L-E to be H-A-P-P-Y!\r\n',10561,0);
INSERT INTO comment VALUES (10859,1555,3558,'Tristan','re: other solutions','2004-01-02 20:25:50',0,'I\'d really like to know what the XOR function does. Some one please tell me!',10857,0);
INSERT INTO comment VALUES (10860,1555,4374,'Richard','re(2): other solutions','2004-01-02 21:47:58',0,'My understanding of the XOR function is that it takes the contents of two computer words and does their bit-by-bit \"exclusive or\" (the input bits have to be different to yield a 1 as the output bit). Assuming 4-bit computer words, for example, XOR(1111,1010)=0101 (i.e. bit by bit complement). An example oriented toward the problem: XOR(1001,0010)=1011, and XOR(1011,1001)=0010 while XOR(1011,0010)=1001.\n\nEdited on January 2, 2004, 11:45 pm',10859,0);
INSERT INTO comment VALUES (10861,1555,4374,'Richard','No Math?','2004-01-02 21:51:47',4,'Is XOR math? Here is a \"solution\" with absolutely no math:\r\n\r\n10 A=123 \r\n20 B=456 \r\n30 PRINT A,B \r\n70 PRINT B,A\r\n\r\nIt does the same thing as the original program as far as an external observer is concerned! \r\n',NULL,0);
INSERT INTO comment VALUES (10862,723,5015,'joel','solution','2004-01-02 22:37:33',0,'ive noticed that they all used cosine law in solving this problem. In more elementary way we could solve that by plotting the vertices to the trinagle in a cartesian plain which has the coordinates of (0,0),(s/2,sã3/2),(s,0). Then use the formula for obtaining the distance between two points and you will get three equations and three unknowns then manipulate it and you will get the value of s=6.76643 cm',NULL,0);
INSERT INTO comment VALUES (10863,1362,5022,'','','2004-01-02 22:38:51',0,'25+34=61\r\n34+25=61',NULL,0);
INSERT INTO comment VALUES (10864,1334,5023,'Juan','re: Big table!','2004-01-02 22:43:00',0,'Jack Squat and SliverKnight are indeed correct. I just wanted to add a few comments:\r\n\r\nA simple trial indicates that the problem is ever expanding for an open form. In that to reach a 3 penny [valence] shell, you must always add another penny. And every penny you add requires at least another penny to complete it.\r\nTherefore a circular or polygonal solution seems required. So that the one penny you add is an existing one. Thus a closed form is required.\r\n\r\nGiven that we need a polygon, we need a basic building block for each side. The 080 cluster of four pennies is the smallest unit where the ends of the \"cluster\" need one and only one penny to complete them. And every other non-linking penny already has its [valence] shell complete.\r\n\r\nObviously silverknight has shown that a 4 sided diamond or square [quadrilateral] is a solution. A pentagon is of course also a solution, etc. However the proof of why a triangle is not a solution may be interesting to a few.\r\n\r\nIf you draw out a triangle solution with the 080 cluster, and then connect the centers of every penny to it\'s nearest neighbors\' center. You will have a lattice of triangles. Now every penny that should make a connection to a neighboring penny has a line of length \"one\" between their centers. Where the unit of length is equal to one penny diameter. Now every line that cannot form a connection [i.e. is not allowed due to it\'s valence shell being already filled], must be assigned a variable. To show that a triangle is possible, you must show that all of the variables must be greater and not equal to one.\r\n\r\nI have not done this problem, however if you try... I think you will show that the solution to this geometry problem is a lattice of equilateral triangles.\r\n\r\n 00\r\n 00 00\r\n 0 0\r\n 080\r\n\r\nTriangle of 080 clusters.\r\n ',10800,0);
INSERT INTO comment VALUES (10865,723,5015,'joel','Solution','2004-01-02 22:48:42',3,'Just plot the vertices of the triangle on the catesian plain which has the coordinates of (0,0),(s/2,s√3/2),(s,0). Then use the distance formula in obtaining 3 equations 3 unknowns. By manipulation you will get the value of s=6.76643 cm',NULL,0);
INSERT INTO comment VALUES (10866,1497,5015,'joel','Solution','2004-01-02 23:02:22',3,'Though its a theorem and already been proven I want to prove it by the calculation of the distance between the midpoint of the hypotenuse and the vertex of the right angle and ive found out that its equal to half of hyptenuse so it lies with the circle',NULL,0);
INSERT INTO comment VALUES (10867,1376,3386,'Victor Zapana','i think this is the answer','2004-01-03 13:13:54',0,'I got this through lotsa computation that I will is too bizarre to type up on this post. So, my answer is about 184.3245837 meters\r\n\r\nNOTE: If you saw an answer here previously that was different, I edited it.\n\nEdited on January 3, 2004, 1:24 pm',NULL,0);
INSERT INTO comment VALUES (10868,1376,4064,'rerun141','re: i think this is the answer','2004-01-03 13:36:07',0,'the dog has to go atleast 200 m. thats the perimeter of the body of soldiers.',10867,0);
INSERT INTO comment VALUES (10869,1376,3386,'Victor Zapana','re(2): i think this is the answer','2004-01-03 14:03:25',0,'then im going with my second answer- 212.5 meters.',10868,0);
INSERT INTO comment VALUES (10870,738,5011,'Katie','easy','2004-01-03 14:24:37',3,'its 36 b/c:\r\nth pattern is like :√1=1 √4=2 √9=3 √16=4 √25=5 so the next would have to be what ever 6 square is which is 36 or it could be like \r\n1+0=1 1+3=4 4+5=9 9+7=16 16+9=25 so the since your adding by each odd # it should be 25+11 which =\'s 36',NULL,0);
INSERT INTO comment VALUES (10871,1376,1301,'Charlie','I get...','2004-01-03 14:58:17',3,'If s is the speed of the dog relative to that of the troop, the time taken would be twice the time taken to go from side to side plus the time taken to get from the trailing edge to the leading edge plus the time taken to get from the head to the trailing edge of the troop:\r\n\r\n2/√(s²-1) + 1/(s-1) + 1/(s+1)\r\n\r\nThis is to be completed in unit time.\r\n\r\nExcel\'s solver makes s be equal to 4.18112545 in order for this to be 1. As the troop is traveling at 50 m per unit of time, the dog is going 209.056272 m per unit of time, and that\'s the distance he\'s traveled.\r\n\r\nThat includes two crosswise traverses taking .246318793 units of time each, during which he travels 51.49449 m each, and the troops had moved 12.31594 m each time.\r\n\r\nThe forward travel took .314354155 units of time, during which the dog traveled 65.71771 m and the troops 15.71771 m.\r\n\r\nThe backward travel took .193008259 units of time during which the dog traveled 40.34959 m and the troops 9.650413 m.\r\n\r\n\n\nEdited on January 3, 2004, 4:27 pm',NULL,0);
INSERT INTO comment VALUES (10872,1376,5028,'GT','','2004-01-03 15:49:47',0,'15o meters. 50m three ways to meet back at D',NULL,0);
INSERT INTO comment VALUES (10873,513,5029,'Jasmine','easy','2004-01-03 17:02:49',0,'change \"this\" to \"that\" so it states \"that sentence does not contain seven words\"',NULL,0);
INSERT INTO comment VALUES (10874,1509,5029,'Jasmine','humm','2004-01-03 17:09:56',0,'13th of march?',NULL,0);
INSERT INTO comment VALUES (10875,543,5029,'Jasmine','humm','2004-01-03 17:17:30',0,'an egg.',NULL,0);
INSERT INTO comment VALUES (10876,537,5029,'Jasmine','?','2004-01-03 17:18:37',0,'shadow or darkness...',NULL,0);
INSERT INTO comment VALUES (10877,861,5029,'Jasmine','?','2004-01-03 17:21:24',0,'fish... i dunno... all in mail never clinking?',NULL,0);
INSERT INTO comment VALUES (10878,860,5029,'Jasmine','easy','2004-01-03 17:23:00',0,'MOUNTAINS!',NULL,0);
INSERT INTO comment VALUES (10879,859,5029,'Jasmine','?','2004-01-03 17:25:09',0,'time?',NULL,0);
INSERT INTO comment VALUES (10880,500,5029,'Jasmine','...','2004-01-03 17:28:00',0,'suicide... seems reasonable, its illegal, but if carried out correctly, you are not able to be punished by the law.',NULL,0);
INSERT INTO comment VALUES (10881,467,5029,'Jasmine','easy','2004-01-03 17:30:00',0,'man',NULL,0);
INSERT INTO comment VALUES (10882,360,5029,'Jasmine','easy','2004-01-03 17:30:46',0,'NOTHING!',NULL,0);
INSERT INTO comment VALUES (10883,315,5029,'Jasmine','?','2004-01-03 17:31:34',0,'himself',NULL,0);
INSERT INTO comment VALUES (10884,1568,4507,'Penny','THE ANSWER (no real program used)','2004-01-03 18:04:42',3,'N=1 and N=13 have zero odds of winning the game. Since N=2 has 1 card of lower value, and N=12 has 1 card of higher value, they have the same odds of winning the game. Similarly N=3 and N=11 have the same odds, N=4 and N=10 have the same odds, N=5 and N=9 have the same odds, and N=6 and N=8 have the same odds. \r\n\r\nWith a deck of 13 cards, with 3 cards drawn at a time, the larger and smaller card discarded, and the middle one returned to the deck, there will be six drawings. In round 1, there are 13 cards, and each card has 3/13 odds of being selected. In round 2, 11 cards with 3/11 odds per card of being selected. In round 3, 9 cards with 1/3 odds per card. In round 4, 7 cards with 3/7 odds per card. In round 4, 5 cards with 3/5 odds. In round 6, 3 cards are left; two will be eliminated, leaving the \"winning card\". \r\n\r\nIn rounds 1-5, the odds of card N surviving the round, are the odds that it survived the prior round (or 1 for round 1) times the odds that it will survive this round.\r\n\r\nThe odds that it will survive this round are the odds that it will not be selected, plus the odds that both it and exactly one smaller card will be selected.\r\n\r\nThe odds that exactly one smaller card will be selected, is the sum of the odds that each smaller card was the only smaller card selected. That is the odds that the smaller card survived the prior round (1 for round 1) times the odds that the smaller card will be selected this round, times the product, for every other smaller card, of the complement of the odds that it survived the prior round (0 for round 1) plus the odds that it did survive the prior round times the complement of the odds that it will be selected in this round.\r\n\r\nIn round 6, the odds for the survival of N=1 and N=13 are zero. For N=2,3,...,12, the odds are the odds that N survived round 5 and exactly one smaller card survived round 5. The latter is the sum, for each smaller card, of the odds that it survived round 5, times the product, for all other smaller cards, of the complement of the odds that it survived round 5. \r\n \r\nNow I was morally certain that the above reasoning produces the correct results. At this point I had the option of tediously computing everything by hand, with the risk of cascading errors, or shamelessly borrowing from Charlie. (I will have to learn how to convert logic into programs as Charlie does. Maybe that will be my 2004 New Years Resolution). \r\n \r\nThe results are: \r\n\r\n 1 has 0.0000000 odds of being the winning card\r\n 2 0.0034965\r\n 3 0.0127146\r\n 4 0.0357067\r\n 5 0.0892845\r\n 6 0.1961927\r\n 7 0.3252101\r\n 8 0.1961927\r\n 9 0.0892845\r\n10 0.0357067\r\n11 0.0127146\r\n12 0.0034965\r\n13 0.0000000\r\n\n\nEdited on January 4, 2004, 2:51 pm',NULL,0);
INSERT INTO comment VALUES (10887,429,5033,'Captain Paradox','re: perfect timing','2004-01-04 11:40:09',0,'If everybody else drank the punch and died, then the entire punch bowl would have to be poisoned. Hence the ice cube solution.',6795,0);
INSERT INTO comment VALUES (10885,1362,4374,'Richard','Null Author?','2004-01-03 19:18:04',4,'Evidently the null author can post a non-null comment, and a good one at that. Who was that masked person? And what is the secret to posting a comment annonymously? ',10863,0);
INSERT INTO comment VALUES (10886,1442,4909,'Brian','in america','2004-01-03 19:33:06',0,'if his wife\'s name was juanita, her response might be \"martes\"',NULL,0);
INSERT INTO comment VALUES (10888,511,5033,'Captain Paradox','re: theoretically, yes','2004-01-04 11:48:59',1,'God would not need a force of infinite mass to push the stone away from. Rather, he/she would only need some sort of refrence point in the universe that the stone is moving away from. If God wanted to give up his/her ability to move it, than it would be possible. But only then.',10400,0);
INSERT INTO comment VALUES (10889,263,5033,'Captain Paradox','overtaking the tortoise','2004-01-04 11:56:45',4,'Say that Achilles moves twice as fast as the tortoise. The race is 8ft, and the tortoise (with a 1ft head start) moves 1ft per second. Therefore, after one second, Achilles is only 1ft behind the turtle. After two seconds, Achilles is even with the turtle at 6ft from his start. In one more second, Achilles will be crossing the finish line while the tortoise still needs another second to finish. Therefore, Achilles can overtake the tortoise. What\'s the philosophy on the paradox?',10691,0);
INSERT INTO comment VALUES (10890,476,5033,'Captain Paradox','Does it have to pertain to the aliens?','2004-01-04 12:00:10',3,'What if you said, \"This sentence is false.\" ? Wouldn\'t that be another vicious circle? It\'s a bit less complicated, but it still works.',NULL,0);
INSERT INTO comment VALUES (10891,82,5033,'Captain Paradox','Time stops forever','2004-01-04 12:06:31',0,'If Zeus had conjured up an infinite number of demons, then he would never finish telling them all to kill Prometheus. Therefore, time would be stopped forever and we would be just frozen in time. Naughty Zeus.',6355,0);
INSERT INTO comment VALUES (10892,1343,5033,'Captain Paradox','The guy under the bull','2004-01-04 12:10:19',0,'If somebody was standing under the bull, would he have been told to understandable?',NULL,0);
INSERT INTO comment VALUES (10893,1556,3386,'Victor Zapana','random related comment','2004-01-04 14:18:44',0,'well, its not impossible at least. The total area of the cubes you need to put in is 1330 cc, while the huge box is 1331 cc. That means that there while be a 1cm cube extra space in there.',NULL,0);
INSERT INTO comment VALUES (10894,1424,4197,'luminita','Diofantic equations','2004-01-04 14:35:41',3,'the unique solution is 420:\r\n\r\nlet the number be \'xyz\'\r\nthe following system of equations gives the solution:\r\nx²+y²+z²=10y+z\r\n(10y+z)²+x²+x=100x+10y+z\r\ny,z = 0,1,2,...9, x=1,2,3,...9\r\n\r\nworking on the equations we obtain:\r\n4x²+4(y-5)²+(2z-1)²=101\r\n99(y²-x)+20yz=0\r\n\r\nthe second equation means that one of following is true:\r\n- (y²-x)<0 and the product yz is multiple of 11 (imposible)\r\n- y²=x and yz=0\r\nif y=0, x=0 and the solution is not a 3 digit number\r\n\r\nThus:\r\nz=0\r\ny ²=x\r\nx²+(y-5)²=25\r\n\r\nthe last equation has possible solutions:\r\nx=3 and y-5=4 or\r\nx=4 and y-5=3 or\r\nx=3 and y-5=-4 or\r\nx=4 and y-5=-3\r\nbut only one verify the condition of y²=x\r\n\r\nso, the final solution (and unique) is \r\nx=4, y=2, z=0, the number beeing 420',NULL,0);
INSERT INTO comment VALUES (10895,1556,4896,'Jaideep','a void ??','2004-01-04 15:32:42',0,'maybe there is allowed a void space of 1cu cm in the box ?',NULL,0);
INSERT INTO comment VALUES (10896,1556,3558,'Tristan','re: random related comment','2004-01-04 17:02:32',0,'That does not necessarily mean that it is possible to pack all the cubes. I think that it might be impossible because of the two 5 cm cubes, and the unusable spaces thay would create. To find a solution, It is important to find good positions for the 5 cm cubes to allow for the others.',10893,0);
INSERT INTO comment VALUES (10897,1362,3558,'Tristan','re: Null Author?','2004-01-04 17:16:50',0,'Interesting... I think it must have been the same thing that sometimes causes comments to disappear, though I\'ve never seen the author disappear, just the title and comment.\r\n\r\nI suppose the anonymous person\'s solution is in base 8? Lowering the base number works well.',10885,0);
INSERT INTO comment VALUES (10898,1376,5026,'sunny','The answer is.........','2004-01-04 17:59:50',0,'it is not an exact answer but approximately this is\r\n203m.',NULL,0);
INSERT INTO comment VALUES (10899,1555,5026,'sunny','solution...','2004-01-04 18:29:43',0,'i hope the solution is\r\nA = A + B;\r\nB = A - B;\r\nA = A - B;\r\nnow the value of A will be 456 and that of B will be\r\n123.',NULL,0);
INSERT INTO comment VALUES (10900,1443,5045,'erin','solution','2004-01-04 18:40:02',0,'A- LIAR(FFF) #1\r\nB- REBEL(FFT) #3\r\nC- KNAVE(FTF) #2\r\nD- KNIGHT(TTT) #4',NULL,0);
INSERT INTO comment VALUES (10901,1556,4982,'Dan Blume','Solution','2004-01-04 20:10:16',3,'Nomenclature (x,y,z) = (left, bottom, front) corner of the cube to be placed.\r\n\r\n5-cubes: (0,0,0), (6,6,6)\r\n Put the 5 cubes in opposite corners\r\n3-cubes: (5,0,0), (8,0,0), (5,3,0), (8,3,0),(5,6,0), (8,6,0), (0,5,0), (0,8,0), (0,5,3), (0,8,3), (5,6,3), (8,6,3)\r\n\r\nThe other twelve 3-cubes go in with the same relationship to the opposite 5-cube. (Subtract each coordinate from (8,8,8))\r\n(0,2,5), (3,2,5), (8,0,5), (8,3,5), (0,2,8), (3,2,8), (0,5,8), (3,5,8), (0,8,8), (3,8,8), (8,0,8), (8,3,8)\r\n\r\nThe remainder is filled in with the 54 2-cubes, and a one cube void in the very center.',NULL,0);
INSERT INTO comment VALUES (10902,1556,1301,'Charlie','solution','2004-01-04 20:17:38',3,'First, if the two 5x5x5 cubes were other than in two diagonally opposite corners of the cube, it would require more single-unit cubes than the one allowed by the 1080 cc taken up by the 2- and 3-cm cubes after the 250 cc of the two 5 cm cubes. For example, even if the two 5-cm cubes were touching vertex-to-vertex, three whole areas of 1-cm thickness would be created with area 5x5 along the faces of the non-outside 5x5x5 cube that don\'t touch the vertex that touches the other cube.\r\n\r\nWorking at it by trial and error, where 11 units can be 3, 3, 3 and 2, or 2, 2, 2 and 5, or 2, 2, 2, 2 and 3, placing cube by cube into the large cube (after the two 5-cm cubes were placed as mentioned above), I came up with a solution that is best described, after the fact, as follows:\r\n\r\nA 6x6x5 rectangular solid subset can be formed from a layer of 4 3-cm cubes laid out in a square formation, overlaid by a layer of 9 2-cm cubes also laid out in a square formation. Six of these solids would then make the 6 x 9 = 54 2-cm cubes and 6 x 4 = 24 3-cm cubes.\r\n\r\nSo place one 4-cm cube and three of the 6x6x5 solids at the bottom of the 11-cm cubical box. One of the 6x6x5 solids will be lying flat (i.e., with its 5-cm dimension upward from the base) taking up a 6 cm by 6 cm square on the base. The other two are laid more vertically, with one of their 6-cm dimensions each vertically, so as to take up a 6 cm x 5 cm rectangle on the base. This occupies the full base partially to a height of 6 cm and the rest to a height of 5 cm. An identical, except mirror-imaged, complex of these 4 items can then be inverted and placed over the original set. This leaves an empty 1-cm cube in the middle.\r\n\r\nWhen originally fitting these together, I did not realize the possibility of the fitting of 4 3-cm cubes and 9 2-cm cubes into a 6x6x5 package, but just tried fitting individual pieces. What resulted, however, was in fact describable in that modular form. The diagrams below show layer-by-layer (1 cm high) the numbered cubes which occupy each 1-cm unit, from top to bottom. The numbers are the order in which I placed the cubes. Each cubic centimeter is labeled with the cube number to which it belongs:\r\n \r\nIn that case, $1=5 1/6 chestnuts, and $60=310 chestnuts.',NULL,0);
INSERT INTO comment VALUES (10968,1445,5088,'eleonora','','2004-01-07 14:25:40',0,'I think it\'s a tooth',NULL,0);
INSERT INTO comment VALUES (10969,1443,5088,'eleonora','my solution','2004-01-07 15:29:46',0,'A is the liar, B is the rebel, C is the knave and D is the knight. A won the race. C came in second, B came in third and D is the last one.\r\n\r\nB in second and C in third, because D tells the truth;\r\nB is the rebel, he said two lies and one truth. \r\nIf B is rebel and D is the knight, so A is the lier. \r\nC is the Knave.',NULL,0);
INSERT INTO comment VALUES (10970,1445,3386,'Victor Zapana','maybe?','2004-01-07 17:12:03',0,'it sounds like a calculator \r\nI coax the lazy of working by using pie\r\nmebe pie refers to pi, the homonym for pi? calculators work with pi, and lessens the workload for the lazy one, though the lazy does work a little to get the calculator working. \r\nI\'m never placed in big use. \r\nreally, really, really big numbers cant be displayed on calculators \r\nTo quit and just add error, \r\nLeaves fear on the loose \r\nmebe it means that to do the computation by hand leaves room for mistake. \r\nWell that\'s just what i think.\r\n\r\n\n\nEdited on January 7, 2004, 5:14 pm',NULL,0);
INSERT INTO comment VALUES (10971,274,4909,'Brian','alternate solution','2004-01-07 19:37:13',0,'with the line positioned in a vertical direction, i would draw an \"s\" to the left of it and convert the line into an \"h\" and write the letters \"orter\" to the right hand side, thus spelling out the word \"shorter\".\r\n\r\ntyvm',NULL,0);
INSERT INTO comment VALUES (10972,1429,5033,'Captain Paradox','re: Give em heck, Harry !!','2004-01-07 22:28:52',0,'I agree with the solution, Penny, but couldn\'t we all try to keep the language on this site sanitary? It makes for easier reading.\r\nThanks',10537,0);
INSERT INTO comment VALUES (10973,1345,5097,'Cindy','My attempt...','2004-01-07 23:21:39',0,'I\'m new at this, so you\'ll have to forgive me if I have posted things that people have already said. But since it is said to be as yet unsolved, here goes. (INHALE)\r\n1) 50 is the most expensive, which leaves the other prices to be 10, 20, 30, 40. Diane spent the most. Possible pairs 50+40=90 and 50+30=80. 90 as a possible pair would mean that 3 girls would have to have bought 40 shirts. So Diane spent $80. The pairs left are 10+50 and 20+40 =60 and 10+40 and 20+30=40.\r\n2)Emily and Diane didn\'t buy the same shirts[3], so Emily didn\'t spend either $30 or $50 on a shirt, so she spent $40 on one. Because Carol spent $40[5], we know she didn\'t spend 30 or $50. The shirt that Alice and Carol bought in common wasn\'t $20[4], so it was $10. So Alice also bought a $50 shirt, Emily a $20 shirt and Betty $20 and $30 shirts. That gives me:\r\nAlice 10+50=60\r\nBetty 20+30=50\r\nCarol 10+40=50\r\nDiane 30+50+80\r\nEmily 20+40=60 okay....\r\n3) Blue and Green are not $10 [2], and Carol bought a blue shirt[2], and spent $10 and $40 on shirts. Therefore, blue is $40. Emily bought a blue shirt. Carol didn\'t buy a green shirt [Green is not 10[2] and she bought a $10 shirt]. Betty bought a red shirt[5], and since Betty and Alice didn\'t spend the same amount on shirts, Alice didn\'t buy a red shirt. Alice and Emily didn\'t buy an orange shirt [4], which means Alice bought a yellow and green shirt. Since Green is not $10 [2], green is $50. So Diane bought a green shirt. And Yellow shirts are $10, so Carol bought a yellow shirt. Emily had to have bought a red shirt [since she didn\'t buy yellow nor green nor orange] Therefore Red shirts are $20 [only amount Emily and Betty have in common]. Leaving Orange shirts to be $30, and they were bought by Betty and Diane. Final Answer:\r\nAlice==> Yellow (10) and Green (50)\r\nBetty==> Red (20) and Orange (30)\r\nCarol==> Blue (40) and Yellow (10)\r\nDiane==> Green (50) and Orange (30)\r\nEmily==> Blue (40) and Red (20)\r\n\r\n Does that make any sense?',NULL,0);
INSERT INTO comment VALUES (10974,1445,5097,'Cindy','ummmm','2004-01-08 00:00:09',0,'What about a chart? Like a pie chart. For organizational and categorizing purposes....just a guess...',NULL,0);
INSERT INTO comment VALUES (10975,1555,1253,'brianjn','Sophisticated programming or Math','2004-01-08 01:26:40',0,'Is the phrase meant to mean \"no sophisticated programming or sophisticated math\"? The solution of \"rerun141\" obviously meets such criteria.',NULL,0);
INSERT INTO comment VALUES (10976,1443,5100,'marky','alright here goes','2004-01-08 01:56:09',3,'okay im new at this so bear with me,\r\nso im choosing a base character of the knight,\r\nif you run through the facts putting him in each position there\'ll be a contridiction in every case except one,that being the real sequence,\r\nso just for the hell of it (and cause im not going through all of them again) D is the knight,\r\nif D is the knight then everything he says is true,making B the rebel,proving C came in second and B came third,rebel agrees with C coming third,the knight proves the rebels other two statements false,giving the rebel his acceptable LIE,LIE,TRUTH, the rebel proves the first two facts of A wrong,since the rebel spot is already taken that proves that A is the liar as it cant have a truth next,therefore C is the knave,the other facts confirm that C\'s pattern is LIE,TRUTH,LIE,\r\nso in the end........1st in the race is the liar:A,second comes the knave:C,third is the rebel B:,and finally the knight:D comes in last..because of all the armour i presume,and cause nice guys finish last',NULL,0);
INSERT INTO comment VALUES (10977,1445,4507,'Penny','How about this?','2004-01-08 03:29:42',3,'\"I coax the lazy of working by using pie. I\'m never placed in big use. To quit and just add error....Leaves fear on the loose. What am I?\" \r\n\r\nHere is my guess at a solution: You are a Pocket Personal Computer.\r\n\r\nExplanation:\r\n\r\nThe puzzle says \"what am I?\", not \"who?\". You are an object, not a person.\r\n\r\n\"Coax\" is common shorthand for \"coaxial cable connection for the Pocket PC\". \"Lazy of working\" is short for \"lazy message evaluation of (net)working\", an advanced software pipelining principle for performance enhancement on Pocket PC\'s.\r\n\r\n\"pie\" = P.I.E. = \"Pocket Internet Explorer\", which is implemented on Pocket PC\'s.\r\n\r\n\"I coax the lazy of working by using pie\", translated, becomes \"I connect to the Internet, through my coaxial connection, and implement lazy network message evaluation in Pocket Internet Explorer to achieve optimal performance.\" \r\n\r\n\"I\'m never placed in big use\" - of course not. You are a Pocket PC. You are a result of miniaturization. \r\n\r\n\"To quit and just add error leaves fear on the loose\" ? A secondary meaning of the word \"fear\" is \"a cause of trouble or error\". To quit a Pocket PC session abruptly can leave data in an inconsistent state and thereby leave \"fear\" (a cause of error) on the system.\r\n\n\nEdited on January 8, 2004, 11:30 am',NULL,0);
INSERT INTO comment VALUES (10978,1443,5103,'tripti','solution','2004-01-08 05:43:21',0,'a-liar\r\nb-rebel\r\nc-knave\r\nd-knight\r\n\r\norder in which they finish the race\r\na-1\r\nc-2\r\nb-3\r\nd-4',NULL,0);
INSERT INTO comment VALUES (10979,723,4197,'luminita','analytical solution (no computer used)','2004-01-08 08:44:39',3,'s=sqrt(25+12sqrt(3))\r\n\r\nProof:\r\ns=side of triangle\r\na=angle PCB\r\n\r\nin PCB and PAC - theorem of cosinus:\r\n16=25+s²-10s(cos(a))\r\n9=25+s²-10s(cos(pi/3-a))\r\n\r\ns²-10s(cos(a))+9=0\r\ns²-5s(cos(a))-5s√3(sin(a))=0\r\n\r\neliminate a\r\ncos(a)=(s²+9)/(10s)\r\nsin(a)=sqrt(1-cos(a)*cos(a))\r\n\r\nthe result is an equation (bi-square):\r\ns^4 - 50s^2 + 193 = 0\r\nthe unique solution satisfying the side of a triangle is:\r\n\r\ns=sqrt(25+12√3)\r\n',NULL,0);
INSERT INTO comment VALUES (10980,731,4197,'luminita','la meme Janette mais autrement coifee!','2004-01-08 09:56:07',3,'2^n+1=7k, k positiv integer\r\n\r\n2^n+1=(2³-1)k\r\n2^n=k2³-(k+1)\r\n\r\nin the right member of the equation it should:\r\nfor the first: k=even to complete a power of 2\r\nfor the second: k=odd cu complete an even number by adding 1.\r\n\r\ni.e. k=0\r\nso 2^n=-1 (impossible)\r\n',NULL,0);
INSERT INTO comment VALUES (10981,1445,4865,'Heartberry','re: How about this?','2004-01-08 11:24:13',1,'WOW! Great guess! :)',10977,0);
INSERT INTO comment VALUES (10982,1581,4507,'Penny','Solution','2004-01-08 11:26:43',3,'[The following solution is erroneous]\r\n\r\nThe original probabilities were:\r\n\r\n(1) Bob to be spared, and warden says \"Charlie\" - 1/3\r\n(2) Charlie is to be spared, and the warden says \"Bob\" - 1/3\r\n(3) Alan is to be spared, the warden flips a coin, Charlie \"wins\", and the warden says \"Charlie\" - (1/2)(1/3) = 1/6\r\n(4) Alan is to be spared, Bob \"wins\" the coin flip, and the warden says \"Bob\" -(1/2)(1/3) = 1/6\r\n\r\nSo the original odds that the warden will say \"Bob\" at all, were 1/3 + 1/6 = 1/2.\r\n\r\nOnce the warden did say \"Bob\", it was no longer possible for Bob to be spared. That leaves only two equally probable outcomes: Charlie to be spared (there was no coin flip), or Alan to be spared (there was a coin flip, and Bob \"won\"). \r\n\r\nThe men reasoned correctly. Their odds of survival increased to 1/2. \n\nEdited on January 8, 2004, 7:00 pm',NULL,0);
INSERT INTO comment VALUES (10983,940,4865,'Heartberry','','2004-01-08 11:33:16',3,'The number 7 on a phone key pad! :) I love this riddle :)',NULL,0);
INSERT INTO comment VALUES (10984,940,4865,'Heartberry','Solution :)','2004-01-08 11:33:52',3,'The number 7 on a phone key pad! :) I love this riddle :)',NULL,0);
INSERT INTO comment VALUES (10985,1581,3172,'SilverKnight','re: Solution','2004-01-08 11:35:51',0,'Penny\'s solution is incorrect.\r\n\r\nIt is unfair of me to say that without explanation of why it is incorrect. (I offer my apologies.) But as the submitter, I don\'t want to stifle other\'s responses. Also, I might have to answer my own submission.\r\n\r\nSimilarly, I don\'t want others to avoid posting further comments, because they assume this has been answered.',10982,0);
INSERT INTO comment VALUES (10986,1581,1920,'Brian Smith','Solution','2004-01-08 11:45:51',3,'The men reasoned incorrectly. Alan still has probability 1/3, but Charlie has probability 2/3.\r\n\r\nAfter Alan says \"Then don\'t tell me now, tell me tomorrow morning\", There are 4 possible scenarios:\r\n\r\n1)Warden must say \"Bob\" (Charlie is pardoned) p=1/3\r\n2)Warden must say \"Charlie\" (Bob is pardoned) p=1/3\r\n3)Warden randomly chooses \"Bob\" (Alex is pardoned) p=1/6\r\n4)Warden randomly chooses \"Charlie\" (Alex is pardoned) p=1/6\r\n\r\nAfter the warden tells Alan that Bob was going to be executed, the possible scenarios are only (1) and (3). Therefore the probability Alan gets the pardon is (1/6)/(1/3 + 1/6) = 1/3, and the probability Charlie gets the pardon is (1/3)/(1/3 + 1/6) = 2/3.',NULL,0);
INSERT INTO comment VALUES (10987,1581,1920,'Brian Smith','re: Solution','2004-01-08 11:49:44',0,'You have made a mistake. You say \"That leaves only two equally probable outcomes Charlie to be spared (there was no coin flip), or Alan to be spared (there was a coin flip, and Bob \"won\")\"\r\nFrom your oun figures, \"Charlie is to be spared\" has probability 1/3 BUT \"There was a coin flip, and Bob \'won\'\" has probability 1/6.',10982,0);
INSERT INTO comment VALUES (10988,1581,2716,'Federico Kereki','Opinion','2004-01-08 11:56:48',1,'Unless I\'m mistaken, Alan\'s chances are still 1/3, but Charles\' went up to 2/3.',NULL,0);
INSERT INTO comment VALUES (10989,1581,4982,'Dan Blume','Different point of view','2004-01-08 12:06:19',0,'Looking at it from a different point of view. What are the odds of Bob\'s name comming up if Bob is not pardoned. Knowing it could only be Alan or Charlie, that gives each of those outcomes 1 in 2. If it is Charlie that is pardoned, then Bob\'s name will come up 100% of the time. If it is Alan that is pardoned, Bob\'s name will come up 50% of the time. This works out to 1/2*1/2 + 1/2*1 = 3/4. Bob\'s name will come up 75% of the time. Since it will come up twice as often if Charlie is pardoned vice Alan is pardoned, then Charlie is twice as likely to have received the pardon. So Charlie should have 2/3 chance of getting the pardon, while Alan still remains at 1/3.',NULL,0);
INSERT INTO comment VALUES (10990,1445,3820,'Joseph ODonnell','re: How about this? from Penny','2004-01-08 13:59:49',0,'Great thought, Penny! I hope you are correct.',NULL,0);
INSERT INTO comment VALUES (10991,453,4718,'Jack Squat','technically speaking','2004-01-08 14:12:03',0,'Mathemagician is right, negative answers need to be looked at too, if you want to get technical. Of course if you really read the problem carefully, the problem only says to \"find\" the square root, it doesn\'t ask to use the square root of the number. The correct answer then becomes +/-16. But that obviously wasn\'t the point of the question!',NULL,0);
INSERT INTO comment VALUES (10992,1581,4197,'luminita','possible solution','2004-01-08 16:03:17',1,'There are 4 possible situations:\r\n1: Bob pardoned, no coin necessary, answer=Charlie, prob = 1/3\r\n2: Charlie pardoned, no coin necessary, answer=Bob, prob = 1/3\r\n3: Alan pardoned, coin face 1, answer=Bob, prob=(1/3)(1/2)=1/6\r\n4: Alan pardoned, coin face 2, answer=Charlie, prob=(1/3)(1/2)=1/6\r\nThe answer beeing Bob, the event 2 is twice probable than event 3, so the probability Alan is pardoned remains 1/3 but the probability of Charlie to be pardoned rise at 2/3.',NULL,0);
INSERT INTO comment VALUES (10993,1581,4507,'Penny','re: Solution','2004-01-08 18:00:49',0,'SilverKnight says that my solution is incorrect. I think so too, now. It isn\'t the first time I have been mistaken. I don\'t know why he felt the need to apologize. \r\n\r\nAfter the warden speaks, the only possibilities are, as you point out, (1) and (3). Since initially (1) was twice as likely as (3), it must remain so. I guess the odds are as you stated them, rather than as I did. Charlie\'s odds are twice Alan\'s, and since they must now total 1, Charlie\'s odds must be 2/3, and Alan\'s 1/3. \n\nEdited on January 8, 2004, 6:37 pm',10986,0);
INSERT INTO comment VALUES (10994,91,5033,'Captain Paradox','Hey Freshter!','2004-01-08 19:10:57',1,'Hey Freshter . . . yes, you got the answer right, but please try not to put the answer in the title of your comment . . . it ruins the surprise for those who see the comment list.\r\nThanks',299,0);
INSERT INTO comment VALUES (10995,1566,3172,'SilverKnight','Is this even possible?','2004-01-08 19:18:18',4,'Yes, it is... my mistake!\n\nEdited on January 8, 2004, 7:50 pm',NULL,0);
INSERT INTO comment VALUES (10996,1581,5115,'James','Idea','2004-01-08 19:40:20',0,'The two men each have a 1/3 probablity of being pardoned. \r\nThe probability of being pardoned was determined by th enumber of names in the hat and the number drawn. \r\nThe information that the warden gives does not change the fact that there were three names in the hat and only one was drawn. \r\nWhile he can confim who is or is not pardoned, he cannot change the probability of one being pardoned because the draw occured in the past. \r\n\r\n(There is actualy a 100% probability that one wil be pardoned and a 0% probability that the other will be, because it has already been determined. But, that doesn\'t change the probability of any name being drawn)',NULL,0);
INSERT INTO comment VALUES (10997,1566,3172,'SilverKnight','solution','2004-01-08 20:06:47',3,'If I had to guess... I\'d say there were 8 solutions.\r\nBut they have duplicates (if you count mirrors and rotations), so only the first two are truly different solutions.\r\n\r\n3 is a rotation of 2\r\n4 is a rotation of 1\r\n8 is a mirror of 1\r\n7 is a mirror of 2\r\n5 is a rotation of 8\r\n6 is a rotation of 7\r\n\r\nand the following is what I think they are:\r\n\r\n \r\n\r\n(from The Tragedy of Coriolanus) \"Before we proceed any further, hear me speak.\" \r\n(from The Tragedy of Julius Caesar) \"Hence! home, you idle creatures get you home:\"\r\n(from The Third Part of Henry the Sixth) \" I wonder how the king escaped our hands.\"\r\n(from The Life and Death of King John) \"Now, say, Chatillon, what would France with us?\"\r\n(from Pericles, Prince of Tyre) \"To sing a song that old was sung,\"\r\n\r\nThe most probable one that will work with the 1st line is \"Hence! home, you idle creatures get you home:\" but probably that is the not the first line in which Sam speaks of. Well, I\'ve probably missed a few plays with 8-word first lines. Please inform us all if I did\r\n\r\n\r\n\r\n\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (11011,1581,5124,'ofma','agree with james!','2004-01-09 17:35:34',0,'agree with james!',NULL,0);
INSERT INTO comment VALUES (11012,1008,5045,'erin','Solution','2004-01-09 18:59:08',0,'I\'d say that the people who have two Es in their name are drinking coffee, and those with one E are drinking soda. So Elizabeth is drinking coffee.',NULL,0);
INSERT INTO comment VALUES (11013,1008,5045,'erin','Solution','2004-01-09 18:59:43',0,'I\'d say that the people who have two Es in their name are drinking coffee, and those with one E are drinking soda. So Elizabeth is drinking coffee.',NULL,0);
INSERT INTO comment VALUES (11014,1584,3558,'Tristan','re: -more Shakespeare lines','2004-01-09 19:44:44',0,'Besides the Tragedy of Julius Caesar, I don\'t think those are the \"more famous plays.\" Also, you are assuming that \":\" is the break between words. While you could be right, I don\'t think that \"247\" decrypts to \"creatures.\"\r\n\r\nHere are the first lines of a few famous Shakespeare plays.\r\n\r\nMacbeth: \"When shall we three meet again\"\r\nRomeo and Juliet: \"Two households, both alike in dignity,\"\r\nA Midsummer Night\'s Dream: \"Now, fair Hippolyta, our nuptial hour\"\r\nThe Two Gentlemen of Verona: \"Cease to persuade, my loving Proteus\"\r\nThe Merchant of Venice: \"In sooth, I know not why I am so sad.\"\r\nOthello: Tush, never tell me! I take it much unkindly\"\r\n\r\nNone of these have 8 words, which is presumably why Victor had to choose a bunch of plays I\'ve never heard of.',11010,0);
INSERT INTO comment VALUES (11015,1379,3558,'Tristan','And the title...','2004-01-09 19:49:20',3,'bETWeen',NULL,0);
INSERT INTO comment VALUES (11016,1270,5126,'melanie','solution ( i think)','2004-01-09 20:38:12',3,'2-mrs chandler, toast, blackbird\r\n4-mrs dennis, bread, sparrow\r\n6-mrs allison, birdseed, thrush\r\n8-mrs emery, cake crumbs, cardinal\r\n10-mrs brewer, suet, robin',NULL,0);
INSERT INTO comment VALUES (11017,1270,5126,'melanie','re: JinCo\'s Solution','2004-01-09 20:39:27',0,'yeah, thats wut i got too.',10268,0);
INSERT INTO comment VALUES (11018,1509,5126,'melanie','solution (its a leapyear!)','2004-01-09 20:55:00',3,'march 15, 1996',NULL,0);
INSERT INTO comment VALUES (11019,1256,5126,'melanie','obvious solution! duh','2004-01-09 21:03:39',3,'hotel road. my duddy is a retired air force airplaner.and u should read the wanderer by sharon creech if u didnt know this answer. duh',NULL,0);
INSERT INTO comment VALUES (11020,1051,5126,'melanie','solution','2004-01-09 21:05:21',0,'obviously anyone who knew their animals would know it was a manatee. if u didnt know this.................um...........',NULL,0);
INSERT INTO comment VALUES (11021,1010,5126,'melanie','no duh its a SOUL!!!!!!!!!!!!!!!!!!!!!!','2004-01-09 21:06:29',0,'hi',NULL,0);
INSERT INTO comment VALUES (11022,1581,5115,'James','','2004-01-09 21:07:14',0,'re: Yep - er, nope\r\n\r\nThere was a 50:50 chance that you world have been concieved a boy or a girl. At the moment of conception, the outcome was determined. Of course, the probability of any event in the past is always 100% (or 0), because it has already happened (or didn\'t happen).\r\n\r\nI\'m saying that Bob has a 100% chance of being executed. There was a one in three chance that his name would be drawn, but it wasn\'t. There is a 100% chance he will be executed if his name isn\'t drawn. The outcome has already been revealed.\r\nFor each of them, there were only two possible outcomes, pardon or execution. However, revealing the outcome for one prisioner does not change the basic probobibility for another.\r\nRemoving one prisioner\'s name from the hat before the drawing would have. But, it doesn\'t work both ways.\r\n',NULL,0);
INSERT INTO comment VALUES (11023,1012,5126,'melanie','oh yeah, im so smarty','2004-01-09 21:08:24',3,'When he was born his father was present. \r\nHis mother died during labor. \r\n\r\nHe was a pastor and married his sister to her husband. \r\n',NULL,0);
INSERT INTO comment VALUES (11024,940,5126,'melanie','well duh','2004-01-09 21:11:30',3,'the seven key on the tellyphone',NULL,0);
INSERT INTO comment VALUES (11025,1584,4507,'Penny','Solution (no computer program used)','2004-01-10 00:53:15',3,'Answer: The two Shakespeare quotes in this puzzle, represented by the two number strings, are the first two lines of Richard III: \r\n\r\n\"Now is the winter of our discontent\r\nMade glorious summer by this sun of York\"\r\n\r\nExplanation:\r\n\r\nSam\'s two number strings contain unfortunate typo\'s: one in the first string and two in the second. Correcting for the three typo\'s, the number strings should be: \r\n\r\n232232:1428:23176:321623251421:247:242827:9182212162327141929:97959391 \r\n\r\n144510:819162710182224:20281422621:330:21151028:202415:207:32162712:13151719\r\n\r\nEach of these encrypted messages has its decryption key appended to it: \"97959391\" at the end of the first number string, and \"13151719\" at the end of the second. \r\n\r\nDecode each of these number strings by applying the decryption keys, then doing ordinary letter substitution on the results (1=A, 2=B, 3=C, etc.)\r\n\r\nStarting with the first string, which has decryption key \"97959391\", subtract these 8 digits from the number string: 9 from the 1st number, 7 from the 2nd, 9 from the 3rd, 5 from the 4rth, 9 from the 5th, 3 from the 6th, 9 from the 7th, 1 from the eighth, and repeating this for the next 8 numbers, etc. \r\n\r\nStarting with \r\n\r\n232232:1428:23176:321623251421:247:242827:9182212162327141929, subtract:\r\n\r\n[23-9][22-7][32-9]:[14-5][28-9]:[23-3][17-9][6-1]:[32-9][16-7][23-9][25-5][14-9][21-3]:[24-9][7-1]:[24-9][28-7][27-9]:[9-5][18-9][22-3][12-9][16-1][23-9][27-7][14-9][19-5][29-9]\r\n\r\nDoing these subtractions and then in each case substituting the appropriate letter by substitution (1-A, 2-B, 3-C, etc), this becomes: \r\n\r\n141523 (NOW) 919 (IS) 2085 (THE) 2391420518 (WINTER) 156 (OF) 152118 (OUR) 4919315142051420 (DISCONTENT) \r\n\r\nNow for Sam\'s second number string:\r\n\r\n144510:819162710182224:20281422621:330:21151028:202415:207:32162712\r\n\r\nThis time apply the decryption key \"13151719\". \r\n\r\n[14-1][4-3][5-1][10-5]:[8-1][19-7][16-1][27-9][10-1][18-3][22-1][24-5]:[20-1][28-7][14-1][22-9][6-1][21-3]:[3-1][30-5]:[21-1][15-7][10-1][28-9]:\r\n[20-1][24-3][15-1]:[20-5][7-1]:[32-7][16-1][27-9][12-1]\r\n\r\nWhich becomes:\r\n\r\n13145 (MADE) 71215189152119 (GLORIOUS) 19211313518 (SUMMER) 225 (BY) 208919 (THIS) 192114 (SUN) 156 (OF) 25151811 (YORK)\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\n\nEdited on January 10, 2004, 6:44 am',NULL,0);
INSERT INTO comment VALUES (11026,1010,3558,'Tristan','re: no duh its a -----!!!!!!!!!!!!!!!!!!!!!!','2004-01-10 02:10:43',0,'In case you didn\'t notice, when you post, it says \"(If posting a solution, don\'t give it away in the subject!).\" But then, you may not notice this comment either.',11021,0);
INSERT INTO comment VALUES (11027,1582,2716,'Federico Kereki','Proof','2004-01-10 09:28:02',3,'This is known as \"Van Aubel\'s Theorem\", and here is a nice proof involving complex numbers. \n\nEdited on January 10, 2004, 9:30 am',NULL,0);
INSERT INTO comment VALUES (11028,1584,3372,'Sam','re: Solution (no computer program used)','2004-01-10 10:31:03',0,'Well done. I tried to make the key something that would catch one\'s eye if they were looking for it, though obviously if it were random and the person didn\'t expect it, it would be much harder to break.\r\nExcuse the typos - I thought I had gone over it pretty thoroughly... :)',11025,0);
INSERT INTO comment VALUES (11029,1582,3372,'Sam','Small problem','2004-01-10 11:18:21',0,'It sounds like they are expected to always intersect. It\'s quite esy to draw an example where they don\'t intersect though - make the quadrilateral a very wide-based, yet short, triangle with the top shaved off. The horizontal line will be formed above the top square.\r\n\r\nHowever, I assume that you just mean the lines would be perpendicular were they to be extended.\r\n\r\nI wonder if someone can provide us with a more intuitive proof then the one Federico linked?',NULL,0);
INSERT INTO comment VALUES (11030,1582,4507,'Penny','re: Proof','2004-01-10 12:42:02',0,'It\'s interesting that you used the work of a famous mathematician to solve this one. Just the other day, CNN announced that another noted mathematician, a Russian named Grigori Perelman, now has a definite answer for \"Poincare\'s Conjecture\", which ranks right up there with \"Fermat\'s Last Theorem\" among famous unsolved (until recently) mathematical problems. Perelman stands to get a cool million dollars for his achievement, although I\'m sure he was motivated by a love of pure mathematics rather than a desire for monetary gain. Details of Perelman\'s coup can be found at:\r\n \r\nhttp://www.theage.com.au/articles/2003/08/02/1059480600718.html \r\n\n\nEdited on January 10, 2004, 12:45 pm',11027,0);
INSERT INTO comment VALUES (11031,1582,153,'TomM','re: Small problem','2004-01-10 13:27:36',0,'>>I wonder if someone can provide us with a more intuitive proof then the one Federico linked?\r\n\r\nMy approach was going to use analytical algebra (Cartesian geometry), and thus would have been similar to the proof Federico linked to. \r\n\r\nIt can also be done with Euclidean geometry as well, by constucting intermediate congruent triangles',11029,0);
INSERT INTO comment VALUES (11032,1443,5138,'Darlene','Taking a guess','2004-01-10 18:23:24',3,'I believe I have the solution to \"The Rebel\"\r\n\r\nC is the The Knave and is the winner\r\nA is the Knight and came in 2nd place\r\nD is the Rebel and came in 3rd place\r\nB is the Liar and came in last place.\r\n\r\nMy name is Darlene Weber and I am new to your sight. My e-mail address is WEDARLE@cs.com. I very much enjoy doing things like this and look forward to being a part of your website.',NULL,0);
INSERT INTO comment VALUES (11033,1581,5140,'Leo','another solution','2004-01-10 22:04:03',3,'There is a chance of 3 out of 4 that Charlie is the one that has been pardoned and only 1 out of 4 that Alan is the one. \r\nInitially there were three possible answers to the question \'who has been pardoned\' but because we have been told that Bob will be executed, there are only two possible outcomes remaing (either Alan or Charlie is pardoned). \r\nIn this situation the probability that Bob would have been named by the warden is 100% if Charlie would have been pardoned, and 50% if Alan would have been the one. So in 3 out of 4 cases the answer \'Bob\' points to the outcome that Charlie has been pardoned and in only 1 out of 4 cases will Alan prove to be the lucky one the next day. Am I right?',NULL,0);
INSERT INTO comment VALUES (11034,1581,5140,'Leo','re: another solution - not!','2004-01-11 05:09:46',0,'Oops, it was late when I wrote that. What I should have said was that thc chances are 2 out of 3 that Charlie is lucky, because in 2 out of 3 (not 3 out of 4) cases the answer \'Bob\' indicates Charlie. I just forgot that in that one of the four outcomes where either A or C are pardoned the answer would be \'Charlie\' - which it wasn\'t :)\r\n',11033,0);
INSERT INTO comment VALUES (11035,1459,4507,'Penny','Solution (no program used)','2004-01-11 21:51:36',3,'What ?? They weren\'t wearing pants ?!?!\r\n\r\nThe first to arrive at the dance was the puzzle answerer, \"B\", wearing a blue shirt, green tie, and green suspenders. He is standing on the left in the photograph. The next person to arrive was wearing a green shirt, white tie, and white suspenders. He is standing on the right in the photo. The third person to arrive was wearing a red shirt, blue tie and red suspenders. He is standing in the middle in the photo. The last person to arrive was wearing a white shirt, red tie and blue suspenders. He is sitting in the photo.\r\n\r\nExplanation.\r\n \r\nI made the following assumptions, from the wording of the puzzle:\r\n\r\n(1) I did not assume that no one wore the same color for any two items of his apparel. In other words, if he wore a blue shirt, he could still have worn a blue tie. Had this been otherwise, it would have been stated explicitly in the puzzle. \r\n(2) From \"...the person with the red shirt...the person wearing the green shirt....the person with the blue shirt...\", each person wore a different color shirt.\r\n(3) From \"...the person with the green suspenders...the person wearing the red suspenders...the person with the white suspenders...\", each person wore different color suspenders. \r\n(4) From \"...the person wearing the red tie.....the person with the blue tie...the person...was wearing a white tie\" ..., each person wore a different color tie.\r\n\r\nFor each of the four people, use three of the letters R (Red), W (White), B (Blue), and G (Green) to represent the color of his shirt, tie, and suspenders, in that order. (e.g. WRB = \"White shirt, Red tie, Blue suspenders\"). Let the \"less than\" symbol, < , indicate an earlier arrival at the dance. ( <> means \"not equal to\"). Let x\'s represent the missing letters. The puzzle can now be summarized in five statements: \r\n\r\n(a)(Rxx < xWx < xxG) or (xxG < xWx < Rxx) \r\n(b) Gxx < xxR < xRx \r\n(c)(Bxx <> xBx) and (Bxx <> xxW) and (xBx <> xxW)\r\n(d) The last arrival was not Bxx, xBx, or xxW\r\n(e) xGx must be either RGx or BGx\r\n \r\n(Therefore the following combinations are disallowed: RWx, RxG, xRR, BBx, xWG, GxR, GRx, BxW, xBW, WGx, and GGx.)\r\n\r\nNow isn\'t this puzzle suddenly a lot easier? What a difference the right use of notation makes ! \r\n \r\nThe only possibility that does not quickly lead to a contradiction of the rules of the puzzle is:\r\n\r\nxxG < GWW < RxR < xRB\r\n\r\nThe only way to fill in the x\'s without contradiction is: \r\n\r\nBGG < GWW < RBR < WRB \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\n\nEdited on January 12, 2004, 11:13 am',NULL,0);
INSERT INTO comment VALUES (11036,1582,3172,'SilverKnight','re(2): Small problem','2004-01-12 00:32:39',0,'For what it\'s worth, I was looking for a \"simpler\" solution that didn\'t involve complex numbers. (When I say \"simpler\", I mean using real numbers only.) What Federico submitted is a valid solution, but certainly, not everyone in Flooble\'s audience is familiar with imaginary numbers and rotating complex vectors by multiplication of -i.\r\n\r\nThat being said, here\'s a nice link to an applet that helps explain this, and perhaps someone may choose to submit a different (perhaps Cartesian) solution.',11031,0);
INSERT INTO comment VALUES (11037,1280,4507,'Penny','Solution','2004-01-12 09:54:19',3,'Answer: The hands of the clock are opposite each other at 4:54 and 33 seconds.\r\n\r\nExplanation:\r\n\r\nThe minute hand moves 360 degrees/hour \r\n= 1/10 degree/second. The hour hand moves 360 degrees/12 hours = 1/120 of a degree/second. At 4 o\'clock, the minute hand is straight up (zero degrees), and the hour hand is at the 4 (120 degrees). T seconds after 4 o\'clock, the minute hand is at T/10 degrees and the hour hand is at (120 + T/120) degrees, and the angle between them is \r\nT/10 - (120 + T/120). When they are pointing in opposite directions, this angle is 180 degrees. \r\n\r\n180 = T/10 - (120 + T/120)\r\n\r\nT = 3273 seconds = 54 minutes + 33 seconds\r\n\r\nSo the hands are opposite each other, 54 minutes and 33 seconds after 4:00.\r\n \n\nEdited on January 12, 2004, 9:58 am',NULL,0);
INSERT INTO comment VALUES (11038,1280,885,'np_rt','Full Solution','2004-01-12 10:36:01',0,'The hour hand moves 360 degrees in 24 hours (1/120 degree/sec) and the minute hand moves 360 degrees in 1 hour (1/10 degree/sec). They are at the exact spot at 12 (noon or midnight).\r\n\r\nObviously the minute hand moves faster than the hour hand. If they are to be exactly opposite each other, the minute hand must travel 180, 540, 900,...,180+360n degrees more than the hour hand if they both start at 12.\r\n\r\nLetting t to be the time in seconds where they are opposite each other,\r\n\r\n(1/10-1/120)*t = 180 + 360n, where n = 0, 1, 2,...\r\nt = 21600/11 + 43200n/11\r\n\r\nThe one that comes right before 6 o clock is 4:54:33.',NULL,0);
INSERT INTO comment VALUES (11039,1280,3224,'Lee','working backwards','2004-01-12 12:47:50',0,'The time taken, T, for a minute hand, traveling at 6 degrees per minute to travel exactly 360 degrees more than an hour hand (traveling at ½ degree per minute) is given by\r\n6T + 360 = ½ T\r\nT = 720/11 minutes. (1 hour 5 minutes 27 seconds (to the nearest second))\r\nSo every 720/11 minutes the hands are in exactly the same position, relative to each other.\r\nSo the hands were opposite, prior to 6 o clock, 720/11 minutes earlier\r\nAt 4:54 and 33 seconds \r\n',NULL,0);
INSERT INTO comment VALUES (11040,1384,3172,'SilverKnight','solution','2004-01-12 14:31:33',3,'One possible solution:\r\n\r\nREPEATED (PEER, DATE)\r\nJUVENILE (JUNE, VILE)\r\nSNOWBALL (SNOB, WALL)\r\nESTIMATE (TIME, SEAT)\r\nANTELOPE (PALE, TONE)',NULL,0);
INSERT INTO comment VALUES (11041,1384,4507,'Penny','Solution (program not used)','2004-01-12 16:42:04',3,'This one yielded without too much fuss to a methodical approach.\r\n\r\nPEER + DATE = DEPARTEE (or REPEATED) \r\nTIME + SEAT = ESTIMATE\r\nWALL + SNOB = SNOWBALL\r\nJUNE + VILE = JUVENILE\r\nTONE + PALE = ANTELOPE\r\n',NULL,0);
INSERT INTO comment VALUES (11042,1459,4507,'Penny','Miraculous Melons ?????','2004-01-12 16:46:14',1,'After solving this one, I tried to look up \"Miraculous Melons\" on the Internet, in an attempt to confirm my answer. The search took me to a pornographic French website !! :0) ',NULL,0);
INSERT INTO comment VALUES (11043,1280,4374,'Richard','Different Answer','2004-01-12 23:58:20',3,'I take the total displacements of the hands as being t and 12t. Then they are opposite whenever t + 6 = 12t - 12k for some integer k. For example, if t = 6, and k = 5 we have the hands at 6 and 12. Solving the condition for t gives t = (6 + 12k)/11, so the hour hand is at 6/11, 18/11, 30/11, 42/11, 54/11, 66/11 (=6) when the minute hand is opposite. 54/11 = 4 9/11 = 4:54:32 8/11.\n\nEdited on January 13, 2004, 1:11 am',NULL,0);
INSERT INTO comment VALUES (11044,1587,4670,'e.g.','Tessellation','2004-01-13 08:48:01',3,'Imagine the complete plane tessellated with large/small circles, such as above. Then, the diameter of the blue circle plus the diameter of the red circle, add to the diagonal of the square.',NULL,0);
INSERT INTO comment VALUES (11045,1587,1301,'Charlie','solution','2004-01-13 09:27:05',3,'A square formed by the center of one of the large blue circles, the points of tangency of this circle with its neighboring circles, and the center of the small red circle, is 1 unit on a side and has as its diagonal the sum of the radii of the large and small circles. The diagonal is √2, so the radius of the center circle is (√2) - 1.',NULL,0);
INSERT INTO comment VALUES (11046,1384,5175,'Surender Taalla','some more !','2004-01-13 10:01:08',0,'\r\nMEDITATE (TIME, DATE)\r\nDETONATE (DATE, TONE)\r\n',11040,0);
INSERT INTO comment VALUES (11047,1587,2716,'Federico Kereki','re: Tessellation','2004-01-13 10:08:19',1,'I assume that a unit square is referred to; if the 2x2 square shown in the picture is meant, then the solution is clearly wrong.',11044,0);
INSERT INTO comment VALUES (11048,1587,4982,'Dan Blume','','2004-01-13 11:23:25',0,'Draw a line diagonally through the square so that it passes through the centers of two of the circles. From the center of the circle to the side of the square create a right triangle. Length of the diagonal from the center to the corner is r*(2^.5). Radius of a circle that you can fit in the corner, is then r*(2^.5)-r.\r\n\r\nEdited on January 13, 2004, 11:24 am\n\nEdited on January 13, 2004, 11:27 am',NULL,0);
INSERT INTO comment VALUES (11049,529,4257,'Jack McBarn','re: no way!','2004-01-13 11:29:28',1,'No, just B.C.',5180,0);
INSERT INTO comment VALUES (11050,529,4257,'Jack McBarn','Yes it was (re: Well, that wasn\'t so intelligent)','2004-01-13 11:32:09',2,'The coin could have been dug up and reburied or it could have been dropped years after.',5784,0);
INSERT INTO comment VALUES (11051,529,4257,'Jack McBarn','re: The official solution of this problem is in error','2004-01-13 11:32:59',0,'No it\'s not. They can\'t predict!',9391,0);
INSERT INTO comment VALUES (11052,1384,1301,'Charlie','re: some more !','2004-01-13 13:06:49',0,'But\r\nMEDITATE (TIME, DATE) \r\nDETONATE (DATE, TONE) \r\nleave other 4-letter words without appropriate combinations, as the idea is to pair all 10 words at the same time.',11046,0);
INSERT INTO comment VALUES (11053,1570,3172,'SilverKnight','solution (spoiler)','2004-01-13 13:39:48',3,' \r\n\r\nX \r\nFIRST did not come first, so:\r\n____ ____ ____ ____ ____\r\n------Fir---Fir---Fir---Fir\r\nSECOND was neither first nor last.\r\n____ ____ ____ ____ ____\r\n-----Fir--Fir--Fir--Fir\r\n-----S----S----S\r\nTHIRD came in one place after FIRST. (This means FIRST can\'t be last, for there is no place after last place.)\r\n____ ____ ____ ____ ____\r\n-----Fir--Fir--Fir\r\n-----S----S----S\r\n----------T----T----T\r\nFOURTH was not second.\r\n____ ____ ____ ____ ____\r\n-----Fir--Fir--Fir\r\n-----S----S----S\r\n----------T----T----T\r\nFo--------Fo---Fo---Fo\r\nFinally, FIFTH was two places below FOURTH (This means that FOURTH can\'t be 4th or last place, for there is no place 2 places after them.)\r\n____ ____ ____ ____ ____\r\n-----Fir--Fir--Fir\r\n-----S----S----S\r\n----------T----T----T\r\nFo--------Fo\r\n----------Fif-------Fif\r\nBecause there is only one horse that could be first place (FOURTH), it must be first. Because we know where FOURTH is, we know where FIFTH is, which is 2 places after. No other horse can be in that place.\r\n-Fo--____ Fif--____ ____\r\n-----S---------S \r\n-----Fir-------Fir\r\n---------------T----T\r\nFIRST cannot be 2nd place because THIRD has to be one place after FIRST, but 3rd place is already filled. So, FIRST but in the remaining spot, 4th. Thus, THIRD must be last.\r\n-Fo--____ Fif--Fir--T\r\n-----S\r\nBecause SECOND remains, it must be in the last spot.\r\n Fo S Fif Fir T\r\nFOURTH SECOND FIFTH FIRST THIRD\r\n',NULL,0);
INSERT INTO comment VALUES (11133,1286,4507,'Penny','re: solution (same as sks) but diff approach','2004-01-19 09:43:07',4,'I hate to nag, but why did you post this elaborate solution? A superficial reading shows that only FOURTH could have finished 1st, and the 2nd place finisher was either FIRST or SECOND. From that, and the other hints, it takes about 3 seconds to solve this one. ',11132,0);
INSERT INTO comment VALUES (11134,1286,1567,'Bryan','re(2): solution (same as sks) but diff approach','2004-01-19 10:26:25',0,'Actually, Penny loves to nag (c\'mon, Penny, be honest!), but I agree with her conclusion.',11133,0);
INSERT INTO comment VALUES (11135,1286,2716,'Federico Kereki','Short solution','2004-01-19 11:50:14',3,'FIRST, SECOND, THIRD and FIFTH couldn\'t be 1st, so FOURTH was 1st, and thus FIFTH was 3rd. FIRST must have been 4th so THIRD can be one place after (5th), and so SECOND was 2nd.\r\n',NULL,0);
INSERT INTO comment VALUES (11136,1599,4374,'Richard','It looks to me like ...','2004-01-19 13:42:34',1,'It looks to me like the number base must be odd. Also, it looks to me like the binomial theorem will be a useful tool to show that at least one of the two numbers must be even, especially in the case where the base is of the form 4k+3.',NULL,0);
INSERT INTO comment VALUES (11137,1574,2899,'Brian Wainscott','Simple approach','2004-01-19 13:52:15',0,'You can always do it simply in 10 weighings..\r\n\r\nTake one coin and designate it the \"master\" coin.. Take each each of the other coins in turn and weigh them against this one. At some point you will find a coin that is heaver or lighter than the master. Also, you will find 5 other coins of the same weight as the master. Once you have done both of these, you are done. This could be as few as 6 weighings, or as many as 10. There is never any point in weighing the last coin, since you know what it must be....\r\n\r\nBut I think Charlie\'s worst case of 9 is best.\n\nEdited on January 19, 2004, 3:30 pm',NULL,0);
INSERT INTO comment VALUES (11143,1574,4189,'John','re: Simple approach','2004-01-19 17:52:38',0,'I like the \"Master Coin\" method. To reduce the maximum weighings from 10 to 9 (thereby tying Charlie\'s method) you can weigh two of the final 3 \"unknown\" coins on the 9th weighing. If they\'re equal, they both belong to whichever category you know 4 of. If they\'re unequal, then they\'re one each, and you know which is which, and you know what the 12th coin must be.\r\n\r\nThere\'s no need to weigh any of the final 3 coins against the Master Coin.\r\n\r\nCheers! :^)',11137,0);
INSERT INTO comment VALUES (11138,1599,1626,'Gamer','re: It looks to me like ...','2004-01-19 14:08:48',3,'The first number is never prime. As long as it\'s written in at least base 3, it\'s divisible by 101010101... times 11; \r\n\r\nFor example, if it was base 5, it would be (6*1)+(6*25)+(6*625)... in base 10.\r\n\r\n\r\nThe second number would be represented by (11*10)+2, and since the first number is 1 more than the second, one of them must be divisible by two. Even times odd plus even is still even and divisible by 2 so it\'s not prime either.\r\n\r\nFor example, 112 in base 5 is (6*5)+2, or 32, in base 6 it\'s (7*6)+2 or 44.',11136,0);
INSERT INTO comment VALUES (11139,1599,4670,'e.g.','Short','2004-01-19 14:08:53',3,'If the first number (1111...11) is in base P, it is (1+)(1+P^2+P^4...); if it has more than two digits, it will be a composite number. Therefore, the first number is just 11, and P must be one less than a prime. Also, P cannot be 2, since that digit is used in the second number, so P is even. \r\nIn the latter case, call the base B; the second number would equal a multiple of B, + 2, which would be even, so it couldn\'t be a prime.',NULL,0);
INSERT INTO comment VALUES (11150,532,5178,'Dan Porter','Another solution','2004-01-20 08:53:44',0,'Before the flood people live 500 years or more having who knows how many children per couple. If heaven only had thousands and not millions or billions then he may have known them on earth.\r\n\r\nAlso, if you think about it. You have 2 parents, 4 grandparents, 8 great grandparents... ect. So if you keep going you exceed the population of the planet well after the death of Christ. Therefore we are all products of some sort of distant incest without reguard to creation vs evolution.',NULL,0);
INSERT INTO comment VALUES (11151,1390,5178,'Dan Porter','They were all wrong','2004-01-20 09:04:01',0,'Cats kill to eat. A rat is a big meal for a cat. Cats always sleep for hours after a big meal. 6 cats might kill 6 rats in 6 minutes but it would be hours at least before any of the 6 killed again. To kill 100 rats in 50 minutes you need 100 cats.\r\n\r\nCats sometimes kill for fun but they also sometimes share prey. All the answers are too low!\n\nEdited on January 20, 2004, 9:09 am',NULL,0);
INSERT INTO comment VALUES (11152,1390,1301,'Charlie','2/3 of an answer','2004-01-20 09:09:16',1,'Ryan\'s answer is based on the assumption that if, as in this case, one cat can kill one rat in 6 minutes, then three cats can kill one rat in 2 minutes. This is because 50 minutes is not evenly divisible by 6 minutes, the killing time for one rat by one cat. After 48 minutes, during which each of Ryan\'s 12 cats has killed 8 rats, for a total kill up to then of 96 rats, Ryan assumes that the remaining 4 rats can be killed in the remaining two minutes by teaming up 3 cats to each of these rats.\r\n\r\nStefanie, loath to make the assumption that just because one cat can kill one rat in 6 minutes that they can team up with the same efficiency, provides enough cats to get the job done in 48 minutes, leaving 9 of the cats with two minutes of rest each and 4 of the cats with 8 minutes rest (9 x 8 + 4 x 7 = 100).\r\n\r\nTom must have convinced the teacher that the cats would get in each other\'s way. I can\'t figure a good mathematical reason for choosing 14, however.\n\nEdited on January 20, 2004, 9:13 am',NULL,0);
INSERT INTO comment VALUES (11153,554,5178,'Dan Porter','Not looking at the solution','2004-01-20 10:49:19',0,'Without looking at the solution I would count up from one. For every number that is not prime I would concatonate 10 to the right end of the string. For every number that is prime I would concatonate 1000 to the right end of the string. \r\n\r\n\r\n10 10 1000 10 1000 10 1000 10 10 10 1000 10 1000\r\n\r\nUsining this method the next 5 digits would be 10101.\r\n\r\nOK just looked at the solution. Seems I had the right idea but not the right answer.\n\nEdited on January 20, 2004, 10:53 am',NULL,0);
INSERT INTO comment VALUES (11154,65,5178,'Dan Porter','seems simple to me','2004-01-20 11:07:00',0,'There are 6 card sides you can see. 3 back and 3 red. Of thoughs 6 possiblities there are 4 loosing combonations and 2 winning combonations. A 1 in 3 chance of winning. Once you see the color there are 2 cards with 4 sides. You know one side of one card so there are 3 hidden sides. Only 1 of the 3 hidden sides will make you win. It is still a 1 in 3 chance of winning.\r\nThis is a very bad bet!',NULL,0);
INSERT INTO comment VALUES (11155,521,4718,'Jack Squat','','2004-01-20 11:23:15',1,'I have to back up DJ\'s answer (mine was 018). Who\'s to say there can\'t be a leading zero? Zip codes are 5 digit numbers, yet there are leading zero zip codes. ',NULL,0);
INSERT INTO comment VALUES (11156,1390,1575,'DJ','re: 2/3 of an answer (FYI...)','2004-01-20 11:37:48',2,'There is a good mathematical reason for all three answers.\r\n\r\n=)',11152,0);
INSERT INTO comment VALUES (11157,1022,5219,'draistal','Full solution to the problem','2004-01-20 11:58:08',3,'To solve this problem of dice rolling, begin by listing all the possible roles that sum to 15. For example, 3,6,6 or 5,5,5. Note that permutations of a role are not needed (otherwise you’ll be listing roles until tomorrow and doing unnecessary extra work). I uncovered a total of 103 different combinations of roles that lead to 15. I found that listing the dice roles in ascending order helped to make sure I didn’t duplicate or miss anything.\r\n\r\nThe next challenge is to find the total number of alternative roles. That means, you role the last die and the sum of your roles exceeds 15 without landing on it. For example, in the case of 5,5,5, you role a 6 instead of the last five. If you role a 4 instead of the last 5, you still have a chance to total to 15 by rolling a 1.\r\n\r\nTo count the total number of alternative combinations, we have to assume that the dice can role the numbers in any order. Thus, for 3,6,6, we assume that 6,3, 3,6 and 6,6 are possible first two role pairs. The fact that 6,6 will only occur 1/5 of the time compared to 6,3 and 3,6’s 2/5 probability is irrelevant to just counting the total number of alternative solutions.\r\n\r\nFor each combination that sums to 15, use the following formula:\r\nIf any number of 1’s are present, add 5 to the total number of alternative solutions\r\nIf any number of 2’s are present, add 4\r\nIf any number of 3’s are present, add 3\r\nIf any number of 4’s are present, add 2\r\nIf any number of 5’s are present, add 1\r\nIf any number of 6’s are present, add 0\r\n\r\nWhy is this? Let’s look at the combination of 15 1’s. Let’s say you have rolled 14 1’s so far. If you don’t role a 1 on your last role, you pass 15. 2, 3, 4, 5, and 6 are alternative roles, so there are 5 total alternative results. Some people may wonder why we don’t add 5 alternatives results for each 1. The reason is that we are only concerned with the very last role. Imagine you having 15 different dice, and you role them all one by one. The first 14 dice all show 1’s. You have only a 1/6 chance that the final role will be a 1, bringing your total to 15. Otherwise you have a 5/6 chance that the total sums to greater than 15 – 5 alternative solutions. If you repeat this same experiment indefinitely, you will always have only 5 alternative solutions at the end.\r\n\r\nNow, this changes with 13 1’s and a 2. At the end of 13 roles, you can have 13 1’s, or you can have 12 1’s and a 2. In the former situation, you need a 2 to hit 15. If you role a 3, 4, 5, or 6, you pass 15. But if you role a 1, you are only at 14, so a 1 takes you to the previously described situation. So, if you need a 2, only 4 alternative solutions exist. If, on the other hand, you have rolled 12 1’s and a 2, you now need a 1. This goes back to the previously described scenario, where there are 5 alternative solutions. So, there are a total of 9 alternative scenarios. You can apply this logic to the remaining 101 dice role combinations. I discovered that in all 961 alternative results could be rolled.\r\n\r\nAdd the alternative results to the to the combinations that sum to 15 to get 1064 total possible combinations given that you must stop rolling once you hit 15 or greater. Divide the 103 sum-to-15 combinations by 1064 to discover that there is only a 9.7% chance of getting 15.\r\n\r\nTo calculate the most frequently occurring number, go back through the 103 combinations and count the number combinations that have any number of 1’s. Do the same for 2’s, 3’s, 4’s, and 5’s. The total number of alternative solutions that sum to 16 equals the results for 1’s + the results for 2’s + … + the results for 5’s. The total number of alternative solutions that sum to 17 equals the results for 1’s + 2’s + 3’s + 4’s. 18 is 1’s + 2’s + 3’s, 19 is 1’s + 2’s, and 20 is only 1’s. I found the following:\r\n\r\nSum of dice roles, total number of occurrences\r\n15, 103\r\n16, 278\r\n17, 246\r\n18, 204\r\n19, 149\r\n20, 84\r\n\r\nThus, 16 is the most common result. \r\n',NULL,0);
INSERT INTO comment VALUES (11158,528,4718,'Jack Squat','sdrawkcab krow','2004-01-20 12:12:27',3,'You might find this solution a bit easier to follow (but maybe not!)\r\n\r\nDefine Old as x and Young as y\r\n\r\nNow start at the end and work the other way: \"when Old was 3x as old as Young\". Let \'a\' be how long ago that was and you get:\r\n\r\n(x-a) = 3(y-a)\r\n\r\nNow look at \"when Young is 3x as old as Old was\". Define \'b\' to be how far into the future that is, and using the fact we just defined Old to be x-a we get:\r\n\r\n(y+b) = 3(x-a)\r\n\r\nNext \"when Old was half as old as Young will be\". Define \'c\' to be how long ago that was, and we just said Young will be y+b we get:\r\n\r\n(x-c) = 1/2(y+b)\r\n\r\nFinally \"Old is twice as old as Young was\". We defined it to be c years ago, so Young was y-c and we get:\r\n\r\nx = 2(y-c)\r\n\r\nNow use x+y = 48 and you have your 5 equations in 5 unknowns. Use whatever algebra tool you like to solve. Matrices are fun.\r\n\r\nReading that over, that might not be that clear!\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (11159,1574,1920,'Brian Smith','There is a solution in . . . .','2004-01-20 12:15:45',0,'There is a solution which only takes eight weighings in the worst case.',NULL,0);
INSERT INTO comment VALUES (11160,1390,4507,'Penny','Solution','2004-01-20 12:25:56',3,'(I have a gnawing feeling about rodent puzzles...)\r\n\r\nRyan: \"If 6 cats kill 6 rats in 6 minutes, then 6 cats kill 1 rat per minute. In 50 minutes they kill 50 rats. Double that number, 12, will kill 100 rats in 50 minutes.\"\r\n\r\nStephanie: \"If 6 cats kill 6 rats in 6 minutes, then 1 cat kills 50(1/6) = 8.33 rats in 50 minutes. 100/8.33 = slightly more than 12. So you need at least 13 cats.\"\r\n\r\nTom reasoned exactly like Stephanie, except that he prudently foresaw the possibility of rodent reproduction during those 50 minutes, and specified one extra cat to counteract it. His total was 14 cats.',NULL,0);
INSERT INTO comment VALUES (11161,1505,5219,'draistal','An unusual approach','2004-01-20 12:26:46',1,'While I know the focus of this site is math, here\'s another approach:\r\n\r\n2 stands by itself, so either it is \"a\" or \"i\"\r\n\"e\" is the most common letter in the English language\r\nThe most common three letter word ending with \"e\" is \"the\"\r\n\r\nFrom there, I was able to pretty quickly deduce the remaining letters without resorting to calculations. I was wondering if anyone else attempted this approach of logical deduction.',NULL,0);
INSERT INTO comment VALUES (11162,1390,2899,'Brian Wainscott','re: 2/3 of an answer','2004-01-20 12:34:50',0,'I don\'t know about the \"teaming up\", but 12 is the straight mathematical answer: each cat kills 8 1/3 rats (whatever killing 1/3 of a rat means....)\r\n\r\n13 also makes sense: Stefanie reasoned that killing 1/3 of a rat makes no sense at all. So 12 cats couldn\'t do it in 50 minutes, there would be 4 rats left over, and another cat is needed. I suppose that it takes a few minutes to CATCH the rat first, then time to kill it, and 2 minutes just isn\'t enough time to do anything.\r\n\r\nBut I\'m also stumped on 14....',11152,0);
INSERT INTO comment VALUES (11163,1390,3172,'SilverKnight','Full solution (even 14)','2004-01-20 12:52:25',3,'If 6 cats kill 6 rats in 6 minutes...\r\n\r\n12 - Ryan\r\nAssumption:\r\nThe number of cats required is proportional to rats and inversely proportional to time required.\r\n\r\nSo, we need to multiply the number of rats by 100/6 and multiply the minutes by 50/6...\r\n\r\nThis means that we multiply the number of cats by 100/6 * 6/50 = 2\r\n6x2 = 12\r\n\r\n\r\n\r\n13 - Stefanie\r\nAssumption:\r\nApparently each cat takes 6 minutes to kill one rat (which is killed at the end of each 6 minute duration).\r\n\r\nIn the initial case, we had 6 cats operating in parallel. If we have 8 times as much time (48 minutes), we will kill 8 times as many rats (8x6=48).. So, if we double the number of cats (12), we\'ll also double the number of rats killed (to 96)..\r\n\r\nWith only 12 cats, we\'d have 96 killed at the end of 48 minutes, and 108 killed at the end of 54 minutes, but in essence we can\'t wait until 54 minutes, so we need another cat to get it up to at least 100 by 50 minutes. This will give us 13 x 7 = 91 killed at the end of 6x7=42 minutes, 104 killed at then end of 48 minutes, (so clearly, we\'ve got our 100 dead at 50 minutes).\r\n\r\n\r\n\r\n14 - Tom\r\nAssumption:\r\nApparently a cat can\'t catch rats alone, but a pair of cats teams up on each rat and take 3 minutes to to kill it (which is killed at the end of each 3 minute duration).\r\n\r\nIn other words 3 pair kills 6 rats in 6 minutes, or:\r\n1 pair kills 2 rats in 6 minutes, or\r\n1 pair kills 1 rat in 3 minutes.\r\n\r\nIn the initial case, we had 3 pair operating in parallel.\r\nIf we have 6 pair operating in parallel, we will get kill 6 rats every 3 minutes.\r\n\r\nSo, at the end of 48 minutes we will have 6 x (48/3) = 96 rats killed. It\'s not until the 51st minute that we will have 6x(51/3) = 102 rats killed, but we need 100 killed by 50 minutes....\r\n\r\nSo, we need to add a 7th pair of cats (total of 14 cats).',NULL,0);
INSERT INTO comment VALUES (11164,1574,2899,'Brian Wainscott','re(2): Simple approach','2004-01-20 13:08:14',3,'John -- good idea!\r\n\r\nI think I can take this further, and get down to 8:\r\n\r\nTake the master, and weigh against the first 5 other coins. If they are all the same, one more weighing will finish the problem. If not, then those 6 are fully known. Here is how to get the other 6 done in 3 weighings.\r\n\r\nCase 1: we know there are 1 heavy and 5 light (or the other way around). Weigh them in three sets of two. As soon as one is not balanced we are done. This takes at most 3 weighings.\r\n\r\nCase 2: we know there are 2 of one kind and 4 of the other (we know which). Label the coins A,B,C,D,E,F. Weigh A vs B and C vs D. If either pair is unbalanced, then weigh E vs F which will also be unbalanced, and the 2 of a kind will be known. If A==B and C==D, then we don\'t have to weigh E and F, they will match. Weigh A vs C. If they match, A==B==C==D, if they don\'t, we know which are the 2 and which are the 4. In either case, we can do it in 3 weighings.\r\n\r\nCase 3: a split 3/3 distribution. Again, label them A,B,C,D,E,F. Weigh A vs B. Sorry, more cases:\r\n\r\nA != B: then we know which is which, and we have 4 coins, split 2/2, and 2 weighings left. Weigh C vs D. If they balance, we know E==F and we can weigh C vs E. If C != D, then we know which is which, and can weigh E vs F and be done.\r\n\r\nA == B: Weigh A vs C. If A == C, we know D==E==F and one more weighing will tell us which set is light. If A != C, we know everything about A, B, C. We can then handle D, E, F using your trick: weigh D vs E and we know everything.\r\n\r\nIn all cases, 8 weighings will suffice.',11143,0);
INSERT INTO comment VALUES (11165,1390,4507,'Penny','The real solution','2004-01-20 13:11:39',3,'If it takes 6 cats 6 minutes to kill 6 rats....\r\n\r\nRyan argued that it takes all 6 cats to kill 1 rat, which they can do in 1 minute.\r\n\r\nStefanie argued that 1 cat can kill 1 rat all by itself, but this takes the cat 6 minutes.\r\n\r\nTom argued that 2 cats must work together to kill 1 rat, and the pair need 3 minutes to do it.',NULL,0);
INSERT INTO comment VALUES (11166,1590,4507,'Penny','A hardy perennial','2004-01-20 14:41:45',3,'In \"A Mathematician\'s Apology\", GH Hardy tells of his visit to the great Indian mathematician Ramanujan. Hardy remarked that the number of his cab was 1729, an uninteresting number. Ramanujan disagreed, noting that 1729 is the smallest number that can be expressed as the sum of two perfect CUBES in two different ways.\r\n\r\n\r\n\r\n\n\nEdited on January 20, 2004, 3:13 pm',NULL,0);
INSERT INTO comment VALUES (11167,1590,3172,'SilverKnight','re: A hardy perennial','2004-01-20 14:49:20',0,'Penny writes:\r\n\"...1729 is the smallest number that can be expressed as the sum of two perfect squares in two different ways.\"\r\n\r\nThis is incorrect (for BOTH questions).\r\n\r\nI would encourage people to VERIFY their solutions before citing some example from the internet.',11166,0);
INSERT INTO comment VALUES (11168,1590,4507,'Penny','re(2): A hardy perennial','2004-01-20 15:07:43',0,'I would encourage people to go to the right website !! That previous one was for a sum of two CUBES..... I did verify the following. \r\n\r\n50 = 5^2 + 5^2 = 1^2 + 7^2 \r\n \r\n65 = 8^2 + 1^2 = 7^2 + 4^2\r\n\r\n\r\n\r\n\n\nEdited on January 20, 2004, 3:17 pm',11167,0);
INSERT INTO comment VALUES (11169,1590,4374,'Richard','re: A hardy perennial','2004-01-20 15:19:23',0,'Actually, according to Hardy\'s \"Ramanujan\" where the anecdote is related, Ramanujan said \"it is a very interesting number, it is the smallest number expressible as a sum of two cubes in two different ways.\" Perhaps, as usual, you are having a bit of fun with old SK? I always enjoy your humor.',11166,0);
INSERT INTO comment VALUES (11170,1590,3172,'SilverKnight','re(3): A hardy perennial','2004-01-20 15:23:54',0,'I see you went back to change your earlier comment from \'squares\' to \'cubes\'....\r\n\r\nThis is why I felt the need to quote your original submission.',11168,0);
INSERT INTO comment VALUES (11171,1590,4507,'Penny','re(2): A hardy perennial','2004-01-20 15:24:28',0,'Thank you. \r\n\r\n50 = 5^2 + 5^2 = 1^2 + 7^2 \r\n65 = 8^2 + 1^2 = 7^2 + 4^2 \r\n\r\n(1729=1^3+12^3=9^3+10^3).\r\n\r\nTo solve puzzles like this, there are three choices:\r\n(1) Be a genius and solve it by intuition, like Ramanujan.\r\n(2) Find the answer on the internet\r\n(3) Write a program\n\nEdited on January 20, 2004, 3:26 pm',11169,0);
INSERT INTO comment VALUES (11172,1590,4507,'Penny','re(4): A hardy perennial','2004-01-20 15:27:40',0,'In this case, changing the original post was not an attempt to cheat, since CUBES could not be an answer to the puzzle, so the post was still wrong.',11170,0);
INSERT INTO comment VALUES (11173,1590,3172,'SilverKnight','re(3): A hardy perennial','2004-01-20 15:30:42',0,'Penny writes,\r\n\"To solve puzzles like this, there are three choices:\r\n(1) Be a genius and solve it by intuition, like Ramanujan.\r\n(2) Find the answer on the internet\r\n(3) Write a program\"\r\n\r\nI would have to agree with that, except that some of us are able to simultaneously choose more than one of those choices.... and I don\'t find my answers on the internet ;-). J/K !',11171,0);
INSERT INTO comment VALUES (11174,1590,4507,'Penny','The fourth way to solve puzzles','2004-01-20 15:55:07',1,'For most puzzles, in addition to sudden intuition, internet searches and software programs, there is a fourth and much more gratifying method of solution: work it out by methodical logic. I can honestly say that that was how I solved \"Word Ladder Construction\", \"Mix and Match\" \"Sequence Fill In\", \"A Timely Manner\", \"Conversing Club\" and \"Shakespeare\'s Numbers\". On another website, I wrote a movie review that solved the riddles of the enigmatic 2003 film \"Swimming Pool\" - I am particularly happy about that feat, since not a few professional movie reviewers were stumped by it.\r\n\r\n\n\nEdited on January 20, 2004, 5:07 pm',NULL,0);
INSERT INTO comment VALUES (11175,184,5178,'Dan Porter','What I got','2004-01-20 15:57:09',0,'Shotting B first 50.5% survival. \r\nShotting C first 72.5% survival. \r\nShotting the air 83.5% survival. \r\n',NULL,0);
INSERT INTO comment VALUES (11176,1589,4374,'Richard','Nonuniform Epsilon?','2004-01-20 18:22:37',4,'There seems to me to be no reason why the same epsilon needs to be used for each point. Why not let each point have its own epsilon?',11148,0);
INSERT INTO comment VALUES (11177,1459,5264,'dan','solution','2004-01-20 21:11:37',0,'ok, so...close, but heres the answer. the first person was wearing a blue shirt, blue suspenders, and a green tie. the second person was wearing a green shirt, green suspenders, and a blue tie. the third person was wearing a white shirt, red suspenders, and a white tie. and the last person was wearing a red shirt, white suspenders, and a red tie. i DID NOT use a program for this, but do not want to go into detail about how i achived this answer. email me at hak77526@comcast.net if u wanna know how i did it...or u can try and prove me wrong ;)',NULL,0);
INSERT INTO comment VALUES (11178,1390,3172,'SilverKnight','re: The real solution','2004-01-20 21:59:26',0,'Nice! I wish I\'d thought of that. ;-)',11165,0);
INSERT INTO comment VALUES (11179,1459,5267,'cogitater','solution','2004-01-21 04:10:33',0,'The solution to \"A Timely Manner\";B is the first to arrive, he wears a blue shirt, green tie, and green suspenders; the 2nd to arrive wears a green shirt, white tie, and white suspenders; third person to arrive wears a red shirt, blue tie and red suspenders; last person in wears a white shirt, red tie and blue suspenders. No program or any other help, just fun to work it out.',NULL,0);
INSERT INTO comment VALUES (11180,1459,5267,'cogitater','re: solution','2004-01-21 04:29:59',0,'Sorry Dan, it doesn\'t work. You have the last person in wearing white suspenders. The description of the photograph eliminates that possibility. The person wearing the white suspenders was on the right in the photograph and was a separate person from the person seated on the floor who was LAST in.',11177,0);
INSERT INTO comment VALUES (11181,846,5271,'philip','re: Solution','2004-01-21 05:18:18',0,'hi brian\r\n\r\nyour maths is impressive but the problem seems simpler than that. if there is twice the snow, then it must have fallen in twice the time. since it takes one hour for the snow height to double the snow must have started one hour previously, ie: at 5:00 am.',5495,0);
INSERT INTO comment VALUES (11182,1289,1920,'Brian Smith','Solution','2004-01-21 09:22:00',0,'This is simple, there are (21*20)/2 ways to choose the lines for the top and bottom and (11*10)/2 ways to choose the lines for the sides.\r\n\r\n21*20*11*10/4 = 11550',NULL,0);
INSERT INTO comment VALUES (11183,1289,3172,'SilverKnight','re: Solution','2004-01-21 09:35:29',0,'well... yeah... but can you NAME them all...? :-)',11182,0);
INSERT INTO comment VALUES (11184,1289,3275,'retiarius','solution','2004-01-21 09:45:39',0,'A 20 x 10 grid is made up of 21 x 11 nodes.\r\nEach node forms a diagonal with (21-1) x (11-1) = 200 out-of-plane nodes.\r\nTotal number of diagonals = 21 x 11 x 200 = 46200\r\nThe diagonals of each rectangle have now been drawn twice.\r\nThe number of rectangles equals half the number of possible diagonals.\r\nTherefore, total number of rectangles = 11550\r\n',NULL,0);
INSERT INTO comment VALUES (11185,1289,4507,'Penny','Question','2004-01-21 10:47:08',4,'Do the solutions posted so far account for all the \"odd\" rectangles, if there are any, like the one formed by (1,10), (5,1), (5,20) and (10,5) (if that is even a rectangle) ? ',NULL,0);
INSERT INTO comment VALUES (11186,1589,153,'TomM','re: Nonuniform Epsilon?','2004-01-21 10:53:31',0,'There is no absolute reason why ε needs to be constant, if we are talking about a finite N number of points, but when we approach infinity, the length of each segment approaches 0 and if we had chosen ε too high for an earlier point, that point will not be in the same segment as its m/(2^n) reference point. It needs to be in the proper segment for any possible proofs of the availability for infinite points.\r\n\n\nEdited on January 23, 2004, 7:49 pm',11176,0);
INSERT INTO comment VALUES (11187,1589,1920,'Brian Smith','This problem is also known as ...','2004-01-21 10:54:39',0,'This problem is also known as the \'18 point problem\'. MathWorld has an article on it here.\r\n',NULL,0);
INSERT INTO comment VALUES (11188,1289,3172,'SilverKnight','re: Question','2004-01-21 11:26:57',0,'Well, those points do not a rectangle make.\r\n\r\nBut, I think, you\'re talking about rectangles that aren\'t ON the integral lattice lines, such as (1,2) (2,1) (4,3) (3,4).\r\n\r\nAnd the previous/posted solutions do not take those into account.\r\n\r\nI think non-lattice rectangles are beyond the scope of this problem (or it would have mentioned rectangles determined by the lattice points, rather than than referencing a 20 by 10 grid).\r\n_________________________\r\n\r\nThat being said, your related question *is* a rather interesting side note... and can be solved similarly to the asked problem (although a little more complicated).\r\n\r\n- SK',11185,0);
INSERT INTO comment VALUES (11189,1589,5256,'Paul','re(2): Solution (Infinite Points)','2004-01-21 11:38:35',0,'Yeah after I went to bed I realized it failed after five. What I should have tried would be\r\n1/2\r\n1/4 3/4\r\n1/8 7/8 3/8 5/8\r\n1/16 15/16 7/16 9/16 3/16 13/16 5/16 11/16\r\n1/32 31/32 ...\r\n\r\nI had first tried starting with just e (as TomM suggested) but I thought starting with 1/2 gave more of a pattern. I\'m pretty sure the above at least works through the first 10 points. Whether it gets up to 17, I don\'t know. Why 17 is the most seems like a tough problem.',11147,0);
INSERT INTO comment VALUES (11190,1289,3372,'Sam','re: Nodes','2004-01-21 11:40:06',0,'This is probably a silly question, but in the counting diagonals method, aren\'t you connecting four diagonals for each rectangle? i.e. from (0,0) to (1,1), (1,1) to (0,0), (0,1) to (1,0) and (1,0) to (0,1)? How come the answer is divided by two and not four?',11184,0);
INSERT INTO comment VALUES (11191,1289,3172,'SilverKnight','re(2): Nodes','2004-01-21 11:46:36',0,'Not silly at all...\r\n\r\nHe counted all diagonals twice... so, yes divide by 2 (and we get the number of unique diagonals).\r\n\r\nBut then each rectangle has TWO of those diagonals... so divide by 2 again (to get the number of unique rectangles).',11190,0);
INSERT INTO comment VALUES (11192,1388,3172,'SilverKnight','re: One solution','2004-01-21 12:02:29',0,'Normally, the square a piece occupies is not considered \'under attack\'. DJ, would you clarify as to whether or not this applies, in this problem?',11115,0);
INSERT INTO comment VALUES (11193,1284,5274,'greg boussard','solution','2004-01-21 14:14:58',0,'There are 64C3 ways of choosing 3 squares. This is the denominator of the probability.\r\n\r\nThe numerator of the probability is all of the possible ways of choosing 3 in the same diagonal. Obviously, the 1 and 2 length diagonals don\'t count. So we are left with: 4 3-length, 4 4-length, 4 5-length, 4 6-length, 4 7-length and 2 8-length diagonals. To find out all ways of choosing three squares in one particular diagonal, we can sum all the ways of choosing three squares in each diagonal.\r\n\r\nHence the numberator is: 4*(3C3) + 4*(4C3) + 4*(5C3) + 4*(6C3) + 4*(7C3) + 2*(8C3) \r\n\r\nI don\'t have a calculator handy.',NULL,0);
INSERT INTO comment VALUES (11194,491,5178,'Dan Porter','Not looking at the solution','2004-01-21 14:34:58',0,'The factors of 225 are 3, 3, 5, 5. To get two fives in the number it must end in 00. To be divisable by 3 twice the sum of the digits must be 9. So the smallest number using only ones and zeros is 11111111100/225=49382716.',NULL,0);
INSERT INTO comment VALUES (11195,1289,5178,'Dan Porter','','2004-01-21 15:46:59',0,'',NULL,0);
INSERT INTO comment VALUES (11196,1289,5178,'Dan Porter','solution','2004-01-21 15:47:31',0,'The number of combos of 2 lines out of N lines is N(N-1)/2. The number of vertical combos times the number of horizontal combos is the total number of rectangles. Therefore 20*19*10*9/2=17100\r\n\r\nAfter reading the other solutions I see I\'m incorrect. The wording tripped me up.\n\nEdited on January 21, 2004, 3:51 pm',NULL,0);
INSERT INTO comment VALUES (11197,638,4718,'Jack Squat','The driver is a moron','2004-01-21 16:49:44',0,'I didn\'t read ALL the posts so I\'m not sure if someone mentioned this, but as usual with Ravioli Raja puzzles, they are open to interpretation. \r\n\r\nWhen getting to the equation y=6x, there are two solutions, 0,0 and 1,6. So an alternative dumb solution is the man\'s car is not moving, and there are inexplicably 3 signs that have 2 zeroes, 2 zeroes and 3 zeroes respectively. However since this driver is so dumb, there are probably only two signs and he read the first one again the second time. Or there aren\'t 3 signs, but one sign that reads \"Baboon food is so good\" and someone has blacked over all the letters but the \'o\'s.',NULL,0);
INSERT INTO comment VALUES (11198,1289,4323,'Benjamin J. Ladd','11,550? Mine was a little bigger than that...','2004-01-21 17:30:46',1,'Okay, here\'s a solution for *ALL* the numbers of squares and rectangles in a 20x10 grid (just in case you ever wondered...)\r\n\r\nIf you apply brute force to the grid (here assumed to be a width of 20 squares and a height of 10 squares) to derive a general formula for the sum of all the rectangles, the final solution is 55 * 20! or 133,809,610,449,715,200,000.\r\n\r\nIf we start by taking the # of 1x1 squares we get:\r\n1x1 = 20 * 10\r\n\r\nThen add this to the # of 1x2 squares:\r\n1x2 = 20 * 9\r\n\r\nAnd 1x3...\r\n1x3 = 20 * 8\r\n\r\n.\r\n.\r\n.\r\n\r\nAnd so on and so forth to...\r\n1x10 = 20 * 1\r\n\r\nAnd then start over with 2x1:\r\n2x1 = 19 * 10\r\n\r\n.\r\n.\r\n.\r\n\r\n2x10 = 19 * 1\r\n\r\nContinuing to apply this method and adding up all of these values, we arrive at the staggering formula:\r\n\r\n10 * 20 + 9 * 20 + 8 * 20 + 7 * 20 + 6 * 20 + 5 * 20 + 4 * 20 + 3 * 20 + 2 * 20 + 1 * 20 + 10 * 19 + 9 * 19 + 8 * 19 + 7 * 19 + 6 * 19 + 5 * 19 + 4 * 19 + 3 * 19 + 2 * 19 + 1 * 19 + 10 * 18 + 9 * 18 + 8 * 18 + 7 * 18 + 6 * 18 + 5 * 18 + 4 * 18 + 3 * 18 + 2 * 18 + 1 * 18 + 10 * 17 + 9 * 17 + 8 * 17 + 7 * 17 + 6 * 17 + 5 * 17 + 4 * 17 + 3 * 17 + 2 * 17 + 1 * 17 + 10 * 16 + 9 * 16 + 8 * 16 + 7 * 16 + 6 * 16 + 5 * 16 + 4 * 16 + 3 * 16 + 2 * 16 + 1 * 16 + 10 * 15 + 9 * 15 + 8 * 15 + 7 * 15 + 6 * 15 + 5 * 15 + 4 * 15 + 3 * 15 + 2 * 15 + 1 * 15 + 10 * 14 + 9 * 14 + 8 * 14 + 7 * 14 + 6 * 14 + 5 * 14 + 4 * 14 + 3 * 14 + 2 * 14 + 1 * 14 + 10 * 13 + 9 * 13 + 8 * 13 + 7 * 13 + 6 * 13 + 5 * 13 + 4 * 13 + 3 * 13 + 2 * 13 + 1 * 13 + 10 * 12 + 9 * 12 + 8 * 12 + 7 * 12 + 6 * 12 + 5 * 12 + 4 * 12 + 3 * 12 + 2 * 12 + 1 * 12 + 10 * 11 + 9 * 11 + 8 * 11 + 7 * 11 + 6 * 11 + 5 * 11 + 4 * 11 + 3 * 11 + 2 * 11 + 1 * 11 + 10 * 10 + 9 * 20 + 8 * 20 + 7 * 20 + 6 * 20 + 5 * 20 + 4 * 20 + 3 * 20 + 2 * 20 + 1 * 20 + 10 * 9 + 9 * 9 + 8 * 9 + 7 * 9 + 6 * 9 + 5 * 9 + 4 * 9 + 3 * 9 + 2 * 9 + 1 * 9 + 10 * 8 + 9 * 8 + 8 * 8 + 7 * 8 + 6 * 8 + 5 * 8 + 4 * 8 + 3 * 8 + 2 * 8 + 1 * 8 + 10 * 7 + 9 * 7 + 8 * 7 + 7 * 7 + 6 * 7 + 5 * 7 + 4 * 7 + 3 * 7 + 2 * 7 + 1 * 7 + 10 * 6 + 9 * 6 + 8 * 6 + 7 * 6 + 6 * 6 + 5 * 6 + 4 * 6 + 3 * 6 + 2 * 6 + 1 * 6 + 10 * 5 + 9 * 5 + 8 * 5 + 7 * 5 + 6 * 5 + 5 * 5 + 4 * 5 + 3 * 5 + 2 * 5 + 1 * 5 + 10 * 4 + 9 * 4 + 8 * 4 + 7 * 4 + 6 * 4 + 5 * 4 + 4 * 4 + 3 * 4 + 2 * 4 + 1 * 4 + 10 * 3 + 9 * 3 + 8 * 3 + 7 * 3 + 6 * 3 + 5 * 3 + 4 * 3 + 3 * 3 + 2 * 3 + 1 * 3 + 10 * 2 + 9 * 2 + 8 * 2 + 7 * 2 + 6 * 2 + 5 * 2 + 4 * 2 + 3 * 2 + 2 * 2 + 1 * 2 + 10 * 1 + 9 * 1 + 8 * 1 + 7 * 1 + 6 * 1 + 5 * 1 + 4 * 1 + 3 * 1 + 2 * 1 + 1 * 1\r\n\r\nWhich looks bad, but can really be grouped together quite easily to make up the following formula:\r\n\r\n20!(10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1) or 55 * 20!\r\n\r\n55 * 20! = 133,809,610,449,715,200,000 rectangles\r\n\r\n(Note: It\'s official, \"I\'m an idiot and didn\'t read the question properly...\")\n\nEdited on January 21, 2004, 5:41 pm',NULL,0);
INSERT INTO comment VALUES (11199,1289,4323,'Benjamin J. Ladd','The real deal: 11,550? Mine was a little smaller than that...','2004-01-21 18:03:47',3,'Okay, here goes round 2:\r\n\r\nSame brute force of an idea as my previous post, but I started at the bottom left of the 10 x 20 grid (10 being the base and 20 being the height) this time and went straight through from level to level always using the bottom left most square as my anchor.\r\n\r\nUsing this method, the first level has 10 unique rectangles:\r\n1x1, 1x2, 1x3 ... 1x10\r\n\r\nThe second level has 9 unique rectangles:\r\n2x2, 2x3, 2x4 ... 2x10\r\n\r\nThis continues eliminating one from each subsequent level all the way until you reach level 11. (Total number of unique rectangles thus far equals 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1). After this point, every single rectangle you draw will not have another single corresponding rectangle at further levels because the base length has already been exceeded (note: the sum of the last 10 levels will therefore be 10 x 10).\r\n\r\nTherefore the final number for all the unique rectangles will be 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 + (10 x 10) = 155.\r\n\r\nIf this has been a confusing solution, I can try to clarify it better. If this helps, here they are all named:\r\n\r\n1x1, 1x2, 1x3, 1x4, 1x5, 1x6, 1x7, 1x8, 1x9, 1x10\r\n2x2, 2x3, 2x4, 2x5, 2x6, 2x7, 2x8, 2x9, 2x10\r\n3x3, 3x4, 3x5, 3x6, 3x7, 3x8, 3x9, 3x10\r\n4x4, 4x5, 4x6, 4x7, 4x8, 4x9, 2x10\r\n5x5, 5x6, 5x7, 5x8, 5x9, 5x10\r\n6x6, 6x7, 6x8, 6x9, 6x10\r\n7x7, 7x8, 7x9, 7x10\r\n8x8, 8x9, 8x10\r\n9x9, 9x10\r\n10x10\r\n11x1, 11x2, 11x3, 11x4, 11x5, 11x6, 11x7, 11x8, 11x9, 11x10\r\n12x1, 12x2, 12x3, 12x4, 12x5, 12x6, 12x7, 12x8, 12x9, 12x10\r\n13x1, 13x2, 13x3, 13x4, 13x5, 13x6, 13x7, 13x8, 13x9, 13x10\r\n14x1, 14x2, 14x3, 14x4, 14x5, 14x6, 14x7, 14x8, 14x9, 14x10\r\n15x1, 15x2, 15x3, 15x4, 15x5, 15x6, 15x7, 15x8, 15x9, 15x10\r\n16x1, 16x2, 16x3, 16x4, 16x5, 16x6, 16x7, 16x8, 16x9, 16x10\r\n17x1, 17x2, 17x3, 17x4, 17x5, 17x6, 17x7, 17x8, 17x9, 17x10\r\n18x1, 18x2, 18x3, 18x4, 18x5, 18x6, 18x7, 18x8, 18x9, 18x10\r\n19x1, 19x2, 19x3, 19x4, 19x5, 19x6, 19x7, 19x8, 19x9, 19x10\r\n20x1, 20x2, 20x3, 20x4, 20x5, 20x6, 20x7, 20x8, 20x9, 20x10\n\nEdited on January 21, 2004, 6:17 pm',NULL,0);
INSERT INTO comment VALUES (11200,1459,5264,'dan','re(2): solution','2004-01-21 18:58:13',0,'good call...grrr, i guess its back to the drawing board',11180,0);
INSERT INTO comment VALUES (11201,1574,4744,'MIKE INCE','will this work','2004-01-21 19:50:35',0,'Take two coins and place them on the balance. One will weigh more than the other if this is the case then it will take 6. If there is a weighing and they are equal leave them to the side. This will be the seventh weighing by taking one of the coins that were equal and balancing it with one of the other coins that you know the weight of.',NULL,0);
INSERT INTO comment VALUES (11202,1289,4374,'Richard','re: The real deal: 11,550? Mine was a little smaller than that...','2004-01-21 20:56:15',0,'The very first comment (by Brian Smith) below nails this one. It is based on the principle, easily verified, that the number of ways to choose i consecutive numbers from 1,2,...,N is N-i+1. Summing these from i=1 to N gives\r\nN(N+1)/2, since they are just 1,2,...,N in reverse order. If a grid has width n and height m, you can choose rectangluar blocks by choosing consecutive blocks horizontally and then stacking these vertically (or vice versa, it doesn\'t matter). Clearly then, a rectangle made up of blocks in this way can be formed in\r\nn(n+1)/2 * m(m+1)/2 = nm(n+1)(m+1)/4 ways. For n=3 and m=2, you get 6*12/4 = 18, which you can easily verify by manual enumeration. For n=10 and m=20 the answer is 11550 just as Brian Smith says.\r\n\r\nEdited on January 21, 2004, 8:59 pm\n\nEdited on January 22, 2004, 1:05 pm',11199,0);
INSERT INTO comment VALUES (11203,1459,5097,'Cindy','My solution','2004-01-21 21:52:50',0,'Here\'s what I got:\r\n\r\n SHIRT TIE SUSPEND. PHOTO\r\n1(B) white green white right\r\n2 green blue green middle\r\n3 blue white red left\r\n4 red red blue sitting\r\n\r\n ',NULL,0);
INSERT INTO comment VALUES (11204,1286,5097,'Cindy','re: seems easy?','2004-01-21 22:26:34',0,'That\'s what I got...',11146,0);
INSERT INTO comment VALUES (11205,1286,4374,'Richard','Below?','2004-01-21 23:12:44',4,'\'FIFTH\' was two places below \'FOURTH\', according to the problem statement. Does this mean the place number of \'FIFTH\' is 2 less than that of \'FOURTH\'? If so, the solution of all the comments below has \'FIFTH\' and \'FOURTH\' reversed.',NULL,0);
INSERT INTO comment VALUES (11206,1270,5097,'Cindy','re(3): JinCo\'s Solution','2004-01-21 23:30:11',0,'Me three',11077,0);
INSERT INTO comment VALUES (11207,1289,4841,'slothman','question of form','2004-01-22 00:23:34',0,'does this problem want to know how many different rectangles I can outline or does it want to know how many forms or rectangles can be created from a 10by20 grid. for example there are 200 1 by 1 rectanges but each is the same. ',NULL,0);
INSERT INTO comment VALUES (11208,1583,4507,'Penny','This has \"write a program\" written all over it','2004-01-22 02:57:33',2,'Only a dummy would try to solve this one manually. It fairly screams WRITE A SOFTWARE PROGRAM TO SOLVE THIS PUZZLE !!!!!!!! \r\n\r\nJust \"grid and bear it\"........\n\nEdited on January 22, 2004, 3:01 am',NULL,0);
INSERT INTO comment VALUES (11209,1459,4507,'Penny','re: My solution','2004-01-22 03:27:33',0,'Cindy, \r\n\r\nThe puzzle states that the person wearing the green tie was also wearing either a red or a blue shirt.\r\n\r\nSorry....',11203,0);
INSERT INTO comment VALUES (11210,1459,5284,'Laura','Solution','2004-01-22 07:17:50',3,'1st arrival had on a green tie, w/blue suspenders, and a red shirt.\r\n2nd arrival had on a white tie, w/white suspenders, and a green shirt.\r\n3rd arrival had on a blue tie, w/ red suspenders, and a blue shirt.\r\n4th arrival had on a red tie, w/green suspenders and a white shirt.',NULL,0);
INSERT INTO comment VALUES (11211,1459,4507,'Penny','re: Solution','2004-01-22 08:43:10',0,'Sorry, this can\'t be right. The only person that came in between the person with the red shirt and the person with the green suspenders was wearing a white tie. Your solution has two such people.',11210,0);
INSERT INTO comment VALUES (11212,1391,1301,'Charlie','Attempt at a computer solution','2004-01-22 11:21:33',1,'The following program fails to find a solution. The program itself tries to produce all possible results and place them in a file with the result at the beginning of each record. That file is sorted and then another program looks for matches with three different equations producing them.\r\n\r\nI had written a program for pluribus 1, but due to a bug (not permuting the numbers) did not find the answer. This program could have some other bug, or the answer is more exotic than allowed for here:\r\n\r\nDEFDBL A-Z\r\n\r\nop$ = \"+-*/^\"\r\nDATA 3,5,18, 10,13,36, 24,27,29\r\nFOR i = 1 TO 3\r\n FOR j = 1 TO 3\r\n READ opnd(i, j)\r\n NEXT\r\nNEXT\r\n\r\nOPEN \"epluribs.txt\" FOR OUTPUT AS #2\r\n\r\nFOR eq = 1 TO 3\r\n DO\r\n FOR op1 = 1 TO 5\r\n err1 = 0\r\n SELECT CASE op1\r\n CASE 1\r\n rslt1a = opnd(eq, 1) + opnd(eq, 2)\r\n CASE 2\r\n rslt1a = opnd(eq, 1) - opnd(eq, 2)\r\n CASE 3\r\n rslt1a = opnd(eq, 1) * opnd(eq, 2)\r\n CASE 4\r\n rslt1a = opnd(eq, 1) / opnd(eq, 2)\r\n CASE 5\r\n IF LOG(opnd(eq, 1)) * opnd(eq, 2) < 300 * LOG(10) THEN\r\n rslt1a = opnd(eq, 1) ^ opnd(eq, 2)\r\n ELSE\r\n rslt1a = 1: err1 = 1\r\n END IF\r\n END SELECT\r\n IF err1 = 0 THEN\r\n FOR op2 = 1 TO 5\r\n err1 = 0\r\n err2 = 0\r\n SELECT CASE op2\r\n CASE 1\r\n rslt2a = opnd(eq, 2) + opnd(eq, 3)\r\n rslt1 = rslt1a + opnd(eq, 3)\r\n CASE 2\r\n rslt2a = opnd(eq, 2) - opnd(eq, 3)\r\n rslt1 = rslt1a - opnd(eq, 3)\r\n CASE 3\r\n rslt2a = opnd(eq, 2) * opnd(eq, 3)\r\n rslt1 = rslt1a * opnd(eq, 3)\r\n CASE 4\r\n rslt2a = opnd(eq, 2) / opnd(eq, 3)\r\n rslt1 = rslt1a / opnd(eq, 3)\r\n CASE 5\r\n IF LOG(opnd(eq, 2)) * opnd(eq, 3) < 300 * LOG(10) THEN\r\n rslt2a = opnd(eq, 2) ^ opnd(eq, 3)\r\n ELSE\r\n rslt2a = 1: err2 = 1\r\n END IF\r\n IF LOG(ABS(rslt1a)) * opnd(eq, 3) < 300 * LOG(10) THEN\r\n rslt1 = rslt1a ^ opnd(eq, 3)\r\n ELSE\r\n rslt1 = 0: err1 = 1\r\n END IF\r\n END SELECT\r\n SELECT CASE op1\r\n CASE 1\r\n rslt2 = opnd(eq, 1) + rslt2a\r\n CASE 2\r\n rslt2 = opnd(eq, 1) - rslt2a\r\n CASE 3\r\n rslt2 = opnd(eq, 1) * rslt2a\r\n CASE 4\r\n rslt2 = opnd(eq, 1) / rslt2a\r\n CASE 5\r\n IF LOG(opnd(eq, 1)) * rslt2a < 300 * LOG(10) THEN\r\n rslt2 = opnd(eq, 1) ^ rslt2a\r\n ELSE\r\n rslt2 = 1: err2 = 1\r\n END IF\r\n END SELECT\r\n\r\n IF err1 = 0 THEN\r\n PRINT #2, rslt1; TAB(30);\r\n PRINT #2, USING \"## \"; eq;\r\n PRINT #2, USING \" # ## ! ## ! ##\"; 1; opnd(eq, 1); MID$(op$, op1); opnd(eq, 2); MID$(op$, op2); opnd(eq, 3)\r\n END IF\r\n IF err2 = 0 THEN\r\n PRINT #2, rslt2; TAB(30);\r\n PRINT #2, USING \"## \"; eq;\r\n PRINT #2, USING \" # ## ! ## ! ##\"; 2; opnd(eq, 1); MID$(op$, op1); opnd(eq, 2); MID$(op$, op2); opnd(eq, 3)\r\n END IF\r\n\r\n NEXT\r\n END IF\r\n NEXT op1\r\n\r\n flag = 0\r\n IF opnd(eq, 1) < opnd(eq, 2) THEN\r\n IF opnd(eq, 2) < opnd(eq, 3) THEN\r\n SWAP opnd(eq, 2), opnd(eq, 3)\r\n ELSE\r\n IF opnd(eq, 3) < opnd(eq, 1) THEN\r\n h = opnd(eq, 1)\r\n opnd(eq, 1) = opnd(eq, 2)\r\n opnd(eq, 2) = opnd(eq, 3)\r\n opnd(eq, 3) = h\r\n ELSE\r\n h = opnd(eq, 3)\r\n opnd(eq, 3) = opnd(eq, 2)\r\n opnd(eq, 2) = opnd(eq, 1)\r\n opnd(eq, 1) = h\r\n END IF\r\n END IF\r\n ELSE\r\n IF opnd(eq, 2) < opnd(eq, 3) THEN\r\n SWAP opnd(eq, 2), opnd(eq, 3)\r\n ELSE\r\n SWAP opnd(eq, 1), opnd(eq, 3): flag = 1\r\n END IF\r\n END IF\r\n PRINT opnd(eq, 1), opnd(eq, 2), opnd(eq, 3)\r\n LOOP UNTIL flag\r\n\r\nNEXT eq\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (11213,1391,1301,'Charlie','re: Attempt at a computer solution -- results','2004-01-22 11:32:29',1,'These are the matches that were found by the program that matched up the output from the program given:\r\n Let\'s write the fraction x=0.abc...zabc...z... Therefore, (x+z)/10= 0.zabc...zabc...zabc...z..., which should be 1.5x. Equating members, x=z/14. With z=4, we get x=0.285714, which ends in 4 as needed, so the number is 285714.',NULL,0);
INSERT INTO comment VALUES (11329,1592,2716,'Federico Kereki','Solution','2004-01-26 13:16:08',3,'This can be seen as a state machine, with probabilistic state changes. You start at the state \"No numbers seen\". With probability 6/6, you change to the state \"One number seen\". At this state, with probability 1/6, you remain there one more throw; with probability 5/6 you change to state \"Two numbers seen\". At this state, with probability 2/6, you remain there one more throw; with probability 4/6 you change to \"Three numbers seen\", and so on. The expected number of throws is 6/6+ 6/5+ 6/4+ 6/3+ 6/2+ 6/1 = 14.7.',NULL,0);
INSERT INTO comment VALUES (11330,1592,1301,'Charlie','solution plus simulation-- and another question or two','2004-01-26 14:02:07',0,'The solution below is the same as Federico Kereki\'s. A reference is given to a similar past puzzle, and I\'ve included a simulation, and a new, more complex question:\r\n\r\nThis is based on Rick\'s Another analytic solution to problem B comment for the puzzle Trading Cards.\r\n\r\nIn order to get 6 rolls, each of which shows a number that had not yet come up, you first have to get one such roll, then a second such roll, etc. Before starting, you expect it will take 1 roll to get the first new number. Once that happens, you expect it to take 6/5 rolls to get some other previously unseen number. To get the third, you expect it to take another 6/4 rolls. The expected times to get each of these fresh numbers can be added, giving \r\n\r\nΣ{i=0 to 5} 6/(6-i) = 14.7\r\n\r\nThe following program evaluates that summation and then simulates 100,000 trials:\r\n\r\nDEFDBL A-Z\r\nFOR i = 0 TO 5\r\n t = t + 6 / (6 - i)\r\nNEXT\r\nPRINT : PRINT\r\nPRINT t\r\n\r\nRANDOMIZE TIMER\r\ntotTook = 0: totTrials = 0\r\nFOR trial = 1 TO 100000\r\n totTrials = totTrials + 1\r\n REDIM had(6)\r\n numHad = 0\r\n DO\r\n r = INT(RND(1) * 6 + 1)\r\n IF had(r) = 0 THEN\r\n had(r) = 1\r\n numHad = numHad + 1\r\n END IF\r\n totTook = totTook + 1\r\n LOOP UNTIL numHad = 6\r\nNEXT trial\r\nPRINT totTook / totTrials\r\n\r\nSome sample output is:\r\n 14.7\r\n 14.7035\r\n\r\n 14.7\r\n 14.70336\r\n\r\n 14.7\r\n 14.70308\r\n\r\n 14.7\r\n 14.70461\r\n\r\n 14.7\r\n 14.71023\r\n\r\n 14.7\r\n 14.68018\r\n\r\nThis method of solution depends on each of the required outcomes having an equal probability of occurrence, so that the expected wait after having acquired, say, 3 different numbers is the same regardless of what those three numbers were. A more complicated solution is needed for questions where not every outcome is the same. Such would be the case if the problem called for rolling a pair of dice, and asking What would be the expected number of rolls needed to have gotten all eleven possible dice totals from 2 through 12?\r\n\r\nAnother question is What are the median and modal numbers for one die being tossed in this procedure--that is, the original question, with expected number replaced with mode or median?\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (11331,1592,3172,'SilverKnight','re: solution plus simulation-- and another question or two','2004-01-26 14:12:22',0,'Charlie,\r\n\r\nThose are interesting questions. At (my) first glance, they seem to require brute forcing (perhaps w/computer) the solution. Is there an analytical way to solve eleven possible dice totals from 2-12, or the mode/median questions?\r\n\r\n- SK',11330,0);
INSERT INTO comment VALUES (11332,1592,1301,'Charlie','re(2): solution plus simulation-- and another question or two','2004-01-26 14:58:49',0,'There is an analytical way of solving the likelihood of having gotten all 11 possible dice totals after n throws. The formula has so many terms that a computer is almost essential. To find the mode and median requires doing this for multiple values of n, and thus could be considered brute force. The mean requires enough to essentially account for \"all the possible\" values of n (the quotes indicating we stop after essentially having probability 1.000000000000000 of having reached the goal), and so is even more of a brute force method. But it doesn\'t get as far down as picking each possible sequence of throws, or be a mere simulation.',11331,0);
INSERT INTO comment VALUES (11333,1399,5212,'kandas','maybe?','2004-01-26 16:53:27',0,'dining',NULL,0);
INSERT INTO comment VALUES (11334,1466,4374,'Richard','re(3): general equation:','2004-01-26 17:10:51',0,'The problem asks \"how could you figure out its surface area using geometric reasoning?\" Ady\'s formulas are correct, but where is the geometric reasoning? Where is there any reasoning? All I see is a set of formulas without any explanation. Developing the surface of the cone is geometric, I contend, and so is finding the untruncated height by similar triangles. Ady\'s formula for the nontrivial part of the surface area is very nice and succinct, and not easy to algebraically deduce from the difference formula that I gave, but it can be found in handbooks such as the one by Alan Jeffrey. But without the geometric explanation, it doesn\'t solve the stated problem.',11315,0);
INSERT INTO comment VALUES (11335,1592,1301,'Charlie','The other answers','2004-01-26 17:28:13',0,'The solution for getting all possible totals for throws of a pair of dice depends on the inclusion/exclusion principle:\r\n\r\nAt any given number of throws having taken place in the trial, the probability of having thrown all the eleven possible totals up until then is the sum of all the individual probabilities of having thrown a 2 through having thrown a 12, minus all 55 (i.e., C(11,2)) pairwise probabilities of having thrown a 2 OR a 3 ... through an 11 OR a 12, plus all 165 triplets of ORed possibilities, etc., alternating adding and subtracting. Taking each ORed set individually that adds up to 2^11 = 2048 terms.\r\n\r\nEach ORed probability is one minus the probability that none of the given set had appeared through that numbered toss of the dice. That is 1 - ((36 - w) / 36) ^ n, where w is the number of ways of rolling the given set and n is the number of throws thus far. For example, if going after the probability of having thrown a 3 or a 5 or a 9, w would be 2+4+4=10. \r\n\r\nA UBASIC program that evaluates this for n = 1 to 2000 is\r\n starting on the 14th Feb 1996 (leapyear) herb climbs up the well with a net gain of 1 foot per day, after 27 days he has climbed 27 feet and on the 28th day he climbs the final 3 feet to get out of the well, therefore he must have got out of the well at the end of the 13th March 1996. Δ π Σ Ω α β θ ω ⁿ º ² ³ √ ¼ ½ ¾ ≠ ≤ ≥ ≈ ∞ ∫ ± → Edited on February 27, 2004, 7:23 pm',NULL,1);
INSERT INTO comment VALUES (11346,1442,5352,'Phil','Eight Days A week','2004-01-27 01:39:50',4,'You Americans haven\'t a clue,\r\nGod created the world in 6 days and rested on the seventh (sunday) if Monday is the 2nd day in the U.S. which day comes between Sunday and Monday',NULL,0);
INSERT INTO comment VALUES (11347,1294,5285,'Ady TZIDON','re: Standard solution','2004-01-27 03:37:37',0,'\r\nz could be 8 as well => x=0.571428 hence the number 571428\r\nady',11328,0);
INSERT INTO comment VALUES (11348,1459,5356,'Sue','Got it, I think','2004-01-27 07:20:50',0,'First to arrive-Green Tie,Blue shirt,Green suspenders\r\nSecond -white tie,green shirt,white suspenders\r\nThird-blue tie,red shirt,red suspenders\r\nLast -red tie,white shirt,blue suspenders',NULL,0);
INSERT INTO comment VALUES (11349,1297,5285,'Ady TZIDON','super easy','2004-01-27 07:46:37',3,'it is surely 1 ( one.)\r\n1999= 1 mod 9\r\nwhich yields 1 in any power.\r\n\r\nady',NULL,0);
INSERT INTO comment VALUES (11350,1286,4507,'Penny','re(2): The easiest puzzle in floobelian history !!!','2004-01-27 08:11:15',0,'Sophea, I don\'t think your answer can be right, since the puzzle says \"\'THIRD\' came in one place after \'FIRST\'\". \r\n',11344,0);
INSERT INTO comment VALUES (11351,1297,3172,'SilverKnight','re: super easy','2004-01-27 09:01:48',0,'Ady,\r\n\r\nI don\'t follow your logic... \r\n\r\n1999 is congruent to 1 mod 9, but why does that mean that the \'sum of digits\' of (1999)^1999 should be one?\r\n\r\n- SK',11349,0);
INSERT INTO comment VALUES (11352,1297,1626,'Gamer','re: super easy','2004-01-27 09:06:13',3,'You haven\'t really proved anything yet... kind of a leap of faith in several spots. Here\'s what Ady\'s trying to say I think.\r\n\r\nFirst of all, when you add the digits of a certain number, you are converting all of them to ones. Conversion to ones is subtracting 9, 99, 999, 9999 from the place value, or some 1-digit number times those numbers. All of these are divisible by 9, so when you add up the digits, you are just taking the number mod 9.\r\n\r\nSince any number 1 mod 9 multiplied by another number 1 mod 9 is also 1 mod 9, the answer is 1. This is because if you express these two numbers (where x and y are integers) as 9x+1 and 9y+1, you get 81xy+9x+9y+1, or 9(9xy+x+y)+1, which is clearly 1 mod 9.',11349,0);
INSERT INTO comment VALUES (11353,1297,4670,'e.g.','re(2): super easy','2004-01-27 09:11:38',3,'Adding the digits of a number, is the same as calculating the residue of dividing it by 9. So, asking for the sum of digits of 1999^1999 is the same as asking for \r\nAfter further reflection, having two lines of 8 people in the middle, and 32 around, would also allow for a solution, so I\'d say \"48 or less\".',NULL,0);
INSERT INTO comment VALUES (11384,1467,3172,'SilverKnight','re: Upper bound (lower bound?)','2004-01-28 14:49:03',0,'I\'m not sure you meant that 32 is a lower bound...\r\n\r\nI quickly came up with an answer with 24.... and I think that it can be done with fewer (but I must run to a meeting)....\r\n\r\n- SK',11383,0);
INSERT INTO comment VALUES (11385,1459,5377,'stewards','','2004-01-28 14:49:19',0,'ill try to look over it some more, and maybe just re-order them, if thats all that i need to do to fix the problem. 4 people, and if my outfit combinations are correct, there are only 24 possible orders that they could arrive in, and i guess 23 of them will be discounted by the problem. ill try to work on it a little more tomorrow if i have the time. anyone else can feel free to try it before i do...not that you really need my permission to read that which has been posted.\r\nSad that im wrong, but glad someone pointed it out to me. I\'d rather know i messed up than through ignorance, think i was right.',NULL,0);
INSERT INTO comment VALUES (11386,1467,1301,'Charlie','re(2): Upper bound (lower bound?)','2004-01-28 14:51:17',0,'I think the \"including anyone who may have been shot already\" means that bullets may fly over their heads--not that they can be killed again.',11384,0);
INSERT INTO comment VALUES (11387,1467,1301,'Charlie','a start','2004-01-28 15:02:06',1,'Assuming that in fact nobody can be killed twice, one way of arranging the people allows for a population of 40:\r\n\r\nForm an 8 pointed star by overlaying two concentric squares with one angled at 45 degrees to the other. Place a person at each of the 8 corners of squares and at each of the 8 intersections of lines from the two squares. The 16 people are now in 8 rows of 4 people. The inner 8 people can be the outer 8 people on a similar smaller concentric scheme. When there are 4 sets of outer people, or 8x5=40 people in all (there being one set of 8 inner people who are not further matched with even-more-inner people), there are 32 sight lines (say aimed counterclockwise each) in which three people are passed over and a final fourth is shot dead.\r\n\r\nThe town must be in a valley so that this is possible--otherwise the mix of tall and short people wouldn\'t allow some to be shot by some bullets and passed over by others.',NULL,0);
INSERT INTO comment VALUES (11388,279,4670,'e.g.','re: Easy solution','2004-01-28 15:09:09',3,'Even simpler: N=lim x-->2003 d/dx (x+x+x+...+x) if there are N x\'s in the sum.',9636,0);
INSERT INTO comment VALUES (11389,1467,1567,'Bryan','After a careful reading, the answer is less than 20','2004-01-28 15:25:14',0,'To find the very fewest villagers that meet the conditions of the problem statement, the barbarians\' bullets must pass completely over the villagers and kill an opposite barbarian on the other side! Note this interpretation is not prohibited by the ambiguous wording of the problem. Consider the villagers arranged thusly: CDE This sentence contains thirty-six letters.\r\n These are easier to construct, but they fullfil the question.',NULL,0);
INSERT INTO comment VALUES (11496,1395,1626,'Gamer','re: Two sentencess','2004-02-01 14:38:08',0,'That goes to a different problem. What he wants is ones that relate to the letters in the sentence.',11495,0);
INSERT INTO comment VALUES (11497,1395,4507,'Penny','re(2): Two sentencess','2004-02-01 16:04:37',0,'Gamer: \"What he wants is ones that relate to the letters in the sentence.\"\r\n \r\nUnless I am totally misreading this puzzle (wouldn\'t be the first time !!), surely there are an infinite number of statements.\r\n\r\nThis sentence has fewer than 100 As, fewer than 100 Cs, fewer than 100 Ds, fewer than 100 Es, fewer than 100 Fs, fewer than 100 Gs, fewer than 100 Hs, fewer than 100 Is, fewer than 100 Ls, fewer than 100 Ns, fewer than 100 Os, fewer than 100 Rs, fewer than 100 Ss, fewer than 100 Ts, fewer than 100 Us, fewer than 100 Vs, fewer than 100 Ws, fewer than 100 Xs, and fewer than 100 Ys. \r\n \r\nThis sentence has fewer than 101 As, fewer than 101 Cs, fewer than 101 Ds, fewer than 101 Es, fewer than 101 Fs, fewer than 101 Gs, fewer than 101 Hs, fewer than 101 Is, fewer than 101 Ls, fewer than 101 Ns, fewer than 101 Os, fewer than 101 Rs, fewer than 101 Ss, fewer than 101 Ts, fewer than 101 Us, fewer than 101 Vs, fewer than 101 Ws, fewer than 101 Xs, and fewer than 101 Ys.\r\n \r\nThis sentence has fewer than 102 As, fewer than 102 Cs, fewer than 102 Ds, fewer than 102 Es, fewer than 102 Fs, fewer than 102 Gs, fewer than 102 Hs, fewer than 102 Is, fewer than 102 Ls, fewer than 102 Ns, fewer than 102 Os, fewer than 102 Rs, fewer than 102 Ss, fewer than 102 Ts, fewer than 102 Us, fewer than 102 Vs, fewer than 102 Ws, fewer than 102 Xs, and fewer than 102 Ys.\r\n\r\netc..... \r\n \r\n\r\n \r\n\n\nEdited on February 1, 2004, 4:05 pm',11496,0);
INSERT INTO comment VALUES (11498,1395,3172,'SilverKnight','re(3): Two sentencess','2004-02-01 16:46:23',0,'LOL... \r\n\r\nI like that answer... but I *think* that DJ means the sentence specifically says exactly how many of each letter it has (rather than saying \'has fewer than\').... In which case, one must take into account the spellings of each number of each letter. (e.g., changing the sixteen in front of the \'Ts\' to a seventeen, would maintain the number of s\'s and t\'s but change the number of e\'s, x\'s v\'s and i\'s... etc...)\r\n\r\nOf course, perhaps, as Penny said, \"I am totally misreading this puzzle (wouldn\'t be the first time)\".',11497,0);
INSERT INTO comment VALUES (11499,1395,3372,'Sam','Hmmmm','2004-02-01 17:10:51',0,'Bah, I think I might give up. I wrote a program for it in about 20 minutes, but haven\'t been able to find anything yet. Perhaps I\'m doing it wrong.\r\n\r\n\r\nMy basic algorithm:\r\n\r\nCreate sentence\r\n\r\n\"Sams wonderfully original sentence contains _ As, _ Bs ...\"\r\n\r\nCount As, insert into first hole. Re-generate sentence.\r\nDo the same for all letters.\r\nLoop until sentence stops changing.\r\n\r\nInserted words: \"No\" \"One\" \"A Couple\" \"Three\" \"Four\" ... \"A Dozen\" ... \"Nineteen\" \"Twenty\" \"Many\"\r\n\r\n\r\nNo dice yet, with any variation on the intitial part of the sentence above.\r\nAnyone have a better method? This one is kind of slow...\n\nEdited on February 1, 2004, 5:13 pm',11498,0);
INSERT INTO comment VALUES (11500,1395,1626,'Gamer','re(4): Two sentencess','2004-02-01 19:57:55',0,'I think DJ, I, or another scholar (I wasn\'t paying too much attention to this problem after I saw it was fine) should have added a line to clarify that when that point was brought up in the queue.\r\n\r\nYou need to say how many letters are in the sentence, not more, not less.',11498,0);
INSERT INTO comment VALUES (11501,1395,1626,'Gamer','This probably doesn\'t count either.','2004-02-01 20:07:33',3,'This sentence contains 2 As, 3 Cs, 4 Es, 2 Hs, 3 Is, 5 Ns, 2 Os, 13 Ss, 4 Ts. ',NULL,0);
INSERT INTO comment VALUES (11502,1395,1626,'Gamer','re: This probably doesn\'t count either (with an and)','2004-02-01 20:09:25',0,'This sentence contains 3 As, 3 Cs, 2 Ds, 4 Es, 2 Hs, 3 Is, 6 Ns, 2 Os, 14 Ss, and 4 Ts.',11501,0);
INSERT INTO comment VALUES (11503,405,5442,'Phil','re(4): more difficult','2004-02-01 20:32:35',0,'if you wrap the paper around a cylinder you can connect all the dots with one line EVEN IF they are points. the trick is to wrap it at some angle, rather than parallel to the edges of the cylinder.',3244,0);
INSERT INTO comment VALUES (11504,1312,5442,'Phil','how i solved it','2004-02-01 21:43:25',0,'This is probably not the most efficient algorithm, but in this case it worked properly.\r\n\r\nI assumed Paul got them all right and made a table of who got what right and wrong.\r\n\r\n Q1 Q2 Q3 Q4 Q5 # RIGHT\r\nPaul R R R R R 5\r\nTodd W W R W R 2\r\nJason R W W W W 1\r\nAlicia R R R W R 4\r\nBebe W W W W W 0\r\n\r\nwe know nobody got all the answers wrong, so one of pauls answers must be wrong. looking at the table i quickly saw that if paul got question 4 wrong then the number of correct solutions would be Paul 4, Todd 3, Jason 2, Alicia 5, Bebe 1; which satisfies the criteria for the solution.\r\n\r\nI guess I got lucky only having to invert one column, but one could make a matrix and just keep inverting columns until the solution presented itself.',NULL,0);
INSERT INTO comment VALUES (11505,529,5442,'Phil','re: The official solution of this problem is in error','2004-02-02 01:26:59',0,'The BC/AD system of dating was imposed by Dionysius Exiguus in 525 AD. So, unless people redated 600-year-old coins, I wouldn\'t believe him.\r\n\r\nInteresting to note was that he calculated the year of Christ\'s birth incorrectly... Oh well.',9391,0);
INSERT INTO comment VALUES (11506,1395,5285,'Ady TZIDON','re: This probably doesn\'t count either.//gamer','2004-02-02 01:48:06',1,'Why not add: ..\'. counting letters only\"...,\r\nadjusting the numbers mutatis mutandis??\r\n\r\nady',11501,0);
INSERT INTO comment VALUES (11507,1443,5267,'cogitater','solution','2004-02-02 02:41:22',0,'Worked on it during the Super Bowl so I may have missed something, but the only initial deduction I saw was that B could not be the knight. The rest was trial and error. A was the liar and won the race, B was the rebel and came in third, C was then knave and came in second, and D was the knight and came in last. Guess I\'ll go look it up now and see how I did.',NULL,0);
INSERT INTO comment VALUES (11508,1270,5267,'cogitater','re(4): JinCo\'s Solution','2004-02-02 03:02:57',0,'It looks as if most people got this one right, why is it rated so high?',11206,0);
INSERT INTO comment VALUES (11509,1543,5267,'cogitater','Comment on solution','2004-02-02 03:27:52',0,'Samo, if as you say, a great number of mathematical proofs rely on questionable assumptions such as step two, then the field of mathematics is unnecessarily complicated by arbitrary semantics. Try this one: Zeus is the father of all gods, Zeus is a god, therefore Zeus is his own father. What is wrong with this proof? Or this one: nobody is perfect, I am nobody, therefore I am perfect. Logic is simpler when unencumbered by arbitrary rules for solution.',NULL,0);
INSERT INTO comment VALUES (11510,1395,1575,'DJ','Similarity','2004-02-02 07:44:57',2,'By a similar statement it is intended that all the statements are identical to this one, aside from the actual number-words used, as in:\r\n\r\nThis sentence has three As, one B, two Cs, two Ds, thirty Es, five Fs, three Gs, ten Hs, seven Is, one J, one K, two Ls, one M, fourteen Ns, twelve Os, one P, eight Rs, twenty three Ss, twenty two Ts, three Us, five Vs, eight Ws, and four Ys.',NULL,0);
INSERT INTO comment VALUES (11511,1607,3372,'Sam','Solution','2004-02-02 08:25:55',3,'Aaron\'s first comment gave his identity away. The only way this could happen is if he said the one thing that only a knave could say: \"I am a liar.\"\r\n\r\nAaron\'s first comment was a lie, therefore his second comment was a truth, therefore Cassie is a knight.\r\n\r\nTherefore Bill was lying on his second comment when he said that Casie was a knave, so Bill is either a knave or a liar.\r\n\r\nBill\'s first comment had to either be \"I am not a knight,\" \"I am not a knave\" or \"I am not a liar\"\r\n\r\nNeither Bill the truth-telling knave nor Bill the liar would have been able to say \"I am not a knave.\" Similarly, both Bill the knave and Bill the Liar would be able to say \"I am not a liar,\" and the friend would not have worked out the puzzle. \r\nTherefore, Bill must have said \"I am not a knight,\" and was therefore telling the truth, and was therefore a knave.\r\n\r\nAaron: Knave\r\nBill: Knave\r\nCasie: Knight',NULL,0);
INSERT INTO comment VALUES (11512,1607,4670,'e.g.','','2004-02-02 08:36:56',3,'A must have said \"I\'m a Liar\", which only allows for his being a Knave; no other could say so. \r\nBill must have said \"I\'m not a Liar\" or \"I\'m not a Knave\", since I couldn\'t tell what he was right then. In the first case he could be a knight or a knave, and in the second case, he could be anything. \r\nA said C was a knight; since A is a knave, and he had already lied, then C *is* a knight. \r\nB said C was a knave; this is false, so we know B (at least sometimes) lies. \r\nIf B had said \"I\'m not a liar\", he could be either a knave or a liar, so as I could tell what he was, he must have said \"I\'m not a knave\", and he actually *was* one.\r\n',NULL,0);
INSERT INTO comment VALUES (11513,1395,2716,'Federico Kereki','Also not acceptable...','2004-02-02 08:59:13',1,'This sentence has plenty of A\'s, C\'s, E\'s, F\'s, H\'s, I\'s, L\'s, N\'s, O\'s, P\'s, S\'s, T\'s and Y\'s, and just one B, D, G, J, K, M, Q, R, U, V, W, X, and Z.\r\n',NULL,0);
INSERT INTO comment VALUES (11514,1583,1920,'Brian Smith','re(2): Very slightly better...','2004-02-02 09:52:16',0,'Yes, all three digits lie in a straight line. Like in a typical word search puzzle puzzle.',11454,0);
INSERT INTO comment VALUES (11515,1509,5452,'Anna','','2004-02-02 10:57:40',3,'He only gains 1 foot every day. On the 30th day he*s still IN the well so he has to take one more day to get OUT. He would get out on March 17th 1996!',NULL,0);
INSERT INTO comment VALUES (11516,315,4865,'Heartberry','re: The solution is wrong!','2004-02-02 11:40:57',1,'The solution makes perfect sense. What you said is correct when you are said that the man who is looking at the picture is the one who is saying that sentence...but you have to keep in mind that his father\'s son (which is himself, the one saying that and looking at the picture), is the person in the picture\'s FATHER. So the man looking at the picture, is the photographed person\'s father :) Which makes the man in the photo, his son :)',4838,0);
INSERT INTO comment VALUES (11517,315,4865,'Heartberry','re: NEVERMIND I WAS WRONG!','2004-02-02 11:43:24',0,'lmao This is why this riddle is so good! I hope you rated it high :) It sure confused a lot of us! But I\'m glad you finally got it! :) Whew! You sure were adamant even though you were wrong :) Good job admitting your err :)',4840,0);
INSERT INTO comment VALUES (11518,1459,5388,'Eliza','solution','2004-02-02 12:32:24',0,'I got the same solution as many people here, and I\'m inclined to think it\'s correct. Here\'s what I did:\r\nBased on clue 2, we know that \"white tie\" came between \"green suspenders\" and \"red shirt.\" If the order is:\r\nred shirt\r\nwhite tie\r\ngreen suspenders\r\n\r\nthen it doesn\'t fit with clue 3, which gives the order:\r\ngreen shirt,\r\nred suspenders\r\nred tie.\r\n(if green shirt #1, red suspenders and red shirt #2, then the two ties clash; green shirt and red shirt can\'t be together; and if red shirt #1, then green shirt and white tie #2, then the two suspenders clash.)\r\n\r\nSo from this, we know the order is:\r\ngreen suspenders\r\nwhite tie\r\nred shirt\r\n\r\nThen, the only way to combine these three with the other group of three (green shirt, red suspenders, and red tie) is:\r\n\r\n#1 - green suspenders\r\n#2 - white tie, green shirt\r\n#3 - red shirt, red suspenders\r\n#4 - red tie\r\n\r\nAny other way it\'s impossible to fulfill the clue about person B (green tie + red or blue shirt)\r\n\r\nThen, filling in:\r\nOnly two shirts are left: blue and white. Blue shirt can\'t be last, so blue shirt is #1, and white shirt is #2.\r\nTherefore, blue tie and white suspenders are #\'s 2 and 3 (not necessarily respectively). #3 is already wearing suspenders, so #3 has a blue tie, and #2 has white suspenders.\r\n\r\nThat leaves us with:\r\n#1 - green suspenders, blue shirt\r\n#2 - white tie, green shirt, and white suspenders\r\n#3 - red shirt, red suspenders, and blue tie\r\n#4 - red tie, white shirt\r\n\r\n#1 needs a tie--only color left is green; and\r\n#4 needs suspenders--only color left is blue.\r\n\r\nFinal answer:\r\n#1 - green suspenders, blue shirt, and green tie\r\n#2 - white tie, green shirt, and white suspenders\r\n#3 - red shirt, red suspenders, and blue tie\r\n#4 - red tie, white shirt, and blue suspenders',NULL,0);
INSERT INTO comment VALUES (11519,1459,5388,'Eliza','small error in typing','2004-02-02 12:36:53',0,'In the solution I posted below, I wrote:\r\n\r\n\"Then, filling in: \r\nOnly two shirts are left: blue and white. Blue shirt can\'t be last, so blue shirt is #1, and white shirt is #2. \"\r\n\r\nI *meant* \"... and white shirt is #4\" Later on, it\'s evident that I included it in #4, but I don\'t know why I wrote #2...',NULL,0);
INSERT INTO comment VALUES (11520,467,5407,'Ashley','re: I dont get it','2004-02-02 13:04:38',0,'The morning/afternoon/evening thing refers to the cycles of life. In the morning (childhood), you crawl on all fours as a baby. In the afternoon (adulthood), you stand on two legs. In the evening (old age), you walk on two legs with the aid of a cane. \r\nThe queue cannot be all liars, for the first would be telling the truth. \r\nSo the queue must have some knights and some liars. The knights must be at the beginning of the queue, and the liars at the end. \r\nIf there were more knights than liars, the last knight would be lying. \r\nIf there were more liars than knights, the first liar would be telling the truth. \r\nThus, there must be the same number of knights and liars, and since the total number must be a prime number, there were TWO people in all, a knight and a liar.',NULL,0);
INSERT INTO comment VALUES (11538,1415,1413,'dave domingo','fun','2004-02-03 13:33:03',0,'I just wanted to be the first to tell you that this puzzle is funny. It made me laugh out loud -- at work. - DD\n\nEdited on February 3, 2004, 1:34 pm',NULL,0);
INSERT INTO comment VALUES (11539,1415,1301,'Charlie','Theoretical minimum that can\'t be done logistically.','2004-02-03 13:40:35',1,'Ideally, the bicycle would be in use all the time and the three hikers would arrive at the destination at the same time.\r\n\r\nLet x be the total number of hours for the trip.\r\nLet b be the hours that the boy is riding the bike.\r\nLet g be the hours that the girl is riding the bike.\r\nLet d be the hours that the dog is riding the bike.\r\n\r\nIf the bicycle is being ridden the whole time then\r\nx=b+g+d\r\n\r\nThey each travel 10 miles:\r\n10=2x+10b, where 10 is the incremental speed added by the bike.\r\n10=2x+10g\r\n10=4x+12d\r\n\r\nThese translate to \r\n12b+2g+2d=10\r\n2b+12g+2d=10\r\n4b+4g+16d=10\r\n \r\nThe last two give d=(10g-5)/6, and then the last one gives\r\n104g = 70, with b=g.\r\n\r\nThe total time, x=b+g+d, would be 85/52 of an hour, the the amounts of time each rides the bike would be 35/52 hour each for the boy and the girl and 15/52 hour for the dog.\r\n\r\nBut there\'s no way the bike could be ridden all the while, as the bike rider would get ahead of the non-riders and would have to leave the bike in place until a walker catches up.\r\n\r\nBut no solution can be lower than 98.08 minutes.',NULL,0);
INSERT INTO comment VALUES (11540,1415,5466,'steve','Solution','2004-02-03 13:59:17',0,'Approximately 3.89 hours.',NULL,0);
INSERT INTO comment VALUES (11541,1415,1413,'dave domingo','i know how but not how fast','2004-02-03 14:19:34',0,'Too-slow scenario: GIRL bikes 5 miles (in 25 minutes), leaves bike and walks the other 5 miles (in 2 hours), finishing the trip in 2 hours 55 minutes. BOY walks first 5 miles, rides second 5 miles, finishes in 2 hours 55 minutes. DOG trots the whole way and finishes in 2 hours 30 minutes.\r\n\r\nImprovement: GIRL rides a little farther before she leaves the bike. DOG takes the bike back a short distance. BOY gets on bike sooner. I haven\'t calculated how far back the dog should take the bike in order to finish at the same time as the humans.\r\n',NULL,0);
INSERT INTO comment VALUES (11542,1415,1413,'dave domingo','solution','2004-02-03 14:37:22',0,'2.75 hours (decimals are a little easier to follow)\r\n\r\nGirl rides 5.4 miles in 0.45 hours; leaves bike; walks 4.6 miles in 2.3 hours.\r\n\r\nDog trots 5.4 miles (to location of bike) in 1.35 hours; takes bike BACK 0.8 miles (to 4.6-mile mark) in 0.05 hours; then trots forward the remaining 5.4 miles in 1.35 hours.\r\n\r\nBoy does same as girl but in reverse order: walks 4.6 miles in 2.3 hours; picks up bike; rides 5.4 miles in 0.45 hours.\r\n\r\nI always use Excel to solve this kind of thing. It allows me to \"compartmentalize\" the mathematical relationships -- so I don\'t have to think about everything at once! \n\nEdited on February 3, 2004, 2:42 pm',NULL,0);
INSERT INTO comment VALUES (11543,1415,3172,'SilverKnight','re: solution','2004-02-03 14:58:07',0,'LOL\r\n\r\nSee what happens, when you don\'t write \"show your work\" in the problem! ',11542,0);
INSERT INTO comment VALUES (11544,1357,5338,'chuck','duh simple','2004-02-03 15:33:42',0,'each number following the is the number of factors the current one has e.g 20 has6 factors, 20,10,5,4,2,1',NULL,0);
INSERT INTO comment VALUES (11545,1603,4507,'Penny','re(2): Solution','2004-02-03 16:15:29',0,'Charlie: \"9 is not prime, but still has a paradox. N must be even to avoid a paradox, and 2 is the only even prime.\"\r\n\r\nI screwed up again. I got the right answer for the wrong reason.\r\n\r\nHere\'s a riddle for you: Is it worse to get the wrong answer for the right reason, or the right answer for the wrong reason? \r\n',11535,0);
INSERT INTO comment VALUES (11546,1603,3172,'SilverKnight','re(3): Solution','2004-02-03 16:27:18',0,'\"Here\'s a riddle for you: Is it worse to get the wrong answer for the right reason, or the right answer for the wrong reason? \"\r\n\r\nMost certainly, the latter is worse.\r\n\r\nThe former, at least, implies one understands the issue at hand (even if he made a mistake). The latter, implies one doesn\'t understand the issue, and (what\'s worse!) he is ignorant of the fact that he doesn\'t understand the issue.',11545,0);
INSERT INTO comment VALUES (11547,1603,4507,'Penny','re(4): Solution','2004-02-03 17:55:01',0,'SK: \"...implies one doesn\'t understand the issue, and (what\'s worse!) he is ignorant of the fact that he doesn\'t understand the issue.\"\r\n\r\nLOL !!!!!!!!!\r\n\r\nThe only worse thing would be somebody copying every single one of his 19 posted problems right off the Internet !!!!! \n\nEdited on February 3, 2004, 8:04 pm',11546,0);
INSERT INTO comment VALUES (11548,1607,3558,'Tristan','Pointing out...','2004-02-03 18:01:11',2,'Don\'t stop the comments yet!\r\n\r\nI point out that none of the below comments have the correct solution. I gave this a D4 for a reason, you know. If you want to know what\'s wrong, try reading the whole problem, not just up to \"Aaron told me that Cassie was a knight.\" There is a trick involved, and you must find it to truly solve the puzzle.\r\n\r\nI also point out that the title and the last sentence contradict each other. What do you know about contradicting statements in a knights and liars puzzle?\r\n\r\nEdited on February 3, 2004, 6:02 pm\n\nEdited on February 4, 2004, 6:23 pm',NULL,0);
INSERT INTO comment VALUES (11549,1607,3172,'SilverKnight','re: Pointing out...','2004-02-03 18:09:15',2,'So, you\'re saying that you, the story teller, are, in fact, a knave... and all your statements (in the problem itself) are, in fact, alternating true and false?\r\n\r\njeez....',11548,0);
INSERT INTO comment VALUES (11550,1415,2899,'Brian Wainscott','Better late than never...','2004-02-03 19:24:17',3,'Me, not the dog!\r\n\r\nI won\'t belabor this, because I\'m sure someone else has already posted this solution:\r\n\r\nThe girl rides 5.4 miles and leaves the bike. When the dog gets to the bike he (she? it?) rides it back 0.8 miles toward the start. When the boy gets to the bike he rides it to the end. They all get there at the same time: 2.75 hours\r\n\r\n------ edit begins here -------\r\n\r\nOK, now that I\'ve read the other posts, I see Dave Domingo got the same answer I did, and SK wants us to show our work. So here is mine (breifly):\r\n\r\nClearly, the problem is symmetric and the boy and girl should each ride the same distance X. Then assuming the \"dog rides it back\" strategy that I\'m using, the time traveled by the girl = X/12+(10-X)/2. The time traveled by the dog will be X/4 + (2X-10)/16 + X/2. Equate and solve for X.\r\n\r\nThis is certainly minimal for this arrangement of travel, and I\'m sure it is the solution sought. But I don\'t know that I can prove it is the minimal time when all possible combinations are considered.\n\nEdited on February 3, 2004, 7:33 pm',NULL,0);
INSERT INTO comment VALUES (11551,1607,3558,'Tristan','re(2): Pointing out...','2004-02-03 19:29:50',2,'I expected someone would say that. I\'m a knight. I can prove it here:\r\n\r\nI am a knight. I am not a knave.\r\n\r\nBut seriously, that\'s enough hints.',11549,0);
INSERT INTO comment VALUES (11552,1618,3558,'Tristan','Clarification','2004-02-03 20:12:43',2,'Each person has a different probability of winning during his or her turn. Everyone has the same chance of winning the whole game. A game is not just a single turn; it only ends when someone wins. ',NULL,0);
INSERT INTO comment VALUES (11553,1415,4374,'Richard','re: Better late than never...','2004-02-03 20:40:21',0,'You and Dave Domingo have certainly dispelled any initial thought that the trip must take 5 hours. However, it seems wasteful that there should be a backward segment, even though it is a short one employing the fastest means of locomotion. Now the dog alone with no bike riding can do the trip in 2.5 hrs which is .25 hr faster than your solutions. So if the boy and girl can alternate riding the bike and walking at an average rate as great as 4 mph, the trip can be done in 2.5 hrs. While it might at first seem that such an alternating sequence can be constructed, it cannot -- if each walks half the time and rides the other half, the average speed will be only 6/7 of 4 mph and it will take 2.91666 hours for them to do the 10 miles. So maybe the backwards segment is not so bad -- it appears to be the only way that both the boy and girl can use the bike for more than half the distance, and thereby get their average speed above 6/7 x 4 mph. Using the backwards segment, the dog loses a bit of its 4 mph unassisted capability, but the boy and girl gain to the point where all three come out with the same average speed.\r\n\n\nEdited on February 4, 2004, 1:01 am',11550,0);
INSERT INTO comment VALUES (11554,1415,5478,'meanie','my answer','2004-02-03 22:04:36',0,'well it says that the three are going for a walk so my guess is 5 hours if the boy and girl walk and the dog trots along with them all at 2 mph. or maybe i\'m just reading too much into the question. ',NULL,0);
INSERT INTO comment VALUES (11555,1601,3558,'Tristan','One way to think about it','2004-02-03 22:32:15',3,'It\'s all in your mind. The mirror technically reflects front and back (or your reflection would face away from you... scary!). Your mind rotates the reflection so it faces away from you, then identifies left and right as right and left. If you were a little insane and irrational, your mind might rotate the reflection so your reflection was upside-down, and then left and right would be fine. ',NULL,0);
INSERT INTO comment VALUES (11556,1415,4507,'Penny','Another meanie on the flooble website ??','2004-02-04 00:00:59',0,'We already have too many meanies.',NULL,0);
INSERT INTO comment VALUES (11557,1607,3172,'SilverKnight','re(3): Pointing out...','2004-02-04 01:01:29',2,'well... I meant the story teller... so not you, but rather your friend is a knave... and the rest follows logically.',11551,0);
INSERT INTO comment VALUES (11558,1415,4830,'Jils','re: Better late than never...','2004-02-04 06:17:46',1,'Well if the dog got there sooner, there would be good time wasted that it could have used in taking the bike back further. However there might be an argument for the boy and girl finishing before the dog....',11550,0);
INSERT INTO comment VALUES (11559,1415,3172,'SilverKnight','re(2): Better late than never...','2004-02-04 06:23:12',0,'In this problem, if *anyone* gets there sooner than another, then an argument can be made showing that the \'extra\' time could have been better used to move the bike to another.\r\n\r\nThey should all finish simultaneously.',11558,0);
INSERT INTO comment VALUES (11560,1302,3136,'Popstar Dave','Solution','2004-02-04 09:20:28',3,'When the first course arrived (cannibal 1) there were 5 other cannibals there to eat him. Therefore it will take 2/5 hours to eat him.\r\n\r\nWhen cannibal 2 comes out, ther are only 4 cannibals left to eat him. Therefore taking 2/4 hours.\r\n\r\nThree cannibals are left to eat cannibal 3, taking 2/3 hours.\r\n\r\n2 cannibals eat cannibal 4 in 2/2 hours.\r\n\r\nAnd the last cannibal eats cannibal 5 in 2/1 hours. \r\n\r\nThus taking a total of:\r\n2/5 + 2/4 + 2/3 + 2/2 + 2/1 Hours\r\n= 4 hours and 34 minutes.\r\n\r\nThis solution assumes that the rate of eating remains constant regardless of the amout of eating already done. \r\n \r\nIt also ignores the fact that if one canibal eats another, he now contains the mass of two cannibals and would theoretically take twice as long to eat. ',NULL,0);
INSERT INTO comment VALUES (11561,1302,3136,'Popstar Dave','Solution (add on)','2004-02-04 09:37:21',3,'Assuming that once a cannibal has eaten another cannibal he now contains the mass of two cannibals and thus takes twice as long to eat (or a proportion of that, depending on how much of another cannibal he has so far eaten), the answer is different. \r\n\r\nAssume the mass of a cannibal is C, and any given cannibal can consume a meal at a rate of C every 2 hours. \r\n\r\nAt the first sitting each of 5 cannibals eats C/5 taking 2/5 hours (=0.4 hr). \r\n\r\nAt the second sitting each of 4 cannibals eats 1.2C/4 taking 1.2*2/4 hours (=0.6 hr).\r\n\r\nAt the third sitting each of 3 cannibals eats 1.5C/3 taking 1.5*2/3 hours (=1 hr).\r\n\r\nAt the fourth sitting each of 2 cannibals eats 2C/2 taking 2*2/2 hours (=2 hr).\r\n\r\nAt the fifth sitting the last cannibal eats 3C taking 3*2 hours (=6 hr).\r\n\r\nThus the meal finishes in:\r\n0.4 + 0.6 + 1 + 2 + 6 = 10 hours. \r\n\r\nThis is the same time that would be taken if the if the final cannibal simply sat down and ate each of the other 5 cannibals in turn (2*5 hours). ',NULL,0);
INSERT INTO comment VALUES (11562,1302,5285,'Ady TZIDON','tasteless solution','2004-02-04 09:38:25',0,'if yhe metabolism is independent of previous meals: \r\n\r\n2*(1/5+1/4+1/3+1/2+1)=4.566666=4h 34\'\r\n\r\notherwise the last one (the survivor) devoured 5 people and this takes 10 hours....\r\n\r\n\r\n\r\nand still hungry.\r\n\r\nady\n\nEdited on February 4, 2004, 9:44 am',NULL,0);
INSERT INTO comment VALUES (11563,1302,4507,'Penny','Solution (...what am I overlooking this time?)','2004-02-04 09:41:16',3,'Answer: 4.5666666667 hours\r\n\r\n(Did you copy/paste this one from Dr. Hannibal Lector\'s autobiography?)\r\n\r\nExplanation:\r\n\r\nIf 1 Cannibal eats 1 person in 2 hrs, then 1 Cannibal eats 1/2 person in 2/2 = 1 hour; he eats 1/3 of a person in 2/3 hour; 1/4 of a person in 2/4 = 1/2 hour, and 1/5 of a person in 2/5 hour.\r\n\r\n5 Cannibals simultaneously eat 1/5 of a person in 2/5 hour. 4 Cannibals simultaneously eat 1/4 of a person in 1/2 hour. 3 Cannibals simultaneously eat 1/3 of a person in 2/3 hour. 2 Cannibals simultaneously eat 1/2 of a person in 1 hour. The last Cannibal eats 1 person in 2 hours.\r\n\r\n2/5 + 1/2 + 2/3 + 1 + 2 = 4.5666666667 hour\r\n ',NULL,0);
INSERT INTO comment VALUES (11564,1302,5285,'Ady TZIDON','re: Solution (...what am I overlooking this time?)','2004-02-04 09:47:33',0,'penny\r\n\r\nmay be you overlook that the portions get bigger..\r\n\r\n the problem is ambiguosly phrased\r\n\r\nady\r\n\r\n\n\nEdited on February 4, 2004, 9:49 am',11563,0);
INSERT INTO comment VALUES (11565,1415,1920,'Brian Smith','Solution','2004-02-04 10:44:36',0,'There are five different time intervals:\r\nt1:boy has bike\r\nt2:boy leaves bike for dog\r\nt3:dog has bike and rides back toward the start\r\nt4:dog leaves bike for girl\r\nt5:girl has bike\r\n\r\nFor the best result everyone (and everything) finishes at the same time. The four following equations can be formulated:\r\n\r\nboy: 12*t1 + 2*t2 + 2*t3 + 2*t4 + 2*t5 = 10\r\ndog: 4*t1 + 4*t2 - 16*t3 + 4*t4 + 4*t5 = 10\r\ngirl: 2*t1 + 2*t2 + 2*t3 + 2*t4 + 12*t5 = 10\r\nbike: 12*t1 - 16*t3 + 12*t5 = 10\r\n\r\nAfter the boy leaves the bike, the bike is (12-4)*t1=8*t1 miles away from the dog. The dog reaches it in t2 hours after the boy drops the bike, therefore 8*t1=4*t2.\r\n\r\nWhen the situation is played in reverse, 8*t5=4*t4 by a similar argument, and t1=t5 and t2=t4\r\n\r\nThis system of eight equations has exactly one solution: \r\nt1 = 9/20 = 27 min\r\nt2 = 9/10 = 54 min\r\nt3 = 1/20 = 3 min\r\nt4 = 9/10 = 54 min\r\nt5 = 9/20 = 27 min\r\nt1+t2+t3+t4+t5 = 55/20 = 165 min = 2 hr 45 min\r\n\r\nThe boy takes the bike for 27 min, leaves it at the 5.4 mile mark and finishes the trip walking.\r\n\r\nThe dog trots for 81 min, finds the bike at the 5.4 mile mark and pedals back toward the start for 3 min, leaves the bike at the 4.6 mile mark and trots the rest of the way.\r\n\r\nThe girl walks for 138 min, finds the bike at the 4.6 mile mark and finishes the trip on the bike.\n\nEdited on February 4, 2004, 2:43 pm',NULL,0);
INSERT INTO comment VALUES (11566,493,2716,'Federico Kereki','Another way','2004-02-04 11:21:08',3,'((0!+0!)^(0!+0!))! = (2^2)! = 4! = 24',NULL,0);
INSERT INTO comment VALUES (11567,1619,5405,'Jer','Extension (A deeper question)','2004-02-04 11:26:12',1,'I like this problem a lot, although I\'ve seen variations before.\r\n\r\nThe most interesting variations (In my opinion) have a missing number that gives multiple possibilities.\r\n\r\n217 has only a single possibility for cube size and method of side painting.\r\n\r\nIf you are told that 8 sides have paint on them, there are 5 possible ways of painting a 2x2x2 cube, so this isn\'t very interesting.\r\n\r\nThere are plenty of examples with two possible size & pattern cominations. For example: 91\r\n\r\nMy question are there any numbers that could yield a lot of solutions? There are 8 ways of painting up to 5 sides of a cube, but some are mutually exclusive, so there can\'t be 8 solutions. How many can there be?\r\n\r\n-Jer',NULL,0);
INSERT INTO comment VALUES (11568,1302,4830,'Jils','Stomach Contents','2004-02-04 11:29:44',0,'Given that the meat would probably take hours to digest, I don\'t think that the mass of the cannibals would change significantly - unless they were prepared to eat the stomach contents as well.',NULL,0);
INSERT INTO comment VALUES (11569,1302,4507,'Penny','re: Stomach Contents','2004-02-04 12:32:01',0,'Jils: \"Given that the meat would probably take hours to digest, I don\'t think that the mass of the cannibals would change significantly - unless they were prepared to eat the stomach contents as well.\"\r\n\r\nThis thread is getting grosser by the minute.',11568,0);
INSERT INTO comment VALUES (11570,1415,1413,'dave domingo','re(2): solution','2004-02-04 12:48:31',0,'That is funny. I am LOL at myself now that you\'ve brought it up. But it didn\'t feel like cheating! \r\n\r\nSeriously, although math was used to set up the problem and to play out the solution, creativity is what \"solved\" the problem. ',11543,0);
INSERT INTO comment VALUES (11571,1302,5484,'P C','A tough meal','2004-02-04 12:56:10',0,'I confirm the solution of Popstar David, although I will explain it differently:\r\n\r\nThe weight of each cannibal increases after each meal, and cannibals remain cannibals, so they devour the stomach contents as well to complete the meal. Assuming that they have infinite appetite, meaning they do not slow down after a meal, then:\r\n\r\nHe ends up having everybody else in his stomach, so it takes simply 5x2=10 hours non-stop.\r\n\r\nIf you calculate the weight of each surviving cannibal after a devouring, you end up with:\r\n1.0, 1.2,1.5,2 and 3 times the original weight.\r\nSince there are 5,4,3,2,1 cannibals that participate, the total time is:\r\n2 hrs x (1/5+1.2/4+1.5/3+2/2+3/1)=10 hours also.\r\n\r\nBon appétit!',NULL,0);
INSERT INTO comment VALUES (11572,1415,3172,'SilverKnight','re(3): solution','2004-02-04 13:02:53',0,'Dave,\r\n\r\nDon\'t get me wrong... I think Excel is a wonderful tool to solve problems... (particularly simultaneous equations with constraint problems).\r\n\r\nAnd you may very well have solved it, on your own, with or without Excel....\r\n\r\nI just meant to point out that a \"solution\" should ideally provide enough information in a clear manner to enable the reader to replicate the thought process/method of solving.\r\n\r\n- SK',11570,0);
INSERT INTO comment VALUES (11573,1415,2899,'Brian Wainscott','re(3): solution','2004-02-04 13:38:30',0,'Dave,\r\n\r\nAs SK points out in his reply, Excel is great. Over the past few months I\'ve been here I\'ve seen several folks use this approach, generally without reproach....',11570,0);
INSERT INTO comment VALUES (11574,1607,2899,'Brian Wainscott','re(4): Pointing out...','2004-02-04 13:51:20',0,'If the knighthood of the story teller is in doubt, perhaps the storyteller is a liar, not a knave.\r\n\r\nTristan notes that the problem title and the last line of the problem contradict each other. But these clearly come from Tristan, not the storyteller. Tristan says this is relevant, but that she is a knight. I\'m not sure that makes sense.... I guess I know what I\'ll be doing during lunch today....',11557,0);
INSERT INTO comment VALUES (11575,1618,5285,'Ady TZIDON','re: Clarification =happy ending','2004-02-04 15:14:30',1,'This Clarification provides an happy ending to very interesting and stimulating problem- not perfectly worded but very original.\r\n\r\nGet us some more!!\r\n\r\nady',11552,0);
INSERT INTO comment VALUES (11576,1415,1413,'dave domingo','re(4): solution','2004-02-04 15:15:36',0,'Right on. And I agree about replicating the thought process.\r\n\r\nWhat I really want to know is where I can find a dog that rides a bike! I\'d like to get a tandem and let the dog do the work. Is that possible? Let\'s say I weigh 180 pounds, the dog weighs 80 pounds, and the tandem bike weighs 40 pounds. If the dog can pedal the bike at 16 mph by itself, it should be able to pedal at 6.4 mph if I ride along (if the gear ratios are perfect). Show my work? OK!:\r\n\r\nTotal weight without me = 40 + 80 = 120\r\nTotal weight with me: = 120 + 180 = 300\r\nRatio = 300 / 120 = 2.5\r\nSpeed divided by ratio = 16 / 2.5 = 6.4\r\n\r\nNow to find the dog....\r\n',11572,0);
INSERT INTO comment VALUES (11577,1607,2899,'Brian Wainscott','re(5): Pointing out...Tristan?!?','2004-02-04 16:19:55',4,'I know you said no more hints, but how about some clarification? How much lying is allowed? As I read the problem, you are trying to specifically limit the things that can be lied about. \r\n\r\nBut when the problem says \"Aaron told me Cassie was a knight\", if this is a lie, under your description what might have happened is Aaron said \"my frog is sick\". This is a lie not about who spoke or when, only about what he said. But if this is allowed, then however I slice it there is not enough information. If the storyteller is a liar, all bets are off. If he is a knave, then half the sentences can be rendered meaningless. I\'ve tickled some info out of things even assuming meaningless statements, but not enough. Now, if \"Aaron said Cassie was a knight\" as a lie can ONLY mean \"Aaron said Cassie was not a knight\", or possibly \"Cassie was a knave/liar\" then I think it can be done. But my reading of the problem leaves too much latitude in the lying for me to get anywhere....\r\n',11574,0);
INSERT INTO comment VALUES (11578,1619,1171,'nikki','re: Extension (A deeper question)','2004-02-04 18:03:26',0,'I\'m not sure I understand what your final question in the last paragraph is.\r\n\r\nAt first I thought you were asking if it was possible to replace the number 217 in the exact same problem statement, but come up with more than one possibility of cube size and painting pattern. But the way you mentioned that scenario in your 5th statement, it seemed like you were explaining that\'s not what you meant.\r\n\r\nAre you asking if there is a way to do your 91 example, but with more than two possible solutions? If so, I haven\'t found one yet. I checked all the ways to paint a cube, up to a 500x500x500 cube, and I found forty-two numbers that would give more than one possible solution. 1 and 8 gave more than two solutions, but the other forty all only gave two (and for just those 40 I checked that a cube bigger than 500x500x500 wouldn\'t have a solution either).\r\n\r\nFor those that are curious, the ones I found were 1, 8, 23, 91, 98, 120, 169, 218, 225, 288, 728, 946, 1156, 1225, 1352, 1657, 1680, 2465, 3176, 8911, 8978, 9800, 11781, 18818, 24571, 29800, 32761, 34133, 37153, 43681, 54289, 63656, 64898, 71288, 78408, 139128, 262088, 298936, 326040, 332928, 765118, 837224.\r\n\r\nlater!\n\nEdited on February 4, 2004, 6:05 pm',11567,0);
INSERT INTO comment VALUES (11579,187,5345,'Rawlyn','Haven\'t read solution but...','2004-02-04 18:25:24',1,'Surely there\'s a correlation between shoe size and age, and similarly between age and spelling ability. There is no mention of the age range of students tested so it\'s hard to know if this could be right - if they were aged 50-60 then the correlations don\'t really count, but if it was a study of students say 4-18 then I reckon I\'m quids in!\r\n\r\nPeace,\r\nRawlyn.\r\n\r\np.s. What on earth is a spelling \"bee\"? ',NULL,0);
INSERT INTO comment VALUES (11580,1607,3558,'Tristan','re(6): Pointing out...Tristan?!?','2004-02-04 18:37:31',0,'\"If anyone lied about what someone said, they didn’t lie about who, when, or whether they said it; they only lied about what the person said.\"\r\n\r\nLet me reword it to make it more clear. If anyone lied about what someone said, they didn\'t lie about who, when or whether they said it (and didn\'t ommit it completely either). The lie only means that the person did not say what was claimed or anything that is essentially the same.\r\n\r\nFor example, if a liar said, \"Cassie said she was a knight,\" than Cassie really could have said, \"I like socks,\" or, \"I am a knave,\" but not, \"I am neither a knave nor a liar.\"',11577,0);
INSERT INTO comment VALUES (11581,1583,5345,'Rawlyn','My algorithm','2004-02-04 18:48:41',0,'Firstly to Brian - I wrote the program in Delphi 6, if you want the source code I\'ll happily email it to you :)\r\n\r\nAnd now for everyone else that\'s interested...\r\n\r\nI used a genetic algorithm to find my solutions. I start with a population of 500 random \"genes\". Each gene is a string of 81 digits (enough to fill the 9x9 grid). I test the genes and find the longest run of consecutive numbers in each, and store this as the \"fitness\" score for each gene. When all the tests are done, a new genepool is generated. For each new gene, two genes are selected using roulette wheel sampling and \"bred\" by mixing them together at random. There is a probability of about 0.001 that a gene will mutate and contain a digit that is different from both parents. The old genepool is replaced with the new genepool and the process begins again.\r\n\r\nSo basically the algorithm is:\r\n\r\nTest, breed, mutate, repeat.\r\n\r\n...But this is the same for pretty much any GA.\r\n\r\nSorry for the poor explanation - I\'m not very good at explaining things like that :P\r\n\r\nPeace,\r\nRawlyn.',NULL,0);
INSERT INTO comment VALUES (11582,1583,3172,'SilverKnight','re: My algorithm','2004-02-04 18:57:26',0,'Not a bad explanation at all... I think they only think you missed was: how you use the \"fitness\" score (in the roulette wheel sampling?) to give the offspring a good chance of improving.\r\n\r\n- SK',11581,0);
INSERT INTO comment VALUES (11583,1331,5345,'Rawlyn','Notes about squirrels','2004-02-04 19:04:26',0,'a) Why would a squirrel need to worry about a path? They can jump quite far you know...\r\n\r\nb) If anyone out there remembers the \"bird brain of Britain\" thing that happened on TV years ago, then you\'ll know that squirrels are highly intelligent when it comes to solving problems, especially if there\'s a dinner in it for them... Any method of prevention will likely take constant maintenance...\r\n\r\nPeace,\r\nRawlyn.',NULL,0);
INSERT INTO comment VALUES (11584,1300,5484,'P C','Diagonals and vertices','2004-02-04 19:24:43',0,'Ms Doe,\r\n\r\nIn a polygon, the number of vertices equals the number of sides it has, as you said, an octagon has eight, a rectangle has 4 etc. However, it does not have to be equal to TWICE the number of diagonals. A rectangle can have UP TO two diagonals, and an octagon can have UP TO 8x5/2=20 diagonals, as stated in the first two solutions.\r\n\r\nThe number of diagonals does not determine the number of vertices, but the number of vertices determine the MAXIMUM number of distinct diagonals one can draw within the polygon.\r\nI go with the first two solutions.\r\nBest regards.',NULL,0);
INSERT INTO comment VALUES (11585,846,5484,'P C','Twice is not twice','2004-02-04 19:51:05',0,'Philip,\r\n\r\nYour argument is correct if you considered that it is the average during the hour that counts. Thus at 7:30 it is twice as much as it was at 6:30, therefore it started at 5:30! Bravo to your brilliant reasoning.\r\n\r\nIf one would try to solve it by Algebra, then let:\r\nt=0 when it started snowing, \r\nt1=time (in hours) when it started plowing (6:00),\r\nk=rate of snow fall, then\r\nsnow accumulated in the first hour (6:00-7:00)\r\nS1=(t0+t0+1)*k/2\r\nsnow accumulated in the second hour (7:00-8:00)\r\nS2=(t0+1+t0+2)*k/2\r\nSince S2=2*S1,\r\n2*(2t0+1)=(2*t0+3)\r\nt0=1/2 (half an hour)\r\nThus the snow storm started at 5:30, since 6:00 is half an hour after it started.\r\n\r\nFor those interested in Calculus, it is possible to do it by Calculus too! The function is simply a straight line.\r\n\r\nBest regards\r\n',NULL,0);
INSERT INTO comment VALUES (11586,543,5490,'cawanda','haha!','2004-02-04 20:00:49',1,'well i personaly thought that it might be pandoras box but what ever',NULL,0);
INSERT INTO comment VALUES (11587,1583,5345,'Rawlyn','re(2): My algorithm','2004-02-04 20:08:21',0,'The higher the fitness score of the gene, the more chance it has of spreading its own attributes amongst the population. It doesn\'t nescessarily give the offspring a good chance of improving, in fact, most new genes are little or no improvement - and quite often worse than their parents. However, once a strong gene is in the population, it stands a good chance of survival and reproduction, so it will quickly \"take over\" the population. Any improvement from there will also have the same effect. Just like genetics - survival of the fittest.\r\n\r\nWas that what you meant? Or did you want me to give a general explanation of roulette wheel sampling?\r\n\r\nPeace,\r\nRawlyn.',11582,0);
INSERT INTO comment VALUES (11588,511,5487,'Peter Lunts','guess','2004-02-04 20:13:59',0,'i think he(she?) can not. If he(she?) is almighty he(she?) can override laws, including the ones he(she?) made and set in stone. He(she?) sort of has a backdoor to everything. ',NULL,0);
INSERT INTO comment VALUES (11589,733,5484,'P C','Another Solution','2004-02-04 20:36:39',3,'First I\'d like to congratulate Charley and Tim Axoy whom I believe have obtained the correction weight of 136.15752 Kg.\r\nA note for Hank: If you still haven\'t found where your problem was, just think that a solid pillar 20x20x200 cm3 weighs only 224 kg, less than the 236.957 kg that you proposed.\r\n\r\nWhat I am posting is an arithmetic method for calculating volumes, a universal formula that is unfortunately not very well known. The formula goes as follows:\r\n\r\nV=H*(A1+4A2+A3)/6\r\n\r\nFor those (e.g. Charlie) who are familiar with numerical integration using Simpson\'s formula, you will see the similitude.\r\n\r\nHere A1 is the area at one end of the solid, A2 is the cross section area in the middle section, and A3 is the area at the other end, and H is the total length or height of the solid.\r\n\r\nTake the case of a rectangle, A1=A2=A3=A, the formula reduces to \r\nVr=H*6A/6=H*A.\r\nFor a cone, A1=0, A2=πr²/4, A3=πr²\r\nVc=H*(0+4*πr²/4+πr²)/6\r\n=πr²H/3\r\nFor a sphere, A1=0, A2=πr², A3=0\r\nVs=2*r*(0+4*πr²+0)/6\r\n=4πr³/3\r\nNow for our familiar pillar,\r\nA1=64√3 (top section)\r\nA3=20*20=400 (bottom section)\r\nA2 is a trapezium, top side is (0+20)/2=10, bottom side is (16+20)/2=18, and the height is the average of 20 and the height of the triangle, equal to 10+4√3, therefore \r\nA2=(10+18)*(10+4√3)/2\r\nThe volume is thereore:\r\nVp=(400+4(140+56√3)+64√3)*200/6\r\n=32000+9600√3 \r\nMass=2.8*Vp\r\n=2.8*(32000+9600√3)\r\n=136.15752 Kg.\r\n\r\nHope you all go out and enjoy this little know formula.\r\n\r\nBest regards.',NULL,0);
INSERT INTO comment VALUES (11590,1467,5352,'Phil','Possible solution','2004-02-04 20:42:13',3,'From the question, we know that there are 32 barbarians, we also know that there is more than 1 villager (Gamer uses plural VILLAGERS in the clue) since all of the barbarians fired at exactly the same time then no-one standing can already be dead, he also uses the phrase \"including any-one who has been shot already\" this implies that there are dead people in the village, i suspect the dead centre of the village is a cemetary (pun intended).\r\n\r\nfrom the info given the answer can be 2. each barbarian fires at the graveyard from his vantage point over the dead bodies of 3 people, his bullet hits the victims at the exact time that other bullets are coming from other shooters.\r\n\r\nthis solution also works with the final answer as 1, but since plurals are used answer must be 2',NULL,0);
INSERT INTO comment VALUES (11591,1583,3172,'SilverKnight','re(3): My algorithm','2004-02-04 20:49:02',0,'That\'s what I meant, thanks!\r\n\r\n(Of course it couldn\'t hurt to go into more detail, such as explanation of roulette wheel sampling.) :-)',11587,0);
INSERT INTO comment VALUES (11592,711,5484,'P C','Charlie','2004-02-04 20:51:39',0,'Thanks for the great solution.\r\n\r\nI could point out that the radius of the sphere could have been obtained by the intersection chord property, namely if two chords of a circle intersect, then l1*l2=l3*l4, where l1+l2=length of the first chord, and l3+l4 the second.\r\nIn this case, l1=3, l2=3, l3=1, therefore \r\nl4=3*3/1=9\r\nThus the diameter is 9+1 cm, therefore radius=5 cm.\r\n\r\nBest regards and keep up the good work.',NULL,0);
INSERT INTO comment VALUES (11593,330,5487,'Peter Lunts','guess','2004-02-04 21:31:03',0,'gran-aunt',NULL,0);
INSERT INTO comment VALUES (11594,330,5487,'Peter Lunts','re: That is not what the first sentence says','2004-02-04 21:34:48',0,'after reading the solution I agree with what Adriane said',9838,0);
INSERT INTO comment VALUES (11595,730,5484,'P C','re: Possible Solution','2004-02-04 21:47:04',0,'Eh... maybe not.\r\nYou may have forgotten the brackets, which forces the evaluation to go from right to left.\r\nI believe Charlie is the first one to have got the good solution.\r\nKeep on posting.',10942,0);
INSERT INTO comment VALUES (11596,250,5487,'Peter Lunts','it depends','2004-02-04 21:49:32',0,'If the man means: \"everything I have said to you so far(including this) is a lie\", then there is a contradiction in him lying AND telling the truth, so this is a paradox.\r\nBut if he means: \"everything that i say to you during this conversation is a lie\", then the answer is either that he\'s lying or it\'s a paradox.',NULL,0);
INSERT INTO comment VALUES (11597,1280,5484,'P C','Yet another answer','2004-02-04 22:17:36',0,'I propose a completely arithmetic solution.\r\n\r\nSince the hour hand takes 60 minutes to move through the equivalent of 5 minutes for the minutes hand, we can say that the hour hand catches up with the minutes hand at the rate of 1/12.\r\nThe same phenomenon (hands opposing, or at 90 degrees, etc.) repeats itself approximately every hour, increased by the rate of 12/11 (the hour hand catches up!):\r\nSo number of minutes before 6 o\'clock before the hands were opposing:\r\n60*12/11=720/11=65min 27+3/11 sec., \r\nor 4:54:32+8/11 \r\nIt happens again at 7:05:27+3/11, etc.\r\n\r\nFor example, when will the two hands be perfectly superimposed after 12:00?\r\nAnswer is 13:05:27+3/11, 14:10:54+6/11, etc.\r\n',NULL,0);
INSERT INTO comment VALUES (11598,1302,5483,'Stu','Gross Guesswork','2004-02-05 04:27:34',3,'Ok, assuming every time the collective eat an individual, the collective inrease by that individual whole, ie. when the 5 eat the 6th at the first sitting, each of the 5 will then be equal to 1 1/5 and so on, my dodgey maths skills spew out 404 minutes??',NULL,0);
INSERT INTO comment VALUES (11599,1305,4906,'stan','Solution','2004-02-05 08:30:09',3,'1/52.\r\n\r\nAssuming no jokers, there are 52 cards in a deck at the start. When we transfer one from A to B, there are 53 cards in B and 51 cards in A. There is a 1/52 chance (case 1) that the transfered card is the king of hearts and a 51/52 (case 2) chance that it is not the king of hearts. In case 1, the odds of the king of hearts being on top of deck B is 2/53; in case 2, the odds are 1/53. So, overall, the odds are:\r\n\r\n(1/52)*(2/53)+(51/52)*(1/53)=53/(52*53)=1/52\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (11600,1305,1301,'Charlie','re: Solution','2004-02-05 08:43:55',3,'Given that the Queen of Hearts was turned up on the first deck, the card that was transferred to deck B is equally likely to be any one of the 51 other cards in the deck, so the probability is\r\n\r\n(1/51)*(2/53)+(50/51)*(1/53)=52/(51*53)=52/2703\r\n\r\nor about 0.0192378838327783943 rather than the 0.0192307692307692307 that 1/52 would be.\r\n\r\n\r\n',11599,0);
INSERT INTO comment VALUES (11601,1305,5499,'winnifred foster','re: Solution','2004-02-05 08:45:02',3,'no because 1 card was added from deck a, meaning there are 53 cards. so the answer is 53:1',11599,0);
INSERT INTO comment VALUES (11602,1305,1920,'Brian Smith','Solution','2004-02-05 09:09:12',0,'There is a 1/51 chance a King of Hearts was the card transferred to deck B, and drawing a King of Hearts in this case is 2/53. \r\n\r\nThere is a 50/51 chance a King of Hearts was not the card transferred to deck B, and drawing a King of Hearts in this case is 1/53. \r\n\r\nThe overall probability of drawing a King of Hearts is (1/51)*(2/53) + (50/51)*(1/53) = 52/2703',NULL,0);
INSERT INTO comment VALUES (11603,1619,5405,'Jer','re(2): Extension (A deeper question)','2004-02-05 09:42:47',0,'Sorry for wording my question so poorly.\r\n\r\nI think you interpreted it right, I want numbers that yield multiple solutions.\r\n\r\n91 does because there could be a 7x7x7 cube painted on two adjacent sides or a 6x6x6 cube painted on 3 sides that share a vertex.\r\n\r\nI\'m not sure 23 can be done in any way except a 3x3x3 cube painted on 4 sides not in a ring. I haven\'t checked the others.\r\n\r\nAre there any numbers that do give _more_ than 2 possible solutions? (besides 1 and 8)\r\n\r\n-Jer',11578,0);
INSERT INTO comment VALUES (11604,1619,1301,'Charlie','re(3): Extension (A deeper question)','2004-02-05 10:35:26',0,'It looks like 23 was a misprint for 25, which does have multiple solutions (5 faces of a 3x3x3 and 1 face of a 5x5x5).',11603,0);
INSERT INTO comment VALUES (11605,1302,5502,'tim','possible solution: semantic issues','2004-02-05 11:04:43',0,'i first tried to solve the problem the same way as penny where in the first \'course\' of the meal, 5 ate 1 (which took 24 mins), in the second, 4 ate 1 (taking 30 mins) etc until the last two remained in course 5. this round took 2 hours, and the total came to 4 hours 34 mins. After seeing that this is not the solution, I considered that the semantics of the word \'consumer\' may be in question. In the 5th course, where 2 people remain, only one of them is technically a consumer. This means that, on these grounds, the time taken for course 5 is additional to the time taken to leave one consumer, and hence only 2 hours 34 minutes is required. \r\nThoughts?',NULL,0);
INSERT INTO comment VALUES (11606,1607,2899,'Brian Wainscott','Solution','2004-02-05 11:04:54',3,'For simplicity, I will refer to the \"storyteller\" as Dan, and use first initials for everyone.\r\n\r\nTristan has basically told us D is not a knight. If D is a liar, there is not enough information to determine everything, so D is a knave.\r\n\r\nHere are the statements as given:\r\n\r\n1 - Aaron and Bill were talking to me.\r\n2 - Aaron told me what he was.\r\n3 - At this point, I could tell what Aaron was.\r\n4 - Bill told me one thing that he wasn’t.\r\n5 - Aaron told me that Cassie was a knight.\r\n6 - I then could figure out what Cassie was.\r\n7 - Bill told me that Cassie was a knave.\r\n8 - I thought about this for a minute.\r\n9 - I soon found that the previous thing Bill said allowed me to know for sure what the last of the three people were\r\n\r\nThere are two cases: the odd statements are false and the even true, or the other way around.\r\n\r\nCase 1: the odd statements are false. I won\'t go into details in this case, but basically there isn\'t enough information to determine either B or C. But there are some interesting points: In (2) A says what he is, and in (3) D does not know what A is. But after A says \"something\" in (5) D knows what C is. A must have said something about C. One possibility is that in (2) A said \"I am a knave\". This would mean A is a knave and telling the truth, or A is a liar. In either case A\'s next statement would be a lie. So in (5) A could have said \"C is not a liar\" (or knight, or knave), and D would know what C is. But D would still not know A. Depending on what B said in (7), D may or may not know what B is, but (9) definitely tells us that in the end, D couldn\'t figure out who was who. If D cannot figure it out at the end, then neither can we, so this case IS unsolvable.\r\n\r\n\r\nCase 2: the even statements are false. This starts out well, because A and B WERE talking to D, so (1) being true works. A says something in (2), and in (3) D knows what A is. Anything a knight can say, a knave can say. Anything a liar can say, a knave can say. But a knave can say \"I am a liar\" or \"I am not a knight\", both of which only a knave can say. Since (2) as reported by D is false, A did not say \"I am a liar\", so in fact A must have said \"I am not a knight\". Thus A is a knave, and was telling the truth when he said this. In (5) A speaks again (lying this time), so we know C is not a knight.\r\n\r\nIn (7) B says C is a knave. In (9) we find that D can deduce everything. Somehow, whatever B said in (4) provided D with enough information to deduce everything.\r\n\r\nWhat might B have said? He did not say \"I am not a XXX\" because we know statement (4) (as reported by D) is false. He may have made a statement that was know by D to be true (or false). In neither case can we determine the veracity if his next statement, so no information is gained by it and D could not solve the problem. B could have said \"I am a knight/knave/liar\". Had he said \"knight\" then again we could not tell the truth or falsehood of any of his statements. Had he said \"I am a knave\" then we know is next statement will be false. This would allow D to determine what C is, but not what B is. But by (9) D can determine who everyone is. If B said \"I am a liar\" the we know he is a knave, his next statement is true, and all is determined.\r\n\r\nSo the conversation that ACTUALLY took place was this:\r\n\r\n1 - Aaron and Bill were talking to me.\r\n2 - Aaron said \"I am not a knight\"\r\n3 - At this point, I could tell Aaron was a knave.\r\n4 - Bill said \"I am a liar\"\r\n5 - Aaron told me that Cassie was a knight.\r\n6 - I then could not figure out what Cassie was.\r\n7 - Bill told me that Cassie was a knave.\r\n8 - I did not think about this for a minute.\r\n9 - I then determined that by (4) B is a knave, and hence by (7) C is a knave.\r\n\r\nThey are ALL knaves.\r\n',NULL,0);
INSERT INTO comment VALUES (11607,1305,4098,'lovejoy','re(2): Solution','2004-02-05 11:46:33',0,'Not so winnifred, there are now TWO kings of hearts in pack B',11601,0);
INSERT INTO comment VALUES (11608,1467,2899,'Brian Wainscott','re: Possible solution','2004-02-05 12:05:01',0,'But if you are going to count the bodies in the graveyard for the sake of having bullets pass over their heads, you have to include them in the total tally of \"villagers.\" After all, the puzzle says the bullets passed over \"villager\'s heads\" and asks for the total number of \"villagers\". If you count corpses in one case you have to count them in both.\r\n\r\nI prefer the 5 villagers scenario: they stand in a cross formation, we put 8 barbarians on each side of the village (in a line, looking over each other\'s heads toward the town), and the barbarians all shoot each other and miss the villagers completely.',11590,0);
INSERT INTO comment VALUES (11609,1583,1920,'Brian Smith','re: My algorithm - re: source code','2004-02-05 12:16:25',0,'I would certainly like to look at the source code.\r\nAttatch the source code as text file \'fillgrid.txt\'. My email is brianscsmithATyahooDOTcom',11581,0);
INSERT INTO comment VALUES (11610,1409,5504,'jason','re: solution','2004-02-05 12:24:55',0,'i understand what you mean by 88 out of 99 is 99% but isnt the highest score for an A 100%...? its the highest number for the letter grade right? 100=A 89=B 79=C 69=D 59=F? I dont like the way the question is worded. im trying to find the question',10844,0);
INSERT INTO comment VALUES (11611,1590,5484,'P C','re(5): A hardy perennial','2004-02-05 12:45:18',0,'Penny,\r\nIn my books, sharing some related information does not make the post wrong. \r\n\r\nAccording to your theory, those who presented more than one answer would also be wrong, because the question requires the SMALLEST number. We read those posts with interest because the additional infformation is related.\r\n\r\nIn closing, I must say I enjoy all your posts, and I congratulate you for suggesting the fourth way to solving a problem, which I believe is the most illuminating way!\r\n\r\nBest regards.',11172,0);
INSERT INTO comment VALUES (11612,1467,3172,'SilverKnight','re(2): Possible solution - only 3 villagers','2004-02-05 13:23:21',3,'Here\'s how you do it with only three villagers (and 12 barbarians).\r\n\r\nThe barbarians line up on either side of the town on a hill... with three villagers lined up with them. Each barbarian shoots the barbarian on the other side at the same height. To have more barbarians, just have them line up further up the hills.\r\n\r\n What I *did* use was a book I had, \"Elementary Theory of Numbers\"... \r\n(signed)\r\nSomeone',11649,0);
INSERT INTO comment VALUES (11651,1607,2899,'Brian Wainscott','re(2): Solution','2004-02-06 12:15:50',0,'By the rules of the problem, D cannot have lied about who spoke. Both A and B spoke to D. It seems to me that this makes the first statement true, and so D cannot be a liar.\r\n\r\nBeyond that, if D were a liar then the actual true statements might be:\r\n\r\nA and B were playing golf.\r\nA said his underwear is purple\r\nAt this point I could not tell what A was.\r\nB told me he ate lemons for breakfast\r\nA told me he has a pet turtle\r\nI then could not figure out what C was\r\nB told me he likes green beans.\r\nI didn\'t think about this at all.\r\nI then could not figure anything out.\r\n\r\nIf this is what really happened then either:\r\n1 - D could not have made the statement\r\n\"A and B were talking to me\" and be a liar\r\nor, if you allow that\r\n2 - D could be a liar and make all the statements as given, but we would not be able to determine what any of the other three are.\r\n\r\nSeems to me that that covers everything. Unless of course you are going to say that the last line \"the puzzle is solvable\" was also uttered by D, in which case the puzzle may NOT be solvable. But I\'ve been presuming that you, Tristan, a knight, said everything before \"A and B were talking to me\" and after \"what the last of the three people were\"\r\n\r\nPretty clever the way the second line of the problem says \"Everyone in the story....\", and D is in the story. We should have picked up on that. But then again, doesn\'t it work out if D is a knight? A could have said \"I am a liar\", B could have said \"I am not a knight\". Then A would be a knave, B a knave, and C a knight. This is the original solution proposed by others, and I don\'t see a problem with it if D is a knight....',11637,0);
INSERT INTO comment VALUES (11652,1476,1920,'Brian Smith','Round Robin','2004-02-06 12:40:52',0,'This puzzle is just asking for a round robin schedule for 12 players:\r\n\r\nDay 1:ab/cd/ef/gh/ij/kl\r\n\r\nDay 2:ak/bc/de/fg/hi/jl\r\n\r\nDay 3:ac/bd/eg/fh/jk/il\r\n\r\nDay 4:af/bk/dg/cj/ei/hl\r\n\r\nDay 5:aj/bi/ck/df/eh/gl\r\n\r\nDay 6:ai/bj/dh/cg/ek/fl\r\n\r\nDay 7:ad/bf/ch/gj/ik/el\r\n\r\nDay 8:ag/bh/ci/ej/fk/dl\r\n\r\nDay 9:ae/bg/hj/fi/dk/cl\r\n\r\nDay 10:ah/gk/ce/fj/di/bl\r\n\r\nDay 11:be/gi/cf/hk/dj/al',NULL,0);
INSERT INTO comment VALUES (11653,1476,1301,'Charlie','solution','2004-02-06 13:09:23',3,'This problem is solved similarly to the original Conversing Club problem, where three people met each day. In that one, the sets could be found by imagining one person\'s name in the center of a circle and the other names surrounding it along that circle. Triangles would be formed, most connecting three points (names) on the circle, but one connecting two points on the circle with the center. The edges that form chords would have to all span different lengths. Then each day, the set of triangles was rotated one position relative to the names, or the names relative to the triangles--same thing.\r\n\r\nThis is similar, except that instead of triangles we just have lines connecting two names. Again, one name is in the center and 11 names are on the circumference, and one line connects the center to a point (call it point 1) on the circle. The chords are among the remaining 10 positions and must each be a different length. One such way is to connect points 2 and 3 for length 1; 4 and 7 for length 3; 5 and 9 for length 5; 6 and 11 for length 5; and 8 and 10 for length 2, summarized as\r\n 2 3 ( 1); 4 7 ( 3); 5 9 ( 4); 6 11 ( 5); 8 10 ( 2)\r\nNote that spans, n, larger than 5 are just formed by the same chord as 11 - n.\r\n\r\nAll the ways of doing this are:\r\n From B\'s statement, C=(B-1)B(B+1). An easier proposal: the two first brothers got to keep their gifts, but the third was left with nothing, so he should marry the princess as a consolation (!) gift.',NULL,0);
INSERT INTO comment VALUES (11854,1622,4507,'Penny','re(2): Out of all the responses so far ......','2004-02-13 12:20:33',0,'Bathtub and codfish were pretty good too.',11838,0);
INSERT INTO comment VALUES (11855,1605,5481,'John','a try','2004-02-13 12:24:38',3,'if we take the shape in 2d(a XY plane in the middle of the cube,where is the max circle of the spheres) and draw a square with it\'s vertices on the center of the circles,it\'s side will have a length of 2 * radius = 2 so it\'s \r\n\r\ndiagonial will have length 2 * √2 .If after we draw a circle in the center of the empty space formed by the circles is diameter will be \r\n\r\nsquare\'s diagonial - 2 * radius of the circle = 2 * √2 - 2 . so i believe that the same holds and for the cube in 3d \r\nand that makes the radius of the central sphere equal to (2 * √2 - 2) / 2 = √2 - 1\r\n\r\nsorry for my terrible english :)\r\n',NULL,0);
INSERT INTO comment VALUES (11856,1605,5481,'John','my solution is completely wrong...:-)','2004-02-13 12:55:12',0,'after rethinking for a minute i show my VERY BIG mistake',11855,0);
INSERT INTO comment VALUES (11857,1623,2716,'Federico Kereki','re(2): Solution','2004-02-13 12:58:55',0,'I\'d rather say that \"leave a gift\" sounds like a testament or legacy, which implies the donor died. Otherwise, you\'d simply say that \"The wizard GAVE a gift...\"',11853,0);
INSERT INTO comment VALUES (11858,1623,5391,'York','re(3): Solution','2004-02-13 13:31:35',0,'Good point',11857,0);
INSERT INTO comment VALUES (11859,1438,1301,'Charlie','Of course you could do this','2004-02-13 13:52:11',1,'Since we now have a super-duper triple inverter, we can use two of those inverted flows as the two inverters in another such scheme, to produce three inverters there, while still having the one inverter left over.\r\n\r\nNo, on second thought, you can\'t, as the input to the second inverter requires the output from the first. Perhaps the original restriction is still true, that you can\'t do more than 2^n-1 inversions with n inverters.\r\n\r\n\n\nEdited on February 13, 2004, 2:20 pm',11850,0);
INSERT INTO comment VALUES (11860,1605,872,'pleasance','another dimension','2004-02-13 14:06:31',0,'As several people have posted, I agree that the answer is √3-1. Here\'s a more general problem: I have an n-dimensional \'n-cube\' of side 4. I pack 2^n \'n-spheres\' of radius 1 packed in it, similarly to the 3 dimensional problem. What\'s the largest \'n-sphere\' I can place in the centre? What happens as n gets larger? \r\n\r\nSurprisingly, the radius of the inner \'n-sphere\' increases with n, and for enough dimensions it will stick out of the sides of the \'n-cube\'! If I\'m not mistaken, it goes to infinity with n, but I\'ll have to do the calculation. ',NULL,0);
INSERT INTO comment VALUES (11861,1420,872,'pleasance','trivia','2004-02-13 14:21:11',0,'Here are a few from \"A collection of word oddities and trivia\", which can be found at http://members.aol.com/gulfhigh2/words.html\r\n\r\nAEGILOPS (alternate spelling of egilops, an ulcer in a part of the eye) is apparently the longest word in W2 which consists of letters in alphabetical order. Aegilops is also also a genus of mollusc and a genus of grass. CHILLLOSS (the opposite of a heatloss) has its letters in alphabetical order, although this word may not be in any dictionary. The title of the film EFIK MOVY was written abcdEFghIjKlMnOpqrstuVwxYz to show the alphabetical-order property. BEEFILY and BILLOWY are the longest such words in OSPD2+. \r\n\r\nTROLLIED seems to be the longest word in W3 with the letters in reverse alphabetical order. There are also SPOON-FEED and SPOON-FED (although these words are usually spelled with hyphens), SNIFFED, SPIFFED, SPOOFED, SPOOKED, SPOOLED, TROOLIE (a palm tree), and TSONECA (a Patagonian language). SPONGED and WRONGED are the longest such words if repeated letters are not allowed. ',NULL,0);
INSERT INTO comment VALUES (11862,1469,3558,'Tristan','???','2004-02-13 14:21:49',1,'It seems to me that there isn\'t enough info here. We\'re only given the values of M, R, and N. R is given twice, I assume to show that the corresponding number is always the same. The blank seems to go right after the number, so I assume that the hint means that 15484 does not equal DP. The blank is leaving the only example of two letters together unknown.\r\n\r\nI don\'t know where to start, though I\'m not that great at cyptography puzzles.',NULL,0);
INSERT INTO comment VALUES (11863,1605,3172,'SilverKnight','re: another dimension','2004-02-13 14:44:54',0,'Actually, it goes to infinity with √n.\r\n\r\nThe answer is actually, √n-1.\r\n\r\nBut, we\'re just talking.... It is a very interesting and related problem to PROVE that this is so. Anyone? ;-)',11860,0);
INSERT INTO comment VALUES (11864,1605,3558,'Tristan','re(2): another dimension','2004-02-13 15:01:39',0,'For an n-dimensional cube, side length 4, with 2^n hyperspheres inside it with radius 1, the radius of the hypersphere fitting inside is √n-1 (As SK said).\r\n\r\nThis is because the diagonal accross the cube is √(n4²). Subtracting the lengths from the corner to the point at which the hyperspheres touch the center hypersphere, I get √(n4²)-2*(1+√(n4²)/4). This simplifies to 4√(n)-2-2√(n)=2√n-2. The radius is then √n-1.\r\n\r\nFor the center sphere to reach the sides of the cube, I\'d say it takes 9 dimensions. I\'m having trouble imagining such a cube, but I think that these \"sides\" would have 8 dimensions themselves.',11863,0);
INSERT INTO comment VALUES (11865,1623,5617,'jen','i know this!','2004-02-13 15:08:53',0,'she marries the dead wizard...it could happen',NULL,0);
INSERT INTO comment VALUES (11866,1605,3172,'SilverKnight','re(3): another dimension','2004-02-13 15:43:19',0,'That\'s pretty good, Tristan... I start having trouble imagining such a cube, when the dimensions exceed 3... :-)\r\n\r\n-SK\r\n\r\nP.S. yup... the sides of a 9-cube have 8 dimensions.',11864,0);
INSERT INTO comment VALUES (11867,537,5618,'Hau Nguyen','out of the ordinary!','2004-02-13 15:44:51',0,'it\'s radiation ',NULL,0);
INSERT INTO comment VALUES (11868,1469,1626,'Gamer','Hints','2004-02-13 19:01:04',0,'The actual number that goes in the blank is 3 numbers, so if it was 123 (which it\'s not), it would read 154123. This isn\'t as important though. It would still make sense if it was 154 123.\r\n\r\nThe other thing (which wasn\'t planned) was the fact that 3=R appears twice. Thinking about why that is may reveal the answer.',NULL,0);
INSERT INTO comment VALUES (11869,1626,5285,'Ady TZIDON','we were all wrong','2004-02-13 19:05:35',3,' I am a long way from home & cannot write a long explanation- may be later. however the answer to the problem as it is worded is 19/49.\r\nShortly: the only pieces that count are 13 dominoes- 7 one-pip pieces and 7 two-pip pieces , 1-2 being counted twice.\r\nLet us divide the population into 3 subsets:\r\nA 6 one-pip pieces ,( all but 1-2)\r\n B 6 two-pip pieces , ,( all but 1-2)\r\nC the 1-2 domino.\r\n\r\nThe first domino is drawn from the union A U C\r\nwith probability of 6/7 belonging to A and \r\nprobability of 1/7 belonging to C.\r\nIf it is from A then it can be complemented by one matching piece from B or the one piece from C 6/7*2/7 =12/49\r\nIf the 1st domino is from C than any one of the B set qualifies: 1/7*6/6=1/7\r\n\r\nSum up 12/49+1/7= 19/49 - thats my answer.\r\n\r\nbtw - 1-1 or 2-2 do not have any special standing . \r\nIf you choose to look on the wrong end of the 1-pip pr 2-pip\r\nit counts exactly as drawing a piece not in A U B U C-\r\nconradicting the conditions stated in the problem.\r\nSimulation taking into account only those 13 pieces will surely confirm my result.\r\n\r\nady\r\n\r\n\r\n\r\n\n\nEdited on February 13, 2004, 7:07 pm',11834,0);
INSERT INTO comment VALUES (11870,1623,3372,'Sam','re: i know this!','2004-02-13 19:11:17',0,'Since it seems as if there could be a logical explanation for any answer, my bet is that this is like one of those \"who\'s to blame\" puzzles, where the answer is supposed to reveal more about the answerer than the question.\r\n\r\n\r\nIn this case, my answer is to assume that we\'re in a polyandrus society, and the king allows the princess to marry all three of the brothers. And the horse for good measure.\r\n\r\n[edit: never mind the title, this isn\'t actually in response to anything...]\n\nEdited on February 13, 2004, 7:11 pm',11865,0);
INSERT INTO comment VALUES (11871,1469,5345,'Rawlyn','re: Hints','2004-02-13 19:25:58',1,'It\'s still not a lot to go by. The thing I find hard to accept about this puzzle is the ambiguity of it all. Presumably you have A solution in mind Gamer, but I don\'t see any evidence to suggest that it\'s the ONLY answer. For example, what reason have I to assume that the next line doesn\'t read \"3 = F\"? None - it\'s pure speculation! If there was more to go by, by means of a message of some sort encoded with your hidden algorithm perhaps, then we might have more to work with.\r\n\r\nFor the mean time, I\'ll go with 1 as my answer. It\'s no more or less likely than any other so I\'m happy with that...\r\n\r\nPeace,\r\nRawlyn.\r\n\r\np.s. Don\'t take it to heart Gamer - just my thoughts :)...',11868,0);
INSERT INTO comment VALUES (11872,1420,5285,'Ady TZIDON','re: trivia ... more','2004-02-14 03:37:38',1,'U say: \" AEGILOPS (alternate spelling of egilops, an ulcer in a part of the eye) is apparently the longest word in W2 which consists of letters in alphabetical order ...\"\r\n\r\nI say : How about FACETIOUS ( one letter more) or even better FACETIOUSLY ( here even Y is counted as an vowel).\r\n\r\n More: \r\n\r\nBuenos Aires and Port-au-Prince are the only capitals using all the vowels..\r\n\r\nAnd how about:\r\n\r\nBOOKKEEPPER (4 doubles in a row!!) assisted by a subBOOKKEEPPER (5 doubles but too artificial...)\r\n Strengths (one consonant only- just like OHIO IOWA and OAHU!!!)\r\n I have a veryloooooooooooooong liiiiiiiiiiiiiiiiist of oddies, but will stop here, concluding with the longest English word:\r\n\r\nSMILES - a whole mile between two S-es.\r\n\r\nady\r\n\r\n\n\nEdited on February 14, 2004, 3:45 am',11861,0);
INSERT INTO comment VALUES (11873,1469,153,'TomM','(re: Hints)','2004-02-14 10:21:31',1,'Well, the category is cryptography, and Gamer says the fact that the \"3=R\" line appears twice is unintentional (a coincidence). There are 3 symbols in \"3=R\" and the most common three letter word is \"the\" which would give us 3 => T, = => H, R => E\r\n\r\nBut, is it reasonable to assume that all the words end in the format -Hx or -Hxx, especially if we\'d be looking for four different \"x\"es, none of them \"E\"',11868,0);
INSERT INTO comment VALUES (11874,1420,1301,'Charlie','re(2): trivia ... more','2004-02-14 11:00:37',0,'Ady says:\r\n\"U say: \" AEGILOPS (alternate spelling of egilops, an ulcer in a part of the eye) is apparently the longest word in W2 which consists of letters in alphabetical order ...\" \r\n\r\nI say : How about FACETIOUS ( one letter more) or even better FACETIOUSLY ( here even Y is counted as an vowel). \"\r\n\r\nBut putting those into alphabetic order makes\r\nACEFIOSTU and ACEFILOSTUY respectively--not the order of the words themselves. Only the vowels of those words had been in alphabetic order, not all the letters.',11872,0);
INSERT INTO comment VALUES (11875,1438,1301,'Charlie','So...','2004-02-14 11:19:13',3,'I don\'t think you actually can invert an arbitrary number of inputs with just 2 inverters. I think the original quote from the internet is correct: with n inverters you can do 2^n - 1 inversions. Put another way, to do i inversions, you need n = ceil(log(i+1)) inverters, using base-2 logarithms.',11859,0);
INSERT INTO comment VALUES (11876,1469,3372,'Sam','re: (re: Hints)','2004-02-14 14:52:44',0,'That\'s a good point, we\'ve been forgetting that this is cryptography, and so possibly the entire set is the message. The title \"Letters to Numbers,\" however, would seem to imply that instead it is simply the substitution code, like people have been thinking.\r\nAnd if it was a message, it still would seem to be impossible. There are absolutely no hooks to help the decryption, and you could insert virtually any message you want, since everything is different.\r\n\r\nAnother hint, perhaps?',11873,0);
INSERT INTO comment VALUES (11877,1328,4507,'Penny','I\'m pretty sure this won\'t be the official solution :-)','2004-02-14 15:00:45',3,'[irony]\r\nNow isn\'t this brilliant ?\r\n\r\n11, 12, 20, 23, 33, 46, 35, 54 72, 47, 75, 98, 59, 96, 124, 71, 117, 150, 83, 138, 176, 95, 159, 202, 107, 180, 228.......\r\n\r\ncan be obtained by merging the following three series: \r\n\r\n11,23,35,47,59,71,83,95,107, (adding ascending multiples of 12 to 11)\r\n12,33,54,75,96,117,138,159,180, (adding ascending multiples of 21 to 12)\r\n20,46,72,98,124,150,176,202,228, (adding acsending multiples of 26 to 20)\r\n[/irony] \n\nEdited on February 14, 2004, 3:20 pm',NULL,0);
INSERT INTO comment VALUES (11878,1469,4507,'Penny','re(2): (re: Hints)','2004-02-14 15:27:48',1,'Gamer wrote: \"The other thing (which wasn\'t planned) was the fact that 3=R appears twice. Thinking about why that is may reveal the answer.\"\r\n\r\nI am guessing that 3=R appears twice because Gamer copy/pasted the word or sentence which is the solution to the puzzle, before encrypting it; and it had whatever \"3=R\" signifies, in both places.\r\n\r\n[64 = M] [3 = R] [154___ = DP] [3 = R] [50= N]\r\n\r\n \r\n',11876,0);
INSERT INTO comment VALUES (11879,1328,5536,'Haiosu','Based on a Fib','2004-02-14 17:03:18',3,'Shift the recursive Fibonacci sequence 3 terms to the left, call it f(n) = 3, 5, 8, 13, 21, 34, 55, ... and apply an incremented base scheme starting with 2. So t(n) = f(n)base(n+1). t(7) = f(7)base(8) = 55 base(8) = 67. Why are there two question marks in the question when it says to find the next number (raises eyebrow)?',NULL,0);
INSERT INTO comment VALUES (11880,1626,3172,'SilverKnight','re: we were all wrong','2004-02-14 18:46:58',0,'Ady,\r\n\r\nWhat you\'re not taking into account (which is what Charlie seems to have been after), are the parts of the problem which read:\r\n\"Two dominoes are picked at random from a standard set of double-sixes...\",\r\nand\r\n\"You look at only one of the two numbers on each domino, choosing at random which end to look at.\"\r\n\r\nIt is not merely sufficient to identify the possible outcomes, but also the likelihood of those outcomes....\r\n\r\n(This would be similar to incorrectly saying that with two normal dice there is a 1/11 chance of rolling each of the 11 totals from 2-12).',11869,0);
INSERT INTO comment VALUES (11881,1626,1301,'Charlie','re: we were all wrong','2004-02-14 19:54:01',0,'\"btw - 1-1 or 2-2 do not have any special standing \"\r\n\r\nThe special standing of the doubles is that when initially chosen they will always fall into the observed set of events. When, say the 1-4 domino is initially chosen, half the time it can\'t fall into the observed situation because the 4 side will be visible. So when the observed situation comes about half of the 1-4 dominos are filtered out, but all of the 1-1 choices remain.',11869,0);
INSERT INTO comment VALUES (11882,1626,153,'TomM','re(2): we were all wrong','2004-02-14 19:58:15',0,'I agree\r\n\r\nFor another perspective on why the answer is not as simple or intuitive as it at first seems, compare SK\'s last post with the discussion on the problem \"3 Cards\" (pid 65).',11880,0);
INSERT INTO comment VALUES (11883,1623,5628,'sandra','','2004-02-14 22:04:55',0,'Why assume the apple is gone? Did she eat the entire apple or did just one bite do the trick... if so then the never rotting apple will be useful in the future (also, seeds could make more magic apples). ',NULL,0);
INSERT INTO comment VALUES (11884,1328,4374,'Richard','link','2004-02-14 23:19:40',0,'http://www.afs-link.com/Brainteaser%20Archive/brainteaser_answers/brainteaser_answer9.html\r\n\r\n(got by googling \"11, 12, 20, 23, 33, 46\" )',NULL,0);
INSERT INTO comment VALUES (11885,1623,5629,'JW','solution??','2004-02-14 23:31:01',0,'the riddle says that the man who saved his daughter\'s life could marry her. the man who actually saved her life was the man with the apple... maybe she marries him??',NULL,0);
INSERT INTO comment VALUES (11886,1438,4374,'Richard','re: So...','2004-02-14 23:48:49',0,'It seems unlikely to me that DJ would make such a major mistake in his problem statement. There are many unintuitive things in Boolean algebra such as the \"Sheffer stroke\" (c. f. http://www.swif.uniba.it/lei/foldop/foldoc.cgi?Sheffer+stroke), which is the \"not both\" Boolean function (better known to circuit designers as \"NAND\") in terms of which every other Boolean function, including negation, can be expressed (\"neither/nor\" aka \"dagger\" aka \"NOR\" has the same property). What is needed is to clearly see why the known method works for 3 inputs--maybe then we will be able to see why it can or cannot be generalized to work for n inputs.\n\nEdited on February 16, 2004, 10:00 pm',11875,0);
INSERT INTO comment VALUES (11887,1605,5178,'Dan Porter','Less otherworldly','2004-02-15 00:22:56',0,'Instead of adding dimensions to the hexahedron why not just use other regular polyhedrons? Try 4 spheres in a tetrahedron or 6 in an octahedron. You could keep the size at 4 or the radius at 1 but not both. Ether way it\'s a task before you ever get to the extra sphere in the center. Now that I think about it 6 spheres in an octahedron is very easy if the radius is 1. OK try a dodecahedron or an icosahedron. ;8^)\r\n\r\nEdited on February 15, 2004, 12:28 am\n\nEdited on February 15, 2004, 12:31 am',NULL,0);
INSERT INTO comment VALUES (11888,1623,5631,'Anne Chen','solution','2004-02-15 03:04:18',0,'none, the person who started the rumor which traveled to the brothers was the really one who saved the princess.',NULL,0);
INSERT INTO comment VALUES (11889,1626,5285,'Ady TZIDON','re(3): we were all wrong AND MAY BE STILL ARE','2004-02-15 04:09:02',1,'Hi\r\n\r\n..\".the answer is not as simple or intuitive as it at first seems, \" \r\n\r\nI never said it was. This is one of the best and certainly the most intriguing problems I found on fl.perp.\r\nAt present time I am on vacation in Austria and have a very limited access to Internet. I will organize my thoughts upon return and post a more detailed explanation- the way I see it. My humble opinion is STILL that it all boils down \r\nto proper definition of how the randomness is achieved.\r\nI hold in high esteem other people´´s considerations but STILL think that my solution is the right one- answering the problem the way it is defined.\r\n\r\nThe sequel to my memo is likely to appear about 48 hours from now.\r\n\r\nady',11882,0);
INSERT INTO comment VALUES (11890,1420,5285,'Ady TZIDON','re(3): trivia ... more','2004-02-15 08:33:01',0,'true-\r\nI just \"went for\" the vowels.\r\n\r\n\r\nady',11874,0);
INSERT INTO comment VALUES (11891,1469,4507,'Penny','GOT IT !!!!!!!!!','2004-02-15 10:08:37',3,'[incredulous]If this isn\'t the right answer, then it sure is one heck of a coincidence !!!![/incredulous]\r\n\r\n170 goes in the blanks.\r\n\r\nExplanation:\r\n\r\n64=M suggests the following relative alphabet numbering scheme:\r\n(1=B 2=C 3=D 4=E 5=F 6=G 7=H 8=I 9=J 10=K 11=L 12=M 13=N 14=O 15=P 16=Q 17=R 18=S 19=T 20=U 21=V 22=W 23=X 24=Y 25=Z 26=A 27=B 28=C 29=D...38=M...64=M...)\r\n\r\n3=R suggests:\r\n(1=P 2=Q 3=R 4=S 5=T 6=U 7=V 8=W 9=X 10=Y 11=Z 12=A 13=B 14=C 15=D 16=E 17=F 18=G 19=H 20=I 21=J 22=K 23=L 24=M 25=N 26=O) \r\n\r\n154=D suggests:\r\n(1=G 2=H 3=I 4=J 5=K 6=L 7=M 8=N 9=O 10=P 11=Q 12=R 13=S 14=T 15=U 16=V 17=W 18=X 19=Y 20=Z 21=A 22=B 23=C 24=D 25=E 26=F 27=G 28=H 29=I...50=D...76=D...102=D...128=D... 154=D...)\r\n\r\n50= N suggests:\r\n(1=Q 2=R 3=S 4=T 5=U 6=V 7=W 8=X 9=Y 10=Z 11=A 12=B 13=C 14=D 15=E 16=F 17=G 18=H 19=I 20=J 21=K 22=L 23=M 24=N 25=O 26=P 27=Q 28=R 29=S 30=T.... 50=N)\r\n\r\nIf you begin to replace each letter of M, R, D, and N in the puzzle with matching letters from their respectively numbered alphabets, you get: \r\n\r\nBPG_PQ (combining the 1st letters)\r\nCQH_QR (combining the 2nd letters)\r\nDRI_RS (combining the 3rd letters)\r\nESJ_ST (combining the 4rth letters)\r\nFTK_TU (combining the 5th letters)\r\nGUL_UV (combining the 6th letters)\r\nHVM_VW (combining the 7th letters)\r\nIWN_WX (combining the 8th letters)\r\nJXO_XY (combining the 9th letters)\r\nKYP_YZ (combining the 10th letters)\r\nLZQ_ZA (combining the 11th letters)\r\nMAR_AB (combining the 12th letters)\r\nNBS_BC (combining the 13th letters)\r\nOCT_CD (combining the 14th letters)\r\nPDU_DE (combining the 15th letters) \r\nQEV_EF (combining the 16th letters)\r\nRFW_FG (combining the 17th letters)\r\nSGX_GH (combining the 18th letters)\r\nTHY_HI (combining the 19th letters)\r\nUIZ_IJ (combining the 20th letters)\r\nVJA_JK (combining the 21st letters)\r\nWKB_KL (combining the 22nd letters)\r\nXLC_LM (combining the 23rd letters)\r\nYMD_MN (combining the 24rth letters)\r\nZNE_NO (combining the 25th letters)\r\nAOF_OP (combining the 26th letters)\r\n\r\nI verified at http://www.refdesk.com/crosswrd.html that the ONLY ONE of the above combinations that can result in a valid English word is by plugging E into DRI_RS, which I got by combining the 3rd letters in the numbering schemes. DRIERS is the only valid word.\r\n\r\nIf E assumes the value of 3 in an alphabetical numbering system, then P=14=40=66=...=170 \r\n\r\n[astonished]If this isn\'t the right answer, it\'s a heck of a coincidence that only DRIERS works in the above combinations!![/astonished]\r\n\r\nP.S. Today (2/15) is the birthday of Galileo (1564) and also the birthday of the computer (ENIAC, the first computer, 1946). There is an odd relationship between the numbers 1564 and 1946.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\n\nEdited on February 15, 2004, 11:50 am',NULL,0);
INSERT INTO comment VALUES (11892,1453,1301,'Charlie','Solution','2004-02-15 10:34:43',3,'2^53 = 9007199254740992 (thus beginning with 9)\r\n\r\n37^35 is 7710105884424969623139759010953858981831553019262380893 (thus beginning with 7)\r\n\r\nOne would expect that the leading digits of powers of numbers would follow Benford\'s Law, a topic that came up in discussing Bascule\'s Book. It was problematic when applied there, due to the limited sizes of books, but here we have an unlimited number of powers of a given number.\r\n\r\nThe following program evaluates as many powers of 2 and of 37 as the internal representation will allow and compares the distribution of leading digits to Benford\'s Law, which states that the fraction of numbers that have leading digit n is log(n+1)/log(n) using base-10 logs for base-10 number representations.\r\n\r\nDEFDBL A-Z\r\nON ERROR GOTO fin\r\nCLS\r\nDIM ct(10)\r\nn = 1\r\nDO\r\n pwr = pwr + 1\r\n n = 2 * n\r\n n$ = LTRIM$(STR$(n))\r\n d = VAL(LEFT$(n$, 1))\r\n ct(d) = ct(d) + 1\r\n IF d = 9 AND pwr < 60 THEN PRINT pwr, n\r\n tot = tot + 1\r\nLOOP\r\nfin:\r\nFOR i = 1 TO 9\r\n PRINT USING \\\"###.## \\\"; tot * (LOG(i + 1) - LOG(i)) / LOG(10);\r\nNEXT\r\nPRINT\r\nFOR i = 1 TO 9: PRINT USING \\\" ### \\\"; ct(i); : NEXT\r\nPRINT : PRINT tot\r\nRESUME fini\r\nfini:\r\nPRINT : PRINT\r\n\r\n\r\nON ERROR GOTO fin2\r\nn = 1: pwr = 0: tot = 0: ERASE ct\r\nDO\r\n pwr = pwr + 1\r\n n = 37 * n\r\n n$ = LTRIM$(STR$(n))\r\n d = VAL(LEFT$(n$, 1))\r\n ct(d) = ct(d) + 1\r\n IF d = 7 AND pwr < 60 THEN PRINT pwr, n\r\n tot = tot + 1\r\nLOOP\r\nfin2:\r\nFOR i = 1 TO 9\r\n PRINT USING \\\"###.## \\\"; tot * (LOG(i + 1) - LOG(i)) / LOG(10);\r\nNEXT\r\nPRINT\r\nFOR i = 1 TO 9: PRINT USING \\\" ### \\\"; ct(i); : NEXT\r\nPRINT : PRINT tot\r\nRESUME fini2\r\n\r\n\r\nfini2:\r\nPRINT\r\nFOR i = 1 TO 9\r\n PRINT USING \\\"###.## \\\"; 100 * (LOG(i + 1) - LOG(i)) / LOG(10);\r\nNEXT\r\n\r\nEND\r\n To what does this refer? Actually, this is a test of posting a comment; was that also? I don\'t have a proof, but the following program shows it always seems to last one more round than the starting number: FOR n = 4 TO 40 giving 4 5 1010..101 = 100^(k-1) +100^(k-2)+...+100+1 = (100^k-1)/(100-1) = (10^2k-1)/(10^2-1) = (10^k+1)(10^k-1)/((10+1)(10-1)) If, after dividing by the denominator, there still remain two factors in the numerator, the number won\'t be a prime. If k=1, we get 1, which isn\'t very interesting. For k=2, the fraction simplifies to 101, which may or not be a prime, depending on the number base. And for k>2, no term is cancelled out, and the number is always composite.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (11989,1624,1301,'Charlie','re(3): Solution','2004-02-18 15:31:10',0,'Mital:\r\n\"u saw \r\n3 min / circle @ 2 & 11 \r\n4 min / circle @ 3 & 6 \r\n6 min / circle @ 1 & 10 \"\r\n\r\nok \r\n\"4 min hand rquires 20 secs to cover normal 5 sec distance so whenever 4 min hand goes 60,120,180 & 240 secs i.e. on 3 , 6 , 9 , 12 other two hands are on exatly on the number of clock, so 4 min hand will be at 3 & 6 because for any other position of that other two hands will be in between the to numbers,\"\r\n\r\nReply:\r\nIn the first part of the above sentence (before the \"so\") you say that 3, 6, 9 and 12 as positions for the 4-min hand all allow the other hands to be on exact positions, but in the latter part you restrict it to 3 and 6. Also, the absolute positions depend on where it started. The 3 and 6 are indeed valid if it starts on 3, but how did you know that? What you know at the beginning is that when the 4-min hand advances 3, 6, 9 or 12 positions, the other hands are on exact positions.\r\n\r\nMital:\r\n\" now 3 min hand is twice as fast as 6 min , with each requires 15 sec & 30 secs for normal 1 min distance, so whenever 3 min hand is on two , 6 min will be at 1.\"\r\n\r\nReply:\r\nAgain, this depends on assuming that the 3-min hand starts on the 2. But even then it is incorrect. If the 3-min hand starts on 2, then three minutes later the 6-min hand will be on the 7 if it was on the 1 to begin with, while the 3-min hand is back at 2.\r\n\r\nMital:\r\n\" & whenever 3 min hand on 11 6 min will be on 10. \"\r\n\r\nReply:\r\nIf the 3-min hand starts on the 2, it will take (11-2)*3/12 = 9/4 minutes to reach the 11. At that time, the 6-min hand will have advanced only half as far--or four and a half positions-- or if it goes once more around, 10 and a half positions-- either way, the 6-min hand would not be at an exact integral position.\r\n\r\n\r\n',11983,0);
INSERT INTO comment VALUES (11990,1394,5658,'Wendy','Here Lassie !','2004-02-18 17:19:47',0,'Impossible to tell really, because when the dog collapses from exhaustion and dies, gravity will take over and drop it anywhere. That is, of course unles it\'s Lassie, and it has a few stand ins to take over..he he.',NULL,0);
INSERT INTO comment VALUES (11991,1643,2899,'Brian Wainscott','re: No Subject','2004-02-18 19:03:50',0,'Nice. This line\r\n\r\n\"If, after dividing by the denominator, there still remain two factors in the numerator, the number won\'t be a prime.\"\r\n\r\nI found a bit confusing at first, but I see now.',11988,0);
INSERT INTO comment VALUES (11992,1503,4507,'Penny','Solution','2004-02-18 19:20:14',3,'If the tribe starts with X offerings, the island will last X turns.\r\n\r\nExplanation: \r\n\r\nIf the tribe initially has X offerings, then its successive holdings are: \r\n\r\nAfter turn 1: X-(2^0)\r\nAfter turn 2: 2[X-2^0]-2^1 = (2^1)X-(2^1)-(2^1)\r\nAfter turn 3: 2[(2^1)X-(2^1)-(2^1)]-2^2 \r\n = (2^2)X-(2^2)-(2^2)-(2^2)\r\nAfter turn 4: 2[(2^2)X-(2^2)-(2^2)-(2^2)]-2^3 \r\n = (2^3)X-(2^3)-(2^3)-(2^3)-(2^3) \r\netc.............. \r\nAfter turn N: (2^[N-1])X-N(2^[N-1]) \r\n = (X-N)*(2^[N-1])\r\n\r\nWhen N=X, X-N=0. The tribe will have zero.\r\n\r\nP.S. You didn\'t mention what tribe this was, but I assume it is a Native American tribe. A Comanche friend of mine once related one of the\r\nfascinating legends that are handed down in her tribe from generation to generation: \r\n\r\n\"This wagon train is heading across the desert, when all of a sudden the wagon master notices that on all sides of the valley, there are Comanche warriors! He quickly forms the wagons into the \'Hollywood\' circle, to protect the families in the train. Nothing happens. Soon, drums are heard pounding out in the distance, BUM, bum, bum, bum, BUM, bum, bum, bum, BUM, bum, bum, bum.......(the famous Hollywood drumbeat from the John Ford movies). The wagon master tells the train, \'I don\'t like the sound of this....\' From out in the distance comes the voice of the Comanche chief: \'Hey, give us a break, paleface! He\'s not our regular drummer!\' \" \n\nEdited on February 18, 2004, 7:21 pm',NULL,0);
INSERT INTO comment VALUES (11993,1509,4098,'lovejoy','re(2): Alternative Solution','2004-02-18 21:18:58',0,'You could be right Phil, but if you are the riddle is a twist, you dont have to have your feet on terra firma to be \"out of the well\" or do you?',11974,0);
INSERT INTO comment VALUES (11994,1469,4507,'Penny','Here\'s a good hint :-)','2004-02-19 05:19:49',2,'Perhaps these are \"language equations\", like these: \r\n\r\n64 = DOTTOH = Disks On The Tower Of Hanoi\r\n64 = S on a C = Squares on a Chessboard\r\n64 = S on a CB = Squares on a Checker Board\r\n64 = TDQ = Thousand Dollar question\r\n64 = YOWIHYWSNM = Years Old When I Hope You Will Still Need Me\r\n\r\n3 = BMSHTR! = Blind Mice, See How They Run!\r\n3 = BGG = Billy Goats Gruff\r\n3 = B in a T = Books in a Trilogy / Bases in a Triangle\r\n3 = B in G = Bears in Goldilocks\r\n3 = B in L of the R = Books in Lord of the Rings\r\n3 = B in the HE = Bones in the Human Ear\r\n3 = B of the USG = Branches of the United States Government\r\n3 = BS (C, E, A) = Bronte sisters (Charlotte, Emily, Anne)\r\n3 = CA in P = Carbon Atoms in Propane\r\n3 = C in a F = Coins in a Fountain\r\n3 = D for J in the B of the W = Days for Jonah in the Belly of the Whale\r\n3 = FH = French Hens (song)\r\n3 = D of the C = Days of the Condor\r\n3 = F in a Y = Feet in a Yard\r\n3 = F of E = Faces of Eve\r\n3 = G in a HT = Goals in a Hat Trick\r\n3 = GNM = Guys Named Mike (movie)\r\n3 = H on the D C = Heads on the Dog Cerberus \r\n3 = LF in an IBP = Little Fishes in an Itty Bitty Pond\r\n3 = LKTLTM = Little Kittens They Lost Their Mittens\r\n3 = L M from S = Little Maids from School\r\n3 = L of M = Legs of Man (in the Isle of Man flag)\r\n3 = LP = Little Pigs\r\n3 = L on a T = Legs on a Tripod\r\n3 = MINPS = Mile Island Nuclear Power Station\r\n3 = M and a B = Men and a Baby (movie)\r\n3 = ME = Minute Egg\r\n3 = M in a L = 3 Miles in a League\r\n3 = M in a B (JKJ) = Men in a Boat (Jerome K Jerome)\r\n3 = M in a TR a DD = Men in a Tub Rub a Dub Dub\r\n3 = OKCF = Old King Cole\'s Fiddlers\r\n3 = P in a BS = Pieces in a Business Suit\r\n3 = P in a HG = Periods in a Hockey Game\r\n3 = P into which AG was D = Parts into which Ancient Gaul was Divided\r\n3 = P of an I = Parts of an Insect\r\n3 = PT = Point Turn\r\n3 = R in a TRC = Rings in a Three Ring Circus\r\n3 = SLM and C = Stooges, Larry, Moe and Curly\r\n3 = S and YO = Strikes and You\'re Out\r\n3 = S in a T = Sides in a Triangle\r\n3 = S make an O = Strikes make an Out\r\n3 = S of CC = Ships of Christopher Columbus\r\n3 = S on CFV = Ships on Columbus\' First Voyage\r\n3 = S on the B of an I = Segments on the Body of an Insect\r\n3 = S to the W = Sheets to the Wind\r\n3 = SYO at the OBG = Strikes You\'re Out at the Old Ball Game\r\n3 = TAL = Times a Lady \r\n3 = WM at B = Wise Men at Bethlehem\r\n3 = W on my W = Wheels on my Wagon (country song)\r\n3 = W in M = Witches in Macbeth\r\n3 = W on a T = Wheels on a Tricycle\r\n3 = Y and a COD = Yards and a Cloud of Dust\r\n3 = on a M = on a Match\r\n3.6 = Mj in a KwH = Megajoules in a Kilowatt Hour\r\n\r\n50 = R to T = Roads to Town (movie)\r\n50 = S on the AF = Stars on the American Flag\r\n50 = S in the U = States in the Union\r\n50 = W to LYL = Ways to Leave Your Lover\r\n50 = Y in a J = Years in a Jubilee\r\n\n\nEdited on February 19, 2004, 7:15 am',NULL,0);
INSERT INTO comment VALUES (11995,1503,2716,'Federico Kereki','Solution','2004-02-19 08:18:28',3,'Let\'s call R(i) the amount of offerings before the i-th turn. R(0)=x Working backwards, R(n)=2R(n-1)-2^n If we substitute n=x, then R(x)= 2^x.R(0) - x.2^x= 2^x.x - x.2^x = 0 so after x turns, the tribe is left with no more offerings.',NULL,0);
INSERT INTO comment VALUES (11996,1637,4507,'Penny','Solution','2004-02-19 09:36:07',3,'21 pigs, 72 chickens, 7 cows\r\n\r\nExplanation\r\n\r\nLet P be the number of pigs, C be the number of chickens, and W be the number of cows. \r\n\r\nP+C+W=100\r\n800 = 8P+C+80W (where P<=99)\r\n\r\nC=100-P-W\r\n800=8P+100-P-W+80W\r\n7P+79W=700\r\n7P=700-79W\r\nP=(700-79W)/7\r\n\r\nSo the first value of 700-79W that is a multiple of 7 will do the trick. e.g. W=7\r\n',NULL,0);
INSERT INTO comment VALUES (11997,1637,5285,'Ady TZIDON','re: Solution OK, abbr. less','2004-02-19 10:24:22',2,'P\r\ne.g. = exempli gratia (for example)\r\ni.e. =id est (namely)\r\n\r\na',11996,0);
INSERT INTO comment VALUES (11998,1637,4507,'Penny','re(2): Solution OK, abbr. less','2004-02-19 10:47:55',0,'LMAO',11997,0);
INSERT INTO comment VALUES (11999,1637,2716,'Federico Kereki','Another way','2004-02-19 12:06:33',3,'Let\'s call C the number of chickens, P the number of pigs, and M the number of cows -- M comes from \"Mooooh!\" ;-) From 8P+C+80M=800 it follows that the number of chickens must be a multiple of 8, so C=8C\', and now we have 8P+8C\'+80M=800, or P+C\'+10M=100. It now follows that P+C\' must be a multiple of 10, so P+C\'=10K, and now we have 10K+10M=100, so K+M=10. Let\'s consider the number of animals: P+C+M=100, so P+8C\'+M=100. But P+C\'=10K, so we get 10K+7C\'+M=100. Now, since K+M=10, 10+9K+7C\'=100, or 9K+7C\'=90. From the latter it follows that C\' must be a multiple of 9, so C\'=9C\". Since C=8C\', therefore C=72C\". As there were 100 animals, C\" can only be 0 or 1; if the former, we\'d need 100 pigs, so it must be the latter, and we get C=72 chickens. As P+C\'=10K, P can be 1, 11 or 21 (31 would be too much), and K would be 1, 2, or 3, so M would be 9, 8 or 7 -- the latter option works out, and we have therefore 21 pigs and 7 cows.∞',NULL,0);
INSERT INTO comment VALUES (12000,234,4507,'Penny','Stop banging the pots','2004-02-19 12:10:13',3,'\"Pots\" is an anagram of \"stop\". And when one opts to post last, one\'s spot is tops in the answer queue.\r\n\r\nYou are an anagram.\r\n\r\n \r\n',NULL,0);
INSERT INTO comment VALUES (12001,1469,4507,'Penny','Getting desperate..... :O)','2004-02-19 12:52:01',1,'I know Gamer said the missing number is 3 digits, but.....Could 92 go in the blanks also ?\r\n\r\nExplanation:\r\n\r\n64=M --> a possible reference to Paul McCartney, author of the song \"When I\'m Sixty-four\".\r\n\r\n3=R --> might refer to the \"3 R\'s\" of our school daze: reading, \r\nwriting and arithmetic.\r\n\r\nThe DP-154 Nokia handheld audio device retails for $92.\r\n \r\n50=N --> conceivably refers to the 50 nations (states) that comprise the United States.\r\n\r\nSo if you put it all together:\r\n\r\n\"I was listening to \'When I\'m sixty-four\' by Paul McCartney and the Beatles [64=M] on my way to school [to study the 3 R\'s], and as the song wafted out of my Nokia handheld player [DP-154], just as I was getting near school [the place to study the 3 R\'s], I felt so glad to be living in the United States [50 states = 50 Nations]. ',NULL,0);
INSERT INTO comment VALUES (12002,1623,4865,'Heartberry','re: A plausible answer','2004-02-19 13:13:14',1,'Now that\'s a good guess! I like the way your mind works :)',11963,0);
INSERT INTO comment VALUES (12003,1494,1301,'Charlie','a proof','2004-02-19 14:17:56',3,' If this were not the case, then the quadrilateral formed by the four points would always have, for any three points chosen to define the circle, the fourth point outside the circle. Erect a radius of the circle as a perpendicular bisector of one of the sides of the quadrilateral that are chords of the circle. A different circle can be made by moving the center backward, away from the chord that it bisects, increasing the radius to be large enough at some point to cause the point formerly outside the circle to be on the circle. But at the same time, the distances from the center on the opposite side also increase so that the point formerly on the circle is now inside the circle. So some point can indeed be made to lie inside such a circle. Edited on February 19, 2004, 2:19 pm',NULL,1);
INSERT INTO comment VALUES (12004,1494,4670,'e.g.','\'Within\' includes \'on\'?','2004-02-19 14:31:20',1,'If \"within the circle\" is assumed to include being on the circle itself, there\'s no need to exclude the possibility of the four points lying on a circle. ',NULL,0);
INSERT INTO comment VALUES (12005,168,4865,'Heartberry','re(2): Other Solution','2004-02-19 14:35:20',1,'Can I just say wow?\r\n\r\nWow.',8490,0);
INSERT INTO comment VALUES (12006,1624,5696,'pierre','unique solution','2004-02-19 14:44:58',3,'The unique solution is :\r\nhand 1 on 11\r\nhand 2 on 10\r\nhand 3 on 6\r\nIt can also be proven that this solution is unique and happens after 5 minutes.\r\n',NULL,0);
INSERT INTO comment VALUES (12007,1637,5696,'pierre','solution','2004-02-19 15:09:37',3,'P=#pigs\r\nC=#chickens\r\nK=#cows\r\n(1)P+C+K=100 ; (2)8P+C+80K=800 ; P=<99\r\n(1) in (2) gives 7P=700-79K\r\nas P and K are interger and 79 is a prime number, K has to be a multiple of 7. As P is >0, the only solution for K is 7, so P=21 and C=72',NULL,0);
INSERT INTO comment VALUES (12008,1494,2716,'Federico Kereki','re: \'Within\' includes \'on\'?','2004-02-19 15:09:40',1,'If you also accept straight lines as zero curvature circles (i.e., of infinite radius, with the center at infinity) then you can also do without the condition about the points not being collinear...',12004,0);
INSERT INTO comment VALUES (12009,1623,5666,'Frank Riddle','re(2): A plausible answer','2004-02-19 15:21:48',0,'My mind works just like yours, Heartberry. Thanks for the compliment, though!',12002,0);
INSERT INTO comment VALUES (12010,1509,5666,'Frank Riddle','re(3): Alternative Solution','2004-02-19 15:26:46',0,'If the riddle has such a twist, it is rather deceptive, as the language clearly is intended to communicate that the snail is inside the well at the bottom. If we allow such semantic \"twists\", the use of logic in solving the riddle is made subordinate to having some sort of \"inside knowledge\", which, obviously, makes the riddle a poor one at best.',11993,0);
INSERT INTO comment VALUES (12011,1469,3372,'Sam','re: Getting desperate..... :O)','2004-02-19 15:27:06',0,'Mmm, yes, I\'d agree with your title if that\'s your final answer..!\r\n\r\nThe problem with that method (*beyond* being completely absurd) is that Gamer said only about ten letters could be transformed using this method. I could create some semi-random connection with any number to any letter if we start reaching like that.\r\n\r\nSo let\'s see... Only a few letters...\r\n\r\nIt could be based on the shape of the letters, perhaps. M is made up of 4 strokes (the 4 in 64?), R has 3... but the rest of them don\'t work...\r\n\r\nPosition in the alphabet...\r\n\r\nM = 13\r\nR = 18\r\nDP = (4 * 16) = 64 (hmmm interesting...) or (4 + 16) = 20\r\nN = 14\r\n\r\nThere doesn\'t appear to be anything special about those number that could limit the set to only 10...\r\n\r\n\r\nHmmmmm.... Still there are no hooks. And still Gamer thinks it\'s difficulty three... Must be something we\'re not seeing, unless that guy\'s gone completely round the bend.\r\n\r\nWhat exactly is it that\'s coincedental about the two 3 = R\'s? The fact that 3 comes up twice (the same letter, whatever it may be in the original message), the fact that R comes up twice (R is used twice in the original message), or that fact that 3 = R both times (the original message and the key word have the same letter in that position both times)? Not that I could see where to go with the answer to that.\r\n\r\nHmmmmmmm\r\n\r\n',12001,0);
INSERT INTO comment VALUES (12012,1509,5666,'Frank Riddle','re(2): A matter of math','2004-02-19 15:29:06',0,'Sorry, lovejoy, I should have read the other comments first. However, I believe our answer is correct, and that SilverKnight has simply neglected to give credit.',11971,0);
INSERT INTO comment VALUES (12013,1503,5696,'pierre','solution','2004-02-19 15:49:18',3,'offers at the being of the year n=2^(n-1).(x-(n-1))\r\nsize of the hole in year n is 2^(n-1)\r\nso 2^(n-1).(x-(n-1))-2^(n-1)=0\r\nso x=n',NULL,0);
INSERT INTO comment VALUES (12014,1494,4507,'Penny','Euler, Feuerbach, et. al.','2004-02-19 18:59:18',1,'I believe this problem is related to deep mathematical analysis involving the \"nine point circle\", which is the circle that can be constructed from any triangle in the plane. Of course I don\'t understand this well enough to copy/paste it without embarrassment, but greater minds than mine can read all about it at:\r\n\r\nhttp://en.wikipedia.org/wiki/Nine_point_circle\r\n \r\n:-) ',NULL,0);
INSERT INTO comment VALUES (12015,1459,5653,'koi_person','solution','2004-02-19 18:59:57',0,'\r\n1st:blue shirt, green tie, green suspenders\r\n2nd:green shirt, white tie, white suspenders\r\n3rd:white shirt, blue tie, red suspenders\r\n4th:red shirt, red tie, blue suspenders\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (12016,1509,5653,'koi_person','solution','2004-02-19 19:12:25',0,'It was a leap year! So herb mush have gotten out March 12, 1996.',NULL,0);
INSERT INTO comment VALUES (12017,1509,5653,'koi_person','re: solution','2004-02-19 19:13:48',0,'My mistake. It was March 13, 1996.',12016,0);
INSERT INTO comment VALUES (12018,1469,1626,'Gamer','getting desperate... for you to solve it!','2004-02-19 19:25:34',2,'I said there was less than 10, because in my opinion, 2 could never appear in a problem like this, and 7 and 9 probably would either unless you think creatively. :)\r\n\r\nOne of my final hints is a philosophical one. \"Equality isn\'t as important as you think.\"\r\n\r\nAlso, this does have something to do with computers, but rather what you would do while using them. Nobody\'s really gotten close enough in the comments I read.',NULL,0);
INSERT INTO comment VALUES (12019,1637,5699,'Kristy','solution','2004-02-19 19:30:30',0,'I would buy 55 pigs and 45 cows.',NULL,0);
INSERT INTO comment VALUES (12020,861,5653,'koi_person','solution','2004-02-19 19:43:22',0,'a sword?',NULL,0);
INSERT INTO comment VALUES (12021,1637,4507,'Penny','re: solution','2004-02-19 19:45:43',0,'45 cows at 80 dollars per cow would come to 3,600 dollars. The problem requires you to use exactly 800 dollars.\n\nEdited on February 19, 2004, 7:46 pm',12019,0);
INSERT INTO comment VALUES (12022,1469,4507,'Penny','re: getting desperate... for you to solve it!','2004-02-19 21:14:12',0,'This is unlikely, since solving it would have required specialized programming knowledge, but this could simply be an assembler program instruction, complete with two operands, both of which are addressed by register 3. 64 might be the instruction op code...\r\n\r\nDP is the well known assemply language \"Divide Decimal\" (Divide Pack) command. M is binary multiply, or 64=M could mean \"Machine instruction with op code 64\"....\r\n\r\n\r\n',12018,0);
INSERT INTO comment VALUES (12023,1205,5670,'tan','Impossible','2004-02-20 00:22:09',0,'25 is indivisible by 3. Here we are dealing with numbers such as 60, 30, 15, 7.5....all divisible by 3. Notice that the question says we can set the timer to double speed at any time, but even so, we are still dealing with arithmetric calcutions of addition and subtraction. The results of these calculations at any time would give a number which is divisble by 3.\r\n\r\nI sure hope someone could prove me wrong, and would be extremely delighted to learn something new if there is an answer to this question.',NULL,0);
INSERT INTO comment VALUES (12024,1494,5670,'tan','No Subject','2004-02-20 00:51:12',0,'I am not sure whether I understand your question correctly, but it seems that it can be disproved easily. Since there are always some points outside a circle, hence one of the points does not have to lie within the circle formed by the other three.',NULL,0);
INSERT INTO comment VALUES (12025,1509,5658,'Wendy','SOLUTION','2004-02-20 07:44:43',0,'Herb began his climb @ 6am Feb.14th. By 10 pm, he had climbed 3 feet. Using the information in the riddel, he slipped down 2 feet overnight. Therefore, @ 6am Feb. 15th, he was 1 foot high.\r\nThis pattern continues thru to March 12th, when Herb reaches the top of the well, but not out yet.\r\nHe finally gets out of the well on March 13th.\r\nP.S., 1996 was a leap year.',NULL,0);
INSERT INTO comment VALUES (12026,1469,4507,'Penny','re(2): getting desperate... for you to solve it!','2004-02-20 07:54:17',1,'64=M could mean....\r\n\r\n64 is the Mantissa\r\n64 is the Multiplier \r\n64 is the Multiplicand\r\n64 is the Machine Op Code\r\n64 Megabytes of Memory\r\na Machine that uses 64-bit addressing\r\n\r\n3=R could mean...\r\n\r\nRegister 3\r\n3 is the Remainder\r\nRepeat 3 times\r\n\r\n154___=DP could mean...\r\n\r\n154___ is the Displacement from Register 3\r\n154 and ___ are the two Displacements from Register 3\r\nDivide Pack (Divide Decimal)\r\n154=D, ___=P\r\n154___ = D*P\r\n\r\n',12022,0);
INSERT INTO comment VALUES (12027,1525,2716,'Federico Kereki','Sum','2004-02-20 08:47:53',3,'If S=√(2+√(2+√(2+...)) then S²=2+S, which can be solved giving S=2. If 2 was replaced with X, then the equation would be S²=X+S, and S would be (1+√(1+4X))/2',NULL,0);
INSERT INTO comment VALUES (12028,1469,1920,'Brian Smith','84?','2004-02-20 09:39:10',0,'Since Gamer went as far as specifying 84 is not the solution, could it be possible to decrypt the puzzle WITH 84 in the blank?',NULL,0);
INSERT INTO comment VALUES (12029,1525,5707,'gulrez','No Subject','2004-02-20 11:07:43',0,'2',NULL,0);
INSERT INTO comment VALUES (12030,1469,1920,'Brian Smith','\"Equality isnt important\" and 84','2004-02-20 11:53:04',0,'I think Gamer\'s statement: \"Equality isn\'t as important as you think.\" simply means that the equal signs are used to obscure the message. Removing the equals and substituting 84 for the blank gives:\r\n\r\n64M\r\n3R\r\n15484DP\r\n3R\r\n50N\r\n\r\nDoes anybody have any ideas on what to do with that?',NULL,0);
INSERT INTO comment VALUES (12031,1469,4507,'Penny','Not 84! ??','2004-02-20 12:00:08',0,'Does Gamer mean \"not 84 factorial\" ???? ',NULL,0);
INSERT INTO comment VALUES (12032,1623,2376,'Jim C','re:','2004-02-20 12:16:12',0,'I\'m with you, Sandra! It would seem to me that one bite would do, and the never-rotting apple is could for at least a few more cures (unless you\'re a complete germophobe and too skeeved to bite off of someone else\'s apple, I guess.\r\n\r\nAnyway, the only thing I feel certain about is that miror-boy is out. AFter all, he may have been helpful, but if the brothers had already heard about the dying princess, they probably could have found out where she was without the mirror. The two bro\'s with the horse and the apple could both argue that they played equally important roles in her recovery, so...',11883,0);
INSERT INTO comment VALUES (12033,1469,1920,'Brian Smith','re: Not 84! ??','2004-02-20 12:20:07',0,'I think he just means 84. 84 factorial is a 127 digit number.',12031,0);
INSERT INTO comment VALUES (12034,1469,4507,'Penny','No Subject','2004-02-20 12:20:13',0,'Gamer wrote:\r\n\r\n\"What number goes in the blank? (Hint: It\'s not 84!) [Penny\'s \"GOT IT !!!!!!!!!\" solution is]...not the solution I had intended, but you have it on the right track. 3=R is there twice because it appears in the original message twice. Here\'s another hint: The letters to numbers isn\'t A=1, B=2; [then \"GOT IT!!!!!!!!!! was NOT on the right track]; in fact, less than 10 letters (by my thoughts) can be translated this way. I said there was less than 10, because in my opinion, 2 could never appear in a problem like this, and 7 and 9 probably would either [you meant, wouldn\'t either?] unless you think creatively. :) One of my final hints is a philosophical one. \'Equality isn\'t as important as you think.\' Also, this does have something to do with computers, but rather what you would do while using them. Nobody\'s really gotten close enough in the comments I read.\"\r\n \r\nWell, this is certainly one of the toughest flooble puzzles. It\'s right up there with the David Lynch film \"Mulholland Dr.\" \r\n\r\n\n\nEdited on February 20, 2004, 12:25 pm',NULL,0);
INSERT INTO comment VALUES (12035,1623,2376,'Jim C','Heart Sick?','2004-02-20 12:20:38',3,'I got it! The youngest guy immediately becomes infatuated with the princess. He becomes completely despondent and heart-broken, knowing that one of his older brothers is gonna nab this babe. Not really paying attention, he takes a bite of the apple and, Voila! His broken heart (a disease in my book, Baby!) is cured and he\'s thumbing his nose at the big boys as he and his bride drive away in the honeymoon carriage.',NULL,0);
INSERT INTO comment VALUES (12036,1623,2376,'Jim C','re(2): sandra','2004-02-20 12:24:35',0,'Hmmmm, If I brought you a pot of my world-class chile, and you told me you ate it and thought it was a little too sweet (Oh, my heart!). I would assume you ate SOME of it, not all of it. In the same vein, she \"ate\" the apple is too vague to point to whether she ate ALL or SOME of it.',11898,0);
INSERT INTO comment VALUES (12037,1623,4865,'Heartberry','re: Heart Sick?','2004-02-20 12:29:01',0,'LOL...you\'re funny :)',12035,0);
INSERT INTO comment VALUES (12038,1525,5614,'Roberto Mattos','Nice','2004-02-20 12:29:14',0,'If we call S the \'n\' term of this sequence, like:\r\nS = √(2+√(2+√(2+...\r\nand we square both sides of the equation, we will reach:\r\nS² = 2+S\r\nS²-S-2=0\r\nS=(1(+/-)√(1+2*4))/2, and considering only the positive solution as valid for our purpose, we reach S=2 as being the limit to this sequence.\r\nAnd if 2 is replaced with X, the solution would be S=((1+√(1+4*X))/2 (again considering only the positive solution as valid for us).',NULL,0);
INSERT INTO comment VALUES (12039,1623,4865,'Heartberry','re(3): sandra','2004-02-20 12:34:39',1,'I agree :) Plus, the fact that the riddle mentions, \"...a magic apple which would never rot...\" makes me wonder why that was part was put in the riddle unless it had something to do with the answer......agree anyone?',12036,0);
INSERT INTO comment VALUES (12040,1469,4865,'Heartberry',':)','2004-02-20 12:44:53',1,'Gamer says that the answer is \"not 84\" so that\'s the answer!\r\n\r\nThe answer is \"not 84\".\r\n\r\nlol just kidding. I have a riddle mind...sorry, I\'ll go back to my riddles and leave you guys alone. ;)',NULL,0);
INSERT INTO comment VALUES (12041,1509,2376,'Jim C','re(3): A matter of math','2004-02-20 13:30:03',0,'I believe Wendy has the answer. On the 12th of March (Day 28), Herb made it to the top of the well (the 30 ft mark), but NOT OUT. Poor guy was just too tuckered out to get that extra couple of inches. It took another day to actually get over the precipice.\r\n\r\nFunny thing is, I was all confused! I had the number of days wrong (I, too originally figured 28), but since I forgot to count Feb 14 as a climbing day, I still got the date right (I think). THEN, after reading your answer, I thought you forgot that it was leap year, but couldn\'t get our dates to jibe. That\'s when I figured out my error and came back to what should be the correct answer--Mar 13 (Which should give ole Herb plenty of time to climb off of the well and find a nice St Patty\'s day party at which to celebrate and get ...............\'well\').',12012,0);
INSERT INTO comment VALUES (12042,1623,2376,'Jim C','re(4): sandra','2004-02-20 13:34:03',0,'Technically, the \'never rot\' statement could have been put in there just so that the apple would remain edible until needed, but I prefer our interpretation, Heart. =0)',12039,0);
INSERT INTO comment VALUES (12043,1469,3372,'Sam','No Subject','2004-02-20 13:36:01',0,'I think I\'ve given up. Gamer\'s last hint \"Also, this does have something to do with computers, but rather what you would do while using them.\" has thown me completely.\r\n\r\n64 is a very common number for computers given that it\'s 2^6, and M is commonly used, as in Megabytes, Megahertz and so on, but the rest don\'t fit in this pattern. 3 is a number rarely seen in computers, unless we start working in other bases, at which point I throw in the towel.\r\n\r\n\r\n\r\n\"what you would do while using them\"....\r\n\r\nwell, I type with my computer, but I see no connection between the letters, numbers, and poitions on my keyboard.\r\n\r\nI do emails and log onto Flooble, but again, no connection spring to mind.\r\n\r\nI program, but as one of Penny\'s solution has showed us once you go there you can make any connection you want.\r\n\r\nI get back pains and drink energy drinks, but I don\'t think this is what Gamer\'s looking for.\r\n\r\n\r\nSo unless a beautiful seed-crystal-like hint comes along, I think I\'ll just wait for the answer to come out... Shows lack of spirit, I know, but no matter.',NULL,0);
INSERT INTO comment VALUES (12044,1640,1920,'Brian Smith','Some thoughts','2004-02-20 14:31:35',0,'1 +\r\n2 +=\r\n3 ++=\r\n4 +=\r\n5 ++++=\r\n6 +===+=\r\n7 ++++++=\r\n8 +=\r\n9 ++=\r\n10 +=+===+=+=\r\n11 ++++++++++=\r\n12 +===+=\r\n\r\nEvery prime p is represented by p-1 \'+\'s followed by an \'=\'. Similarily every power of a prime p^n is represented by p-1 \'+\'s followed by an \'=\'.\r\n\r\n6 and 12 also have the same pattern, so I suspect the pattern is based on the prime factors of the number .\r\n\r\nI will conjecture:\r\n13 ++++++++++++=\r\n14 ?\r\n15 ?\r\n16 +=\r\n17 ++++++++++++++++=\r\n18 +===+= [same as 6, 12]\r\n19 ++++++++++++++++++=\r\n20 +=+===+=+= [same as 10]',NULL,0);
INSERT INTO comment VALUES (12045,1640,2899,'Brian Wainscott','re: Some thoughts','2004-02-20 15:11:27',0,'That seems good to me. For the entries that are not a power of a prime, what could we have? Look at 6:\r\n\r\n6 +===+=\r\n\r\nTo me this looks like \"2==2\", which has 3 terms (+=, ==, +=). And 6 has 2 and 3 as its only factors.\r\n\r\nThis also works with 10:\r\n\r\n+=+===+=+= would be 22==22, 5 terms total, and 10=2*5. So possible answers for 14 and 15 would be:\r\n\r\n14 +=+=+===+=+=+=\r\n15 ++=++====++=++=\r\n\r\nor 15 might possibly be:\r\n\r\n15 ++=++===++=++=\r\n\r\ndepending on whether the separator is === or == in this case.\r\n\r\nBut I\'m not really happy with this, and have no idea what would happen when you get to 30 (the first number with 3 distinct primes in its factorization)\r\n\r\n',12044,0);
INSERT INTO comment VALUES (12046,1469,1626,'Gamer','re: :)','2004-02-20 15:17:41',0,'I\'m going to go ahead and post the solution. This really wasn\'t supposed to be this hard... was supposed to be like a morning problem.',12040,0);
INSERT INTO comment VALUES (12047,1469,4507,'Penny','Re: Official solution','2004-02-20 15:51:32',0,'\"Gamer is a good person\"....\r\n\r\nYes, I can see why a message like that would need to be encrypted....\r\n\r\nLOL...Just kidding. Good puzzle !! ',NULL,0);
INSERT INTO comment VALUES (12048,1469,5285,'Ady TZIDON','Person , you are a good gamer','2004-02-20 16:36:58',1,'Although I never even came close to solve this puzzle I must admit that I enjoyed the process of\r\ntrying.\r\nThe puzzle deserves a \"5\" and that is the vote I have casted.\r\nRe-reading all the comments, \"y compris \" the hints leaves me shocked - how none of us saw the text.\r\nNice and above all ORIGINAL problem.\r\n\r\n 36yQy 27mN U ALL!!\r\n\r\nady',NULL,0);
INSERT INTO comment VALUES (12049,1640,4507,'Penny','re: Some thoughts','2004-02-20 17:05:12',0,'Never mind...I just re-read your post....\r\n\r\nWhy can\'t we delete our posts ? I\'d like to delete mine.\n\nEdited on February 20, 2004, 5:13 pm',12044,0);
INSERT INTO comment VALUES (12050,1623,5617,'jen','anne\'s solution','2004-02-20 17:21:11',0,'so true, so true ',NULL,0);
INSERT INTO comment VALUES (12051,1525,3558,'Tristan','extraneous solutions','2004-02-20 17:25:04',1,' I think everyone (should) agree that if S is the solution, then S©÷-2=S. The problem here is that there are extraneous solutions. Of course, S can\'t be negative, and the negative solution must account for negative square roots. There is another extraneous root though. ¡Ä©÷-2=¡Ä, at least as far as I know. I don\'t believe in this answer of course, but is my belief only enough proof? I can think of ways to prove it beyond reasonable doubt, but not truly prove it, if you know what I mean. ...well i hope it is. call me young (which i am, lol) but i read a book in my reading class \"myths and folklore\" which basically had this story in it...i think..lol.. neither sons gets the girl, they were fighting and the kingg piccked another man to marry her. its logic for kids story since it alwaays has to be fair and not about winning. well tell me im wrong, but thats my answer is it ... ¡îx + ©÷¡îx + ©ø¡îx + etc... ??? Right you are, TomM...My killer firewall was doing it. Thanks !!!!! Penny Partners Bill, Teddy and Gary sit in chairs a reasonable distance apart. They each hold a common handheld calculator (which is not a computer anyone can hack, and hardly \"special equipment\" -- almost all grade school kids have one). Bill says: \"We will now each enter on our calculators the number of partners we know to be innocent. Then we will copy that number into the calculators\' memory, and then erase it from the display, so that no one can look over and see anyone else\'s number. After each has done that, I will walk around and place each calculator (all with zero on their displays) into a black bag. I will then remove the three calculators from the bag and display the memory of each one. After I examine each one, I will erase its memory, so that no one can come around later and dust them for fingerprints. If they all say \'1\', we are innocent. But if one of them says \'2\', then Monica\'s future baby was fathered by one of us.\" Edited on February 22, 2004, 10:30 am',NULL,1);
INSERT INTO comment VALUES (12097,1458,5653,'koi_person','so easy','2004-02-21 19:29:44',0,'If you can\'t use an object to make the cigarette then you must, logically, use energy and the cigarette itself. Just use the flame from a match or lighter or the concentrated light of a magnifying glass. The cigarette will then burn and overbalance. Why did you give this a 5 difficulty?',NULL,1);
INSERT INTO comment VALUES (12098,1652,4507,'Penny','A better solution just came along','2004-02-21 19:38:34',3,' Partners Bill, Teddy and Gary are alone together in a large conference room in the office. Gary is 30 feet from Bill and Teddy. Secretary Monica is away from the office, conferring with her lawyer. Bill enters the number 100 on a calculator, and hands it to Teddy. Only Bill and Teddy know that the original number is 100. Teddy mentally computes the sum of 100 plus the number of partners he knows to be innocent, then purges the calculator\'s memory and enters that sum. He then walks 30 feet over to Gary and hands him the calculator. Gary mentally computes the sum of the number on the calculator and the number of partners he knows to be innocent, purges the calculator\'s memory, enters that sum, and walks 30 feet back to Bill and hands it back to him. If Teddy is guilty, he puts 102 on the calculator. Gary sees that the number is 102, but doesn\'t know whether the original number was 100 or 101, so he doesn\'t know whether Teddy is guilty. Gary puts 103 on the calculator. Bill sees that the number is 103, which confirms that one of Gary and Teddy is guilty. Bill announces that one of the partners is guilty. If Gary is guilty, Teddy puts 101 on the calculator. Gary sees that the number is 101, and since he knows that he himself is guilty, he surmises that the original number was 100. Gary puts 103 on the calculator. Bill sees 103 and knows that one of Teddy and Gary is guilty. Bill announces that one of the partners is guilty. If Bill is guilty, Teddy puts 101 on the calculator. Gary sees that the number is 101, but doesn\'t know whether the original number was 100 or 99, and so does not know whether Teddy is guilty or not. Gary puts 102 on the calculator. Bill sees that the number is 102, as he knew it would be, and since he knows that he himself is guilty, he announces that one of the partners is guilty. If none are guilty, Teddy puts 101 on the calculator. Gary sees that the number is 101, but doesn\'t know whether the original number was 100 or 99, and so does not know whether Teddy is guilty or not. Gary puts 102 on the calculator. Bill sees that the number is 102, and since he knows that he himself is innocent, he now announces that none of them is the father of Monica\'s baby. Edited on February 21, 2004, 10:06 pm',NULL,1);
INSERT INTO comment VALUES (12100,1623,5735,'maeve','another possibility','2004-02-21 22:14:57',0,'maybe two of the sons are married it never says they arent?!?!?',NULL,0);
INSERT INTO comment VALUES (12101,1509,5735,'maeve','No Subject','2004-02-21 22:20:10',3,'march 15',NULL,0);
INSERT INTO comment VALUES (12102,1652,4507,'Penny','re: A better solution just came along','2004-02-21 22:50:41',0,' If a calculator is too much \"extra equipment\", let Bill write 100 on a scrap of paper and hand it to Teddy. Teddy reads the scrap of paper, puts it in his mouth and swallows it, writes the new number on another scrap of paper and hands it to Gary. Gary reads that scrap, swallows it, writes the next number on a third scrap of paper and hands it to Bill. Or is this too hard to swallow ? Then Bill whispers 100 in Ted\'s ear. Ted whispers a number in Gary\'s ear. Gary whispers a number in Bill\'s ear. Edited on February 21, 2004, 11:48 pm',12098,1);
INSERT INTO comment VALUES (12099,1607,1626,'Gamer','Problems noted?','2004-02-21 21:35:49',0,'When I was solving this, I came to the conclusion that the friend was a knight. First of all, all the stuff in the intro is true. There isn\'t any break between the story and the who \"these people told me this\" part.\r\n\r\nSecond of all, I think if this was reworded without the \"for sure\" part, it would be better. When I solved this, I found out that the people were what they were \"for sure\" because everything checked out in the end; what they were before that part didn\'t contradict what they were now. Such a listener to the actual story may have thought the same thing.\r\n\r\nAlso, remember that the title isn\'t a statement in the puzzle. It could even be directly misleading, so I didn\'t know that I was supposed to take it into consideration.',NULL,0);
INSERT INTO comment VALUES (12103,343,4507,'Penny','Solution','2004-02-21 23:52:25',3,' A bear killed them. They swallowed poison. They were struck by lightning. Somebody murdered them. They died of old age. They died of bird flu. They killed each other.... Edited on February 21, 2004, 11:55 pm',NULL,1);
INSERT INTO comment VALUES (12104,1525,5728,'sandy','re: a guess','2004-02-22 00:55:00',3,' y did my symbols change?? ¡îx + ©÷¡îx + ©ø¡îx + etc... I think this Al-Gore-ithm is correct, but I\'m tired, and I am still reeling from that \"Letters to Numbers\" puzzle. But anyway... A guilty partner will know that the other two are innocent. An innocent partner will only know that he himself is innocent. So if the 3 partners are A, B and C, A whispers an arbitrary number X into B\'s ear. Only A and B know what X is. B mentally adds to X the number of partners that B knows to be innocent, and whispers that number into C\'s ear. C mentally adds to it the number of partners that C knows to be innocent, and whispers that number back into A\'s ear. If the number A hears back from C is X+3, he knows that either B or C has added 2, and A can announce that somebody is guilty. If A hears X+2, and A knows that he (A) is guilty, he will announce that somebody is guilty. If A hears X+2 and knows that he (A) is innocent, he will announce that all three are innocent. Case 1: A is guilty. A whispers 6 to B, B whispers 7 to C, C whispers 8 to A, A declares that someone is guilty (since A knows that A is guilty). Case 2: B is guilty. A whispers 6 to B, B whispers 8 to C, C whispers 9 to A, A declares that someone is guilty. Case 3: C is guilty. A whispers 6 to B, B whispers 7 to C, C whispers 9 to A, A declares that someone is guilty. Case 4: Nobody is guilty. A whipsers 6 to B, B whispers 7 to C, C whispers 8 to A, A decalres that eveyone is innocent (since A knows that A is innocent). If someone is guilty but A and B are innocent, A won\'t be able to tell if it\'s Case2 or Case 3, and B won\'t know if it\'s Case 1 or Case 3. If someone is guilty but B and C are innocent, B won\'t know if it\'s Case 1 or Case 3, and C (who doesn\'t know what number A originally whispered to B) won\'t know if it\'s Case 1 or Case 2. If someone is guilty but A and C are innocent, A won\'t know if it\'s Case 2 or Case 3, and C won\'t know if it\'s Case 1 or Case 2. Edited on February 22, 2004, 2:51 am',NULL,1);
INSERT INTO comment VALUES (12106,1652,3372,'Sam','re: Or more simply.....','2004-02-22 02:55:36',0,'I think all your answers so far have been basically good, but I\'m slightly confused at your round-a-bout way of having them name the number of partners that they know are innocent. Would it not be the same thing is they name the number of *guilty* partners - i.e. they just add one if they did it and nothing if they didn\'t? \r\n\r\nIt just seems slightly more intuitive. No different in the end, though.',12105,0);
INSERT INTO comment VALUES (12107,1652,4507,'Penny','re(2): Or more simply.....','2004-02-22 03:29:03',0,' Thanks, Sam. If each one adds the number he knows to be guilty (0 or 1) instead the number he knows to be innocent (1 or 2) it works just as well, with the appropriate small modifications. You\'re all very close, and I\'ll say that the next five rows have been correctly predicted by at least one person. You\'ve all noticed the little patterns, such as the pattern with prime numbered rows. Think of a more unifying pattern that will cause the patterns you have observed. It might be simpler than you expect. I don\'t quite understand that algorithm, but it would seem to me that it doesn\'t successfully predict the rows already shown. As far as real hints, I think that the columns are equally important as the rows. Edited on February 22, 2004, 4:33 pm',NULL,1);
INSERT INTO comment VALUES (12110,1464,5285,'Ady TZIDON','my solution','2004-02-22 17:49:31',3,'Consider the following table:\r\n 10^n ( 10^n )mod7 \r\n 10 3 \r\n 100 2 \r\n 1000 6 \r\n 10000 4 100000 5\r\n 1000000 1 \r\n 10000000 3 etc\r\nClearly for any n-digit number we can add 7 for so many times to get O at the end.\r\nReversing the n-digit number ending with a zero- we get an (n-1)digit number. \r\nRepeating this routine n-1 times we get a one digit number say m . m is not a zero.\r\nFor m=1 STOP, WE\'RE DONE.\r\nFor m=3 add 7 1 time, inverse - you get ONE.\r\nFor m=5 add 7 5 timeS ,inverse - you get FOUR.\r\n For m=4 add 7 8 timeS ,inverse - you get SIX .\r\nFor m=6 add 7 2 timeS ,inverse - you get TWO.\r\nFor m=2 add 7 14 timeS ,inverse - you get ONE.\r\n For m=8 add 7 6 timeS ,inverse - you get FIVE.\r\n\r\nSPECIAL CASE: For m=7 add 7 - 1 time only ,inverse - you get 41 THEN add 7 7 timeS and inverse- you get NINE,\r\n\r\nFor m=9 add 7 3 timeS ,inverse - you get THREE,\r\nfollowing the links we always get ONE\r\n.\r\n\r\nq.e.d/\r\nady\r\n',NULL,0);
INSERT INTO comment VALUES (12111,1624,5751,'Mitch Mullings','I think me knows it!','2004-02-22 19:59:31',0,'If you take the hands of each at 1, 2 and 3 and put them 5 normal minutes ahead, you get the answer. Allow me to explain. The hand on the 1 will be the hand to take 6 minutes for a full circle. In one normal minute, it takes 10 seconds or 2 numbers ahead to make the equivalent. It goes from 1, to 3, to 5, to 7, to 9 and finally to 11. The numbers just said are taken from every 1 normal minute. The hand on the 2 will be the hand to take 3 minutes to complete a full cycle. In 1 normal minute, it takes 20 seconds or 4 numbers ahead to make the equivalent. It goes from 2, to 6, to 10, to 2, to 6, and then to 10. Finally, The hand on the 3 will be the hand to take 4 minutes to complete a cycle. In 1 normal minute, it takes 15 seconds or 3 numbers ahead to make the equivalent. It goes from 3, to 6, to 9, to 12, to 3, and finally to 6. Pretty good, eh? I\'ll try to solve more! Ta-ta for now!',NULL,0);
INSERT INTO comment VALUES (12112,1623,5670,'tan','2 solutions here!','2004-02-22 20:21:03',0,' 1. Marry the horse. The poor thing had to carry 3 men. Without the horse, the mirror and the apple are rendered useless. Who knows, he is a handsome prince turned into a horse by the wizard? 2. Marry the youngest. He will be the most faithful husband. The eldest can always look at other girls bathing with his mirror. The second can go to any place to do his hanky panky and get back before his wife wakes up. The youngest, what can he do? The king could repay the youngest son with his \'apple of the eye\'. An apple which is lousier, considering it gets old and will rot someday :) ady wrote: \"RE: \' Reverse the digits of N.\' N was defined as an 1-digit number.\" Initially it was a 1-digit number, and then it keeps getting incremented by 7 at that LOOP. :-) There has to be. The whisper-in-the-ear algorithm falls prey to the possibility of \"bugs\" or listening devices. The puzzle states: \"The king was grateful, and indeed intended to let one of them [obviously one of the brothers] marry the princess. But it had taken the cooperation of all three brothers to save her. Which one did the king decide should marry his daughter?\" So she didn\'t marry the wizard or the guy who started the rumor, and she didn\'t marry all three of the brothers. (She didn\'t marry the horse either, wiseguy !!) The puzzle states that she married one of the three brothers. Edited on February 23, 2004, 5:45 am',NULL,1);
INSERT INTO comment VALUES (12129,1652,153,'TomM','re: Is there a method that doesn\'t involve whispering ?','2004-02-23 06:38:06',0,'Using the same algorithm as the whispering or (previously) the calculator, and reverting to the urn mentioned in the problem: Bill drops an arbitrary (but known to him) number of \"balls\" into the urn. Ted and Gary drop one or none in. Bill drops or doesn\'t drop and removes the \"dummy\" balls. If a ball remains, ...',12127,0);
INSERT INTO comment VALUES (12130,1645,1301,'Charlie','solution','2004-02-23 08:33:34',3,' One set is the intersection of the planes y=k;z=kx for any real k. Another is x=k;z=ky for all real k. Expressed parametrically: Set one: y=k;x=t;z=kt That there are no others is shown by the fact that for the line to be straight while both x and y vary, y must be in the form ax+b. Then the equation for z becomes z=x(ax+b) = ax²+bx, but if a is not zero, this is not linear, so a must be zero (so long as x is not a constant) and y a constant. Interchange x and y in the above for the other way of looking at why not both x and y can vary. I totally agree with you on that. I feel that if the riddle solution is someone other than one of the 3 brothers, it will be a faulty and, sorry to say, but stupid solution and I will rate it low. I\'m not usually harsh like that, but it is very clear to me (just as it is to you Penny) that the solution will be one of the 3 brothers. So I am sticking to my original answer that it is the youngest son, who gave of his apple because he is the only one who fully gave his gift away and without him, the princess would not have been cured. But that doesn\'t sound like much of a \"riddle\" solution, so I understand why everyone is reaching and digging deeper. Can\'t wait till they post the solution! Isn\'t that the same kind of thing as the white/black marble, one of the other partners could potentially see if/how many balls were put into the urn? How about this: Everyone leaves the room except Bill. He places a pen in the center of the table, pointing in a particular direction, such as toward the window, etc (known only to him). He leaves the room, and each of the other partners enters, one at a time, and if they are guilty, they rotate the pen 90°. Afterward, they all reenter the room, and if the pen has moved (or if he himself is guilty), Bill announces that one of the partners is indeed responsible. If not, he tells the others accordingly. Of course, if perhaps one could tell by listening if the pen was moved or not, then perhaps something slightly more complicated coud be devised; for instance, clockwise = innocent, counter-clockwise = guilty. If the pen is reversed, the other two partners are innocent, if it lies in its original orientation, one is guilty. Gee wiz it\'s time. Gnaws Iron and bites steel-rust Grinds hard stones-erosian(bad spelling) Slays kings-natureal old age Beats mountains-agian erosian We seem to have several suggestions of a similar nature, adding something on, be it a number on a calculator, whisering, marbles in an urn, etc. The only question is how to prevent \'bugging\'. I would suggest something like this (other variations obviously possible): Have a trusted fourth person put several black marbles in an urn, counting exactly how many. Each partner adds a handful of identical marbles, say 5 if he\'s guilty, 6 if he\'s innocent, or whatever. Count out the marbles at the end, after being told how many you started with. At a glance, no one could count the marbles that were already in there, so that problem is solved, and peeking to see if someone is adding 5 or 6 marbles is also difficult. They could even turn out the light when someone is adding his marbles etc. Edited on February 23, 2004, 12:42 pm',NULL,1);
INSERT INTO comment VALUES (12138,1640,1920,'Brian Smith','Solution','2004-02-23 13:06:27',3,' For every integer n, there is an integer f which is the product of the prime factors of n. The nth element is f symbols long. The kth symbol in an element is \'+\' if the gcd of f and k is 1, otherwise the symbol is \'=\'. Example 1: n=12 Example 2: n=10 Continuing this algorithm for n=13 to 20 yeilds: Brian Wainscott asked what would happen for n=30: +=====+===+=+===+=+===+=====+= Uhh, is this as easy as it sounds? The pitcher was a relief pitcher who came in after the team was already losing. Let y be the vertical distance between the top of the box and where the ladder touches the wall. Similarly, let x be the horizontal distance between the box and where the ladder touches the ground. Then, by similar triangles, y/3 = 3/x, so xy = 9. By Pythagoras, (x + 3)² + (y + 3)² = 12², or Now note that (x + y)² = x² + 2xy + y² = x² + y² + 18. Hence (x + y)² + 6(x + y) - 144 = 0. Rejecting the negative root, x + y = 3(sqrt(17) - 1). Now we have the sum and product of the roots, so we can write down the quadratic: z² - 3(sqrt(17) - 1)z + 9 = 0. (With roots x, y.) For maximum height, x < y, and so So the answer is (3/2)*(sqrt(17) + 1 - sqrt(14 - 2*sqrt(17))). Good question, but it took outside information which was bad. ㇠First some assumptions: Also, it is assumed that the distance from the top of the pencil measured to the bottom, along its central axis, is 144 times the difference in the two diameters. As the difference determines the angle or slope of a ruling along the conical surface and that angle would be maintained all the way to the tip of a full cone (and since the problem didn\'t give us the actual top and bottom radii), we can substitute a full cone of height 288 and base diameter of 2. The slant height of this cone is √(1+288²). The semicircle traversed by the contact of the base with the slanted surface is then π√(1+288²). The circumference of the base is 2π, so the ratio of the length of the semicircle to the circumference of the base is √(1+288²)/2, or about 144.0008680529392. This is the number of times the pencil would spin on its axis while going from base uphill to base downhill. Edited on February 24, 2004, 9:43 am',NULL,1);
INSERT INTO comment VALUES (12147,1642,5614,'Roberto Mattos','My thought','2004-02-23 17:59:53',0,'Let\'s name L = length of the pencial, D = wider diameter and d = smaller diameter.\r\nIf we say, for example, that L = 144, D = 1, d will be 0 and the pencil will rotate over its extremity with d = 0 and it will have to rotate half of the perimeter of a circle with radius = 144. So, the distance to cover will be 2 x Pi x 144 / 2. As the perimeter of the extremity that will be rolling is given by 2 x PI x (1/2), we conclude that it will be necessary exactly 144 rotations. ',NULL,0);
INSERT INTO comment VALUES (12148,1163,3558,'Tristan','creative solution','2004-02-23 18:48:02',3,' I\'m not computer literate, so I decided to make up my own bogus computer language I call T++. In it, all the commands I used are valid, two single quotes make a double quote, and close quotes look the same as open quotes. If that doesn\'t make sense, then maybe it still would to the computer that can use T++. BTW, yes, I am awesome. Great job! But let it be known that there is more than one way to explain this same pattern. I used a different way in the official solution (but I knew well there were other ways). But the pattern in essence is the same. Let the given number be n and suppose first that n is not a multiple of 7. Since the powers of 10 repeatedly cycle through 1,3,2,6,4,5,... mod 7, there are always nonnegative k and m such that n+7k=10^m which then reverses to 1. If n is a multiple of 7, then there is a nonnegative k such that n+7k=77...7 so that n+7(k-2)=77...763 . Reversing, 3677...7 cannot be a multiple of 7, however. For 36 is congruent to 1 mod 7, while 10^m is never congruent to 0 mod 7, making it impossible for 36*10^m+77...7 to be congruent to 0 mod 7. Congratulations on your obtaining the exact solution in terms of radicals. But this assumes that the \"length\" of the pencil is the length of the line where the cylindrical surface of the pencil is tangent to the slanted flat surface. Ordinarily the length of a pencil is from the center of the top to the center of the bottom. If that is what is 144, then the other (which is a slant height) is √(1+144²)(D-d), to be used in your calculations, rather than 144(D-d). That\'s why I consider √(1+144²)≈144.0008680529392 to be more exact than 144. ...is just to put the whole thing in quotation marks. Then it must be true. (Every quote is true in the sense that it is a reiteration of something). \"According to W. Quine Either specification that I gave originally does in fact include lines other than those that go through the origin. (Only two lines fitting the criteria actually pass through the origin: one coincident with the x-axis and one coincident with the y-axis.) I had specified the intersection of the planes y=k;z=kx for any real k and x=k;z=ky for all real k. That y=k, for values of k that differ from zero, precludes going through the origin, as y is zero at the origin. Likewise for the case of x equals a non-zero k. In my parametric form: It is true that all the lines I give pass through the x-axis or y-axis, and therefore look like they pass through the \"origin\" of a given x-z plane or y-z plane taken as a 2-dimensional cartesian system. But this in fact represnts the actual case: no other straight lines exist on the surface. In your solution set: x=x0, y=y0+b*t, z=x0*y0 + b*x0*t So any given one of these lines still has x as a constant--x0 rather than k-- and the slope of z relative to y is b*x0/b, which is still x0, or my k, and when y is zero (so that y0=-b*t), z = x0*(-b*t) + b*x0*t, which is indeed equal to zero also. So your set is the same as mine, once given the proper caveat that z0=x0*y0, which you failed to include. Excellent point, Charlie. It would never occur to most people (not to me, anyway) to be that precise. Do you work for NASA ? \"How far does each wheel travel at the end of one mile?\" Of course each wheel and each tire travelled a mile. If the puzzle had asked \"for what distance was each tire affixed to a wheel on the axle\", then 0.6 mile would have been the correct answer. LOL !!!!!!! Edited on February 24, 2004, 12:49 pm',12159,1);
INSERT INTO comment VALUES (12162,1420,1183,'fwaff','re(2): trivia ... more','2004-02-24 10:16:35',0,'Since when has \'keeper\' contained a double \'p\'? Is this another English English vs US English difference?',11872,0);
INSERT INTO comment VALUES (12163,1654,5614,'Roberto Mattos','No Subject','2004-02-24 10:28:39',0,'You have 5 tires to ride 3 miles, so 0.6 miles per tire. \r\nThe solution that minimizes the number of exchange tires requires you to exchange one tire each 0.2 miles. Ady\'s solution minimizes the number of pit stops, but considering that little Suzy should be a lazy lady, probably she would be bored stopping for two tires exchange, so it is more likely she would prefer frequent pit stops, taking a snack and exchanging her tire. So, my suggestion would be begin with tires 1,2,3 and after 0.2 miles use 1,2,4, then 1,5,4, then 3,5,4 and finally 3,5,2. And I agree with Penny, each tire \'travels\' one mile and rides 0.6 miles... :) ',NULL,0);
INSERT INTO comment VALUES (12164,1654,1183,'fwaff','re: Solution - further pedantry','2004-02-24 10:35:21',0,'The problem states that Suzy took two spare TYRES with her, not wheels. Therefore each wheel travelled the full mile fixed to an axle.',12158,0);
INSERT INTO comment VALUES (12165,1642,1183,'fwaff','re(3): Trying to be even more exact','2004-02-24 10:49:17',0,'I reckon Charlie\'s got too much common sense for NASA, he\'s more likely to work for RKA (Russian Space Agency). \r\n\r\nNASA spent millions developing a pen to work in zero gravity, RKA astronauts used a pencil.',12160,0);
INSERT INTO comment VALUES (12166,1642,1301,'Charlie','re(4): Trying to be even more exact','2004-02-24 10:53:25',0,'And NASA sent a rocket to Mars a few years back, where one component used metric units while another expected English units, and the capsule crashed.',12165,1);
INSERT INTO comment VALUES (12167,1642,1183,'fwaff','re(5): Trying to be even more exact - dumb question','2004-02-24 11:02:30',0,'OK so what are \'English units\'? On the island we have \'Imperial\' units eg feet and inches (1 inch =25.4mm) are these the same thing? I\'ve heard the term \'English\' being applied to snooker/pool balls to mean screw and also heard it in relation to muffins to differentiate between bread and cakes, but never in relation to units of measure. \r\nThanks in advance.',12166,0);
INSERT INTO comment VALUES (12168,1654,5285,'Ady TZIDON','wheels wheel me and tyres tire me','2004-02-24 11:11:08',1,'Being a newcomer to this puzzle-web I am not accustomed to all the tricks and innuendos carefully camouflaged in every nook and cranny of the text.\r\nBut put some blame on lazy Suzanne: all she knows\r\nis ..\" to exchange wheels so that each of them travels an equal distance.\" T R A V E L S !!!\r\n\r\nSo the question is moot- she can do it any way she wants- the hardware travels with her, mounted or not. -And there is nothing to solve.\r\n\r\nAm I right or am I???\r\nady\n\nEdited on February 24, 2004, 11:17 am',NULL,0);
INSERT INTO comment VALUES (12169,1497,5528,'shawn','semi-circle theorem','2004-02-24 11:26:10',3,' Since the centre of the circle lies on the mid-point of the hypotenuse, each of the two halves is the radii, hence the circle will pass through them definitely. For the third point, the one having the right angle, it is known that the angle in a semi-circle is 90 degrees and vice-versa, i.e. if a chord subtends 90 degree angle at any other point, the circle must pass through that point. Hence, proved. Since the centre of the circle lies on the mid-point of the hypotenuse, each of the two halves is the radii, hence the circle will pass through them definitely. For the third point, the one having the right angle, it is known that the angle in a semi-circle is 90 degrees and vice-versa, i.e. if a chord subtends 90 degree angle at any other point, the circle must pass through that point. Hence, proved. Lee, I certainly hope you\'re not planning to be driving a car in the next 24 hours. Penny I just tried to roll a physical pencil through 0.0008680529392 of a spin. It can\'t be done. 1500 miles? 5 tires each travel 1200 miles, but 4 are being used constantly 5*1200 / 4. By the way, I keep my gun in very nice condition. The product can be rewritten as (n^2+3n+1)^2 - 1. This proves it is not a square unless n=0, -1, -2, or -3. None of those values are positive integers which the problem asks for. The product cannot be a perfect cube either. If it was, then the values n*(n+1)*(n+2)*(n+3) and (n^2+3n+1)^2 would satisfy a special case of Catalan\'s Conjecture (case with p,q = 2,3). It has been proven that the only nontrivial solution for the special case is 8=2^3 and 9=3^2. 8, 9 implies n^2+3n+1 = 3, which has no rational roots. Edited on February 24, 2004, 3:41 pm',NULL,1);
INSERT INTO comment VALUES (12185,1644,3172,'SilverKnight','re: Not a square','2004-02-24 15:46:53',0,'F.K., I think there\'s a number out there something to do with graph theory that holds the world record for being the largest number ever used in a meaningful calculation. Whatever it\'s called (Grahams Number I think), it used a new symbol to somehow represent nested powers. At a glance I\'d say it\'s possible to vastly increase the size of the best solution given by Nick Reed using the symbol. Whatever it is and however it works. Peace, Rawlyn. I didn\'t realise the solution has been submitted, but I\'ll put my answer in before I look. I work it out to be.... C1 #\'s 0,1,2,3,5,7 C2 #,s 0,1,2,4,6,8 I\'m using the 6 as also the 9. Let n=3182, given n the following equation would be sqrt(3182*3183*3184*3185)=sqrt(102711556278240)=10134671 the above has been done with microsoft excel so if the maths is wrong, dont blame me! Edited on February 24, 2004, 7:25 pm',NULL,1);
INSERT INTO comment VALUES (12190,1644,5352,'Juggler','re: I think i have one, oh no i haven\'t','2004-02-24 19:30:00',0,' I\'ve just realised my (sorry Bill Gates\'s) Microsoft Excel cant add up 10134671 x 10134671 = 102711556278241 Sorry, i\'m just going to chastise myself. lol I could live with March 13th, if we assume he couldn\'t roll over the edge of the well at the top on the 12th. Hehe, if he\'s lovelorn, maybe it\'s because Mrs. Snail is waiting for her clumsy husband at the top. In that case, he won\'t have to wait for St. Patty\'s day.......... Gamer\'s comment is insightful, and allows for the quickest solving of the cubic problem. There is not a single error in the statement, and the logic used is, well, obvious without explanation, but, in the hopes of un-obfuscating Ady, here goes: Listing only the first twelve perfect cubes, one sees both the cube of 12, which is 1728, and the consecutive cubes of 9 and 10, namely, 729 and 1000. The sum of 729 and 1000 is 1729, about which Gamer commented, \"If, from the number 1728, you add the one at the beginning (which is a perfect cube, hence the comment is relevant and not random) to the end, you also have a perfect cube (or rather, a sum of two obvious perfect cubes). In short, the only thing we should be striving to eschew in this case is comments that are simultaneously rude and incorrect. lets call them tires 1, 2, 3, 4, 5 5 choose 3 = 10 combinations: 123, 124, 125, 134 ,135, 145, 234, 235, 245, 345 starting with 123, change the tires according to the sequence as above for every 0.1 mile. a less hassle combination would be: 123, 234, 345, 451, 512 where she changes the tires every 0.2 mile. let n(n+1)(n+2)(n+3)=d^2 or n(n+1)(n+2)(n+3)=c^3 thinking in terms of factors, the highest common factor n and (n+3) can have is 3. d^2 shld be a number with prime factors having even powers and c^3 shld be a number with prime factos having powers which are multiples of 3. n=2 :2x3x4x5 is not a square nor a cube n=3 :3x4x5x6 is not a square nor a cube for n>3, n(n+1)(n+2)(n+3) would ALWAYS some prime factors which stand alone by themselves. As we know, a perfect square would have prime factors where the powers are even. since 3 is the highest common factor 2 of the terms in n, n+1, n+2, n+3 (a consecutive of 4 numbers) hence for n>3, n(n+1)(n+2)(n+3) has to have some other prime factors bigger than 3 and they appear only once. hence showing that a perfect square or cube cannot exists. in special cases where one of the terms in n, n+1, n+2, n+3 is a perfect square, we can easily prove that although some prime factors larger than 3 may have powers which are even, the other three terms will DEFINITELY NOT be a perfect square, hence there still exists some prime factors which exist alone. same reasoning goes for cube. Edited on February 25, 2004, 7:12 pm',NULL,1);
INSERT INTO comment VALUES (12198,1602,5285,'Ady TZIDON','re(3): A way to do it.===> NO WAY, not quite','2004-02-25 04:20:09',1,'Dear FR,\r\nThanks for trying to \" unobfuscate\" me.\r\n\r\nPlease comment why \"...the cube root of 12, 1728, you..\" etc\r\nis compatible with \" There is not a single error in the statement..\".\r\nThe issue of 1728 ===>1+728 is clear, believe me.The issue of \" the cube root of 12\".... much less.\r\n\r\nady\r\n\r\n',12192,0);
INSERT INTO comment VALUES (12199,1637,5788,'Tempe Everson','Solution','2004-02-25 08:34:39',0,'I have a solution for the chickens, pigs and cattle problem, but I\'m new to this site. Am I supposed to post a solution once I\'ve found it?',NULL,0);
INSERT INTO comment VALUES (12200,1637,5788,'Tempe Everson','Solution','2004-02-25 08:56:37',0,'I have a solution for the chickens, pigs and cattle problem, but I\'m new to this site. Am I supposed to post a solution once I\'ve found it?',NULL,0);
INSERT INTO comment VALUES (12201,1655,4507,'Penny','Solution','2004-02-25 09:26:50',3,' How can one get lead to float? Place it in mercury. 64! just glue one inside of each other put the 1 insidee the 8 and those inside of the 64 :-) lol, you just need to put the cigarette under some intense light place the lump of lead in a room with a huge fan on the floor that directs airflow upwards and that can create such a current as to overcome the gravitational force exerted on the lead. with the fan on at the right speed the lead should float in the air. bonus doofus answer: put it in outer space The number 2^(1002!) is a perfect power with bases 2^2=4, 2^3=8, 2^4=16, . . . . 2^1000, 2^1001, 2^1002. Then, the number 2^(1002!)+1 is a palindrome of at least three digits in bases 2^2=4, 2^3=8, 2^4=16, . . . . 2^1000, 2^1001, 2^1002. All of the palindromes begin with a \'1\', end with a \'1\' and all the digits in between are zeros. Can anyone come up with a smaller number? Edited on February 25, 2004, 3:03 pm',NULL,1);
INSERT INTO comment VALUES (12210,1655,2899,'Brian Wainscott','Solution','2004-02-25 15:35:25',3,'Place it in a tub of mercury and it will float, no problem.',NULL,0);
INSERT INTO comment VALUES (12211,1553,1301,'Charlie','A solution','2004-02-25 15:35:30',3,' 2^(2^101)+2^(2^100)+1 is palindromic in base 2^(2^100), where it is \"111\". In base 2^(2^99) it is written \"10101\". In base 2^(2^98) it is written \"100010001\". The cycle length doubles each time, so by the time you get to base 2 (i.e., base 2^(2^1)), the cycle length is 2^100, having 2^100-1 zeroes between the 1\'s. For a more interesting, but larger number, 2^(2^101)+2^(2^100+1)+1 is \"121\" in base 2^(2^100), and it works similarly in all the bases except with a 2 in the middle instead of a 1. It fails, however, when we get to base 2, so we\'d have only 99 of them. So we really should use 2^(2^102)+2^(2^101+1)+1, starting with \"121\" in base 2^(2^101), and working down to base 2^(2^2), i.e., base-4. After seeing Brian Smith\'s solution, it struck me we don\'t need that highest power of the base except for the one case. So just start with 2^(2^101)+1, which is \"101\" in base 2^(2^100), then \"10001\" in base 2^(2^99), \"100000001\" in base 2^(2^98), etc. Edited on February 25, 2004, 3:39 pm',NULL,1);
INSERT INTO comment VALUES (12212,1553,1301,'Charlie','re: A solution -- oh, I see','2004-02-25 15:43:50',0,' Oh, I see it\'s 1000 different values of b. Substitute 1000 for the 100 in my solution. If both my solution and Brian Smith\'s withstand scrutiny (it does get a little confusing keeping track of those powers of 2), 2^(2^1001) is smaller than 2^(1002!), as 2^1001 is a 302-digit number and 1002! is a 2,574-digit number. Edited on February 25, 2004, 3:58 pm',12211,1);
INSERT INTO comment VALUES (12213,1644,5799,'red_sox_fan_032003','not a square','2004-02-25 17:42:49',0,' to make it a square try looking at product of means and product of extremes N(N+3),(N+1)(N+2) n^2+3n,n^2+3n+2 inconsistent now subbing in X=n^2+3n you have X*(X+2) but you need this product to equal perfect square so x^2+2x=z^2 X^2+2x-z^2=0 look at discriminant b^2-4ac=4-4z^2which is only positive if Z=0,1 which you can prove can\'t be achieved for x(x+2)=z!!!! Just set up a matrix since fifth is two behind fourth, fourth must be 1,2,3 but fourth can\'t be 2nd and fourth finishing 3rd leads to inconsistencies turn the drinks into \'currency\' and realize Ben is owed 3 drinks/units while everyone else owes 1 unit/drink net!!! a little easy for this site.... ady, hehe, okay, so I missed the \"root\". But, your original message seemed to pooh pooh Gamer\'s reply, and you even commented that you couldn\'t tell what he meant because of the errors! So, do you get it or not? FR Well, since we\'re having so much fun with this, how\'s this: Swallow it and do the backfloat until you die. Once you are dead, the lead will still float, but I suppose your dead body could then be considered \"boatlike\", thus disqualifying this method. The total distance travelled is one mile per each of three tire locations for a total of 3 tire/miles. With five tires, each would travel 3/5 miles. The easiest way to do this is to go 2/5 miles. Replace two wheels. Go 1/5 mile. Change the only original tire left (it\'s through) with one that was taken off first. Go 1/5 mile and change that tire with other originally removed tire. 1/5 more and you are there. I can only think of one pair of positve positive integers that apply 2^4 & 4^2 its just 1/4 of the area of a circle with radius 1 the answer is pi/4 Take the lump of LEAD, rearrange the letters, and you get.... DALE.....Dale Petranech was a legendary swimming champ of the early 80\'s.... I\'m certain that this is the answer Charlie is looking for. :-) Edited on February 26, 2004, 2:40 pm',NULL,1);
INSERT INTO comment VALUES (12237,1553,1575,'DJ','Shorter Still?','2004-02-26 15:17:08',2,' Those formulae work, but the numbers are enormous .. my intended answer yields a somewhat large number as well, but on a substantially smaller order. For example, say you were looking for a number that worked for just 7 values of b, instead of 1000. 2^(7!) is 1518 digits long, 2^(2^8)+2^(2^7+1) is 78 digits long, but mine is only three digits long in decimal. So, while your answers are perfectly fine, there is still much room for optimization. Remember, if you are in, say, base 25, a value of 22 is still a single digit (even though we don\'t have a way to represent it as such with the current system). In other words, if you want an ideal solution, your palindromes will probably contain more than just zeroes and ones. Maybe we should disband this site and start a google fanclub instead.. I\'ve never had the chance to be first before :D No idea about the puzzle though! Peace, Rawlyn. Hmm... might as well just put the lump of lead on the table and announce to the world that it\'s floating on wood... Just a thought (not a scientist here, just going through random problems), but if the amount of lead were small enough, would surface tension on some plain ol\' H2O hold it up? Peace, Rawlyn. replace sin(c) with sin(180-(a+b))= sin(a+b)= cos(a)sin(b)+ sin(a)cos(b) take partial with respect to A,B and set =0 probably leads to angle A= angle B etc. \"of at least three digits\" - is that at least three digits in base 10? I read it that the number must have at least three digits in any of the bases. If it is only three digits in base 10 that sheds a whole new light on the subject. In a way it still doesnt make sense. If it\'s base three in base 10 only then it\'s palindromic in in infinite number of high bases anyways. In other words, I dont understand the question lol Peace, Rawlyn. How can one get lead to float? I\'m surprised no smart-aleck thought of this before now: Take \"lead\"; replace \"d\" with \"f\"; move \"f\" to the front; Replace \"e\" with \"o\"; add \"t\" at the end; and you suddenly have: float !!!!!!! (I know this puzzle is in the Science section...Well, isn\'t spelling a science ?) Edited on February 26, 2004, 7:47 pm',NULL,1);
INSERT INTO comment VALUES (12250,1553,1575,'DJ','re: How many digits? Confused here.','2004-02-26 20:57:22',0,' No, it must have at least three digits in each base to count .. <i>any</i> number is a single digit when the value of the base is larger than the number itself, for an infinite number of bases. This problem could move to the algorithms category, and instead of specifically naming 1000 in the problem, I could have said, \"Given any positive integer k, how how to find a number that is a b-palindrome, of at least three digits, for at least k different values of b.\" I picked 1000 just as a large number to eliminate someone finding \"by accident\" a solution for a specific smaller number, had I chosen one. My reference to \"three digits in decimal\" was referring not to the solution of the cited problem, but the simpler case of finding a value that works for only 7 digits. The point was that, while the previously offered methods do indeed work, the one I have produces substantially smaller numbers. let x =sqrt(2+sqrt(2)....) then x=sqrt(2+x) x^2=2+x x=2,-1 has to be positive so x =2!!! Ryan wasn\'t commenting on the wrong problem. He was commenting on the \"new problem\" that I put in the post he was replying to. I used to do that all the time -- put new problems in posts of existing problems. But I stopped doing that. It is a violation of flooble rules. DJ: \"Maybe we should disband this site and start a google fanclub instead..\" When in pain, DJ, always be prompt to remind yourself that there is nothing shameful about it and nothing prejudicial to the mind at the helm, which suffers no injury either in its rational or its social aspect. In most cases the saying of Epicurus should prove helpful, that \"Pain is never unbearable or unending, as long as you remember its limitations and do not engage in fanciful exaggerations.\" Bear in mind also that, although we do not realize it, many other things which we find uncomfortable are, in fact, of the same nature as pain: feelings of lethargy, for example, or a feverish temperature, or loss of appetite. When inclined to grumble at any of these, tell yourself that you are giving in to pain. this isnt very hard here are a few hints what numbers are still #\'s upside down, try inverting the square of the #\'s 1 to sqrt 500 i.e. 1 to 22 squared but even more of a hint since when reversed the number is greater than 500 that eliminates some more possibilities He can tell anywhere from zero to 5 lies; any more would require at least one pair of successive lies. So: There\'s exactly 1 way of telling zero lies. The ways of telling one lie are C(10,1) = 10 The ways of telling two lies are more complicated. The two lies can\'t be successive (when laid out as a plan, they can\'t be adjacent). The two lies divide the remaining eight true statements into three groups, the first and last of which might be empty, but the middle needs at least one to separate the lies. There is a formula for the number of ways three non-negative integers (including the possibility of zero) can add up to a given number, n, based on choosing which two of n+2 objects shall be partitions rather than counted objects: C(n+2,2). Before we use this, we must separate out the fact that the middle of the three numbers to be added must be at least one. So, of the 8 truths, there must be 1 in the middle group, and then the remaining 7 must be in the three groups, so the number of ways is C(7+2,2)=36. Similarly for three lies, there are four groups of truths, the middle two of which have at least one. The lies and required truths account for 5, leaving 5 more truths to be distributed among the four groups of truths: C(5+3,3)=56. For four lies, there are five groups of truths, the middle three of which have at least one, leaving only three optional truths to be distributed among the five groups: C(3+4,4)=35. For five lies, there are six groups of truths, the middle four of which have at least one, leaving only one optional truth to be distributed among the six groups: C(1+5,5)=6. These ways total 144. Excellent! Can\'t the nth Fibonacci number be gotten in 1 step, rather than a number proportional to log(n)?: F(n)=[(phi^n)/sqrt(5)+.5], where [] represents the floor function, so that [ +.5] represents rounding to the nearest integer, and phi is the golden ratio. (I tried using the square root symbol in the new editor, but got garbage. I also tried viewing source and pasting in the ampersand code for phi, but that didn\'t work either.) Edited on February 27, 2004, 11:08 am',12259,1);
INSERT INTO comment VALUES (12266,1653,5285,'Ady TZIDON','re(2): Fibo again att:Charlie','2004-02-27 11:57:21',1,'Charlie,\r\n\r\na thanks for the complement\r\nb yes , this is the formula but it implies using a calculator. The \"logarithmic \" procedure needs squares only\r\ngoing like f(17)===> (f8),( f9)====>(f4),( f5) etc \r\n\r\nc there is a similar question on this web (climbing the stairs\" 2002 - look up c0mment #4.\r\n d Enjoy\r\n\r\nady\r\n\r\n90',12265,0);
INSERT INTO comment VALUES (12267,1644,5799,'red_sox_fan_032003','part of solution','2004-02-27 12:35:23',0,' try looking at product of means and product of extremes N(N+3),(N+1)(N+2) n^2+3n,n^2+3n+2 now subbing in X=n^2+3n you have X*(X+2) but you need this product to equal perfect square,perfect cube the only common factor they can have is 2. If X is odd it is easy to show that they have no common factors therefore since X and X+2 can\'t both be perfect squares/cubes there is no solution. So this leaves case of X is even èIf d is the distance between the tips, then d² = 4² + 3² - 2*4*3*cosè by the law of cosines. That comes out to (25 - 24 cosè)^(½) Its derivative is ½ (25 - 24 cosè)^(-½)*24*sinè The second derivative has in the numerator (apart from a factor of 12): cosè(25 - 24 cosè)^(½) - 12*sin²è/(25 - 24 cosè)^(½) In an Excel spreadsheet, if è is to be in cell B1, then d can be placed in B2 with formula =(25-24*COS(B1))^0.5, and its derivative in B3 with =12*SIN(B1)/B2. To make the second derivative zero, we put the two parts of its numerator in B4 and C4 (=COS(B1)*B2 and =12*(SIN(B1))^2/B2). In D4 we put B4-C4, and used the solver to equate the latter to zero. The derivative of d with respect to è is at its maximum, 3 units per radian, when the distance, d, is <FONT face=Arial size=2>2.645751311 and the separation is <FONT face=Arial size=2>0.722734248 radians, or <FONT face=Arial size=2>41.40962211 degrees. parametrize the two curves 4cos(60t) i +4sin(60t)j sub in Ai +BJ 3cos(t)i +3sin(t)j sub in Ci+Dj note minute hand moves 60 times faster than hour hand distance = sqrt( (A-C)^2+ (B-D)^2 ) want to maximize first derivative so set second derivative equal to zero!!! You write \"note minute hand moves 60 times faster than hour hand.\" A careful analysis shows that the minute hand only moves 12 times faster than the hour hand. For when the hour hand moves from 12 to 1, it moves 1/12 of 360 degrees and in the same time the minute hand moves the full 360 degrees. But this may have no bearing on the problem at hand anyway. Theta gotten from the toolbar above the comment entry window does not work for me either. It looks OK when inserted into the edit window, but when displayed in the final text, it comes out wrong. I never could get the special character buttons to work in the old system either, so I haven\'t lost anything. It would be nice, though, if everything worked for everybody the way it obviously is supposed to. Edited on February 27, 2004, 5:28 pm',12270,1);
INSERT INTO comment VALUES (12275,1565,1301,'Charlie','re(3): Spreadsheet solution.','2004-02-27 17:11:02',0,'Were you intending that first character to be a letter e with a grave accent? ... It\'s showing up that way at least on my browser, and it shows up where I had intended a theta, using that toolbar.',12274,1);
INSERT INTO comment VALUES (12276,513,5815,'matt runchey','No Subject','2004-02-27 17:32:32',0,'Ive seen this puzzle before, it is not a new one. This problem is so old.... I can\'t believe that everyone hasn\'t heard it yet. I heard it like 50 times already',NULL,1);
INSERT INTO comment VALUES (12277,1565,4374,'Richard','re(4): Spreadsheet solution.','2004-02-27 17:36:39',0,' I edited my previous comment so yours no longer applies. Sorry. However, please read my edited comment. For me, the toolbar special characters give eratic results in the final displayed text. If I put in the top row from the toolbar it comes out as ÄðÓÙáâèù and is supposed to be capital delta, pi, capital sigma, capital omega, alpha, beta, theta, and omega. Edited on February 27, 2004, 5:38 pm',12275,1);
INSERT INTO comment VALUES (12278,1648,5815,'matt runchey','lol','2004-02-27 17:36:49',0,'lol i dont know what this problem is about, but it has probly been used before. It is hard to think of mew, original problems like that when there are already so many out there.',NULL,1);
INSERT INTO comment VALUES (12279,1653,5815,'matt runchey','good problem','2004-02-27 17:38:59',0,' I like this problem because it is one like you would see in mathcounts. d=sqrt(7). I wrote a long solution, but it didn\'t save. Grr... Rather than write it again, I\'m just gonna post the important points. Hopefully, someone can follow it and make sure the math is correct. Consider them to start at 12 o clock so both the minute and the hour are at 0 degrees. The minute hand travels at 6 degrees/min. The hour hand travels at 0.25 degrees/min. At time t, the minute hand is at 6t degrees and the hour hand is at 0.25 degrees. Converting from polar to Cartesian coordinates gives the minute hand to be at (4cos(6t), 4sin(6t)) and the hour hand to be at (3cos(0.25t), 3sin(0.25t)). Applying the distance formula and using (cosx)^2+(sinx)^2=1 and cos(x-y)=cosx*cosy+sinx*siny simplifies the distance into d=sqrt(25-24*cos(5.5t)). d\'=66*sin(5.5t)/sqrt(25-24cos(5.5t)). Also, defining f=d^2. Then f\'=2d*d\'. f\'\'=2*(d\')^2+2d*d\'\'. For the distance to increase most rapidly, d\'\'=0. Hence f\'\'=2*(d\')^2. f=25-24*cos(5.5t), f\'=132*sin(5.5t), f\'\'=726*cos(5.5t). Setting f\'\'=2*(d\')^2 would simplify into This simplifies into a quadratic in terms of cos(5.5t). Solving yields cos(5.5t) = 3/4 or 4/3. Only 3/4 is valid. It can be verified that this gives a maximum instead of a minimum. Plugging cos(5.5t) into the formula for d yields sqrt(7). (Clever pun, Mr. Porter.....) Edited on March 1, 2004, 11:39 pm',NULL,1);
INSERT INTO comment VALUES (12288,1565,5285,'Ady TZIDON','re: Spreadsheet solution.===.>best and final','2004-02-28 08:35:51',1,'CHARLIE \r\nPlease see my last post-\r\nYour solution is OK\r\n\r\nHowever please note the \"round \" numbers:\r\nd^2= 7\r\ncos( A)=3/4\r\nd(speed)/d(A)=3 units/radian\r\n\r\nady\r\n\r\n ',12269,0);
INSERT INTO comment VALUES (12289,1565,5285,'Ady TZIDON','Best and final','2004-02-28 08:56:55',3,'I GOOFED ,\r\nIn my last post which provided a fast but totally\r\nwrong answer I started with a false statement:\r\n\" If distance increases most rapidly so does its square...\". SAYS WHO??\r\n\r\nGIGO* - ALL THE REST IS WRONG.\r\n(* GARBAGE IN --GARBAGE OUT)\r\n\r\nMy reasessment is as follows:\r\nfor A=.001 to 1.7\r\nevaluate D=((25-24cos(A+.0001))^.5 D=distance\r\n DD=((25-24cos(A+.0001))^ .5 DD=D increased\r\nrate= (DD-D)/.0001\r\n\r\nChecking the table for max. rate and refining the \r\nsearch in the neigborhood-we get nice and round numbers:\r\n\r\nmax rate= 3\r\ndistance= sqrt(7)\r\ncos(angle)=3/4\r\n\r\nThis corraborates Charlies solution, however without referring explicitly to calculus-just examining the deltas\' (=inreases) ratio.\r\nady\r\n\r\n\r\n\r\n\n\nEdited on February 28, 2004, 9:02 am',NULL,0);
INSERT INTO comment VALUES (12290,1642,4507,'Penny','re(2): But on the other hand....','2004-02-28 08:59:49',0,' LOL !!!! I was just kidding !!!!!!!! I\'m surprised no one else has noticed that this puzzle is a repeat. It is not a duplicate, so I did not object to it in the waiting queue, but it is the same puzzle as \"Climbing the Stairs\" (pid 190). If you look at this site, you will see that \"Climbing the Stairs\" (called Leonardo\'s leaps on that page) is the inverse of \"Chairs in a Row- the anti-social version\" (empty chairs correspond to steps tread on, full chairs to skipped steps); and the \"teachers\" version corresponds to this puzzle if teachers are liars. The link button placed the URLs in quotes and pre-appended the URL http://perplexus.info so the links don\'t work. The correct urls are: http://perplexus.info/show.php?pid=190 and http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibpuzzles.html/ Edited on February 28, 2004, 11:04 am',NULL,1);
INSERT INTO comment VALUES (12293,1653,4507,'Penny','Re: Fibonacci','2004-02-28 11:31:37',1,' I have a warm spot in my heart for Leonardo Pisano of Pisa (known to history by his nickname, Fibonacci ), because one of my most beloved professors, Dr. Nanini, was a graduate of the University of Pisa. Fibonacci has been called \"the most brilliant meteor flashing past the dark background of the European Middle Ages\". Although he was one of the brightest minds in the history of mathematics, his contribution is not sufficiently appreciated. The importance of Fibonacci\'s mathematical creativity is assessed properly by Russian mathematician Prof. Vasil\'ev: Edited on February 28, 2004, 11:36 am',NULL,1);
INSERT INTO comment VALUES (12294,1653,5285,'Ady TZIDON','re: Repeat: I DID IT MAY WAY','2004-02-28 12:29:03',2,'Tom,\r\nTo your \"I\'m surprised no one else has noticed that this puzzle is a repeat. It is not a duplicate, so I did not object to it in the waiting queue, but it is the same puzzle as \"Climbing the Stairs\" (pid 190). \"...\r\n\r\nI respond: \r\n\r\nI noticed it- see comment #7 to the current puzzle:\r\n\r\n\r\n\" ....c There is a similar question on this web (climbing the stairs\" 2002 - look up c0mment #4. \r\n\"....\r\n\r\nViva Fibonacci !!\r\n\r\nady',12292,0);
INSERT INTO comment VALUES (12295,1653,4374,'Richard','re: Re: Fibonacci','2004-02-28 12:49:42',0,' \"(known to history by his nickname, Fibonacci )\" which means \"Bonacci\'s son\" and seems to me to be less of a nickname than just an identifier. See http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibBio.html for an excellent rundown on the guy. The first question is simply \'is it possible?\'. 1. a2-b3 2. e4-b1 3. e2-d3 4. b3-d1 5. b1-a2 6. d3-c4 7. a4-c2 8. c2-e4 9. d1-c2 10. c4-e2 11. a2-c4 12. c2-b1 13. e2-d1 14. d1-a4 15. c4-b3 16. b1-d3 17. b3-a2 18. d3-e2 Yes. the next question is \'are there wasted moves in this example?\' You tell me. The first question is simply \'is it possible?\'. 1. a2-b3 2. e4-b1 3. e2-d3 4. b3-d1 5. b1-a2 6. d3-c4 7. a4-c2 8. c2-e4 9. d1-c2 10. c4-e2 11. a2-c4 12. c2-b1 13. e2-d1 14. d1-a4 15. c4-b3 16. b1-d3 17. b3-a2 18. d3-e2 Yes. the next question is \'are there wasted moves in this example?\' You tell me. Gamer wrote: \"The new graphic looks cool :) Thanks to whomever made it.\" You\'re welcome. Glad you like it. Edited on February 29, 2004, 11:03 am',NULL,1);
INSERT INTO comment VALUES (12316,1564,1301,'Charlie','solution','2004-02-29 11:24:09',3,' 10^40 = 2^40 * 5^40 The divisors of 10^40 can, therefore, have zero through 40 factors equal to 2 and zero through 40 factors equal to 5. Combining these choices, there are 41*41=1681 divisors of the first number. The second number, similarly, can have 2 appear as a factor zero to 60 times and 5 as a factor zero to 30 times, for 61*31 = 1891 divisors. But some of these 1681+1891 numbers are divisors of both numbers and therefore have been counted twice. Those are the numbers that have 2 as a factor zero to 40 times and 5 as a factor zero to 30 times, accounting for 41*31=1271 divisors, so we get 1681+1891-1271 = 2301 divisors. 10^40 has 41*41 integers that can divide it, because the integers can be 2^(0 to 40)*5^(0 to 40). Similarly, 20^30 has 61*31 integers that can divide it. To get rid of the ones counted twice, I find the GFC of the two, which is 2^40*5^30. The number of integers that divide this is 41*31. So the total number of integers that divide at least one is 41*41+61*31-41*31=1681+620=2301 If x is the original number then 3x is the number after the digit 3 has been moved from back to front. We set up a long division of 3 into 3x to get the original number. It starts So the next digit after the 3 in the dividend is 1, as that is the first digit in the quotient, before which the 3 was appended to make the dividend. After a couple of turns of this we get: <U>103 The last digit so far is 3, but this is not the end, as it still leaves a remainder of 1. We must continue until the last digit is 3 but there is no remainder. The following program continues the algorithm: PRINT quot$ The underlines didn\'t come out right in those long-division examples, but the long division is supposed to look like this: 103 I\'m sorry, you are right. You did mention it. I don\'t know how I missed it. <my face is red> :-| Therefore, a good place to start would be to write out the multiplication, using ... to indicate the unknown digits in both the product and the multiplicand. Then, (X+3)/10= 0.3abc...3abc...3abc..., which must be equal to 3X. Equating, we get X=3/29, which works out to be 0.1034482758620689655172413793..., so our number is 1034482758620689655172413793.\n\nEdited on March 1, 2004, 12:01 pm',NULL,0);
INSERT INTO comment VALUES (12335,124,5759,'Pieater','Answear','2004-03-01 12:42:04',0,'I believe it\'s easy because Arley pays more, but if the other dude pays bigger coins then he would pay more money. ',NULL,1);
INSERT INTO comment VALUES (12338,1651,3992,'Jane Doe','one way of looking at it...','2004-03-01 15:38:22',3,'1. Let\'s assume that the first statement was made by the Saudi Arabian. Then the statement is true. So Saudi Arabia gets the Gold.\r\n Assuming the first statement is true, the second statement must have been made by the Romanian, because the Qatarian cannot be talking about his own country while the first statement is true. Therefore the statement is false. So Qatar gets either Silver or Bronze and Saudi Arabia gets either Gold or Silver.\r\n Assuming the first statement is true and the second false, let\'s also assume that the third statement was made by the Qatarian. The statement is false as he is not talking about his own country, so Romania gets Silver. \r\nThe final places are as follows:\r\nSaudi Arabia - Gold\r\nRomania - Silver\r\nQatar - Bronze\r\n\r\n2. Let\'s assume that the first statement was made by the Romanian. The statement is false, so Saudi Arabia gets either Silver or Bronze. \r\n Assuming that the first statement is false, let\'s also assume that the second statement was made by the Qatarian. This statement is true, so Qatar gets either Gold or Silver\r\n Assuming that the first statement is true and the second one is false, let\'s say that the third statement was made by the Saudi Arabian. It is a false statement, so Romania gets Silver.\r\nBased on this situation, the results are as follows:\r\nQatar - Gold\r\nRomania - Silver\r\nSaudi Arabia - Bronze\r\n\r\n3. Let\'s assume that the first statement was made by the Qatarian. It is false, so Saudi Arabia either gets Silver or Bronze. \r\n Assuming that the first statement is false, let\'s say that the second statement was made by the Saudi Arabian. It is a true statement, so Qatar gets either Silver or Bronze. \r\n Assuming that the first statement and second statements are true, let\'s say the third one was made by the Romanian. It is true, so Romania gets the Bronze. \r\nSo, \r\nQatar - Gold\r\nSaudi Arabia - Silver\r\nRomania - Bronze \r\n\r\n4. Now let\'s assume that the first statement was made by the Qatarian. It is false, so Saudi Arabia gets either Silver or Bronze.\r\n With the first statement assumed true, let\'s say the second statement was made by the Romanian. It is false, so Saudi Arabia gets either Gold or Silver.\r\n With the first and second statement being true, let\'s say that the third statement was made by the Saudi Arabian. It is false, so:\r\nRomania - Gold\r\nSaudi Arabia - Silver\r\nQatar - Bronze\r\n\r\n5. Let\'s say that the first statement was made by the Romanian. It is false, so Saudi Arabia gets etiher Silver or Gold.\r\n With the first statement assumed true, let\'s say the second statement was made by the Saudi Arabian or the Qatarian; it is true so Qatar gets Gold and Saudi Arabia gets Silver.\r\n The Qatarian or the Saudi Arabian could not have made the last statement, because Romania could not have gotten the Gold or Silver based on the first two assumptions. Therefore, the final places are:\r\nQatar - Gold\r\nSaudi Arabia - Silver\r\nRomania - Bronze.\r\n\r\nNow, based on all the different situations, the following statements were made: \r\n\r\nThe first statement was made by the Qatarian, the second statement was made by the Saudi Arabian, and the third statement was made by the Romanian. \r\n\r\n..and the final places should be: \r\n\r\nGold - Qatar\r\nSilver - Saudi Arabia\r\nBronze - Romania \r\n\r\n',NULL,0);
INSERT INTO comment VALUES (12339,1351,5852,'Coda','Easy','2004-03-01 16:05:26',0,'First day on the site, and the first problem I could figure out! The problem with the paragraph is that the last word of each line is repeated on the next line. ',NULL,1);
INSERT INTO comment VALUES (12340,1651,4507,'Penny','Solution','2004-03-01 16:15:13',3,' Edited on March 1, 2004, 6:52 pm',NULL,1);
INSERT INTO comment VALUES (12341,1302,5852,'Coda','Solution','2004-03-01 16:15:18',3,'Assuming the cannibals ate at a steady rate, it would take 4 hours 34 minutes until just one consumer remained. However, considering that the remaining cannibal would have to eat the equivalent of over 2 people, it is highly improbable that he could finish in such a short space of time. ',NULL,1);
INSERT INTO comment VALUES (12342,1653,5840,'michelle','No Subject','2004-03-01 21:59:22',0,'3,628,800',NULL,1);
INSERT INTO comment VALUES (12343,625,3750,'mohan','re(2): Solution','2004-03-02 00:10:40',0,'SK, be kind! (i got your drift, though, as i had a similar reaction.)\r\n\r\nyour comment was pretty funny, however.\r\n ',10223,0);
INSERT INTO comment VALUES (12344,1530,4374,'Richard','re: Standard solution','2004-03-02 01:10:08',0,'I am fascinated by this non-practical problem and the method you give. Can you give a reference for the method? Replacing 3 in the problem with 2, I get the 18-digit number 105263157894736842. Replacing 3 with n, there will be an answer (perhaps itself containing an internal repeating answer) with 10n-2 digits if 10n-1 is prime, i.e. when n=2,3,6,8, and 9. When 10n-1 is prime, the (10n-2)-digit answer will be the smallest possible whenever the index of 10 mod 10n-1 is coprime to 10n-2 as it is for n=2,3, and 6. Thus the minimal answer for n=6 has 58 digits.',12334,1);
INSERT INTO comment VALUES (12345,1651,5285,'Ady TZIDON',' SECOND OPINION','2004-03-02 03:22:13',3,'re: my previous post.\r\nI erred\r\nQ1 S2 R3 is the right and unique answer.\r\n\r\nady\r\n\r\n\r\n\n\nEdited on March 2, 2004, 3:31 am',NULL,0);
INSERT INTO comment VALUES (12346,1467,5857,'hunter','I think this is the answer','2004-03-02 06:48:56',0,'My answer is 33 if my answer is right tell me and i will tell you how i got it and thank you',NULL,0);
INSERT INTO comment VALUES (12347,1526,2716,'Federico Kereki','re: A switch solution - maybe not the optimal one...','2004-03-02 07:03:49',1,'The numbering is wrong... \"a3b2\" should be \"a2b3\", and so on. Also, the two first moves can be switched, and so can the two last moves, so there are four solutions.',12336,0);
INSERT INTO comment VALUES (12348,1410,5857,'hunter','re(2): solution','2004-03-02 07:10:09',0,'what you said is convincing (SilverKnight) but what if hour, minute and second hand do not jerk and turn around smoothly will your answer be right',11444,0);
INSERT INTO comment VALUES (12349,1530,1301,'Charlie','re(2): Standard solution','2004-03-02 08:34:50',3,' This didn\'t use the \"standard\" solution, but here\'s a rundown for various move-by and multiply-by values, with the length of the number shown below the number: Move the 2 , mult. by 2 . Produced by OPEN \"movxmulx.txt\" FOR OUTPUT AS #2 PRINT #2, quot$ CLOSE intersting interesting ((i^2)e)^(i* pi) (e^[i*pi/2]^2^(i*pi)*1) e(-pi^2) or 5.1723*10^-5 - e^(-ð²). Can it be that the toolbar is now working? Evidently not. So how does one get pi to come out as the Greek letter? Edited on March 2, 2004, 1:32 pm',12360,1);
INSERT INTO comment VALUES (12363,1661,1301,'Charlie','re: too easy for this site','2004-03-02 13:30:16',0,' I\'m not sure what your line of reasoning is, but you are missing the minus sign--the result is negative. I\'m sure also that your next-to-last line is intended to have a ^, which is missing also. F equals the area of TCRS, and G equals the area of VRYZ. BST and SZV are similar to BAC. Maximizing F+G equals minimizing the sum of the areas of BST, SZV, and ZAY. Let\'s call BC=2L so the height of ABC is 1/L. If BT=2H, then the area of BST is H^2/L^2. If SV=2K, then the area of SZV=K^2/L^2. Finally, ZY=2L-2H-2K, so the area of ZAY=(L-H-K)^2/L^2. Maximizing F+G equals minimizing (H^2+K^2+(L-H-K)^2)/L^2. Differentiating with regard to H and K and equating to zero, shows that this is minimum if H=K=L/3, and in that case, F+G equals 2/3 of the total area. \r\nPS. In the first draft of this text, I had written \"parallel to BC\", which made no sense, instead of \"parallel to AC\".\n\nEdited on March 2, 2004, 2:45 pm',NULL,0);
INSERT INTO comment VALUES (12365,1632,3172,'SilverKnight','re: Possible solution','2004-03-02 14:13:25',4,'F.K., you wrote: I\'m pretty sure he intended a parallel to AC, not BC, forming parallelograms with the same areas as F and G, and leaving two similar triangles. Not the same approach I had, but it works, so .. I like it. =) Interestingly enough, I\'ve had the same problem before the rich text editor, when submitting this very problem. When I submitted this problem, all the symbols came out fine, using those codes with the ambersand and stuff. But when I editted it, the pi symbol was in the text box instead of the code, and then after submitting the edit, it came out as some wierd symbol. I think that it\'s the lower case Greek delta. Anyway, I did bring it up in a thread here quite a while ago. Edit: the link wasn\'t working, at least not for me. I can\'t figure out what\'s wrong, but the url is http://perplexus.info/forum.php?fid=5&tid=283 Edited on March 2, 2004, 8:17 pm',12361,1);
INSERT INTO comment VALUES (12376,1632,5352,'Juggler','Layman\'s Maths','2004-03-03 02:07:02',1,' For this I needed to add some figures into the picture, I called the line BC = 10cm, dropping a perpendicular line from A to an intersection of BC, say A-A\', i called this length 10cm also, this gives us an area for the triangle of 50cm², (base x 1/2 height) now i need to insert 2 squares into the triangle, i used the equation ½height x ½width (5cm x 5cm) for the first (F) and ¼height x ¼width (2.5cm x 2.5cm) for the second (G) from this i can now work out area of F+G to be 25cm²+6.25cm²=31.25cm² this is 62.5% of the original triangles area To prevent a given number from being relatively prime to the rest in the set of ten, it must share a prime factor. Prime factors that are 11 or larger need not be considered, as only one number in any range of ten can have such a prime as a factor. In any span of ten numbers, five will be even (divisible by 2), leaving five that are still possible candidates for being relatively prime. There can be three numbers that contain 3 as a factor, but at least one of these was already disqualified by being even, so the 3\'s can only reduce the candidates by 2, leaving 3 candidates for relative primeness. Only two of the numbers in the range can be divisible by 5, but again, one is even, so only one is removed from candidacy now, leaving 2 candidates. At most two numbers in the range can be divisible by 7, and again, only one can be odd, so at most one candidate is disqualified, leaving at least one that\'s still relatively prime to the rest. As we\'ve run out of primes under 11, we\'ve shown that at least one number of the ten is relatively prime to the rest. The only possible prime factors the ten numbers might share are 2, 3, 5 and 7. The positions of multiples of these primes within any given range (including ranges of 10) therefore shift in a cycle of 2*3*5*7=210 numbers. Therefore we can check the first 220 numbers to find those numbers that do not have any one of these as a factor. They are listed below, together with the difference between it at the previous number on the list: 1 None of the differences is greater than 10, so every group of ten will have at least one. In fact, there are only two points in the cycle where the distance is farther than 8: 1-11, and 199-211. In the first instance (to be repeated at 211-221), 7 (or 217) is the only multiple of that number within the group bounded by numbers on the list and so serves as a relative prime until 1 (or 211) is reached on the one side or 11 (or 221) on the other. In the other range, 199-211, 203 is a multiple of only 7 and again the only such multiple in the range, and so serving as a relative prime within that group. Thus any set of eight consecutive integers has at least one member that is relatively prime to the others in the set. Edited on March 3, 2004, 9:10 am',NULL,1);
INSERT INTO comment VALUES (12383,1657,1301,'Charlie','Extension in the other direction','2004-03-03 09:50:20',0,' Reducing the span to 8 as in my previous post makes it easier in one sense to get relative primes, in having fewer numbers that might share a factor, but harder in another in reducing the eligible candidates for being the relative prime. So extension in the other direction could be of intereste. The following program checks spans of 11 for numbers that are relatively prime and finds that the widest gap between numbers that are in fact prime relative to their preceding 10, is 10, so any span of 11 consecutive numbers contains at least one that is relatively prime to the rest: max = 2 * 3 * 5 * 7 * 11 I\'d like to thank Ady for pointing out that it is not necessary to use squares, but i\'d like to add that for the particular figures that i used in the example, squares are required. if the height and base of the triangle were of differing lengths, then the \"square\" objects would in fact be rectangles and the calculation would still work. The official solution is given in \"Problem #6\" at the following website. (If you get \"URL not found on this server\", copy/paste it into your web browser). http://www.geneseo.edu/~towsleyg/PUTNAM%20PROBLEM%20ARCHIVE.htm Edited on March 3, 2004, 1:09 pm',NULL,1);
INSERT INTO comment VALUES (12386,1632,1575,'DJ','re(3): We are not square (in my original post, they are)','2004-03-03 13:39:12',1,' \"for the particular figures that i used in the example, squares are required.\" Why? If you assume that they need be squares, then you are not finding the maximum of anything, just calcluating an area. In fact, when you maximize the areas, the two rectangles will have the same height (one third of the height of the triangle), so both will never be squares (the bottom one is obviously much wider). Five locks, and five keys. The chest could only be opened when all five people are present (which, in turn, satisfies that at least three of them must be present. Ah, the old \"only if\" versus \"if and only if\" loophole .. represent odd # as 2K+1 then odd^2-1 =(2K+1)(2K+1)-1 4k^2+4K =4K(K-1) but since either K or K-1 is even a 2 can be pulled out from one of them leaving 4K(k-1)/8 as an integer Edited on March 3, 2004, 6:51 pm',NULL,1);
INSERT INTO comment VALUES (12394,1668,5285,'Ady TZIDON','re(2): key answer +an EXTRA key for GAMER','2004-03-03 18:15:00',3,'\r\nG\'\r\n\r\nNeither the proof nor the actual distribution of the keys was requested, but I will obliged you. I felt that something should be left for others. Anyway:\r\n\r\nWhy is this minimum? If there was a lock for which 2 or fewer people had keys, the 3 or more people left over would be unable to open the box, which is unacceptable; so all locks must share their keys among 3 or more people. Now if there was some 3-person group that was not the set of key owners for a lock, the group consisting of the remaining 2 people would be able to open the box, since it shares at least one person with every other 3-person group, and every group with 4 people or more. Hence every 3-person group must be the set of key owners for some lock, which means that any solution must use at least the locks and keys above (you can use more if you like.) \r\n\r\nAs to the distribution list - simply follow the solution and\r\nallocate the keys: subsets of a group 1,2,3,4,5 are:\r\n123,124,.....345\r\nall members of the first 3-tuple get EACH the A-key for lock A\r\nall members of the SECOND 3-tuple get EACH the B-key for lock B\r\n....YHE LAST SUBSET the J-kay\r\n\r\nHope you find it satisfactory.\r\n\r\nady',12392,0);
INSERT INTO comment VALUES (12395,1668,3172,'SilverKnight','re(3): key answer +an EXTRA key for GAMER','2004-03-03 18:17:24',0,'An example of Ady\'s suggest distribution would be:\r\n Any two of these people must lack a key to at least one lock. But then the other three must all have a key to that lock; otherwise there would be three people who couldn\'t unlock it. There are 10 groups of 2 people among 5. Therefore 10 is the minimum number of locks, and 5 the minimum number of keys (one per person). OK, let\'s start afresh, the only reason i said squares was because the dimensions of the theoretical triangle i used were such that the outcome of the shapes F & G were both squares, maybe this is unfortunate, So to re-iterate the area of F should be equal to ½Height x ½Base, while the area of G should be ¼Height x ¼Base, giving us areas of F=50% total area and G=12.5% total area. F+G=62.5% I have since recalculated with the DJ\'s recommendations and have got better results (66.66%) thanks for that I also realise where i went wrong, i was trying to get the largest area possible with the first rectangle and then doing the same with the second, this is clearly wrong as the calculations show that if the rectangular heights are the same then the smaller rectangle will more than make up for the shortfall in the first. I guess this long drawn out explanation as actually been an apology of sorts, i shall refrain posting any more comments on maths related issues until i am more sure of what is being asked Sorry, Phil (Juggler) Since locks are expensive and keys are cheaper, i believe i have come up with a better solution, 5 Locks and 10 Keys. call the locks A, B, C, D, E. Albert holds lock A and key 1 + a copy of Key 3 This way only three people ever need to be at the chest to open it but 2 people cannot Edited on March 3, 2004, 7:45 pm',NULL,1);
INSERT INTO comment VALUES (12402,1668,3172,'SilverKnight','re: Explanations','2004-03-03 19:53:15',0,'Gamer is absolutely correct. Juggler wrote: \"5 Locks and 10 Keys. call the locks A, B, C, D, E. call the Keys 1, 2, 3, 4, 5. Albert holds lock A and key 1 + a copy of Key 3 Dear Juggler: How would Albert, Brenda and David unlock the 5th lock ? Ooops :-) Once again, another short sighted explanation, i\'ll get bac to you with a better one soon. I must agree with Axorion/Dan here. The fact that the hour hand moves is irrelevant because we only need to consider the relative movement of the hands. We can say that relative to the minute hand, the hour hand is moving counter-clockwise around a point 4 inches away from the point of the minute hand (the center of the clock). Relative to the minute hand, the hour hand keeps the same speed. The time when the distance is increasing most is when the hour hand is moving in the opposite direction. The direction is determined by the line tangent to the circle, at the point of the hour hand. So at this moment, the point of the minute hand is on the tangent line. So, using the pythagorean theorum, the distance is ã(4^2-3^2) or ã7. It seems to me like what you\'re proposing is just a less straightforward way (but I could be wrong). I hope I was thorough enough and not too thorough. \"Therefore 10 is the minimum number of locks, and 5 the minimum number of keys (one per person).\" I\'m wondering how anyone can open 10 unique locks with 5 keys. The minimum of keys is 30 because at least 3 of the people have to have the key for any of these ten locks. Edit: I see what you meant now, but I don\'t think that you could have five keys that each open a different set of locks. Edited on March 3, 2004, 8:31 pm',12396,1);
INSERT INTO comment VALUES (12409,1668,4507,'Penny','re(3): Solution (Penny\'s)','2004-03-03 22:18:47',0,' Edited on March 4, 2004, 8:02 am',12408,1);
INSERT INTO comment VALUES (12410,1565,5178,'Axorion','re(2): why calculus','2004-03-03 22:30:56',0,'Think of it this way. The rate of both hands is a constant so adding or subtracting them will still be a constant rate. Take a battery operated clock. Remove the second hand. Glue a small block to the minute hand. Glue the block to a piece of glass. Now look through the glass at the clock. The hour hand will be moving counter clockwise at a uniform rate slightly slower than a minute hand normally moves clockwise. The tip of the hour hand will be at a constant speed but changing direction. When the tip of the hour hand is moving directly away from the tip of the minute hand we have our max increase. This is at 90° to the unknown segment or as Tristan put it, the point of tangent of a line through the tip of the minute hand to the circle drawn by the hour hand.\r\n\r\nI never took calculus although I can do a bit of it. I have found that many problems can be simplified through geometry, algebra, trigonometry, logic and common sense. Of course it helps that I can count the sides of complex polyhedrons in my head. I\'m also an accomplished programmer so if it get over my head I can always do successive approximation. Now if I could only remember that mandatory meeting I was reminded is in five minutes I might go back to school and have a cool job! \r\n\n\nEdited on March 3, 2004, 10:54 pm',12397,0);
INSERT INTO comment VALUES (12411,1328,5384,'Larry','Solution','2004-03-03 23:19:54',3,' Haven\'t read the other posts, so this may be redundant. The numbers are Fibonacci numbers starting with 3 in base 2, then 5 in base 3, 8 in base 4, 13 in base 5, 21 in base 6, and 34 in base 7. The next 2 numbers are: 45 (55 in base 8) Oops, sorry, messed up my bases there. Haven\'t read the other posts, so this may be redundant. The numbers are Fibonacci numbers starting with 3 in base 2, then 5 in base 3, 8 in base 4, 13 in base 5, 21 in base 6, and 34 in base 7. The next 2 numbers are: 67 (55 in base 8) As far as the philosophy of what makes the best answer (now I have read the other posts), I think there should be something akin to esthetic points for \"cleverness\" or \"uniqueness of ideas\". So for this series combining Fib with a changing base seems to me to be \"better\" than, say, a \"kicked up a notch\" geometric series. But then that\'s just me. Then again, sometimes I mess up translating bases. I agree that the customer expected 1/6 plus 5 chestnuts. Let X be the number in question. Let Y = FLOOR(LOG(X)). According to the problem, X and Y... (X-3)/10 + 3*10^Y = 3*X Multiply both sides of that equation by 10... X - 3 + 3*10^(Y+1) = 30*X Subtract X from both sides. 3*10^(Y+1) - 3 = 29X So the left side of that equation must be divisible by 29. Or, stated in another way, 3*10^(Y+1) is congruent to 3 mod 29. which implies 10^(Y+1) is congruent to 1 mod 29. Now all we do is find power of 10 that is congruent to 1 mod 29. Since 29 is a prime number, Fermat\'s theorem tells us that... 10^28, 10^57, 10^86, etc. are congruent to 1 mod 29. More generally put, 10^(29*n+28) is congruent to 1 mod 29 for every integer n >= 0. Which means Y+1 = 29*n+28 where n is an integer. And that in turn tells us that... 29*X = 3*10^(29*n+28) - 3 where n is an integer >= 0 Take n=0 for example. 29*X = 3*10^28 - 3 29*X = 29999999999999999999999999997 X = 1034482758620689655172413793 So, to sum that up... the general formula for the complete set of answers is X = (10^(29*n+28)-1)*3/29 where n is an integer >= 0 X is guaranteed to be a whole number because we found the set of power of 10 that have the right congruency in mod 29. And thus everything\'s in order here. Final , complete answer... The Final Standings:- 1. Saudi Arabia 2. Romania 3. Qatar Reasoning: The Romanian was the person who spoke 2nd i.e. \"Qatar ended in a higher place than Saudi Arabia\". Since he was not speaking about his country, he was lying and Qatar ended in a LOWER place than Saudi Arabia. The person who spoke first was Saudi Arabian and Saudi Arabia did end up winning the gold. The 3rd person, was the Qatarian and since he was not speaking about his country, he was lying. Hence, Romania was NOT the worst. This implies that... Saudia Arabia is First(GOLD Winner), Romania is 2nd (since it wasn\'t the worst and wasn\'t the best either), and Qatar was third(finishing lower than Saudi Arabia) Is it correct? lol Edited on March 4, 2004, 3:43 am',NULL,1);
INSERT INTO comment VALUES (12418,1530,5892,'empraptor','re: complete set of answers, mathy reasoning *** correction','2004-03-04 03:44:36',0,' The general formula should read X = (10^(28*n) - 1) * 3 / 29 where n is an integer >= 1 I made a mistake in doing modular math. 10^(29*n+28) is NOT congruent to 1 mod 29 for all n. For example, 10^(29+28) = 1-^57 is congruent to 10 mod 29. Because 10^28 is congruent to 1 mod 29, 10^28 * 10^28 should also be congruent to 1 mod 29. If you extend this reasoning, 10^(28*n) is congruent to 1 mod 29 for all integer n >= 0. Of course, while n=0 does satisfy the equation we set up to model the problem statement, it is not a valid solution because X=0 in that case. So we limit n to >= 1. Brianjn wrote: \"Solution: 9 keys, 4 people get 2 but one soul gets 1 such the table distribution is obeyed.\" If you think about it for a while, you realize that you don\'t need more keys than there are people: 5. Because the multiple keys that a given person possesses can be replaced by one key that unlocks all the locks that each of the multiple keys unlocks. Edited on March 4, 2004, 4:54 am',12417,1);
INSERT INTO comment VALUES (12421,1668,5893,'Stelian Trandafir','Possible Solution','2004-03-04 07:28:29',0,' Hi all I have a possible solution to the problem: if you have a combination of 5 people of which any 3 have to be able to open all the locks then you have to have a C(5,3)=10 unique locks and 3 cheys per lock = 30 keys divided by 5 people = > 6 keys/ person Stelian Trandafir wrote: \"6 keys/ person\" And then you replace each person\'s 6 keys with one key -- one key that unlocks everything those 6 keys collectively unlocked. 1 key/person I am working on the assumption that one lock can be opened with one key or its copies and there is no masterkey to open 6 or more locks. That is the point of the problem as I see it. As simple and realistic as it can be. How realistic is it that a key opens 6 different locks and another key opens the same 5 locks as the previous one but not the 6-th...? I disagree. If the \"Master Keys\" scenario looks realistic to you then this will be even more realistic: Only one lock that \"senses\" that 3 different keys have been used and opens the chest. Then 5 different keys will be distributed to each person. The lock might even have 5 holes that count the number of keys that have been used at once. That solves it. Of course, but that was not the point of the exercise. The keys are simple keys which open exactly one lock. The locks are simple locks which can be opened only by keys made for the lock. Multiple keys can be made for any lock. Stelian Trandafir wrote: \'Only one lock that \"senses\" that 3 different keys have been used and opens the chest. Then 5 different keys will be distributed to each person. The lock might even have 5 holes that count the number of keys that have been used at once. That solves it. Of course, but that was not the point of the exercise.\' I don\'t think that solves it at all. The puzzle states that no fewer than three people must be present to open the chest. Sheesh....... Now you clarify this ! The idea that one key opens exactly one lock detracts from the attractiveness of the puzzle. (In my humble opinion, of course). There must still be 10 locks. More shortly........ Let the edge of the cube be 1. Each truncation would remove a right tetrahedron with an edge of 1/2. The volume of the tetrahedron is (1/6)*(1/2)*(1/2)*(1/2)=1/48. The total volume of all eight removed tetrahedra is 8*(1/48)=1/6. Then, the volume of the truncated cube is 1-1/6=5/6 Brian, Not to further dwell on this puzzle, the solution 10locks, 3 keys per lock 30 keys in total is correct or not? Edited on March 4, 2004, 11:34 am',NULL,1);
INSERT INTO comment VALUES (12434,1530,2716,'Federico Kereki','re(2): Standard solution','2004-03-04 11:37:01',0,'I\'m pretty sure I saw this method in a book by Martin Gardner -- but as it was many years ago, and Gardner wrote many books, it\'s impossible for me to be more specific; sorry!',12344,0);
INSERT INTO comment VALUES (12435,1668,4507,'Penny','Revised solution to revised puzzle','2004-03-04 11:54:41',3,' Lock 7 is redundant of lock 4 Lock 9 is redundant of lock 8 I\'m sure this has been covered already, but not nearly as clearly as it should. It\'s been proposed that we should only need 10 locks and 30 keys, but maybe figuring out how to distribute them is a problem. Everyone I\'ve seen so far has given the arrangement, and then shown how their arrangement solves the problem. The simplest approach is to simply say, if the lock will be opened if and only if at least three people are present, then any given pair should be unable to unlock at least one lock. That\'s where the 10 locks comes from, the 10 combinations of 2 people out of a group of 5. Make those assignments first: Read this as A and B alone should be unable to open lock 1. Thus, C, D, and E should all have a key to that lock, and the same reasoning follows for the other 9 locks. The assignment of keys follows naturally from there: I realize this is redundant of what other people have posted, but without the right method this can get way too messy .. Edited on March 4, 2004, 12:32 pm',12435,1);
INSERT INTO comment VALUES (12442,1668,4507,'Penny','re: Really Simple','2004-03-04 12:47:17',0,' Compare this to your original \"Poor solution\" post. It wasn\'t \"really simple\" then. This seems to be a case of 20-20 hindsight, after you read all the other 32 posts. (Post #9 stated \"Any two of these people must lack a key to at least one lock. But then the other three must all have a key to that lock; otherwise there would be three people who couldn\'t unlock it.\") No offense. I do the same thing all the time. Edited on March 4, 2004, 12:49 pm Edited on March 4, 2004, 1:47 pm',12439,1);
INSERT INTO comment VALUES (12443,1530,5892,'empraptor','re(2): complete set of answers, mathy reasoning *** correction #2','2004-03-04 14:31:13',0,'Argh... another correction - minor this time. The general formula is right the way I left it in my last correction. The way we see the colour wheel with red, blue and green is exactly the same way that the r g b receptors in our retinas perceive light. However, we can indeed use different colours to achieve approximate results of cyan, magenta and yellow (but they will not be exactly the same, because of the way our retinas perceive the light). Light can be additive or subtractive, so we can get the various colours by mixing spectral light in varying combinations no? For instance, we see Yellow when Red and Green are optically mixed by being placed close together or are being presented together in rapid succession. It simply depends on the mixture/combinations or the succession in which the colours are being presented. Charlie wrote: \"Why not use your original solution (comment #6) and just have a separate key for each lock: 10 locks and 30 keys?\" That would have been the logical thing to do. Why didn\'t I think of that ? (Don\'t answer that !!) :-) This was the best kind of flooble puzzle. It didn\'t require either a google lookup or a software program (contrary to what I said before). It really stimulated thought and creativity, as did Gamer\'s \"Letters to Numbers\" puzzle. \"Open by Majority\" and \"Letters to Numbers\" are the kinds of puzzles that really make flooble worthwhile. A is the girl You go right Edited on March 5, 2004, 1:07 am',12447,1);
INSERT INTO comment VALUES (12456,1672,5899,'john','easy on the eye','2004-03-05 02:10:43',0,'Objects do not have color. They are only coated with a substance that reflects light of a certain wavelength. Assuming they are illuminated with white light, coating (A) will reflect red light stronger than the other wavelengths, which are still present in varying degrees, but overpowered. Coating (B) green. A mixture of both coatings will be seen to reflect yellow because of destructive interference.The red wavelengths cancel out the green, leaving yellow as the strongest remaining reflective wavelength. Using lasers for illumination in our experiment, this is not the case. A red helium-neon laser, and a green argon laser mixed together will not produce yellow light. So light is not additive after all.',NULL,0);
INSERT INTO comment VALUES (12457,460,5903,'blackberry brambles','What\'s a rotation?','2004-03-05 07:17:36',0,' Great puzzle! We have found three different solutions (over an equal number of weeks...). Now we\'re not sure if we have finished or not. Say we have a solution on a board where the bottom right square is black. If we put exactly the same solution on a board with a white bottom right square, is that a new solution or simply a rotation? (This is the same as picking up the pieces in the first puzzle with a ten-pin-bowling-like set of pincers, and then spinning the board 180 degrees and dropping the pieces back down. Does this count as a rotation?) Any two of these people must lack a key to at least one lock. But then the other three must all have a key to that lock; otherwise there would be three people who couldn\'t unlock it. So there are at least 10 locks, since there are 10 groups of two people among 5. It is a waste of time to look for a solution with less than 10 locks. The proposition to be proved seems counter-intuitive. Suppose there are a subset of 10 towns on each side, and each is connected to each of the others in these subsets, so there are ten roads of each of the 10 allowed colors. Now remove two roads of the same color, say color 10. Then add another town on one side of the divide and connect it to the two towns on the other side which had a road removed. The only color available at either of these towns is color 10, but the two new roads can\'t both be color 10. In order for the proposition to be true, we must prove it\'s possible to reassign the whole remainder of the network so as to free up different colors at these two towns. Um....never mind...Two roads are adjacent if they leave the same town..... Are we to assume that Alexton and Brighton are neat and tidy divisions of Albinia ? Because if I were allowed to \"gerrymander\" Albinia wildly enough into odd shaped fragments, and then arbitrarily unite the fragments into two states Alexton and Brighton, I\'m pretty sure I could come up with a map that would not permit your puzzle\'s hypothesis. Edited on March 5, 2004, 5:46 pm',NULL,1);
INSERT INTO comment VALUES (12461,19,5759,'Pieater','No Subject','2004-03-05 12:05:19',0,' What\'s in my package? would be the question I would axe because (assumably) you know what is in the package. Bob\'s brother would lie about it and Bob would tell you the truth. That\'s a rotation. After looking at this for a while, I think I found a possible loophole rendering the proof disprovable. Say town A is in Alexton and town B in Brighton. There are 11 roads connecting the two. This obviously doesn\'t work out and was not how it was meant to be. I think where it says \"It is known that no town is connected with more than 10 others.\" it should actually say \"It is known that no town is connected with more than 10 roads.\" I think that with this wording it may be provable. On the other hand, I\'m not sure how to actually prove it yet. Aaron could also have meant that no two roads connect the same two towns, as the previous commenters have interpreted it, but I think we can go a little further. Not really in reply to this comment, but to extend... in a way... Two wavelengths of light won\'t add to a new wave, like John said, it\'s really the brain that adds them together. For example if there was red+green light around, you would see red+green, and interpret it as yellow. The reason for this is that if there was actual yellow light, you would also see it as red+green and interpret it as yellow. Also, I suppose light is an exception to most energy waves in the way that 2 waves won\'t add to each other and make a wave with greater magnitude. It\'s not like sound where if you make two waves slightly out of tune, the magnitude would oscillate. Well, I think that demonstrated my (lack of) knowledge of physics well. http://www.ams.org/new-in-math/cover/colorapp4.html Also Robin J. Wilson\'s book \"Introduction to Graph Theory,\" 4th ed., pp. 94-95 for a short proof. This problem is an instance of a theorem of graph theory attributed to Denes Koenig, c. 1916. there are only two possibilities that either and c are innocent or b and c are innocent; if b is not killer means he can assist. but if that is not so,the other possibility b and c being innocent, their statements mean b : if a is not innocent, then c must not be guilty (justified). c : if b was not the killer, d must have had something to do with the crime (justified). a : if b is \'not\' guilty of something, then c is innocent. (lie inverted justified). d : he is not innocent. (lie inverted justified). but then who exactly killed the Professor among a and d ? A can\'t be the killer. Neither can C. This can be seen instantly because their statements starts with \"If x is guilty.\" If A or C were guilty, then this first part of the conditional would be false, so the entire conditional would be true, so they would be telling the truth. Since guilty people can\'t tell the truth, they can\'t be guilty. Note that there is only one way to access squares like a1, a8, h1, and h8. This means that if your knight ever lands on a square like b3, c2, b6, c7, f2, g3, f7, or g6 his next move must include the corner square followed by the opposite exit square. If we are aiming for SK\'s extra credit than we are seeking a 64 move pattern which ends where it begins, and as such makes the starting square irrelavant. Also if we are seeking to earn his EXTRA extra credit we might imagine a symmetry where each corner is hit with equal distribution. I put the numbers 1, 17, 33 and 49 in each of the corners in order counter-clockwise but this fails when I notice that the knight must alternate black and white squares. Therefore the symmetry must be balanced over the breadth of 32 moves as opposed to 16. I believe it\'s in the eye of the beholder. Consider 2 beams of monochromatic light of different colors. The electromagnetic energy of the combination is the sum of 2 sine waves of different frequecies. This is where the addition comes in. Inside the retina, the light falling on individual cones stimulates an electrical response in the optic nerve. Add another wavelength and you add the response of additional cones. Pigments in paint absorb certain frequencies of light, so adding paint colors is additive with respect to absorption of light, but subtractive with respect to the reflected light (which then may strike someone\'s retina) And that\'s my story. There is also something called the Land effect, which I believe is a higher brain function that interprets the colors we see in comparison to the overall background color. This is why a white shirt still looks white even if the color of the light changes. This effect isn\'t perfect, however, and if viewed in pure red light, the white shirt will look red. I also recall hearing about an experiment in which photographs were taken through monochromatic filters. If the same scene was photographed with 2 different color filters, then the images were projected and superimposed, and then the test subject viewed the scene with 3-D glasses (one red lense, one green lense for example) then the scene would look normal with all the true colors. There was some specific wavelength (I assume related to the cones specific sensitifities) such that the 2 colors had to be one higher and one lower for the final picture to look right. Land invented the polaroid camera, I believe. The 3 jugs are A 12 liters, B 8 liters, and C 5 liters: A B C 12 0 0 (from A to B) 4 8 0 (from B to C) 4 3 5 (from C to A) 9 3 0 (from B to C) 9 0 3 (from A to B) 1 8 3 (from B to C) 1 6 5 (from C to A) 6 6 0 And I have that on the authority of the late, great science writer Isaac Asimov. Asimov wrote that when relativity of motion is taken into consideration, it is just as true to say that the sun rotates around the earth, as it is to say that the earth spins on its axis. Naturally we prefer the latter interpretation, but not because it is more truthful. It is not. Truth and falsehood are not involved. We prefer the spinning earth model because it is simpler. This is the principle of Occam\'s Razor. Edited on March 6, 2004, 9:44 pm',NULL,1);
INSERT INTO comment VALUES (12479,198,2561,'Aaron','What if?','2004-03-07 00:01:58',1,' What if he turned right on every third crossroad (repeating two lefts and a right, two lefts and a right)? Then, isn\'t it possible that he could enter a loop on the first left turn, which came back to that crossroad on the second left turn, and get him stuck in a loop? I know it\'s not in the problem, but I saw this \'old\' problem in the Bonus section, and I wondered if it is true for any fixed pattern of moves.. This solution isn\'t symmetrical, but it is a re-entrant tour. A1 - B3 - D4 - B5 - C7 - A8 - B6 - D7 - E5 - G4 - F2 - H1 - G3 - E2 - C1 - A2 - B4 - D3 - C5 - A6 - B8 - C6 - A7 - C8 - D6 - E8 - G7 - H5 - F4 - H3 - G1 - F3 - H2 - F1 - E3 - D1 - B2 - A4 - C3 - D5 - E7 - G6 - H8 - F7 - G5 - E4 - D2 - B1 - A3 - C4 - A5 - B7 - D8 - 36 - F8 - H7 - F6 - G8 - H6 - F5 - H4 - G2 - E1 - C2 - A1\r\n For my method, I actually took out a chess set and took 4 paths that went 3 quarters around the board and didn\'t overlap and connected them all in the upper-left corner. Adding to the comments Eric made, there are 64 squares on the board. For a symmetrical pattern in four section, which would seem natural, each \'section\' of moves would need to include 16 squares, distributed equally with some sort of radial symmetry. What I did, then, is to start in each corner, and make the same move simultaneously in all four corners (to make sure that none of the patterns crosses another), and trying to get the patterns to end up in a position to move into the next corner. I\'m not sure if that will work; it\'s late and I haven\'t really thought about it, but it seems good enough.. This beautiful puzzle goes back to the days of Leonhard Euler and before. One simple strategy in Knight\'s Tours is to start in a corner and keep rotating in the same direction, moving on the outer edges of the board. a8; b6; a4; b2; d1; f2; h1; g3; h5; g7; e8; c7; a6; b4; a2; c1; e2; g1; h3; g5; h7; f8; d7; b8; c6; a5; b3; a1; c2; e1; g2; h4; g6; h8; f7; d8; b7; c5; d3; f4; e6; d4; f3; e5; c4; a3; b1; d2; f1; h2; g4; h6; g8; e7; c8; a7; b5; c3; e4; f6; d5; e3; f5; d6 This is neither re-entrant nor symmetrical. Not even Garry Kasparov can visualize all possible Knight\'s Tours in his head. To achieve a Knight\'s Tour which is both symmetrical and re-entrant, without being allowed to write a program, you must do a lot of trial and error and backtracking. Edited on March 7, 2004, 6:38 am',NULL,1);
INSERT INTO comment VALUES (12489,1565,5384,'Larry','Oops, this time I got it, sans spreadsheet solver','2004-03-07 10:04:01',3,' OK, this time I just started with the law of cosines getting d as a function of theta, then took d\' and d\" and I got the same answer as Charlie\'s original post. But I got it without using the solver on the spreadsheet. Call the angle x, it\'s too hard to figure out how to write a theta d=sqrt(25-24cos(x)) d\'=12sin(x)/d setting d\" to zero gives: 0=cos(x)sqrt(25-24cos(x)) - 12 sin^2(x) / sqrt(25-24cos(x)) multiply both sides by sqrt(25-24cos(x)) gives: cos(x)(25-24cos(x)) - 12 sin^2(x) cos^2(x) - (25/12) cos(x) + 1 = 0 so cosine is .75 Better late than never, and that\'s my final story I went on google to look for a site that would allow you to try the tour and didn\'t give you a solution. I swear that I didn\'t look at any solutions. I got this. That\'s http://www.geocities.com/allentownchess/knightstour.html, in case the link doesn\'t work. After trying it many times, I developed a little technique. I split the tour into four parts. Each part goes around in a circle in almost the same path. For example, in the grid below, the numbers represent the number of the path. The paths go together to complete the whole square. 3221 I hope that turns out. As you can see, the four paths come in from the left and come out on the bottom. I also thought up other transformations for all four paths to move at once. Unfortunately, for this to work out, the paths have to go in a circle, and they all must connect. I\'m having trouble making it both symmetrical and connective. I\'ve tried radial symmetry, symmetry over a line, over a dot, but I can\'t get it to work out. Here\'s some other transformations: 1234 412 AAAAAAAAUUUUUUUGGGGGGGGGGGGGGGHHHHHHH!!!!!!!!! I can\'t get those arrows to work! And the link too! It would have been clearer if I could fix them. Edited on March 7, 2004, 1:41 am Edited on March 7, 2004, 1:41 am Edited on March 7, 2004, 1:43 am Edited on March 7, 2004, 1:44 am Edited on March 7, 2004, 1:50 am',NULL,1);
INSERT INTO comment VALUES (12485,1565,5384,'Larry','Calculus solution','2004-03-07 01:49:03',3,' You do need calculus to get the maximum or minimum. Figured out d as a function of time I just filled 2 sheets of paper with formulae for d, d\', and d\" I came up with a time of about 2:23 and a distance of 4.551 I started with theta_M(t)=pi/2 - 2pi t and theta_H(t)=pi/2 - (pi/6)t where t is in hours d(t)=sqrt[25 - 24cos{(11/6)pi t}] d\'(t)= [22 sin{(11/6)pi t}] / d(t) d\"(t) was very tedious but setting it to zero eventually led to a quadratic expression in cos(x) where x= (11/6)pi t (2pi - 1) (cos(x))^2 - (25 pi/12) cos(x) + 1 =0 solving this gives cos(x)= {0.1785, 1.0603} but the cosine can\'t be greater than 1, so only 0.1785 can be valid. then x= 1.3913 radians; t=(6x)/(11 pi)=2.384 hours unless of course I made a math error. And that\'s my story The answer is x + 1 years This can be proved by induction Let\' s say we start with x = 1, then it will last for 1 year 1 | 1 1 0 2|0 for x= 2 we will have 1| 2 1 2 2|2 0 0 4|0 Similarly for x we will have x + 1 Regards JK When I posted this reply, this was a puzzle with XX as the subject, and everything else blank. Is this like a Zen Buddhist koan ? Edited on March 7, 2004, 12:37 pm',NULL,1);
INSERT INTO comment VALUES (12492,1575,4507,'Penny','Possible solutions','2004-03-07 12:52:57',3,' [This reply was posted at a time when this puzzle consisted only of the heading XX]. (1) The sound of one hand clapping ? (2) The complete list of reasons to re-elect Bush in November ? (3) A photo of the interior of the Cleveland Browns SuperBowl Trophy display ? Edited on March 7, 2004, 12:53 pm',NULL,1);
INSERT INTO comment VALUES (12493,1575,5285,'Ady TZIDON','possible solutions','2004-03-07 13:09:48',3,'1.What men know about women\r\n2. A PERFECT statement -no errors.\r\n3. A full list of non-personal parameters affecting politician\'s decision\r\n\r\nhave fun!!\r\nady',NULL,0);
INSERT INTO comment VALUES (12494,685,1301,'Charlie','re(2): The official solution is entirely mistaken','2004-03-07 15:42:33',0,'I think Penny was pointing out that it is Occam\'s Razor that prefers the spinning earth to the Sun going around the earth. It is General relativity (with Mach\'s principle) that says each is equally good, or at least equivalent.',12487,1);
INSERT INTO comment VALUES (12495,1575,5885,'George','Smells like badly written JavaScript','2004-03-07 15:53:31',0,'Is this the solution?',NULL,0);
INSERT INTO comment VALUES (12496,1575,5384,'Larry','Logic or Biology?','2004-03-07 15:56:30',1,' Chromosome pattern of a female: XX Or perhaps the average ability of females to think logically as opposed to emotionally. Edited on March 7, 2004, 5:23 pm',12500,1);
INSERT INTO comment VALUES (12502,1575,5352,'Juggler','The Perfect Solution','2004-03-07 17:30:17',3,' Edited on March 7, 2004, 5:33 pm',NULL,1);
INSERT INTO comment VALUES (12503,1575,3172,'SilverKnight','re(2): I\'m probably lost, but...','2004-03-07 17:41:20',0,'\r\nI\'m onto something; it\'s hard to see, but it has to do with serendipity. Edited on March 8, 2004, 8:12 am',12501,1);
INSERT INTO comment VALUES (12504,1575,5352,'Juggler','Another better solution','2004-03-07 17:44:05',3,' I\'m onto something; it\'s hard to see, but it has to do with a Juggling Gypsy. Nice One DJ, did you just cut and paste this puzzle off the Internet ? :-) By the way, it is possible that the same thing happened to the text defining this problem that happened to the WMD. Yes, the text MAY have been deleted, but it could have been hidden inside another file, or transferred from this website to another website. Or hidden somewhere on the hard drive. I once lost a file for several months and eventually found it inside a stock portfolio folder dealing with the S&P 500 stock SPDR (ie it was inside a spider hole). By the way, WMD are still around somewhere, we just haven’t found them yet.<o:p></o:p> <o:p> </o:p> Edited on March 7, 2004, 8:27 pm',NULL,1);
INSERT INTO comment VALUES (12514,1575,4507,'Penny','I think I have the solution','2004-03-07 20:37:32',3,' DJ posted this as an eloquent protest against the shameful Martha Stewart guilty verdict. The problem is presented exactly as it is intended to be (I had said that I would post a comment to that effect when the problem was made live, but another scholar pushed the problem before I had the chance). There are no errors in display, javascript, or (presumably) with your vision. Four people have solved the problem already; maybe the rest of you would be able to if you tried, instead of pretending to be clever. Notes: Problems submitted by scholars have to wait in queue and go through voting, just like those by anyone else. This is an original problem (no copy-and-paste for me). As far as I know, I am mentally sound. Martha Stewart got what she deserved. Edited on March 8, 2004, 4:38 am',NULL,1);
INSERT INTO comment VALUES (12518,1575,1183,'fwaff','I\'m not lost, I\'m number five','2004-03-08 04:27:40',3,'I\'m onto something; it\'s hard to see, but it has to do with fearing me',NULL,1);
INSERT INTO comment VALUES (12519,1666,4507,'Penny','Yes it does, Deb','2004-03-08 06:00:16',0,':-)',NULL,1);
INSERT INTO comment VALUES (12520,1575,5352,'Juggler','re: Full solution (No joke this time)','2004-03-08 06:41:56',1,'So close but You\'re not quite there',12517,1);
INSERT INTO comment VALUES (12521,1575,4830,'Jils','re: Full solution (No joke this time)','2004-03-08 06:56:52',1,' They also all said \"1\'m onto something\" I\'m going to have a guess at 71 and 92. The gaps seem to be getting bigger (the sum of the 3rd and 4th preceding gaps +1). I don\'t think this can be right though as I can\'t see how the series gets going in the first place..... DuCk: \"I\'m onto something; it\'s hard to see, but it has to do with.....blah blah blah\" Would you please let me in on the joke ? All I can see is a subject line that reads XX and everything else blank. That phrase is not found on the Internet. Is this a browser issue -- can other people see something that I can\'t ? This is really getting silly. [comment deleted by poster] Edited on March 8, 2004, 4:06 pm',NULL,1);
INSERT INTO comment VALUES (12547,1307,5898,'paul','No Subject','2004-03-08 20:03:40',0,'>`_`<',NULL,1);
INSERT INTO comment VALUES (12548,1422,5898,'paul','No Subject','2004-03-08 20:13:32',0,'ko-ni-chi-wa',NULL,1);
INSERT INTO comment VALUES (12549,1297,5898,'paul','No Subject','2004-03-08 20:17:08',0,'1+9+9+9=28',NULL,1);
INSERT INTO comment VALUES (12550,1666,5952,'Sunwoo Lee','the answer?','2004-03-08 20:28:45',0,' wouldn\'t the answer be that B was the killer, and A helped? -_-;; When I copy/paste this, that lame phrase \"I\'m onto something, it\'s hard to see...\" suddenly appears. What a crock. Can I change the rating I gave this one from 5 to 0 ? Edited on March 8, 2004, 10:46 pm',NULL,1);
INSERT INTO comment VALUES (12553,1575,5384,'Larry','I thought of this earlier','2004-03-09 00:11:11',0,'<CENTER class=content> <FORM> \r\n <INPUT onblur=checkentry(this); style=\"BORDER-TOP-STYLE: none; BORDER-RIGHT-STYLE: none; BORDER-LEFT-STYLE: none; BACKGROUND-COLOR: transparent; BORDER-BOTTOM-STYLE: none\" size=2 name=entry> <INPUT style=\"WIDTH: 359px; HEIGHT: 31px\" type=hidden size=44 value=\"I\'m onto something; it\'s hard to see, but it has to do with _____...\" name=copytext> I thought of a hidden message earlier, but when I cut and pasted into either Word or Notepad, nothing showed up. When pasting into perplexus then it does show up. hmmm right idea, wrong word processor. Edited on March 9, 2004, 12:12 am Edited on March 9, 2004, 12:12 am Edited on March 9, 2004, 12:14 am',NULL,1);
INSERT INTO comment VALUES (12554,1533,5352,'Juggler','The Sliding Rooks. ver1.2','2004-03-09 04:47:48',4,' Ok so that was easy What about the smallest number of moves when it is not possible to move the same piece on consecutive turns? Is it also possible to do this in 10 moves? Edited on March 9, 2004, 5:03 am',NULL,1);
INSERT INTO comment VALUES (12555,1575,1686,'DuCk','re: Oh brother (+hint)','2004-03-09 07:43:27',0,'Penny, I\'ll help you out, but I just don\'t wanna post the process of solving it yet. The only hint I can give w/o blowing the puzzle is \"in a purely SUBJECTive manner use the tab button.\" I hope that\'s not too much or too little.',12552,1);
INSERT INTO comment VALUES (12556,1575,4507,'Penny','re(2): Oh brother (+hint)','2004-03-09 07:53:21',0,' Thanks, dude, but I had already figured that much out all by myself. \"I\'m onto something, it\'s hard to see, but it has to do with ____\" Fill in the blank. Controlled substances ? \"I\'m onto something, it\'s hard to see, but it has to do with controlled substances.\" Just kidding....lol ....she knew all about the Archimedes Principle. She took one of the ice cubes, put it in the ungraduated glass pitcher, and measured the amount of fluid that was displaced. (We must assume that she could perform this measurement, since the puzzle states that \"To make matters worse I had not paid attention to how full I had made the trays so we couldn\'t just refill them and see how much they held.\") Archimedes Principle: The principle that states that a body immersed in a fluid is buoyed up by a force equal to the weight of the displaced fluid. The principle applies to both floating and submerged bodies and to all fluids, i.e., liquids and gases. It explains not only the buoyancy of ships and other vessels in water but also the rise of a balloon in the air and the apparent loss of weight of objects underwater. In determining whether a given body will float in a given fluid, both weight and volume must be considered; that is, the relative density, or weight per unit of volume, of the body compared to the fluid determines the buoyant force. If the body is less dense than the fluid, it will float or, in the case of a balloon, it will rise. If the body is denser than the fluid, it will sink. Relative density also determines the proportion of a floating body that will be submerged in a fluid. If the body is two thirds as dense as the fluid, then two thirds of its volume will be submerged, displacing in the process a volume of fluid whose weight is equal to the entire weight of the body. In the case of a submerged body, the apparent weight of the body is equal to its weight in air less the weight of an equal volume of fluid. The fluid most often encountered in applications of Archimedes\' principle is water, and the specific gravity of a substance is a convenient measure of its relative density compared to water. In calculating the buoyant force on a body, however, one must also take into account the shape and position of the body. A steel rowboat placed on end into the water will sink because the density of steel is much greater than that of water. However, in its normal, keel-down position, the effective volume of the boat includes all the air inside it, so that its average density is then less than that of water, and as a result it will float. Edited on March 9, 2004, 8:51 am',NULL,1);
INSERT INTO comment VALUES (12559,1575,2561,'Aaron','p\'raps','2004-03-09 10:12:41',3,' I\'m onto something; it\'s hard to see, but it has to do with alimony... nifty :) first she marked how full the pitcher was. when she knew the level of the tea she filled the measuring cup with four cups of tea. she then added ice cube to the pitcher untill the tea reached the level it was at befor she removed the tea. she then added the tea back in. Penny, Captain Paradox and some others (I think), you\'re close, but not quite there. Does anyone remember the Scavenger Hunt that was (is?) on this site? I had just been thinking about that before I saw this puzzle, and so quickly guessed at a way of discovering the solution. The line you guys are quoting is most of the answer, but that blank can\'t be filled with just anything... Joshua Quintana: \"she then added ice cube to the pitcher untill the tea reached the level it was at befor she removed the tea\" You are assuming that the ice cubes will cause the tea to reach that level exactly. That is a pretty sound assumption, since she did find ice cubes equal to 4 cups of water. I\'d say your solution is the correct one. Edited on March 9, 2004, 12:01 pm Edited on March 9, 2004, 12:19 pm',12561,1);
INSERT INTO comment VALUES (12564,1675,4507,'Penny','All the solutions so far...','2004-03-09 13:00:27',0,' ...are more or less variations on the Principle of Archimedes. Did anybody run through the streets naked, shouting \"Eureka !!\", like old Archimedes did when he discovered it ? Edited on March 9, 2004, 1:04 pm',NULL,1);
INSERT INTO comment VALUES (12565,587,5963,'Vincent','A solution','2004-03-09 13:30:09',0,'Pour half of a full barrel into an empty barrel. That gives you 6 Full\r\nBarrels, 9 Half-Full Barrels, and 6 Empty Barrels. 2 Full Barrels per\r\nson, 3 Half-Full barrels per son, and 2 Empty Barrels per son. Each son\r\ngets an equal amount of Full, Half-Full, and Empty barrels.\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12566,1498,5963,'Vincent','A solution','2004-03-09 13:39:52',0,'I\'m assuming on this that the one problem that comes in per Sunday has\r\nalready come in. So she has 1/(20^5) chance of reading a different\r\nproblem each time she clicks on \"Random Problem\". I\'m also assuming\r\nthat she reads the new problems each day AFTER the two new problems\r\nhave come in each day. Which means the next day (Monday) she will have\r\n1/(20^5)*1/(22^5) chance of reading a new problem each time she clicks\r\non \"Random Problem\". This will go progressive each day ending up in an\r\nequation something like this,\r\n1/(20^5)*1/(22^5)*1/(24^5)*1/(26^5)*1/(28^5)*1/(30^5)*1/(31^5)*1/(32^5)\r\nchance of reading all the different problems by the next Sunday evening.\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12567,1533,5964,'Jay','I think this should do it','2004-03-09 14:08:07',0,'E5-E2\r\nA1-A4\r\nA5-E5\r\nE5-E3\r\nE1-A1\r\nA1-A3\r\nA3-D3\r\nE2-A2\r\nA2-A3\r\nA3-C3\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (12568,1592,5963,'Vincent','A solution','2004-03-09 14:15:17',0,'(1/6)*6 is the minimum number of rolls that can be made if you get a\r\ndifferent roll each time. If you don\'t get all six numbers on the\r\ninital six rolls you keep rolling up till infinity because there is no\r\nguarantee that you will get all six numbers on a fair 6-sided die. The\r\nequation for larger rolls will be (1/6)*(6+i) i being a varible that\r\nwill be incremented by one each roll after the sixth roll.\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12569,1575,5965,'ozz','solution','2004-03-09 14:45:03',0,'I\'m onto something; it\'s hard to see, but it has to do with sea...',NULL,0);
INSERT INTO comment VALUES (12570,1670,5964,'Jay','If not base 12 then perhaps','2004-03-09 14:45:35',0,'Are these the two missing numbers 73 and 94',NULL,0);
INSERT INTO comment VALUES (12571,1666,4670,'e.g.','re: solution','2004-03-09 14:48:09',1,'When someone says \"If XXX then YYY\", and XXX is false, it doesn\'t\r\nfollow that YYY is also false. Your argument \"C says if b was the\r\nkiller D had nothing to do with it but B is innocent so D had something\r\nto do with it\" isn\'t correct.\r\n\r\n',12551,1);
INSERT INTO comment VALUES (12572,1575,5965,'serious','re: solution','2004-03-09 14:48:36',0,'I\'m onto something; it\'s hard to see, but it has to do with sea...',12569,0);
INSERT INTO comment VALUES (12573,1680,3992,'Jane Doe','an unimaginative solution - but an honest one!','2004-03-09 15:18:18',0,' It is somewhat difficult to construct a \'magic square\' without using prime numbers between 1 and 9. The next smallest magic quare you can construct looks like this: 1669 199 1249 619 1039 1459 829 1879 409 You can construct this square using consecutive prime numbers which form the smallest possible magic constant - a magic constant is where the numbers along any line will sum up in a magic square (and I got that textbook definition from my math textbook). I cannot show the formula because I am not tech-savvy enough to format it so that it will appear correctly on the screen! e.g. is correct. \"If I won the lottery last week, I have a lot of money today\" is a true statement. But \"I won the lottery last week\" can be false, and \"I have a lot of money today\" can still be true. But if you replace \"if\" with \"if and only if\", then the falseness of the antecedent does imply the falseness of the consequent. If I were bitten by a rabid dog, I would say \"I will survive if and only if I get the rabies vaccine\". Then if I don\'t get the rabies vaccine [the antecedent is false], I will not survive [the consequent is false]. I heard this claim in the early 70\'s, supposedly a kid in Africa had discovered it. But I never heard an explanation. Here is my set of conditions: I\'m onto something; it\'s hard to see, but it has to do with those disgusting and revolting (yet strangely loveable) mariachi rodents playing their guts out on the new Quizno\'s commercials. Edited on March 9, 2004, 6:17 pm',NULL,1);
INSERT INTO comment VALUES (12580,1575,4507,'Penny','re: No Subject','2004-03-09 18:19:22',0,' The real \"brain teaser\" is: Why is anyone taking this puzzle seriously ? >The real \"brain teaser\" is: Why is anyone taking this puzzle seriously ? Well, to start with, not everyone has gotten it. Of the last three answers (Ozz\'s, Serious\' and Banjamin\'s), only one was correct. The other two were trying to answer using other people\'s answers as a guide. Plus, you seem to take it seriously - you keep coming back here to write more! ;) I\'m with you, Penny... This problem was by far my favorite and the ensuing thread that resulted in the apparent lack of a problem just had this one destined for glory. I must confess that I was equally disappointed when I \"found out\" what I initially just glanced over. But, on the whole, it\'s still been great fun to read everyone else\'s responses. 2 is out of the question, because it would make some, but not all of the sums even. I decided that there would have to be at least 4 pairs of primes that add up to the same number so these pairs could be on opposite sides. I found by brute force what numbers would have many pairs of primes that could sum up to it. After trying it, I eventually came to 90, which has a whopping 10 pairs of primes that will sum to it. That doesn\'t mean that 90 is the sum for each row, just the sum for of opposite outer primes. So anyway, expect another comment from me with a solution. Edited on March 9, 2004, 7:18 pm',NULL,1);
INSERT INTO comment VALUES (12586,1680,3558,'Tristan','re: lower square - failure','2004-03-09 19:32:03',1,' Hmph. I was brute forcing this using pairs summing up to 90. After a few failed tries, I thought of a proof of the lack of possibilities there. Take the two opposite columns. Their total sum must be 270, because of the three pairs it includes. Therefore, each row and column must add to 135. Then, the middle number must be 45, which isn\'t a prime. Similarly, the sum of opposite numbers can\'t be any multiple of ten. Pushing this further, if the sum of opposite numbers is x, then the sum of each column must be 1.5 * x, and the middle number .5 x. Therefore, the sum of opposite sides must be double of a prime, and the sum of each row triple of a prime. I hope this helps others if they happen to be searching the same way I am. Were you disappointed? You shouldn\'t be, if you really solved the puzzle. I\'ll say that to people who have actually solved this, it is very obvious who solved it and who just looked at other comments or copied/pasted. Some people don\'t seem to know that they haven\'t really solved this one, but if you do solve it, you\'ll know. You don\'t even have to know what a source code is to solve this. to give a form let our magic square look like this: (x-a) (x+d) (x+c) (x+b) ( x ) (x-b) (x-c) (x-d) (x+a) Without loss of generality, all variables in this case can be considered positive. comparing sums of opposite columns teaches us that b=a+c comparing sums of top and bottom rows teaches a=c+d and likewise b=2c+d I fail to understand your solution. \"first she marked how full the pitcher was.\" The pitcher is empty. The tea is in the Pyrex measuring cup. \"she then added ice cube to the pitcher untill the tea reached the level it was at befor she removed the tea.\" The level of the tea doesn\'t change if it\'s in the Pyrex while you\'re adding ice cubes to the pitcher. The tea can\'t reach the \"level it was at befor\" if it isn\'t even in the same container. ....by midnight I will have a Visual Basic console application that will accept a number N, then compute the first N primes (using the Sieve of Eratosthenes), then find all the 3X3 magic squares among them. btw...\"composed of 9 prime numbers (not the numbers from 1-9)\"...didn\'t you mean to say \"2-7\" ? It goes without saying that 1 and 9 can\'t be in the solution. \r\n \r\n \r\n \r\n \r\n Edited on March 10, 2004, 8:11 am',NULL,1);
INSERT INTO comment VALUES (12598,1698,4670,'e.g.','Solution','2004-03-10 08:41:47',3,'It\'s impossible -- you\'d have to travel at infinite speed.\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12599,1698,4670,'e.g.','An explanation','2004-03-10 08:46:24',2,'Going from A to B at 15 mph takes 80 minutes. Every magic square can be written as: For all the entries to be prime, a cannot be a mult of 2 or 3 and b and c both must be mult of 6. If we allow 1 in our prime magic square; a=1, b=6, c=30 yields: I didn\'t know any formula but looking at the square: A B C D E F G H I and using A+B=G+E=F+I, B+E=G+I etc got to C-E=E-G etc and came up with the fact that all the lines must be in arithmetic series\'s. (eg, ABC is in sequence, so is GEC etc). This seems to be true of the example solutions given. Also then the total of each line had to be 3 times the middle number. I would be interested to know how/if this relates to Brian\'s answer. Since 1442897 is just over 1,000,000, the cube root must be slightly over 100. If it was 110, its cube would be 1331000, still too small by a little. Since we want the last digit cubed to end in 7, the last number must be 3, making the answer 113 This has to be worth another go: Half the tea is emptied from the measuring jug into the empty pitcher and icecubes are added to the measuring jug one by one slowly so they melt and the jug is again full (this is how the grits got burned - the ice had to melt). All the contents are then tipped into the pitcher and the same number of icecubes again are added and stirred. I don\'t see the Eureka factor here (sorry Penny) - as if it were a quick solution (and Mrs Boy is no fool) the grits would have been fine. Unfortunately, speeds do not average linearly over distance. Traveling distances D1 and D2 at speeds R1 and R2, takes times T1=D1/R1 and T2=D2/R2, resp. The average speed is thus (D1+D2)/(T1+T2)= 1/(W1/R1+W2/R2) where W1=D1/(D1+D2) and W2=D2/(D1+D2). For this problem W1=W2=1/2 so the average speed is 1/(1/2R1+1/2R2) which is known as the \"harmonic mean\" of R1 and R2 -- it is the reciprocal of the ordinary mean of the reciprocals. Thus with R1=15 and R2=45, the average speed would be 1/(1/30+1/90)=1/(4/90)=22.5. It is clear that 1/(1/2R1+1/2R2) < 1/(1/2R1)=2R1 -- to get the average speed to equal 2R1 would require R2=\"infinity.\" Edited on March 12, 2004, 4:30 pm',12611,1);
INSERT INTO comment VALUES (12613,263,5759,'Pieater','No Subject','2004-03-11 09:02:44',0,'The reason is obvious,but I believe that the tortise has super-turtle power and can use his jet pack to fly faster than Achilles could run. Otherwise the points would never be the same because achilles would overtake the turtle and they would move at different speeds.',NULL,1);
INSERT INTO comment VALUES (12614,1532,1171,'nikki','re: Quick question:','2004-03-11 09:09:04',0,' \"When you are taking away the 1/8 area of each square face, do you mean from the original cube regardless of what has been taken away, or do you mean 1/8 of the area of the remaining face? I hope this question makes sense.\" I see what you mean, but I don\'t think that is what the problem is asking. I think (but I\'m not 100%) that it would matter what order you chopped off the corners, so you would get different answers. Also, Gamer says \"this truncation of a vertex takes away 1/8 of the ORIGINAL AREA from each of 3 square faces.\" Hope this helps. Later! Let’s call the length of one edge of the cube x (x > 0). So the volume of the full cube is x^3 and the area of one full face is x^2. Intuitively I know that in order to truncate the corner of a cube and create an equilateral triangle, you must remove the same distance along each of the 3 edges. As a proof, I guess I could say, lets call the distances removed along each edge a, b, and c (a,b,c > 0). So the 3 edges of the new equilateral triangle are: Sqrt(a^2 + b^2) Sqrt(a^2 + c^2) Sqrt(b^2 + c^2) Since this is an equilateral triangle, Sqrt(a^2 + b^2) = Sqrt(a^2 + c^2) a^2 + b^2 = a^2 + c^2 b^2 = c^2 since a,b,c > 0 b = c Similarly we can also find that a = b or a = c, leading us to a = b = c. Moving on, let’s find out what that distance is. Truncating a corner removes an area of (a^2)/2 from the area of the face (x^2). So (a^2)/2 = 1/8 * (x^2) 4 * a^2 = x^2 2 * a = x a = x/2 This makes sense, because you can picture a square being made up of 8 right triangles (divide the square in half horizontally, then vertically, and then cut each of those 4 quadrants in half diagonally). Now we have to calculate the volume of the removed corner as a function of a. The formula for the volume of a pyramid is 1/3*base*height. Well, since all the faces of the pyramid are triangles, I can call the \"base\" one of the right triangle sides, making the height = a. So… V = 1/3*(1/2*a^2)*a = 1/6*a^3 = 1/6*(1/2*x)^3 = 1/6*1/8*x^3 Since we remove 8 corners, the total volume removed from the original cube is 8*V = 8*1/6*1/8*x^3 = 1/6*x^3. So the volume of the new solid is x^3 – 1/6*x^3 = 5/6*x^3. So the new volume would be 5/6 the original volume. Later! You will give me either one or more digits. If you give me two, I\'ll add them together. If the new number is greater 9, I\'ll repeat the addition until I get a number less than or equal to nine. If it is nine, the missing digit is nine; otherwise, I will then subtract this number from nine. That is the missing digit. It works on the same basis as the old \"casting out nines\" method of checking long sums. Adding the digits of a number produces another number with the same remainder when divided by 9. Repeating the addition eventually results in a single digit which is that remainder. Because of this rule, and the commutative property of addition, Two numbers with the same digits, albeit in a different order, leave the same remainder when divided by nine. Therefore, their difference is divisible by nine -- which means that the digits eventually add up to nine. It was necessary to specify that the missing digit be non-zero because there is no way to distinguish a missing zero from a missing nine. Each digit: a(10^n) = a +9a(10^[n-1])+9a(10^[n-2])+...+9a(10^1)+9a(10^0) Entire number:A= Σa(10^a)=Σa+Σ(9aÓ10^n) Therefore A-Σa is divisible by 9 => A and Σa leave the same remainder when divided by nine. Examples: 123 = 100(1)+10(2)+3=99(1)+1+9(2)+2+3 = 1+2+3+99(1)+9(2)=(1+2+3)+9(1+11[2]) 4567 = 1000(4)+100(5)+10(6)+7 = 4+4(999)+5+5(99)+6+6(9)+7 = 4+5+6+7+4(999)+5(99)+6(9) = (4+5+6+7)+9[4(111)+5(11)+6) Edited on March 11, 2004, 11:36 am',NULL,1);
INSERT INTO comment VALUES (12618,1668,5352,'Juggler','Another way of looking at it.','2004-03-11 11:40:17',3,' I have a solution that can work, but another item is required, A second smaller chest to house 3 keys. there will only be one lock on the smaller chest and three keys will be distributed to 3 of the 5 people. inside the chest there is another set of 3 keys, one for each lock that needs to be on the chest. the locks on the main chest are distributed such that one person can reach only one lock at a time and the lock is not a standard padlock, it is the type that once the key is removed or even let go of, the lock will close itself, in the UK we call these Yale locks, as a result of this 3 people need to operate the locks simultaneously. therefore 4 locks are required and 6 keys. Edited on March 11, 2004, 11:42 am',NULL,1);
INSERT INTO comment VALUES (12619,568,5852,'Coda','Answer is Wrong! (My oppinion)','2004-03-11 13:09:38',0,' The posted answer is wrong! When it says ...how could you remove the coin without taking the cork out or breaking the bottle? It means without taking the cork out of the bottle neck. The situation was simulated by DEFDBL A-Z for 200,000 trials, producing 2 23 .50595 so apparently, likelihood of 7 or more repetitions of a birthday requires more than the 600 allowed for. But with this information we have enough to check out answers that we get from more theoretic analysis, and then use that theoretic analysis to determine what size array to allow for. The probability that one given birthday will appear exactly r times among n people is p(n,r) = C(n,r)*(1/365)^r*(364/365)^(n-r). Then the probability that it appears at least r times among n people is P(n,r) = 1 - p(n,0) - p(n,1) - ... - p(n,r-1). (That\'s a capital P defined in terms of small p, in case the fonts don\'t make that clear.) The difficulty is then finding the probability that any birthday occurs at least r times among n people. If the events were mutually exclusive, we could add the probabilities (that is just multiply the probability for a given birthday by 365). But they are not mutually exclusive--more than one date might occur r or more times. To allow for this, we could use inclusion/exclusion to subtract out the pairwise ANDed conditions (of two birthdays both being represented), as each had been counted though only one represented a new \"success\". Defining now P(m,n,r) as the event of m different dates each having at least r occurrences among n people, with P(1,n,r) being just the previously defined P(n,r), the overall sought probability is C(365,1)*P(1,n,r) - C(365,2)*P(2,n,r) + C(365,3)*P(3,n,r) - C(365,4)*P(4,n,r) + ... , where the first term is the oversimplified (exclusivity-assumed) 365*P(n,r). The problem is that these pairwise (and higher multiple-wise) probabilities are hard to calculate. However, we can make an approximation by assuming that they are independent (though they are also not actually independent). For example, the probability that January 1 is present among a group of 50 people is 1-(364/365)^50 = 0.1281817426688633092, as is the probability that January 2 is present. The probability that both are present is 0.0161437857620377809. If we assumed their presences were independent, we\'d have multiplied the individual probabilities (i.e., squared the probability of one), and used 0.0164305591536266927, which is not very different, but is indeed different. The exact calculation was possible for this any-occurrence case, but becomes more difficult for multiple-occurrence cases. The following program calculates the probabilities as an approximation by treating the compound conditions as independent and carrying the inclusion/exclusion to the possibility of 5 different dates meeting the criteria: 5 point 10 and it finds 2 24 0.516892911505135457193064552705280701875673521049 so the original simulation program was expanded to up to 2000 people per trial, with the following results: 2 23 .50643 and our approximation calculations agree well with our simulation results. We had already known the 23 for the case of 2 occurrences. Three occurrences looks like 87 or 88, ... twelve occurrences require something like 1596-1599. The approximation calculation went beyond the original scope and calculated for thirteen occurrences also. Edited on March 11, 2004, 2:12 pm',NULL,1);
INSERT INTO comment VALUES (12621,1680,5777,'Thalamus','re(2): If all goes well today.....','2004-03-11 14:44:17',4,'Penny, Smallest prime 3x3 magic square with \'5\' Smallest magic square with \'7\' Smallest magic square without any 1-9 A very interesting pair of magic squares: If we make the assumption that 1442897 has an integral cube root, we can conclude it must be 113. From the information given, we can deduce that the answer must be between 110 and 120 since 110 cubed must be 1331000 and 120 cubed is 1728000. The only digit which cubed results in a final digit of 7 is 3, hence 113. With the conditions as stated in the problem, the amount of remaining singles after all the ten dollar bills have been picked up is 6. An equation to solve the problem is x^2 = 10a + b, with the added condition that a is an odd number since the first brother gets an additional ten dollar bill. Running through the first ten squares, we find that only 2^2 = 16, and 4^2 = 36 display an odd number in the tens position. We know that checking the first ten squares is sufficient for if we add ten to any of the solutions so far: (x+10)^2 = x^2 + 20x + 100= 100+20x + 10a + b which again exhibits the same behavior in the tens and singles digits. I found the first two by hand using the matrix equation from my first post. The other three were found using a computer program searching all primes up to 300. I got lucky when I found the twin prime squares. Extending the algorithm found 159 prime magic squares with all entries less than 1000. If the number 1 is included, there are four more. After modifying the algorithm slightly, I found that there were 15,858 solutions with all entries less than 10,000. There are 41 more solutions when 1 is included. The program I used is below. It is written for UBASIC 8.74. P is the largest prime in a solution, and B and C are solution parameters: 10 Start=37 Mr. Boy took the tea and poured it into the ungraduated glass pitcher of unknown volume, and put the ice in the heated 4 cup graduated pyrex measuring cup, the ice melted, they used the measuring cups to measure the ice, and poured them into the glass pitcher with the tea. Im pretty sure thats the answer. Instead of looking for stubs on the streets, Charlie should try to find a decent job if he wants to pay for his cigars. After \'assembling\' and smoking 5 cigars with his 25 stubs, he would have 5 new stubs he would not have to search on the streets and could produce a 6th cigar. So, he could smoke 6 cigars and would have 1 stub left. But in fact, if the stub represents 20% of the cigar, we could consider that he smokes only 0.8 of the cigar each time, so he would have smoked 4.8 complete cigars and would have 1 stub left... With 20 stubs he would have smoked 4 cigars and would remain with 4 stubs left, that is not good enough for makind a full cigar. If he is not willing to wait for the full cigar, we could consider that he would make a 0.8 cigar and would smoke that till he have 1 stub left (so he would have smoked 4.8 cigars, or 3.84 cigars with the 80% consideration)... Charlie: go work!!! First, contrary to the above report, I do not smoke; it\'s a disgusting and vile habit. However, back to the problem at hand: The first question has already been answered. The second question has more interpretive possibilities. Apparently a cigar is 4/5 usable, with a 1/5 unusable stub. So, being left with 4 stubs, after having smoked 4 cigars, Cheap can make a cigar of 3/5 usable tobacco and 1/5 unusable stub. As this cigar is only 3/5 usable instead of the usual 4/5, it could in some sense be counted as 3/4 of a cigar, as we are counting the use of 4/5 of a cigar as having smoked the cigar: so he smokes 4 and 3/4 cigars, in that sense. Toggler is similar to Lights Out, and \"Chasing the Lights\", a technique mentioned in the solutions, produces, for the 4x4 case an immediate solution in 10 moves--not as good as the 4 moves that is possible. A brute force search by computer program finds: 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 where a 1 indicates to toggle that switch and 0 indicates to leave that one alone. There are various rotations/reflections present, but two, reflections of each other, have the minimum 4. 0 0 0 1 1 A brute force search for 4x4 Triggler does not find any solution. The program is as follows: DECLARE SUB vary (r%, c%) PRINT \"--------\" END SUB vary (r, c) checkIt: END SUB It is based on the fact that three times triggering a cell returns that cell and its neighbors to their original positions, so there are only three possibilities for any given cell: do not trigger, trigger once or trigger twice. The brute force program for Toggler is similar except it has only two states per cell, and can be found in the discussion of Lights Out. The difference will be a multiple of 9; not necessarily a multiple of 99. Neither is the sum of the digits in a multiple of 99 always 18; but similarly, the sum of digits in a multiple of 99 is a multiple of 9. and if the pole has width W, 2*[sqrt(2) - W] I\'m picturing the pole at a 45 degree angle with its midpoint touching the corner and its ends touching the outer walls jammed in place. But by symmetry, if it could jam into that position then it can keep going and jam out of that postion as it completes the turn. But I think I scratched the paint. I think you knew you were in trouble when you said you could probably jam it into place. Picture the pole already in place at 45 degrees, touching both walls. To get out of there the far end would have to turn inwards towards the center of the hall, which means that the near end would have to turn outwards away from the center (remembering that the pivot is right in the center of the pole). Since the pole is already up against the wall, it can\'t do this. And, like you said (but the other way round), if it can\'t get out of that position, it couldn\'t have gotten into that position. As for the real answer. Well, I\'ll leave that to someone with more time on their hands... Consider a line of length L that touches both outer sides of the corridor, and the inner corner. Let the line extend beyond the inner corner by x units on one side, and y on the other. Then, by similar triangles, y = 1/x. By Pythagoras, L² = (1 + x)² + (1 + 1/x)² = z² + 2z = (z + 1)² - 1, where z = x + 1/x. By the Arithmetic Mean-Geometric Mean inequality, the minimum value of z = x + 1/x is 2, when x = 1. (Or consider (sqrt(x) - 1/sqrt(x))² >= 0.) Since (z + 1)² - 1 is an increasing function for z >= -1, the minimum value of L² occurs when z = 2. Hence the minimum of L² = 8, and of L = 2×sqrt(2). This is the shortest line; hence the longest pole. There are five colors of shirts in $10 increments, with the most expensive costing $50, meaning that they cost 10, 20, 30, 40 and 50 dollars in some order. Since each girl bought two different shirts, possible totals are: We know that Diane spent $80 on thirty- and fifty-dollar shirts, and Emily did not buy any shirts of the same colors as she did [3]. Thus, Emily either spent $10 and 40 or $20 and 40, and we know for sure that she did buy a forty-dollar shirt. Also, we are told that Carol bought the other forty dollar shirt [5]: Carol\'s blue shirt was not ten dollars [2]; it must have been forty dollars. The ten-dollar shirt was not green [2], orange [4], or red [5]; it must have been yellow: That the length 2 * sqrt (2) is just long enough to not be a possible solution... You can\'t \"Austin Powers\" the pole if the given length restricts any movement whatsoever. Theoretically, the length of this hypothetical pole should be just shy (infinitesimally smaller) than 2 * sqrt (2). Here I have a quick question: are we assuming the width of this pole to be nonexistent--that the pole is just a line? If not, this problem might be practically solved if we also include the smallest measurement we will allow for adjusting the pole back and forth (given a 5 cm diameter cylindrical pole, 1/2 cm rotation shouldn\'t be too far out of the question...) [Comment deleted by poster] Edited on March 14, 2004, 9:33 am Edited on March 14, 2004, 10:08 am',NULL,1);
INSERT INTO comment VALUES (12658,1681,6011,'jas','answer?','2004-03-14 10:51:47',0,'10 ft\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12659,1693,1301,'Charlie','thoughts','2004-03-14 12:16:18',1,' The first 10 multiples of 2^76 are with 2^76 itself being a 23-digit number. To produce a 76-digit number, 2^76 must be multiplied by a 53- or 54-digit number (between 13,234,889,800,848,442,797,942,539,073,119,405,657,052,993,774,414,062 and 132,348,898,008,484,427,979,425,390,731,194,056,570,529,937,744,140,625). The last digit can\'t be a 7, so it must be a 6. In order for the 76-digit number to start with only 6s and 7s, the multiple of 2^76 must start between 87... and 89... or between 100... and 102..., with the ellipses representing another 51 digits. This is based on the following table of multiples of 2^76, and allows for carries from lower order digits: 86 6497976280428631814045696 Now where to go from here is a question. The choices here are among 6 sets of starting digits. If we follow through each of these by trial division, at each stage there are more choices. This is unfortunate from the point of view of finding the correct sequence of choices, but the great variety does assure us there is likely a solution, as, when we get to the last 23 digits, they have to come out as consisting solely of 7\'s and 6\'s, and there are 2^23=8,388,608 such 23-digit numbers, out of 10^23 23-digit numbers altogether. If there are 6 possibilities each step of the way of trial divisions, they multiply to a 40-digit number by the time you\'ve chosen 52 digits for the multiplier. Edited on March 14, 2004, 2:35 pm',12659,1);
INSERT INTO comment VALUES (12661,1693,1301,'Charlie','more thoughts (actually solution--spoiler)','2004-03-14 13:48:25',3,' Working from the right, the problem is not quite as bad as working from the left, but at each stage in choosing a multiplier, you are presented with two choices of a digit. For example, here\'s one where the only choice of 6 was at the rightmost position; from there on only 1 was chosen to produce a 6 in the product: 916 69211003172937520251928576 where the left number is the multiple and the right is the product up to that point as we build the multiplier from right to left. Another set of choices looks like this: 66 4986819005910345345662976 but the resulting set of digits in the product is still the same. In fact the same set is produced by randomly choosing which of the two should be used at each step: 916 69211003172937520251928576 So what if we continue? At the end we get: 60323785355017521615381548200199638897190843742219575360695242527202826527017533487543311497704930616 which multiple of 2^76 is 4557936353285720092883266666766767776667766777666667776766677767667676666776766667777767666677766776777777777777666766667776 and if we take the last 76 digits of this, the result is indeed divisible by 2^76, and so is the answer: 6667776766677767667676666776766667777767666677766776777777777777666766667776 Edited on March 14, 2004, 1:49 pm Edited on March 14, 2004, 1:53 pm',NULL,1);
INSERT INTO comment VALUES (12662,1693,3735,'Nick Hobson','Answer','2004-03-14 13:48:27',3,' 6667776766677767667676666776766667777767666677766776777777777777666766667776 = 88247290723637794367680048552939376696792027490086866 × 276. In general, there exists a k-digit number, written exclusively with 7s and 6s, divisible by 2k. The proof is by induction. For k = 1, 6 is divisible by 21. Let nk be a k-digit number, written exclusively with 7s and 6s, divisible by 2k. If nk = 0 (mod 2k), then nk = 0 or 2k (mod 2k+1). Note that: So we can choose, respectively, nk+1 = 6×10k + nk or 7×10k + nk = 0 (mod 2k+1). Hence result. The induction gives an explicit means of constructing nk. Edited on March 14, 2004, 2:09 pm',NULL,1);
INSERT INTO comment VALUES (12663,1693,3558,'Tristan','maybe?','2004-03-14 13:51:27',1,' If you multiply by 7*576, you\'ll get 7*1076. If you add 276 * 3*575, you\'ll get 7.6*1076. If you add 276 * 4*574, you\'ll get 7.76*1076 If we continue in this fashion and find some kind of pattern, we may be able to find a solution. Edit: I\'ve realized since that 1076 is a 77 digit number Edited on March 14, 2004, 10:33 pm',NULL,1);
INSERT INTO comment VALUES (12664,1693,1301,'Charlie','calculations provided by ...','2004-03-14 13:59:50',0,' The random-choice method, carried out far enough for the solution, was found using: 10 D=2^76 Since Cheap Charlie really only needs to use 4/5 of each cigar for it to count as a \"full cigar\", we need only to divide 25/5 cigars by 4/5. This is 25/4, or 6.25 cigars. Similarly, he would smoke 20/5 cigars divided by 4/5 for the second case. This is exactly 5 cigars. The only way for this to really work out in real life though, as e.g. said, is if Cheap borrows stubs and gives them back. In the second case, Cheap would need to borrow a stub and make a cigar to smoke, then give back the stub left over. In the first case, Cheap would need to borrow four stubs, then smoke 1/5 of the cigar, or 1/4 of the amount he would normally get from each cigar. Then, Cheap would return the rest of the cigar. [x][x][x][x] [.][.][.][x] [.][.][.][.] [.][.][.][.] [.][.][.][.] Side + Top + Bottom Pi*(a+b)* sqrt[h^2 + (b-a)^2] + Pi*a^2 + Pi*b^2 The geometric explanation for the top and bottom is obvious. But for the truncated cone, we need the slant height, S, which is the hypoteneuse of a right triangle with sides (h) and (b-a). So a cylindar whose radius is the average of the top and bottom of the truncated cone; and whose height is the same as the slant height of the truncated cone should have the same side area. And that\'s my story. Edited on March 15, 2004, 11:53 am',NULL,1);
INSERT INTO comment VALUES (12672,1697,1171,'nikki','No Proof, though','2004-03-15 13:42:58',3,' Looks like the Fibonacci numbers, but I can\'t prove it. 1, 1, 2, 3, 5, 8, 13... Later! When Pascal\'s triangle is made in non-lopsided fashion, each number is the sum of the numbers directly above-and-left and above-and-right. In the lopsided manner presented, each number is the sum of the number directly above and the one above and to the left. Each number that is directly above is part of the preceding diagonal line. Each number that is above and to the left is part of the diagonal line before that. So no number is added in that is not part of one of the two preceding diagonal lines Also, every number on the diagonal before the current one has a number just below it and so is included in the current diagonal. Also every number in the diagonal before that has a number down and to the right of it and also is represented in the current diagonal. So every number on one of the two preceding diagonals is included in the current line. No number so included is included more than once. Therefore the sum of the numbers on the current diagonal equals the sum of the numbers on the preceding diagonal plus the sum of the numbers on the diagonal before that. This meets the definition of the Fibonacci sequence. Pascal\'s triangle may be written down in terms of the binomial coefficients (n,m) as (0,0) For m < 0 and m > n, (n,m) = 0. Now (n,0) + (n-1,1) + (n-2,2) + ... = (n-1,0) + (n-2,1) + (n-3,2) + ... + (n-1,-1) + (n-2,0) + (n-3,1) + ... because each term of the top line of this formula is the sum of the two terms that lie below it in the next two lines, according to the usual formula (n,m) = (n-1,m) + (n-1,m-1) used to form Pascal\'s triangle. For n=0 and 1, the totals are each 1. Hence the result is the Fibonacci numbers because the lines of the formula are three consecutive diagonal sums of the type being treated in this problem, related by the Fibonacci recurrence relation F(n) = F(n-1) + F(n-2). Edited on March 15, 2004, 7:23 pm',NULL,1);
INSERT INTO comment VALUES (12676,158,4323,'Benjamin J. Ladd','Yeah, I thought about that too, DJ...','2004-03-15 20:31:03',0,' But since the letters represent digits and not just integers, the already hard equation would be MUCH harder to solve. Here goes: A(10E+F)(10H+I) + D(10B+C)(10H+I) + G(10B+C)(10E+F) = (10B+C)(10E+F)(10H+I) Or... 100AEH + 10AEI + 10AFH + AFI + 100DBH + 10DBI + 10DCH + DCI + 100BGE + 10BGF + 10CEG + CFG = 1000BEH + 100BEI + 100BFH + 10BFI + 100CEH + 10CEI + 10CFH + CFI And that\'s just a nightmare. 1- surfing, acrylic 2- hang gliding, oil 3- motorcycle, wtercolor 4- windmill, tempera hmmm..... 5x5 triggler solution: Mrs B pours half the tea into the pitcher (graduated cup 2/4 full) and throws in ice cubes till liquid level is 3cups. Adds these cubes to pitcher and pours off (ice melted off cubes in hot tea) till cup again 2/4 full. Repeats four times. That sequence is too logical, and Dr. Levik would have realized it could be logically deduced. The sequence was probably an arbitrary one, like: So Agent Argent keyed in 5; the door opened, and he thwarted Dr. Levik. Edited on March 17, 2004, 6:18 am',12681,1);
INSERT INTO comment VALUES (12686,1694,5285,'Ady TZIDON','SOLUTION','2004-03-16 12:19:10',3,'ANS:33\r\n\r\nSTRUCTURE:\r\nReplace n by concatenation of its prime factors in increasing order.\r\n\r\n1 2 3 (22 5 23 7 222 ) 33 25 11 223 etc\r\n\r\nady\r\n',NULL,0);
INSERT INTO comment VALUES (12687,1694,5285,'Ady TZIDON','re(2): Solution','2004-03-16 12:22:53',1,'I told you once and I told you twice:\r\n\r\nYou cannot define a series by providing some members\r\n\r\nSee for yourself...\r\n\r\nady',12685,0);
INSERT INTO comment VALUES (12688,1692,5520,'sassy','4x4 solution','2004-03-16 12:37:01',3,' This is the board: 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 In any order, click squares 3,8,9 and 15. ...don\'t you know the difference between a series and a sequence ? What is your mal-ady ????? (just kidding....) Each letter in the original message was replaced by its index multiplied by one more than the index (the nth letter is replaced by n(n+1)). Here\'s a little script that reads the code and prints out the result. I modified it slightly, simply replacing the dashes with spaces and using the spaces to delimit sections to be parsed. The line breaks were not present in the original code; I added them just so they would fit on this page. vals[] is an array that contains the translated letters at their indexed positions (vals[2]=\'a\', vals[30]=\'e\', etc.). That seemed easier than trying to do the math backwards. When run, this code outputs: Similar to how Charlie solved the 3-bug problem... Let\'s consider the vector diagram of a pursuer and pursuee pair of bugs. Calling each vector V, the component of the pursuee\'s motion that is parallel to the pursuer\'s is 1/2*V AWAY from the pursuer. So this is a 2:1 ratio as well, but now the pursuee is moving away from the pursuer instead of towards it. In the 3-bug problem, you can solve for the distance travelled by saying \"distance of the pursuer\" + \"parallel distance of the pursuee\" = 10, and using the ratio found you get x + 0.5x = 10 In this case, we still have x and 0.5 x, but it is now x - 0.5x = 10. If just changing that sign doesn\'t sit well with you, think of it this way: The pursuer needs to travel the distance of the edge, PLUS the distance the other bug runs away from it. So x = 10 + 0.5x, which is the same thing. So x = 20 inches. Regardless of what the puzzle says, the only thing I know for a fact is that Evil Dr. Levik is no fool. Regarding the intelligence of Silv- I mean Agent Argent, I make no observation. Therefore, Dr Levik, being no fool, would not be so stupid as to arrange for some sequence test that could be broken after seeing just three out of five of the prior numbers. This means that the sequence is either completely arbitrary, or Dr Levik cleverly chose a sequnce that could head off in any number of directions (as Ady shows us) in order to lull the poor Argent into a false sense of security. Since the question asks \"What number did he type *and what happened*?\", my answer is that he saw the alternating primes as being part of the sequence, punched in the next prime (11), promptly fell into the dungeon, and is solving lateral thinking problems and riddles even as we speak. www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A014088 www.mathcad.com/library/LibraryContent/puzzles/soln28/soln28.html i think the following solution works. BOOL LinkedList::containsLoop(link* first) { link* slow = first; link *fast = slow ->next; while(fast) { if(slow == fast){ return TRUE; // the list contains a loop as the slow and // fast pointer are same } slow = slow ->next; fast = fast ->next ->next; } return false; } SilverKnight I dont think we can have soln with O(1). Since the problem requires atleast one pass through the list, we can have a soln with O(n). In my case, if the fast reaches the end of the list, we can safely say there is no loop in the list which takes only actually n/2 comparisons where n is the length of the list } BOOL LinkedList::containsLoop(link* first) { link* slow = first; link *fast = slow ->next; while(fast) { if(slow == fast){ return TRUE; // the list contains a loop as the slow and // fast pointer are same } slow = slow ->next; fast = fast ->next ->next; } return false; } Isn\'t it easier to simply take one ice cube, immerse it, and measure the fluid that is displaced ? Like Mrs. Boy, Archimedes was no fool, either. Edited on March 17, 2004, 6:46 am',12684,1);
INSERT INTO comment VALUES (12702,1545,5777,'Thalamus','re: Solution','2004-03-17 07:27:37',0,'Prabhakhar, Ady, I\'d go with your first answer, 17 is divisible by 1 and itself, so it doesn\'t satisfy the 2nd statement 37 is a good number. Juggler 53 is found by: DATA 2,3,5,7,11,13,17,19 which also finds larger numbers: 53 The average of 3 and 7, which I think everyone will agree are the only two digits in the number 37, is 5, which I also think everyone will agree is an odd number (hence, it is not even). Also, any number is divisible by itself (if you have 17 apples, can you split them into 17 equal groups?). Thus, any number below 20 is by definition also divisible by a number below 20. The lowest number that meets all the criteria, and the solution to this problem, is 53, as Charlie has already stated in his apparently much-overlooked solution. Lee, yuour assertion that water volume = ice volume is incorrect. In fact, ice floats because it has a lesser density than ice. If it had the same density, it wouldn\'t float (though it wouldn\'t sink either...) As ice has a lesser density, the same amount (say, in moles) of it will occupy a greater volume. A simple experiment performable in your home to illustrate this. Take a clear glass, and fill it mostly full with water. Add some ice (one or two cubes - not enough to create a full layer at the top of the glass), and then fill the remainder of the glass with water until the surface tension is all thats stopping the water from overflowing the edge. Notice that the ice is floating above the level of the water. Now wait for the ice to melt... If the volume of the iced-water stayed the same, wneh it melted, the water would have overflowed - but I\'ll bet that it didnt! I used Excel to solve for the side of the square, using the law of cosines. cos(APB) = (1+4-S^2)/4 The factor of 2 times the square of the side in the last is due to the side being not the side of the square but the diagonal of the square. This was solved so that The total of the three angles is 2*pi. S comes out to 2.797933, and angle APB is 2.356194 radians, or 135 degrees. This assumes that the point P is inside the square. The same Pythagorean relationships make the distance to D the same even if point P is outside the square, but the side is smaller, and I haven\'t worked out what the angle would be for that, but it would be acute (having drawn it on graph paper, with the locus of points at a 1:2 ratio from A vs. B,being a circle and the locus of points at a 2:3 ratio from B vs.C; therefore these are two intersecting circles with the points of intersection being the two possible locations for P, with the side shrinking in absolute size when the outer point is chosen). Edited on March 17, 2004, 10:04 pm',NULL,1);
INSERT INTO comment VALUES (12732,1706,885,'np_rt','Solution (Excel-Aided)','2004-03-17 22:19:04',0,' For the first part, draw lines parallel to the sides of the square through P. Let the segment parallel to AD intersect AB at E and the segment parallel to AB intersect AD at F. There\'s an intersection at the other sides too but it\'s not necessary to discuss it since it breaks the other sides into the same lengths as these sides. Let AE=w, BE=x, AF=y, DF=z. Applying the Pythagorean theorem 4 times, AP^2=w^2+y^2 = 1 You can get w^2+z^2 by adding the first and the third equation and then subtracting the 2nd to arrive at w^2+z^2=1+9-4=6. Therefore, DP^2=6 --> DP=sqrt(6). As for the 2nd part, I could not get an analytical solution so I used Excel Goal Seek. It would be nice if someone can come up with an analytical solution. Let APB be J, BPC be K, CPD be L, and DPA be M. Also, let the side of the square be length s. Apply the law of cosines 4 times yields s^2=5-4cosA We have 5 equations and 5 unknowns. I couldn\'t come up with an analytical solution. So I defined cosA, cosB, cosC in terms of s^2. Then I found A, B, and C and used the fifth equation to find D. I used Excel Goal Seek to find s^2 such that the fourth equation applies. The results I got are:\r\n s=2.797921, A=2.356172, B=1.125229, C=1.061036, D=1.740749. (Radians). The required angle is A (135 degrees). Since it has such a nice answer, I assume it can be done analytically but I have no idea how it\'s done. 1. the taxi driver is on foot 2. the taxi driver is reversing. Edited on March 18, 2004, 7:40 am',NULL,1);
INSERT INTO comment VALUES (12737,1718,1171,'nikki','Ideas','2004-03-18 07:49:37',1,' I didn\'t read Juggler\'s yet, so maybe these ideas aren\'t novel, but I was thinking either (a) the taxi driver was walking (taxi drivers don\'t ALWAYS drive their taxi) or (b) he was driving, but he was backing up a bit because he missed his pickup/dropoff point, so he was facing the right way, but GOING the wrong way. That\'s all I have. Later! There are two possible answers, one with p outside the square and one with p inside the square. Let A be at (0,0), B at (d,0), C at (d,d) and D at (0,d). Using the distance formula: From this it is easy to find (DP)^2 = 6, as noted by others. Using the equations for AP and BP, x can be expressed in terms of d: Similarily, AP and DP can be used express y in terms of d: Substituting the expressions for x and y into x^2 + y^2 = 1 yeilds an equation in d: ((d^2 - 3)/(2d))^2 + ((d^2 - 5)/(2d))^2 = 1 The equation can be reduced to d^4 - 10d^2 + 17 = 0. This gives two positive values for d: sqrt(5 - 2*sqrt(2)) and sqrt(5 + 2*sqrt(2)). If d = sqrt(5 - 2*sqrt(2)) then P is located at x = (1-sqrt(2))/sqrt(5 - 2*sqrt(2)), y = -sqrt(2)/sqrt(5 - 2*sqrt(2)) In this case, using the law of cosines on triangle APB gives: The equation reduces to 1/sqrt(2) = cos(angle APB) which means angle APB is 45 degrees. If d = sqrt(5 + 2*sqrt(2)) then P is located at x = (1+sqrt(2))/sqrt(5 + 2*sqrt(2)), y = sqrt(2)/sqrt(5 + 2*sqrt(2)) In this case, using the law of cosines on triangle APB gives: The equation reduces to -1/sqrt(2) = cos(angle APB) which means angle APB is 135 degrees. Solution summary: There are two solutions. In both solutions the length of DP is sqrt(6). In the first solution P inside the square and angle APB=135 degrees. In the second solution P is outside the square and anlge APB=45 degrees. Edited on March 18, 2004, 11:43 am',NULL,1);
INSERT INTO comment VALUES (12741,1718,6073,'Russ','my thoughts','2004-03-18 09:39:36',0,' 1: they could be on a one way street high above the city, like a one way road up a mountain or something, and they can tell the car down in the valley-area is a taxi due to the taxi light on the top, but are powerless to stop it. 2: the one way street goes into a neighboring town, where they don\'t have jurisdiction, and the taxi has just crossed over the town line. Dump the tea into the glass pitcher. Fill the 4 cup Pyrex container. Dump the 4 cups into an ice cube tray. How many cubes does it make. Then add this number of cubes to the ice tea. Something is telling me that it would be helpful to take advantage of the fact that there are two As. Later! 18 It is extremely simple to rotate it an even number of spaces, to put the G in one of the other corners. Just push the E, S, Y, or the first A into the middle, rotate the other pieces around, and put the letter back where it goes. To move it an odd number of times, and start the G on an edge, it gets more tricky. You have to take advantage of the fact that there are two As, one that starts on the edge, while the other ends up on an edge. If you just use the same method, push one A into the middle and put it back on the edge where it goes, you\'ll end up with an A in the wrong corner (GMERSAAY instead of GAMERSAY, something like that). So, the trick is getting the second A to be the one in the middle. To do so, you have to just switch their positions -- put the second A where the first one is, and leave the first in the middle. Then, when you rotate them around, the space for the second A ends up on the edge. Switching the As took me 12 moves: The rest is trivial, and took me six moves to complete: That\'s a total of 18 moves. The second part can\'t be improved upon (if you rotate the outside in the other direction, it takes 9 moves instead of 6). Perhaps, though, there is a more efficient way to switch the two As, so my answer isn\'t final, yet ... ... well, almost my final answer. The minimum number of moves to put the G on the right middle is 24: The minimum for putting the G at the bottom is 22: and for the left is 20: Edited on March 19, 2004, 11:39 am',12768,1);
INSERT INTO comment VALUES (12770,1737,5809,'Jer','Source of confusion','2004-03-19 12:28:38',0,'Here is the problem as I see it.\r\nWhen I read \"the average of the digits is an even number between 3 and 9\" my brain interpreted \"even\" as \"whole number\"\r\n\r\nI assume this is because I know the average of a set of numbers is not usually a whole number.\r\n\r\nIn fact, had the orginal statement used \"whole\" rather than \"even\" the solution whould be 37 - the conclusion I jumped to.\r\n\r\nAlthough the wording as it stands is _not_ ambiguous, is can be wrongly interpreted.\r\n\r\nA better wording may be\r\n\r\n- the average of the digits is an even whole number between 3 and 9\r\n\r\nFor a really easy problem this one has sparked quite the discussion.\r\n\r\n-Jer',NULL,0);
INSERT INTO comment VALUES (12771,1770,5384,'Larry','10 seconds of thought','2004-03-19 13:51:42',1,' My first thought was 21, but then I realized that the show doesn\'t end until ALL monkeys are back home. So I think we want a set of numbers such that the sum of the numbers is 21 and the product of the numbers is maximum; and also that the numbers are prime relative to each other. And that\'s my story after thinking for 10 seconds. Since one arrow starts and ends in each circle, the individual circles must be connected together in larger circles of the arrows. To create the largest number of whistle blows, the product of the lengths of all the circles must be as large as possible (providing the numbers are all prime and different). The only combinations of numbers that fit are (13,5,3) and (11,7,3). 13 * 5 * 3 = 195 11 * 7 * 3 = 231 Therefore the largest number of whistle blows is 231, with the circles arranged in circles of lengths 11, 7 and 3. I disagree that all the numbers of the Loop Sizes have to be prime. What we are dealing with is a situation where you need to find a set of whole numbers (that cannot include 1) whose sum is 21 and whose Least Common Multiple is maxmized. A solution I found is 2, 3, 4, 5, and 7. The least common multiple is 2^2 * 3 * 5 * 7 = 420. I don\'t know if that is the maximum solution, but I\'m sure Charlie will provide an exhaustive proof of the maximum =) Later! Yes, the exhaustive proof is DECLARE SUB try (n!) FOR n = 2 TO 19 FUNCTION gcd (a, b) FUNCTION lcm (a, b) SUB try (n) which tries all the ways of different numbers, in ascending sequence, can add up to 21, and keeps track of the highest product thus far. Its successive \"bests\" end up with your solution: 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 5 2 2 2 2 2 2 2 3 4 2 2 2 2 2 2 2 7 2 2 2 2 2 2 4 5 2 2 2 2 2 3 3 5 2 2 2 2 3 3 7 2 2 2 3 3 4 5 2 2 2 3 5 7 2 3 4 5 7 i\'ve never seen a problem like this one before Here\'s a list of the best that can be done with varying numbers of circles from 6 to 50: Rarely do duplicated numbers appear. Of course they add nothing, any more than a 2 on a list that contains 4, but they use up the remainder of the circles. [Please see \"I invented the Internet] Edited on March 20, 2004, 10:51 am',NULL,1);
INSERT INTO comment VALUES (12783,1801,1301,'Charlie','Most of a solution','2004-03-20 11:23:31',3,' As the lengths, areas, volumes, etc. are all of unit size, the total value of each of these will just be a count of the number of edges, faces, cubic pieces, etc. When transitioning from a given dimensional space to the next, say from a square to a cube, this can be said to be done by moving the original shape perpendicular to itself, during which process, each k-dimensional element traces out one element of k+1-dimension, but also leaves an initial and final impression of itself. To illustrate, as a square is moved through the third dimension to trace out a cube, each of its vertices traces out a new edge, making 4 edges to the cube so far considered. Each vertex also leaves an initial and final impression of itself, so the 4 vertices of a square lead to 8 vertices of the cube. Meanwhile, the 4 edges of the square also leave their initial and final impressions; adding these 8 to the 4 edges traced by the vertices makes 12 vertices all together. Finally, each edge traces out a square, making 4 faces, plus the original square leaves its initial and final impression, making a total of 6 faces on the cube. The points (vertices) themselves are never generated by lower-dimensional pieces, and so just double each successive dimension: two end-points of a line segment, 4 vertices of a square, 8 vertices of a cube, 16 vertices of a hypercube. Where V, E, F, and S represent vertices, edges, faces and solids. So a 4-dimensional hypercube has 32 edges, and if they are of unit length, the total length is 32. There are 24 2-d faces having a total area of 24. There are 8 cubic surface volumes, each of unit volume, making the total volume of the hypersurface of the hypercube 8. The above presents a recursive way of getting the figures for successive dimensions. As for a direct formula for a given spot on the chart (where each number is twice the number just above it plus just 1 times the number up and to the left from it), that will take some more thought, but probably is related to combinations, as it is quite similar to the formation of Pascal\'s triangle. Edited on March 21, 2004, 8:39 am',NULL,1);
INSERT INTO comment VALUES (12784,865,853,'Matthew Bobbins','Whats the question?','2004-03-20 11:27:50',0,'lets say i answered yes. then the correct answer to the question \"is no the correct answer to this question\" yes. yes, no is the correct answer. that makes no sense, so what is the ACTUAL question? its incomplete.',NULL,0);
INSERT INTO comment VALUES (12785,513,853,'Matthew Bobbins','ermmm...','2004-03-20 11:30:37',0,'you\'ve changed the question, so it is false.',NULL,0);
INSERT INTO comment VALUES (12786,1770,6104,'shea','our solution','2004-03-20 15:02:27',0,' We think it\'s 21 To find the formula for the number of s-dimensional components in a cube of c dimensions, you need to consider how the components of varying dimensions relate to each other. As is shown in the chart in the first comment, the number of 0-dimensional components (vertices) is given by 2c. There are c dimensions at right angles to each vertex, so c edges can be drawn from each. Each edge connects 2 vertices, so divide by 2 to find the number of edges. There are (c-1) faces at right angles to each edge, and each face has 4 edges, therefore the number of faces is the number of edges multiplied by (c-1) and divided by 4. For cubes, there are (c-2) from each face, and each cube has six faces, so multiply the faces by (c-2) and divide by 6. To calculate the number of Here you can see the resemblance to the Pascal sequence (which defines the terms of Pascal\'s triangle). A slight variation is all that is necessary. The general equation is: 2^(c-s) c! s! (c-s)! This is the formula for the number of edges / faces / cubes etc. Since the c-dimensional cube has side length of one unit, the formula holds for this question. For a c-dimensional cube with side length n units, the s-dimensional surface area is given by the number of s-dimensional components multiplied by n^s. \"Is the answer no?\" is the question. Can you define \"ACTUAL\" question? Edited on March 21, 2004, 10:22 pm',NULL,1);
INSERT INTO comment VALUES (12791,1735,6109,'hamish thompson','solution','2004-03-20 23:35:17',0,'they have al got smaller words in them',NULL,1);
INSERT INTO comment VALUES (12792,1735,4507,'Penny','re: solution','2004-03-21 01:28:33',0,' hamish thompson wrote: \"Solution: they have all got smaller words in them\". Almost all words have smaller words in them. Consider the preceding sentence: \"Almost all words have smaller words in them\". Every word in that sentence has a smaller word in it. \"Almost\" has \"most\" in it. \"All\" has \"a\" in it. \"Words\" has \"or\" in it. \"Have\" has \"a\" in it. \"Smaller\" has \"all\" in it. \"In\" has \"I\" in it. \"Them\" has \"hem\" in it. So that\'s like saying \"Solution: they all consist of letters.\" Edited on March 21, 2004, 7:03 am',12791,1);
INSERT INTO comment VALUES (12793,1718,6089,'Iain','Yet another solution','2004-03-21 04:50:08',0,' Who says the taxi driver is on that street? There could be two parallel one-way streets, and the police spot the taxi driver on the other street. If the two streets were very long, or started and finished in different places, there would be little point doing anything, as it would be imposible to catch up. Not a very good question, as there are so many possible answers. I haven\'t seen what the official soulution is yet, or read any of the comments, but here\'s my answer. Point to one of the doors and ask the monk \"If I were to ask you if this door leads to the garden, would your answer be \"Zim\"? Since you are nesting a question within your question, you will get a truthful answer regardless of whether the monk is a knight or liar. He will either answer truthfully about a true answer to your hypothetical question, or answer falsely about a false answer to your hypothetical question. If the door does in fact lead to the garden, then the monk\'s answer would mean \'yes\'. If \"zim\" means yes, then the monk would answer \"zim\" meaning \"yes, I would answer \'yes\'\". Likewise, if \"zim\" means no, then the monk would still answer \"zim\" meaning \"no, I would not answer \"no\'\". If the door does not lead to the garden, then the monk will answer \"dahl\". (If his answer is anything other than \"zim\", you know you pointed to the wrong door.) Great Riddle. lg(x) = ln(x)/ln(2) Plotting the graphs of y = sin(x) and y = ln(x)/ln(2) shows that they intersect at x ¡Ö 1.919. There are no other solutions, since the graph of y = ln(x)/ln(2) quickly becomes > 1 as x increases and < 1 as x decreases. Without looking at anyone elses answers or comments... 1/2 n are knights, 1/2 n are liars. Thomas and Richard are both liars. The campers are seated in alternating pairs of knights and liars. Richard is seated between two pairs of knights, so there is one fewer liar in the circle. This is the only way it works. Excellent riddle. Very tough. (Haven\'t read any posts yet.) Aaron told the friend \"I am a liar\". This is the only thing he could say that would reveal what he really was. Obviously he is a knave who was lying. The next thing Aaron said was that Cassie was a knight, so this had to be the truth. Bill said Cassie was a knave, which was a lie, so Bill is either a knave or a liar. Since Bill\'s second statement (about Cassie) was a lie, then If he were a knave his first statement would have been the truth, which must have been either \"I\'m not a liar, or I\'m not a knight\". If he were a liar, his first statement could only have been \"I\'m not a liar.\" If that had been his statement, then the friend would not have been able to tell whether he was a liar or a knave. Since the friend was able to determine what he was, Bill\'s statement must have been \"I\'m not a knight\". So the friend was able to determine that he was a knave. Run down: Aaron and Bill are knaves, Cassie is a knight. Seems easy. I\'ll have to read the comments now. (stopped reading comments at the post to which this replies.) Well, based on your statements in the puzzle, it doesn\'t make sense for you to be either a liar or a knave, so if you must be one of the three (which I doubt), then you must be a knight.<o:p></o:p> Your friend certainly could be a knight, since it was assumed he was telling the truth to arrive at the previous given solutions, and that led to no unresovable contradictions. From what he said, the statements can\'t all be lies, so he can\'t be a liar. If his first statement were false, then his second would have to be also, so his first statement must be true. So everyone being a knave gives us another possible solution. (now on to the remaining comments) The last statement right now is: \"I soon found that the previous thing Bill said allowed me to know for sure what the last of the three people were.\" This statement meanst that only because of the last statement, my friend knew what the last of the three people were. It means that without that last statement, my friend wouldn\'t have known. _____________________________________________________ To the scholar that reads this: I\'d like to have this editted, but Gamer must have forgotten that I can\'t edit it myself. I believe it is 315. Three seperate groups of circles, one of 5, one of 7, and one of 9. Rearranging the rows so that the first letters are in alphabetical order gives: A W E T O T N T E V Reading down the columns (ignoring the first) gives the question: WHAT IS THE SMALLEST NUMBER SO THAT ALL C A M U H I R L C Z ITS LETTERS ARE IN ALPHABETICAL ORDER So the question is, \"What is the smallest number so that all its letters are in alphabetical order?\" Checking the numbers one to twelve: One - x None of the numbers thirteen to nineteen will work, because the \"teen\" section is not in alphabetical order. Therefore, the number must be an integer multiple of ten, because all other numbers will contain the numbers one to nine at some point. Neither twenty nor thirty satisfy this, but forty does. So the answer is forty. First, It\'s important to note that in propostional logic, any conditional statement with a false antecedent is considered true. If A were guilty, then his statement is false so the antecedent must be true and the consequent false, but that would mean that both B & C are also gulity making too many killers, so A must in fact be innocent. If B is innocent then C must be guilty, meaning his statement is false, but the antecedent of C\'s statement is false so his statement would be true therefore B can\'t be innocent. Both A\'s and B\'s statements then leave C innocent and therefore D the remaining culprit. Since C\'s statement must be true, and the consequent of his statement is false, the antecedent must also be false. So B is the accomplice and D is the killer. Several options: One - as Penny says, they all consist of letters Two - specifically, they all consist of letters, derived from the Greek, in standard use today. Three - they are all taken from the English language Four - they all mean different things Five - I haven\'t spoken any of them out loud in conversation during the last year. Six - they have all been listed as having something in common in a puzzle at http://perplexus.info Seven - none of them could sensibly be used to describe a bucket Eight - they all fit into this stupid sentence: A fleet of haggard bibliophiles rode hogback into a sweltering downdraft of devilment-cauing irtrons. Nine - they can all be used to create a moronic list of things that they have in common that you\'ve just wasted valuable seconds of your life reading. There\'s probably some sensible things as well, but frankly I don\'t have time for them. Check out \"Letters to numbers\", the best, subtlest, most challenging, most original, cleverest flooble puzzle I have ever seen. http://perplexus.info/show.php?pid=1469 Edited on March 21, 2004, 6:07 pm',12806,1);
INSERT INTO comment VALUES (12811,1341,6028,'Barrett Hasseldine','re: Integer infinity','2004-03-21 21:46:06',0,'Umm, I think you\'ll find that Q (the rational numbers) are countable (aleph naught in cardinality)...\r\nA \'1-1 Correspondence\' can be seen if you take a matrix, each element being an ordered pair in NxN. Each element in the matrix represents a different quotient in Q. Follow the matrix from top left, then snakeing your way away from (1,1) towards the bottom right of the infinite matrix you have created a bijection...',10787,0);
INSERT INTO comment VALUES (12812,1223,6114,'logischer Verstand','an answer','2004-03-21 22:54:44',3,'The sum of all the numbers would be 14,751 by using the equation given in the next part. Pour half (2 cups) of tea into the pitcher. Richard: \"Penny must be on spring break or she probably would have already commented...\" It ain\'t Spring yet, dude. Besides, embarrassment over my many egregious blunders in that thread drove me to silence. I originally failed to distinguish between degrees and radians, resulting in an absurdly large result. Then Charlie had to tell me how to subtract negative numbers (it is very tricky...you have to add a positive number...), and even SilverKnight, who is usually my most ardent admirer, started to criticize me... :o) But I did have the correct formula. :-) Edited on March 22, 2004, 1:19 am',12803,1);
INSERT INTO comment VALUES (12816,1651,6116,'Galendir','The Solution is false!','2004-03-22 01:33:32',0,' Edited on March 22, 2004, 1:37 am',NULL,1);
INSERT INTO comment VALUES (12817,1735,4507,'Penny','I\'m afraid that will be the Official Solution...','2004-03-22 02:04:54',0,'...that all these words contain smaller words. That will be absurd, of course, since almost every word in this present post contains a smaller word.....',NULL,1);
INSERT INTO comment VALUES (12818,525,6126,'Kancelot To','No Subject','2004-03-22 03:31:55',0,'It never says that all thouse people were going to St. Ives, so therefore, 1 is the solution.',NULL,1);
INSERT INTO comment VALUES (12819,467,6126,'Kancelot To','No Subject','2004-03-22 03:33:08',0,'heard of this one, a person',NULL,1);
INSERT INTO comment VALUES (12820,859,6126,'Kancelot To','?','2004-03-22 03:34:08',0,'huh?',NULL,1);
INSERT INTO comment VALUES (12821,1721,4507,'Penny','I would say','2004-03-22 08:34:33',3,' Water (H2O) Edited on March 22, 2004, 8:35 am',NULL,1);
INSERT INTO comment VALUES (12822,1721,4670,'e.g.','No doubt about it','2004-03-22 08:47:27',3,'Good ol\' water!!\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12823,1721,1920,'Brian Smith','DHMO','2004-03-22 09:03:37',3,' The compound is Dihydrogen Monoxide (DHMO) Read all about the dangers of DHMO at www.dhmo.org Edited on March 22, 2004, 9:11 am',NULL,1);
INSERT INTO comment VALUES (12824,50,6114,'logischer Verstand','wrong addition','2004-03-22 09:45:43',3,'The addition in the problem was done wrong just for trickery. To\r\nsolve the problem, one must first take into account that the desk\r\nmanager has $25, the bellboy has $2, and each farmer has $1. \r\nThus, $25+$2+$1+$1+$1=$30. No missing dollar.\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12825,1721,1686,'DuCk','I once had this on a test','2004-03-22 09:51:23',3,'I once had this question on an exam in hydrology except the question was, do you think this substance should be banned and why? Of course I missed it, coming up with some dumb reasoning, but it was a cool question anyhow. And of course the answer was, no because it\'s water.',NULL,1);
INSERT INTO comment VALUES (12826,488,6114,'logischer Verstand','answer','2004-03-22 09:56:39',3,'pi. The value of pi\'s digits is through the number of letters per word. e.g.: Sir (3), I (1) bear (4) a (1)...\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12827,1721,6132,'Philip Carey','Dangerous compound','2004-03-22 10:12:53',0,'I believe the answer is water.',NULL,1);
INSERT INTO comment VALUES (12828,980,6089,'Iain','re:No Subject','2004-03-22 12:10:15',0,'Just as a point, a lying knave is quite capable of saying \"I am a liar\".',8597,1);
INSERT INTO comment VALUES (12829,1721,6134,'chuma','re: Dangerous compound','2004-03-22 12:30:14',0,'the answer is definately water',12827,0);
INSERT INTO comment VALUES (12830,1540,4507,'Penny','Question for anyone','2004-03-22 13:18:10',4,' \"Also, each of these rectanges [rectangles?] is similar in proportion to the whole sheet.\" Could you please be a little more precise ? Do you mean that the ratio of the width to the height of the individual rectangles is the same as the ratio of the width to the height of the entire sheet ? Edited on March 22, 2004, 1:24 pm',NULL,1);
INSERT INTO comment VALUES (12831,1540,4374,'Richard','Solution','2004-03-22 13:31:52',3,'The rectangles are similar to the whole sheet but must be oriented the other way. If the height is X then (15/9) : (X/4) = X : 15 which makes X=10.',NULL,1);
INSERT INTO comment VALUES (12832,1540,4507,'Penny','re: Solution','2004-03-22 13:35:25',0,' I get it..... Height/width of the sheet is equal to width/height of each rectangle.... Isn\'t that clever.... That\'s what similar means ... you learn something new every day ... Indeed you do. I was afraid that the answer to this one would be \"Cannot be determined\", as was the Official \"Solution\" to http://perplexus.info/show.php?pid=1394&op=sol LOL !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Edited on March 22, 2004, 1:58 pm',12833,1);
INSERT INTO comment VALUES (12835,1540,6089,'Iain','A different solution','2004-03-22 14:02:26',3,' In this solution, I am assuming that the width is the shortest side of a rectangle. Let X be the height of the sheet. Let A be the height of the small rectangles, and B be the width. 4A = 15 9B = X 3.75/X = B/15 X = 22.5 inches Sorry - didn\'t read the question properly. 4 rows, 9 columns - the width must be the longest side. I was wrong (much as it pains me to admit it) But it\'s not water... It is in fact, Dihydrogen Monoxide. Check out the FAQ on the web page and go through the bullet points: Brian Smith was right. If each little rectangle measurements are a x b units, then either:<p> the first way leads to 4ab = 9ab so it has to be the other way <p> There are 2 answers: <p> Width 15, Height 22.5 (little rectangles 3.75 x 2.5) or <p> just so the ratio between sides is 2 to 3 and that\'s my story Edited on March 22, 2004, 3:13 pm',NULL,1);
INSERT INTO comment VALUES (12842,1540,1301,'Charlie','re: Solution','2004-03-22 15:21:37',0,' Hmmm.... This gets down to a definition of width and length. Actually the question called for \"width and height\", rather than \"length\", changing the emphasis somewhat. When width is contrasted with length, we think of the width as the shorter dimension, but when width is contrasted with height, we think of the width as whichever one was horizontal, while height is vertical, regardless of which dimension is smaller or larger. Gamer indicates 4 rows and 9 columns, indicating that the division by four is vertical (separated by horizontal lines) and the nine is horizontal (separated by vertical lines). If the width stretches across the columns and the width is 15, then the height is 10, as another previous post indicated. get it? H20 with 10^(-7) moles per liter H+ ions, and Specifically (cf. Penny\'s post): dihydrogen = H2 monoxide = O dihydrogen monoxide = H2O Perhaps there is no sequence - the minions are being watched by camera, and any who hesistate to enter a number will be plunged into the hideous storm of brain teasers. Agent Argent simply enters any number, goes through the door and confronts Dr. Levik, who merely presses a secret button concealed in his high-backed leather chair, and plunges our hero into a pool filled with pirhana fish, while stroking his long-haired white cat. I changed the problem to reflect these concerns. I knew what I meant; why couldn\'t you just recieve my telepathy? :) Actually my original problem was 15 inches long, how wide is it? and somehow it got changed. So of course the answer would be 10 then, but this problem is fine too I suppose. One third of twelve is \"lv\" I have a nagging suspicion that \"Rocket Scientist\" (who as duty compels me to bring forth is in fact a mere novice of 6 posts) is really our old and very good friend \"Yo.\" Really, no other conclusion seems likely. Takers? novice you are, benjamin 12 or 24 hours 30 minutes 0 seconds lol i dint say that the triangles CMY and DMX are congruent. i meant that in order to prove it , one way of doing it is to prove that they are congruent well... there is a sure-fire way to get MX = MY, which is CPCTC (correspoding parts of congruent triangles are congruent) after either figuring out if triangle CMY is congruent to DMX, or figure out YMB is congruent to XMA... hmm i already notice vertical angles, so mebe u gotta use SAS or SAA? also... u no that angle D is congruent to angle B because they share the same arc CA. Similarly, angle C and A are congruent because they share the same arc BD. one more thing... u can prove that triangle CMB is similar to AMD by AAA, but their congruence cant be proven just yet (if possible) Edited on March 24, 2004, 4:42 pm',NULL,1);
INSERT INTO comment VALUES (12954,1689,6159,'Shanna','Answer','2004-03-24 17:03:50',0,'Prove that Point M is the midpoint of points X & Y. Hmm... They switch horses, and tie on the way there, so that they both win. Victor: Triangles CMY and DMX are not congruent. You can\'t prove it because it\'s not always true. However, you are correct that triangles CMB and AMD are similar. Shanna: Look at the diagram a bit more. If I recall my geometry, AM * MB = CM * CD = PM * PQ. Maybe this will help? I say that we draw an auxillary reflection over the diameter, and prove that the points reflect to each other. (x²+2x+3) (1x²+[2*1x]+3) You are supposed to put 1 in front of xso the answer to the equasion is 6x which is not divisable by 35 You can be banned for personal attacks and vulgar profanity, yo yo. This is your second warning. Edited on March 22, 2004, 7:45 pm',12852,1);
INSERT INTO comment VALUES (12867,1735,4507,'Penny','yo yo, do really want to be here ?','2004-03-22 19:47:53',0,'I don\'t think so',12864,1);
INSERT INTO comment VALUES (12868,1737,6142,'Maghann','and the answer is','2004-03-22 20:36:34',0,'23',NULL,0);
INSERT INTO comment VALUES (12869,1721,4323,'Benjamin J. Ladd','The ugly truth is I\'m an idiot...','2004-03-22 22:23:46',0,' I am (very seriously) failing chemistry II this semester. I have an aversion to the subject that goes beyond disgust and loathing... Anyway, on a better note, www.dhmo.org may be the funniest website ever constructed. Man, do I feel stupid. And thanks go out to all those who pointed out that dihydrogen monoxide IS in fact water. I\'ve come up with 420. It\'s five loops, of 2, 3, 4, 5, and 7 circles. Ignoring the 2 at the start (because it\'s a factor of 4) that leaves you with 2 * 3 * 4 * 7, or 420. (Well, actually 419, because it doesn\'t start the dance with a whistle) Cups is a measurement of volume. Water, when frozen, while retaining the same mass (weight) increases in volume. If you were wanting to find the answer in cups of water, the displacement concept that everyone here has suggested would not be accurate, as you would be calculating the volume of ice, not water. Of course, that means that this problem is insoluble given the tools we have at hand, but then again you could just choose to ignore the difference in volume between the states of water. pppy wrote: \"...the displacement concept that everyone here has suggested would not be accurate, as you would be calculating the volume of ice, not water....\" That is not what the problem asks. It does not ask for the volume of ice cubes. It asks, what is the number of ice cubes required to produce a volume of four cups of water. Obviously, that would be the number of ice cubes equal in weight to four cups of water, because the weight of water does not change significantly when it freezes, and the displacement concept of Archimedes determines that weight very nicely. An ice cube will be equal in weight to the volume of water it displaces. Please don\'t try to outsmart Archimedes. Not even Albert Einstein could do that. You seem to have used a method which ignores the similararity of the rectangles and tries to find what the proportions would be if the rectangles were squares. Why is everyone being so dumb? Everyone is taking this way out of proportion. Firstly, dihydrogen monoxide and water ARE THE SAME THING!! Why does everyone have to try and be funny and say that they are not. The first one may have been funny a long time ago, but people keep repeating it, and it is getting boring. Plus, this should not be able to degenerate into a thing where people are just insulting other people for absolutely no reason. Some people just don\'t know when to stop. This was a good puzzle, as puzzles go. And as puzzles go, it went. Don\'t worry about yo and his insults. He is obviously 5 years old, and his mommy will log him off pretty soon. Edited on March 23, 2004, 7:36 am',12877,1);
INSERT INTO comment VALUES (12879,1721,6089,'Iain','The ancient art of diplomacy','2004-03-23 08:41:17',0,'See, when he reads that, he\'s just going to get more annoyed.',12878,1);
INSERT INTO comment VALUES (12880,1721,4507,'Penny','re: The ancient art of diplomacy','2004-03-23 08:44:25',0,'He\'ll get so annoyed that he\'ll remove that nice \"a\" that makes \"biatches\" a euphemism....',12879,1);
INSERT INTO comment VALUES (12881,1718,1920,'Brian Smith','Another answer','2004-03-23 08:48:54',0,'The one way street was being used as a detour due to construction. Every car was going down the street in the wrong direction.',NULL,1);
INSERT INTO comment VALUES (12882,1688,4323,'Benjamin J. Ladd','This tour is of...','2004-03-23 09:15:20',3,' Alphabetical state capitals. So the next two in the sequence are LA and ND; the capitals of which are Baton Rouge and Bismarck, respectively. Edited on March 23, 2004, 9:16 am',NULL,1);
INSERT INTO comment VALUES (12883,1688,4507,'Penny','Tour de force','2004-03-23 09:23:24',3,' I finally solved a SilverKnight puzzle..... They visited New York (capital Albany), Maryland (Annapolis), Georgia (Atlanta), Maine (Augusta), and Texas (Austin). Then they went to Louisiana (Baton Rouge), North Dakota (Bismarck)....etc...etc...Kansas (Topeka), and New Jersey (Trenton) last of all. But...how did they get from Maine to Texas without \"visiting\" any other states ???? Edited on March 23, 2004, 9:27 am Edited on March 23, 2004, 1:09 pm',NULL,1);
INSERT INTO comment VALUES (12884,1688,4323,'Benjamin J. Ladd','re: Tour de force','2004-03-23 09:33:12',0,'They flew there, Penny (on a private jet of course as I\'m sure the Honolulu to Indianapolis leg doesn\'t exist on any public carrier). I don\'t think flying consitutes \"visiting\" even though you\'re passing through the states. Maybe they burrowed?',12883,1);
INSERT INTO comment VALUES (12885,1688,4507,'Penny','re(2): Tour de force','2004-03-23 09:38:58',0,' Benjamin J. Ladd: \"Maybe they burrowed?\" Or, since they began in New York, they Burrough-ed. Or maybe since they ended in Mexico, they \"burro-ed...\" Edited on March 23, 2004, 9:48 am',12885,1);
INSERT INTO comment VALUES (12887,1737,5528,'shawn','re: and the answer is','2004-03-23 10:49:55',4,'isnt the average 3+2/2=5/2=2.5, which is less than 3..',12868,1);
INSERT INTO comment VALUES (12888,1688,1301,'Charlie','re(3): Tour de force','2004-03-23 11:12:03',0,'that would be boroughed (NYC)',12885,1);
INSERT INTO comment VALUES (12889,1644,4507,'Penny','looking in the mirror, yo yo','2004-03-23 11:17:15',0,':-)',12855,1);
INSERT INTO comment VALUES (12890,718,6114,'logischer Verstand','a possibility','2004-03-23 12:06:51',3,'The smallest number I could get is (1/3)^2=.1111111111111111\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12891,1688,4507,'Penny','re(4): Tour de force','2004-03-23 12:46:45',0,' Charlie, do you expect a Midwestern hick like me to spell Borough correctly ? Edited on March 23, 2004, 12:47 pm',12888,1);
INSERT INTO comment VALUES (12940,1549,1301,'Charlie','thoughts','2004-03-24 08:35:39',1,' Numerically, combining 3, 12, 5 and 7 with just multiplication and division doesn\'t seem to make it possible to come up with 11. Perhaps it\'s really a word problem, with one third of \"twelve\" being \"el\". But the extra \"even\" is 4/5 of \"seven\", not 1/5. Besides that, taking \"divide\" literally, we\'d have to separate the third taken from \"twelve\" to surround whatever we take from \"seven\". Have some tylenol handy, in case you get that \"run down\" feeling. Tylenol 3 is good for the brian!!! Running down while the tylenol is in your system is bad It\'s going to be \"guest\". Edited on March 23, 2004, 2:04 pm',12853,1);
INSERT INTO comment VALUES (12896,1688,4507,'Penny','Alternative solution','2004-03-23 14:17:41',3,' Louisiana and North Dakota were the next two states on the itinerary, but the next two states \"visited\" were Louisiana and Arkansas (passing through, on the way to North Dakota). How\'s that for making a STATEment ? By the way, \"yo\", if you\'re reading this, I hope you like your new username, \"Guest User\". You could work through it, finding possible 19-digit numbers and square roots - but that wouldn\'t be quick, would it? The first approximation would just count the relative frequency of perfect squares to numbers in the 19-digit range. As the derivative of x^2 is 2x, and the square root of a 19-digit number beginning with 7 is going to be about 2,500,000,000 (the best I can do without a calculator), the squares are going by at a rate equal to about 5,000,000,000 times that of their square roots. So the first approximation of the probability is 1/5,000,000,000. However, the last digit being 9 increases the chances that you have a perfect square: 1/5 of perfect squares end in 9, twice that which you\'d expect if the last digit were uniformly distributed over the digits, so at this level of sophistication, we increase the probability to 1/2,500,000,000. At the next level of sophistication, 1/25 of perfect squares end in 49, which is four time what you\'d expect, so instead of multiplying our original estimate by 2, we multiply by 4, and the probability is now estimated at 1/1,250,000,000. Of course in order to determine that 1/25 of perfect squares end in 49, you\'d need a table of squares of numbers from 1 to 100. Why anyone would have one lying around, I don\'t know, as a computer can produce one at any time; its only advantage is being allowed in this puzzle. (Yes, I cheated by producing it on the fly via computer.) One could continue on, with probabilities of ending in 549, 249, 749, 449, 549 and 849, and allow for the equal probability that the hundreds position could be any one of the given spare digits, but that is beyond what I\'d want to do without a computer. Edited on March 23, 2004, 3:01 pm',NULL,1);
INSERT INTO comment VALUES (12899,1540,6152,'Rocket Scientist','re(2): answer','2004-03-23 14:55:56',0,'But Aren\'t rectagles just squares with two longer sides? TO find the proportions of the similarities would not be difficult, therefore the lines in a square are the same as the lines in a rectangle',12876,1);
INSERT INTO comment VALUES (12900,1546,1301,'Charlie','with a computer (or a table of squares)','2004-03-23 14:57:04',1,'It turns out that a number with 49 as its last two digits can be a perfect square only if the hundreds digit is even. This has probability 1/2 of happening. However, if it is even, the probability that is a square is 8 times what it otherwise would be, leaving us with just the same probability of four times the most naive estimate, i.e., it is still 1/1,250,000,000.',12898,1);
INSERT INTO comment VALUES (12901,1546,6089,'Iain','Wording dispute','2004-03-23 14:59:21',4,'Does a person who is really, really, REALLY good at mentally calculating square roots count as a \"device\"?',NULL,1);
INSERT INTO comment VALUES (12903,1721,6152,'Rocket Scientist','re: What do you mean, getting ?','2004-03-23 15:05:05',0,'I do not comprehend how you came to the conclusion that yo is merely five years of age, when infact there is no indication that yo is even a man, he may be some psychopathic robot that is trying to take over website forums. Logic dictates that you re-evaluate your original assumption.',12878,1);
INSERT INTO comment VALUES (12904,1721,6152,'Rocket Scientist','re: chillax','2004-03-23 15:07:11',0,'Well hello there good citizen. I have invented many rockets in my time, that crazy cylindrical one from apollo 13, that was mine!!',12902,1);
INSERT INTO comment VALUES (12906,1546,2716,'Federico Kereki','Some thoughts','2004-03-23 15:12:39',1,'If the number is a square, the sum of its digits should be 0, 1, 4, or 7. \r\n\r\nThe 14 digits sum to 1.\r\n\r\nIf we picked 8, 5, 4, 7 and 2, the sum would be 0, so the number could be a square.\r\n\r\nIf we picked 8, 5, 4, 7 and 5, the sum would be 3, so it couldn\'t be a square.\r\n\r\nAnd so on...\r\n\r\nNote, however, that this is a feasibility check; even if the sum is one of the four values, it can easily be not a square.',NULL,0);
INSERT INTO comment VALUES (12907,1721,6152,'Rocket Scientist','re(3): chillax','2004-03-23 15:18:02',0,' I PROGRAMED YOU, AND I CAN UN...PROGRAM YOU!!!! And if i may, logic dictated that since i created the craft the you were programmed into, that could only mean that you are infact merely a earth dwelling....life form. the wording is kinda funky but if you look at it this way... twelve has 6 letters 1/3 of that is 2 letters if you take the middle 2- E & L and add it to seven minus the S (1/5 of the word) it equals eleven. You were infact created on this earth, so you are inface merely an earthling, a human you are not, but an earthling you are. There are five different combinations of the six numbers that can be chosen: Summing the total of all the numbers for each combination gives: 24578 = 9 Therefore the only possible combinations are 24558 or 25578, assuming that the numbers must sum to 0, 1, 4 or 7. If the hundreds digit must be even, then for 24558 it must be either 2, 4, or 8; and for 25578 it must be either 2 or 8. This gives 36 possible arrangements of the digits for 24558, and 24 for 25578. Therefore the probability that the number is a perfect square is at max 1/60. Seems strange why you would count the 5 numbers by themselves without counting the other 14 numbers :) Also, this is just like mental cube root, you should only use mental math or possibly paper (though it\'s not needed) My first thoughts had to do with the one\'s place digit. The one\'s place of any square number is as follows, in the form of One\'s digit of X : One\'s digit of X^2 0:0 1:1 2:4 3:9 4:6 5:5 6:6 7:9 8:4 9:1 So, out of these 10 possibilities, a 9 for the squared number shows up twice. So how about the answer being a 1/5 probability of the 19 digit number being a perfect square? This is probably too simple and naive of an approach, but I thought it was possible that all the other information was supposed to be distracting/misleading. I figured this idea was worth embarassing myself =) Otherwise, I like Charlie\'s approach with the 1(even digit)49 concept. Obviously I summed the other 14 digits as well - I\'m not stupid. Yes, but there would be several more digits before the last, so the answer isn\'t just one fifth. I think the extra information is probably there for a reason, though I could be wrong. I don\'t know how to spell borough either, but once they got to North Dakota, they might well have burrr-oughed. [Well I sure hope I deleted this post in time] Edited on March 23, 2004, 9:39 pm',NULL,1);
INSERT INTO comment VALUES (12930,234,5352,'Juggler','Penny\'s not top','2004-03-23 23:12:57',0,' You are \"A Gran Ma\" Penny might not be top, but it was great comment. How can I put this lightly? No, you\'re wrong, I mean hypercube. \"Supercube\" is a term that doesn\'t exist, according to the dictionary. In fact, it specifically asks whether I really meant \"hypercube.\" To those confused by the apparent lack of a comment to reply to: This comment was in reply to a deleted comment by a banned user. You say: <<you say: \"This has probability 1/2 of happening\" etc Your possibilities are based on the number being a square. The probability I gave of the 100\'s position being even was in general, not based on it\'s being a square. The probability was 1/2, as each of the 6 tiles was equally likely to have come from the 100\'s position (again, disregarding whether the number is a square or not), and half the digits are even. My calculation of the square probability, based on that alone, was then computed based on the necessity of the 100\'s position to be even in order to produce a square. >>Aren\'t rectagles just squares with two longer sides? No, they aren\'t. A square is specifically a rectangle with all sides of equal length. The equation there was based on the sides of the the small rectangles being equal. They cannot be squares, since they are similar to a 9x4 version of themselves. A 9x4 combination of squares cannot be a square. :-) \r \r \r \r \r \r \r \r \r \r \r \r \r \r Shouldn\'t yum, arsenic be higher then? Since it has been exposed to a larger audience? Like if you think about it what if the 10 people who voted on yum, arsenic voted on changing chameleons? There is most probably a chance it\'s score will go down. So basically what i\'m trying to suggest is that the top-rated problems should be arranged by score then ties would be settled by number of votes.',1072,'Alan','2003-01-27 10:45:32');
INSERT INTO forumpost VALUES (105,24,3,'Re: Top-rated Problems','This makes sense, yes. What do you think, levik?',250,'Nick Reed','2003-01-27 11:03:46');
INSERT INTO forumpost VALUES (106,24,3,'Re: Top-rated Problems','Another thing to consider is that perhaps it would be a good thing to drive users toward less exposed problems? If quality is really the issue, then additional votes could drive the problem down in the rankings fairly quickly.',103,'friedlinguini','2003-01-27 12:22:54');
INSERT INTO forumpost VALUES (107,24,3,'Re: Top-rated Problems','yo friedlinguini the driving down the ranks in the problems isn\'t a bad thing. Its what we want. That is the purpose of showing the top rated the problems so if problems are voted on more and ranks are altered more accurately this is good thing. But for friedlinguini\'s point about certain problems having least exposure... why not make a \"least voted on\" problem page. ',1072,'Alan','2003-01-27 15:26:08');
INSERT INTO forumpost VALUES (108,24,3,'Re: Top-rated Problems','It\'s a good suggestion. I\'ve been meaning to do this for quite a while now, but since nobody noticed up til now, never took the time. It should now display problems with more ratings higher than ones with less if they have the same score.',1,'levik','2003-01-27 18:10:25');
INSERT INTO forumpost VALUES (109,25,5,'Scholar Level','Although I know this may not be that good of a question but what are the \"contributions\" that promote a journeymen to a scholar?',1072,'Alan','2003-01-28 03:14:38');
INSERT INTO forumpost VALUES (110,23,3,'Re: Two a day?','I like the idea of 2 per day, but maybe make it an irregular thing. For example, post one puzzle 2-3 times per week and two puzzles 2-3 times per week. I don\'t support multiple postings on weekends though, cause I\'m one of those at-work types of puzzlers...(I don\'t even have reliable net access at home). I don\'t have any trouble catching up on Mondays when I\'ve missed a couple of problems, so I don\'t think that will be a huge hurdle for others.',775,'Cory Taylor','2003-01-28 08:28:35');
INSERT INTO forumpost VALUES (111,25,5,'Re: Scholar Level','Unless levick has changed the proceedure, becoming a scholar is not an automatic promotion like the other levels.\r in my opinion the best questions for flooble are ones that have \"set in stone\" answers. This may even include 2+2=? (Although this is to simple for the site. Also questions in logic can also have set in stone answers such as \" why are manholes round?\" or \"Why does ice float in water\" (I just submitted that so don\'t try to) Sorry but i think because of the fact that many problems of these type have come in, we all should be on the same page when it comes to voting. One last comment, Ravi if you are reading this and think that some of your problems fit the \"unneeded\" standards then could you please make a comment and levik, since there are 200 problems in the queue and a lot of users would be frustrated having to wait 6.6 months for their problems to go through that if you could use your special admin tool and view all the problems and check the one\'s that have ravi\'s comment then delete them i think it would really speed the process up, or, just check all \"riddles\" in the queue. Although i know this a lot to ask i really don\'t want a great question like \"why does ice float in water\" have to wait 6.6 months to get posted. Thank you',1072,'Alan','2003-02-21 10:47:06');
INSERT INTO forumpost VALUES (139,32,5,'Sorry to bug you again levik','But I\'ve noticed that there is no preview option for forum posts, and when i type something long out like i did in the library i would like to check it and make it look professional. Thank you',1072,'Alan','2003-02-21 10:49:42');
INSERT INTO forumpost VALUES (140,31,4,'Re: Riddles','Regarding your first comment, I agree, though I\'d expand the set of problems from names to anything that assumes some sort of cultural bias. This would include that \"South of England\" problem that was in the queue some time ago. I also agree that having to scramble around flooble itself is not a productive exercise. That said, I don\'t think it\'s so bad to refer to other problems as long as a hyperlink is provided. \r \r \r \r \r don\'t try to argue he wouldn\'t try during an operation for two reasons. 1. even without trying he\'s still gonna do better than that other guy. \r \r P.S in one of my pending problems trickiest pearls i need to have that table in my solution tat i was talking about modified. i entered in the pre command as you had said',1072,'Alan','2003-04-01 13:30:38');
INSERT INTO forumpost VALUES (433,74,4,'Re: New for you page','Actually that date idea would work well for me. everytime i go on flooble i check everything. Anyone else wanna give their input?',1072,'Alan','2003-04-01 13:32:56');
INSERT INTO forumpost VALUES (434,21,3,'Re: Puzzles','Wrong Number Cory :) lol :)',979,'Ravi Raja','2003-04-01 19:41:42');
INSERT INTO forumpost VALUES (435,73,7,'Re: hello!','Yes I have a few but the queue (list of pending problems) is too long. It might take some time.',979,'Ravi Raja','2003-04-01 19:48:05');
INSERT INTO forumpost VALUES (436,77,4,'Re: Congratulations to me','Congrats \"Journeyman\" Cory, now wishing you a happy journey on this site :)',979,'Ravi Raja','2003-04-01 20:04:21');
INSERT INTO forumpost VALUES (437,77,4,'Re: Congratulations to me','Although i really never liked the concept of asking for a promotion in some way i think on your next \"scholar recruitment\" me, ravi raja and cory taylor (I put me first because of grammar) should be the first one\'s made to scholars. Ravi\'s posted lots of problems, Cory has a lot of comments, and i have a combination as well as ideas for the site in the forum, although they are sometimes suggestions. ',1072,'Alan','2003-04-02 16:15:52');
INSERT INTO forumpost VALUES (438,78,7,'Hello all','Hello all,\r Greaty minds think alike eh?:)',1072,'Alan','2003-04-20 07:05:50');
INSERT INTO forumpost VALUES (648,100,4,'Re: Discovered leviks login password','What you said in your second post was what I was saying in my first post Ravi. :) So Bryan and any possible hackers know who is who, but there is no sense in telling us (except for the e-mail possibly) because both could claim to be Bryan. \r 2 as aamir said the site does look more professional just one thing perhaps this could be an option given to students only. A guest really should not be allowed to have any access over their comments adn wouldn\'t be able to (since they have no accounts.)',1072,'Alan','2003-04-21 12:27:49');
INSERT INTO forumpost VALUES (668,105,4,'Re: Uh, this is the REAL Bryan','well one thing we should do is take into consideration tim is nine years old and the math he is learning in school most probably wouldnm\'t allow him to solve peculiar pillar. So for tim to generate a solution? Also it would make sense that a lot of bryans comments were rude. Why? because when tim got access to bryans account he would\'ve read the library forum... especially the thread that had \"about tim axoy\" in its heading. ',1072,'Alan','2003-04-21 12:36:03');
INSERT INTO forumpost VALUES (669,97,5,'I am a pi genius.','Pi=exactly 3.14.\r Some possible solutions. 1. Create or type up a \"rules of submission\" document when the submit a problem link is clicked. This would either be a seperate page before the problem or right above the problem being made. 2. users are told by notes when their problems are visible in the queue. (there are so many major flaws with this i won\'t begin to describe them you should be able to figure them out yourself)',1072,'Alan','2003-04-25 10:29:53');
INSERT INTO forumpost VALUES (746,114,5,'Re: From Liars and knights to Logic','clever',775,'Cory Taylor','2003-04-25 10:52:35');
INSERT INTO forumpost VALUES (747,118,4,'Solution posted?','I think all the problems in the queue (and waiting problems as well) have solutions, but I didn\'t post them so people can\'t look at it and ruin the puzzle for themselves.\r 2 colors and 3 colors were perfect examples of problems that could\'ve been condensed. Also problem condensing will make the queue move along quicker.',1072,'Alan','2003-04-27 06:14:34');
INSERT INTO forumpost VALUES (765,117,4,'Re: Problem condensing','I doubt that the submitter of 2 colors and 3 colors was stretching things out to get more posted puzzles. I can only assume he was following in a tradition such as Tricky Pearls, Trickier Pearls and Trickiest Pearls. Each is different and each has a different method of solution. \r 1. for all problems in the queue run the queue calculation function (meaning it should be done manually) and this would be the last time it is done with its current code. now this forms an \"order\" in which the problems with qw=1 are organized. What should happen: This jumping penomenon which cory talks about will now no longer happen. It WOULD still happen in the qw=2 line though but this is good as it allows author\'s who submit a lot of puzzles to have there puzzles dispersed over a mathematically regulated amount of time (where number of puzzles submitted, day of week, current posting policies, number of puzzles contributed by specific users,etc. calculate to give this time.) Do not get confused by my last line. I\'m not say program a dispension system that works like that. i am saying thta my solution will cause that to happen, (and with one simple code modification)',1072,'Alan','2003-04-29 10:31:24');
INSERT INTO forumpost VALUES (781,121,5,'Deleting my own pending problems','How would I delete my own pending problems? Since a few are lateral thinking puzzles, I would rather not cause the voters the trouble of tu-inf them.',1645,'luvya2003','2003-04-29 11:05:11');
INSERT INTO forumpost VALUES (782,111,3,'Re: Computer/Programming puzzles','Dunno. Have you written one yet?',103,'friedlinguini','2003-04-29 11:22:01');
INSERT INTO forumpost VALUES (783,36,4,'Re: New QW thread','Have you considered making a FAQ section? I was wondering how the QW system worked too, and this might be a good addition to that (or is there one I don\'t know about?)',1626,'Gamer','2003-04-29 11:22:33');
INSERT INTO forumpost VALUES (784,36,4,'Re: New QW thread','You guys have a lot of interesting ideas. Honestly, I didn\'t even think that the current QW system was \"broken\". Certainly, I foresaw the jumping to be an issue, but did not think that the amount of it has reached a critical level. (I myself have two problems in the queue destined - hopefully - for the Algorithms sections)\r Yes I to, am in STRONG favour of having the ability to delete your own problems. I noticed a problem i submitted a while ago and saw its queue position. it was 116!!!!! The ability to delete your own problems might bring it down to maybe around 100. Also the queue granularity needs to be changed indefientely. so that way problems 1-2=qw1 3-4=qw2. This would make thing way quicker but ravi will still hold two spots in the queue(that is a LOT) I believe the queue has reached the point where the size of the queue is now officially on a constant uphill rise.(Not of new problems, but of total problems) especially with new users constantly submitting lateral thinking problems. (which will become more apparent over time.) We NEED these changes. Please let us have a discussion/vote on it in this forum. if foer it say \"yes\" followed by a paragraph break.(only if you want to justify it or try to sway other people\'s opinions.) If not say \"no\" The reason i didn\'t post it in response to the original thread is because I thought this should be a library thread where the more \"experienced users of flooble could vote on this. Ok i know thats a little to sketchy but here\'s what i\'m proposing the vote be on. Changing the queue granularity so that problems 1-2 have qw=1 3-4 have qw=2 and 5-6 have qw=3 etc. As for deleting your own problems you COULD vote on that but thats not the main discussion here. Anyways first vote \"yes\"',1072,'Alan','2003-05-01 15:23:46');
INSERT INTO forumpost VALUES (808,121,5,'Re: Deleting my own pending problems','When I looked I think just the date changes and not the queue order. I still don\'t understand why my problems are ordered the way they are in the \"__ problems pending\" page.',1626,'Gamer','2003-05-02 02:04:45');
INSERT INTO forumpost VALUES (809,124,7,'A little french in the Flooble.com world','Hi.\r Ok now that that\'s cleared up its time for what I wanted to say in the can or cannot message posting thread but decided to do it here anyway. Firstly, A LOT of things in the people truly don\'t make sense, and jut to let everyone know, I believe in NONE of the old testament. Why? well let me ask you this. Who wrote the old testament? The answer. Prophets!! Now wait a minute. Do you believe in miss cleo? I doubt you do. so why believe in prophets. If you do justify your belief by saying that the prophets are \"holy\" well then I can just say miss Cleo has the \"power of the African shaman\" (at least this is what I think it was, no offense meant to any ethnic group) OK now here\'s something that doesn\'t make sense. Noah had to build an ark and collect to of every animal in order to sail across the ocean in order to save all the animals. Well how could Noah traverse the whole world and collect two of every animal? Especially since only some animals live on continents that are surrounded by water? how could he retrieve these animals if the ark wasn\'t even built yet? Another thing the bible says is that Noah lived to be around 700 years old (a number around that) Do u mean to tell me that all this technology we have has decreased our life span by 600 years? Now another point to counter. \"you cannot disprove god\'s existence\" You cannot prove it either. The only thing you CAN do is formulate a theory that best describes a way god can exist. And my theory about him being a phase of our existence and not really have an impact on our world definitely is a theory that fits quite well. Here\'s another point that was said (or the gist of it) \"you cannot prove evolution\". I\'ll make two points about this 1. \"you cannot disprove evolution\" (The point I\'m trying to make is that saying you cannot prove or disprove something is easily contradictable) 2. Although it is true evolution has not been 100% proven it has been proven to a degree, a degree so high it is believable and widely acceptable in today\'s world (Just as D.N.A test\'s are submittable evidence in court, they are not 100% proven, but because it has such a high percentage it is acceptable) Also dj, you talked about c-14 dating techniques that proved humans and dinosaurs lived at the same time. If this c-14 dating was true then that means it showed humans lived in the age of dinosaurs (beyond 6,000 years ago/4,000 B.C) which not only disproves your 6\'000 year existence concept but this is also incorrect because that means humans have survived the ice age, (another phenomenon which has also been proven. Now about the new testament, I DO believe in Jesus, BUT I do not believe Jesus was the son of god. Why. Right before Jesus dies he said this. \"my god, my god, why have you forsaken me\" Now supposedly Jesus, god and the holy spirit are one (the holy trinity) Now according to Jesus (or god since jesus=god) god has killed him which means god killed Jesus, which means god killed god. How could god kill himself and still exist. this means he didn\'t kill himself. (This is yet another paradox) Now see a lot will now say Jesus was resurrected from the dead, But by who? God didn\'t exist, he was dead (because Jesus was dead) so who resurrected Jesus? noone which means he never died. But then the bible said he died so the bible is wrong!!! Well in any scenario something is wrong Also a lot of people ask how you explain miracles. Well lets say someone was cured of cancer and the doctor\'s can\'t explain it and it was a \"miracle\" Ok well firstly do we know of any cure\'s for cancer? No. So how would the \"miracle scientists\" (or whatever they\'re called) be able to look for whatever cured the cancer? They wouldn\'t. So these miracle scientists are basically looking for something that they don\'t know what it is, and then when they can\'t find it, they justify it as a \"miracle\" Thats just a person saying \"I don\'t know what it is, and because I know everything it is therefore unexplainable\" We DON\'T know everything. These miracles are products of people\'s belief that humans are close to perfect technology. We are not. I thank anyone who read all this. I will post more as the debate goes on and I look forward to reading your arguments, your beliefs that may persuade me to a new form of belief (That\'ll be a VERY hard task), and anyone who was persuaded by my arguments. I will be open to suggestion when I read your comments, please be open to mine. Also, Please excuse any gramaratical errors i have made as i did not proofread this.',1072,'Alan','2003-05-04 13:53:44');
INSERT INTO forumpost VALUES (832,128,3,'Re: The existence of god','One day Achilles ran a race with a tortiose. The tortiose had a 100 meter head start, and they ran. Now the question is, did they ever catch up? This is like a question of religion. You can argue and argue and argue about it, and all you will get is anger and not a lot more.\r Secondly i have not made this debate to be malicious. It just came and I knew it would be a good topic to talk about.\r Thirdly, well despite my vain attempt in the first paragraph about me talking about not calling other\'s belief\'s insulting names e.g piddly, I was ignored. I tried to make sure that people opinion\'s would be respected, but i guess that was a little to much for some. Dj, I have not called or insulted your beliefs in anyway, please don\'t insult mine. I hope that this is not to hard to handle. You can believe my beliefs are stupid, just please don\'t say it. Since you have a strong belief in the bible you should know what goes around comes around. Fourthly, well evolution seems to be a big debate now so I shall explain two simple concepts that give evolution a degree of accuracy proving that it may have happened. Another concept that supports evolution is wisdom teeth. A lot of people have to get them removed. Why? because there is no room for them. Over the years wisdom teeth removal rate has gone up. But god has created man in his own image, and god is perfect. Why would there be a flaw in the creation of man? To sum up evolution you say there is no more proof. Well tell what has MORE proof. God just did it? or: All the reasoning behind evolution(which has explanation behind it) happened? And as to your point about the tracks, as you have said yourself almost every dating technique is inaccurate so how can you say both footprints were made near the same time. On top of that, prints CAN be remade. By comparing cement to mud you were comparing an apple to an orange. Mud allows to be remolded when re-wet, cement doesn\'t. So how do you know the mud in which the fossil was contained was not changed in order to allow footprints once again. as fpr the debate I made about miracles, that was in response to your argument (or possibly someone else\'s)asking \"how do you explain bones magically healed, and diseases gone leaving doctor\'s baffled\" and i did a very good job of explaining that in my first paragraph.',1072,'Alan','2003-05-05 12:36:41');
INSERT INTO forumpost VALUES (844,127,4,'Re: auto-log out un-post','i am on ie 4, but just today the phenomenon happened to me again while i was typing my second post in the existence o god thread. I took a long time to type it up so i think the site might have an in-active=sign-out type thing going. (don\'t worry i ctrl+c right before i posted it and found out it never posted so it was just a matter of looging in and using ctrl+v)',1072,'Alan','2003-05-05 12:45:21');
INSERT INTO forumpost VALUES (845,127,4,'Re: auto-log out un-post','wait let me re-word that, and tell me if it sounds like programming language(i\'ve always wanted to learn) ahem I believe the problem may be a Oh yes by the way dj. I NEVER said god was dead. My point about jesus killing himself was merely me finding a contradiction within the bible, and me saying that god is a \"phase\" in our existence, that does not mean he is dead.',1072,'Alan','2003-05-06 14:00:10');
INSERT INTO forumpost VALUES (858,128,3,'Re: The existence of god','Yes, I would... Being bound by laws is the whole idea behind a utopia... :) But I don\'t care about this whole religion mess.',1626,'Gamer','2003-05-06 16:06:49');
INSERT INTO forumpost VALUES (859,125,4,'Re: Bait and switch','Now gamer what bryan does is sort of acceptable, but submitting blank problems was a definate thing people should not be doing.',1072,'Alan','2003-05-06 16:40:55');
INSERT INTO forumpost VALUES (860,128,3,'Re: The existence of god','I to would like to see a Utopian world (of course to this you would have to eliminate emotion so i guess i would want a world that is extremeley close to a utopia. But Gamer let me ask you this. Would just saying \"god did it\" and not figuring out the keys to science allow us to achieve this utopian world. Definetely not. In order for a utopian world to exist the following must happen. We must reach all knowledge and every person must fully understand all the laws of existence, which is possible (not in the next couple thousand years)by things like genetic engineering, stem-cell research etc.',1072,'Alan','2003-05-06 16:48:10');
INSERT INTO forumpost VALUES (861,128,3,'Re: The existence of god','Before I chuck in my two penn\'orth I should make it clear that I\'m an atheist, but that does not mean that I don\'t respect the views of others. Clearly religion is a subject that stirs up great emotions (why else would somebody strap a load of C4 to themselves and blow up a bus?) so I\'m sure that you could read what I\'m about to say and see dozens of \'implied insults\' should you wish to interpret it that way. However, please note that none are intentional and all I\'m trying to do is put a different perspective to the debate. \r Anyways fl made a very good point about how we have \"faith\" in science to. The real question is what faith will benefit mankind the most? I choose science. There may be limits to it(as i believe quantum mechanics is only a theory, correct me if i\'m wrong) but then again there is still so much more we could learn between science and quantum mechanics. I guess if humans ever reach all the limits stated above, we will know all the laws of existence.',1072,'Alan','2003-05-07 10:26:04');
INSERT INTO forumpost VALUES (865,129,7,'Greetings and ??','Greetings,\r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r P.S for the riddle limitation (if it were to be put in place) I think that users who are submitting problems will just put their riddles under logic so perhaps a no riddle note (which would also state any riddle submitted under a false category with inappropriate rank will be deleted when it reaches the queue)',1072,'Alan','2003-06-20 15:06:42');
INSERT INTO forumpost VALUES (1315,185,4,'Re: The queue needs help now!','Yes... Just say \"Any riddle submitted not under riddles will take up a queue-weight spot and be deleted anyway\"... The queue-weight thing is what discourages people from just submitting problems. :)',1626,'Gamer','2003-06-20 16:27:20');
INSERT INTO forumpost VALUES (1316,186,6,'Log?','In some of the problems it has maths terms like \'log\'. I\'m only 13, so I don\'t know what that means. Perhaps there could be a page with different math terms and symbols, explaining what they mean for people like me. Or am I the only one?',1919,'Lewis','2003-06-21 09:57:57');
INSERT INTO forumpost VALUES (1317,186,6,'Re: Log?','Lewis, a log can be explained as a measure of the order of magnitutde of a number. As the log gets larger, the number which it is derived from grows exponentially. To expand this idea into a strict definition, it is important to have a knowledge of exponents. For example, 2^5 or 10^3. If you don\'t understand this yet, then you\'ll need to figure this out first, as logs are simply an application of a particular relationship using exponents.\r to skip two lines and \r Now thats the rant that was involved in my problem but heres my general opinion. Don\'t just look at a problem and then say nothing, comment on why you won\'t give it a thumbs up. A lot of times a person will say \"It just doesn\'t interest me\" Well We\'re are evaluating if problems are siteworthy not If they interest us or not is irrelevant unless you think others will not be interested. So in conclusion please look and evaluate every problem and don\'t leave it sitting there. i think dancing 2 would\'ve been a pretty good problem for the algorithms category to.',1072,'Alan','2003-11-04 15:52:51');
INSERT INTO forumpost VALUES (2207,300,5,'Re: Scavenger Hunt','lol i tried. truth is im not really up to challenge 4 heh',3386,'Victor Zapana','2003-11-04 18:20:47');
INSERT INTO forumpost VALUES (2208,300,5,'Re: Scavenger Hunt','hmm.. i see i got from another site that ie6 is more ActiveX friendly while netscape is more java friendly. is that why?',3386,'Victor Zapana','2003-11-04 18:23:41');
INSERT INTO forumpost VALUES (2209,300,5,'Re: Scavenger Hunt','It looks like Silverknight just went right up those challenges after you added the free t-shirt. I didn\'t know Flooble had t-shirts! That\'s so cool! Unfortunately, I have internet explorer. I was having trouble doing something on challenge 4, and at first I thought it was just because I was doing it wrong or something. Well, I always have that other browser...',3558,'Tristan','2003-11-04 19:01:27');
INSERT INTO forumpost VALUES (2210,300,5,'Re: Scavenger Hunt','lol, yeah, I\'m just a sucker for free t-shirts... :-)\r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r BTW, congrats on making Journeyman. Does that mean I can complain to you if I think my puzzles are taking too long to get posted?',2839,'FatBoy','2003-12-01 11:24:47');
INSERT INTO forumpost VALUES (2521,301,3,'Re: WOOHOO!!!','Thanks (and frankly, I\'m ashamed I didn\'t do it earlier...)\r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r Now heres some of the real thing.\r \r \r \r\nHow would you go about measuring a 45 minute time interval with just these two ropes?','The solution to this problem is fairly elegant.\r\n \r\nRealize that if a rope takes an hour to burn from end to end, we can reduce that time to half an hour by lighting up both ends simultaneously. (This will work, even though the rope burns unevenly.)\r\n \r\nSo, we light up one rope from both ends, and the other rope from just one end. At the point that the first rope is completely consumed, we know that half an hour has elapsed.\r\nAt this moment, the second rope still has half an hour to burn. \r\n \r\nBut we can reduce that to 15 minutes by lighting the second end of the second rope now, and when that rope is gone, we know that it\'s been 30 + 15 = 45 minutes.','2002-03-28',20031120232101,NULL,3,3,0,3.83,20020328000000,0);
INSERT INTO problem VALUES (5,4,2,1,'Pick a box!','You are shown three boxes, and told that one of them contains a prize. You are then asked to pick one box, and if that box is the one with the prize, you will win it. After picking a box, you are shown that one of the other two boxes is empty, and offered a chance to change your selection.\r\n \r\nShould you do this? Would changing your choice to the other remaining box affect your odds of winning? Why or why not?','Switching your choice would actually double your odds, and would be the smart thing to do. Here\'s why:\r\n \r\nLet\'s say you start off by picking an arbitrary box. Let\'s call it box (A). Let\'s also call the other two boxes (B) and (C). Since the chance of the prize being in a particular box is 1/3, your selected box, (A), will be the winner one out of three times.\r\n \r\nWhich means you will lose the other two times, when the prize will be in either box (B) or box (C). Now the problem states that you are shown that one of these boxes is empty. But of course one of them has to be empty since the prize cannot be in both of them. And of course the odds of the prize being in either (B) or (C) are not affected by revealing which box the prize is not in. \r\n \r\nSo let\'s say the box revealed to be empty is (B). If the chance of the prize being in either (B) or (C) is 2/3, and we know that it\'s definitely not in (B), that means that we can say that the probability is 2/3 that it is in (C) - and 1/3 that it is in (A).\r\n \r\nThus changing your choice raises your chance of winning from one out of three to two out of three.\r\n \r\nYou can see the statistics of this here.\r\n \r\nUpdate: Here\'s a more intuitive explanation...\r\n \r\nAt the time you make your initial guess and pick one box, the prize is either contained in that box, or not contained in it. \r\n \r\nIf the prize is in the box you picked, changing your choice is obviously the wrong thing to do. \r\n \r\nHowever, if you were initially wrong, then the prize is in one of the other two boxes. After one of those boxes is revealed to be empty, the prize will most definitely be in the last remaining box, so you should definitely switch.\r\n \r\nSo you stay with your choice if you are initially correct, and switch if you were wrong. Now the chance that you were right with your first guess is 1/3, and that you were wrong - 2/3, so in two out of three cases a switch makes sense.','2002-03-28',20031119155147,NULL,3,3,0,3.83,20020328000000,0);
INSERT INTO problem VALUES (6,5,2,1,'Make four equilateral triangles','An equilatteral triangle is a triangle in which all three sides have the same length. How can one arrange six equal-length match sticks so that the result contains four equilatteral triangles?','The idea here is to not confine yourself to a flat surface.\r\nBy building a pyramid out of the matches (3 matches for the base, and 3 more as the edges meeting at the top), you make the 4 triangles needed (One at the base, and three more are the faces of the pyramid).','2002-03-28',20030824232101,NULL,2,3,0,2.50,20020328000000,0);
INSERT INTO problem VALUES (7,4,2,2,'Simple coins','I toss two coins and look at the outcome.\r\nI then tell you that at least one of the coins is showing up as \"tails\". What is the chance that the other one is showing \"tails\" as well?\r\n \r\n(from techInterview.org)','The probability is 1/3. \r\n \r\nWhile it may seem like it should be 1/2, this is not so. This problem can be restated as follows:\r\n \r\n\"When two coins are tossed, what is the probability that they both show tails, given that at least one is showing tails?\"\r\n \r\nWhen two coins are thrown, there can be four possible equally likely outcomes: T-T T-H H-T and H-H. Now the H-H possibility is discarded, since at least one of the coins is showing tails. Of the other three, only one outcome yields the desired result, and since they are all equally likely, the probability of getting that outcome is 1/3.','2002-04-09',20031009232103,NULL,2,3,0,3.82,20020409000000,0);
INSERT INTO problem VALUES (10,6,2,1,'Four people on a bridge.','Four people need to cross a bridge at night. They have one flashlight for the four of them, but the bridge is only wide enough for two to cross at a time. Because it\'s so dark, anyone crissing the bridge must do so with the flashlight. \r\n \r\nPerson A can walk across in 1 minute. Person B takes 2 minutes; person C -- 5 minutes, and finally person D needs a full 10 minutes to cross.\r\nNaturally, if two people are crossing the bridge, they move with the speed of the slower person.\r\n \r\nWhat is the shortest amount of time it will take for all four to get to the other side?','The shortest time is 17 minutes.\r\n \r\nThe key to this problem is that to minimize the time spent, we need to have persons C and D to cross together. However, to avoid one of them having to make the trip back, we need to ensure that when they cross, someone is waiting for them on the other side to take the flashlight back.\r\n \r\nSo we send A and B to the other side first. (This takes 2 minutes.) Then one of them returns with the flashlight (it doesn\'t matter who - the result will come out the same, but let\'s assume A comes back - making the total elapsed time 3 minutes.) Now C and D cross together, taking 10 minutes (and bringing our total to 13). B then takes the flashlight and returns to help A get across - taking 2 minutes to go each way, and yielding the result of 17 minutes.\r\n \r\n(You can verify that the result is the same if it is B and not A who returns with the flashlight initially.)','2002-04-14',20030717232102,NULL,2,3,0,3.89,20020414000000,0);
INSERT INTO problem VALUES (11,6,2,1,'A busy bee','A bicyclist starts his ride home from a point 10 miles away from his house going 5 miles per hour (assume the road is a perfect straight line). At the same time, a bee, initially sitting on his helmet (always wear your helmet!), takes off and flies toward the house at the speed of 15 miles per hour.\r\n \r\nUpon reaching the house, the bee turns right around and flies back toward the bicyclist. When it reaches him it turns around again and flies back to the house. The bee keeps doing this until the man finally arrives at the house himself.\r\n \r\nWhat total distance did the bee cover by that point in time?','The solution to this problem is much easier than most people initially think.\r\n \r\nThe key here is not to start doing the arithmetics by seeing how long each \"segment\" of the bee\'s flight is.\r\n \r\nRather, notice that we know both the bicyclist\'s speed, and the distance he needs to travel. Dividing 10 miles by 5 miles/hour we calculate that the total time it took for the bicyclist to get home is 2 hours. Now we realize that for those 2 hours, the bee has been going back and forth at a constant speed of 15 miles per hour, meaning that it would have traveled exactly 30 miles.','2002-04-15',20031209232101,NULL,3,3,0,3.56,20020415000000,0);
INSERT INTO problem VALUES (12,6,2,1,'A Bookworm’s meal',' \r\nThe volumes are identical in size, each has a front and a back cover that is a millimeter thick on each side, and the pages of each are a 10mm thick stack of paper from the first page to the last.\r\n \r\nIf a bookworm starts its meal on the first page of the first volume (already inside the front cover), how long will it take to eat his way through to the last page of the second volume (inside the second volume’s back cover)?',' \r\nSo rather than having to eat through two sets of pages and two covers, the worm\'s meal is actually much shorter - consisting of the front cover of the first book and the back cover of the second book.\r\n \r\nTogether they are 2 millimeters thick, so the worm will spend only 1 hour on the meal, not 11 hours as you may initially think.','2002-04-19',20031209232101,NULL,3,3,0,3.50,20020419000000,0);
INSERT INTO problem VALUES (14,4,2,1,'A crazy passenger','A line of 100 airline passengers is waiting to board the plain. They each hold a ticket to one of the 100 seats on that flight. (For convenience, let\'s say that the Nth passenger in line has a ticket for the seat number N.)\r\n \r\nUnfortunately, the first person in line is crazy, and will ignore the seat number on their ticket, picking a random seat to occupy. All the other passengers are quite normal, and will go to their proper seat unless it is already occupied. If it is occupied, they will then find a free seat to sit in, at random.\r\n \r\nWhat is the probability that the last (100th) person to board the plane will sit in their proper seat (#100)?','The solution to this one is pretty mathimatically involved.\r\n \r\nThe crazy passenger that boards first has an equal chance of getting on any of the 100 seats. Therefore, the probability of this person sitting in a particular seat k is 1/100.\r\n \r\nNow for any value of k, all the passengers up to k will board and take their seats as normal. Then the k-th passenger will find themselves out of a seat, and pick a random seat, in effect, becoming the crazy passenger for a problem with 101 - k passengers.\r\n \r\n(For example if the crazy person takes the tenth seat, passengers 2 through 9 will be seated normally, and when passenger 10\'s turn comes, they can be considered the crazy passenger first in line of 91 people boarding a plane with 91 seats.)\r\n \r\nLet us define P(n) as the probability that the last of n passengers boards their proper place under the conditions of the problem. So for solution, we are looking to find the value of P(100).\r\n \r\nIn a situation with n passengers, the first, \"crazy\", passenger can take any of the seats 1 .. n with the probability of 1/n. Also, given some seat number k that the crazy passenger may occupy, the problem will become that of 1+n-k passengers.\r\nTherefore, we can say that \r\nWhat we would like to do is see what the value of P(n) is in terms of P(n-1). \r\n(Hint: it\'s quite large)','The number is 105263157894736842. Hey, I said it was quite large, didn\'t I?\r\n \r\nStart by realizing that the second to last digit of the original number is 4. (This is because the new number\'s last digit has to be double the old last digit which was two. And the new last digit is the original next to last digit - everything gets shifted when you move the 2 to the front). \r\n \r\nNext write down: \r\nIs it ever possible for all chameleons to become the same color? (Why or why not?)','Forall chameleons to become of the same color, the number of chameleons of any two colors must become the same. (Then they all meet, and turn into chameleons of the third color.)\r\n \r\nIn other words, the difference between chameleon populations must become 0.\r\n \r\nInitially, this difference is 2 between red and green, 2 between green and blue and 4 between red and blue.\r\n \r\nWhenever two different color chameleons meet, they become the third color. That means that if chameleon ofcolor A meets one of color B, they turn to color C. Thus the populations for A and B have gone down by 1 each, and the population of C has gone up two. Therefore, the difference between A and C, and B and C has been changed by 3. (The difference between A and B is obviously unchanged.)\r\n \r\nSince there is no amount of adding or subtracting 3 that can turn either 2 or 4 into 0, there is no way for the population to ever become the same color.','2002-04-19',20040324232101,NULL,4,3,0,4.25,20020419000000,0);
INSERT INTO problem VALUES (17,5,2,18,'10 trees','You are working for a farmer, who gives you ten trees to plant. He tells you:\r\n \r\n\"I want you to plant these ten trees in five rows. There must be exactly four trees in each row. \" \r\n \r\nHow do you plant the trees?',' \r\nBy planting them in the star shape shown, you can easily achieve what was asked of you.','2002-04-21',20030407232101,NULL,2,3,0,4.00,20020421000000,0);
INSERT INTO problem VALUES (21,8,2,1,'A game of Nim','This game is a variation of the old Eastern game \"Nim\".\r\n \r\nStarting with a deck of cards, two players take turns removing cards from the deck. During his turn a player may take one, two or three cards. The winner is the person who takes the last card (or cards) from the deck.\r\n \r\nThere is a strategy that the first player can follow in order to assure his victory, but this strategy will not work for all the deck configurations.\r\n \r\nWhat is this strategy, which of the following decks will it work for, and why?\r\n \r\n(This doesn\'t work for 3 cards because the second player will just take them all, nor for 5 cards, because the second player will take one leaving the first player with 4.)\r\n \r\nSo taking this a step further, a deck of 8 cards is also a winning deck for player one, since no matter what player two does, player one can make sure that the deck will contain four cards after his turn.\r\n \r\nIn fact, the strategy is to make sure that the deck contains the number of cards that\'s a multiple of four after your turn.\r\n \r\nPlayer one can only use this strategy with the 54 card deck by taking two cards from it. All the other cards already contain a number of cards that\'s a multiple of four, and with these, the game can be won by the second player if he follows the strategy.','2002-04-23',20040115232102,NULL,3,3,0,3.86,20020423000000,0);
INSERT INTO problem VALUES (18,7,2,1,'How many pages?','When setting the type for a book, a publisher wanted to use a particular font to number the book\'s pages. They found that they needed 2775 digit characters for the whole book. \r\n \r\nHow many pages does the book contain?','This one is a straight arithmetics problem.\r\n \r\nThe first 9 pages of the book, (pages 1 through 9) need 9 digits to enumerate (one per page).\r\n \r\nNext, getting into the double digits, we have 90 pages (10 thorugh 99), for a total of 180 digits.\r\n \r\nIt\'s easy to calculate that if the book had more than 1000 pages, it would need at least \r\n \r\nSo, to calculate the number of three-digit pages, simply subtract 189 from 2775 and divide by three:\r\n \r\nTo make the matter worse, one of the brothers is a pathological liar who never tells the truth, while the other never lies. Not only do you not know which is the liar and which tells the truth, but also, you do not know wether Bob is the liar or not.\r\n \r\nUpon meeting the brothers, you can ask one short question of either of the brothers (but not both) to establish with certainty which of the two is Bob. (It is possible to do this with a question of four to five words.)\r\n \r\nWhat question would you ask?','Ask one of them \"Is Bob a liar?\".\r\n \r\nThere are four possibilities:\r\n \r\nSimilarly, you can ask if Bob tells the truth, and reverse the answers\' meanings.','2002-04-22',20030603232102,NULL,3,3,0,3.50,20020422000000,0);
INSERT INTO problem VALUES (20,5,2,1,'A fly on a cube',' \r\nA fly, sitting in the vertex (A) of this cube must travel the surface of the cube until it arrives at the vertex (G).\r\n \r\nIf the fly cannot leave the surface of the cube, what is the shortest path for the fly to take between the two points?','The shortest path is for the fly to travel to the poing exactly in the middle of (D) and (E), and then head straight for (G) from there.\r\n \r\nThe reason is that if you \"unfold\" the cube, and bring the faces ABED and DEGF into one plane, it will become obvious that this is actually a \"straight line\" path between (A) and (G).\r\n \r\n(The fly can also travel through the midpoint between (F) and (D).)','2002-04-23',20040229232101,NULL,2,3,0,3.30,20020423000000,0);
INSERT INTO problem VALUES (22,8,2,1,'Matching pairs','A standard deck of 52 cards is shuffled, and we take cards from its top in pairs.\r\n \r\nIf both are of a red suit, I take both cards.\r\nIf both are black - you take them.\r\nIf they are different colors - we put them in the discard pile.\r\n \r\nIf at the end of the deck you have more cards than I, I will pay you a dollar.\r\n \r\nIf I have more cards, or if we have the same amount of cards, I pay you nothing.\r\n \r\nWhat is a fair \"admission price\" to play this game?\r\n \r\n(from techInterview.org)','When the game is finished, let\'s say you took X pairs,\r\nI got Y pairs, and Z pairs were discarded.\r\n \r\nThat means there were 2*X + Z black cards, and 2*Y + Z red cards played. Since in a standard deck, there is an equal amount of red and black cards in it, therefore, 2*X + Z = 2*Y + Z and X = Y.\r\n \r\nWe would always get an equal number of cards at the end of the game, and therefore I would always win. This game is not fair at all, and the only fair admission price for it is nothing.','2002-04-23',20031230232102,NULL,3,3,0,3.50,20020423000000,0);
INSERT INTO problem VALUES (23,2,2,1,'Bob and his brother, revisited','You are to meet Bob and his brother again. Imagine you still don\'t know which one of them is Bob, and wether or not Bob always lies or tells the truth.\r\nIn other words, let\'s say you never solved the first problem.\r\n \r\nBut this time, your task is to find out wether or not Bob, whichever brother he is, will lie to you.\r\n \r\nIt is possible to find this out with a short question to either one of the brothers. (A question consisting of four to five words.) What will you ask?','A mirror image of the original Bob and his brother problem, the question to ask in this case is \"Are you Bob?. \r\n \r\nIf the person you ask is\r\n \r\nAnd 12111/3 = 4037 with no remainder.','2002-04-24',20040301232101,NULL,2,3,0,2.11,20020424000000,0);
INSERT INTO problem VALUES (25,6,2,1,'A clock tower','A clock tower bell sounds to mark off every hour with the number of bells equal to the hour (three consecutive bells sound at three o\'clock, etc). The last bell marks the exact beginning of the hour. \r\n \r\nThe sounding of the bells for six o\'clocks starts at 30 seconds before six.\r\n \r\nAssuming that the bells are always evenly and equally spaced in time, how long before noon must the sounding of the bells begin?','While the six o\'clock bells take 30 seconds, it is incorrect to assume that each bell takes 5 seconds. If you think about how the bells are sounded, you will realize that they are instaneous, and it is the periods between the bells that make up for the time delay.\r\n \r\nFor six bells, there are five pauses, adding up to 30 seconds, which means that each pause takes 6 seconds.\r\n \r\nFor the bells to strike twelve times, there will be 11 such pauses, taking 66 seconds. That means that to mark noon, the clock tower starts ringing its bells one minute and six seconds before.','2002-04-24',20031209232101,NULL,3,3,0,2.38,20020424000000,0);
INSERT INTO problem VALUES (26,6,2,1,'An inconsistent climber','A mountain climber is journeying up a mountain trail. He starts out with the sunrise, and gets to the peak just as the sun is setting. Throughout the day, he moves with inconsistent speed, slowing down to rest a few times.\r\n \r\nHe spends the night at the top, and in the morning sets out downward, reaching basecamp by nightfall. (Even though the going is easier, he stops a number of times to admire the scenery and rest.)\r\n \r\nIs there an altitude on the mountain slope for which the climber was at that exact altitude at the same point during both days? Why or why not?','Let\'s call our climber \"Bill\". Imagine a climber \"John coming down the mountain in the same exact way that Bill comes down it, but a day earlier.\r\n \r\nIn other words, John is coming down the mountain on the same day as Bill is ascending it. Now with Bill going up, and John going down, the two men will be on the same altitude at some point in the day.\r\n \r\nBecause Bill going down and John going down will follow the same path, John will, at that poing, be at the same altitude as Bill will be in 24 hours. So, that is the point in time that Bill is at the same altitude on both the days.\r\n','2002-04-25',20030509232101,NULL,2,3,0,3.00,20020425000000,0);
INSERT INTO problem VALUES (27,9,2,1,'A surprise exam','A professor tells his class that he will give them a surprise examination sometime next week.\r\n \r\nFor our purposes, an examination is considered a \"surprise\" if on that day, the class is not 100% sure that they will get an examination. (If they only suspect it, the examination can still be a surprise.)\r\n \r\nHaving given the class this warning, is it still possible for the professor to give them a surprise examination next week? (Assume that he will not give them an exam if it will not be a surprise.)','The paradox here is in the reasoning that the professor cannot \"surprise\" his class with an exam on friday - since they know that they will get an exam this week, and didn\'t get one in the first four days of the week, they will know that friday must be the day, and so it is no longer a surprise.\r\n \r\nBut then by the same logic, since now the exam can only be given on Mon - Thu, giving it on Thursday, the last possible day, would not be a \"surprise\" either.\r\n \r\nThis way, we can eliminate all the other days of the week one by one, and by this logic, the professor cannot give the students a surprise exam.\r\n \r\nHowever as soon as the class knows that the professor cannot give them a surprise exam during the week, the exam can be given on any of the days and be a surprise (since the class doesn\'t expect it).','2002-04-26',20031124232101,NULL,3,3,0,3.67,20020426000000,0);
INSERT INTO problem VALUES (28,2,2,1,'Mr and Mrs Brown','Mr and Mrs Brown are a little strange. When they are awake, their judgement about everything is absolutely perfect. When they are asleep however, it is exactly the opposite.\r\n \r\nThat is, if Mr Brown is awake and thinks that something is true, then it will always be true. But if he were to be sleeping and dreaming something to be true, it would always turn out to be false.\r\n \r\nOnce, late at night, Mr Brown was under the impression that Mrs Brown is asleep. At that very point in time, Mrs Brown was also thinking about her husband. Was she under the impression that he was asleep or that he was awake?','There are two possibilities here:\r\n \r\nAs you see, in both cases Mrs Brown thinks that Mr Brown is sleeping.','2002-04-26',20030809232100,NULL,2,3,0,3.29,20020426000000,0);
INSERT INTO problem VALUES (29,10,2,1,'Getting to the Knights\' city','You are stranded in a land with only two big cities. \r\nKnightville is populated only by Knights, and Liarville - only by liars. Naturally, you wish to get to Knightville, where you hope to find help.\r\n \r\nDuring your travels, you meet a resident of these parts, who must have come from one of the two cities, but you do not know which.\r\n \r\nWith one simple question, how do you find out what direction Knightville lies in?','Ask the person to point out the direction of his home city.\r\nA Knight will point to Knightville, and so will a Liar, so you will know where to go even without knowing the nature of the person you are speaking to.','2002-04-26',20040209232104,NULL,1,3,0,3.64,20020426000000,0);
INSERT INTO problem VALUES (30,10,2,1,'Escaping the dungeon','You are trapped in a dungeon, and see two doors in front of you. One is a way out, andther will lead to certain death.\r\n \r\nTwo people are standing in front of these doors, one of them a Knight, another - a Liar. Naturally, you do not know who is who, but they know each other\'s true nature.\r\n \r\nBoth the people know which way is correct, but you can only ask one question of one of them before making your choice.\r\nWhat will you ask?','Ask: \"Which door will the other person tell me to use?\" \r\n \r\nNo matter who the person you ask is, they will point to the door leading to death.\r\n \r\nTake the other one.','2002-04-26',20030911232101,NULL,2,3,0,2.83,20020426000000,0);
INSERT INTO problem VALUES (31,9,2,1,'Where\'s the Bee facing?','Remember the busy Bee? The one that kept flying from the bicyclist to his home and back as he approached it?\r\n \r\nWell, at the instant when the person finally got to his house, which way was the Bee facing? (Assume that the Bee\'s turns are instantaneous - that it can go from facing the house to facing the cyclist in no time.)','This is a paradox (as the category implies).\r\n \r\nThe bee will be making an infinite series of turns before the biker gets home. We can assign each leg of its flight a number stating from one: \r\nSince there are an infinity of these short flights, there will be a one to one correspondence between them and the infinity of counting numbers.\r\n \r\nTo say that at the end of infinity the bee is facing either the biker or the house would be to imply that the last counting number is either even or odd.\r\n \r\nWhich is of course impossible given that there is no last counting number.','2002-04-27',20040225103947,NULL,4,3,0,3.90,20020427000000,0);
INSERT INTO problem VALUES (32,10,2,1,'A Banquet','At a banquet attended by 45 Liars and Knights, everybody sat at a big round table.\r\n \r\nAt the end of the feast, each of the attendees was asked about their neighbors, and each stated that they were seated between one Liar and one Knight.\r\n \r\nAs it later turned out, two of the Knights were mistaken in their statements.\r\n \r\nHow many Knights, and how many Liars were in attendance at the banquet?','There must be some Liars at the table, as the knights would not otherwise claim that they were sitting next to Liars.\r\n \r\nFor a Liar to state that he was sitting between a Knight and another Liar, he must actually be sitting either between two Liars or two Knights.\r\n \r\nBut if we have two Liars next to one another, we can have no Knights at the table, since if we have a K-L-L combination, the Liar in the middle would be sitting between a Knight and a Liar, and thus would have told the truth.\r\n \r\nIf everyone at the table were Liars, they could say that they sat between a Liar and a Knight and still be true to form, but the problem states that there were at least two Knights at the table, so we must conclude that no two Liars were sitting next to one another.\r\n \r\nIn fact the only feasible setup seems to be a repeated sequence of two Knights followed by one Liar: \r\nNote that since the total number of people - 45 - can be divided evenly by 3, the last person at the table - a Liar, would be sitting between Knight #44 and Knight #1: \r\nIf both were sitting between Liars, that means two of the \"K-K-L\" sequences turned into \"K-L\". But then the order would be \"shortened\" by two people, which would create a \"mismatch\" at the end of the table: \r\nThe same problem occurs if we try to seat both errant Knights between two Knights each.\r\n \r\nThe only possible solution, is to have one of the mistaken Knights sit between two Liars, and the other - between two Knights. The result - the balance of Knights to Liars is unchanged - of the 45 guests, 30 are Knights, and 15 are Liars.','2002-04-27',20030821232101,NULL,4,3,0,3.56,20020427000000,0);
INSERT INTO problem VALUES (33,2,2,1,'Incorrect information.','Four people think of a number, and then proceed to each tell you something about it.\r\n \r\nSo we move on and assume B lied. Then the number is not a divisor of 150. But the only three two digit numbers that are divisible by 25 are 25, 50 and 75, all of which are divisors of 150. So B isn\'t the culprit either.\r\n \r\nIf C was the liar, then the number is indeed 150, which can\'t happen because it must have two digits according to A. \r\n \r\nFinally if D lied, the number is not divisible by 25. This is possible with all other statements still being true. (For example if the number is 10 or 30.)\r\n \r\nTherefore we know it\'s D that is the liar here. (Unfortunately we still cannot determine the number exactly.)','2002-04-27',20040112232101,NULL,3,3,0,3.44,20020427000000,0);
INSERT INTO problem VALUES (34,7,2,1,'Erasing digits','Digits from 1 to 9 are written on the board.\r\n \r\nA student erases a few of them, and instead writes the digit(s) of their product. (For example if he erases 4, 3 and 7 he would write the digits 8 and 4 since 4 * 3 * 7 = 84.) He also writes a few other random digits on the board.\r\n \r\nHe repeats this process until only one digit remains on the board. What is this digit and why?','The last digit left will be zero.\r\n \r\nThe digits initially on the board include a \"5\", which will result in either another 5 when multiplied by an odd digit, or in a 0 if multiplied by an even one.\r\n \r\nOnce a zero appears on the board, it is impossible to erase by these rules, since multiplying anything by zero still results in a zero.\r\n \r\nTherefore, if there is only one number remaining, zero is it.','2002-04-27',20030418232102,NULL,3,3,0,2.88,20020427000000,0);
INSERT INTO problem VALUES (35,7,2,1,'2001 digits','A string of 2001 digits begins with a \"6\". Any number formed by two consecutive digits is divisible by either 17 or 23. \r\n \r\nWhat is the last digit in this sequence?\r\n \r\nWhat if the sequence had 2002 digits?','First write down all the two digit multiples of both numbers:\r\n \r\nNow, starting with a 6, there are two paths we can take (since 2 of the above numbers start with 6):\r\n \r\nIt is obvious that we can repeat pattern B as many times as we need, and come back to a 6 every 5 digits. So a digit number n where n mod 5 = 1 will always be a 6, and since 2001 mod 5 = 1 the 2001st digit is a 6.\r\n \r\nThe 2002nd digit can be a 9, but can also be an 8, since we can branch into the dead end pattern A here because we have no need to continue the sequence further.','2002-04-29',20031104232103,NULL,2,3,0,4.20,20020429000000,0);
INSERT INTO problem VALUES (36,2,2,1,'A Mad tea party','The Mad Hatter, March Hare and Dormouse are sitting down for a tea party. They sit at a table with twelve chairs, and twelve cups of tea.\r\n \r\nEach day at six o\'clock, everyone moves over two seats to the left or to the right (if any of those seats are free), then if there is tea in the cup at their seat, each one drinks it so the cup becomes empty.\r\n \r\nAfter this, Alice comes and fills one of the empty cups on the table with tea again.\r\n \r\nProve that Alice can make sure that there are at least six full teacups on the table every day just before six.','Each of the tea-drinking characters has a \"parity\" that they must stick to: if they start out with an even numbered seat, they must always stay even, or if they start out odd, they must stay odd. This is because they must always move 2 seats over, and the total number of seats is even.\r\n \r\nAn \"odd\" character will never get to an \"even\" seat, and vise versa.\r\n \r\nThere are two possibilities here:\r\n \r\nAssuming that a different veneer is needed for each square of the board, what is the maximum number of such veneers that the artisan will require to do the job?\r\n','First, realize that the scratch is continuous. If the scratch is in one square, it will be in an adjacent square only if there is some point where the scratch crosses the border between them, and it will be in a non-adjacent square only if there is a sequence of adjacent squares for which the previous statement is true. The length of the scratch is one more than the number of boders crossed. [A curved scratch could possibly double back into an already counted square, lowering the expected total, but the problem states the scratch is a straight line.]\r\n \r\nSecond, realize that when it crosses the border between two adjacent squares, the scratch is also crossing the border between two adjacent ranks or two adjacent columns. [Again, a straight line cannot double back to cross twice.]\r\n \r\nThere are 8 columns, and so there are 7 borders between pairs of columns. Similarly, there are 7 borders btween pairs of ranks. The maximum number of borders that the scratch can cross is 14, so the length of the scratch is 14 + 1= 15. \r\n \r\n(Submitted by TomM)','2002-04-30',20040225103933,NULL,3,3,0,3.00,20020430000000,0);
INSERT INTO problem VALUES (38,5,2,1,'An extra square',' \r\nShape A is actually slightly concave, while B is a little convex. If you draw the two shapes one on top of the other, B will slightly stick out, with the difference being a rombus-shaped area that is exactly one square unit in area.','2002-04-30',20030824232101,NULL,3,3,0,4.00,20020430000000,0);
INSERT INTO problem VALUES (39,6,2,1,'Opening doors','Imagine a row of 100 closed doors. Now, make 100 passes along the row, and at each pass \"toggle\" the doors whose number is divisible by the number of the pass. (By \"toggle\", we mean to open a closed door, or close an opened one.)\r\n \r\nFor example, on the first pass, we will toggle all the doors, on the second, we will toggle only the even-numbered doors, on the third - only doors whose number is divisible by three, and so on.\r\n \r\nAt the end of the 100 passes, how many doors will be left open?\r\n \r\n(from techInterview.org)','Since we \"toggle\" the doors, we can realize that the only doors that are open at the end of the exercise are the ones that are toggled an odd number of times. We also know that a door is toggled once for each divisor that it has.\r\n \r\nBut divisors come in pairs. By definition, if N is divisible by M, there is also some other number K = N/M which N will be divisible by.\r\n \r\nThe only way around this is when K = M, which means that N = M \r\n(So 4 can be broken into 1*4 and 2*2, meaning it will be open on the first, closed on the second and re-opened on the fourth passes.)\r\n \r\nSince there are 10 perfect squares between 1 and 100, that\'s how many doors will stay open.','2002-05-01',20030601232101,NULL,3,3,0,3.25,20020501000000,0);
INSERT INTO problem VALUES (40,11,2,38,'The odd coin','In a pile, there are 11 coins: 10 coins of common weight and one coin of different weight (lighter or heavier). They all look similar. \r\n \r\nUsing only a balance beam for only three times, show how you can determine the \'odd\' coin.\r\n \r\nOpen problem (i cannot solve this myself): how many more coins (with the same weight as the ten) can we add to that pile so that three weighing still suffices? My conjecture is zero, though my friend guessed that adding one is possible. The best bound we can agree upon is < 2.','Divide the 11 coins into three trios and one pair. Let the trios be A,B,C. Weigh A against B. Then weigh A against C. From this we can determine whether the odd coin lies in any of the trio or not. \r\n \r\nCase 1: the odd coin does not lie in any trio. \r\nThis happens when both weighings are balanced. Then the odd coin must be in the pair. Take any one coin from any trio (which are not odd), then weigh against any coin from the pair. If it shows balance, then the other coin from the pair is odd. If it is not balanced then the one on the balance (from the pair) is odd. Then we are done by three weighings.\r\n \r\nCase 2: the odd one lies in the trio.\r\nIf this is the case, then we can deduce which trio contains the odd coin, since, we have only three possibilities: \r\nAnd also, we can easily check that we can determine whether the odd coin is lighter/heavier. Now take the trio where the odd coin is supposed to be. Then weigh any two of them: if it is equal then the third one is odd; if not then the lighter/heavier of them (depending on our observation earlier) is odd. We are done with three weighings. ','2002-05-01',20040204232103,NULL,3,3,0,3.25,20020501000000,0);
INSERT INTO problem VALUES (41,10,2,1,'A trial','Three people, A, B and C, (each one of whom is either a Liar or a Knight) are brought before a tribunal for a crime that was commited. \r\n \r\nThe court records have since been partially lost, and it is only known that A testified that C was the guilty one. The testimony of the other people is unavailable.\r\n \r\nIt is known that as the court found that only one of the people turned out to be a Knight, but that he was also the one guilty of the crime.\r\n \r\nWho was it?','Since the guilty party was a Knight, it could not have been A, since he testified that the crime was commited by someone else. (If he was a Knight and was guilty he would have to admit his guilt.)\r\n \r\nSo A was a Liar. Which means that his testimony about C\'s guilt was false, and C was also innocent (though a Liar as well).\r\n \r\nThat leaves us with B who must have been the honest culprit.','2002-05-02',20030601232101,NULL,2,3,0,2.60,20020502000000,0);
INSERT INTO problem VALUES (42,4,2,1,'Trading cards','A trading card series has 200 different cards in it, which are sold in 5-card packages.\r\n \r\nEach package has a random sampling of the cards (assume that any card of the 200 has an equal chance of being in a package).\r\n \r\nOn the average, how many packages will need to be bought to collect the complete series if...\r\n ','After a long tenure on the \"Unsolved\" list, there have been some users who posted solutions agreeing with one another in their results.\r\n \r\nPlease refer to the comments on this problem to read them.','2002-05-03',20030626232102,NULL,3,3,0,4.18,20020503000000,0);
INSERT INTO problem VALUES (43,7,2,38,'Class act','31 students in a row were numbered 1,2,...,31 in order. The teacher wrote down a number on the blackboard.\r\n \r\nStudent 1 said \"the number is divisible by 1\", \r\nThe teacher remarked: \"Very well pups, but two of you gave a wrong statement, and those two sit besides each other\". Determine those two.','Easy if we use elimination (it helps to list down the numbers and cancel as we go along).\r\n \r\nThe number is even for obvious reason, so cancel 1 and 2.\r\n \r\nIf the number is not divisible by any odd n>1, then it is not divisible by 2n. but n and 2n is not beside each other, so we may cancel n and 2n for n=3,5,7,9,11,13,15. \r\n \r\nBy further elimination of number with no possible neighbor, we cancel 4,8,12,31. \r\n \r\nAlso, \r\ndivisible by 4,5 => divisible by 20\r\ndivisible by 3,8 => divisible by 24\r\ndivisible by 4,7 => divisible by 28.\r\n \r\nThen we can cancel 20,24,28 which in turn cancels 19,21,23,25,27,29.\r\n \r\nThat leaves only the pair (16,17), which is the answer if we can verify the existence of a number which satisfies the condition.\r\n \r\nHowever, this is straightforward, any number\r\n8.7.11.13.17.19.23.25.27.29.31k\r\n(where k is odd and not divisible by 17) works. \r\n ','2002-05-02',20030728232102,NULL,3,3,0,3.67,20020502000000,0);
INSERT INTO problem VALUES (44,2,2,1,'A Queen\'s decree','A Queen of an island kingdom was concerned about the high level of infidelity among the island\'s men, so she gathered all the married women of the island and made the following announcement:\r\n \r\n\"There is at least one unfaithful husband in our kingdom. All the wives know of all the unfaithful husbands, but know nothing about their own husband. You are not allowed to discuss your husband with any of the other women, but if it becomes known to you that your man is unfaithful, you must shoot him at midnight of the following night.\"\r\n \r\n(Assume a shot anywhere on the island is heard at any other point on the island.)\r\n \r\nAfter thirty nine nights of uneasy quiet, on the fortieth night the gunshots echoed across the island. How many men were shot that night, and why? (Assume the wives are all super smart.)','If every wife on the island knows about all the other women\'s husbands, but not her own, she will either:\r\n \r\nThus if there is one cheating husband, his wife will know about no other cheaters. But since the queen said that there is at least one exists, she will realise that the cheater is her husband, and kill him in the first night.\r\n \r\nIf there are two cheaters, their wives will only know of one cheater each. They will also know that if the one cheater they know about is the only cheater on the island, he will be killed the first night. (See above.) Since they do not hear a shot the first night, they will realize that there are more than one cheaters on the island, and the second one is their husband. So they will shoot their husbands on the second day.\r\n \r\nIn general, if there are N cheaters, their N wives will know of N-1 husbands, and expect these people to be shot on the N-1\'st night. When no shooting happens, they realise that there are actually one more cheaters than they know about, and that their husband is the extra one. The N are then shot on the Nth night.\r\n \r\nThus, if the shots were fired on the 40th night, that means that 40 of the husbands were unfaithful.','2002-05-03',20030811232101,NULL,4,3,0,4.33,20020503000000,0);
INSERT INTO problem VALUES (45,5,2,1,'Half a cube','Try to do this without any visual aids:\r\n \r\nImagine a perfect cube that is placed on a horizontal surface resting on its point (A), so that the opposite point (B is in the air directly above it. (The long diagonal of this cube (AB) would thus be perpendicular to the surface.)\r\n \r\nThe cube is then cut in half with a horizontal cut - parallel to the surface it is standing on, at the height equal half the length of AB, resulting in two equal shapes.\r\n \r\nWhat is the cross-section of such a cut?','The cross section of the cut is a regular hexagon.\r\n \r\nThe high and the low vertices of the cube each have three edges connected to them. The other six (of the total twelve) edges of the cube, form a \"zig-zag ring\", that if un-linked and flattened out would look like this: \r\nHowever, the worker will not work without getting the day\'s pay up front, and you do not wish to give him more than his due for the fear that he will take it and leave. Therefore, you realised that you must cut some of the links on the chain.\r\n \r\nWhat is the smallest number of links you will need to cut, so that you can make sure that the worker receives one link for every day that he works, but not more?','The answer to this problem is \"one link\". This might be surprising to people who have heard a similar problem where the payment was a bar of gold, rather than a chain.\r\n \r\nBy cutting the third link of a chain open, you end up with the one broken link, a two-link piece of chain on its left, and a four-link piece on its right.\r\n \r\nThen make the payments as follows:\r\n \r\nWhen the men did wake, they looked at each other, saw the black marks and began laughing. Each one thought that his two friends had the mark, while his own forhead was clean.\r\n \r\nSuddenly, one of them stopped laughing, having realized that his forhead must be dirty as well. How did he arrive at this conclusion?','The sages were initially laughing as they all thought that the other two were the only ones with the dirty forehead. The fact that the other two were also laughing didn\'t alarm them, as they could be laughing at one another.\r\n \r\nThen one sage thought:\r\n\"If my forehead is clean, then the second sage is laughing at the third one. But then the third one would see that the second one is laughing, and if my forehead was clean would undestand that the second sage is laughing at him. He would then realize that his forehead is dirty, and stop laughing. The fact that he doesn\'t, means that he thinks the second sage is not laughing at him, but rather laughing at me. That means he sees that my forehead is dirty. I better stop laughing.\"','2002-05-05',20030406232102,NULL,3,3,0,3.25,20020505000000,0);
INSERT INTO problem VALUES (48,4,2,1,'Population control','In one nation, having a daughter is traditionally prefferable to having a son. Therefore, a couple will continue to have children until a daughter is born. Once they have a daughter, they will stop. (Assume that it is possible for a couple to have an unlimited number of children)\r\n \r\nIf the chance of a boy or a girl being born is equal, what would be the ratio boys to girls in this country?\r\n','Assume the country has N families. Since every family will have children until a daughter is born, they will have N daughters.\r\n \r\nBut there is a 1/2 chance that the first child will be a boy, making for N/2 \"firstborn\" boys.\r\n \r\nThere is also a 1/4 chance that the second child will be a boy as well, for a total of N/2 + N/4 boys among the first- and second-born.\r\n \r\nIt is easy to see that after each child, the chance that all the children are boys is reduced by 1/2, so the total number of boys is equal to N/2 + N/4 + N/8 + ..., an infinite series that adds up to N.\r\n \r\nSo the ratio of boys/girls in the country will actually be 1 to 1, unaffected by the strange custom.','2002-05-05',20031225232101,NULL,4,3,0,3.80,20020505000000,0);
INSERT INTO problem VALUES (49,5,2,1,'Two ways up','A tower, 200 feet high, has an elevator inside it, and a spiral stairway winding its way around the tower at a constant 30 degree angle with the horisontal.\r\n \r\nGiven the tower\'s radius of 10 feet, what is the difference between the distance covered by a person going up in the elevator, versus one climbing the stairs?','The tower\'s radius actually plays no part in the problem. \r\n \r\nThe elevator will obviously move exactly 200 feet from the bottom of the tower to the top.\r\n \r\nTo calculate the length of the stairs, imagine it \"uncoiled\" from the tower, and flattened out on a flat surface. You will be looking at a right triangle with the height of 200 feet, and the angles of 30 and 60, where the length of the hypotenuse is what we are trying to find.\r\n \r\nWe can use a simple trigonometric equasion: \r\nSo the length of the stairway is only twice the length of the elevator shaft.','2002-05-05',20030824232101,NULL,3,3,0,2.33,20020505000000,0);
INSERT INTO problem VALUES (50,6,2,65,'Missing dollar','Three poor farmers visit the big city for the first time. In the town, they visit a cheap hotel. \r\nThe hotel owner is farmer-friendly: he has a room for 3 persons which costs only 30 dollars. \r\n \r\nSo, the farmers agree to pay $10 each. They pay and go to their room. \r\n \r\nBut then, the hotel owner realises that he has forgotten his super discount. The farmers only had to pay $25. \r\nSo, he calls the bell-boy and tells him to give the farmers their $5 back. \r\n \r\nBut the bell-boy thinks: \"You can\'t split 5 by 3 well. If I give them their $5, they\'ll probably have a fight.\" \r\nSo he keeps $2 for himself and gives the other $3 to the farmers. \r\n \r\nNow, the farmers each paid $9, that\'s $27 in total, and the bell boy kept $2. But together, that\'s $29! \r\n \r\nWhat happened to the missing dollar? \r\n\r\n \r\n','There is no missing dollar; the arthmetic 27+2 makes no sense in the context of the problem. \r\nEach farmer paid nine dollars, for a total of 27 dollars. Of that 27, the bell-boy kept two and the rest ($25) went to the hotel. \r\n\r\nTherefore, the correct equation is: \r\n\r\n27 - 2 = 25 \r\n\r\n \r\n','2002-05-06',20040322232104,NULL,2,3,0,3.15,20020506000000,0);
INSERT INTO problem VALUES (51,7,2,65,'Cows','A few weeks ago a farmer died. And the will he left behind... fortunately his three sons had had a good education. \r\nHis will was as follows: \r\n \r\nBut, since the sons had a good education, they came up with a solution. \r\nThey lent a cow from the neighbour. \r\nWhy? Then they had 18: \r\n \r\nWhat do you think about the sons\' education? \r\n\r\n \r\n','The sons didn\'t get their intelligence from their father: \r\n1/2 + 1/3 + 1/9 = 9/18 + 6/18 + 2/18 = 17/18 \r\n \r\nIn other words, the farmer left 1/18 of his inheritance undivided! \r\n','2002-05-06',20040113232102,NULL,2,3,0,3.43,20020506000000,0);
INSERT INTO problem VALUES (52,5,2,65,'The groove around the moon','Imagine you would have to put a rope around the moon. Since the moon is 1,738,000 metres in diameter, this is a hard task. \r\nFinally you have managed to get the rope around the moon but... it is one meter short. \r\n \r\nYou decide to dig a groove all around the moon, so that the shorter rope suffices. How deep must this groove be? \r\n(Assume the Moon to be a perfect sphere.)','The outline of a circle is always 2 * Pi * R (R = the radius). \r\nTherefore, the radius will have to decrease by:\r\n100 centimetres / (2 * Pi) = \r\n100 / 6,28 = R = 15,92 cm. \r\n \r\nSo, to put the cable tightly around the moon the groove should be 15,92 centimetres deep. \r\nWhich is still a huge task if you want to gid this deep all around the moon.\r\n \r\nThe fun thing is, that the depth of the groove does not depend on the radius of the object you are digging it in. \r\n \r\nYou could as well \'dig a groove\' in the globe on your desk: it would still have to be 15,92 centimetres. \r\n','2002-05-06',20040307180728,NULL,3,3,0,2.62,20020506000000,0);
INSERT INTO problem VALUES (53,5,2,1,'Four bugs','Four bugs are located in the corners of a square, 10 inches on the side. They are arranged like this: \r\nEach bug will home in exactly on its target, reguardless of the target\'s motion, so their paths will be curves spiraling toward the center of the square where they will meet.\r\n \r\nWhat distance will each of the bugs have covered by then?','The answer is 10 inches. \r\n \r\nFirst thing to notice is the symmetry. Each bug will home in on its target at exactly the same speed, and each will approach the center at exactly the same speed. This means that the four bugs will always form a square. \r\n \r\nSince they form a square, their travel paths will always be at right angles to one another. That means that at any given instant, Bug B\'s motion does not take it any closer or any further away from Bug A. Hence, Bug B\'s motion does not increase or decrease the distance Bug A must travel. \r\n \r\nSo Bug A must travel the 10 inches that was separating the two bugs at the start. This applies for the other bugs as well.\r\n \r\n(Solution submitted by friedlinguini)','2002-05-07',20040201232103,NULL,4,3,0,3.89,20020507000000,0);
INSERT INTO problem VALUES (55,10,2,1,'Another trial','Residents A, B and C, each of whom are either a Liar or a Knight are brought to stand trial for a crime only one of them commited.\r\n \r\nEach person accused one of the other two, but the records do not show who exactly. As it turned out, A was the only Knight of the three.\r\n \r\nCuriously enough, if each person switched their testimony, and accused the remaining suspect (not themselves, and not who they accused originally), then B would come out to be the only Knight.\r\n \r\nWho was the real culprit in the case?','Since each person accused someone else, and since A turned out to be a Knight, his accusation was true. And therefore, he could not be guilty.\r\n \r\nLikewise, B was not guilty, since - in the second case - if he were to testify that someone (not him) was the culprit, he would be telling the truth. Which means he didn\'t do it.\r\n \r\nLeaving us with C, who must have been guilty by elimination.','2002-05-08',20030821232101,NULL,2,3,0,3.80,20020508000000,0);
INSERT INTO problem VALUES (56,6,2,62,'Who owns the fish?','On a street are five houses, side by side, painted five different colours. In each house lives a person of different nationality. The five residents each drink a different beverage. The five residents each smoke a different brand of smokes. The five residents each have a different kind of pet.\r\n \r\nHints:\r\n \r\nWe do, however know that the chord (shown in red) - a line whose ends are on the outer circle and which is tangent to the inner circle - has a length of 10 inches.\r\n \r\nWhat is the area (shaded in light-blue) between the two circles?','Ler\'s say the small circle has the radius r and the big one\'s is R. Then what we need to find is: \r\nBecause A-B is a tangent to the inner circle, it is perpendicular to C-P, and A-P-C makes a right triangle, with R for the hypotenuse, and r and 100/2 for legs. Use the pythagorean theorem: \r\nAt your disposal is a scale, and two weights: a 5 pound one and a 9 pound one. \r\n \r\nHow can you complete this job in only 9 weighings?',' \r\nWhen the man at the back of the line was asked \"Do you know your hat color?\", he replied \"No\". When the man that was second in line was then asked \"Do you know your hat color?\" he replied \"No\". When the man at the front of the line was asked \"Do you know your hat color?\" he replied \"Of course\". \r\n \r\nWhat color of hat was the man at the front of the line wearing?','If the first man saw that the second and third men were wearing black hats, he would be able to know that his is white (since there are only two black hats). The fact that he did not know his hat color means that he either saw one black hat and one white, or two white hats.\r\n \r\nThe second man realized this. He knew that he and the third man could not both have black hats on. Therefore, if he saw the man in front of him wear a black hat, he would immediately know that his was white. Since he didn\'t know the color of his hat, he must have seen a white hat on the third man.\r\n \r\nThe third man, realizing this, deduced that his hat is white.','2002-05-08',20030418232102,NULL,3,3,0,2.86,20020508000000,0);
INSERT INTO problem VALUES (61,12,2,149,'Weekend Rider','A knight was riding through the forest on Saturday when he came upon an inn. After stabling his horse he joined the other patrons for a quiet drink. The knight thoroughly enjoyed himself and decided to stay for a few days. When the time came for him to leave, he had stayed three days, but, the strange thing is he left on Saturday!\r\n \r\nHow can this be?','The knight\'s horse was named \"Saturday\".','2002-05-09',20040129232106,NULL,2,3,0,2.00,20020509000000,0);
INSERT INTO problem VALUES (62,2,2,1,'Tricky Area',' \r\nThat problem is solved using some (moderately) tricky geometry. But if you know that the problem is solvable, it\'s actually pretty easy to solve by simply using the formula for the area of the circle and a bit of logic.\r\n \r\nCan you do it?','The problem asks us to determine the area between the circles by simply knowing the length of the longest chord. The fact that it\'s solvable, means that the radii of the two circles are not important, and as long as the chord stays the same length, the solution won\'t change.\r\n \r\nImagine then, a scenario where the inner circle\'s radius is zero. The area should still be the same since changing the radius shouldn\'t matter. But then the 10 inch chord becomes the diameter of the large circle. Since the inner circle\'s area is zero, the area between the circles is equal to the area of the bigger one: \r\nYou both see only one side of the card. At this point he says that if the bottom side is the same as the top, he will take your money. If the other side is different, you double it. He explains that by now one of the cards is ruled out - if you\'re seeing red, the card cannot be a double black card, and vise versa - so you have a 50/50 chance of winning.\r\n \r\nIs this a fair game? Why or why not?','The dealer is of course trying to trick you. His logic that one of the two possible cards is a winner is flawed. Let\'s say the card is showing a red face. The dealer would have you believe that it is either a red-black card or a red-red card, and therefore your chance of winning is 50/50.\r\n \r\nBut in reality, there are three possibilities:\r\n \r\nAs you can see, only one of these is a winning combination, so your odds of winning are 1/3. Therefore, the payout is not enough to make the game fair.\r\n','2002-05-11',20031201232101,NULL,3,3,0,3.50,20020511000000,0);
INSERT INTO problem VALUES (64,8,2,1,'A game of 15','Two players play this game. Numbers from 1 to 9 are layed out in a row. Players take turns putting a coin on one of the numbers that does not yet have a coin on it. Player one puts his coins head-up, and player two -- tails-up.\r\n \r\nThe winner of this game is the first person to have their coins on three numbers that add up to 15. (For example if a player has coins on 1, 6 and 9, they can win the game by putting a coin on either 8 or 5.)\r\n \r\nIs there a strategy for playing this game? Is there a sure-fire way of winning?','Consider the following table: \r\nTaking turns putting a coin on these numbers is equivalent to a game of tic-tac-toe. A person who has the magic square above to refer to is at a significant advantage, and though as with regular tic-tac-toe, victory is never assured, they will always be able to avoid defeat.','2002-05-10',20030620232102,NULL,4,3,0,4.00,20020510000000,0);
INSERT INTO problem VALUES (66,9,2,1,'The (in)famous Barber','In a certain small town, there is a barber named Bill. Since Bill is the only barber in the town, he decides that he will shave all the town\'s residents who do not shave themselves, but (obviously) not the ones who do.\r\n \r\nIf Bill follows this rule, will he shave himself or not?','The answer to this one is that Bill the barber cannot follow his own rule the way it is stated. If he shaves himself he is breaking it by shaving someone who shaves himself. If he doesn\'t - he breaks the rule by not shaving someone who doesn\'t shave himself.','2002-05-14',20031226232103,NULL,3,3,0,3.35,20020514000000,0);
INSERT INTO problem VALUES (67,7,2,1,'Fat Cats','Three fat cats can eat three fat rats in three minutes. How long will it take for thirty three fat cats to eat sixty six fat rats?','The answer is six minutes. The reason being is that in the first scenario the ration of cats to rats is 1:1, which lets us calculate that one fat cat needs one minute to eat a fat rat.\r\n \r\nIn the second scenario the ratio becomes 1:2, so it will take two times longer.','2002-05-14',20040229232101,NULL,2,3,0,2.88,20020514000000,0);
INSERT INTO problem VALUES (68,13,2,1,'Digits','Can you find the rule used to order the ten digits here? \r\n \r\nIt takes this car 5 hours to go from town A to town B. The return trip only takes 4 hours.\r\n \r\nFind the distance between the two towns.','First, label the uphill distance X, the level ground distance Y, and downhill distance Z. (This is for the first trip. On return X becomes the downhill distance and Z becomes uphill.) We are looking for the total distance, or X + Y + Z\r\n \r\nThe time to travel a distance D at a particular speed V is D/V. Therefore we know that for the trip from A to B the following holds true: \r\nWhen they leave the shop, they notice that both fathers have spent 21 shillings more than their respective sons. Moreover, each of them paid per book the same amount of shillings as the number of books that he bought. \r\n \r\nThe difference between the number of books that Alex bought and that Peter bought is five. \r\n \r\nWho is the father of Tim? \r\n','For each father-son couple holds: the father bought x books for x shillings each, the son bought y books for y shillings each. The difference between their expenses is 21 shillings, thus x^2 - y^2 = 21. \r\n \r\nSince x and y are whole numbers (each book costs a whole amount of shillings), there are two possible solutions: (x=5, y=2) or (x=11, y=10). Because the difference between Alex and Peter is 5 books, this means that father Alex bought 5 books and son Peter 10. This means that the other son, Tim, bought 2 books, and that his father is Alex. \r\n','2002-05-16',20031231232101,NULL,3,3,0,3.86,20020516000000,0);
INSERT INTO problem VALUES (71,2,2,117,'Light bulb','A light bulb is hanging in a room. Outside of the room there are three switches, of which only one is connected to the lamp. In the starting situation, all switches are off and the bulb is not lit. \r\n \r\nYou are allowed to enter the room only once (the bulb is not visible from outside). How can you determine which of the three switches turns on the light bulb? \r\n','To find the correct switch (1, 2, or 3), turn switch 1 on and leave it like that for a few minutes. After that you turn switch 1 back off, and turn switch 2 to on. Now enter the room. If the light bulb is lit, then you know that switch 2 is connected to it. If the bulb is not lit, then it has to be switch 1 or 3. Now touching the light bulb, will give you the answer: if the bulb is still hot, then switch 1 was the correct one; if the bulb is cold, then it has to be switch 3. \r\n','2002-05-16',20030729232116,NULL,2,3,0,3.25,20020516000000,0);
INSERT INTO problem VALUES (72,10,2,1,'Who has the key?','An adventurer found a locked treasure chest in a dungeon.\r\nHe tracked down three brothers (each either a Liar or a Knight) one of whom has the key to open the chest.\r\n \r\nEach made a statement:\r\n \r\nThe adventurer knows that at least one of the three is a Liar, and at least one - a Knight. Who has the key?','If A had the key, he would be a Knight, but so would B and C. Since at least one of the three is a Liar, this cannot be.\r\n \r\nIf B had the key, all three turn out to be Liars, and that is also impossible, since at least one is a Knight.\r\n \r\nThus, it\'s C who has the key, making both him and B Knights, and A a Liar.','2002-05-17',20040128232101,NULL,2,3,0,2.60,20020517000000,0);
INSERT INTO problem VALUES (73,13,2,1,'Fill in the blank','What is the \"row heading\" of the third row (marked with the question mark) in the table shown below? \r\n(6 + 11 + 7)/6 = 24/6 = 4\r\n \r\n(8 + 4 + 12)/8 = 24/8 = 3\r\n \r\n(10 + 55 + 15)/10 = 80/10 = 8\r\n \r\n(Another valid solution, submitted by Happy and yielding the same answer, is to multiply the terms of a row and use the left-most digit of the result.)','2002-05-20',20040225103933,NULL,3,3,0,3.40,20020520000000,0);
INSERT INTO problem VALUES (74,5,2,1,'Triominoes',' \r\nProve that a square, 2^n cells to the side, with one square cell removed from the corner can be covered with triomino pieces without any overlapping or going over the border for any natural value of n. The triominos can be rotated.\r\n \r\n(For example if n = 1, the result is a triomino shape to begin with - a 2 x 2 square with one cell removed.)','This problem is solved with \"recursion\".\r\n \r\nConsider a square with 2^n cells on each side, one corner cell removed. Now, let us prove that it can be filled with triominos if we know for a fact that this can be done to a similar shape with 2^(n-1) on each side. Here\'s our smaller shape: \r\nSince 2^n is twice as much as 2^(n-1), the smaller shape\'s side is 2 times less than the bigger shape. The big shape can be divided into four parts like this: \r\nBut in placing the smaller shape into the three areas, we can rotate them, so that their removed corner is in the center of the big shape. This will result in a triomino-shaped hole in the center of the big shape, which we can fill with one additional triomino piece.\r\n \r\nThus, we have shown that if the \"imperfect square\" of 2^(n-1) cells on each side can be tiled with triominos, one with 2^n sides can be as well. Since for n=1, the shape is a triomino piece, and therefore can be tiled, all natural values of n>1 will result in a \"tilable\" shape.','2002-05-21',20030829232101,NULL,3,3,0,3.60,20020521000000,0);
INSERT INTO problem VALUES (75,6,2,1,'The hands of a clock','Anne and Mike have an argument about the hands of the clock:\r\n \r\nAnne: \"The minute hand takes one hour to make a complete circle. Therefore, it will pass the hour hand once every hour!\"\r\n \r\nMike: \"But by the time the minute hand has made a full circle, the hour hand will have moved 1/12th of the circle ahead. And by the time the minute hand gets to that spot, the hour hand will have moved forward yet again. This will continue indefinitely, so it is obvious that contrary to what it may seem like, the minute hand will never pass the hour hand.\"\r\n \r\nIn reality, how often does the minute hand pass the hour hand?','The hour hand takes 12 hours to make a full revolution around the face of the clock. The minute hand will have made 12 revolutions in that period of time, so it must have overtaken the hour hand (12 - 1 = 11) times.\r\n \r\nSince the hands are moving at a constant rate, each period between the clock hands\' meeting is equal, and therefore they take place 12 hours / 11 times = 12/11th of an hour apart. (This is roughly 66 minutes, but you can calculate it exactly if you wish.)','2002-05-23',20031212232102,NULL,2,3,0,3.30,20020523000000,0);
INSERT INTO problem VALUES (76,11,2,1,'Pearls','You have nine pearls, one of which is (as is usually the case in these problems) fake. You know that the fake pearl weighs less than the others, but it is (of course) impossible to distinguish from the others in any other way.\r\n \r\nWhat is the minimum number of weighings that must be performed to find the fake pearl? How would you go about it?','Divide the pearls into three groups: pearls A:(1,2,3) B:(4,5,6) and C:(7,8,9).\r\n \r\nFirst, weigh the three pearls of A against the three pearls of B. If one of them weighs less than the other, then the fake pearl is in that group. Otherwise, it\'s in group C.\r\n \r\nHaving determined which group the pearls are in, take two pearls of that group, and weigh them. If one is lighter, then that one is fake. If they are both the same weight, then the fake one is the one you didn\'t put on the scale.\r\n \r\nThus we can determine the fake pearl in only two weighings.','2002-05-23',20030726232103,NULL,3,3,0,2.71,20020523000000,0);
INSERT INTO problem VALUES (77,4,2,1,'A blue taxi','A crime has occured in Carborough, involving a taxi. The police interviewed an eyewitness, who stated that the taxi involved was blue.\r\n \r\nThe police know that 85% of taxis in Carborough are blue, the other 15% being green. They also know that statistically witnesses in these situations tend to be correct 80% of the time - which means they report things wrong the other 20% of the time.\r\n \r\nWhat is the probability that the taxi involved in the crime was actually blue?','Let\'s say the city has a total of 100 taxis (this way we can have a one to one relationship between taxis and percent).\r\n \r\nOf these 100, 85 are blue, and 15 are green. Let\'s look at both cases:\r\n \r\nWe know that the witness said they saw a blue taxi. There is a total of 68+3 = 71 percent chance for that to happen. Of those 71%, 68% of the time the taxi will in truth be blue. Thus the probability of the taxi being blue is 68/71 = approximately 95.8%','2002-05-24',20030908232101,NULL,4,3,0,3.56,20020524000000,0);
INSERT INTO problem VALUES (78,2,2,1,'Light at the end of the tunnel','A man was walking through a tunnel. He is 1/4 of the way through when he hears a train approaching the tunnel from behind him.\r\n \r\nIf he turns and runs back, he will make it out of the tunnel just as the train is entering it (and will save himself by a hair). If he goes forward to the far end of the tunnel, he will also just barely make it, emerging from the tunnel just as the train is about to catch up to him.\r\n \r\nIf the man\'s running speed is 7 miles per hour, how fast is the train moving?\r\n \r\n(from techInterview.org)','If the man were to start running back, he would have to run 1/4 the length of the tunnel, and reach the start of the tunnel just as the train is entering it.\r\n \r\nSince he would run at the same speed either way, he could also run forward, and by the time he ran the same 1/4 of the tunnel, the train would still be just entering it. At this point, the person is at the half-way point of the tunnel, having started 1/4 of the way in, and ran 1/4 more.\r\n \r\nNow in the time it will take the man to reach the far end of the tunnel, the train will catch up to him. Therefore, the man will have run 1/2 of the tunnels length in the same period of time that the train covered its entirety. Therefore, the train\'s speed is twice that of the man, or 14 miles per hour.','2002-05-26',20030603232103,NULL,3,3,0,3.88,20020526000000,0);
INSERT INTO problem VALUES (79,4,2,1,'A birthday gamble','For Cathy\'s birthday, her uncle decided to make her a deal. He took ten singles and ten one hundred dollar bills, and asked Cathy to divide them into two piles as she saw fit. He would then blindfold her, and thoroughly shuffle each pile of bills, so that the order was completely random. Finally, he would put each pile in a separate box.\r\n \r\nCathy is to pick one of the two boxes at random, and then pick out a random bill from that box (still blindfolded). She would get to keep whatever bill she pulls out.\r\n \r\nNaturally, Cathy prefers to get a $100 bill. What strategy should she use in breaking up the bills into two piles to maximize her chance of getting a hundred?','Since there\'s no way to affect the box Cathy will pick, in order to maximize her odds of finding the $100, she has to maximize the odds of finding it in each box separately.\r\n \r\nThe biggest chance to find $100 in a box (100%) can only occur if there is nothing in that box but $100s. However, the more $100s we put into one box, the lower the chance of finding $100 will be in the other.\r\n \r\nThus it would be prudent for Cathy to put one $100 bill into one box, and put everyhting else into the other box.\r\n \r\nThis way the odds of \"victory\" for box 1 are 100% and the odds for box 2 are 9/19, or 47.4%, with the overall chance of victory at 73.7%','2002-05-28',20030601232101,NULL,3,3,0,3.29,20020528000000,0);
INSERT INTO problem VALUES (80,5,2,117,'Out for a walk','There are some points on Earth for which the following is true:\r\n \r\nStarting from one of these points, you can walk 1 km South, then 1 km East, then 1 km North, and you will wind up back where you started from.\r\n \r\nOne such point is the North Pole. Where are others?','You can not start 1 km away from the South Pole, if you did, you would not be able to do the second leg of the journey. \r\n \r\nShort answer: These points are at a distance from the South Pole roughly equal to (1 + 1/2(pi)n) km , for some positive integer n. \r\n \r\nLong answer: On a sphere of radius R, the distance d measured on the surface is along an arc of a great circle (that\'s indeed the shortest possible distance). If the \"radius\" d of a circle is measured in that way, its circumference is only 2pi[R sin(d/R)] (since the bracketed quantity is the actual radius of that circle in 3D space). For small values of x=d/R, we have sin(x) » x (1-x ^2/6), and 1/sin(x) » 1/x (1+x ^2/6). \r\n \r\nBefore we apply this to the above situation, we may stop to consider what is theoretically the best value to use for R around the South Pole (this may seem like a ludicrous concern --and it is-- but we are already into ludicrous precision at this point, so we may as well learn something from this): First, consider the Reference Ellipsoid (the defined regular shape with respect to which professionals are charting the irregularities of the Earth\'s so-called \"sea-level\", which is an equipotential surface averaged over time at each point of the Globe). Its \"equatorial radius\" is defined as precisely equal to a=6378137 m, whereas the \"polar radius\" (i.e. half the distance between the North Pole and the South Pole) is about 6356752.3141404 m. This makes the radius of curvature of the Meridian at the South Pole equal to a 2/b or 6399593.6258639 m, for this surface of reference. Now, the South Pole is not at sea level, but on an elevated plateau at about 2835 m of altitude (with an unbelievably thick layer of about 8800\' feet of ice, which accounts for almost 95% of that altitude). This altitude is to be essentially added to the radius of curvature of the \"sea-level\" reference meridian. Therefore, if the surface at the South Pole was perfectly level and smooth, it would be extremely close to the surface of a sphere with a radius R of about 6402428 m. This would make the tiny quantity 1/(6 R ^2 ) (used in the \"final\" result below) equal to about 4.066 10^-9 \r\nAll told, we may now state with more (ludicrous) precision that \"home\" is at a distance from the South Pole very close to: \r\nSet A = { 2,3,4,6 } \r\nWhat is the probability that two randomly chosen elements from B would add up to be more than the product of two randomly chosen elements from A?\r\n\r\n','There are six ways to pick a pair of numbers from a set of four. For set A, the possible pairs and their products are:\r\n \r\nFor set B, the pairs and their sums are:\r\n \r\nOut of the possibilities listed, the outcomes where the sum of a pair from B is greater than a product of a pair from A is as follows:\r\n \r\nIn all, we have 6+5+2+2 = 15 possibilities to meet the condition required, out of a total 36 possible outcomes. This the probability is 15/36','2002-05-29',20030326065623,NULL,3,3,0,3.00,20020529000000,0);
INSERT INTO problem VALUES (82,9,2,1,'The guilty demon','As the story goes, Prometheus stole fire from the gods of Olympus and gave it to humans. This made Zeus very angry. Prometheus was told to return the fire by 1:00pm, an order that he defied.\r\n \r\nTo punish Prometheus for his disobedience, at 1:00 pm, Zeus paused time (he can do this as a god), and conjured up an infinite number of demons. To the first demon he said: \r\n \r\nSo he kept ordering each of his demons to kill Prometheus in half the time of the demon before. After giving orders to all the demons, Zeus un-paused time again and waited.\r\n \r\nAt two o\'clock, Prometheus was dead, and the council of gods was none too happy about it. They told Zeus:\r\n \r\n\"But none of my demons could possibly have killed Prometheus!\" answered Zeus. How can this be?','The reason this is a paradox, is that for any given demon, N, there exists a demon N+1 who would have killed Prometheus earlier.\r\n \r\nTo say that some demon actually did kill the hero is equivalent to saying that there exists a maximum counting number N for which there is no N+1.','2002-05-29',20031209232101,NULL,3,3,0,4.08,20020529000000,0);
INSERT INTO problem VALUES (83,2,2,1,'The general\'s journey','A French foreign legion general must make a trip across the deserts of Tunis to a remote outpost. He must travel on foot from the nearest town, and the distance is such that it will take a person six days to cover it.\r\n \r\nThe problem is that a person on foot can only carry enough water and provisions to last him four days. The general can take with him any number of assistants to help him carry the supplies, but they must be fed as well, and cannot be left stranded in the desert.\r\n \r\nHow will the general make it across, and how many assistants will he need to help him? (Find the smallest number.)','The general starts out from the town with two assistants.\r\n \r\nAfter one day of marching, one assistant will turn back to the town, leaving the general and the remaining assistant a total of 8 days worth of supplies.\r\n \r\nAt the end of the second day, six rations will be left. At this point, the second assistant turns back and takes two of the rations with him - enough to make it to town. The general, now four days away from his destination has four rations left, so he will make it.\r\n','2002-05-29',20030726232103,NULL,3,3,0,4.29,20020529000000,0);
INSERT INTO problem VALUES (84,18,2,117,'The race','You are in a straight 400 m race. You overtake the last person. \r\n \r\nWhat position are you in now?','If the last person was in front of you, how could he be last? My best guess, your position is seated... in the back of a police car for interferring with the race.\r\n','2002-05-29',20040107232101,NULL,1,3,0,2.00,20020529000000,0);
INSERT INTO problem VALUES (85,2,2,117,'Ties','There are 3 gentlemen in a meeting: Mr. Yellow, Mr. Green and Mr. Brown. They are wearing yellow, green and brown ties. Mr. Yellow says: \r\n \r\n\"Did you notice that the color of our ties are different from our names?\" \r\n \r\nThe person who is wearing the green tie says:\r\n \r\n\"Yes, you are right!\" \r\n \r\nWho is wearing what color of tie?\r\n','We know that Mr Yellow was not wearing a yellow tie because of his statement. He also was not wearing the green tie because the one wearing the green tie agreed to his statement.\r\n \r\nTherefore, Mr Yellow was wearing a brown tie. Mr Green was wearing a yellow tie. And Mr Brown was wearing the green tie.','2002-05-29',20030904232102,NULL,2,3,0,2.00,20020529000000,0);
INSERT INTO problem VALUES (86,14,2,117,'Proof','Prove that 3.999... = 4\r\n',' \r\nJohn asks Tom: \r\n \r\n\"Is your house number bigger than 50?\" \r\n \r\nTom answers him, but he lies. (John doesn\'t know that he\'s lying) John continues to ask: \r\n \r\n\"Is your house number a multiple of 4?\" \r\n \r\nTom answers and again, he lies. Then John asks: \r\n \r\n\"Is your house number the square of an integer?\" \r\n \r\nTom answres, but this time he tells the truth. \r\nFinally, John asks: \r\n \r\n\"Is the first digit of your house number 3?\" \r\n \r\nAfter Tom answers (we don\'t know if he lied or not) John declares Tom\'s house number, but he is wrong! \r\nWhat is Tom\'s house number?\r\n','Tom\'s house number is 81. \r\nSince John asked if the first digit is 3, he thought the number was smaller than 50, \r\nbut we know that Tom lied about that, so the number we\'re looking for is bigger than 50. \r\nAfter John asked that, he was certain he had the number, so that means that Tom must have said that the number was indeed the square of an integer, and is a multiple of 4. (That is the only way John could have narrowd down his options to only one) \r\nSince he lied about being a multiple of 4, and told the truth about being the square of an integer, we now know that his house number is bigger than 50, isn\'t a multiple of 4, and is the square of an integer. \r\nThe only number between 8-100 that fits that description is 81. \r\n','2002-05-30',20030904232102,NULL,4,3,0,4.20,20020530000000,0);
INSERT INTO problem VALUES (88,2,2,117,'Yum, arsenic!','In a far away land, it was known that if you drank poison, the only way to save yourself is to drink a stronger poison, which neutralizes the weaker poison. \r\n \r\nThe king that ruled the land wanted to make sure that he possessed the strongest poison in the kingdom, in order to ensure his survival, in any situation. So the king called the kingdom\'s pharmacist and the kingdom\'s treasurer, he gave each a week to make the strongest poison. Then, each would drink the other one\'s poison, then his own, and the one that will survive, will be the one that had the stronger potion. \r\n \r\nThe pharmacist went straight to work, but the treasurer knew he had no chance, for the pharmacist was much more experienced in this field, so instead, he made up a plan to survive and make sure the pharmacist dies. On the last day the pharmacist suddenly realized that the treasurer would know he had no chance, so he must have a plan. After a little thought, the pharmacist realized what the treasurer\'s plan must be, and he concocted a counter plan, to make sure he survives and the treasurer dies. \r\n \r\nWhen the time came, they king summoned both of them. They drank the potions as planned, and the treasurer died, the pharmacist survived, and the king didn\'t get what he wanted. \r\n \r\nWhat exactly happened? \r\n','The treasurer\'s plan was to drink a weak poison prior to the meeting with the king, then he would drink the pharmacist strong poision, which would neutralize the weak poision. As his own poison he would bring water, which will have no affect on him, but the pharmacist who would drink the water, and then his poison would surely die.\r\n \r\nWhen the pharmacist figured out this plan, he decided to bring water as well. So the treasurer who drank poision earlier, drank the pharmacist\'s water, then his own water, and died of the poison he drank before. The pharmacist would drink only water, so nothing will happen to him. And because both of them brought the king water, he didn\'t get a strong poison like he wanted. \r\n','2002-05-29',20030823232101,NULL,3,3,0,4.50,20020529000000,0);
INSERT INTO problem VALUES (89,12,2,117,'Time is an illusion','Two people are talking long distance on the phone. One is in an East-Coast state of the US, the other is in a West-Coast state of the US. The first asks the other \r\n\r\n \r\n\"What time is it over there?\" \r\n \r\nUpon hearing the answer, the person says, \r\n \r\n\"That\'s funny. It\'s the same time here!\". \r\n \r\nHow can this be?','One is in Eastern Oregon (in Mountain time), the other in Western Florida (in Central time), and it\'s the Autumn daylight-savings changeover day at 1:30 AM (give or take 29 minutes).\r\n','2002-05-29',20040129232107,NULL,4,3,0,3.00,20020529000000,0);
INSERT INTO problem VALUES (90,12,2,117,'Twins','One day Kerry celebrated her birthday. \r\n \r\nTwo days later her older twin brother, Terry, celebrated his birthday.\r\n \r\nHow can this be, assuming that the difference in twins\' ages can be a few minutes, but not over an hour?','At the time she went into labor, the mother of the twins was travelling by boat. The older twin, Terry, was born first early on March 1st. The boat then crossed the International Date line (or any time zone line) and Kerry, the younger twin, was born on February the 28th. In a leap year the younger twin celebrates her birthday two days before her older brother. \r\n','2002-05-29',20031026232101,NULL,3,3,0,2.71,20020529000000,0);
INSERT INTO problem VALUES (91,5,2,117,'Wood','A standard piece of wood (one that can be found at just about any wood store), is cut with two straight cuts. After being cut, the wood will fit perfectly through three holes: circle, square, and triangle. What piece of wood was used, and how was it cut?','A dowel. Standing the dowel on end, it would be cut from the bottom (opposite) side edges, up at an angle. From the cutting view, this would make a triangle. Turn the wood to face the cut side, you have a square (as long as the angle is correct), and from the bottom, it\'s a circle. \r\n','2002-05-29',20030409232101,NULL,3,3,0,2.75,20020529000000,0);
INSERT INTO problem VALUES (92,5,2,227,'Diagonal length','The diameter of the circle (O), (XY) is 12cm. \r\n \r\nTwo adjacent vertices of the square (ABCD) lie on the diameter of that circle, while the other two vertices lie on the circumference of the circle. \r\n \r\n \r\nWhat is the length of a diagonal of this square (DB)?\r\n','Consider the triangle OBC. It\'s a right triangle with the hypothenuse equal to the radius of the circle (6cm), and its short leg (OC) is half the length of the long leg (BC).\r\n \r\nLet\'s designate the length of OC as x. then: \r\nHow many attempts do you expect to make on the average (statistically) before making it out?','Let\'s say that the average number of doors you have to go through is N. Since you will always end up in front of the same five doors after a failed attempt, your chance of making it out in each round are equal to 1/5th.\r\n \r\nThat is to say that there\'s a 0.8 chance that you\'ll be right back where you started, with one more attempt wasted, and still (on the average) N of them to go. Therefore \r\n(This solution was submitted by Nick Reed. See comments for a more general solution.)','2002-06-05',20040225103933,NULL,3,3,0,3.75,20020605000000,0);
INSERT INTO problem VALUES (95,5,2,227,'Enclosed area','What is the maximum area that could be enclosed by a piece of string 132 cm long? What shape would that area take?\r\n \r\nWhat is the minimum area that could be enclosed by the same string? What shape will it take?','The greatest area of a shape with a given perimeter is achieved when that shape is a circle. Rigorous proof of this is beyond the scope of the given problem, but once this is assumed as true, the calculations become easy:\r\n \r\nIf the length of a string is 132cm, and it is layed out in a circle, its length will be the length of the circle\'s circumferrence. Thus \r\nConsider the right triangle OMB. Its hypothenuse, OB is the circle\'s radius. The angle OBM is 30 degrees, since it\'s half the size of CBM which is 60. The length of MB is 3cm.\r\n \r\nSince the cosine of an angle is equal to the length of its adjacent leg over the length of a hypothenuse, we have: \r\nWhat are the values of x and y?','Consider the definition of a log, and you will see that loga(b) = 1/(logb(a)).\r\n \r\nLet\'s say that logy(x) equals some number A. Then A + 1/A = 43. This can be written in the form: A^2 + 1 = 43A.\r\n \r\nSolving this quadratic equation yields A = 43.977 or A = 0.023. (These two values are reciprocal of one another, so they are identical for our purposes)\r\n \r\nNow to solve the problem, take any number (such as 2) and raise it to the power of 42.977. As you can see, there is an infinite number of solutions, but none of them are particularly elegant.','2002-06-04',20040102232102,NULL,4,3,0,2.53,20020604000000,0);
INSERT INTO problem VALUES (99,7,2,248,'Make the most of these digits','You can use the digits 1,2,and 3 once only and any mathematical symbols you are aware of, but no symbol is to be used more than once. The challenge is to see if you can make the largest numbers.\r\n \r\nHere are some numbers to set the ball rolling: 321, 21to the third power, (3/.1)to the second power.\r\n \r\n(levik: I guess this is more of a competition)','While we may never know the actual \"maximum\" number, the victory in this little contest goes to \r\nNick Reed, for his submission of \r\nTo see the solution, refer to the excellent thoughts posted by our visiotrs, in particular TomM\'s step by step elimination guide.','2002-06-05',20031009232104,NULL,3,3,0,3.14,20020605000000,0);
INSERT INTO problem VALUES (101,7,2,257,'100 Herbivores','There are a total of 100 animals: cows, sheep and buffaloes. These 100 animals ate 100 bunches of grass.\r\n \r\nEvery cow ate 5 bunches, every buffalo ate 3 bunches and every sheep ate only 1/3 bunch. \r\n \r\nHow many cow, sheep and buffalo are there? You only know that there is at least one of every kind of animal.','A very thorough solution to this problem was posted HERE by Ender, and I won\'t bother repeating it.\r\n \r\nTo sum it up though, there are three possibilities:\r\n \r\nOne day, the three were sitting on a bench when the king\'s herald stopped by to deliver a message to one of them.\r\n \r\nHe asked the man sitting on the left side of the bench:\r\n \r\n\"Who\'s that sitting in the middle? To which the man replied: \"Why that\'s Abe\".\r\n \r\nHe then asked the man in the middle directly:\r\n \r\n\"What\'s your name?\" and got the answer \"My name\'s Carl.\"\r\n \r\nConfused, he asked the man on the right:\r\n \r\n\"Who is that sitting in the middle?\" and was immediately told: \"That\'s Bill, of course!\"\r\n \r\nCan you help the king\'s herald figure out who is who?','The man in the middle cannot be Abe, since Abe, being a Knight, would just tell the herald who he is, instead of claiming to be Carl.\r\n \r\nThat means that Abe is one of the other men on the bench, either to the left of the middle, or to the right of it. But the man on the left told the herald that the middle man is Abe, so he cannot be a Knight. That leaves the man on the right, who must be Abe.\r\n \r\nWhich means that the man in the middle is Bill, since Abe told the truth. \r\n \r\nCarl then must be the man sitting on the left side, and he has decided to lie about his name in this case.','2002-06-11',20030830232101,NULL,2,3,0,2.85,20020611000000,0);
INSERT INTO problem VALUES (103,5,2,153,'Chocolate!','I can\'t take credit for this. It was submitted to a quiz page on the CBC\'s (Canadian Broadcasting Co) website by Professor Maria Klawe of the Computer Science department at the University of British Columbia. But I thought our group would enjoy it.\r\n \r\nRemember when a bar of plain milk chocolate was scored to allow you to break it evenly into smaller pieces?\r\n \r\nWhat is the smallest number of breaks needed to divide a 4 by 8 chocolate bar into single squares, where each break splits any one of the pieces along an original horizontal or vertical line of the bar? Your answer should explain why your number is the smallest possible.','The answer is 31. \r\n \r\nIn fact, every allowed way of the breaking the chocolate bar into single squares will take 31 breaks. This is because each break you make increases the number of pieces you have by exactly 1. For example, you start with 1 piece and after your first break you have 2 pieces no matter what break you choose to make. \r\n \r\nSimilarly, after two breaks, you have three pieces, and after three breaks, four pieces. Since you end with 32 pieces (namely the 32 single squares in the bar), you must have made exactly 31 breaks.','2002-06-12',20030801232102,NULL,2,3,0,3.44,20020612000000,0);
INSERT INTO problem VALUES (104,7,2,153,'The Tennis Tournament','Another problem from the CBC website, this one submitted by Prof. Peter Rosenthal of the Mathematics Department of the University of Toronto:\r\n \r\n This is a question about a tennis tournament. It\'s organized so that in each round players are randomly paired. If there is an odd number of players, the extra player sits out the round. Losers are all eliminated from the tournament. The rounds continue in the same way until there is only one person remaining, who becomes the champion. The question is: If there are X people who enter the tournament, how many matches will be played in the tournament?','I asked a question about organizing a tennis tournament. In each round entrants are randomly paired, if one is left over, she sits out a round. Each loser is eliminated from the tournament. \r\n \r\nThe process goes on until the final, and someone wins the championship. How can you know, given the number of entrants, how many matches will be played? You might have tried to do this in a complicated way, by counting and dividing, over and over. \r\n \r\nHere\'s a better approach. Each match has a loser, and everyone except the champion loses exactly one match. So the number of matches is equal to the number of matches lost, which is the number of entrants minus 1 for the champion. \r\n \r\nIf there are X entrants, then there have to be x-1 losers, and x-1 matches.','2002-06-13',20030404232102,NULL,2,3,0,2.60,20020613000000,0);
INSERT INTO problem VALUES (105,11,2,1,'A four-way division','Four friends are gathered at a pub. They have in front of them two 8-pint trankards full of beer, and an empty 3-pint mug.\r\n \r\nSince they are still sober, they quickly calculate that they have 16 pints for the four of them, which comes out to an even 4 pints per person.\r\n \r\nCan they divide the beer equally with the containers they have available?','A few solutions were arrived at by our visitors. \r\n \r\nHere is one by Nick Reed. \r\n \r\nSee other comments for some additional ones.','2002-06-12',20040225103933,NULL,4,3,0,3.71,20020612000000,0);
INSERT INTO problem VALUES (106,10,2,250,'Bob\'s Hat','Three friends, Alan, Bob and Cecil, sit down at a park bench. Each of them is a Knight or Liar and each knows what the other two are.\r\n \r\nForgetful Bob, well known for his flamboyant hats that are either red, white or blue, asks Alan: \"What colour hat am I wearing today?\"\r\n \r\nAlan replies: \"There is a chance Cecil would tell you it\'s blue. If you saw it, there is a chance you would say it is white.\"\r\n \r\nBob sighs, \"I should have asked Cecil - he always tells me the truth...\"\r\n \r\nWhat colour hat is Bob wearing?','Let\'s take the statements one at a time:\r\n \r\n1) A says \"There is a chance C would tell you it\'s blue\"\r\n \r\nA would only say this if:\r\n \r\n2) A says to B \"If you saw it, there is a chance you would say it is white\"\r\n \r\nA would only say this if:\r\n \r\nCombining these with the options from point 1 results in:\r\n \r\n3) B says \"C always tells me the truth\"\r\n \r\nB would only say this if:\r\n \r\nCombining these with the options from point 2 results in:\r\n \r\nSo, although we don\'t know who is who, we know the hat is Red.','2002-06-13',20030806232101,NULL,4,3,0,3.67,20020613000000,0);
INSERT INTO problem VALUES (107,7,2,122,'The Dating Game','Sally and Sue have a strong desire to date Sam. They all live on the same street yet neither Sally or Sue knows where Sam lives. The houses on this street are numbered 1 to 99. \r\n \r\nSally asks Sam, \"Is your house number a perfect square?\". He answers. Then Sally asks \"Is it greater than 50?\". He answers again. Sally thinks she now knows the address of Sam\'s house and decides to visit. When she gets there, she finds out she is wrong. This is not surprising, considering Sam answered only the second question truthfully. \r\n \r\nSue, unaware of Sally\'s conversation, asks Sam two questions. Sue asks \"Is your house number a perfect cube?\". He answers. She then asks \"Is it greater than 25?\". He answers again. Sue thinks she knows where Sam lives and decides to pay him a visit. She too is mistaken as Sam once again answered only the second question truthfully. \r\n \r\nIf Sam\'s house number is less than the numbers of the houses where Sue and Sally live, and that the sum of all three of their numbers is a perfect square multiplied by two, what are Sally\'s, Sue\'s, and Sam\'s house numbers?\r\n',' \r\nSince Sally thinks she has enough information, we deduce that Sam answered his house number was a perfect square greater than 50. (answering Yes to both) There are two of these {64,81} and Sally must live in one of them in order to have decided she knew where Sam lives. Sam answered only the second question truthfully, so his house number is greater than 50, but not a perfect square. \r\n \r\nSince Sam answered Sue\'s second question truthfully, he had to have answered yes to \"Is is greater than 25?\". Sue was able to deduce Sam\'s number, so he also must have said it was a perfect cube. Cubes greater than 25: {27, 64}. Sue must live in one of these houses to deduce Sam\'s number.\r\n \r\nSince Sam\'s number is greater than 50 and is less than Sue\'s number, she must live in 64. Since Sue and Sally are not roommates (we\'re told there are three numbers), Sally must live in 81. \r\n \r\nGiven Fact: the sum of their numbers is a perfect square multiplied by two. \r\n \r\nSue + Sally + Sam = 2 p^2 (for p an integer) \r\nApplying the constraint that Sam\'s number is greater than 50 and less than 64, it looks like Sam = 55 (p = 10). \r\n \r\nIn summary, \r\n(Source: Primrose Puzzles, who apparently got this from rec.puzzles :)','2002-06-14',20031215232102,NULL,4,3,0,4.09,20020614000000,0);
INSERT INTO problem VALUES (113,15,2,257,'Maximum Value','We have : \r\n(Remember the category)','The maximum value is 8.\r\n \r\nThere are two sets of values that yield this value:\r\n \r\nSee friedlinguini\'s first comment on this problem (later a different solution is presented by vohonam)\r\n ','2002-06-19',20040225103933,NULL,5,3,0,3.00,20020619000000,0);
INSERT INTO problem VALUES (109,14,2,227,'More Logs','If \r\nBy definition of the log function, loga(b^2) is equal to 2*loga(b).\r\n \r\nThus, log 2(9) = 2 * log 2(3) = 2x','2002-06-17',20040102232102,NULL,1,3,0,1.67,20020617000000,0);
INSERT INTO problem VALUES (111,16,2,257,'Measure that angle',' \r\nThe \"official\" one, posted by vohonam and arranged neatly by TomM is here.\r\n \r\nAlso noteworthy, is a solution posted by Nick Reed which he has been kind enough to dedicate a page to.\r\n \r\nThank you guys.','2002-06-18',20040225103933,NULL,5,3,0,4.38,20020618000000,0);
INSERT INTO problem VALUES (116,15,2,257,'Funny Stuff !','Given: \r\n(This means : You have an angle A, you divide Angle A into 3 Angles B,C,D. And B=C=D=A/3)\r\n \r\nNote: vohonam clarified that the problem actually only gives you a straightedge, not a ruler.','This is one of the ancient geometric problems that people have been puzzling about.\r\n \r\nWhile it can be solved given a precise ruler with the use of trigonometry, no solution has yet been found with just a straightedge.','2002-06-19',20030904232102,NULL,5,3,0,3.75,20020619000000,0);
INSERT INTO problem VALUES (118,2,2,153,'The party','Alice and Bill threw a party and invited four other couples. As each couple arrived there were greetings, including handshakes.\r\n \r\nLater in the evening, Bill asked everyone, including Alice how many people they shook hand with. Every answer was different. No one shook hands with his or her own partner.\r\n \r\nHow many hands did Alice shake?','There were ten people at the party. No one shook hands with his or her own partner (and couldn\'t have shaken with him/herself), so the maximum handshakes a person could have made was 8. The minimum is 0.\r\n\r\n \r\n\r\nThere are 9 numbers between 0 and 8, inclusive, and 9 different answers, so each number was used as an answer once.\r\n \r\nThe person who shook hands eight times shook with everyone but his partner, so none of them can be the person who did not shake at all, so she must be \"8\'s\"partner.\r\n \r\nAfter eliminating \"0\" and \"8\", the same logic shows that \"7\" and \"1\" must be partners, then \"6\" and \"2\",followed by \"5\" and \"3\". \"4\'s\" partner must have also shaken 4 hands. But no two people answered the same. However, Bill did not answer the question, so he is the missing\"4\" Alice is his partner, so she is the other \"4\"','2002-06-20',20030829232101,NULL,4,3,0,3.40,20020620000000,0);
INSERT INTO problem VALUES (120,14,2,227,'logs and sins','sin(x) = lg(x)\r\n \r\nGive all values for x.','A full solution was posted by friedlinguini here','2002-06-24',20040225103933,NULL,3,3,0,2.25,20020624000000,0);
INSERT INTO problem VALUES (124,2,2,257,'A better deal','Yoric the worker came to a fair looking for a job. \r\n \r\nThere, Arley, an artisan, offered him the following terms:\r\n \r\n\"I wil pay you once every 67 days, one gold coin for a day of work, minus five coins for upkeep - a total of 62 coins in all!\"\r\n \r\nSuddenly a competing artisan named Bentley interrupted:\r\n \r\n\"Don\'t work for Arley, come work for me instead. I will also give you one coin a day, minus five for upkeep, but I will pay you every 57 days instead of 67. That\'s right, stick with me, and you\'ll get your 52 coins a whole ten days faster!\"\r\n \r\nEven though he wasn\'t very good at math, Yoric was a smart fellow and quickly figured out who was offering a better deal. Can you do it without using a calculator or performing complex fractional arithmetics?','Boiling down the terms of the two merchants, we can establish the following:\r\n \r\nArley: will pay Yoric 1 coin per day, with a five coin deduction every 67 days.\r\n \r\nBentley: will pay Yoric 1 coin per day, with a five coin deduction every 57 days.\r\n \r\nObviously, even without doing the math, Yoric is better off working for Arley.','2002-06-21',20031104232103,NULL,2,3,0,2.29,20020621000000,0);
INSERT INTO problem VALUES (125,6,2,103,'MU','(from Gödel, Escher, Bach: an Eternal Golden Braid by Douglas R. Hofstadter)\r\n \r\nStart with a single sequence of letters: MI\r\n \r\nThe goal is to apply a series of manipulations to this sequence to produce MU.\r\n \r\nThe allowable manipulations are:\r\n \r\n1. If the sequence ends in I, you can append U\r\n \r\n2. If the sequence begins with M, you can duplicate the string after M, e.g. MIII can be replaced by MIIIIII or MIMU can be replaced by MIMUIMU \r\n \r\n3. If the sequence contains III, you can replace the III with U, e.g. UIIIM can be replaced by UUM.\r\n \r\n4.If the sequence contains UU, you can delete the UU, e.g. \r\nUUM can be replaced by M or MIUUI can be replaced by MII.\r\n \r\nThese rules are all one-way; you can\'t take a U and replace it with III.\r\n \r\nIs it possible to reach MU from MI? If so, what series of steps would you take to get there? If not, why not?','It is not possible.\r\n \r\nThe trick is in the number of I\'s. Define f(s) as the number of I\'s in a string s. To start with, f(MI) = 1, and our goal is f(MU) = 0. Note that f(MI) is not divisible by 3, whereas f(MU) is. In order to reach MU, we have to get f(s) to be divisible by 3 for some s in the series of transformations.\r\n \r\nLet\'s see what happens when each o the rules is applied, changing f(s) to f(s\'):\r\n \r\n1. f(s\') = f(s). No change. \r\nSince the number of I\'s is not divisible by 3 to start with, and none of the transformations can change that, it is not possible to reach MU.','2002-06-20',20030601232101,NULL,4,3,0,3.20,20020620000000,0);
INSERT INTO problem VALUES (123,7,2,288,'Amoebas!','An amoeba propagates by simple division; each split takes three minutes to complete. When such an amoeba is put into a glass container with a nutrient fluid, the container is full of amoebas in one hour.\r\n \r\nHow long would it take for the container to be filled if we start with not one amoeba, but two?','Don\'t rush to say \"half an hour!\". Think about it. \r\n \r\nIn the original scenario we are starting with one ameoba. But in three minutes, this will become two ameobae, which then take the remaining 57 minutes of the hour to fill up the container.\r\n \r\nThus, it will take 57 minutes to go from two to full.','2002-06-20',20030708232102,NULL,1,3,0,3.11,20020620000000,0);
INSERT INTO problem VALUES (128,10,2,250,'The Camping Trip','A number of Knights and Liars went on a camping trip. Having pitched their tents for the night at the end of a long day\'s hike, Thomas (the best cook by far) settled down near the camp fire to make stew whilst everyone else sat in a circle around him, watching. Looking around, Thomas noticed that each person seemed to be sat between two people they knew, whereas Thomas himself knew no-one except his good friend Richard. So, getting everyone\'s attention, he asked a person at random in the circle the following question:\r\n \r\n\"You and the two people that are sitting next to you: Is there an odd number of Liars in that little group?\"\r\n \r\nThe person replied. Thomas asked another person at random, and that person gave the same reply as the first. Again and again he asked and every time the reply was the same. Finally, having asked everyone else and always receiving the same reply, he turned to Richard and asked the question once more. Surprisingly, Richard answered differently to everyone else.\r\n \r\nThinking for a moment, Thomas asked Richard: \"Are you sitting between two Knights?\", to which Richard smiled and gave the same reply as he had previously.\r\n \r\nNodding, Thomas declared: \"So, the Knights are outnumbered by the Liars here!\", and turned back to making the stew once more.\r\n \r\nIf \"n\" people in total went on the camping trip, how many Knights and Liars are there, and what are Thomas and Richard?','From the round of questioning we realise we have two options: Everyone answered No and Richard answered Yes, or everyone answered Yes and Richard answered No.\r\n \r\nLet\'s assume Richard answered Yes:\r\n \r\nSo (using the notation where we represent the people in the circle as a line of K\'s and L\'s, with Richard\'s position marked by brackets) we have either: \r\nApplying this to our above options gives us: \r\nTherefore it is impossible that Richard answered Yes.\r\n \r\nSo, Richard answered No:\r\n \r\nSimply that everyone else must be sat between one Knight and one Liar.\r\n \r\nSo, we get: \r\nIn the second option the reverse is true: there is one more knights than liars in the circle \r\nThere are 4 possibilities:\r\n \r\nRichard is a Knight, Thomas is a Knight: There would be x knights and x+1 liars in the circle - including Thomas this would change to x+1 of each - there is no majority and Thomas wouldn\'t lie about this - IMPOSSIBLE\r\n \r\nRichard is a Knight, Thomas is a Liar: There would be x knights and x+1 liars in the circle - including Thomas this would change to x+2 liars - the liars are in the majority, but Thomas wouldn\'t tell the truth - IMPOSSIBLE\r\n \r\nRichard is a Liar, Thomas is a Knight: There would be x+1 knights and x liars in the circle - including Thomas this would change to x+2 knights - the knights are in the majority, and Thomas wouldn\'t lie about this - IMPOSSIBLE\r\n \r\nRichard is a Liar, Thomas is a Liar: There would be x+1 knights and x liars in the circle - including Thomas this would change to x+1 of each - there is no majority and Thomas would lie about the fact.\r\n \r\nTherefore, both Richard and Thomas are Liars, and the group has an equal split of Knights and Liars (i.e. n/2 of each)','2002-06-23',20040321232101,NULL,4,3,0,4.50,20020623000000,0);
INSERT INTO problem VALUES (127,6,2,288,'Coffee and Cream','A spoonful of cream is taken from a cup of cream and put into a cup of coffee. The coffee is then stirred. Then a spoonful of this mixture is put into the cup of cream. \r\n \r\nIs there now more cream in the coffee cup or more coffee in the cup of cream?','Assume the cups each contains 90 units of liquid, and a spoon will fit 10 units (these numbers are used for convenience, the solution will work with any numbers)\r\n \r\nAfter we put the spoon of cream into cofee, the coffee cup has 90 units of coffee and 10 units of cream. The cream cup has 80 units of cream.\r\n \r\nIf we stir the coffee cup thoroughly and take a spoonfull from it, the spoon full will contain a representative proportion of each liquid: 9 units of coffee and 1 unit of cream. (Thus 81 and 9 units of each is left in the cup.)\r\n \r\nPouring the liquid in the spoon back into the cream cup will yield 81 units of cream and 9 units of coffee in that cup.\r\n \r\nThus the proportions in both cups will be identical.','2002-06-21',20031212232102,NULL,2,3,0,3.12,20020621000000,0);
INSERT INTO problem VALUES (129,17,2,103,'The Coca-Cola Diet','The way to lose weight is to burn more energy than you take in. One way of burning energy is to maintain your temperature at a steady 37°C (98.6°F).\r\n \r\nHow much energy is required with a can of Coca-Cola? The standard formula is that the amount of energy required is:\r\n \r\n(amount of substance) x (specific heat) x (change in temperature)\r\n \r\nWhat are the numbers for a can of Coke? The can I have here says it contains 355 mL. If I were to serve it cold in a glass with melting ice, it would start off with a temperature of 0°C. I don\'t know the exact specific heat of Coke, but I think it\'s fair to assume it\'s in the ballpark of the specific heat of water (1 calorie per mL per degree C). Coke is mostly water, anyway. Substituting those numbers gives:\r\n \r\n355 x 1 x 37 = 13,135 calories.\r\n \r\nUnder the Calories heading on the side of the can, I read 140. Even allowing for large differences between the physical properties of water and the physical properties of Coke, that\'s a tremendous difference. Every can of Coke ought to actually burn a net 12,995 calories if it\'s served cold. These numbers can easily be verified by anybody who wants to buy a can of Coke (Disclosure: I own a little bit of stock in the Coca-Cola Company).\r\n \r\nDrinking Coke ought to help people lose weight like crazy. So why hasn\'t the Coca-Cola diet caught on?','A distinction needs to be made between regular calories (cal) that are used in physics and chemistry, and Kilo-calories (Cal) - used in nutrition.\r\n \r\n1 Cal = 1,000 cal\r\n \r\nSo the 13,000 some (chemical) calories in the problem are only equivalent to about 13 Cal - food calories. The rest of the 140 Cal in a can of Coke comes from nutritional value of its ingredients (sugars and such).','2002-06-24',20030807232101,NULL,4,3,0,2.33,20020624000000,0);
INSERT INTO problem VALUES (130,10,2,153,'Lost in the catacombs','You are on the island of Knights and Liars exploring an ancient monastery. The old, worn guidebook that the abbot loaned has helped you navigate the catacombs and find all of the interesting old crypts. You are heading back out to garden, still following your guidebook, when you come to a pair of ornately carved doors.\r\n \r\nThe guidebook describes the two doors: \"At this point there are two doors. One will return you to the garden. You must be careful not to open the other door, because beyond it is a sheer drop into the cesspit. The ladder that the monks used to access the chamber was removed when the new wing of the abbey was built with modern plumbing.. Carved on each door in the ancient language is its destination. The door to the garden is marked....\"\r\n \r\nAt this point, the page is torn. You think to yourself, \"maybe, if I\'m very careful....\" but when you look at the doors, you see that the way they are constructed, you cannot open a door without stepping through.\r\n \r\nYou are about to despair when you hear approaching footsteps. Someone is coming! A monk comes into view. He is wearing a red sash and carrying a basket of food. You remember the ceremony you watched this morning., and realize that he is headed for a meditation chamber deep in the catacombs and will remain there for three days. So much for just following him out.\r\n \r\nYou remember that the Abbot (a Knight) told you that during the time of their purification, monks are under a vow of near silence. They areallowed to speak only one word per day, in answer to a yes-or-no question. But they must speak it in the ancient language. You remember that \"Zim\" is one of the words, but you don\'t remember whether it is \"yes\" or \"no.\" (Although you can\'t remember it, the other word is \"Dahl.\")\r\n \r\nCan you ask one question and learn which door to take without knowing either whether the monk is a Knight or a Liar, or whether \"zim\" means \"yes\" or \"no\"?\r\n \r\nThis puzzle is, I believe, original to me. It was influenced by the books of Raymond Smullyan, which I haven\'t read in many years. If this should prove to be a re-working of one of his puzzles, I apologize.\r\n','My original answer had been:\r\n \r\nYou could ask the following question:\r\n \r\nIf I were to ask you if \"Zim\" means \"yes,\" would I get the same answer as if I were to ask a liar if the left door leads to the garden?\r\n \r\nThe answer will always be \"Dahl\" if you should take the left door and \"Zim\" if you should take the right door. \r\n \r\nIt was one of two equivalent questions (more if you count variations in exact wording)based on comparing two questions (one about the meaning of \"Zim,\" the other about the doors) asked of two people (the monk and a hypothetical known liar)\r\n \r\nBut Nick Reed found a way to incorporate the \"Zim\" clause into the main question. His question \"If I asked you \'does this door lead to the garden?\', would you say Zim?\" is just as correct, and is more elegant.','2002-06-25',20040321232101,NULL,5,3,0,4.58,20020625000000,0);
INSERT INTO problem VALUES (131,4,2,251,'Maze','You\'re trapped in a maze. There is a way out. Path junctions are all 3-way. \r\n \r\nIf you use the strategy of always taking the path going right, what will happen?\r\n \r\n(Note: This problem is deliberarely vague.)','My puzzle as far as i know, corrections welcome..\r\n \r\nSince the maze\'s structure is not specified, then\r\na random treatment is in order. In this way the path you\r\ntake at any point is a random variable.\r\n \r\nThere are two possibilities in the long term:\r\n \r\nThe 2 possibilities are then:\r\n \r\nSo the best answer to the question is:\r\n \r\nIf they both said it in 1932, how old are were they at the time?','If the last two digits of the child\'s birthyear form a number x, then the child has stated that (s)he is x years old. Or, in other words x more years has passed since the child\'s birth. \r\n \r\nIn that case, the last two digits of the year would be 2*x (or, for x > 50, 2*x - 100) Since the actual year in which the statement was made is 1932, we have 2*x = 32 for x = 16\r\n(the child\'s age) or 2*x - 100 = 32 for x = 66 (the grandmother\'s age)','2002-06-25',20040314232102,NULL,2,3,0,3.17,20020625000000,0);
INSERT INTO problem VALUES (133,7,2,227,'Matchstick Frenzy','A heap of 48 matches are divided into three groups. \r\n \r\nIf I take as many matches from the first group as there are in the second group and add them to the second, and then take as many from the second group as there are in the third group and add them to the third, and finally take as many from the third group as there are in the first group and add them to the first group, the number of matches in each heap would be equal.\r\n \r\nHow many matches were in the three groups originally?','Let\'s say there were originally X, Y and Z matches in piles one, two and three respectively. After all the manipulations, each pile has 16 matches (48/3 = 16).\r\n \r\nThe first pile contains twice what it did after we took as many matches as there were in the second pile:\r\n16 = 2*(X-Y) (eq. 1)\r\n \r\nThe second pile contains twice what it did originally minus what the third pile contained: \r\n16 = 2*Y - Z (eq. 2)\r\n \r\nFinally, the third pile contains twice what it did originally minus what the first pile contained having had\r\nmatches taken to put into the second pile:\r\n16 = 2*Z - (X-Y) (eq. 3)\r\n \r\nWe solve these equations: \r\nAn old man has a boat and needs to cross the river, the problem is he has three things he needs to get across the river\r\na chicken, a dog, and a sack of grain.\r\nHe has three problems: \r\n \r\nHow does he get across with all three items intact?\r\n',' \r\nThe painter understands that he will have to throw away some of the paint, but wants to get the correct amount of the right mixture with as little waste as possible. How should he do it?\r\n','Since there are 4 pints of Black and 2 pints of White by halving the mixture (Ridding 3 pints) he would get 2 pints of Black and 1 pint of White in the mixture. By adding 3 pints of White paint he would get 4 pints of White paint along with the remaining 2 pints of Black paint thus solving his problem with minimum wastage.','2002-06-29',20030731232126,NULL,2,3,0,3.38,20020629000000,0);
INSERT INTO problem VALUES (136,16,2,227,'The Unknown Side','ABC is a triangle:\r\n \r\nBut as it happened, my airplane arrived at the airport 1 hour earlier. So I walked from the airport directly to my friend\'s house. On the way to her house, I met her driving to pick me up. I got into the car, and we drove me to the house. This way, I arrived at the house at 11:40.\r\n \r\nHow long did I spend walking?\r\n(The only thing known about my walking speed and my friend\'s driving speed is that they are different and they are constant.)\r\n','If my friend was able to drive back to her house 20 minutes earlier than she was supposed to, and she was driving at the same constant speed in both directions, that means she spent 10 minutes less going each way.\r\n \r\nSo she met me ten minutes before getting to the airport, and therefore, her drive back was also ten minutes shorter. \r\n \r\nIf I had arrived at the airport an hour before my designated arrival time, but was picked up ten minutes before that same time, it follows that I spent 50 minutes walking out to meet my friend.','2002-07-02',20030326065623,NULL,3,3,0,4.00,20020702000000,0);
INSERT INTO problem VALUES (139,2,2,1,'Mutually friendly','Prove that any group of six people contains either 3 mutual friends or 3 mutual strangers.\r\n \r\n(For the purpose of this problem any pair of people must be either friends or strangers.)','Imagine the six people. Of them, some person X either has at least three friends among the other 5, or at least three strangers.\r\n \r\nIf X has at least three friends, (call them A, B and C), then either the three of them are all mutual strangers (and satisfy the condition), or at least two of them are friends, and then the these two plus X are the three people that satisfy the condition.\r\n \r\nThe above paragraph applies likewise to the case where A, B and C are strangers to X.','2002-07-01',20030522232102,NULL,2,3,0,2.50,20020701000000,0);
INSERT INTO problem VALUES (140,14,2,227,'Equation games','Can you design an equation with two unknowns and still find the value of one?','This is more of a \"game\" than a problem. See the comments on this one for various equation that fit the demands of the puzzle, as well as the strategy for deriving them.','2002-07-03',20030708232102,NULL,2,3,0,3.17,20020703000000,0);
INSERT INTO problem VALUES (141,11,2,250,'The unplugged bath','(This is an old chestnut of a puzzle, but with a slight twist)\r\n \r\nIt takes six minutes for just the cold tap to fill my bath with water.\r\n \r\nThe hot tap fills the bath at the same rate, but unfortunately (due to some strange plumbing) after the hot tap has been running for three minutes its supply of water shuts off for a full two and a half while the hot water tank refills and reheats - after the two and a half minutes, the hot tap commences dispensing water once again.\r\n \r\nWith the plug pulled out, a full bath empties (at a uniform rate) in only four minutes.\r\n \r\nWith the hot water tank full and the plug pulled out, how long will it take my bath to fill if I turn both taps on?','The cold tap dispenses 1/6 of a bath-full of water every minute.\r\n \r\nSo, with both taps running and the plug out the bath fills by: 1/6 + 1/6 - 1/4 = 1/12 every minute\r\n \r\nSo, for the first 3 minutes we gain (3 * 1/12). Then for the next 2.5 minutes (as the hot water tank refills and \r\nthe hot tap is off) we lose (2.5 * 1/12).\r\n \r\nSo, an obvious solution to the problem would be to say it takes 24 * 5.5 minutes (132 minutes) to fill the bath.\r\n \r\nThis answer is wrong.\r\n \r\nAfter 18 * 5.5 minutes, the tank is full, and the bath has 18/24 (9/12) of it\'s water in it.\r\n \r\nTotal time: 18 * 5.5 + 3 = 102 minutes.','2002-07-03',20031031232101,NULL,3,3,0,3.43,20020703000000,0);
INSERT INTO problem VALUES (143,4,2,251,'Bascule\'s Book','Bascule is reading a book.\r\nWhat is the probability that the first digit of the page he is on is 1, 2, 3, 4 or 5?\r\n \r\na) obtain an expression \r\nSome discussion has occured on the topic of wether the book is equally likely to have anywhere from one to infinity pages, or if the book\'s thickness follows a standard distribution curve.\r\n \r\nSee comments on this problem for more details.','2002-07-03',20030422055620,NULL,5,3,0,3.00,20020703000000,0);
INSERT INTO problem VALUES (144,6,2,227,'Marching Messenger','(This is from CTK exchange)\r\n \r\nA column of soldiers is 25 miles long and they march 25 miles a day. One morning a messenger started at the rear of the column with a message for the guy up front. The messenger began to march and gave the message to the guy up front and then returned to his position by the end of the day. Assume that the messenger marched at the same rate of speed the whole time. How many miles did the messenger march?','A solution to this problem was posted by TomM in \r\nthis comment.','2002-07-05',20040225103933,NULL,5,3,0,4.20,20020705000000,0);
INSERT INTO problem VALUES (145,5,2,304,'Circular Logic','A name which has nothing to do with this question \r\n(well almost nothing)\r\n \r\nWhat percentage of the circle is shaded? (The quadrangle shown in the picture is a square with one of the vertices in the circle\'s center.)\r\n \r\n \r\nA full circle is 360 degrees \r\n \r\n360/360 = 1 = 100% = full circle\r\n \r\n90/360 = 1/4 = 25% = answer','2002-07-03',20040314232102,NULL,2,3,0,1.85,20020703000000,0);
INSERT INTO problem VALUES (146,7,2,304,'Number favorites',' \r\nWhat numbers do I like?\r\n(This question appears on IQ tests all the time)','The person likes perfect squares.\r\n \r\n2500 = 50 * 50 \r\nSolution courtesty of John Orapello','2002-07-03',20031201232101,NULL,1,3,0,1.71,20020703000000,0);
INSERT INTO problem VALUES (147,2,2,304,'Eggalicious','You have to boil a single egg for exactly nine minutes.\r\n \r\nAll you have are two hourglasses, able to measure (in sand) seven and four minutes, respectively.\r\n \r\nHow quickly, using only these two hourglasses, can you boil an egg?','The trick to solving this problem is realising that you are dealing with hourglasses which can be reversed.\r\n \r\nThe following solution would not be possible with other time measuring devices:\r\n \r\n \r\nEach is asked in turn if they know the color of their own hat. The answers are: \r\n \r\nWhat color is Carl\'s hat and how does he know?\r\n \r\n(Taken from http://einstein.et.tudelft.nl/~arlet/puzzles/logic.html)','The hats are not all white. This means that if Albert did not know his hat color, he saw at least one black hat among Bill and Carl. Otherwise he would have known his own hat to be black.\r\n \r\nBill must have realised this. He saw Albert\'s hat color, and also saw Carl\'s. He knew that Albert\'s statement meant that either he or Carl (or both) is wearing a black hat.\r\nHad he seen Carl in a white hat, he would immediately know his hat to be black. The fact that he did not make this guess let Carl know that his hat color was black.\r\n','2002-07-15',20030527232101,NULL,2,3,0,3.75,20020715000000,0);
INSERT INTO problem VALUES (149,7,2,227,'Addition','maybe you have seen this before.... \r\nSecond, we have FOR + T + T + carry = SIX. Since both of the top digits changed, that means there is a carry to the column with the O and the F. Since the 0 is already used, and the maximum carry is 2 (9+9+9 = 27 for the first column, 9+9+9+2=29 for any other column), that mean we must be adding enough to roll over from 9 to 1 in the 1000\'s column, a carry of 2 from the 100\'s column. So O=9, I = 1, and S = F+1. This also forces S to be 3,4,7, or 8, since it can\'t be either a used number or one more than a used number. Likewise, F must be 2,3,6, or 7.\r\n \r\nThird, to have a carry of 2, that means R+T+T must be greater than 20. Since 0 and 1 are both used, that means x is at least 2, so R+T+T is between 22 and 28. If T was the highest unused value (8), and since we have a carry of 1 (T + 5 + 5 = T, carry 1), R would have to be 6 or 7 (5 is already used). Likewise, if R was 8, T would have to be 7. So R is 6, 7, or 8; and T is 7 or 8.\r\n \r\nNow, two out of 6, 7, and 8 are used for R and T, so since S and F must be consecutive, they now must be 2, 3, or 4. Since either S or F will have be be 3, that raises the new minimum for R+T+T to be 24, forcing R to be 7, T to be 8, and X to be 4. This then forces F to be 2, and S to be 3.\r\n \r\nThus far, we have N=0, E=5, O=9, I=1, R=7, T=8, X=4, F=2, and S=3. The only usused letter is Y, and the only unused value is 6, so Y=6, giving us: 29786 + 850 + 850 = 31486, which checks.\r\n \r\n(Posted by Ender)','2002-07-08',20040225103933,NULL,4,3,0,4.00,20020708000000,0);
INSERT INTO problem VALUES (150,6,2,1,'A grid of people','Imagine a \"grid\" of people: some number of people arranged in a number of rows and columns in a rectangular formation.\r\n \r\nWe designate person A as the shortest person in the group of the tallest people of each row. We then designate person B as the tallest person in the group of shortest people in each column.\r\n \r\nWho is taller, A or B?','There are 4 cases to consider:\r\n \r\nA and B are the same person \r\nA and B are in the same row \r\nA and B are in the same column \r\nA and B are in different rows and columns \r\nAs you see in all cases but the specialized case where A and B are the same person, A must be the taller of the two.','2002-07-09',20031213232102,NULL,3,3,0,3.57,20020709000000,0);
INSERT INTO problem VALUES (151,7,2,1,'Self-Descriptor','Find a number ABCDEFGHIJ such that A is the count of how many 0\'s are in the number, B is the number of 1\'s, and so on.\r\n \r\n(Taken from http://einstein.et.tudelft.nl/~arlet/puzzles/logic.html)','The number is 6210001000. Ender explains in his comments why it is the only possible answer.','2002-07-10',20040225103933,NULL,3,3,0,3.60,20020710000000,0);
INSERT INTO problem VALUES (154,2,2,1,'A locked safe','(Puzzle by Raymond Smullyan)\r\n \r\nThere is a safe containing millions of dollars – unfortunately the combination is written on only one card, and that card has been accidentally locked inside the safe! If the wrong combination is used, the lock will jam and the only way to open the safe would be to blow it up, destroying the contents.\r\n \r\nA combination is a string of digits from 0 through 9. It can be any length and contain any number of digits occurring any number of times; 90915 is a combination; so is 2133127; so is 5. Certain combinations will open the lock, certain combinations will jam the lock, and the remaining combinations will have no effect whatever (these last are called neutral).\r\n \r\nThe small letters x and y will represent arbitrary combinations, and by xy is meant the combination x followed by the combination y; for example, if x is 213 and y is 3812, then xy is 2133812. By the reverse of a combination is meant the combination written backwards; for example, the reverse of 3812 is 2183. By the repeat xx of a combination x is meant the combination followed by itself; for example, the repeat of 3182 is 31823182.\r\n \r\nNow, some of the combinations are related to other combinations. There are five properties of this relation:\r\n \r\n \r\nFind the shortest possible combination that will open the lock.\r\n \r\n\r\n\r\nNotes/Clues:\r\n \r\nTo find a number that opens the lock, it is necessary to find a number that relates to itself, which then, by property E, can neither be neutral nor jam the lock, and must open it. The shortest number that relates to itself presumably has the form of xx2 or x2x2, where x is a series of 1s, 5s, and 9s that gives the steps needed to find that very number.\r\n \r\nTo find the number, it is best to work backwards. Starting with xx2: \r\nNow, working backwards again for x2x2: \r\nFinally, a simple relation must be noted:\r\n \r\nTherefore, there are two 8-digit solutions, 92591522 and 95951522.','2002-07-16',20030815084936,NULL,5,3,0,4.04,20020716000000,0);
INSERT INTO problem VALUES (157,16,2,153,'Circular Logic II','In qball\'s Circular Logic, we were asked to determine the Area of the region common to a circle and a square, one vertex of which was at the center of the circle. The figure was drawn to show that e (the edge of the square) was greater than r (the radius of the circle), and the Area resolved to 25% that of the circle, or πr²/4.\r\n \r\nBut what if e were less than r? The second and third verteces would be inside the circle, and the Area becomes a function of e (expressed as a fraction of r). When e is less than r/(√2), the fourth vertex is within the circle, and the area of the common region becomes the area of the square e²\r\n \r\nBut what is the function f(x) such that A=f(e) for r ≥ e ≥ r/(√2) ?\r\n \r\nNote: we already know that f(r) = πr²/4, and f(r/(√2)) = r²/2, because although the derivative of the greater function becomes discontinuous at these points, the function itself does not.\r\n \r\nIt was a comment by Manolo on the page for the original Circular Logic problem that suggested this one to me.\r\n','The common area can be divided into three sections: \r\n \r\ntwo right triangles with legs e and √(r² - e²) (The total area of bot triangles is e[√(r² - e²)])\r\n \r\n\r\nand a sector of the circle with angle A, where Angle A = 90º - 2(invcos e/r) (the area of the sector is (πr²)(A/360º)\r\n \r\nThe final form of the area function (in the specified range) is f(e) = e[√(r² - e²)] + (πr²)([90º - 2(invcos e/r)]/360º)\r\n \r\nWhen e = r, the triangles degenerate into line segments with area 0, and angle A becomes 90º The final area is πr²/4.\r\n \r\nWhen e = r/(√2), √(r² - e²) is also r/(√2), The triangles cover an area of r²/2 and Angle A becomes 0, causing the sector to degenerate into a line segment of area 0\r\n \r\nNote: this solution was found using geometry, Solving it using analytic algebra or calculus might give valid answers with a different form.','2002-07-19',20030326065623,NULL,4,3,0,3.00,20020719000000,0);
INSERT INTO problem VALUES (158,7,2,122,'Three Fractions',' A/BC + D/EF + G/HI = 1 Each of three fractions has a one-digit numerator and a two-digit denominator. The three fractions together add up to one. Place the nine digits 1-9 into the fractions to make the equation correct. There is only one answer: 5/34 + 7/68 + 9/12 = 1 (Source: Nob Yoshigahara, c/o Scot Morris in OMNI, April 1994) Smith, Jones and Brown were great friends. After Brown\'s wife died, his niece kept house for him. Smith was also a widower, and lived with his daughter. When Jones got married, he and his wife suggested that they all live together. Each one of the party (male and female) was to contribute $25.00 on the first of the month for household expenses, and what remained at the end of the month was to be equally divided. \r\nThe first month\'s expenses were $92.00. When the remainder was distributed, each received an even number of dollars without fractions. How much money did each receive, and why? Mrs. Jones was the daughter of Smith and the niece of Brown, so there were but four persons. $100 was contributed, $92 spent, and each received $2 in the distribution. (Origin: Sam Loyd) \r\nWhenever two chameleons of the same color met, they would fight to the\r\ndeath and the victor would become stronger and change color (eg white to yellow). Black chameleons would fight eternally.\r\n \r\nThe small island of Ula was initially populated by a\r\ngroup of fighting chameleons. For this group\r\n \r\na) the colors present each had an equal number of\r\nchameleons (for example, group = 3 black, 3 green and 3 yellow)\r\n \r\nb) it was not made up entirely of white chameleons\r\n \r\nAfter all the possible fighting was done, there remained one black and\r\ngreen and no blue or orange chameleons.\r\n \r\nHow many white chameleons remained in the island?\r\nProve it.','The island of Ula is really a huge adding machine,\r\nwhose basic mechanism is chameleons. Once youve realised this, its a matter of translation (:)\r\n \r\na): all the number added are equal. this type\r\nof addition has a name, multiplication:\r\n \r\nchameleons per color * colors present = survivors\r\nn * c = s\r\n \r\nb): c != 1 (im using != as not equal)\r\n \r\n\"After all the fighting..\": n != 1.\r\n \r\nWe know that s = 1010XX, s = 101000-101011 = 40-43.\r\n41 and 43 are prime, and s = n * c.\r\nsince n != 1 != c, s != 41,43\r\n \r\nso s = 40, 42 = 101000, 101010.\r\n \r\nNo white chameleons left, regardless of yellow.\r\n \r\nYou can also prove this systematically, by obtaining\r\nall initial combinations which result in 1010XX and\r\nfinding all with white = 0. This would inadvertently\r\nprove that 41,43 are prime.\r\n \r\nBtw, confusion aside, i dont think this puzzle deserved a rating of 1 :)','2002-07-30',20030723232102,NULL,3,3,0,2.89,20020730000000,0);
INSERT INTO problem VALUES (164,14,2,251,'No calculus','Define: \r\nwhere f\'(x) = gradient (or slope) of f(x) at x = x.\r\n \r\nProve that: \r\nwithout using calculus.','Define a tangent y = Ax + B of y = x^2.\r\n \r\nwe have\r\n \r\nx^2 = Ax + B, \r\nbecause Ax + B is a tangent, there is only one root to this\r\nquadratic equation, so in the quadratic formula\r\n \r\nb^2 - 4ac = 0.\r\n \r\nwhich in the formula \r\nleads to\r\n \r\nx =-b/2a =-(-A)/2*1 \r\nsince in y = Ax + B, A is\r\nthe gradient, then\r\n \r\nd/dx(x^2) = 2x','2002-07-31',20030626232103,NULL,4,3,0,3.14,20020731000000,0);
INSERT INTO problem VALUES (165,16,2,227,'Math on the playground','A circular playground has 2 parellel roads running through it. Their lengths are 112m and 50m. The perpendicular distance between these roads is 92m. \r\n \r\nFind the diameter of the playground.','Solution here by TomM.\r\n \r\nAnswer here by Cheradenine\r\n','2002-08-02',20040225103933,NULL,3,3,0,3.17,20020802000000,0);
INSERT INTO problem VALUES (166,6,2,1,'A pyramid of balls','Consider a triangular pyramid of balls, constructed by placing each ball (except those on the bottom) in the hollow formed by the three balls under it. If such a pyramid has 12 balls on the side of the bottom level, how many balls in total does it contain?','Let\'s call one of the pyramid\'s faces it\'s \"front\".\r\n \r\nFor any given level of balls N, (as counted from the top), the \"front row\" will contain N balls. For example the first row from the top, will have 1 ball \"in front\", the second one will have two, and so on till at level 12, there are 12 balls along the front face of the pyramid.\r\n \r\nIn the row behind the front row, where will be one ball present for each space between two balls in the front row. Since for level N, there would be N-1 such hollows, the row behind the front row on level N would contain N-1 balls: 11 on the 12th level, 1 on the second, and the first level does not have a second row.\r\n \r\nGenerally, each row further from the front face of the pyramid will have one less ball in it than the row before. Therefore, for any level N, the number of balls in the level would be N+(N-1)+(N-2)+...+1. This can be expressed as N*(N+1)/2\r\n \r\nSo if we have 12 levels, We need to calculate the sum of\r\nN*(N+1)/2 for N from 1 to 12. After a lot of arithmetics, this comes out to be 364.\r\n \r\n(TomM has managed to further reduce the equation here)','2002-08-02',20040225103933,NULL,2,3,0,2.83,20020802000000,0);
INSERT INTO problem VALUES (167,12,2,437,'Big and Little Indian','There is a Big Indian and a Little Indian. The Little Indian is the Big Indian\'s son, but the Big Indian is not the Little Indian\'s father. How is this possible?','The Big Indian was the Little Indians mother.','2002-08-05',20040129232107,NULL,1,3,0,2.36,20020805000000,0);
INSERT INTO problem VALUES (168,12,2,437,'The Good Book','I have a book where the forward comes after the epilogue, the end is in the first half of the book, and the index comes before the introduction.\r\nWhat book is it?','The dictionary.','2002-08-05',20040319232102,NULL,1,3,0,3.62,20020805000000,0);
INSERT INTO problem VALUES (172,14,2,251,'Odd Sum','Prove that the sum of consecutive odd numbers beginning at 1 (eg 1, 3, 5, ..) always adds up to a perfect square','Consider the sum of n odd numbers \r\nWe can pair up symmetrical elements \r\nThe largest odd number is 2n - 1. If \r\nS = each pair * number of pairs \r\nIf n is odd, the numbers do not pair \r\nS = (each pair * number of pairs) + center \r\n(See the comments for other interesting ways to prove \r\nthis)','2002-08-08',20040105232102,NULL,2,3,0,4.20,20020808000000,0);
INSERT INTO problem VALUES (171,15,2,251,'Definite Integral','Let f(x) = √(1-x²)\r\n \r\nFind the definite integral\r\nof f(x) between x = 0 and x = 1\r\n','An integral is the area under a curve\r\n \r\nf(x) = y = √(1-x²) \r\na bell should ring at this point. this\r\nis the equation of a circle radius = 1 centered at 0,0. because x² is a 2-to-1 function and the limits are x=0-1, only 1/4 of the area contributes. \r\n \r\nA = πr²/4 = π/4.\r\n \r\nSo the value of the integral is\r\nπ/4','2002-08-06',20040229232101,NULL,3,3,0,3.20,20020806000000,0);
INSERT INTO problem VALUES (173,16,2,122,'String around the Cylinder','A cylinder 90 cm high has a circumference of 24 cm. A string makes exactly 5 complete turns around the cylinder while each of its two ends touch the cylinder\'s top and bottom respectively. \r\n \r\nHow long is the string?',' Imagine cutting the cylinder along the string and then unrolling the cylinder. The string becomes the hypotenuse of a right triangle whose height is 90cm and whose base is 5 * 24 cm (120cm). The Pythagorean Theorem then reveals the length. 90^2 + 120^2 = 150^2 Thus, the string is 150 cm. \r\na) this problem is solvable \r\nor \r\nb) this problem is unsolvable','Jacob Frugal submits a detailed analisys for this problem here.','2002-08-12',20040225103933,NULL,4,3,0,3.00,20020812000000,0);
INSERT INTO problem VALUES (175,7,2,1,'Zero to a Hundred in 1996','Using the digits in 1996 and any operations (but not mathematical constants), try to write equations that have the numbers from 0 to 100 as the answer.\r\n \r\nFor example with 1995:\r\n \r\nProvide as many as you can. Digits 1,9,9 and 6 do not have to appear in order. (But each digit has to be used - 1 and 6 once, 9 twice.)\r\n \r\nThis is more of a game than a puzzle','To avoid all the extra typing here, I will refer you to Nick Reed\'s excelent solutions for the problem:\r\n\r\n \r\nNick missed a couple of the numbers in his posts, but you can find the solutions to those last ones by going through the comments.','2002-08-15',20040225103933,NULL,3,3,0,3.57,20020815000000,0);
INSERT INTO problem VALUES (176,12,2,448,'Cops and Robbers','There is a shoot-out going on behind a school somewhere in the US. The shoot-out is between a group of cops and a band of robbers. One of the robbers was shot in the heart, and one of the police officers was shot in the head. Neither died, but instead went to the sidelines to watch, talk, and laugh. \r\n \r\nThe police managed to get the robbers under control, but the robbers were not sent to jail. This is not a game between children. Can you answer these questions?\r\n \r\n1. Why didn\'t those shot die? \r\n2. a state police academy (You may not be familiar with this unless you are from the US. Here they are used to train each state\'s police squads.)\r\n \r\n3. The robbers are police in thug\'s clothing, so to speak.\r\n \r\n4. I hope you have caught on to this by now. This is a training activity for a police academy. The robbers are studing to become police officers just like the men/women that played the cops. The simulation is a shoot-out between police an a band of neighborhood thugs. This way, both groups get practise for a mission that they may someday face.\r\n \r\n\r\n The guns being used are laser guns. If you are shot in a vital organ, you are considered dead and go sit and watch from the sidelines, but if you are sot in something a little less important, a timer is set with the aproximate time it takes for a persom to bleed to death. Once that runs out, you are also considered dead. \r\n \r\n The cops won because they either \"killed\" or captured all of the robbers, or the robbers made a retreat. Had all the officers been killed, the robbers would have gotten away.','2002-08-17',20040129232107,NULL,2,3,0,1.92,20020817000000,0);
INSERT INTO problem VALUES (177,12,2,448,'Imprisoned! (Possibly for Insanity)','You are trapped in a room with a window and a door. The window is of indestructible glass, and the door has no knobs or locks. There is a hole in the floor with a ping-pong ball in it. If you can get the ball out, the door will open. The hole is only wide enough for the ball, which rules out just sticking your hand in to pull it out. There is also a vent in the wall that is made out of some weird superstrength alien metal that won\'t break and a lightbulb is hanging from the ceiling as well. You have a few objects with you that might help. They are:\r\n \r\n \r\nAnd your most important ally, your brain. (Not that it\'s neccesarily a very good one, of course!)\r\n','If your ally has served you well, you would have guessed that all you have to do is spit in the hole and make the ball float to the top. If your ally is really perverted, you could always have used another one of your bodily functions, too.','2002-08-18',20031104232103,NULL,3,3,0,2.50,20020818000000,0);
INSERT INTO problem VALUES (178,2,2,1,'A Pack of Prudent Pirates','After a long season of plunder, a pirate team of five Prudent Pirates has amassed a booty of 500 golden coins. Before they part their ways, the five decide to divide the treasure.\r\n \r\nThey that they will each propose a division strategy in order of their seniority: first the oldest pirate will propose the strategy for the division of coins. All five will then vote on it, and if at least half vote \"Yes\", the strategy will be used to divide the coins. If the majority rejects the plan however, the oldest pirate will be killed, and the whole process will be repeated with the remaining pirates, with the second oldest proposing his strategy.\r\n \r\nSince all the pirates are very prudent, each one will want to claim as many coins for himself without getting killed. Given this, how many coins will each of the pirates (5 - 1, with 5 being the oldest) get, and why? What strategy will the oldest pirate propose?','Consider a situation with one pirate. He will simply claim all the coins for himself.\r\n \r\nWith two pirates (2 and 1), 2 will propose a \"strategy\" where he gets all the coins, vote for it, and thus will walk away with all the booty, leaving 1 with nothing.\r\n \r\nIf we have 3 pirates, 3 will need one more vote to avoid getting killed. He knows that if his strategy is not adopted, he will be killed, and the situation will become the equivalent of a 2-pirate setup, in which 1 will get nothing. Thus, if 3 offers 1 a single coin, 1 will accept, since he will lose even that by declining the strategy. Thus 3 would be able to abscond with 499 of the coins, having given 2 nothing.\r\n \r\nWith 4 pirates, 4 will try to bribe 2, who would gain nothing in the 3-pirate scenario. 2 will have to take 1 coin from 4, or else take nothing from 3. Thus 4 will give 2 one coin, and get his vote for a total of 50% of the vote, leaving 1 and 3 emptyhanded.\r\n \r\nWe come to the 5 pirate scenario. #5 needs two more votes to reach the 50% threshold. He can get them by offering 1 and 3 one coin each. (Remember, they get nothing if 4 proposes his strategy). They will accept so as not to lose everything, and 5 will go home with 498 coins, leaving 2 and 4 with nothing.','2002-08-19',20031030232101,NULL,3,3,0,4.42,20020819000000,0);
INSERT INTO problem VALUES (179,12,2,448,'Water, Water Everywhere','Here is a riddle for you:\r\n \r\nWhat is it, that gets wetter as it dries?','A towel. Sorry for the corny-ness!','2002-08-19',20040129232107,NULL,1,3,0,2.54,20020819000000,0);
INSERT INTO problem VALUES (180,17,2,448,'Forensic Fancy','You have a little beaker with an unknown amount of acid indicator solution in it. Over this beaker, you have a tube marked in ml. increments. This tube is marked backwards, it starts at 0 at the top and goes to 25 at the bottom. This tube contains 25ml. of hydrocloric acid (.01 concentration), which will drip out one drop at a time into the beaker. The acid indicator will eventually turn magenta and you will then close off the tube.\r\n \r\nOn one such test you recorded that you started out with 10.2ml in the tube. You used it down to the 24.8ml area. At which time you refilled the tube to 12.1ml. You shut off the tube at 13.1ml, when the acid indicator was a nice shade of magenta. \r\n \r\nNow, please give me the equation for how much acid indicator was in the beaker in mols, and use it to actually find how much was in it, also in mols. For bonus points, tell me how this equation would be helpful in certain forensic investigations.\r\n \r\nYou wouldn\'t think a 13 yr. old would want to put you through such a hard time of it, would you? ^_^\r\n\r\n','The equations looks like this:\r\nfinal volume-initial volume= x ml base >>>\r\n(x ml)(L/1000ml)(.1 mol/L)=y mol base >>>\r\n(y mol base)(1 mol acid/ 1 mol base)(1/10ml)(1000ml/L)=z mol\r\n\r\nsoooo....plugging the info you have about the experiment you get this equation and this answer:\r\n\r\n24.8-10.2 + (13.1-12.1)= 15.6ml >>>\r\n(15.6ml)(1L/1000ml)(.1mol/L)=.00156 mol\r\n(.00156mol base)(1 mol acid/ 1 mol base)(1/10ml)(1000ml/L)=.156mol acid\r\n\r\nSo now you know that there was .156 mol acid in the beaker. This would be handy to know if you wanted to figure out how much of a contaminating substance was in a wide range of liquids, from drinks to rivers.\r\n\r\n\r\n\r\n','2002-08-20',20030601232101,NULL,4,3,0,2.71,20020820000000,0);
INSERT INTO problem VALUES (183,2,2,1,'Smart prisoners always get a break','100 prisoners are put into solitary cells. There\'s a central living room with one light bulb; the bulb is initially off. No prisoner can see the light bulb from his or her own cell. Every day, the warden picks a prisoner at random, and that prisoner goes to the central living room. While there, the prisoner can toggle the bulb if he or she wishes. Also, the prisoner has the option of asserting the claim that all 100 prisoners have been to the living room. If this assertion is false (that is, some prisoners still haven\'t been to the living room), all 100 prisoners will be shot for their stupidity. However, if it is indeed true, all prisoners are set free and inducted into MENSA, since the world can always use more smart people. Thus, the assertion should only be made if the prisoner is 100% certain of its validity.\r\n \r\nThe prisoners are allowed to get together one night, to discuss a plan. What plan should they agree on, so that eventually, someone will make a correct assertion?\r\n \r\n(From http://www.ocf.berkeley.edu/~wwu/riddles/intro.shtml)','The prisoners need to designate a \"counter\" from among themselves.\r\n \r\nEveryone who is not the counter, upon coming to the living room will turn the light on if\r\n \r\nThe counter, starting with a count of zero, upon coming to the living room, will do the following:\r\n \r\nWhen the counter\'s count reaches 99, he knows that 99 other people have been to the living room. Since he has also been there, he can safely announce that all the prisoners have visited the living room.','2002-08-27',20030829232101,NULL,4,3,0,4.33,20020827000000,0);
INSERT INTO problem VALUES (182,14,2,227,'Primary Problem','Prove that there exists an infinitely large number of primes.','Suppose that there exists a finite amount of Primes and the list is as follows:\r\n \r\n(p1, p2, p3.....pn).\r\n \r\nn being the amount of primes.\r\n \r\nNow we shall assume that the integer obtained by multiplying the primes is \"N\".\r\n \r\nTherefore N = (p1 p2 p3.....pn).\r\n \r\nN is obviously not Prime because it is divisible by all the other primes.\r\n \r\nNow we shall add 1 to N.\r\n \r\n\"N+1\" will not be divisable by any of the other primes since it is not a multiple of the primes that were given. Hence N + 1 is a Prime. \r\n \r\nBut N + 1 is also larger than any of the primes that were given, thus it contradicts our first assumption of the list given was complete. Therefore the list will have no end.','2002-08-21',20040208015243,NULL,4,3,0,3.29,20020821000000,0);
INSERT INTO problem VALUES (184,4,2,1,'Three for all','You are in a free-for-all shootout involving three people, and by some rotten luck, you are the worst shooter of the group. You, shooter A, hit your target 33% of the time. \r\nThe other two, B and C, have 50% and 100% accuracy respectively.\r\n \r\nAt least you get to shoot first, with B going after you, and C going last. Everyone takes turns shooting until all but one are dead.\r\n \r\nWho will you fire at in the first round to maximize your odds of survival?','If player C survives to the end of the first round, he will definitely kill one of the remaining contestants. Assuming both A and B are still alive, he will have to chose one of them to shoot.\r\n \r\nSince B will have a higher chance of killing C, it is reasonable to assume that C will shoot at B and not at A.\r\n \r\nB knows this, and when it\'s his turn to shoot, he will shoot at C rather than at A.\r\n \r\nThus, if both B and C are alive after A\'s turn, A is guaranteed survival in the first round, plus the first shot in the second at whichever opponent survives the first.\r\n \r\nHowever, if A shoots and kills B, he is sure to be killed by C who will only have one targer to shoot at. If A shoots and kills C, he has a 50% chance of being killed by B with the next shot, without a chance to shoot at B first.\r\n \r\nTherefore, it is to A\'s advantage that both B and C survive his turn. Therefore, he is better off missing deliberately than shooting either of the other participants.\r\n \r\n(You can look here for a more statistically thorough solution.)','2002-08-27',20030724232103,NULL,4,3,0,3.57,20020827000000,0);
INSERT INTO problem VALUES (185,6,2,1,'Electric car','You have an electric car that you want to use to transport some batteries 1,000 miles. You have 3,000 batteries, but your car can only carry 1,000 of them at once. In addition, for each mile that it travels, the car will need to use up one battery in order to power itself. \r\n \r\nHow many unspent batteries will you be able to transfer to your destination?','The answer is 533 1/3 cells.\r\n \r\nTo achieve this, load the car with 1000 cells, drive out 200 miles, drop 600 cells, and return back with the 200 cells you have left (200 + 200 + 600 = 1000).\r\n \r\nRepeat this once more, and you will have 1200 cells at the 200 mile mark. \r\n \r\nNow, load the remaining 1000 cells and drive out to 200th mile. By the time you get there, you will have 800 left, making 2000 with the 1200 that are there already.\r\n \r\nLoad 1000 onto the car, and drive to mile 533 (a 333 mile drive from mile 200). Unload 334 cells there, and drive back to 200. Pick up the remaining 1000 cells and go to mile 533 again. (You will have 667 cells in your car, and 334 on the ground.)\r\n \r\nPick up 333 of the cells, leaving one on the ground. Your car is now full.\r\n \r\nYou could now drive straight to the finish line (467 miles) and get there with 533 cells remaining, but here\'s a trick that will let you transport a whole extra 1/3 of a cell:\r\n \r\n \r\nYou are now at mile 533 1/3, with 1000 full power cells. This means that if you drive straight to mile 1000, you will use up 466 2/3 cells, leaving 533 1/3 intact for delivery.\r\n \r\nThanks to Ender for submitting this solution','2002-08-29',20040225103933,NULL,4,3,0,4.29,20020829000000,0);
INSERT INTO problem VALUES (186,7,2,1,'Prime Pairs','Pairs of primes separated by a single number are called prime pairs. Examples are 17 and 19. Prove that the number between a prime pair is always divisible by 6 (assuming both numbers in the pair are greater than 6).\r\n \r\n(From http://www.ocf.berkeley.edu/~wwu/riddles/intro.shtml\r\n)','Let\'s say the prime numbers in a given prime pair are a-1 and a+1. Since both are greater than six, neither can be divisible by either 2 or 3.\r\n \r\nBut if a-1 is not divisible by 2, a must be divisible by 2.\r\n \r\nAlso, if you take any three consecutive numbers, one of them must be divisible by 3, and since neither a-1 nor a+1 are, then a must be.\r\n \r\nSince a has to be divisible by both 2 and 3, it must be divisible by 6 as well.','2002-09-01',20040131232101,NULL,4,3,0,3.83,20020901000000,0);
INSERT INTO problem VALUES (187,12,2,1,'Feet make you smarter?','Researchers have found that statistically, there is a direct positive relationship between students\' shoe sizes and their results on spelling tests and spelling bees. (That is, students with larger shoe sizes tend to do better.) \r\n \r\nCan you explain this correlation?','The trick to this problem is realising that spelling tests and bees are generally participated in by children, whose feet grow as they get older. Older kids tend to do better at these events than younger ones.','2002-09-03',20040129232107,NULL,2,3,0,2.77,20020903000000,0);
INSERT INTO problem VALUES (190,7,2,1,'Climbing the stairs','A stairway has 100 steps. You can climb it by one step at a time, or by two steps. How many different ways to ascend this stairway exist?','Let\'s define F(n) as the number of ways to climb a stair of n steps either one or two steps at a time.\r\n \r\nConsider the last step you will take. It will either be a \"single\" step, if you are now at step n-1, or a \"double\" step if you are at n-2. (You could take a single step from n-2 to n-1, but that wouldn\'t be your last step in climbing the n-step stairway).\r\n \r\nFor each of the above last steps, you will have had a multitude of ways of getting to either n-1 or n-2. Actually, if you think about it, standing on n-1, you could have gotten there in F(n-1) ways. Likewise, you had F(n-2) ways to get to step n-2. \r\n \r\nSince in each case, the next step will be your last, and there is only one way to take it, the total number of ways to reach n is \r\nYou see a moving bus on the streets of New York as shown. Is this bus moving towards A or towards B (assume it\'s not backing up)?','Note that on the picture we do not see the door of the bus. In the US, bus doors appear on the right side of the bus (or on both sides, but in any case, if a side of the bus is missing a door, it HAS to be the left side).\r\n \r\nThis means that the bus is heading towards A.','2002-09-06',20031015232102,NULL,2,3,0,3.00,20020906000000,0);
INSERT INTO problem VALUES (189,12,2,122,'How many letters?','How many letters are in the answer to this question?\r\n','0 \r\nThere are many possible solutions.','2002-09-04',20040129232107,NULL,1,3,0,2.87,20020904000000,0);
INSERT INTO problem VALUES (195,8,2,1,'Coins on the round table','This game is played by two players at a round table. They each take turns placing identical coins onto the table\'s surface. No two coins can overlap, and the entirety of the coin\'s surface must rest on the table. The loser of the game is the first person who is unable to put down a coin because there is no more room.\r\n \r\nWhich of the players has a winning strategy? What is it?\r\n \r\nMouse over for a hint: \r\nAs his first move, he should set his coin at the very center of the table. For each subsequent move, he should place his coin exactly opposite of where his opponent set the coin last, picking a spot diametrically opposite to his opponent\'s. This way, the pattern of coins on the table will always be symmetrical with respect to the center, and therefore any spot the second player chooses will have a corresponding empty spot of the same size on the other side of the table.','2002-09-08',20031123232103,NULL,4,3,0,3.80,20020908000000,0);
INSERT INTO problem VALUES (196,2,2,1,'Calendar Cubes','A businessman has two cubes on his desk. Each cube has a number on each of its sides. Every day, the businessman arranges the cubes in such a way that the upward facing numbers display the day\'s date.\r\n(Note that both cubes are always used for this, so on the 7th of the month, the cubes\' surfaces display \"07\".)\r\n \r\nHow are these cubes numbered? (I.E. What numbers are on which cube? - call them C1 and C2.)\r\n \r\n(From http://www.ocf.berkeley.edu/~wwu/riddles/intro.shtml)\r\n','The trick to this problem is realising that by turning a \"6\" upside down, we can make a \"9\". Since there are only a maximum of 31 days in a month, we will never need a 6 and a 9 simultaneously.\r\n \r\nBecause each month as an 11th and a 22nd, both the cubes will need to have the numbers 1 and 2 on them. Also, because each of the digits needs to appear next to a zero (for the first 9 days of the month), zero should also be on both cubes. \r\n \r\nThis leaves us with three free spots on each cube, where we need to put the numbers 3, 4, 5, 6, 7, and 8.\r\n \r\nSo, \r\nThe challenge is accepted, and play starts. After a few moves, the experienced players throw up their hands in disgust, and pay off the bet.\r\n \r\nQuestion 1: What happened?\r\n \r\nQuestion 2: Having accepted the challenge, what ought the experienced players to have done in order to win?','What happened? The duffer just copies each expert\'s move to the other board. He is thus guaranteed to achieve either two draws or one win and one loss.\r\n \r\nThe bet having been accepted, what should the experts do to avoid this? My favorite answer is to set up two chess clocks. If the duffer is copying experts\' moves, his white game will always consume more time than the expert\'s white game, and his black game will always consume more time than the expert\'s black game. If the experts play a reasonably balanced but slow game, they can arrange for the duffer to run out of time on both clocks before either expert does.\r\n','2002-09-10',20031209232102,NULL,3,3,0,4.10,20020910000000,0);
INSERT INTO problem VALUES (198,5,2,1,'Trianglia','Trianglia is a jacked-up island where no road has a dead end, and all the crossroads are \"Y\" shaped.\r\n \r\nThe young prince of Trianglia mounts his horse, and is about to go on a quest to explore the land of Trianglia. He gets to the road by his palace, when the mother queen comes out and shouts: \r\n \r\n\"But Charles, how will you find your way back?\". \r\n \r\n\"Don\'t worry Elizabeth\", the prince replies, \"I will turn right in every second crossroad to which I arrive, and left otherwise. Thus I shall surely return to the palace sooner or later.\" \r\n \r\nIs the prince right?\r\n \r\n(From http://www.ocf.berkeley.edu/~wwu/riddles/intro.shtml)','Jim Lyon posted a very well-worded solution here.','2002-09-11',20040225103933,NULL,4,3,0,4.00,20020911000000,0);
INSERT INTO problem VALUES (199,7,2,1,'Men of Smallvile','A few facts about the male population of Smallvile:\r\n \r\nIf even one number from 0 to N-1 is not represented, there are no longer enough numbers for all the male residents to have a different hair count.\r\n \r\nSince we know that the number 1003 in not represented, N cannot be such that N-1 >= 1003. Thus, N <= 1003, and 1003 is the maxumum number of men living in Smallvile.','2002-09-12',20030708232102,NULL,3,3,0,3.00,20020912000000,0);
INSERT INTO problem VALUES (200,2,2,122,'Calendar Cubes pt 2',' Okay, you\'ve figured out how to display all of the days of the month using two cubes in \r\n\"Calendar Cubes\". Now here\'s your next challenge: Spell the months of the year with a letter on each face of three cubes. Use lowercase three-letter English abbreviations for the names of all twelve months (e.g., \"jan\", \"feb\", \"mar\"). The lower case is necessary because in order to spell out every month, you\'ll need 19 different letters (abcdefgjlmnoprstuvy) but you only have 18 faces to put the letters on. However, the \"n\" can be turned upside down to become a \"u\". The same goes for \"d\" and \"p\". With these at hand, the blocks can be assigned: Block 1: a, c, f, n/u, s, v Block 2: b, d/p, l, m, n/u, t Block 3: e, g, j, o, r, y \r\nWhere does he end up?\r\n \r\nHow far did he go?\r\n \r\nHow many times did he circumnavigate the earth? (For these purposes, this means travel through 360 degrees of longitude.)','He ends up at the North Pole.\r\n \r\nFor each meter he travels, he ends up 1/sqrt(2) meters north. Since the distance from the equator to the north pole is 10,000 kilometers, he travels a total of that times sqrt(2), or 14,142 kilometers.\r\n \r\n3 (from a mathematical point of view): For each increment of longitude he travels, he crosses an amount of latitude equal to that increment times the cosine of his current latitude. That is:\r\n \r\nd(lat) = d(lon) * cos(lat)\r\n \r\nRe-arranging this and integrating, we get\r\n \r\nd(lon)/d(lat) = 1/cos(lat)\r\n \r\nlon = ln(tan(lat/2+pi/4))\r\n \r\nThis approaches infinity as lat approaches 90 degrees, so the traveller circumnavigates the Earth an infinite number of times.\r\n \r\n3 (from an engineering point of view): Rearranging the final equation from (2) to solve for lat yields\r\n \r\nlat = 2*arctan(exp(lon)) - pi/2\r\n \r\nAfter passing through 360 degress of longitude, our traveller is at 89 degrees 5 minutes 13 seconds north, or 23.8 kilometers from the north pole. After 720 degrees of longitude, he\'s only 44.4 meters from the pole. After 1080 degrees of longitude, he\'s about 8 centimeters from the pole. Assuming our traveler is human, this is less than his width. Therefore, part of him is at the pole, and he circumnavigates the earth somewhat less than 3 times. (The rest of the mathematical circumnavigations is just spinning like a top.)\r\n \r\nI enjoy the disparity (mathematically infinite, but enginneringwise less than 3) of this puzzle.','2002-09-25',20030710232102,NULL,4,3,0,4.43,20020925000000,0);
INSERT INTO problem VALUES (202,11,2,153,'Escape from the Tower','This classic was written by Dr Charles Dodgson, aka Lewis Carroll, author of the Alice books.\r\n \r\nA captive queen and her son and daughter were shut up in the top room of a very high tower. Outside their window was a pulley with a rope around it, and a basket fastened to each end of the rope of equal weight. They managed to escape with the help of this and a weight they found in the room, quite safely. It would have been dangerous for any of them to come down if they weighed 15 lbs more than the content of the other basket, for they would do so too quick, and they also managed not to weigh less either.\r\n \r\nThe one basket coming down would naturally of course draw the other basket up.\r\n \r\nThe queen weighed 195 lbs, daughter 105, son 90, and the weight 75 lbs.\r\n \r\nHow did they all escape safely?','(a) The weight is sent down; the empty basket comes up.\r\n \r\n(b) The son goes down; the weight comes up.\r\n \r\n(c) The weight is taken out; the daughter goes down; the son up.\r\n \r\n\r\n(d) The son gets out; the weight goes down; the empty basket up.\r\n \r\n\r\n(e) The queen goes down; daughter and weight come up; daughter gets out.\r\n \r\n\r\n(f) The weight foes down; empty basket up.\r\n \r\n\r\n(g) Son goes down; weight comes up.\r\n \r\n\r\n(h) Daughter removes weight, and goes down; son comes up.\r\n \r\n\r\n(i) Son sends down weight; empty basket comes up.\r\n \r\n(j) The son goes down; weight comes up.\r\n \r\n(k) Son gets out; the weight falls to the ground.','2002-09-19',20031111232103,NULL,3,3,0,3.62,20020919000000,0);
INSERT INTO problem VALUES (203,17,2,213,'Radiators','It\'s well-established in physics that black or dark-colored objects radiate heat faster and more effectively than light-colored objects.\r\n \r\nSo, in almost every building that uses steam heat, why are the radiators painted silver or some other very light color?','Radiators aren\'t meant to heat buildings via radiation, they\'re meant to heat buildings via convection.\r\n \r\nIf the radiator were painted a dark color, the radiant heat would make you uncomfortably warm on the side facing the radiator, while leaving you cool on the side away from the radiator. By painting them a light color, they minimize the heat radiation. \r\n \r\nBy minimizing the heat radiation, the heat convection is relatively maximized. The radiator heats the air in its vicinity; that air circulates around the room.','2002-09-26',20030529232102,NULL,2,3,0,2.88,20020926000000,0);
INSERT INTO problem VALUES (204,11,2,153,'The Rings','Mary has an unusual ring. It is made up of a set of three interlocking ringlets, each set with a large gemstone, a diamond, a ruby, and a sapphire. It is very valuable and the insurance company insists it be kept locked in their vault, except on those occassions where Mary is wearing it. Because of this, Mary had a copy made, which she wears on lesser occassions.\r\n \r\nToday she attended an affair in which she was able to convince the insurance company that she needed to wear the original. Half an hour after returning home the insurance rep called to let her know he was on his way to pick up the ring.\r\n \r\nMary then realized that she\'d absent-mindedly taken off the ring and put it in her jewelry box, where she keeps the copy.\r\n \r\nWhen it\'s not on her finger, the ring separates into its componants, so Mary was looking at six nearly identical ringlets, two with blue stones, two with red, and two with white. \r\n \r\nShe needs to separate the genuine ringlets from the copies. She knows that each of the ringlets in each set weighs the same.(That is the genuine ringlets each weigh the same, and the copies each weigh the same.) She also knows that a copy weighs less than its original.\r\n \r\nThe only scale she has that is delicate enough to properly weigh the ringlets is a small balance scale she uses to measure headache powders and sleeping draughts (she can\'t swallow pills), but the weights tha she uses for her medicine are of an order too small for the ringlets. She will have to weigh them against each other. She could do it in three weighings by trying each against its counterpart, but she is certain to be \"caught\" before she finishes, and either her insurance will go up, or the company will be \"forced\" to not allow her to wear the ring any more.\r\n \r\nIs there a way to separate the six ringlets in two weighings?','Yes. One possible sequence:\r\n\r\n \r\nFirst weighing: put a white and a red in one pan, a white and a blue in the other.\r\n \r\nCase I (they balance): Since you don\'t have four genuine or four copies, you must have two of each. Switch the whites, so that the copies are together in one pan and the orginals in the other to determine which is which. The unweighed ringlets can each only go in one set.\r\n \r\nCase 2 (they don\'t balance):\r\n \r\nIn this case, you have either three copies and one genuine, or three genuine and one copy, or you have two heavies vs two lights. Either way, you\'ve isentified the whites. \r\n \r\nCarefully set them aside and note which color the genuine white was paired with. Put the red and blue you weighed in one pan and the other two in the other pan.\r\nIf they do not balance, the heavier pan has two originals and the lighter, twoo copies. If they balance, the ringlet that was partnered with the genuine white was also genuine, and it\'s new parner is a copy, and the other two can be worked out from there.','2002-09-20',20030415232102,NULL,3,3,0,3.50,20020920000000,0);
INSERT INTO problem VALUES (205,2,2,558,'Four Perfect Logicians','Four perfect logicians, who all knew each other from being members of the Perfect Logician\'s Club, sat around a table \r\nthat had a dish with 11 apples in it. The chat was intense, and they ended up eating all of the apples. Everybody had at \r\nleast one apple, and everyone knew that fact, and each \r\nlogician knew the number of apples that he ate. They didn\'t know how many apples each of the other ate, though.\r\n \r\nThey agreed to ask only questions that they didn\'t know the answers to.\r\n \r\n \r\nKurt figured out how many apples each person ate. Can you do the same?','Alonso ate 1, Bertrand ate 2, George had 3 and Kurt ate the remaining 5 apples. A few full solutions are presented in the comments for this problem.','2002-09-24',20030621232102,NULL,4,3,0,3.60,20020924000000,0);
INSERT INTO problem VALUES (206,12,2,103,'Oh, No! Not Again!','What do the following items have in common? \r\n\r\nThe La Brea Tar Pits \r\n\"I want you write a computer program that plays tic-tac-toe \r\nlegally and runs through ALL the possible combinations of the game, and finds out the total.\"\r\n \r\nThe students settle down to work..\r\n \r\nAn hour later, a student gets up and proclaims \"I\'ve got it! The number of possible combinations in a game is 344,242.\"\r\n \r\nAt which point another student quickly replies, \"I haven\'t finished yet, but I\'m sure \r\nFred made a mistake in his program.\"\r\n \r\nWhy?\r\n \r\n \r\n(Tic Tac Toe = Noughts and Crosses)','The total combinations can be partitioned into first\r\nmove groups. Positions starting at corners and sides\r\nare indistinguishable. This means that each of \r\nTotal = 4*(Corner) + 4*(Side) + Middle\r\n \r\nIn Middle games, the second move is inevitably a \r\ncorner or side. Because the middle mark is in the middle, symmetry still applies, as in the previous calculation.\r\n \r\nT = 4C + 4S + (4C\' + 4S\') \r\nThe number given by the first student is not divisible\r\nby 4. So even though the second student does not know\r\nthe exact value, he knows fred´s suggestion is incorrect.','2002-09-27',20040115232103,NULL,3,3,0,3.67,20020927000000,0);
INSERT INTO problem VALUES (210,7,2,1,'Egg drop','You have two identical eggs, and are given the task of figuring out the highest floor of a 100-story building from which an egg can be dropped safely (meaning that it doesn\'t break). You have no prior information about this matter, so for all you know a fall from the first floor might break the egg, but then again, it might be strong enough to survive a 100-story drop.\r\n \r\nYou need to conduct experiments by dropping the eggs from various levels in the building to solve the problem. You are allowed to break both eggs as long as you come up with an answer.\r\n \r\nFind a strategy to minimize the maximum number of drops you would have to do. What is this number? (For example if your strategy is dropping an egg from first, then second, then third floors, and so on until it breaks, the maximum number of drops is 100.)','An efficient stragegy for finding the threshold floor using only two eggs, would be to use the first to establish a range of floors that contains the threshold, and then using the second to pinpoint the actual floor within that range.\r\n \r\nSo we will throw the first egg off of floors \r\nNow our goal is to find the values for Xi that will make our strategy most efficient. Intuitively, it would seem that the ranges of floors should be equal to minimize the needed attempts. However, on further thought, we will see that since higher ranges need more attempts to reach, they should contain less floors, to balance out the total number of attempts used.\r\n \r\nThe optimal solution is: \r\nDoes the ant ever reach the far end of the band? If so, when?\r\n','During the first second, the ant traverses 1/1000 of the band. When the band stretches, he\'s still 1/1000 of the way to the end. During the second second, the band is 2 meters long, so he only traverses 1/2000 of the band. In general, during the nth second the ant traverses 1/(1000*n) of the rubber band. So, for the time up to and through the nth second, he has traversed:\r\n \r\n1/1000 + 1/2000 + 1/3000 + ... + 1/(1000*n)\r\n \r\nAs n grows large, this series increases without bound. When the value of this series reaches 1, the ant will be at the far end of the rubber band. Therefore, mathematically speaking, the ant will reach the end.\r\n \r\nThe series above takes as many terms to reach one as the following series takes to reach 1000:\r\n \r\n1/1 + 1/2 + 1/3 + ...\r\n \r\nThis takes between e^999 and e^1000 terms. So, the ant takes roughly e^1000 seconds to reach the end.\r\n \r\nBut wait. e^1000 seconds is inconcievably huge, roughly 10^426 years. By way of comparison, the universe is only about 10^10 years old, and is expected to suffer complete heat death before 10^100 years.\r\n \r\nSo yes, the ant gets there, but it takes him 10^326 universe lifetimes to do so. At the end of this time, the rubber band is 10^426 meters, or 10^418 light-years long. Assuming that the rubber band weighs 10 grams (reasonable for a 1 meter band), it has about 10^24 atoms, and the mean distance between atoms when fully stretched is 10^394 light-years. The known size of the universe is only about 10^10 light-years, so the rubber band is stretched much further than that.\r\n \r\nAll of which goes to show that, mathematics notwithstanding, the ant will never reach the end.','2002-10-03',20040324232102,NULL,3,3,0,4.53,20021003000000,0);
INSERT INTO problem VALUES (215,7,2,606,'Square of an Odd','Take any odd number and square it. It will invariably be a multiple of 8 plus 1. So (odd)^2=8n+1 where n is an integer. Show why this is always so. Also show what the pattern for n is.','Z = an even number \r\n(Z+1)^2 = z^2+2z+1 \r\n \r\nso we\'re trying to prove that \r\nso \r\n(2w)^2 + 2(2w) = 8n \r\n8*[w*(w+1)/2] = 8n //notice that I turned the 4 into 8/2 \r\nIf you multiply two integers together, and at least one of them is even, the product will be even. Therefore, w*(w+1) is even, since one of them has to be even, and one of them has to be odd. So if [w*(w+1)] is even, then [w*(w+1)]/2 is an integer, equal to the n that we started with (8n+1)\r\n \r\nIt just so happens that [w*(w+1)]/2 = the sum of all the non-negative integers up to and including w (0 + 1 + 2 + 3 + ...... + w). So that is the pattern for n (0, 1, 3, 6, 10, 15).\r\n \r\n1^2 = 8(0) + 1 \r\nIt is decided that the three of them will divide the 8 sandwiches equally, and then Al and Bert will divide the $8. After lunch, Bert picks up four of the dollars. but Al says that it is not fair. He says he should have more. Carl agrees that All should have nore. He says that since Al contributed 5 of the sandwiches and Bert contributed 3, Al should get $5 and Bert should get $3\r\n \r\nIs this the most fair division of the money?\r\n \r\n(The site I found this on calls it a \"classic\" puzzle, but does not give any other information about its source.)','No.\r\n \r\nEach man ate 2 2/3 sandwiches. Since Bert brought 3 sandwiches, he only \"sold\" 1/3 of a sandwich to Carl. Al, who brought 5 sandwiches, \"sold\" 2 1/3 sandwiches to Carl: 7 times as much! Al should get $7, and Bert should get $1.','2002-10-02',20030908232101,NULL,2,3,0,3.78,20021002000000,0);
INSERT INTO problem VALUES (217,11,2,1,'Tricky Pearls','You have been given 10 bags of pearls. You are told that one of the bags is full of those cheap plastic kind of pearls, but the other nine are the real deal. Naturally, you cannot tell the difference just by looking. However, you know that the fake pearls weigh 9 grams each, while the real ones are one gram heavier and weigh 10.\r\n \r\nArmed with a very presice scale, you could weigh a pearl from each bag until you find the fake one by weight, but that would take up to 10 weighings. Can you do it in less?','Take a pearl from bag 1, 2 pearls from bag 2, 3 pearls from bag 3, etc.\r\n \r\nWeigh this pile of pearls you have. If they were all real, the result would weigh 10*(1+2+3+4+...+10) = 550 grams.\r\n \r\nBecause some of the pearls are fake, your result will be less.\r\n \r\nIf it\'s one gram less, then the bad pearls are in bag 1. If the difference is 2 grams, then bag #2 is the culptit, etc.\r\n \r\nThus the problem is solvable in one weighing.','2002-10-08',20031030232101,NULL,2,3,0,3.78,20021008000000,0);
INSERT INTO problem VALUES (218,11,2,122,'Trickier Pearls',' \r\nYour boss liked how you solved the Tricky Pearls problem and has now given you a new one.\r\n \r\nYou have 5 bags of pearls. You are told that each bag contains either all genuine pearls, or all fake pearls. Real pearls weigh 10 grams and fake pearls weigh 9 grams. \r\n \r\nArmed with a very precise scale, how can you figure out which bags contains the fake pearls with the fewest number of weighings?\r\n If every bag contains genuine pearls, the total weight should be 10*(1+2+4+8+16) grams or 310 grams. \r\nNow X can be viewed as a binary representation of which bag is fake. Here\'s how to decode it: If X >= 16g, then bag 5 must contain fake pearls. Subtract 16g from X and continue to next step.\r\n \r\nIf X >= 8g, then bag 4 must contain fake pearls. Subtract 8g and continue.\r\n \r\nIf X >= 4g, then bag 3 is fake. Subtract 4g.\r\n \r\nIf X >= 2g, then bag 2 is fake. Subtract 2g.\r\n \r\nIf X >= 1g, then bag 1 is fake.\r\n \r\nI place one dollar on the table. I repeatedly flip a coin. Each time the coin comes up heads, I double the money on the table. The first time the coin comes up tails, you take the money and the game is over.\r\n \r\nWhat\'s a fair admission price for the game?\r\n \r\nWould you play the game with me for $100?','The probability that the nth flip is tails is 1/2^n. The amount of money won if the nth flip is tails is 2^(n-1).\r\n \r\nMathematically speaking, the value of the game is:\r\n \r\n1/2 * 1 + 1/4 * 2 + 1/8 * 4 + ...\r\n \r\nwhich equals\r\n \r\n1/2 + 1/2 + 1/2 + ...\r\n \r\nSo, mathematically speaking, the value of the game is infinite.\r\n \r\nIn practical terms, however, you\'ll soon be limited by the amount of money I have. (That is, there will soon come a point where I am incapable of doubling the money on the table.) So, the series ends at that point. In reality, the series only has as many terms as log2 of the money I have, and the value of the game is 1/2 that.\r\n \r\nSo, if I have about $1000, the value of the game is $5. If I have about $1,000,000, the value of the game is $10. If I have $1,000,000,000, the value of the game is $15. Even if I\'m Bill Gates, the value is less than $20.','2002-10-09',20030911232101,NULL,3,3,0,3.50,20021009000000,0);
INSERT INTO problem VALUES (220,7,2,122,'Mmm... nuggets.','At a certain nation-wide fast food chain, you can get chicken nuggets in boxes of 6, 9, and 20. What is the maximum number of nuggets you could ask for such that no combination of the 3 sizes will give you exactly what you wanted?',' \r\nIf the number is divisible by 3, then just using the 6 and 9 boxes can fulfill the order. Fill as much as you can with the 6 boxes, and if there\'s 3 left over, take away one box and replace with 9. The only exception to this is 3 nuggets, of course. \r\n \r\nIf the number is not divisible by 3, then first use a box of 20. If the remaining number of nuggets is divisible by 3, then use the first strategy to fill the rest.\r\n \r\nIf the number is STILL not divisible by 3 after using the box of 20, then use a second box of 20. Now the remaining number MUST be divisible by 3 (otherwise it should\'ve met one of the above two criterias). Use 6 and 9\'s to fill the rest of the order.\r\n \r\nHowever, if the remaining number was 3, then 6 and 9 can\'t be used. So the maximum number that can\'t be fulfilled is 2*20+3 = 43 nuggets.\r\n \r\n(source: Math Puzzles Index)\r\n \r\nCurrently, the largest named measure of data is the yottabyte (YB), which is exponentially greater than the zettabyte, exabyte, petabyte, terabyte, and so on. The yottabyte is approximately equal to 5X * 10^6, where X is equal to all printed matter that exists on our planet. More definitively, 1 YB=2^80 Bytes.\r\n \r\nThe highest-density digital tape (which is the highest-density medium currently in common use) made by one of the world\'s leading manufacturers stores data at a density of 124,000 bpi (bits-per-inch). Assume zero overhead for error-correction and -detection.\r\n \r\nAt a tape thickness of 8.9 microns, what must the diameter of a roll of tape be in order to store one YB of data, assuming that it is wrapped around a spool with a diameter of 0.5 inches and assuming that there is no space between the layers of tape?',' \r\nTo find the diameter of the roll of tape:\r\n \r\nI. Find the length of the tape:\r\n \r\n \r\n \r\nII. Using Step I, find the area of the \"side\" of the \"piece\" of tape.\r\n \r\n \r\n \r\nIII. Find the area of the end of the spool (a = π r²): \r\n \r\nIV. Add the areas of steps II and III: \r\n \r\nV. Given IV, find the circle\'s diameter (2 * (√(A/π))): \r\n \r\nVI. To make this number a bit more manageable, let\'s convert to miles: \r\n \r\nThis is roughly 37% of the diameter of the planet earth and almost one and one half times the diameter of our moon. Now that\'s a Lotta Yotta!\r\n \r\nThe entire equation can be expressed as:\r\n \r\n Alan and Bob are trying to figure out two numbers. They know that both numbers are integers between 1 and 100 (but not 1 or 100). Alan knows the product of the numbers, and Bob knows the sum. Their conversation goes as follows: \r\nAlan: I can\'t tell what the two numbers are. What are the two numbers? \r\nThe first person can\'t work out the numbers, hence at least one of the numbers is not a prime number\r\n \r\nThe second person knew that the first couldn\'t work out the numbers, hence the sum of the numbers is such that it cannot be represented as a sum of two prime numbers. Let\'s call the possible sums, i.e. numbers that cannot be represented as a sum of two prime numbers, \"Good sums\", and number pairs that sum up to a \"Good Sum\", \"Good Pairs\".\r\n \r\nNow the first person can work out the numbers, hence if the number that he know is represented as a product of two numbers in all possible ways, only one pair is a \"Good Pair\". Let\'s call all such products \"Good Products\".\r\n \r\nThe second person now can tell the numbers, hence if the sum is represented as a sum of two numbers in all possible ways, and the product of all these ways is calculated, only one of these products is a \"Good Product\".\r\n \r\nNow we are ready for some calculations \r\n \r\nIt\'s easy to check that only the following numbers cannot be represented as sums of two prime numbers:\r\n \r\n11, 17, 23, 27, etc. These are all odd numbers X so that X-2 is not a prime number. \r\n \r\nNow that we have all \"Good Sums\", we\'ll have to check each of those to satisfy the other statements.\r\n \r\nChecking 11 \r\n \r\nWe are now checking if 11 is a possible sum of the numbers sought. Possible ways of representing 11 as a sum of two numbers are: 2+9, 3+8, 4+7 and 5+6.\r\n \r\nCorresponding products are: 18, 24, 28 and 30\r\n \r\nLet?s see if 18 is a \"Good Product\". It can be represented as a product of two numbers in the following ways: 2x9 and 3x6. 2+9 is a \"Good Sum\" according to the \"Good Sums\" slide, and 3+6 is not a \"Good Sum\", hence 18 is a \"Good Product\"\r\n \r\n24 can be represented as a product of two numbers in the following ways: 2x12, 3x8 and 4x6. 2+12 is not a \"Good Sum\", 3+8 is a \"Good Sum\" and 4+6 is not a \"Good Sum\", hence 24 is a \"Good Product\" as well.\r\n \r\nThus we have at least two pairs (2,9) and (3,8) so that their sum is 11 and their product is a \"Good Product\", hence 11 cannot be the sum of the sought numbers, as the person knowing the sum couldn\'t make his final statement.\r\n \r\nChecking 17 \r\n \r\nWe are now checking if 17 is a possible sum of the numbers sought. Possible ways of representing 17 as a sum of two numbers are: 2+15, 3+14, 4+13, 5+12, 6+11, 7+10 and 8+9.\r\n \r\nCorresponding products are: 30, 42, 52, 60, 66, 70 and 72.\r\n \r\nLet\'s see if 30 is a \"Good Product\". It can be represented as a product of two numbers in the following ways: 2x15, 3x10 and 5x6. 2+15 is a \"Good Sum\" according to the \"Good Sums\" slide, 3+10 is not a \"Good Sum\", 5+6 is a \"Good Sum\", hence 30 is not a \"Good Product\" (because of the two \"Good Sums\")\r\n \r\n42 can be represented as a product of two numbers in the following ways: 2x21, 3x14 and 6x7. 2+21 is a \"Good Sum\", 3+14 is a \"Good Sum\", hence 42 is not a \"Good Product\" either.\r\n \r\n52 can be represented as a product of two numbers in the following ways: 2x26 and 4x13. 2+26 is not a \"Good Sum\", and 4+13 is a \"Good Sum\", hence 52 is a \"Good Product\". \r\n \r\n60 can be represented as a product of two numbers in the following ways: 2x30, 3x20, 4x15, 5x12 and 6x10. 2+30 is not a \"Good Sum\", 3+20 is a \"Good Sum\", 4+15 is not a \"Good Sum\", 5+12 is a \"Good Sum\", 6+10 is not a good sum. Here we have two good sums (3,20) and (5,12) hence 60 is not a \"Good Product\".\r\n \r\nContinuing with the same logic we\'ll find that 66, 70 and 72 are not \"Good Products\" either. Thus, for the sum of 17 we found only 1 \"Good Product\": 52. Thus, the pair (4,13) is a possible solution to the problem.\r\n \r\nChecking other \"Good Sums\" \r\n \r\nWe won\'t check all other \"Good Sums\" here, however the by applying the logic described in the previous slides you can see that there is no other \"Good Sum\" so that one and only one of the corresponding products is a \"Good Product\" within the limitations of the problem (i.e. numbers less than 100).\r\n \r\nThus the final answer is: 4 and 13.\r\n \r\n(source: Tech Ed ) In Self-Descriptor, we found a number ABCDEFGHIJ such that A is the count of how many 0\'s are in the number, B is the number of 1\'s, and so on. I wonder... what if the number didn\'t have to be 10 digits long? Find the smallest whole number such that the left-most digit describes the number of 0s in the number, the next digit describes the 1s, etc. Prove that it\'s the smallest.\r\n \r\n1210\r\n \r\nTry to find a number less than 1210: ABCD, or ABC, or AB, or A.\r\n \r\nA: Can\'t be zero. If A >= 3, then the number would have be over 3001 (in order to state that there are at least 1 3\'s in the number). If A = 2, then to be under 1210, the number would have to be exactly 200 which is not self-describing. Thus, A = 1.\r\n \r\nB: Since A = 1, B >= 1. B cannot be 1 because then we\'d have 2 1\'s. if B >= 3, then the number would have to be over 1300. Thus B = 2.\r\n \r\nC: Since B = 2, C >= 1. If C = 1, this would fulfill B\'s count. \r\n \r\nD: Since we stated that A is 1, there must be one zero in the number. D = 0 fulfills this condition.\r\n \r\nThus, the smallest self-describing number is 1210.\r\n \r\nWhat is the total percentage of red balls in the jar?','This turns out to be a more difficult (and somewhat deceptive) problem than I first thought.\r\n \r\nThe answer is that 75% of the balls are red. This is because the only viable solution seems to be when there are a total of 4 balls, and 3 of them are red. (You cannot get the same results with 8 balls 6 of which are red, etc)\r\n \r\nTomM has submitted a fairly rigorous proof to this in the problem\'s comments.','2002-10-17',20030814232101,NULL,4,3,0,4.00,20021017000000,0);
INSERT INTO problem VALUES (227,9,2,658,'Oh my, Protagoras','A Lawyer named Protagoras teaches law for a hefty fee. He advertises his skills as a teacher by offering his students a contract, which states that they do not have to pay him until they have won their first case. If the student loses their first case, then they don\'t have to pay Protagoras at all. \r\n \r\nOne student of Protagoras sees a loophole, takes the course and fininshes it. After that, the student avoids arguing any cases. \r\nSince the student has not yet won his first case, he avoids paying Protagoras. \r\n \r\nProtagoras feels cheated, and sues the student for his fee. When the case comes to trial, the student represents himself. If the student loses the case, then by the terms of their original agreement, there is no fee for the course. If the student wins the case however, then, since its the student\'s first case, there will be a fee. (But, of course, winning the case means that the student doesn\'t have to pay the fee, while losing it means that the fee must be paid.) \r\n \r\nWill the student be obliged to pay Protagoras\' fee or not?\r\n','This paradox is mostly of legal nature, as it is to be decided in the court of law. Depending on the procedure followed by the judge/jury they may (or may nor) be able to come to a deceision at their discression.\r\n \r\nIrene provided some interesting historical background (and corrections) to this problem in the comments.','2002-10-19',20031209232102,NULL,3,3,0,2.92,20021019000000,0);
INSERT INTO problem VALUES (228,12,2,1,'Errors','There is three errors in thise riddle. \r\n \r\nWhat are they?','The expected answer is:\r\n \r\nIf the riddle only has two errors, then saying that it has three errors is clearly wrong. Therefore, there is a total of three errors. However if that\'s the case, then the error on the third line is not an error at all, and the problem really only has two errors.\r\n \r\nThis sort of cirtcular logic should lend this problem in the Paradoxes\r\ncategory, as it\'s very similar to the statement that claims to be false.','2002-10-21',20040225103933,NULL,1,3,0,3.77,20021021000000,0);
INSERT INTO problem VALUES (229,19,2,122,'Curiouser and curiouser','Why is a raven like a writing desk?',' This is a famous riddle by Lewis Carroll\'s Alice in Wonderland. There is no official answer. However in his 1896 book, he wrote in the preface: \r\n\"Enquiries have been so often addressed to me, as to whether any answer to the Hatter\'s Riddle can be imagined, that I may as well put on record here what seems to me to be a fairly appropriate answer, viz: `Because it can produce a few notes, tho they are very flat; and it is nevar put with the wrong end in front!\"\r\n \r\nFamous puzzle maven, Sam Loyd, gives two other possible answers: \r\nUnfortunately, when Billy came home from school, he had five friends with him. Not to be stumped, Mom asked Billy and another boy to share a seat for a while. Then she put the second guest into the second seat, the third into the third seat, the fourth into the fourth seat. Then looking at the remaining empty (fifth) seat, she said to the boy sharing Billy\'s chair:\r\n \r\n\"You can now go sit this this last seat. Since you are Billy\'s fifth guest, everyone should now be seated.\"\r\n \r\nDid Billy\'s mom really manage to put six people into five seats?','The trick here, is that Billy\'s mom only seated five people (naturally). The last boy to be seated was not really the fifth guest, as Mom said, but the first guest.\r\n \r\nHe just got counted twice.','2002-10-24',20040107232101,NULL,1,3,0,2.33,20021024000000,0);
INSERT INTO problem VALUES (231,7,1,1,'Niners','The set of numbers {9, 99, 999, 9999, ...} has some interesting properties. One of these has to do with factorization. Take any number n that isn\'t divisible by 2 or by 5. You will be able to find at least one number in the set that is divisible by n. Furthermore, you won\'t need to look beyond the first n numbers in the set.\r\n \r\nProve it. \r\n \r\n(from http://www.ocf.berkeley.edu/~wwu/riddles/)','','2002-10-23',20030813232100,NULL,4,3,0,4.14,20021023000000,0);
INSERT INTO problem VALUES (232,8,2,688,'How many openings?','How many possible openings are there in the game of chess, if we define an that opening consists of each player making their first 3 moves?\r\n \r\n(With one move there are 400 possible openings)','Original solution:\r\n \r\n\"a LOT! you will HAVE to use a computer program to figure this one out or spend years trying to without using a computer\"\r\n \r\nOf course, this being perplexus, we did use a computer:\r\n \r\nYou are looking through a small hole at a corner of a standard six-sided playing die, as shown above. (The picture is showing that there are spots in the corners that you see. It does not imply absence of any other spots.)\r\n \r\nDetermine at least one of the faces of the die that you are seeing.','Standard playing dice have faces arranged in a way that opposite face values always add up to 7.\r\n \r\nThe picture shows the three partly visible faces that have a dot in the corner. The only face to not have a dot in the corner is 1, which means that 1 is definitely not one of the visible faces.\r\n \r\nHowever this means that the face opposite 1 has to be one of the three. That face is 6.','2002-10-26',20040323232103,NULL,3,3,0,3.46,20021026000000,0);
INSERT INTO problem VALUES (234,12,2,688,'What am I','I make Marriage A Grim Era and turn your Mother in law into a Woman Hitler.\r\n \r\nIf you have ever asked someone to \"stop banging the pots\", you have used me before. \r\n \r\nWhat am I?','I\'m an Anagram! (Letters of a word or phrase rearranged to spell out a different word or phrase.)','2002-10-29',20040129232107,NULL,1,3,0,3.00,20021029000000,0);
INSERT INTO problem VALUES (235,4,2,213,'World Series','What is the probability of a world series ending after 4 games? After 5 games? 6 games? 7 games?\r\n \r\nAssume that each team has equal probability of winning each game, regardless of who has won the previous games.\r\n \r\n(For the baseball-challenged, the World Series ends after one team has won 4 games. Ties are not possible.)','In order to have a 4-game series, games 2..4 must end the same way as game 1. p = 1/8\r\n \r\nIn order to have a 5-game series, games 1..4 must be split 3-1, then game 5 must be won by the leader. The probability of splitting 3-1 is 4 * 1/16 * 2 = 1/2. So overall, for a 5-game series, p = 1/4.\r\n \r\nIn order to have a 6-game series, games 1..5 must be split 3-2, then game 6 must be won by the leader. The probability of splitting 3-2 is 10 * 1/32 * 2 = 5/8. So overall, for a 6-game series, p = 5/16.\r\n \r\nIn order to have a 7-game series, games 1..6 must be split 3-3. The probability of this is 20 * 1/64 = 5/16.\r\n \r\nThe above calculations all rely on the binomial distribution. The factors of 2 are there to account for the possibility of either team winning. (That is, when I calculate the probability of going 3-0, it counts the probability of the NL team leading 3-0 plus the probability of the AL team leading 3-0.)','2002-10-30',20030415232102,NULL,3,3,0,3.40,20021030000000,0);
INSERT INTO problem VALUES (236,16,2,227,'Quarter intersection Problem','Below is an image of a square, 7 cm to a side, with four quarter-circles inscribed into it as showm. \r\n \r\nFind the area of the shaded region in the center.\r\n \r\n \r\n\"The product of their ages is 36\". \r\n \r\nWhen I still couldn\'t find their ages he said:\r\n \r\n\"Ok. I\'ll give you another clue: the sum of their ages is same as the number of my house\". \r\n \r\nI knew the number but still couldn\'t calculate their ages. So the man gave me a last hint, he said:\r\n \r\n\"My eldest daughter lives upstairs\". \r\n \r\nFinally I was able to find their ages. Can you?','First, we find the prime factorization of 36:\r\n \r\n36 = 1 * 2 * 2 * 3 * 3\r\n \r\nNow, find all groupings of these factors into 3 numbers (and their sums):\r\n \r\nIf I knew the sum of the daughters\' ages, and that didn\'t help me, it means that the sum must have been 13. (Any other sum would yield a unique solution, but 13 is repeated twice in the list.)\r\n \r\nThe last bit of information seems pretty useless, but it let me know that there exists an eldest daughter. Of the two combinations adding up to 13, (1,6,6) and (2,2,9), the first one has two older daughters of the same age. The fact that there is an eldest daugher means that the daughers\' ages MUST be 2, 2 and 9.','2002-10-31',20030914232101,NULL,3,3,0,3.40,20021031000000,0);
INSERT INTO problem VALUES (238,11,2,707,'Water Works','You have a 5 gallon jug and a 3 gallon jug. \r\nYou have no other measuring devices.\r\n \r\nMeasure out exactly 4 gallons of water (Assume you have a river handy, or some other limitless water supply). \r\n\r\n\r\n','We will use \"(X,Y)\" after each step to indicate how much water is in each jug. X will be the amount in the 5 gallon jug, Y - the 3 gallon one.\r\n \r\n \r\nVoila! You now have 4 gallons in the 5 gallon jug.','2002-11-02',20030504232102,NULL,2,3,0,2.30,20021102000000,0);
INSERT INTO problem VALUES (239,16,2,227,'Big Circle, Little Circle',' \r\nA circle has a radius of 14 cm. Another circle has a radius of 7 cm. The centre of the second circle lies on the circumference of the first. Find The common area for both circles.\r\n \r\n(P.S -The answer might not be elegant)','The answer is approximately 68.75 \r\n \r\nThe comments submitted by our users provide a few methods for solving it.','2002-11-03',20030831232101,NULL,4,3,0,3.29,20021103000000,0);
INSERT INTO problem VALUES (240,16,2,227,'Special triangle in any triangle','Prove or disprove, that the points of intersection of the adjacent trisectors of the angles of any triangle are the vertices of an equilateral triangle. (In other words, that for any yellow triangle, the green triangle will be equilateral, given that the thinner lines trisect their respective angles.)\r\n \r\nCharlie has pointed out that a proof is available here.','2002-11-05',20030901232101,NULL,5,3,0,3.86,20021105000000,0);
INSERT INTO problem VALUES (261,4,2,1,'Ants on a triangle','Three ants are arranged on vertices of a triangle, one ant to a vertex. At some moment, all the ants begin crawiling along the sides of the triangel. Each one crawls along one of the two sides that connect to the vertex it is sitting on, with an equal probability of picking either.\r\n \r\nAssuming that all the ants move with an equal speed, and that they keep crawling forever in the same direction along the triangle, what are the odds that no two will collide?','Each ant can either start moving in a clockwise direction, or a counterclockwise direction. Since the odds of either occuring are equal (50%), and there are 3 ants, we have 2*2*2 = 8 equally likely \"states\" that can result.\r\n \r\nThe only way for the ants to not collide is for all of them to start moving in the same direction: either clockwise, or counterclockqise. \r\n \r\nOf our given 8 possibilities, these are only 2. Thus there is a 2/8 = 1/4 chance that no collisions will take place.','2002-11-20',20040229232101,NULL,2,3,0,2.88,20021120000000,0);
INSERT INTO problem VALUES (256,7,2,746,'Princeton\'s Prime Problem','Prove that every prime number other than 2, can be expressed as a difference of two squares.\r\n \r\n - Princeton Math Club Website','As Jim Lyon explains:\r\n \r\nAny prime number other than 2 has to be odd, and therefore can be expressed as 2*k+1, where k is an integer.\r\n \r\nTake the difference between k2 and (k+1)2, \r\nusing simple algebra, (k+1)2 - k2 = 2*k+1.\r\n \r\nSo not only is the prime other than two expressed as a difference of two squares, but it is a difference ot the squares of two specific consecutive numbers. \r\n \r\nsin^2 x = AB^2/AC^2 \r\nTherefore sin^2 x + cos^2 = (AB^2 + BC^2)/AC^2\r\n \r\nBut AB^2 + BC^2 = AC^2 (Pythogorean Thoerem)\r\n \r\nThrough substituition AC^2/AC^2 = 1\r\n \r\nSo sin^2 x + cos^2 = 1','2002-11-07',20031009232104,NULL,1,3,0,2.50,20021107000000,0);
INSERT INTO problem VALUES (248,12,2,746,'A locked 7-11?!','If a 7-11 store is open 24 hours a day, 7 days a week, 365 days a year, then why are there locks on the doors?','This problem doesn\'t really have a very satisfying answer.\r\nThere are a few practical reasons, most pretty mundane, such as in the case of emergency/holidays why even a 24/7 store might want to lock its doors.','2002-11-11',20030909232101,NULL,2,3,0,2.13,20021111000000,0);
INSERT INTO problem VALUES (249,13,2,746,'What\'s Next?','What row of numbers comes next? (This is a tough one!)\r\n \r\nIs he telling you the truth or is he lying? ','This is or is not a paradox depending on wether or not the man has said anything else to you.\r\n \r\nA lot of people assume that if the statement \"I always lie\" is false, then the statement \"I always tell the truth\" must be true. But in reality, the opposite of \"I always lie\" is \"I sometimes don\'t lie.\"\r\n \r\nIt is obvious that the man cannot be telling the truth, since if he is telling the truth, he must be lying. However, if he is lying when saying \"Everything I tell you is a lie\", then in reality, at least something (not everything) that he tells you should be the truth.\r\n \r\nIf this statement is the only thing he ever tells you, then we reach a paradox: it\'s like a statement saying that it\'s false.\r\n \r\nHowever, if the man then proceeds to tell you something else, something that is true, then there is no paradox: he has lied to you about always lying. Some of what he tells you is truthful.','2002-11-12',20040202232102,NULL,3,3,0,2.79,20021112000000,0);
INSERT INTO problem VALUES (251,12,2,746,'Half or not','A woman has 7 children, half of them are boys.\r\nHow can this be possible? ','ALL the children are boys, so 1/2 half are boys and so is the other half.','2002-11-14',20040212232105,NULL,1,3,0,3.42,20021114000000,0);
INSERT INTO problem VALUES (252,7,2,746,'Equation drawing','How can you make the following equation true by drawing only one straight line:\r\n \r\n5+5+5=550\r\n \r\nCan you figure it out? ','Draw a line on the first plus sign that turns it into a 4! The equation then becomes true:\r\n \r\n545+5=550','2002-11-10',20030626232103,NULL,3,3,0,3.12,20021110000000,0);
INSERT INTO problem VALUES (253,17,2,756,'H2O','If hydrogen (H) is combustible and oxygen (O) is combustible, why does water (H2O) water not explode?','This problem is a little misleading, as it compares apples and oranges (Or atoms to molecules as it were). It is meaningless to talk about the combustibility of hydrogen (H) as an atom. Since combustion is a chemical reaction, it is a molecule of Hydrogen (H2) which we can say is combustible. \r\n \r\nHowever, with a molecule, its atoms play only a part of determining wether or not it is combustible. A big part is also played by the bonds between the molecules atoms. As such, we can have two very reactive substances (hydrogen and oxygen gases) combine to form a very stable substance - water.','2002-11-13',20031015232102,NULL,3,3,0,2.60,20021113000000,0);
INSERT INTO problem VALUES (254,16,2,540,'Square wheels?','On what kind of surface would a square wheel function the same as a round wheel?\r\n ','After much discussion here, TomM\r\nGoogled\r\nthis problem and found the surface producing smooth motion with a square wheel.\r\n \r\nLevik meanwhile, proposed a way to find an answer addressing the letter of the problem.','2002-11-15',20040225103933,NULL,4,3,0,3.67,20021115000000,0);
INSERT INTO problem VALUES (255,16,2,706,'Chessboard Puzzle','Take a chessboard, it has 64 squares. Now cut off any two corner squares which are diagonally opposite. \r\n \r\nYou are given many rectangular bits of paper which have area equal to that of two such squares kept side by side. The PROBLEM is to cover the modified chess board with such pieces of paper. \r\n \r\nNo overlapping or folding is allowed. All the pieces should lie on the area of the modified chess board. Is this possible, and if not why?','Nick Reed\'s comment provides a perfect solution to the puzzle. \r\n \r\nTo reiterate: it cannot be done. Removing two diagonally opposite squares will result in a chessboard with 32 squares of one color, and 30 of another. Since one 2x1 piece of paper will always cover one square of each color, you would need an equal number of black and white squares to cover the whole board.','2002-11-17',20040225103933,NULL,3,3,0,2.60,20021117000000,0);
INSERT INTO problem VALUES (257,5,2,746,'Checkers trick','How many squares can be drawn on a checkers board, given that these squares should consist of whole black-white squares (the ones that are already painted on the board)?','The total number of squares on the board is equal to the number of 1x1 squares (64) + the number of 2x2 squares + .... + number of 8x8 squares (1).\r\n \r\nIn general, the number of NxN squares on an 8x8 board can be obtained by figuring out the number possible positions for the upper-left corner of the smaller square. For example, if dealing with 7x7 squares, there are only 4 possible positions for its upper-left corner, and therefore, there are only 4 possible 7x7 squares on an 8x8 board.\r\n \r\nA formula for this function F(N) is pretty easy to deduce: F(N) = (9-N)2\r\n \r\nSo, the overall sum is \r\n \r\nF(1) + F(2) + F(3) + F(4) + F(5) + F(6) + F(7) + F(8) = \r\nL = 2πR\r\n \r\nLabel the big circle\'s radius Rb, and the four smaller radii R1, R2, R3 and R4.\r\n \r\nIt\'s easy to see that R1 + R2 + R3 + R4 = Rb.\r\n \r\nThe sum of the small circles\' perimeters is 2πR1 + 2πR2 + 2πR3 + 2πR4\r\n \r\nor 2π * (R1 + R2 + R3 + R4). From the equation above we can substitute in the sum of small radii for the large one to get \r\n \r\n2πRb, or the perimeter of the large circle.','2002-11-19',20030821232101,NULL,2,3,0,2.67,20021119000000,0);
INSERT INTO problem VALUES (262,14,2,227,'Alphabet Multiplication','(a-x) (b-x) (c-x) (d-x)........(z-x)=????\r\n \r\n\r\n\r\n','When multiplying the expressions one of the expressions would be (x-x) which is = 0. So the product of the expression would also be 0.','2002-11-21',20030326065623,NULL,1,3,0,3.64,20021121000000,0);
INSERT INTO problem VALUES (263,9,2,746,'Achilles and the Tortoise','Suppose that the swift Achilles is having a race with a tortoise. Since the tortoise is much slower, she gets a head start. When the tortoise has reached a given point a, Achilles starts. But by the time Achilles reaches a, the tortoise has already moved beyond point a, to point b. And by the time Achilles reaches b the tortoise has already moved a little bit farther along, to point c. Since this process goes on indefinitely, Achilles can never catch up with the tortoise.\r\n \r\nHow can this be?\r\n \r\nTaken from - http://members.aol.com/kiekeben/zeno.html','This is known as Zeno\'s paradox, a series of paradoxes dealing with infinite series of infinitely small components. Here is another:\r\n \r\nThe Racetrack (or Dichotomy) \r\nOne can never reach the end of a racecourse, for in order to do so one would first have to reach the halfway mark, then the halfway mark of the remaining half, then the halfway mark of the final fourth, then of the final eighth, and so on ad infinitum. Since this series of fractions is infinite, one can never hope to get through the entire length of the track (at least not in a finite time). \r\n \r\n\r\nStart ____________________1/2__________3/4_____7/8__15/16... Finish \r\n \r\nJust as one cannot reach the end of the racecourse, one cannot even begin to run. For before one could reach the halfway point, one would have to reach the 1/4 mark, and before that the 1/8 mark, etc., etc. As there is no first point in this series, one can never really get started (this is known as the Reverse Dichotomy). \r\n \r\n','2002-11-22',20031217232101,NULL,3,3,0,3.00,20021122000000,0);
INSERT INTO problem VALUES (270,12,2,794,'Mystery of the babies','I was at the hospital waiting for my little cousin to be born. I began talking to another couple. The husband said \" My wife just gave birth to 2 babies. They are not twins.\" \r\n \r\nConfused, I said \"Huh?\". \r\n \r\n\"Yes\" he said, \"They were both born today within minutes of each other.\"\r\n \r\nI assumed that they must have been born in different years but he assured me that this was not so. I figured out what the deal is with these babies. Can you?','The babies are not twins. They have another sister (or brother), they are triplets (or quadruplets, etc.) ...','2002-11-27',20040211232108,NULL,1,3,0,3.17,20021127000000,0);
INSERT INTO problem VALUES (265,20,2,103,'Had Had','Punctuate and capitalize the following so that it makes sense:\r\n \r\njane while john had had had had had had had had had had had a much better effect on the teacher\r\n','Jane, while John had had \"had,\" had had \"had had.\" \"Had had\" had had a much better effect on the teacher.\r\n \r\nJohn wrote \"had\". \r\nAt least that\'s what I think it means.','2002-11-23',20031127232102,NULL,3,3,0,2.80,20021123000000,0);
INSERT INTO problem VALUES (274,18,2,794,'The impossible task...or is it?','There was once a man named Harold. Harold was from England. The king would always get upset with Harold because it seemed like Harold never failed at anything and the king was jealous. \r\n \r\nSo one day, the king was determined to prove Harold a failure. He drew a line across the floor. He said: \r\nHow is this possible?','The king did not specify that Harold must actually shorten the line itself. So Harold drew a secong line across the floor, longer than the first. Therefore, the line that the king drew is shorter. ','2002-12-03',20040107232101,NULL,2,3,0,2.45,20021203000000,0);
INSERT INTO problem VALUES (266,6,2,251,'In the Act','A mother is 21 years older than her son,\r\nand in 6 years time\r\nthe son will be one\r\nfifth of her age.\r\n \r\nWhere is the father?','S = son\'s age, M = mother\'s age\r\n \r\nS + 21 = M \r\nsubstitute for M:\r\n \r\n5(S + 6) = S + 21 + 6 \r\nso the solution is:\r\n \r\nAll over the mother!\r\n \r\n(i heard this as a joke, sorry i couldnt resist such cheap humor..)','2002-11-25',20031212232103,NULL,2,3,0,3.86,20021125000000,0);
INSERT INTO problem VALUES (267,6,2,122,'Word Rebus','What\'s being described here?\r\n \r\nThe first few triangle numbers are 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120. In other words you start by adding one, then two then, three etc. The formula for these is (n(n+1))/2. \r\n \r\nNext square numbers which we learn as N squared. But they can also be expressed as ((n(n+1))/2) + ((n(n-1))/2). Here the first few are: 1, 4 ,9 ,16, 25, 36, 49. In this case, instaed of adding 1 then 2 then 3 you add 1 then 3 then 5 then 7 (i.e. every other number).\r\n \r\nNext are pentagonal numbers which are also comprised of dots where the Nth pentagonal number is the number of dots in the figure. The first few are: 1, 5, 12, 22, 35, 51. Notice how first you add 1 then 4 then 7 then 10 then 13 (i.e. every third number). The formula is ((n(n+1))/2) + ((2)(n(n-1))/2). \r\n \r\nCan you find a pattern in N-gons and prove it?','Check the comments to this problem for a solution. A few were submitted.','2002-11-30',20030803232102,NULL,5,3,0,4.25,20021130000000,0);
INSERT INTO problem VALUES (272,7,2,746,'Jack and George\'s number trick','There are two people, Jack and George.\r\nBoth men represent a digit.\r\nThe sum of Jack\'s digit and Georges digit is 14. \r\n \r\nIf you position Jacks digit in the ten\'s place and Georges digit in the one\'s place, the number you get is 36 more than the number you get when you put Georges digit in the ten\'s place and Jacks digit in the one\'s place. \r\n \r\nWhich two digits do Jack and George represent? ','Given:\r\n \r\n[author unknown, but also unusual]','Unlike most paragraphs with more than a few words, this one doesn\'t contain the letter E - the most common letter in the English language.','2002-12-03',20030823232102,NULL,2,3,0,3.42,20021203000000,0);
INSERT INTO problem VALUES (278,12,2,831,'Share!','There are 6 oranges in a bag, and 6 kids in the class. The teacher wants to give each kid one orange, but still have one in the bag... \r\n \r\nWhat does she do?','Simple: give 5 of the kids an orange each, and the 6th kid gets the orange in the bag!','2002-12-02',20040211232108,NULL,2,3,0,2.62,20021202000000,0);
INSERT INTO problem VALUES (279,7,1,746,'Zero to 150 in 2003','Take the digits 2, 0, 0 and 3. Make equations equating to all the integers from 1 to 150 using these digits according to the following rules:-\r\n \r\na) The above digits are the only digits to be used and no other digits should appear anywhere in the equation (except on the side where the answer will be).\r\n \r\nb) Use of any mathematical symbols are allowed.\r\n \r\nc) The digits 2, 0, 0 and 3 should appear in the given order in the equation. e.g - 0 + 2 + 3 + 0 = 5 is not acceptable.\r\n \r\nd) When using the mathematical symbols try using the most simplest forms as much as possible.\r\n','Brian Smith came up with a solution using the basic arithmetic operations (+, -, ÷, ×), exponentiation (a^b), factorial (x!), square root (√y), trigonometric functions (sin, cos, tan), and rounding (floor, ceil). \r\nHere is the list, which is also featured on a webiste he created where you will be able to find any updates: http://www.geocities.com/brianscsmith/zeroto150in2003.html. \r\nMost recently, DJ suggested some improved methods, which are shown on that site and reflected in this list.\r\n \r\nNotes: 0!=1. floor x is x rounded down the the nearest integer; ceil x is x rounded up to the nearest integer. Trigonometric functions are calculated in radians. Digits may be concatenated to form other numbers (20, 003..). The listed methods use the fewest operations found to obtain each number. Grouping () is not counted as an operation.\r\n You\'re trapped in a room far away from home. There\'s a door with a keyhole, but it is locked. \r\nIn the room, there is: \r\nFind three ways of escaping the room using word play. \r\nAnd once you\'re outside, you can scream and scream and scream until your throat is a little hoarse. Then ride the horse to home! :) \r\n\"See that moving sidewalk? Why don\'t you run on it, and then when you reach the end turn back and run to where you started from? I meanwhile will run the same path, but right next to it rather than on it.\"\r\n \r\nYonette thought about it and said:\r\n \r\n\"But I don\'t see the point... We both run with the same speed, and it\'s the same distance. Sure, I will gain a bit on you while the sidewalk increases my speed, but then I will just lose the advantage while I\'m running back and we will arrive at the same time.\"\r\n \r\nAssuming Xavier and Yonette do run with the same speed, who will win the race?','Initially one would think Yonette is right: she will gain some time running with the moving sidewalk by benefiting from its speed, but then lose just as much time when going back.\r\n \r\nBut if you think about it, Yonette will obviously spend less time running faster than she will running slower. (Since the distance will remain the same)\r\n \r\nTherefore, even though her base speed is the same as Xavier\'s, her average speed will be less, and thus she will lose the race.','2002-12-05',20030602232102,NULL,3,3,0,3.60,20021205000000,0);
INSERT INTO problem VALUES (320,2,2,853,'Two Barbers','A Man is visiting a town and decides to get his hair cut. \r\n \r\nHe asks a boy where he can find a barber and the boy says there are only two barbers in the town. \r\n \r\nThe boy shows him the first one. Inside the barber has hair all over the floor, dirt everywhere and long \r\nuneven hair. \r\n \r\nHe goes to the other one and sees the barber is dressed in pristine clothing, well cut, and his floors are well swept and clean.\r\n \r\nThe man changes his mind and goes to the other barber.\r\n \r\nWhy does he do this?','Since there are only two barbers in the town, it is obvious that they must be cutting each other\'s hair. Therefore, the barber with the good cut must have gotten it from the other guy, whose hair is messy, while giving him the bad haircut.\r\n \r\nTherefore, the barber with the messy hair must be better at what he does.','2002-12-27',20030916232101,NULL,2,3,0,3.58,20021227000000,0);
INSERT INTO problem VALUES (284,13,2,775,'What came first?','Find the first number in the following series. (there may be more than one answer?)\r\n \r\n?, 2 ,3 , 8, 30, 144, 840, 5760, 45360...','my answer is infinity, the series is calculated as follows. a(n)=n!/(n-1). term 1 is 1!/(1-1) or 1/0.\r\n \r\nI expect that (by visual inspection) an answer of zero may be possible somehow as well, but I can\'t find it.\r\n \r\nlevik: Actually, 1/0 is not infinity, it\'s undefined, as Dulanjana can probably explain to us. It is one divided by a number APPROACHING zero (and thus infinitely small) that will result in infinity. So I guess the answer is that the fist term is undefined, unless we can come up with a different rule for the sequence.','2002-12-04',20030404232102,NULL,3,3,0,3.40,20021204000000,0);
INSERT INTO problem VALUES (314,22,2,775,'Crackers','Can you crack the code used to transform the following numbers and come up with the final number?\r\n\r\n \r\n(hint by levik: the encoding is such that it will only work on some numbers, not all integers)','The answer is 4444\r\n \r\nIn each number, the transformation has the number of digits equal to the first digit. Each of the digits contained is then the rank of the following numbers.\r\n \r\ni.e. 2461289=18 because the first digit is 2 (telling us there are 2 digits in the answer), the next digit is 4, showing that the first digit is the fourth of the original number (1), and the next number is the sixth digit of the original number (8)','2002-12-25',20030928232101,NULL,4,3,0,3.64,20021225000000,0);
INSERT INTO problem VALUES (304,7,2,873,'Prime Time','There are 362,880 different numbers that use the digits 1 to 9 exactly once (like 187,432,569). \r\n \r\nOf these, what percentage are prime numbers?','An old problem \r\n Please see the solutions in the comments. \r\n\r\nThe answer is - 0%. \r\nAll those numbers add up to 45 or 5 * 9. \r\nAll are divisible by 9. ','2002-12-17',20040214232101,NULL,2,3,0,3.50,20021217000000,0);
INSERT INTO problem VALUES (305,2,2,873,'A Drinking Problem','Four people are in a bar. \r\n \r\nBen owes Glen a drink. Glen owes Rhen two drinks. Rhen owes Sven three drinks. Sven owes Ben four drinks. \r\n \r\nTo settle up, what is the minimum number of drinks that need to be bought by who for whom?','Another problem passed to me. \r\nGlen, Rhen and Sven should all buy Ben a drink. \r\nThe answer is 3. ','2002-12-18',20030617232102,NULL,2,3,0,3.40,20021218000000,0);
INSERT INTO problem VALUES (287,7,2,794,'Lockers','There is a wall with 1000 closed lockers on it. A person walks down the hall opening every other locker. Then the next person opens every 3rd locker. The next opens every fourth locker. The next every fifth locker. \r\n \r\nOnce this has been done, how many lockers are still closed? \r\n','The solution to this depends largely on the method which the people follow when opening the locker doors. Once this is established, figuring out th eanswer comes down to arithmetics.\r\n \r\nComments from our visitors suggest some possible assumptions/solutions.','2002-12-06',20030518232102,NULL,2,3,0,3.00,20021206000000,0);
INSERT INTO problem VALUES (288,12,2,873,'Quick Brown Fox','What is so unusual about this sentence?\r\n \r\n\"The quick brown fox jumped over the lazy dogs.\"','The sentence has every letter of the alphabet in it.','2002-12-07',20040209232105,NULL,1,3,0,2.31,20021207000000,0);
INSERT INTO problem VALUES (299,12,2,873,'What Do I Have?','I am holding a collection of items in my hands. \r\nI want to divide it into different groups, but I can only see one half of each item in my hands. \r\nI can easily divide the items into the same amount of groups: \r\nWhat do I have?','A deck of cards. \r\nYou are one of 20 logicians worldwide to receive this letter. You don\'t know each other, but you all think alike. An address is given, and you are told that if a letter is received from one and only one of you, all 20 will equally split a large sum of money. If no letters are received, or more than one, no prize.\r\n \r\nWhat would you to for a chance of winning the prize? What could you do in order to maximise the probability of winning? ','If you simply send a letter, so will all the others, 20 letters equals no prize. If you don\'t, no one will, no prize.\r\n \r\nSo, you must introduce a random element, not controlled by yourself. For example, send a letter with the address slightly wrong, or with slightly insufficient postage. Different post offices will handle this differently, and most likely some, but not all, of the letters will arrive. That gives you a chance at the prize.\r\n \r\nA more methodic approach is to base your decision of whether to send a letter or not on a random event, such as rolling dice. All the others will roll dice too, but will get different results, so only some will send letters. \r\n \r\nTo maximise your probability (as someone suggested in the comments) roll a \"d20\" - a 20 sided die - and only send the letter if you roll a 20. A probability calculation shows that this yields the best odds, with a surprising 37.7% chance that only one of you will roll a 20 and send a letter. Better odds than predicting post office behaviour, surely!','2002-12-08',20030919232102,NULL,3,3,0,3.08,20021208000000,0);
INSERT INTO problem VALUES (290,7,2,227,'Pi problem','Prove that \'pi\' is irrational.\r\n ','Cale Gibbard submitted a link to \r\nhttp://pi314.at/math/irrational.html\r\nwhere the proof can be found.','2002-12-11',20031205232101,NULL,5,3,0,3.00,20021211000000,0);
INSERT INTO problem VALUES (300,13,2,873,'The A, BB, CCs','What is the next entry in the series?\r\n \r\nA, BB, CC, DD, E, F, G, H, II, JJ, K, LL, MM, NN, OO, PP, QQ, RR, SS, T, UU, VV, WW, X, Y, ______.','ZZ. \r\nD + M = R \r\n\r\nThis problem was passed on to me.','2002-12-15',20030415232102,NULL,3,3,0,3.80,20021215000000,0);
INSERT INTO problem VALUES (294,4,2,875,'9 labels and 9 jars','There are 9 jars each with unique labels.\r\n \r\nSomeone has come and removed all the labels and mixed them up.\r\n \r\nIf you put the labels back on the jars (without knowing the contents), what is the expected number of labels which would match the contents?','As friedlinguini (here) and Cheradenine (here) show, the number of jars is actually irrelevant, and the expected result will always be one correclty labelled jar.','2002-12-09',20040225103933,NULL,4,3,0,3.50,20021209000000,0);
INSERT INTO problem VALUES (295,4,2,746,'Return of the hats','Three players enter a room and a red or blue hat is placed on each\r\nperson\'s head. The color of each hat is determined by a coin toss,\r\nwith the outcome of one coin toss having no effect on the others.\r\nEach person can see the other players\' hats but not his own.\r\n \r\nNo communication of any sort is allowed, except for an initial\r\nstrategy session before the game begins. Once they have had a\r\nchance to look at the other hats, the players must simultaneously\r\nguess the color of their own hats or pass. The group shares a\r\nhypothetical $3 million prize if at least one player guesses\r\ncorrectly and no players guess incorrectly. What strategy should they use to maximize their chances of success?\r\n \r\n(From - http://www.princeton.edu/~sjmiller/riddles/riddles.html)','TomM has submitted a solution here that would allow the players to win the prize three out of four times.','2002-12-10',20040225103933,NULL,3,3,0,3.83,20021210000000,0);
INSERT INTO problem VALUES (296,13,2,873,'Seven Entry Series','What is the next number in this series: \r\n \r\n341, 39, 602, 50, 1003, 64, _______?','I had too much time on my hands and thought this one up. \r\nThis is an original problem. ','2002-12-11',20030507232102,NULL,5,3,0,2.25,20021211000000,0);
INSERT INTO problem VALUES (297,8,2,746,'Safety from the queen',' \r\n(From - http://www.princeton.edu/~sjmiller/riddles/riddles.html)','Jen provides a solution here,\r\nbut is it the only one? (Symmetry aside)','2002-12-12',20040225103933,NULL,2,3,0,3.50,20021212000000,0);
INSERT INTO problem VALUES (298,7,2,873,'Unconventional Question','An enthusiastic math student was asked to write a sentence incorporating his new knowledge about prime numbers. Though you could spend time correcting him on his conventions, can you still give him the numerical answer he is looking for?\r\n \r\nThis is an original problem.','2002-12-13',20030802232102,NULL,4,3,0,2.93,20021213000000,0);
INSERT INTO problem VALUES (306,7,2,873,'subtractiOn','If This is an original problem.','2002-12-19',20040219232102,NULL,2,3,0,3.25,20021219000000,0);
INSERT INTO problem VALUES (307,18,2,890,'A flawed proof?','Given: a=b. Applying some basic identity transformations, we get: \r\nYou\'re sure you can find the lake, and walk around it if necessary, but visibility might be poor. Where should you arrange to meet to be sure of finding each other?\r\n \r\nThere is a simple solution to this problem, which outdoorsy types should be familiar with.','Lakes may have many inflows, but only one outflow. Arrange to meet at the lake\'s outflow. \r\n\r\nIt was stated that you could walk around the lake, so presumably you would be able to find a place to cross the outflowing stream if necessary. One could also solve this by agreeing to meet on the true left bank of the outflow (true left = left bank when facing downstream).','2002-12-29',20030626232103,NULL,2,3,0,3.00,20021229000000,0);
INSERT INTO problem VALUES (330,18,2,816,'Fill in the blank logic','Donna is the daughter of Donnetta.\r\nDonnetta is the granddaughter of Donnetta\'s sister, Donnita. Donnita has never met Donna. Donnetta is the _______ of Donna\'s mother.\r\n\r\n\r\n Found in the Mindstretch Calendar by Terry Stickels ','As the first sentence states, Donna is the mother of Donnetta.\r\n \r\nTherefore, \"Donnetta\" is the name of Donna\'s mother.\r\n \r\nThe rest is trickery.','2003-01-04',20031104232104,NULL,2,3,0,3.45,20030104000000,0);
INSERT INTO problem VALUES (310,6,2,873,'L,E,T,T,E,R,S','What is the next letter in this sequence? \r\nThis is an original problem.\r\n','2002-12-11',20030709232101,NULL,2,3,0,3.14,20021211000000,0);
INSERT INTO problem VALUES (311,2,2,873,'Dances with Wolves','Dances runs around a track in sixty seconds. Wolves, running in the opposite direction around the track, meets Dances every twenty seconds. How long does it take for Wolves to run around the track? \r\n-Problem modified from UNL Math Day\r\n','After 60 seconds, Dances has completed one lap and Wolves must have completed two laps, since they will meet for the third time. \r\nA Duplicates are allowed? \r\nProblem modified from UNL Math Day with help from friedlinguini\r\n','If duplicates are allowed, you should choose the integers to be as close to e as possible. \r\n\r\nIf duplicates are not allowed, the maximum product is still generally found when all the numbers are as close as possible to e.\r\n \r\nInspection shows that 2, 3, 4, 6, 7 is better than 1, 2, 3, 4, 5, 7, so the maximum product is 2*3*4*6*7=1008. ','2002-12-23',20030731144340,NULL,2,3,0,3.29,20021223000000,0);
INSERT INTO problem VALUES (313,5,2,873,'Sugar Cubes','Three cubes of volume 1, 8, and 64 are glued together. \r\n-Problem taken from UNL Math Day\r\n','The total surface area of the three cubes (before any gluing occurs) is 96 + 24 + 6 =126. \r\nBrothers and Sisters I have none, \r\nWhose picture is the man looking at?','For some reason people sometimes think the man is looking at a picture of himself.\r\n \r\nIn reality, this would only be true if he said he was looking at his father\'s son (given that he has no brothers or sisters).\r\n \r\nHowever, since he is looking at someone whose father is his father\'s son (himself), we can tell he is looking at a picture of his son.','2002-12-30',20030901232101,NULL,2,3,0,3.60,20021230000000,0);
INSERT INTO problem VALUES (316,15,2,103,'Enough Rope to Shoot Yourself in the Foot','A rope with its two ends held in place forms a curve called a catenary (assuming that the stiffness of the rope is negligible). A catenary takes the shape of the function: \r\nIf a 50-foot rope hangs by its ends from two flagpoles, one 50 feet tall and one 40 feet tall, and at its lowest point is 20 feet above the ground, how far apart are the flagpoles?','0 feet. They are right next to each other. The rope is simply doubled up on itself, and despite the category, no calculus is actually needed.\r\n \r\n(It takes 30 feet of rope to reach from the 50 foot top of pole 1 to the low point of 20 feet. The remaining 20 feet are needed to go back up to the 40 foot elevation of pole 2.)','2002-12-22',20030414232101,NULL,2,3,0,3.25,20021222000000,0);
INSERT INTO problem VALUES (317,2,2,939,'The Punched-Out Numeral','Two women and two men entered a cafeteria and each pulled a ticket (There\'s a illustration, but I can\'t post it here... It\'s a rectangle with numbers from 5-100 that go by 5 cents, 10 cents, 15 cents...etc) \r\n1. The four ordered the same food and had he same numeral punched out on their ticket (the retangle is the ticket).\r\n \r\n2. Each of the four had exactly four coins.\r\n \r\n3. The two women had the same amount of money in coins, though no denomination (value) of coin was held by both women; the two men had the same amount of money in coins, though no denominationof coin was held by both men.\r\n \r\n4. Each of the four paid the exact amount inndicated by the numberal that was punched out on his or her ticket.\r\n \r\nWhich numeral was punched out on each ticket?\r\nNOTE: \"Coins\" may be pennies (1 cent), nickles (5 cents), dimes (10 cents), quarters (25 cents), half dollar (50 cents) or silver dollar.','Submitted \"Solution\":\r\n \r\n\r\nI don\'t have a solution, if anyone has one, please send it to me! It\'s my math project and just the answer is worth 65 points!!! I will fail if I don\'t have the right answer!! Please~~~\r\n(BTW, the answer is NOT 40 cents or 80 cents. My teacher checked her answer keys...)\r\n\r\n \r\nlevik:\r\n \r\nHmmm. We\'re not generally in business of doing others\' homework here, and if I saw this earlier, the problem may not have been posted. It\'s probably too late for you anyway, given that it was delayed in voting.\r\n \r\nOur visitors have provided a solution in the comments, that I don\'t see a point in copying here.','2002-12-27',20030414232101,NULL,5,3,0,3.25,20021227000000,0);
INSERT INTO problem VALUES (344,12,2,1048,'Barrel','Tim and Adam made a bet.Tim bet Adam that he could put something into his barrel to make it lighter. They first weighed the barrel. Then Adam left the room while Tim pondered a solution.One hour later, Adam returned, and they weighed the barrel once again. The barrel was indeed lighter. What did Tim put in the barrel?','A hole.','2003-01-12',20031003232102,NULL,1,3,0,2.38,20030112000000,0);
INSERT INTO problem VALUES (355,17,2,1072,'Passing through zero','A car is travelling in one direction at 80 km/h and a fly is coming from the opposite direction at 5km/h. (So its velocity is -5 km/h, since it\'s in the opposite direction.)\r\n \r\nThe fly hits the windshield of the car and is now travelling at 80km/h. In order for the fly to achieve the speed of 80km/h it\'s speed must have passed from -5km/h to 80km/h. (Meaning it must pass through the speed of zero) Therefore if the fly passes through a speed of 0km/h and the car is in contact with the fly the car must also pass through that speed of 0km/h. \r\n \r\nThis seems to mean that everytime a car gets hit by a fly it will completely stop. Why is this not so?','Np_rt\'s solution gives a good detailed solution in the comments. \r\n(It\'s here)','2003-01-19',20040225103933,NULL,2,3,0,3.38,20030119000000,0);
INSERT INTO problem VALUES (323,12,2,227,'Important Day','An important day is held on the 14th of march at 1:59 am somewhere in America. can you guess what this day is called?\r\n \r\nHint - Look at the figures closely!','March 14 at 1:59am, with the March being the third month gives the first 6 digits of the number Pi. \r\n\r\n3.14159 \r\n\r\nSo this day is called \"Pi-day\" \r\n','2002-12-29',20030720232102,NULL,2,3,0,3.00,20021229000000,0);
INSERT INTO problem VALUES (325,2,2,873,'Which Game?','Five of your relatives are having a Sunday Football party. You have to decide which one you are going to by solving the problem of how they are related to you, what snacks they are serving, and what team they are cheering for. \r\nTheir names are Pat, Chris, PJ, Stacey, and Bobbi. They are your Cousin, Uncle, Mother, Brother, or Sister. They serve Popcorn, Chips, Carrot Sticks, Pizza, or Cookies. They cheer for the Broncos, Raiders, Packers, Cowboys, or Dolphins. \r\n \r\nThe cookies are not served while watching the Packers or Raiders. Pat isn’t your brother (your brother doesn’t serve cookies or pizza.) \r\nPJ is your cousin (and doesn’t serve cookies or carrot sticks) who watches the Dolphins. \r\nYour sister doesn’t watch the Broncos or the Packers; and the Packers fan doesn’t serve carrot sticks. Chris is not your brother. \r\nWhen you go to Bobbi’s house, pizza is served, but Bobbi is not your uncle. \r\nArrange the numbers in the grid above in such a way that no two adjecent cells (horizontally, vertically or diagonally) have consecutive number in them. For example 1 must not be next to 2.\r\n(The letters are shown so that you can easily refer to specific individual boxes.)\r\n \r\n(From: http://www.ocf.berkeley.edu/~wwu/riddles/intro.shtml)','There are a total of eight numbers that we need to distribute.\r\n \r\nCells \"C\" and \"F\" each have 6 adjacent cells. That means that whatever numbers we assign to these two cells, they will be surrounded by all the remaining numbers except for one. That means we cannot place a number in these cells if it has two neighboring numbers among the set. Thus, \"C\" and \"F\" must be populated by 1 and 8, since these numbers only have one neighbor.\r\n \r\nOnce we do this, the rest becomes fairly easy, yielding the final result: \r\nOne letter is missing: a \"J\" - for June. There are a total of three months in a year starting with a \"J\", and of them, only \"June\" is also a woman\'s name. So Jason\'s gilrfriend\'s name is June.\r\n\r\n','2003-01-02',20040318232101,NULL,1,3,0,3.21,20030102000000,0);
INSERT INTO problem VALUES (331,4,2,775,'Hey coach, that\'s unfair!','A first baseman is fortunate enough for his team to be playing in the World Series. When game one is about to start, he asks the coach if he\'s going to play. The coach responds \"despite the fact that you have a higher batting average than our rookie first baseman, we\'re up against a left handed pitcher today, and he has a better average against lefties than you, so I\'m going to play him\". Well, the fellow figures that this is fair enough, baseball being a game of averages and all, and happily sits out the first game, knowing that the team will come up against a right hander at some point, giving him a chance to play.\r\n \r\nSure enough, game 2 is set to start, and the opponents are starting a right handed pitcher. The fellow asks the coach if hes going to play today. The coach responds \"well, I know that you have a better average overall, but today we\'re facing a rightie, and our rookie has a better average against righties than you do, so we\'re going to play him today\".\r\n \r\nSo, the regular player, who has a better average against pitchers in general, has a lower average against BOTH left and right handers????? The player feels cheated. How did this happen?\r\n \r\nFor reference, the players batting average is calculated using the following formula: \r\nRookie - LH 3/8=.375, RH 7/30=.233, Total (3+7)/(8+30)=.263\r\n \r\nRegular - LH 58/166=.349, RH 80/356=.224, Total (58+80)/(166+356)=.264\r\n \r\nThere are obviously many other sets of numbers that create this situation','2003-01-05',20030404232102,NULL,3,3,0,2.83,20030105000000,0);
INSERT INTO problem VALUES (354,2,2,1072,'The 3 cans','There are 3 cans containing different foods.\r\nNuts in one can.\r\nSliced Peaches in juices in another and the third can contains sliced oranges in juices.\r\nSomeone has steamed off and switched the labels of all the cans so every can will have a label that is not the actual food inside it.\r\nCan you figure out which cans contain which foods without opening any?\r\n','Well first you have to shake each can. The one that has the rattle is the can of nuts. The food for whatever label that is on the can of nuts must therefore be in the can that does not have the nuts label.(If it was in the can with the nuts label that would mean that one can of food still has its original label) \r\n \r\nThen the label of that can (the one that does not contain the nuts or the nuts label) must be the food in the can with the nuts label.','2003-01-18',20030626232103,NULL,2,3,0,2.92,20030118000000,0);
INSERT INTO problem VALUES (334,12,2,1016,'What am I?','What\'s in a song, but not in a tune? \r\nWhat\'s in the sun, but gone in the night \r\nWhat are the five \"little airy creatures\"?\r\n','The creatures are Vowels','2003-01-06',20030408232102,NULL,2,3,0,2.29,20030106000000,0);
INSERT INTO problem VALUES (339,18,2,853,'Sally\'s Silly Walk','Last Sunday, when sally went for a walk, \r\nWas sally imagining all this?\r\nNo, everything in the long sentence is right, except it has been punctuated incorrectly.\r\nChange the punctuation so that it reads correctly, with out changing a single word.','Last Sunday, when sally went for a walk, \r\nThere was a mirror behind the fountain. when the lady she raised her head she saw that the man behind her had a knife in his upraised fist. she screamed. the man lowered his knife and both of them started to laugh. \r\n \r\nWhat is Going on? ','The lady had the hiccups. Her boss was trying to stop them by scaring her.','2003-01-08',20030720232102,NULL,1,3,0,2.15,20030108000000,0);
INSERT INTO problem VALUES (343,12,2,1048,'Two men and the mountains','Two men are laying dead beside a cabin in the side of a mountain.\r\n \r\nHow did they die?','They died in a plane crash. The \"cabin\" this riddle refers to is the \"cabin\" of a plane. The plane had crashed into the side of the mountain.','2003-01-16',20040323232103,NULL,2,3,0,1.57,20030116000000,0);
INSERT INTO problem VALUES (351,6,2,775,'A special word','There is something special about the English word \"facetiously\". \r\nTomM offers an explanation \r\nhere\r\n','2003-01-15',20040225103933,NULL,3,3,0,4.31,20030115000000,0);
INSERT INTO problem VALUES (348,12,2,979,'Guessme One','They call me a man, but I\'ll never have a wife. \r\n \r\nWhat/Who am I? \r\n','A Snowman \r\n \r\nThey call him a man (SnowMan), but he\'ll never have a wife. \r\nAt this point in the party everyone is seated in a circle and must guess the colour of their own hat. If they do they get 100 dollars. \r\n \r\nEvery person can make a guess of yellow, red or blue and nothing else. Every person gets two such guesses but these can be made in any order. (That is one need not make both his guesses one right after the other.)\r\n \r\nIn order to win with one of your two guesses you must say the colour of your own hat. How can every person guarantee themselves the money? (How can they have a 100% chance of guessing the colour of their hat correctly?)','The first person would say the colour of the person\'s hat beside them (remember he\'s not breaking any rules because he is saying one of the three colours he is allowed to)\r\nWhen every person in the circle knows the colour of their hat they would then use their second guess to say the colour of their hat and collect their money','2003-01-17',20030722232103,NULL,2,3,0,2.73,20030117000000,0);
INSERT INTO problem VALUES (400,4,2,1072,'BlackJack','When playing a game of blackjack, what are the odds that you will be dealt BlackJack on the first deal? Assume you are playing with one opponent and your opponent is the dealer.\r\n \r\nNote: 10, jack, queen and king all are worth 10. Aces are worth 11.\r\nYou have blackjack when the values of both your cards add up to 21. There is only one deck of cards being dealt out.','4.65% (Check comments)','2003-02-12',20030508232102,NULL,2,3,0,3.50,20030212000000,0);
INSERT INTO problem VALUES (356,18,2,1072,'The walkaround','Two men meet each other and one says to the other \"I bet you I can walk around you three times, and before I walk around you the third time you will move your feet off of that spot you\'re standing on. On top of that i will do it without hitting or touching you in any physical way.\"\r\n \r\nThe other man says \"I bet you 20 bucks you can\'t.\" After saying this he stood still and was preparing for the man to circle around him.\r\n \r\nHe circled him once.\r\n \r\nHe circled him twice. At this point the man trying to stand still threw his arms up in disgust realizing that he lost.\r\n \r\nWhat happened?','After the first man circled him twice he then stood and waited. Since he was allowed to walk around he could go to the bathroom, eat and do many other things as long as he didn\'t circle him the third time. Since the other man had to stand still he could not do these things. He then realized that the first man never would circle him a third time causing him to have to move in order to do normal day to day activities.','2003-01-23',20030930232102,NULL,1,3,0,2.10,20030123000000,0);
INSERT INTO problem VALUES (357,12,2,794,'The Slow But Rewarding Ride','A very old rich man was in the hospital awaiting death. He called for his two sons to see him before he died. He said to his sons, \"I want you each to find a horse and ride it to the next town. The owner of the horse that arrives last will recieve my entire fortune.\" The sons were both very confused as to how they would get to the next town last. \r\n \r\nThey both started their ride to the next town, each trying desperately to go slower than the other. Just when they were about to give up, they both had an idea of how to inherit the money.\r\n \r\nWhat was it?','They each jumped on the other person\'s horse. Thus whoever came first would have his actual horse come last, therefore winning the contest.','2003-01-24',20040324232102,NULL,2,3,0,3.18,20030124000000,0);
INSERT INTO problem VALUES (358,5,2,1072,'Triangles to Squares','You have 8 wooden right-angle isosceles triangles (the lengths of the two lines that make up the right angle are equal). These are numbered from 1 to 8. Every single triangle is equal in size. Using these triangles how many DIFFERENT squares can you make. (Not neccesarily all at once)\r\n \r\nNote: A square must be entirely wooden in order for it count. A square cannot have the exact same combination of triangles that have already been used.e.g if you used triangles 1 and 2 in one combination you can never have a square made from only triangles 1 and 2. (However triangles 1 and 3 would make a distinct square)','Well first you must realize that there are 3 ways to make these triangles. \r\n \r\n1.Two triangles with thier long sides touching. There are 28 different squares you can make using 2 trangles.\r\n \r\n2.Four triangles with all their right angles touching. There are 70\r\n \r\n3.All 8 triangles put together(this is done by having all the triangles be put into squares of two then those 4 squares being put into a supersquare)There is only 1.\r\n \r\nSo altogether there are (28+70+1) triangles that cane be made. So that means there are 99 different squares you can make.\r\n','2003-01-20',20030410232102,NULL,3,3,0,3.60,20030120000000,0);
INSERT INTO problem VALUES (359,8,2,1072,'Mancala','In the game of mancala there is a board with 2 rows of 6 holes.(To make this easier imagine these rows travelling from left to right) \r\n \r\nIn each of these holes there are 4 gems. Also, At the end of each row is a special cup. (this cup is not included as one of the 6 holes) Everytime you drop a stone into this cup you guarantee yourself that gem. \r\n \r\nIn order to get gems into that cup you must pick up all the gems in any 1 hole and drop 1 gem in every hole ahead of it in order from left to right. If you drop it in your rightmost hole you then drop 1 in your cup and proceed dropping along your opponents cups from right to left.(still from your point of view.)\r\nFor those who are still confused you are pretty much picking up all the gems in one hole and dropping them one at a time counter-clockwise in every hole and cup you come across.\r\n \r\nIf the last gem you drop lands in your cup you get to go again. \r\n \r\nSo the question I ask you is this: What is the maximum number of gems that can be on your side that can be sunk on 1 turn(including everytime you get to go again)? Also, how would they have to be set up?\r\n \r\n(Still not clear on the rules? Play it here)','(your cups from left to right):\r\n \r\n5 3 1 2 0 14 \r\n \r\n(how to sink them all):\r\n \r\nYou must sink in order from right to left every hole of beads that will allow you to go another turn. \r\n \r\nPlease note there may be larger combinations than this.','2003-01-21',20030508232102,NULL,2,3,0,3.57,20030121000000,0);
INSERT INTO problem VALUES (360,19,2,794,'Requires all knowlege','What is greater than God, You have a freakish friend who only drinks pure distilled water. And keeps jars of them stored up in his basement.\r\n\r\n When you went over to visit him, he offered you a glass. To prove to you how pure his water is, he got a pH meter and measured the pH. To his surprise, the pH was not 7!\r\n\r\n Shouldn\'t the pH of pure water be 7 at 25 degrees? What happened? And was the pH greater or less than 7?',' The pure water reacted with the carbon dioxide in the air and formed an acidic solution via the following reactions:\r\n\r\n CO2 + H2O <--> H2CO3 The numbers in parentheses represent the charge on the ion. Reactions like these are why CO2 and other gases are called \"dry acids.\" And since the solution was acidic, its pH was less than 7 (probably somewhere between 5-6).\r\n\r\n This is similar to how acid rain is formed; which forms from sulfur dioxide and nitrogen oxides.\r\n\r\n I know this was a bit tough and abstract but it is a science question.','2003-02-11',20031124232102,NULL,3,3,0,3.00,20030211000000,0);
INSERT INTO problem VALUES (394,17,2,885,'pH of water again','After your freakish friend \r\n(from the other pH problem)\r\nfound out that it was carbon dioxide in the air that made his water acidic, he made sure that all his jars are air-tight and vacuumed out all the air in his jars immediately after the purification. How big of a freak is that?!\r\n \r\nDuring one hot summer day, you and he just finished playing basketball. You went over to his house and again, he offers you a glass of his purified water. And to ensure that it\'s pure, he measures the pH of it right after he pours it out (so that it doesn\'t get in contact with the air too long).\r\n\r\n And again, the pH of the water is not 7! What happened this time?',' The pH of water depends on the amount of ionization of the water, which in turn depends on the temperature of the water. It\'s only at a temperature of 25 degrees celsius and a pressure of 1 atmosphere (pressure doesn\'t really make any difference) that the pH of water is 7.\r\n\r\n So this time, the water is indeed pure, just that the pH is different due to the different temperature.','2003-02-15',20040225103947,NULL,3,3,0,2.67,20030215000000,0);
INSERT INTO problem VALUES (362,2,2,1138,'Christmas Returns',' \r\nMrs. Holly made these five returns (not necessarily in order): Zach\'s gift, the jeans, the article bought at Banana Republic, the item of apparel that the recipient didn\'t like, and the one to the 5th store in the order. \r\nErica\'s gift, which wasn\'t the one returned because it was too small, wasn\'t the one purchased at American Eagle Outfitters. \r\nImmediately after returning the hat to one mall store, Mrs. Holly returned Mindy\'s gift to another retailer. \r\nThe item returned to Abercrombie and Fitch wasn\'t the one that was too large. \r\nThe article Mrs. Holly took back to Banana Republic, which wasn\'t Erica\'s, wasn\'t the one that was the wrong color. \r\nImmediately after returning Tara\'s gift, Mrs. Holly returned the item that was too small; immediately after returning the too small article, Mrs. Holly returned the sweatshirt. \r\nThe shorts weren\'t the too large item. \r\nMindy\'s gift wasn\'t the one returned because it was the wrong style. \r\nThe item of apparel returned to the Gap, which wasn\'t Mindy\'s, wasn\'t the sweatshirt. \r\nMrs. Holly didn\'t return the jacket to American Eagle. \r\nThe jeans weren\'t Tara\'s. \r\nIn consecutive order first-to-last, Mrs. Holly made these three returns: the one to the Gap, Erica\'s gift, and the article that was the wrong color. \r\n\r\n','1st - Banana Republic, Tara\'s shorts were the wrong style\r\n \r\n2nd - The Gap, Ben\'s jeans were too small\r\n \r\n3rd - Abercrombie and Fitch, Erica didn\'t like her sweatshirt\r\n \r\n4th - American Eagle Outfitters, Zach\'s hat was the wrong color\r\n \r\n5th - Eddie Bauer, Mindy\'s jacket was too large\r\n \r\n(Stolen from http://crpuzzles.com/logic/logic0147.html)\r\n','2003-01-26',20030414232101,NULL,3,3,0,3.40,20030126000000,0);
INSERT INTO problem VALUES (363,2,2,979,'The Three Logicians -','Here is a list of words: \r\n \r\n(ii) The logicians were then told their three letters could be arranged to spell one of the words in the list above.\r\n \r\n(iii) When each logician was asked in turn, “Do you know which word the letters spell?,” the first logician answered, “Yes,” then the second logician answered, “Yes,” and then the third logician answered, “Yes”.\r\n \r\nWhich word did the letters spell?\r\n','From (i), (ii) and (iii), the first logician to answer “Yes” must have been told a letter that occurred only once in the list. So the first logician was told either H, R, P, D or V. \r\n \r\nThen the second logician knew the first logician was told either H, R, P, D or V. So the second logician knew the word was not TOE. Then the second logician knew what the word was if told T or E(some new letter), or if told the second letter of PAD that occurred only once in the list: P or D. \r\n \r\nThe third logician knew the first logician was told either H, R, P, D or V and knew the second logician was told either T, E, P or D. So the third logician knew the word was not OAR. So the third logician knew what the word was if told O(some new letter), but would not know what the word was if told A. \r\n \r\nThen rather than PAD or VAT, the letters spelled HOE. ','2003-01-22',20030616232102,NULL,4,3,0,3.85,20030122000000,0);
INSERT INTO problem VALUES (364,2,2,979,'Fathers and Sons','Statement A: Both fathers always tell the truth or both fathers always lie. \r\n \r\nStatement B: One son always tells the truth and one son always lies.\r\n \r\nStatement C: Statement A and Statement B are not both lies. \r\n \r\nHere are a few facts given related to the statements above and the men who made them:\r\n \r\n(i) Albert made one of the statements, his father made another of the statements, and his son made the remaining statement.\r\n \r\n(ii) Each father and son mentioned in the statements refers to one of the three men.\r\n \r\n(iii) Each man either always tells the truth or always lies.\r\n \r\nWhich statement – A, B or C – was made by Albert? \r\n','See the solution here, courtesy of TomM.','2003-01-27',20040319232102,NULL,4,3,0,4.17,20030127000000,0);
INSERT INTO problem VALUES (365,2,2,979,'How Many Children ?','“We – A, B and C – each have some children.\r\n \r\n(i) A has at least one girl and twice as many boys as girls.\r\n \r\n(ii) B has at least one girl and three times as many boys as girls.\r\n \r\n(iii) C has at least one girl and three more boys than girls. \r\n \r\n(iv) When I tell you the number of children we have – a number less than 25 – you will know how many children I have, but not how many children each of the others has. Altogether we have……..”\r\n \r\nWho is the speaker and how many children does the speaker have? \r\n','From (i), it is clear that A has at least 3 children and the number of children A has form the following sequence:\r\n3, 6, 9, 12, 15, 18, 21, 24, ……..\r\n \r\nFrom (ii), it is clear that B has at least 4 children and the number of children B has form the following sequence:\r\n4, 8, 12, 16, 20, 24, ……..\r\n \r\nFrom (iii), it is clear that C has at least 5 children and the number of children C has form the following sequence:\r\n5, 7, 9, 11, 13, 15, 17, 19, 21, 23, ……..\r\n \r\nThen the total number of children is at least 12 and, from (iv), at most 24. Also, if the total number of children is even, A must have an odd number of children, and if the total number of children is odd, then A must have an even number of children. \r\n \r\nThe total number of children cannot be 13 because, no three numbers, one from each sequence can give us a total of 13. The total cannot be 12, 14, 15, 16 or 17 because then the number of children each had would be known, contradicting (iv). The total cannot be 18, 20, 21, 22, 23 or 24 because then no number of children could be known for anybody, again contradicting (iv). So, the total number of children has to be equal to 19. \r\n \r\nWhen the total is 19, A must have an even number of children and from the sequences, this number must not be greater than 19 – (4+5), which is equal to 10. So, A must have 6 children. Then B and C together must have 13 children. Then B must have either 4 or 8 children. Now, if B has 4 children, then it is clear that C has 9 children and if B has 8 children, then C has 5 children. \r\n \r\nSo, now it is clear that the speaker is ‘A’.\r\n','2003-01-28',20030901232101,NULL,3,3,0,2.70,20030128000000,0);
INSERT INTO problem VALUES (366,2,2,979,'Bank Robbery','A cop arrested four suspects for the bank robbery. When he interviewed them, each made two statements. From his infrared lie-detector he knew that each man made one \"true\" and one \"false\" statement. As a result, he soon found out the culprit. \r\n \r\nGiven the following statements, can you determine who the culprit was?\r\n \r\n‘A’ said: “I did not do it. B did.”\r\n \r\n‘B’ said: “A did not do it. C did.”\r\n \r\n‘C’ said: “B did not do it. I did.”\r\n \r\n‘D’ said: “C did not do it. A did.”\r\n \r\n\r\n','D was the culprit.\r\n \r\nEach man gave one ‘did’ and one ‘did not’ statement.\r\nSo, if the ‘did’ statement is true, so must the ‘did not’ be true. But this is impossible, one of the two statements must be false in each case. Therefore each ‘did’ statement is false, and each ‘did not’ statement true. \r\n \r\nThis rules out A, B, C, leaving D as the culprit.\r\n','2003-01-29',20040324232102,NULL,3,3,0,2.31,20030129000000,0);
INSERT INTO problem VALUES (367,6,2,979,'Have A Nice Day !!','When tomorrow is yesterday, today will be as near to Sunday as today was when yesterday was tomorrow.\r\n \r\nWhat day is it?','\"Today\" is Sunday. \r\n \r\nSee the explanation \r\n(a) The Heart isn’t next to the Club.\r\n \r\n(b) No card is next to its immediate senior in rank. \r\n \r\n(c) The colors of the suits alternate. \r\n \r\n(d) The king and Queen are facing opposite directions. \r\n \r\nIdentify the four cards and their correct order. \r\n','King of Hearts - Jack of Spades - Ace of Diamonds - Queen of Clubs\r\n \r\nor\r\n \r\nQueen of Clubs - Ace of Diamonds - Jack of Spades - King of Hearts\r\n \r\nor\r\n \r\nKing of Clubs - Jack of Diamonds - Ace of Spades - Queen of Hearts\r\n \r\nor\r\n \r\nQueen of Hearts - Ace of Spades - Jack of Diamonds - King of Clubs','2003-01-30',20030613232102,NULL,3,3,0,2.83,20030130000000,0);
INSERT INTO problem VALUES (369,2,2,979,'Puppies','Here are some statements about puppies. Of course, you may not agree with all of them. But just suppose they were ALL correct, what conclusion could you draw from them?\r\n \r\n(i) No puppy that chases cats is unteachable.\r\n \r\n(ii) No puppy without a black nose will play with a Kangaroo.\r\n \r\n(iii) Puppies with floppy ears always chase cats.\r\n \r\n(iv) No teachable puppy has a loud bark.\r\n \r\n(v) No puppies have black noses unless they have floppy ears.\r\n','PUPPIES WHICH PLAY WITH KANGAROO DO NOT HAVE A LOUD BARK\r\n \r\nor, \r\n \r\nNO PUPPY WITH A LOUD BARK PLAYS WITH KANGAROOS.\r\n \r\nThis conclusion is arrived at as follows: \r\n \r\nAll puppies which play with kangaroos have black noses (ii)\r\n \r\nWhich means they have floppy ears (v)\r\n \r\nWhich means they chase cats (iii)\r\n \r\nWhich means they are teachable (i)\r\n \r\nWhich means they do not have a loud bark (iv)\r\n','2003-01-30',20030519232102,NULL,3,3,0,2.67,20030130000000,0);
INSERT INTO problem VALUES (370,6,2,979,'Book Worms','There were three brothers Albert, Bertrand and Charles. \r\n \r\nAlbert lent to Bertrand and Charles as many books as they had initially.\r\n \r\nAfter some time Bertrand gave as many books to Albert and Charles \r\nas many as they now have. \r\n \r\nAfter sometime Charles did the same thing.\r\n \r\nAt the end each one of them had 24 books.\r\n \r\nFind the books each orginally had. ','Let Albert, Bertrand and Charles have initially a, b and c number of books with themselves.\r\n \r\nGiven that in the first division, Albert gives away to Bertrand and Charles as many books they initially had, so now the number of books each of them have after the first division are:\r\n \r\nAlbert: (a – b – c); Bertrand: 2b, Charles: 2c\r\n \r\nIn the second division, Bertrand gives away to Albert and Charles as many books they now have. That is, the number of books they have after the first division, so now the number of books each of them have are: \r\n \r\nAlbert: 2(a – b – c); Bertrand: (3b – a – c); Charles: 4c\r\n \r\nIn the third division, Charles gives away to Albert and Bertrand as many books they now have. That is, the number of books they have after the second division, so now the number of books each of them have are:\r\n \r\nAlbert: 4(a – b – c); Bertrand: 2(3b – a – c); Charles: (6c – a – b)\r\n \r\nNow, from the problem, we have:\r\n \r\n(a – b – c) = 6 --------(1)\r\n \r\n(3b – a – c) = 12 --------(2)\r\n \r\n(6c – a – b) = 24 --------(3)\r\n \r\nSolving the above three equations, we get: a = 39, b =21 and c =12\r\n \r\nSo, the number of books each originally had is:\r\n \r\nAlbert: 39 Books, Bertrand: 21 Books and Charles: 12 Books.\r\n','2003-02-01',20030326065623,NULL,3,3,0,3.00,20030201000000,0);
INSERT INTO problem VALUES (619,14,2,979,'Primes','If x and (x² + 8) are both primes, then prove that (x³ +16) is also a prime.','First, we need to realize that for any whole number n, one of n+1, n, or n-1 is divisible by three.\r\n \r\nAlso, if n is prime, then n is not divisible by three (unless n=3), so either n+1 or n-1 is divisible by three. In that case, \r\nTherefore, the only time that n and n²+8 will both be prime is if n is equal to three. In this situation, x³+16=43 is indeed prime, so we have proven the original supposition.','2003-09-09',20031015232103,NULL,3,3,0,4.57,20030909155054,0);
INSERT INTO problem VALUES (431,6,2,979,'Three Playing Cards','There are three playing cards face-up on the table.\r\n \r\nA diamond is on the left of a spade.\r\n \r\nAn eight is on the right of a king.\r\n \r\nA ten is on the left of heart.\r\n \r\nA heart is on the left of a spade.\r\n \r\nFrom left to right, what are the three playing cards?\r\n','A diamond is on the left of a spade. \r\nAn eight is on the right of a king. \r\nA ten is on the left of heart. \r\nA heart is on the left of a spade. \r\n \r\nFrom the first three statements, we can clearly observe the following: \r\n \r\nThe rightmost card cannot be a diamond or a heart or an king or a ten. \r\n \r\nSo, obviously the rightmost card has to be a Eight Of Spades.\r\n \r\nNow from the second and fourth statements it is clear that the card in the middle is none other than the King Of Hearts leaving the leftmost card to be the Ten Of Diamonds.\r\n \r\nSo, the order of the three playing cards from left to right are:\r\n \r\nTen Of Diamonds, King Of Hearts, Eight Of Spades.','2003-02-26',20031121232101,NULL,2,3,0,2.44,20030226000000,0);
INSERT INTO problem VALUES (372,7,2,979,'License Number','Albert remarked that even when it is turned upside down, the number plate of his car still made sense. \r\n \r\nHe observed that this would however increase the registration number on it by 8505. \r\n \r\nGiven, all of the four digits in the number is different, find out what was his car license number? \r\n','The answer is 1096\r\n \r\nRick provides an excellent soluiton here','2003-01-31',20040225103933,NULL,2,3,0,2.80,20030131000000,0);
INSERT INTO problem VALUES (373,12,2,979,'Guessme Two','Twice ten are six of us,\r\n \r\nSix are but three of us,\r\n \r\nNine are but four of us;\r\n \r\nWhat can we possibly be?\r\n \r\nWould you know more of us,\r\n \r\nTwelve are but six of us,\r\n \r\nFive are but four, do you see?\r\n\r\n','They are the \"Number of LETTERS\" of a word.\r\n \r\nLike twice ten means twice of 3(since the word ten contains three letters), which is equal to 6, Six are but three(the word six contains three letters)....and so on....which also explains \'Twelve are but six of us,Five are but four.\'\r\n','2003-02-01',20030725232102,NULL,2,3,0,3.12,20030201000000,0);
INSERT INTO problem VALUES (374,6,2,979,'Family Problem','A family gathering included one grandfather, one grandmother, two fathers, two mothers, four children, three grandchildren, one brother, two sisters, two sons, two daughters, one father-in-law, one mother-in-law and one daughter-in-law. \r\n \r\nWhat can be the minimum number of people present in the gathering? ','The party consisted of altogether seven people and they are: Three children (two girls and a boy), their father and mother, and their father’s father and mother. \r\n \r\nIt will be found that these in their various relations to each other, fill all the characters named.\r\n \r\nThus the father in relation to his own father, is also a son, and so on. ','2003-02-03',20031216232100,NULL,2,3,0,2.71,20030203000000,0);
INSERT INTO problem VALUES (426,4,2,1301,'Dice Proposition','If a pair of dice are thrown repeatedly until a 7 is thrown, what is the probability that all the other possible numbers from 2 through 12 will have been thrown by the time the 7 has been thrown?\r\nAs a preliminary, what is the probability that 2, 11 and 12 will all have been thrown before the first 7?\r\n \r\n','In the preliminary, P(2 and 11 and 12) = P(2) + P(11) + P(12) – P(2 or 11) – P(2 or 12) – P(11 or 12) + P(2 or 11 or 12). You can verify the formula by seeing how many times each possible truth value is added in or subtracted out. All except the desired probability are cancelled by equal adding and subtracting. The individual probabilities are based on the number of ways of the sought combinations divided by that plus the 6 ways of getting a 7: Thus 1/7 + 2/8 + 1/7 – 3/9 – 2/8 – 3/9 + 4/10 = 2/105 = 0.0190476…\r\n \r\nThe main problem has a similar formula, involving 1023 terms, and has the result 0.005257704… By the way this corresponds to 189.197 to 1 odds against.\r\n','2003-02-22',20030326065623,NULL,5,3,0,3.50,20030222000000,0);
INSERT INTO problem VALUES (377,12,2,979,'Guessme Three','Five hundred begins it, \r\n \r\nFive hundred ends it,\r\n \r\nFive in the middle is seen;\r\n \r\nFirst of all figures,the first of all letters,\r\n \r\nTake up their stations between.\r\n \r\nJoin all together, and then you will bring;\r\n \r\nBefore you the name of an eminent king.\r\n \r\nGuess What/Who am I ? \r\n\r\n','The answer is \"David\".\r\n \r\nTomM provides a detailed explanation here','2003-02-01',20040225103933,NULL,3,3,0,3.88,20030201000000,0);
INSERT INTO problem VALUES (378,12,2,979,'Guessme Four','Who makes it, has no need of it.\r\n \r\nWho buys it, has no use for it.\r\n \r\nWho uses it can neither see nor feel it.\r\n \r\nGuess What/Who am I ?\r\n','It\'s a coffin. The maker has no need for it. Neither has the buyer. Whoever it\'s meant for is dead, and can\'t see or feel it.','2003-02-04',20040221232101,NULL,2,3,0,3.00,20030204000000,0);
INSERT INTO problem VALUES (379,12,2,979,'Guessme Five','Whoever makes it, tells it not.\r\n \r\nWhoever takes it, knows it not.\r\n \r\nAnd whoever knows it wants it not.\r\n \r\nGuess What/Who Am I ?\r\n','Fake (counterfeit) money','2003-02-04',20031106232104,NULL,2,3,0,3.25,20030204000000,0);
INSERT INTO problem VALUES (380,7,2,979,'Plus and Minus','Frame at least 8 different equations by inserting plus and minus signs only into 1,2,3,4,5,6,7,8,9; to give a total of 100.\r\n \r\nFor example: 123 - 45 - 67 + 89 = 100\r\n \r\n(The numbers must stay in the normal ascending order from 1 to 9).\r\n\r\n\r\n\r\n','Jim Lyon lays out the goods here\r\n \r\nfriedlinguini though, also gets brownie points for his attempt','2003-02-05',20040225103933,NULL,3,3,0,3.00,20030205000000,0);
INSERT INTO problem VALUES (381,12,2,979,'Guessme Six','What has six legs, two heads, four ears and two hands, and walks on four feet? ','It\'s a man riding a horse.','2003-02-05',20030806232101,NULL,1,3,0,2.50,20030205000000,0);
INSERT INTO problem VALUES (382,12,2,979,'Guessme Seven','Two bodies have I,\r\n \r\nThough both joined in one.\r\n \r\nThe more still I stand, \r\n \r\nThe quicker I run. \r\n \r\nGuess What/Who Am I ?\r\n','It\'s an hourglass... Or should that be \"a hourglass\"?.. Hmm...','2003-02-06',20030720232102,NULL,3,3,0,2.20,20030206000000,0);
INSERT INTO problem VALUES (383,12,2,979,'Guessme Eight','I have a nose but cannot smell,\r\nI have two eyes but cannot see.\r\n \r\nI have a head, a chest, a neck, but none are any use to me.\r\n \r\nI cannot walk, I cannot run, I can\'t abide to see the sun.\r\n \r\nMy day of birth is the eve of my life. \r\n \r\nGuess What/Who am I ?\r\n','SNOWMAN \r\n','2003-02-08',20040324232102,NULL,2,3,0,1.67,20030208000000,0);
INSERT INTO problem VALUES (466,17,2,1301,'Sunlight over the World','Do different parts of the world receive different amounts of sunshine during the year? Ignore clouds, or consider only what is received either on the cloud tops or surface, whichever is available. Is it the same at the poles as at the equator? ... the northern and the southern hemispheres?\r\n \r\n Consider two interpretations of the above: (1) number of hours per year that the sun is up, (2) the total insolation (total solar energy received per unit of area of the ground) received during the year, weaker when the sun is low near the horizon than when it is high in the sky. (1) For various latitudes, the following table shows the hours the sun is up over the course of one year: The sun is up more time in mid latitudes north and south than at either the equator or the pole, but also more time in the northern than in the southern hemisphere. The latter difference is the result of the sun being north of the equator for more time than south, because the earth is farther from the sun in northern summer and therefore moving more slowly in its orbit. Overall, the sun is up over half the time as atmospheric refraction raises the apparent sun near the horizon, and also the sun is considered up when any part of the solar disk is above the horizon. That effect also causes the mid-latitude excess, as those latitudes benefit from a prolonged daily slantwise passage of the sun through the horizon. (2) For various latitudes the following is the integrated amount of insolation over the course of a year. The units are arbitrary, rather than calories per square centimeter per year or the like, but are in proportion to the amount received: The poles suffer from the fact that the sun is lower on the horizon there even when it is up. Also, while the sun is closer during southern hemisphere summer, summer lasts longer in the northern hemisphere, as mentioned above. For more details see http://www.wiskit.com/marilyn/sunshine.html. The item had originally appeared, ambiguously worded without a clarification as to which meaning was meant, in Marilyn vos Savant\'s Parade column. Marilyn had answered that the sun shone over every part of the world for exactly half the time during the year, either for 6 months straight as at the poles or 12 hours every day as at the equator or some compensation of summer vs. winter elsewhere. This ignores the eccentricity of the earth’s orbit that causes the sun to be north of the equator more than south, and the raising of the low sun by atmospheric refraction. The above URL is in the Marilyn is Wrong web site. \r\nand often by the vain possessed,\r\n \r\nheard by the deaf, seen by the blind.\r\n \r\nI give the troubled spirit rest. ','\" NOTHING \" is the correct answer.\r\n \r\nNOTHING is scorned by the meek and humble minded\r\n \r\nthe vain possesses NOTHING \r\n \r\nthe deaf hears NOTHING and the blind sees NOTHING\r\n \r\nand NOTHING gives the troubled spirit rest.\r\n\r\n','2003-02-08',20040209232105,NULL,2,3,0,2.17,20030208000000,0);
INSERT INTO problem VALUES (395,13,2,834,'Complete the series','There is a logical pattern to the following series of numbers. What are the next three numbers in the series?\r\n \r\n15 21 25 27 33 35 39 ... \r\n','45, 49, 51. The series consists of 2-digit odd numbers excluding primes. \r\n \r\n(Certainly some of the more involved patterns that our visitors have submitted can hold true as well.)','2003-02-10',20030326065623,NULL,3,3,0,3.33,20030210000000,0);
INSERT INTO problem VALUES (390,12,2,1016,'Life Cycle in Color','It\'s black when it\'s not in use, it\'s red when it\'s in use, and it\'s grey when you\'re done using it. What can this be??','Charcoal or coal.','2003-02-05',20031127232102,NULL,3,3,0,2.82,20030205000000,0);
INSERT INTO problem VALUES (689,4,2,834,'Make it Even','Timothy and Urban play a game with two dice. But they do not use the numbers. Some of the faces are painted red and the others blue. Each player throws the dice in turn. Timothy wins when the two top faces are the same color. Urban wins when the colors are different. Their chances are even. \r\n \r\nThe first die has 5 red faces and 1 blue face. How many red and how many blue are there on the second die? \r\n','Each die has 6 faces. When two dice are thrown, there are 36 equally possible results. For chances to be even, there must be 18 ways of getting the same color on top. Let X be the number of red faces on the second die. We have: 18 = 5X + 1(6 - X) \r\nX = 3 \r\nThe second die must have 3 red faces and 3 blue faces. ','2003-03-30',20030823232102,NULL,3,3,0,4.29,20030330031555,0);
INSERT INTO problem VALUES (392,6,2,834,'The Rope','Two fifty foot ropes are suspended from a forty foot ceiling, about twenty feet apart. \r\n \r\nArmed with only a knife, how much of the rope can you steal?','Almost all of it. Tie the ropes together. Climb up one of them. Tie a loop in it as close as possible to the ceiling. Cut it below the loop. Run the rope through the loop and tie it to your waist. Climb the other rope (this may involve some swinging action). Pull the rope going through the loop tight and cut the other rope as close as possible to the ceiling. You will swing down on the rope through the loop. Lower yourself to the ground by letting out rope. Pull the rope through the loop. You will have nearly all the rope. \r\n','2003-02-07',20031216232100,NULL,3,3,0,2.80,20030207000000,0);
INSERT INTO problem VALUES (397,20,2,794,'3 From 1','What one-syllable word can be transformed into a three-syllable word by adding only one letter? ','Are. By adding an \"a\" it becomes area, a three-sylabble word. \r\n \r\n(Some more solutions are submitted by our visitors in comments)','2003-02-11',20031031232101,NULL,1,3,0,3.75,20030211000000,0);
INSERT INTO problem VALUES (399,5,2,1072,'Folding Square','You have a square piece of paper and you do not know its length or width. \r\n \r\nWhat is the minimum number of folds required in order for the paper to only show 1/16 of its original size, 2/16 of it\'s original size, 3/16 of its original size........15/16 of its original size.\r\n \r\nNote: You do not know where halfway marks or quarter marks lie on this piece of paper therefore you must use folds to mark these areas. You are allowed to use folds as guides to make other folds.','1/16 4 folds ','Charlie has taken the trouble to show all work here.','2003-03-01',20040303215126,NULL,3,3,0,3.60,20030301000000,0);
INSERT INTO problem VALUES (465,7,2,1299,'Composite numbers','Find 2000 consecutive composite numbers.\r\n \r\n(Of course you can\'t do this by trial and error alone)\r\n \r\nFor those who do not know what a composite number is, it is any integer greater than 1 that is not prime. (4, 6, 8, 9, ...)','Since you can\'t possible think of some random 2000 consecutive composite integers, you need to think of some relation or formula.\r\n \r\nObjects placed on one side of the balance could be counter-balanced by a weight on the other side of the balance to determine the object\'s weight.\r\nAlso, the object and a weight(s) could be placed on one side of the balance and counter balanced to determine its weight, if necessary. \r\n \r\nBy using only these 5 weights, the ancients were able to determine the weight of objects weighting 1, 2, 3, ..., 120, 121 grams. What are the 5 weights that the archeologists found?','Delvin posted a soltion here','2003-02-13',20040303215126,NULL,3,3,0,3.83,20030213000000,0);
INSERT INTO problem VALUES (621,16,2,979,'Resting Sphere','There is a perfect sphere of diameter 100 cms. resting up against a perfectly straight wall and a perfectly straight floor. \r\n \r\nHow did the five men and the five dogs cross the river? ','Let the five men be represented by A, B, C, D, and E. Let the five dogs be represented by a, b, c, d, and e. Let the dog that can operate the boat be dog a.\r\n \r\na, b, and c cross the river. a comes back alone and takes back d. a goes back and says behind while B, C, and D cross the river. Now A, a, E, and e are on the starting shore, and B, b, C, c, D, and d are on the destination shore. D and d return; A and a cross. C and c go back, and C, D, and E cross. Now dogs c, d, and e are on the starting shore, and everyone else is on the destination shore. a goes back and returns with c and d, then goes back and returns with e.\r\n \r\n***\r\n \r\nSince this is a little confusing, look at DJ\'s solution here for a better explanation of what is happening, as well as a diagram of the enumerated steps in the solution.','2003-09-15',20040225103933,NULL,3,3,0,2.50,20030915072731,0);
INSERT INTO problem VALUES (405,5,2,834,'Nine dots',' \r\nDrew: We are of the same type. \r\nNow, what are each?\r\n\r\n','The two contradict each other, so one is a knight and one is a liar.\r\nThat means they are of different types, so Drew must be a liar because he lied and Mohammad must be a knight because he told the truth.','2003-04-30',20031107232102,NULL,1,3,0,2.56,20030430014843,0);
INSERT INTO problem VALUES (968,14,2,1567,'We put the \'fun\' in function','Consider the function f(x)=ln(x)/√x\r\n For the second part, let y=f(x). For x=-1, y=ln(-1)/i From this arrangement, we see that y=pi (Euler\'s law).','2003-07-01',20040120232103,NULL,4,3,0,3.00,20030701020344,0);
INSERT INTO problem VALUES (1267,10,2,1567,'Know Who Your Friends Are','A traveler passing through the land of liars and knights stops in at a pub, where he meets a group of six friendly locals. Their stories all are funny, but he doesn\'t know which ones to believe, so he asks them (tactfully) who the liars and knights are in the group. They make one statement each: Amery: Cuthbert and Fredo are both liars. Which of the men are liars, and which are knights? \r\nNumber the six statements 1-6 and nickname the men A-F. Start by assuming E is a liar. Then statements 2 and 3 are false, making B and C liars. If D is a knight, statement 4 is true, making A a liar and statement 1 false. Since C is a liar, F must be a knight, making statement 6 true, making A a knight, which contradicts an earlier assumption. Therefore D is not a knight. If D is a liar, statement 4 is false, and since B is a liar, A must be a knight, so statement 1 is true, making F a liar, so statement 6 is false, and since A is a knight, D must be a knight, which contradicts the original assumption. Since D can be neither a liar nor a knight when starting from the assumption that E is a liar, this assumption must be wrong. Therefore E is a knight and statement 5 is true, so C and D are also knights. From statement 4, A and B are both liars, so from statement 2, F must be a liar. In summary: the liars are Amery, Brant, and Fredo, and the knights are Cuthbert, Derek, and Everard.','2003-09-05',20040121232101,NULL,3,3,0,3.20,20030905135459,0);
INSERT INTO problem VALUES (1505,14,2,1645,'Crypto-Phrase','6-342-30-2-132 / 420-72-30 / \r\n12-240-20-30 / 420-240 / \r\n342-30-506-30-2-156 / 2 / \r\n42-2-182-240-462-380 / \r\n272-72-342-2-380-30 / 2-210-20 / \r\n90-420-380 / 2-462-420-72-240-342:\r\n \r\n420-240 / 6-30 / 240-342 / \r\n210-240-420 / 420-240 / 6-30; \r\n420-72-2-420 / 90-380 / 420-72-30 / \r\n306-462-30-380-420-90-240-210. \r\n \r\n ~552-90-156-156-90-2-182 / \r\n 380-72-2-132-30-380-272-30-2-342-30\r\n \r\n Note: Each letter of every word is separated by a dash and each word is separated by a slash.','The code is determined by replacing each letter with a value -- for the nth letter of the alphabet, the value is n(n+1). \r\nFully translated, the message reads:\r\n \r\n \r\nIf you were to shuffle the deck (consider the cards to be random after shuffling) and take off the first 4 cards, (such that the first card is thousands place, the second card is the hundreds place, so on), what is the probability that this number will be a perfect square?? Also, how would you find this probability without \"trial and error\" or \"brute force\"?','If you look at a list of squares (0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100) you will note there isn\'t any 2, 3, 7, or 8 in the ones place. \r\nWhen growing peanuts the following happens:\r\n \r\nWhen a company packages 1000 peanuts in one bag they take peanuts randomly from a giant bin that contins all the peanuts grown. What are the odds that there will be 1000 individual nuts?','In a series of posts (see comments), Charlie explains why the probability of this is roughly 1 in 55 cases.','2003-02-18',20030724232104,NULL,3,3,0,3.67,20030218000000,0);
INSERT INTO problem VALUES (467,19,2,1419,'Riddle of the Sphinx','What has Four legs at the Morning, ','A (wo)man. Crawling on all fours as a baby, walking on two feet as a grown person, and hobbling on a cane as an old person.','2003-03-11',20040319232102,NULL,2,3,0,3.20,20030311000000,0);
INSERT INTO problem VALUES (408,7,2,1072,'Dancing','In a popular dancing game there are 4 directions: up, down, left, right. In the game these arrows may appear once every quarter-note or eight-note. Also two arrows may appear at the same time in the same beat. Three or four arrows cannot. \r\n \r\nIn a song that is 1 minute long and plays at 1 bar(4 quarter notes) every 4 seconds, what are the total possible number of different dances that can exist.','11^120\r\n \r\nThere are 120 segments of the song each with 11 possible arrow possibilities. None, up, down, left, right and the 6 combinations.','2003-02-16',20030326065623,NULL,2,3,0,4.00,20030216000000,0);
INSERT INTO problem VALUES (693,11,2,1072,'Creating 5 weights','A long time ago some ancients needed to make 5 weights that could weigh any amount of weight up to 121 grams. \r\n \r\nThe ancients though, had only a 1 gram weight and 120 grams of clay(which they would later make into weights. So with only a scale, 120 grams of clay and a 1 gram weight how would you create all the other weights needed to weigh any amount up to 121 grams? \r\n \r\nWhat is the minimum amount of weighings required to do this?\r\n','First measure out clay equal to the 1 gram weight. Take that 1 gram of clay and put it on the side with the weight. Measure out 2 grams of clay now. Take the 1 gram of clay and the 2 grams of clay and you have the 3 gram weight. \r\n \r\nUsing the one and 3 gram weight on one side, measure out 4 grams of clay twice, then using the 1 gram weight get 1 more gram of clay. Put the two 4 gram weights together along with the 1 gram of clay and you have your 9 gram weight. \r\n \r\nNext take all the wieghts you have (1,3,9=13 grams)and put them on one side of the scale. Now measure out an equivalent amount of clay twice, then measure out 1 gram of clay. Take all this clay and now you have your 27 gram weight. \r\n \r\nAll the leftover clay is now your 81 gram weight. Thus resulting in 8 weighings.','2003-03-24',20040225103947,NULL,2,3,0,3.60,20030324000000,0);
INSERT INTO problem VALUES (410,7,2,1254,'Fruity math','Using only the digits 0-9, but not 3 or 5, solve for each letter:\r\n \r\nGRAPE - PLUM = APPLE\r\n \r\nYou can only use one digit for each letter.','94872 - 7160 = 87712 \r\n \r\n(Look in the comments by our visitors for a solution)','2003-02-17',20030326065623,NULL,3,3,0,3.83,20030217000000,0);
INSERT INTO problem VALUES (411,6,2,1072,'The flooble question','At flooble there are 40 problems in the queue. (this may not be true but lets just pretend it is.) A few crazy hackers somehow manage to promote themselves to scholars. On the first day the first hacker will vote thumbs up on all problems displayed.(The 10 most recent) On the second day the second hacker votes thumbs down on every second problem. On the third day the third hacker votes thumbs up on every third problem. And so on and so on. (When it gets to the eleventh day the eleventh hacker will do what the first hacker did) How many days will it take for every problem in the queue to be live on the site?\r\n \r\nNote: For those who don\'t know there are only 10 problems that can be voted thumbs up or thumbs down every day and these problems are the 10 least recent. Also a problem with three thumbs up will be posted to the site and taken out of queue. Only one problem can be posted to the site per day. Also if a problem gets 3 thumbs down it is deleted.\r\n \r\nBtw: for those who like an extra challenge what if one problem is submitted every 3 days? \r\n \r\nAlso: A hacker will always vote before a problem becomes live.','Charlie ran a computer simulation that shows that the last problem is posted on day 201. If one problem is posted once every 3 days the queue would never be exhausted. You could also read the comment list to find out more.\r\n ','2003-02-18',20030529232103,NULL,4,3,0,3.75,20030218000000,0);
INSERT INTO problem VALUES (421,2,2,1299,'So obvious....?','Why do you think manholes are round in shape?\r\n \r\n(You need to think a little crooked for this )','If the manhole was of any other shape, say some polygon, then the it will have a diagonal which is longer than the sides. So the cover can fall in through the hole, hence creating a dangerous hole in the road. But a circle having a fixed diameter avoids this.','2003-02-19',20040229232101,NULL,3,3,0,3.40,20030219000000,0);
INSERT INTO problem VALUES (476,9,2,1440,'Aliens','Aliens have taken you aboard their ship. You will be asked to make a statement. If the statement is true you will be blasted into atoms. If it is false you will be ejected into space. One statement can get you out alive. What is it and how does \r\nit spare you?\r\n ','By telling the aliens that they will eject you into space, you will effectively make them unable to do either and still conform to their rules.\r\n \r\nIf what you said is true and they plan to eject you, they would have to blast you - but then the statement is no longer true, and they have to eject you once again. It\'s a vicious circle.','2003-03-15',20031210232104,NULL,3,3,0,3.43,20030315000000,0);
INSERT INTO problem VALUES (477,17,2,1301,'Earth Slowing Down','The earth\'s rotation is slowing down due to the friction against the tidal bulge produced by the moon\'s and sun\'s gravitation. The variation is irregular but in general after 100 years the earth has rotated about .25° less than it would have if the rate were the same as at the beginning of the 100 years. That corresponds to one minute\'s worth of rotation. \r\nIn how many different ways can this be achieved ?\r\n ','See Charlie\'s solution in this comment.\r\n ','2003-05-30',20040225103933,NULL,3,3,0,2.14,20030530015424,0);
INSERT INTO problem VALUES (536,14,2,979,'27 Weights','Suppose you have 27 weights weighing: 1², 2², 3², 4², ........, 25², 26² and 27² grams respectively. \r\n \r\n(a)How can you group them into three groups so that each group has the same weight ?\r\n \r\n(b) Is it possible to divide it into more than three groups satisfying the same conditions ? ','See Gamer\'s comments on this problem for the solutions to the different parts.','2003-05-31',20030608042519,NULL,3,3,0,4.00,20030531030408,0);
INSERT INTO problem VALUES (414,12,2,1299,'Greetings','If I sent this message to all of my friends and relatives at a particular time of the year, what would i be tryin to say to them?\r\n \r\n\"ABCDEFGHIJKMNOPQRSTUVWXYZ\"\r\n\r\n','Since the only aplhabet missing in the set is L, it\'s \"no L\" or Noel....or just Merry Christmas!','2003-02-18',20040323232104,NULL,3,3,0,2.25,20030218000000,0);
INSERT INTO problem VALUES (417,13,2,775,'Sequential seasonings','Can you fill in the blanks in the following sequence? \r\n \r\n1,1,4,2,7,3,17,4,20,?,37,6,47,5,51,?,61,3,70,3,9?,2,100,1','Pair the numbers off into groups of two. Then, in each set, the first number represents an ordinary number, while the second is the number of \"digits\" the Roman numeral representation of the number includes. \r\n \r\nSo in (1,1), the RN for 1 is (i), which is 1 letter, while in the pair (47,5), the RN for 47 is (XLVII), which is 5 letters long. Following this, the first unknown is 2 (XX), the second is 2(LI), and the third is 0, the only number properly created in the nineties with just two symbols (I believe that the correct representation of 99 is XCIX, not IC). The first number in each pair is simply chosen to disguise the relation.','2003-02-19',20030723232103,NULL,4,3,0,4.00,20030219000000,0);
INSERT INTO problem VALUES (534,4,2,1301,'Probability of All of a Set','Prove that the probability of occurrence of all of a given set of events A(1) through A(n) is equal to the sum of the individual probabilities minus the sum of the probabilities of all pairs of events, A(i) OR A(j) plus the sum of all triples of events, A(i) OR A(j) OR A(k), ..., plus (-1)^(n-1) times the n-tuple A(i) OR ... OR A(n). \r\n \r\nProve for the specific cases of n = 3 and n = 10, and the general case.','Consider a state space in which the area, volume or hypervolume is proportional to the probability of events contained in the subset of space. This is easiest to visualize in the case of n=3, where the Venn diagram\'s 8 regions (bounded, so as to delimit even the null area) can be made proportional in area to the probability of each combination of events, say A(1) AND A(2) AND NOT A(3), or the outside, NOT A(1) AND NOT A(2) AND NOT A(3).\r\n \r\nA formal mathematical proof for the general case can start with an already-proved theorem from Feller’s Introduction to Probability Theory and Its Applications, vol. 1, 2nd edition. That theorem has the ORs interchanged with ANDs: P(A OR B OR C … OR Z) = P(A)+P(B)+…+P(Z) – P(A AND B) – P(A AND C) … - P(Y AND Z) + P(A AND B AND C) + … +P(X AND Y AND Z) – P(A AND B AND C AND D)…\r\n \r\nLet’s start with events A(1)’, A(2)’, …, A(n)’. Then P(A(1)’ OR … OR A(n)’) = P(A(1)’) + P(A(2)’) + … + P(A(n)’) – P(A(1)’ AND A(2)’) - … - P(A(n-1)’ AND A(n)’) + …\r\n \r\nwhere each ANDed even multiple of events is subtracted out and every ANDed odd multiple is added in.\r\n\r\nThen consider the events A(1), A(2), A(3), …, A(n), defined as NOT A(1)’, NOT A(2)’, NOT A(3)’, …, NOT A(n)’. Similarly then, A(1)’ is the event NOT A(1), etc. Then P(A(1)’ OR … OR A(n)’) is P(NOT A(1)’ OR … OR NOT A(n)’). By De Morgan’s law this is P(NOT(A(1) AND A(2) AND A(3) … AND A(n))). By the definition of probability P(NOT x) = 1- P(x), so this becomes 1 – P(A(1) AND … AND A(n)).\r\n \r\nDe Morgan’s law and negation can then also convert the right side into 1 – P(A(1)) + 1- P(A(2)) + … + 1- A(n) – (1-P(A(1) OR A(2))) - … - (1-P(A(n-1) OR A(n))) + …\r\n \r\nSo we have 1 – P(A(1) AND … AND A(n)) = 1 – P(A(1)) + 1- P(A(2)) + … + 1- A(n) – (1-P(A(1) OR A(2))) - … - (1-P(A(n-1) OR A(n))) + …\r\n \r\nIf we subtract 1 from each side, and then multiply each side by –1, we get\r\nP(A(1) AND … AND A(n)) =1 – (1 – P(A(1))) – (1- P(A(2))) - … - (1- A(n)) + (1-P(A(1) OR A(2))) + … + (1-P(A(n-1) OR A(n))) - …\r\n \r\nNow, the individual events as well as all odd ORed combinations have double negatives, therefore positive, and the even combinations of ORed events have negative. But there are all those 1’s. Adding them, taking into consideration their signs, they total 1 – nC1 + nC2 – nC3 + … +/- nCn, the last term having absolute value 1 and positive sign if n is even and negative if odd. This is, however, the set of coefficients of (a-b)^n and in this instance a and b are both zero so a-b is zero and (a-b)^n is zero. Therefore all the 1’s cancel out, and the formula is the one we are trying to prove.\r\n\r\n\r\n\r\n','2003-03-13',20030326065623,NULL,5,3,0,3.50,20030313000000,0);
INSERT INTO problem VALUES (420,6,2,834,'Harder Puzzle','If the puzzle you solved before you solved the puzzle you solved after you solved the puzzle you solved before you solved this one, was harder than the puzzle you solved after you solved the puzzle you solved before you solved this one, was the puzzle you solved before you solved this one harder than this one?\r\n ','The puzzle was indeed harder than this one.\r\n \r\nSee the posted comments for a solution.','2003-02-21',20030705232102,NULL,3,3,0,3.67,20030221000000,0);
INSERT INTO problem VALUES (422,7,2,1299,'Counting digits','How many digits are there in 2^1000 (2 to the power of 1000)?\r\n ','Ender has provided the solution in the comments list\r\n \r\nAnyway, 2^1000 = 10^(1000*log2) = 10^(301.03)\r\n \r\nSo you can round the exponent to 301.\r\n \r\nSo including the 1 and the 301 zeroes, the answer is 302 digits.','2003-02-20',20030326065623,NULL,3,3,0,4.14,20030220000000,0);
INSERT INTO problem VALUES (424,2,2,1344,'Men, Women and Pets','There are 3 women (1,2,3), 3 men (A,B,C), 3 dogs and 3 cats\r\n \r\nCan you figure out who is married to who, and how many animals of each kind that person has?','E Woodford was the first to post the correct answer\r\nhere','2003-02-21',20040225103933,NULL,3,3,0,3.00,20030221000000,0);
INSERT INTO problem VALUES (427,12,2,1299,'Talking gibberish','A guy walks into a restaurant. Half an hour later the waiter hands him a bill. The guy immediately says:\r\n \r\n\"102004180\"\r\n \r\nThe waiter being a rather smart chap, waitering only because of the recession, immediately understood what he meant... but do you?\r\n','This one is a play on the sounds of the words.\r\nWhat the customer actually said was \" One ought to owe nothing for one ate nothing\". Just try saying 102004180 pronouncing the first 0 as \"nought\", the second 0 as \"Oh\" , the third 0 and fourth 0 as \"nothing\".','2003-02-23',20040121232101,NULL,3,3,0,2.00,20030223000000,0);
INSERT INTO problem VALUES (428,12,2,1299,'Lateral thinking','A stranger walks into a bar and puts a pound coin on the counter and asks for half a pint of bitter. The barmaid asks him whether he would like Guinness or Worthington. The stranger asks for Guinness. Another complete stranger comes into the bar, puts a pound on the counter and also asks for half a pint of bitter. The barmaid immediately pulls half a pint of Guinness. How did she know what the second man, who was completely unknown to her, wanted? \r\n \r\n(think in a crooked way for this one)','The key here is the money or the pound being paid.\r\nHalf a pint of Guinness (Batemans) costs exactly one pound, while Worthington costs 90p. The first stranger put down a £1 coin on the counter. The second man put down a 50p piece and five 10p coins. If he had wanted Worthington he would only have put down 90p.','2003-02-24',20040323232104,NULL,3,3,0,3.00,20030224000000,0);
INSERT INTO problem VALUES (429,12,2,1299,'Death came','A man went to a party and drank some of the punch. Late for another appointment, he then left early. Everyone else at the party who drank the punch subsequently died of poisoning. \r\n \r\nWhy did the man not die? \r\n ','The ice cubes used in the punch contained poison. The poison spread to the punch only after the ice melted and hence the man who left early escaped.','2003-02-24',20040121232101,NULL,3,3,0,2.33,20030224000000,0);
INSERT INTO problem VALUES (432,10,2,979,'Who is Guilty ?','Alan, Barry and Carl (each either a Knight or a Liar) were rounded up by the cops yesterday, because one of them was suspected of having stolen money from the bank. The three brothers made the following statements under very intensive questioning:\r\n \r\nAlan: I\'m innocent. \r\n \r\nBarry: I\'m innocent. \r\n \r\nCarl: Barry is the guilty one. \r\n \r\nIf only one of these men is a Knight, who stole the money?\r\n','We can see that both Barry and Carl contradict each other. So obviously, one of them is bound to be a liar and one a Knight. \r\n \r\nAlso, we see that if we consider Carl as the Knight then we see that it violates the given conditions of the problem. Hence, Barry is the Knight and Carl and A are both Liars and thus proving that A stole the money.','2003-02-27',20031212232103,NULL,1,3,0,2.42,20030227000000,0);
INSERT INTO problem VALUES (434,2,2,979,'Black and White','Imagine that you have three boxes, one containing two black balls, one containing two white balls, and the third containing one black ball and one white ball.\r\n \r\nThe boxes were originally labelled for their contents (BB - WW - BW) but someone has inadvertently switched the labels so that now every box is incorrectly labelled.\r\n \r\nWithout looking inside, you are allowed to take one ball at a time out of any box that you wish, and by this process of sampling, you are to determine the contents of all three boxes.\r\n \r\nWhat is the smallest number of drawings needed to do this? \r\n','You need only take one ball to re-label the jars properly. The key is that all the labels are wrong. So, the jar labeled BW has either all black balls or all white balls. Take one ball from that jar, and figure out which one it is.\r\n \r\nNow, if this is the black jar, then the jar labeled \"black\" is really the white jar, and the remaining one is mixed.\r\n \r\nOn the other hand, if the first jar is white, then the jar labelled \"white\" is actually black, the remaining being mixed once again.\r\n \r\nAs you see, there are only two possibilities, and you can figure out which one is actually true by removing the ball from the jar whose label says its mixed.','2003-02-25',20030621232102,NULL,2,3,0,3.00,20030225000000,0);
INSERT INTO problem VALUES (1621,7,0,1626,'Sum Rotation','Here\'s a hard problem I remember reading somewhere.\r\n \r\n\r\nWhat is the probability for each person to win during their turns?\r\n','The probabilities are: 3/20 for the first player, 3/17 for the second, 3/14 for the third, and 3/11 for the last. \r\n\r\nSince the chance of anyone winning in a round is 3/5 and they all have even chances of winning, they must each have 3/20 chance of winning in a round. The players who don’t go first, however, have a chance that they may not get to take their turns at all. So, the players who don’t go first actually have a better chance to win during their turns, provided that their turns come. \r\n\r\nYou divide the chance of winning by the chance of getting a turn, and you get the chance of winning during the turn. \r\n','2004-01-27',20040203221611,NULL,2,3,0,3.00,20040127130121,0);
INSERT INTO problem VALUES (1888,13,0,3386,'Musical Munchies','Fill in the missing numbers in the sequence.\r\n \r\n5, 3, 8, 2, 2, ?, 1, 2, 6, ?, 7, ?','This sequence involves musical solfeggio notes (DO, RE, MI, FA, SOL,...). First group everything into groups of 2. The first number signifies solfeggio notes from 1 to 8(1= DO, 2= RE, 3= MI, 4= FA, ... 8= DO). The second number signifies the number of letters in the standard way of writing the solfeggio note. Thus, for the first pair (5,3) 5= SOL, and SOL has 3 letters. Thus, all the unknowns are the number 2.','2004-01-01',20040324232101,NULL,2,3,27,0.00,00000000000000,459);
INSERT INTO problem VALUES (673,4,2,1301,'The Flooble Code','A book titled The Bible Code introduced the topic of equidistant letter sequences (ELS), described below, for finding words “hidden” in text. That book referenced the Hebrew Bible, but prompts a question about finding any given word in any, say, English-language text.\r\n \r\nFor simplicity, and to better match the Hebrew, spaces and punctuation are removed. A particular text that I have in mind, thus crunched, has 284,939 characters remaining (letters and digits). How many times would you expect to find the word FLOOBLE as an equidistant letter sequence in the text? Ignore case. The word can start at any of the 284,939 characters and proceed by skipping any constant number of letters forward or backward. So, for example, if the 11,000th character were an F and the 10,000th an L, and the 9,000th an O, etc. that would be one occurrence. Of course we don’t expect always to find such decimally round spacings. The question again, How many do we expect to find?\r\n \r\nThe absolute and relative frequencies of the relevant letters in the text are:\r\n \r\nThe occurrences are (the letters of FLOOBLE capitalized): \r\n1. Exactly one of these ten statements is false. \r\n \r\n2. Exactly two of these ten statements are false. \r\n \r\n3. Exactly three of these ten statements are false. \r\n \r\n4. Exactly four of these ten statements are false. \r\n \r\n5. Exactly five of these ten statements are false. \r\n \r\n6. Exactly six of these ten statements are false. \r\n \r\n7. Exactly seven of these ten statements are false. \r\n \r\n8. Exactly eight of these ten statements are false. \r\n \r\n9. Exactly nine of these ten statements are false. \r\n \r\n10. Exactly ten of these ten statements are false. \r\n \r\nWhich of the above statements will be true and which of them will be false, if you remove the word \'Exactly\' from all the statements ? \r\n','If all 10 are false then this is exactly what the 10th asserts. But if it\'s true, we get a contradiction since then not all 10 are false. Hence, at least one is indeed false. On the other hand, no two of the statements may be true simultaneously; for they make contradictory assertions. Therefore, exactly one of them is true while the remaining nine are false. This is what is claimed by the ninth statement. This is true too.\r\n \r\nAnd for the second part, \"The First Five are TRUE and the Last Five are FALSE\".\r\n\r\n','2003-02-25',20030601232102,NULL,3,3,0,4.00,20030225000000,0);
INSERT INTO problem VALUES (674,14,1,979,'Three numbers','If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3, what is the largest value that x can have ?','','2003-11-17',20040116232103,NULL,3,3,0,3.00,20031117133422,0);
INSERT INTO problem VALUES (2072,20,0,2716,'Ordered letters','Can you find a number that, when written in letters, has its letters in alphabetical order?','FORTY','2004-02-19',20040324232101,NULL,2,3,22,0.00,00000000000000,429);
INSERT INTO problem VALUES (1826,5,0,3558,'3-d grid hunting','Find two regular tetrahedra that share a face placed in a way such that each vertex has integer coordinates.','Here is a visual of the tetrahedrons, where the numbers represent the vertices and their z values (depth). \r\n\r\n0∙∙∙∙ \r\n\r\nOf course, there are infinite solutions, but this is the smallest one.\r\n','2003-11-19',20040324100726,NULL,2,3,1,0.00,00000000000000,11);
INSERT INTO problem VALUES (1817,14,0,3386,'Pizza Slice','A.) You have a pizza and a pizza slicer. The pizza slicer is a little rusty, so you can only cut 10 straight lines through the pizza before the slicer breaks apart. \r\nAt most how many slices from 1 pizza can you get if you cut through the pizza all 10 times? \r\nB.) Do the question from Part A, but now the pizza slicer can now slice through 100 times before breaking apart. \r\nC.) How many slices can be made if you cut n straight cuts through the pizza? \r\n(Note for all questions: A slice does not have to be in equal size. In addition, when you cut through the pizza, it goes from one point on the circle to another point, to create a \"chord.\")','A.) 56 \r\nB.) 50051 \r\nC.) 0.5 (n^2 + n + 2) or equivalent.','2003-11-19',20040324232101,NULL,1,3,16,0.00,00000000000000,366);
INSERT INTO problem VALUES (441,6,2,979,'Flowers','How many flowers do I have if all of them are roses except two, all of them are tulips except two, and all of them are daisies except two? ','There are two possible solutions: \r\n \r\n\"But now the two digits in my age, both prime, are the reverse of the two in your Dad\'s age\". \r\n \r\nHow old is Grandma?','Grandma was 72 years old.\r\n \r\nHow old were Albert and Bertrand the last time they met? ','Albert and Bertrand were 2 and 5 years old repectively the last time they met.\r\n \r\nTry to use common short words. There\'s at least one solution with a total of 93 letters.','One solution, with 93 letters total is: \r\nComputer programming skills are useful in solving this puzzle. Word lists of a couple hundred thousand words are available such as at: \r\nHowever, you need to go to http://www.puzzlers.org/secure/wordlists/dictinfo.php and click on the appropriate word list, then save the file to your own computer or server to use them. \r\n\r\n \r\nA good way is to form thirteen two-dimensional arrays of words (one for each of the anagrammed words) with the two indices representing the first and last letters, but in alphabetical order rather than as specifically first or last, so that enough and heroine would both be filed in the same slot, so only a triangle of the matrix would be populated. Present each of these arrays as the number of letters in the smallest word fitting the category, then manually go through these 13 arrays looking to complete an alphabetic set, taking into consideration the rarity of letter pairs and sparsity of some of the arrays. That is, start with the most sparsely populate array so you\'re not later forced to look for an array position there that is not populated, but also look for fortuitous Q\'s, X\'s, etc. \r\nAs a final step you could then program something to swap letters among the different anagrammed numbers to see if lower letter counts could be gotten by such swaps.','2003-03-19',20030817232102,NULL,5,3,0,3.25,20030319000000,0);
INSERT INTO problem VALUES (445,6,2,979,'Time For Breakfast','A, B and C just finished their breakfast. One of the boys had apples, another bananas and the third, grapes. If only one of the following four statements is true, who had what for breakfast?\r\n \r\nC had bananas. \r\n \r\nC did not have grapes. \r\n \r\nB did not have grapes. \r\n \r\nB did not have apples. \r\n','If we assume the first statement to be true, then we see that the second statement is also true. So, obviously the first statement is false implying C did not have bananas. Therefore, either A had bananas or B.\r\n \r\nLeast Significant Non-Zero Digit of n!\r\nLet p(k) be the least significant non-zero decimal digit of k! The\r\nfirst several values of this sequence are\r\n 2,6,4,2,2,4,2,8,8,8,6,8,2,8,8,6,8,2,4,4,8,4,6,4,4,8,4,6,8,... \r\n \r\nCan we directly determine the kth term for any given k? Also, what\r\nis the asymptotic distribution of the digits? To answer these\r\nquestions, let L(k) denote the least significant non-zero decimal \r\ndigit of the integer k. Writing n! in the form\r\n \r\n n! = (2^a2)(5^a5)(3^a3)(7^a7)...\r\n \r\nwe can let (n!)\' denote this same number divided by its highest\r\npower of 10, i.e.,\r\n \r\nLikewise, the least significant digits of the sequence p^k, k=1,2,..\r\nfor every odd prime ending with the digit 3 or 7 has a period of four,\r\nwhile those ending with 9 have a period of two, and those ending with\r\n1 have a period of one. Thus, all these periods are divisors of four.\r\nOf course, the least significant digits of 2^k also have a period of\r\nfour, i.e., {2,4,8,6}.\r\n \r\nAlso, as we multiply successive integers to generate n!, we always\r\nhave more powers of 2 than of 5, so the value of L(n!) is easily\r\ncomputed recursively as L(L(n)L((n-1)!)) unless n is a multiple of \r\n5, in which case we need more information. As a result, the values \r\nof L(n!) come in fixed strings of five, as shown below\r\n \r\nFrom the above tabulations we can extract the essential patterns \r\nfor L((5^k n)!)\r\n \r\nTo illustrate, consider the case of the decimal number n=1592. In\r\nthe base 5 this is n=22332. Now we enter the above table at row \r\nk=4=0 (mod 4) in the block beginning with 0, which is 06264. The\r\nleading digit of n (in the base 5) is 2, so we check the digit in\r\nposition 2 of this block to give L((2*5^4)!) = 2. Then we enter \r\nthe table at row k=3 (mod 4) in the block beginning with 2, which\r\nis 26648, to find L((2*5^4 + 2*5^3)!) = 6.\r\n \r\nThen in the row k=2 (mod 4), the block beginning with 6 is 64244, \r\nand we find L((2*5^4 + 2*5^3 + 3*5^2)!) = 4. From this we know we\'re\r\nin the block 48226 in row k=1 (mod 4), so we have L((2*5^4 + 2*5^3 + \r\n3*5^2 + 3*5)!) = 2. Finally, we enter the row k=0 (mod 4) in block \r\n22428 to find the result\r\n \r\nThis process essentially acts as a kind of \"filter\", taking consecutive\r\ndigits from the set {0,1,2} and outputing digits from the set {1,2},\r\njust as the decimal algorithm takes a stream of digits from the set\r\n{0,1,...,9} and outputs a stream of digits from the set {2,4,6,8}.\r\nFor the base-3 filter, a continuous stream of \"0\" input digits will\r\nleave the output unchanged, i.e., it will retain the previous output\r\nvalue. On the other hand, a continuous stream of \"2\" input digits\r\nwill cause the output to oscillate between 1 and 2 on each step. A\r\ncontinuous stream of \"1\" input digits will act like \"0\" when the\r\nparity is even, and will act like \"1\" when parity is odd, with the\r\nresult being that the output will change state on the odd steps.\r\n','2003-12-21',20040104121146,NULL,4,3,0,2.67,20031221095348,0);
INSERT INTO problem VALUES (1256,12,2,2341,'Road Signs','One afternoon, a retired air force pilot and his family were driving through Texas on a vacation. They pass a road sign. One of the children remarks on the fact that the sign is named after a newspaper comic. \r\n \r\nAfter about five minutes, they pass another sign, which reads, \"Golf Road\". As soon as they pass it, the man turns to his wife and says he knows what the next sign will say, and that he\'ll bet her twenty dollars that he\'s right. She agrees, and they drive on. After passing the next road sign, the wife finds that her husband is right, and hands him twenty dollars.\r\n \r\nWhat did the last sign say and how did the man know?','The key was that he was a retired air force pilot.\r\n \r\nThe military, and other organizations, use words to represent letters when talking via radio, etc, to avoid confusion of the many similar sounding letters.\r\n \r\nThe international standard for this is the NATO alphabet:\r\n \r\nAlpha Bravo Charlie Delta Echo Foxtrot Golf Hotel India \r\nJuliet Kilo Lima Mike November Oscar Papa Quebec Romeo \r\nSierra Tango Uniform Victor Whiskey Xray Yankee Zulu\r\n \r\nThe one for F is Foxtrot, which is the name of a comic in the paper. Golf is for G. The one for H is hotel, so, seeing the pattern of Foxtrot and Golf, he correctly guessed Hotel Road.','2003-08-27',20040223232101,NULL,4,3,0,3.10,20030827073252,0);
INSERT INTO problem VALUES (1266,13,2,1626,'Sequence Group','I didn\'t come up with this problem, but I still think it\'s a good one. \r\nThe number plate showed the bus number as a perfect square and also if the plate was turned upside down, the number would still be a perfect square. I came to know from the bus company they had only five hundred buses numbered from 1 to 500.\r\nFrom this I was able to deduce the number. \r\n \r\nCan you find out the bus number and the other one, too ?','The only numbers that can be turned upside down and still be read as a number are 0,1,6,8 and 9.The numbers 0,1 and 8 remain remain the same when turned over, but 6 becomes 9 and 9 becomes 6.Therefore the possible numbers on the bus were 9,16,81,100,169 or 196. However the number 196 is the only number which becomes a perfect square when turned over (as 961 is the square of 31). \r\n \r\nJust to give an incentive to Harry to deliver the glasses intact I offered him 30 paise for every glass delivered safely and threatened to forefeit 90 paise for every glass he broke. On settlement, Harry received 24 Rupees from me.\r\n \r\nHow many glasses did Harry break ?\r\n \r\n( Given: 1 Rupee = 100 Paise )','Let us assume that \'G\' is the number of glasses delivered intact and \'B\' be the number of glasses broken. Then, the amount earned = 30G paise and the amount forfeited = 90B. \r\n \r\n\"Please give me some 2 rupees stamps, six times as many one rupee stamps, and for the rest of the amount make up some 5 rupee \r\nstamps.\"\r\n \r\nCharles thought for a few moments and finally she handed over the exact fulfilment of the order to the man. \r\nHow did he do it and how many stamps of each type did he give to the man ?','Let \'x\' be the number of 2 Rupees stamps (obviously the number of 1 Rupee stamps is then equal to \'6x\') and \'y\' be the number of 5 Rupee stamps. \r\n \r\nEach of the 8 dealers bought the same number of animals and paid at the rate of Rupees 17 for each cow, Rupees 2 for each sheep and Rupees 2 for each pig. My friend received from the dealer in total Rupees 285.\r\n \r\nHow many animals in all did he have and how many of each kind ?\r\n \r\n(Given: 1 Rupee = 100 Paise)','We know that there were five droves with an equal number of animals in each drove and therefore the number must be divisible by 5. As every dealer bought the same number of animals, the number must also be divisible by 8. Hence the number must be a multiple of 40.\r\n \r\nWhat are the numbers ?','Let the numbers be chosen as (n-1), n and (n+1). \r\n \r\nHow many steps do they have to take before they are both stepping out on the right foot together ?','They will never step out with their right feet together.','2003-03-07',20040106232105,NULL,3,3,0,2.75,20030307000000,0);
INSERT INTO problem VALUES (453,14,2,979,'What is the Number ?','Which is the number that, multiplied by 3, then increased by three-fourths of the product, divided by 7, diminished by one-third of the quotient, multiplied by itself, diminished by 52, the square root found, addition of 8, division by 10, gives the number 2 ?\r\n ','The number is 28.\r\n If you were to close your eyes and pick them at random, how many marbles must you take out to be sure that there are at least two of one color among the marbles picked out ?','Suppose you draw three marbles from the box, then there is a possibility that all three are of different colors (though it is always possible that the first two drawn are of the same color, but here we are to find the number of balls to be drawn such that we are sure that at least two among them are of the same color).\r\n \r\nNow, if you draw a fourth marble from the box, then it has to be one of a \'Green\', a \'Yellow\' or a \'Blue\' marble, which implies that now we are sure to have at least two marbles of the same color.\r\n \r\nTherefore, the answer is: Four marbles.','2003-03-14',20040108232102,NULL,1,3,0,1.33,20030314000000,0);
INSERT INTO problem VALUES (456,14,2,979,'Charity or Party?','A number of us went out together to a charity fete one day. Our party consisted of four different professional groups, namely – 25 writers, 20 doctors, 18 dentists and 12 bank employees. We spent altogether Rs. 1330.\r\n \r\nLater it was found that 5 writers spent as much as 4 doctors, that 12 doctors spent as much as 9 dentists and that 6 dentists spent as much as 8 bank employees.\r\n \r\n[Or, in other words: \"A Writer spent (4/5) times the amount spent by a Doctor, a Doctor spent (3/4) times the amount spent by a Dentist and a Dentist spent (4/3) times the amount spent by a Bank Employee].\r\n \r\nHow much did each of the four professional groups spend ?','Given, 5 Writers spent as much as 4 Doctors, 12 Doctors spent as much as 9 Dentists and 6 Dentists spent as much as 8 Bank Employees.\r\n \r\nThus, we have the following conclusion: The Writers spent Rupees 350, the Doctors also spent Rupees 350, the Dentists spent Rupees 420 and the Bank Employees spent Rupees 210. Thus they spent altogether Rupees 1330.\r\n\r\n\r\n','2003-03-23',20040109232104,NULL,3,3,0,1.83,20030323000000,0);
INSERT INTO problem VALUES (457,14,2,979,'Rupees and Paise','I entered a store and spent one-half of the money that was in my wallet. When I came out I found that I had just as many paise as I had rupees and half as many rupees as I had paise when I went in.\r\n \r\nHow much money did I have with me when I entered the store ? \r\n \r\n( Given: 1 Rupee = 100 Paise ).','I had entered the store I must have had with me 99 Rupees and 98 Paise. \r\n \r\nWhen I spent exactly half the amount I initially had, I had left with me 49 Rupees and 99 Paise, which clearly shows that when I came out of the store, I had as may Paise as I had Rupees and half as many Rupees as I had Paise when I entered the store.\r\n\r\n\r\n\r\n','2003-03-16',20030625232103,NULL,3,3,0,4.00,20030316000000,0);
INSERT INTO problem VALUES (458,13,2,1373,'Number Alert','Two numbers are missing in this pattern:\r\n \r\n2, 4, 11, 37, 153, ??, ???\r\n \r\nWhat are they? ','617 and 3091 because you take the first # and multiply it by 1 and add 2 to the #. Then you multiply the # by 2 and add 3. Then you continue on in that order intil you reach the number.','2003-02-27',20030907232101,NULL,2,3,0,2.17,20030227000000,0);
INSERT INTO problem VALUES (460,8,2,1301,'Non-Attacking Chess Pieces','Arrange all 8 chess pieces of one set (no pawns) on a 5x6 board so no piece attacks another. Never mind that they\'re all the same color--it\'s \"friendly fire\". Be sure that the two bishops are on opposite-colored squares. There are 6 ways, not counting reflections and rotations. \r\n ','Caps and + are black squares. lower case and space are white squares. (h or H stands for knight (horse)).\r\n ','Method 1: The distribution is the binomial distribution for 2,000,000 trials with p=1/2. We want the random variable to have the value 1,000,000. This occurs with probability C(2000000,1000000)/2^2000000, where C(n,r) is the combinations of n things taken r at a time. The numbers involved are too large to compute directly, but we can use logarithms and the definition of C(n,r). As C(n,r) = n!/(r! (n-r)!), and an approximation for ln(x!) that is excellent for large values of x is: \r\nAlan says:\r\n \r\nGiven that no two people told the truth the same number of times, which statements were true and which were false?\r\nGot this puzzle from graylabyrinth.com.','Frank always tells the truth and Eric always lies. Bob lied once (#4); David twice (3,4); Alan three times (2,3,5) and Chuck four times (only #3 was true). ','2003-03-03',20031123232104,NULL,4,3,0,3.25,20030303000000,0);
INSERT INTO problem VALUES (463,4,2,885,'Duel',' One day your rival invites you out to an old fashion duel. The rules are as follows:\r\n Clearly, whoever shoots first has a distinct advantage. So your friends suggests flipping a coin for it. Little did you know that your rival uses a coin rigged in such a way that the probability of getting heads is only 1/3.\r\n\r\n If you chose heads, what is the probability of you winning the duel?',' The first thing to do is to calculate the probability of winning if you shoot first.\r\n The probability of you winning if you shoot first is the sum of all P(n)\'s, which forms an infinite geometric series, assuming you guys can shoot forever, with the first term a=1/2 and the ratio r=1/4. Using the formula for the sum of this infinite geometric series (which converges), S=a/(1-r), you\'d end up with a probability of 2/3. And consequently, the probability of winning for the person shooting second is 1/3.\r\n\r\n Next there are two cases to consider, one where the coin lands heads and other tails.\r\n Now, if you were to choose tails, your probability of winning would be 5/9.','2003-03-06',20030907232101,NULL,3,3,0,3.60,20030306000000,0);
INSERT INTO problem VALUES (469,2,2,979,'Around The World','While walking in a park, one morning, I found a Hundred Rupee note on one of the park benches. I picked it up, noted the number and took it home.\r\n \r\nIn the afternoon the plumber called on me to collect his bill. As I had no other moey at home, I settled his account with the Hundred Rupee note that I had found.\r\n \r\nLater I came to know that the plumber paid the note to his milkman to settle his monthly account , who paid it to his tailor for the garments he had made.\r\n \r\nThe tailor in turn used the money to buy an old sewing machine, from a woman who lives in my neighbourhood. This woman incidentally, had borrowed Hundred Rupees from me sometime back to buy some household appliance. She, remembering that she owed me a Hundred Rupees, came and paid the debt.\r\n \r\nI recognized the note as the one that I had found on the park bench, and on careful examination, I discovered that the note was counterfeit. \r\n \r\nHow much was lost in the whole transaction and by whom ?','Nothing was lost or gained. The person who found the note settled his plumber\'s account using that note, the plumber paid the note to his milkman to settle his monthly account , who paid it to his tailor for the garments he had made and the tailor in turn used the money to buy an old sewing machine, from a woman who lives in the neighbourhood of the person who found the note. Now the woman owed the author a Hundred Rupees and she came and paid the debt using the same note, thus forming a complete circlewith the note returning back to the person who found it. \r\n \r\nAnother possible reasoning that we can give for the problem regarding the gains and losses after all the transactions are over is: \r\n \r\nA person who has no prior knowledge of which numbers appear on the slips - but who does know that there are \'N\' slips - is to blindly pull slips from the box one by one. The person looks at each slip, then either agrees to accept that number (of Rupees) and quit or decides to go on and choose another slip.\r\n \r\nNote that the person looks at each slip as he/she proceeds, and then decides whether to quit or to go on. That person can go forward, but cannot go back. If no choice is made by the time the \'N\'th slip is reached, then the person must accept the number (of Rupees) on the \'N\'th slip.\r\n \r\nDoes there \" EXIST \" a \'Best Strategy\' for the person ? If \" YES \", then what is that strategy ? (Here the term \" Best Strategy\" means that the person will get the greatest amount of Rupees).','Let us fix a value ‘k’, where k lies between 0 (inclusive) and N and consider the strategy that rejects the first k slips and then accepts the slip thereafter that has a number greater than the maximum among the ones observed on each of the first k slips that have been rejected. Let W be the event that the slip with the highest number is chosen and the person wins when this strategy is employed. Also, for i = 1,2,….,N, let B(i) be the event that the slip with the highest number is in position ‘i’. Exactly one of the events B(i), i = 1,2,….,N, must occur and so, upon conditioning on which event does occur, we obtain: \r\n \r\nP(W) = [Summation from i = 1,2,….,N] P{W | B(i)}P{B(i)} \r\n \r\nor, P(W) = (1/N)[Summation from i = 1,2,….,N] P{W | B(i)}\r\n \r\nThe final equality follows because the slip with the highest number is equally likely to be in any of the N positions and so, P{B(i)} = 1/N, for all i. Now since we are employing the strategy of rejecting the first k slips, it follows that there is no chance of obtaining the slip with the highest number if it is among the first k. \r\n \r\nConsequently, P{W | B(i)} = 0, if i is less than or equal to k.\r\n \r\nOn the other hand, if the slip with the highest number is in position i, where i is greater than k, then this slip will be selected if the highest number on the first (i – 1) slips is among the first k. \r\n \r\nHowever, conditional on the slip with the highest number being in position i, it is easy to see that all possible orderings of the other slips remain equally likely, which implies that each of the first (i – 1) slips is equally likely to be the one with the highest number on them. \r\n \r\nHence we obtain that: P{W | B(i)} = {k/(i – 1)}, if i is greater than k.\r\n \r\nFrom the previous results we have: \r\n \r\nP(W) = (k/N)[{Summation from i = (k+1),(k+2),….,N}1/(i – 1)]\r\n \r\nor, P(W) = (k/N)[{Summation from j = k,(k+1),(k+2),….,(N – 1)} (1/j)]\r\n \r\nNow, if we select (k/N) to be equal to (1/e), where e = 2.718281828459045 \r\n(approximately), then we have P(W) = 1/e\r\n \r\nThat is, the strategy that lets approximately the fraction (1/e) of all the slips go by and then accept the first one thereafter that is the greater than the maximum number yet observed (among the first k slips that have been rejected) has probability equal to (1/e) which is approximately equal to 0.37 of obtaining the slip with the highest number. \r\n \r\nSo, the best strategy is to reject the first k (= N/e) slips and then accept the slip thereafter which will bear the number greater than the maximum number observed in the first k slips rejected. ','2003-03-18',20040111232101,NULL,5,3,0,3.71,20030318000000,0);
INSERT INTO problem VALUES (472,17,2,1183,'Water level','I’m sitting in a boat in a pool. In the boat with me is a cannonball. What happens to the level of the pool if I take the cannonball out of the boat and drop it into the pool? Does the level increase, decrease or stay the same?\r\n ','The level drops.\r\n \r\nWhen the cannonball is in the water it is displacing a volume of water equivalent to the volume of the cannonball.\r\n \r\nWhen the cannonball is in the boat the volume of water displaced is related to the mass of the cannonball. Since the cannonball has a greater density than the water, then the volume of water displaced is greater than the volume of the cannonball.\r\n \r\nTherefore more water is displaced when the cannonball is in the boat than when it is in the water.\r\n\r\nFor a more scientific answer (with formulae!) see friedlinguini\'s first posting.\r\n','2003-03-10',20040309232103,NULL,2,3,0,4.00,20030310000000,0);
INSERT INTO problem VALUES (474,20,2,1437,'Four words','What are the only 4 words in the English language that end in \"dous\"?\r\n ','They are:\r\n \r\n(Plus some others that our users thought of/looked up)','2003-03-05',20030704232102,NULL,2,3,0,2.60,20030305000000,0);
INSERT INTO problem VALUES (696,2,2,1072,'Calendar Cubes pt 3','In the problem Calendar cubes you figured out the maximum amount of days you could fit on two cubes by putting numbers on both cubes and using the faces of the cubes to combine and make more numbers. To represent months you may use Next we see how many days can be represented. once again combination 12 could represent 1,2 and 12. On top of that depending how you write these numbers a 21 can also be represented. Follow that two up with a 3 and you\'ve got 3 and 23 represented. Then follow that up with a 0 to create two more numbers (since it is now in a ring). This makes 30 and 10(upside down 1 and 0). Next we use a number 6 on one face to represent 6 and 9. Lastly any other number on the last face except 5. This gives us 10 digits(excluding 30 since not all months have it.) 8x10=80, Now we add 9 because only 9 of the months on the cube have 30 days.(this is why we needed september and december) Thus, giving us a grand total of 89 days. But one more day can be represented using the zero on the number cube and the s(for september) on the other cube we can make the zero the letter O for october and the S of september as a 5, thus giving us one more day. \r\n \r\nMaking the grand total 90 days.','2003-04-06',20040225103947,NULL,4,3,0,2.50,20030406045802,0);
INSERT INTO problem VALUES (478,17,2,1301,'Earth\'s Momentum','The earth\'s rotation rate is slowing down because of friction against the tidal bulges caused by the gravitation of the moon (major factor) and the sun (lesser factor). The earth\'s rotational energy is dissipated as heat, but where is the angular momentum going, and what physical mechanism brings that momentum there?\r\n ','The angular momentum is being transferred to the moon\'s revolution about the earth, bringing it to a higher orbit (the distance more than compensates for the slower speed of higher orbits). The mechanism is that the friction of the earth\'s rotation on the tidal bulges pushes those bulges out ahead of being directly beneath the moon. Those bulges pull on the moon with the same force that the moon is pulling on them. Specifically, the leading one has greater pull than the one on the opposite side of the earth, and gives a tug on the moon in the same direction as it is travelling, nudging it into a higher orbit, which paradoxically is slower, but is the same direction as if the moon had a rocket pushing out it\'s trailing side.','2003-03-12',20031224232100,NULL,3,3,0,3.00,20030312000000,0);
INSERT INTO problem VALUES (480,2,2,1299,'Hats off','Three convicts A,B and C were about to be executed. When they begged for a last chance, the hangman decided to let them battle it out with their wits.\r\n \r\nThe man in the center {B}, must have realised that and realises that the man in front of him C has a hat of a colour different from his own i.e. if the person in front C has a white coloured hat, then his own is black and vice versa.\r\n','2003-03-11',20030630232102,NULL,2,3,0,3.25,20030311000000,0);
INSERT INTO problem VALUES (738,20,2,1567,'Who Ordered the Pi?','What is the next number in this sequence? 1, 4, 9, 16, 25, pi The sequence is not arbitrary. Create a mathematical function that generates this sequence.','Like most questions (in life, as in Flooble-space), there is more than one possible answer. One solution is to define the nth term of this sequence as\r\n \r\nn^2 + (pi-36)(n-1)(n-2)(n-3)(n-4)(n-5)/5!\r\n \r\nFor n=1 to 5, the second term equals zero. 36 + (pi-36)6!/5! = 6*pi - 180','2003-04-21',20040324144953,NULL,4,3,0,2.50,20030421015726,0);
INSERT INTO problem VALUES (482,12,2,979,'Inside Out','You throw away the outside and cook the inside. Then you eat the outside and throw away the inside.\r\n \r\nWhat did you eat? ','Corn on the cob.','2003-03-21',20040307232104,NULL,3,3,0,2.43,20030321000000,0);
INSERT INTO problem VALUES (483,2,2,979,'Monkeys and Coconuts','Five men were stuck in a desert island. The island was plentifully supplied with coconuts, fortunately, and they spent the first day gathering the coconuts, heaping them in a great pile. \r\n \r\nThat night, one of the men was sleepless at the thought that everyone would fight over the coconuts at daybreak. So he arose, crept to the pile, and counted out the coconuts. Except for one coconut, it was possible to divide the pile into five equal portions. He gave the extra coconut to the monkey (who was the only other living being on the island besides those five men), buried his share of the coconuts, then went back to a sound sleep leaving the rest again in a pile. \r\n \r\nThen another man got up and stole to the pile with the same object in mind. Again there was one coconut left over. The second man gave the spare coconut to the monkey, buried (what he thought was) his fair share, and went back to sleep, again leaving the remaining coconuts in one pile. \r\n \r\nOne by one, the remaining men got up and did the same and everytime the monkey got his share of one coconut. \r\n \r\nIn the morning, the men divided whatever coconuts remained into five equal piles, each taking his share and saying nothing about the night just past.\r\n \r\nWhat is the minimum number of coconuts the five men assembled on the first day, if in the Final Division: \r\n \r\n(a)There was again one coconut left over and the men (as usual) gave it to the monkey. \r\n \r\n(b) There was no coconut left over for the monkey. \r\n\r\n','Let initially there be ‘x’ coconuts in the pile. \r\n \r\nNow, for the first part of the problem, the number of coconuts remaining (after the fifth man finished dealing with the pile) is one more than a multiple of 5, i.e., (a) 5y + 1 (say) whereas for the second part, i.e., (b) the number of coconuts remaining is an exact multiple of 5, i.e., 5y (say) where ‘y’ is the number of coconuts each man receives in the final division. \r\n \r\n1024x - 15625y = 11529 for (a) and \r\n \r\nFrom these equations, we obtain:\r\nx (minimum) = 15621 for (a) and \r\n \r\nThus the number of coconuts left after each of the men finished dealing with the pile are: \r\n \r\n10, 40, 90, 61, 52, 63, 94, ? , ?\r\n \r\n(Explain how you arrived at your result).\r\n','The next two numbers of the given sequence are: 46 and 18.\r\n \r\nHere are the numbers in the given sequence :10, 40, 90, 61, 52, 63, 94, which are nothing but the whole squares of the first seven natural numbers written with the positions of their digits (Units and Tens Place) interchanged.\r\n \r\nSo, obviously the next two numbers have to be the squares of 8 and 9, written in a simlar fashion.\r\n \r\nTherefore the required numbers are: 46 and 18.\r\n ','2003-03-25',20040111232101,NULL,4,3,0,2.67,20030325000000,0);
INSERT INTO problem VALUES (486,4,2,979,'Happy Birthday','Find the least positive integer \'N\' so that, in a room containing \'N\' people, the odds that two of the people have the same birthday (not the year, just the day) are more than 50%.\r\n \r\n[Note: Forget about Leap Year. Assume that a year has 365 days and that people are born randomly throughout the year].\r\n','We fix ‘N’ and determine the probability that no two people, in a room of N people, have the same birthday. Say that the people are P(1),P(2),….,P(N). Now person P(1) may have any of the 365 days of the year for his birthday without contradicting the condition that no two people in the room will have the same birthday. Once person P(1) has fixed a birthday, then person P(2) is not allowed to have that birthday if we are to maintain distinct birthdays. Thus person P(2) has 364 choices for his/her birthday, then person P(3) has 363 choices for his/her birthday, and so it goes,(if we are to maintain distinct birthdays).\r\n \r\nIn summary, the total number of birthday combinations for ‘N’ people, with no two being the same, is: (365)(364)(363)……..[{365 – (N – 1)}]\r\n \r\nThe total number of all possible birthday distributions among ‘N’ people, without regard for duplication or lack of duplication, is: (365)(365)(365)……..(365) (‘N’ times)\r\n \r\nTherefore, the probability that N people in a room will all have distinct birthdays is:\r\n \r\nWe now start multiplying the fractions together. When the product falls below ½, we are finished. The last fraction that we multiplied in will tell us what ‘N’ should be [because the last fraction you multiplied in was [{365 – (N – 1)}/365].\r\n \r\nWe multiply together 23 terms to obtain a probability of 0.4927027. Using only 22 terms yields a probability of 0.5243046. Clearly the least value of ‘N’ to yield a probability of less than 1/2 that each person in the room will have a distinct birthday is N = 23.\r\n \r\nTherefore, we conclude that if there are 23 people in a room then the odds are better than even (in fact the odds are P=1-0.4927027=0.5072973) that two of them will have the same birthday.','2003-03-27',20030404104733,NULL,3,3,0,3.67,20030327073850,0);
INSERT INTO problem VALUES (805,13,2,1301,'Next in Line','What\'s the number that follows in this sequence, and what is the sequence\'s significance?\r\n \r\n0,1,2,9,44,265,...','The next number is 1854, and after that comes 14833. \r\nNumerically the number in position n is n times the sum of the two preceding terms. \r\nThe meaning of the sequence is the number of derangements of n objects. That is, each is the number of ways n objects can be rearranged so that none is in its right position, as in the case of mismatched labels. If you have one can and one label there are zero ways to mismatch them. If there are two cans and two labels there is only one way to mismatch them. With three cans and three labels there are two ways of mismatching them all. With four cans and four labels there are nine ways of mismatching them all, etc.','2003-05-12',20030703232103,NULL,3,3,0,2.60,20030512075701,0);
INSERT INTO problem VALUES (807,7,2,1767,'Tetra-productial numbers','Show that there are infinitely many integers n such that:\r\n \r\n1) All digits of n in base 10 are strictly greater than 1.\r\n ','Brian\'s solution is very elegant. You can find it here.','2003-05-13',20040225103933,NULL,3,3,0,2.00,20030513070946,0);
INSERT INTO problem VALUES (808,16,2,1767,'Regular Pentagon (Classic)','Show, how given a distance r, one can construct a regular pentagon, whose circumradius is r, using only ruler and compass...\r\n ','Charlie offers his solution here.\r\n ','2003-05-15',20040225103933,NULL,5,3,0,2.50,20030515092248,0);
INSERT INTO problem VALUES (809,7,2,1767,'10001, 100010001, ....','Consider the following sequence:\r\n \r\nShow that at every moment, there were 2 people at the party who had shaken hands the same number of times.','Trevor Leitch\'s solution is very clear. It\'s found here.','2003-05-22',20040225103933,NULL,3,3,0,2.75,20030522014853,0);
INSERT INTO problem VALUES (811,7,2,1767,'Ascending numbers!','Let\'s call n an ascending number, if it has the following 2 properties:\r\n \r\nHow many ascending numbers are there?','I like Charlie\'s solution!','2003-05-25',20040225103933,NULL,3,3,0,4.00,20030525050044,0);
INSERT INTO problem VALUES (813,11,2,1707,'Many coins - one fake','Given a balance scale that is sure to break after X weighings, find an equation for the largest number of coins N, from which you can determine a fake coin that has the wrong weight if\r\n \r\nA: You know whether the fake is lighter or heavier\r\n \r\nB: You do not know whether the fake is lighter or heavier\r\n \r\n(Assume only one of the N coins is fake)','Pleasance offers solutions here and expands on the second part here.\r\n \r\nAlso of interest is this post by Sanjay','2003-05-14',20040225103933,NULL,5,3,0,4.00,20030514083051,0);
INSERT INTO problem VALUES (488,12,2,979,'Yes Sir!','Sir, I bear a rhyme excelling,\r\n \r\nIn mystic force and magic spelling.\r\n \r\nCelestial sprites elucidate,\r\n \r\nAll my own striving can\'t relate.\r\n \r\nWhat Am I ?\r\n','The number \"PI\", the digits of which are illustrated by the length of each word in the riddle. ','2003-03-31',20040106232105,NULL,5,3,0,3.73,20030331014000,0);
INSERT INTO problem VALUES (489,7,2,979,'Father And Grandfather','Both my Father and my Father\'s Grandfather were born in years that can be expressed as [(m)^n - (n)^m], where \'m\' and \'n\' are both positive integers. In which years were they born ?\r\n \r\n(Note: (a)^b implies: \'a\' raised to the power of \'b\', or \'a\' multiplies \'b\' number of times).','My Father was born in the year 1927 which can be expressed as: \r\n \r\n[(2)^(11) - (11)^(2)] (= 2048 - 121) and my Father\'s Grandfather was born in the year 1844 which can be expressed as: [(3)^(7) - (7)^(3)] (= 2187 - 343).','2003-04-02',20030808232102,NULL,4,3,0,4.00,20030402014335,0);
INSERT INTO problem VALUES (490,14,2,979,'Perfect Squares','Show that the numbers of the form: \r\n \r\n444444....4444888888....8889\r\n \r\n[Where there are \'k\' Fours, \'(k-1)\' Eights and \'Exactly One\' 9],\r\n \r\nare always perfect squares.\r\n \r\n(For example the sequence of numbers: 49, 4489, 444889, ....etc. and so on are always perfect squares).','Let the given number be 444444……4444888888……8889, where the digit 4 appears ‘k’ times, the digit 8 appears ‘(k – 1)’ times and the digit 9 appears exactly once (and always in the unit’s place). \r\n \r\nLet N(k) = 444444……4444888888……8889, where the digit 4 appears ‘k’ times, the digit 8 appears ‘(k – 1)’ times and the digit 9 appears exactly once.\r\n \r\nN(k) – 1 = 444444……4444888888……8888, where both the digits 4 and 8 now appear ‘k’ times.\r\n \r\nTherefore, it is clear that {N(k) – 1} is divisible by the number 111111……1111, where there are ‘k’ 1’s and the quotient thus obtained will be 4000000……0008, where there is exactly one 4 (the leftmost digit) and exactly one 8 (the rightmost digit) separated by ‘(k – 1)’ zeros (0’s) in between. \r\n \r\nAlso, we can see that the numbers 408, 4008, 40008, 400008, ……and similar numbers with exactly one 4 (the leftmost digit) and exactly one 8 (the rightmost digit) separated by any number of zeros (0’s) in between is an exact multiple of 6, giving quotients 68, 668, 6668, 66668,…… (with the same number of 6’s in the quotient as there are number of zeros in the dividend). \r\n \r\nHence, the number 4000000……0008, where there is exactly one 4 (the leftmost digit) and exactly one 8 (the rightmost digit) separated by ‘(k – 1)’ zeros (0’s) in between is also a multiple of 6, the quotient being 666666……6668, where there are ‘(k – 1)’ 6’s and one 8.\r\n \r\nSo, from the above results, the number {N(k) – 1} can be written as the product of two factors as follows:\r\n \r\n{N(k) – 1} = 444444……4444888888……8888, where both the digits 4 and 8 now appear ‘k’ times.\r\n \r\n= (666666……6666)x(666666……6668), where there are ‘(k)’ 6’s in the first factor and ‘(k – 1)’ 6’s and one 8 in the second factor.\r\n \r\nAgain, the two factors can be rewritten in the form: \r\n \r\n(666666……6667 – 1)x(666666……6667 + 1), which is of the form (A – 1)(A + 1); and A = 666666……6667, where there are ‘(k – 1)’ 6’s and ONE 7. \r\n \r\nThus, we now have the following form for N(k): \r\n \r\n{N(k) – 1} = (A – 1)(A + 1) \r\n \r\nor, N(k) – 1 = (A)^2 – 1\r\n\r\nor, N(k) = (A)^2, where A = 666666……6667, where there are ‘(k – 1)’ 6’s and ONE 7.\r\n \r\nThus proving that every number of the form 444444……4444888888……8889, [where the digit 4 appears ‘k’ times, the digit 8 appears ‘(k – 1)’ times and the digit 9 appears exactly once (and always in the unit’s place)], is always a PERFECT SQUARE.\r\n','2003-04-05',20030412041205,NULL,5,3,0,4.00,20030405045807,0);
INSERT INTO problem VALUES (491,7,2,979,'Zeros And Ones','What is the smallest integer greater than 0 that can be written entirely with zeros and ones and is evenly divisible by 225? \r\n ','The prime factorization of 225 is 5*5*3*3. So the answer will be both a factor of 25 and of 9. \r\n \r\nAll factors of 25 end in either 00, 25, 50, or 75. The only one of these composed of 0\'s and 1\'s is obviously 00, so the answer must end in 00.\r\n \r\nNow, we know that if the sum of digits of a number is divisible by 9 then the number itself is also divisible by 9. Note that this is true for 3 also. \r\n \r\nSince we are to find a series of zeros and ones which will be divisible by 9, we get the following: \r\n \r\nThe smallest number consisting of all 1\'s and divisible by 9 is thus 111,111,111. Adding the two zeros at the end results in the answer to the problem: 11,111,111,100.\r\n','2003-04-08',20040204232104,NULL,2,3,0,3.00,20030408014131,0);
INSERT INTO problem VALUES (492,6,2,979,'The Reindeers','You are given the following clues, from which you have to determine that order of the nine reindeers:\r\n \r\nComet behind Rudolph, Prancer and Cupid.\r\n \r\nDetermine the order of the nine reindeers .\r\n','Here is the explanation, showing all the steps using which I have arrived at the conclusion. Here is the order of the reindeers:\r\n \r\nComet is behind (Rudolph, Prancer and Cupid) ----------(1)\r\n \r\nHere I would like to mention that as in (1), it is given that Comet is behind (Rudolph, Prancer and Cupid), I have written the names of the three within brackets because their order is not given. So it means that the three reindeers within brackets can be in any order.\r\nSince Comet is behind Rudolph (1) and Rudolph is behind Prancer (4), we can write:\r\n \r\n(Where the direction arrows ‘ X - Y’ signifies that Y is behind X or X is in front of Y).\r\n \r\nWhich is our required order of the nine reindeers.\r\n \r\n1st: PRANCER\r\n \r\n','SOLUTION:\r\n \r\nWe know that (0)! (pronounced as Zero -Factorial), is equal to 1.\r\n \r\nSo, using four zeros, we can arrive at the result of 24 as follows: \r\n \r\n[ (0)! + (0)! + (0)! + (0)! ] !\r\n \r\nThat is, the factorial of the sum of the factorials of four zeros, each taken separately), giving 4!, which is equal to 24.\r\n','2003-04-09',20040319232102,NULL,4,3,0,1.80,20030409014933,0);
INSERT INTO problem VALUES (494,2,2,979,'Envelopes','There are three envelopes and exactly two statements are written on each of the envelopes. The statements on one of the envelopes are BOTH TRUE, the statements on the other envelope are BOTH FALSE and the remaining envelope has ONE TRUE and ONE FALSE statement. Here is what is written on the three envelopes:\r\n \r\nFirst Envelope:\r\n \r\nSecond Envelope:\r\n \r\nThird Envelope:\r\n \r\nWhich envelope contains the formula ?','Let us assume that the Formula is in Envelope 1. In that case both the statements on the First Envelope as well as on the Second Envelope are False, violating the given conditions of the problem. So the Formula is not in Envelope 1.\r\n \r\nNext assume that the Formula is in Envelope 2. In this case we see that one statement written on each of the Second and Third envelopes is True and the other is False. Again violating the given conditions of the problem. So the Formula is not in Envelope 2.\r\n \r\nFinally let us assume that the Formula is in Envelope 3. Now we see that the statement (a) on the First Envelope is True whereas statement (b) is False. Both the statements on the Second Envelope are True and both the statements written on the Third Envelope are False, thus satisfying all the conditions of the problem. \r\n \r\nHence we conclude that the Formula is in Envelope 3.','2003-04-10',20030531232102,NULL,2,3,0,2.67,20030410014032,0);
INSERT INTO problem VALUES (495,2,2,979,'The Two Logicians','Two logicians place cards on their foreheads so that what is written on the card is visible only to the other logician. Consecutive positive integers have been written on the cards. The following conversation ensues: \r\n \r\nA: \"I don\'t know my number.\" \r\n \r\nB: \"I don\'t know my number.\" \r\n \r\nA: \"I don\'t know my number.\" \r\n \r\nB: \"I don\'t know my number.\"\r\n \r\n........ n statements of ignorance later.......... \r\n \r\nA or B: \"I know my number.\" \r\n \r\nWhat is on the card and how does the logician know it? ','If A saw 1, he would know that he had 2, and would say so. Therefore, A did not see 1. A says \"I don\'t know my number.\" \r\n \r\nIf B saw 2, he would know that he had 3, since he knows that A did not see 1, so B did not see 1 or 2. B says \"I don\'t know my number.\" \r\n \r\nIf A saw 3, he would know that he had 4, since he knows that B did not see 1 or 2, so A did not see 1, 2 or 3. A says \"I don\'t know my number.\" \r\n \r\nIf B saw 4, he would know that he had 5, since he knows that A did not see 1, 2 or 3, so B did not see 1, 2, 3 or 4. B says \"I don\'t know my number.\" \r\n \r\n........ n statements of ignorance later ........ \r\nif X saw n, he would know that he had n + 1, since he knows that ~X did not see 1 ... n - 1, so X did see n. X says \"I know my number.\" \r\n \r\nAnd the number is n + 1. \r\n','2003-04-11',20030503232103,NULL,3,3,0,2.50,20030411052827,0);
INSERT INTO problem VALUES (496,2,2,979,'The Four Mathematicians','Four mathematicians have the following conversation:\r\n \r\nA: I am insane.\r\n \r\nYou are also given that:\r\n \r\nPure mathematicians tell the truth about their beliefs. \r\n \r\nDescribe the four mathematicians. ','There are four possible kinds of mathematicians:\r\n \r\nPure and sane, Pure and insane,\r\nApplied and sane, Applied and insane.\r\n \r\nThe first step is to determine what each kind of mathematician would say about themselves:\r\n \r\nPure and sane: \"I am pure and sane.\" \r\n \r\nPure and insane: \"I am applied and sane.\" \r\n \r\nApplied and sane: \"I am pure and insane.\" \r\n \r\nApplied and insane: \"I am applied and insane.\" \r\n \r\nNote that the applied and insane mathematician is lying about a lie so is actually speaking the truth. \r\n \r\nNext consider the first statement by A, \"I am insane.\" Based on the four groups there are two that will say they are insane:\r\n \r\nThe applied and sane, The applied and insane. \r\nWhat these two groups have in common is that both are applied, thus we can determine that A is applied.\r\n \r\nBy the same logic we can determine that B is sane, C is insane, and D is pure.\r\n \r\nNow we know one of the two characteristics of each mathematician. Next jump to the last statement by D, \"C is sane.\" We already know that D is pure so he actually believes that C is sane. However we also know that C is infact insane so D\'s belief must be incorrect. Since he is not deliberately telling a lie her belief is incorrect, making him insane. So D is pure and insane. \r\n \r\nLet review what we know thus far:\r\n \r\nA: applied, B: sane, C: insane,\r\nD: pure and insane.\r\n \r\nNext look at what B says about D, \"D is insane.\" This is a true statement and since B is already sane we can conclude that he is also pure. Now we have:\r\n \r\nA: applied, B: sane and pure, \r\nC: insane, D: pure and insane.\r\n \r\nNext consider what C says about B, \"B is applied.\" This is not true since B is pure. We already know C is insane thus he must also be pure. If he were applied he would be lying about a lie, thus telling the truth. Now we have:\r\n \r\nA: applied, B: sane and pure, \r\nC: pure and insane, D: pure and insane. \r\n \r\nFinally consider A\'s second statement, \"C is pure.\" C is pure thus A is making a true statement. However A is applied, thus she thinks she is telling a lie. So A is lying about an incorrect belief, making a true statement. Since A\'s belief is incorrect he must be insane. Thus:\r\n \r\nA: applied and insane, B: pure and sane, C: pure and insane, \r\nD: pure and insane. ','2003-04-12',20030713232102,NULL,3,3,0,3.40,20030412040800,0);
INSERT INTO problem VALUES (497,14,2,979,'Leaving Las Vegas','A courier pigeon departs Las Vegas for Reno at the same time as another courier pigeon departs Reno for Las Vegas. Both pigeons fly at constant speeds, although different from each other. They cross paths 2x miles from Las Vegas. After each arrives at their destination they immediately turn around, going back and forth without breaks. They cross paths the second time x miles from Reno.\r\n \r\nWhere will they cross paths the third time?\r\n','First solve for x. Assume that the distance between Las Vegas and Reno is 1. Call \'r\' the pigeon that starts in Reno and \'v\' the pigeon that starts in Las Vegas. For any given amount of time the ratio of the distance traveled by \'r\' to \'v\' will be the same. This ratio at the first meeting is (1-2x)/2x. At the second meeting this ratio is (2-x)/(1+x). Equating these two ratios: (1-2x)/2x = (2-x)/(1+x).\r\n \r\n1, 11, 31, 4113, 612314, ? , ? \r\n \r\n(Explain how you arrived at your result).\r\n','The first number is 1. So, the number of 1\'s is 1. Hence we say that there is \"One 1\", which is written as \"1 1\" or 11. Therefore, we get the next number of the sequence as 11. \r\n \r\nNow, in the sequence (beginning from the very first number), we have in total \"Three 1\'s\", which can be written as \"3 1\", thus obtaining the third term of the sequence as \"31\". \r\n \r\nAgain proceding as before, we see that in the entire sequence (from the first term till the third one), there are altogether \"Four 1\'s and One 3\" which is now written as \"4 1 1 3\", giving us the fourth term of our sequence as \"4113\". Using similar reasoning, we get the fifth term (which is already given) as \"612314\".\r\n \r\nApplying the same logic and reasoning, we obtain the next two numbers of the given sequence as:\r\n \r\n\"8112332416\" (EIGHT 1\'S, ONE 2, THREE 3\'S, TWO 4\'S and ONE 6), and \r\n \r\n\"1113253342618\" (ELEVEN 1\'S, THREE 2\'S, FIVE 3\'S, THREE 4\'S, TWO 6\'S and ONE 8).\r\n','2003-04-16',20030626232103,NULL,3,3,0,4.25,20030416014616,0);
INSERT INTO problem VALUES (499,19,2,979,'Paradox or a Riddle','Four jolly men sat down to play; \r\n \r\nAnd played all night till break of day; \r\n \r\nThey played for money and not for fun, \r\n \r\nWith separate scores for every one. \r\n \r\nYet when they came to square accounts, \r\n \r\nThey all had made quite fair amounts! \r\n \r\nCan you the paradox explain?\r\n \r\nIf no one lost, how could all gain?','The Four men were musicians playing at a dance hall; they were not playing cards as one might suppose. At the end of the performance they were all paid and so they all gained.','2003-04-18',20040130232103,NULL,4,3,0,3.00,20030418015648,0);
INSERT INTO problem VALUES (500,19,2,979,'Crime and Punishment','A certain crime is punishable if attempted but not punishable if committed. \r\n \r\nWhat is it? ','Suicide. While technically it is always illegal, successful suicide cases cannot be prosecuted because the \"perpetrator\" is dead.\r\n ','2003-04-20',20040130232103,NULL,2,3,0,2.80,20030420061248,0);
INSERT INTO problem VALUES (501,12,2,979,'Uninvited Guests','At night they come without being fetched, \r\n \r\nWhat are they?\r\n ','The Stars.','2003-04-22',20040323232104,NULL,2,3,0,2.00,20030422014548,0);
INSERT INTO problem VALUES (502,6,2,979,'Numbers And Words','\r\n\r\n\r\n\r\nStart spelling each word as you count, starting with one.\r\n \r\nHow high do you have to count before you reach a number that has the letter \"a\" in it?\r\n','One Thousand. \r\n \r\nYou don\'t say one hundred and one.\r\n \r\nThat\'s like saying 7 tens and 8.\r\n','2003-04-23',20030508232103,NULL,2,3,0,2.00,20030423014532,0);
INSERT INTO problem VALUES (503,14,2,979,'Ladders Without Snakes','There is a 6 metres wide alley. Both walls of the alley are perpendicular to the ground. Two ladders, one 10 metres long, the other 12 metres, are propped up from opposite corners to the adjacent wall, forming an X shape. All four feet of each ladder are firmly touching either the corner or the wall. The two ladders are also touching each other at the intersection of the X shape.\r\n \r\nWhat is the distance from the point of intersection from the ground? ','Let us consider the foot of one of the ladders as the origin. The width of the alley is given to be equal to 6. Thus if we consider the alley to be the axis of x and the wall from the origin (as assumed) to be the axis of y, then the coordinates of the four feet of the two ladders are: (0,0),(6,8) for the First Ladder and (6,0),{0,(108)^(1/2)} for the Second Ladder.\r\n \r\nNow the equation of the two ladders are: \r\n \r\nThe next statement is \"False\".\r\n \r\nSo now the only possibility is that the First statement is False. Now, according to this assumption, the Second statement is False, which says that the Frist (Previous) statement is False, thus making it True. Again a contradiction. \r\n \r\nHence the First statement is neither True nor False. \r\nSimilarly for the Second one.\r\n','2003-04-24',20031209232102,NULL,3,3,0,2.83,20030424015301,0);
INSERT INTO problem VALUES (505,14,2,979,'Generation Gap','The following relationships hold among the ages of the members of a family of four. (All ages are integral). \r\n \r\n(a) The mother is three times as old as the daughter was when the father was the same age as the mother is now. \r\n \r\n(b) When the daughter reaches half the age the mother is now, the son will be half as old as the father was when the mother was twice the age the daughter is now.\r\n \r\n(c) When the father reaches twice the age the mother was when the daughter was the same age as the son is now, the daughter will be four times as old as the son is now.\r\n \r\nGiven that one of their ages is a perfect square, what are the four ages ?','Let the prsent ages of the Father, Mother, Son and Daughter be F, M, S and D respectively. \r\n \r\nSo, obviously the following can be the cobinations of their ages in years: (In the order: Father, Mother, Son, Daughter):\r\n \r\nTherefore, their respective ages are:\r\n \r\nOne of the students replied: “We have all been studying a whole number of years, the sum of our years of studying is equal to the number of years you have been teaching and the product of our years of studying is 180”. \r\n \r\n“I’m sorry”, replied the Professor after some thought, “but that doesn’t give me enough information”.\r\n \r\n“Yes, you’re right”, agrees another of the students. “But if we told you that one of us were into double figures in our years of study, then you could surely answer your question”.\r\n \r\nHow long had each of the four been studying ?\r\n','Let the years of study of the four students be a,b,c and d respectively. \r\n \r\n3 + 3 + 4 + 5 = 15 \r\n \r\nNow, since the Professor was not able to tell the years of study of his four students, even after knowing their sum, implies that the sum has to be either equal to 18 or 22, in which case he had the following possibilities:\r\n ',' W T N L I T ? \r\nThe sequence is that of first letters of each word in \"What\'s The Next Letter In This Sequence\".','2003-07-03',20030923232102,NULL,1,3,0,3.29,20030703085039,0);
INSERT INTO problem VALUES (510,12,2,979,'The Three Friends','I give you a group of three. \r\n \r\nOne is sitting down and will never get up.\r\n \r\nThe second eats as much as is given to him, yet is always hungry. \r\n \r\nThe third goes away and never returns.\r\n \r\nWhat are they? ','Stove, Fire and Smoke.','2003-04-29',20040106232106,NULL,3,3,0,2.50,20030429014718,0);
INSERT INTO problem VALUES (511,9,2,979,'Can Or Cannot','Can the omnipotent God create a stone which he(she?) him(her?)self Cannot carry?\r\n \r\n(Note: blasphemy added by levik. Disregard if offensive)','This is pretty much a theological question, without a definite solution. Read the user comments for some discussion on it.\r\n \r\nWhat? Did you really expect a definitive answer?','2003-04-30',20040204232105,NULL,3,3,0,3.71,20030430075454,0);
INSERT INTO problem VALUES (513,9,2,979,'True Or False - Part 2','Obviously the following statement is \'False\':\r\n \r\nSo we correct the sentence by changing it to:\r\n \r\nWe know that the First statement is False and so now can we conclude that the Second statement is True ?','While this vaguely resembles a paradox, it is not truly one. Since there are two distinct sentences, there is nothing tying one to another. Therefore, they are both false:\r\n \r\nSentence one is false because it has five words and claims it has seven.\r\n \r\nSentence two is false because it has seven words and claims it does not.\r\n \r\nSince each one references itself exclusively, and there are no external influences, this is not a paradox.','2003-05-07',20040227232102,NULL,2,3,0,2.29,20030507015800,0);
INSERT INTO problem VALUES (514,14,2,979,'Pumpkins','Five pumpkins are weighed two at a time in all ten sets of two. The weights are recorded as 16, 18,19, 20, 21, 22, 23, 24, 26, and 27 pounds. All individual weights are also integers.\r\n \r\nHow much does each pumpkin weigh? ','The weights of the five pumpkins are:\r\n ','Let S be a non-empty subset of N (the set of Natural Numbers). Let k be an element of S. Then k is a natural number. \r\n \r\n(a)Chad loves the girl who is in love with David. \r\n \r\nThere is no mutual love interest (nobody loves the person who loves them back). Nobody is homosexual or narcisstic. \r\n \r\nEllen loves Chad who loves Mary who loves David who loves Gloria who loves Arthur who loves Helen who loves Bruce who loves Ellen.\r\n','2003-05-03',20030518232102,NULL,3,3,0,3.00,20030503211644,0);
INSERT INTO problem VALUES (1031,7,2,1645,'7-11','A customer at a 7-11 store selected four items to buy, and was told that the cost was $7.11. He was curious that the cost was the same as the store name, so he enquired as to how the figure was derived. The clerk said that he had simply multiplied the prices of the four individual items. The customer protested that the four prices should have been ADDED, not MULTIPLIED. The clerk said that that was OK with him, but, the result was still the same: exactly $7.11. What were the four prices? (Do NOT count sales tax.)','If a, b, c, d are the prices of the items expressed in (whole) cents, what we are told is that a+b+c+d = 711 and abcd = 711000000 = 26 32 56 79. \r\n\r\nSo, one (and only one) of the amounts, say a, is a multiple of 79. This is, of course, less than 9 times 79 (which is 711), and may thus only be 1,2,3,4,5,6, or 8 times 79 (7 times 79 is ruled out, because it does not divide 711000000). These 7 possibilities translate into the following equations: \r\n\r\n1. a=79, b+c+d=632, bcd=9000000 \r\n2. a=158, b+c+d=553, bcd=4500000 \r\n3. a=237, b+c+d=474, bcd=3000000 \r\n4. a=316, b+c+d=395, bcd=2250000 \r\n5. a=395, b+c+d=316, bcd=1800000 \r\n6. a=474, b+c+d=237, bcd=1500000 \r\n7. a=632, b+c+d=79, bcd=1125000 \r\nNow, the product of 3 positive numbers of given sum is greatest when they are all equal, which means that the product bcd cannot exceed (b+c+d)3/27. This rules out the last three of the above 7 cases. \r\n \r\nIn the first three cases, on the other hand, the sum b+c+d is not a multiple of 5, so at least one of b,c,d (say d) is not either. This means that the product bc must be a multiple of the sixth power of 5. Since neither b nor c can be large enough to be a multiple of the fourth power [625 is clearly too big a share of 711, leaving only 7 cents for two items in the first case and nothing at all in the other two] we must conclude that both b and c are multiples of 125 (the cube of 5). \r\n\r\n\r\nTherefore, only the fourth case can be valid, so that a=$3.16. \r\na=316, b+c+d=395, bcd=2250000. \r\n \r\nSince the sum b+c+d is a multiple of 5, and at least one of these three is a multiple of 5, either only one is, or all three are. The former possibility is ruled out since this would imply for the single multiple of 5 to be a multiple of 56=15625, which would by itself be (much) larger than the entire sum of 395... So, b, c, and d are all multiples of 5, and we may let b=5b\', c=5c\', d=5d\', where b\'+c\'+d\'=79 and b\'c\'d\'=18000. \r\n\r\nNow, it\'s not possible that all three of these new variables are divisible by 5 (otherwise their sum would be). It\'s not possible either to have a single one of them divisible by 5, because it would then have to be a multiple of 53=125 and exceed the whole sum of 79. Therefore, we must have a multiple of 25 (say b\'=25b\") and a multiple of 5 (say c\'=5c\"): 25b\"+5c\"+d\'=79 and b\"c\"d\'=144. It is then clear that b\" can only be 1 or 2. If b\" was 2, then we would have 5c\"+d\'=29 and c\"d\'=72, implying that c\" is a solution of x(29-5x)=72 or 5x2-29x+72=0. However, this quadratic equation does not have any real solutions, because its discriminant is negative. Therefore, b\" is equal to 1 and b=5(25b\")=125=$1.25. \r\n\r\nThe whole thing thus boils down to solving 5c\"+d\'=54 and c\"d\'=144, which means that c\" is solution of x(54-5x)=144 or 5x2-54x+144=0. Of the two solutions of this quadratic equation (x=6 and x=4.8), we may only keep the one which is an integer. Therefore c\"=6, c\'=30, c=150=$1.50. \r\n\r\nFinally, d\'=144/c=24 which means d=5d\'=120=$1.20. \r\n \r\nAs the order of the items is irrelevant, the problem has therefore a unique solution and the only possible costs of the 4 items are (in the order \"discovered\" above): \r\n\r\n$3.16, $1.25, $1.50, $1.20. \r\n \r\n\r\nSpecial thanks to Numercicana.com','2003-07-11',20030718065014,NULL,3,3,0,3.80,20030711093456,0);
INSERT INTO problem VALUES (518,14,2,979,'The Two Trains','Two trains, A and B, leave their respective starting points at the same time and travel in opposite directions. They travel at constant speeds, and pass at point M. One travels at twice the speed of the other. If one of the trains leaves five minutes late they pass at a point 2 miles from point M.\r\n \r\nWhat is the speed of the slow train, in miles per hour?\r\n','As long as both trains are moving they will always meet at a point 1/3 of the way between their two positions. Lets say the initial positions for the slow train is 0 and the fast train is 3x. Thus if they both left on time they would meet at point x. Let\'s assume that in 5 minutes the slow train can travel u units of distance and the fast train can cover 2u units. \r\n \r\nAssume first the slow train leaves late. At the moment the slow train does leave the fast train will be at point 3x-2u. The meeting point will be 1/3 of the way between 0 and 3x-2u = (3x-2u)/3 = x-2u/3. We also know the distance from this point to x is 2 miles. In other words x-(x-2u/3)=2 ... 2u/3=2... u=3. \r\n \r\nIt is not necessary but we can also calculate u if the fast train leaves late. In this case when the fast train does leave from point 3x the slow train will already be at point u. The meeting point will be u+(3x-u)/3 = x+2u/3. Again the distance between this point and x is 2 miles. In other words (x+2u/3)-x=2 ... 2u/3=2 ... u=3.\r\n \r\nNow we just plug what we know into the d=rt formula (distance=rate * time). The distance is one unit, which equals 3 miles. The time is 5 minutes, or 1/12 of an hour. So we have 3=r*(1/12) ... r=36 m.p.h..\r\n','2003-05-10',20030515023116,NULL,3,3,0,3.00,20030510033923,0);
INSERT INTO problem VALUES (519,14,2,979,'Paint My Love','Your paint inventory consists of 60 gallons of blue, 40 gallons of red, and 30 gallons of yellow. To make purple paint you mix equals parts of blue and red. To make orange paint you mix equal parts of red and yellow. To make green paint you mix equal parts of blue and yellow. Purple paint sells for $6 a gallon, orange for $20, and green for $9.\r\n \r\nThere is a fixed disposal charge for every unused gallon. How much of each of purple, orange, and green paint should you mix to maximize profits if the disposal cost is (a) $4 per gallon, and (b) $6 per gallon.\r\n','SOLUTION:\r\n \r\n(a) Purple=20, Orange=60, Green=0, revenue=$1120 \r\n \r\n(b) Purple=70, Orange=10, Green=50, revenue=$1070\r\n','2003-05-12',20040120232104,NULL,3,3,0,3.50,20030512001053,0);
INSERT INTO problem VALUES (520,6,2,979,'Hearts And Spades','Three playing cards, removed from an ordinary deck, lie face down in a horizontal row. \r\n \r\nImmediately to the right of the King there\'s a Queen or two. \r\n \r\nImmediately to the left of a Queen there\'s a Queen or two. \r\nImmediately to the left of a Heart there\'s a Spade or two. \r\nImmediately to the right of a Spade there\'s a Spade or two. \r\nName the three cards in order. ','Let\'s label the clues as follows:\r\n \r\n(1) To the right of the King there\'s a Queen or two. \r\n \r\n(2) To the left of a Queen there\'s a Queen or two. \r\n \r\n(3) To the left of a Heart there\'s a Spade or two. \r\n \r\n(4) To the right of a Spade there\'s a Spade or two. \r\n \r\nFrom clues 1 and 2 we can infer that a king is on the left and a queen on the right and the middle card is either a queen or 2.\r\n \r\nFirst consider the possibility that a 2 is in the middle. If there are two consecutive spades (from clue 4) then then three cards must be the king of spades, 2 of spades, queen of hearts. If to the right of a spade there is a 2 (again from rule 4) then the three cards are the kings of spades, a two of unknown suit, and the queen of hearts. So if we assume a 2 in the middle it is not certain what the suit of the 2 is. \r\n \r\nNext consider the possibility that a queen is in the middle. Clue 4 tells us there must be two consecutive spades, since there is no 2. Both queens can not be spades since they are from the same deck, thus the left and center cards must be spades. Clue 3 tells us the right queen is a heart. So the three cards would be the king of spades, queen of spades, and queen of hearts.\r\n \r\nSo a 2 in the middle does not lead to a definitive answer, but a queen in the middle does. The question implies there is just one possible answer. Therefore there is a queen in the middle, leading to the final answer of king of spades, queen of spades, and queen of hearts.','2003-05-14',20030721232103,NULL,2,3,0,3.00,20030514014755,0);
INSERT INTO problem VALUES (521,14,2,979,'Three Digit Number','Find a three-digit number containing three different digits where the following are all perfect squares:\r\n \r\n ','916 is the required number (assuming that all the digits of the number are positive, that is non-zero).\r\n \r\n(Note: Hyphens \'-\' are not to be counted as a Line Segment).','The number is: TWENTY NINE.','2003-05-17',20030522020215,NULL,2,3,0,1.50,20030517041442,0);
INSERT INTO problem VALUES (524,12,2,979,'Guessme Ten','Pronounced as one letter,\r\n \r\nI met a man with seven wives.\r\n \r\nEach wife had seven sacks;\r\n \r\nEach sack had seven cats;\r\n \r\nEach cat had seven kits.\r\n \r\nKits, cats, sacks, wives;\r\n \r\nHow many were going to St. Ives?\r\n\r\n','Only one person (that is ME) was going so St. Ives, which becomes obvious from the meaning of the word \"MET\". \r\n \r\nE = 0\r\n \r\nHow old is Old ?','Old is 30 Years and Young is 18 Years.','2003-05-24',20030808232102,NULL,3,3,0,4.00,20030524034629,0);
INSERT INTO problem VALUES (529,2,2,979,'Archaeological Problem','An archaeologist claims he found some gold coins dated 64 B.C.\r\n \r\nDo you believe him? ','Before Christ was born, nobody knew when exactly He would be born, so there was no way specify what year it was B.C. \r\n','2003-05-22',20040319232102,NULL,2,3,0,2.89,20030522073220,0);
INSERT INTO problem VALUES (530,7,2,979,'Ten-Digit Numbers','Find all ten digit numbers each containing the digit from 0 to 9 once and only once, with the property that the successive pairs of digits from left to right are divisible by 2,3,4,5,6,7,8,9 and 10.\r\n \r\n[In other words: The two-digit number formed with the \'N\'th digit and the \'(N+1)\'st digit is divisible by \'(N+1)\', where N = 1,2,3,4,....,9].','There are only two numbers satisfying the given property, and they are: 1872549630 and 7812549630.\r\n\r\n\r\n\r\n','2003-05-27',20030602015241,NULL,3,3,0,4.00,20030527020638,0);
INSERT INTO problem VALUES (532,12,2,979,'Adam and Eve','A man died and went to Heaven. There were thousands of other people there. They were all naked and all looked as they did at the age of 21. He looked around to see if there was anyone he recognised. He saw a couple and he knew immediately that they were Adam and Eve.\r\n \r\nHow did he know? ','He recognized Adam and Eve as the only people without navels. Because they were not born of women, they had never had umbilical cords and therefore they never had navels. \r\n','2003-05-28',20040209232106,NULL,2,3,0,2.42,20030528015036,0);
INSERT INTO problem VALUES (533,14,2,979,'The Strange Number','What is the smallest number which leaves a remainder:\r\n \r\n[ In other words: Find the Least number which when divided by \'N\' leaves a remainder \'(N-1)\', for N = 1,2,3,4,........,9,10].','The smallest number satisfying the given property is 2519.','2003-05-29',20040303215126,NULL,3,3,0,3.20,20030529015205,0);
INSERT INTO problem VALUES (537,19,2,979,'And another Hobbit Riddle','It cannot be seen, cannot be felt,\r\n ','DARKNESS','2003-06-13',20040317232102,NULL,3,3,0,2.92,20030613100308,0);
INSERT INTO problem VALUES (538,14,2,979,'Primary Product','Do there exist three integers in Arithmetic Progression whose product is prime ? \r\nIf Yes, then what are the three integers and if No, then why ?\r\n \r\n[Note: The numbers: x1, x2, x3, x4, x5, x6,........ are said to be in Arithmetic Progression if (x2 - x1) = (x3 - x2) = (x4 - x3) = (x5 - x4) = ........ and so on].\r\n','We know that the numbers: x1, x2, x3, x4, x5, x6,........ are said to be in Arithmetic Progression if (x2 - x1) = (x3 - x2) = (x4 - x3) = (x5 - x4) = ........ and so on.\r\n \r\nSo, if the product of three numbers in Arithmetic Progression is a prime, then it is obvious that two of the numbers have to be (-1) and (+1) and the third number has to be negative and at the same time must satisfy the condition that the three numbers are in Arithmetic Progresion. \r\n \r\nThus we can now easily find out that the third number is none other than (-3) and the product of these three integers: (-3), (-1) and (1) is a prime whose value is 3. \r\n','2003-06-02',20030811232101,NULL,2,3,0,3.33,20030602071643,0);
INSERT INTO problem VALUES (540,19,2,979,'Horses On Hills','Thirty white horses on a red hill,\r\n \r\nFirst they champ,\r\n \r\nThen they stamp,\r\n \r\nThen they stand still.\r\n \r\nWhat am I talking about ?\r\n','The author is of course referring to teeth in the mouth.\r\n ','2003-06-06',20040130232103,NULL,2,3,0,2.83,20030606021200,0);
INSERT INTO problem VALUES (541,12,2,979,'Faces and Eyes','An eye in a blue face\r\n \r\nSaw an eye in a green face.\r\n \r\n\"That eye is like to this eye\"\r\nSaid the first eye,\r\n \r\n\"But in low place\r\nNot in high place.\"\r\n','Sun on the Daisies.','2003-06-10',20040204232105,NULL,3,3,0,1.86,20030610015146,0);
INSERT INTO problem VALUES (542,12,2,979,'Leg Byes','No legs lay on one-leg, two-legs sat near on three-legs, four legs got some.\r\n ','Fish on a little table, man at table sitting on a stool, the cat has the bones.','2003-06-16',20040203232101,NULL,3,3,0,2.29,20030616084401,0);
INSERT INTO problem VALUES (543,19,2,979,'Umpteenth Hobbit Riddle','A box without hinges, key, or lid,\r\n \r\nYet golden treasure inside is hid.\r\n','Eggs.','2003-06-17',20040316232104,NULL,3,3,0,2.78,20030617015247,0);
INSERT INTO problem VALUES (544,12,2,979,'Red And Black','Take one out and scratch my head,\r\n \r\nI am now black but once was red.\r\n \r\nWhat Am I ?','A Match or A Match Stick.','2003-06-18',20040223232101,NULL,1,3,0,1.67,20030618015322,0);
INSERT INTO problem VALUES (554,13,2,979,'Sequence 1','What are the next 5 digits in the following series? \r\n \r\n10101000101000101000 ','10000 is the answer. The series begins with the number 3, and continues through 22, giving a 1 for each prime number, and a 0 for each number that is not prime. \r\n \r\njoke, burst, allude, father, midday, observes, horizontal',' Each word has a palindromic synonym: gag, pop, refer, dad, noon, sees, level','2003-09-16',20031104232104,NULL,4,3,0,4.40,20030916145753,0);
INSERT INTO problem VALUES (1571,6,0,1626,'Another Pack of Prudent Pirates','The five pirates have found another 500 gold coins and wonder how to split them up. This time they say that unless a majority (more than 1/2) say yes to a plan, the one that proposed that plan will get killed and they will move on to the next plan. The order of plan making starts with 5, then 4, 3, 2, 1. \r\nHow much time does the watch lose or gain ? \r\n','The minute and the hour hand meet 11 times in 12 hours in normal watch i.e. they meet after every (12 * 60) / 11 minutes \r\n \r\n(This is roughly 25 seconds every hour)','2003-07-05',20040120232104,NULL,3,3,0,3.25,20030705045738,0);
INSERT INTO problem VALUES (566,11,2,979,'Thirsty Farmer','A farmer needs 8 gallons of water. He has only three unmarked buckets, two 6 gallon and one 11 gallon bucket. \r\n \r\nHow can he collect 8 gallons of water using three unmarked buckets? Provide solution with minimal water wastage. \r\n','Fwaff has posted a solution that wastes only 10 gallons of water. See it here','2003-07-09',20040225103933,NULL,3,3,0,3.00,20030709033505,0);
INSERT INTO problem VALUES (567,2,2,979,'Contest','P, Q, R, and S ran for a contest. \r\nA, B, C made the following statements regarding results.\r\n \r\n1. A said either P or S will definitely win. \r\n \r\nWho has made the correct statement and who has won the contest? ','B has made the correct statement and R has won the contest. \r\n\r\n','2003-07-15',20031017232101,NULL,2,3,0,2.56,20030715020449,0);
INSERT INTO problem VALUES (568,6,2,979,'Coin And Bottle','If you put a coin in an empty bottle and insert a cork into the neck of the bottle, how could you remove the coin without taking the cork out or breaking the bottle? \r\n ','Push the cork into the bottle and shake the coin out. ','2003-07-16',20040311232102,NULL,2,3,0,2.57,20030716014355,0);
INSERT INTO problem VALUES (569,2,2,979,'Box, Locks and Keys','You want to send a valuable object to a friend securely. You have a box which can be fitted with multiple locks, and you have several locks and their corresponding keys. However, your friend does not have any keys to your locks, and if you send a key in an unlocked box, the key could be copied en route.\r\n \r\nHow can you send the object securely? ','Put the valuable object into the box, secure it with one of your locks, and send the box to your friend. Your friend should then attach one of his own locks and return it. When you receive it again, remove your lock and send it back. Now your friend can unlock his own lock and retrieve the object. ','2003-07-18',20030801232103,NULL,4,3,0,3.29,20030718073557,0);
INSERT INTO problem VALUES (2235,2,0,4106,'Bakar3','kjk','khjk','2004-03-23',20040324232101,NULL,3,3,9,0.00,00000000000000,285);
INSERT INTO problem VALUES (571,2,2,979,'Refrigerator and Ice-Cubes','You have an old-fashioned refrigerator with a small freezer compartment capable of holding seven ice cube trays stacked vertically. But there are no shelves to separate the trays, and if you stack one tray on top of another before the ice cubes in the bottom tray are fully frozen, the top tray will nestle into it, and you won\'t get full cubes in the bottom tray. You have an unlimited supply of trays, each of which can make a dozen cubes. \r\n \r\nWhat\'s the fastest way to make full-sized ice cubes? ','You can make 120 cubes (10 full trays) in the time it takes to freeze two trays. First, fill four of the trays with water and turn the other three upside down and use them to space the four apart. That gives you 48 cubes. Next, empty the four trays and put two ice cubes in diagonally opposed corners of each of six of the trays. Fill the remaining holes -- and the entire seventh tray -- with water. Using the ice cubes to hold the trays apart, stack all seven (the seventh tray should go on top), and freeze them. You\'ll get an additional 72 cubes. You can get 72 cubes for every batch except the first, for which spacer ice cubes are not yet available. ','2003-07-19',20030908232101,NULL,4,3,0,3.50,20030719025443,0);
INSERT INTO problem VALUES (1423,7,2,2489,'Mental Arithmetic','I can multiply any three-digit number by 1667 in my head, usually in less than 10 seconds. \r\n \r\nAlso, to make it even more impressive, I come up with the digits of the result in proper order (not in reverse!)\r\n \r\nHow can I do this?','METHOD:\r\n \r\n1667 is not used. The calculation uses your number only. It involves division not multiplication and hence the answer starts with the most significant digit.\r\n \r\nDivide your number by 6. This gives the first 2 or 3 digits of the answer.\r\n \r\nMultiply the remainder by 5.\r\n \r\nPut this remainder by 5 in front of your original number and divide by 3. This gives the rest of the answer.\r\n \r\nExample\r\n \r\n1667 x 872\r\n \r\nDivide 872 by 6 = 145 remainder 2\r\n \r\nMutiply remainder by 5 = 10\r\n \r\nPut in front of number and divide by 3\r\n \r\n10872/3 = 3624 \r\n \r\nThus 1667 x 872 = 1453624 \r\nThe cook\'s injuries need surgical treatment. The surgeons\' injuries are minor but open. It turns out they brought the equipment necessary for the cook\'s surgery with them, and they can use the campfire to sterilize the tools. But there are only two rubber gloves. Because of the different surgeons\' skills, all three of the surgeons are needed to operate on the cook, in sequence. \r\n \r\nHow can this be done without any of them being exposed to the blood of any of the others? ','The first surgeon operates with the first glove (glove A) inside the second glove (glove B). The second surgeon operates using just glove B. The third surgeon operates using glove A, turned inside out, inside glove B. ','2003-07-21',20031013232101,NULL,3,3,0,3.00,20030721015225,0);
INSERT INTO problem VALUES (574,6,2,979,'Escape','Four prisoners escape from a prison. The prisoners, Mr. East, Mr. West, Mr. South, Mr. North head towards different directions after escaping. The following information of their escape was supplied:\r\n \r\nThe escape routes were North Road, South Road, East Road and West Road. \r\n \r\n1. None of the prisoners took the road which was their namesake. \r\n \r\nWhat road did each of the prisoners take to make their escape? ','Lewis was the first with a solution here','2003-07-23',20040225103933,NULL,2,3,0,1.50,20030723014847,0);
INSERT INTO problem VALUES (575,6,2,979,'Some Good Ideas','Substitute digits for the letters to make the following relation true. \r\n \r\nNote that the leftmost letter can\'t be zero in any word. Also, different digits represent different values.','S = 8; O = 7; M = 9; E = 5; G = 4; D = 3; I = 1; A = 6.','2003-07-24',20030801232103,NULL,3,3,0,2.67,20030724014521,0);
INSERT INTO problem VALUES (576,6,2,979,'The Lonely Dog','Can you find the word \"dog\" in the following word search puzzle?\r\n \r\n\"That that is is that that is not is not is that it that is it.\" \r\n','\"That that is, is; that that is not, is not; is that it? That is it.\" ','2003-07-27',20030801022002,NULL,3,3,0,2.60,20030727034425,0);
INSERT INTO problem VALUES (578,20,2,979,'Six Letters And Eight Words','What word begins with \'h\', ends with \'n\', contains six letters, and contains eight words besides itself without transposing a single letter? \r\n ','\"Herein.\" The words it contains are: \"he,\" \"her,\" \"here,\" \"ere,\" \"re,\" \"rein,\" \"I,\" and \"in.\" \r\n \r\nTwo more possiblities suggested in comments are \"HATPIN\" and \"HITMAN\".','2003-07-31',20030805085952,NULL,3,3,0,3.00,20030731061233,0);
INSERT INTO problem VALUES (579,13,2,979,'Sequence 2','What is the next number in the following series? \r\n \r\n1, 2, 4, 13, 31, 112, ? \r\n','Convert the numbers to decimal numbers from base 5 numbers, to get the following sequence: 1, 2, 4, 8, 16 , 32 , ? \r\n \r\n\"Would you be able to enter a guilty verdict if you knew that such a verdict would condemn the defendant to death?\"\r\n \r\nThe person replied: \"No. I beleive that human life is the most important thing, and must be preserved above all else.\"\r\n \r\nThe lawyer asked: \"So you will hold to this even though it may keep you off this jury?\"\r\n \r\n\"Yes,\" the person replied.\r\n \r\nHow did the lawyer know he was lying?','If the prospective juror was telling the truth about human life being of paramount importance, he would pretend to change his mind in order to be able to influence the jury from within.','2003-03-13',20040301232102,NULL,2,3,0,2.57,20030313000000,0);
INSERT INTO problem VALUES (582,13,2,1474,'Find the rule...','The following are the smallest 9 elements of an infinite set of integers: \r\n\r\n0,1,5,6,25,76,376,625,9376 \r\n\r\nWhat rule generates the set? What are the next two values?\r\n','These are the automorphic numbers, base 10. The square of each number has the original number as the least significant digits. E.g. 9376 * 9376 = 87909376 \r\n\r\nThe next two values are 90625,109376. \r\n\r\nSee also http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A003226\r\n','2003-03-13',20030420232102,NULL,4,3,0,3.33,20030313000000,0);
INSERT INTO problem VALUES (586,13,2,979,'Sequence 3','What is the next number in the following series : \r\n \r\n5, 20, 24, 6, 2, 8, ? \r\n','The sequence is found by, starting with 5, multiply, add, divide, and subtract 4 in that order:\r\n \r\nHow can the barrels and wine be evenly divided? ','The most efficient solution is to take two of the half-full barrels and dump each of them into another half-full barrel, resulting in two full barrels and two empty barrels.\r\n \r\nThis make, in all, nine full barrels, three half-full barrels, and nine empty barrels. \r\n\r\nDick Van Dyke \r\nPeter Sellers \r\nSean Connery \r\nDavid Niven and \r\nWoody Allen. \r\n\r\nThe answer is not that they are all famous actors. \r\n\r\nSean Connery (obviously) played James Bond\r\nbut so did Peter Sellers, David Niven and Woody Allen (all in the 1967 movie Casino Royale)\r\n\r\nDick Van Dyke never played Bond that I know of but did star as Caractacus Potts in the film version of Ian Fleming\'s children\'s classic Chitty Chitty Bang Bang \r\n the title is a clue for two reasons: first obviously because \"bang bang\" is a part pf the name Chitty Chitty bang bang but also because \"Bang bang, kiss kiss\" is the way that a European movie critic once famously summarized the plot of all Bond films ','2003-10-30',20040311232102,NULL,1,3,0,1.38,20031030124356,0);
INSERT INTO problem VALUES (1470,20,2,1567,'Words in Common 8','What do the following words have in common? tamper, spied, mister, decal, ashtray, uniformed, sneaky, refined','When the third letter of each word is removed, a new word is formed: Furthermore, the removed letters, in order, spell \"mischief\".','2003-10-16',20031104232104,NULL,4,3,0,1.88,20031016142353,0);
INSERT INTO problem VALUES (599,11,2,979,'The Three Jugs','You have a 12 litre jug, an 8 litre jug, and a 5 litre jug. None of the jugs have any markings on them. The 12 litre jug is full, and the other two are empty. \r\n \r\nHow can you divide the 12 litres of water in such a way that two of the jugs (the 12 litre and the 8 litre jugs) have exactly 6 litres of water in them, and the third (the 5 litre jug) is empty? ','Fill the 8 liter jug with the 12 liter jug, leaving 4 liters in the 12 liter jug. \r\n \r\nAlso, DJ presented a table here that shows the seven steps to the simplest solution:\r\n \r\nOne sales man sold one box out of them and then he says, \"I have the same number of red and blue balls left over.\" \r\n \r\nWhich box is sold out?','He sold the box with 29 balls. \r\nThe total number of balls: 5 + 7 + 14 + 16 + 18 + 29 = 89. \r\nWe assign values to the coefficients a, b and c by throwing a die. \r\n \r\nWhat is the probability that the equation will have real roots ?','Look at DJ\'s solution here.','2003-08-20',20040225103933,NULL,3,3,0,3.00,20030820082343,0);
INSERT INTO problem VALUES (603,18,2,979,'One Equals Two','Given \'x\' not equal to 0, let us consider the follwoing relation:\r\n \r\nx + x + x + .... +x (added \'x\' times) = x²\r\n \r\nDifferentiating both sides with respect to x, we get:\r\n \r\n1 + 1 + 1 + 1 + .... + 1 (\'x\' times) = 2x \r\n \r\n(Since the derivative of x² with respect to \'x\' is 2x).\r\n \r\nSo we now have:\r\n \r\nx = 2x\r\n \r\nCancelling \'x\' from both sides, we have:\r\n \r\n1 = 2\r\n \r\nNow the very obvious question follows:\r\n \r\nWhere is the flaw ?\r\n','Firstly, the above relation holds only for positive integral values of x, and secondly, when we are differentiating with respect to x, the number of times the 1\'s are occurring is still equal to x, which is not possible, since on differentiation all the x\'s are changing to 1\'s. \r\nMr. X\'s wife and mother are not blood relatives. \r\nMr. X\'s son is the youngest of all four and is blood relative of each of them. \r\nHence, Mr. X is the engineer.\r\n \r\nNow, Mr. X is the engineer, and obviously he is both younger than his mother and a blood relative to her.\r\nFrom 2, then, Mr. X\'s mother can not be the doctor.\r\n \r\nSo the Doctor is either his wife or his son. \r\nN-1 must be a multiple of 16, since we are dealing with natural numbers and the average of N-1 numbers is a rational number which reduces to have 16 as the denominator.\r\n \r\nAlso, the average for the first n natural numbers is just n/2. 16²=256, so 271/16 is just a little more than 16. By inspection, we can guess that there were 33 numbers, with an average of a little more than 16, and after 1 is erased, the average of the remaining n-1 numbers is also relatively close to 16.\r\n \r\nFor 32 numbers to have an average of 271/16, their sum must be 271×2=542. The total of the first 33 numbers is 561, a difference of 19, so 19 must have been the number that was removed.\r\n \r\nCharlie posted a solution based on the algebraic formulas involved, here. \r\nFirst, we need to realize that the first 9 one-digit numbrs provide 9 digits. 180 digits come from the 90 two-digits numbers, 2700 digits come from the 900 three-digit numbers, and so on. The set of n-digit numbers will provide 9n×10^n digits to the list.\r\n \r\nBased on this, we get:\r\n \r\nDigits 1-9 come from the 1-digit numbers. \r\nSo, the 40000th digit must be the 1111th digit of the sequence of 5 digit numbers. \r\n \r\nWe also know that 1111=222×5+1, so the 1111th digit of this set is the first digit of the 223rd 5-digit number.\r\n10222 is the 223rd 5 digit number, which means that 1 is the 40000th digit of the overall sequence. ','2003-08-29',20031009182740,NULL,3,3,0,2.00,20030829073111,0);
INSERT INTO problem VALUES (1515,5,2,3182,'A horse\'s rope','Two ranchers shared a circular corral of 10-meter radius. One rancher wanted to tie his horse to one point on the fence and allow him to graze on just half the area of the corral. How long should the horse\'s rope be to make the portion available to this horse be equal to half the area of the corral?','Solution: \r\nTry to obtain a transcient ecuation describing the comparison of both areas, all of this relating every area with trigonometry and finally solving for the variable or distance (the \"rope\") \r\n \r\nAnswer: 11.5872847303m','2003-12-05',20040104122834,NULL,2,3,0,2.75,20031205064926,0);
INSERT INTO problem VALUES (1863,9,0,3372,'Short Long Numbers','What is the smallest positive integer not specifiable in less than twenty-five syllables?','There are an infinite number of positive integers. There are only a finite number of words in the English language at any one time, and so there are only a finite number of phrases of twenty-four syllables or less. Therefore, the majority of integers must not be specifiable in less than twenty-five syllables. \r\n\r\nIf we have a set of positive integers, there must be a least member. Therefore, there must be a smallest positive integer not specifiable in less than twenty-five syllables. \r\n\r\nBut doesn\'t the specification \"the smallest positive integer not specifiable in less than twenty-five syllables\" have less than twenty-five syllables?\r\n \r\nTherefore, the smallest positive integer not specifiable in less than twenty-five syllables can in fact be specified in less than twenty-five syllables. Thus, the least member of the set isn\'t really a member of the set after all. Therefore there is no smallest member. Without a smallest member, the entire set collapses. \r\n\r\nSo does that mean that there are no numbers not specifiable in less than twenty-five syllables? Of course not, or we could only have a finite number of integers. So what\'s wrong? And is that Gödel I see lurking round the corner again...?\r\n \r\nThis paradox is known as Berry\'s Paradox, and was published by Russell in the begining of the last century.','2003-12-06',20040324232101,NULL,4,3,2,0.00,00000000000000,102);
INSERT INTO problem VALUES (1858,5,0,4374,'Half Squared','Given a square piece of paper, show how by creasing and folding only, a square of half the area of the original can be obtained.','Crease the line between the midpoints of the top and bottom and same for line between the midpoints of the left and right sides. Then fold down the corners.','2003-12-02',20040323232102,NULL,1,3,1,0.00,00000000000000,22);
INSERT INTO problem VALUES (1513,13,2,3172,'Flawless Series?','What are the next three numbers in this sequence?\r\n6, 28, 496, 8128, ... ?\r\n\r\nPlease explain how you determined these three numbers.','The next three numbers in this sequence are: \r\n(a) How many yellow birds were seen in all?\r\n \r\nSo five yellow birds were seen (the one B saw, the one C saw, the one A and C saw, the one B and C saw, and the one all three saw), and two non-yellow birds were seen (the one A saw and the one A and B saw) by the group. \r\n','2003-08-30',20040104232102,NULL,2,3,0,2.20,20030830093421,0);
INSERT INTO problem VALUES (611,2,2,979,'The Confusion','Four gentlemen (A, B, C, and D) went to an expensive restaurant to dine. They checked their coats, hats, gloves, and canes at the door (each of the gentlemen had one of each). But when they checked out, there was a mix up, and each of the men ended up with exactly one article of clothing (a pair of gloves is considered a single article of clothing) belonging to each one of the four.\r\n \r\nA and B ended up with their own coats, C ended up with his own hat, and D ended up with his own gloves. A did not end up with C\'s cane.\r\n \r\nState whose coat, hat, gloves, and cane each of the gentlemen ended up with. ','A had his own coat, B\'s hat, C\'s gloves, and D\'s cane. \r\nMany methods for solving this problem were offered in the comments, including Charlie\'s deductive method here and DJ\'s solution by grid here.','2003-09-02',20040225103933,NULL,3,3,0,2.79,20030902141555,0);
INSERT INTO problem VALUES (1496,9,2,3172,'On the house?','Alan and Bob each own a bar. Alan\'s is in very northern New York, and Bob\'s is just across the border in Canada. \r\n\r\nB, C, F, H, I, K, N, O, P, S, U, V, W & Y.','They are all the single letter symbols for elements on the periodic table. \r\nBoron, Carbon, Flourine, Hydrogen, Iodine, Potassium, Nitrogen, Oxygen, Phosphorus, Sulfur, Uranium, Vanadium, Tungsten & Yttrium.','2003-11-01',20031113232102,NULL,3,3,0,4.00,20031101084355,0);
INSERT INTO problem VALUES (1538,22,2,2682,'Nothing but flowers','23-923-29279-1541-53-122-21574-20999-1541-437-19-14-74-166-43-159941-671','Factorise the numbers and sort the prime factors of each number in ascending order. \r\nNow assosciate the first 26 prime numbers with the letters of the alphabet. (2=A, 3=B, 5=C...) \r\nBy substituting the prime factors with the letters you get: \r\nIFTHISISPARADISEIWISHIHADALAWNMOWER \r\nIf you wonder where this comes from, use google ;)','2003-12-12',20040104122502,NULL,4,3,0,4.25,20031212141255,0);
INSERT INTO problem VALUES (1539,22,1,1626,'Middle order',' \r\nOn which day of the week does Bob tell the truth?','Charlie offers a detailed solution here\r\n ','2003-03-17',20040225103933,NULL,3,3,0,4.00,20030317000000,0);
INSERT INTO problem VALUES (1522,14,2,3275,'The Ladder','A 3\' cube sits on level ground against a vertical wall. A 12\' ladder on the same ground leans against the wall such that it touches the top edge of the box.\r\n \r\nHow far from the wall must the foot of the ladder be, if it is to reach maximum height whilst meeting the foregoing conditions?\r\n','Let Pythagorus sleep.\r\nThe 12ft ladder meets the ground at angle a.\r\nThe edge of the 3ft box divides the ladder into 2 lengths whereby:\r\n\r\n12 = 3/sin a + 3/cos a\r\n4 sin a cos a = cos a + sin a\r\n2 sin 2a = cos a + sin a\r\n4 sin^2 2a = cos^2 a + sin^2 a + 2 sin a cos a\r\n4 sin^2 2a = 1 + sin 2a\r\n4 sin^2 2a - sin 2a - 1 = 0\r\nsin 2a = (1 ± (1 + 16)^½)/8\r\n\r\na must be positive therefore the 2 values of 2a are 39.82 and 140.18 degrees.\r\n\r\nFor maximum height the distance of foot of ladder from the wall = 12 cos (140.18/2) = 4.09\r\n','2003-12-09',20040223232101,NULL,2,3,0,3.80,20031209090230,0);
INSERT INTO problem VALUES (624,7,2,979,'What Happened ?','What happened in the middle of the twentieth century that will not happen again for 4,000 years ?\r\n \r\n(Hint: See the category).','The year 1961. It reads the same upside down. This will not happen again until the year 6009.','2003-09-23',20031009200618,NULL,2,3,0,1.00,20030923083427,0);
INSERT INTO problem VALUES (625,16,1,979,'Two Spheres','There are two spherical balls, each of radius 100 cm., lying on a perfectly horizontal floor and touching each other.\r\n ','Consider the remainders obtained when the given 181 square integers are divided by 19. If n is any integer then n is congruent modulo 19\r\nto one of the numbers 0, 1, 2, . . ., 18 and hence n^2 is congruent to 0, 1, 4, 9,16, 6, 17, 11, 7 or 5.\r\n \r\nIf this is so why does ice float in water?','If you look at the comment list and view rosalind\'s comment you will see the answer.','2003-03-23',20031210232104,NULL,2,3,0,2.67,20030323000000,0);
INSERT INTO problem VALUES (637,7,2,979,'Check Mate','Two brothers share a flock of x sheep. They take the sheep to the market and sell each sheep for $x. At the end of the day they put the money from the sales on the table to divide it equally. All money is in $10 bills, except for fewer than ten excess $1 bills. One at a time they take out $10 bills. The brother who draws first also draws last.\r\n \r\nThe second brother complains about getting one less $10 bill so the first brother offers him all the $1 bills. The second brother still received a total less than the first brother so he asks the first brother to write him a check to balance the things out.\r\n \r\nHow much was the check? ','There is a good solution by nikki here','2003-10-06',20040225103933,NULL,3,3,0,3.80,20031006081951,0);
INSERT INTO problem VALUES (638,14,2,979,'Formula None Racer','A car is travelling at a uniform speed.\r\n \r\nWhat is the speed of the car?\r\n','45 mph\r\n \r\nLet the two digit number be represented by 10x+y.\r\n \r\nAfter one hour, the milestone shows the number 10y+x. \r\nAfter another hour, the milestone shows 100x+y. \r\nThen, we have: \r\nTherefore, the milestones mentioned read: 16, 61 and 106.\r\n \r\nNow, since the car traveled 45 miles each hour, it is clear that the speed of the car is 45 mph.','2003-10-03',20040121232101,NULL,3,3,0,2.86,20031003080029,0);
INSERT INTO problem VALUES (1625,7,0,1626,'A Simple Difference','I am thinking of two positive integers. If x is the sum of them and y is the product of them, prove that √(x²-4y) is the difference of my two numbers.','Calling the two numbers a and b: \r\nHere is the proof that 1 dollar = 1 cent. Is there an error in my calculations?','The trick in this \"proof\" lies in the part the transition from 100 cents to 10 cents x 10 cents. \r\n \r\nIn reality, it is meaningless to multiply cents by cents (since we would get a non-existant unit of cents squared). 100 cents is actually simply 10 * 10 cents, or 10 * (1/10 dollar) or 1 dollar - as we all know.','2003-05-03',20030802232102,NULL,3,3,0,2.80,20030503033015,0);
INSERT INTO problem VALUES (643,4,2,979,'The Last Baby','A baby is added to a hospital nursery. Before the baby was added there were two boys in the nursery and an uncounted number of girls. After the new baby is added a baby is selected at random among all the babies. The selected baby is a boy. \r\n \r\nWhat is the probability that the added baby was a girl? ','We apply Baye\'s Theorem here:\r\n \r\nLet events A1,...,Ak form a partition of the space S such that P(Aj)>0 for j=1,...,k, and let B be any event such that P(B)>0. Then for i=1,...,k,\r\n \r\nP(Ai|B) = P(Ai)*P(B|Ai) / Sum for j=1 to k of P(Aj)*P(B|Aj).\r\n \r\nNow let,\r\n \r\nB=boy selected\r\n \r\nA1=boy added\r\n \r\nA2=girl added\r\n \r\ng=number of girls before baby \r\nis added.\r\n \r\nP(A2|B) = (1/2)*(2/(3+g)) / [(1/2)*(2/(3+g)) + (1/2)*(3/(3+g))] = 0.4','2003-10-08',20031118092729,NULL,4,3,0,2.57,20031008074421,0);
INSERT INTO problem VALUES (1659,7,0,1626,'Sum of Cubes','Prove that the sum of perfect cubes (starting with 1) is always a perfefct square.\r\n \r\nHowever, you see that there are only 99 pigs for sale. The only other animals there are chickens for 1 dollar each, and cows for 80 dollars each.\r\n \r\nIf there are enough chickens and cows for you to buy as many as you wanted, how can you end up buying 100 animals using exactly 800 dollars?','72 chickens \r\nIf a/b=11/21, then 11b-21a=1, and a and b should be as large as possible but less than 99, which works out to 45/86. For the other side you find 43/82.','2004-02-16',20040324232101,NULL,3,3,20,0.00,00000000000000,410);
INSERT INTO problem VALUES (1643,7,2,2561,'Binary Primes','How many primes, written in usual base 10, have digits that are alternating 1s and 0s, beginning and ending with one?\r\n \r\nFor example (not necessarily prime): \r\nSo the only way you\'ll get a prime is if one of those two factors is 99.','2004-02-18',20040229143647,NULL,4,3,0,3.50,20040218131458,0);
INSERT INTO problem VALUES (1644,7,1,2561,'Looking for n','Let n be the smallest positive integer such that n(n+1)(n+2)(n+3) can be expressed as either a perfect square or a perfect cube (not necessarily both). \r\n\r\nFind n, or prove that this is not possible.','(n+1)(n+2) = n² + 3n + 2 and n(n+3) = n² + 3n. So their product is (n2 + 3n + 1)² - 1. Hence n(n + 1)(n + 2)(n + 3) is 1 less than a square, so it cannot be a square. \r\n \r\nOne of n+1, n+2 must be odd. Suppose it is n+1. Then n+1 has no factor in common with n(n + 2)(n + 3), so n(n + 2)(n + 3) = n³ + 5n² + 6n must be a cube. But (n + 1)³ = n³ + 3n² + 3n + 1 < n³ + 5n² + 6n < n³ + 6n² + 12n + 8 = (n + 2)³, so n³ + 5n² + 6n cannot be a cube. \r\n \r\nSimilarly, suppose n + 2 is odd. Then it has no factor in common with n(n + 1)(n + 3) = n³ + 4n² + 3n, so n³ + 4n² + 3n must be a cube. But for n >= 2, (n + 1)³ < n³ + 4n² + 3n < (n + 2)³, so n³ + 4n³ + 3n cannot be a cube for n >= 2. The case n = 1 is checked by inspection: 24 is not a cube.','2004-02-24',20040321232102,NULL,3,3,0,4.40,20040224145201,0);
INSERT INTO problem VALUES (648,4,2,979,'Same Name','Suppose there are n people in an office. At Christmas they have a random gift exchange in which every name is writen on scraps of paper, mixed around in a hat, and then everyone draws a name at random to determine who they are to get a gift for.\r\n \r\nWhat is the probability nobody draws their own name? ','The required probability is: \r\n \r\n(1) - (1) + 1/(2!) - 1/(3!) + 1/(4!) - 1/(5!)+ 1/(6!) - 1/(7!) + ........\r\n \r\nWhich is approximately equal to (1/e), where e = 2.71828 (approx.).','2003-10-11',20031104014520,NULL,4,3,0,4.00,20031011072714,0);
INSERT INTO problem VALUES (649,4,2,979,'Playing With Marbles','You choose one of two identical looking bags at random. One bag has three black marbles and one white marble. The other has three white marbles and one black marble.\r\n \r\nAfter choosing a bag you draw one marble out at random. You notice it is black. You then put it back and draw another marble out of the same bag at random.\r\n \r\nWhat is the probability that the second marble drawn is black? ','The probability of event A happening given that event B already happened is the probability of A and B happening divided by the probability that B happened. This can be pressed as P(A|B)=P(A and B)/P(B).\r\n \r\nIn this case A is drawing a black marble and B is having already drawn a black marble.\r\n \r\nP(A and B) = (1/2) * [(3/4)^2 + (1/4)^2] = 5/16.\r\n \r\nTheredore, P(B) = 1/2.\r\n \r\nP(A|B) = P(A and B)/P(B) = (5/16)/(1/2) = 10/16 = 5/8. \r\n','2003-10-13',20040322232106,NULL,3,3,0,2.83,20031013150427,0);
INSERT INTO problem VALUES (650,2,2,979,'Penny Problem','You are blindfolded before a table. On the table are a very large number of pennies. You are told 128 of the pennies are heads up and the rest are tails up. \r\n \r\nHow can you create two subgroups of pennies, each with the same number of heads facing up? ','Create a subgroup of any 128 pennies. Then flip over all 128. That group of 128 and the group of all the remaining pennies will have the same number of heads facing up. ','2003-10-14',20040324232102,NULL,3,3,0,3.92,20031014073708,0);
INSERT INTO problem VALUES (651,14,2,979,'Remainder','If \'p\' be a prime, then what is the remainder when (p - 1)! is divided by p? \r\n','The solution to this problem is that the remainder in such a case will always be equal to (p - 1), which is \'WILSON\'S THEOREM\' which states that: \'p\' divides [(p - 1)! + 1] if and only if \'p\' is a prime and therefore, whenever (p - 1)! is divided by \'p\', the remainder thus obtained will be equal to (p - 1).','2003-10-16',20031205100633,NULL,3,3,0,3.86,20031016093545,0);
INSERT INTO problem VALUES (1660,17,0,1626,'The Monkey Tail Hunter','You are standing a far ways away from the base of a tree from which a monkey is hanging on a branch exactly 5 meters above the ground. \r\nHow many locks would be needed, and how many keys?','Ten locks and thirty keys are needed. Each lock would have three keys made to unlock it. Each person would get six different keys. Call the locks 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0. Each person would get their keys following the table below.\r\n \r\n2, 3, 5, 11, 23, 29, 41, 53, _ , _ .\r\n \r\nAlso mention the rule that the numbers follow.','The given series comprises of all the prime numbers \'p\' such that \'(2p +1)\' is also a prime and such primes are known as Germain Primes. So the next two numbers of the given sequence are: 83 and 89.','2003-10-23',20031104015237,NULL,3,3,0,2.60,20031023145912,0);
INSERT INTO problem VALUES (1666,2,2,2716,'Murder by Logic','Professor Z was killed by one of his four students, who was helped by another of the four. His students declared: \r\nA: If B is guilty of something, then C must be innocent. \r\nAs everybody should know, guilty parties always lie, and innocent people always tell the truth. Who killed the professor, and who was his accomplice?','D\'s declaration is worthless: were he innocent or guilty he could have said so. \r\nSuppose C was guilty: as he would lie, then B should be the killer, but D would have to be involved too, making three guilty parties; it follows that C was innocent. \r\nSuppose B was innocent: A could be innocent or guilty. If A was innocent, then C would have to be guilty, but we showed C was innocent, so A couldn\'t be innocent. If A was guilty, since he lied, B and C must have been guilty -- and that\'s contradictory. As A cannot be either guilty or innocent, B cannot be innocent; he is guilty. \r\nSince B is guilty, A must be innocent, and C must be too (which we had already proved). \r\nWe have now that B and D are guilty, but if B was the killer, then D would be innocent (as C said) so B must have been the accomplice, and D the killer.\r\n','2004-03-05',20040316135514,NULL,3,3,0,3.43,20040305142125,0);
INSERT INTO problem VALUES (658,2,2,979,'Mathematician Versus Detective','The police commissioner hired a mathematician to help at a crime scene. At the scene were between 100 and 200 glasses of wine. Exactly one glass was poisoned. The police lab could test any sampling for poison. A group of glasses could be tested simultaneously by mixing a sample from each glass. The police commissioner desired only to minimize the maximum possible tests required to determine which exact glass was poisoned.\r\n \r\nThe mathematician started by asking a detective to select a single glass at random for testing. \"Wouldn\'t that waste a test?\", the detective asked. \"No, besides I\'m in a gambling mood.\", the mathematician replied. How many glasses were there? ','If the goal is to minimize the maximum number of tests then that maximum for n glasses is log2n (log to the base 2 of n), rounded up.\r\n \r\nIf the number of glasses is a power of 2 (32, 64, 128, 256, etc.) then the correct procedure on the first step would be to test exactly half the glasses. Then test half of the glasses in the positive half next. Keep repeating this procedure. Each step will narrow down the field of poisoned glasses by a factor of 2. \r\n \r\nIf the number number of glasses is not a power of 2 then there are lots of ways you can test them and still achieve the same maximum number of tests. One way would be to find the closest power of 2 less than n, set this many glasses aside, and then test the others. The only n for which this remainder is 1, between 100 and 200, is 129. In the case of 129 the first test would likely be negative. Then proceed with the procedure for testing 128. Between the first test and the log2128 the maximum number of tests is 8.','2003-11-05',20031224232100,NULL,3,3,0,3.40,20031105085658,0);
INSERT INTO problem VALUES (1698,14,1,2130,'A to B','You need to go from point A to point B, and then back to point A. Points A and B are 20 miles apart. You go to point B at a constant speed of 15 miles per hour. If you want your overall speed to be 30 miles per hour, how fast would you have to go from point B back to point A?','It would be impossible to obtain an overall speed of 30 miles per hour, unless you somehow magically went from B to A instantaneously. ','2004-03-10',20040322232106,NULL,2,3,0,1.33,20040310081813,0);
INSERT INTO problem VALUES (1699,5,0,1626,'The right pentagon','There is a pentagon ABCDE such that angles A, C, and E are all right angles. (C\'s right angle is outside the pentagon.) \r\nEveryone should know that sum of all integers from 1 to n is n*(n+1)/2. So the sum of additional pieces cut will be n*(n+1)/2. Finally add 1 because we start with 1 piece: n*(n+1)/2 + 1.','2003-10-27',20031104014845,NULL,3,3,0,2.50,20031027145311,0);
INSERT INTO problem VALUES (661,6,2,979,'Tiger - Man','A man is standing on a rock in the middle of a circular lake of radius 1. There is a tiger on the shore of the lake that can run four times as fast you can swim, however the tiger can not swim. The tiger is hungry and always attempts to keep the distance between the two of you at a minimum.\r\n \r\nHow can you safely swim to shore? ','Until you are more than 1/4 of the radius away from the rock you can swim fast enough so that you can stay 180 degrees away from the tiger. Regardless of which direction the tiger moves around the circle you swim the other way, always keeping 180 degrees away, and moving outward with leftover energy. \r\nBefore long you will be 1/4 of the radius away from the center and the tiger will be 180 degrees away. At this point swim straight to the point on the shore furthest from the tiger. You will be able to get there in 3/4 units of time, while it will take the tiger pi/4 =~ 0.7854 units of time.\r\n\r\n','2003-10-29',20040322232106,NULL,4,3,0,4.29,20031029154535,0);
INSERT INTO problem VALUES (662,14,2,979,'Foreign Puppy','A man wishes to sell a puppy for $11. A customer wants to buy it but only has foreign currency. The exchange rate for the foreign currency is 11 round coins = $15, 11 square coins = $16, 11 triangular coins = $17.\r\n \r\nHow many of each coinage should the customer pay? ','Let x be the number of circular coins, y be the number of square coins, and z be the number of triangular coins. \r\n \r\nThus:\r\nx*(15/11) + y*(16/11) + z*(17/11) = 11. \r\n \r\nMultiplying by 11:\r\n \r\n15x + 16y + 17z = 121. \r\n \r\nHere we have to use trial and error method. I divided 121 by 15 to get 8 plus a remainder of 1. It is then obvious that x=7, y=1, and z=0 would solve the equation.','2003-10-31',20031229232105,NULL,3,3,0,3.50,20031031123306,0);
INSERT INTO problem VALUES (663,7,2,979,'Fair and Square','Jack and Jill each have marble collections. The number in Jack\'s collection in a square number.\r\n \r\nJack says to Jill, \"If you give me all your marbles I\'ll still have a square number.\" Jill replies, \"Or, if you gave me the number in my collection you would still be left left with an even square.\" \r\n \r\nWhat is the fewest number of marbles Jack could have? ','25\r\n \r\nJack has 25 marbles and Jill has 24. If Jill gives Jack all her marbles, he will have 49(7²), and if Jack gives Jill the number in her collection, he will be left with one, which is a square.\r\n \r\nThis ignores the trivial case where Jill has 0 marbles, since they problem says they each have marble collections, they must each have some marbles in their collections.\r\n \r\nDJ provided a good proof of why this is the minimum here.','2003-11-03',20040313214119,NULL,3,3,0,2.33,20031103080516,0);
INSERT INTO problem VALUES (1790,14,0,3386,'Volunteers','Six Komosomol members volunteered to saw large logs into half-yard logs to heat the school. The 3 leaders of pairs were Volodya, Petya, and Vasya. \r\nVolodya and Misha would saw up 2-yard logs. Petya and Kostya would say up 1 1/2-yard logs. Vasha and Fedya would saw up 1-yard logs. (These are all first names.) \r\nThe next day the school bulletin praised the good work of teams led by Lavrov, Galkin, and Medvedev. Lavrov and Kotov sawed logs into 26 small logs, Galkin and Pastukhob, 27, and Medvedev and Yevdokimov, 28. (These are all last names.) \r\nWhat is Pastukhov\'s first name?\r\n \r\n(from The Moscow Puzzles by Boris Kordemsky)','Sawing 2-yard logs produces a number of half-yard logs divisible by 4; sawing 1 1/2-yard logs, divisible bu 3; 1-yard logs, divisible by 2. Pastukhov\'s team\'s 27 logs is not divisible by 2 or 4, so it is the 1 1/2-yard log team of Petya and Kostya. The team leader is Petya Galkin, so Pastukhov\'s first name is KOSTYA','2003-11-11',20040324232101,NULL,1,3,10,0.00,00000000000000,292);
INSERT INTO problem VALUES (1902,14,0,5033,'Abdul and Saeed',' Two salt sellers are sitting in an Arabian Marketplace trying to impress tourists.\r\n \r\n The first, Abdul, starts talking with a lady nearby.\r\n \r\n \"I have only five weights and a scale, but with them I can measure any weight from 1g to 31g!\"\r\n \r\n Of course, Abdul uses the binary system, with weights of 1g, 2g, 4g, 8g, and 16g. The lady is very impressed, but Saeed counters with his own genius.\r\n \r\n \"I have but five weights and a scale as well, but I can measure any weight from 1g to 242g!\"\r\n \r\n Well, both the lady and Abdul were very amazed at this system. Can you figure out what weights Saeed uses?',' Saeed uses weights of 1g, 3g, 9g, 27g, and 81g. Like Abdul, he can add weights together to measure weights like 4 and 10. But he can use subtraction as well!\r\n \r\n3 plus salt_______________9 plus 1\r\n \r\n The 1 and 9 add up to 10, but the three on the other side of the scale makes it the same as if there was a 7g weight on one side and none on the other!\r\n \r\n This system works for all the amounts from 1 to 242.','2004-01-12',20040323232102,NULL,4,3,1,0.00,00000000000000,40);
INSERT INTO problem VALUES (666,7,2,979,'This Way and That Way','ABCDE * 4 = EDCBA. Solve for A,B,C,D, and E where each is a unique integer that can take any value from 0 to 9. ','A = 2; B = 1; C = 9; D = 7; E = 8.\r\n \r\nTaking into account all possible ways to keep dogs in the kennels, what\'s the average number of dogs I can place?','SEE LATER','2004-02-11',20040324232101,NULL,3,3,18,0.00,00000000000000,389);
INSERT INTO problem VALUES (1794,22,0,3386,'Looking Through the Looking Glass','Asdi qPraadhm slHoksbrpqoaaksncjsgekve qpoIlakn ckdcEocoxoelqkxopsdr awkadFonaksd qwkasoDm Asja fKjffdarfodufuiisdst. asjwHejhowfahuxt cbuAwogm iaSi wkbiDixn akeEdafncvuggudlhusiqwxshoxh?','Orange. Every fourth letter, if combined makes coherent words. Combine the words to form the question: \"I am orange in color and am a fruit. What am I?\" The answer is simple.','2003-11-12',20040324232101,NULL,2,3,11,0.00,00000000000000,309);
INSERT INTO problem VALUES (669,14,2,979,'Two Boats and A River','Two boats on opposite sides of a river head towards each other at different speeds. When they pass each other the first time they are 700 yards from one shoreline. They continue to the opposite shoreline, turn around, and move towards each other again. When they pass the second time they are 300 yards from the other shoreline.\r\n \r\nHow wide is the river? (Assume both boats travel at a constant speed and ignore factors such as turn-around time and the current of the river). ','Define the following variables:\r\n \r\nw=width of river\r\n \r\ns1=speed of first boat\r\n \r\ns2=speed of second boat\r\n \r\nt1=time until boats meet the \r\nfirst time\r\n \r\nt2=time until boats meet the \r\nsecond time\r\n \r\nI shall arbitrarily say that both boats are 700 yards from the shore of original of the first boat at time t1. \r\n \r\nThe following equations can be inferred from the information given:\r\n \r\n(1) w=t1*(s1+s2)\r\n \r\n(2) s1*t1=700 \r\n \r\n(3) w+300=s1*t2\r\n \r\n(4) 2w-300=s2*t2\r\n \r\nAdding equations (1) and (2) we get:\r\n \r\n(5) 3w=t2*(s1+s2)\r\n \r\nSubstituting s1+s2=w/t1 from equation (1) we get:\r\n \r\n3w=t2*r/t1\r\n \r\n3w*t1=r*t2\r\n \r\n(6) 3*t1=t2\r\n \r\nCombining equations (3) and (6):\r\n \r\n(7) w+300=3*s1*t1\r\n \r\nCombining equations (2) and (7):\r\n \r\nw+300=2100 \r\n \r\nw=1800','2003-11-13',20031213153006,NULL,4,3,0,2.50,20031113142048,0);
INSERT INTO problem VALUES (670,14,2,979,'50 - Digit Number','A number of 50 digits has all its digits equal to 1 except the 26th digit. If the number is divisible by 13, then find the digit in the 26th place.','3\r\n \r\nFirst, notice that 111111 is divisible by 13 (13×8547). So, 11111100 is also divisible by 13 (13×854700), and so on. Also, the sum of any multiples of 13 will also be divisible by 13, which includes any string of 6n 1s (where n is any integer), and obviously those numbers followed by any number of 0s.\r\n \r\nThus, the number formed by 24 1s is divisible by 13: \r\nFinally, their sum is a multiple of three: \r\nThus, 11111111111111111111111113111111111111111111111111 is divisible by 13, and the digit in question is 3.','2003-11-15',20040316075547,NULL,3,3,0,3.50,20031115073332,0);
INSERT INTO problem VALUES (671,14,2,979,'Calculation Mistake','A boy was asked to calculate the arithmetic mean of ten positive integers each of which had 2 digits. \r\n ','In traditional logic this is an impossible scenario. A universe containing a sword that cuts through \"anything\" cannot also contain a shield that \"nothing\" can cut through. These two items are mutually exclusive.\r\n \r\nAlan proposes an interesting alternate solution: the sword would be able to cut through the shield, but take an infinitely long time to do so (for example penetrating 50% in the first second, 25% more in the next, etc.) ','2003-03-17',20031209232103,NULL,3,3,0,3.40,20030317000000,0);
INSERT INTO problem VALUES (676,14,1,979,'Sides Of A Triangle','The sides of a triangle are in arithmetic progression and its area is 3/5th the area of an equilateral triangle with the same perimeter.\r\n \r\nFind the ratio of the sides of the triangle.','','2003-11-23',20040130232103,NULL,3,3,0,4.14,20031123111321,0);
INSERT INTO problem VALUES (1852,22,0,3386,'2(A,0,1) 471(S,6,2) 294(L,4,2)','223(S,4,1) \"80(C,2,1)\" 76(I,1,1) 239(E,5,2). \r\n','Title: A Spelling Lesson \r\nQuestion: Spell \"cat\" in English. \r\nAnswer: cat \r\nEach letter corresponds to a prime number. The first letter, A, corresponds with the first prime number, 2. The second letter, B, corresponds with the second prime number, 3. It goes all the way to the last letter, Z, corresponding to the 26th prime number- 103. The first number (not in the parentheses) is the sum of the prime numbers corresponding to the letters in the word. The letter in the parentheses is the first letter of the word. The first number in the parentheses is the number of consonants in the word. The second number is the number of vowels. ','2003-11-30',20040324232101,NULL,5,3,25,0.00,00000000000000,446);
INSERT INTO problem VALUES (1835,13,0,3386,'Mikhail\'s Sequence','The brilliant mathematician, Mikhail, decided to impress his sons. So, he decided to make a hard sequence. Later that day, he shows his sons the sequence: \r\n1, 2, 11, 11252, 16025186939242511, ... \r\nThe sons were stumped. They couldn\'t even get the pattern. But can you? What is the pattern to this sequence? BONUS: What\'s the next number (be afraid, its gonna be huge)?','The pattern is x^4 - 3(x^3) + 5(x^2) - 1. \r\nBONUS: I didn\'t solve it. Possibly someone will post it up. It will be about 58-60 digits total.','2003-11-24',20040324232101,NULL,5,3,23,0.00,00000000000000,431);
INSERT INTO problem VALUES (678,4,2,979,'Spider and Fly','A spider eats 3 flies a day. Until the spider fills his quota a fly has a 50% chance of survival if he attempts to pass the web.\r\n \r\nAssuming 5 flies have already made the attempt to pass, what is the probability that the 6th fly will survive the attempt? ','Using the binomial distribution, the probability that n flies out of 5 have been eaten is combin(5,n)*(1/2)^5, where combin(5,2)=5!/(n!*(5-n)!). \r\n \r\nThe probability that 0 flies were eaten is combin(5,0)*(1/2)^5=1/32.\r\n \r\nThe probability that 1 fly was eaten is combin(5,1)*(1/2)^5=5/32.\r\n \r\nThe probability that 2 flies were eaten is combin(5,2)*(1/2)^5=10/32.\r\n \r\nSo the probability that the spider is still hungry is 1/32 + 5/32 + 10/32 = 16/32 = 1/2. \r\nThe probability the spider is full is 1-1/2=1/2. Thus the probability of a successful attempt to pass is (1/2)*1 + (1/2)*0.5 = 0.75 .\r\n','2003-11-25',20031224232100,NULL,3,3,0,3.50,20031125085759,0);
INSERT INTO problem VALUES (1836,13,0,3386,'Mikhail\'s Sequence 2','After much thought, brilliant mathematician Mikhail thought that his sequence was a little too hard for his sons. So, he made another one that is easier. He showed it to his sons later that day: \r\n6, 10, 4, 9, 6, 11 \r\nThen he asked what would be the next number in this sequence. After much thought, the sons had no clue what was the next number. So, Mikhail said, \"This sequence cannot continue once you have the next number.\" After much thought, the sons figured out the next number. What was the next number?','11. This is because the sequence is the number of letters in the continents, in alphabetical order (Africa, Antarctica, Asia, Australia, Europe, North America, and South America) The number of letters in them are 6, 10, 4, 9, 6, 11, and 11. After 11, there would be no more numbers in the sequence, for there are no more continents.','2003-11-24',20040324232101,NULL,3,3,23,0.00,00000000000000,432);
INSERT INTO problem VALUES (1875,14,0,2130,'Square Root','Without using trial and error, find the least positive integer value for x when the following equals a perfect square. Tell how you obtained your answer. √(98*38*x) Note: I\'m not sure if the symbol used before the (98*38*x) is supposed to be the square root symbol. I think it is, but if it\'s not supposed to be, pretend it is;)','x=19. I figured if I could make 98*38 into a perfect square with a positive integer left over, x could equal the integer leftover. Divide 38 by 2, you get 19. Multiply 98 by 2, you get 196, the square of 14. So you get √(196*19²). If you multiply two perfect squares you get another perfect square. Since 19 is prime, it can\'t be anything lower.','2003-12-20',20040323232102,NULL,2,3,1,0.00,00000000000000,29);
INSERT INTO problem VALUES (683,20,2,794,'Mysteries of the English Language','A man who only spoke Greek came to America for the first time. He realized that he needed to learn English, so he took a class. When questioned by his teacher, \"How do you spell fish?\" he replied \"g-h-o-t-i\". The teacher was very surprised as to how he could get such an answer since he was learning English so well. He asked the man, \"How did you get that answer?\" When the man replied, the teacher accepted his answer with a chuckle. What was his answer?\r\n \r\nHint: Think about the many oddities of the English language.','G-H-O-T-I\r\n \r\nWhen you say \"enough\", the \"gh\" is pronounce like an \"F\" \r\nWhen you say \"women\" the \"o\" is pronounced like an \"I\" \r\nWhen you say \"caution\" the \"ti\" is pronounced like an \"SH\". \r\nTherefore \r\nG-H-O-T-I, can be pronounced like \"fish\"','2003-03-20',20030725232103,NULL,3,3,0,3.00,20030320000000,0);
INSERT INTO problem VALUES (684,2,2,834,'The Plan','There is an island with 10 inhabitants. One day a monster comes and says that he intends to eat every one of them but will give them a chance to survive in the following way:\r\n \r\nIn the morning, the monster will line up all the people - single file so that the last person sees the remaining 9, the next person sees the remaining 8, and so on until the first person that obviously sees no one in front of himself. The monster will then place black or white hats on their heads randomly (they can be all white, all black or any combination thereof). \r\nThe monster will offer each person starting with the last one (who sees everyone else\'s hats) to guess the color of his/her own hat. The answer can only be one word: \"white\" or \"black\". The monster will eat him on the spot if he guessed wrong, and will leave him alive if he guessed right. All the remaining people will hear both the guess and the outcome of the guess. The monster will then go on to the next to last person (who only sees 8 people), and so on until the end. \r\nThe monster gives them the whole night to think. \r\n \r\nThe Task:\r\n \r\nDevise the optimal strategy that these poor natives could use to maximize their survival rate. \r\n \r\nAssumptions:\r\n \r\n \r\nLet us say that guy #10 (first to speak, and sees the hats of the remaining 9) says \"white\". That should mean to everybody else that he sees an odd number of white hats. At this time guy #9 will either be wearing a white or a black hat. If he is wearing a white hat he will only see an even number of white hats, and since guy #10 said that there is and odd number of white hats, guy #9 will know that he is wearing white and will say it. But if guy #9 is wearing a black hat, he will see an odd number of white hats (just like #10 did), and thus will know that he is wearing a black hat and will say it. No matter what #9 answers, guy #8 (who heard guy #10 and guy #9) can now easily incorporate the color of hat on guy #9 into the original answer of guy #10. This will allow #8 to know if he should see an odd or even number of white hats in front of him to determine his own hat color. The same thing repeats with #7-1. And they all get it right except of course #10, though he may get lucky. \r\n','2003-03-21',20031217232102,NULL,3,3,0,4.00,20030321000000,0);
INSERT INTO problem VALUES (786,13,2,1660,'Cool sequence 2','Here is a cool sequence.\r\n \r\n1,10,101,1020,10301,______,_______...\r\n \r\nWhat numbers go in the two blanks?\r\n\r\n ','The first blank should be 104030. \r\n \r\nHe calmly continued on his way, without bothering to notify the police. \r\n \r\nWhy not? \r\n\r\n\r\n','Answer:\r\nThe collective noun for crows is a murder and it was a murder of crows that Clem saw. \r\n','2003-04-03',20040323232104,NULL,3,3,0,3.15,20030403014022,0);
INSERT INTO problem VALUES (687,17,2,834,'The floating mystery','A cork, say from a wine bottle, is held by a robotic clamp at the bottom of a bucket of water and released the moment the bucket is dropped off the side of a tall building. What will happen to the cork during the fall? Will it float to the top of the bucket normally, slower than normal, faster than normal, or not at all? \r\n \r\nAssume that there is no air resistance to slow the bucket down. \r\n','The cork will stay at the bottom of the bucket and not float up at all during the fall, since the cork, the bucket and the water all fall at the same acceleration g (neglecting air resistance as all good physics questions do). The buoyant force of the water does not push the cork upward in this case since in free fall the buoyant force is zero. In other words, a cork only floats up when the water around it is heavier and pushes it up. In free fall the water is weightless, as is the cork and bucket, so there is no force to push the cork to the top of the bucket. \r\n','2003-03-26',20031124232102,NULL,3,3,0,3.80,20030326072104,0);
INSERT INTO problem VALUES (688,17,2,834,'Boiled eggs?','Sam Rottenegger got some free tickets to go and see his least favorite band. Sam, feeling a little unruly, stopped at the corner store so he could bring a 1/2 dozen eggs with him to the concert. \r\n \r\nThe concert was packed and the tunes where so loud that Sam could hardly stand it. He started making his way through the crowd when one of the eggs broke in his pocket and ran down the inside of shirt. Sam squirmed with disgust but thought how great it would be to see that yellow ooze on the band members. \r\n \r\nIt took him 60 grueling minutes to make his way close enough to launch his attack. Sam chucked one right at the bass player but it just bounced off him without breaking. \r\n \r\n\"Odd,\" Sam thought, but every one of the 4 eggs he threw just landed unbroken. He never got to throw the 5th as security removed Sam promptly. Sam, now half deaf, bruised, battered, and confused looked closely at the egg and noticed it wasn\'t exactly raw anymore. Frustrated, Sam chucked the egg over his shoulder hitting an Officer who gladly gave him a free nights stay at the Bars Inn. \r\n \r\nSo what happened to the eggs that caused them not to break? Note that they were totally raw when he brought them in. \r\n','High volume sound waves at certain frequencies can cause the proteins in an egg to stick together almost like when it is boiled. Thus the eggs bounced like a hard boiled egg instead of breaking. \r\n','2003-03-27',20031028232101,NULL,3,3,0,3.67,20030327200659,0);
INSERT INTO problem VALUES (690,17,2,834,'Cool it fast...','A blacksmith wishes to cool his hot piece of steel as rapidly as possible. He has a bucket of ice-water and a bucket of oil (at room temperature). Which bucket should he dump his steel into? \r\n \r\n','Answer:\r\nHe should put the steel into the oil as the liquid will lower the temperature quicker. The water will actually boil as it touches the metal, but that gas will insulate the hot steel from the rest of the cooling water. \r\n','2003-04-01',20031108232108,NULL,3,3,0,2.50,20030401023122,0);
INSERT INTO problem VALUES (692,17,2,1549,'Rise of an object-Physics','If a 7kg object is thrown straight upwards at a speed of 10m/s(meters per second)\r\n \r\nTo what height will it rise?\r\n\r\nnote: gravitational constant = -9.8m/s','Of course as you know the answer is 5.1m\'s (This is just about the same with or without air resistance)explainations are given in the comments. There are many ways of getting to this solution. Try to see how many you can come up with.\r\n \r\nI would post full explainations but they would take up a lot of space(I tried). ','2003-04-01',20040303215126,NULL,3,3,0,3.33,20030401082701,0);
INSERT INTO problem VALUES (697,7,1,979,'House Numbers','Mr. X and Mr. Y live in the same avenue with only 9 houses between them. The number on their houses were both prime, and Mr. X found that he could express the number of his house as the sum of the squares of the digits of Mr. y\'s house number. \r\n \r\nWhat is the probabilty of both decks being in the EXACT same order after shuffling?','VERY low. \r\n \r\nThe answer is 1 in 52!, which works out at approximately 1 in 8.06 x 10^67\r\n','2003-03-22',20030823232102,NULL,2,3,0,2.67,20030322000000,0);
INSERT INTO problem VALUES (698,7,2,979,'Squares and Cubes','What are the two smallest positive whole numbers the difference of whose squares is a cube and the difference of whose cubes is a square ?\r\n\r\n','6 and 10 are the two smallest such numbers which satisfy the conditions of the given problem.','2003-12-06',20040104121504,NULL,2,3,0,3.67,20031206105652,0);
INSERT INTO problem VALUES (1840,13,0,3172,'You can\'t have your cake and eat it too.','What are the next 4 digits in the sequence: \r\n1/A + 1/B + 1/C = 1.','There are only 3 unique solutions. {A,B,C}: {3,3,3}, {2,3,6}, and {2,4,4}.\r\n \r\nAlso if negative numbers are included, the enswer will be any set in the form of {-X,1,X}\r\n \r\nEnder provides an explanation here .','2003-07-18',20040225103933,NULL,2,3,0,3.33,20030718015520,0);
INSERT INTO problem VALUES (700,16,2,1301,'Equidistant points on the Axes','Two points, A and B, are on the Cartesian plane at (-1,4) and (9,6).\r\n \r\nA. What point on the x-axis is equidistant from each of these two points? \r\n \r\nB. What point on the y-axis is equidistant from these two points?','The locus of all points equidistant from the two points is the perpendicular bisector of the line segment bounded by the two points. The perpendicular bisector goes through the point midway between them, (4,5), and has a slope that is the negative of the reciprocal of the slope of the segment. The segment\'s slope is 1/5, so the slope of the perpendicular bisector is -5. Its equation is y=-5x+b and b has to satisfy 5=-5(4)+b, so b=25 and the line sought is y=-5x+25. \r\nPart A: That linear function intersects the x-axis when y=0, so 0=-5x+25, and x=5. \r\nAlternatively, the Pythagorean relationship would give (x+1)^2+4^2 = (9-x)^2+6^2, which also solves to x=5. \r\nFor part B, since the equation of the perpendicular bisector is -5x+25, if we substitute x=0, we get y=25. Or, (-1)^2+(y-4)^2 = 9^2+(y-6)^2, which also solves to y=25.','2003-03-28',20030821232101,NULL,2,3,0,3.40,20030328062759,0);
INSERT INTO problem VALUES (701,14,2,775,'Mystery Numbers','I have chosen 3 different whole numbers less than 10, and have found several simple combinations that lead to perfect squares. Calling the numbers x,y, and z, the following combinations all yield a perfect square as the answer. (A perfect square is a number that has a whole number square root).
\r\nWhy?:If it is solvable or unsolvable,then it has a solution,and if it has a solution,then it is solvable or unsolvable.\r\n
\r\nWhy?:If it is unsolvable,then it does not have a solution,and if it does not have a solution,then it is unsolvable.\r\n
\r\n1:(avb)<->c,Given.
\r\n2:b<->(~c),Given.
\r\n3:(avb)<->(~b),Consequence of 1 and 2.
\r\n4:b->(avb),Tautology.
\r\n5:(avb)->(~b),Consequence of 3.
\r\n6:b->(~b),Consequence of 4 and 5.
\r\n7:(b->(~b))->(~b),Tautology.
\r\n8:~b,Consequence of 6 and 7.
\r\n9:c,Consequence of 2 and 8.
\r\n10:c->(avb),Consequence of 1.
\r\n11:avb,Consequence of 9 and 11.
\r\n12:(avb)&(~b),Consequence of 8 and 11.
\r\n13:((avb)&(~b))->a,Tautology.
\r\n14:a,Consequence of 12 and 13.\r\n
THE ONLY WINNING MOVE IS
NOT TO PLAY\r\n* . . . . . . . * . . . . . . . . . . . . * . .\r\n. . . . . . * . . . . . . . * . * . . . . . . .\r\n. . . . * . . . . . . * . . . . . . . . * . . .\r\n. . . . . . . * . . . . . * . . . * . . . . . .\r\n. * . . . . . . . . . . . . . * . . . . . . . *\r\n. . . * . . . . . * . . . . . . . . * . . . . .\r\n. . . . . * . . . . . . * . . . . . . . . . * .\r\n. . * . . . . . . . * . . . . . . . . * . . . .\r\n--------------- --------------- ---------------\r\n\r\n. . . * . . . . . . . . * . . . . . * . . . . .\r\n* . . . . . . . * . . . . . . . * . . . . . . .\r\n. . . . * . . . . . . . . . . * . . . . . . * .\r\n. . . . . . . * . . . * . . . . . . . . * . . .\r\n. * . . . . . . . * . . . . . . . . . . . . . *\r\n. . . . . . * . . . . . . . * . . * . . . . . .\r\n. . * . . . . . . . * . . . . . . . . * . . . .\r\n. . . . . * . . . . . . . * . . . . . . . * . .\r\n--------------- --------------- ---------------\r\n\r\n. . . . * . . . . . . . . . * . . . . . * . . .\r\n* . . . . . . . * . . . . . . . * . . . . . . .\r\n. . . * . . . . . . * . . . . . . . . . . . . *\r\n. . . . . * . . . . . . . . . * . . . . . * . .\r\n. . . . . . . * . . . . . * . . . . * . . . . .\r\n. * . . . . . . . . . * . . . . . . . . . . * .\r\n. . . . . . * . . * . . . . . . . * . . . . . .\r\n. . * . . . . . . . . . * . . . . . . * . . . .\r\n--------------- --------------- ---------------\r\n\r\n. . . . * . . . . . . . * . . . . . . . . * . .\r\n. . * . . . . . . . . . . . * . . . * . . . . .\r\n* . . . . . . . * . . . . . . . * . . . . . . .\r\n. . . . . . * . . . . * . . . . . . . . . . . *\r\n. * . . . . . . . * . . . . . . . . . * . . . .\r\n. . . . . . . * . . . . . . . * . * . . . . . .\r\n. . . . . * . . . . . . . * . . . . . . . . * .\r\n. . . * . . . . . . * . . . . . . . . . * . . .\r\n--------------- --------------- ---------------\r\n
\r\n',NULL,0);
INSERT INTO comment VALUES (5424,835,1301,'Charlie','re: solution','2003-06-03 08:30:47',0,'As for the programming exercise, this is what I used. The first part finds all 92 (as it turns out) solutions. Phase 2 then reads the file produced in part 1 and copies to a second file only those that are not trivial rotations/reflections of one that had come before.\r\n\r\nDECLARE SUB placeQueen (col!)\r\nDIM SHARED board(8, 8), ct\r\n\r\nOPEN \"8queens.txt\" FOR OUTPUT AS #1\r\nplaceQueen 1\r\nPRINT ct\r\nCLOSE\r\n\r\nphase2:\r\n\r\nOPEN \"8queens.txt\" FOR BINARY AS #1\r\nOPEN \"8queensc.txt\" FOR OUTPUT AS #2\r\nrow$ = SPACE$(16)\r\nFOR soln = 1 TO ct\r\n stPos = (soln - 1) * 18 * 9 + 1\r\n FOR row = 1 TO 8\r\n GET #1, stPos + (row - 1) * 18, row$\r\n FOR col = 1 TO 8\r\n IF MID$(row$, col * 2 - 1, 1) = \"*\" THEN\r\n board(row, col) = 1\r\n ELSE\r\n board(row, col) = 0\r\n END IF\r\n NEXT\r\n NEXT\r\n good = 1\r\n FOR solRef = 1 TO soln - 1\r\n stPos = (solRef - 1) * 18 * 9 + 1\r\n FOR row = 1 TO 8\r\n GET #1, stPos + (row - 1) * 18, row$\r\n FOR col = 1 TO 8\r\n IF MID$(row$, col * 2 - 1, 1) = \"*\" THEN\r\n board2(row, col) = 1\r\n ELSE\r\n board2(row, col) = 0\r\n END IF\r\n NEXT\r\n NEXT\r\n FOR rotRef = 1 TO 7\r\n bad = 1\r\n FOR r = 1 TO 8\r\n FOR c = 1 TO 8\r\n SELECT CASE rotRef\r\n CASE 1\r\n r2 = 9 - r\r\n c2 = c\r\n CASE 2\r\n r2 = 9 - r\r\n c2 = 9 - c\r\n CASE 3\r\n r2 = r\r\n c2 = 9 - c\r\n CASE 4\r\n r2 = 9 - c\r\n c2 = r\r\n CASE 5\r\n r2 = 9 - c\r\n c2 = 9 - r\r\n CASE 6\r\n r2 = c\r\n c2 = 9 - r\r\n CASE 7\r\n r2 = c\r\n c2 = r\r\n END SELECT\r\n IF board(r, c) <> board2(r2, c2) THEN bad = 0: EXIT FOR\r\n NEXT\r\n IF bad = 0 THEN EXIT FOR\r\n NEXT\r\n IF bad THEN good = 0: EXIT FOR\r\n NEXT\r\n IF good = 0 THEN EXIT FOR\r\n NEXT\r\n IF good THEN\r\n stPos = (soln - 1) * 18 * 9 + 1\r\n FOR row = 1 TO 9\r\n GET #1, stPos + (row - 1) * 18, row$\r\n PRINT #2, row$\r\n NEXT\r\n ct2 = ct2 + 1\r\n END IF\r\nNEXT\r\nPRINT ct2\r\n\r\nSUB placeQueen (col)\r\n FOR row = 1 TO 8\r\n good = 1\r\n FOR c = 1 TO col - 1\r\n IF board(row, c) THEN good = 0: EXIT FOR\r\n r = row - (col - c)\r\n IF r > 0 THEN\r\n IF board(r, c) THEN good = 0: EXIT FOR\r\n END IF\r\n r = row + (col - c)\r\n IF r < 9 THEN\r\n IF board(r, c) THEN good = 0: EXIT FOR\r\n END IF\r\n NEXT\r\n IF good THEN\r\n board(row, col) = 1\r\n IF col = 8 THEN\r\n ct = ct + 1\r\n FOR r = 1 TO 8\r\n FOR c = 1 TO 8\r\n IF board(r, c) THEN\r\n PRINT #1, \"* \";\r\n ELSE\r\n PRINT #1, \". \";\r\n END IF\r\n NEXT\r\n PRINT #1,\r\n NEXT\r\n PRINT #1, \"--------------- \"\r\n ELSE\r\n placeQueen col + 1\r\n END IF\r\n board(row, col) = 0\r\n END IF\r\n NEXT\r\nEND SUB\r\n\r\n',5423,0);
INSERT INTO comment VALUES (5425,538,1301,'Charlie','re: One and Only','2003-06-03 08:48:16',0,'While the Random House dictionary defines prime number\r\n\r\na positive integer that is not divisible without remainder by any integer except itself and 1, with 1 often excluded\r\n\r\nmathematicians would almost always exclude 1, rather than just \"often\". Otherwise prime factorizations would not be unique. For example, 15 = 3 x 5 becomes 15=3x5 or 15=3x5x1 or 15 = 3x5x1x1 or 15=3x5x1x1x1, etc.',5419,0);
INSERT INTO comment VALUES (5426,442,1919,'Lewis','Solution','2003-06-03 09:03:34',3,'If Grandma is 45 years older then the two digits of their ages must have a difference of 5.\r\nThe only single digit prime numbers with a difference of five are 2 and 7. 27 + 45 = 72, so Grandma is 72 and the dad is 27.',NULL,0);
INSERT INTO comment VALUES (5427,836,2129,'Sanjay','re(2): Bang for the Buck','2003-06-03 09:37:45',0,'It also states that \'everyone will want to do what is best for them\'. The only way to reconcile the seemingly conflicting requirements of \'at least one bid\' and \'freedom to choose the best strategy\' is the interpretation that \'in order for the dollar to be won, there must be at least one bid\'. \r\n 1\r\n2)2\r\n
\r\nso place a 1 to the right in the dividend:\r\n\r\n 1\r\n2)21\r\n 2 \r\n 01\r\n
\r\nrequiring a zero in the quotient, and also to the right in the dividend, and brought down:\r\n\r\n 10\r\n2)210\r\n 2 \r\n 010\r\n
\r\nleading to a 5 in the quotient and dividend:\r\n\r\n 105\r\n2)2105\r\n 2 \r\n 010\r\n 10\r\n 05\r\n
\r\nleading to a 2, etc.\r\n\r\nuntil eventually a 04 (not a 05) appears at the bottom that has to be divided by 2, so a 2 can be placed at the rightmost portion and zero out the bottom subtraction.',NULL,0);
INSERT INTO comment VALUES (5457,865,103,'friedlinguini','Recursion','2003-06-04 04:46:53',0,'Nope, the correct answer is, \"Nope, the correct answer is, \"Nope, the correct answer is, \"Nope, the correct answer is... (etc)',NULL,0);
INSERT INTO comment VALUES (5458,844,1660,'Tim Axoy','DJ or .?','2003-06-04 05:31:19',4,'When this problem first appeared on the site,the author was DJ.\r\nNow it is ..\r\nDid DJ or . make this?',NULL,0);
INSERT INTO comment VALUES (5459,865,1660,'Tim Axoy','re: Recursion','2003-06-04 05:35:43',0,'Is that sentence ∞ly long?',5457,0);
INSERT INTO comment VALUES (5460,836,2075,'Matt','','2003-06-04 06:03:37',0,'As the first bid nobody would bother risking 1 dollar for a 1 dollar return therefore 99 cents is the best first and only bid. If you can\'t bid this first then don\'t bother. \r\n\r\nIf 99 cents was made as the only bid, there would be no previous chain of \'one upmanship\' to contend with therefore nobody else would bother bidding at all. So you would make 1 cent per lot.\r\n ',NULL,0);
INSERT INTO comment VALUES (5461,844,1919,'Lewis','re: DJ or .?','2003-06-04 06:55:10',0,'Umm... DJ posted it, but either he\'s changed his name or there\'s been a mistake. If you click on the dot it still says \'Hi I\'m DJ....\' or something in the about bit.',5458,0);
INSERT INTO comment VALUES (5462,865,2231,'Trevor Leitch','re: er','2003-06-04 06:58:09',0,'How about \"maybe\"?',5452,0);
INSERT INTO comment VALUES (5463,847,1686,'DuCk','Solution','2003-06-04 08:40:25',0,'Defining \"moisture content\" as the weight of the wet potatoes minus the weight of the potatoes when completely dry over the weight of the wet potatoes times 100, we find the solution of:\r\n\r\nat MC=98% ==> potatoes weigh 50lbs\r\nat MC=50% ==> potatoes weigh 2lbs',NULL,0);
INSERT INTO comment VALUES (5464,847,1567,'Bryan','solution','2003-06-04 08:40:30',3,'The original hundred pounds is 99 lbs water and 1 lb potato solids. When The moisture gets to 98%, the solids must account for 2%.
If 2%=1 lb, then 98%=49 lbs. Thus, at 98% moisture content, the potatoes weigh 50 lbs total.
R = S*t*dL/dt
or, solving for dL,
dL = [R/(S*t)]*dt
R/S *ln(t) from T to T+1 = 2*R/S *ln(t) from T+1 to T+2
canceling out the R/S terms,
ln(T+1)-ln(T) = 2*[ln(T+2)-ln(T+1)]
3*ln(T+1)= 2*ln(T+2)+ln(T)
ln[(T+1)^3]=ln[T*(T+2)^2]
(T+1)^3= T*(T+2)^2
T^3+3T^2+3T+1=T^3+4T^2+4T
T^2+T-1=0
T=(-1±sqrt5)/2
T=0.6180 hours (approximately 37 minutes) or T=-1.618
GONE
GOND
GOLD
WOLD
WOLFB C B A _ _ _ _\r\n\r\nSuppose, then, that the answer to #1 is \'C.\'\r\nC _ _ _ _ _ _ _\r\nObviously, then, it is the first \'C,\' and number three is \'D.\'\r\nC _ D _ _ _ _ _\r\nAlso, number two must be \'D.\'\r\nC D D _ _ _ _ _\r\nFrom that, number 4 is \'B.\'\r\nC D D B _ _ _ _\r\nThat means that there are two questions with \'B\' as their answer, one of which is this question, and one of which is in the last four questions.\r\n\r\nSuppose, first, that the fifth answer is \'B.\'\r\nC D D B B _ _ _\r\nThat means that three of the four even-numbered questions are answered with either \'B\' or \'C\'. Number two is not, and four is, so numbers six and eight must both be either \'B\' or \'C.\'\r\nHowever, since we have that there are only two Bs altogether, which are already placed, six and eight must both be \'C.\'\r\nC D D B B C _ C\r\nAn answer of \'C\' to question six means that the answer to #5 is \'A,\' but that has already been penned as \'B.\' So, the last assumption must be false.\r\nC D D B B C _ C\r\n\r\nSuppose, then, that number six is \'B.\'\r\nC D D B _ B _ _\r\nThat answer stipulates that number seven is \'A.\'\r\nC D D B _ B A _\r\nAn answer of \'A\' there says that there are two instances of consecutive \'D\' answers. There is already one, but with the currently assumed answers, there is no way to fit in another match.\r\nSo, the last assumption, again, must be false.\r\nC D D B _ B A _\r\n\r\nSuppose that the answer to number seven is \'B.\'\r\nC D D B _ _ B _\r\nThat says that nowhere in the problem are two consecutive answers of \'D,\' but we already have one instance.\r\nTherefore, this cannot be the case.\r\nC D D B _ _ B _\r\n\r\nFinally, for the previous assumption to be valid, the answer to number eight must be \'B.\'\r\nC D D B _ _ _ B\r\nThat answer says that there are exactly three Ds, and not three of any other answer in the set of problems. Two have been placed already as answers to numbers two and three, and the final \'D\' must answer one of the fifth, sixth, or seventh questions.\r\nFurther, we know (given these assumptions) that there is exactly one more \'D,\' and therefore no way to make another pair of consecutive Ds other than the pair already made.\r\nSo, the answer to number seven must be \'C.\'\r\nC D D B _ _ C B\r\n\r\nNow, there are two answers left, one of which is \'A\' (from the general assumptions based on question 6) and the other which is \'D\' (from the current answer to question eight.\r\nLooking at number six, we already have answered questions seven and eight. So, the \'A\' must be number five or six, and the answer to question six is \'A\' or \'C.\'\r\nHowever, we know that it must be one of \'A\' or \'D\' (for reasons stated above).\r\nTherefore, it must be \'A.\'\r\nC D D B _ A C B\r\nFinally, the third \'D\' must answer question five.\r\nC D D B D A C B\r\nThat answer implies that two of the four even-numbered questions in the problem are answered with either \'B\' or \'C.\'\r\nInspecint these answers, that is indeed the case (they are D, B, A, B).\r\nDouble checking the other answers with their questions:\r\nThe answer to #2 is \'D\' (1)\r\nThe answer to #4 is \'B\' (2)\r\nThe first answer of \'C\' is to question #1 (3)\r\n\'B\' correctly answers exactly two questions (4)\r\nThere are 2 even-numbered answers of \'B\' or \'C\' (5)\r\nThe last (and only) answer of \'A\' in the solution set is to question six (6)\r\nTwo consecutive Ds appear only once in the solution set (7)\r\nThere are exactly three Ds and not three of any other respose letter (8)\r\n\r\nEverything checked so [a] valid solution is\r\nC D D B D A C B\r\n11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111S\r\nLastly, to perform a thorouth check, what happens if we assume number one to be \'D\'?\r\nD _ _ _ _ _ _ _\r\nIf that is the case, number two is \'A.\'\r\nD A _ _ _ _ _ _\r\nFrom that, number four must be \'D.\'\r\nD A _ D _ _ _\r\nAlso, since (as stated in the introduction) no Cs have been placed, but one of the first four must be a \'C,\' which in this case must he answer to number three.\r\nD A C D _ _ _ _\r\n\r\nFrom the answer of \'D\' to number 4, there are four Bs in the problem. None have been placed yet in the fire time,\r\nTherefore, the remaining four blanks must all be Bs.\r\nD A C D B B B B\r\nThis last assumption is quite easily disproven by any of the latter four questions.\r\nD A C D B B B B\r\n\r\nSo, the only valid possibility for the answers is as follows:\r\n\r\n
',NULL,0);
INSERT INTO comment VALUES (5570,905,1575,'DJ','re: Solution','2003-06-08 00:51:27',0,'(Excuse the typos in the previous post; the line of 111s and the incomplete final list of answers were of course unintended, as well as anything else I may have missed)',5569,0);
INSERT INTO comment VALUES (5571,826,1660,'Tim Axoy','Dunno','2003-06-08 02:32:58',0,'This seems like no flaw.',NULL,0);
INSERT INTO comment VALUES (5572,905,1660,'Tim Axoy','HARD!','2003-06-08 02:43:35',0,'This is so hard!\r\nGive me a hint.',NULL,0);
INSERT INTO comment VALUES (5573,845,693,'Jun','Solution','2003-06-08 04:37:32',0,'I guess the answer would be 22, since going by the examples given, there would be two 2s making it 22.',NULL,0);
INSERT INTO comment VALUES (5574,845,1626,'Gamer','re: Solution','2003-06-08 04:48:26',3,'I thought about that... but the number machine only seems to work on numbers beginning with 1_ or 21_\r\n\r\n2x gives yy... so x = 2 and y = 2. But 2 doesn\'t seem to work.\r\n\r\nSince 10^?+x will never equal x, we must be looking at the last sequence.\r\n\r\nSo... 2 __ = __ __\r\n\r\nBut putting the first sequence into the second one, you get\r\n\r\n2(1 __)=(__)(__)\r\n\r\nSo 21 followed by a number equals the same number twice.\r\n\r\nSince 121 gives 21, 2121 gives 2121.\r\n\r\nThis number must be 21, so 121 gives itself.\r\n\r\n\r\n',5573,0);
INSERT INTO comment VALUES (5575,848,1301,'Charlie','Another non-obscure 6-step solution','2003-06-08 04:56:42',0,'It seems the only words that differ by one letter from WOLF are GOLF, ROLF, WOLD and WOOF. For a 5-step solution you can\'t get GOLF, but must use the next-least-obscure word, ROLF.\r\n\r\nGamer provided a 6-step solution using GOLF. Another is:\r\n\r\nLONE\r\nHONE\r\nHOLE\r\nHOLD\r\nGOLD\r\nGOLF\r\nWOLF\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (5576,845,1301,'Charlie','re(2): Solution','2003-06-08 05:02:57',0,'What\'s with the last line: \"This number must be 21, so 121 gives itself\"?\r\n\r\nThe line preceding that gave a correct answer, \"2121 gives 2121\".',5574,0);
INSERT INTO comment VALUES (5577,845,1626,'Gamer','re(3): Solution','2003-06-08 06:56:20',0,'No, that line means the solution.\r\n\r\nBecause when you combine the statments, you get \"21y gives yy\", and subtracting a y from both sides, you get \"21 gives y\", so y must be 21.\r\n\r\nWhen I said 121 gives itself, I mean 121 = x for the second rule. 2 121 = 21 21. I found y, then figured out what x was. Then I could figure out what the number that gives itself.',5576,0);
INSERT INTO comment VALUES (5578,905,1567,'Bryan','re: DJ\'s Solution','2003-06-08 09:13:59',0,'Bravo, DJ! In retrospect, I think this one is as much a test of patience as it is of deduction!',5569,0);
INSERT INTO comment VALUES (5579,455,1919,'Lewis','Solution','2003-06-08 10:24:10',3,'The answer is four.\r\n\r\nIf you were trying to get two marbles of the same colour, and there are three colours, the most you can pick out without two of a colour is three - one of each colour.\r\n\r\nTherefore the next one you pick out has to be the same colour as one of the others, so the answer is four.\r\n\r\nThis problem was a little easy, so I decided to work out the probabilities.\r\n\r\nWhen you pick out the first one, it means there are only three of that colour left. So the probability that the second will be the same is 3/11.\r\n\r\nIf you didn\'t get the same colour, then you\'ll have two different colours, each with three of the same in the bag, and the remaining colour will have four in the bag. This means that the probability of getting a colour you already got is 3/5.\r\n\r\nAnd if you still didn\'t get a duplicate colour, the next one has a probability of 1, seeing as there is no other different colours.',NULL,0);
INSERT INTO comment VALUES (5580,845,1301,'Charlie','My Solution','2003-06-08 10:35:49',3,'Since 1x gives x, 121 gives 21, which is not itself (121 is not 21).\r\n\r\nHowever, since when x gives y, then 2x gives yy, let 121 be the x and 21 be the y (as one gives the other per the first paragraph), then 2121 gives 2121, that is itself, as 2121 is indeed 2121.',5577,0);
INSERT INTO comment VALUES (5581,836,1626,'Gamer','re(6): Solution','2003-06-08 11:08:25',0,'I just thought of something. Could you (or someone bidding for you) bid on the dollar yourself? This would make the bid of 99 cents a bad idea, or even bidding a dollar for the first bid have problems.\r\n\r\nIf you bid 99 cents and I bid a dollar, (I being the person who is auctioning off the dollar, or the person bidding for/with the auctioneer), I would get your bid of 99 cents.\r\n\r\nEven if you bid a dollar (as your first bid), I would bid a dolllar and a cent. Then I would lose one cent, but gain your bid of a dollar.\r\n\r\nEven if you bid two dollars, then I would bid two dollars and a cent. I would still have a net win of 99 cents against what anyone bid.',5568,0);
INSERT INTO comment VALUES (5582,154,2374,'John Tate','ANSWER!','2003-06-08 11:13:25',3,'92951522 is the answer!',NULL,0);
INSERT INTO comment VALUES (5583,1,2374,'John Tate','Give up.','2003-06-08 11:14:28',4,'How do you?',NULL,0);
INSERT INTO comment VALUES (5584,1,2374,'John Tate','Saw','2003-06-08 11:16:11',0,'I saw the solution.',NULL,0);
INSERT INTO comment VALUES (5585,845,2374,'John Tate','It is...','2003-06-08 11:18:11',0,'...2121.\r\nSince 121 gives 21,2121 gives 2121.\r\nWe can find an i such that for any number x,ix gives xx,so ii will give itself.\r\n21x gives xx since 1x gives x,and so 21 is an i.\r\n2121 must give itself.\r\nGood problem,Tim.',NULL,0);
INSERT INTO comment VALUES (5586,254,2129,'Sanjay','Slip Sliding Away','2003-06-08 12:56:40',0,'I just saw this problem for the first time.
LONF
WONF
WOLF
WONF - sarcastic tossing of the head, meant to convey annoyance at one\'s parents for their abject cluelessness about all things adolescent -- considered very, very slang.
u1j2u3i4j5,j1v2\'v3b1n1c2j3m4h5o1w2p3f4j5x6,z1g2v3j1v2j1u2\r\n',5595,0);
INSERT INTO comment VALUES (5599,892,1567,'Bryan','re(2): t1v2d3x4x5k1q2n3i4 HELP','2003-06-09 08:53:47',0,'Sorry, should say \"a certain appeal.\"',5598,0);
INSERT INTO comment VALUES (5600,892,1919,'Lewis','Solution','2003-06-09 09:07:55',3,'Thanks to friedlinguini\'s hint, I have the solution.\r\n\r\nThe title is - Add It!\r\nThe problem says - What is two plus one?\r\nAnswer(cryptic) - u1j2u3i4j5',NULL,0);
INSERT INTO comment VALUES (5601,892,1626,'Gamer','h1q2r3h4k1q2e3!','2003-06-09 09:09:13',0,'h1q2r3h4k1q2e3z1q2x3u1y2r3!(b1p2g3p1v2k3i4w5y6x1j2r3h1g2w3j1v2u1q2r3)',NULL,0);
INSERT INTO comment VALUES (5602,540,2406,'Cameron','Solution!','2003-06-09 09:10:42',0,'Ahh.. a hobbit riddle. Teeth!',NULL,0);
INSERT INTO comment VALUES (5603,892,1919,'Lewis','re: Solution','2003-06-09 09:10:42',3,'Whoops, wasn\'t finished there.\r\n\r\nAnswer(normal) - three\r\nTo work it out go the number of letters back stated after each letter, eg x1 is one letter before x, so is w.',5600,0);
INSERT INTO comment VALUES (5604,860,2406,'Cameron','Solution!','2003-06-09 09:11:32',0,'A mountain!',NULL,0);
INSERT INTO comment VALUES (5605,859,2406,'Cameron','Solution','2003-06-09 09:14:17',3,'I love Hobbit riddles! The solution is:\r\n\r\nTime',NULL,0);
INSERT INTO comment VALUES (5606,892,1626,'Gamer','s1g2: t1q2o3y4y5o6v7v8','2003-06-09 09:15:33',2,'v1j2d3x4j1u2s1k2j3l4y5!',5600,0);
INSERT INTO comment VALUES (5607,892,1919,'Lewis','re: h1q2r3h4k1q2e3!','2003-06-09 09:16:39',0,'z1g2v3x1g2o3p4e1q2q3i4',5601,0);
INSERT INTO comment VALUES (5608,892,1919,'Lewis','re: s1g2: t1q2o3y4y5o6v7v8','2003-06-09 09:20:26',0,'z1g2v3!',5606,0);
INSERT INTO comment VALUES (5609,205,2379,'Dark','Sol','2003-06-09 09:27:31',0,'As long as bertrand had more apple(s) than alonso, and george had more than bertrand, and kurt has the leftover(s) of at least one, then the answer would be correct.',NULL,0);
INSERT INTO comment VALUES (5610,311,2379,'Dark','I like this one, I can actually solve it','2003-06-09 09:33:06',0,'30 seconds',NULL,0);
INSERT INTO comment VALUES (5611,734,1660,'Tim Axoy','re: solution','2003-06-09 10:19:41',0,'Did I really do this solution?',4226,0);
INSERT INTO comment VALUES (5612,824,2379,'Dark','I did this in gr. five with Mr. Houston','2003-06-09 10:32:07',3,'answer: He was standing on a block of ice(rope is noose around his neck and tied to ceiling fixture) as time went by, ice melted and he died.\r\n',NULL,0);
INSERT INTO comment VALUES (5613,859,2374,'J','Hmmm....','2003-06-09 10:33:24',0,'Hmmm....',NULL,0);
INSERT INTO comment VALUES (5614,859,2374,'J','Answer','2003-06-09 10:33:51',3,'Time.',NULL,0);
INSERT INTO comment VALUES (5615,860,2379,'Dark','re: Straight from the source','2003-06-09 10:37:55',0,'he supposes that it\'s a mountain, so, it\'s not necessarily right. + mountains change through time(deposition and erosion)+ has not roots',5591,0);
INSERT INTO comment VALUES (5616,532,2379,'Dark','','2003-06-09 10:43:53',3,'I believe that everyone else was born a baby and as they aged, they would all seem the same age at 21, when adam and eve were \"born\", they were mature, therefore, at age 21, they would have been 21 years past their mature age. they would look like they were in their forties/fifties',NULL,0);
INSERT INTO comment VALUES (5617,702,2379,'Dark','Umm, I don\'t get it...','2003-06-09 10:57:32',1,'a revolving door with an odd amount of sections?',NULL,0);
INSERT INTO comment VALUES (5618,734,1919,'Lewis','re(2): solution (cheater)','2003-06-09 11:17:31',0,'Tim - you copied and pasted Bryan\'s solution. That\'s not allowed!',5611,0);
INSERT INTO comment VALUES (5619,842,2376,'Jim C','re(2): hmm..','2003-06-09 11:20:55',0,'There are some great theories here. The broken glass is especially elegant. But the Simon Says answer is perfect. He obeyed when he shouldn\'t have and lost the game. Losing always made me sulk when I was young (now I\'ve gotten used to it, I just brood! =0)',5333,0);
INSERT INTO comment VALUES (5620,860,1626,'Gamer','re(2): Straight from the source','2003-06-09 12:41:22',0,'Well I am not quite sure that you are correct either. If I don\'t believe in \"destiny\", in other words, I am given free will... my family tree isn\'t decided already. And it grows anyway...\r\n\r\nPlus, how do you believe that a family tree is \"tall\" since it is only an idea... Even if you pick out the people, nobody is taller than a tree, unless you bend the rules lots. (which isn\'t called for in riddles like these)',5615,0);
INSERT INTO comment VALUES (5621,442,2129,'Sanjay','A non mathematical approach','2003-06-09 14:37:25',0,'For Grandma to be older than Dad the digits must be in descending order in her age, and ascending in Dad\'s. someone we know did not steal the wallet.\r\n\r\nDwayne says that Allan is a liar, so they cannot both be knights.\r\nA B C D E F\r\n\r\nCalvin says that they [Allan and Dwayne] are [liars], so he is a liar. From this, Eddy did not steal it.\r\nA B C D E F\r\n\r\nEddy says that he did not steal it, so he is a knight.\r\nTherefore, Calvin did not steal it.\r\nAlso, there are only four knights.\r\nA B C D E F\r\n\r\nBarry also says Calvin is a liar, therefore he (Barry) is telling the truth.\r\nFrom that, then, we know that he did not steal it and Allan also did not.\r\nA B C D E F\r\n\r\nFred says that Barry did not steal it, so Fred must be a knight.\r\nA B C D E F\r\n\r\nIf Fred is telling the truth, then Allan is a liar, and Fred did not steal it.\r\nA B C D E F\r\n\r\nSince Dwayne says (truthfully) that Allan is a liar, he is a knight.\r\nTherefore, Dwayne is also telling the truth when he says that he did not steal it.\r\nA B C D E F\r\n\r\nSo, none of the six stole the wallet?\r\nThe knights are Barry, Dwayne, Eddy, and Fred, while Allan and Calvin are lying.\r\n\r\nPerhaps you (the author) are a liar, your wallet is not really missing, nobody stole it, you really can figure out if they are truthtellers, and you never asked a few questions anyway, you liar. You\'re not even sure that all the men are either knights or liars.',NULL,0);
INSERT INTO comment VALUES (5652,917,1920,'Brian Smith','Perception and Reality','2003-06-10 15:07:47',0,'I got Allan & Carl are liars and the rest knights and no one stole the wallet. But usually these problems require one of the parties involved is guilty.\r\n\r\nI noticed in Barry\'s statement \"I KNOW Allan did not steal it.\" And in Eddy\'s statement \"I KNOW Calvin did not steal it.\"\r\n\r\nThe key to the puzzle may be that one of the statements is a flawed judgement. Either Barry or Eddy percieves someone innocent but in reality is guilty.',NULL,0);
INSERT INTO comment VALUES (5653,541,1920,'Brian Smith','Some thoughts','2003-06-10 15:11:51',0,'The \'eye in a blue face\' is the sun in the sky. I dont know about the \'eye in a green face.\'',NULL,0);
INSERT INTO comment VALUES (5654,836,2373,'ryan smith','re(3): Dollars and Sense','2003-06-10 15:43:19',0,'Please don\'t misunderstand my reasoning. Here are my two key points:\r\n\r\n-ANY bid puts money at risk.\r\n\r\n-Bidders can calcualte their potential gains and losses for a potential bid. I.e. They are capable of thinking: \"If I bid X, I may win Y or I may lose Z.\" Such immediate outcome perception is reasonable for any gambling problem. Consider a silly guess a card problem (52 cards, guess the top card): If I bet $1, I may win $52 or I may lose $1. There is so extraordinary logical foresight required.\r\n\r\nSo, a second bid of a dollar undoubtedly risks (or commits) $1.00 for zero possible return. There is no logical motivation for this bid. The moment the second bidder utters \"I bid $1.00\" they are bound to either lose $1.00 or win NOTHING. A bidder understanding this is not a \"long term impact\", it it part of the reasoning process for any bid!\r\n\r\nIf the first bid is 98 cents, an imperfect logician in the crowd may reason that if they bid 99 cents they can make 1 cent. So, there is some logical motiviation for a second bid of 99 cents.\r\n\r\nAlso, you\'ve mentioned that a second bid invariably starts a bidding war. Prove it. Someone bids $2 against $1. Both are down $1. Bidding war?\r\n\r\n',5646,0);
INSERT INTO comment VALUES (5655,836,2373,'ryan smith','re(3): Dollars and Sense','2003-06-10 15:47:38',0,'I get the picture.\r\n\r\nBut if we\'re widening the scope of this problem like that, the best strategy is robbing the auctioneer at gun point in the parking lot. \r\n',5635,0);
INSERT INTO comment VALUES (5656,917,1575,'DJ','re: Perception and Reality','2003-06-10 15:51:45',0,'I was thinking something like that, but it seems that a knight who always told the truth would certainly \'know\' if they said they did, the implication of that being that if they know something to be true, then it certainly should be true.\r\n\r\nThat said, it seems to be the only really plausible explanation (and it would certainly account for the strange title of the problem). If that is the case, Allan or Calvin (incidentally, one of the liars) must have taken the wallet, and somehow Barry or Eddy is mistaken in what they \'know.\'\r\n\r\nGood observation!',5652,0);
INSERT INTO comment VALUES (5657,541,2423,'Michael Pepin','Answer to Faces & Eyes','2003-06-10 16:52:36',3,'Eye in a blue face = SUN (1st eye in high place)\r\n\r\nEye in a green face = SUN FLOWER (eye in low place)',NULL,0);
INSERT INTO comment VALUES (5658,824,2423,'Michael Pepin','','2003-06-10 16:55:56',1,'this is too easy',NULL,0);
INSERT INTO comment VALUES (5659,541,2425,'Lunch Box','Answer:','2003-06-10 17:15:14',0,'It\'s the sun and it\'s reflection in a body of water.',NULL,0);
INSERT INTO comment VALUES (5660,541,2426,'Will H','Answer','2003-06-10 17:15:27',0,'I believe this was a riddle from The Hobbit.\r\nThe answer is the sun looking down on a sunflower',NULL,0);
INSERT INTO comment VALUES (5661,540,2426,'Will H','Answer','2003-06-10 17:22:41',0,'The answer, of course, is teeth, or if you want to go with the answer straight from the Hobbit, chestnuts (which is old british slang for teeth).',NULL,0);
INSERT INTO comment VALUES (5662,538,2184,'mark hartman',' maybe not too easy?','2003-06-10 18:15:14',0,'-3 x -1 x 1 = 3; 3 is a prime. A good puzzle, since it appears that if x, x+a, and x+2a are the numbers in progression, then we can prove that x divides the product, implying that the product is not prime. The trick is to notice that the product can be -x, in which case the product can be prime.\r\n',NULL,0);
INSERT INTO comment VALUES (5663,917,2428,'gordo packard','P&R redux','2003-06-11 00:53:40',0,'The trouble with saying that the truth tellers are mistaken is, allowing for this would not allow for a solution to ANY logic problem of this sort. Hey, maybe Barry stole it while he was drunk and just doesn\'t remember. Maybe Allen doesn\'t realize that Fred is reading lips and believes that he can hear. If we assume that this problem follows the standard parameters, the only solution, given the data, is that none of the six is the thief. I think this problem is just badly worded. If the wallet was lost instead of stolen, the final question should be, \"what happened to the wallet?\" If a person other than the six stole it, that person should have been mentioned.',NULL,0);
INSERT INTO comment VALUES (5664,405,2415,'hemalatha','solution','2003-06-11 01:56:16',3,'go from point g(1,1) to (4,1),then draw a line from (4,1) to (1,4)passing through b(3,2) and f(2,3).then draw the line from (1,4) to g(1,1).now draw the line from g(1,1) to c(3,3).',NULL,0);
INSERT INTO comment VALUES (5665,288,2415,'hemalatha','solution','2003-06-11 02:01:56',3,'All the english alphabets are present in the sentence.',NULL,0);
INSERT INTO comment VALUES (5666,274,2415,'hemalatha','solution','2003-06-11 02:14:39',3,'he drew a longer line just parallel to the previous one.',NULL,0);
INSERT INTO comment VALUES (5667,900,1301,'Charlie','solution','2003-06-11 02:58:55',3,'There are 16 different letters represented in the words, so each of the different letters must be present exactly once in the grid. The letter A is used twice in one word and so must be returned to in forming that word (PALACE).\r\n\r\nThe letter A is adjacent to 7 different letters (L, C, G, I, P, F and R) in the various words. Therefore the A must be in one of the central 4 positions, so that it has 8 neighbors-the 7 that it needs plus exactly one that it doesn\'t need.\r\n\r\nSince the letter A needs to be adjacent to P and I, and the letter E must be adjacent to N (because of FRAGMENT) and T (because of COMET), the straight-line words AGE and PINT must be parallel and adjacent to one another and going in the same direction.\r\n\r\nAGE and PINT can\'t be diagonal, as PINT would have to be in one of the two major diagonals in order to fit, and then AGE would be in an adjacent diagonal with only 3 letters; but that would place A outside the central square of 4 and is thus no good.\r\n\r\nThus AGE and PINT must be both either vertical or horizontal, and with A not on an edge, so the A is orthogonally connected to the I and diagonally connected to P and N, and then further, the N is the only letter adjacent to A whose adjacency is not really needed, so any future letters placed next to A must be from the remainder of the required set (L, C, F and R).\r\n\r\nThe C must be next to the A and the E (from PALACE), and so must be orthogonally adjacent to the G in AGE (obviously the other side from the N in PINT). The O in COMET is horizontally connected to the C, but cannot be next to the A as it\'s not one of the remaining 4 to be connected to A, and it cannot be next to the E, as that would leave no room for the M between the O and the E. Therefore AGE and PINT must be vertical rather than horizontal so that CO can proceed horizontally away from this pair, as in the following diagram:\r\n\r\n P\r\n AI\r\nOCGN\r\n ET\r\n
\r\n\r\nNote that this diagram may be reversed left-right, or up-down, as we don\'t yet know where the optional space will come about for the W. At the end, we can adjust by flipping left-right or reversing the order of the rows to place the W in the upper left corner of the final result.\r\n\r\nThe M in COMET must be placed in the only position adjacent to both the O and the E. The R in ARCHLY must then be in the only position next to both the A and the C. The H in archly must then be placed above the O in the above diagram as it must be adjacent to the C, but going below the O would not allow enough room to complete ARCHLY (and the L must be next to the A anyway). That being said, the L must go in the only position left that\'s adjacent to the O and the A. The Y must go to the top left, leaving room for the F to go next to the A by the P.\r\n\r\nThat leaves us with:\r\n\r\nYLFP\r\nHRAI\r\nOCGN\r\n MET\r\n
\r\n\r\nSo the only place for the W on this diagram is the lower left, which we get to the upper left by reversing the order of the rows:\r\n\r\n\r\nWMET\r\nOCGN\r\nHRAI\r\nYLFP\r\n
\r\n\r\nwhich is the answer.\r\n',NULL,0);
INSERT INTO comment VALUES (5668,541,1575,'DJ','ask Tolkien','2003-06-11 03:29:53',3,'\"Ss, ss, ss,\" said Gollum.. \"Sss, sss, my preciouss\" .. \"Sun on the daisies it means, it does.\"',NULL,0);
INSERT INTO comment VALUES (5669,917,103,'friedlinguini','re: Perception and Reality','2003-06-11 03:59:46',1,'I thought of that. If you call perception into the question, then all statements go out the window, since anybody could be mistaken. The \"I know\" statements could be interesting if they were made by liars (in which case the statements become indeterminate), but when I went through it, they were only made by knights, so both the knowing part and what was known must be true.',5652,0);
INSERT INTO comment VALUES (5670,900,1301,'Charlie','Other big words','2003-06-11 05:23:54',0,'Other (besides fragment) words of 8 letters or more that can be found in the solution grid are:\r\n\r\n 10: acromegaly, engagement, engraining, frangipane, frangipani, ingraining\r\n 9: centenary, garagemen\r\n 8: arginine, carapace, engaging, engining, flagrant, flanging, fragrant, garaging, graining, integral, morainal, tenement, alanine\r\n \r\nfound by:\r\n \r\nDECLARE SUB searchGrid (row!, col!, w$, posn!)\r\nDIM SHARED grid$(4, 4)\r\n\r\nDATA wmet,ocgn,hrai,ylfp\r\n\r\nFOR row = 1 TO 4\r\n READ r$\r\n FOR col = 1 TO 4\r\n grid$(row, col) = MID$(r$, col, 1)\r\n NEXT\r\nNEXT\r\n\r\nOPEN \"\\words\\words.txt\" FOR INPUT AS #1\r\nOPEN \"bogwords.txt\" FOR OUTPUT AS #2\r\nDO\r\n LINE INPUT #1, w$\r\n IF LEN(w$) > 2 THEN\r\n FOR row = 1 TO 4\r\n FOR col = 1 TO 4\r\n IF grid$(row, col) = LEFT$(w$, 1) THEN\r\n searchGrid row, col, w$, 2\r\n END IF\r\n NEXT\r\n NEXT\r\n END IF\r\nLOOP UNTIL EOF(1)\r\nCLOSE\r\nEND\r\n\r\nSUB searchGrid (row, col, w$, posn)\r\n FOR r = row - 1 TO row + 1\r\n IF r > 0 AND r < 5 THEN\r\n FOR c = col - 1 TO col + 1\r\n IF c > 0 AND c < 5 THEN\r\n IF row <> r OR col <> c THEN\r\n IF MID$(w$, posn, 1) = grid$(r, c) THEN\r\n IF posn = LEN(w$) THEN\r\n PRINT w$\r\n PRINT #2, USING \"### &\"; LEN(w$); w$\r\n ELSE\r\n searchGrid r, c, w$, posn + 1\r\n END IF\r\n END IF\r\n END IF\r\n END IF\r\n NEXT\r\n END IF\r\n NEXT\r\nEND SUB\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (5671,11,1919,'Lewis','Easy Solution','2003-06-11 05:48:57',3,'Okay - because the road is straight, the bee is always travelling three times the speed of the cyclist (assuming he doesn\'t take any time turning).\r\n\r\nThe cyclist travelled 10 miles so the bee travelled 30 miles.',NULL,0);
INSERT INTO comment VALUES (5672,917,1715,'Jonny Doe','Fred??','2003-06-11 07:03:23',1,'I think that we managed to determine that Allan and Calvin are both liars while every one else are knights, but who stole the wallet.\r\n
x x x x
x x x x
P I N T
x x x x
x A G E
P I N T
L R C x
F A G E
P I N T
L R C M
F A G E
P I N T
O C G N
H R A I
Y L F P',NULL,0);
INSERT INTO comment VALUES (5675,919,1567,'Bryan','Most realistic solution','2003-06-11 08:13:52',3,'Let Fa, Fb, Sa, and Sb represent the ages of the four people in question. Sa=1.5*Sb and all ages are multiples of 5, so assume Sb=10 and Sa = 15. Son B will be twice his age in Sb years, at which time Son A\'s age will be Sa+Sb, so
Fb=2*(Sa+Sb)=2*25=50. Fa=2*(Fb-Sa)=2*(50-15)=70. So the four ages are:
Father B is 50
Son A is 15
Son B is 10
Since he wants to do what is best for him, he will want to \'win\' the auction at no financial cost to himself. Hence he will make the bid.
He will not want to back a losing proposition. Hence he will not make the bid.
Again, he will not want to back a losing proposition. Hence he will not make the bid.|1|
\r\nWith two guesses, you can find the answer out of three numbers. Guess the middle value, and either you have guessed correctly, or the answer is the higher or lower value, in which case you must use the second guess to find the correct answer.\r\n1 |2| 3
\r\nHere\'s where it gets tricky.\r\n\r\nIn order to ever find the number, it is therefore necessary to have no more than three numbers to choose from when you get down to your last two guesses.\r\nIf you have seven numbers with three guesses, and you guess the middle value, then either you are correct, or the answer is either in the higher three or the lower three, in which case you can determine it from the final two guesses.\r\n1 2 3 |4| 5 6 7
\r\n\r\nSimilarly, with four guesses, you must narrow it down to no more than seven possibliities with the first guess, so if you guess the middle value out of 15 numbers, you have either guessed correctly or eliminated all but 7 of the choices.\r\n1 2 3 4 5 6 7 |8| 9 10 11 12 13 14 15
\r\n\r\nIn general, a single guess with x choices will narrow it down to at most (x-1)/2 possibile values for the next guess. With n guesses, you can narrow it down to (and guess) a single number out of 2^n-1 possiblities by guessing the median value each time.\r\n\r\nHowever, the problem does not require that you may guess only a single value. Rather, it says that you may guess \"anything you like,\" and will be answered with whether (or not) the number in question is \"higher or lower then (sic) your guess.\"\r\nGiven that, it is possible to guess a range of values instead of a single value.\r\n\r\nWith one or two guesses, the range you would guess is a single value anyway, and the number of choices you can narrow down are the same.\r\n\r\nRecall that with three guesses, your first guess must narrow the field down to no more than three values.\r\nIf, then, you guess a range of three values, with three higher and three lower numbers, you can be assured of being able to narrow down your last two guesses.\r\n1 2 3 |4 5 6| 7 8 9
\r\nTherefore, you can find a single number out of 9 values (instead of 7) by guessing the range.\r\n\r\nIn general, a guess of the middle range of x values will narrow it down to x/3 possibilities for the next guess, instead of (x-1)/2, and actually the operation is ternary instead of binary.\r\nWith n+1 guesses (since the last guess is always needed for the actual number, even after you have narrowed it down), you will in this manner be able to find a single number out of 3^n possibilites.\r\n\r\nIf you have five guesses, you can find the answer out of 3^4=81 possible values.\r\nThis is not enough, but with six guesses, you can find and guess a single value out of 3^5=243 numbers.\r\nTherefore, to find a number out of the 100 values between 1 and 100, you need six guesses.\r\n\r\n..\r\nMy first guess would be \"82 to 90.\"\r\n\r\nIf it is correct, then you have only 9 values to deal with and will find the number in three more guesses for a total of four (or possibly three).\r\nIf the answer is higher, then you have 10 values from 91 to 100, and will find the number in at most four more guesses, but it would be possible to do it in two or three more.\r\nIf the answer is lower, then you have 81 values, so it will five more guesses (four if the number is one less than a multiple of three), for a total of six.\r\nMy reasoning behind that is, at least it\'s easy math when you have 81 values.\r\n',NULL,0);
INSERT INTO comment VALUES (5835,96,1575,'DJ','re: solution','2003-06-17 17:45:04',2,'Remember that when you draw the altitude, the outside edge of the triangle is no longer 6 cm, but 3 cm.\r\nThis edge is opposite the 60° angle, so the length of the hypotenuse is 3 cm/sin 60°, which is equal to 2√3.\r\n\r\nYou were off by a factor of two I think because you forgot that the 6 cm is not an edge of the 3-60-90 triangle you were considering.',5812,0);
INSERT INTO comment VALUES (5836,544,1686,'DuCk','Solution','2003-06-18 02:11:44',3,'A match',NULL,0);
INSERT INTO comment VALUES (5837,903,1686,'DuCk','Solution','2003-06-18 02:23:39',0,'Cube 1 ==> C,U,R,H,O,J\r\nCube 2 ==> A,L,D,T,M,W\r\nCube 3 ==> V,F,Z,I,P,G\r\nCube 4 ==> E,B,Y,K,S,N',NULL,0);
INSERT INTO comment VALUES (5838,544,2465,'peter','solution','2003-06-18 02:25:23',3,'a match\r\n',NULL,0);
INSERT INTO comment VALUES (5839,542,2465,'peter','solution?','2003-06-18 02:35:17',3,'no legs (a bucket) rests on one leg (the foot) of a woman (two legs) sat on a stool (three legs) milking a cow, while four legs (a cat) had the cream',NULL,0);
INSERT INTO comment VALUES (5840,544,1919,'Lewis','Easy','2003-06-18 02:59:11',3,'A matchstick.\r\nTake one out of the match box and scratch the head on the sandpaper.\r\nIt was red, but once it burns it becomes black.',NULL,0);
INSERT INTO comment VALUES (5841,544,2376,'Jim C','Don\'t get burnt.','2003-06-18 05:00:37',1,'Hey, there are a lot of matches out there these days that aren\'t red.\r\nAnd what about an alternative solution? A pencil eraser. They\'re usually red until you atually erase something, then they\'re black (or gray at least =0).',NULL,0);
INSERT INTO comment VALUES (5842,544,1919,'Lewis','re: Don\'t get burnt.','2003-06-18 05:39:13',3,'But when you use a pencil eraser you\'re not scrathcing it\'s head.\r\n\r\nWith a match, generally they are red. Or, instead of the answer being \'a match\' it could be \'a match with a red head\'.',5841,0);
INSERT INTO comment VALUES (5843,908,1919,'Lewis','Nickel?','2003-06-18 06:49:07',4,'I\'m from England, and I don\'t know how much a nickel is worth. What is it?',NULL,0);
INSERT INTO comment VALUES (5844,908,1919,'Lewis','re: Nickel? (Never mind, I know now)','2003-06-18 06:54:54',0,'Don\'t bother answering - I found out that it\'s five cents.',5843,0);
INSERT INTO comment VALUES (5845,908,1919,'Lewis','Solution (After all that)','2003-06-18 07:06:19',3,'We just have to find as many ways to make 100 with 5, 10, 25 and 50. There are:\r\n50 + 50\r\n50 + 25 + 25\r\n50 + 25 + 10 + 10 + 5\r\n50 + 25 + 10 + 5 + 5 + 5\r\n50 + 25 + 5 5\'s\r\n50 + 5 10\'s\r\n50 + 4 10\'s + 2 5\'s\r\n50 + 3 10\'s + 4 5\'s\r\n50 + 2 10\'s + 6 5\'s\r\n50 + 10 + 8 5\'s\r\n50 + 10 5\'s\r\n\r\nThat is eleven ways, so there are 11 ways to make 100 from those coins. We can find more ways by replacing 50 with one of the other ways, but each time there is one less way. So the amount of ways is 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 66.\r\n\r\nI confused myself, so this might be wrong :)',NULL,0);
INSERT INTO comment VALUES (5846,908,1715,'Jonny Doe','Solution','2003-06-18 08:00:46',3,'40',NULL,0);
INSERT INTO comment VALUES (5847,908,1301,'Charlie','The list','2003-06-18 09:39:45',3,' 50 x 0 ; 25 x 0 ; 10 x 0 ; 5 x 20\r\n 50 x 0 ; 25 x 0 ; 10 x 1 ; 5 x 18\r\n 50 x 0 ; 25 x 0 ; 10 x 2 ; 5 x 16\r\n 50 x 0 ; 25 x 0 ; 10 x 3 ; 5 x 14\r\n 50 x 0 ; 25 x 0 ; 10 x 4 ; 5 x 12\r\n 50 x 0 ; 25 x 0 ; 10 x 5 ; 5 x 10\r\n 50 x 0 ; 25 x 0 ; 10 x 6 ; 5 x 8\r\n 50 x 0 ; 25 x 0 ; 10 x 7 ; 5 x 6\r\n 50 x 0 ; 25 x 0 ; 10 x 8 ; 5 x 4\r\n 50 x 0 ; 25 x 0 ; 10 x 9 ; 5 x 2\r\n 50 x 0 ; 25 x 0 ; 10 x 10\r\n 50 x 0 ; 25 x 1 ; 10 x 0 ; 5 x 15\r\n 50 x 0 ; 25 x 1 ; 10 x 1 ; 5 x 13\r\n 50 x 0 ; 25 x 1 ; 10 x 2 ; 5 x 11\r\n 50 x 0 ; 25 x 1 ; 10 x 3 ; 5 x 9\r\n 50 x 0 ; 25 x 1 ; 10 x 4 ; 5 x 7\r\n 50 x 0 ; 25 x 1 ; 10 x 5 ; 5 x 5\r\n 50 x 0 ; 25 x 1 ; 10 x 6 ; 5 x 3\r\n 50 x 0 ; 25 x 1 ; 10 x 7 ; 5 x 1\r\n 50 x 0 ; 25 x 2 ; 10 x 0 ; 5 x 10\r\n 50 x 0 ; 25 x 2 ; 10 x 1 ; 5 x 8\r\n 50 x 0 ; 25 x 2 ; 10 x 2 ; 5 x 6\r\n 50 x 0 ; 25 x 2 ; 10 x 3 ; 5 x 4\r\n 50 x 0 ; 25 x 2 ; 10 x 4 ; 5 x 2\r\n 50 x 0 ; 25 x 2 ; 10 x 5\r\n 50 x 0 ; 25 x 3 ; 10 x 0 ; 5 x 5\r\n 50 x 0 ; 25 x 3 ; 10 x 1 ; 5 x 3\r\n 50 x 0 ; 25 x 3 ; 10 x 2 ; 5 x 1\r\n 50 x 0 ; 25 x 4\r\n 50 x 1 ; 25 x 0 ; 10 x 0 ; 5 x 10\r\n 50 x 1 ; 25 x 0 ; 10 x 1 ; 5 x 8\r\n 50 x 1 ; 25 x 0 ; 10 x 2 ; 5 x 6\r\n 50 x 1 ; 25 x 0 ; 10 x 3 ; 5 x 4\r\n 50 x 1 ; 25 x 0 ; 10 x 4 ; 5 x 2\r\n 50 x 1 ; 25 x 0 ; 10 x 5\r\n 50 x 1 ; 25 x 1 ; 10 x 0 ; 5 x 5\r\n 50 x 1 ; 25 x 1 ; 10 x 1 ; 5 x 3\r\n 50 x 1 ; 25 x 1 ; 10 x 2 ; 5 x 1\r\n 50 x 1 ; 25 x 2\r\n 50 x 2\r\n\r\nfrom:\r\nDECLARE SUB changeIt (n!, tot!)\r\nDATA 50,25,10,5\r\nDIM SHARED den(10), denCt(10)\r\nDIM SHARED ct, nickCt\r\nFOR i = 1 TO 4: READ den(i): NEXT\r\n\r\nchangeIt 1, 0\r\n\r\nPRINT ct, nickCt\r\n\r\nSUB changeIt (n, tot)\r\n num = 0\r\n DO\r\n denCt(n) = num\r\n remain = 100 - tot - num * den(n)\r\n IF remain < 0 THEN EXIT DO\r\n IF remain = 0 THEN\r\n ct = ct + 1\r\n IF n = 4 THEN nickCt = nickCt + num\r\n FOR i = 1 TO n\r\n IF i > 1 THEN PRINT \";\";\r\n PRINT den(i); \"x\"; denCt(i);\r\n NEXT\r\n PRINT\r\n ELSEIF n < 4 THEN\r\n changeIt n + 1, tot + num * den(n)\r\n END IF\r\n num = num + 1\r\n LOOP\r\nEND SUB\r\n\r\nThe count is indeed 40, and the program also totals the number of nickels involved in each solution. That count indicates how many more solutions would be achieved by allowing pennies as each nickel could or could not be converted to 5 pennies. That count does indeed add up to 252, which, added to the 40 without pennies gives the original 292 quoted by the teller\r\n\r\n 40 252',NULL,0);
INSERT INTO comment VALUES (5848,544,2470,'talia','my first one!','2003-06-18 09:56:39',0,'it\'s a match! (duh, i guess). ah, well, you have to start somewhere.',NULL,0);
INSERT INTO comment VALUES (5849,542,2426,'Will H','Solution','2003-06-18 10:51:28',0,'I love Hobbit riddles\r\nThe answer is a fish (no legs) on a one legged table (one leg), a man (two legs) sitting on a stool (three legs), and a cat (four legs) gets the bones',NULL,0);
INSERT INTO comment VALUES (5850,544,2426,'Will H','Solution','2003-06-18 10:55:43',0,'The was from the movie Batman Forever, wasn\'t it?Anyway... the answer is a match',NULL,0);
INSERT INTO comment VALUES (5851,543,2426,'Will H','Solution','2003-06-18 10:59:43',0,'You\'ve beat me to just about every one, Ravi.\r\nThe answer of course, is an egg.',NULL,0);
INSERT INTO comment VALUES (5852,906,1902,'Hank','Answer','2003-06-18 11:36:23',1,'162 (i think)\r\n\r\nevery number (1-9) is used 20 times for numbers 1-99.\r\n\r\n100 - 199 uses the number one 100 times. All of the other numbers are used only 20 times again.\r\n\r\n1 - 161 uses 100 ones. ',NULL,0);
INSERT INTO comment VALUES (5853,906,2472,'jono','Numbers','2003-06-18 12:06:47',0,'Hank is not so far of the solution is 163 he must have forgot about the extra one didgit in 11 and 111',NULL,0);
INSERT INTO comment VALUES (5854,906,1626,'Gamer','re: Numbers','2003-06-18 12:30:56',3,'Say what? I counted all the 10 1s used as ones place digits, and 10 1s in the 10s place digits. 11 counts twice because it fits both criteria.\r\n\r\nThere are 20 already, so every number you count past adds 1, and every one that ends in 1 counts and every 110-119 counts 1. So for 1-99 plus 100-119, there are 20+20+10+2 or 52 numbers. Then from 120-162 there are 43 numbers (hundreds-place 1s), and 5 ones-place 1s. which makes a total of 100 1s.\r\n\r\nWhich means the first number after this that uses a 1 is 163, which is the answer.',5853,0);
INSERT INTO comment VALUES (5855,906,1301,'Charlie','solution','2003-06-18 15:31:27',3,'The shopkeeper should have paid more attention to Benford\'s Law, which figures in the puzzle Bascule\'s Book. The digit 1 is going to be used more than any other.\r\n\r\nThe numbers 1-9 use 1 1.\r\nThe numbers 10-99 use 10 1\'s in the tens position and 9 in the units position for a total of 19, bringing the running total to 20.\r\n\r\nNumbers 100-199 use 100 1\'s in the hundreds position plus another 20 duplicating 1-99, so this overshoots the mark, so lets go back to the count of 20 for 1-99.\r\n\r\n100-119 use 20 in the hundreds pos, 10 in the 10\'s pos and 2 in the units pos, for a total of 32, bringing the running total to 52.\r\n\r\n120-129 use 10 in the hundreds pos and 1 in the units for a total of 11, bringing the running total to 63.\r\n\r\nThe ranges 130-139, 140-149, and 150-159 likewise use 11 each, bringing the running total to 96.\r\n\r\n160-162 use the remaining 4. Customer 163 finds no 1\'s left.\r\n\r\nA simple program verifies our answer:\r\nDO\r\n i = i + 1\r\n i$ = LTRIM$(STR$(i))\r\n FOR j = 1 TO LEN(i$)\r\n s = VAL(MID$(i$, j, 1))\r\n ct(s) = ct(s) + 1\r\n NEXT\r\n PRINT i,\r\n FOR j = 0 TO 9\r\n PRINT ct(j);\r\n NEXT\r\n PRINT\r\n IF i / 40 = INT(i / 40) THEN DO: LOOP UNTIL INKEY$ > \"\"\r\nLOOP\r\n\r\n 158 25 95 36 36 36 35 26 26 26 25\r\n 159 25 96 36 36 36 36 26 26 26 26\r\n 160 26 97 36 36 36 36 27 26 26 26\r\n 161 26 99 36 36 36 36 28 26 26 26\r\n 162 26 100 37 36 36 36 29 26 26 26\r\n 163 26 101 37 37 36 36 30 26 26 26\r\n 164 26 102 37 37 37 36 31 26 26 26\r\n\r\nThe next most popular digit is 2, with only 37 sold by the time the 1\'s run out.',NULL,0);
INSERT INTO comment VALUES (5856,405,2456,'joy','','2003-06-18 16:37:41',0,'this one is easy...go through a,b,c keep going past til you get in a straight line with f and h then go diagnol through f and h and keep going til you are under g and d then go up through g and d to a and then go diagnol down through e and i',NULL,0);
INSERT INTO comment VALUES (5857,903,1575,'DJ','an aside','2003-06-18 18:33:37',1,'Just wanted to bring up something someone mentioned in the queue:\r\n\r\nOften, puzzles like this are solved when a certain face of a cube can be oriented different ways to represent more than one character (see the <a href=http://perplexus.info/show.php?pid=196>Calendar Cubes series, and others), like using the same face for a 6 and a 9.\r\n\r\nAlthough it is not necessary to solve this problem, as there are exactly 23 letters in the words, and a J is stipulated in the introduction, as is the fact that each face bears a different letter.\r\nWe can still try to see if it is possible.\r\n\r\nStart with the solution that several people have found:\r\n\r\nA D L M T W\r\nB E K N S Y\r\nC H J O R U\r\nF G I P V Z\r\n
\r\n\r\nTwo letters that can be represented by the same face are N and Z.\r\nIn the solution, they appear on different cubes. As this solution is unique, there are certain direct or indirect reasons that those two letters cannot be on the face of the same cube.\r\nFor example, if you replaced the word \'HAZY\' with the \'HANY\' and tried to solve the problem that way, thinking it will yield a solution in which the same face is used, you will find that it is impossible.\r\n\r\nSimilarly, I and H (which could be rotations of each other) appear on different cubes. Moreover, they are in the same word (KITH), and certainly could not be represented by the same face.\r\n\r\nLastly, M and W are 180° rotations of each other. These letters do appear on the same cube, so if you removed the W, for instance, each word with a W in it could still be read with an upside-down M.\r\nAll the faces must still bear a different letter, so the now-extra face must contain a Q or an X, which were omitted from the original problem.\r\n\r\nThus, an alternate solution might be:\r\n\r\nA D L M T _\r\nB E K N S Y\r\nC H O R U _\r\nF G I P V Z\r\n
\r\nin which one of the blanks contains a J, and the other blank is filled with either a Q or an X (four possible arrangements this way).\r\n\r\nThere are no other letters that could be represented with the same face.\r\n\r\nTherefore, there are perhaps five ways to solve this problem.',NULL,0);
INSERT INTO comment VALUES (5858,542,1575,'DJ','and the winner is...','2003-06-18 19:15:33',3,'\"Fish on a little table, man at table sitting on a stool, the cat has the bones.\"',NULL,0);
INSERT INTO comment VALUES (5859,544,1732,'Helen','the answer','2003-06-19 00:20:43',0,'it\'s a match',NULL,0);
INSERT INTO comment VALUES (5860,544,2479,'Lonne','scab?','2003-06-19 01:09:27',0,'That\'s weird, I immediately thought of a scab - it was once red (with blood), then turns into a black scab which you scratch and it\'s red again. Okay, I guess it doesn\'t quite make sense.',NULL,0);
INSERT INTO comment VALUES (5861,542,2479,'Lonne','copycat','2003-06-19 01:26:08',0,'stop copying Tolkien',NULL,0);
INSERT INTO comment VALUES (5862,906,1686,'DuCk','Answer Only','2003-06-19 02:04:17',3,'the homeowner who can\'t buy their complete house number would be #163 as all of the 1s would have been sold.',NULL,0);
INSERT INTO comment VALUES (5863,929,1902,'Hank','Solution','2003-06-19 04:21:21',3,'My quick answer is 0 (zero)\r\n\r\nI think that perfect squares only end in 1,4,9,6,5',NULL,0);
INSERT INTO comment VALUES (5864,544,2190,'mike','solution','2003-06-19 05:16:27',0,'that sounds like a match to me',NULL,0);
INSERT INTO comment VALUES (5865,929,1626,'Gamer','re: Solution','2003-06-19 05:35:13',4,'Wow, that was a short lived problem... *sigh*, but do you know why that is?\r\n\r\nI think this might stump some people when they first look at it. (I would hope so)',5863,0);
INSERT INTO comment VALUES (5866,929,1902,'Hank','re(2): Solution','2003-06-19 05:40:59',0,'the number in the ones column is 1-9, when doubled the number in the ones column is 1,4,9,6,5',5865,0);
INSERT INTO comment VALUES (5867,922,1626,'Gamer','re: The Trick (Full Solution)','2003-06-19 05:45:47',0,'I might argue that there is nothing the person could say if your first range is the answer. For example, if you were saying \"82 to 90\" and the number was 87, he would have to say \"That\'s it!\", but then you wouldn\'t know what it was. Or he could say \"Both\", which would pose another problem...\r\n\r\nIn any case, this problem is not in \"tricks\", so you shouldn\'t be looking for any easy way out in my opinion.',5834,0);
INSERT INTO comment VALUES (5868,922,1626,'Gamer','Is this right?','2003-06-19 05:54:07',1,'I still get 6 guesses and not 7. Using DJ\'s good method (at the top, guessing 1 number and not a range), you know the number after:\r\n\r\n0 guesses if there is no more than 1 number\r\n1 guess if there are no more than 3 numbers\r\n2 guesses if there are no more than7 numbers\r\n3 guesses if there are no more than 15 numbers\r\n4 guesses if there are no more than 31 numbers\r\n5 guesses if there are no more than 63 numbers\r\n6 guesses if there are no more than 127 numbers\r\n\r\nSo, you can figure the number out using 6 guesses.\r\n\r\nI think DJ\'s trick is a creative idea though, but may not have been what the author intended.',NULL,0);
INSERT INTO comment VALUES (5869,693,2430,'lalit','solution','2003-06-19 07:35:29',3,'the weights must be 1,3,9,27,81\r\nlalit',NULL,0);
INSERT INTO comment VALUES (5870,693,2430,'lalit','','2003-06-19 07:35:52',3,'the weights must be 1,3,9,27,81\r\nlalit',NULL,0);
INSERT INTO comment VALUES (5871,693,2430,'lalit','','2003-06-19 07:35:53',3,'the weights must be 1,3,9,27,81\r\nlalit',NULL,0);
INSERT INTO comment VALUES (5872,722,1919,'Lewis','Solution','2003-06-19 09:44:19',3,'Fill the 11.\r\nUsing that fill the 3 & 6, leaving 2 in the 11.\r\nPut the two in the car.\r\nEmpty the 3 & 6 into the eleven, and fill the rest up from the pump.\r\nPut the eleven into the car.\r\n2 + 11 = 13, and there is no gasoline wasted.',NULL,0);
INSERT INTO comment VALUES (5873,685,1919,'Lewis','Solution','2003-06-19 09:52:44',3,'The sentence is........... FALSE.\r\nThat is because the sun doesn\'t rise - the Earth spins making it seem like the sun is rising, but it isn\'t.',NULL,0);
INSERT INTO comment VALUES (5874,929,2129,'Sanjay','No entry for squares','2003-06-19 10:35:11',3,'Perfect squares always end in 0,1,4,5,6 or 9.
1*1=1
2*2=4
3*3=9
4*4=16
5*5=25
6*6=36
7*7=49
\r\nOr not.',NULL,0);
INSERT INTO comment VALUES (5934,924,1919,'Lewis','Solution','2003-06-21 08:17:12',3,'We need to change the final teams to amounts of the same symbols so that we can compare them.\r\n\r\n2$ + % + * = 3$ so the second team can be written as 3$.\r\n\r\nNow we have to change the first team to $.\r\n\r\n2@ = 3$ - 2% - *\r\n2! = 3$ - 2% - 3*\r\n4! = 6$ - 4% - 6*\r\n2@ + 4! = 9$ - 6% - 7*.\r\n= 2@ + 4! = 9$ - 6$ - *\r\n= 2@ + 4! = 3$ - *\r\n\r\nSo the second team will win because they are stronger by 1*.',5932,0);
INSERT INTO comment VALUES (5935,434,1919,'Lewis','Solution','2003-06-21 08:23:18',3,'Erm.. 1.\r\n\r\nTake a ball from the box marked BW. Because all of the labels are incorrectly placed, whatever colour comes out the box will have two of that colour (either BB or WW).\r\n\r\nThe box marked BB or WW (whichever colour you picked out) will have to be the other option out of BB and WW, otherwise one will have the correct label.\r\n\r\nThese are the possible situations.\r\n\r\nTake a ball from box marked BW. It is:\r\n1. White. Therefore the box marked WW is actually BB and the box marked BB is actually BW.\r\nOr\r\n2.Black. Then, the box marked BB is actually WW and the box marked WW is actually BW.',NULL,0);
INSERT INTO comment VALUES (5936,911,1919,'Lewis','re: Hint #1 ???','2003-06-21 08:30:45',4,'Erm.. I\'m more confused now than I was before.\r\n\r\nPerhaps another hint is needed?\r\n0\r\n(0)\r\n(0)0\r\n((0))\r\n(0)00\r\n(0)(0)\r\n(0)000\r\n(((0)))\r\n((0))0\r\n(0)0(0)\r\n\r\nIs the answer something mathematical or not, because that sequence means nothing to me.',5933,0);
INSERT INTO comment VALUES (5937,902,1919,'Lewis','re: ************************','2003-06-21 09:08:25',0,'Once again. PLEASE DONT GIVE AWAY THE ANSWER IN YOUR SUBJECTS! Or at least in your case, part of the answer',5906,0);
INSERT INTO comment VALUES (5938,911,1575,'DJ','Hint #2','2003-06-21 11:02:55',2,'Hint: These are just the numbers 1 through 10, expressed differently. And despite the presence of zero (if you use the first hint), you can\'t express zero this way.',NULL,0);
INSERT INTO comment VALUES (5939,932,2121,'Chaz','DERR RETARDED','2003-06-21 16:15:28',0,'Its an electric train, and as far as I know they produce no smoke.',NULL,0);
INSERT INTO comment VALUES (5940,921,2121,'Chaz','re: solution','2003-06-21 16:19:44',0,'you forgot that you have to cut off his shlong and make him eat it.',5905,0);
INSERT INTO comment VALUES (5941,835,1301,'Charlie','re: I don\'t get it.','2003-06-21 17:24:10',0,'The idea is to place as many queens so that no queen is currently, without any further positioning, attacking any other. And color doesn\'t count. Geometrically this just means as many queens as will fit on the board so that no two queens are in the same row or column or diagonal straight line.',5918,0);
INSERT INTO comment VALUES (5942,932,2496,'anoop','re(3): Old Smokie','2003-06-21 21:26:16',0,'I could be wrong .. but I used vector mechanics to analytically solve this problem. You can also do it graphically. \r\n\r\nDraw a cordinate (xX\' - yY\') like a big plus sign\r\nwhere x = north, X\' = south, y = West, Y = East\r\nFrom the origin, draw a line at 45 degree angle which is 7.1 cm long (to represent 71 km/h)\r\nFrom the other end of this line (the end that is farther from teh origin), draw aline vertically up 3.1 cm long.\r\n\r\nJoin the other end of this vertical line to the origin, measure the length, and the angle.\r\n\r\nI am trying to draw a picture:\r\n\r\n N |\r\n |\r\n |\r\n |\r\nW-------------------- E\r\n |\\\r\n | \\\r\n | \\\r\n | \\ |\r\n | 7.1 \\ |3.1\r\n | \\ |\r\n | \\|\r\n |\r\n S\r\n\r\nThanks for your review.\r\n\r\n\r\n\r\n',5931,0);
INSERT INTO comment VALUES (5943,932,2489,'nellie','re(4): Old Smokie','2003-06-22 05:19:51',0,'I understand what you say, which is exactly what you would do to plot your true position when sailing into a tide.\r\nMy point was that the smoke would not itself be moving forward at all to set against the wind speed. Vector triangles do not therefore appear relevant.\r\nI\'m being a bit pedantic I know, but that\'s what these puzzles seem to be all about and thus, good fun.\r\nThanks.',5942,0);
INSERT INTO comment VALUES (5944,937,1575,'DJ','hmm','2003-06-22 05:50:33',1,'Everyone should get this...\r\nAll people have one,\r\nRight next to their head',NULL,0);
INSERT INTO comment VALUES (5945,937,1919,'Lewis','Solution','2003-06-22 05:55:51',3,'Its an ear!\r\nThe 2nd line made me think it was, but the 3rd line confirmed it.',NULL,0);
INSERT INTO comment VALUES (5946,921,2080,'Tristan','¿ Solution ¿','2003-06-22 08:07:52',0,'No, Don\'t take it, you payed $10 for that drink, if he drinks it, you win $5, he used you to get a $10 for $5, you lost $5, and your drink, you just got humiliated.',NULL,0);
INSERT INTO comment VALUES (5947,865,1919,'Lewis','No, no, no, no, no, ...Or is it yes?','2003-06-22 08:23:43',3,'Well, this is easy - its no.\r\nHang on, i mean yes.\r\nNo, i meant no.\r\nYes.\r\nNo.\r\nYes.\r\n\r\nEither way there is a contradition',NULL,0);
INSERT INTO comment VALUES (5948,448,1919,'Lewis','Helpful Harry','2003-06-22 08:38:56',3,'If Harry had delivered all the glasses intact, he would have recieved 30 rupees.\r\n\r\nIf he broke a glass, he would not only have to pay the 90 paise \'fine\', but also lose his 30 paise pay. So, every glass he broke takes away 120 paise.\r\n\r\n30-24= 6 rupees, or 600 paise.\r\n120 goes into 600 5 times, so Harry broke 5 glasses.',NULL,0);
INSERT INTO comment VALUES (5949,921,2507,'Kimii','easy to solve','2003-06-22 10:29:36',0,'you pay ten dollars for your drink, so a five dollare wager would be a rip off! ',NULL,0);
INSERT INTO comment VALUES (5950,544,2507,'Kimii','re: solution','2003-06-22 10:38:07',0,'ahhh. duh!!! how could i have been so stupid not to notice that?!?!?1',5864,0);
INSERT INTO comment VALUES (5951,824,2507,'Kimii','Easy, i think...','2003-06-22 10:43:27',0,'well, he would have stood on a block of ice and put the noose around him, and waited for the ice to melt.',NULL,0);
INSERT INTO comment VALUES (5952,501,2507,'Kimii','duh','2003-06-22 10:52:17',0,'that was one of the most simple puzzles i have ever heard. stars!!!',NULL,0);
INSERT INTO comment VALUES (5953,37,1575,'DJ','but','2003-06-22 15:51:25',0,'If you assume the scratch can have width to it, what is the limit of the width? Since it\'s not stated in the problem, I say the scratch is horizontal through the middle of the board, and a little more than 6 squares wide. Therefore, you will have to replace all 64 squares (and use 64 veneers).',NULL,0);
INSERT INTO comment VALUES (5954,908,1,'levik','official soluiton','2003-06-22 17:23:32',4,'DJ: there seem to be some issues with the solution you have submitted (as pointed out by Charlie and TomM)\r\n\r\nYou seem to include permutations (50-25-25 and 25-50-25 are counted as different results.)\r\n\r\nYou did not mention 50c + 5x10 as an outcome.\r\n\r\nPlease review the solution.',NULL,0);
INSERT INTO comment VALUES (5955,921,2436,'Chris','Agreement?','2003-06-22 23:25:49',4,'Jon, is there a soloution to this problem, or is this a test to \"find the sucker\"? Most readers seem to agree that taking a five dollar wager with a ten dollar drink on the line is a ripoff, regardless of whether or not it can be done. If it can be done, let us know so I can make money and impress folks at bars...',NULL,0);
INSERT INTO comment VALUES (5956,924,1575,'DJ','Different Solution','2003-06-22 23:34:56',3,'Start with equations based on the matches listed as ties:\r\n\r\n* + % = $\r\n3$ = 2@ + 2% + *\r\n@ = ! + *\r\n\r\nFrom these, derive a few simple forms:\r\n\r\n2* + 2% = 2$\r\n3* + 3% = 3$\r\n2@ = 2! + 2*\r\n\r\nCombine these with the second given equation:\r\n\r\n3$ = 2@ + 2% + *\r\n3* + 3% = 2!+ 2* + 2% + *\r\n% = 2!\r\n\r\nFinally, compare the final match:\r\n\r\n4! + 2@ (?) 2$ + % + *\r\n4! + 2! + 2* (?) 2* + 2% + % + *\r\n6! + 2* < 6! + 3*\r\n\r\nTherefore, the right-hand side wins by a *.\r\n\r\nThere are any number of numerical values that can be assigned to the characters. ! and * can be assigned any arbitrary values, including zero, with no regard to which is greater.\r\n% is then twice !, @ is the sum of ! and *, and $ is the sum of % and *.\r\n\r\nIt should be noted that while negative values also fit the system algebraically, if * is assigned a negative value, then naturally the left-hand side wins instead of the right (the right has an extra
These are: 512, 256, 128, 64, 32, 8, 2, 1 lbs \r\nK L L K L L K L L K\r\nL L K L L K L L K L\r\nL K L L K L L K L L\r\nK L L K L L K L L K\r\nL L K L L K L L K L\r\nL K L L K L L K L L\r\nK L L K L L K L L K\r\nL L K L L K L L K L\r\nL K L L K L L K L L\r\nK L L K L L K L L K K=34\r\n\r\nL K L L K L L K L L\r\nK L L K L L K L L K\r\nL L K L L K L L K L\r\nL K L L K L L K L L\r\nK L L K L L K L L K\r\nL L K L L K L L K L\r\nL K L L K L L K L L\r\nK L L K L L K L L K\r\nL L K L L K L L K L\r\nL K L L K L L K L L K=33\r\n
\r\nThese arrangements give us 34 and 33 knights out of 100, respectively, which is not enough.\r\nSo, there must be another way to arrange them, or the grid must be yet bigger.\r\n\r\nThat\'s all I have for now.',NULL,0);
INSERT INTO comment VALUES (5992,912,1567,'Bryan','Stuck again','2003-06-24 10:52:52',0,'I haven\'t even figured out how to get to level 4!',NULL,0);
INSERT INTO comment VALUES (5993,957,1919,'Lewis','A Few Thoughts','2003-06-24 10:58:45',1,'KLLKLLK\r\nLKLLKLL\r\nLLKLLKL\r\nKLLKLLK\r\nLKLLKLL\r\nLLKLLKL\r\n\r\nThis pattern meets the criteria that all can say that they are standing next to people of the opposite type - all the knights are by liars and all the liars are by a mixture of knights and liars - but only 33% are knights, so I don\'t know how you could add a few more knights in.',NULL,0);
INSERT INTO comment VALUES (5994,937,2540,'dEADzONE','Solution','2003-06-24 11:04:28',0,'It\'s the ear...the timpani is the eardrum.\r\nThe \"hammer\", \"anvil\" and \"stirrup\" are the three bones of the middle ear, and the \"canal\" is the Eustuchian canal connected to the bones.',NULL,0);
INSERT INTO comment VALUES (5995,957,158,'Ender','Solution?','2003-06-24 11:29:20',1,'Playing around with symbols, I noticed a diamond patern kept appearing when I\'d try to optimize the knights ( .\'s are liar, |\'s are knights):\r\n\r\n..|..\r\n.|.|.\r\n|...|\r\n.|.|.\r\n..|..\r\n\r\nWhile on a single patern, it doesn\'t produce a high enough percentage, repeating it does. It looks like this generates a 3:8 (37.5%) ratio:\r\n\r\n|...|...\r\n.|.|.|.|\r\n..|...|.\r\n.|.|.|.|\r\n|...|...\r\n.|.|.|.|\r\n..|...|.\r\n.|.|.|.|\r\n\r\nThis has 24 knights out of 64 people. However, 4 liars are surrounded by 3 knights only (no liars), so it appears that I need to make the dimensions large enough that some of the outside knights can be turned into liars (the extra 0.5%). At 20x20, there are 150 knights, but 148 are needed; however, there are 9 knights that have to be changed. At 40x40, I have 600, I only need 592, but 19 need to be changed.\r\n\r\nAfter looking at it, 1/4 of the rows and 1/4 of the columns need 1 knight changed. If a corner knight is changed and the rows/columns are a multiple of 4, than you can subtract 1 from this because of the knight being both on a row and column.\r\n\r\nSo in a NxN square, there are (3/8)*N*N knights, with (37/100)*N*N needed, resulting in (1/200)*N*N extra. If N is a multiple of 4, then (1/2)*N-1 knights will need to be changed. So solving:\r\n(1/200)*N*N > N/2-1\r\nN*N > 200*N/2-200\r\nN*N - 100*N + 200 > 0\r\n2 <= N <= 98\r\nSo 98x98 is the smallest number of rows/columns that might work with this solution. However, that is not a multiple of 4, so I think 100x100 will be needed.',NULL,0);
INSERT INTO comment VALUES (5996,912,1,'levik','Thoughts...','2003-06-24 11:43:38',2,'So to get to the \"next\" level (call it \"N\") (after 1) you need to have an arrangement similar to the one shown in \"Turn 1\": \r\n\r\nLevel N:.. ......\r\nLevel N-1: ...a..\r\nLevel N-2: .bc...\r\n\r\n\r\nB would then jump over C then A to get to level N.\r\n(B cannot start out sitting below A, since A had to jump over something to have gotten to level N-1, and that checker is now gone)\r\n\r\nSo it seems that the lowest theoretical \"cost\" of moving a checker to N is equal to the cost of N-1 plus twice the cost of N-2.\r\n\r\nFrom the problem though, it seems there is some additional expense after level 3 (otherwise the cost for N=4 would be 16, not 20.)',NULL,0);
INSERT INTO comment VALUES (5997,957,1626,'Gamer','re: Solution?','2003-06-24 12:26:41',2,'I think that will work... Good idea! :)\r\n\r\nTo help rephrase what Ender was saying\r\n\r\nJust have a\r\n\r\n|...\r\n.|.|\r\n..|.\r\n.|.|\r\n\r\n4x4 repeating sequence that tiles the field that Kazzam wants to use.\r\n\r\nThe only problem is that then the bottom and right side of Kazzam\'s field have a lone liar (per unit of 4). To fix this, you would need to change the bottom right knight to a liar in each case...\r\n',5995,0);
INSERT INTO comment VALUES (5998,957,2541,'K','Am I missing something','2003-06-24 13:02:38',0,'The text says at least 37%. The answer would then be a simple alternating pattern, with 50% of each, as 50% represents at least 37% of the whole. As such, a simple grid 10x10 would suffice.',NULL,0);
INSERT INTO comment VALUES (5999,957,1575,'DJ','re: Am I missing something','2003-06-24 13:08:09',0,'If you have an alternating grid, such as the red and black squares on a checkerboard, each knight is surrounded by all liars (which we want), and each liars is surrounded by all knights. However, being a liar, he will not say that he is surrounded by all knights, and the arrangement fails.\r\n\r\nTo solve this problem, we need to find an arrangement for which each knight is surrounded by all liars, but each liar is next to at least one other liar (so he can lie and say that all his neighbors are knights).',5998,0);
INSERT INTO comment VALUES (6000,957,1626,'Gamer','re: Solution?','2003-06-24 13:17:29',1,'I would double both sides first in the equation:\r\n\r\n(1/100)*N*N>=N-2\r\n\r\nThen upon multiplying by 100, I see from both sides I see\r\n\r\nN*N>=100(N-2)\r\n\r\n(N-2)(N+2)+4 is equal to N*N,\r\n\r\nSo then (N+2)+4/(N-2)>=100\r\n\r\n\r\n\r\nIf N+2 = 100, then 4/(100-4) would be small but positive. For each number N is less than 98, 4/N-2 would have to be 1 more. But that couldn\'t happen, so the lowest is 98.\r\n\r\nAs for the 1 larger thing, looking at the pattern, you could have these last two rows\r\n\r\n|...\r\n.|.|\r\n\r\nThen change the | to a . (as allowed by the 2n-1), and it should work.\r\n',5995,0);
INSERT INTO comment VALUES (6001,912,1567,'Bryan','re: Thoughts...','2003-06-24 16:08:05',0,'Getting to level 3 is pretty straight forward. It can be done with an arrangment like
o o o
CHEAT
QUEEN
MESSY
STEAM
SPINE
TOTEM
ASHES
SPEED
HURRY
JESUS
ZIPPY
SCOLD
GOODS
FUNNY',NULL,0);
INSERT INTO comment VALUES (6007,183,1626,'Gamer','re: My solution','2003-06-25 03:14:52',0,'I don\'t think that\'s legal... You can\'t leave anything there or take anything, but that is a good idea...',2271,0);
INSERT INTO comment VALUES (6008,957,158,'Ender','re(2): Solution?','2003-06-25 04:11:57',1,'The problem asks for an even number of rows and columns. Should that be equal number?\r\n\r\nIf so, I believe it can be solved with a 49x49 square. On odd numbers, no knights need to be changed in the 4x4 pattern I used.\r\n',6002,0);
INSERT INTO comment VALUES (6009,824,2547,'janelle','re: Death Theory','2003-06-25 05:04:14',0,'but wouldn\'t there be a trail of water where the truck rolled out of the room?',5443,0);
INSERT INTO comment VALUES (6010,958,2341,'Pickels','Solution','2003-06-25 06:23:53',3,'I got Reese Witherspoon for my answer. I had a little trouble with the first part, but after I got a few, it was pretty easy.',NULL,0);
INSERT INTO comment VALUES (6011,958,950,'sarah','Answer','2003-06-25 08:16:31',0,'Reese Witherspoon',NULL,0);
INSERT INTO comment VALUES (6012,957,158,'Ender','re(3): Solution?','2003-06-25 08:30:18',1,'The diamond pattern is 4x4, so allowing partial repeats of the pattern gives different results. Note that no knights need to change on odd numbers. I believe 49 is the smallest number using this diamond pattern (discounting n < 4, since the statement requires n > 10).\r\n\r\nThese all assume this is the top left corner, with the pattern repeated down and right as needed:\r\n|...\r\n.|.|\r\n..|.\r\n.|.|\r\nOn ones where the knights change, I made the second to bottom row and second to last column entirely liars.\r\n\r\nIf (n mod 4 = 0):\r\n-----------------\r\nNumber of knights minus changed knights:\r\n(3/8*n*n) - ((1/2)*n-1) = 1/8*(3n^2-4n+8)\r\n\r\nSolving inequality (number of knights >= 37%):\r\n1/8*(3n^2-4n+8) >= 37/100*n^2\r\nn^2 - 100n + 200 >= 0\r\n2 <= n <= 98\r\nn = 100,104,108,...\r\n\r\n\r\nIf (n mod 4 = 1):\r\n-----------------\r\nNumber of knights in n-1 square plus knights in columns-1 plus knights in rows-1 plus corner knight:\r\n(3/8*(n-1)*(n-1)) + ((1/4)*(n-1)) + ((1/4)*(n-1)) + 1\r\n= 1/8( 3*n^2 - 2*n + 7 )\r\n\r\nSolving inequality:\r\n1/8( 3n^2 - 2n + 7 ) >= 37/100*n^2\r\nn^2 - 50n + 175 >= 0\r\n3 <= n <= 47\r\nn = 49,53,57,...\r\n\r\n\r\nIf (n mod 4 = 2):\r\n-----------------\r\nNumber of knights minus changed knights:\r\n(3/8*(n^2) + 1/2) - (n/2) = 1/8*(3n^2 - 4n + 4)\r\n\r\nSolving inequality:\r\n1/8*(3n^2 - 4n + 4) >= 37/100*n^2\r\nn^2 - 100n + 100 >= 0\r\n1 <= n <= 99\r\nn = 102,106,110,...\r\n\r\n\r\nIf (n mod 4 = 3):\r\n-----------------\r\nNumber of knights in n+1 square minus knights in columns+1 minus knights in rows+1 plus knight in corner (was taken out twice - by rows and columns):\r\n3/8*(n+1)*(n+1)- (1/2)(n+1) - (1/2)(n+1) + 1\r\n= 1/8*(3n^2 - 2n + 3)\r\n\r\nSolving inequality:\r\n1/8*(3n^2 - 2n + 3) >= 37/100*n^2\r\nn^2 - 50n + 75 >= 0\r\n1 <= n <= 49\r\nn = 51,55,59,...\r\n',6008,0);
INSERT INTO comment VALUES (6013,937,2551,'mary armstrong','','2003-06-25 09:55:23',3,'the answer to what can i be is an \"ear\"',NULL,0);
INSERT INTO comment VALUES (6014,937,2551,'mary armstrong','solution','2003-06-25 09:58:49',3,'you are an \"ear\"',NULL,0);
INSERT INTO comment VALUES (6016,965,1902,'Hank','this might work','2003-06-25 11:03:01',0,'A - liar\r\nB - knight\r\nc - knave\r\n\r\nB 1st\r\nA 2nd\r\nC 3rd',NULL,0);
INSERT INTO comment VALUES (6017,965,158,'Ender','My solution','2003-06-25 11:07:33',3,'I broke the statements down by person, to make it easier to find a knave. Then, since there were only 6 combinations possible, I then wrote down each combination and the truthfulness for each statement.\r\n\r\nStatements:\r\nA:A was 1st. C was not 1st. A was 1st.\r\nB:A was not 1st. B was 1st. B was not 2nd.\r\nC:B was not 1st. C was 1st. B was not 2nd.\r\n\r\nOrder: A,B,C\r\nA:T,T,T\r\nB:F,F,F\r\nC:T,F,F - not valid\r\n\r\nOrder: A,C,B\r\nA:T,T,T\r\nB:F,F,T - not valid\r\nC:T,F,T\r\n\r\nOrder: B,A,C\r\nA:F,T,F\r\nB:T,T,T\r\nC:F,F,T - not valid\r\n\r\nOrder: B,C,A\r\nA:F,T,F\r\nB:T,T,T\r\nC:F,F,T - not valid\r\n\r\nOrder: C,A,B\r\nA:F,F,F\r\nB:T,F,T\r\nC:T,T,T\r\n\r\nOrder: C,B,A\r\nA:F,F,F\r\nB:T,F,F - not valid\r\nC:T,T,F\r\n\r\nThere is only one valid combination (C,A,B). So Ajax is a liar is the stable, Balthazar is a knave in the pighouse, and Cicero is a knight in the stableboy’s room.\r\n',NULL,0);
INSERT INTO comment VALUES (6018,965,1575,'DJ','More Thoughts (Soulution)','2003-06-25 11:38:36',3,'There are two ways to look at the statements (as far as the alternating statements of a knave). Either each set of statements in a line counts as a single statement which are both true or false, and the next group of statements is the opposite (if, of course, that person is a knave); or the first statement is true, the second is false, etc, regardless of the lines in the problem.\r\n\r\nFirst assume that they count together. That means that both sentences in any one line have the same value (true/false), and if we know one, we know the other.\r\nBased on my original assumption that B cannot be first (or there will be no full solution), B must be a liar or a knave. His first set of statements must be false, since he says, \"I was first,\" and we are assuming that can\'t be the case.\r\nAlso, the first part of that statement (\"No you didn\'t\") must be false, so Ajax was first.\r\nThe first part of Cicero\'s first statement (\"You were not,\" referring to B being first) must be true. Therefore, his second statement (\"I arrived first\") must also be true, but we already have that Ajax was first. Both cases cannot be true, so that must mean that the statements in a line do not count together.\r\n\r\nTherefore, each statement counts independently, but we know that every other statement by any of the people has the same value.\r\nAssuming still that B is not first, his second statement must be false. He is not a knight; we know that his other two statements are the same, but could both be true (if B is a knave) or false (if he is a liar). There is no way of figuring this out from his statements alone (as those are the only ones he made).\r\nIf Balthazar\'s second statement is false, then Cicero\'s first statement, which denies it, must be true. Therefore, he (Cicero) is not a liar, but the next statement (\"I arrived first\") could be true or false, depending on whether he is a knight or a knave. His third statement, however, must also be true, and Balthazar did not arrive second. Therefore, Balthazar arrived third.\r\nB\'s last statement, which agrees with Cicero\'s last statement that is true, must also be true. Therefore, B is a knave, and his first statement (\"No you didn\'t\" in response to A\'s \"I arrived first\") must be true, as well as the third. Therefore A did not arrive first; he arrived second and Cicero was first.\r\n\r\nTherefore, a little more inspection shows that all of Ajax\'s statements are false; he must be a liar. Also, Cicero\'s statements are all true; he is a knight.\r\n\r\nThe men, in the order they arrived, are:\r\n1st: Cicero, knight\r\n2nd: Ajax, liar\r\n3rd: Balthazar, knave',NULL,0);
INSERT INTO comment VALUES (6019,965,1567,'Bryan','re: My solution','2003-06-25 11:41:32',0,'This is a great method of cutting through the chaff to get to the solution! I\'ll have to make my next puzzle in such a way that it can\'t be solved this way -- you make it seem too easy!\r\n\r\nSomeone could work through the logic \"frontwards\" to get to the answer, although I doubt they would want to now.',6017,0);
INSERT INTO comment VALUES (6020,936,1171,'nikki','Solution','2003-06-25 11:49:10',3,'\r\nFirst, I hope N >= 10.\r\n\r\nSecond, there are two ways that the weighing could happen (because the wording wasn\'t specific). One way is to have the item on one side of the scale all alone, and various weights on the other. The other way is to allow weights on both sides of the scale. Here are the solutions to each way:\r\n \r\nItem vs. Weights:\r\n8 Weights are needed. 512, 256, 128, 64, 32, 8, 2, and 1.\r\n\r\nItem and Weights vs. Weights:\r\n4 Weights are needed. The Item and Weights 16, 4, and 1 on one side. Weight 1024 on the other.\r\n\r\nAs for the second part of the equation, the answers are the same. Due to the nature of the weights (all being a power of 2) you gain nothing by having more than one of each weight. Using two of Weight 2^m is silly because 2*2^m = 1*2^(m+1). 2^(m+1) is also a power of two so that weight should be on hand, so it would be better to use that one than two of another.\r\n\r\nLater!',NULL,0);
INSERT INTO comment VALUES (6021,7,1171,'nikki','People! Get a clue!','2003-06-25 12:18:47',0,'\r\nFor all of the people out there who STILL believe the answer is 1/2, let me ask you this:\r\n\r\nForget about the person saying anything at all. If two coins are flipped, what are the chances both are heads? Some of you have used the logic that tossing HT is the same as tossing TH. If that is the case then your answer to my question would be 1/3 instead of the correct 1/4. So clearly there is something lacking in that logic.\r\n\r\nAnd to Charlie and anyone who agrees with him, did you even read the problem statement? It was written quite clearly. The person definitively tells you that one of the coins is a Tail, not \"the person told you what one of the coins was.\" Your whole theory about a person\'s preference for announcing Heads or Tails is irrelevent. In this case we are dealing with a person who said Tails, period. All that did was eliminate the HH possibility.',NULL,0);
INSERT INTO comment VALUES (6022,902,1575,'DJ','=\\','2003-06-25 13:31:58',0,'Just because I mistakely left out a line of the problem, I hardly think it deserves a rating of 1.\r\n.. ohwell ..',NULL,0);
INSERT INTO comment VALUES (7524,610,3202,'Jill','Solution','2003-08-30 11:23:16',0,'a.)5 yellow birds b.) 2 other color birds\n\nEdited on August 30, 2003, 11:23 am',NULL,0);
INSERT INTO comment VALUES (7525,610,3248,'Kelsey','Solution','2003-08-30 12:26:03',0,'There were 5 yellow birds and 2 non-yellow birds spotted.\n\nEdited on August 30, 2003, 12:33 pm',NULL,0);
INSERT INTO comment VALUES (7526,610,3248,'Kelsey','RE:Solution','2003-08-30 12:26:51',0,'Each person spotted 4 birds. All the birds C spotted were yellow. That means that the bird all of them spotted was yellow (1 yellow, 0 non-yellow). That also means that the bird C and A both spotted is yellow and the bird C and B both spotted is yellow (3 yellow, 0 non-yellow). The bird only C spotted also must have been yellow. A spotted 2 yellow birds and 2 non-yellow birds. The 2 yellow birds A spotted were: the bird all three of them spotted and the bird that C and A both spotted. That means that the bird A and B spotted and the bird that only A spotted were non-yellow (4 yellow, 2 non-yellow). 1 of the 3 yellow birds that was spotted was the bird all three of them saw. Another one was the bird that both B and C spotted. The non-yellow bird B spotted was the one that both B and A spotted. That leaves the bird that just B spotted to be yellow (5 yellow, 2 non-yellow).\r\n\r\n\n\nEdited on August 30, 2003, 12:41 pm',NULL,0);
INSERT INTO comment VALUES (7527,499,3292,'Angelo','Alternate answer','2003-08-30 12:56:08',1,'They could have been playing BINGO!',NULL,0);
INSERT INTO comment VALUES (7528,610,3206,'Lawrence','Simple Solution','2003-08-30 13:49:51',0,'Giving the birds number as to whom they were seen by makes this one easy. They each see one that others don\'t see, so 1,2,3. Each pair sees one that the third doesn\'t see, so 4,5,6. And they all see one bird 7. As follows.\r\n\r\nA-1467\r\nB-2457\r\nC-3567\r\n\r\nSince C saw four yellow ... \r\nA-14YY\r\nB-24YY\r\nC-YYYY\r\n\r\nSince A only saw two yellow, then 1 and 4 are not yellow, so\r\nA-NNYY\r\nB-2NYY\r\nC-YYYY\r\n\r\nB saw three yellow, so the last bird was yellow.\r\n\r\nSo the seven birds look like this\r\n1-N\r\n2-Y\r\n3-Y\r\n4-N\r\n5-Y\r\n6-Y\r\n7-Y\r\n\r\nThe answer?\r\n(a)5\r\n(b)2',NULL,0);
INSERT INTO comment VALUES (7529,257,3206,'Lawrence','Answer','2003-08-30 14:01:53',0,'There are (9-n)^2 squares you can form, where n is the number of squares. It\'s really (8-n+1)^2, the +1 is because it is inclusive of the starting point. So n goes from 1 to 8, there are 64+49+36+25+16+9+4+2+1= 204.',NULL,0);
INSERT INTO comment VALUES (7530,255,3206,'Lawrence','Hmmm...','2003-08-30 14:25:49',0,'It\'s not possible because there is a 6x6 square in the middle and along the outside two areas of 13 each with an effective width of 1. There will always be 2 blocks that are at best, diagonal. but never vertical or horizontal. As soon as you decide to stagger anything, you\'ll always be left with 1 empty block, and eventually, the 2 not together.\r\n',NULL,0);
INSERT INTO comment VALUES (7531,254,3206,'Lawrence','Solution','2003-08-30 14:46:41',3,'Kinda cool ... Tell me if I\'m right. If you think about the way a circle rolls on a flat surface, that flat surface is effectively a bunch of squares lined up side by side. Now imagine one square that has sides of length equal to one half of the cirle all lined up next to each other. And now you have the answer. The surface is a bunch of one half circles lined up side by side, i.e. a 180 degree semi-circles lined up like upside down bowls next to each other. The length of the arc of these semicircles is equal to the length of the side of the square.\r\n\r\nHow would you do it with a triangle?',NULL,0);
INSERT INTO comment VALUES (7532,251,3206,'Lawrence','Maybe ...','2003-08-30 15:00:42',3,'I was thinking there was some siamese twin thing her, but then it dawned on me ... they are all hermaphrodites!!!',NULL,0);
INSERT INTO comment VALUES (7533,250,3206,'Lawrence','Solution','2003-08-30 15:08:34',3,'Yep, he\'s lying. If he were telling the truth, then this statement would contradict itself. So he is lying. If he is lying, then he just can\'t be a an all-the-time truth teller. So he\'s lying now, but he doesn\'t tell the truth all the time. He also can\'t be an all the time liar, otherwise that contradicts this statement. So sometimes this guy lies, and this is one of those times.',NULL,0);
INSERT INTO comment VALUES (7534,252,3206,'Lawrence','Solution','2003-08-30 15:53:27',0,'Put a / on the = making it a NOT EQUAL sign, and then it is true.',NULL,0);
INSERT INTO comment VALUES (6024,15,1575,'DJ','Another method','2003-06-25 16:07:43',3,'Rather than long division, it is possible to solve by filling in a multiplication problem.\r\n\r\nWe know that the first digit must be a 1, since it is half of a number starting with 2. So, a multiplication problem, with ... representing the missing digits in the product and in the multiplicand, would be:\r\n\r\n1...2\r\n* 2\r\n21...\r\n\r\nTherefore, the last digit in the product must be a 4 (from 2*2):\r\n\r\n1...42\r\n* 2\r\n 4\r\n21...4\r\n\r\nThe next to last digit is an 8 (4*2):\r\n\r\n1...842\r\n* 2\r\n 4\r\n 8 \r\n21...84\r\n\r\nAnd then a 6 (from 8*2=16):\r\n\r\n1...6842\r\n* 2\r\n 4\r\n 8\r\n 16 \r\n21...684\r\n\r\nContinuing thus:\r\n\r\n1...36842\r\n* 2\r\n 4\r\n 8\r\n 16\r\n 12 \r\n21...3684\r\n\r\n1...736842\r\n* 2\r\n 4\r\n 8\r\n 16\r\n 12\r\n 6 \r\n21...73684\r\n\r\n1...4736842\r\n* 2\r\n 4\r\n 8\r\n 16\r\n 12\r\n 6\r\n 14 \r\n21...4736842\r\n\r\n1...94736842\r\n* 2\r\n 4\r\n 8\r\n 16\r\n 12\r\n 6\r\n 14\r\n 8 \r\n21...9473684\r\n\r\n1...894736842\r\n* 2\r\n 4\r\n 8\r\n 16\r\n 12\r\n 6\r\n 14\r\n 8\r\n 18 \r\n21...89473684\r\n\r\n1...7894736842\r\n* 2\r\n 4\r\n 8\r\n 16\r\n 12\r\n 6\r\n 14\r\n 8\r\n 18\r\n 16 \r\n21...789473684\r\n\r\n1...57894736842\r\n* 2\r\n 4\r\n 8\r\n 16\r\n 12\r\n 6\r\n 14\r\n 8\r\n 18\r\n 16\r\n 14 \r\n21...5789473684\r\n\r\nThe next digit we find will be a 1 (the zero from 5*2=10 plus the carried 1), which is what we are looking for. However, there is another 1 carried over from this, so that will not do. We will keep going until we find a 1 with no carry over.\r\n\r\n1...157894736842\r\n* 2\r\n 4\r\n 8\r\n 16\r\n 12\r\n 6\r\n 14\r\n 8\r\n 18\r\n 16\r\n 14\r\n 10 \r\n21...15789473684\r\n\r\n1...3157894736842\r\n* 2\r\n 4\r\n 8\r\n 16\r\n 12\r\n 6\r\n 14\r\n 8\r\n 18\r\n 16\r\n 14\r\n 10\r\n 2 \r\n21...315789473684\r\n\r\n1...63157894736842\r\n* 2\r\n 4\r\n 8\r\n 16\r\n 12\r\n 6\r\n 14\r\n 8\r\n 18\r\n 16\r\n 14\r\n 10\r\n 2\r\n 6 \r\n21...6315789473684\r\n\r\n1...263157894736842\r\n* 2\r\n 4\r\n 8\r\n 16\r\n 12\r\n 6\r\n 14\r\n 8\r\n 18\r\n 16\r\n 14\r\n 10\r\n 2\r\n 6\r\n 12 \r\n21...26315789473684\r\n\r\n1...5263157894736842\r\n* 2\r\n 4\r\n 8\r\n 16\r\n 12\r\n 6\r\n 14\r\n 8\r\n 18\r\n 16\r\n 14\r\n 10\r\n 2\r\n 6\r\n 12\r\n 4 \r\n21...526315789473684\r\n\r\n1...05263157894736842\r\n* 2\r\n 4\r\n 8\r\n 16\r\n 12\r\n 6\r\n 14\r\n 8\r\n 18\r\n 16\r\n 14\r\n 10\r\n 2\r\n 6\r\n 12\r\n 4\r\n 10 \r\n21...0526315789473684\r\n\r\nThe next digit in the number will be a 1 (from 0*1=0 added to the carried 1). Since there is no carry over from the doubled zero, we can end here. The final multiplication is:\r\n\r\n105263157894736842\r\n* 2\r\n 4\r\n 8\r\n 16\r\n 12\r\n 6\r\n 14\r\n 8\r\n 18\r\n 16\r\n 14\r\n 10\r\n 2\r\n 6\r\n 12\r\n 4\r\n 10\r\n2 \r\n210526315789473684\r\n',NULL,0);
INSERT INTO comment VALUES (6025,924,2562,'Chii','solution','2003-06-25 22:11:14',0,'saying the $=100 if *% = $ is evenly matched then * and % must both equal 50\r\n\r\n$$$=300 and taking the facts from a while ago %+ *+%= 150 then if @%*%@ = $$$ then the @ must equal 75\r\n\r\nin the fourth one!*=@ so if @ is 75 and * is 50 then ! is 25\r\n\r\nthen (! + @ + ! + ! + @ + != 250) & (% + $ + * + $= 300)\r\n\r\nSO! [!@!!@! < %$*$]',NULL,0);
INSERT INTO comment VALUES (6026,822,2562,'Chii','----','2003-06-25 22:30:26',0,'Take me to the Gold.',NULL,0);
INSERT INTO comment VALUES (6027,940,158,'Ender','Solution','2003-06-26 03:38:46',0,'The 7 key on a phone.\r\n\r\nWhat tipped me off was the star clue. Since it couldn\'t be a computer keyboard, I thought of what else had a star key.',NULL,0);
INSERT INTO comment VALUES (6028,908,1575,'DJ','Challenge','2003-06-26 04:15:29',4,'Good job, now here\'s a challenge:\r\n\r\nCan anyone give a logical or formulaic explanation (other than brute force) as to why the answer is specifically 40?',NULL,0);
INSERT INTO comment VALUES (6029,912,1575,'DJ','re(2): Thoughts...','2003-06-26 04:29:08',2,'To get to level 4, start by creating the arrangement needed for level 3, but one unit higher. This takes 12 moves. \r\n\r\nAnother 8 are then needed to reach level 4, for a total of 20.',6001,0);
INSERT INTO comment VALUES (6030,912,1567,'Bryan','re(3): Thoughts...','2003-06-26 05:19:26',1,'DJ, you said to create the arrangement needed for level 3, but one unit higher. I know that\'s what I need to do, but I don\'t see how to do it. Getting 5 checkers across on level 1 can be done a number of ways, but then how do I get 3 across on level zero beneath them? Call it mental block, but I\'m just not seeing it.',6029,0);
INSERT INTO comment VALUES (6031,940,1626,'Gamer','re: Solution','2003-06-26 06:40:58',0,'Wow! This is a good riddle :D',6027,0);
INSERT INTO comment VALUES (6032,965,950,'sarah','i think...','2003-06-26 07:14:45',0,'I went through different options systamatically but once i found one i think works i havent checked other options so there may be others:\r\nHaving Ajax telling the truth would not work no matter who of the others was a liar or a knave. \r\n\r\ni then tried with Ajax being the liar, Balthazar beind a knight and Cicero the knave...this worked and the order of people i got is Balthazar, Ajax and then Cicero so:\r\nBalthazar: spare bunk\r\nAjax: stable\r\nCicero: pighouse',NULL,0);
INSERT INTO comment VALUES (6033,940,1919,'Lewis','Copied from Braingle','2003-06-26 08:10:59',4,'Luvya - both of your riddles are copies of riddles found on Braingle.com.\r\n\r\nOne is \r\nhttp://www.braingle.com/11657.html\r\n\r\nand the other is\r\nhttp://www.braingle.com/4087.html\r\n\r\nThese were submitted by different users, so they can\'t be ones that you submitted to Braingle and Flooble under a different name.',NULL,0);
INSERT INTO comment VALUES (6034,965,1567,'Bryan','re: i think...','2003-06-26 08:15:03',0,'I don\'t think your solution works. If Balthazar is a knight, he would be first. Then Cicero says, \"You were not!\" (lying), \"I arrived first,\" (lying), and \"Well, Balthazar did not arrive second,\" (telling the truth). Cicero makes three statements, although the first two are made back to back without anyone else saying something in between.',6032,0);
INSERT INTO comment VALUES (6035,963,1575,'DJ','First Thoughts','2003-06-26 08:47:42',0,'My first idea is that the numbers represent letters of the alphabet, perhaps with some of the letters paired. Possible letters, then (with A=1 to Z=26), are:\r\n3=C, 2=B, 21=U, 1=A, 11=K, 13=M, 14=N, 4=D\r\nOr, if A=0 and Z=25, these are:\r\n2=D, 2=C, 21=V, 1=B, 11=L, 13=N, 14=O, 4=E\r\n\r\nI also venture that somehow the clue in parentheses (it\'s clever) is significant...the second possibility contains all the letters of \'clever\' except for R (17)...\r\n\r\nOkay, I\'m lost.',NULL,0);
INSERT INTO comment VALUES (6036,940,1575,'DJ','re: Copied from Braingle','2003-06-26 09:15:54',0,'Lewis, I think that you\'ll find a lot of the problems on this site, or on any site, can be found elsewhere on the Internet, especially the less difficult ones.\r\n\r\nWhat sets this site apart, in my opinion, is the fact that the general caliber of the problems is much higher. The voting system is set up not to maximize the number of problems, as many sites do, but to make sure that the problems on the site are thought out and interesting.\r\n\r\nAs a side note, I\'m willing to bet that I could find links to ¾ of the problems on the site, being displayed somewhere else on the web. However, I would also wager (as I have been looking for a long time) that few collections of puzzles have as many \'good\' problems as the one right here.\r\n\r\n=)',6033,0);
INSERT INTO comment VALUES (6037,963,1626,'Gamer','re: First Thoughts','2003-06-26 09:22:46',1,'I think the important clue is the name of the question. And I will say (It\'s clever)? isn\'t any more or less important than the other 8 words. But good ideas DJ! :)\r\n\r\nIt sounded from the queue that clues might need to be dropped about this puzzle... Is this a good idea?',6035,0);
INSERT INTO comment VALUES (6038,158,1575,'DJ','Hmmm','2003-06-26 09:29:07',0,'I was wondering why no one had attempted putting the fractions together with common denominators to create a SOP equation.\r\n\r\nAEFHI + BCDHI + BCEFG = BCEFHI\r\n\r\nThen I got the equation .. scary.\r\n\r\nI wonder if there is a good way to solve this, other than trial-and-error.',NULL,0);
INSERT INTO comment VALUES (6039,963,1902,'Hank','Additional thoughts','2003-06-26 09:33:01',0,'three, two, one, one, one, three, one, four, one, one\r\n\r\nIII, II, I, I, I, III, I, IV, I, I\r\n\r\nupside down on a calculator: iihieiiise (i\'s could be l\'s)\r\n\r\nnote: there are no commas (is it one number)',NULL,0);
INSERT INTO comment VALUES (6040,902,1626,'Gamer','It\'s ok','2003-06-26 09:34:22',1,'I gave it a rating of 5 to calm you down :D',NULL,0);
INSERT INTO comment VALUES (6041,940,1626,'Gamer','re(2): Copied from Braingle','2003-06-26 09:40:27',0,'I would just say \"I never saw them there\"... And the \"life or death\" problem that luvya submitted (in the queue), I would guess that most of the puzzling people know about it already. I would agree with DJ, we have a queue that helps filter out the good riddles from the wierd ones, and the duplicates.\r\n\r\nPlus, I know Hobbit riddles fall under the same catergory. Even though they are somewhere else, they still are good, and would belong on this site if they weren\'t copied, so they should if they were copied. :)',6036,0);
INSERT INTO comment VALUES (6042,963,1919,'Lewis','re(2): First Thoughts','2003-06-26 09:49:46',0,'Yeah - we need a hint. Just to point us in the right direction..',6037,0);
INSERT INTO comment VALUES (6043,963,1626,'Gamer','re(3): First Thoughts','2003-06-26 09:53:52',2,'The numbers don\'t relate to eachother... They relate to... something else... :)\r\n\r\n(So 3 doesn\'t affect 2, and 2 doesn\'t affect 1... in other words, if you only knew the numbers and nothing else, the sequence wouldn\'t make sense)\r\n\r\nI don\'t think this is really a sequence, but others seemed to think it was (and the discussion on sequences did), so I put it in sequences...',6042,0);
INSERT INTO comment VALUES (6044,963,1575,'DJ','re(4): First Thoughts','2003-06-26 10:41:51',1,'This comment and your first one (\"any more or less important than the other 8 words\") lead me to think that the numbers are somehow related to the 8/10 words in the problem. But, the number of letters (4 2 3 6 2 4 5 7 3 6) or syllables (1 1 1 2 1 1 2 2 1 2) don\'t seem to help, so I\'m still at a loss..',6043,0);
INSERT INTO comment VALUES (6045,963,2567,'j j','maybe?','2003-06-26 10:45:29',0,'it must be morse code or something. I, of course, happen to know NONE of that.',NULL,0);
INSERT INTO comment VALUES (6046,963,1575,'DJ','re(5): First Thoughts (Finally!)','2003-06-26 10:45:38',3,'A statistic.\r\n\r\nAs soon as I posted that last comment, I got it...the numbers refer to the letters above. So, the third letter in \"What\" is \"a,\" the second letter in \"is\" is \"s,\" and so one, until we come up with:\r\nA S T A T I S T I C\r\n\r\nSo, the question is \'reused\' with the numbers to give the answer.',6044,0);
INSERT INTO comment VALUES (6047,965,1575,'DJ','re(2): i think...','2003-06-26 10:54:22',0,'If you consider each set of sentences in a line as a single statement, for the purposes of the knave\'s statements, then there is no problem with Cicero\'s statements. The discrepancy with sarah\'s solution, though, lies in Ajax\'s second line, in which his first statement becomes true while the second is false.',6034,0);
INSERT INTO comment VALUES (6048,963,1567,'Bryan','re(6): First Thoughts (Finally!)','2003-06-26 11:18:00',0,'Arggh! Now that I see it, it seems so easy.',6046,0);
INSERT INTO comment VALUES (6049,963,1626,'Gamer','re(6): First Thoughts (Finally!)','2003-06-26 11:37:19',3,'Yes! You got it! The answer is not a number, but a statistic... :)',6046,0);
INSERT INTO comment VALUES (6050,963,1626,'Gamer','re(7): First Thoughts','2003-06-26 11:41:46',4,'Do you think this problem should stay in sequences? ',6049,0);
INSERT INTO comment VALUES (6051,963,1919,'Lewis','re(8): First Thoughts','2003-06-26 12:16:06',0,'I think its sort of cryptography, but if you put it in that it might make it seem more obvious...\r\n\r\nOh well, I say change it to Cryptography.',6050,0);
INSERT INTO comment VALUES (6052,924,2569,'yaman','solution','2003-06-26 13:09:31',0,'since %*=$ theright hand side is =$$$=@%*%@\r\n\r\nsince !*=@ the left hand side = @@@@@@-****\r\nsubtract LHS from RHS---if the answer is negative then LHS wins if it is positive then RHS wins\r\nRHS - LHS\r\n=%*% - @@@@ + ****\r\n=$$ - @@@@ + ***\r\n=@%@ - @@@@ + ***\r\n=% - @@ + ***\r\n=% - %**+ ***\r\n=*\r\nThe positive answer proves that the right hand side would win\r\n',NULL,0);
INSERT INTO comment VALUES (6053,963,1626,'Gamer','re(9): First Thoughts','2003-06-26 13:19:27',1,'I think it should go into general personally. :)',6051,0);
INSERT INTO comment VALUES (6054,965,2569,'yaman','some thoughts','2003-06-26 13:41:02',0,'ok\r\nthe last two statement are either both true or both false\r\n\r\nif they are bith false then AJAX is the knight\r\nBUT then either Cicero or Balthazar has to be the knave, and sice their second statements are untrue one of thier 1st statements would have to be true\r\nBUT none of them are\r\nTHUS ajax is not the knight and the last 2 statements are true\r\n\r\nthus ajax is the liar\r\nso \r\n\r\nand either cicero or balthazar is the knight\r\nAjax did not arrive first\r\n\r\nsince Balthazar says that Ajax didn\'t reach 1st---which is true---i guess that balthazar is the knight\r\n\r\n\r\nBUT\r\nif Cicero is knight then rest of question easier\r\nbewcause then Cicero came 1st and he gets the bunk i the stable boy\'s room.\r\nAjax came 2nd and thus gets the barn\r\n\r\nand Balthazar came 3rd so he gets the pighouse\r\nand thus cicero is the knave\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (6055,924,2570,'Daniel Ciguenza','Possible solution','2003-06-26 15:24:57',0,'Assume all symbols represent positive numbers.\r\n* = a\r\n% = b\r\n$ = c\r\n@ = d\r\n! = e\r\n\r\nrewrite the expressions as...\r\n1. a + b = c\r\n2. 3c = 2d + 2b + a\r\n3. d = e + a\r\n\r\nnow start removing variables..\r\na = c - b (from 1 above), therefore\r\nd = e + (c - b) (from 3 above), therefore\r\n3c = 2(e + c - b) + 2b + (c - b) (from 2 above)\r\n\r\ncontinuing...\r\n3c = 2e + 2c - 2b +2b + c - b\r\n3c = 2e + 3c - b\r\n2e = b\r\n\r\nCarrying these to the match in question...\r\nrewrite the expression as...\r\nLHS <-> RHS\r\n!@!!@! <-> %$*$\r\n\r\n4e + 2d <-> 2c + b + a\r\n\r\nNow, remove as many variables as possible by introducing expression ascertained above...\r\n4e + 2d <-> 2c + b + (c - b)\r\n4e + 2d <-> 3c\r\n4e + 2(e + c - b) <-> 3c\r\n4e + 2e + 2c - 2b <-> 3c\r\n6e - 2b <-> c\r\n3b - 2b <->\r\nb <-> c\r\n\r\nBack to the original expression of a + b = c ...\r\n\r\na is assumed to be positive, therefore c is greater than b and the RHS wins.',NULL,0);
INSERT INTO comment VALUES (6056,921,2570,'Daniel','re(2): easy to solve','2003-06-26 16:19:26',0,'No, your net loss would be $5 and a $10 drink. For if you win the bet, you have lost the drink.',5978,0);
INSERT INTO comment VALUES (6057,963,1253,'brianjn','Relationship?','2003-06-26 19:47:47',0,'This is a sequence of sorts, being a one to one relationship.',NULL,0);
INSERT INTO comment VALUES (6058,963,1575,'DJ','Category','2003-06-26 20:22:41',0,'I think the problem certainly fits under \'Cryptography,\' but once that is established, the solution is somewhat gieven away, or at least hinted at. \'Sequences,\' on the other hand, is a total misnomer, and made the puzzle nearly impossible to solve without a few hints. Perhaps \'General\' would be the best place for this particular problem.',NULL,0);
INSERT INTO comment VALUES (6059,965,2436,'Chris','re(3): i think...','2003-06-27 03:33:31',1,'Ajax\'s second line is curious. I think, at least, he is lying or telling the truth. \"That\'s a lie! I arrived first, as I said before.\" The second part, \"...as I said before.\" is true.\r\n',6047,0);
INSERT INTO comment VALUES (6060,464,1626,'Gamer','re(2): Solution?','2003-06-27 04:03:26',0,'Yes... in my opinion thia is like figuring out 2^100 and counting digits rather than using logs and other mathematics...\r\n\r\nI have no idea on this one, so Charlie\'s solution might be necessary.',3120,0);
INSERT INTO comment VALUES (6061,554,158,'Ender','Wild guess','2003-06-27 04:14:58',0,'10100?\r\nAll I have noticed so far is that you can look at the sequence as being: \r\n10 101000 101000 101000\r\nSo my current guess is that the series is just 10 followed by 101000 ad infinitum.',NULL,0);
INSERT INTO comment VALUES (6062,554,1567,'Bryan','Is the problem right?','2003-06-27 05:14:17',0,'I remember that when this problem was in the queue, it started with 01 and had 22 digits. Is this puzzle correct as is?',NULL,0);
INSERT INTO comment VALUES (6063,554,979,'Ravi Raja','re: Is the problem right?','2003-06-27 05:22:24',0,'Yes Bryan, the problem is alright. I had left a note when the problem was in the queue itself mentioning that there was something wrong with the one written previously (the one which you say began with 01 and there were 22 digits), but later when I went through the problem once again I found a mistake, corrected it and left a note regarding that fix.',6062,0);
INSERT INTO comment VALUES (6064,554,251,'Cheradenine','a minimal approach','2003-06-27 05:44:27',1,'a sequence is minimally defined by 3 elements\r\n\r\n101010 0 010100 0 101000\r\n\r\nthe elements are split by a separator, 0, acting like a \',\'\r\n\r\nthe elements are logically shifted to the left\r\n\r\nthus\r\n\r\n101010 0 010100 0 101000 -> 0 010000\r\n\r\nthe next 5 digits are 00100',NULL,0);
INSERT INTO comment VALUES (6065,554,1575,'DJ','Thinks','2003-06-27 06:02:56',0,'Hmm, let\'s see...\r\nThe number of digits to each \'section\':\r\n1: 1 1 1 1 1 1 1\r\n0: 1 1 3 1 3 1 3\r\nor: 1 1 1 1 1 3 1 1 1 3 1 1 1 3 overall\r\n\r\nBinary equivalents?\r\n1: 1\r\n2: 10\r\n5: 101\r\n10: 1010\r\n21: 10101\r\n42: 101010\r\n84: 1010100\r\n168: 10101000\r\n...\r\nA few terms are doubled, a few are doubled plus one (duh, that\'s what tacking on to a binary number does...)\r\n\r\nPerhaps:\r\n10 101000 1000101000\r\nleading to:\r\n10 101000 1000101000 101000101000\r\n\r\nAlthough, I suppose that is no different than:\r\n10 101000 101000 101000 101000 ...\r\n\r\nYeah, no clue.',NULL,0);
INSERT INTO comment VALUES (6066,965,1575,'DJ','re(4): i think...','2003-06-27 07:41:47',0,'That\'s an interesting point...but I think it\'s part of the smae false statement. Had he said, \"I arrived first. This I said before.\" as two separate statements, I think the problem would prove unsolvable.',6059,0);
INSERT INTO comment VALUES (6067,969,1715,'Jonny Doe','Solution','2003-06-27 08:01:53',0,'Alex - Knight, Not Guilty\r\nBill - Liar, Not Guilty\r\nCarl - Knight, Not Guilty\r\nDave - Liar, Guilty\r\nEddy - Liar, Guilty',NULL,0);
INSERT INTO comment VALUES (6068,836,1919,'Lewis','re: If you know each other....','2003-06-27 08:13:14',0,'What does everyone else think about it, because everybody\'s stopped commenting on this problem. :(',5921,0);
INSERT INTO comment VALUES (6069,969,1575,'DJ','Observations (spoiler)','2003-06-27 09:14:39',3,'Let\'s look at each man\'s pair of statements.\r\n\r\nThe only way Alex\'s first statement is false is if Bill and Eddy are both guilty.\r\nIf this is not the case, his first (and therefore both) statement is true, and Dave is guilty.\r\nTherefore, we have only two cases for the guilty parties, based on the fact that Alex is either a knight or a liar:\r\n1. Bill & Eddy\r\n2. Dave & ??\r\n\r\nLooking at Bill\'s statements, his first will only be true if Alex and Carl are both guilty.\r\nIf that is not the case, then the second statement is false, as well, and Eddy is guilty.\r\nTherefore, there are two possible cases for the guilty parties based on Bill\'s statements:\r\n1. Alex & Carl\r\n2. Eddy & ??\r\n\r\nCombining these two conclusions, we see that there are only two possiblities for the robbers:\r\n1. Bill & Eddy\r\n2. Dave & Eddy\r\nEither way, Eddy is guilty, and his partner in crime was Bill or Dave.\r\n\r\nCarl\'s first statement, then, must be true, since we know Eddy is guilty.\r\nTherefore, he is a knight, and his second statement is true as well, so Bill is not guilty.\r\n\r\nWe can stop there; as we know that Dave and Eddy are the guilty parties.\r\n\r\nContinuing on, we see that Dave is a liar, as is Eddy.\r\n\r\nAltogether, the robbers are Dave and Eddy.\r\nAlex and Carl are knights; Bill, Dave, and Eddy are liars.',NULL,0);
INSERT INTO comment VALUES (6070,912,2129,'Sanjay','re(3): Thoughts...(moves vs checkers)','2003-06-27 10:23:55',0,'There are 8 checkers in the arrangement needed for level 3. Once you have created this arrangement, one unit higher, you will need only 7 moves and not 8 to reach level 4. \r\n 1 (24) 1 1 1.0000\r\n 2 (23) 4 5 2.2361\r\n 3 (22) 9 14 3.7417\r\n 4 (21) 16 30 5.4772\r\n 5 (20) 25 55 7.4162\r\n 6 (19) 36 91 9.5394\r\n 7 (18) 49 140 11.8322\r\n 8 (17) 64 204 14.2829\r\n 9 (16) 81 285 16.8819\r\n10 (15) 100 385 19.6214\r\n11 (14) 121 506 22.4944\r\n12 (13) 144 650 25.4951\r\n13 (12) 169 819 28.6182\r\n14 (11) 196 1015 31.8591\r\n15 (10) 225 1240 35.2136\r\n16 ( 9) 256 1496 38.6782\r\n17 ( 8) 289 1785 42.2493\r\n18 ( 7) 324 2109 45.9239\r\n19 ( 6) 361 2470 49.6991\r\n20 ( 5) 400 2870 53.5724\r\n21 ( 4) 441 3311 57.5413\r\n22 ( 3) 484 3795 61.6036\r\n23 ( 2) 529 4324 65.7571\r\n24 ( 1) 576 4900 70.0000\r\n
\r\nWhich shows the square size in parentheses.\r\n\r\nThese are listed by the size of the square of possible placement, the total possibilities for that size, the total thus far and that total\'s square root.\r\n\r\nThe first time there is a perfect square is indeed at line 24, so a size 24 board to begin with is the smallest for which this will work, and the final board is 70x70.\r\n',NULL,0);
INSERT INTO comment VALUES (6088,918,1902,'Hank','My solution','2003-06-30 04:45:08',3,'where n=the length of the sub-square\r\nn = {1,2,3...24)\r\nit is the sum of (25-n)^2 for all of n.\r\n\r\n=4900\r\n\r\nthe square root of 4900 is 70, and the board is then 70x70',NULL,0);
INSERT INTO comment VALUES (6089,970,103,'friedlinguini','Quick and Dirty Solution','2003-06-30 06:56:18',3,'Generate two random numbers between a and b between 1 and 5. There are 25 possible combinations. Divide those combinations into groups of 3. There are seven groups, plus four left over. If the generated combination falls into one of these groups, return a number corresponding to that group. Otherwise, try again. C++ code would look something like:\r\n\r\n\r\nwhile (true)\r\n{\r\n int a = rand5();\r\n int b = rand5();\r\n int c = (a - 1) * 5 + b - 1;\r\n int result = (c % 3) + 1;\r\n\r\n if (result <= 7)\r\n return result;\r\n} C,A,U,T,H,B\r\ncube #2 ==> L,E,K,Q,D,Y\r\ncube #3 ==> O,P,R,Z,V,S\r\ncube #4 ==> G,I,N,M,F,W\r\n',NULL,0);
INSERT INTO comment VALUES (6093,973,950,'sarah','i think','2003-06-30 07:24:18',0,'i don\'t really know but i think that Jim was in a different area to bob and so needed an area code first.',NULL,0);
INSERT INTO comment VALUES (6094,973,1072,'Alan','Ok Read this','2003-06-30 07:42:23',0,'It has nothing to do with area. Look at the category and try to thinkl outside the box. I believe the problem. A recent riddle may give you a clue to solving this.',NULL,0);
INSERT INTO comment VALUES (6095,970,2572,'derek','Possible Solution','2003-06-30 07:52:56',1,'run the random function 7 times, for say variables a to g.\r\n\r\nsum = a + b + c + d + e + f + g\r\n\r\nrandom7 = (sum mod 7) + 1',NULL,0);
INSERT INTO comment VALUES (6096,970,103,'friedlinguini','re: Possible Solution','2003-06-30 08:05:55',0,'Unfortunately, this makes \'middle\' numbers much more likely to turn up than the outliers, and the problem stated that all results must have an equal chance.',6095,0);
INSERT INTO comment VALUES (6097,973,1902,'Hank','What a problem','2003-06-30 08:11:19',3,'I think that this is one of the most abiguous problems I\'ve heard.\r\n\r\nObviously, the area code or maybe he was in a school and had to dial a certain number to get out.\r\n\r\nAlso, the problem first says that he got the worng house (which means that he did get through, but not to the correct house), then it says \'once again, he didn\'t get through\'\r\n\r\nMy guess is that technology has made us (and Jim) forget about the troubles of pay phones. I think that he didn\'t put money in the pay phone.',NULL,0);
INSERT INTO comment VALUES (6098,973,1301,'Charlie','Another possibility','2003-06-30 08:37:56',3,'He has speed calling 8, which uses digits 2 - 9 to dial a prestored number, and he dialed the 7 after a long enough pause that the system took the 9 to be a speed-dial number and dialed that number.',NULL,0);
INSERT INTO comment VALUES (6099,973,2231,'Trevor Leitch','Thoughts','2003-06-30 08:50:17',1,'Alan\'s tip gave me an idea; on the phone, each number can also represent some letters:\r\n\r\n9 - WXYZ\r\n7 - PQRS\r\n6 - MNO\r\n6 - MNO\r\n4 - GHI\r\n1 - (no letters)\r\n9 - WXYZ\r\n\r\nUsing these, the first five digits of the phone number could spell WRONG... thus, he dialled WRONG-19 or WRONG-1X or something. \r\n\r\nI don\'t know how that might relate to an answer though. Some possibilities:\r\n\r\n1) In whatever country Bob (or indeed Alan) is from, there\'s a directory service for wrong numbers which starts out with WRONG.\r\n2) Jim\'s friend is Bob Wrong, and the \"wrong house\" is actually Bob\'s house.\r\n3) There is another family named Wrong who vainly chose their phone number to reflect that fact.\r\n\r\nUnfortunately, none of these strike me as an obvious answer. Hopefully someone can use this posting to come up with something which closer approximates the solution.',NULL,0);
INSERT INTO comment VALUES (6100,970,1301,'Charlie','re: Quick and Dirty Solution','2003-06-30 08:50:42',0,'Where you say \r\nint result = (c % 3) + 1; \r\nI assume you mean 7 rather than 3, but then I don\'t see the reason for checking that it\'s less than or equal to 7.\r\n\r\nUnder this assumption, however, while c can be anything from 0 to 24, when taken mod 7, zero through three will come up more often than four through six (on a 4-to-3 ratio) as 0-6 is one complete set; 7-13 is another; 14-20 another, but 21-24 are an incomplete set, re-representing what are now overrepresented digits.',6089,0);
INSERT INTO comment VALUES (6101,970,1301,'Charlie','solution','2003-06-30 08:52:22',3,'The best way to consider sequences of 5 possibilities or 7 possibilities is to consider them as base-5 or base-7 numbers. In order to do so, we\'ll reduce the 5-possibility random digit by 1, to get 0 - 4, and after converting to base-7, increment each digit by 1 to get the desired 1 - 7.\r\n\r\nNo power of 5 is an integral multiple of a power of 7 because any number is factorable uniquely into primes. So there is always going to be some loss of information. For example, if we take two random numbers from 1-5 (or a two-digit base-5 number), to get 25 possibilities, that is not even enough for a two-digit base-7 number, so if we express the result as a base-5 number, 0-24, and convert to base-7, we\'ll get, in that base, a number from 0-33 (base 7). If we were to just take the last digit, 0 through 3 would be overrepresented, any such digit appearing 4 times for every 3 times that a digit such as 4 through 6 appears. So we\'d have to throw away numbers greater than 26 (base 7), which is 20 in decimal, or 40 in base-5, then take the last base-7 digit.\r\n\r\nAs the rand5 function, as I\'ll call it, is expensive to call, we want to minimize losses where we have to throw out a fraction of such results.\r\n\r\nIdeally, if there were no losses due to the incommensurability of base-5 and base-7 numbers, we\'d get log(5)/log(7) base-7 digits for every base-5 digit. That\'s about .8271, or about 83% as many random digits from 0-6 (or 1-7) as from 0-4 (or 1-5). That\'s because a base-7 digit has more information than a base-5 number.\r\n\r\nSo there are two items we need to take into consideration in deciding how many base-5 digits we should group together: the number of base-7 digits we get for every group of n base-5 digits, and how many whole such groups we must throw away to avoid a bias in favor of some digits. We saw above that if we use just two base-5 digits, we only get one base-7 digit, but we also must throw away 4/25 or 16% of our entire throughput, so we actually get only .5*.84 = 42% as many base-7 digits as we require base-5 digits.\r\n\r\nThe following table shows the results for various choices in the grouping of base-5 digits:\r\n\r\n 2 1 25 7 21 0.84000 0.42000\r\n 3 2 125 49 98 0.78400 0.52267\r\n 4 3 625 343 343 0.54880 0.41160\r\n 5 4 3125 2401 2401 0.76832 0.61466\r\n 6 4 15625 2401 14406 0.92198 0.61466\r\n 7 5 78125 16807 67228 0.86052 0.61466\r\n 8 6 390625 117649 352947 0.90354 0.67766\r\n 9 7 1953125 823543 1647086 0.84331 0.65591\r\n10 8 9765625 5764801 5764801 0.59032 0.47225\r\n11 9 48828125 40353607 40353607 0.82644 0.67618\r\n12 9 244140625 40353607 242121642 0.99173 0.74380\r\n13 10 1220703125 282475249 1129900996 0.92561 0.71201\r\n14 11 6103515625 1977326743 5931980229 0.97190 0.76363\r\n15 12 30517578125 13841287201 27682574402 0.90710 0.72568\r\n16 13 152587890625 96889010407 96889010407 0.63497 0.51591\r\n17 14 762939453125 678223072849 678223072849 0.88896 0.73209\r\n18 14 3814697265625 678223072849 3391115364245 0.88896 0.69141\r\n19 15 19073486328125 4747561509943 18990246039772 0.99564 0.78603\r\n20 16 95367431640625 33232930569601 66465861139202 0.69695 0.55756\r\n21 17 476837158203125 232630513987207 465261027974414 0.97572 0.78987\r\n
\r\nIn the various columns:\r\n\r\nThe number of base-5 digits that go in, the resulting number of base-7 digits that result, five raised to the given power, and seven raised to the power of the number of base-7 digits, followed by the largest integral multiple of that power of 7 that is not greater than the power of 5 shown. The fraction of that over the number that is the power of 5 is the portion of throughput that need not be thrown away--we just throw away the first base-7 digit--is shown next. Finally is shown the ratio of base-7 to base-5 digits multiplied by the fraction kept.\r\n\r\nIn the two-base-5-digit example, we saw we can get only one base-7 digit, as there are only 25 possible two-base-5-digit results. Then 7^1 is of course 7, but three times this (or 21) will fit into 25, so it doesn\'t matter we throw away the first base-7 digit (0-2). But as a result we keep only 21/25 of our throughput, or 84%, and 84% of 50% is the 42% we figured earlier.\r\n\r\nIf we choose to accumulate 21 base-5 digits, we\'ll get 17 base-7 digits, and as you can see from the last column, get almost 79% as many base-7 digits as base-5 go in, not too far from the theoretic 82.7% of the ideal case. Going to 23 base-5 digits would give us 78.991% instead of the 78.987 we get at 21, but accumulating such large numbers would exceed the precision available in the language I used.\r\n\r\nThe subroutine is:\r\n\r\nDEFDBL A-Z\r\nFUNCTION rand7\r\n STATIC seed\r\n IF seed = 0 THEN\r\n DO\r\n seed = 0\r\n FOR i = 1 TO 21\r\n seed = seed * 5 + rand5 - 1\r\n NEXT\r\n LOOP WHILE seed > 465261027974413#\r\n DO WHILE seed > 232630513987206#\r\n seed = seed - 232630513987207#\r\n LOOP\r\n END IF\r\n q = INT(seed / 7)\r\n r = seed - q * 7 + 1\r\n seed = q\r\n rand7 = r\r\nEND FUNCTION\r\n
\r\nNote the STATIC seed.\r\n\r\nIt keeps this value--the built base-5 number (actually stored in the internal binary format of the computer, but conceptually just a number)--from call to call to this function, until it has been depleted. The first DO...LOOP WHILE throws away seeds greater than 2*7^21-1 (the subtraction of one as we\'re zero-based). The second DO WHILE...LOOP in effect gets rid of the first base-7 digit.',NULL,0);
INSERT INTO comment VALUES (6102,970,103,'friedlinguini','Optimal Solution','2003-06-30 09:04:07',3,'In Quick and Dirty Solution, every time through the loop, the algorithm must generate two random numbers. However, this isn\'t always necessary. If the first pair of numbers doesn\'t generate a good result, there is still a \'wasted\' random number. That is, the loop must repeat if c is calculated to be 21, 22, 23, or 24. Each of these four is equally likely, so there is a \'free\' random number with four possibilities. This number can be reused in conjunction with another number from rand5 to generate more possible answers. The code could be changed so that if an iteration through the loop does not provide an answer, then we reuse the variable a to show which of the four \'remainder\' values is used. Since there are not necessarily 5 possible values for a, we need another variable, aSize, to show how large a pool a is picked from. Note that if a is picked from too small a pool (such as 1), we need to regenerate a from scratch using rand5.\r\n\r\nThe revised solution might look like:\r\n\r\nint a = rand5() - 1;\r\nint aSize = 5;\r\n\r\nwhile (true)\r\n{\r\n int groupSize = aSize * 5 / 7;\r\n\r\n if (groupSize == 0)\r\n {\r\n a = rand5() - 1;\r\n aSize = 5;\r\n continue;\r\n }\r\n\r\n int b = rand5() - 1;\r\n int c = a * aSize + b;\r\n int result = (c % groupSize) + 1;\r\n\r\n if (result <= 7)\r\n return result;\r\n\r\n int aSize = aSize * 5 - 7 * groupSize;\r\n a = c - 7 * groupSize;\r\n}n to represent the number of expected calls needed when you already have a value for a, and when n is a particular value for aSize. To start off,\r\n\r\nE = 1 + E5\r\n\r\nbecause after calling rand5 once, we have an aSize of 5.\r\n\r\nIn the E5 case, we need to call rand5 once more. This leads to 25 possible combinations. If we take this result in groups of 3, there are 4 different possible remainder values. Thus,\r\n\r\nE5 = 1 + 4/25 * E4\r\n\r\nWith E4, another call to rand5 will give 20 possible combinations. Here, we use groups of 2, which will give 6 possible remainder values. Thus,\r\n\r\nE4 = 1 + 6/20 * E6\r\n\r\nContinuing this pattern,\r\n\r\nE6 = 1 + 2/30 * E2\r\nE2 = 1 + 3/10 * E3\r\nE3 = 1 + 1/15 * E1\r\n\r\nRemember that if aSize is 1, it isn\'t useful; we have to start over. Thus,\r\n\r\nE1 = E.\r\n\r\nWe can now start substituting backwards to obtain a single equation in terms of E.\r\n\r\nE3 = 1 + 1/15 * E\r\nE2 = 1 + 3/10 * (1 + 1/15 * E) = 1 + 3/10 + 3/150 * E = 13/10 + 1/50 * E\r\nE6 = 1 + 2/30 * (13/10 + 1/50 * E) = 1 + 13/150 + 1/750 * E = 163/150 + 1/750 * E\r\nE4 = 1 + 6/20 * (163/150 + 1/750 * E) = 1 + 163/500 + 1/2500 * E = 663/500 + 1/2500 * E\r\nE = 2 + 0.16 * (663/500 + 1/2500 * E) = 2 + 663/3025 + 1/15625 * E = 6713/3025 + 1/15625 * E\r\n\r\nSolving this last equation for E finally gives:\r\n\r\nE = 6713/3025 / (1 - 1/15625)\r\n= ~2.219\r\n',NULL,0);
INSERT INTO comment VALUES (6103,970,103,'friedlinguini','re(2): Quick and Dirty Solution','2003-06-30 09:12:31',0,'Actually, what I was thinking, but failed to write is:\r\n\r\nint result = (c / 3) + 1;\r\n\r\nI brain-farted and managed to mix up the modulo and division operators.\r\n\r\nWith the correction in place, different values for c give these results:\r\n\r\n0-2: 1\r\n3-5: 2\r\n6-8: 3\r\n9-11: 4\r\n12-14: 5\r\n15-17: 6\r\n18-20: 7\r\n21-23: 8 (which fails the comparison test, and thus causes the loop to re-run)\r\n24: 9 (as above)\r\n\r\nI think I managed to do that in my other snippet as well. Serve me right for not testing my code...',6100,0);
INSERT INTO comment VALUES (6104,973,2588,'Jessi','may sound like a stupid answer','2003-06-30 09:17:06',0,'Bob simply gave Jim the wrong number?',NULL,0);
INSERT INTO comment VALUES (6105,973,1301,'Charlie','Another solution','2003-06-30 10:29:01',3,'That was the phone number of Bob\'s house. But Bob was out visiting a different house. Since Jim wanted to speak to Bob, he should have called the other house, hence he actually called the wrong house for speaking to Bob at that time.',NULL,0);
INSERT INTO comment VALUES (6106,973,1626,'Gamer','re: Another solution','2003-06-30 11:31:14',1,'I think this is a lateral thinking problem... any problem that has so many answers must be...',6105,0);
INSERT INTO comment VALUES (6107,970,1626,'Gamer','re: solution','2003-06-30 13:26:10',0,'Sorry if I missed something, but when you use really high numbers (like 5^7), wouldn\'t that need 7 attempts to find a random number? This means you are already up to 7 uses at minimum.\r\n\r\n',6101,0);
INSERT INTO comment VALUES (6108,836,1626,'Gamer','re(2): If you know each other....','2003-06-30 13:30:17',2,'Well, we have kind of exhausted all the possibilites... For one thing, I think I addressed the point of \"If you know eachother\" in a post below.',6068,0);
INSERT INTO comment VALUES (6109,82,2589,'alex','i don\'t get it.....','2003-06-30 13:43:00',0,'assuming you can get past the entire....\"infinite time\" flaw....the problem starts out saying zeus created these demons to kill prometheous....and ended with him saying that it shouldn\'t have been possible because there would always be another demon who should\'ve killed him sooner...soooooo..if he knew that none of the demons could acomplish this...why the hell did he create them in the first place?...i thought he WANTED prometheous killed....there\'s your paradox.',NULL,0);
INSERT INTO comment VALUES (6110,970,1301,'Charlie','re(2): solution','2003-06-30 15:14:41',0,'My assumption was that this random number generator (of integers between 1 and 7) would be called several times, not just once. I see that that\'s not stated in the problem, but I guess I just didn\'t (don\'t) see a need for just one random number, but rather some stochastic trials that need integers from 1 - 7.\r\n\r\nBut yes, if you need only one random number, choosing just two integers from 1-5 and using fl\'s techniques would be superior.',6107,0);
INSERT INTO comment VALUES (6111,973,2571,'Rob','Yet another solution','2003-06-30 19:00:16',1,'I heard a math problem once, where a kid switched the numbers on a calculator. Maybe something like that? Bob switched the numbers somehow? Yeah, sounds stupid. Still, this is under tricks, so someone may be doing something like that. Bob giving him the wrong number is a good answer though.',NULL,0);
INSERT INTO comment VALUES (6112,973,2591,'Kate','re: Thoughts','2003-06-30 19:05:23',0,'I agree about the number letters, but I don\'t agree with the possibilities. What I think is that the word \"WRONG\" probably means that \"wrong phone number.\" Another one is that the when Trevor Leitch mentioned about the two extra numbers 1 and 9 would maybe just extra numbers, or when Trevor said \"WRONG-1X\" if you take out the \"X\" it would be saying \"wrong one.\"',6099,0);
INSERT INTO comment VALUES (6113,903,2563,'rajesh','','2003-06-30 19:07:15',3,'I Got The Solution :)\r\n\r\nThe 6 Letters are\r\n\r\ncruohj\r\naldmwt\r\nvfpgiz\r\neybsnk\r\n',NULL,0);
INSERT INTO comment VALUES (6114,274,2563,'rajesh','Solution','2003-06-30 21:04:10',3,'Harold drew a longer line next to the line drawn by the king in parallel. this made the line drawn by the king shorter.',NULL,0);
INSERT INTO comment VALUES (6115,307,2563,'rajesh','Solution','2003-06-30 21:11:55',3,'a=b.\r\ntherefore we cannot cancel (a-b) on both sides as it amounts to 0 which can\'t be cancelled',NULL,0);
INSERT INTO comment VALUES (6116,973,1183,'fwaff','Yet another possibility','2003-06-30 22:19:46',3,'On the phone in my office I need to dial 9 to get an outside line. If Jim\'s works on the same principle then he\'s only really dialled 766419.',NULL,0);
INSERT INTO comment VALUES (6117,946,2428,'gordo packard','re: Common solution','2003-06-30 23:21:06',0,'Wouldn\'t it be unfortunate if the person who told you about the substitution was lying, and had replaced the \"death\" paper with another \"life\" paper, knowing you would probably tear up, eat, or burn the paper you chose?',6080,0);
INSERT INTO comment VALUES (6118,946,2563,'rajesh','My Solution','2003-06-30 23:46:35',3,'Tell the authorities to pick instead saying that you can\'t bear to see the word written on the paper u choose. Well, whichever they pick , they get the paper with DEATH written on it. Voila ! U Are set free !',NULL,0);
INSERT INTO comment VALUES (6119,836,1919,'Lewis','re(3): If you know each other....','2003-07-01 01:45:41',0,'Oh yeah.... that was sooo long ago though that I forgot about it.... :0(',6108,0);
INSERT INTO comment VALUES (6121,957,158,'Ender','Please post more about Solution','2003-07-01 02:53:00',0,'Could you please post a picture of the solution? (using |\'s for knights and .\'s for liars will allow it to fit, at least according to preview)\r\n\r\nI tried the official solution, and I can\'t get it to work. I needed to change n/2-1 to get all of the liars on both the side and the bottom of the square. With only changing n/4, I only can fix the side or the bottom.\r\n',NULL,0);
INSERT INTO comment VALUES (6122,968,1301,'Charlie','solution','2003-07-01 03:00:44',3,'1. As the natural log function decreases without limit (increases without limit in the negative direction) as its argument approaches zero from the positive side, and at the same time √x becomes closer to zero but still positive as x approaches zero, the function f(x)=ln(x)/√x also decreases without limit as x approaches zero, or in a less formal, looser terminology, approaches negative infinity.\r\n\r\n2. In a famous equation, incorporating all the major building-block numbers and operations, e^(iπ)+1 = 0, or\r\ne^(iπ)=-1 (by the way that π is a pi; it\'s sometimes hard to read in this font.)\r\nor\r\nln(-1)=iπ\r\n\r\nAs √(-1) is by definition i, we have iπ/i = π. The answer to the second part is pi.',NULL,0);
INSERT INTO comment VALUES (6123,946,2588,'Jessi','re: Common solution','2003-07-01 03:16:39',0,'I agree to a certain extent, I think he should say to the authorities that he will agree to have the sentence which is opposite of what he picks...am I right?',6080,0);
INSERT INTO comment VALUES (6124,516,2588,'Jessi','i liked this one','2003-07-01 03:57:01',0,'I liked this brainteaser, but is there a certain system one would follow to arrive at this solution, or is it trial and error?',NULL,0);
INSERT INTO comment VALUES (6125,970,103,'friedlinguini','re(3): solution','2003-07-01 05:17:58',0,'Actually, I think it\'s possible to combine ideas from both techniques for an even better solution. Store a and aSize as static variables. Upon successfully finding a result in my technique, set aSize to groupSize and a to (c % groupSize) (and this time I mean that modulo operator!). This allows ensures that the rand5 function is never called more times than necessary at any point.',6110,0);
INSERT INTO comment VALUES (6126,970,1301,'Charlie','re(4): solution','2003-07-01 05:38:24',4,'If I\'m interpreting your description correctly, the non-static version of your algorithm averages about 2.219 calls to rand5 for each base-7 digit. My algorithm averages 1.266 calls to rand5 per base-7 digit given that a large number of them will be needed. I take it that applying STATIC to your technique will actually bring it down to the theoretical 1.209 calls per digit; is that correct? (that\'s log(7)/log(5)).',6125,0);
INSERT INTO comment VALUES (6127,970,103,'friedlinguini','re(5): solution','2003-07-01 05:56:59',0,'I\'m not sure. I haven\'t tested it. I do have yet another solution to the problem that I believe is theoretically optimal, which I will post shortly.',6126,0);
INSERT INTO comment VALUES (6128,916,2592,'ben young','this works for me','2003-07-01 06:53:00',0,'LQEKDY\r\nCUATHB\r\nFMWNGI\r\nRZSOVP',NULL,0);
INSERT INTO comment VALUES (6129,970,103,'friedlinguini','Another look at optimality','2003-07-01 06:55:26',0,'Here is a solution that I believe wastes no information from any of the rand5 calls at all. What\'s interesting about this one is that I believe it is possible in some cases to generate a result without calling rand5 at all! However, it requires an arbitrary-precision math library (maybe something like Mathematica) to run.\r\n\r\nThe idea is similar to Charlie\'s large base 5 and base 7 integer ideas, and also gets some inspiration from the algorithm from Arithmetic Encoding.\r\n\r\nImagine a number x such that 0 ≤ x < 1. If you convert it to base 7, you have a string of digits between 0 and 6. If values of x are evenly distributed in the interval, each digit can be an integer between 0 and 6 with equal probability for each possible value. Add 1 and you have a possible return value for the function. x in base 7 represents an infinite list of random values that can be used in the solution--all you have to do is determine x.\r\n\r\nUnfortunately, we don\'t have a function for generating a random real number with infinite precision. We do, however, have the rand5 function. What we do is slap down a decimal point and use a string of rand5 calls to generate x in base 5.\r\n\r\nWe can\'t call rand5 an infinte number of times. However, that\'s OK because we don\'t need an infinte number of results. We can use rand5 to approximate x to greater and greater precision by adding single digits one right after the other. If we call rand5 n times, we have a lower bound on x to within 5^(-n). Moreover, if you add 1 to the last digit you added (carrying 1s to keep it the number in base 5), you have an upper bound on x with similar precision.\r\n\r\nSo what you do is convert these upper and lower bounds to base 7. Compare these numbers digit by digit. If corresponding digits are equal, you have a known digit of x.\r\n\r\nHere\'s the algorithm:\r\n\r\n// BigInt - an integer type that can hold arbitrarily\r\n// large values.\r\n// Rational - a numeric type that supports rational\r\n// numbers using a numerator and denominator of type BigInt\r\n// Both types support all normal mathematical operations\r\n// plus exponentiation.\r\n// In addition, Rational has a member function for finding\r\n// the nth digit after the decimal point in base b.\r\nstatic Rational x(0);\r\nstatic BigInt i5(0);\r\nstatic BigInt i7(0);\r\n\r\n++i7;\r\n\r\nwhile (x.digit(i7, 7) != (x + 1 / BigInt(5).exp(i5).digit(i7, 7))\r\n{\r\n ++i5;\r\n x += BigInt(rand5()) / BigInt(5).exp(i5);\r\n}\r\n\r\nreturn x.digit(i7, 7) + 1;\r\n\r\nI think this algorithm is optimal for any number of calls, using Charlie\'s theoretical minimum of log(7)/log(5) calls to rand5 per number generated.',NULL,0);
INSERT INTO comment VALUES (6130,973,1072,'Alan','Well','2003-07-01 07:23:25',2,'I really don\'t like posting in my own problems but I think I\'ll just say this trevor is on the right track, and the answer has nothing to deal with phone numbers in certain locations, switching numbers or anything of that nature. Thats why the category is tricks. Gamer you\'re right if someone were to just ask this it would be lateral thinking but this is in the category tricks for a reason. To prevent that.',NULL,0);
INSERT INTO comment VALUES (6131,85,2376,'Jim C','Where\'s Mister Black and Blue?','2003-07-01 07:57:24',3,'OK, I hate to nit pick, but nowhere in the puzzle was it stated that the ties were the same colors as the name. For all we know, Mr yellow is wearing a purple and orange paisley!\r\n\r\nAnyway, since Mr yellow can\'t be wearing yellow, and we know he\'s not wearing green (unless he is talking to himself), we know he is wearing brown. So Brown is wearing green and Green is wearing yellow. ',NULL,0);
INSERT INTO comment VALUES (6132,946,2376,'Jim C','\'shaky\' response','2003-07-01 08:02:01',3,'OH, C\'mon! I\'m too nervous to pick a paper. Just look at my hands! Tell you what, you pick one and whatever is left in the hat will be mine...',NULL,0);
INSERT INTO comment VALUES (6133,971,1301,'Charlie','Algebraic Solution','2003-07-01 09:45:39',3,'In the following function, I make use of a check that a given number n is between two other numbers a and b, by checking if (a - n)*(n - b)>=0, so as to avoid checking two possible orders of size.\r\n\r\nIf both segments are vertical, they can \"intersect\" only if they are at the same x coordinate, and then only if at least one of the endpoints of oneone line lies between the endpoints (y values) of the other.\r\n\r\nIf only one segment is vertical that segment must lie between the x limits of the other segment, and the equation of that line is computed and the y value at the vertical segment\'s x value must lie between that segment\'s end y values.\r\n\r\nOtherwise the equations of the two lines are checked. If the lines are parallel (same slopes) they must be coincident for any intersection, and at least one end x coordinate of one must lie between the other segment\'s end x coordinates.\r\n\r\nIf the lines are not parallel, the point of intersection is found by solving simultaneously, and the x coordinate of the point of intersection must lie between the x coordinates of the endpoints for each of the two segments.\r\n\r\nDEFDBL A-Z\r\nDECLARE FUNCTION intersects# (Ax#, Ay#, Bx#, By#, Cx#, Cy#, Dx#, Dy#)\r\nDIM SHARED pi\r\n\r\npi = ATN(1) * 4\r\n\r\nDO\r\n INPUT x1, y1, x2, y2, x3, y3, x4, y4\r\n PRINT intersects(x1, y1, x2, y2, x3, y3, x4, y4)\r\nLOOP\r\n\r\nFUNCTION intersects (Ax, Ay, Bx, By, Cx, Cy, Dx, Dy)\r\n \' Lines segments are A-B and C-D\r\n false = 0: true = NOT false\r\n\r\n \'exceptional cases first:\r\n IF Ax = Bx THEN\r\n IF Cx = Dx THEN \' both segments vertical\r\n IF Cx <> Ax THEN intersects = false: EXIT FUNCTION\r\n IF (Cy - Ay) * (By - Cy) >= 0 OR (Dy - Ay) * (By - Dy) >= 0 OR (Ay - Cy) * (Dy - Ay) >= 0 OR (By - Cy) * (Dy - By) >= 0 THEN\r\n \'C between A and B or D between A and B or A between C and D or B between C and D\r\n intersects = true: EXIT FUNCTION\r\n ELSE\r\n intersects = false: EXIT FUNCTION\r\n END IF\r\n ELSE\r\n IF (Dx - Ax) * (Ax - Cx) < 0 THEN\r\n \' Ax not between Cx and Dx\r\n intersects = false: EXIT FUNCTION\r\n END IF\r\n slope = (Dy - Cy) / (Dx - Cx)\r\n yForx = slope * (Ax - Cx) + Cy\r\n IF (By - yForx) * (yForx - Ay) >= 0 THEN\r\n \'line at Ax (which is also Bx) is between Ay and By\r\n intersects = true: EXIT FUNCTION\r\n ELSE\r\n intersects = false: EXIT FUNCTION\r\n END IF\r\n END IF\r\n ELSEIF Cx = Dx THEN\r\n IF (Bx - Cx) * (Cx - Ax) < 0 THEN\r\n \' Cx not between Ax and Bx\r\n intersects = false: EXIT FUNCTION\r\n END IF\r\n slope = (By - Ay) / (Bx - Ax)\r\n yForx = slope * (Cx - Ax) + Ay\r\n IF (Cy - yForx) * (yForx - Dy) >= 0 THEN\r\n \'line at Cx (which is also Dx) is between Cy and Dy\r\n intersects = true: EXIT FUNCTION\r\n ELSE\r\n intersects = false: EXIT FUNCTION\r\n END IF\r\n ELSE\r\n slopeA = (By - Ay) / (Bx - Ax)\r\n slopeC = (Dy - Cy) / (Dx - Cx)\r\n IF slopeA = slopeC THEN\r\n yForx = slopeA * (Cx - Ax) + Ay\r\n IF yForx <> Cy THEN intersects = false: EXIT FUNCTION\' parallel non-coincident lines\r\n \' what remains are segments sharing the same line\r\n IF (Cx - Ax) * (Bx - Cx) >= 0 OR (Dx - Ax) * (Bx - Dx) >= 0 OR (Ax - Cx) * (Dx - Ax) >= 0 OR (Bx - Cx) * (Dx - Bx) >= 0 THEN\r\n intersects = true: EXIT FUNCTION\r\n ELSE\r\n intersects = false: EXIT FUNCTION\r\n END IF\r\n ELSE\r\n x = (slopeA * Ax - slopeC * Cx + Cy - Ay) / (slopeA - slopeC)\r\n IF (Ax - x) * (x - Bx) >= 0 AND (Cx - x) * (x - Dx) >= 0 THEN\r\n \' x coord of point of intersection of lines is within\r\n \' x boundaries of both segments\r\n intersects = true: EXIT FUNCTION\r\n ELSE\r\n intersects = false: EXIT FUNCTION\r\n END IF\r\n END IF\r\n END IF\r\n\r\nEND FUNCTION\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (6134,971,1301,'Charlie','Geometric Solution','2003-07-01 09:54:13',0,'The geometric solution checks that ACBD is a non-concave quadrilateral, after having checked a couple of special cases where an endpoint of one line coincides with that of another.\r\n\r\nDECLARE FUNCTION norm# (x#)\r\nDECLARE FUNCTION atan2# (y#, x#)\r\nDEFDBL A-Z\r\nDECLARE FUNCTION intersects# (Ax#, Ay#, Bx#, By#, Cx#, Cy#, Dx#, Dy#)\r\nDIM SHARED pi\r\n\r\npi = ATN(1) * 4\r\n\r\nDO\r\n INPUT x1, y1, x2, y2, x3, y3, x4, y4\r\n PRINT intersects(x1, y1, x2, y2, x3, y3, x4, y4)\r\nLOOP\r\n\r\nFUNCTION atan2 (y, x)\r\n IF x = 0 THEN\r\n atan2 = pi / 2 * SGN(y)\r\n ELSE\r\n IF x < 0 THEN\r\n atan2 = ATN(y / x) + pi\r\n ELSE\r\n atan2 = ATN(y / x)\r\n END IF\r\n END IF\r\nEND FUNCTION\r\n\r\nFUNCTION intersects (Ax, Ay, Bx, By, Cx, Cy, Dx, Dy)\r\n \' Lines segments are A-B and C-D\r\n false = 0: true = NOT false\r\n\r\n \'exceptional cases first:\r\n \'end point of one line is end point of another:\r\n IF Ax = Cx AND Ay = Cy OR Ax = Dx AND By = Dy OR Bx = Cx AND By = Cy OR Bx = Dx AND By = Dy THEN\r\n intersects = true: EXIT FUNCTION\r\n END IF\r\n\r\n angle1 = atan2(Cy - Ay, Cx - Ax)\r\n angle2 = atan2(By - Cy, Bx - Cx)\r\n angle3 = atan2(Dy - By, Dx - Bx)\r\n angle4 = atan2(Ay - Dy, Ax - Dx)\r\n a1 = norm(angle2 - angle1)\r\n a2 = norm(angle3 - angle2)\r\n a3 = norm(angle4 - angle3)\r\n a4 = norm(angle1 - angle4)\r\n \r\n \' check if end point of one line is along another line:\r\n IF a1 = 0 OR a2 = 0 OR a3 = 0 OR a4 = 0 THEN intersects = true: EXIT FUNCTION\r\n \'check if all colinear but no overlap\r\n IF a1 = pi AND a2 = pi AND a3 = pi AND a4 = pi THEN\r\n intersects = false: EXIT FUNCTION\r\n END IF\r\n\r\n\r\n IF a1 > 0 OR a1 = 2 * pi THEN\r\n IF (a2 > 0 OR a2 = 2 * pi) AND (a3 > 0 OR a3 = 2 * pi) AND (a4 > 0 OR a4 = 2 * pi) THEN\r\n intersects = true\r\n ELSE\r\n intersects = false\r\n END IF\r\n ELSE\r\n IF (a2 < 0 OR a2 = 2 * pi) AND (a3 < 0 OR a3 = 2 * pi) AND (a4 < 0 OR a4 = 2 * pi) THEN\r\n intersects = true\r\n ELSE\r\n intersects = false\r\n END IF\r\n END IF\r\nEND FUNCTION\r\n\r\nFUNCTION norm (x)\r\n n = x\r\n DO UNTIL n <= pi\r\n n = n - 2 * pi\r\n LOOP\r\n DO UNTIL n > -pi\r\n n = n + 2 * pi\r\n LOOP\r\n norm = n\r\nEND FUNCTION\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (6135,973,1626,'Gamer','re: Well','2003-07-01 11:09:47',4,'Sorry to sound doubtful, but the catergory doesn\'t prevent the fact that all the solutions are logical. And many of them ARE tricks... And why do you say \"The solution\"? Aren\'t all the solutions logical?',6130,0);
INSERT INTO comment VALUES (6136,971,1567,'Bryan','An easier way','2003-07-01 12:27:50',3,'If line segments AB and CD intersect, then points C and D will fall on opposite sides of AB (or one will fall directly on AB), and similarly, points A and B will fall on eith side of (or on) CD. Therefore, one means of determining if line segments AB and CD intersect is as follows:
It is a straight-forward exercise to write an algorithm to perform this function, so one is not included here.',NULL,0);
INSERT INTO comment VALUES (6137,971,103,'friedlinguini','Solution','2003-07-01 13:03:47',3,'The two segments intersect if and only if C and D do not lie on the same side of the line through AB and A and B do not lie on the same side of the line through CD.\r\n\r\nSo the trick is finding out which side of a line a point lies upon. Probably the most straightforward way to do this is to convert the line to its implicit form: L(x, y) = Px + Qy + R. If L(x, y) > 0 then <x, y> is on one side of the line, if L(x, y) < 0 then <x, y> is on the other side, and if L(x, y) = 0, then <x, y> is on the line.\r\n\r\nIt\'s possible to find P, Q, and R by solving some system of linear equations, but there are some shortcuts that can be taken. Assume that we\'re looking for the values corresponding to the line through A and B. <P, Q> is actually a vector that points perpendicular to the line. The direction of the line through A and B is given by <Bx - Ax, By - Ay>.\r\n\r\nIn 2D, it\'s easy to find one vector that is perpendicular to another: just switch the x and y coordinates, and multiply one of them by -1 (try it and see).\r\n\r\nThis means that we can use <By - Ay, Ax - Bx> for our perpendicular vector. The length of the vector doesn\'t really matter, just its direction. This gives us P = By - Ay and Q = Ax - Bx.\r\n\r\nTo find R, just plug one of the points (say, A) into the function. Since the point is on the line, the function evaluates to 0. Thus,\r\n\r\nL(Ax, Ay) = P Ax + Q Ay + R = 0\r\n(By - Ay) Ax + (Ax - Bx) Ay + R = 0\r\nAxBy - AxAy + AxAy - AyBx + R = 0\r\nR = AyBx - AxBy\r\n\r\nTo see whether C and D lie on the same side of the line, substitute them into L(x, y) and multiply the results together. If the value is positive, they intersect.\r\n\r\nL(Cx, Cy) L(Dx, Dy) = [(By - Ay)Cx + (Ax - By)Cy + AyBx - AxBy][(By - Ay)Dx + (Ax - By)Dy + AyBx - AxBy]\r\n= (ByCx - AyCx + AxCy - ByCy + AyBx - AxBy)(ByDx - AyDx + AxDy - ByDy + AyBx - AxBy)\r\n\r\n(I won\'t bother multiplying these together, as I think it will make the expression even uglier)\r\n\r\nTo see whether A and B lie on the same side of the line through C and D, just switch the A\'s and B\'s with the C\'s and D\'s:\r\n\r\n(DyAx - CyAx + CxAy - DyAy + CyDx - CxDy)(DyBx - CyBx + CxBy - DyBy + CyDx - CxDy)\r\n\r\nThe whole algorithm can thus be written in one statement:\r\n\r\nreturn (ByCx - AyCx + AxCy - ByCy + AyBx - AxBy) * \r\n (ByDx - AyDx + AxDy - ByDy + AyBx - AxBy) > 0\r\n && (DyAx - CyAx + CxAy - DyAy + CyDx - CxDy) *\r\n (DyBx - CyBx + CxBy - DyBy + CyDx - CxDy) > 0;\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (6138,971,103,'friedlinguini','re: Solution','2003-07-01 13:07:26',0,'OK, probably should have finished converting to legal code:\r\n\r\nreturn (By*Cx - A*yCx + Ax*Cy - B*yCy + Ay*Bx - Ax*By) *\r\n (By*Dx - Ay*Dx + Ax*Dy - By*Dy + Ay*Bx - Ax*By) > 0\r\n && (Dy*Ax - Cy*Ax + Cx*Ay - Dy*Ay + Cy*Dx - Cx*Dy) *\r\n (Dy*Bx - Cy*Bx + Cx*By - Dy*By + Cy*Dx - Cx*Dy) > 0;',6137,0);
INSERT INTO comment VALUES (6139,914,2563,'rajesh','Solution','2003-07-01 22:47:24',3,'Ya! It will be the last place bcos u wont look anywhere afterwards. :)',NULL,0);
INSERT INTO comment VALUES (6140,971,1301,'Charlie','re: Solution','2003-07-02 03:40:46',4,'When I use\r\nAx, Ay, Bx, By, Cx, Cy, Dx, Dy equal to\r\n 1,3,4,1,3,1,5,3\r\nso that AB is from (1,3) to (4,1) and CD is from (3,1) to (5,3), which intersect,\r\n\r\nI get the following values:\r\nBy * Cx - Ay * Cx + Ax * Cy - By * Cy + Ay * Bx - Ax * By = 5\r\nBy * Dx - Ay * Dx + Ax * Dy - By * Dy + Ay * Bx - Ax * By = 1\r\nDy * Ax - Cy * Ax + Cx * Ay - Dy * Ay + Cy * Dx - Cx * Dy = -2\r\nDy * Bx - Cy * Bx + Cx * By - Dy * By + Cy * Dx - Cx * Dy = 4\r\n\r\nThen, while 5*1 > 0, (-2)*4 < 0 so the ANDed condition fails. What went wrong here?\r\n',6137,0);
INSERT INTO comment VALUES (6141,974,1567,'Bryan','First guess','2003-07-02 04:43:59',0,'My first guess is to use the word \"tile,\" since this seems to be verse of some sort, and \"tile\" rhymes with \"while\" in the second line. Rhyming is good; I like rhymes.
If the guy was telling a lie and both papers say LIFE, then you are saved.
If the guy was telling a lie and he hadn\'t switched any paper and you draw LIFE, then you are saved.
If the guy was telling a lie and he hadn\'t switched any paper and you draw DEATH then you are decidedly unlucky and you will die. But since you don\'t know whether he was being truthful or telling a lie you are no worse off getting rid of the paper.
Angular velocity of hour hand = 30 deg/hr
Angular velocity of minute hand = 360 deg/hr
let angle covered by hour hand before meeting minute hand next, be x deg.
In the same time, the minute hand would have travelled 360+x deg
Hence, x = 360/11 deg
= 360/11/30 hr
= 1 hr, 5 min, & 27.2727.. sec
which is a litte over 25 sec per hour (25.174825.. sec/hr to be precise)',NULL,0);
INSERT INTO comment VALUES (6226,400,2129,'Sanjay','Change the official solution','2003-07-05 09:14:20',0,'Its a shame that the official solution to this problem continues to be 4.65%, when the actual solution, as ably pointed out by fwaff, is 4.83%
Odds for being dealt a Blackack = 32 to 631
Odds against being dealt a BlackJack = 631 to 32.\r\nFOR i = 1000 TO 9999\r\n n$ = LTRIM$(STR$(i))\r\n n1$ = RIGHT$(n$, 1) + MID$(n$, 3, 1) + MID$(n$, 2, 1) + LEFT$(n$, 1)\r\n n = VAL(n1$)\r\n IF i * 10 = n + i THEN PRINT i\r\nNEXT\r\n
',6234,0);
INSERT INTO comment VALUES (6237,976,1301,'Charlie','re(2): Solution','2003-07-06 06:09:26',0,'I meant to say \"no other solutions even with digits allowed to be repeated\".',6236,0);
INSERT INTO comment VALUES (6238,974,2632,'allison','ive got a guess','2003-07-06 09:55:19',3,'i think it\'s tile because the second-to-last letter in line 1 is n, line 2 is l, line 3 is n, so line 4 should be l. Tile\'s the only one that has the second-to-last letter \"l\"',NULL,0);
INSERT INTO comment VALUES (6239,441,2632,'allison','re: Already not the latest... solution','2003-07-06 09:59:32',0,'I agree.',2988,0);
INSERT INTO comment VALUES (6240,976,153,'TomM','Non-algorithmic solution','2003-07-06 13:02:15',0,'Yes, you can use a program to \"brute-force\" test every four digit number, but it is better if you can find it and prove it without crunching all of those numbers.\r\n\r\nFirst, as Lewis said, the first and last digits must add up to 10. \r\n\r\nSecond, since the first digit of the five digit number can only be 1, the first digit of the four digit number can only be 1. \r\n\r\nSo the number is of the form 1xx9\r\n\r\nThird, since 1xx9 + 9xx1 = 1xx90 = 10(1xx9), then 9xx1 = 9(1xx9). Since 9xx1 is divisible by 9, and 1xx9 and 9xx1 have the same digits, then by the \"casting out nines property\" 1xx9 must be divisible by 9. And also, the two middle numers must add to either 8 or 17.\r\n\r\nIf I were inclined to crunch numbers, I would only need to crunch 1089, 1179, 1269, 1359, 1449, 1899, and 1989. The last three contain duplicated digits and are thus disqualified. So we have reduced the \"pool\" from 10!/6! = 5040 (Already reduced from 10,000 by the no duplicates rule) to 4. \r\n\r\nBut perhaps we can reduce it further. At this point it becomes necessary to identify the digits by unique variables. abcd, where a=1 and d=9.\r\nwe get:
\r\n\r\nThis gives us a=1, b=0, c=8, d=9 or 1089 as a unique solution. \r\n',NULL,0);
INSERT INTO comment VALUES (6241,543,2635,'wink','oh i know!','2003-07-06 18:53:54',0,'its gotta be some sort of alien treasure chest. see, the aliens know how to get the treasure inside without an opening.. maybe they can move through walls? anyways. so no one can open it. no hinges, key, or lid, but golden treasure inside is hid. they must have hidden them choclate coins! what a great prize! or maybe its just a piggy bank? becuase golden treasure as in pennies!',NULL,0);
INSERT INTO comment VALUES (6242,230,2635,'wink','i will explain','2003-07-06 19:08:20',0,'if you draw it on a paper, it will look something like this\r\n\r\nSeat Seat Seat Seat Seat\r\n| \\ \\ \\ | /\r\n| \\ \\ \\ | /\r\n| \\ \\ \\ | /\r\nBilly Guest1 Guest2 Guest3 Guest4 Guest5',NULL,0);
INSERT INTO comment VALUES (6243,976,2373,'ryan smith','Solution (Algebraic)','2003-07-06 20:04:10',3,'I like the other solutions.\r\n\r\nHere\'s how I approached it:\r\n\r\nThe number is \"abcd\" (where a,b,c,d are 0-9), then:\r\n\r\n1000a+100b+10c+d+1000d+100c+10b+a = 10(1000a+100b+10c+d),\r\n\r\ncollecting terms:\r\n\r\n8999a+890b-10c-991d = 0\r\n\r\nsince 991(9)=8919 < 8999, and by inspection:\r\n\r\na=1, d=9, and so, b=0 and c=8,\r\n\r\nsolution: 1089.\r\n\r\nIt\'s interesting to note that the constants of the equation (*) have the only those digits as in the answer. Conicidence or a hint to a general solution?',NULL,0);
INSERT INTO comment VALUES (6244,974,2373,'ryan smith','re(3): Easy','2003-07-06 20:16:58',0,'Yes, I do. Thankfully Mirriam-Webster (www.m-w.com) backs me up.\r\n\r\nI agree with the poster who said that B, C, and D each have one syllable.\r\n\r\n',6213,0);
INSERT INTO comment VALUES (6245,806,2449,'Gt Vegita','eh..','2003-07-06 21:02:26',0,'If he were to follow the edges, around all corners of the cube, not only would he have a specific path, but it would enable him to consume the center last.',NULL,0);
INSERT INTO comment VALUES (6246,987,1183,'fwaff','re(2): More solutions in that number','2003-07-06 21:48:01',0,'Once again I think this is a difference in English English and US English. My understanding is that \'fuze\' is a common US variant of \'fuse\'.\r\n\r\nI think that this problem is impossible if you use common proper English English words. The problem comes in getting from a word of the form **zz to one either of the form **z* or ***z. However, since the problem states \'common\', but does not explicitly state \'proper\' then the transition could be made using common slang.',6219,0);
INSERT INTO comment VALUES (6247,980,1715,'Jonny Doe','Solution','2003-07-07 03:24:35',0,'Jimmy is a knave but Jonny can be either Knight or Knave. If I had to choose one I would choose knight since both his statements are true.',NULL,0);
INSERT INTO comment VALUES (6248,980,1301,'Charlie','re: Solution','2003-07-07 03:31:37',0,'Since both Johnny\'s statements are true and they were made in succession, he must be a knight, as a knave would have lied on one of the two statements.',6247,0);
INSERT INTO comment VALUES (6249,980,1919,'Lewis','Solution','2003-07-07 05:15:57',3,'Jimmy says \'I am a knave\', so he is either a liar or a knave telling the truth, which would make his other statement false.\r\n\r\nJohnny says that Jimmy is not a knight, which is true, so he is either a knave or a knight. If he is a knave his other statement would also be false.\r\n\r\nSeeing as they both claim each other are knaves, if they were knaves that would be the lying statement, but thats a contradiction.\r\n\r\nThis means that Johnny is a knight and Jimmy is a knave who\'s first statement was true.',NULL,0);
INSERT INTO comment VALUES (6250,987,1575,'DJ','re(3): More solutions in that number','2003-07-07 05:58:46',0,'I agree with Trevor..I have never seen the word \'fuze\' before, let alone in common usage. My solution has one more step (by the way, yours would considered eight, not seven), but using words that I think everyone will at least agree that they have seen before and know the meaning.',6246,0);
INSERT INTO comment VALUES (6251,918,1575,'DJ','re: Difficulty change','2003-07-07 06:28:20',0,'You\'re right, but I didn\'t even think about it and I was gone when it was in voting and posted. Maybe levik can do some \'posthumous\' editing...',6086,0);
INSERT INTO comment VALUES (6252,980,1183,'fwaff','re: Solution','2003-07-07 06:32:25',3,'It\'s possible to slightly shorten Lewis\'s logic as follows:\r\n\r\nJimmy says \'I am a knave\', so he is either a knave telling the truth or a liar - in either instance his second statement must be false, therefore Johnny is either a knight or a liar.\r\n\r\nJohnny says \'Jimmy is not a knight\' which is true, therefore Johnny must be a knight. Johnny the knight also says \'Jimmy is a knave\' which must also be true.\r\n\r\nSo we have Johnny is a knight and Jimmy is a knave.',6249,0);
INSERT INTO comment VALUES (6253,980,2376,'Jim C','I\'m Jimmy and I\'m not a Knave!','2003-07-07 07:33:25',3,'C\'mon! This was too easy!\r\nJimmy told the truth--he is a knave. Johnny told the truth both times--Jimmy is not a Knight, he\'s a Knave. And Jimmy lied--Johnny is not a knave.\r\n\r\nJimmy Knave\r\nJohnny Knight.',NULL,0);
INSERT INTO comment VALUES (6254,976,2376,'Jim C','Thank God I have all of MY digits!','2003-07-07 08:14:27',3,'OK, pseudoalgebraically:\r\n\r\n((1000A+100B+10C+D)+(1000D+100C+10B+A))/10 = 1000A+100B+10C+D\r\n\r\nsimplify the left, and multiply both sides by ten:\r\n\r\n1001A+110B+110C+1001D = 10000A+1000B+100C+10D\r\nSubtract the left:\r\n0= 8999A+890B-10C-991D\r\n\r\nIf you look at the puzzle, we have one more equation at our disposal. Since the combined numbers must be divisible by ten, the sum must end in zero, so A + D = 10, and D = 10-A.\r\n\r\nSubstitute for D:\r\n0 = 8999A+890B-10C-9910+991A\r\n9910 = 9990A+890B-10C\r\nWe can divide by ten to simplify:\r\n991 = 999A+89B-C\r\n\r\nOK. Now lets use logic (thus the pseudoalgebra only).\r\nWe know A is a non-zero integer (otherwise we\'d be working with a three digit number), so 89B-C must be negative. The only way this is possible would be for B to be zero (since even a positive 89 would make a negative impossible).\r\n\r\nSo B = 0, leaving 991 = 999A-C\r\nSince C must be a single integer, A can\'t be greater than one. Substituting 1 for A:\r\n-8 = -C\r\nThus far we have\r\nA = 1\r\nB = 0\r\nC = 8\r\nand, since A+D = 10\r\nD=9\r\n\r\n1089+9801 = 10890\r\n10890/10 = 1089\r\n',NULL,0);
INSERT INTO comment VALUES (6255,976,2376,'Jim C','re: Non-algorithmic solution','2003-07-07 08:22:05',0,'That was great! I especially like the \"First digit must be 1\" reasoning. It took me a good 5 minutes to realize this must be true, since we are adding single digits, the first digit of the sum MUST be 1, and since we know we are simply dividing that sum by 10, all of the digit places (1,2,3,4) must match, with a zero in the fifth place.\r\n\r\nExcellent, and thanks for the additional exercise in figuring out the answer BEFORE asking you a stupid question =0).',6240,0);
INSERT INTO comment VALUES (6256,987,1301,'Charlie','re(4): More solutions in that number','2003-07-07 08:25:18',0,'According to the Random House dictionary, meaning 1 of fuze is \"a mechanical or electronic device to detonate an explosive charge, esp. as contained in an artillery shell, a missile, projectile, or the like.\", while meaning 2 is a reference to \"fuse\" meaning number 1, which is \"a tube, cord, or the like, filled or saturated with combustible matter, for igniting an explosive.\" Also \"fuse\" has a secondary meaning that refers to the primary meaning of \"fuze\". As to the distinction between these meanings, I admit I don\'t see much, except that if what\'s detonated is a missile or projectile the z spelling is preferred.\r\n\r\nI do see however that \"futz\" and \"putz\" are labeled slang, the latter somewhat vulgar as former senator D\'Amato had found out. \r\n\r\nAs to the number of steps, I\'d consider that to be the number of changes, which equates to all the words but not counting the beginning word, but counting the goal word. In that instance the solutions provided previously are 7 steps.',6250,0);
INSERT INTO comment VALUES (6257,187,2376,'Jim C','Ummm, that was spelling, not counting, right?','2003-07-07 09:42:58',3,'I know, i know. The bigger feet give them a bigger surface to write crib notes on, right?\r\n\r\nDuh! How about, bigger feet equals older age (in general--this was a statistical study, after all).',NULL,0);
INSERT INTO comment VALUES (6258,686,1919,'Lewis','re: maybe a solution','2003-07-07 10:04:41',3,'But that wouldn\'t stop him from panicking, as the problem states that he \'calmly continued on his way\'. Aslo, he could just show someone else who could talk. (All this is if it was a murder as in crime, not crows, which I know the solution is)',3906,0);
INSERT INTO comment VALUES (6259,988,1301,'Charlie','observation','2003-07-07 11:01:40',1,'If the special characters are the only thing that counts and their placement in the plaintext message is arbitrary, I see that they are all characters that can be found on the numeric row of keyboard keys. The keys, in turn are\r\n 3 4 2 8 2 5 4 2 5 2 3 8 2 4 4 2 2 2 5 5 8 5 3 2 3 2 3 2 4 5 4 3 4 2\r\n\r\nI don\'t know if this means anything, or the fact that the 9 and 0 are absent (no parentheses included).',NULL,0);
INSERT INTO comment VALUES (6260,988,1919,'Lewis','re: observation','2003-07-07 11:10:40',1,'The problem with that is the different keyboard layouts. The only symbols in the problem that appear on my keyboard on the numberic keys are $ and %, which are 4 and 5 respectively.',6259,0);
INSERT INTO comment VALUES (6261,988,2635,'wink','re: observation','2003-07-07 11:15:33',0,'maybe it has something to do with the telephone numbers? i don\'t know. usually it has something to do with the telephone becuase it so damn popular.. dang kids these days wont use the old fashioned telegram..',6259,0);
INSERT INTO comment VALUES (6262,988,1919,'Lewis','Some thoughts','2003-07-07 11:17:34',1,'Perhaps the different sections of words cut up by the symbols can be put together? \r\n\r\nPerhaps words with matching symbols have some relation or hidden meaning?\r\n\r\nIf what Charlie said is right, then perhaps the numbers of the symbols relate to certain letters in that word or words in the paragraph?\r\n\r\nI don\'t know. This is confusing!',NULL,0);
INSERT INTO comment VALUES (6263,988,2129,'Sanjay','re: observation','2003-07-07 11:34:25',0,'Since there isn\'t any !,^,or &, I suppose 1,6,and 7 are also missing, in addition to 9 and 0.\r\nd s f m g\r\n 6 10 21 23 25\r\n 12 20 41 40 54\r\n 18 30 61 57 83\r\n 24 40 81 74 112\r\n 30 50 101 91 141\r\n
\r\nConsiderations:\r\nThe first row has the grandmother to young to be a parent to either the father or the mother.\r\n\r\nThe second row is conceivable if the grandmother gave birth to the mother at age 14.\r\n\r\nThe third row is presumably the sought answer with the grandmother having given birth to either the mother at age 26 or the father at age 22, and the mother having given birth at ages 27 and 39.\r\n\r\nThe third row is also conceivable with the grandmother having given birth to the father at age 31 and the mother having given birth at ages 34 and 50.\r\n\r\nThe last row has an age of 141, which age I don\'t think anyone has reached, and the mother would have had to have given birth at age 61.',NULL,0);
INSERT INTO comment VALUES (6497,984,2667,'Viet','re: solution','2003-07-16 08:58:01',0,'#2 don\'t fit in if the son is 20 then the father b 39 and if the grandmother is 54 it mean it gave birth to either the father or mother at age 14 or 15 itz just don\'t fit',6495,0);
INSERT INTO comment VALUES (6498,984,2667,'Viet','re: Solution','2003-07-16 09:32:22',0,'wouldn\'t 2. be F+1=Sx2 since in one year the father will b twice meaninf if sone is 10 the father b 19 this year??',6496,0);
INSERT INTO comment VALUES (6499,984,2742,'abdi','my solution','2003-07-16 10:07:09',0,'Daughter: 12\r\nSon: 20\r\nMother:34\r\nFather:40\r\nGrandmother:58',NULL,0);
INSERT INTO comment VALUES (6500,568,2743,'marinos','that\'s very easy','2003-07-16 10:21:09',0,'You just push the cork from the neck of the bottle to fall into the bottle and then you can get your coin out of the bottle ;-)',NULL,0);
INSERT INTO comment VALUES (6501,1008,2743,'marinos','probably','2003-07-16 10:34:31',0,'Probably she is drinking both coffee and soda because she is Eliza + Beth (LOL what a stupid answer) :-)',NULL,0);
INSERT INTO comment VALUES (6502,984,1171,'nikki','re(2): Solution','2003-07-16 12:51:08',0,'\r\nActually Charlie is right - the wording of the statement must be considered carefully. It doesn\'t say:\r\n\r\n\"In one year, the father will be twice as old as the son is NOW\"\r\n\r\nThink of the statement as saying \"Let one year of time pass. At that point the father will be twice as old as his son.\"\r\n\r\nDoes that help, Viet?\r\n\r\nLater!',6498,0);
INSERT INTO comment VALUES (6503,1032,2716,'Federico Kereki','re: Wild Guess','2003-07-16 15:03:50',0,'I agree, but it should be PN, KT, BP, RK, QN, KG. If a knight is valued as 3.0, the bishop usually counts as 3.5. Furthermore, the king\'s worth is considered \"infinity\", since losing it means a defeat.',6414,0);
INSERT INTO comment VALUES (6504,568,2373,'ryan smith','Another Solution','2003-07-16 15:16:22',3,'Well, if you couldn\'t push the cork down the neck of the bottle you could always toss the whole thing into a furnace. The cork would burn, the bottle would melt (not break!), and the coin would be yours. Just let it cool down a bit before picking it up.\r\n\r\nThis, of course, depends on the melting points of the bottle and the coin. But, I\'m pretty sure that most glasses will melt before most metals do.\r\n\r\nAlso, you could burn the cork (that might prove difficult), or dissolve it with an acid (one that doesn\'t affect metal).',NULL,0);
INSERT INTO comment VALUES (6505,1008,2724,'PRIVATE','i say it\'s.....','2003-07-16 22:33:38',0,'ElizabEth is probably drinking coffEE!!!',NULL,0);
INSERT INTO comment VALUES (6506,567,2724,'PRIVATE','i\'m dumb, but i think it\'s...','2003-07-16 22:47:02',0,'i say b indirectly made the correct statement by not outright disquallifying r to win. in my view this is the only possible way that one of them can be right and two others wrong.',NULL,0);
INSERT INTO comment VALUES (6507,903,2724,'PRIVATE','i got it.....','2003-07-16 23:34:43',0,'Process of elimination makes life easy for us here. You start with the first word, cave.\r\nC must be cube 1, (or cube alphalpha or whatever you want to name it ) \r\nA for cube 2, V for three, and E for four.\r\n\r\nAfter determining that, you simply isolate the possibilities from here on.\r\n\r\nafter following the lengthy, if easy, process one comes up with:\r\n\r\nFor cube 1:\r\nC U R H O (and don\'t forget the never used J)\r\n\r\nFor cube 2:\r\nA L W D T M\r\n\r\nFor cube 3:\r\nV F G P Z I\r\n\r\nFor cube 4:\r\nE B Y N K S',NULL,0);
INSERT INTO comment VALUES (6508,924,2724,'PRIVATE','GOT IT!','2003-07-17 01:14:42',0,'OKAY, I HATE ARBITRARY SYMBOLS, BUT HERE GOES:\r\n\r\nOK WE HAVE THE GIVEN:\r\n\r\n*% = $\r\n$$$ = @%*%@\r\n@ = !*\r\n\r\nFIRST LETS CONBINE THE GIVEN INTO SOMETHING THAT MAY MAKE A LITTLE MORE SENSE...\r\nSINCE *% = $, LETS SUBSTITUTE ***%%% FOR $$$ ON THE LEFT SIDE OF THE MIDDLE EQUATION OF THE GIVEN. AND SINCE @ = !* LETS SUBSTITUTE !* FOR EVERY @ IN THE RIGHT SIDE OF THE SAME EQUATION.\r\n \r\nTHEREFORE WE HAVE:\r\n\r\n***%%% = ***%%!!\r\n\r\nOF CORSE WE ELIMINATE 3 *\'S AND 2 %\'S FROM BOTH SIDES OF THE EQUATION AND THAT LEAVES US WITH\r\n\r\n% = !! .....(THE KEY)\r\n\r\nNOW TO ANSWER THE QUESTION WE SIMPLY SUBSTITUTE AS WE DID BEFORE, \r\n\r\nINSTEAD OF:\r\n\r\n!@!!@! = %$*$\r\n\r\nWE USE: \r\n\r\n!!!!!!** = ***%%%\r\n\r\nAND SINCE WE KNOW NOW THAT % = !!, WE USE:\r\n\r\n!!!!!!** < !!!!!!***\r\n\r\nAS U CAN SEE NOW EVERYTHING CANCELS EXCEPT FOR 1 * ON THE RIGHT SIDE, MAKING THE RIGHT THE STRONGER SIDE!!!',NULL,0);
INSERT INTO comment VALUES (6509,1012,2732,'gary','solution','2003-07-17 03:30:49',0,'the man was born in front of (before) is father, made a \"markedly favorable impression\" upon (killed) his mother, and performed the wedding ceremony (married) his sister.',NULL,0);
INSERT INTO comment VALUES (6510,1012,979,'Ravi Raja','My Guess !!','2003-07-17 04:55:18',1,'I guess that his father was in front of him when he was born, therefore it has been said that he was born before his father and his mother died after giving birth. This boy then grew up to be a minister and therefore had the right to marry his sister. ',NULL,0);
INSERT INTO comment VALUES (6511,984,2667,'Viet','re: Solution','2003-07-17 06:49:08',0,'okai your rite i didn\'t notice at first but the son also grow a year too my fault',6496,0);
INSERT INTO comment VALUES (6512,1036,1626,'Gamer','One solution','2003-07-17 08:36:58',2,'I got POUNDING as one solution :)\r\n\r\nNotes: ING is 30,\r\nED is 5\r\nS is (of course) 19\r\nSTR is 57',NULL,0);
INSERT INTO comment VALUES (6513,984,1301,'Charlie','re(2): Solution','2003-07-17 09:10:50',0,'if the son were 10 and the father 19, or the more realistic example of the son 20 and father 39, then next year the son would also be 1 year older, and 20 is not twice 11, and 40 is not twice 21. That is, 2 says that next year the father will be twice as old as the son is then, not as the son is now.',6498,0);
INSERT INTO comment VALUES (6514,984,1301,'Charlie','re: my solution','2003-07-17 09:19:27',0,'In one year the father will be 41 and the son 21, so the father won\'t then be twice his son\'s age.\r\n\r\nWhen the daughter is twice 12 she\'ll be 24. When the mother was 10 years younger than that, that is 14, was 20 years ago. At that time the grandmother was 38 and the mother 14, so the grandmother would have been more than twice as old as the mother was.',6499,0);
INSERT INTO comment VALUES (6515,1036,1921,'Travis Taylor','','2003-07-17 11:02:30',0,'THIRTY = 100',NULL,0);
INSERT INTO comment VALUES (6516,1036,1921,'Travis Taylor','re:','2003-07-17 11:04:18',0,'so is FIFTY-ONE',6515,0);
INSERT INTO comment VALUES (6517,1036,1301,'Charlie','program for finding them','2003-07-17 11:44:52',1,'This program, given a word list (it\'s set up for bogwords.txt) finds matching words under each criterion:\r\n\r\nOPEN \"bogwords.txt\" FOR INPUT AS #1\r\nOPEN \"wval100a.txt\" FOR OUTPUT AS #2\r\nOPEN \"wval100b.txt\" FOR OUTPUT AS #3\r\n\r\nDO\r\n LINE INPUT #1, w$\r\n w$ = LCASE$(w$)\r\n t1 = 0: t2 = 0\r\n FOR i = 1 TO LEN(w$)\r\n v1 = ASC(MID$(w$, i, 1)) - ASC(\"a\") + 1\r\n v2 = 27 - v1\r\n t1 = t1 + v1: t2 = t2 + v2\r\n NEXT\r\n IF t1 = 100 AND t2 = 100 THEN PRINT w$\r\n IF t1 = 100 THEN PRINT #2, w$\r\n IF t2 = 100 THEN PRINT #3, w$\r\nLOOP UNTIL EOF(1)\r\n
',NULL,0);
INSERT INTO comment VALUES (6518,1036,1301,'Charlie','mathematical note','2003-07-17 11:50:20',1,'No word will be found on both lists, that is the list of words equalling 100 with the initial value assignments and those equalling 100 with the reversed value assignments. That\'s because in the reversed value, each letter is worth 27 minus what it was worth in the first set. So a word of length n and value v in the original valuation of the letters will have value 27n-v in the reversed valuation. If we want both the old and the new value to be 100 that would be 27n - 100 = 100, or 27n = 200, which is impossible as 27 doesn\'t go into 200 evenly.',NULL,0);
INSERT INTO comment VALUES (6519,1036,1626,'Gamer','re: mathematical note','2003-07-17 12:07:27',4,'What words have you found Charlie? I would be interested... :)',6518,0);
INSERT INTO comment VALUES (6520,243,1171,'nikki','re(2): Solution','2003-07-17 12:17:37',0,'I\'m not sure I understand your comment. First, Happy\'s solution started with \"Draw a right triangle.\"\r\n\r\nSecond, trig is not restricted to right triangles. Trigonometry has to do with the sides and angles of any triangle, not just right triangles.\r\n\r\nLater!',1607,0);
INSERT INTO comment VALUES (6521,1036,1301,'Charlie','Words for part A','2003-07-17 16:39:10',3,'The computer finds for part A (A=1,...,Z=26):\r\nabatements, abettors, absconders, acclimation, accumulate, acknowledge, acolytes, acquitted, activates, addressing, adiabatically, adulthood, advantaging, adverting, affectation, airdrops, alienation, alkalinize, alternated, ambulating, amiableness, amphiboles, amputees, analysis, anchoritic, anginous, animaters, annually, answerable, anterior, apoplectic, appeasers, appertain, applying, appointed, apropos, aquamarine, arbitrages, archdiocesan, archenemies, arrests, arrivals, asbestos, atonally, attitude, attunes, auctorial, audiophile, augments, autoclave, automated, avocation, avouching, awfully, backswept, backtracking, backwardly, baguettes, balletomane, bandwagons, barkeepers, bedazzles, bedposts, beginnings, benediction, bespreading, bestirred, bestridden, bettering, bevellers, bewitching, biathlons, bipartite, birthmark, biweeklies, blasphemes, blastoffs, blazoning, blissful, bolstered, boondoggled, bootblacks, bootery, boozers, borrowed, boskiest, botanist, bouillon, boulevard, boundary, bowknot, boycott, breviary, bronchus, bronzy, browser, bruiting, burnished, byplays, cacophony, camphorate, candidature, cannibalized, captaincies, cardiograph, carotenes, carouser, carpenter, carroty, caryatids, catechisms, causeries, censurable, centipedes, ceramicist, chaplaincies, charwomen, chastening, chemurgy, cherishing, chimpanzee, chondrule, choppers, chortles, chromium, chucklers, clarifiers, cleanliest, clinically, clockwise, clotting, clumsier, coarsest, coasters, coattails, colleagues, collecting, commandeered, companion, comport, condensate, confabulate, confederated, congeners, congenital, congress, conjoint, conjugated, conjunct, connivance, conniver, consigns, contented, cookout, coonskin, corkiest, corridor, costumed, cotters, coulombs, courses, courter, cousins, coverlet, coverup, coyness, crankiest, cravenly, creepiest, creosote, crimsoned, crudity, cruising, crummier, crusts, culture, curettage, cutlets, cutout, cutups, debarkation, debaucheries, decalcomanias, declarative, declension, decorous, deescalating, defections, deflators, degausses, deliberates, delineating, deliquesce, delivery, delouses, demobilize, demodulate, denominate, denounces, depletion, deploring, derogating, desegregated, desiccative, designers, desolates, despatches, deterring, dewberry, diagonally, digestive, dinginess, disarranged, discernible, discipline, disclaiming, discommode, discredited, disjoint, dislodging, distancing, distrait, divinely, diviners, divorcees, dockyards, dominates, dooryard, doubleheader, doughty, draftsmen, driveling, drizzle, droopier, drossy, dualities, ducklings, ebullient, ecstasies, egoistical, ejections, electives, elephants, elsewhere, emasculate, embodiment, emboldening, embowers, emendation, emptily, encapsuled, encumbers, enlivens, entrains, envoys, equalized, equipages, espouse, eulogize, eventual, evolves, excavates, excellent, excerpted, excoriate, execrates, exigencies, explains, explodes, extendible, extracted, falseness, falsities, farrows, fatalistic, fatherhood, fattiest, feldspars, ferments, ferrites, ferryman, filtering, finitely, firebricks, flagellates, fluorine, flurry, foredoomed, forefoot, forewarn, forgiver, forsaking, fountain, freshest, friendlier, furcular, garnishes, gauntlet, gauntly, generating, geographer, germanely, gladiolus, glimpses, glissando, glittered, glorifies, glutamate, godparent, goldbricks, governs, grappling, graybeards, grenadiers, grimiest, groggily, grouper, grouts, grovelled, grumpy, guarantied, guttier, gypsies, halftones, hammerers, haranguing, harmonics, harrying, healthily, hegemonies, hemoglobin, highways, hinderers, hirsute, hitchhikes, hobbyist, hollandaise, hollering, holograph, honeycomb, honoring, hooligans, hooters, hospital, hotness, housemen, howlers, humblest, hungrier, hussies, hydrates, identifies, ideologies, imbroglio, immature, immitigable, impaneling, imported, impotence, inadequacy, inanities, inapplicable, incubating, inductees, inefficient, infernos, inferring, inflation, ingrown, inkiness, innately, innovate, inoculate, insecticide, intellect, interbreed, interfaces, interfere, irritate, isolates, jimmying, jostles, judiciary, junkets, keyboards, keyholes, kibitzer, kissers, knothole, knouts, kohlrabies, lacquerer, lagniappes, lambskins, laminating, landscaping, languished, largeness, lavenders, leaderless, leaseholds, liberalism, liberator, ligaments, lightest, lightning, likelihood, liminess, limpidly, loginess, lowlands, lubricant, luckiest, macrocosm, magnetize, mailboxes, maintains, mantises, marauders, marinates, marshalcy, martinet, martingale, masochism, mastoids, matchless, matrons, maximize, measurer, mercantile, mercurial, merganser, merrily, midpoint, mimickers, minuses, minuter, mirrored, miscopy, misdirect, miseducate, mittens, moderates, molecular, mollifies, moodiest, morphemic, motors, mourns, mousier, mufflers, mummify, nastily, negotiated, neoclassic, nesters, nestling, nihilist, ninepins, nonbreakable, noncausal, nondairy, nonhuman, nosebleeds, nostalgic, notional, novellas, nucleates, nutty, obscenely, operetta, orients, ornament, oscillated, osculated, outflank, outlined, outrank, outreached, outset, overboard, overbore, ovulated, palpitate, panderers, panhandling, papists, paramecium, parleyer, pastiches, pasture, pathless, pedagogues, pedicures, penchants, percents, performed, perilune, permits, personage, personal, perturb, phalanxes, pharisees, phlebitis, piggybacks, pilaster, pilloried, pistachio, pitying, plastered, plateaux, playgirl, playoffs, plebiscite, plenties, plenums, plummet, plunging, pocketing, postdate, posting, postpaid, potbellied, pothook, potpies, pounding, pouring, powders, practicing, preadapts, predeceases, predicates, preeners, preformed, preludes, preordain, prepays, presser, prevent, primary, printer, problems, procured, producer, profaning, profiles, profuse, progeny, proofing, propjet, proscenia, prosier, publicly, pumpkin, pursue, pussy, putter, pyritic, quadrangle, qualmish, quarry, quarter, quicklime, quints, radarscope, radiocarbon, raillery, raincoats, rasters, ravelling, ravisher, reaccusing, rearguing, reattaches, receptor, reciprocal, recreating, redeploy, redesigns, redounds, redrying, referring, refinancing, refinery, refuting, regimented, regressed, regroup, regrown, reimpose, reissued, remedying, renovate, repress, reprint, reprobate, repulsed, reputable, reradiates, reschedule, researcher, resents, reshipped, reshuffle, residues, resolved, responded, restaging, restocked, restore, resumes, resurfaced, retaught, retiring, retrenched, reversal, revives, rewound, rewraps, ricochets, ridicules, riptides, rituals, riverbank, roadblocks, roadster, rockiest, roomful, roommate, ruddiest, rulings, sagebrush, saintly, salacious, satiating, savory, schematics, scrapbook, screwier, sculpted, scuttle, secreting, selective, semaphore, septicemia, services, session, settles, setups, shadowing, shakedown, shakeups, sharpens, shattered, shibboleth, shipyard, shivers, shooter, shortcake, shovels, shredders, shrewder, shrieking, sightly, simulate, siphons, skewers, skimpier, sleepyhead, slenderer, slithered, slumps, slyest, smirching, smirking, smitten, smokers, sneerful, snipers, snivels, snobbery, snubbers, socialism, sodomite, soother, soughing, sources, soybeans, spacewalked, sparkler, spenders, spiciest, spirited, splashy, spouted, sprucer, squares, squaws, squint, staggerer, stagiest, stalemated, standards, stanzas, starers, starfish, starling, status, steamers, stemming, steppes, stockier, stonier, stooges, stools, stoves, strains, strangled, straws, stress, striding, striker, stuccos, styles, sublimes, subsume, sucrose, suffocated, sunders, sunnier, surcharge, surely, swankier, swashing, sweatier, sweetened, swifter, swimmer, swirls, swollen, syndicate, tabernacles, tailcoats, tailgating, tailspin, tallying, tangents, tattooed, taxying, telegrams, telephone, telescope, temperance, temporal, tensely, tetanus, tetrahedra, thalidomide, theists, therefore, thickening, thievish, thirty, thorny, threatened, thriver, thumbnail, tinkerer, toboggans, toilets, tolerated, tooting, towards, towers, traction, transom, trembling, triplet, triply, troller, tropics, troths, trounced, trudging, truism, tsunamic, tubules, tularemia, tummies, turkey, turnoff, tussled, twisted, typefaces, unaltered, unavailable, unbeholden, unbeloved, unbounded, unbridgeable, unbroken, unchaining, uncombined, underdone, undergird, underlay, undress, unequaled, unfasten, unfreeze, unhorse, unironed, unkempt, unmanly, unmown, unrelated, unshelled, unwarned, unwove, upsets, urbanized, urologic, urticaria, useless, utensil, vacuums, variety, varnished, venation, venially, verbalize, verdicts, vinous, violins, vivifier, volleyed, vortical, vouchsafe, voyaging, warpers, watchdogs, wattles, weariest, weeniest, whenever, whirling, whiskey, whisking, whistled, wholesale, whooper, whorish, wigglers, windfalls, wirehaired, wizards, woodblock, wriggles, writing, wronger, yappers, ',NULL,0);
INSERT INTO comment VALUES (6522,1036,1301,'Charlie','Words for Part B','2003-07-17 16:41:23',3,'For part B (A=26,...,Z=1) the computer finds:\r\n\r\nabbey, acrid, acronym, action, actuary, acutest, adonis, adores, adverts, airports, aligns, alimony, alumna, amazons, anatomy, aneurysm, ankles, antlers, apostasy, ardent, arming, arrowroot, ascent, asthma, atomists, atomize, atwitter, austere, bacon, bakery, ballot, balsa, basal, basils, bassist, batiks, batten, befog, bequest, betters, bevies, bilge, blazons, blocks, blusters, bonbon, bonnets, booing, bootee, border, brazers, bricks, brownest, bucket, bulbuls, burled, burring, cages, cahoot, calumny, calves, calyxes, canary, capers, carats, catch, cation, caved, ceder, chain, chalk, chantry, charms, chewer, china, chrome, citing, citric, civvies, clamor, clean, climax, codify, comics, conchs, conger, controls, converts, coolest, copying, corkers, cosmic, counsel, countess, courier, cowslips, creed, creels, critic, crossers, crowing, cruller, cruppers, cubed, cumber, curiously, cushion, czarism, demote, detritus, diatom, dictums, dimmer, dirges, dodge, dodoes, dollar, dominos, dopants, dossier, dotard, dotting, dousing, drably, draggy, draper, dresses, drivels, drogues, dunned, earthly, efforts, ejects, elates, elide, embers, emoted, enacts, ensuing, entirety, envelop, environs, equators, erupted, eruptive, espresso, estates, eternity, evoked, existent, expressly, extrudes, extrusive, facet, fades, falter, faunas, filler, filters, fissures, flake, flaxen, flecky, flight, flouters, fluidly, fluting, fogyish, fonder, footstep, foppish, forever, forsooth, frames, frappe, fretwork, fudges, furriest, galley, gallows, galosh, gamma, garish, glares, gloria, glorious, glossary, glummer, glutted, goober, gothic, gourdes, goutiest, grade, grievous, gripper, groused, grudge, grunted, gunpoint, gurgles, hansoms, harbor, hawing, haywire, hefter, hemmer, hence, hickory, hinges, holder, hollers, holsters, homiest, hostlers, housesit, howitzers, hulled, humane, hurling, husking, hustled, iliad, image, impact, incests, incubus, inmate, insane, insects, instants, instructs, ironies, jazziest, jocosity, jogger, jordan, juggle, juicily, junkies, kaolin, knead, knitters, knotted, kolinsky, kowtowed, kraals, kuchen, lagers, lamed, lance, lappets, larkspur, lassoer, lathery, legion, leisure, liking, lipped, lizards, locals, lockouts, lodges, looked, lopping, lovably, lovingly, lunettes, lutanist, luxuriously, magma, manual, margin, masted, maulers, medal, meiosis, mensch, mercer, metiers, mewled, mimosas, mincer, miscues, misled, misrules, misterms, mitotic, modules, moltenly, monkish, mortally, motherly, mottled, mouthful, murkiest, muteness, myriads, naked, nappers, neighs, nerving, netting, neuroses, neutrino, newsman, newsworthy, noisier, nonhero, nonunion, notably, novelist, nubbin, obeyers, ocelots, oiliest, oilskin, omelets, ominously, opacity, ostmarks, outhouses, outscore, outvoting, ovaries, overawe, overflow, overlap, overrule, oversee, overtures, overwise, pacers, panics, papacy, parred, parvenus, passports, patsies, pebbly, pellets, pelted, pepped, pertness, phallus, phenols, phoned, picker, pinned, pismire, plague, plainly, planar, plasma, plastery, playpen, pockets, pointers, poising, poisonous, polarity, polders, politest, pongee, porgies, powerful, preexist, presents, presumes, products, prolongs, protean, protects, proteins, provide, puddle, pullman, punitive, purveyed, pushovers, pussycats, queerer, querying, quietest, quinine, racists, raged, railway, raisers, raisins, ranees, ranted, ratting, reach, realtor, rebuke, rebuses, recaps, recoil, reeker, refill, refuge, reinter, remoras, rentals, reputed, rescuer, resowed, retitle, retrying, reviler, revival, revivify, rewriter, riches, ridges, rifted, rimmed, ripoffs, ripping, riskier, roamers, rockers, rooking, roulette, rubdowns, rudders, rugged, rumbler, rumpled, samovar, sawmill, scenery, scrape, sculptors, secant, secrets, securer, sedans, sedulous, seethe, seiners, seizing, sensuously, seriously, serology, serpents, sesame, shadows, shaker, shelver, shoppers, shortcuts, shorted, shrieks, shrikes, shticks, shutdowns, siding, sierras, signal, signify, silently, skivvies, skulkers, skylarks, sleekly, slimmer, slipknot, slipover, slithery, slitted, slotting, slowpoke, slugger, slurping, smashups, smiled, snapper, snorting, snowdrops, soared, sonatas, soulfully, southerly, spartan, spottiest, squeezer, stairway, stammer, stance, starved, sternal, stertorous, stifler, stillest, stilted, stipples, stolidly, stopping, stronger, stupidity, subitem, subsoils, subsystem, success, sudsiest, suffuses, sulkiest, sultriest, supplier, surcoats, sureties, surpriser, survivals, swearer, sweetest, swooning, syncopes, synodic, syringes, taking, tallest, tapped, tardily, tarnish, tarrier, tartness, teasel, tempters, tenting, tertiary, thrombus, tilled, tinnier, tiptoed, tolling, tonality, toppings, townships, toxemic, trawlers, treble, tribal, tribune, trifles, trinkets, troublous, tsunamis, turbine, turgidly, tutorial, twinned, tzarina, unclose, unhand, unsettle, unsinful, unsorted, untaxed, untoward, unwonted, unyoking, uppermost, upraise, upstage, vapidly, varmints, viceroys, vicunas, viewing, vitrines, vivace, volition, voluble, waited, walkers, wangle, wartime, waterway, wearers, whippets, whittles, widowers, wigwags, willies, winged, wintrier, wiriness, wishing, wombed, woodier, woodmen, workdays, workings, worthier, wrappers, wrongful, xeroxing, yeomanry, yeshiva, zapping, zillions, zombies',NULL,0);
INSERT INTO comment VALUES (6523,1036,1575,'DJ','Programming Solution','2003-07-17 17:10:34',3,'I wrote the following small javascript program to find all the possible words. I used the ENABLE word list, which is just a text file of all acceptable Scrabble words, also used often for programming purposes such as this. Here is the first program:\r\n\r\nlist=\"aa aah aahed (ENABLE LIST) ... zymurgy zyzzyva zyzzyvas\";\r\nwords=list.split(\" \");\r\nvar count=0, long=0, short=100;\r\nfor (i=0; i<words.length; i++) {\r\n var word=words[i];\r\n var total=0;\r\n for (c=0; c<word.length; c++) {\r\n char=word.charAt(c);\r\n value=word.charCodeAt(c)-96;\r\n total+=value;\r\n }\r\n if (total==100) {\r\n document.write(word + \", \");\r\n count++;\r\n if (word.length<short) {\r\n short=word.length;\r\n shortest=word;\r\n }\r\n if (word.length>long) {\r\n long=word.length;\r\n longest=word;\r\n }\r\n }\r\n}\r\ndocument.write(\"<br><br>Total words: \" + count);\r\ndocument.write(\"<br>Longest = \" + longest);\r\ndocument.write(\"<br>Shortest = \" + shortest);\r\n\r\nThis will take each word in order and add up the value of its letters, count the total number of matches, and keep track of the longest and shortest words found.\r\ncharCodeAt is a function that returns the ASCII value of a letter (starting with a=97).\r\nThen, to find the reverse order, I changed the (value=..) line to:\r\n\r\nvalue=123-(word.charCodeAt(c));\r\n\r\nBoth lists are way too long to post here. The results were:\r\n\r\nForwards (a=1...z=26):\r\nTotal words: 1921\r\nLongest = adiabatically\r\nShortest = nutty\r\n\r\nBackwards (a=26...z=1):\r\nTotal words: 1263\r\nLongest = luxuriously\r\nShortest = caca\r\n',NULL,0);
INSERT INTO comment VALUES (6524,1036,1575,'DJ','re: Programming Solution','2003-07-17 17:23:08',3,'I posted the text files with both lists: here and here (some browsers might be a little sketchy about displaying a text file consisting of one really long line; in which case just right click and save the target file to your computer).',6523,0);
INSERT INTO comment VALUES (6525,171,2670,'saad','solution?','2003-07-17 18:29:05',0,'i got 2/3',NULL,0);
INSERT INTO comment VALUES (6526,171,2670,'saad','re: solution?','2003-07-17 18:37:24',0,'ha, nevermind , a bit off, im dumb...',6525,0);
INSERT INTO comment VALUES (6527,1036,1919,'Lewis','re: Words for part A','2003-07-17 21:00:32',0,'Wow - I originally had one for each, and I knew there would be more, but I didn\'t think there would be that many.',6521,0);
INSERT INTO comment VALUES (6528,1019,1301,'Charlie','solution?','2003-07-18 02:29:31',1,'{3,3,3}, {2,4,4} and {2,3,6} work, but I can\'t prove it\'s a complete list (other than shuffling around which is A, which B and which is C).',NULL,0);
INSERT INTO comment VALUES (6529,1019,158,'Ender','partial solution','2003-07-18 03:59:27',3,'Let us make a starting constraint, that A, B, and C must be written in increasing order (A <= B <= C). Any solution can be organized this way, so it won\'t affect the solutions.\r\n\r\nA=0: Invalid.\r\n\r\nA=1: 1+1/B+1/C=1. 1/B + 1/C must be 0, so B and C = infinity. No valid solution.\r\n\r\nA=2: By the starting restraint, B cannot be 1.\r\n_____B=2: 1/2+1/2+1/C=1. 1/C=0. C = infinity. Nope\r\n_____B=3: 1/2+1/3+1/C=1. 1/C=1/6. C = 6.\r\n_____B=4: 1/2+1/4+1/C=1. 1/C=1/4. C = 4.\r\n_____B>4: The largest value, by the starting restraint, is 1/2+1/5+1/5=9/10.\r\nThus, there are two valid answers that have a lowest value of 2: (2,3,6) and (2,4,4)\r\n\r\nA=3: By the starting restraint, B cannot be 1 or 2.\r\n_____B=3: 1/3+1/3+1/C=1. 1/C=1/3. C = 3.\r\n_____B>3: The largest value, by the starting restraint, is 1/3+1/4+1/4=5/6.\r\nThus, there is one valid answer that has a lowest value of 3: (3,3,3)\r\n\r\nA>3: The largest value, by the starting restraint, is 1/4+1/4+1/4 = 3/4. No other solutions.\r\n\r\nHowever, integers are considered any of the natural numbers (positive, zero, or negative). So what happens when we allow negatives?\r\nB=1: 1/A+1/1+1/C=1 => 1/A+1/C=0 => 1/C=-1/A => C=-1*A\r\nSo the solution is all members of the set (-X,1,X)\r\n\r\nNow we add that infinite list to the set. I\'m not sure how to prove out all solutions involving one negative number (it can be shown that none involve two negatives or three negatives, though).\r\n\r\nSo the answer to the question appears to be:\r\n(2,3,6), (2,6,3), (3,2,6), (3,6,2), (6,2,3), (6,3,2), (2,4,4), (4,2,4), (4,4,2), (3,3,3), and all (-X,1,X) (and its permutations)\r\n',NULL,0);
INSERT INTO comment VALUES (6530,1019,2682,'exoticorn','re: solution?','2003-07-18 04:02:13',0,'Yes, that\'s the complete solution. It\'s pretty straightforward to prove.\r\nLet\'s assume that we are not interested in permutations and define A<=B<=C.\r\nNow, since 1/A, 1/B and 1/C have to be 1/3 on average, A (the smallest number of the solution) has to be either 2 or 3.\r\nFor A=3, {3, 3, 3} is obviously the only solution.\r\nFor A=2, 1/B and 1/C have to be 1/4 on average, so B has to be either 3 or 4 (2 obviously doesn\'t work), so {2, 3, 6} and {2, 4, 4} are the only remaining solutions.',6528,0);
INSERT INTO comment VALUES (6531,1019,158,'Ender','re: partial solution','2003-07-18 04:20:33',0,'This is to prove that all solutions involving negative integers are of the set (-X,1,X).\r\n\r\nFirst, there can be no solutions where all three are negative, since three negatives would sum to a negative value, and we need a sum of 1. Thus, no solutions involve three negative numbers.\r\n\r\nSecond, there can be no solutions where two numbers are negative. If A and B were both negative, the largest value 1/C can have is 1 (when C = 1). That would mean 1/A + 1/B would need to sum to 0 or greater, but two negatives can only sum to a negative number. Thus, no solutions involve two negative numbers.\r\n\r\nThird, We need to prove that there is only one solution to 1/A+1/B+1/C=1 for a negative A. We can rewrite this as 1/B+1/C=1+1/A, and all A, B,and C must now be greater than 0.\r\nWe want solutions other than (-X,1,X), so neither B or C can now 1. We can write that as 1 < B and 1 < C. This gives us: 1/B + 1/C = 1 + 1/A; 1 < B; 1 < C; 1 <= A\r\nThus, B and C can be no smaller than 2, so the largest value on the left hand side is 1/2 + 1/2 = 1. But we need this to be 1 + 1/A! Thus, there are no valid solutions involving negative numbers that are not of the set (-X,1,X).\r\n\r\nSo my previous answer stands as complete.',6529,0);
INSERT INTO comment VALUES (6532,86,2376,'Jim C','re: Problem with 2 Solutions','2003-07-18 05:52:30',0,'Gamer hit it exactly! The proof is amusing and brings up great discussions cocerning infinite decimals, but the fact is 39.99999... - 3.99999... is not exactly the same as 36.000...\r\n\r\nBasically, you have an \"Infinity minus 1\" issue. We can make it work in a practical sense because we assume that the \"limit as we approach infinity\" is an absolute number rather than the theoretical \"limit\" that it truly is. The \"Proof\" makes an assumption that isn\'t truly proveable.',4024,0);
INSERT INTO comment VALUES (6533,568,2376,'Jim C','re: hmmm...','2003-07-18 05:55:15',0,'Actually, you did \"remove\" the cork. You just didn\'t do it with your hands.',6488,0);
INSERT INTO comment VALUES (6534,568,2755,'walker','Is this alowed?','2003-07-18 06:07:36',0,'So you can\'t break the bottle - can you drill a hole through the cork?',NULL,0);
INSERT INTO comment VALUES (6535,823,2744,'Russ','Solution','2003-07-18 06:31:55',0,'This is my first Flooble response. I think the answer is 1 in 9, or approx. 11%.',NULL,0);
INSERT INTO comment VALUES (6536,823,2744,'Russ','re: Solution','2003-07-18 06:38:20',0,'Oops - I see I made a mistake. The outcomes would be 2x2x2, three of those would have one head only; therefore, 3 of 8 would be the correct probability of getting just one head.',6535,0);
INSERT INTO comment VALUES (6537,1036,1183,'fwaff','re(2): challenge','2003-07-18 07:17:07',0,'Travis\'s answers got me wondering whether or not any numbers exist where the total letter value is equal to the number. \r\n\r\nAt the risk of re-opening the bucket of snakes regarding written numbers, the smallest one I found is: 251 (two hundred and fifty one)\r\n\r\nIf the word \'and\' is excluded then I don\'t believe that there are any such numbers, at least for a=1...z=26.',6516,0);
INSERT INTO comment VALUES (6538,1036,1301,'Charlie','re(2): Words for part A','2003-07-18 08:04:45',0,'In the word list I used, of 74,780 words, the mean and standard deviation of the total values for part A were 100.86 and 35.6. For part B they were 130.18 and 41.8. So a value of 100 is quite near the mean for part A.',6527,0);
INSERT INTO comment VALUES (6539,569,2682,'exoticorn','solution','2003-07-18 08:05:43',3,'You send key#1 in the box locked with lock#2.\r\nYou send key#2 without a box.\r\nThe friend unlocks the box, takes key#1 and sends the box back.\r\nYou send the object in the box locked with lock#1.\r\nThe friend unlocks the box with key#1, takes out the object and congratulates you on your cleverness... ;)',NULL,0);
INSERT INTO comment VALUES (6540,569,2489,'nellie','No problem','2003-07-18 09:09:08',0,'If the question really is how to send the object securely, simply lock the box. How your friend opens the box is a different question and is not the question that is asked.',NULL,0);
INSERT INTO comment VALUES (6541,1036,1301,'Charlie','re(3): challenge','2003-07-18 09:42:16',0,'Without the word \"and\", I also don\'t think such a thing is possible. The following program verifies this for numbers 1 through 100,000. After that, I can\'t see any number words adding up to the value of the number itself as the size in words grows approximately as the size in digits, which is only logarithmically related to the value of the number.\r\n\r\nDECLARE SUB enterNum ()\r\nDECLARE SUB ProcPiece (piece$, MajorPower!)\r\nDATA one,two,three,four,five,six,seven,eight,nine\r\nDATA ten,eleven,twelve,thirteen,fourteen,fifteen,sixteen,seventeen\r\nDATA eighteen,nineteen\r\nDATA twenty,thirty,forty,fifty,sixty,seventy,eighty,ninety\r\nDATA thousand,million,billion,trillion,quadrillion,quintillion,sextillion\r\nDIM SHARED unit$(19), ten$(10), major$(7)\r\nFOR i = 1 TO 19\r\n READ unit$(i)\r\nNEXT\r\nFOR i = 2 TO 9\r\n READ ten$(i)\r\nNEXT\r\nFOR i = 1 TO 7\r\n READ major$(i)\r\nNEXT\r\nDIM SHARED name$, num$\r\nFOR n = 1 TO 100000\r\n num$ = LTRIM$(STR$(n))\r\n\' enterNum\r\n IF num$ = \"0\" THEN\r\n name$ = \"zero\"\r\n ELSE\r\n name$ = \"\"\r\n MajorPower = 0\r\n DO\r\n l = LEN(num$): IF l > 3 THEN l = 3\r\n piece$ = RIGHT$(num$, l)\r\n num$ = LEFT$(num$, LEN(num$) - l)\r\n CALL ProcPiece(piece$, MajorPower)\r\n MajorPower = MajorPower + 1\r\n LOOP WHILE LEN(num$) > 0\r\n END IF\r\n tVal = 0\r\n FOR i = 1 TO LEN(name$)\r\n lt$ = MID$(name$, i, 1)\r\n IF INSTR(\"abcdefghijklmnopqrstuvwxyz\", lt$) > 0 THEN\r\n tVal = tVal + ASC(lt$) - ASC(\"a\") + 1\r\n END IF\r\n NEXT\r\n IF tVal = n THEN PRINT n\r\n\' IF tVal = 100 THEN PRINT n\r\nNEXT\r\n\r\nSUB enterNum\r\n DO\r\n INPUT \"Enter number:\", num$\r\n num$ = LTRIM$(RTRIM$(num$))\r\n num = 1\r\n FOR i = 1 TO LEN(num$)\r\n IF INSTR(\"0123456789\", MID$(num$, i, 1)) = 0 THEN num = 0: EXIT FOR\r\n NEXT\r\n IF num = 0 THEN PRINT \"Must be numeric.\"\r\n LOOP WHILE num = 0\r\nEND SUB\r\n\r\nSUB ProcPiece (piece$, MajorPower)\r\n piece = VAL(piece$)\r\n n$ = \"\"\r\n IF piece > 99 THEN\r\n n$ = unit$(piece \\ 100) + \" hundred \"\r\n piece = piece MOD 100\r\n END IF\r\n IF piece > 19 THEN\r\n n$ = n$ + ten$(piece \\ 10)\r\n piece = piece MOD 10\r\n IF piece > 0 THEN n$ = n$ + \"-\": ELSE n$ = n$ + \" \"\r\n END IF\r\n IF piece > 0 THEN n$ = n$ + unit$(piece) + \" \"\r\n IF n$ > \"\" THEN name$ = n$ + major$(MajorPower) + \" \" + name$\r\nEND SUB\r\n\r\n',6537,0);
INSERT INTO comment VALUES (6542,1036,1301,'Charlie','re(3): challenge','2003-07-18 10:02:14',0,'A modification to use the word \"and\" shows that 251 and 259 are the only two that now produce a value equal to themselves. The modified ProcPiece subroutine is:\r\n\r\nSUB ProcPiece (piece$, MajorPower)\r\n piece = VAL(piece$)\r\n n$ = \"\"\r\n IF piece > 99 THEN\r\n n$ = unit$(piece \\ 100) + \" hundred \"\r\n piece = piece MOD 100\r\n IF piece > 0 THEN n$ = n$ + \"and \"\r\n END IF\r\n IF piece > 19 THEN\r\n n$ = n$ + ten$(piece \\ 10)\r\n piece = piece MOD 10\r\n IF piece > 0 THEN n$ = n$ + \"-\": ELSE n$ = n$ + \" \"\r\n END IF\r\n IF piece > 0 THEN n$ = n$ + unit$(piece) + \" \"\r\n IF n$ > \"\" THEN name$ = n$ + major$(MajorPower) + \" \" + name$\r\nEND SUB\r\n\r\n',6537,0);
INSERT INTO comment VALUES (6543,974,1626,'Gamer','re(4): Easy','2003-07-18 15:54:57',2,'Yes, this has 10 syllables in each line, and every other line rhymes, but that\'s not all that\'s here... There is a deeper reason to the wierd words (including the make up of runshine and mathways, and usage of \"cat gas\" and \"Too far making\")',6244,0);
INSERT INTO comment VALUES (6544,569,1575,'DJ','re: solution','2003-07-18 18:33:07',0,'I think that if you send a key without a box, it\'s the same as sending it in an unlocked box, and not \'secure\' as you want it to be.',6539,0);
INSERT INTO comment VALUES (6545,569,1575,'DJ','Possible Solution','2003-07-18 18:34:01',3,'If your friend has a lock, you can send the locked box, and he can add a lock of her own and send it back.\r\nThen, you remove your lock, send the box back one more time, and he can remove his own lock and open the box.\r\n\r\nThat way, you never send the box unlocked, and never have to send a key at all.',NULL,0);
INSERT INTO comment VALUES (6546,569,153,'TomM','re: Possible Solution','2003-07-18 19:39:45',0,'Yes, this is not only the traditional answer, but the \"key\" to secure encryption of electronic documents. Since each of you choose an encryption code key that you share with no one else, no one can decrypt any of the three encrypted versions (your encryption, bothe encryptions, your friend\'s encryption.)',6545,0);
INSERT INTO comment VALUES (6547,971,1253,'brianjn','re: Points on an ellipse','2003-07-18 22:33:46',1,'Back to my previous ask, \"is there a property (etc)..\", I have thought just a bit further.\r\n\r\nIf two lines are to intersect, then there is a common area within which arcs of half their lengths must overlap. \r\n\r\nIs this what levik means by \"How would you determine ...?\"\r\n\r\n ',6270,0);
INSERT INTO comment VALUES (6548,569,2682,'exoticorn','re(2): solution','2003-07-19 01:20:08',0,'Yes, the one key is sent insecurely, but the point is that the box with the corresponding lock has already arrived at the friend before the key for it is sent. Therefore copying this key doesn\'t help someone sitting between the sender and his friend. (To open the box he needs the copied key BEFORE the locked box goes through his hands.)\r\n\r\nIn fact, i just realised that my solution was overly complicated, the second key&lock isn\'t neccessairy.\r\n\r\nJust send the locked box with the valuable object first and the key only after the box has arrived.',6544,0);
INSERT INTO comment VALUES (6549,569,2682,'exoticorn','re: Possible Solution','2003-07-19 01:24:32',0,'While that would certainly work, IF the friend had his own set of key+lock, the problem doesn\'t give us any information about whether this is the case. So the solution to the problem shouldn\'t depend on this.',6545,0);
INSERT INTO comment VALUES (6550,571,1626,'Gamer','Maybe','2003-07-19 04:01:37',2,'I would fill four trays with water, and put the first tray in, then a tray bottom-side up, then a tray right side up with water, and so on. You can fill it that way with 4 at a time\r\n',NULL,0);
INSERT INTO comment VALUES (6551,571,2489,'nellie','possible solution','2003-07-19 06:58:23',0,'Maybe I\'ve missed something in the question but the trays will be either 3 x 4 or 2 x 6 and can therefore be stacked altnately at right angles to each other.',NULL,0);
INSERT INTO comment VALUES (6552,823,2766,'Angelo','coin problem','2003-07-19 07:57:55',3,'There are eight possibilities and three of them have one head so it\'s 3/8.',NULL,0);
INSERT INTO comment VALUES (6553,567,2766,'Angelo','My solution...','2003-07-19 08:12:42',3,'R won the race therefore making it B that made the only correct statement.',NULL,0);
INSERT INTO comment VALUES (6554,571,2703,'Mr. Spock','Wrong answer','2003-07-19 08:28:17',0,'Hmmm, we do not know the dimensions of the freezer compartment or the trays, we only know it will hold seven ice cube trays stacked vertically. However with an unlimited supply of trays why not break them apart in order to construct shelving such that six vertical trays could be inserted vertically with a bit of a little gap (less than or equal to a tray height / 5 between each that is)',NULL,0);
INSERT INTO comment VALUES (6555,571,1919,'Lewis','My Idea','2003-07-19 09:47:39',3,'Fill one ice cube tray and put it in, then put an empty one upside down on top of it. This will not \'nestle\' into the other one, and you can then place another water-filled tray on top, and so on, until you get 4 trays with water in and 3 trays without.',NULL,0);
INSERT INTO comment VALUES (6556,571,1626,'Gamer','re: Wrong answer','2003-07-19 09:50:11',1,'My guess is the freezer will just barely fit the ice trays, so they can\'t be stacked in any way (like an alternating patern) by atlternating every other row.\r\n\r\nI don\'t know if putting them at right angles is not allowed, but would imagine the ice cubes wouldn\'t be full size in some instances of this.\r\n\r\nI also think the goal is to keep the trays intact, and not cut them apart. Otherwise this would be an easy problem.',6554,0);
INSERT INTO comment VALUES (6557,946,2771,'Joe','re(2): Common solution','2003-07-19 19:04:29',0,'well if you pulled it out and it said \"LIFE\" then you obviously wouldent tear, swollow, or burn it',6117,0);
INSERT INTO comment VALUES (6558,571,2771,'Joe','re(2): Wrong answer','2003-07-19 19:31:53',0,'but even if the freezer \"just barely\" fits the ice cube trayes then you should be able to stack them in a pattern upside down from each other if all trayes are the same dimensions',6556,0);
INSERT INTO comment VALUES (6559,980,2773,'Jeff','re: Answer','2003-07-19 22:47:05',0,'I agree. If knaves truly alternate between truth and lies - meaning that they must tell one and then the other - then this is the only possible solution.',6402,0);
INSERT INTO comment VALUES (6560,571,1626,'Gamer','re(3): Wrong answer','2003-07-20 02:52:26',2,'Yes, I think that\'s a good answer, and is the one I submitted in \"Maybe\", below. :)',6558,0);
INSERT INTO comment VALUES (6561,1018,1301,'Charlie','hmmm...','2003-07-20 04:49:28',1,'There doesn\'t seem to be a limit as to the number of sets that satisfy the equation. \r\n\r\nThe equation becomes\r\nbc=ac+ab, or\r\nbc=a(b+c), or\r\na = bc/(b+c)\r\n\r\nThe following program seems to produce solutions going on and on:\r\n\r\nDECLARE FUNCTION gcd# (x#, y#)\r\nDEFDBL A-Z\r\nsum = 1\r\nDO\r\n sum = sum + 1\r\n FOR b = 1 TO sum / 2\r\n c = sum - b\r\n a = b * c / sum\r\n IF a = INT(a) THEN\r\n IF gcd(gcd(a, b), c) = 1 THEN\r\n PRINT a, b, c, sum\r\n END IF\r\n END IF\r\n NEXT\r\nLOOP\r\n\r\nFUNCTION gcd (x, y)\r\n dnd = x: dvr = y\r\n IF dnd < dvr THEN SWAP dnd, dvr\r\n DO\r\n q = INT(dnd / dvr)\r\n r = dnd - q * dvr\r\n dnd = dvr: dvr = r\r\n LOOP UNTIL r = 0\r\n gcd = dnd\r\nEND FUNCTION\r\n a²bc = ab²c + abc²\r\n\r\nDividing by abc gives us a = b + c\r\n\r\nSome examples: \r\n\r\n\r\n\r\n A B C a b c\r\n 1 2 2 2 1 1\r\n 2 3 6 3 2 1\r\n 3 4 12 4 3 1\r\n 10 14 35 7 5 2\r\n 20 36 45 9 5 4\r\n 330 555 814 37 22 15\r\n 969 1330 3570 70 51 19\r\n1189 2030 2870 70 41 29\r\n\r\nBecause of your weeding out of triples which are multiples of other triples, b and c are mutually prime in all your examples. The pattern would have been more difficult to determine and to generate without that step. \r\n\r\nYou can generate A, B, and C by \r\n\r\n1) Set any random b\' and c\';\r\n2) Set b = (b\')/d; Set c = (c\')/d (d = GCF(b\',c\')*\r\n3) Set a = b + c\r\n4) Set A = bcd; Set B = acd; Set C = abd\r\n\r\n*GFC(b\',c\') means the Greatest Common Factor shared by b\' and c\'\r\n\r\n ',6561,0);
INSERT INTO comment VALUES (6564,1018,153,'TomM','re: Pattern (re: hmmm...)','2003-07-20 07:15:11',0,'The algorithm at the end of my last reply generates all triples that satisfy the initial equation, including triples that Charlie weeded out because they are multiples of other triples (4,2,2) or because c < b (2,6,3). To weed these out, add steps \r\n1A) If c < b return to step 1)\r\n2A) If d > 1 return to step 1)',6563,0);
INSERT INTO comment VALUES (6565,567,2703,'Mr. Spock','Proof by Contradiction','2003-07-20 08:13:14',0,'There are three scenarios, Firstly lets suppose Scenario A - 1 is correct and 2 and 3 are not. From 1) we know either P or S won. Lets suppose P won that would be contradictory because 3) would be correct also. Lets suppose S won that would prove 2) correct also, contradictory. Scenario A thus fails. Scenario C - 3) is correct and 1) are 2) are not. From 3) we know either S or R won. Either case proves 2) correct also which is a contradiction. Thus the only possibility is Scenario B - 2) is correct and 1) and 3) are not. We then know from 1) P and S lost, from 2) gives us no additional help and from 3) Either S or R won. Therefore R won with B making the onlt correct statement. ',NULL,0);
INSERT INTO comment VALUES (6566,571,2703,'Mr. Spock','Right Answer','2003-07-20 09:25:49',0,'I will make the non implicit assumption that each tray is of indentical n x 2 rectangular dimension and n > 1. Begin by filling four of the trays with water and seperating them using three upsidedown trays, 8n cubes will be produced. This much is obvious but there is a trick to now producing additional cubes. Now empty the trays, By my assumption you will then have enough cubes now to stick 2 in alternating diagonal corners of each of six empty trays. Do this, fill up all the remaining holes of these 6 trays with water and put it back in the freezer with a seventh tray entirely filled with water at the top. This will produce 14n-12 cubes. Utilizing this process is your most efficient method of cube production under the current scenario. So after c freezing cycles you will have 8n +(c-1)*(14n-12) cubes.',NULL,0);
INSERT INTO comment VALUES (6567,1018,1301,'Charlie','re: Pattern (re: hmmm...)','2003-07-20 10:47:49',0,'Or, eliminating one set of variables:\r\n\r\n1) Set any random b and c; \r\n2) Set d = GCF(b,c) \r\n3) Set a = b + c \r\n4) Set A = bc/d; Set B = ac/d; Set C = ab/d \r\n\r\n',6563,0);
INSERT INTO comment VALUES (6568,571,2571,'Rob','Solution','2003-07-20 16:45:28',3,'Sell your infinite number of ice trays and buy a new fridge. \r\n Assuming that this is the kind of fridge where you have a actual refrigerator as well as a freezer, why not just use both compartments? Then you use Gamer\'s solution, only with even more space.',NULL,0);
INSERT INTO comment VALUES (6569,573,1686,'DuCk','possibility...','2003-07-21 02:30:56',0,'I\'m not sure if i\'m understanding the situation correctly, but if each surgeon only needs one glove to operate, and the requirement is that the glove must be clean to operate then I would say surgeon 1 uses the first glove. Surgeon 2 uses the second glove. Surgeon 3 then takes surgeon 1\'s glove and put\'s it on, and then takes surgeon 2\'s glove and turns it inside out and put\'s it over the other glove (leaving a clean glove on both sides) and finishes the operation up.',NULL,0);
INSERT INTO comment VALUES (6570,573,1919,'Lewis','re: possibility...','2003-07-21 02:34:58',1,'I was thinking along those lines too, but when you said \'Surgeon 3 then takes surgeon 1\'s glove and put\'s it on, and then takes surgeon 2\'s glove and turns it inside out and put\'s it over the other glove\' it should be the other way round (He puts surgeon 1\'s glove on upside down and then puts surgeon 2\'s glove on the normal way round.',6569,0);
INSERT INTO comment VALUES (6571,573,1919,'Lewis','re(2): possibility...','2003-07-21 02:35:57',0,'*I meant inside out, not upside down',6570,0);
INSERT INTO comment VALUES (6572,571,1919,'Lewis','re: Solution','2003-07-21 02:39:30',1,'The whole point of a \'freezer\' is that it freezes. Putting water in a \'refrigerator\' will keep it cool, but will not turn it to ice.',6568,0);
INSERT INTO comment VALUES (6573,573,1301,'Charlie','re(2): possibility...','2003-07-21 02:54:05',0,'If surgeon 3 puts on surgeon 1\'s glove inside out, he is exposed to the patient\'s blood. ',6570,0);
INSERT INTO comment VALUES (6574,573,1301,'Charlie','re: possibility...','2003-07-21 02:55:37',0,'If surgeon 3 puts on surgeon 1\'s glove he is exposed to surgeon 1\'s blood. In addition, turning the outer glove inside out exposes the patient to surgeon 2\'s blood.',6569,0);
INSERT INTO comment VALUES (6575,573,1301,'Charlie','solution','2003-07-21 03:04:15',3,'There are only four glove surfaces as well as four people. Each surface therefore must be associated with only one person.\r\n\r\nThe first surgeon wears both gloves. The outer glove must then remain the outer (or only) glove each remaining time to keep that outer surface toward the patient.\r\n\r\nThe second surgeon then wears only that outer glove.\r\n\r\nThe third surgeon then turns the first surgeon\'s inner glove inside out and puts it inside the second surgeon\'s only glove (the original surgeon\'s outer glove), so that the surface reserved for the patient remains outside and the two surfaces contaminated by the previous two doctors are facing each other between the two gloves.\r\n\r\nBut how does each doctor perform surgery with only one hand? ',NULL,0);
INSERT INTO comment VALUES (6576,1018,2716,'Federico Kereki','A (partial?) solution','2003-07-21 07:59:33',1,'For integer P, Q, setting A=PQ, B=P(P+Q), C=Q(P+Q) gives a solution.',NULL,0);
INSERT INTO comment VALUES (6577,1018,2716,'Federico Kereki','A (partial?) solution','2003-07-21 07:59:33',0,'For integer P, Q, setting A=PQ, B=P(P+Q), C=Q(P+Q) gives a solution.',NULL,0);
INSERT INTO comment VALUES (6578,1018,2716,'Federico Kereki','re: A (partial?) solution','2003-07-21 08:07:14',1,'For the general problem 1/A=1/B+1/C+...+1/Z, you can get a solution by picking integer number b, c, ... z, setting A=bc...z, and letting X=A/x.(b+c+...+z).',6576,0);
INSERT INTO comment VALUES (6579,573,2760,'Fay Duncan','solution','2003-07-21 08:10:52',3,'One surgeon does the surgery while the other two tell him/her how to do their portion of the surgery.',NULL,0);
INSERT INTO comment VALUES (6580,1021,1567,'Bryan','solution','2003-07-21 09:49:19',3,'It seems that all three partygoers must be 44, and since 44x44 = 1936, this would be the age of the third person in the year 1980.
\r\nSample output:\r\n\r\nNumber of hoops: 3\r\n\r\n A | |\r\n B | |\r\n C | |\r\nStarting position\r\n\r\n | | |\r\n B | |\r\n C | A\r\nMove hoop A from pole 1 to pole 3\r\n\r\n | | |\r\n | | |\r\n C B A\r\nMove hoop B from pole 1 to pole 2\r\n\r\n | | |\r\n | A |\r\n C B |\r\nMove hoop A from pole 3 to pole 2\r\n\r\n | | |\r\n | A |\r\n | B C\r\nMove hoop C from pole 1 to pole 3\r\n\r\n | | |\r\n | | |\r\n A B C\r\nMove hoop A from pole 2 to pole 1\r\n\r\n | | |\r\n | | B\r\n A | C\r\nMove hoop B from pole 2 to pole 3\r\n\r\n | | A\r\n | | B\r\n | | C\r\nMove hoop A from pole 1 to pole 3\r\n\r\nAnd, the requested case with n=5:\r\n\r\nNumber of hoops: 5\r\n\r\n A | |\r\n B | |\r\n C | |\r\n D | |\r\n E | |\r\nStarting position\r\n\r\n | | |\r\n B | |\r\n C | |\r\n D | |\r\n E | A\r\nMove hoop A from pole 1 to pole 3\r\n\r\n | | |\r\n | | |\r\n C | |\r\n D | |\r\n E B A\r\nMove hoop B from pole 1 to pole 2\r\n\r\n | | |\r\n | | |\r\n C | |\r\n D A |\r\n E B |\r\nMove hoop A from pole 3 to pole 2\r\n\r\n | | |\r\n | | |\r\n | | |\r\n D A |\r\n E B C\r\nMove hoop C from pole 1 to pole 3\r\n\r\n | | |\r\n | | |\r\n A | |\r\n D | |\r\n E B C\r\nMove hoop A from pole 2 to pole 1\r\n\r\n | | |\r\n | | |\r\n A | |\r\n D | B\r\n E | C\r\nMove hoop B from pole 2 to pole 3\r\n\r\n | | |\r\n | | |\r\n | | A\r\n D | B\r\n E | C\r\nMove hoop A from pole 1 to pole 3\r\n\r\n | | |\r\n | | |\r\n | | A\r\n | | B\r\n E D C\r\nMove hoop D from pole 1 to pole 2\r\n\r\n | | |\r\n | | |\r\n | | |\r\n | A B\r\n E D C\r\nMove hoop A from pole 3 to pole 2\r\n\r\n | | |\r\n | | |\r\n | | |\r\n B A |\r\n E D C\r\nMove hoop B from pole 3 to pole 1\r\n\r\n | | |\r\n | | |\r\n A | |\r\n B | |\r\n E D C\r\nMove hoop A from pole 2 to pole 1\r\n\r\n | | |\r\n | | |\r\n A | |\r\n B C |\r\n E D |\r\nMove hoop C from pole 3 to pole 2\r\n\r\n | | |\r\n | | |\r\n | | |\r\n B C |\r\n E D A\r\nMove hoop A from pole 1 to pole 3\r\n\r\n | | |\r\n | | |\r\n | B |\r\n | C |\r\n E D A\r\nMove hoop B from pole 1 to pole 2\r\n\r\n | | |\r\n | A |\r\n | B |\r\n | C |\r\n E D |\r\nMove hoop A from pole 3 to pole 2\r\n\r\n | | |\r\n | A |\r\n | B |\r\n | C |\r\n | D E\r\nMove hoop E from pole 1 to pole 3\r\n\r\n | | |\r\n | | |\r\n | B |\r\n | C |\r\n A D E\r\nMove hoop A from pole 2 to pole 1\r\n\r\n | | |\r\n | | |\r\n | | |\r\n | C B\r\n A D E\r\nMove hoop B from pole 2 to pole 3\r\n\r\n | | |\r\n | | |\r\n | | A\r\n | C B\r\n | D E\r\nMove hoop A from pole 1 to pole 3\r\n\r\n | | |\r\n | | |\r\n | | A\r\n | | B\r\n C D E\r\nMove hoop C from pole 2 to pole 1\r\n\r\n | | |\r\n | | |\r\n | | |\r\n | A B\r\n C D E\r\nMove hoop A from pole 3 to pole 2\r\n\r\n | | |\r\n | | |\r\n | | |\r\n B A |\r\n C D E\r\nMove hoop B from pole 3 to pole 1\r\n\r\n | | |\r\n | | |\r\n A | |\r\n B | |\r\n C D E\r\nMove hoop A from pole 2 to pole 1\r\n\r\n | | |\r\n | | |\r\n A | |\r\n B | D\r\n C | E\r\nMove hoop D from pole 2 to pole 3\r\n\r\n | | |\r\n | | |\r\n | | A\r\n B | D\r\n C | E\r\nMove hoop A from pole 1 to pole 3\r\n\r\n | | |\r\n | | |\r\n | | A\r\n | | D\r\n C B E\r\nMove hoop B from pole 1 to pole 2\r\n\r\n | | |\r\n | | |\r\n | | |\r\n | A D\r\n C B E\r\nMove hoop A from pole 3 to pole 2\r\n\r\n | | |\r\n | | |\r\n | | C\r\n | A D\r\n | B E\r\nMove hoop C from pole 1 to pole 3\r\n\r\n | | |\r\n | | |\r\n | | C\r\n | | D\r\n A B E\r\nMove hoop A from pole 2 to pole 1\r\n\r\n | | |\r\n | | B\r\n | | C\r\n | | D\r\n A | E\r\nMove hoop B from pole 2 to pole 3\r\n\r\n | | A\r\n | | B\r\n | | C\r\n | | D\r\n | | E\r\nMove hoop A from pole 1 to pole 3\r\n\n\nEdited on September 9, 2003, 12:33 am',NULL,0);
INSERT INTO comment VALUES (7746,946,3372,'sam','Trick the prisoner','2003-09-08 13:45:33',0,'Most importantly, since everyone\'s heard of this answer, if you were the guy who wants you killed you would replace both papers with life, and then tell the prisoner the story above. The prisoner will then happily eat one of the papers, confident that he has tricked everyone, only to be sent to his death...\r\n\r\nPS, The solution to pick out the label of the hat is also good. I wonder what they\'d do with \"Do not machine wash\"?',NULL,0);
INSERT INTO comment VALUES (7747,1341,3172,'SilverKnight','Solution (I think)','2003-09-08 14:44:25',3,'Either way... you do \"process\" all the marbles.\r\n\r\nWell... let\'s start with (B):\r\n1 16\r\n2 13\r\n3 12\r\n4 9\r\n5 8\r\n6 9\r\n7 6\r\n8 7\r\n9 5\r\n10 5\r\n11 2\r\n12 5\r\n15 2\r\n16 1\r\n18 2\r\n20 2\r\n24 2\r\n25 1\r\n30 2\r\n36 1\r\n
\r\n------\r\nNumbers without a way of being formed, such as 13 or 14, are not shown.\r\n\r\nSo the best 6 numbers to have on your card are 1,2,3,4,5 and 6.\r\n\r\nThe different dice falls that produce these first 6 numbers are:\r\n\r\n1x 1 1+ 1 1+ 2 1+ 3 1+ 4 1+ 5\r\n1- 2 1x 2 1x 3 1x 4 1x 5 1x 6\r\n2- 1 1- 3 1- 4 1- 5 1- 6 2x 3\r\n2/ 2 2x 1 2+ 1 2x 2 2+ 3 2+ 4\r\n2- 3 2- 4 2- 5 2- 6 3+ 2 3x 2\r\n3- 2 3- 1 2/ 6 3+ 1 4+ 1 3+ 3\r\n3/ 3 3- 5 3x 1 4x 1 5x 1 4+ 2\r\n3- 4 3/ 6 3- 6 5- 1 6- 1 5+ 1\r\n4- 3 4- 2 4- 1 6- 2 6x 1\r\n4/ 4 4- 6 5- 2\r\n4- 5 5- 3 6/ 2\r\n5- 4 6/ 3 6- 3\r\n5/ 5 6- 4\r\n5- 6\r\n6- 5\r\n6/ 6\r\n
\r\n-------\r\nThe first column shows falls that produce 1; the second,2; etc.\r\n\r\nNote that 2,1 is different from 1,2 as they are different ways that the dice can fall. The indication of the operator between them is not meant to imply the order in which the numbers are given to the operation. That is, for example, 2/6 and 6/2 are both shown for producing 3, as they are different falls of the dice that can produce 3 by division, but obviously 2 has to be the divisor and 6 the dividend.\r\n\r\nAlso note what is important: a given fall of the dice can be counted only once. For example, a fall of 2,2 counts for just one way of producing 4; you can make it addition or make it multiplication, but it still counts as only 1 way, as we\'re counting ways of the dice falling, not your choice of how to make the number. Only one way is shown on the above chart, to reflect that fact.',NULL,0);
INSERT INTO comment VALUES (6606,1037,2798,'Wayne','proposed solution','2003-07-22 18:37:21',0,'I ran the numbers on a spreadsheet, and the most commonly occuring sums, differences, products, and quotients are 1,2,3,4,5, and 6 (each occurs 10 or more times). This is therefore my guess for the solution.',NULL,0);
INSERT INTO comment VALUES (6607,569,2682,'exoticorn','re(4): solution','2003-07-23 00:55:59',0,'If we allow an interceptor to impersonate the friend in all actions and communications, I don\'t think there is a solution short of delivering the packet personally. (Or having the friend collect it himself, for the more lazy ones ;) ',6591,0);
INSERT INTO comment VALUES (6608,571,2489,'nellie','cubes','2003-07-23 01:09:13',0,'If we are being pedantic, then the question asks how to produce \'cubes\' (plural). To produce one cube is not enough.',NULL,0);
INSERT INTO comment VALUES (6609,397,1575,'DJ','re: Yet Another','2003-07-23 01:52:06',0,'But \'vide\' is not a word, except in Latin -- and it has two syllables',4629,0);
INSERT INTO comment VALUES (6610,574,1919,'Lewis','Solution','2003-07-23 02:19:18',3,'From the clues we know:\r\n\r\nMr East went North.\r\nMr West went East.\r\nMr South went West.\r\nMr North went South.',NULL,0);
INSERT INTO comment VALUES (6611,574,1575,'DJ','Solution','2003-07-23 02:22:50',3,'There is not much problem here.\r\nSince South didn\'t go south, as East and West did not, North did.\r\nNorth did not go west, neither did West, or East, so South went west.\r\nEast did not go east, south, or west; he went north.\r\nWest, then, went east.\r\n\r\nIn sum:\r\nNorth -> south\r\nEast -> north\r\nSouth -> west\r\nWest -> east',NULL,0);
INSERT INTO comment VALUES (6612,574,2722,'Jack Putz','Duuuuuhhhh','2003-07-23 03:02:14',0,'East went North\r\nWest went East\r\nNorth went South\r\nSouth went East',NULL,0);
INSERT INTO comment VALUES (6613,574,1715,'Jonny Doe','re: Duuuuuhhhh','2003-07-23 04:23:31',0,'How can Mr. West & Mr. South take the East road? I think you meant Mr. South went WEST.\r\n\r\nDuuuuuuuuuhhhhhhhhhhh',6612,0);
INSERT INTO comment VALUES (6614,1010,1715,'Jonny Doe','How about ....?','2003-07-23 04:34:19',1,'Sound.\r\n\r\nIt can not be felt, seen or touched. Everyone\'s body are making sounds like heart beating, talking and more. It is always debated, for example who never heard the quetion if a tree falls in the forest and no one is there does it make a sound? And last music is sound.',NULL,0);
INSERT INTO comment VALUES (6615,574,2804,'adrian','Solution','2003-07-23 04:38:06',3,'Mr East cannot go east, did not go south or west therefore went North\r\nMr West cannot go west, did not take the south road, Mr east took north so must have gone east\r\nMr South cannot go south therefore must go west\r\nMr North has only south left',NULL,0);
INSERT INTO comment VALUES (6616,984,2798,'Wayne','','2003-07-23 04:47:56',0,'I agree with Charlie\'s 2nd, 3rd, or 4th solutions from 7/16. I personally favor #3 , because most women don\'t give birth at either ages 14 or 50, though it\'s indeed possible. Thank goodness for Cramer\'s rule and Excel, which calculates determinants so quickly. Otherwise, I wouldn\'t have finished nearly so soon',NULL,0);
INSERT INTO comment VALUES (6617,574,1626,'Gamer','Pretty easy','2003-07-23 06:40:02',1,'I personally wouldn\'t have voted this one onto the site, as it is too easy in my opinion. As long as you don\'t get cocky (the cocky ones always come up with wrong answers), you will get it',NULL,0);
INSERT INTO comment VALUES (6618,574,1626,'Gamer','Pretty easy','2003-07-23 06:40:02',1,'I personally wouldn\'t have voted this one onto the site, as it is too easy in my opinion. As long as you don\'t get cocky (the cocky ones always come up with wrong answers), you will get it',NULL,0);
INSERT INTO comment VALUES (6619,573,2809,'William','Solution','2003-07-23 06:55:38',3,'Each doctor wears one glove on the hand that is wounded and they share the fourth glove never turning it inside out.',NULL,0);
INSERT INTO comment VALUES (6620,397,1919,'Lewis','re(2): Yet Another','2003-07-23 07:32:43',0,'vide is a word (believe it or not) according to my parent\'s overly-sized overly-old dictionary, and is pronounced with 1 syllable. Perhaps its one of those words that doesn\'t get used any more, but the latin meaning is still around.',6609,0);
INSERT INTO comment VALUES (6621,573,2810,'Brett Zabek','Solution','2003-07-23 08:02:43',3,'There are 2 gloves (A and B). The first surgeon wears both gloves (A and B)on one hand, Glove A on top of Glove B. The second surgeon wears glove A.\r\nThe third surgeon reverses Glove B and places the Glove A over it.',NULL,0);
INSERT INTO comment VALUES (6622,571,2811,'chrissy','solution','2003-07-23 08:19:07',3,'the question only asks what the fastest way to make full size cubes is, it says nothing about how many you have to make, so the answer has to be just to fill one tray with water, put it in the freezer, and freeze it to make full-sized ice cubes',NULL,0);
INSERT INTO comment VALUES (6623,573,2272,'Clinton Heath','My solution','2003-07-23 08:50:56',0,'First off, it doesn\'t say that the surgeons each have one injured hand, so the solution must work with the surgeons having open wounds on both hands.\r\nIf Dr. Moe must operate on Curley the cook first, followed by Dr. Larry, and finally by Dr. Shemp, here is a possible solution.\r\nThey\'re surgeons, so why can\'t they operate on each other? Dr. Shemp puts on the rubber gloves and closes Dr. Moe\'s wounds, leaving Dr. Moe free to operate on Dr. Larry (after having sterlilized the instruments). Then after re-sterilizing the instruments, Dr. Moe then begins the operation on Curley while Dr. Larry closes the wounds on Dr. Shemp\'s hands. Of course I am assuming that with the wounds closed, they are no longer in danger of being exposed to the blood of any of the others.',NULL,0);
INSERT INTO comment VALUES (6624,1020,2667,'Viet','clueless','2003-07-23 09:03:56',4,'what is permutation??',NULL,0);
INSERT INTO comment VALUES (6625,1020,1919,'Lewis','re: clueless','2003-07-23 09:19:48',1,'I dont know what permutations are either, but from looking at this it could be to do with different combinations of those numbers, as there is 720 ways of arranging 1,2,3,4,5 & 6 (I think).\r\n\r\nIf that is correct, then as for the actually question, my guess would be it starts with 4, as each starting number has 120 combinations of other numbers. Obviously in numberical order the first 120 would start with one, then the second 120 would start with two.\r\n\r\nThe 361th would then be 412356. For the 5 digits after the four we can apply the same method to find the number is 425631. This is all assuming that my guess at what a permutation is is correct, and that my calculations are also correct (we can always hope, eh).',6624,0);
INSERT INTO comment VALUES (6626,1020,2682,'exoticorn','re(2): clueless','2003-07-23 09:34:13',3,'You are right about the permutations, and also about the 361st, but I think you made a mistake inbetween that and the 407th.\r\nAccording to my calculations, it is 426513. 425631 appears to be the 401st one.',6625,0);
INSERT INTO comment VALUES (6627,1020,1301,'Charlie','solution','2003-07-23 09:44:07',3,'Let\'s first look at the question coming from the other direction. What permutation is, say 365241? We can see in this example that as prior to this permutation there are all the ones starting with 1 or 2, plus some more. The ones that start 1 or 2 number 2*5!, as the remaining five digits after either the 1 or the 2 can be rearranged in 5! permutations. But also some permutations beginning with 3 also precede 365241. How many? Those beginning 31, 32, 34, and 35 certainly, and some beginning 36. The ones beginning with one of the former group of four pairs number 4*4! as each of the four pairs can be followed by any permutation of the remaining 4 digits. Note that in each position the choices contributed to the total are the digit in the given position minus 1 minus the number of digits to the left which are lower than this digit, all multiplied by the factorial of the number of digits remaining. Thus in the next position, 5 - 1 - 1 (as there is one digit, the three, preceding the 5 lower than 5) is multiplied by 3!. The 5 - 1 - 1 = 3 accounts for beginnings of 361, 362, and 364, each with 3! permutations available for the later digits. Thus the number of permutations of the first six digits that lexicographically precede 365241 is given by:\r\n\r\n2*5! + 4*4! + 3*3! + 1*2! + 1*1! + 0*0! = 357,\r\n\r\nso that 365241 is the 358th permutation of the first 6 digits in lexicographical order.\r\nGoing in the reverse direction, we can see that the first 5! of the 6! permutations are devoted to those beginning with the digit 1. The next 5! to those with 2, etc. We merely need to divide by 5!: the quotient is the factor of 5! to use; the remainder is further divided by 4!, and the quotient there is the factor of 4!, etc. Thus if we wish to know the 358th permutation of the six digits, we divide 357 (the number of permutations prior) by 5!, giving a quotient of 2 and a remainder of 117; when this is divided by 4! we get 4 with a remainder of 21; when that\'s divided by 3! we get a quotient of 3 with a remainder of 3. Continuing in this fashion we get as quotients the entire sequence of coefficients of the factorials shown above:\r\n\r\n2, 4, 3, 1, 1, 0 (by the way the last one is always zero)\r\n\r\nFrom this sequence we can reconstruct the permutation: There are 2 digits with lexicographic priority over (lower than) the first digit, which must therefore be 3. Of the digits other than 3, there are 4 with priority over the second digit, which is therefore 6. Of the digits other than 3 or 6, three have priority over the third digit (these three therefore being 1, 2, and 4) so the third digit is 5. Of the digits other than 3, 6, and 5, only one has priority over the fourth digit, which is therefore 2. Of the digits other than 3, 6, 5, and 2, only one has priority over the next, which is therefore 4. You can see where we go from there in reconstructing the original 365241.\r\nNow to get back to the originally proposed 407th permutation of the first 6 digits in lexicographical order: \r\n\r\n406/5! = 3 with remainder 46\r\n46/4! = 1 with remainder 22\r\n22/3! = 3 with remainder 4\r\n4/2! = 2 with remainder 0\r\n\r\nThe series of coefficients is therefore 3, 1, 3, 2, 0, 0.\r\n\r\nSo 3 are prior to the first digit which is therefore 4.\r\nThen 1 previously unused (1) are prior to the second digit which is therefore 2.\r\nThen 3 previously unused (1, 3, 5) are prior to the third digit which is therefore 6.\r\nThen 2 previously unused (1, 3) are prior to the fourth digit which is therefore 5.\r\nThen 0 previously unused are prior to the fifth digit which is therefore 1.\r\nThen the remaining digit is 3.\r\n\r\nThe reconstructed permutation is therefore 4, 2, 6, 5, 1, 3 as being the 407th in lexicographic (or 426513 numeric) order.\r\n\r\nThis can be verified via the \"brute force\" method of invoking the PERMUTE function (Permutations) 406 times starting with \"123456\".',NULL,0);
INSERT INTO comment VALUES (6628,1037,2813,'Dan','Solution','2003-07-23 11:00:57',0,'Well, using the numbers 0,1,2,3,4, and 5 would guarantee a win in this game because the smallest difference between two 6-sided dice is zero (same number on each die) and the largest is 5 (rolling a 1 and a 6), Therefore, no matter what is rolled on the two dice, these numbers will always hold a winner.',NULL,0);
INSERT INTO comment VALUES (6629,1020,1626,'Gamer','Another Solution','2003-07-23 11:28:56',3,'Here\'s how I would do it.\r\n\r\nThe 1-120 permutations begin with 1,\r\nThe 121-240 permutations begin with 2,\r\nThe 241-360 permutations begin with 3,\r\nThe 361-480 permutations begin with 4,\r\nThe 481-600 permutations begin with 5,\r\nThe 601-720 permutations begin with 6,\r\n\r\nSo the 407 permutation must begin with 4.\r\n\r\nThe 361-384 permutations begin with 41\r\nThe 385-408 permutations begin with 42\r\nThe 409-432 permutations begin with 43\r\nThe 433-456 permutations begin with 45\r\nThe 457-480 permutations begin with 46\r\n\r\nSo the 407 permutation begins with 42.\r\n\r\nYou could continue this method to find the answer. I think an easier way is seeing the last permutation (numerically) that begins with 42 is the 408 permutation, which is 426531; the digits after 42 are highest to lowest. So the 407 term must be 426513',NULL,0);
INSERT INTO comment VALUES (6630,573,1626,'Gamer','re: Solution','2003-07-23 11:43:14',0,'They only have two gloves, not four gloves :)',6619,0);
INSERT INTO comment VALUES (6631,397,1626,'Gamer','re(3): Yet Another','2003-07-23 12:37:25',1,'I think this is like one of those word-meld things where if it\'s an obscure word, it doesn\'t count much :)',6620,0);
INSERT INTO comment VALUES (6632,788,1626,'Gamer','re: SOLUTION','2003-07-23 12:52:04',4,'Actually isn\'t cock a female rooster? So would groin be a neccessary term in this case?\r\n',6196,0);
INSERT INTO comment VALUES (6633,1010,2828,'Glo','Hmm...','2003-07-23 14:29:21',0,'Wouldn\'t it be soul? Souls cannot be seen felt are touched, but are believed by some to be inside of everyone, and there is soul music.',NULL,0);
INSERT INTO comment VALUES (6634,571,1626,'Gamer','re: solution','2003-07-23 15:48:57',0,'If you can make more than 12 ice cubes per hour (assuming it takes an hour to freeze them) then that\'s not the fastest way',6622,0);
INSERT INTO comment VALUES (6635,569,2833,'maddi','think i got it','2003-07-23 16:32:18',0,'you send the key seprate in a box with a lock that your friend has or . . .\r\n\r\njust hand the thing to him',NULL,0);
INSERT INTO comment VALUES (6636,1037,1301,'Charlie','re: Solution','2003-07-23 16:33:20',0,'I\'m sure the idea is not to have just one number come up, but a whole row of them. Some might interpret this as all the six numbers chosen, but I think it refers to an ordinary 5x5 bingo card with 24 numbers printed (free space in the middle), and the six are what you would never want to have missing from your card.\r\n\r\nSecond, zero is not a positive integer as it\'s neither positive nor negative.\r\n\r\nThird, There are only 6 ways that the numbers can come out equal on the two dice, and that\'s the only way to get zero.',6628,0);
INSERT INTO comment VALUES (6637,1037,2833,'maddi','huh?','2003-07-23 16:35:16',0,'dude, in trying to read this, i got like labrith lost',6605,0);
INSERT INTO comment VALUES (6638,574,2833,'maddi','yup :)','2003-07-23 16:49:56',3,'Mr. North went South, Mr. South went West, Mr. West went East and Mr. East went North.\r\n\r\n\r\nno i did not cheat or look at other anwsers',NULL,0);
INSERT INTO comment VALUES (6639,569,2834,'Ryan','Solution (Maybe)','2003-07-23 16:53:46',0,' Just send the box locked. It never said that the friend had to open the box or anything. It just said to send it to him/her securely.',NULL,0);
INSERT INTO comment VALUES (6640,1018,2133,'spinoza','solution','2003-07-23 17:01:56',0,'solution:\r\nB,C are equal even no\'s (say 2k each)\r\nA is half of either B or C.\r\n\r\nproof:\r\ncase 1- B odd & C odd\r\non taking LCM and adding you\'ll get sum of two odd numbers in the numerator, which is even and product of two odds in the denom, which is odd. \r\nThus the result shall be a non integer.\r\n\r\ncase 2- B odd & C even\r\non taking the LCM and adding you\'ll get an even no. above B and odd above C. result: sum is odd. the denominator shall be even. hence non integer result.\r\n\r\ncase 3- B even and C even but both contain unequal powers of two.\r\non taking the lower power of 2 common from both numbers in the denominator this becomes a case 2 problem.\r\n\r\ncase 4 - B and C are equal even numbers(say 2k each).\r\n1/A = 1/2k + 1/2k\r\n = 2/2k\r\n = 1/k\r\nhence A = k.\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (6641,1018,2133,'spinoza','oops','2003-07-23 17:05:25',0,'made a mistake with case 2, sorry\r\n',NULL,0);
INSERT INTO comment VALUES (6642,568,1919,'Lewis','Would the solution work??','2003-07-23 22:18:17',4,'I read Ravi\'s solution where you push the cork into the bottle. This surely wouldn\'t work. Corks are bigger at one end so that they stay in the bottleneck when pushed in. You couldn\'t push the whole cork into the bottle.',NULL,0);
INSERT INTO comment VALUES (6643,230,1919,'Lewis','Solution','2003-07-23 22:20:50',3,'At the start, she sat Billy and the first guest. Then she sat the others and at the end said the one sharing Billy\'s seat was the fifth guest. Since he/she was counted twice, only five people were seated, and one person wasn\'t even mentioned.\r\n',NULL,0);
INSERT INTO comment VALUES (6644,1036,1919,'Lewis','Another Challenge','2003-07-24 00:40:22',4,'Here\'s another challenge for you to try:\r\n\r\nEither find a word that has the same value both ways (doesn\'t have to be 100, because, as Charlie proved, that\'s impossible) OR prove that it is also impossible.',NULL,0);
INSERT INTO comment VALUES (6645,132,1919,'Lewis','Solution','2003-07-24 00:52:26',3,'The child\'s age is easy. Half of 32 is 16. So he was born in 1916 and was 16 when he made the statement.\r\n\r\nFor granny\'s age, we can start from 1800. That was 132 years previously. Half of 132 is 66, so granny was born in 1866 and was 66 when she made the statement.',NULL,0);
INSERT INTO comment VALUES (6646,574,2731,'Venisha','ok','2003-07-24 01:40:08',0,'mr East took the north rd\r\nmr WEst took the east rd\r\nMr south took the west rd\r\nmr north took the south rd',NULL,0);
INSERT INTO comment VALUES (6647,1010,2839,'Andrwe Mitchell','','2003-07-24 01:53:19',0,'I agree that the most obvious answer is soul, but I like Johnny D\'s different take on it. Only one problem wth it the existence of sound is not really in debate UNLESS we play a little fast and loose and since sound exists in debates then its existence is \"in debate\"\r\nnah, I guess that does not work either, sorry',NULL,0);
INSERT INTO comment VALUES (6648,90,1919,'Lewis','re: Why international waters????','2003-07-24 04:08:05',1,'If that was the case, then Terry would be the younger of the twins. The reason its in international waters is so that it would go back a day.',6590,0);
INSERT INTO comment VALUES (6649,574,2843,'sunnyrae','solution','2003-07-24 05:14:44',3,'Mr East went North, Mr West went East, Mr North went South, Mr South went West',NULL,0);
INSERT INTO comment VALUES (6650,1021,2843,'sunnyrae','solution','2003-07-24 05:49:01',0,'1980\r\nthey are all 44, born in 1936',NULL,0);
INSERT INTO comment VALUES (6651,574,1575,'DJ','re: Pretty easy','2003-07-24 05:54:56',0,'I said the same thing when it was in queue, but everyone else seemed to think this was a great problem..',6618,0);
INSERT INTO comment VALUES (6652,575,2843,'sunnyrae','a possible solution','2003-07-24 05:55:01',3,' 9285\r\n +5224\r\n---------\r\n 14509\r\n\r\nI don\'t know if it\'s right but it works',NULL,0);
INSERT INTO comment VALUES (6653,575,1919,'Lewis','re: a possible solution','2003-07-24 05:58:14',1,'I\'m not sure if that works because you have both E and G being worth five. I think by \'Also, different digits represent different values\', it means different letters mean different values, so two lettters cannot be worth the same.\r\n',6652,0);
INSERT INTO comment VALUES (6654,575,2667,'Viet','sunnyrai was close','2003-07-24 06:35:41',0,' 9 2 8 5 \r\n+ 7 2 2 4\r\n----------\r\n1 6 5 0 9\r\n\r\nhe was so close just a lil mistake',NULL,0);
INSERT INTO comment VALUES (6655,575,1183,'fwaff','A solution','2003-07-24 06:36:27',3,' 8795\r\n+4773\r\n-----\r\n13568\r\n\r\nI couldn\'t find an elegant way to solve this so ended up using trial and error with a modicum of logic thrown in.\r\n\r\nI started on the basis that I=1, and then worked through the options for increasing values of D. This solution worked at D=3 so there may be more for higher values of D, I\'ll have a look tomorrow.',NULL,0);
INSERT INTO comment VALUES (6656,575,2667,'Viet','i woould like to delete the oone before','2003-07-24 06:36:51',0,'would like to delete that post',6654,0);
INSERT INTO comment VALUES (6657,575,1183,'fwaff','re: A solution','2003-07-24 06:55:41',3,'The options for the other letters reduce dramatically as D increases so it took much less time than I thought to work out the other combinations. I believe that my previously posted solution is unique.\r\n',6655,0);
INSERT INTO comment VALUES (6658,261,1919,'Lewis','I dont like ants. They bite me.','2003-07-24 07:58:45',3,'Call the ants ant 1,2 & 3.\r\n\r\nThe direction ant 1 goes doesn\'t matter.\r\n\r\nAnt 2 has a 1/2 chance of picking the same way as ant 1.\r\n\r\nAnt 3 has a 1/2 chance of picking the same direction as the other two ants.\r\n\r\nThus, the probability of the ants never colliding is 1/4.\r\n',NULL,0);
INSERT INTO comment VALUES (6659,1037,1919,'Lewis','re: Solution','2003-07-24 08:02:59',1,'0 isn\'t a positive integer so you can\'t use that number. Also, 6 has more ways of being made than 5. (See Charlie\'s solution)\r\n\r\nBTW, why has nobody rated this yet? I would like to know what people think of my problems.',6628,0);
INSERT INTO comment VALUES (6660,1022,2489,'nellie','A start','2003-07-24 09:03:20',0,'I\'m not a die person or a maths person but to ensure a total of 15 or more might require 15 throws in which case the least likely total would be 15. I\'ll leave the rest to others.',NULL,0);
INSERT INTO comment VALUES (6661,1022,1919,'Lewis','re: A start','2003-07-24 09:07:59',1,'Thats not strictly true because you could get 15 other ways, like 5,5,5.',6660,0);
INSERT INTO comment VALUES (6662,1022,1919,'Lewis','Solution','2003-07-24 09:15:11',3,'I would say the least likely total is definitely 20 as the only way that can happen is if the sum so far was 14 and then you rolled a 20.\r\n\r\nThe ways of getting 15 or over are:\r\n\r\nAlredy on... ---------- Rolled---Totals\r\n9-------------------------6-------15\r\n10---------------------5 or 6-----15 and 16\r\n11-------------------4,5 or 6-----15,16 and 17\r\n12-----------------3,4,5 or 6-----15,16,17 and 18\r\netc.\r\n\r\nAs you can see the number that comes up every time is 15, so I think 15 would be the most common.',NULL,0);
INSERT INTO comment VALUES (6663,1022,1919,'Lewis','re: Solution','2003-07-24 09:17:08',0,'Whoops, that should be:\r\n\r\n...sum so far was 14 and then you rolled a 6.',6662,0);
INSERT INTO comment VALUES (6664,1022,1301,'Charlie','The probabilities','2003-07-24 12:45:59',3,'Let p(n;g) be the probability that n will be the first number at or greater than g.\r\n\r\nIf 0<=g-n<=5, p(n;g) = p(n;g-1) + p(g-1;g-1)/6, as the event can be achieved if either\r\n1) n is the first number achieved at or higher than g-1, assuring the same for g+1 or\r\n2) The first number achieved at or higher than g-1 was g-1 itself, and then an (n-g) was rolled, the latter with a likelihood of 1/6.\r\n\r\nIf we start with choosing g = 1, p(6;1) through p(6;1) are all 1/6.\r\n\r\nThereafter we just need to use the recursion formula above. In the below table, the numbers listed start, for each g, at n=g, rather than 1 each time, as that at n=g is the earliest non-zero value:\r\n\r\nn f(n) Sn\r\n0 2 2\r\n1 2 4 = 2 + 2\r\n2 1 8 = 2 + 4 + 2\r\n3 -1 13 = 4 + 8 + 1\r\n4 -4 20 = 8 + 13 - 1\r\n5 -8 29 = 13 + 20 - 4\r\n6 -13 41 = 20 + 29 - 8\r\n7 -19 57 = 29 + 41 - 13\r\n8 -26 79 = 41 + 57 - 19\r\n
\r\nSo, the numbers in the blanks should be 41 and 57.',NULL,0);
INSERT INTO comment VALUES (6797,133,1171,'nikki','Backwards thinking','2003-07-29 12:56:40',3,'Friedlinguini got the answer by working through the problem forward. I found the answer working backwards:\r\n\r\nIn the end, each pile had 16 matches. So the final state is:\r\n16 16 16\r\n\r\nThe last statement says \"Take as many from the 3rd group as there are in the 1st group and add them to the 1st group.\" Well, this means that the quantity in the 1st group is going to get doubled, and we know the result will be 16 matches, so before we follow the last instruction, the 1st group had 8 matches. The 8 matches that double group 1 came from group 3 so our second to last state is:\r\n8 16 24\r\n\r\nNext we deal with \"Take as many from the 2nd group as there are in the 3rd group and add them to the 3rd.\" So now the quantity in the 3rd group is going to get doubled, and we know the result will be 24 matches. So before we follow the second to last instruction, the 3rd group had 12 matches. The 12 matches that double group 3 came from group 2 so our third to last state is:\r\n8 28 12\r\n\r\nAnd finally (well, firstly) the first statement says \"Take as many matches from the 1st group as there are in the 2nd group and add them to the 2nd.\" This time the quantity in the 2nd pile is going to be doubled and we know the result will be 28, so before we follow this instruction the 2nd group had 14 matches. These 14 matches came from group 1, so our initial state is:\r\n22 14 12\r\n\r\nTada! Later!',NULL,0);
INSERT INTO comment VALUES (6798,1050,1575,'DJ','New Challenge','2003-07-29 13:00:37',0,'Yes, I\'m pretty sure five steps is the fewest it will take to make either of the transitions. Now, see how many different ways you can find to do it! Besides the few already posted, I have some other unique solutions as well.',NULL,0);
INSERT INTO comment VALUES (6799,434,2913,'Caitlin','','2003-07-29 16:55:13',3,'Um... one. lol....',NULL,0);
INSERT INTO comment VALUES (6800,38,2913,'Caitlin','','2003-07-29 16:57:08',0,'By rearanging the shanpes u get an extra space. ',NULL,0);
INSERT INTO comment VALUES (6801,1043,1575,'DJ','Solution','2003-07-30 02:09:54',3,'Starting with the second clue, there are only 2 pairs of digits that are each other\'s square root, 2 and 4, and 3 and 9 (unless you count 0 and 1).\r\nThat means the minutes past the hour is one of :24, :42, :39, or :93. Obviously, 93 is too large.\r\nPutting in the number for the hours section that makes a total of 60, we have 36:24, 18:42, and 21:39.\r\n36, now, is greater than 23 and is too large. That leaves 18:42 and 21:39. 4 + 2 is not 81, but 9 + 3 is 12.\r\n\r\nSo, the answer is 18:42.\r\n\r\nInterestingly, the first clue could be eliminated, since for both :24 and :42, the total of the digits is 6, or 60 when reversed, which is too large.',NULL,0);
INSERT INTO comment VALUES (6802,1043,2918,'Jay','Time','2003-07-30 02:15:54',0,'What about 21H39',NULL,0);
INSERT INTO comment VALUES (6803,1043,1301,'Charlie','re: Solution','2003-07-30 02:37:10',0,'I\'m sure 21:39 is what you meant.',6801,0);
INSERT INTO comment VALUES (6804,1043,2839,'Andrew Mitchell','Solution','2003-07-30 02:41:13',3,'You must not be a civilian resident in the US since you use a 24 hour clock\r\nadn you looked at it at 21:39 or 9:39 PM to us yanks',NULL,0);
INSERT INTO comment VALUES (6805,1050,1301,'Charlie','re: New Challenge','2003-07-30 02:50:51',3,'Starting with SOFT:\r\n sort\r\n fort\r\n fart\r\n hart\r\n hard\r\n-------\r\n sort\r\n port\r\n part\r\n hart\r\n hard\r\n-------\r\n sort\r\n tort\r\n tart\r\n hart\r\n hard\r\n-------\r\n sort\r\n wort\r\n wart\r\n hart\r\n hard\r\n-------\r\n sort\r\n wort\r\n wart\r\n ward\r\n hard\r\n-------\r\n sort\r\n wort\r\n word\r\n ward\r\n hard\r\n\r\n... and from there:\r\n bard\r\n bare\r\n base\r\n ease\r\n easy\r\n-------\r\n card\r\n care\r\n case\r\n ease\r\n easy\r\n-------\r\n card\r\n cart\r\n cast\r\n east\r\n easy\r\n-------\r\n hare\r\n bare\r\n base\r\n ease\r\n easy\r\n-------\r\n hare\r\n care\r\n case\r\n ease\r\n easy\r\n-------\r\n hart\r\n cart\r\n cast\r\n east\r\n easy\r\n-------\r\n hart\r\n fart\r\n fast\r\n east\r\n easy\r\n-------\r\n hart\r\n mart\r\n mast\r\n east\r\n easy\r\n-------\r\n hart\r\n part\r\n past\r\n east\r\n easy\r\n\r\nReductions to 4 steps in each part would require using SORD, SARD on the one hand and HAST (as in \"thou hast\") on the other.\r\n\r\nI\'ve considered wort ok because of the recent popularity of the supplement St. John\'s wort.\r\n\r\n',6798,0);
INSERT INTO comment VALUES (6806,1043,1575,'DJ','re: Solution','2003-07-30 03:01:46',0,'Err..after all that, I meant to say that the answer is 21:39.',6801,0);
INSERT INTO comment VALUES (6807,205,2839,'Andrew Mitchell','Solution','2003-07-30 03:02:29',3,'The only way Kurt couls know is if he ate 5 apples himself.\r\n\r\nBertrand had to have eaten more than one apple (or he would have answered \"no\" to Alonso)\r\n\r\nGeorge Must have eaten more than two because he would have deduced that Bertrand would have had to have eaten more than one.\r\n\r\nNone of the first three ate more than 4 total because than they would have known they had eaten more than the people they questioned\r\n\r\nthis narrows the field but not enough. So Kurt must have used his own knowledge of how many he ate\r\nA ate 1, B ate 2, G ate 3, and Kate 5',NULL,0);
INSERT INTO comment VALUES (6808,840,2898,'dorkdork','won\'d wat itz ??','2003-07-30 04:19:10',0,'gravity.',NULL,0);
INSERT INTO comment VALUES (6809,842,2898,'dorkdork','ummmmm?','2003-07-30 04:26:04',0,'the other child (boy) was the one that stompp-ed away.',NULL,0);
INSERT INTO comment VALUES (6810,940,2898,'dorkdork','absolut answere','2003-07-30 04:34:04',0,'#7 on telephone reciever!!!',NULL,0);
INSERT INTO comment VALUES (6811,766,2898,'dorkdork','etc., etc., etc.....','2003-07-30 04:44:54',0,'they could have been murdered, they could have choked, they could of had heart-attacts, who knows. It could be a # of things.',NULL,0);
INSERT INTO comment VALUES (6812,766,2898,'dorkdork','very clever.-silvis.','2003-07-30 04:49:00',0,'they were fish! How brilliantly clever of silvis.',NULL,0);
INSERT INTO comment VALUES (6813,1043,2921,'Salem Dunbar','solution?','2003-07-30 07:10:30',0,'21:39 is the only one I could find any other square root would be too large for the clock.',NULL,0);
INSERT INTO comment VALUES (6814,1043,2921,'Salem Dunbar','re: solution?','2003-07-30 07:12:29',0,'Sorry I meant to say, any other square root would be too small or too large for the clock. ',6813,0);
INSERT INTO comment VALUES (6815,865,2898,'dorkdork','maybe?','2003-07-30 07:34:55',0,'yes.',NULL,0);
INSERT INTO comment VALUES (6816,1043,2667,'Viet','i don\'t kare wat u all say','2003-07-30 07:35:16',3,'i say the answer is 3:42 if im wrong this sux badly cuz i haven\'t figure one problem yet',NULL,0);
INSERT INTO comment VALUES (6817,1043,2667,'Viet','re: i don\'t kare wat u all say','2003-07-30 07:41:23',0,'i meant 2:39 yea thats my answer ',6816,0);
INSERT INTO comment VALUES (6818,1043,2667,'Viet','re(2): i don\'t kare wat u all say','2003-07-30 07:52:44',3,'damnit the answer is 4:39 and this is why\r\n\r\n2nd clue state that 1 digit is the square root ofthe other in the min hand so option are \r\n42 24 39 93 in the min hand there are only 60 so 93 is out\r\n\r\nthe 1rst clue say the number in the hour plus the min = 60 so it\'z either \r\nmin hour\r\n42 18\r\n24 36\r\n39 21\r\nthe third clue say the min sum equal the hour reverse \r\nonly 39 and 21 qualifies this \r\neveryone thought the time b 21:39\r\nbut they forgot the hour hand is on 21 not 21 hours so when the hand is on 21 the hour is 4 o clock yea following me the min stay so i say the time is 4:39 finnally there you go hope itz rite cuz thats alot of typing',6817,0);
INSERT INTO comment VALUES (6819,1043,2667,'Viet','re(3): i don\'t kare wat u all say','2003-07-30 08:02:18',0,'ahhhhhhhhhhhhhhhh f*ck it God damn did see the first part where they mention bout digital the proove me all wrong if itz a normal clock mayb',6818,0);
INSERT INTO comment VALUES (6820,1049,1575,'DJ','Starters','2003-07-30 09:10:58',1,'Here are the few that struck me right off:\r\n\r\n
\r\n2 + 4 + 6 = 12 points.. go me!',NULL,0);
INSERT INTO comment VALUES (6821,174,1919,'Lewis','Solution','2003-07-30 10:45:06',3,'This problem is solvable. Why? Because I just solved it.',NULL,0);
INSERT INTO comment VALUES (6822,84,1919,'Lewis','re: No! You cannot! You cannot overtake the last person! No,no,no!','2003-07-30 11:54:14',3,'You can - if you are not in the race or if you are lapping him/her :p',4092,0);
INSERT INTO comment VALUES (6823,1049,1567,'Bryan','(5)','2003-07-30 11:54:25',0,'The values in the 5th sequence are the days of the month in three-week intervals, starting with January 1, in a non-leap year such as this year. Starting on 1/1 (month/day), the date every three weeks is: 1/22, 2/12, 3/5, 3/26, 4/16, 5/7, 5/28, 6/18, and 7/13. Thus the answer to the 5th sequence is 13.\r\n\r\nI got the same answers as DJ on (2) and (4) but missed (1), so my score so far is 19. Woo-hoo!',NULL,0);
INSERT INTO comment VALUES (6824,84,1919,'Lewis','re(2): No! You cannot! You cannot overtake the last person! No,no,no!','2003-07-30 11:55:08',3,'Ooooopsy---you can\'t lap in a straight race. :( But you can still not be in the race',6822,0);
INSERT INTO comment VALUES (6825,842,2925,'Danny','haha this one is easy','2003-07-30 15:55:29',0,'she has 3 children with the names: One Boy, Him, and He',NULL,0);
INSERT INTO comment VALUES (6826,1043,2373,'ryan smith','re(4): i don\'t kare wat u all say','2003-07-30 19:59:22',0,'See, you got one.\r\n\r\nAnyway, dude you\'re a riot.\r\n\r\n',6819,0);
INSERT INTO comment VALUES (6827,1049,1183,'fwaff','Solutions for 7 & 8','2003-07-30 21:17:13',3,'Series 7 gives the first number after the decimal point for the square root of the number...\r\n\r\nsqrt(1)=1.00 so the 1st number is 0\r\nsqrt(2)=1.41 so the 2nd number is 4\r\nsqrt(3)=1.73 so the 3rd number is 7\r\nsqrt(4)=2.00 so the 4th number is 0\r\netc, etc\r\nso the ? comes from sqrt(13)=3.60 ie 6\r\n\r\nSeries 8 comes from multiplying different prime numbers together...\r\n\r\n2x3=6\r\n2x5=10\r\n2x7=14\r\n3x5=15\r\n3x7=21\r\netc,etc\r\nso the ? is 38 (=2x19)\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (6828,66,2775,'tyler','Here is the RIGHT answer','2003-07-30 21:33:11',0,'He will shave himself once... because before he gives himself his first shave, he will have been a town resident that doesn\'t shave himself. Upon giving himself his first shave, he now becomes someone who shaves himself, thereby making him unable to give himself a shave.',NULL,0);
INSERT INTO comment VALUES (6829,66,2775,'tyler','Here is the RIGHT answer','2003-07-30 21:33:32',0,'He will shave himself once... because before he gives himself his first shave, he will have been a town resident that doesn\'t shave himself. Upon giving himself his first shave, he now becomes someone who shaves himself, thereby making him unable to give himself a shave.',NULL,0);
INSERT INTO comment VALUES (6830,576,1919,'Lewis','Solution','2003-07-31 01:22:45',3,'Starts column 8 row 3 (8 along the top and 3 down) and moves diagonally down-right.',NULL,0);
INSERT INTO comment VALUES (6831,576,2731,'Venisha','','2003-07-31 02:04:45',0,'starts in the 3rd row. 8th letter. D \r\nthen the 4th row. 9th letter. O\r\nthen the 5th row. 10th letter.G\r\n\r\nDOG',NULL,0);
INSERT INTO comment VALUES (6832,576,2899,'Brian Wainscott','Solution','2003-07-31 05:27:33',3,'Yes. Starting with the d in row 3 column 8, and going down to the right.\r\n\r\nMy first inclination was to answer \"No, I can\'t\", which seems to me a perfectly valid solution.....who are YOU to tell ME what I can and can\'t find.... But of course that is the easy way out....',NULL,0);
INSERT INTO comment VALUES (6833,1038,2932,'Scott','The money','2003-07-31 06:06:21',1,'The question of \'did Mike gain or lose money on the transactions\' is not affected by the bike\'s worth. Mike spent (lost) $40 total and gained a bicycle. ',NULL,0);
INSERT INTO comment VALUES (6834,578,1301,'Charlie','solution','2003-07-31 07:47:30',3,'The word HEAVEN contains HE, HEAVE, EVE, EVEN, AN, HAVE, HEN and A. (I assume it\'s OK to drop letters that fall between letters of the found words, so long as letters are not transposed.) More obscure words in this one are AVE, EAVE and HA.',NULL,0);
INSERT INTO comment VALUES (6835,578,2839,'Andrew Mitchell','solution maybe','2003-07-31 08:00:05',3,'This may be a cheat, I am not sure if you can skip letters but here goes...\r\n\r\nHASTEN\r\n1) HA\r\n2) HAS\r\n3) HAST (archaic)\r\n4) HASTE\r\n5) A\r\n6) AS\r\n7) ATE\r\n8) HATE',NULL,0);
INSERT INTO comment VALUES (6836,578,1575,'DJ','Solution','2003-07-31 09:20:03',3,'I was thinking that we weren\'t allowed to drop letters for this problem .. and there is one common word with 8 common words in it:\r\n\r\nHATPIN\r\nHA\r\nHAT\r\nA\r\nAT\r\nPI\r\nPIN\r\nI\r\nIN\r\n\r\n
\r\nSome more obcure examples:\r\nHEREIN\r\nHE\r\nHER\r\nHERE\r\nERE\r\nRE\r\nREIN\r\nI\r\nIN\r\n\r\nHEREON\r\nHE\r\nHER\r\nHERE\r\nERE\r\nRE\r\nEON\r\nO\r\nON\r\n\r\nHASTEN\r\nHA\r\nHAS\r\nHAST\r\nHASTE\r\nA\r\nAS\r\nTEN\r\nEN\r\n\r\n
\r\nIf the letters do not have to be consecutive, it is possible to find more:\r\nHAPTEN\r\nHA\r\nHAT\r\nHATE\r\nHE\r\nHEN\r\nA\r\nAPT\r\nAPE\r\nAT\r\nATE\r\nAN\r\nPEN\r\nTEN\r\n\r\nHARDEN\r\nHA\r\nHARD\r\nHARE\r\nHAD\r\nHE\r\nHEN\r\nA\r\nARE\r\nAD\r\nAN\r\nRE\r\nDEN\r\n\r\nHARKEN\r\nHA\r\nHARK\r\nHARE\r\nHE\r\nHEN\r\nA\r\nARK\r\nARE\r\nAN\r\nRE\r\n\r\nHASTEN\r\nHA\r\nHAS\r\nHAST\r\nHASTE\r\nHAT\r\nHATE\r\nHE\r\nHEN\r\nA\r\nAS\r\nAT\r\nATE\r\nAN\r\nTEN\r\n\r\nHATPIN\r\nHA\r\nHAT\r\nA\r\nAT\r\nAN\r\nTI\r\nTIN\r\nPI\r\nPIN\r\nI\r\nIN\r\n\r\nHEAVEN\r\nHE\r\nHEAVE\r\nHEN\r\nHA\r\nHAVE\r\nHAVEN\r\nEAVE\r\nEVE\r\nEVEN\r\nA\r\nAVE\r\nAN\r\n\r\nHEREIN\r\nHE\r\nHER\r\nHERE\r\nHEN\r\nHI\r\nERE\r\nRE\r\nREIN\r\nI\r\nIN\r\n\r\nHIDDEN\r\nHI\r\nHID\r\nHIDE\r\nHE\r\nHEN\r\nI\r\nID\r\nIDE\r\nDEN\r\n
',NULL,0);
INSERT INTO comment VALUES (6837,576,2912,'Talon5000','Agnostic','2003-07-31 10:48:50',0,'\r\n dgooddodgooddo\r\n odoogggdodgogg\r\n ogogdooDgooddd\r\n dgdoooggOogdgo\r\n ogdgogdgoGgogd\r\n dddgddodoogdoo\r\n odgoggdooggood\r\n\r\nDid you hear about the dyslexic agnostic?\r\nHe wondered if there is a dog.',NULL,0);
INSERT INTO comment VALUES (6838,152,2912,'Talon5000','solution','2003-07-31 11:00:56',3,'the only way albert will know his own hat color is if both hats in front of him are white, his is black because they are not all white. so after he says no, bill and carl know that both their hats are not white. the only way for bill to know his hat color, now, is if carl\'s hat is white, his hat must be black since from albert\'s statement both are not white. bill didn\'t know, so carl\'s hat much be black.',NULL,0);
INSERT INTO comment VALUES (6839,1,2912,'Talon5000','cool','2003-07-31 11:04:58',0,'i think i\'ve seen a problem like this before, but i still had to look at the answer...',NULL,0);
INSERT INTO comment VALUES (6840,135,1919,'Lewis','Solution','2003-07-31 11:08:37',3,'The painter\'s mixture is currently 4 black and 2 white but he needs 2 black and 4 white. He should pour away half of his mixture to leave him with 2 black and 1 white, then just add the other 3 white.\r\n\r\nNow he has 2 black and 4 white, which is what he needed, with only 3 pints of paint wasted.',NULL,0);
INSERT INTO comment VALUES (6841,578,1301,'Charlie','computer search','2003-07-31 11:12:28',3,'From a computer search, with more obscure words removed:\r\n\r\nharden: hard hare had he hen are an den a\r\nhasten: has haste hat hate he hen as at ate an ten a (12 words)\r\nherein: he her here hen hi ere rein in I (9)\r\nhereon: he her here hero heron hen ere eon on\r\nheroin: he her hero heron hen hi eon on in I (10)\r\nhidden: hi hid hide he hen id in den\r\n',NULL,0);
INSERT INTO comment VALUES (6842,578,1575,'DJ','javascript solution','2003-07-31 12:03:00',3,'Charlie\'s comment gave me an idea. Here\'s a programming solution the other way (without skipping letters), using the ENABLE list (wordList[] is an array of all the words):\r\n\r\nfunction find(word) {\r\n for (var w=0; w<wordList.length; w++) {\r\n wrd=wordList[w];\r\n if (word==wrd)\r\n return true;\r\n }\r\n return false;\r\n}\r\n\r\nvar hn=new Array();\r\nfor (var w=0; w<wordList.length; w++) {\r\n word=wordList[w];\r\n if (word.length==6) {\r\n if (word.charAt(0)==\'h\') {\r\n if (word.charAt(5)==\'n\')\r\n hn[hn.length]=word;\r\n }\r\n }\r\n}\r\n\r\nfor (var h=0; h<hn.length; h++) {\r\n var count=0;\r\n Word=hn[h];\r\n Len=Word.length;\r\n document.write(Word + \":<br>\");\r\n for (var c=0; c<Len; c++) {\r\n for (var len=1; len<=(Len-c); len++) {\r\n word=Word.substr(c, len);\r\n if (find(word) & word.length<6) {\r\n if (count!=0)\r\n document.write(\\\", \\\")\r\n document.write(word);\r\n ++count;\r\n }\r\n }\r\n }\r\n document.write(\\\"<br>Total: \" + count + \"<br><br>\");\r\n}\r\n\r\nThis returned the following list:\r\n\r\nhadron:\r\nha, had, a, ad, on\r\nTotal: 5\r\n\r\nhaemin:\r\nha, hae, haem, a, ae, em, mi, i, in\r\nTotal: 9\r\n\r\nhagdon:\r\nha, hag, a, ag, do, don, on\r\nTotal: 7\r\n\r\nhappen:\r\nha, hap, a, pe, pen, en\r\nTotal: 6\r\n\r\nhapten:\r\nha, hap, a, apt, ten, en\r\nTotal: 6\r\n\r\nharden:\r\nha, hard, a, ar, de, den, en\r\nTotal: 7\r\n\r\nharken:\r\nha, hark, a, ar, ark, ken, en\r\nTotal: 7\r\n\r\nharmin:\r\nha, harm, a, ar, arm, mi, i, in\r\nTotal: 8\r\n\r\nharpin:\r\nha, harp, a, ar, pi, pin, i, in\r\nTotal: 8\r\n\r\nhasten:\r\nha, has, hast, haste, a, as, ten, en\r\nTotal: 8\r\n\r\nhatpin:\r\nha, hat, a, at, pi, pin, i, in\r\nTotal: 8\r\n\r\nhausen:\r\nha, a, us, use, sen, en\r\nTotal: 6\r\n\r\nhazzan:\r\nha, a, a, an\r\nTotal: 4\r\n\r\nheaven:\r\nhe, heave, eave, a, ave, en\r\nTotal: 6\r\n\r\nhempen:\r\nhe, hem, hemp, em, pe, pen, en\r\nTotal: 7\r\n\r\nherein:\r\nhe, her, here, er, ere, re, rei, rein, i, in\r\nTotal: 10\r\n\r\nhereon:\r\nhe, her, here, er, ere, re, eon, on\r\nTotal: 8\r\n\r\nheroin:\r\nhe, her, hero, er, i, in\r\nTotal: 6\r\n\r\nhetman:\r\nhe, het, et, ma, man, a, an\r\nTotal: 7\r\n\r\nhidden:\r\nhi, hid, i, id, de, den, en\r\nTotal: 7\r\n\r\nhodden:\r\nho, hod, od, odd, de, den, en\r\nTotal: 7\r\n\r\nhoddin:\r\nho, hod, od, odd, din, i, in\r\nTotal: 7\r\n\r\nhoiden:\r\nho, i, id, de, den, en\r\nTotal: 6\r\n\r\nholden:\r\nho, hold, old, olden, de, den, en\r\nTotal: 7\r\n\r\nholpen:\r\nho, holp, pe, pen, en\r\nTotal: 5\r\n\r\nhoyden:\r\nho, hoy, oy, de, den, en\r\nTotal: 6\r\n\r\nhyalin:\r\nya, a, al, li, lin, i, in\r\nTotal: 7\r\n\r\nhyphen:\r\nhyp, he, hen, en\r\nTotal: 4\r\n
\r\nSo, there are quite a few words with more than 8, but the one I found before is still the only one with all common or \'acceptable\' words.',NULL,0);
INSERT INTO comment VALUES (6843,576,1575,'DJ','re: Agnostic','2003-07-31 12:08:20',0,'That\'s my joke, and you messed it up:\r\n\r\nDid you hear the one about the insomniac dyslexic agnostic amnesiac?\r\nHe stayed up all night trying to remember if there really is a dog.',6837,0);
INSERT INTO comment VALUES (6844,428,2869,'tammy','Possible','2003-07-31 12:14:52',0,'The second man stated \"I\'ll have what he\'s having.\"',NULL,0);
INSERT INTO comment VALUES (6845,576,2921,'Salem D','possible solution','2003-07-31 15:11:44',0,'if you start at row three col. 8 with d, you can spell dog by moving down and to the right for each of the following letters.',NULL,0);
INSERT INTO comment VALUES (6846,578,1299,'Anoop','Answer','2003-07-31 15:38:42',0,'well the first word that popped into my head was heroin and it seems to fit i think with the possible 8 words being - \r\n\r\nhe, her, hero, heron, i, on , eon, in',NULL,0);
INSERT INTO comment VALUES (6847,1038,2938,'nakia','true answer','2003-07-31 16:45:37',0,'he lost $20 in the transactions.',NULL,0);
INSERT INTO comment VALUES (6848,577,2938,'nakia','The True Solution is right before your very eyes!','2003-07-31 17:24:05',0,'That! That is. Is that? That is not. Is not! Is that it? That is it.',NULL,0);
INSERT INTO comment VALUES (6849,578,2944,'verizon','re: computer search','2003-08-01 02:05:28',0,'charlie, you\'re the best!',6841,0);
INSERT INTO comment VALUES (6850,1045,2839,'Andrew Mitchell','Solution','2003-08-01 02:37:02',3,'1806\r\neach number is the product of the previous number multiplid by that number plus 1\r\n\r\n1 * (1+1) =2\r\n2 * (2+3) =6\r\n6 * (6+1) = 42\r\n42* (42+1) = 1806',NULL,0);
INSERT INTO comment VALUES (6851,1049,1575,'DJ','Some more answers','2003-08-01 03:10:00',3,'Here are some more that I figured out, or at least that I think I can explain. I\'ve included the answers other people have come up with:\r\n\r\n
\r\nOverall, I think I myself completely solved numbers 1, 2, 4, and 6.\r\nMy answer to number three is iffy, and probably not the intended solution, but I\'m taking it.\r\nFor number five, I noticed that that the difference between both pairs of ascending terms was the same, 21, and I guessed it was some sort of mod scale. I got different values, though; some 30, some 31, and the second one even came out to 28! .. If I had been awake that would have been easy. Anyway, I corrected Bryans answer (three weeks from June 18 is July 9, not 13), so I\'m claiming those points as well.\r\nNumber seven I would have gotten in a few weeks, or years. I\'ll relinquish those points.\r\nFor the values in number 8, I had noticed that each had exactly two different prime factors, but I was thinking too much. I mulled over the order, trying to find a pattern, and missed the simple ascension of the results. I would take only half of those points, but 21 doesn\'t divide by two very evenly, so I\'ll just take them all.\r\nI didn\'t get the last one, and no one else has yet either.\r\n\r\nTotal: 2 + 4 + 5 + 6 + 9 + 12 + 21 = 59.\r\nLooks like I still failed..\r\nActually, for number seven, I did notice that the postions of the zeroes (1, 4, 9) were the perfect squares. So, that would eventually have led to me listing the square roots of the numbers, and making the same observation that fwaff did. It\'s not my fault he blurted out the answer before I had the chance! So, I deserve those points too.\r\n\r\nMy total score then is: 2 + 4 + 5 + 6 + 9 + 12 + 15 + 21 = 74.\r\nAnd hey, I only missed the last sequence. Too bad you guys each only got one or two ...\r\n\r\n=P',NULL,0);
INSERT INTO comment VALUES (6852,1045,1575,'DJ','solution','2003-08-01 03:33:55',3,'The differences between consecutive terms is:\r\n1 + 1 = 2, 2 + 4 = 6, 6 + 36 = 42 ..\r\n\r\nThis makes it fairly easy to see that each term is added to its square to get the next term:\r\n42 + 1764 = 1806',NULL,0);
INSERT INTO comment VALUES (6853,120,1575,'DJ','re: log?','2003-08-01 03:52:55',0,'Also, just to avoid any confusion, it should be noted that log(x) does not generally refer to the natural logarithm, base e, but to the common logarithm, base 10, (except in advanced level mathematics texts, and then only rarely).\r\n\r\nIn general, the convention is:\r\nlog(x) is base 10\r\nln(x) is base e\r\nlg(x) is base 2\r\nlogb(x) or logb(x) has some base b',1269,0);
INSERT INTO comment VALUES (6854,1049,872,'pleasance','sequence 3','2003-08-01 05:53:35',0,'I thought of (3) as a calendar, not a clock, but it\'s much the same as DJ\'s answer. Pairing the numbers off, we get 1/12, 1/1, 1/2, or December first, January first, February first, so to continue we would have March first, 1/3, the next two numbers in the series being 1 and 3. It just occurred to me that this doesn\'t work in the US, where dates are usually written the other way round.\r\n\r\nAlternative solution: We could read the numbers as months, giving us January, December, Jan., Jan., Jan., February. Then the sequence is obviously the first month in which it snowed on Mount Pooka-Pooka in consecutive winters, beginning with the winter of 1837/8 and up to 1842/3. Unfortunately, the next in the series refers to the infamously warm dry winter of 1843/4, when it didn\'t snow at all. Just kidding. Sorry. ',NULL,0);
INSERT INTO comment VALUES (6855,1045,2667,'Viet','thoughtz','2003-08-01 08:28:55',0,'DJ solution sound better and is more understanding and andrew i didn\'t get how you get 6 or you must have typed it wrong 2*(2+1)=6',NULL,0);
INSERT INTO comment VALUES (6856,1038,2947,'jeremy','he is even.','2003-08-01 09:06:20',0,'Through all his transactions he ended up losing $40, but due to the fact that the bike is worth $40, in a sense he breaks even.',NULL,0);
INSERT INTO comment VALUES (6857,1043,2947,'jeremy','21:39','2003-08-01 09:30:24',0,'*Read the first sentence \"24 HOUR DIGITAL CLOCK\"\r\n This means there are no hands, just numbers.\r\n*Now for my solution of 21:39, 21+39=60, 3 is the square root of nine and 3+9=12 which reversed is 21.\r\n \r\n21:39\r\nNow everyone else stop you petty b****ing',NULL,0);
INSERT INTO comment VALUES (6858,1063,2899,'Brian Wainscott','','2003-08-01 10:18:03',3,'Moe is born in 1932, and hence is older.\r\n\r\nFor the grandfather clocks to show the same time, the fast one must gain 6 hours, and the slow one lose 6 hours. This will take (6 hours)x(60 minutes/hour)x(60 seconds/minute) / (10 seconds/hour) hours, which is exactly 90 days.\r\n\r\nIf they set the clocks on January 31, 1979, they will agree again at noon on May 1, 1979 (each reading 6 o\'clock). Hence this is Moe\'s 47th birthday.\r\n\r\nIf they had set the clocks in 1980 (had Moe been born in 1933), then the latest they could have agreed is April 30th, not may, due to 1980 being a leap year.',NULL,0);
INSERT INTO comment VALUES (6859,1063,1567,'Bryan','Tricky ...','2003-08-01 10:24:26',3,'Since one clock gains as much time every hour as the other loses, the next time both clocks will show exactly the same time is when one has gained 6 hours and the other has lost 6 hours, since antique grandfather clocks have a 12-hour cycle.
Bert: I won.
Coby: I didn\'t win.
Dave: Bert won.
Ed: I came 4th.\r\nA: 4\r\nE: 3\r\n0: 1\r\n1: 1\r\n2: 5\r\n3: 3\r\n4: 11\r\n5: 1\r\n6: 0\r\n7: 2\r\n8: 2\r\n9: 2\r\n
\r\nJust to check, that does add up to 35.\r\n\r\nThe hint says that the title is significant somehow, as well as the grid of letters. It contains 10 letters, 9 of which are distinct.\r\nIf the clue in the title is simple the fact that this code is tricky, it\'s unnecessary. I\'m still lost..\r\n\r\nAnyone?',NULL,0);
INSERT INTO comment VALUES (7055,994,2839,'FatBoy','Solution','2003-08-11 09:37:09',0,'Barry whent to church',NULL,0);
INSERT INTO comment VALUES (7056,567,2839,'FatBoy','Solution','2003-08-11 09:38:54',0,'b is correct\r\nr wins',NULL,0);
INSERT INTO comment VALUES (7057,1103,1301,'Charlie','solution','2003-08-11 09:43:59',3,'Assuming the robbers know whether to start by going clockwise or counterclockwise, and that any given number can appear any number of times, and in succession, there are 60^5 possible combinations. That\'s 777.6 million combinations. On average, then, the robbers would have to try 388.8 million times, thus averaging 388.8 British billion pounds in order to get 100 British billion pounds, or an expected loss of 288.8 billion pounds.',NULL,0);
INSERT INTO comment VALUES (7058,1101,1301,'Charlie','thoughts','2003-08-11 09:46:27',1,'Maybe it\'s just a programmer\'s prejudice, but they could be hexadecimal digits since no letters are used beyond F, but this is not hinted at by any of the clues, and B, C, D and F are not used, as also 6 is not used.',NULL,0);
INSERT INTO comment VALUES (7059,1103,2129,'Sanjay','re: solution','2003-08-11 10:23:44',0,'Why would you assume that the robbers know whether to start by going clockwise or counterclockwise when the problem clearly states that \'they don\'t have a clue what the code is\'.
Leaving but twelve in the first one.
Then dumping the four and repeating twice more,
He had four in the first and the last one.
For every inch of its level
By pouring the four ‘til its level matched before
He had four plus one units, the devil!',NULL,0);
INSERT INTO comment VALUES (7070,1073,2899,'Brian Wainscott','Another solution','2003-08-11 16:02:47',3,'(I won\'t even TRY verse...sorry to disappoint you, but believe me you are better off...)\r\n\r\nTaking into account that the glasses are negligibly thick, we can do this:\r\n\r\nplace the 4 unit glass inside the 16 unit glass, and push it all the way over to one side (say, the left). Then tip the 16 unit glass to the left until the right bottom edge of the 16 unit glass just reaches the water level. There will be 5 units left in the 16 unit glass.\r\n\r\nLoose proof: the 4 unit glass has half the diameter of the 16 unit glass. If we left it out and tipped the 16, we would have 8 units. So the only thing is to show that the 4 unit glass displaces exactly 3 units. Since it has half the diameter, then the right edge of the 4 unit glass is directly over the center of the 16 unit glass. Thus when tipped, the water level is exactly half way up the 4 unit glass. Now if you think of the 4 unit glass as 2 2 unit glasses (one on top of the other) it is obvious: the lower one is completely submerged, and the upper one is half under the water, and half out of the water. Thus 3 units are displaced, so the total remaining is 5.',NULL,0);
INSERT INTO comment VALUES (7071,177,3026,'drew','Air Pressure','2003-08-11 16:46:02',3,'It\'s possible to suck the ball out without actually using your mouth. The curtains could be waved in front of the vent and force enough air out of the vent (for a short time) to make the ball be pushed out of the hole by the air pressure behind it. It\'s not a very feasible solution, but technically it is possible.',NULL,0);
INSERT INTO comment VALUES (7072,1103,3075,'Daniel','solution','2003-08-11 17:13:20',0,'Any question asking how many ways you can pick a certain number of anything from the whole set of anything (in this case how many ways can you pick 5 different numbers from 60. You use the format 60 choose 5 (on pascal\'s triangle that is 60 down starting with 0 on the first line and 5 to the left or right starting with 0 on the 1 column.) Algebraically this may be found by 60!/(60-5)!5!=54615120 which means that there is a 1:54615120 chance of getting the right combination. Therefore statistically they need to try it 50% *1 times, to probably get it. Therefore they need to try 27307561 different combinations in order to probably get it. This means that they will probably be fined 27307561000000 pounds. Therefore they will probably make 99999999972692439000000 . The payoff minus the fines. Sorry for such a long solution, I wanted my first one to be a good one.',NULL,0);
INSERT INTO comment VALUES (7073,1103,3075,'Daniel','re: daniel\'s solution','2003-08-11 17:25:09',1,'I just read over my solution and realize my reasoning and the entire answer itself is completely incorrect. Sorry about that. Furthermore, you might assume as in most locks that you start going in one direction, after you get to the next number, in order for the mechanism to lock, you must go in the next direction. Therefore there are only twice as my options. ',7072,0);
INSERT INTO comment VALUES (7074,1060,2951,'Jim Breaux','Solution','2003-08-11 21:12:37',0,'I don\'t know if this is the solution that you are looking for but, for each word, switching the first and last letters forms a new word.\r\n\r\nnail becomes lain, etc...',NULL,0);
INSERT INTO comment VALUES (7075,1073,2130,'ethan','very creative','2003-08-11 23:29:36',0,'Very creative, DJ. I like the poetry. Well done.',NULL,0);
INSERT INTO comment VALUES (7076,958,3080,'nich','','2003-08-12 04:10:18',0,'1 word- yawnz',NULL,0);
INSERT INTO comment VALUES (7077,19,3075,'Daniel','solution','2003-08-12 05:37:18',0,'You ask \"Who would your brother say is bob?\". This would lead to a lie each time and so you would then know that the opposite is true.',NULL,0);
INSERT INTO comment VALUES (7078,1106,1686,'DuCk','my thoughts','2003-08-12 07:48:43',0,'not sure if i\'m doing this right, but wouldn\'t the probability of a person doing all of the activities listed be the probabilities of the person doing each individual event multiplied together? If so, I obtain the probability for a person to be a smoker, drinker, driver, and computer owner to be:\r\n\r\n(1/4.8)*(23/37)*(26/33)*(83/100) = .084688\r\n\r\nwhich means that approximately 84688097 (.084688*1,000,000,000) people in the country would smoke, drink, drive and own a computer.',NULL,0);
INSERT INTO comment VALUES (7079,1106,1301,'Charlie','re: my thoughts','2003-08-12 09:26:10',0,'That certainly looks right to me.',7078,0);
INSERT INTO comment VALUES (7080,35,2839,'FatBoy','solution','2003-08-12 09:40:50',3,'2001 = 6\r\n2002 = 9\r\n\r\nthe only possible sequence is 69234 repeating\r\n',NULL,0);
INSERT INTO comment VALUES (7081,1103,2899,'Brian Wainscott','re: solution','2003-08-12 15:22:15',1,'Sorry Daniel, but I think you missed a couple of points:\r\n\r\n1 - for opening a safe, order matters. The combination 1-2-3-4-5 is NOT the same as the combination 1-2-3-5-4. In this sense it is really a permutation that opens the safe, not a combination (hence, I think, the use of the word \"code\" in the puzzle, instead of \"combination\"). This would increase the number of codes from 60 choose 5 to 60!/55!\r\n\r\n2 - There is not necessarily a restriction that the numbers in the code be distinct, so the true number of codes is more likely 60^5, giving you Charlie\'s answer.\r\n',7072,0);
INSERT INTO comment VALUES (7082,1089,1567,'Bryan','An observation','2003-08-12 18:40:55',0,'I can\'t find an instance where n^2 + 3 is a perfect cube, let alone with the caveat that n + 3 is a perfect cube as well. My answer is \"no,\" but I cannot prove it.',NULL,0);
INSERT INTO comment VALUES (7083,1089,1626,'Gamer','re: An observation','2003-08-12 19:34:35',0,'I have been playing around with variables, and am pretty sure it can\'t happen, but am not positive.',7082,0);
INSERT INTO comment VALUES (7084,1089,3083,'xanthophobic','??','2003-08-12 20:02:50',0,'doesn\'t 1 work? am i wrong? that sounds too easy',NULL,0);
INSERT INTO comment VALUES (7085,1089,103,'friedlinguini','re: ??','2003-08-12 20:31:48',0,'Well, no. 4 is not a perfect cube.',7084,0);
INSERT INTO comment VALUES (7086,1089,3083,'xanthophobic','re(2): ??','2003-08-12 21:03:44',0,'ohh that\'s why, i was thinking square not cube',7085,0);
INSERT INTO comment VALUES (7087,1058,775,'Cory Taylor','re(2): ~50%','2003-08-12 21:11:48',0,'well done. You acheived about 7% better than I could figure out, though I used much the same strategy. I wasn\'t able to come up with anything useful when weighing more than one coin per side at a time (though this doesn\'t mean it isn\'t the best...). However, with a (genuine) reference coin I gained my % points back, well, almost. My success rate was 4/10 + 6/10*4/9 +6/10*5/9*4/8=79/90, or a little better than 86.9%.',7066,0);
INSERT INTO comment VALUES (7088,1089,1626,'Gamer','More Ideas','2003-08-12 22:34:19',1,'Looking at the one\'s place:\r\n\r\n0 0 0\r\n1 1 1\r\n2 4 8\r\n3 9 7\r\n4 6 4\r\n5 5 5\r\n6 6 6\r\n7 9 3\r\n8 4 2\r\n9 1 9\r\n\r\nSince the ones place of n^2 + 3 can end in any digit, it comes down to the squares. Since squares can only end in a certain way, this means that n^2+3 must be the cube of something ending in 2, 3, 4, 7, 8, 9.',NULL,0);
INSERT INTO comment VALUES (7089,1074,979,'Ravi Raja','The Number','2003-08-13 00:23:14',0,'Is the answer to the first part : 1921111111 ',NULL,0);
INSERT INTO comment VALUES (7090,1111,2839,'FatBoy','I\'m not sure I get the rules','2003-08-13 08:23:24',1,'I can do it in four moves\r\nPASSER\r\nPSASER\r\nSPASER\r\nSPASRE\r\nSPARSE\r\n\r\nI guess I can also do it in five moves\r\nPASSER\r\nPASSER (with \"s\"s reversed\r\nPSASER\r\nSPASER\r\nSPASRE\r\nSPARSE\r\n\r\nis this what you were after or am I not getting it?',NULL,0);
INSERT INTO comment VALUES (7091,1111,1301,'Charlie','re: I\'m not sure I get the rules','2003-08-13 08:39:39',3,'It would seem that indeed the only way to stretch this out to exactly 5 steps is to interchange the two S\'s at some point. The four steps that do the work are interchanging pos. 2&3, 1&2, 5&6 and 4&5. These can be in any order so long as 2&3 gets done before 1&2, and 5&6 before 4&5. That\'s six possible orders. The switching of the two S\'s at 3&4 can be done at any time they are still together. There seems to be no other possibilities.\r\n\r\nA computer search gives the following possibilities:\r\n\r\n 3 4 2 3 1 2 5 6 4 5\r\n 3 4 2 3 5 6 1 2 4 5\r\n 3 4 2 3 5 6 4 5 1 2\r\n 3 4 5 6 2 3 1 2 4 5\r\n 3 4 5 6 2 3 4 5 1 2\r\n 3 4 5 6 4 5 2 3 1 2\r\n 5 6 3 4 2 3 1 2 4 5\r\n 5 6 3 4 2 3 4 5 1 2\r\n 5 6 3 4 4 5 2 3 1 2\r\n
\r\nwhere the program is\r\n\r\ns0$ = \"passer\"\r\nFOR t1 = 1 TO 5\r\n s1$ = LEFT$(s0$, t1 - 1) + MID$(s0$, t1 + 1, 1) + MID$(s0$, t1, 1) + MID$(s0$, t1 + 2)\r\n FOR t2 = 1 TO 5\r\n s2$ = LEFT$(s1$, t2 - 1) + MID$(s1$, t2 + 1, 1) + MID$(s1$, t2, 1) + MID$(s1$, t2 + 2)\r\n FOR t3 = 1 TO 5\r\n s3$ = LEFT$(s2$, t3 - 1) + MID$(s2$, t3 + 1, 1) + MID$(s2$, t3, 1) + MID$(s2$, t3 + 2)\r\n FOR t4 = 1 TO 5\r\n s4$ = LEFT$(s3$, t4 - 1) + MID$(s3$, t4 + 1, 1) + MID$(s3$, t4, 1) + MID$(s3$, t4 + 2)\r\n FOR t5 = 1 TO 5\r\n s5$ = LEFT$(s4$, t5 - 1) + MID$(s4$, t5 + 1, 1) + MID$(s4$, t5, 1) + MID$(s4$, t5 + 2)\r\n IF s5$ = \"sparse\" THEN PRINT t1; t1 + 1, t2; t2 + 1, t3; t3 + 1, t4; t4 + 1, t5; t5 + 1\r\n NEXT\r\n NEXT\r\n NEXT\r\n NEXT\r\nNEXT\r\n',7090,0);
INSERT INTO comment VALUES (7092,1111,3087,'Scott','Solution','2003-08-13 09:32:54',0,'passer\r\npsaser\r\nspaser\r\nspasre\r\nsparse',NULL,0);
INSERT INTO comment VALUES (7093,1074,1575,'DJ','re: The Number (Ravi imitation)','2003-08-13 09:53:10',0,'Well if you look at your answer again please you see that you have a 9 in your answer but the last digit in your number is a 1 when there are really two 9s, one in the blank and one in the statement itself. So if you would please take another look at your answer I think you will see where you went wrong thank you.',7089,0);
INSERT INTO comment VALUES (7094,1074,979,'Ravi Raja','re(2): The Number (Ravi imitation)','2003-08-13 10:30:07',0,'Thank You DJ for pointing out my mistake. I just did not notice that or whatever but please tell me one thing. Why did you mention in your subject \"Ravi imitation\" ? I did not get that part. ;)',7093,0);
INSERT INTO comment VALUES (7095,787,2839,'FatBoy','solution','2003-08-13 11:04:20',3,'a is a liar\r\nb is a knight',NULL,0);
INSERT INTO comment VALUES (7096,1111,3090,'Crystal','Solution','2003-08-13 12:55:18',0,'I got it.\r\nPASSER\r\nPSASER\r\nPSASRE\r\nSPASRE\r\nSPARSE',NULL,0);
INSERT INTO comment VALUES (7097,1089,3032,'gregada','Another idea','2003-08-13 12:55:21',0,'There are also negative integers to think about...',7088,0);
INSERT INTO comment VALUES (7098,1058,2899,'Brian Wainscott','re(3): ~50%','2003-08-13 13:24:47',4,'Thanks -- but the weighing 1 vs 1 was Ryan\'s idea originally. I was trying more complex things, and I don\'t know if I would have thought of this without reading his post.\r\n\r\nHowever, my calculator tells me that 4/10 + 6/10*4/9 + 6/10*5/9*4/8 = 83.3%\r\n\r\nThe fractions make sense to me (4 chances in 10 the first coin is bad, 6/10*4/9 the first is good and the second is bad, 6/10*5/9*4/8 that both the first and second are good and then the one you randomly pick from the remaining 8 is bad).\r\n\r\nAm I missing something here?',7087,0);
INSERT INTO comment VALUES (7099,1089,2899,'Brian Wainscott','I can\'t resist....','2003-08-13 13:32:28',0,'There are no such integers. I have a remarkable proof, which the text box of this web page is too small to contain.',NULL,0);
INSERT INTO comment VALUES (7100,848,2839,'FatBoy','solution in 5','2003-08-13 14:14:26',3,'I have not read the solution or everybody\'s comments but I can do it in 5 steps\r\n\r\nlone\r\ndone\r\ndole\r\nrole\r\nrolf (a form of massage)\r\nwolf',NULL,0);
INSERT INTO comment VALUES (7101,848,2839,'FatBoy','re(5): Out and about','2003-08-13 14:24:25',0,'It seems silly to respond this late in the game but Rolf is not a mispelling of ralph nor is in onomatopoetic. Its a common (if painful) form of massage. I\'ve read entire articles about it in Time and Newsweek (albeit this was back in the 1980s)',5564,0);
INSERT INTO comment VALUES (7102,1107,1301,'Charlie','solution','2003-08-13 14:46:16',3,'Use the formula distance = rate x time.\r\n\r\nLet the distance (height of the grass) be measured in units in which the current height of the grass is 1. Let the rate at which a cow eats the grass be c and the rate at which grass grows r. Then, as distance = rate * time,\r\n\r\n1=(40c-r)*40\r\n1=(30c-r)*60\r\n\r\nRespectively these are equivalent to \r\n1600c-40r=1\r\n1800c-60r=1\r\n\r\nSolving, 1200c = 1, or\r\nc=1/1200\r\nthen\r\nr=1/120\r\n\r\nIf d is the number of days the pasture would last if 20 cows were to graze on it, the formula becomes\r\n1=(20/1200)d\r\nor\r\n1=(1/60 - 1/120)d = d/120\r\nso d = 120 days, the answer.\r\n\r\nAs an aside, we can see that 10 cows grazing would exactly balance the growth rate of the grass, so 10 is a sustainable number of cows with no time limit.\r\n\r\nBut again, 120 is the answer to the question posed.',NULL,0);
INSERT INTO comment VALUES (7103,1107,1301,'Charlie','re: solution','2003-08-13 14:48:04',0,'That line\r\n1=(20/1200)d \r\n\r\nshould of course be\r\n1=(20/1200 - 1/120)d \r\n',7102,0);
INSERT INTO comment VALUES (7104,1111,3032,'gregada','re: Solution','2003-08-13 15:38:50',0,'i think Crystal means that the first moves is changing PASSER to PASSER by switching S\'s.',7096,0);
INSERT INTO comment VALUES (7105,1089,979,'Ravi Raja','re: An observation','2003-08-14 04:27:33',0,'Do you think that aproof is necessary Bryan. It will be done only if you can provide a counterexample to prove that the statement does not hold, that is both the expressions cannot be Perfect Cubes.',7082,0);
INSERT INTO comment VALUES (7106,1089,979,'Ravi Raja','My Idea','2003-08-14 04:27:41',1,'Just put n = 5 and observe that (n+3) is a perfect cube but (n²+3) is not. This is one example and there may exist infinitely many such counterexamples. ',NULL,0);
INSERT INTO comment VALUES (7107,1089,979,'Ravi Raja','Is there a Solution ??','2003-08-14 04:29:05',0,'Did Jayaram submit a solution to this problem ?',NULL,0);
INSERT INTO comment VALUES (7108,1089,1575,'DJ','re: My Idea','2003-08-14 07:25:55',0,'Well, I tried n=4, and n+3 is 7, which isn\'t a perfect cube, so I think that it\'s impossible for n+3 to be a perfect cube.\r\n\r\n.. You could prove that it\'s possible, of course, by finding a single example, but no number of counterexamples will ever serve as sufficient disproof.',7106,0);
INSERT INTO comment VALUES (7109,1094,1919,'Lewis','Solution','2003-08-14 07:31:09',3,'The only way to finish with 7 is to have either the twins\' ages product finish 1 and the other brother\'s age finish with 7, or vice versa, or have a 3 and a 9. By trying different combinations we find that:\r\n\r\nThe twins ages are 9. 9*9=81\r\nThe other brother is 7 years old. 81*7=567.',NULL,0);
INSERT INTO comment VALUES (7110,499,2839,'FatBoy','A little verse...','2003-08-14 07:50:14',3,'I do not read what others write,\r\nere I post a solution.\r\nSo please forgive, if you find trite\r\nmy little contribution.\r\n\r\nI know these four, I surely do.\r\nWe meet quite frequently\r\nwith nary a loss they all accrue\r\nbecause all four play poker with me\r\n',NULL,0);
INSERT INTO comment VALUES (7111,1094,1575,'DJ','Analysis','2003-08-14 08:05:05',3,'The prime factorization of 567 is 3×3×3×3×7.\r\n\r\nSince there are four factors of three, there are three ways mathematically to multiply three numbers, two of which are equal, to get 567:\r\n\r\n1×1×567 = 567\r\n3×3×63 = 567\r\n9×9×7 = 567\r\n\r\nOf these, the second is possible, but the third is the only really plausible answer, and probably what we are looking for.\r\nThe twins are 9, and the other brother is 7.\r\n\r\nPerhaps, to further eliminate the other possibilites other than by inspection, it could have been said that the twins were older than the other brother, or something like that.',NULL,0);
INSERT INTO comment VALUES (7112,1094,2561,'Aaron','','2003-08-14 08:09:35',0,'7, unless he is 63 and his brothers are 3 haha',NULL,0);
INSERT INTO comment VALUES (7113,1111,2561,'Aaron','idk','2003-08-14 08:11:11',0,'you can\'t do it, unless switching the two Ss at the beginning is a valid move, then it\'s easy',NULL,0);
INSERT INTO comment VALUES (7114,226,3095,'Paula Bilton','Red ball... Red ball','2003-08-14 08:16:42',0,'Easy - if you know probability!\r\npabrtr',NULL,0);
INSERT INTO comment VALUES (7115,1094,1626,'Gamer','re: Analysis','2003-08-14 08:24:57',0,'I think saying the twins had a younger brother would be a great thing to say... :)',7111,0);
INSERT INTO comment VALUES (7116,924,2839,'FatBoy','Solution','2003-08-14 08:43:26',3,'Since $ = * + % (eq. a)\r\nThen $ + $ + $ = @ + % + * + % + @ (eq b)\r\ncan be converted to $ + $ = @ + % + @\r\nby subtracting equal terms from both sides\r\ngathering like figures we get:\r\n2 ($) = 2(@) + % (eq. d)\r\n\r\nDevide both sides by 2 you get\r\n$ = @ + %/2\r\n\r\nsince eq (a) tell us $ = * + %\r\nwe can combine to get\r\n@ + %/2 = * + %\r\nwhich simplifies to\r\n@ = * + %/2\r\neq. c tells un @ = ! + *\r\ntherefore\r\n* + %/2 = ! + *\r\nsimplifies to\r\n%/2 = ! or 2(!) = % (eq. e)\r\n\r\nso when !+ @ +! + ! + @ +! faces % + $ + * + $\r\nusing equation e we can say\r\n\r\n% + % + @ + @ is facing % + $ + * + $ \r\n\r\nequation d lets us then say that\r\n\r\n% + % + @ + @ is facing % + % + @ + @ + *\r\n\r\nsince % + % + @ + @ cancels form both sides we can see that the right side wouls win\r\n\r\nsorry if this is not elegant but it is how my brain worked it out\r\n',NULL,0);
INSERT INTO comment VALUES (7117,1094,3095,'Paula','Solution','2003-08-14 09:31:50',0,'The other brother is 63 yrs old',NULL,0);
INSERT INTO comment VALUES (7118,1094,3095,'Paula','re: Solution','2003-08-14 09:51:42',0,'Just kidding!!! That would make the twins 3 yrs old!!!! The other brother is 7 yrs old and the twins are 9 yrs old.',7117,0);
INSERT INTO comment VALUES (7119,1094,2839,'FatBoy','','2003-08-14 11:56:40',0,'',NULL,0);
INSERT INTO comment VALUES (7120,1094,2839,'FatBoy','arrrggghhhh','2003-08-14 11:59:48',3,'seems I posted a non -solution\r\n\r\nteh most likely posibility is the the twins are 9 and the other brother is seven,\r\nbut it could concievably be that the brother is 63 and the twins are 3',NULL,0);
INSERT INTO comment VALUES (7121,600,1567,'Bryan','Solution','2003-08-14 14:28:27',0,'The box of 29 balls is sold, leaving 5, 7, and 18 of one color and 14 and 16 of the other. No other groupings from five boxes splits evenly.',NULL,0);
INSERT INTO comment VALUES (7122,600,1686,'DuCk','re: Solution','2003-08-14 14:34:47',0,'same result here --> 29',7121,0);
INSERT INTO comment VALUES (7123,467,2839,'FatBoy','re: Stupid answer','2003-08-14 15:19:07',0,'Even though its a classic, I have always hated this Riddle.\r\nTerry Pratchett in his book Pyramids does a great job of taking it apart',4836,0);
INSERT INTO comment VALUES (7124,600,2839,'FatBoy','2 Solutions (but one\'s a cheat)','2003-08-14 18:46:59',3,'the buses tag number was 196 (13^2)\r\nupside down it would be 961 (31^2)\r\n\r\nThe other answer is simpler and reversable but I don\'t think it counts\r\nthat is using the numbers 001 and 100\r\nI don\'t think it counts because cool math people always seam to snub the lowly one as a perfect square (although it is)',NULL,0);
INSERT INTO comment VALUES (7125,600,2839,'FatBoy','oops','2003-08-14 18:47:58',0,'sorry folks my previous solution was for en entirly different puzzle',NULL,0);
INSERT INTO comment VALUES (7126,600,2839,'FatBoy','now my solution for THIS one','2003-08-14 18:49:13',3,'The box that was sold had 29 in it leaving the following boxes \r\n5,7,14,16,1\r\n5,7,18 were one color\r\n14, 16 were the other',NULL,0);
INSERT INTO comment VALUES (7127,447,2839,'FatBoy','2 solutions (ones a cheat)','2003-08-14 19:02:32',0,'frst solution tag number is 196 (13^2)\r\nupside down is 962 (31^2)\r\n\r\notehr answer\r\n001 and 100',NULL,0);
INSERT INTO comment VALUES (7128,447,1626,'Gamer','Not really','2003-08-14 21:40:04',0,'Usually leading zeroes are illegal for a number. 1 isn\'t expressed as 0001, 1.000 or 0001.00000000 or such in our numbering system when talking about exact numbers.',NULL,0);
INSERT INTO comment VALUES (7129,600,1575,'DJ','Simple','2003-08-15 07:34:02',3,'After you remove the one box, the remaining total must be able to be split evenly in half; therefore there must be an even total number of balls left. The overall total number is 89, so the box removed must have an odd number of balls in it, eliminating half of the possibilites.\r\n\r\nThe first thing I then tried in my head, removing 29 to leave 60, showed that 14+16 and 5+7+18 indeed both add up to 30. Further inspection shows that it doesn\'t work out if the box with either 5 or 7 balls is removed.\r\n\r\nOther than knowing that the box has an odd number of balls in it, I\'m not sure how this would be approached other than simple trial and error (not that it\'s that hard).',NULL,0);
INSERT INTO comment VALUES (7130,1110,2561,'Aaron','Simple','2003-08-15 08:42:47',0,'Well, the probability of making the first shot is 80%, times the probability of the second shot is 80%, so the probability of either is only 64%.',NULL,0);
INSERT INTO comment VALUES (7131,616,2839,'FatBoy','answer','2003-08-15 08:58:07',0,'The statements in lines two and 4 can not both be true (they are made on different days and Bob only tels the truth once a week). Therefore Bob must tell the truth one of those four days and, in any case, lies on Thursday, Saturday an Sunday (the other three days). This being the case the statement in line three can not be made on any of those three days since it would be true.\r\n\r\nSince the second day can not be Thursday, Saturday or Sunday, it must be monday, tuesday wednesday or friday. THerefore the first day must be either Sunday Monday Tuesday or THursday\r\n\r\nBut the first day can not be THursday b/c then the first adn last statements (which can not both be false becasue that would cause there to be at least two days when Bob told the truth) would both fall on days when Bob lies\r\n\r\nThat leaves Sunday Monday and tuesday for the first day\r\n\r\nTHis leave 5 possibilites\r\na)Sunday is the first day and Bob is lying that day\r\nb)Monday is first day and Bob is lYing that day\r\nc)Monday is first day and bob is telling the truth\r\nd)Tuesday is first day and Bob is lying \r\ne)Tuesday is first day and Bob is telling the truth.\r\n\r\nc and e are eliminated because the statemetn \"I lie on Mondays and Tuesdays\" can\'t be true on Monday or Tuesday.\r\n\r\nsince this leaves no option where Bob can be telling the truth on the first day that means two things 1) the third day must be his truthful day and (since the statement on teh first day is false) His truthful day must be Monday or Tuesday.\r\n\r\nThe only possible first day to allow teh third day to be Monday or tuesday is Sunday so Bob tells the truth on Tuesday',NULL,0);
INSERT INTO comment VALUES (7132,1110,3109,'Roger','re: Simple','2003-08-15 09:25:59',0,'no...that is the probability of getting both of them.\r\nTo only make one shot of two you take 80% times 20% and get 16% chance of only making one.',7130,0);
INSERT INTO comment VALUES (7133,500,3111,'Richard','aint got a clue but.....','2003-08-15 10:42:08',0,'suicide- thts just a stupid answer aint it?',NULL,0);
INSERT INTO comment VALUES (7134,574,3111,'Richard','solution','2003-08-15 11:07:04',0,'Mr East took the north road.\r\nMr West took the east road\r\nMr South took the west road\r\nMr North took the soth road\r\n\r\ni might have got this wrong because of rushing',NULL,0);
INSERT INTO comment VALUES (7135,1110,2899,'Brian Wainscott','re(2): Simple','2003-08-15 11:11:09',3,'no..that is the probability of getting just the first one.\r\nTo make only one shot of two you take 80% * 20% for making the first and missing the second, plus 20% * 80% for missing the first and making the second, and get a 32% chance of making only one of the two. The complete breakdown is:\r\n\r\n64% of making both (80% * 80%)\r\n%32 of making exactly one (80%*20% + 20%*80%)\r\n%4 of making neither (20%*20%)',7132,0);
INSERT INTO comment VALUES (7136,1110,1567,'Bryan','re(3): Simple','2003-08-15 11:52:31',3,'Actually, Roger was right, although he did not explain why. Whether the player hits his first shot or not, he gets a second shot, so the first shot can do nothing but help him and he will therefore try his best. Result: 80%.\r\n A B C D E F G H I J K L M N O P Q R S T U V W X Y Z\r\nA o x x x x x x x x x x x x x x x o x x\r\nB x x x x x x x x\r\nC x x o x x x x x o x x x o x x x x x x x\r\nD x x o x x x x x o x x x\r\nE x x x x x x x x\r\nF x x x x x x x x x x\r\nG x x x o o x x x x\r\nH x x x o o x x x x\r\nI x x x x x x x x x x x x\r\nJ x x o x x x x x o x x x o x x x x x x x\r\nK x x x x x o x x o x x x x\r\nL x x x x x\r\nM x x x x x x\r\nN x x x x x x x x\r\nO x x o x x x x x o x x x o x x x x x x x\r\nP x x x x x o x x o x x x x\r\nQ\r\nR x x o x x x x x o x x x\r\nS x x x x x x x x x x\r\nT x x x x x x x x x x\r\nU x x x x x x x x x x x x\r\nV x x x x x x x\r\nW o x x x x x x x x x x x x x x x o x x\r\nX x x x x\r\nY x x x x x x x x x\r\nZ\r\n
\r\nwith Q and Z absent because they aren\'t on the cubes.\r\n\r\nThe x\'s indicate they can\'t be together and the o\'s that they must be together.\r\n\r\nAllowable letters to share with the ones already on our cubes are:\r\nAW: BLMTU\r\nCOJ: ENVX\r\nPK: BDGHILNRVXY\r\nS: BDEFGHLMNRSUVY\r\n\r\nT appears only on the AW cube, and I only on the PK list, so they must actually be on those respective cubes.\r\n\r\nThen TURN prevents U from appearing on what\'s now the AWT cube.\r\n\r\nThen going back through the words one by one, letters can be placed on the appropriate cubes:\r\n\r\nAWTLBM\r\nCOJXEN\r\nPKIYDR\r\nSFVUHG',NULL,0);
INSERT INTO comment VALUES (7169,1115,3136,'Dave Cheetham','','2003-08-17 12:21:44',0,'I\'m going with the same method, assuming that vertical lines on C and D are the same through half rotations.\r\nLCM(35,27,42,17)=32130\r\n32130/35=918 rotations of A',NULL,0);
INSERT INTO comment VALUES (7170,1110,3136,'Dave Cheetham','','2003-08-17 12:23:40',0,'Not being a basketball player myself, I\'d go with 32% (2*0.8*0.2) but that\'s just because I don\'t know the rebound rules!',NULL,0);
INSERT INTO comment VALUES (7171,600,3136,'Dave Cheetham','','2003-08-17 12:26:48',0,'He\'s sold the box of 29. \r\nNow the 14 and 16 are one colour, the 5, 7, 18 are the other colour.',NULL,0);
INSERT INTO comment VALUES (7172,1094,3136,'Dave Cheetham','','2003-08-17 12:32:09',0,'9/7 or 63/3 or ...\r\nThese solutions all assume that age can only be measured in integer intervals. Technically there are infinite solutions that satisfy:\r\ny=567/x^2',NULL,0);
INSERT INTO comment VALUES (7173,1106,3136,'Dave Cheetham','Solution using proportions','2003-08-17 12:51:45',0,'Proportion of Smokers = 0.208333\r\nProportion of Drinkers = 0.787879\r\nProportion of Drivers = 0.621622\r\nProportion of Computer Owners = 0.83\r\n\r\nTherefore proportion of (Smoker AND Drinker AND Driver AND Computer Owner) \r\n= 0.208333*0.787879*0.621622*0.83\r\n= 0.084688\r\n= 84688097 people',NULL,0);
INSERT INTO comment VALUES (7174,1103,3136,'Dave Cheetham','','2003-08-17 13:12:19',0,'Surely they only get one go at the safe within a reasonable time frame. I assume a £1 million fine would also include a hefty jail term. However this assumption doesn\'t effect my solution.\r\n\r\nFor each go at 60^5 combinations:\r\nProbability = 1/60^5\r\n = 0.0000001286% of getting £100 billion.\r\nTherefore, their expected cash inflow is £1286.0023\r\n\r\nHowever, they may get it wrong:\r\nProbability = 99.9999998714% of losing £1 million.\r\nTherefore, their expected cash outflow is £999999.9987\r\n\r\nGiving their overall expected cash flow:\r\n= £1286.0023 - £999999.9987\r\n= -£998713.9905\r\n\r\nTherefore, they can expect to lose £998713.9905 each time they try to crack the safe.',NULL,0);
INSERT INTO comment VALUES (7175,1074,3136,'Dave Cheetham','Overactive Curiosity','2003-08-17 13:25:14',0,'Grrr... Damn me and my overactive curiosity. I was most of the way through working it out and I peeked at the answer. That takes all the fun out of it! Now I\'ve gotta find a new problem!',NULL,0);
INSERT INTO comment VALUES (7176,228,3136,'Dave Cheetham','','2003-08-17 13:42:51',0,'\"is\", \"errors\" & \"thise\"\r\n\r\nBut there\'s two errors in my answer...',NULL,0);
INSERT INTO comment VALUES (7177,1015,3136,'Dave Cheetham','','2003-08-17 13:51:21',0,'The man was OBVIOUSLY walking on his hands. That meant the numbers were upside down.\r\nOh and it should be noted that the shop he was handstand-walking towards was called \"11-L\".',NULL,0);
INSERT INTO comment VALUES (7178,929,3136,'Dave Cheetham','Good Q','2003-08-17 13:55:17',0,'It was a good question Gamer, definately had me thinking until I looked at the first comment. ',NULL,0);
INSERT INTO comment VALUES (7179,1110,1575,'DJ','re: how to win','2003-08-17 14:50:41',1,'Whoa, buddy...that all may sound good, but nothing that would even happen in a game..\r\n\r\nFirst, the ultimate strategy in this case would invariably be to try to make both foul shots and put the game into overtime. So, he will always try to make the first shot.\r\n\r\nThen, if he makes the first shot, the strategy is unchanged. He is always going to try to make the second shot if he had made the first.\r\n\r\nIf he misses the first shot, then making the second shot will do no good. They\'ll still be down by a point, and the other team gets the ball with only 1.7 seconds left.\r\n\r\nThe only viable choice here is to intentionally miss the second shot, hoping for a teammate to get the rebound and put the ball back up for two points and a tie.\r\n\r\nAlso, do you know how hard it is to bounce a ball off the backboard, from the free throw line (15 feet away), and make it out to the three-point line (20-24 feet out)? Add that to the fact that he has only one teammate back there, with a man on him, and his other three teammates are between him and the basket -- they\'re not going to try it. Not that it changes the answer to this question at all, except that he\'s probably more likely to accidentally make the shot if he\'s trying to put it out to the 3-point line than dropping it inside the key.\r\n\r\nEven still, 2 foul shots by an 80% shooter in a two-point game is far from hopeless, so while miracles do indeed happen every day, one will likely not even be necessary for this game.',7148,0);
INSERT INTO comment VALUES (7180,842,3143,'Vito','got it!','2003-08-17 22:28:10',0,'The mother told her child to stomp away, sit down, and sulk. The child obeyed...yes???',NULL,0);
INSERT INTO comment VALUES (7181,1121,3144,'rose albrecht','You Got Me!','2003-08-18 01:50:35',0,'I was stumped. I couldn\'t figure it out. There seemed to me that there were 3 possible solutions, Very clever that the knight would be the clue that lets you figure this out. This was difficult for me to figure out.',NULL,0);
INSERT INTO comment VALUES (7182,1112,2203,'kyle','re: solution','2003-08-18 02:15:26',0,'wow! my pea hurts just thinking about it.',7168,0);
INSERT INTO comment VALUES (7183,599,2682,'exoticorn','solution','2003-08-18 08:36:36',3,'Jugs: 12 0 0\r\nfill the 8 litre jug from the 12 litre one, then fill the 5 litre jug from the 8 litre one.\r\nJugs: 4 3 5\r\nEmpty the 5 litre jug into the 12 litre one, and the 8 litre one into the 5 litre one.\r\nJugs: 9 0 3\r\nFill the 8 litre jug from the 12 litre one, then the 5 litre one from the 8 litre one.\r\nJugs: 1 6 5\r\nFinally empty the 5 litre one into the 12 litre one.\r\nJugs: 6 6 0',NULL,0);
INSERT INTO comment VALUES (7184,599,1575,'DJ','Solution','2003-08-18 09:55:13',3,'Here are the amounts in each jug for the method I came up with, step by step:\r\n\r\n 12 8 5\r\n------------\r\n 12 0 0\r\n 4 8 0\r\n 4 3 5\r\n 9 3 0\r\n 9 0 3\r\n 1 8 3\r\n 1 6 5\r\n 6 6 0\r\n\r\n
\r\nThat is the shortest solution I could find, requiring seven steps.',NULL,0);
INSERT INTO comment VALUES (7185,599,2839,'FatBoy','Solution','2003-08-18 10:23:33',0,'use the 12 liter jug to fill the 8 liter jug\r\nleaving 4 liters in the 12 liter jug.\r\nUse the 8 liter jug to fill the 5 liter jug this leaves 4 L. in the 12 L jub,\r\n 3 L in the 8 L jug \r\n 5 L in the 5 L jug\r\nEmpty the 5 L. Jug into the 12 L. Jug and then empty the 8 L. jug into the (now empty) 5L jug\r\nThis leaves\r\n 9 L in the 12 L jug\r\n 0 L in the 8 L jug\r\n 3 L in the 5 L jug\r\nFill the 8 L jug from teh 12 L jug\r\nThis Leaves\r\n 1 L in the 12 L Jug\r\n 8 L in the 8 L jug\r\n 3 L in the 5 L jug\r\nTop off the 5 L jug from the 8 L jug this leaves:\r\n 1 L in the 12 L jug\r\n 6 L in the 8 L jug \r\n 5 L in the 5 L jug\r\npoor the 5 L jug baack into the 12 L jug adn you are done',NULL,0);
INSERT INTO comment VALUES (7186,1121,3146,'TheGreatOne','Solution','2003-08-18 11:27:14',3,'Got the solution !\r\n\r\nBenny\'s a Knave and Lenny\'s ia a Liar.\r\n\r\nThought process:\r\n\r\nGiven the problem there are three possible combinations:\r\n\r\nBenny Lenny\r\nLiar Knave\r\nKnave Liar\r\nKnave Knave\r\n\r\nIf one knows that Lenny is a Liar then only can she figure out what Benny is , hence the answer\r\n\r\ncheers',NULL,0);
INSERT INTO comment VALUES (7187,1112,1686,'DuCk','re: solution','2003-08-18 12:27:44',0,'I\'ve got mine written down on scraps of paper but came up with the same thing. Awesome description, Charlie! Must have taken you forever to type it.\r\n\r\nAnswer:\r\n\r\nA,L,M,T,W,B\r\nX,O,C,N,E,J\r\nI,K,R,D,P,Y\r\nS,F,H,G,U,V',7168,0);
INSERT INTO comment VALUES (7188,234,2839,'FatBoy','solution','2003-08-18 13:31:53',3,'anagrams',NULL,0);
INSERT INTO comment VALUES (7189,946,3146,'TheGreatOne','re: \'shaky\' response','2003-08-18 15:35:53',0,'I would def. do this ;)',6132,0);
INSERT INTO comment VALUES (7190,914,3146,'TheGreatOne',':)','2003-08-18 15:39:15',3,'That\'s because you stop looking when you find the \"thing\" !',NULL,0);
INSERT INTO comment VALUES (7191,1122,3091,'Hans','solution','2003-08-18 17:07:49',1,'The Liar is telling you which door they will tell, which is not the exit, and a door that the Knight would not offer as your exit.\r\n\r\nThe Knight is telling you which door is not an exit and is picking a door that the Liar could offer as the exit.\r\n\r\nWith this, none of the answers given could be your exit regardless of who is the Liar or Knight.\r\nDoor D leads you out. \r\n',NULL,0);
INSERT INTO comment VALUES (7192,1089,3151,'Jason Asher','A preliminary thought for half of a solution','2003-08-18 18:01:22',0,'One can easily prove that n cannot be odd:\r\n\r\nSuppose that n = 2m + 1 for an integer m, and further suppose that q^3 = n^2 + 3 for an integer q. Then by substitution we would have that q^3 = 4m^2 + 4m +4 = 4(m^2 + m + 1).\r\n\r\nBy considering the prime factorization of q^3 we see that in order for the above equation to be true, m^2 + m + 1 must be\r\neven (for else there will not be sufficient powers of 2 in q^3).\r\nHowever, this is impossible as that expression always results in an odd output for integral entries.\r\n\r\nHow does that sound?',NULL,0);
INSERT INTO comment VALUES (7193,1089,2899,'Brian Wainscott','re: A preliminary thought for half of a solution','2003-08-18 19:31:32',0,'Looks correct -- that takes care of half of them.\r\n\r\nI don\'t see a similar analysis for even n.\r\n\r\nMaybe some headway could be made mod p (p prime)?',7192,0);
INSERT INTO comment VALUES (7194,1122,2781,'Jonathan Shaw','Solution','2003-08-19 02:58:47',0,'It has to be D',NULL,0);
INSERT INTO comment VALUES (7195,1112,2781,'Jonathan Shaw','solution','2003-08-19 03:15:43',0,'Cube 1: ALWBMT\r\nCube 2: OCENJX\r\nCube 3: HGUVSF\r\nCube 4: DRYPKI',NULL,0);
INSERT INTO comment VALUES (7196,1134,1686,'DuCk','Solution','2003-08-19 07:30:18',3,'The word is Startling and it decomposes as follows: \r\n\r\nStartling\r\nstarting\r\nstaring\r\nstring\r\nsting\r\nsing\r\nsin\r\nin\r\nI',NULL,0);
INSERT INTO comment VALUES (7197,374,2839,'FatBoy','It seems to me..','2003-08-19 07:36:41',3,'That there cold be as few as four people there',NULL,0);
INSERT INTO comment VALUES (7198,374,2839,'FatBoy','re: It seems to me..','2003-08-19 07:38:41',0,'In defense of my answer, the riddle does not specify that the relations mentioned must have theri recipricol partners present.\r\nby this I mean a man is someones son whether or not his father is present',7197,0);
INSERT INTO comment VALUES (7199,1134,2840,'Becky','re: Solution','2003-08-19 08:22:33',0,'Very Nice, did you already know it or figure it out?',7196,0);
INSERT INTO comment VALUES (7200,355,2839,'FatBoy','Humpf','2003-08-19 08:26:24',1,'THe car most certainly does not pass through 0 MPH the cars velocity does not change more than very slightly.\r\nThe fly accelerates in the direction of the car as it comes in contact with it.\r\n\r\nThink of it from the cars\'s frame of reference. In that frame of reference teh car is stationaryn and the fly in flying toward it at 85km/h. when the fly hits the car it comes to a halt (in the car\'s frame of reference) it does not move the car more than fractionally.',NULL,0);
INSERT INTO comment VALUES (7201,1134,1301,'Charlie','computer search','2003-08-19 08:59:50',3,'Solving via computer, and deleting lines with more uncommon words produces the following list:\r\n\r\n(This includes a couple of extra sequences starting with startling, and the more common starting words include cleansers, restarted, roadsters, splatters, stampeded, starlings, strapping, trampling, trappings and wrappings.)\r\n\r\nabridgers abridges bridges ridges rides rids rid id I\r\nabridgers abridges bridges ridges rides ride rid id I\r\nabridgers abridges bridges ridges ridge ride rid id I\r\nabridgers abridges bridges brides rides rids rid id I\r\nabridgers abridges bridges brides rides ride rid id I\r\nabridgers abridges bridges brides bides bids bid id I\r\nabridgers abridges bridges brides bides bide bid id I\r\nabridgers abridges bridges brides bride ride rid id I\r\nabridgers abridges bridges brides bride bide bid id I\r\nabridgers abridges bridges bridge ridge ride rid id I\r\nabridgers abridges bridges bridge bride ride rid id I\r\nabridgers abridges bridges bridge bride bide bid id I\r\nabridgers abridges abridge bridge ridge ride rid id I\r\nabridgers abridges abridge bridge bride ride rid id I\r\nabridgers abridges abridge bridge bride bide bid id I\r\nabridgers abridger abridge bridge ridge ride rid id I\r\nabridgers abridger abridge bridge bride ride rid id I\r\nabridgers abridger abridge bridge bride bide bid id I\r\ncleansers cleanses cleanse cleans clans cans can an a\r\ncleansers cleanses cleanse cleans clans clan can an a\r\ncleansers cleanses cleanse cleans clean clan can an a\r\ncleansers cleanser cleanse cleans clans cans can an a\r\ncleansers cleanser cleanse cleans clans clan can an a\r\ncleansers cleanser cleanse cleans clean clan can an a\r\npilasters plasters pasters pastes pates pats pat at a\r\npilasters plasters pasters pastes pates pate ate at a\r\npilasters plasters pasters pastes pates pate pat at a\r\npilasters plasters pasters pastes paste pate ate at a\r\npilasters plasters pasters pastes paste pate pat at a\r\npilasters plasters pasters pastes paste past pat at a\r\npilasters plasters pasters paster paste pate ate at a\r\npilasters plasters pasters paster paste pate pat at a\r\npilasters plasters pasters paster paste past pat at a\r\npilasters plasters plaster laster later late ate at a\r\npilasters plasters plaster paster paste pate ate at a\r\npilasters plasters plaster paster paste pate pat at a\r\npilasters plasters plaster paster paste past pat at a\r\npilasters piasters pasters pastes pates pats pat at a\r\npilasters piasters pasters pastes pates pate ate at a\r\npilasters piasters pasters pastes pates pate pat at a\r\npilasters piasters pasters pastes paste pate ate at a\r\npilasters piasters pasters pastes paste pate pat at a\r\npilasters piasters pasters pastes paste past pat at a\r\npilasters piasters pasters paster paste pate ate at a\r\npilasters piasters pasters paster paste pate pat at a\r\npilasters piasters pasters paster paste past pat at a\r\npilasters piasters piaster paster paste pate ate at a\r\npilasters piasters piaster paster paste pate pat at a\r\npilasters piasters piaster paster paste past pat at a\r\npilasters pilaster plaster laster later late ate at a\r\npilasters pilaster plaster paster paste pate ate at a\r\npilasters pilaster plaster paster paste pate pat at a\r\npilasters pilaster plaster paster paste past pat at a\r\npilasters pilaster piaster paster paste pate ate at a\r\npilasters pilaster piaster paster paste pate pat at a\r\npilasters pilaster piaster paster paste past pat at a\r\nrestarted restated restate estate state sate ate at a\r\nrestarted restated restate estate state sate sat at a\r\nrestarted restated restate estate state stat sat at a\r\nroadsters roasters rasters raters rates rats rat at a\r\nroadsters roasters rasters raters rates rate ate at a\r\nroadsters roasters rasters raters rates rate rat at a\r\nroadsters roasters rasters raters rater rate ate at a\r\nroadsters roasters rasters raters rater rate rat at a\r\nroadsters roasters rasters raster rater rate ate at a\r\nroadsters roasters rasters raster rater rate rat at a\r\nroadsters roasters roaster raster rater rate ate at a\r\nroadsters roasters roaster raster rater rate rat at a\r\nroadsters roadster roaster raster rater rate ate at a\r\nroadsters roadster roaster raster rater rate rat at a\r\nshinglers shingles singles singes sines sins sin in I\r\nshinglers shingles singles singes sines sine sin in I\r\nshinglers shingles singles singes sings sins sin in I\r\nshinglers shingles singles singes sings sing sin in I\r\nshinglers shingles singles singes singe sine sin in I\r\nshinglers shingles singles singes singe sing sin in I\r\nshinglers shingles singles single singe sine sin in I\r\nshinglers shingles singles single singe sing sin in I\r\nshinglers shingles shingle single singe sine sin in I\r\nshinglers shingles shingle single singe sing sin in I\r\nshinglers shingler shingle single singe sine sin in I\r\nshinglers shingler shingle single singe sing sin in I\r\nsparkling sparking sparing spring sprig prig pig pi I\r\nsplatters platters platter latter later late ate at a\r\nsplatters platters platter latter later late ate at a\r\nsplatters splatter platter latter later late ate at a\r\nsplatters splatter platter latter later late ate at a\r\nstampeded stampede stamped tamped tamed tame tam am a\r\nstampedes stampede stamped tamped tamed tame tam am a\r\nstarlings starling staring string sting sing sin in I\r\nstartling starling staring string sting sing sin in I\r\nstartling starting stating sating sting sing sin in I\r\nstartling starting staring string sting sing sin in I\r\nstrapping trapping rapping raping aping ping pig pi I\r\nstrapping trapping rapping raping aping ping pin in I\r\nstrapping trapping rapping raping aping ping pin pi I\r\nstrapping trapping rapping raping aping ping pig pi I\r\nstrapping trapping rapping raping aping ping pin in I\r\nstrapping trapping rapping raping aping ping pin pi I\r\nstrapping trapping tapping taping aping ping pig pi I\r\nstrapping trapping tapping taping aping ping pin in I\r\nstrapping trapping tapping taping aping ping pin pi I\r\nstrapping trapping tapping taping aping ping pig pi I\r\nstrapping trapping tapping taping aping ping pin in I\r\nstrapping trapping tapping taping aping ping pin pi I\r\nstringers stingers singers singes sines sins sin in I\r\nstringers stingers singers singes sines sine sin in I\r\nstringers stingers singers singes sings sins sin in I\r\nstringers stingers singers singes sings sing sin in I\r\nstringers stingers singers singes singe sine sin in I\r\nstringers stingers singers singes singe sing sin in I\r\nstringers stingers singers singer singe sine sin in I\r\nstringers stingers singers singer singe sing sin in I\r\nstringers stingers stinger singer singe sine sin in I\r\nstringers stingers stinger singer singe sing sin in I\r\nstringers stringer stinger singer singe sine sin in I\r\nstringers stringer stinger singer singe sing sin in I\r\nstringier stingier stinger singer singe sine sin in I\r\nstringier stingier stinger singer singe sing sin in I\r\nstringier stringer stinger singer singe sine sin in I\r\nstringier stringer stinger singer singe sing sin in I\r\ntramplers trampers tampers tamers tames tams tam am a\r\ntramplers trampers tampers tamers tames tame tam am a\r\ntramplers trampers tampers tamers tamer tame tam am a\r\ntramplers trampers tampers tamper tamer tame tam am a\r\ntramplers trampers tramper tamper tamer tame tam am a\r\ntramplers trampler tramper tamper tamer tame tam am a\r\ntrampling tramping tamping taping aping ping pig pi I\r\ntrampling tramping tamping taping aping ping pin in I\r\ntrampling tramping tamping taping aping ping pin pi I\r\ntrappings trapping rapping raping aping ping pig pi I\r\ntrappings trapping rapping raping aping ping pin in I\r\ntrappings trapping rapping raping aping ping pin pi I\r\ntrappings trapping rapping raping aping ping pig pi I\r\ntrappings trapping rapping raping aping ping pin in I\r\ntrappings trapping rapping raping aping ping pin pi I\r\ntrappings trapping tapping taping aping ping pig pi I\r\ntrappings trapping tapping taping aping ping pin in I\r\ntrappings trapping tapping taping aping ping pin pi I\r\ntrappings trapping tapping taping aping ping pig pi I\r\ntrappings trapping tapping taping aping ping pin in I\r\ntrappings trapping tapping taping aping ping pin pi I\r\nwrappings wrapping rapping raping aping ping pig pi I\r\nwrappings wrapping rapping raping aping ping pin in I\r\nwrappings wrapping rapping raping aping ping pin pi I\r\nwrappings wrapping rapping raping aping ping pig pi I\r\nwrappings wrapping rapping raping aping ping pin in I\r\nwrappings wrapping rapping raping aping ping pin pi I\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (7202,1134,1301,'Charlie','re: computer search-- the program','2003-08-19 09:05:00',0,'DECLARE SUB subtlet (w$)\r\nDECLARE FUNCTION isWord! (w$)\r\nDIM SHARED hist$(10)\r\n\r\nCLS\r\nOPEN \"bwords9.txt\" FOR BINARY AS #1\r\nOPEN \"9lets.txt\" FOR OUTPUT AS #3\r\nw$ = SPACE$(9)\r\n\r\nDO\r\n GET #1, , w$\r\n hist$(LEN(w$)) = w$\r\n subtlet w$\r\nLOOP UNTIL EOF(1)\r\n\r\nCLOSE\r\n\r\nFUNCTION isWord (w$)\r\n n = LEN(w$)\r\n IF w$ = \"i\" THEN isWord = 1: EXIT FUNCTION\r\n w1$ = SPACE$(n)\r\n IF n > 2 THEN\r\n OPEN \"bwords\" + LTRIM$(STR$(n)) + \".txt\" FOR BINARY AS #2\r\n ELSE\r\n OPEN \"words\" + LTRIM$(STR$(n)) + \".txt\" FOR BINARY AS #2\r\n END IF\r\n l = LOF(2) / n\r\n low = 1: high = l\r\n DO\r\n mid = INT((low + high) / 2)\r\n GET #2, (mid - 1) * n + 1, w1$\r\n IF w1$ = w$ THEN isWord = 1: CLOSE 2: EXIT FUNCTION\r\n IF w1$ < w$ THEN low = mid + 1: ELSE high = mid - 1\r\n LOOP UNTIL low > high\r\n isWord = 0\r\n CLOSE 2\r\nEND FUNCTION\r\n\r\nSUB subtlet (w$)\r\n FOR i = 1 TO LEN(w$) \' STEP LEN(w$) - 1\r\n w2$ = LEFT$(w$, i - 1) + MID$(w$, i + 1)\r\n IF isWord(w2$) THEN\r\n hist$(LEN(w2$)) = w2$\r\n IF LEN(w2$) = 1 THEN\r\n FOR j = 9 TO 1 STEP -1\r\n PRINT hist$(j); \" \";\r\n NEXT\r\n PRINT\r\n FOR j = 9 TO 1 STEP -1\r\n PRINT #3, hist$(j); \" \";\r\n NEXT\r\n PRINT #3,\r\n ELSE\r\n subtlet w2$\r\n END IF\r\n END IF\r\n NEXT\r\nEND SUB\r\n\r\n',7201,0);
INSERT INTO comment VALUES (7203,1134,1301,'Charlie','re(2): computer search-- the program','2003-08-19 09:07:50',0,'By the way, in the line\r\n\r\n FOR i = 1 TO LEN(w$) \' STEP LEN(w$) - 1 \r\n\r\nthe latter part is commented out by the apostrophe. When not commented out it limited the dropping of letters to the first and last letter of each successive word.',7202,0);
INSERT INTO comment VALUES (7204,1134,1686,'DuCk','re(2): Solution','2003-08-19 12:16:01',0,'Becky, are you doubting my skills? LOL! No, I actually knew that. From where? I don\'t know...',7199,0);
INSERT INTO comment VALUES (7205,1134,1686,'DuCk','re: computer search','2003-08-19 12:18:36',0,'I am fully convinced.........Charlie........is a genius!!!',7201,0);
INSERT INTO comment VALUES (7206,1114,1626,'Gamer','Specifications?','2003-08-19 15:27:24',4,'Does this mean C = H and I = N? Also, are only integers allowed? Somehow I thought they were, but I read through the problem and it doesn\'t say anything about that...',NULL,0);
INSERT INTO comment VALUES (7207,1114,1301,'Charlie','solution -- analysis plus trial and error','2003-08-19 15:53:55',3,'Assuming that C must in fact be equal to H and I equal to N, we know\r\n\r\np=ej\r\nl=5g\r\ni=5g-k-j\r\nn=5g-k-j\r\nh=ej-k-g\r\nc=ej-k-g\r\nn=5g-k-j\r\nf=ej-k-2g-e\r\nf=5g-k-2j-5\r\n\r\nfrom these last two, 7g=ej+2j-e+5\r\n\r\nThus various combinations of e and j produce what may or may not be valid (integral) g. We can then try various combinations of a and k to see if the product q is equal to d+h+l and to m+n+p where d=a+b+c and m is a+e+i.\r\n\r\nNot wanting to do this by hand, I made a program:\r\n\r\nCLS\r\nsum = 2\r\nDO\r\n FOR j = 0 TO sum\r\n e = sum - j\r\n g = (e * j + 2 * j - e + 5) / 7\r\n IF g = INT(g) AND g >= 0 THEN\r\n FOR k = 0 TO 50\r\n FOR a = 0 TO 50\r\n IF e * j - k - 2 * g - e > 0 AND 5 * g - k - j > 0 THEN\r\n IF a * (e * j - k - 2 * g - e) * k = a + 5 + 2 * (e * j - k - g) + 5 * g THEN\r\n IF a + e + 5 * g - k - j + 5 * g - k - j + e * j = a * (e * j - k - 2 * g - e) * k THEN\r\n PRINT USING \"####\"; a;\r\n PRINT USING \"####\"; 5;\r\n PRINT USING \"####\"; e * j - k - g;\r\n PRINT USING \"####\"; a + 5 + e * j - k - g\r\n\r\n PRINT USING \"####\"; e;\r\n PRINT USING \"####\"; e * j - k - 2 * g - e;\r\n PRINT USING \"####\"; g;\r\n PRINT USING \"####\"; e * j - k - g\r\n\r\n PRINT USING \"####\"; 5 * g - k - j;\r\n PRINT USING \"####\"; j;\r\n PRINT USING \"####\"; k;\r\n PRINT USING \"####\"; 5 * g\r\n\r\n PRINT USING \"####\"; a + e + 5 * g - k - j;\r\n PRINT USING \"####\"; 5 * g - k - j;\r\n PRINT USING \"####\"; e * j;\r\n PRINT USING \"####\"; a * (e * j - k - 2 * g - e) * k\r\n PRINT \"-\"\r\n DO: LOOP UNTIL INKEY$ > \"\"\r\n END IF\r\n END IF\r\n END IF\r\n NEXT\r\n NEXT\r\n\r\n END IF\r\n NEXT\r\n sum = sum + 1\r\nLOOP\r\n\r\nthe first several resulting arrays are:\r\n\r\n 21 5 11 37\r\n 5 3 3 11\r\n 11 3 1 15\r\n 37 11 15 63\r\n-\r\n 19 5 9 33\r\n 5 1 3 9\r\n 9 3 3 15\r\n 33 9 15 57\r\n-\r\n 11 5 15 31\r\n 5 6 4 15\r\n 15 4 1 20\r\n 31 15 20 66\r\n-\r\n 9 5 10 24\r\n 5 1 4 10\r\n 10 4 6 20\r\n 24 10 20 54\r\n
\r\n-\r\nof which the second has the desired highest number of 57.',NULL,0);
INSERT INTO comment VALUES (7208,687,3026,'Drew Skau','Density','2003-08-19 18:04:50',3,'Under normal gravitational conditions, the cork would float to the top because the water is denser. The speed the cork moves to the top of the bucket relative to the force the water is displacing it with. Since there is no force of gravity acting on the bucket or its contents during free fall, the cork should not float. If the cork were floating to begin with it would not sink either.',NULL,0);
INSERT INTO comment VALUES (7209,777,1575,'DJ','re:','2003-08-19 18:50:00',1,'You are mistaken..a plane is not another word for a line. A plane is an infinite 2-dimensional region, like a piece of paper that never ends, while line only has one dimension, stertching infinitely in either direction.\r\n\r\nWhat you described is a line segment, part of a line with two definite endpoints, and an infinite number of points between them, since between any two points another point can be placed.',6909,0);
INSERT INTO comment VALUES (7210,1114,1575,'DJ','Solution','2003-08-19 18:52:28',0,'Other than trial-and-error (or having a computer do it for you), can anyone come up with a way to logically explain how to get the answer? The numerical answer is out there now, but this problem hasn\'t been laid to rest just yet..',NULL,0);
INSERT INTO comment VALUES (7211,1089,1626,'Gamer','Even idea?','2003-08-19 18:54:00',2,'If n was even, then n² must end in 0, 4 or 6. This means that n²+3 must end in 3, 7 or 9, and this means b³ (the perfect cube) ends with the same numbers, so b must end with 3, 7, 9\r\n\r\na, (the one whose cube is n + 3), must end in 1, 3, 5, 7, 9. \r\n\r\nEnds with:\r\n\r\nn a b\r\n0 7 7\r\n2 5 3\r\n4 3 9\r\n6 9 9\r\n8 1 3',NULL,0);
INSERT INTO comment VALUES (7212,1114,3167,'Dino','The solution isn\'t hard if you...','2003-08-20 05:00:59',0,'assume that the resulting matrix is symmetrical across the NW-SE line. It\'s pretty easy to write simple equations for the various lines in the matrix and solve them with that assumption. I found two similar solutions.',NULL,0);
INSERT INTO comment VALUES (7213,263,3163,'Evan','The tortoise and the hairy Paradox','2003-08-20 05:51:53',0,'The question does not even resemble the \"cant reach the wall going half way each time\" problem\r\nThe turtle would win in that situation if he kept a constant rate of acceleration and achilles ran at a constant unchanging velocity(even if faster than the turtle)',NULL,0);
INSERT INTO comment VALUES (7214,1114,1183,'fwaff','re: Solution - no trial and error or computers','2003-08-20 08:07:52',3,'As Dino has already observed, the square is symmetrical about the AFKQ diagonal. The question tells us that B=5, C=H, I=N. We can also deduce that Q=57 since the highest value in the grid is 57 and Q > all the other values (assuming that they are all positive integers). This transforms the grid to:\r\n\r\nA 5 C D\r\n5 F G C\r\nC G K 5G\r\nD C 5G 57\r\n\r\nSo we have the following equations:\r\n\r\nA+5+C=D\r\n5+F+G=C\r\nC+G+K=5G\r\nD+C+5G=57\r\nA*F*K=57\r\n\r\nThe only factors of 57 are 1,3 and 19, therefore {A,F,K} = {1,3,19}. Which also gives:\r\n\r\nA+F+K=23\r\n\r\nNow we have 6 equations and 6 unknowns. By numerous substitutions through the above equations it\'s possible to get to:\r\n\r\n2A-3F=35\r\n3G=28-A ie G=9-(A-1)/3 \r\n\r\nThe first of these shows that A>F, therefore A = 3 or 19.\r\nThe second equation shows that (A-1) must be divisible by 3.\r\nTherefore the two equations show that A=19.\r\n\r\nSubstituting this back through the equations gives the same grid that Charlie obtained with his program.',7210,0);
INSERT INTO comment VALUES (7215,718,3169,'Yoseph','re: Possible solution','2003-08-20 08:10:21',0,'ã(2^-31*e) \r\nisn\'t this bigger than\r\n(2^-31*e)\r\nwhen you square root a number lower than one it\'s square root is bigger than the original number.',7147,0);
INSERT INTO comment VALUES (7216,1134,2840,'Becky','re(3): Solution','2003-08-20 08:17:34',0,'I would NEVER doubt you my dear. Hey, I can\'t figure any of this stuff out. ',7204,0);
INSERT INTO comment VALUES (7217,718,3169,'Yoseph','What\'s wrong','2003-08-20 08:20:31',0,'Does zero count: 1+2-3=0\r\nIf this is the solution then it\'s a very misleading question and you should be shot Alan.\r\ntan(2^-(31!)) is the closest to zero I could get assuming you can\'t use more numbers like e(2.8) or other algegbraic notations of values like pi. \r\n',NULL,0);
INSERT INTO comment VALUES (7218,1114,1301,'Charlie','can it be shown ...','2003-08-20 08:32:47',4,'... that the solution must be symmetric with respect to the major NW-SE diagonal?',NULL,0);
INSERT INTO comment VALUES (7219,912,3169,'Yoseph','re: Impossible?','2003-08-20 08:35:58',0,'It\'s not impossible you need 20 peices to get to level 4 I worked that one through and it works, 5 is harder and I did it but I\'m trying to find the lowest number of attempts. You can jump pieces over each other on the back lines i.e. in the same line 0 to 0 and remove the piece you jumped off the board. level four isn\'t very hard, why so much trouble with it. DJ maybe you can show a worked solution, showing twenty moves in the style posed in the question is a bit long.\r\n',6072,0);
INSERT INTO comment VALUES (7220,602,2572,'derek','solution','2003-08-20 09:51:27',3,'there is 19.907% probability the solution is real\r\n\r\nfor each a, b, and c from 1 to 6, calculate b^2-4ac, and if it is >= 0, then the quadratic has real roots',NULL,0);
INSERT INTO comment VALUES (7221,602,1575,'DJ','Full Solution','2003-08-20 10:14:16',3,'The probability is a little less than 1/5.\r\n\r\nThe quadratic equation states that if\r\nax²+bx+c=0,\r\nthen\r\nx=[-b±√(b²-4ac)]/2a.\r\n\r\nThe part under the radical, b²-4ac, is called the determinant, because it determines what types of roots the equation will have. If the determinant is zero, then that term drops out, leaving one real root to the equation. If it is positive, there are two real roots, and if it is negative there are two imaginary or complex roots.\r\n\r\nI will assume for this problem, since it\'s not stated, that the condition of \'real roots\' includes a single real root, and we are looking for the probability that b²-4ac will be nonnegative.\r\n\r\nAnother way of saying that b²-4ac is nonnegative, is saying that:\r\nb²≥4ac .\r\nFurther:\r\n¼b²≥ac .\r\n\r\nLet\'s say we roll die B first. There are six possible values, of course. There are 6×6=36 possible ways to roll ac, and if we determine ¼b², this must be greater than or equal to ac.\r\n\r\nIf b is 1, then ¼b²=¼, and it is impossible for ac to be less than this. Therefore there is a probability of zero that the equation will have real roots if b=1.\r\n\r\nIf b=2, then ¼b²=1. The only way the could form a valid equation is if a and c are both 1, leaving -1 as the only root to the equation. Therefore, if b is 2, there is a 1/36 chance that the equation will have real roots.\r\n\r\nIf b=3, then ¼b²=9/4=2¼. There are three ordered pairs (a, c) for which this will work: (1, 1), (1, 2), and (2, 1). The probability of any of these is 3/36=1/12.\r\n\r\nIf b=4, ¼b²=4, and the valid values of (a, c) are:\r\n(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (3, 1), (4, 1). The chance of any of these is 8/36=2/9.\r\n\r\nIf b=5, ¼b²=25/4=6¼, and (a, c) must be one of:\r\n(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (4, 1), (5, 1), (6, 1). 14 of the 36 combinations are valid, so the chance of getting one of them is 14/36=7/18.\r\n\r\nFinally, if b is 6, ¼b²=9, and (a, c) can be any of:\r\n(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (5, 1), (6, 1). These are 17 out of 36 values.\r\n\r\nIn sum, the chance of b showing up as any given value is, of course, 1/6. The overall probability of finding any of the permutations described here is 1/6 of their sum, or: 1/6(0+1/36+1/12+2/9+7/36+17/36), or 43/(36×6). This evaluates to 0.199074074074..., which is the probability we are looking for.\r\n\r\nAnother approach could be to list all the valid ordered sets (a, b, c) of of 6×6×6=216 possible values. There will be 43, of course, yielding the same probability as above. The 43 valid ordered sets are:(1, 2, 1), (1, 3, 1), (1, 3, 2), (1, 4, 1), (1, 4, 2), (1, 4, 3), (1, 4, 4), (1, 5, 1), (1, 5, 2), (1, 5, 3), (1, 5, 4), (1, 5, 5), (1, 5, 6), (1, 6, 1), (1, 6, 2), (1, 6, 3), (1, 6, 4), (1, 6, 5), (1, 6, 6), (2, 3, 1), (2, 4, 1), (2, 4, 2), (2, 5, 1), (2, 5, 2), (2, 5, 3), (2, 6, 1), (2, 6, 2), (2, 6, 3), (2, 6, 4), (3, 4, 1), (3, 5, 1), (3, 5, 2), (3, 6, 1), (3, 6, 2), (3, 6, 3), (4, 4, 1), (4, 5, 1), (4, 6, 1), (4, 6, 2), (5, 5, 1), (5, 6, 1), (6, 5, 1), (6, 6, 1). As we can see, there are indeed 43 sets. Any other values will produce a negative determinant, so our solution is complete.',NULL,0);
INSERT INTO comment VALUES (7222,602,1301,'Charlie','re: solution','2003-08-20 10:19:30',0,'A program for doing this is:\r\nDEFDBL A-Z\r\nFOR a = 1 TO 6\r\n FOR b = 1 TO 6\r\n FOR c = 1 TO 6\r\n IF b * b > 4 * a * c THEN\r\n ct = ct + 1\r\n ELSEIF b * b = 4 * a * c THEN\r\n ct2 = ct2 + 1\r\n END IF\r\n NEXT\r\n NEXT\r\nNEXT\r\nPRINT USING \"##.########\"; ct / (6 * 6 * 6); ct2 / (6 * 6 * 6); ct / (6 * 6 * 6) + ct2 / (6 * 6 * 6)\r\n\r\nwhich counts separately the cases where there are two distinct real roots from those cases where there is a double root. The results come out:\r\n\r\n 0.17592593 0.02314815 0.19907407\r\nso the 19.9% probability of real roots is broken down into a 17.6% probability of two distinct real roots and 2.3% probability of a double real root.\r\n',7220,0);
INSERT INTO comment VALUES (7223,602,1575,'DJ','re: Full Solution','2003-08-20 10:39:21',1,'One other point I should make:\r\n\r\nIf it is said that there must indeed be two distinct real roots (a single real root where b²=4ac is no longer valid), then the sets (a, b, c) corresponding to (1, 2, 1), (1, 4, 4), (2, 4, 2), (4, 4, 1), and (3, 6, 3) would not be valid.\r\n\r\nThis eliminates 5 of the original 43 valid sets, leaving 38, for an overall probability of 38/216(=19/108), which evaluates to 0.17592592592... .\r\nThe chance of having exactly one real root, incidentally, is 5/216=.023148148148... .',7221,0);
INSERT INTO comment VALUES (7224,602,979,'Ravi Raja','Regarding the Problem: Levik','2003-08-20 10:59:06',0,'Levik: Could you please check the power of x in my problem. In place of 2 it has become I, or is it that I am seeing like that. I mean is there a problem with my comp or something like that or has it been posted like that? Could you please change it and correct it?',NULL,0);
INSERT INTO comment VALUES (7225,912,1575,'DJ','re(2): Impossible?','2003-08-20 11:14:54',0,'Actually, Yoseph, I\'ve been trying to show how to get to level 4 in twenty moves myself. I have the mathematical proofs that it is possible, but I want to put up the actual method to level 4 -- that lack is the only reason I haven\'t posted a solution. So, if you could post even the start of your method, I\'ll type it all out and post a full solution. By the way, good job for figuring it out! =)',7219,0);
INSERT INTO comment VALUES (7226,599,3171,'snapp','sloution','2003-08-20 12:50:32',1,'if the 12 litre jug is called a, the 8 litre jug b, and the 5 litre jug c then:\r\n\r\nA into B \r\nB into C\r\nC into A\r\nB into C\r\nA into B\r\nB into C\r\nC into A\r\n\r\n???\r\n',NULL,0);
INSERT INTO comment VALUES (7227,1089,3151,'Jason Asher','Solution','2003-08-20 13:33:56',0,'Three cheers for analytic number theory:\r\n\r\nIf both (n + 3) and (n^2 + 3) were perfect cubes, then their product would be a perfect cube as well.\r\n\r\nHowever, (n + 3)(n^2 + 3) = n^3 + 3n^2 +3n + 9 is bounded between the functions (n + 1)^3 and (n + 2)^3 for all values of n less than -3 and greater than zero, and thus cannot be a perfect cube in those instances. One then verifies that for the remaining four cases the above fact does not hold.\r\n\r\nProof of the above claims:\r\n(n + 1)^3 = n^3 + 3n^2 + 3n + 1\r\nThis is always 8 less than the polynomial in question, and thus forms a lower bound.\r\n(n + 2)^3 = n^3 + 6n^2 + 12n + 8\r\nsubtracting our polynomial from this we get:\r\n3n^2 + 9n - 1 which is greater than zero for values of n in the range described above.\r\n\r\nFurthermore, n^2 + 3 takes the values 12, 7, 4, and 3 for the remaining cases, none of which are perfect cubes.\r\n\r\nQED.\r\n\r\nCheers! Let me know what you think.',NULL,0);
INSERT INTO comment VALUES (7228,924,3171,'snapp','','2003-08-20 13:52:53',0,'i think that algerbra would be better taught using such a method',NULL,0);
INSERT INTO comment VALUES (7229,511,3171,'snapp','That one is good','2003-08-20 14:04:56',0,'i think i\'ll ask my religous family members\r\n',NULL,0);
INSERT INTO comment VALUES (7230,504,3171,'snapp','wording','2003-08-20 14:11:25',0,'i think that the solution might need rewording:\r\n\r\nif we assume that the fist statement is true, then the second statement is false. then the second statement is logically equivelent(spelling?) \"the previous statement is False.\" which would prove our assumtion wrong. \r\n\r\nThen starting with the assumption that the first statement is false. Then the second statement is conter to your assumtion again.\r\n\r\nIts the same answer just a different wording i think.\r\n',NULL,0);
INSERT INTO comment VALUES (7231,672,3171,'snapp','spliting the sheild','2003-08-20 14:15:12',0,'What if the sword kept cutting the sheild in half? Spliting the sheild doesn\'t mean that its destroyed and the splitting action can continue on to infinity.',NULL,0);
INSERT INTO comment VALUES (7232,476,3171,'snapp','would this work?','2003-08-20 14:17:55',0,'this statement is false?',NULL,0);
INSERT INTO comment VALUES (7233,49,3026,'Drew Skau','Not Completely Possible','2003-08-20 14:19:05',1,'The person going up the stairs would not walk exactly 10 feet from the center {right against the wall}. Chances are they would walk a fes feet away from the wall which would increase the radius. Without this information the best possible answer would be an approximation.',NULL,0);
INSERT INTO comment VALUES (7234,1138,3172,'Not Applicable','SOLUTION','2003-08-20 14:41:51',3,'The answer is 13467 (134 is double 67).\r\n\r\nEasily verified with the following C code:\r\n(which shows in the second column the only integral square root...)\r\n\r\n13467*3 = 40401 which is the square of 201.\r\n\r\n#include \"stdafx.h\"\r\n#include \"math.h\"\r\n\r\nint main(int argc, char* argv[])\r\n{\r\n int x, y;\r\n for (x=50; x<100; x+=1)\r\n {\r\n y=(200*x)+x;\r\n printf(\"%d\\t%f\\n\",y,sqrt(3*y));\r\n }\r\n return 0;\r\n}',NULL,0);
INSERT INTO comment VALUES (7235,1138,158,'Ender','Solution','2003-08-20 14:49:53',3,'The number is 13467. 67*2 = 134, and 13467*3 = 40401 = 201*201\r\n\r\nThis is how I found the number:\r\nThe splitting the number in two requirement means the number had to start with a 1. The largest value the second half could have is 99, and 2*99 = 198. So the number has to be between 10050 and 19899. Also, the digit in the hundreds place must be an even number, since it comes from another number being multiplied by 2.\r\n\r\nTripling those numbers gives a range of 30150 to 59697. The square roots of those numbers are 173.64 and 244.33. So that means a number between 174 and 244 that gets squared and divided by three.\r\n\r\nSince the number that is squared gets divided by 3, that means the starting number must be a multiple of 3, so it must be one of 174, 177, 180, 183, ..., 237, 240, 243; a list of 24 numbers.\r\n\r\nAt this point I decided to just do trial-and-error, since 24 is a reasonably small number of iterations, and found the above answer.',NULL,0);
INSERT INTO comment VALUES (7236,777,3172,'Your buddy','re: solution','2003-08-20 15:49:51',0,'When I first thought of a solution, I began with a point and the circle around it (of radius one meter) which must be of different color than the center. Then pick any two points on that circle exactly one meter apart (a one meter chord), and of course, they\'re the same color.\r\n\r\nIt boils down to your triangle. I like your triangle better. :-P',4384,0);
INSERT INTO comment VALUES (7237,1138,1626,'Gamer','Trial and error?','2003-08-20 15:54:17',0,'There\'s a way to do it without trial and error... (which is what a program is) but I like your method Ender! :)',NULL,0);
INSERT INTO comment VALUES (7238,672,3172,'Your buddy','re: Ideal answer','2003-08-20 15:55:47',0,'Short of \"What happens when an irresistable force meets an immovable object? *An inconceivable event*\", I think Alan\'s response is probably the best.',3305,0);
INSERT INTO comment VALUES (7239,602,1626,'Gamer','Vocabulary mistake','2003-08-20 16:00:48',4,'I heard the b²-4ac was called the discriminant... Where did I hear that from?',NULL,0);
INSERT INTO comment VALUES (7240,1107,3163,'Evan','','2003-08-20 16:18:36',0,'I thought maybe if 3/4 cows gives you 3/2 grazing time then 1/2 of the cows would give you 3\\1 grazing time or 40*3=120 but im a retard',NULL,0);
INSERT INTO comment VALUES (7241,1138,1575,'DJ','Full Solution','2003-08-20 16:31:07',3,'13467\r\n\r\nFor a 5-digit number to be \'split\' into two parts, one of which is double the other, the parts must of course have three and two digits, respectively.\r\n\r\nLet x represent the two-digit number (which must be between 50 and 99). 2x is then the three-digit number. To make the five-digit number, these three digits must be moved two places to the left, so we multiply by 100.\r\n\r\nTherefore, the five-digit number is represented by 201x, where x is the two-digit number in question. If we triple this number, we have a perfect square, equal to 603x.\r\n\r\nThe prime factorization of 201 is just 3×67, so we have that 3×3×67×x is a perfect square. There are two ways for this to happen; x must be equal to 3×3×67, so that the resulting number is 603², or x must equal 67=603, so that the resulting number is (3×67)(3×67)=201². We already know that x has only two digits, so the latter is the case.\r\n\r\nTherefore, the five digit number is 13467, which is equal to 201².',NULL,0);
INSERT INTO comment VALUES (7242,369,1575,'DJ','re: do not agree with solution','2003-08-20 16:54:12',0,'That\'s true; a puppy with a black nose may not necessarily play with kangaroos. The statement in the solution, however, simply states that if a puppy plays with a kangaroo, he must have a black nose. This is always true.',6693,0);
INSERT INTO comment VALUES (7243,1138,1575,'DJ','re: Full Solution','2003-08-20 17:21:04',1,'In the previous post, \"x must be equal to 3×3×67, so that the resulting number is 603², or x must equal 67=603\" should read \"x must be equal to 3×3×67=603, so that the resulting number is 603², or x must equal 67.\" The \"=603\" was an afterthought, and I accidentally put it in the wrong place.\r\n\r\nAlso, the multiplication symbol (×) and the variable x are distinguishable, but very similar. I hope it\'s clear enough which is which.',7241,0);
INSERT INTO comment VALUES (7244,602,1575,'DJ','re: Vocabulary mistake','2003-08-20 19:02:38',0,'You are right, of course; the quantity b²-4ac is called the discriminant of the quadratic equation.\r\n\r\nA determinant is a value assigned to square matrices of numbers, useful in determining whether a system of equations has a nontrivial solution, as well as other applications.\r\n\r\nIt has been some time since I have had to use either of these terms by name, which led to their confusion.',7239,0);
INSERT INTO comment VALUES (7245,1138,2707,'Gordon Steel','Five Digit Numbers','2003-08-20 19:09:35',0,'We know that the last two digits can range from a low of 50 to a high of 99. Therefore, the first three digits can range from 100 to 198 but exclude all even numbers. Thus the number of combinations that we need to investigate to 50. The solution is 13,467. Clearly, 67 x 2 is equal to 134. Three times 13,467 is 40,401, which is the square of 201.\r\n\r\nGsteel ',NULL,0);
INSERT INTO comment VALUES (7246,602,2707,'Gordon Steel','Quadratic Equation Coefficients','2003-08-20 19:35:28',0,'If I recall my high school algebra correctly, there were two basic categories of numbers involved in factoring a quadratic equation: imaginary roots (that involve the peculiar concept of the square root of negative 1) and real roots (all others). If the die thrown is normal, it would have the integers 1 through 6 or the six faces. Therefore, the probabily of having real roots is 100%. It is also possible to determine the probability that the roots of the equation are integers, but this would take a bit more work.\r\n\r\nG. Steel',NULL,0);
INSERT INTO comment VALUES (7247,602,1575,'DJ','re: Quadratic Equation Coefficients','2003-08-20 23:33:13',1,'What you have said is correct, the roots of a quadratic equation can be real or imaginary, but it is not true that integral coefficients ensure that the roots will be integral, rational, or even real at all.\r\n\r\nIf you have a quadratic equation ax²+bx+c=0, then the quadratic states that the values of x are shown by:\r\n -b ± √(b²-4ac)\r\nx = --------------\r\n 2a\r\n\r\n
\r\nThis kind of equation can have one or two real roots, or two imaginary roots.\r\nThe part under the radical sign, b²-4ac, called the discriminant, determines the types of roots the equation will have.\r\n\r\nIf the discriminant is zero, then the square root drops out and you have one rational root.\r\n\r\nIf the discriminant is a perfect square, you will have two rational roots.\r\n\r\nA rational root will be integral iff the denominator, 2a, is a \'clean\' factor of the numerator.\r\n\r\nIf the discriminant is positive, but not a perfect square, the equation has two irrational roots.\r\n\r\nIf the discriminant is negative, then you have the square root of a negative number, which is a complex (imaginary) number, involving (as you said) i, which is defined as a number that, when squared, yields -1. For example, √(-4) could be rewritten as √(4×-1)=√2×√(-1)=2i.\r\n\r\nTo solve this problem, you need to find the probability that for the coefficients determined by the dice (a, b, and c), the value of the discriminant will be nonnegative. If 4ac is greater than b², which is certainly possible with values ranging from 1 to 6 for all three coefficients, then the discriminant will be negative and the roots will be imaginary.',7246,0);
INSERT INTO comment VALUES (7248,1168,1301,'Charlie','solution','2003-08-21 08:56:00',3,'There are 12 ways altogether of making a knight\'s tour starting at the upper left corner and going to the lower right corner. The specification of the starting and ending positions as well as the non-square rectangular shape of the board prevent there being variations that are strict reflections or rotations of the board.\r\n\r\nHowever, there is another symmetry involved: ten of the twelve ways consist of five pairs that are the reverse of one another. That is, if the path taken by the knight is retraced backwards from the end to the beginning, but considering the board rotated 180 degrees, the result is the other solution of the pair. If those are counted as being mere reflections, then the number of possible \"ways\" goes down to 7. Two ways are their own rotated reverse, and five pairs are mutual rotated reverses.\r\n\r\nOn the below list, the squares are marked with the order in which the knight occupies the square. The solutions are numbered. A solution which is the rotated reverse of a previous solution is marked also with which numbered solution it is the reverse of. The two solutions that are their own rotated reverse are marked with an asterisk.\r\n\r\nThe list is:\r\n\r\n\r\n 1 18 3 14 7\r\n 4 13 8 19 10 1\r\n 17 2 11 6 15\r\n 12 5 16 9 20\r\n---------------\r\n 1 18 3 14 7\r\n 10 13 6 19 4 2\r\n 17 2 11 8 15\r\n 12 9 16 5 20\r\n---------------\r\n 1 18 9 14 5\r\n 8 13 4 19 10 3\r\n 17 2 11 6 15\r\n 12 7 16 3 20\r\n---------------\r\n 1 18 5 14 7\r\n 10 13 8 19 4 4\r\n 17 2 11 6 15\r\n 12 9 16 3 20\r\n---------------\r\n 1 18 5 14 9\r\n 6 11 8 19 4 5 *\r\n 17 2 13 10 15\r\n 12 7 16 3 20\r\n---------------\r\n 1 12 5 16 9\r\n 6 15 10 19 4 6 rev 1 \r\n 11 2 13 8 17\r\n 14 7 18 3 20\r\n---------------\r\n 1 12 5 16 9\r\n 6 17 10 13 4 7\r\n 11 2 19 8 15\r\n 18 7 14 3 20\r\n---------------\r\n 1 18 5 14 9\r\n 6 15 10 19 4 8 rev 3 \r\n 11 2 17 8 13\r\n 16 7 12 3 20\r\n---------------\r\n 1 18 5 12 9\r\n 6 15 10 19 4 9 rev 4 \r\n 17 2 13 8 11\r\n 14 7 16 3 20\r\n---------------\r\n 1 16 5 12 9\r\n 6 13 10 19 4 10 rev 2 \r\n 17 2 15 8 11\r\n 14 7 18 3 20\r\n---------------\r\n 1 18 7 14 3\r\n 6 13 2 19 10 11 rev 7 \r\n 17 8 11 4 15\r\n 12 5 16 9 20\r\n---------------\r\n 1 12 7 16 3\r\n 6 17 2 11 8 12 *\r\n 13 10 19 4 15\r\n 18 5 14 9 20\r\n
\r\n---------------\r\n\r\nThe program to produce this is:\r\nDECLARE SUB showSoln ()\r\nDECLARE SUB nextMove (soFar!, row!, col!)\r\nDIM SHARED maxRow, maxCol, lastMove, tot\r\nmaxRow = 4: maxCol = 5\r\nlastMove = maxRow * maxCol\r\n\r\nDIM SHARED board(maxRow, maxCol)\r\nDIM SHARED hist(100, maxRow, maxCol)\r\nboard(1, 1) = 1\r\n\r\nOPEN \"kngttour.txt\" FOR OUTPUT AS #1\r\nnextMove 1, 1, 1 \' 1 move so far, at 1,1\r\nCLOSE\r\n\r\nPRINT tot\r\n\r\nEND\r\n\r\nSUB nextMove (soFar, row, col)\r\n newMove = soFar + 1\r\n FOR r = row - 2 TO row + 2 STEP 4\r\n IF r > 0 AND r <= maxRow THEN\r\n FOR c = col - 1 TO col + 1 STEP 2\r\n IF c > 0 AND c <= maxCol THEN\r\n IF board(r, c) = 0 THEN\r\n board(r, c) = newMove\r\n IF newMove = lastMove THEN\r\n IF r = maxRow AND c = maxCol THEN\r\n tot = tot + 1\r\n showSoln\r\n END IF\r\n ELSE\r\n nextMove newMove, r, c\r\n END IF\r\n board(r, c) = 0\r\n END IF\r\n END IF\r\n NEXT\r\n END IF\r\n NEXT\r\n FOR r = row - 1 TO row + 1 STEP 2\r\n IF r > 0 AND r <= maxRow THEN\r\n FOR c = col - 2 TO col + 2 STEP 4\r\n IF c > 0 AND c <= maxCol THEN\r\n IF board(r, c) = 0 THEN\r\n board(r, c) = newMove\r\n IF newMove = lastMove THEN\r\n IF r = maxRow AND c = maxCol THEN\r\n tot = tot + 1\r\n showSoln\r\n END IF\r\n ELSE\r\n nextMove newMove, r, c\r\n END IF\r\n board(r, c) = 0\r\n END IF\r\n END IF\r\n NEXT\r\n END IF\r\n NEXT\r\nEND SUB\r\n\r\nSUB showSoln\r\n FOR r = 1 TO maxRow\r\n FOR c = 1 TO maxCol\r\n hist(tot, r, c) = board(r, c)\r\n NEXT\r\n NEXT\r\n FOR r = 1 TO maxRow\r\n FOR c = 1 TO maxCol\r\n PRINT #1, USING \\\"###\\\"; board(r, c);\r\n NEXT\r\n IF r = INT(maxRow / 2) THEN\r\n PRINT #1, USING \\\"####\\\"; tot;\r\n FOR i = 1 TO tot\r\n Rev = 1\r\n FOR cChk = 1 TO maxCol\r\n FOR rChk = 1 TO maxRow\r\n IF board(rChk, cChk) + hist(i, maxRow - rChk + 1, maxCol - cChk + 1) <> lastMove + 1 THEN\r\n Rev = 0\r\n EXIT FOR\r\n END IF\r\n NEXT\r\n IF Rev = 0 THEN EXIT FOR\r\n NEXT\r\n IF Rev THEN EXIT FOR\r\n NEXT\r\n IF Rev THEN\r\n IF i = tot THEN\r\n PRINT #1, \" *\";\r\n ELSE\r\n PRINT #1, \" rev\"; i;\r\n END IF\r\n END IF\r\n END IF\r\n PRINT #1,\r\n NEXT\r\n PRINT #1, STRING$(maxCol * 3, \"-\")\r\nEND SUB\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (7249,602,3074,'Adam Sisco','Nice solution DJ','2003-08-21 10:55:01',0,'I like your approach to that solution DJ, good work!',NULL,0);
INSERT INTO comment VALUES (7250,173,3074,'Adam Sisco','Pythagoras','2003-08-21 11:07:21',0,'I find it rather interesting that this soup can question can be applied to the old pythagoras theorem.',NULL,0);
INSERT INTO comment VALUES (7251,1138,3183,'Daniel Gordon','Solution','2003-08-21 11:35:50',3,'The number is 13,467',NULL,0);
INSERT INTO comment VALUES (7252,940,3143,'Vito','ring ring','2003-08-21 11:38:03',0,'gotta be the number 7 on a telephone',NULL,0);
INSERT INTO comment VALUES (7253,1122,2839,'FatBoy','solution','2003-08-21 13:04:49',0,'D',NULL,0);
INSERT INTO comment VALUES (7254,1112,3184,'Donna','Solution','2003-08-21 14:19:17',3,'Cube 1;A, L, W, B, M, T\r\nCube 2:X, O, C, E, J, N\r\nCube 3:I,K, P, R, D, Y\r\nCube 4:S,F, V, U, G, H\r\n',NULL,0);
INSERT INTO comment VALUES (7255,1116,3172,'Your buddy','FULL SOLUTION (in C)','2003-08-21 15:50:00',3,'apologies that my indentions don\'t come through the HTML (but I don\'t want to type the non-breaking space character ;-)\r\n\r\n#include \"stdafx.h\"\r\n#include \"stdlib.h\"\r\n\r\nint F(int i, int j, int x)\r\n{\r\n if (i == 0)\r\n {\r\n return(x*x-j-1);\r\n }\r\n if (i == (x-1) )\r\n {\r\n return( (x-2) * x + j - x + 2);\r\n }\r\n if (j == (x-1) )\r\n {\r\n return( (x-1)* x - i);\r\n }\r\n if (j == 0)\r\n {\r\n return( (x-2) * (x-2) + i - 1) ;\r\n }\r\n return (F(i-1, j-1, x-2));\r\n}\r\n\r\nint main(int argc, char* argv[])\r\n{\r\n int i,j;\r\n int x = atoi(argv[1]);\r\n\r\n for (i=0; i\r\n\r\nC:\\tc\\BIN>spirals 7\r\n48 47 46 45 44 43 42\r\n25 24 23 22 21 20 41\r\n26 9 8 7 6 19 40\r\n27 10 1 0 5 18 39\r\n28 11 2 3 4 17 38\r\n29 12 13 14 15 16 37\r\n30 31 32 33 34 35 36\r\n\r\nC:\\tc\\BIN>spirals 8\r\n63 62 61 60 59 58 57 56\r\n36 35 34 33 32 31 30 55\r\n37 16 15 14 13 12 29 54\r\n38 17 4 3 2 11 28 53\r\n39 18 5 0 1 10 27 52\r\n40 19 6 7 8 9 26 51\r\n41 20 21 22 23 24 25 50\r\n42 43 44 45 46 47 48 49\r\n
\r\n----------\r\n----------',7256,0);
INSERT INTO comment VALUES (7261,1116,1301,'Charlie','re(2): solution','2003-08-21 16:54:31',0,'I\'ll try pre again:\r\n\r\nn=7\r\n 36 35 34 33 32 31 30\r\n 37 16 15 14 13 12 29\r\n 38 17 4 3 2 11 28\r\n 39 18 5 0 1 10 27\r\n 40 19 6 7 8 9 26\r\n 41 20 21 22 23 24 25\r\n 42 43 44 45 46 47 48\r\nn=8\r\n 63 62 61 60 59 58 57 56\r\n 36 35 34 33 32 31 30 55\r\n 37 16 15 14 13 12 29 54\r\n 38 17 4 3 2 11 28 53\r\n 39 18 5 0 1 10 27 52\r\n 40 19 6 7 8 9 26 51\r\n 41 20 21 22 23 24 25 50\r\n 42 43 44 45 46 47 48 49\r\n
\r\n-----------\r\n-----------\r\n',7259,0);
INSERT INTO comment VALUES (7262,1168,1626,'Gamer','Without trian and error?','2003-08-21 17:11:59',4,'How could you figure it out without using \"trial and error\"... like a program that does a thing like that?\r\n',NULL,0);
INSERT INTO comment VALUES (7263,1168,1626,'Gamer','re: Without trial and error?','2003-08-21 17:13:13',0,'If your program didn\'t use that, sorry! I don\'t know how to read basic, but it looked like that.',7262,0);
INSERT INTO comment VALUES (7264,1116,3172,'Your buddy','re(3): solution','2003-08-21 17:28:26',0,'You are absolutely correct in what my program does! It DOES go the opposite way for odd N....
This is because the problem specified a \"descending spiral\"....
\r\nI interpret this to mean the upper left corner has the HIGHEST valued number. My program is consistent with this notion. It is left as an exercise to the reader (easy enough) to change my code to always have the \'1\' to the right of the \'0\'.',7261,0);
INSERT INTO comment VALUES (7265,1122,3187,'duckpotter','liars and knights','2003-08-21 18:47:45',0,'is it d?',NULL,0);
INSERT INTO comment VALUES (7266,735,3182,'Antonio','Solution','2003-08-21 19:09:41',3,'According to the cosines law, an angle theta can be obtained using the tetrahedron side L and the height of the triangles H. Since a tetrahedron has te same sides, it is made of 4 triangles with same sides L, so their internal angle is 60 degrees and is equal to √/2, H becomes √3*L/2.\r\nSo theta becomes ArcCos[1/3].\r\nWe make a new rectang triangle with an hypotenusa equals to the already used height H (√3*L/2) and the angle theta on one vertex. With these two values, we obtain the bottom of the triangle instead of the full height of the tetrahedron. The bottom of the triangle is H/3.\r\nSubtracting H-(H/3) gives 2*H/3.\r\nFinally we make a rectang triangle where the hipotenusa is R2 (Radius of the external sphere), the bottom side 2*H/3 and the side left R1 (Radius of the internal sphere), and by angle relation, the angle between R2 and R1 is the already described theta (ArcCos[1/3]). So we obtain R1= √3*L/(3*Tan[ArcCos[1/3]]).\r\nR2=R1/(Cos[ArcCos[1/3]])=3*R1=√3*L/(Tan[ArcCos[1/3]]).\r\n\r\nTHE RATIO OF RADII OF THE TWO SPHERES IS (R2/R1)=3\r\n\r\nNote: I prefered to use the trigonometric function ArcCos[theta] in this problem, but it can be done using Pitagora\'s theorem.',NULL,0);
INSERT INTO comment VALUES (7267,705,3182,'Antonio','Solution','2003-08-21 19:46:48',3,'The only angle where every face can be touching their sides (of every pentagon) is 63.434948823 degrees. So, 63.434948823 + 180 = 243.434948823 degrees from face to face in the external part of the dodecahedron',NULL,0);
INSERT INTO comment VALUES (7268,705,3182,'Antonio','Re: Solution','2003-08-21 20:02:48',3,'Well, according to the answer given, may past solution gives the external angle 243.434948823 degrees (63.434948823 + 180), but a CNC machine doesn\'t make a 12 side dice from the inside (at least I haven\'t seen one), you have to give an external reference. But to prove my point, 360 - 243.434948823 = 116.565051177 degrees.\r\n\r\nThe angle that I used at my last solution (63.434948823 degrees) is the basis an icosahedron in Geodesic geometry, I have studied it for 8 years.',NULL,0);
INSERT INTO comment VALUES (7269,734,3182,'Antonio','Solution','2003-08-21 20:41:52',0,'Again, the basis for Geodesic geometry is the icosaherdon, the external angle is 63.434948823+180=243.434948823 degrees and the internal angle is 180-63.434948823=116.565051177 degrees. ',NULL,0);
INSERT INTO comment VALUES (7270,734,3182,'Antonio','My last solution is wrong this is the real one','2003-08-21 21:47:11',0,'Sorry, I posted a wrong solution, but the real one to this problem is:\r\n\r\nAngle=360-ArcSin[1/(√3*Tan[36])]-ArcTan[Sin[63.434948823/2]/(Tan[36]-Sin[63.434948823/2]*√(3*Tan[36]²-1))]\r\nAngle=138.189685105\r\n\r\nWhere again is used the angle 63.434948823',NULL,0);
INSERT INTO comment VALUES (7271,1112,3190,'Shelly','Solution','2003-08-21 22:26:53',0,'cube 1: albmtw\r\ncube 2: xocnej\r\nCube 3: ikyprd\r\nCube 4: sfvuhg',NULL,0);
INSERT INTO comment VALUES (7272,692,3182,'Antonio','Solution','2003-08-22 01:17:33',3,'Since V=D/t, A=V/t\r\nThe velocity V is an average Velocity V=(V1-V2)/2\r\nV2=0\r\nV1=10/2 m/sec\r\nA=g=-9.81m/sec² since the object goes up, g=9.81m/s²\r\nt=V1/A =10/(2*9.81) sec\r\nD=V1²/A=10²/(2*9.81)=5.09683m\r\n\r\nNote: The mass is not used',NULL,0);
INSERT INTO comment VALUES (7273,405,3182,'Antonio','Solution','2003-08-22 01:39:34',3,'Move from coordinates:\r\n1.- 1,1 to 1,4\r\n2.- 1,4 to 4,1\r\n3.- 4,1 to 1,1\r\n4.- 1,1 to 3,3',NULL,0);
INSERT INTO comment VALUES (7274,313,3182,'Antonio','Solution','2003-08-22 02:09:03',3,'I don´t know if the face at the bottom counts, but if it doesn\'t, the smallest area I found was 90 square units. If the bottom faces count, the smallest ares would be 111 square units',NULL,0);
INSERT INTO comment VALUES (7275,313,3182,'Antonio','Solution','2003-08-22 02:17:20',3,'Arrange the cubes so that one face of the one with volume 8 is glued with the one of volume 64 and another face facing to the ground. Then the little one with volume 1 glue it in the corner touching the ground, the one with volume 8 and the one with volume 64.\r\n\r\nThis arrange would give an area of:\r\n80+16+11+3=110',NULL,0);
INSERT INTO comment VALUES (7276,260,3182,'Antonio','Solution','2003-08-22 02:25:28',3,'I posted a comment about proportionality, but the problem seems very easy because you have to choose the diameters of the little circles in order to fill the large diameter. So, 2*Pi*R1+2*Pi*R2+2*Pi*R3+2*Pi*R4=2*Pi*R5 All 2*Pi terms are cancelled and you get R1+R2+R3+R4=R5 the sum of all perimeters are the same as the big perimeter as the sum of all radii are the same as the large radius. ',NULL,0);
INSERT INTO comment VALUES (7277,96,3182,'Antonio','Solution','2003-08-22 02:38:11',3,'You form a rectangular triangle with an angle of 30 degrees and the bottom side is 3cm. With this information you get the radius of the circle:\r\nR=3/Cos[30]=6/√3\r\nDiameter=2*R=12/√3=6.92820323027\r\n',NULL,0);
INSERT INTO comment VALUES (7278,92,3182,'Antonio','Solution','2003-08-22 03:11:55',3,'Form a rectangular triangle of sides L, L/2 and an hypotenusa of R (in this case 6cm). With this triangle use the Pitagoras theorem and obtain L.\r\nIt gives L=12/√5\r\nSo, because it is a square, every side is equal, to obtain the diagonal you simply multiply L*√2=12*√2/√5=7.58946638437',NULL,0);
INSERT INTO comment VALUES (7279,57,3182,'Antonio','Solution','2003-08-22 05:31:02',3,'Make a rectangular triangle of sides 5, R1 and an hypotenusa of R2. Using Pitagoras theorem we get 25=R2²-R1²\r\nThe area between the two circles is Pi*R2²-Pi*R1²=Pi*(R2²-R1²). So we simply put 25 instead of R2²-R1² and the result is:\r\nArea=25*Pi=78.5398163398 in²',NULL,0);
INSERT INTO comment VALUES (7280,603,3172,'Your buddy','I think I've got it...','2003-08-22 08:40:55',3,'The problem lies with your differentiation of both sides. The operation of differentiation is valid only on well defined mathematical functions. \"1 + 1 + 1 + ... + 1 (\'x\' times)\" is not a well defined function; it is an algorithm (specifying to add 1 repeatedly), whereas \"2x\" is a well defined function.\r\n\r\nTherefore, the resulting equation is faulty.',NULL,0);
INSERT INTO comment VALUES (7281,603,1301,'Charlie','flaws','2003-08-22 08:43:50',3,'There are two major flaws:\r\n1. The function is defined only for integers, so is not at all continuous and therefore has no derivative.\r\n\r\n2. When differentiating the left side, it was done for a fixed value of x (as a fixed number of terms, but that number is dependent on x). But by definition differentiation has to vary depending on the change in x.\r\n\r\nRelated to the latter is that the description of the function on the left side contains within itself mere English words to take the place of a mathematical function, and thereby hopes to avoid the necessary mathematical treatment. That is,\r\n\r\nx + x +...+x (x times) \r\n\r\nreally is saying\r\nx * x\r\nwhich everyone agrees is x²\r\n\r\nthen as both the left hand and the right hand x are changing (not just the left hand one), the correct formula to apply is the product rule. To differentiate x * x you get x * 1 + 1 * x, which is indeed 2x, rather than x.',NULL,0);
INSERT INTO comment VALUES (7282,599,3190,'Shelly','Solution','2003-08-22 09:25:53',0,'Pour the 12 litre jug into the 8 litre jug until full. Pour the 8 litre jug into the 5 litre jug until full. Pour the 5 litre into the 12 litre, making the 12 litre have 9 litres of water. Pour the 8 litre jug (holding 3 litres), into the 5 litre jug. Pour the 12 litre jug into the 8 litre jug until full. Pour the 8 litre jug into the 5 litre jug until full. Finally pour the 5 litre jug into the 12 litre jug.',NULL,0);
INSERT INTO comment VALUES (7283,1008,3190,'Shelly','Solution','2003-08-22 09:29:33',0,'Elizabeth is drinking Coffee',NULL,0);
INSERT INTO comment VALUES (7284,1121,3190,'Shelly','guess!','2003-08-22 09:44:48',0,'Lenny is a Liar and Benny is a knave?',NULL,0);
INSERT INTO comment VALUES (7285,227,3196,'Dan Erickson','Here is my ingenious solution','2003-08-22 11:37:39',0,'If the student loses, the court will order him to pay Protagoras. The student will immediately appeal, this time using a different lawyer to represent him, rather than representing himself. If he wins the appeal, he is home free -- clearly he does not have to pay. If he loses the appeal, he will appeal again, again using a different lawyer to represent him. He will keep this up until (a) he runs out of appeals, at which time he will pay Protagoras; (b) Protagoras dies of old age, which means the student won\'t have to pay; (c) he wins one of the appeals, upon which he won\'t have to pay.\r\n\r\nIf the student wins, the court will free him of his debt to Protagoras. Then Protagoras will immediately appeal, citing the legal ground of \"changed circumstances\" - the student has already won his first case, and so in this second case, Protagoras will argue, successfully, that the student must pay the debt. The student will pay Protagoras.\r\n\r\nTo sum up:\r\n\r\nThe student probably will NOT pay if he LOSES the original case (unless he exhausts the appeal process), but probably WILL pay if he wins the original case. This is a pleasing example of a paradox that the Ancient Greeks were so brilliant at creating. \r\n',NULL,0);
INSERT INTO comment VALUES (7286,1089,506,'Ferran Muiños','Solution following Jason\'s','2003-08-22 11:52:58',1,'If both (n+3) and (n^2+3) were perfect cubes, the product (n+3)(n^2+3) = n^3+3n^2+3n+9 = (n+1)^3 + 8 = (n+1)^3 + 2^3 will be a perfect cube, right. Now one can see geometrically that if we take any cube formed by n^3 smaller cubic units, we can\'t construct a greater cube by adding 8 cubic units to the original cube, for any n. Thus the assumption is false.',NULL,0);
INSERT INTO comment VALUES (7287,227,3196,'Dan Erickson','re: Here is my ingenious solution','2003-08-22 12:00:40',0,'I think I can improve on that !!\r\n \r\n(a) If the student loses this, his first case, the court will order him to pay Protagoras. The student will immediately appeal, this time using a different lawyer to represent him, rather than representing himself. In this appeal, his lawyer will argue, successfully, that the student has not won his first case, and so must not pay Protagoras. Obviously the court will agree. The student is home free -- clearly he does not have to pay.\r\n(b) On the other hand, if the student wins this, his first case, the court will free him of his debt to Protagoras. Then Protagoras will immediately appeal, citing the legal ground of \"changed circumstances\" - the student has just won his first case, and so in this second case, Protagoras will argue, successfully, that the student must pay the debt. The student will pay Protagoras.\r\n',7285,0);
INSERT INTO comment VALUES (7288,603,3198,'JohnE','Flaw in the Program','2003-08-22 12:31:41',0,'The flaw in the program is that when you assign x=1, 1 squared is still 1 not 2. Therefore, the equation 1 + 1 + 1 + 1 +1 .... +1 (\'x\' time) should equal x instead of 2x.',NULL,0);
INSERT INTO comment VALUES (7289,1094,2129,'Sanjay','re(2): arrrggghhhh','2003-08-22 13:29:23',0,'The woman would have to be fertile for 63 years.',7146,0);
INSERT INTO comment VALUES (7290,573,3197,'gabbo','Similar','2003-08-22 15:54:13',0,'warning explicit content :)\r\n\r\nThis one seems similar to another one i heard, \r\n\r\nGeorge wants to have sex with three prostitutes, but he only has 2 condoms, how can he @#!% all the women without risk.\r\n\r\n\r\nbtw...these surgens are pretty good to only need to use one hand) ',NULL,0);
INSERT INTO comment VALUES (7291,602,2707,'Gordon Steel','Die Based Coefficients','2003-08-22 18:33:51',0,'A six-sided die tossed randomly to determine the coefficients for a, b, and c of a quadratic equation can yield 6 x 6 x 6 = 216 unique equations. We want to determine those that have real roots. We can do so by eliminating those with imaginary roots. We need to find all values of a,b and c such that 4AC is greater than B^2. For a = b = 1, there are 36 combinations of 4AC that are greater than 1 squared. For a b of 2, there are 35 values of AC such that 4AC >4. For an b of 3, there are 33 values of AC such that 4AC exceeds 9. For a B of 4 the total is 28, for 5 the total is 22 and for 6 the total is 19. Thus we have 173/216, or 80.1% probability of irrational roots.\r\n\r\nGordon Steel',NULL,0);
INSERT INTO comment VALUES (7292,1179,1567,'Bryan','A guess to get things started','2003-08-22 18:40:55',0,'Since there are thirteen \"Canadian\" letters listed in the puzzle, perhaps they have to do with the 13 Canadian provinces and territories. The letters a, c, and g might pertain to each of the three territories, with the other letters referring to the ten provinces. I already tried the names of the provinces and their capitol cities to no avail, but there still might be a connection here.',NULL,0);
INSERT INTO comment VALUES (7293,1179,1626,'Gamer','Another guess','2003-08-22 20:01:39',1,'Maybe it has something to do with the French alphabet or something like that...',NULL,0);
INSERT INTO comment VALUES (7294,1179,1575,'DJ','Clueless','2003-08-22 23:01:10',0,'I was thinking along the same lines as Bryan, and I checked all the Canadian provinces, territories, and their capitals, with no luck. On the other hand, I also remember Cory saying that the \'Canadian\' part was a hint that may be useful to Can-Am solvers, but wasn\'t crucial to the problem, so I doubt it has anything to do with that.\r\nFrench uses the same Latin alphabet as English, but some letters can be modified with accent marks and symbols. These symbols, though, only modify the vowels a, e, i, o, and u, as well as c.\r\n\r\nOther common methods used in puzzles like this one, such as the number of strokes required to draw each character or the number of curved or straight lines in each (or the capital letters), number of syllables or rhymes when saying the letter, all fail. I was thinking of maybe the way the letters themselves are pronounced in French, except I don\'t know how that is (I only speak English and Spanish). Past that, I have no bright ideas...',NULL,0);
INSERT INTO comment VALUES (7295,1179,3202,'Jill Gudmundson','Still Trying...','2003-08-22 23:08:04',0,'I tried the same things as DJ. I have nothing useful to add, though I did notice that the letters a, c, g could stand for America, Canada, and Greenland...but I don\'t see how this would connect with the rest of it.',7294,0);
INSERT INTO comment VALUES (7296,602,979,'Ravi Raja','re: Vocabulary mistake','2003-08-23 01:11:19',0,'Yes Gamer, I had said that when the problem was in the queue and there were a few doubts regarding the real roots or may be something else. So I had posted a comment saying that the condition for the existence of real roots means the vanishing of the discriminant.',7239,0);
INSERT INTO comment VALUES (7297,45,3182,'Antonio','Solution','2003-08-23 02:49:06',3,'Well, I imagine any of the corner of the cube, it has 3 faces, and on the opposite side is the same corner but rotated so that those tree faces fit with the other mentioned. A cube has 6 faces, so if we cut it horizontally, every face has to be \"seen\". I say that the figure appears after the cut would be an hexagon. ',NULL,0);
INSERT INTO comment VALUES (7298,602,2912,'Talon5000','re(2): Vocabulary mistake','2003-08-23 03:16:50',4,'Do you mean that a number \'vanishes\' when it is negative? And the comment you are replying to is one sentence saying that the name of the term is discriminant insteead of determinant, and nothing about the roots or \"may be something else.\" You wrote the problem, and that comment made less sense to me than anything anyone else has said...did I miss something?',7296,0);
INSERT INTO comment VALUES (7299,1094,3196,'Dan Erickson','Here is my solution','2003-08-23 04:14:05',0,'Let the ages of the brothers be A, A, and B.\r\nAxAxB=567\r\nB=567/(AxA)\r\nThere AxA, a square number, must divide evenly into 567. But 567=3x3x3x3x7, so clearly 9 is the only square number that divides into 567. Therefore A=3 and B=63\r\nThe \"other one\" is 63 years old. The twins are 3.\r\n(To the objection that this in impossible...NOT SO. The artist Picasso was conceiving children in his 90\'s. So Picasso could have children with such disparate ages as 63 and 3.) ',NULL,0);
INSERT INTO comment VALUES (7300,1094,3196,'Dan Erickson','re: Here is my solution','2003-08-23 04:20:51',0,'Not so fast, Einstein. 81 (3x3x3x3) is a square number that divides into 567 also !! So A=9 and B=7 is also a solution. The twins could be 9 and the other one 7. This solution would not require the virility of a Picasso. ',7299,0);
INSERT INTO comment VALUES (7301,908,3196,'Dan Erickson','Here is one take on this.','2003-08-23 05:01:05',0,'Here are the exhaustive possibilities:\r\n \r\nhalf-dollars quarters dimes nickels\r\n------------ -------- ----- -------\r\n 2 0 0 0 \r\n 1 2 0 0 \r\n 1 1 2 1\r\n 1 1 1 3\r\n 1 1 0 5\r\n 1 0 5 0\r\n 1 0 4 2\r\n 1 0 3 4\r\n 1 0 2 6\r\n 1 0 1 8\r\n 1 0 0 10\r\n 0 4 0 0\r\n 0 3 2 1\r\n 0 3 1 3\r\n 0 3 0 5\r\n 0 2 5 0\r\n 0 2 4 2\r\n 0 2 3 4\r\n 0 2 2 6\r\n 0 2 1 8\r\n 0 2 0 10\r\n 0 1 7 1\r\n 0 1 6 3\r\n 0 1 5 5\r\n 0 1 4 7\r\n 0 1 3 9\r\n 0 1 2 11\r\n 0 1 1 13\r\n 0 1 0 15\r\n 0 0 10 0\r\n 0 0 9 2\r\n 0 0 8 4\r\n 0 0 7 6\r\n 0 0 6 8\r\n 0 0 5 10\r\n 0 0 4 12\r\n 0 0 3 14\r\n 0 0 2 16\r\n 0 0 1 18\r\n 0 0 0 20\r\n-------------------------------------\r\nA total of 40 combinations. 40 different ways for her to give you change, ranging from 2 half-dollars to 20 nickels. \r\n ',NULL,0);
INSERT INTO comment VALUES (7302,599,3206,'Lawrence','3 jugs, one cycle','2003-08-23 05:50:45',3,'The solution to this works pretty much round robin from 12 to 5 to 8. Once 8 is full, empty 8 back to 12, then whatever is left in 5 goes into 8. Then restart the cycle from 12 to 5 to 8 until 8 is full, empty 8 to 12, then remaining contents of 5 to 8, and start again.\r\n\r\nStart with contents 12-0-0 (jugs in capacity order of 12-8-5)\r\n1. From 12 to 5 = 7-0-5\r\n2. From 5 to 8 = 7-5-0\r\n3. From 12 to 5 = 2-5-5\r\n4. From 5 to 8 = 2-8-2\r\n5. 8 is full, so from 8 to 12 = 10-0-2\r\n6. Empty remaining from 5 to 8 = 10-2-0\r\n7. Restart cycle like at #1, i.e. 12 to 5 = 5-2-5\r\n8. 5 to 8 = 5-7-0\r\n9. 12 to 5 = 0-7-5\r\n10. 5 to 8 = 0-8-4\r\n11. 8 is full, so from 8 to 12 = 8-0-4 \r\n12. Empty remaining from 5 to 8 = 8-4-0\r\n13. Restart Cycle like at #1 & #7, so 12 to 5 = 3-4-5\r\n14. 5 to 8 = 3-8-1\r\n15. 8 is full, so empty 8 into 12 (almost done)= 11-0-1\r\n16. Empty remaining 5 to 8 = 11-1-0\r\n17. Restart 12 to 5 = 6-1-5\r\n18. Empty 5 into 8 = 6-6-0, and we are DONE!',NULL,0);
INSERT INTO comment VALUES (7303,1134,3122,'Gert','solution','2003-08-23 06:44:40',3,'Startling - starting - staring - string - sting - sing - sin - in - I',NULL,0);
INSERT INTO comment VALUES (7304,1112,3206,'Lawrence','Spreadsheet helps','2003-08-23 07:35:59',3,'Always start with vowels, and go from there. Neither a Z nor a Q\r\n\r\nABLMTW\r\nDIKPRY\r\nCEJNOX\r\nFGHSUV\r\n',NULL,0);
INSERT INTO comment VALUES (7305,53,3182,'Antonio','Solution','2003-08-23 08:35:52',3,'If every bug moves at the same time, then every bug follow the other at 90 degrees forming an exact square, but the trayectory resembles an spiral towards the center of the original configuration of the 10in square. My point of understanding the problem is different than that of levik\'s: If every bug is moving, than every \"step\" they take they are closer to each other and so on... They follow a bug that is getting closer and closer. I imagine this problem as a mere change of scale of the square respect to an angle of inclination. This angle of inclination opens from 0 to 45 degrees, so is just like a seen a growing square and at the same time rotating until it stops with its sides equal to 10in. In this particular problem, we assume that all the bugs walk with exactly the same speed, this gives the characteristic of a change of scale in the square. So measuring the position of a single bug respect to a reference angle (in this case from the center of the square), and at the same time adjusting the scale of the square respect to the same angle, we get to know the real trayectory of one bug. Makeing a simple program to sum every infinitesimal part of that trayectory would give a real aproximation of the perimeter or distance. \r\nMy result:\r\nDistance covered of a single bug = 7.7422806275 in',NULL,0);
INSERT INTO comment VALUES (7306,532,3196,'Dan Erickson','Got it !!!!!','2003-08-23 08:48:43',0,'He could see at once that neither had a navel.',NULL,0);
INSERT INTO comment VALUES (7307,1206,3207,'Kathryn','Solution to Breakfast','2003-08-23 09:40:58',3,'This was a pretty simple problem.\r\n\r\nAl: bacon, eggs, milk; Will: bacon pancakes coffee; Bob: ham, eggs, milk; Chuck: ham, eggs, milk; Peter: sausage, pancakes, tea; Ned: sausage, eggs, tea.\r\n\r\nDo you need to know how I figured?',NULL,0);
INSERT INTO comment VALUES (7308,1116,3074,'Adam Sisco','Neat','2003-08-23 10:13:16',0,'Nice Question, I\'ve been getting into some programming competitions this year and these kind of mathematical qestions are the kind I love to see.',NULL,0);
INSERT INTO comment VALUES (7309,1206,1575,'DJ','Full Solution','2003-08-23 12:56:13',3,'Al: Eggs, bacon, and milk\r\nBob: Pancakes, ham, and coffee\r\nChuck: Eggs, ham, and milk\r\nNed: Eggs, sausage, and tea\r\nPeter: Pancakes, sausage, and tea\r\nWill: Pancakes, bacon, and coffee\r\n\r\nMethod:\r\nThere are six boarders altogether.\r\n\r\nThere are two tea drinkers, two coffee drinkers, and two milk drinkers (6).\r\n\r\nAlso, since there are three different sides, and Mrs. Finnegan will not prepare a single dish for any one person, there must be two people who have each.\r\n\r\nMore than two of them pancakes (6), and more then two of them have eggs (7), so there must be three who have each:\r\n\r\nP\r\nP\r\nP\r\nE\r\nE\r\nE\r\n
\r\nBoth of the sausage-eaters have tea (6).\r\nSince no two people have exactly the same breakfast, one must have eggs and the other pancakes.\r\n\r\nP S T\r\nP\r\nP\r\nE S T\r\nE\r\nE\r\n
\r\nThat takes care of one of the \"pancake-eaters.\"\r\nThe other two boarders with pancakes must both have coffee (6), so one must have ham and one bacon.\r\n\r\nP S T\r\nP H C\r\nP B C\r\nE S T\r\nE\r\nE\r\n
\r\nThe last two boarders both have eggs.\r\nAlso, they both have milk milk, so again, one must have ham and one has bacon.\r\n\r\nP S T\r\nP H C\r\nP B C\r\nE S T\r\nE H M\r\nE B M\r\n
\r\nNow to figure out who has what meal.\r\nBob has ham (2) and coffee (5); he must be the second boarder with pancakes.\r\n\r\nP S T\r\nP H C - Bob\r\nP B C\r\nE S T\r\nE H M\r\nE B M\r\n
\r\nChuck is the other boarder with ham:\r\n\r\nP S T\r\nP H C - Bob\r\nP B C\r\nE S T\r\nE H M - Chuck\r\nE B M\r\n
\r\nAl does not like sausage (1).\r\nHe is also not the boarder with pankcakes and bacon (and coffee) (1). Therefore, he must have eggs, bacon, and milk:\r\n\r\nP S T\r\nP H C - Bob\r\nP B C\r\nE S T\r\nE H M - Chuck\r\nE B M - Al\r\n
\r\nNed, who does not like pancakes (4), is the last person with eggs.\r\n\r\nP S T\r\nP H C - Bob\r\nP B C\r\nE S T - Ned\r\nE H M - Chuck\r\nE B M - Al\r\n
\r\nFinally, Peter does not like bacon (3).\r\nHe must be the remaining boarder with sausage, and Will, who isn\'t picky, has pancakes and bacon:\r\n\r\nP S T - Peter\r\nP H C - Bob\r\nP B C - Will\r\nE S T - Ned\r\nE H M - Chuck\r\nE B M - Al\r\n
\r\nIn sum, here\'s what each has:\r\n\r\nAl: Eggs, bacon, and milk\r\nBob: Pancakes, ham, and coffee\r\nChuck: Eggs, ham, and milk\r\nNed: Eggs, sausage, and tea\r\nPeter: Pancakes, sausage, and tea\r\nWill: Pancakes, bacon, and coffee\n\nEdited on August 25, 2003, 10:03 pm',NULL,0);
INSERT INTO comment VALUES (7310,1179,775,'Cory Taylor','narrowing the hint','2003-08-23 13:32:23',0,'DJ, you\'ve come very close to the grouping requirement with one of your suggestions (one more logical leap and you\'ll be there), however it has nothing to do with French - in fact it has eerything to do with speaking english. My previous hint probably wont make sense until you see the answer, and then only if you\'re up on your pop culture, however, I have just given you more hints than are immediatly obvious..',NULL,0);
INSERT INTO comment VALUES (7311,1179,775,'Cory Taylor','Important Problem Modification','2003-08-23 13:34:39',0,'Resulting from an unfortunate brain fart, the second part of the question should include the letters a, c, and i - not a, c, and g.\r\n\r\nSorry to all this mislead.',NULL,0);
INSERT INTO comment VALUES (7312,1206,1575,'DJ','re: Solution to Breakfast','2003-08-23 14:16:55',0,'I didn\'t really look at your solution until I had figured out mine. Then, I noticed that they were different.\r\n\r\nYou should have double-checked your list against the clues one last time; #5 says that Bob has coffee, but your Bob has milk. Also, #6 says that two of the pancake eaters have coffee, but you only have two pancake-eaters, one of whom is drinking tea. Since this was a pretty simple problem, you must have made a pretty simple mistake, somewhere, I guess...\r\n\r\nRemember the first two rules to any problem: show your work, and check yoru answer!',7307,0);
INSERT INTO comment VALUES (7313,1206,1626,'Gamer','re: Full Solution','2003-08-23 14:29:50',2,'DJ, the two rules of posting is always check your answer (if you did you would have seen it was all bold) and check your work (if you did you would notice some of it is scrolling off the page)',7309,0);
INSERT INTO comment VALUES (7314,1206,1575,'DJ','re(2): Full Solution','2003-08-23 15:06:02',0,'I don\'t know what you\'re insinuating, but I tried to preview the comment and it was too long. I did double-check it; the only typo in the whole entry was one missing backslash (so it showed <b> instead of </b>), and the scrolling off the edge is a problem with the way the page is handling the &pre> tag, not with anything I did. So, if my \'answer\' is wrong because it all showed up bold, then, I apologize. Do you want me to try again?',7313,0);
INSERT INTO comment VALUES (7315,1206,1626,'Gamer','re(3): Full Solution','2003-08-23 15:26:42',4,'Yes please... I don\'t know if others know what the solution is.\r\n\r\nI am just figuring out pre tags, but it seems like they force the script over like they always have. So when it\'s in pre tags it will keep typing over and over and over even if you run out of space. Is that right or have my observations led me astray?',7314,0);
INSERT INTO comment VALUES (7316,1206,1301,'Charlie','re(3): Full Solution','2003-08-23 15:32:13',0,'When entering text with pre and /pre, the next paragraph after the closing /pre never word wraps. After closing a pre with /pre on this venue it\'s always a good idea to put a short paragraph just after the closing /pre. Lacking anything to put in a short paragraph, I usually put a line of hyphens.',7314,0);
INSERT INTO comment VALUES (7317,573,1301,'Charlie','re: Similar','2003-08-23 15:46:41',0,'Similar also is three conventioneers, one streetwalker and two condoms.',7290,0);
INSERT INTO comment VALUES (7318,1179,1575,'DJ','Solution','2003-08-23 20:13:33',3,'The letters listed are the ones that, when pronounced, are an English word:\r\neh, bee, see, gee, eye, jay, oh, pea, queue, are, tee, you, why.\r\nI\'m guessing the \'Canadian\' reference was to the first letter, which is pronounced \'eh.\'\r\n\r\nAs to the second grouping, perhaps those are the ones that can be spelled more than one way (sea, see; eye, aye), although I don\'t know of a spelling for \'a\' besides \'eh.\'\r\n\r\nAny ideas?',NULL,0);
INSERT INTO comment VALUES (7319,1179,3136,'Popstar Dave','re: Solution','2003-08-23 20:49:42',0,'I had a similar thought. Except that \"q\" could be \'queue\' or \'cue\', \"t\" could be \'tee\' or \'tea\', and \"u\" could be \'you\' or \'ewe\'. Also, \'em\' and \'en\' are both words. \r\nSo now I\'m not too sure.',7318,0);
INSERT INTO comment VALUES (7320,1179,1626,'Gamer','re(2): Solution','2003-08-23 21:55:04',0,'I heard that, but I don\'t know what em or en means... surely they aren\'t common words.',7319,0);
INSERT INTO comment VALUES (7321,52,3182,'Antonio','Solution','2003-08-24 03:16:48',3,'Moons perimeter = 1,738,000*Pi = 5460088.03194 mts\r\nRope = 5460088.03194 - 1 = 5460087.03194 mts\r\nNew diameter = 5460087.03194/Pi = 1737999.68169 mts\r\n\r\nGroove\'s depth = (1,738,000 - 1737999.68169)/2 = .159155 mts ',NULL,0);
INSERT INTO comment VALUES (7322,49,3182,'Antonio','Solution','2003-08-24 04:05:48',3,'I imagine a rectang of bottom 20*Pi=62.8318530718ft and a height of 200ft, we draw a 30 degree line at the lower left corner and measure the hypotenuse that results in the interior of the rectang. The rectang contains 5 rectangular triangles with an hypotenuse of 72.5519745694ft and one final rectangular triangle with an hypotenuse of 37.240127152ft. We just sum all hypotenuses and it gives 5*72.5519745694 + 37.240127152 = 400ft\r\n\r\nThe difference would be 400ft - 200ft = 200ft ',NULL,0);
INSERT INTO comment VALUES (7323,1115,3206,'Lawrence','Simple LCM','2003-08-24 05:59:40',3,'This is a simple Least Common Multiple problem, remember those? Luckily I recently took the GMAT, and spotted it immediately. So you break each down to it\'s primes, then pick the highest power of each prime from each number and multiply. That gives you the number of teeth, then simply divide by the number of teeth for A to get the solution.\r\n\r\nFor A, 35 = 7 x 5\r\nFor B, 27 = 3 x 3 x 3\r\nFor C, 84 = 2 x 2 x 3 x 7\r\nFor D, 34 = 17 x 2\r\n\r\nTherefore the LCM = 2 x 2 x 3 x 3 x 3 x5 x 7 x 17 = 64,260\r\n\r\nDivide that by the number of spokes for each to get the number of revolutions for each.\r\n\r\nRevs for A = 1836\r\nRevs for B = 2380\r\nRevs for C = 765\r\nRevs for D = 1890',NULL,0);
INSERT INTO comment VALUES (7324,38,3182,'Antonio','Solution','2003-08-24 06:04:17',3,'Green triangle area = 8*3/2 = 12\r\nSky blue triangle area = 5*2/2 = 5\r\nOrange-yellow area in A = 15\r\nOrange-yellow area in B = 8*2 = 16\r\n\r\nThe area of the figure A is 12 + 5 + 15 = 32\r\nThe area of the figure B is 12 + 5 + 16 = 33\r\nFigure B is bigger than A, so we subtract B - A = 33 - 32 = 1\r\n\r\nThe extra square in B comes from the diference of the figures A and B, representing an invisible figure in A composed by 2 triangles of sides √29, √73 and √194. The area of these two triangles will give an area of 1, the extra square.',NULL,0);
INSERT INTO comment VALUES (7325,1115,3206,'Lawrence','re: Simple LCM','2003-08-24 06:09:18',0,'OK, you got me. Didn\'t get the visual on this one. Half a rotation works too, no kiddin\'. I feel like that guy from the Holy Grail that went flying into the pit.',7323,0);
INSERT INTO comment VALUES (7326,1110,3206,'Lawrence','Simple Enough','2003-08-24 06:18:54',3,'There are only 4 possible outcomes: \r\n1. Make both - prob .8 x .8 = .64 \r\n2. Miss both - prob = .2 x .2 = .04\r\n3. Make first, miss second - prob = .8 x .2 = .16 \r\n4. Miss first, make second - prob = .2 x .8 = .16\r\n\r\nYou can just add #s 3 and 4, OR you could\'ve done 1 - (#1 +#2) = 1 - (.64 + .04) = .32\r\n\r\nHope I get this one, unlike the gears. Don\'t think half a rotation on the bball matters here, though.',NULL,0);
INSERT INTO comment VALUES (7327,1110,3206,'Lawrence','re: Simple Enough','2003-08-24 06:23:22',0,'Guess that\'s why these are riddles. The obvious is never the answer. If you miss the first, you wouldn\'t attempt to make the second. You did see Larry Bird though, stealing the ball with about 5 seconds left and making the shot back when in the playoffs, right. Could happen.',7326,0);
INSERT INTO comment VALUES (7328,6,3182,'Antonio','Solution','2003-08-24 06:37:20',3,'Form an equilatteral triangle, then put a match from the middle of the bottom side to the middle of one of the other sides, use another match and put it the same way but with the other side, finally put a match parallel to the botom match but intersecting the upper vertex of the first triangle and at the same time touching the end points of the previous arranged two matches. \r\n ',NULL,0);
INSERT INTO comment VALUES (7329,600,3206,'Lawrence','Hmm, should I?','2003-08-24 06:39:18',0,'OK, I\'m 0 for 2 on my last 2, but 2 for 2 on the first two, so here goes.\r\n\r\nAdding all the balls up, you come up with 89 balls. Subtracting the number of balls for each box has to be an even number, otherwise you wouldn\'t have the same red and blue. This eliminates 3 of the boxes. Then you have to figure how you could add up to the half number remaining -- you like my poor English?\r\n\r\nLike so\r\n89 - 5 = 84\r\n89 - 7 = 82\r\n89 - 14 = 75, but odd, so no good\r\n89 - 16 = 73, also odd, so no good\r\n89 - 18 = 71, also odd so no good\r\n89 - 29 = 60\r\n\r\nWith the remaining balls, you have to add up to half of one of the above, 41, 42, or 30. 30 works out well, because 7 + 5 + 18 = 30, and 16 + 14 = 30. The others don\'t add up. Therefore, the box of 29 was sold.',NULL,0);
INSERT INTO comment VALUES (7330,1094,3206,'Lawrence','Another Simple one, I hope','2003-08-24 06:46:15',0,'Pulling out the prime factors, you come up with 3x3x3x3x7 = 567. So the twins are each 3 x 3 = 9 and the other is 7.',NULL,0);
INSERT INTO comment VALUES (7331,1211,1575,'DJ','Starters','2003-08-24 07:08:25',2,'I won\'t post a full solution now, but there is one useful point that could be made. For any point (x, y), the point will only be invisible if x and y share a common factor. For example, if they both have a factor of some number n, such that x=an and y=bn, then the point (x, y)=(an, bn) will always be invisible because the point (a, b) will be in the way.\r\n\r\nIn other words, if the two coordinates of a point share any common factor, there will be some point directly between the given point and the origin, found by factoring out the common term from both values.',NULL,0);
INSERT INTO comment VALUES (7332,1179,1575,'DJ','re(2): Solution','2003-08-24 07:09:13',0,'Yeah, you\'re right about the seconds part; that was just my only guess.\r\nHowever, I\'m fairly certain that my first guess is correct, as \'em\' and \'en\' are not really words. If you find them in the dictionary, they are listed as the pronunciation of the letter itself (if you counted that, then all letters would be valid), or as a prefix. In printing, an \'em\' is used to describe the amount of space a capital M takes up, or a square of a certain size that defines a font, while an \'en\' is half that width, but neither is a common or accepted word.\r\n\r\nMaybe I should change my answer to, these are the letters that, when pronounced, could also be a common, acceptable, everyday English word.',7319,0);
INSERT INTO comment VALUES (7333,1111,3206,'Lawrence','Vague','2003-08-24 08:05:00',0,'OK, I got this one in about 2 seconds after simply moving them and doing it in 4,then realizing you had to switch the 2 S\'s. However, the directions say something about doing something to form \"another common word.\" Thing is that word another can throw you off here. Looked at it for about 10 more minutes, then looked at your solution. This one was vague. Yeah, I\'m that guy from your class who complained about the one question he got wrong on the test because of poor wording -- hahaha. Let it go, man, let it go. hahaha',NULL,0);
INSERT INTO comment VALUES (7334,1211,1626,'Gamer','Solution','2003-08-24 09:14:39',3,'I hope I can post a solution to this and not spoil it for the rest of you... It\'s actually a cool problem :)\r\n\r\nIt has been my opinion that x or y needs 2 DIFFERENT factors. If its factors are all the same, then x, y and x, y+1 couldn\'t be both invisible. (Also, 1 doesn\'t count as a factor here.)\r\n\r\nThis excludes all powers of 2, 3... and prime numbers. (A space means no and an = means yes.)\r\n\r\n 1\r\n 2\r\n 3\r\n 4\r\n 5\r\n=6\r\n 7\r\n 8\r\n 9\r\n=10\r\n 11\r\n=12\r\n 13\r\n=14\r\n=15\r\n 16\r\n 17\r\n=18\r\n 19\r\n=20\r\n=21\r\n=22\r\n 23\r\n=24\r\n 25\r\n\r\nThe lowest numbers where x and x+1 are both yes is 14 and 15, and the lowest other set are 20 and 21.\r\n\r\nIt happens that these two pairs work.\r\n\r\n(14,20) is blocked by (7,10)\r\n(14,21) is blocked by (2,3)\r\n(15,20) is blocked by (3,4)\r\n(15,21) is blocked by (5,7)',NULL,0);
INSERT INTO comment VALUES (7335,1206,3206,'Lawrence','Solution','2003-08-24 10:51:13',0,'Based on all the clues we know that some eat ham, some have sausage and some bacon, so there \r\n\r\nare exactly two of each meat, because Mrs. F won\'t cook any item for just one. Same with \r\n\r\nthe beverages.\r\n\r\nLooking only at #6, we know the following\r\n\r\nThe sausage eaters have tea, so\r\n\r\nentree([e]gg,[p]ancake)/meat([b]acon,[h]am,[s]ausage)/beverage([c]offee,[t]ea,[m]ilk)\r\n?st\r\n?st\r\n\r\nsince all meals are different then one st has pancakes, the other eggs, so\r\n\r\nest\r\npst\r\n\r\nFrom #6, we can fill in most of the rest of the meals\r\n\r\nest\r\npst\r\np?c\r\np?c\r\n??m\r\n??m\r\n\r\nBob drinks coffee (#5), and has Ham (#2), so\r\n\r\nest\r\npst\r\nphc - Bob\r\np?c\r\n??m\r\n??m\r\n\r\nAgain, since no two meals are exactly alike, and there are exactly 2 of each meat we can \r\n\r\nfill in much of the rest\r\n\r\nest\r\npst\r\nphc - Bob\r\npbc\r\n?bm\r\n?hm\r\n\r\nThere are more than 2 eggs (#7), so the last two had to be eggs\r\n\r\nest\r\npst\r\nphc - Bob\r\npbc\r\nebm\r\nehm\r\n\r\nThe other ham was Chuck, from #2, so \r\n\r\nest\r\npst\r\nphc - Bob\r\npbc\r\nebm\r\nehm - Chuck\r\n\r\n\r\nAl doesn\'t eat sausage, so he is either pbc or ebm, BUT Al sit\'s next to the boarder who \r\n\r\neats bacon and pancakes (pb?), so Al eats ebm, NOT pbc\r\n\r\nest\r\npst\r\nphc - Bob\r\npbc\r\nebm - Al\r\nehm - Chuck\r\n\r\nNed doesn\'t like pancakes, so he is est\r\n\r\nest - Ned\r\npst\r\nphc - Bob\r\npbc\r\nebm - Al\r\nehm - Chuck\r\n\r\n\r\nPeter doesn\'t like Bacon, so he must be pst. And Will fills in the last spot.\r\n\r\nest - Ned\r\npst - Peter\r\nphc - Bob\r\npbc - Will\r\nebm - Al\r\nehm - Chuck\r\n\r\n\r\nWhy do these things sound so much easier when you write them than when you actually do them?',NULL,0);
INSERT INTO comment VALUES (7336,1138,3206,'Lawrence','Solution','2003-08-24 11:35:15',0,'This one is easy with a spreadsheet application. The \"split\" thing tells you that the last two numbers are from 50 to 99, and the first two are double the last. When you do that and concatenate the numbers then triple and squareroot, the number just pops out at you. Your number is 13467, when tripled is 40401, the squareroot of which is 201.',NULL,0);
INSERT INTO comment VALUES (7337,1038,3206,'Lawrence','Solution','2003-08-24 11:47:29',0,'Easiest way to do this is cash flow for Mike and see how that compares to the $40.\r\n\r\nMike is out (20) when he pays for it, then sells it for 30, he\'s up +10, then he pays $40 for it, so he\'s out (30). Then he gets 50, so he\'s up +20. He then pays $60 for it, so he\'s out (40). The bike is worth 40, so he\'s at break even. No need to see what money he\'s out each time, just figure the net outflow of cash, i.e. $40, and there it is.',NULL,0);
INSERT INTO comment VALUES (7338,571,3206,'Lawrence','Solution','2003-08-24 12:04:39',3,'Well, if it\'s ok, fill one, then put an empty one on top of that upside down, then another full one, then an upside-down empty, then a full, then an upside down empty, then a full. That will make you 4. Then put those on bottom and do the same thing, full-empty-full on top, then when that\'s done, put the 6 frozen on bottom and the last one filled to be frozen on top. It\'ll take three cycles. Meanwhile, buy a damn icemaker.',NULL,0);
INSERT INTO comment VALUES (7339,567,3206,'Lawrence','Solution','2003-08-24 12:19:48',0,'B made the correct statement because R wins.\r\n\r\nRestated as to who can win in each statement\r\n1. P,S\r\n2. Q,R,S\r\n3. P,Q\r\n\r\nLook at the above and eliminate duplicates, only R can win.',NULL,0);
INSERT INTO comment VALUES (7340,1008,3206,'Lawrence','Solution','2003-08-24 12:24:28',0,'All those drinking coffee have 2 e\'s in their names. The others are drinking soda. Elizabeth has 2 e\'s, so she is drinking coffee, which also has two e\'s. Cream and two sugars, please.',NULL,0);
INSERT INTO comment VALUES (7341,946,3206,'Lawrence','Solution','2003-08-24 12:40:47',0,'I\'ll have a piece of paper in my hand that says LIFE on it when I put my hand into the hat, that\'s what I\'ll do. Or I could just pull out both of them that are in there, and everyone would know. Then I\'m gonna beat the person who did that, so they\'ll probably kill me anyhow. it\'s really a no win situation.',NULL,0);
INSERT INTO comment VALUES (7342,1211,1575,'DJ','Full Solution','2003-08-24 13:00:05',3,'(14, 20), (15, 20), (14, 21), (15, 21)\r\n\r\nThe first thing to do is find out where the \"visible\" and \"invisible\" points are. A point will be visible iff its coordinates are relatively prime, that is, x and y have no common factors. On the same line of reasoning, a point is invisible iff its coordinates have at least one common factor.\r\n\r\nTherefore, to make a square, we need to find two consecutive values that have two consecutive common factors. Before we start, let\'s note a few things:\r\nA prime number n will never have two adjacent invisible points, since its only invisible points will be of the form (x, n) or (n, y) when x or y is a factor of n.\r\nSimilarly, any number with only one prime factor (a perfect square, cube, etc) will also only have invisible points when the other coordinate is a multiple of its prime factor.\r\n\r\nTherefore, we are looking for two consecutive values that each have more than one prime factor.\r\n 0 - all but (0, ±1) and (±1, 0) are invisible\r\n 1 - all values are visible\r\n 2 - prime\r\n 3 - prime\r\n 4 - perfect square\r\n 5 - prime\r\n* 6 - factors of 2 and 3\r\n 7 - prime\r\n 8 - perfect cube\r\n 9 - perfect square\r\n* 10 - factors of 2 and 5\r\n 11 - prime\r\n* 12 - factors of 2 and 3\r\n 13 - prime\r\n* 14 - factors of 2 and 7\r\n* 15 - factors of 3 and 5\r\n\r\n
\r\nFinally, we have some values.\r\n14 and 15, then, must be the lower of the two sets of coordinates. So, to match 14, the other values will be an odd multiple of 7 and either of the adjacent even numbers; to match 15, we just need adjacent multiples of 3 and 5. So, the odd multiple of 7 needs to also be a multiple of 3 or 5. The smallest way to do this (which is what we are looking for), of course, is just to multiply 3 and 7 to get 21. Happily, we see that one of the neighboring even numbers, 20, is indeed a multiple of 5. So, there is our answer. Also, any reflection or rotation is the same distance from the origin, so there are really eight squares:\r\n( 14, 20), ( 15, 20), ( 14, 21), ( 15, 21)\r\n( 20, 14), ( 21, 14), ( 20, 15), ( 21, 14)\r\n(-14, 20), (-15, 20), (-14, 21), (-15, 21)\r\n(-20, 14), (-21, 14), (-20, 15), (-21, 14)\r\n( 14, -20), ( 15, -20), ( 14, -21), ( 15, -21)\r\n( 20, -14), ( 21, -14), ( 20, -15), ( 21, -14)\r\n(-14, -20), (-15, -20), (-14, -21), (-15, -21)\r\n(-20, -14), (-21, -14), (-20, -15), (-21, -14)\r\n\r\n
\r\nThese are all equivalent.\r\n\r\nAnother way to find these squares is to realize that all we need multiples of four distinct primes. Obviously, this will be minimized if we use the lowest primes (2, 3, 5, 7), so we could have just written out a list of all the numbers that have at least two of these primes as factors:\r\n6, 10, 12, 14, 15, 18, 20, 21 ..\r\n\r\n
\r\nWe can stop there.\r\nWe have already found two consecutive pairs, 14 and 15, and 20 and 21, the same ones as before, and we didn\'t have to look far.\r\nWe didn\'t have to look far to find the same answer.\n\nEdited on August 25, 2003, 10:18 pm',NULL,0);
INSERT INTO comment VALUES (7343,924,3206,'Lawrence','Solution','2003-08-24 13:03:58',3,'For line 2, replace the $$$ with it\'s equivalent in line 1.\r\n*%*%*% = @%*%@\r\n\r\n and then using line 3 replace the @\r\n*%*%*% = !*%*%!*\r\n\r\nget rid of the *** from each side\r\n%%% = !%%!\r\n\r\ntherefore\r\n!! = %\r\n\r\nSubstitute for the line we for which we are attempting to determinine a winner:\r\n\r\nFor the left side, simply replace the @ using line 3\r\n!!*!!!*!\r\n\r\nFor the right side, use a bit of everything we\'ve discovered\r\n!!*!!**!!\r\n\r\nboth of these have 5 !s, but one has 3*, the other 2*. Therefore, the right side, or %$*$ wins by *.',NULL,0);
INSERT INTO comment VALUES (7344,914,3206,'Lawrence','George Carlin was here?','2003-08-24 14:12:54',1,'Who would keep looking after they find something? This is a George Carlin rip-off, which may be a rip-off from somewhere else, who knows.',NULL,0);
INSERT INTO comment VALUES (7345,919,3206,'Lawrence','re: Most realistic solution','2003-08-24 14:29:44',0,'Wording of the problem is a bit risky ... if Sa is 1.5 times OLDER than Sb, then he is actually Sa = 1.5Sb +Sb, in which case Sa is 25, and both fathers are 50. 1.5 times the age of is better. When you say 1.5 times older than, then the difference is what you are referring to. As I end my sentence in a preposition, which is acceptable these days, I\'ll just say, so what, right. This is just for fun.',5675,0);
INSERT INTO comment VALUES (7346,900,3206,'Lawrence','Solution','2003-08-24 15:30:37',0,'This one was fun. And I love that game.\r\n\r\nFirst thing you do is figure out all the letters. Adding the W makes an even 16. Then figure out what letters go next to which. A has 7 letters next to it, so it must go in one of the four middle places. C, O, R, E (interesting that it comes out to core) all have 4 letters and are best candidates for the other 4 middle spots. The letters in PINT don\'t need much, so probably on the side. Lining that up with AGE as A needs its letters, you start putting things where they go, and then BAMMO! The only thing I can\'t spell is archly. My C and O are horizontal, right to left, but can\'t do it. Then I realize AGE and PINT are linear, not necessarily right to left or top to bottom. Flipping those and putting things right again made it all better.\r\n\r\nHere it is ...\r\n\r\nWMET\r\nOCGN\r\nHRAI\r\nYLFP',NULL,0);
INSERT INTO comment VALUES (7347,917,3206,'Lawrence','Solution','2003-08-24 16:03:21',0,'Far as I can tell, none of these guys has my wallet. Since they either lie or tell the truth, the easiest way to figure it is to pick one and assume one way, then go until the theory breaks. I assumed Allen told the truth, which leads to the deaf man, Fred, being a liar about not being deaf, so Barry stole it. If Barry stole it, he is lying about not stealing it and therefore also about Allen not stealing it, but is it possible they both stole it. OK, having been born and raised in New Orleans, I had to say it is possible they worked together, but not here, right. So Allen is a liar, go from there, noone stole it. That\'s it. And I looked and looked again, and one more time. You left your wallet on the counter, I don\'t know, but these guys don\'t have it.',NULL,0);
INSERT INTO comment VALUES (7348,541,3206,'Lawrence','Solution','2003-08-24 16:06:48',0,'God in blue sky (blue face? maybe), Jesus or man on green earth, green being the face of the planet.',NULL,0);
INSERT INTO comment VALUES (7349,845,3206,'Lawrence','re: solution','2003-08-24 16:34:22',0,'You are so right. I came up with 2 as well. How 2121 works is beyond me. Going right to left, the first 2 gives 11. Crazy, I\'m just saying.',5810,0);
INSERT INTO comment VALUES (7350,905,3206,'Lawrence','Solution','2003-08-24 17:04:46',0,'I started with Q3 and assumed C for Q1 was right and went from there.\r\nSo Answer #3 is (D)1.\r\n\r\nSo Answer #1 to be (C)D\r\n\r\nSo Answer #2 is (D)\r\n\r\nLeft 4 alone for now.\r\n\r\nI looked at #6 and realized one of the last questions was A. Then went on to #7. As of right now, D occured consecutively once,\r\n\r\nso Answer #7 is (C)1.\r\n\r\nThen looked at number 8 and decided it had to be D or C, I opted for D on a hunch, \r\n\r\nso Answer #8 is (B)D\r\n\r\nB is now right twice and I don\'t want it thrice, \r\nso Answer #4 is (B)2\r\n\r\nand Answer #5 is (D)2.\r\n\r\nLeaving #6 to answer itself as the last, and only Question with A as the answer\r\n\r\nAnswer #6 is (A)6\r\n\r\nSo the answer key \r\n\r\n1 C\r\n2 D\r\n3 D\r\n4 B\r\n5 D\r\n6 a\r\n7 C\r\n8 B',NULL,0);
INSERT INTO comment VALUES (7351,905,3206,'Lawrence','re: Solution','2003-08-24 17:07:34',0,'When I said, I left 4 alone for now, that can\'t be right, because since 2 is D, 4 is B which meant B darn well better only show up twice, which it did.',7350,0);
INSERT INTO comment VALUES (7352,848,3206,'Lawrence','Six is good enough','2003-08-24 17:22:22',3,'LONE\r\nHONE\r\nHOLE\r\nHOLD\r\nHOOD\r\nWOOD or HOOF\r\nWOOF\r\nWOLF',NULL,0);
INSERT INTO comment VALUES (7353,1179,1575,'DJ','Second part?','2003-08-24 17:34:57',1,'One thing I noticed, when typing my last comment, about the words \"eh,\" \"see,\" \"sea,\" \"eye,\" and \"aye,\" is that none of them are spelled using the letter they are supposed to sound like. However, there is still the consideration of \"cue\" for q, although \"queue\" is spelled using the q. So, perhaps the answer to the second part is that these letters sound like words that can\'t be spelled using the letter itself?',NULL,0);
INSERT INTO comment VALUES (7354,859,3206,'Lawrence','Solution','2003-08-24 17:43:10',0,'Never read the Hobbit, but I think it would have to be TIME, i.e. erosion, decay, old age, etc.',NULL,0);
INSERT INTO comment VALUES (7355,847,3206,'Lawrence','The incredible shrinking potato ...','2003-08-24 17:51:17',3,'Well, at 100 lbs, there\'s 1 lb of potato and 99 lbs of water. The 1 lb of potato will remain constant. At 98%, then the 1 lb of potatoes is now 2% of the weight, so the water is now 49 lbs and the potato 1 lb, so it weighs 50 lbs. When you finally get to the point of 50%-50%, the 1 lb of potato is still 1 lb, and the other equally sized 50% is also 1 lb, so you have a 2 lbs of incredible shrinking potato.',NULL,0);
INSERT INTO comment VALUES (7356,847,3206,'Lawrence','Genetics and percentages','2003-08-24 18:04:53',0,'Have you ever heard that chimps and man are 97% the same genetically? Or that no man is more than 99.7 percent different than any other man, genetically speaking? This bothers me, not because of the genetics, but because of the math. How many instructions are there per genome? Billions, trillions, right? I mean I\'m not a geneticist, but that\'s what I hear. So if we are 97 % the same, then we are 300,000,000+ instructions different than all of them. I\'d really like to get a number on this, because if it\'s in the low billions, then there is someone genetically exactly like you somewhere in the world of 6.3 billion people, heck more than one even. You do the math.',NULL,0);
INSERT INTO comment VALUES (7357,835,3206,'Lawrence','Solution','2003-08-24 18:20:18',0,'I came up with 8, thinking like a Knight I started in one corner then up 2 over 1 until I got to the end and carried it over. A8, B6, C4,D2,E7,F5,G3,H1. How\'s that? Can\'t be more than 8.',NULL,0);
INSERT INTO comment VALUES (7358,836,3206,'Lawrence','Solution','2003-08-24 18:33:45',0,'Bid 99 cents, I suppose. Anything less leaves me open to a bid that someone could trump. Since there is nothing to gain, i.e. nothing to \"Win\" by bidding a dollar, noone would, according to your rules, and not this utopian society. What I would do is wait for the first bid. Or I could wait to see if anyone else bids, and be the second, and bid 99 cents, then the auctioner makes some money off the other chump.\r\n\r\nIn this world though, someone would bid a dollar just to screw me out of my 99 cents. The best thing to do would be to make a deal with the dollar holder, and then bid a dollar SECOND, and split the take with the dollar holder. Would be hard to convince the dollar holder to do that though. So I\'ll stick with 99 cents.',NULL,0);
INSERT INTO comment VALUES (7359,538,3206,'Lawrence','Solution','2003-08-24 18:41:08',0,'-3, -1, 1 multiply to 3 which is prime, and they are 2 apart from each other in Arithmetic Progression. Anything else would be divisible by something, and therefore not prime. Prime numbers are only positive starting at 2, so this is all I can come up with.',NULL,0);
INSERT INTO comment VALUES (7360,824,3206,'Lawrence','Check your stopwatch','2003-08-24 18:46:55',0,'I got this one pretty quickly. He hung himself by standing on an ice cube. Middle of the desert is a big hint because it melted quickly. Lucky bastard.',NULL,0);
INSERT INTO comment VALUES (7361,844,3206,'Lawrence','Solution','2003-08-24 19:08:53',0,'This one is just math ...\r\n\r\nThe rate of the escalator, r steps per second, is assumed to be constant. If the escalator were stopped, there would be a certain number of steps or distance to travel. I called that distance d.\r\n\r\nThat distance is the same all three days and therefore we have 2 equations to set up. The total distance covered is the same each trip all three days.\r\n\r\nDay one took me 30 seconds to get to the top and day two took me half of 36 or 18 seconds.\r\n\r\nSo on day one\r\nd steps = 30 steps + r(30 seconds)\r\n\r\non day two\r\nd steps = 36 steps + r steps/second(18 seconds)\r\n\r\nsimply subtract one equation from the other to get\r\n0 = -6 steps + 12 steps r\r\n6 = 12 r\r\n1/2 = r\r\n\r\nTo check it, you go half a step per second on the escalator at its own rate, so on day one in 30 seconds he went 15 steps by the escalator\'s rate only, plus the 30 he climbed, that\'s 45 steps.\r\n\r\nOn Day Two, the escalator takes him 9 steps in 18 seconds, and he climbed 36, so there are 45 steps. BINGO. He\'s tired, the escalator takes 90 seconds to get him up the 45 stairs at half a stair per second. The end.',NULL,0);
INSERT INTO comment VALUES (7362,1179,3202,'Jill','re: Second part?','2003-08-24 20:12:10',0,'Ok...assuming that the letters are the pronunciations for english words (which btw \"a\" could be eh or a) maybe the Canadian bit comes in because a, c, and i are the only letters in the word Canadian left....seems a little lame but ... no other ideas at this time. ',7353,0);
INSERT INTO comment VALUES (7363,1026,3043,'Angel','possible solution?','2003-08-25 01:56:26',0,'i think the answer is 8 total bags of coins.\r\nyou start out with 7 bags of 12 gram coins and 1 bag of 11 gram coins.\r\nsplit the 8 bags into groups of 2 and weigh one of the groups of 4 bags. if the weight is divisible by 12 then the other group has the bag of fake coins. if not, then the group weighed has the fake coins.\r\nthen split the group with the fake coins in 2, and weigh one of the groups with 2 bags. if the weight is divisible by 12 then the other group has the fake coins.\r\nyou are then left with 2 bags. one with real coins and one with fake. weigh either one of them and divide the weight by 12. you will then know which is fake and which is real.',NULL,0);
INSERT INTO comment VALUES (7364,1015,3223,'Michael Glass','re: No Subject','2003-08-25 03:05:43',0,'I\'m sure he was going there to pick up a case of dnL',7177,0);
INSERT INTO comment VALUES (7365,605,3225,'Jenna','','2003-08-25 09:14:46',1,'There is more than one solution to this problem.\r\n\r\n\r\nI would say Mr. X is the Engineer, and his son is the Doctor.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (7366,605,1301,'Charlie','solution','2003-08-25 09:18:50',3,'You can tell who the Engineer is, but not the Doctor. \r\n\r\nThe son is the youngest, and is also a blood relation to all the others, so by (2) he cannot be the Engineer.\r\n\r\nBy (3), if Mr.X\'s mother were the Engineer, she and the Doctor would be blood relatives. But her blood relatives here are all male, and this would violate rule (1). So Mr.X\'s mother is not the Engineer.\r\n\r\nBy (3), if the wife were the Engineer, she\'d be a blood relative to the Doctor, but her only blood relative here is the son, whose being the Doctor would require the Engineer to be male by (1). So the wife cannot be the Engineer.\r\n\r\nThe Engineer must actually be Mr.X.\r\n\r\nSince the Engineer is male, rule (1) has no further consequences--the Doctor can be either male or female.\r\n\r\nIf the mother were the Doctor, rule (2) would be violated, so the mother is not the Doctor.\r\n\r\nRule (3) has no further effect, as the Engineer is not a female.\r\n\r\nThe Doctor could be either the wife or the son without violating any of the statements.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (7367,605,1575,'DJ','Solution','2003-08-25 10:44:55',3,'A statement of the form \"if A, then B\" can be ignored if A is not true.\r\n\r\nIf the doctor is a female younger than the engineer, and the engineer is a male, then all three statements can be ignored.\r\nThis is possible only if Mr. X is older than his wife, and he is the engineer while she is the doctor.\r\n\r\nIf the first \"if\" statement is true, and the other two are still false, we have another valid solution. This happens when the doctor and engineer are both males, and the engineer is older than the doctor.\r\nThere are only two men in the problem, so this occurs when Mr. X is the engineer and his son is the doctor.\r\n\r\nSuppose only the second \"if\" statement is true. That means the doctor is a female, the engineer is a male that is younger than the doctor, and they are not blood relatives.\r\nEither of the men (Mr. X and his son) could be younger than either of the women, so we just need to find a man and woman that aren\'t blood relatives. The son is a blood relative to each of the other three, and Mr. X is a blood relative to his mother and his son.\r\nTherefore, this only occurs when Mr. X is the engineer, his wife is the doctor, and she is older than him.\r\n\r\nIf only the third \"if\" statement is true, then the doctor and engineer are both female, the engineer is older than the doctor, and they are blood relatives. Since the only two women in the problem are not blood relatives, this will never happen.\r\n\r\nIf both of the first two \"if\" statements are true, then both the engineer and the doctor are male, but they are not blood relatives; this is not possible.\r\n\r\nSimilarly, if the second and third \"if\" statements are both true, they are blood relatives and they are not blood relatives; we have an obvious contradiction.\r\n\r\nFinally, if the first statement is true, both are males, and the third will never be true.\r\n\r\nThat is the entire realm of possiblity, and there are three combinations of the parity of the statements that yield a valid conclusion. Two of these are equivalent, except for whether Mr. X or his wife is older, so there are two disctinct possiblities for who are the doctor and the engineer.\r\n\r\n
',NULL,0);
INSERT INTO comment VALUES (7368,1117,1301,'Charlie','a proof','2003-08-25 13:17:23',1,'This proof uses 8 points; I don\'t know if that\'s minimal:\r\n\r\nTake a grid of points at the vertices of tesselated equilateral triangles of side length 1. Take one equilateral triangle with sides 2 units long. Either all three vertices are the same color (in which case we\'ve met the desired condition) or two are one color and one is another. Call the two of the same color A and the odd color B, and set the points (as well as 5 neighboring points of the grid labeled with digits) out as below:\r\n\r\n\r\n 2 A\r\n 4 1 3\r\n B 5 A\r\n
\r\n\r\nPoint 1 must be either color A or color B.\r\n\r\nIf it is color A, then point 2 must be color B to avoid the triangle 1,2,top-existing-A from being all A; and point 3 must be color B to prevent 1,3, top-existing-A from being all A. But then triangle 2,3,original-B form an equilateral triangle that\'s all B.\r\n\r\nIf on the other hand point 1 is color B, then point 4 must be color A to avoid 1,B,4 from being all B; and point 5 must be color A to prevent 1,5,B from being all color B. But then triangle 4,5,original-top-A is all A.\r\n\r\nThis exhausts the alternatives: somewhere along the line we had an equilateral triangle with vertices of all one color.',NULL,0);
INSERT INTO comment VALUES (7369,1117,2899,'Brian Wainscott','Another proof','2003-08-25 17:35:34',0,'I have a proof by contradiction that uses 7 points:\r\n\r\nSuppose there are no such monochrome equilaterial triangles.\r\nCall the colors Red and Blue. Pick two Red points a and b in the plane\r\n(if you can\'t do this, Blue triangles are pretty easy to\r\ncome by...)\r\n\r\nRotate/translate/whatever your coordinate system (or your brain) so\r\nthat one of these points a is at (0,0) and the other b is at (1,0). Now\r\nconsider the points below (Sorry about the strange formatting, please ignore the _, I couldn\'t get this system to line things up nicely):\r\n\r\n __1\r\n _2_3\r\n a_b_4\r\n _5\r\n\r\nwhich are spread out at the corners of equilaterial triangles. Since\r\n(a,b,2) is not a Red triangle, 2 is Blue. Similarly for 5.\r\nNow, (2,4,5) form an equilaterial triangle, so that 4 must be Red.\r\nSo far then we have:\r\n\r\n __1\r\n _B_3\r\n R_R_R\r\n _B\r\n\r\nWhere R=Red, B=Blue. 3 must be Blue, since (3,b,4) form a triangle\r\nand b and 4 are Red. But then if 1 is Blue, we have a Blue triangle\r\n[(1,2,3) in the original numbering]. If 1 is Red, we have a\r\nRed triangle [(1,a,4) in the original numbering]. So either 1 is\r\nsome third color, or monochrome triangles do in fact exist.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (7370,605,3239,'paul','I have real solution!!!','2003-08-25 22:02:10',0,'The engineer is the son and the doctor is Mr. X\'s mother!\r\n\r\nI drew 4 people and labeled them and then I see wat is possible for the answers and i got the answer. No one told me the answer so dont think i cheated.\r\n\r\nP.S. I\'m only 12 lol',NULL,0);
INSERT INTO comment VALUES (7371,605,1626,'Gamer','Blood Relative?','2003-08-25 22:48:57',4,'I don\'t think the question was put in as to what exactly a blood relative is. I don\'t know and I would guess others don\'t either.',NULL,0);
INSERT INTO comment VALUES (7372,605,1575,'DJ','re: Blood Relative?','2003-08-25 22:58:42',0,'A person is a blood relative if they are directly related (not by marriage). Siblings, parents, children, etc, are blood relatives. Spouses and in-laws are not.',7371,0);
INSERT INTO comment VALUES (7375,605,3245,'sandy','the REAL solution, oops','2003-08-26 07:41:06',3,'ignore what the clue is telling u and read what it isnt telling u, \r\n1. the engineer must be older \r\n2.the dr is female \r\n3.engineer is male \r\nhence, the engineer is mr x, and his wife is the dr, both the son and mother are ruled out in the equation \r\n\r\ndr.bossie.cleo \r\n',NULL,0);
INSERT INTO comment VALUES (7376,1247,1183,'fwaff','Solution','2003-08-26 08:41:01',3,'The answer is M.\r\n\r\nAssigning numbers to each letter of the alphabet such that A=1, B=2,...,Z=26, the given letters produce:\r\n\r\n2, 3, 5, 7, 11, 17, 19, 23\r\n\r\nThese are all prime numbers less than 26. The only one missing is 13 (=M).',NULL,0);
INSERT INTO comment VALUES (7377,605,1301,'Charlie','re: the REAL solution, oops','2003-08-26 08:49:02',0,'How is the son ruled out?',7375,0);
INSERT INTO comment VALUES (7378,605,1301,'Charlie','re: solution','2003-08-26 08:51:15',0,'Regardless of whether Mr.X is younger than his wife, his wife could still be the doctor.\r\n\r\nThe statement\r\n2. If the Engineer is younger than the Doctor, then the Engineer and the Doctor are not blood relatives. \r\ndoes not say \"Only if...\", just \"If...\".',7373,0);
INSERT INTO comment VALUES (7379,605,1301,'Charlie','re: I have real solution!!!','2003-08-26 08:53:15',0,'But statement 2 says that If the Engineer is younger than the Doctor (which would be the case in your solution), then the Engineer and the Doctor are not blood relatives (but they would be blood relatives in your solution). \r\n',7370,0);
INSERT INTO comment VALUES (7380,1117,1567,'Bryan','5-point proof','2003-08-26 10:59:20',3,'Start with any two points, one red (R) and one blue (B). The point midway between them will obviously match the color of one point or the other. For the sake of argument, let\'s suppose it is red. B\r\nR R B\r\n X
Note that point X is equidistant from the two blue points as well as from the two red points. Whichever color it is, we have an equilateral triangle.',NULL,0);
INSERT INTO comment VALUES (7381,1247,3091,'Hans','re: Solution','2003-08-26 11:37:45',0,'I concur!\r\nM is missing.',7376,0);
INSERT INTO comment VALUES (7382,1117,3248,'Kelsey','re: 5-point proof','2003-08-26 15:29:18',0,'Brian\r\nI believe that the problem is asking for the fewest number of points so that no matter how you rearrange the colors you will always have an equilateral triangle with all of the same color points. If you place the two different colors in different positions but still keeping the five points you have there isn\'t an equilateral triangle meeting the condition. For example you can rearrange them like this:\r\n r \r\nb r b\r\n r \r\nThere is no equilateral triangle meeting the conditions in this arrangement. ',7380,0);
INSERT INTO comment VALUES (7383,1117,3248,'Kelsey','re(2): 5-point proof','2003-08-26 15:39:07',0,'Sorry \r\nMy diagram should have looked like this:\r\n__R\r\nB___R___B\r\n__R',7382,0);
INSERT INTO comment VALUES (7384,1247,3241,'catherine','missing letter','2003-08-26 15:50:51',0,'the letter m which would denote the prime number 13.',NULL,0);
INSERT INTO comment VALUES (7385,1144,1626,'Gamer','Pushed?','2003-08-26 16:00:45',4,'Ummm... I didn\'t see this in the queue... Did it get pushed when I was away today?',NULL,0);
INSERT INTO comment VALUES (7386,1247,3248,'Kelsey','','2003-08-26 16:39:29',0,'\"M\" is missing. The \"M\" represents the number 13 which is a prime number.',NULL,0);
INSERT INTO comment VALUES (7387,1117,1575,'DJ','re(2): 5-point proof','2003-08-26 16:51:48',1,'No; if the problem were asking for the fewest number of points so that you can rearrange the colors any way you want, that\'s what it would have said.\r\n\r\nWe are looking for the fewest number of points needed to prove that such a triangle must exist, which is exactly what Bryan has done.\r\n\r\nBy the way, 5 points (two of one color and two of another, with a fifth point that makes a triangle with both pairs) must be the minimum number of points.',7382,0);
INSERT INTO comment VALUES (7388,1112,3250,'Khanh','','2003-08-26 17:40:38',3,'The solution of the problem is that the first cube consists of the letters:G, H, B, T, M, and I; the second cube:O, C, E, N, J, and X; the third cube:A, U, V, F, W, and S; and the forth cube:D, R, K, Y, P, and L.',NULL,0);
INSERT INTO comment VALUES (7389,1144,3091,'Hans','Continuation','2003-08-26 17:56:55',0,'Therefore, no short kangaroos who are smart... ought to go swimming.\r\n\r\nDoes the kangaroo drive? ',NULL,0);
INSERT INTO comment VALUES (7390,903,3250,'Khanh','','2003-08-26 17:59:26',3,'The 1st cube has the letters:C, U, R, H, O, and J; the 2nd cube has: A, L, D, G, K, and M; the 3rd cube has:V, F, P, W, Z, and I; and the 4th cube has:E, B, Y, T, N, and S.',NULL,0);
INSERT INTO comment VALUES (7391,916,3250,'Khanh','','2003-08-26 18:19:29',3,'The 1st cube contains the letters:W, M, I, N, F, and G; the 2nd cube contains:A, S, V, O, U, and B; the 3rd cube contains:R, T, H, C, Q, and Z; and the 4th cube contains:P, E, D, Y, K, and L.',NULL,0);
INSERT INTO comment VALUES (7392,824,3250,'Khanh','','2003-08-26 18:32:48',3,'The man was standing on a block of ice in the middle of the desert so the ice melted quickly. And when it melted, he didn\'t have anything to stand on so he hung himself.',NULL,0);
INSERT INTO comment VALUES (7393,1206,3241,'catherine','my solution','2003-08-26 19:02:04',0,'Al: egg, bacon, milk\r\nBob: pancake, ham, coffee\r\nChuck: egg, ham, milk\r\nPeter: Pancake, sausage, tea\r\nNed: egg, sausage, tea\r\nWill: pancake, bacon, coffee',NULL,0);
INSERT INTO comment VALUES (7394,1206,3241,'catherine','re: my solution','2003-08-26 19:54:26',0,'are we supposed to show our workings out? sorry, I\'m new and dont know the rules.\r\nI started by checking off on a grid the given data statements (pos and neg) as in 1,2,3,4,5. It can then be established that the only one left for Al to sit next to who could have bacon and pancakes is Will. He could therefore be eliminated as a ham, sausage or egg eater. Nor can he drink tea, as it\'s the sausage eaters that do. (6)\r\nChuck and Bob eating ham, can\'t drink tea.\r\nFrom (6) and (1), Al not being a sausage eater cant be a tea drinker...this leaves only Peter and Ned to do so as each beverage must appear twice.\r\nTherefore Peter and Ned must also eat sausage. (Peter cant eat bacon or the ham that is chuck and Bob\'s). But they must not both eat pancakes as well or would have identical breakfast. We know from (4) that Ned doesnt eat pancakes, therefore Peter must, while Ned eats egg. So far we know that Peter eats pancakes, sausage and tea and Ned eats egg, sausage and drinks tea. Sausage and tea are out for anyone else. \r\nAs both Bob and Chuck have reserved the ham, Al and Will (already a proven bacon eater) must eat the bacon. \r\nWe know that there can only be at most 3 pancake eaters to satisfy (7). Peter we know is a pancake eater who drinks tea, therefore Bob who drinks coffee must also be a pancake eater for there to be 2 coffee drinking pancake eaters (6).`And Will, who we established as a pancake eater must be the other coffee drinker. That leaves Al, Chuck and Ned to be egg eaters. (Ned we knew already was one). With Bob and Will drinking coffee and the tea already taken by Peter and Ned, that leaves Al and Chuck to drink milk.\r\nWe have thus established all of my previous post.\r\n',7393,0);
INSERT INTO comment VALUES (7395,605,3241,'catherine','','2003-08-26 20:58:30',0,'i cant get past there being at least rwo possible solutions: Mr X as Engineer and the doctor being either a)the son or b) Mr X\'s wife. \r\nBoth of these options seem to satisfy the 3 points. \r\nIf Mr X is the engineer (3) becomes irrelvant. If the doctor is the son, (1) is satisfied. If the doctor is the wife then (1) is irrelevant. If the son is the doctor then (2) is irrelevant. If the wife is the doctor, Mr X can be either older or younger than her without violating (2) as they are not blood relatives.\r\nAs to Mr X\'s mother: If she was the engineer the doctor would (to satisfy 3) have to be a male to be blood related to her (mr x or his son) but if that was the case (1) would be violated. \r\nOld Mrs X would seem ineligible to be either the doctor or th3e engineer for the following reasons:\r\nIf Mr X\'s mother is the doctor then the only possible candidates will be younger, and therefore ineligible (2) as all but Mr X\'s wife are her blood relatives. Could Mrs X\'s wife be an engineer and be older than her mother-in-law? Possible, but in that case (3) would be seem to be violated because the two women presumably arent blood relatives. A possibility still exists if Mr X\'s wife is a cousin of some kind (perhaps old Mrs\'s X\'s much older sibling\'s child?) and thus could still be a blood relative of her mother-in-law. In that case (2) would be irrelevant.\r\nOld Mrs X cannot be an engineer without the doctor being female too (1). Again for (3) to apply, her daughter-in-law would have to be a relative(say,niece or nephew who married her cousin, Mr X). Precluding such scenarios, we will leave out old Mrs X as a candidate for any position and be left with Mr X as engineer and either his wife or his son as doctor.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (7396,1117,3248,'Kelsey','re(3): 5-point proof','2003-08-26 20:59:23',0,'The problem states what is the fewest number of points needed to prove an equilateral triangle with the same color on all the points exists. I\'m not saying you can rearrange the colors any way you want but if someone told you they had five points arranged in the fashion that bryan had and that they were going to randomly select one of two colors for each point you can\'t prove that one of those triangles meets the condition. That is all I am trying to say.',7387,0);
INSERT INTO comment VALUES (7397,1117,1575,'DJ','re(4): 5-point proof','2003-08-26 21:14:49',0,'The very first part of the proof is that you start with two points that are different in color. In your diagram, those two points have the same color.\r\n\r\nThe proof lies not only on the number of points or even solely by virtue of their arrangement, but it hinges on how you select the points.\r\n\r\nYou have to start with two differently-colored points, and similarly, the last two points chosen depend on whatever the color of the midpoint happens to be.\r\n\r\nThe problem doesn\'t say that all points have to be randomly selected, and indeed, they cannot be.',7396,0);
INSERT INTO comment VALUES (7398,311,3206,'Lawrence','Cakewalk','2003-08-26 23:03:02',0,'This one is easy. Wolves goes 2/3 and Dances 1/3 every time they meet. They meet three times, so Wolves went 2 laps and dances, 1. So it takes Wolves 30 seconds to do a lap.',NULL,0);
INSERT INTO comment VALUES (7399,1144,3241,'catherine','my tentative solution','2003-08-26 23:26:31',0,'No short kangaroos who are smart should drive a car. If they do, they will be caught in a confusion of rules:\r\nIf they drive, they will, being smart, wear sunglasses and look silly. Being short, they will sneeze and therefore be avoided. As sneezers they won\'t dance on tightropes. But it forces them to eat peanut butter (as all non-tightope dancers who dont eat it are tall). Being avoided, non-tightrope dancers would mean they had spikey hair. As spikey haired, silly looking non-tightrope dancers, they \'may\' swim, but as peanut butter eating, silly looking creatures they should not. \r\n(In the 4th statement:\'no one ought\' doesnt say one could NOT swim, but since our kangas are smart, we\'ll assume they would do what is best. Similarly, statement 2\'s \'may\' isnt a \'must\' so they are not compelled to swim, but then rule 4 would seem to make rule 2 at best imcomplete, possibly false)\r\nAll the kangas have to do to avoid this confusion is not drive. They need not look silly or be avoided. They are free to swim, dance tightropes and eat or not eat peanut butter so long as they dont try to avoid both tightrope dancing and peanut butter eating (or they wouldnt be short). If the kangaroos can deal with the social ostracism i.e.looking silly and being avoided (a moot point whether smart kangas would choose this) they might prefer the former scenario and drive or not drive and just decide not to swim. \r\n What do you think? ',NULL,0);
INSERT INTO comment VALUES (7400,410,3206,'Lawrence','Solved','2003-08-27 00:21:56',0,' GRAPE or APPLE\r\n- PLUM + PLUM\r\n APPLE GRAPE\r\n\r\nM is obviously 0, because E - M = E\r\n\r\nA = G-1, so (A,G)=(1,2)(6,7)(7,8)or(8,9)\r\n\r\nP+P Obviously carries, so P = 6,7,8,9\r\n\r\nBut if P=9, then P+L = some number, carry a one, P+P+1 would equal 1P. So P = 8,7 or 6. From here I plugged a few for the AG thing I talked about before and came up with the answer.\r\n\r\n94872-7160=87712\r\nGRAPE-PLUM=APPLE',NULL,0);
INSERT INTO comment VALUES (7401,1144,2912,'Talon5000','answer','2003-08-27 01:26:31',0,'...will go driving.\r\n\r\nIf a short smart kangaroo goes driving, then we also know:\r\nHe does not dance on tight ropes, he has sneezing fits, he wears sunglasses and looks silly, he eats peanut butter, he is avoided, and he has spikey hair.\r\n\r\nSince he looks silly and eats peanut butter, he ought not go swimming. Since he is smart, I\'ll assume he will do as he ought.\r\n\r\nSince he looks silly, has spiky hair, and does not dance on tight ropes, he may go swimming. I\'ll assume this means that there is a possibility that he will go, or that he can go.\r\n\r\nBased on that interpretation of those statements, that makes a contradiction, so the kangaroo must not go driving.',NULL,0);
INSERT INTO comment VALUES (7402,408,3206,'Lawrence','','2003-08-27 01:38:35',0,'',NULL,0);
INSERT INTO comment VALUES (7403,408,3206,'Lawrence','Solution','2003-08-27 01:39:27',3,'\r\nMore than 23040. (actual solution at the end) Let\'s see.\r\n\r\nIf I understood this correctly, it\'s not a simple permutation. I assumed that an up arrow and a right arrow in the same beat could be considered different than an up arrow then a right arrow. Therefore there are 4x3=12 ways to choose two, but you could also just choose 1, so there are really 16 ways to choose arrows for the beats.\r\n\r\nI also assumed that by \"per beat\" you meant \"per note,\" NOT two if it\'s an eighth note and one if it\'s a quarter. If I was wrong about that, well, I blame you. Hahaha.\r\n\r\nSo when you look at it, you have to figure out how many notes you\'re dealing with per bar and multiply that times 16. Well, a bar could be all quarter notes (1way@4notes), 3 quarter notes and one set of eighth notes, but wait. A set of eighth notes need not appear as a set. One eighth note could appear at the beginning, the other at the end. Yikes. It\'s a combination thing. For 3 Quarter and 2Eighth there are 5 choose 2 combo (or 5 choose 3 combo, the answer is the same). So there are 5!/3!*2!=10. For 2Quarter and 4Eighth there are 6!/4!*2!=15. For 1QUarter and 6 Eighth, there are 7 choose 1, or 7. And there\'s only one way to have 8 eighths. SO there is a total of 34 different ways for the notes to go per bar. BUT you can\'t simply multiply can you. The number of notes now matters, SO you multiply the number of ways times the number of notes times the 16 arrow permutations per note...\r\n\r\n4Q 1*4*16=64\r\n3Q2E 10*5*16=800\r\n2Q4E 15*6*16=1440\r\n1Q6E 7*7*16=784\r\n8E 1*8*16=128\r\n\r\nFor a total of 3216 dance arrangements per bar. There are 15 bars per minute, so 48,240. Wow that was a good one. Did I actually get it right?',NULL,0);
INSERT INTO comment VALUES (7404,408,3206,'Lawrence','hmm...','2003-08-27 01:43:42',0,'So you said the arrow things were a combination and not a permutation, but what\'s with the 120 thing? I did miss out on the \"there could be nothing on each beat,\" but I just don\'t get the same time same beat and 120^11 thing.',NULL,0);
INSERT INTO comment VALUES (7405,1107,3224,'Lee','solution','2003-08-27 01:53:11',3,'(my first post - this is practise)\r\n\r\nLet C be a cow-day - the amount of grass a cow eats in a day.\r\nSo,\r\na) In 40 days the field + 40 days growth supplies 1600C\r\nb) In 30 days the field + 60 days growth supplies 1800C\r\nClearly the extra 20 days growth provides the extra 200C\r\nFrom this we see that the field grows at a rate to feed 10 cows without depleting (200C/20)\r\nThere must therefore be 1200C worth of grass in the field (derived from either a) or b))which would take the extra 10 cows from the question 120 days to get through',NULL,0);
INSERT INTO comment VALUES (7406,918,3206,'Lawrence','Solution','2003-08-27 02:01:54',3,'70\r\n\r\nTo see how many subsquares of a certain size there are, start with 23. That you can start in the upper left corner and then shift once right, once down, then left for a total of 4. For 22, you can do the same going twice right and twice down, including the first spots, it\'s a 3x3 move or 9. So the solution is simply the sum of 1 through 24 squared which comes to 4900, the squareroot of which is 70. Not too tough.',NULL,0);
INSERT INTO comment VALUES (7407,1144,3241,'catherine','re: answer','2003-08-27 03:19:59',0,'Talon5000, I see we both observed the ambiguity in the 2 swimming rules, but you explained it so much more neatly than I did! \r\nI\'m curious how others will answer.',7401,0);
INSERT INTO comment VALUES (7408,1206,3250,'Khanh','','2003-08-27 11:58:57',3,'For breakfast, Al has: bacon, eggs, and milk; Will has: bacon, pancakes, and coffee; Bob has: ham, pancakes, and coffee; Chuck has: ham, eggs, and milk; Peter has sausage, pancakes, and tea; and Ned has: sausage, eggs, and tea.',NULL,0);
INSERT INTO comment VALUES (7409,1256,3206,'Lawrence','Possible Solution','2003-08-27 12:21:58',0,'Is it the newspaper comic? I\'m guessing that the first sign had a couple of things written on it, i.e. the next few exits. Five minutes later, he sees \"Golf Road,\" and knows that the next exit is the comic strip one. Good enough?',NULL,0);
INSERT INTO comment VALUES (7410,202,3206,'Lawrence','Solution -- not too tough','2003-08-27 13:07:46',0,'Queen (195)in one side, daughter (105) in other with weight (75) totalling 180. Queen is now down, daughter and son and weight up. Daughter (105)and son (90) get in opposite baskets, the daughter is now down, the son and the weight up. Put the son (90) in one and the weight(75) in the other, and the son is down.',NULL,0);
INSERT INTO comment VALUES (7411,1144,1575,'DJ','re: answer','2003-08-27 13:13:27',0,'Sorry, that wasn\'t supposed to be misleading. I changed the wording to make it more clear (by the way, that is the conclusion I was looking for).',7401,0);
INSERT INTO comment VALUES (7412,202,3206,'Lawrence','re: Solution -- not too tough','2003-08-27 13:21:31',0,'Easy because I didnt\' visualize the problem. It has to be up for one to get in, and they get in one at a time, and the seesaw effect of getting in and getting out. This one was good, and similar to another I have seen before. Didn\'t read the whole thing, just saw weight in first which is obvious because a person in first would die, so here goes.\r\n\r\n1 Weight in weight goes down -- QDS/W\r\n2 Son in, son down, weight up -- QDW/S\r\n3 Take weight out, send Daughter down, son up -- QSW/D\r\n4 Son gets out, daughter gets out, weight goes in and down,\r\nso QS/DW\r\n5. Daughter gets in with weight, queen gets in up top, and now she\'s down. DSW/Q\r\n6. Daughter gets out, queen gets off, weight comes down. DS/QW\r\n7. Son gets in, weight up, son down -- DW/SQ\r\n8. Daughter takes weight out, and hops in, so the son comes up. SW/DQ\r\n9. Son gets out, daughter gets out, weight in, weight to the ground. S/QDW\r\n10. Son gets in, weight comes out, son gets out. W/SDQ\r\n\r\nLOOK OUT! The weight comes crashing down. All three knew that was gonna happen, and stayed clear. Now what to do for transportation? Did anyone else have flashbacks of being a kid and the heavy kid got off the seesaw and blammo?',7410,0);
INSERT INTO comment VALUES (7413,605,3261,'Anna','solution','2003-08-27 13:50:32',0,'I think the son is the Doctor and Mr. X is the engineer. ',NULL,0);
INSERT INTO comment VALUES (7414,196,3206,'Lawrence','Neat','2003-08-27 13:51:09',0,'The key to this one is realizing that a 6 and a 9 look the same if you just turn the cube around. Also, you only need a 31 and 30, so 3 need only be on one cube. Both will need 0,1,2.\r\n\r\nC1 = 0 1 2 3 4 5\r\nC2 = 0 1 2 6 7 8 (flip the 6 for the 9)\r\n\r\nCheers!',NULL,0);
INSERT INTO comment VALUES (7415,190,3206,'Lawrence','Solution','2003-08-27 14:24:48',0,'The solution is too large for my spreadsheet, I\'ll tell you what, but I am assuming I can do, two steps once or up to 50 times, and the rest ones. The rest, or number of single steps, comes out to 100-(2n) where n is the number of times I took two steps. So for every n, there are (100 - 2n) + n spots for which you can have any combination, i.e. combination 100-n chose 2. So there is a combination of 100-n choose n for n = 0 to 50.\r\n\r\nThat comes out to 573,147,844,013,817,000,000\r\n',NULL,0);
INSERT INTO comment VALUES (7416,190,3206,'Lawrence','re: A new approach with no proof','2003-08-27 14:28:31',0,'I did it differently, using combinations and summing them all up in a spreadsheet. Came up with the same answer. Who\'s Fibonacci and what is this magic sequence both you and the author of this discuss, pray tell?',1092,0);
INSERT INTO comment VALUES (7417,189,3206,'Lawrence','This was easy','2003-08-27 14:32:34',0,'The answer is FOUR. Just go through the numbers and see which has the same number of letters as the number itself. Zero, One, Two, Three, FOUR, Five, Six Seven, Eight, Nine, Ten from here it gets worse as numbers get higher and words just don\'t get long enough.',NULL,0);
INSERT INTO comment VALUES (7418,605,3262,'richard','Solved','2003-08-27 14:44:52',3,'Father is the engineer and the son is the doctor.\r\n\r\nYou can eliminate many of the scenarios using the \"if the doctor is male, the engineer is male\" premise. List the five scenarios and the only one that does not violate any rules is the father as engineer and son as doctor.',NULL,0);
INSERT INTO comment VALUES (7419,633,3263,'James','ice is less dense than liquid water','2003-08-27 15:10:10',0,'solid water i.e. ice is actually less dense than liquid water and that is why it floats. Water is one of the few substances that actually has this property. Water is actually most dense at 4 degrees celsius. Ice is less dense than liquid water because of something called hydrogen bonds that form between water molecules. In ice, a nice structured latice is formed which makes more empty space between molecules. When water is at 4 degrees celsius the molecules are actually packed closer together than at any other temperature making the water most dense at that temperature. ',NULL,0);
INSERT INTO comment VALUES (7420,607,3172,'Your buddy','spoiler','2003-08-27 15:13:41',3,'The Professor wrote 1-33 on the board.... and the student deleted #19.',NULL,0);
INSERT INTO comment VALUES (7421,607,2995,'H','My solution','2003-08-27 15:22:02',0,'The 16 in the denominator hints that (N-1) is divisible by 16. Then the numerator would have to be 271x, where x = (N-1)/16. Thus, we must find a number n = 16x+1 whose summation is at most n greater than 271x\r\n\r\nIf N-1 were to equal 16, then N itself would be 17. However, then Sum(N-1) would be at most 152 (if 1 was deleted), which obviously cannot be the case. \r\n\r\nTrying N-1 = 32, we find a solution. At N = 33, Sum(N) = 561, and 271x=542. 561-542=19.\r\n\r\nThus, it was the number 19 that was deleted',NULL,0);
INSERT INTO comment VALUES (7422,607,3172,'Your buddy','re: spoiler','2003-08-27 15:24:46',0,'If you\'d like an easy way to solve this...\r\n\r\nrecognize that the 271/16 can\'t be reduced any further, therefore the total (to create that average) must be 16 numbers totalling 271, or 32 numbers totalling 542, or 48 numbers totalling 813, etc.\r\n\r\nSince the professor wrote Natural numbers and the student took one away, we\'re talking about 1-17 less one of the digits, or 1-33 less one of the digits, or 1-49 less one of the digits, etc.\r\n\r\nIf we total the first 17 numbers, we find the total is 153. TOO LOW! We can\'t subtract one number and find the requisite 271.\r\n\r\nIf we total the first 49 numbers, we find the total is 1225. TOO HIGH! We can\'t subtract one number and find the requisite 813.\r\n\r\nBut (we probably would\'ve tried this by now), if we total the first 33 numbers, we find the total is 561... hmmm.... we need a total of 542.... so subtract 19! And there we go.\n\nEdited on August 27, 2003, 3:27 pm',7420,0);
INSERT INTO comment VALUES (7423,187,3206,'Lawrence','Is this it?','2003-08-27 15:35:58',3,'Well, older children generally have bigger feet and more education, so they probably can spell more words. So probably because they are older and more educated. Hello.',NULL,0);
INSERT INTO comment VALUES (7424,1144,3241,'catherine','re(2): answer','2003-08-27 15:45:42',0,'Thanks DJ, we now have a clear contradiction in the 2 swimming rules if the kangaroos drive. They \'will\' swim (statement 2) but, being smart will always do what they ought to do (statement 4) and therefore simultaneously wont swim (5).\r\nTo avoid the contradiction, the smart short kangaroos do not drive.',7411,0);
INSERT INTO comment VALUES (7425,1144,3241,'catherine','re(3): answer','2003-08-27 15:51:28',0,'and p.s. I\'m giving it a 5 rating for being such a humorous yet also challenging and absorbing problem. I hope I assume right that a 5 is better than a 1 in our rating system?',7424,0);
INSERT INTO comment VALUES (7426,185,3206,'Lawrence','Just a guess','2003-08-27 15:59:37',3,'OK, I\'m feeling lazy, so let\'s do this the simple way -- 334. If I load up and go 333 from Point A toward point B, then drop off 334 and return, I just make it back to my 2000. Then if I go to 333, and drop off the dead batteries, pick up 333 of the 334, then go 166 miles and drop off all but 449 of my batteries, i.e. 334, at the 500 mile marker. I can return to Point A, picking up my one remaining at mile 333. Then I can pick up my last 1000 batteries and head to 500 where I dump my 500 dead ones, pick up the 334 live, and go the rest of the way with 334 live left when I arrive at point B.\r\n\r\nI never studied algorithms in school, so I dunno if that\'s the most efficient way, but I like it.',NULL,0);
INSERT INTO comment VALUES (7427,605,3241,'catherine','re: Solution','2003-08-27 16:15:44',0,'I came to the same conclusions as you (that Mr X is engineer and either his wife or son is the doctor) but am unsure about your argument in one part starting:\r\n\'If the doctor is a female younger than the... engineer...This is possible only if Mr. X is older than his wife, and he is the engineer while she is the doctor.\'\r\nStatement 2 says \'If the engineer is younger than the doctor...\', but it doesnt say \'if and only if\' or \'only if.\'\r\nTherefore the possibility seems to remain that the engineer and doctor could be non-blood relatives in either case. Am I missing something?',7367,0);
INSERT INTO comment VALUES (7428,607,1301,'Charlie','another method','2003-08-27 16:16:27',3,'The sum of the first n natural numbers is n(n+1)/2. Subtracting a deleted number,d, gives n(n+1)/2-d, making the average (n(n+1)-d)/(2(n-1)).\r\n\r\nWith the 271/16 average, this makes\r\nd=(n(n+1)-542(n-1))/2\r\n\r\nThis is negative for n<32.\r\n\r\nWhen n=32 the result for d has a fraction; n = 33 gives d=19; for n>33, d would be larger than n, and thus is impossible.\r\n\r\nSo N is 33 and 19 was the deleted number.',NULL,0);
INSERT INTO comment VALUES (7429,607,1575,'DJ','Solution Method','2003-08-27 16:39:21',3,'19 was removed from the first 33 counting numbers.\r\n\r\nThe average of a set of numbers is their sum divided by the number of terms.\r\n\r\nThe average of the first n counting numbers is simply (n+1)/2; their sum is n(n+1)/2.\r\nWith a little manipulation, this becomes n²/2 + &n/2.\r\nFor the purposes of this problem, the average can also be rewritten as (n²/2 + n/2)/n.\r\n\r\nIf a some term b is removed from the set, the sum is reduced by the value of b, and the total number of terms is reduced by one. The average now will be (n²/2 + n/2 - b)/(n-1).\r\n\r\nWe are given that this is equal to 271/16:\r\n(n²/2 + n/2 - b)/(n-1) = 271/16\r\n16(n²/2 + n/2 - b) = 271(n-1)\r\n8n² + 8n - 16b = 271n - 271\r\n8n² - 263n +271 - 16b = 0\r\n\r\nThere are an infinite number of solutions to this, now, except that we know that n and b are both integers. Furthermore, given the form of the average, n is one more than a multiple of 16.\r\n\r\nSolving for b and substituting (16i+1) for n, where i is some positive integer, we get:\r\n16b = 8(16i+1)² - 263(16i+1) +271\r\n16b = 8(256i² + 32i + 1) - 263(16i) - 263 + 271\r\n16b = 8(256)i² + 8(32)i - 263(16)i +16\r\nb = 128i² - 247i + 1\r\n\r\nNow, we can just plug in values for i until we get a result for b that is a positive integer 1<b 1 B\r\n 2 A\r\n 3 B\r\n 4 A\r\n 5 B\r\n 6 A\r\n 7 D\r\n 8 C\r\n 9 B\r\n10 A\r\n\r\n
\r\nPhew!\n\nEdited on August 28, 2003, 10:27 pm',NULL,0);
INSERT INTO comment VALUES (7481,605,3224,'Lee','re: (All in the family)','2003-08-29 00:22:19',0,'Lawrence,\r\n\r\nJust before your conclusion you state,\r\nIf Mom is the Engineer, that violates #3, because she and her hubby must be related.\r\nYou had already ruled out Mom as an engineer so this point is moot.\r\nIf it had started;\r\nIf Mom is the Doctor.. (the only occupation left to address)\r\nthe sentence would have finished\r\n...then she is older than her husband.\r\nYou would have been in the \'inconclusive\' camp.\r\n \r\nThe natural choice would be the son as the Doctor since we can be 100% sure he is younger than his father.',NULL,0);
INSERT INTO comment VALUES (7482,1148,3224,'Lee','fundamental symbols?','2003-08-29 00:59:06',0,'I, like Dacre, will feel a little \'cheated\' if more than +-*/ need to be used (cheated out of a half hour of my life!)- maybe DJ will surprise us.\r\nIf we do need to go beyond these four symbols which do you think is more fundamental? (which would you learn first at school). Or, which of the proffered equations would a child most likely work the answer out to be 55?\r\nSqr root comes first but would a \'child\' understand \'factorial\' before \'0.4 doesn\'t need the zero\'? \r\nI think .4 is neater than 4! so I\'m going with,\r\n44root4/.4*4 =55 (really just a rearrangement of Your Buddy\'s second offering)',NULL,0);
INSERT INTO comment VALUES (7483,263,3206,'Lawrence','Well','2003-08-29 01:19:31',0,'Because of your definition, that\'s why. The limit to this infinite problem is the point at which rabbit actually catches up to hair. It\'s kinda like traveling on a line segment, but only going a certain percentage, then going that same percentage of the remainder. You\'d never get to the end of the line segment, but the end exists. There are a theoretical infinite number of points.',NULL,0);
INSERT INTO comment VALUES (7484,602,979,'Ravi Raja','re(3): Vocabulary mistake','2003-08-29 02:15:55',0,'Well Talon, the two words \'Discriminant\' and \'Determinant\' are two different things and not the same. In this problem you need the former and not there\'s no use of the latter one. Secondly I did not mean to say that the number vanishes but the discriminant vanishes, that is the expression under the \'square root\'.',7298,0);
INSERT INTO comment VALUES (7485,1184,3224,'Lee','Another stab at it.','2003-08-29 02:15:55',0,'6 tells us it\'s 3 digits.\r\nThe last 2 digits must be strictly ascending/descending and divisible by 19 or 20\r\n_38 _20\r\n_57 _40\r\n_76 _60\r\n _80\r\nThe difference between the first and last number being at least 5 gives us 9 choices\r\n(257,357,457,876,976,320,420,520,540)\r\nwhich we can narrow down because the sum of the digits need to be 10-20 (clue 2)\r\n(257,357,457)\r\nTest for divisibilty by 3 (clue 3)\r\n=357\r\nGreat question Gamer - I think reading the posts gives a good insight into how different people attack the same problem (note to self; must calm down brown-nosing)\r\n\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (7486,865,3288,'James','re: oh no !!!!!!!','2003-08-29 05:27:23',0,'You say the answer is indeterminate, but don\'t you first have the answer the question with no? Sounds like a yes or no question, so indeterminate is unaplicable, so in order to \'answer\' the question with \'indeterminate\', you must first answer the question with \'no\' so say that the question is wrong and that the answer is indeterminate.\r\nThen by that the answer would truely be \'no\', and you\'re contradicting yourself.',7458,0);
INSERT INTO comment VALUES (7487,608,1183,'fwaff','Solution','2003-08-29 08:37:23',3,'The answer is 1, the reasoning is as follows:\r\n\r\nThere are 9 one-digit numbers, 90 two-digit numbers, 900 three-digit numbers,...., 9*(10^n) n-digit numbers.\r\n\r\nThis means that:\r\n\r\nDigits 1-9 come from the 1-digit numbers\r\nDigits 10-189 come from the 2-digit numbers\r\nDigits 190-2889 come from the 3-digit numbers\r\nDigits 2890-38889 come from the 4-digit numbers\r\nDigits 38890-488889 come from the 5-digit numbers\r\n\r\nSo the 40000th digit must be the 1111th digit of the sequence of 5 digit numbers.\r\n\r\n1111 = 222x5 + 1\r\n\r\nSo the 1111th digit is the first digit of the 223rd 5 digit number. 10222 is the 223rd 5 digit number, which means that 1 is the 40000th digit of the overall sequence.',NULL,0);
INSERT INTO comment VALUES (7488,1184,1301,'Charlie','Maximal Brute Force','2003-08-29 08:57:40',3,'357 is also found by the following program:\r\nDECLARE SUB ProcPiece (piece$, MajorPower!)\r\nDATA one,two,three,four,five,six,seven,eight,nine\r\nDATA ten,eleven,twelve,thirteen,fourteen,fifteen,sixteen,seventeen\r\nDATA eighteen,nineteen\r\nDATA twenty,thirty,forty,fifty,sixty,seventy,eighty,ninety\r\nDATA thousand,million,billion,trillion,quadrillion,quintillion,sextillion\r\nDIM SHARED unit$(19), ten$(10), major$(7)\r\nFOR i = 1 TO 19\r\n READ unit$(i)\r\nNEXT\r\nFOR i = 2 TO 9\r\n READ ten$(i)\r\nNEXT\r\nFOR i = 1 TO 7\r\n READ major$(i)\r\nNEXT\r\nDIM SHARED name$, num$\r\nFOR i = 100 TO 1000\r\n IF i <> 900 THEN\r\n i$ = LTRIM$(STR$(i))\r\n s = 1: up = 0: down = 0: eq = 0\r\n FOR j = 1 TO LEN(i$)\r\n dig$ = MID$(i$, j, 1)\r\n s = s + VAL(dig$)\r\n IF j > 1 THEN\r\n IF dig$ > prevDig$ THEN\r\n up = 1\r\n ELSEIF dig$ < prevDig$ THEN\r\n down = 1\r\n ELSE\r\n eq = 1\r\n END IF\r\n END IF\r\n prevDig$ = dig$\r\n NEXT\r\n IF s > 10 AND s <= 20 AND up + down + eq = 1 THEN\r\n s = 0\r\n IF i MOD 2 = 0 THEN s = s + 1\r\n IF i MOD 3 = 0 THEN s = s + 1\r\n IF i MOD 5 = 0 THEN s = s + 1\r\n IF s = 1 THEN\r\n s = 0\r\n IF i MOD 17 = 0 THEN s = s + 1\r\n IF i MOD 19 = 0 THEN s = s + 1\r\n IF s = 1 THEN\r\n i2 = VAL(MID$(i$, 2))\r\n s = 0\r\n IF i2 MOD 19 = 0 THEN s = s + 1\r\n IF i2 MOD 20 = 0 THEN s = s + 1\r\n IF s = 1 THEN\r\n num$ = i$\r\n name$ = \\\"\\\"\r\n MajorPower = 0\r\n DO\r\n l = LEN(num$): IF l > 3 THEN l = 3\r\n piece$ = RIGHT$(num$, l)\r\n num$ = LEFT$(num$, LEN(num$) - l)\r\n CALL ProcPiece(piece$, MajorPower)\r\n MajorPower = MajorPower + 1\r\n LOOP WHILE LEN(num$) > 0\r\n s = 0\r\n IF INSTR(name$, \"j\") > 0 THEN s = s + 1\r\n IF INSTR(name$, \"l\") > 0 THEN s = s + 1\r\n IF INSTR(name$, \"q\") > 0 THEN s = s + 1\r\n IF INSTR(name$, \"v\") > 0 THEN s = s + 1\r\n IF INSTR(name$, \"x\") > 0 THEN s = s + 1\r\n IF INSTR(name$, \"z\") > 0 THEN s = s + 1\r\n IF s = 1 THEN\r\n diff = ABS(VAL(MID$(i$, LEN(i$) - 2, 1)) - VAL(RIGHT$(i$, 1)))\r\n IF diff > 1 AND diff < 6 THEN\r\n s = 0: ix = 0\r\n DO\r\n ix = INSTR(ix + 1, name$, \\\"e\\\")\r\n IF ix > 0 THEN s = s + 1\r\n LOOP UNTIL ix = 0 OR ix = LEN(name$)\r\n IF s = 3 OR s = 5 OR s = 7 THEN\r\n PRINT i\r\n END IF\r\n END IF\r\n END IF\r\n END IF\r\n END IF\r\n END IF\r\n END IF\r\n END IF \' not 900\r\nNEXT\r\n\r\nSUB ProcPiece (piece$, MajorPower)\r\n piece = VAL(piece$)\r\n n$ = \"\"\r\n IF piece > 99 THEN\r\n n$ = unit$(piece \\ 100) + \" hundred \"\r\n piece = piece MOD 100\r\n\' IF piece > 0 THEN n$ = n$ + \"and \"\r\n END IF\r\n IF piece > 19 THEN\r\n n$ = n$ + ten$(piece \\ 10)\r\n piece = piece MOD 10\r\n IF piece > 0 THEN n$ = n$ + \"-\": ELSE n$ = n$ + \" \"\r\n END IF\r\n IF piece > 0 THEN n$ = n$ + unit$(piece) + \" \"\r\n IF n$ > \"\" THEN name$ = n$ + major$(MajorPower) + \" \" + name$\r\nEND SUB\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (7489,608,3275,'retiarius','The solution again','2003-08-29 09:25:07',0,'I agree.\r\n\r\nA number with 40,000 digits is made from 9 x 1-digit, 90 x 2-digit, 900 x 3-digit, 9000 x 4-digit, N x 5-digit numbers. That equals 39889 + N x 5-digit numbers. The first 22 x 5-digit numbers give the last 110 digits of a 39999-digit number. The next digit to arrive is 1.\r\n',NULL,0);
INSERT INTO comment VALUES (7490,608,2899,'Brian Wainscott','Agreed','2003-08-29 11:11:01',0,'My C program gives the same answer. Just doing a reality check....',NULL,0);
INSERT INTO comment VALUES (7491,830,3274,'Dacre','Real situation (I think)','2003-08-29 11:35:17',1,'I think I am right in saying that on ice rinks that when they re-surface , to get rid of lines created by skaters, they use hot water.',NULL,0);
INSERT INTO comment VALUES (7492,608,3172,'SilverKnight','re: Agreed','2003-08-29 11:36:04',0,'why didncha post your C program? (I mean since you went and bothered writing it...)',7490,0);
INSERT INTO comment VALUES (7493,1148,3275,'retiarius','Another Approach','2003-08-29 11:46:04',0,'If we consider the following numbers are to Base 7 then we have:\r\n\r\n44 x 4/4 + 4 + 4 = 55\r\n\r\n44 Base 7 is 32 Base 10\r\n55 Base 7 is 40 Base 10\r\n',NULL,0);
INSERT INTO comment VALUES (7494,1122,3274,'Dacre','A bit obvious I\'m afraid','2003-08-29 12:06:08',3,'Since both keepers are effectively saying the same thing, and the door letters can be swapped about, it can only possibly be the door they are not talking about.',NULL,0);
INSERT INTO comment VALUES (7495,183,3274,'Dacre','Possible solution','2003-08-29 12:25:18',3,'Haven\'t read any other comments - but surely not simply on the 100th day - so some-one is going to have warn if they have been there more than once ie turn it on. But then how does some-one else say they\'ve been there twice?\r\nWhat about changing it depending if the day is odd or even - ie it\'s on on a even day, so that many people visited minus one if on, nope that won\'t work either. Aaarrgh! Don\'t want to read answer... but.. \r\nPossible options for code in room:\r\nDay number?\r\nOff\r\nOn\r\nunscrewed?\r\ndirection of side of bulb - turn it 3.6 degrees only on first visit?',NULL,0);
INSERT INTO comment VALUES (7496,1010,3274,'Dacre','re: I differ on my answer....','2003-08-29 12:43:34',3,'Who debates the existance of rhythm?\r\n\r\nSurely it\'s Soul?',6752,0);
INSERT INTO comment VALUES (7497,27,3259,'srikumar','not true','2003-08-29 13:23:04',0,'the logic is flawed in a way that it permanently eliminates fri and proceeds to eliminate the rest of the week in a similar fashion.it should be kept in mind that when we try to remove thur, wed etc then we automatically bring back fri and all the remaining days to the list.hence only one day, most obivously fri, can be eliminated applying this logic. so the professor can conduct a suprise test. ',NULL,0);
INSERT INTO comment VALUES (7498,250,3259,'srikumar','fuzzy logic','2003-08-29 13:38:55',0,'If the statement is true then obivously it would be self contradictry. the answer therefore is MAYBE. this kind of logic forms the basic of fuzzy logic systems.',NULL,0);
INSERT INTO comment VALUES (7499,690,3259,'srikumar','wrong','2003-08-29 13:56:23',0,'the given explaination is incorrect because the phenomena < aka film boiling > occurs only at much higher temperature than the conventional temp used in forgeing steel. only when the a substance is sufficiently hot and dipped in water will the water vapour film be sustainable for providing the said thermal insulation, surely not for steel forging temperature.',NULL,0);
INSERT INTO comment VALUES (7500,608,2899,'Brian Wainscott','re(2): Agreed (with code)','2003-08-29 14:55:54',0,'Caveat: I don\'t know how to make this\r\ntext box preserve spaces, so the indentation is shot. Also, I know itoa would probably be faster than sprintf, but I\'m lazy -- what\'s a microsecond or two anyway... \r\n\r\n#include <stdio.h>\r\n#include <stdlib.h>\r\n#define TARGET 40000\r\nmain()\r\n{\r\n char s[50000], *cp, ss[10];\r\n int i,j,len;\r\n cp = s;\r\n s[0]=0;\r\n len=0;\r\n for(i=1; len < TARGET+2 ; i++) {\r\n sprintf(ss,\"%d\",i);\r\n j=strlen(ss);\r\n strcpy(cp,ss);\r\n cp += j;\r\n len += j;\r\n }\r\n printf(\"character %d = %c\\n\",TARGET,s[TARGET-1]);\r\n}\r\n',7492,0);
INSERT INTO comment VALUES (7501,1184,3291,'cobra','educational guess','2003-08-29 15:05:01',0,'seven hundred and sixty-five\r\n(found four E\'s)\r\n1.B 2.A 3.C 4.B 5.B 6.A 7.D,E 8.A 9.? 10.A',NULL,0);
INSERT INTO comment VALUES (7502,1184,1301,'Charlie','re: educational guess','2003-08-29 15:22:19',0,'For 765, 3.B and 3.C both work.',7501,0);
INSERT INTO comment VALUES (7503,1184,1575,'DJ','re: educational guess','2003-08-29 16:00:26',0,'The problem says that each question has a single unique answer.\r\n765 is divisible by 3 and 5 (3).\r\n65 is not divisible by 19 or 20 (6).\r\nSeven hundred sixty five is spelled using both V and X (7).\r\nE appears four times in seven hundred sixty five (9) (which you noticed, and could have been a sign to keep looking).',7501,0);
INSERT INTO comment VALUES (7504,1118,2899,'Brian Wainscott','My attempt','2003-08-29 16:00:54',0,'HOT\r\nHIT\r\nFIT\r\nFIR\r\nAIR\r\nFIR\r\nFIG\r\nBIG\r\nBAG',NULL,0);
INSERT INTO comment VALUES (7505,1118,2995,'H','My solution','2003-08-29 16:07:02',0,'Here\'s my best:\r\n\r\nH O T\r\nH I T\r\nH I M\r\nA I M\r\nA I R\r\nA I D\r\nB I D\r\nB A D\r\nB A G\r\n\r\n3 steps for each meld...\r\n',NULL,0);
INSERT INTO comment VALUES (7506,1148,1575,'DJ','re: fundamental symbols?','2003-08-29 16:17:48',0,'Why would you feel cheated? The problem does not say only \'fundamental\' symbols are to be used which would indeed imply only the use of + = × ÷. It certainly doesn\'t say to find the answer that a child would most likely come up with.\r\n\r\nActually, the word \'basic\' is only used in reference to the first part of the problem, but I think that ! and √ could be considered basic (not \"fundamental\") operations anyway, as opposed to trigonometric or calculus operators.\r\n\r\nIn any case, I think factorial and square root would be allowable, but I\'m not especially fond of considering a decimal point to be a mathematical symbol in this context (or, consequently, the bar for a repeating decimal).\r\n\r\nSo, these are the rules, if a little late:\r\nGood symbols:\r\n+, -, ×, ÷ (fundamental arithmetic); !, √ (other basic operations); || (absolute value)\r\n\r\nBad symbols:\r\nsin, cos, tan (trig functions); floor, ceil (rounding); .¯ (decimals and repeating digits), e, π (mathematical constants)\r\n\r\nBy the way, exponentiation is not a symbol at all, but since 3³ uses only the two digits, it\'s perfectly fine. Don\'t know how that\'s useful here, though...',7482,0);
INSERT INTO comment VALUES (7507,1118,2912,'Talon5000','re: My solution','2003-08-29 17:01:39',1,'Actually, that\'s four steps for each (three intermediate words). I don\'t think it\'s possible to get three steps for either, because each step would need to contain one of the letters of the second word.\r\nAOT, HOR, BIR, AAR, and AIG are not words.\r\nHIT is, but then AIT and HIR are not words, so four must be the minimum number of steps.\r\n\r\nThere can only be so many ways to do that, even, how many of them work?',7505,0);
INSERT INTO comment VALUES (7508,1184,2912,'Talon5000','re: Minimal Brute Force','2003-08-29 17:02:59',4,'What do you mean by \'minimal brute force\'? That seems to be a lot more work than everyone else did..',7480,0);
INSERT INTO comment VALUES (7509,1118,3241,'cat','my solution','2003-08-29 17:53:46',0,'hot\r\nhat\r\nfat\r\nfar\r\nfir\r\nair\r\nfir\r\nfig\r\nbig\r\nbag',NULL,0);
INSERT INTO comment VALUES (7510,1118,3241,'cat','re: my solution 2','2003-08-29 18:00:40',0,'nah, could be better:\r\nhot,hit,fit,fir,air,fir,fig,big,bag',7509,0);
INSERT INTO comment VALUES (7511,605,3241,'cat','but wait','2003-08-29 18:59:04',0,'Consider statement 2:\r\nIf the Engineer is younger than the Doctor, then the Engineer and the Doctor are not blood relatives.\r\nThis only says in effect, if A then B. This doesnt necessarily imply if not-A then not-B. That would have to have been specified by \"Only if\"\r\nIf MrX is engineer and is older than his wife, they can still be unrelated; statement 2 simply becomes irrelevent. Therefore I believe that the wife is still an equal contender with her son for being the doctor.',NULL,0);
INSERT INTO comment VALUES (7512,1184,1575,'DJ','re(2): Minimal Brute Force','2003-08-29 22:57:43',0,'\"Brute force\" would be like going through all the numbers from 1 to 1000 and eliminating them one at a time.\r\nOther people listed out all the multiples of 19 and 20, and went through each of those numbers (a form of brute force or trial-and-error), which is obviously better, but not ideal.\r\n\r\nThe only brute force in my solution was listing out the 5 two-digit multiples of 19, and going through the final three choices for the number. Everything else was based on logical deductions, directly from the clues, to minimize the trial-and-error that would need to be done.\r\n\r\nA computer program is a form of brute force (as Charlie has humorously noted) since it really goes through all possible numbers until it finds a match (although it goes much faster than we could ever go through them).',7508,0);
INSERT INTO comment VALUES (7513,1118,3202,'Jill','More of the same','2003-08-29 23:15:45',0,'I went with\r\nhot\r\nhit\r\nhim\r\naim\r\nair\r\nfir\r\nfig\r\nbig\r\nbag',NULL,0);
INSERT INTO comment VALUES (7514,1184,1626,'Gamer','re: Maximal Brute Force','2003-08-30 00:07:15',0,'Although I appreciate your want for a programming assignment, wouldn\'t this take more time to set up? :)',7488,0);
INSERT INTO comment VALUES (7515,1118,3206,'Lawrence','Can\'t touch this ...','2003-08-30 00:07:19',0,'3 + 3 = 6!!!!! \r\n HOT ...\r\n1. HIT\r\n2. FIT\r\n3. FIR\r\n AIR\r\n1. FIR\r\n2. FAR\r\n3. BAR\r\n BAG\r\n\r\nCan anyone beat that?',NULL,0);
INSERT INTO comment VALUES (7516,865,1626,'Gamer','re(2): oh no !!!!!!!','2003-08-30 00:22:29',0,'In other words, indeterminite means you DO know the answer because indeterminite isn\'t the same as no, and so the answer is no if it\'s indeterminite',7486,0);
INSERT INTO comment VALUES (7517,441,3026,'Drew Skau','Who can count?','2003-08-30 00:27:55',3,'The difficulty rating isn\'t accurate. It should say zero.\r\nThree, one tulip, one rose, and one daisy, or two, none of them are tulips, roses, or daisies.',NULL,0);
INSERT INTO comment VALUES (7518,608,3206,'Lawrence','Solution','2003-08-30 00:39:45',0,'I did it with a spreadsheet ...\r\n\r\nRange #digits Count of Range digxcount Remaining to 40000\r\n1 to 9 1 9 9 9 39991\r\n10 to 99 2 90 180 189 39811\r\n100 to 999 3 900 2700 2889 37111\r\n1000 to 9999 4 9000 36000 38889 1111\r\n10000 to 10221 5 222 1110 39999 1\r\n\r\nWhen you get to 9999 there are only 1111 spots left to go. The next numbers are five digits each. So divide 1111 by 5 and come up with 222.2. Since .2 = 1/5 it is the first number after the 222 digit. Well that\'s clearly a 1.\r\n\r\nIn the end of the spreadsheet clip above, you are 1 away from 40000, so the next number is a 1 -- the first digit of 10222.',NULL,0);
INSERT INTO comment VALUES (7519,1184,3206,'Lawrence','re(2): Note to Gamer','2003-08-30 00:45:33',0,'Hahaha. Sounds like you\'ve been doing this a while. I suppose you get some inane stuff, eh? Better to post it once than answer it over and over.\r\n\r\nCheers!!!\r\nL',7475,0);
INSERT INTO comment VALUES (7520,1118,1575,'DJ','re: Can\'t touch this ...','2003-08-30 01:04:35',0,'Well.. that\'s still four moves for each, like everyone else has had so far.\r\n\r\nBut no, no one can beat that, since (like has already been mentioned) AOT, HOR, AIT, HIR, AAG, BIR, and AIG are all not words, four is the lowest possible. There are, as we have seen, many possible ways to do that, and there are still a few more that haven\'t been mentioned yet.',7515,0);
INSERT INTO comment VALUES (7521,777,3297,'jamie','Smart ass solution','2003-08-30 02:52:30',0,'Bracket the statement into \" colored (every single point on that plane){meaning the entire plane} (one of two colors)\" Assume that (one of two colors) means one color from a possible selection of two, so the painter either painted the entire plane green, or the entire plane red (or whatever colors you want). Then the entire plane is the same color and any two points exactly one meter apart will be the same color. ',NULL,0);
INSERT INTO comment VALUES (7522,1148,3224,'Lee','re:(fundamental symols)2','2003-08-30 07:05:04',0,'My reference to being \'cheated\' was by myself of my own time. I jumped in convinced you had a solution with just the four arithmetic symbols and since the first part was relatively straight forward hit the poser with that in mind. Opening your mind to other symbols gives the number flexibility to \'solve\' the problem in a variety of ways. I was just posing the question of which (of the \'solutions\') people think may be the \'neatest\' - that which could be done at the earliest age (I knew about sqr roots about 7 years before factorials)',NULL,0);
INSERT INTO comment VALUES (7523,20,3182,'Antonio','Solution','2003-08-30 08:13:15',3,'√5*L where L one side of the cube.',NULL,0);
INSERT INTO comment VALUES (7535,610,3241,'cat','','2003-08-30 20:19:35',3,'A total of 7 birds are distributed as follows with yellow birds denoted by \'y\' and non yellow bird denoted by \'n\'. \'_\'signifies a place holder containing no bird.\r\n\r\nA B C\r\ny y y\r\nn _ _\r\n_ y _\r\n_ _ y\r\nn n _\r\n_ y y\r\ny _ y\r\n\r\na) there are 5 yellow birds\r\nb) there are 2 non yellow birds.\r\n\r\n\r\nEdited on August 30, 2003, 8:26 pm\n\nEdited on August 30, 2003, 8:28 pm',NULL,0);
INSERT INTO comment VALUES (7536,1117,3206,'Lawrence','How about ...','2003-08-30 20:42:11',0,'The MOST you need is a seven point proof, because you won\'t be able to place the eighth.\r\n\r\nStart with 3 adjacent, and then start adding so that you don\'t have three in a triangle. The best way ends up being having a diagonal row of one color and a diagonal row of the other. So you have 7 points. Zig-zag causes problems around 5 points. HOw\'s that? \r\n',NULL,0);
INSERT INTO comment VALUES (7537,102,3206,'Lawrence','Why it\'s ...','2003-08-30 21:44:50',0,'... Mr. Bill!!! Seriously, assuming knights don\'t lie, that is. If it were Abe, he\'d have to say, \"I\'m Abe.\" If it were Carl, then Carl told the truth, but the other two lied, so Abe doesn\'t exist. Ergo, it must be Bullshit Bill, making the first man Crafty Carl and the last Honest Abe.',NULL,0);
INSERT INTO comment VALUES (7538,99,3206,'Lawrence','','2003-08-31 00:06:16',0,'',NULL,0);
INSERT INTO comment VALUES (7539,99,3206,'Lawrence','Solution','2003-08-31 00:10:16',0,'Haven\'t looked at the others, but yours gave me an idea. How about ((2/.1)^3)! -- that\'s a factorial, not a simple exclamation point.\r\n\r\nThat would be (20^3)! = (20x20x20)! = 8000! raise to the power of Pi too, if that\'s allowed before factorial.\r\n\r\nThat comes to ... holy cow, you broke my spreadsheet. There aren\'t enough bytes in a number to hold the answer apparently. The FACT() function didn\'t work, so I checked. Going backwards from 8000 down and multiplying it got to 7922 where the result was 1.501 x (10^300) But there are stilll the last 7921 numbers to multiply that against.\r\n\r\nI need to a refresher and some more math courses, because I probably could have done something with natural logs here too.',NULL,0);
INSERT INTO comment VALUES (7540,1144,3241,'cat','one more thing :-)','2003-08-31 00:24:23',1,'If short kangaroos want to increase their height all they have to do is give up peanut butter eating and tightrope walking :-)',NULL,0);
INSERT INTO comment VALUES (7541,808,3182,'Antonio','Solution','2003-08-31 03:43:05',3,'With the distance r, we open the compass with a distance r, then we mark two distances r in the X axis and a distance r to the Y axis, to form a rectangular triangle of sides r and 2r. It\'s hypotenusa must be √5*r, so we find the midpoint of the hypotenusa (√5*r/2) and open the compass to get the distance of the middle of such hypothenusa. To that lenght, we add the middle of r (r/2) so in the compass we have an opening equal to (.5*r+.5√5*r) or ((1+√5)/2)*r that is the golden ratio. So, with the golden ratio founded, we simply find the intersection of such distance just by puting the compass origin un the endpoint of the initial distance r. We get an isoceles triangle of sides r, and two sides with lenght of the golden ratio. We open the compas to a lenght r and draw a light circular reference where the next vertex could be, we do this from one vertex of sides golden ratio and r. We open the compass with the lenght of golden ratio and put the origin in the vertex thas has tow sides of the golden ratio, from there we intersect the golden ratio distance with the previously marked circle. We make the same operation to find the vertex next to the vertex of twice the golden ratio. We could find all the vertex makeing the same operation, and voila! we have a perfect pentagon. I assume that all of you know how to draw a perpendicular line and get the midpoint of a given line using a compass, because I didn\'t mentioned in order to write less. ',NULL,0);
INSERT INTO comment VALUES (7542,236,3182,'Antonio','Solution','2003-08-31 06:00:14',3,'Imagine only the bottom side of the square and two arcs with their centers on the endpoints of the refered bottom side. The arcs intersect forming a characteristic of an imaginary equilatteral triangle. From the left vertex of the square to the intersection of the arcs, it has an inclination of 60 degrees. The diagonal from opposite vertex in the square, has an inclination of 45 degrees, so 60-45 = 15 degrees, we form a right triangle of one angle equal to 15 and an hypotenusa equals to the radius of one arc, that is 7cm. With this triangle we obtain the two sides (7*Sin(15) and 7*Cos(15)), these sides will help us to obtain the proper areas in order to obtain the final of the shaded region. The shaded region is composed by the area of a square with a side equal to 2*7*sin(15) and 4 circular sections that are very small, but they all count. These circular sections are obtained by first obtaining the linear relation of the proportional area that the circular segments relate to the total area of the circle with a radius of 7cm. We subtract an isoceles triangle formed by a side equal to 2*7*sin(15) and two equal sides of 7cm. To the proportional area of the small circle segment we subtract the mentioned isoceles triangle and we get one of the four circle segment areas. So we multiply this area times 4 and add the area previously calculated of the square of side 2*7*sin(15). \r\nArea = (49/3)*(12*sin(15)*(sin(15)-cos(15))+Pi) = 15.4421904378 cm²\r\nNote: I did not write how to obtain the area of the isoceles triangle or the value of one of the four circle segment areas, I posted my final ecuation of the total area, so any area obtained is within the final ecuation.',NULL,0);
INSERT INTO comment VALUES (7543,239,3182,'Antonio','Solution','2003-08-31 07:49:32',3,'Since the problem is in the geometry section, it is solved using the proportionality of angle-area. Using trigonometric telations, the general formula would be:\r\nArea = (1/360)*[ R1²*Pi*(180-acos[(2*R2²-R1²)/(2*R2²)]) + 2*R2*(R2*Pi*acos[(2*R2²-R1²)/(2*R2²)]-180*R1*cos((acos[(2*R2²-R1²)/(2*R2²)])/2)) ]. Where 0≤R1≥R2 and R1≤R2≥∞\r\n\r\nWith R1=7cm and R2=14cm, the common area is: 68.7502555449cm²\r\n\r\nNo calculus needed.',NULL,0);
INSERT INTO comment VALUES (7544,1260,3304,'Andrew','Solution','2003-08-31 08:46:14',0,'You\'re on the wrong side of the road , WATCH OUT!',NULL,0);
INSERT INTO comment VALUES (7545,1118,3275,'retiarius','The English Language','2003-08-31 09:44:46',0,'Word games are difficult when there are many variations of English around the globe. Ait is a word for island or eyot and is not uncommon where I come from. Therefore,\r\n\r\nHOT\r\nHIT\r\nAIT\r\nAIR\r\nAIT\r\nBIT\r\nBAT\r\nBAG ',NULL,0);
INSERT INTO comment VALUES (7546,1260,2572,'derek','solution','2003-08-31 10:26:50',3,'slow',NULL,0);
INSERT INTO comment VALUES (7547,1260,2604,'Koren','solution','2003-08-31 11:42:00',3,'You\'re going the wrong way on a one-way street on which people are encouraged to drive SLOW.',NULL,0);
INSERT INTO comment VALUES (7548,1260,1575,'DJ','hmm','2003-08-31 19:35:20',0,'Either you\'re driving on the wrong side of the road, going the wrong way on a one-way street, or the local department of transportation is rather incompetent. Better make sure the stripe to your right is painted white (unless, of course, that is painted incorrectly as well)...',NULL,0);
INSERT INTO comment VALUES (7549,1260,3310,'Danielle Kirkpatrick','solution','2003-08-31 20:40:31',3,'You\'re in the wrong lane! The message should say \"SLOW\" to the person facing the correct way.',NULL,0);
INSERT INTO comment VALUES (7550,1260,3206,'Lawrence','Solution','2003-08-31 21:50:12',0,'Well, that would be SLOW written upside-down, which means I am probably going the wrong way down a one way street.',NULL,0);
INSERT INTO comment VALUES (7551,1260,3206,'Lawrence','re: Solution ... or ...','2003-08-31 21:51:57',0,'You may just be on the wrong side of the road.',7550,0);
INSERT INTO comment VALUES (7552,297,3206,'Lawrence','Solution','2003-08-31 21:59:21',3,'A1,B3 C5 ... The pawns go at D2,E2, and E4. This is remarkable like the one where they asked what\'s the most number of queens you can put on a regular 8x8 chess board without any of them being able to attack each other',NULL,0);
INSERT INTO comment VALUES (7553,29,3206,'Lawrence','Possibly ...','2003-08-31 23:47:22',0,'This may be ludicrous, but if there are only two directions, you could ask him which way he goes home. If he is a liar, then he\'ll point to Knightville. If he is a knight he\'ll tell you how to get to knightville. There has to be a better answer, because the liar would send you to nowhere land.',NULL,0);
INSERT INTO comment VALUES (7554,25,3206,'Lawrence','Response','2003-08-31 23:59:47',0,'There are therefore 5 intervals of 6 seconds, so for 12 there would be 11 intervals of 6 seconds, or 66 seconds prior to noon.',NULL,0);
INSERT INTO comment VALUES (7555,240,3182,'Antonio','Solution','2003-09-01 04:22:23',3,'Imagine a triangle composed by sides A, B, C and angles thetaA, thetaB, thetaC (the opposite side of thetaA is A, the opposite side of thetaB is B and the opposite side of thetaC is C). Align such triangle to a Cartesian coordinate plane (X axis and Y axis) in a way that the vertex in thetaA touches the origin of the X axis and Y axis, also the vertex at thetaC touches the X axis pointing towards +infinite. To calculate the sides of the special triangle, I used intersecting linear equations, and the coordinates of such special triangle are:\r\nX1=C*sin(thetaB/3)*tan(thetaA+thetaB/3)/(sin(thetaA+thetaB/3)*[tan(thetaA+thetaB/3)-tan(2*thetaA/3)])\r\nX2=B*tan(180-thetaC/3)/(tan(180-thetaC/3)-tan(thetaA/3))\r\nX3=B*sin(thetaC+thetaB/3)*[tan(180-thetaC-thetaB/3)-tan(180-2*thetaC/3)]-A*sin(thetaB/3)*tan(180-thetaC-thetaB/3)/(sin(thetaC+thetaB/3)*[tan(180-thetaC-thetaB/3)-tan(180-2*thetaC/3)])\r\nY1=X1*tan(2*thetaA/3)\r\nY2=X2*tan(thetaA/3)\r\nY3=(B-X3)*tan(2*thetaC/3)\r\nThe distances of such triangle can finally be tested and prove that it is an equilateral triangle or not. \r\nL1=√((X2-X1)²+(Y2-Y1)²)\r\nL2=√((X3-X2)²+(Y3-Y2)²)\r\nL3=√((X3-X1)²+(Y3-Y1)²)\r\nIf such triangle is equilateral then L1, L2 and L3 must all be the same length. An examples:\r\n1.- A triangle with thetaA=30 degrees, B=10 and C=6, has an equilateral special triangle with sides L1=L2=L3= 0.92271409\r\n2.- A triangle with thetaA=50 degrees, B=3 and C=4, has an equilateral special triangle with sides L1=L2=L3= 0.5862669748\r\nSolution: the special triangle is always an equilateral triangle.\r\nNote: With the values of thetaA, B and C you can find all other values for a real existent triangle using the law of cosines.',NULL,0);
INSERT INTO comment VALUES (7556,190,3274,'Dacre','re(2): who\'s Fibonacci? Simple answer','2003-09-01 06:33:49',0,'You may have guessed, but Fibonacci was a maths guy who came up with the following sequence used in all manner of maths inc. expanding brackets. \r\nBasically, forms a triangle with numbers by adding one asbove and adding extra line ie:\r\n\r\nLine 1: 1\r\nLine 2: 1 1\r\nLine 3: 1 2 1\r\nLine 4: 1 3 3 1\r\nLine 5: 1 4 6 4 1\r\nLine 6 1 5 10 10 5 1\r\netc.\r\n\r\nYou get the idea. It\'s used in so much stuff it\'s not true.',7416,0);
INSERT INTO comment VALUES (7557,1200,1183,'fwaff','Solution','2003-09-01 08:31:11',3,'t1ea4ri0sc5nm4sa1dp4e\r\n\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (7558,1200,1626,'Gamer','re: Solution','2003-09-01 09:34:33',0,'m0ya4rw3db0em2kc7e(i0ft2tc4s)a1dr1d',7557,0);
INSERT INTO comment VALUES (7559,297,1626,'Gamer','re: Solution','2003-09-01 09:39:08',0,'It says 5 queens and 3 pawns or 3 queens and 5 pawns, not 3 queens and 3 pawns',7552,0);
INSERT INTO comment VALUES (7560,417,1626,'Gamer','re: this is not a sequence','2003-09-01 09:47:21',0,'A sequence is any amount of numbers that have a particular order. This has a particular order... :)',3981,0);
INSERT INTO comment VALUES (7561,183,3206,'Lawrence','Possibly ...','2003-09-01 10:10:51',0,'Well, I am assuming that everyone can see the light in the living room from their cell because of it\'s central location. Since only one per day is allowed, then the inmates can count the number of days, right? So if they toggle on the day when they are new, and don\'t toggle if they\'ve toggled before, then the other inmates can simply count the number of days that the switch has been toggled. Once it has been toggeled 100 times, the next inmate can make the proper assertion. \r\n\r\nThe answer in short ... toggle only the first time you are randomly selected. Count the day only if the light is toggled.',NULL,0);
INSERT INTO comment VALUES (7562,544,3206,'Lawrence','Solution','2003-09-01 10:15:48',0,'I was going to say a pencil ... when you erase it goes from red to black. But then I read the subject line \"don\'t get burnt\" and realized you are a match.',NULL,0);
INSERT INTO comment VALUES (7563,1200,1301,'Charlie','L3yS4m','2003-09-01 10:44:18',0,'T2ss4ml3ss0om2hi9nt2tt1eo2yt4sIp4du0pi0nt1ea4ss0of1ri0st2tG3r\'sf6ec3ri0sr1d.',NULL,0);
INSERT INTO comment VALUES (7564,190,1301,'Charlie','re(3): who\'s Fibonacci? Simple answer','2003-09-01 10:56:56',0,'Actually, the triangle you mention is usually associated with Blaise Pascal (Pascal\'s Triangle), not Fibonacci, though the triangle was known in China much before the time of either one. Fibonacci popularized arabic numerals in the west, but mostly his name is attached to the sequence\r\n\r\n1,1,2,3,5,8,13,21, ...\r\n\r\nwhere each term is the sum of the two preceding terms.',7556,0);
INSERT INTO comment VALUES (7565,337,3206,'Lawrence','Solution','2003-09-01 12:15:21',0,'Well, if you are speaking of seconds as in seconds, minutes, hours, then there are 60*60*24*365=31536000 in a normal year, in a leap year 60*60*24*366=3162240. OR if you are talking about the second of each month, then there are 12.',NULL,0);
INSERT INTO comment VALUES (7566,1200,1183,'fwaff','re(2): Solution','2003-09-01 12:29:18',0,'Ip4rd2kc7e.\r\nw2td2s\"o4s\"m2n???',7558,0);
INSERT INTO comment VALUES (7567,1200,1575,'DJ','w2a..','2003-09-01 12:32:21',3,'h2yc2pt2si0sc7g!\r\nm2ea1ep3a(ik2w,o6l)a1do4e.',NULL,0);
INSERT INTO comment VALUES (7568,334,3206,'Lawrence','How about ...','2003-09-01 12:34:53',0,'The letter \"s\"',NULL,0);
INSERT INTO comment VALUES (7569,325,3206,'Lawrence','Solution','2003-09-01 13:50:09',0,'This is a process of elimination process witht the following results:\r\n\r\nPJ Cousin Popcorn Dolphins\r\nPat Uncle Chips Broncos\r\nChris Sister Cookies Cowboys\r\nStacey Brother CarrotSticks Raiders\r\nBobbi Mother Pizza Packers\r\n\r\nI\'m a Saints fan, and my family sucks. Let\'s eat Pizza!',NULL,0);
INSERT INTO comment VALUES (7570,315,3206,'Lawrence','Solution','2003-09-01 13:54:23',0,'My son. Since I have no brother, my father\'s son is me myself. So the answer is my son.',NULL,0);
INSERT INTO comment VALUES (7571,1051,3206,'Lawrence','Are you ...','2003-09-01 13:59:11',0,'a manatee (also known as a sea cow)',NULL,0);
INSERT INTO comment VALUES (7572,1010,3206,'Lawrence','Answer','2003-09-01 14:00:54',3,'Soul ... you also have your own food.',NULL,0);
INSERT INTO comment VALUES (7573,1012,3206,'Lawrence','Answer','2003-09-01 14:04:21',0,'Born before his father: \"before\" meaning \"in front\" of his father, not before in time\r\n\r\nKilled his mother: during child birth, she died\r\n\r\nMarried his sister: he became a priest, judge, justice of the peace, captain or something like that and presided over the wedding of his sister',NULL,0);
INSERT INTO comment VALUES (7574,990,3206,'Lawrence','Baseball rules','2003-09-01 14:08:17',0,'Well, on a strike three passed ball, or simply one that hits the ground, the runner can advance to first base. So that\'s what happened, a bunch of strike threes end up being passed balls, so they scored runs that way.\r\n\r\nIs a passed ball considered an error though?',NULL,0);
INSERT INTO comment VALUES (7575,532,3206,'Lawrence','Answe','2003-09-01 14:21:19',3,'No belly buttons, born, they were created. Adam may have had a nasty scar around his ribs too, hahahaha.',NULL,0);
INSERT INTO comment VALUES (7576,840,3206,'Lawrence','Answer','2003-09-01 14:26:22',0,'Ton ... backwards, that\'s not, and forward, it\'s heavy.',NULL,0);
INSERT INTO comment VALUES (7577,501,3206,'Lawrence','Answer','2003-09-01 14:32:16',0,'Stars?',NULL,0);
INSERT INTO comment VALUES (7578,686,3206,'Lawrence','Possible answers','2003-09-01 14:34:36',0,'He saw someone hunting, but that\'s ok in the country.\r\n\r\nHe saw someone fishing\r\n\r\nHe went by a slaughterhouse. Or someone was hacking up a chicken for dinner ... this is the country.',NULL,0);
INSERT INTO comment VALUES (7579,1200,1301,'Charlie','re(3): Solution','2003-09-01 14:56:14',0,'u11yt1ef2tu2db0yb6sm3s\"c4s\"l2kl2e\"o4s\",b1ti0t\'sn1t.',7566,0);
INSERT INTO comment VALUES (7580,1200,1301,'Charlie','stuck--can\'t be chicken matzos, can it?','2003-09-01 15:19:11',0,'I\'ms3ko0n\"m4s\".',7557,0);
INSERT INTO comment VALUES (7581,1260,3320,'benji','roadway riddle','2003-09-01 16:09:18',0,'slow',NULL,0);
INSERT INTO comment VALUES (7582,1149,1301,'Charlie','solution','2003-09-01 17:27:01',3,'\"Luckily\" the truth-tellers\' names begin with T, and the liars\' with L.\r\n\r\nIf the male sailor were Terry, the male soldier would be Lee, a liar. But the male solder claims this to be true, so the male sailor can\'t be Terry and the Male soldier can\'t be Lee. However since the male soldier is a liar, he must be Loren.\r\n\r\nAlso his second statement is false, so Tracy is indeed stationed in Afghanistan, and the female sailor is therefore a truth teller.\r\n\r\nThus the female sailor, a truth teller, is not Loren, so the male sailor is a liar, and the male soldier is therefore not Lee. But since the male soldier is also a liar, he is Loren, while the male sailor is Lee.\r\n\r\nThus the males lie and the females tell the truth. Thus the female sailor is indeed not Terry, so the female soldier must be Terry while the female sailor is Tracy.\r\n\r\nThis establishes the names. Now for the stationings.\r\n\r\nWe\'ve established that Tracy (who is the female sailor) is indeed stationed in Afghanistan. As Tracy\'s other statement is true, a sailor is stationed in Hawaii, and the only other sailor is Lee, he is stationed in Hawaii.\r\n\r\nNow comes the hard part: it does not say anywhere that anyone is in fact stationed in Texas. Nor does a liar state that someone is not stationed in Texas--only a truth teller says this.\r\n\r\nI would say the puzzle poser wants us to say that Terry, the female soldier, is stationed in Texas, and that Loren, the male soldier is stationed in Kuwait. But actually, either could be stationed in Kuwait and the other in an unmentioned location. So the possibilities are:\r\n\r\n\r\nMale soldier-Loren Kuwait Kuwait unknown\r\nFemale soldier-Terry Texas unknown Kuwait\r\nMale sailor-Lee Hawaii Hawaii Hawaii\r\nFemale sailor-Tracy Afghanistan Afghanistan Afghanistan\r\n
\r\n----------\r\n(hoping that the pre comes out ok on the above so the columns appear.)\r\n',NULL,0);
INSERT INTO comment VALUES (7583,1200,1626,'Gamer','Say what? I can\'t decipher half these...','2003-09-01 17:46:13',0,'I1\'sh2dt0os1ew2tt1ew3sa1ei0nt1ea5s! :) ',NULL,0);
INSERT INTO comment VALUES (7584,1149,3202,'Jill','Solution','2003-09-01 20:17:19',0,'Loren - male soldier - Kuwait\r\nTerry - female soldier - Texas\r\nLee - male sailor - Hawaii\r\nTracy - female sailor - Afghanistan\r\n\r\nThe way I came to this conclusion was by looking for inconsistancies indicating a liar. We know right away the male sailor is Lee or Loren, because he says the two liars are the male soldier and the female sailor. Only one of them can be a liar because they disagree as to whether Tracy is in Afghanistan. We can then easily find that the other liar is the male soldier because he says that Terry is the male sailor and we already found this to be false. Ok so now we know who the liars are and who\'s telling the truth. \r\n\r\nSince we know the female soldier is telling the truth when she says that Terry is not the female sailor (who is also telling the truth) we know that Terry is the famale soldier and Tracy is the female sailor. Lee must be the male sailor since he lies about being the male soldier. This leaves Loren as the male soldier.\r\n\r\nOk...so where are they? Tracy tells us that she is in Afghanistan and that Lee is in Hawaii. We know the other two are in Texas or Kuwait (we are told so) and since Terry is telling the truth when she says Loren is not in Texas, Loren must be in Kuwait and Terry must be in Texas.\n\nEdited on September 1, 2003, 8:17 pm',NULL,0);
INSERT INTO comment VALUES (7585,378,1626,'Gamer','A change? :)','2003-09-01 20:27:30',0,'If the last line was \"The person who it\'s for doesn\'t want it.\" as I have sometimes seen it, it might be harder :)',NULL,0);
INSERT INTO comment VALUES (7586,1149,1301,'Charlie','re: solution','2003-09-01 20:51:42',0,'I see the puzzle now makes the answer unambiguous by changing the female soldier\'s second statement statement to indicate there is in fact someone stationed in Texas. So the first column of stationments in my solution is the unique correct one.',7582,0);
INSERT INTO comment VALUES (7587,1149,2716,'Federico Kereki','Short solution','2003-09-01 21:02:25',3,'The male soldier and the female sailor disagree as to where is Tracy stationed, so one is a truth teller and other a liar.\r\n\r\no2y, I\'m d2e, i0fn0oo1e e2e i0s,h2a.\r\nOkay, I\'m done, if no one else is, haha.\r\nH2e\'s w2e I\'v0ef5d (o0ra5d ) s0of1r:\r\nHere\'s what I\'ve figured (or assumed) so far:\r\n\r\nt1e q5n\r\nthe question\r\nw2t i0sy2r f6e f2d a1d c3r?\r\nwhat is your favorite food and color?\r\n\r\nt1e a4r i0sc5n m4s a1d p4e \r\nthe answer is chicken m....s and purple\r\n\r\nm0ya4r w3d b0em2k c7e (i0ft2t c4s ) a1d r1d \r\nmy answer would be milk chocolate (if that counts) and red\r\n\r\nL3y S4m\r\nLousy System\r\nT2s s4m l3s s0om2h i9n t2t t1e o2y t4s I p4d u0p\r\nThis system lacks so much information that the only things I picked up\r\ni0nt1e a4s s0of1r i0st2t G3r\'s f6e c3r i0sr1d\r\nin the answers so far is that Gamer\'s favorite color is red\r\n\r\nI p4r d2k c7e. \r\nI prefer dark chocolate\r\nw2t d2s \"o4s\" m2n???\r\nwhat does \"o4s\" mean???\r\n\r\nw2a...\r\nwhoa...\r\nh2y c2p t2s i0sc7g!\r\nholy crap this is confusing!\r\nm2e a1e p3a (i k2w, o6l ) a1d o4e. \r\nmine are pizza (i know, original) and orange.\r\n\r\nu11y t1e f2t u2d b0yb6s m3s \"c4s\" l2k l2e \"o4s\", b1t i0t\'sn1t. \r\nunfortunately the font used by b......s makes \"c4s\" look like \"o4s\", but it\'s not.\r\n\r\nI\'m s3k o0n\"m4s\". \r\nI\'m stuck on \"m4s\".\r\n\r\nI1\'s h2d t0os1e w2t t1e w3s a1e i0nt1e a5s! :) \r\nIt\'s hard to see what the words are in the answers! :)\r\n
',NULL,0);
INSERT INTO comment VALUES (7590,865,3324,'William Beer','Is no the correct answer...?','2003-09-02 00:53:45',0,'Never.',NULL,0);
INSERT INTO comment VALUES (7591,1149,3206,'Lawrence','Solution','2003-09-02 02:30:56',3,'The male soldier and female sailor cannot both be telling the truth because their respective statements 2 are contradictory. By naming the male soldier as Lee, and female sailor as Loren, the Male Sailor has exposed him/herself as a liar. Therefore, the female soldier is telling the truth. Because the male soldier says that the male sailor is Terry, and we\'ve already established the male sailor to be a liar, we now know that the male soldier is the other liar, so the female soldier is telling the truth. Working through their statements will lead to the following conclusion:\r\n\r\nLoren is the Male Soldier stationed in Kuwait,\r\nTerry is the Female Soldier stationed in Texas,\r\nTracy is the Female Sailor stationed in Afghanistan, and\r\nLee is the Male Sailor stationed in Hawaii.',NULL,0);
INSERT INTO comment VALUES (7592,1260,3326,'kiri','Solution','2003-09-02 03:46:14',0,'You are driving on the wrong side of the road and the cryptic message is actually SLOW which you would see if you were driving from the opposite direction.',NULL,0);
INSERT INTO comment VALUES (7593,1200,1183,'fwaff','re: Ig2e (I give) - missing words','2003-09-02 06:42:19',0,'m4s = madras\r\nb6s is probably browsers, but could be bagpipes!\r\n\r\nLewis: Aren\'t you English? I think f7e and c4r would have made it more of a challenge for the US contingent.',7589,0);
INSERT INTO comment VALUES (7594,323,3274,'Dacre','Just to be pedantic...','2003-09-02 07:34:48',3,'No wonder I couldn\'t get it!\r\nThis doesn\'t work if you are sensible and use the British method and put the day then the month. This way makes far more sense as it goes Day Month Year - ascending time scales.\r\nAnd more importantly, it\'s British. \r\n:-P',NULL,0);
INSERT INTO comment VALUES (7595,1200,1301,'Charlie','re: Ig2e (I give)','2003-09-02 08:50:12',0,'b6s is browsers\r\nand L3y is Lossy, rather than Lousy (loses information).\r\n\r\n... and l3s is loses, rather than lacks.\r\n\n\nEdited on September 2, 2003, 8:54 am',7589,0);
INSERT INTO comment VALUES (7596,1058,1920,'Brian Smith','Better than 50%','2003-09-02 09:44:56',0,'I got a 5/6 = 83.33% success rate using a known genuine coin and a 29/35 = 82.86% success rate without a known genuine coin.',NULL,0);
INSERT INTO comment VALUES (7597,912,1920,'Brian Smith','20 checkers to level 4','2003-09-02 09:58:10',0,'This arrangement of checkers can be used to reach level 4.\r\n\r\n4 4 1 1 1 1 1\r\n 1 1 1 2 2\r\n 3 3 3 2 2 2\r\n 3 2\r\n
\r\n*************\r\n\r\nFirst, use the checkers marked with 1\'s to reach level 3 (in the 5th column). Second, use the checkers marked with 2\'s to reach level 1 underneath the level 3 checker. Third, use the checkers marked with 3\'s to place a checker at level 0 one column to the left of the checker at level 3. Finally, use the checkers marked with 4\'s to place a checker at level 4.',NULL,0);
INSERT INTO comment VALUES (7598,1186,3275,'retiarius','Some solutions','2003-09-02 10:06:21',0,'1. Lost and gone forever\r\n2. Going undercover\r\n3. Too hot for TV\r\n4. \r\n5. Home in the heart\r\n6. Every dog has his day\r\n\r\nI\'ll have my day as soon as I\'ve done 4. I\'ll be back.',NULL,0);
INSERT INTO comment VALUES (7599,1186,1301,'Charlie','re: Some solutions','2003-09-02 11:36:27',0,'I would phrase 5 as \"Home is where the heart is\" (the more familiar expression) and 6 as \"Every dog has its day\" (the wordie shows a word against a word, which is an it).',7598,0);
INSERT INTO comment VALUES (7600,1186,1575,'DJ','re: Some solutions','2003-09-02 11:37:12',0,'Those are the same ones I figured out, except I took #5 to mean \"Home is where the heart is.\" Still drawing blank on #4, as well...',7598,0);
INSERT INTO comment VALUES (7601,1058,2899,'Brian Wainscott','re: Better than 50%','2003-09-02 11:57:17',0,'Great -- but how did you get these numbers?',7596,0);
INSERT INTO comment VALUES (7602,1186,1183,'fwaff','re(2): Some solutions','2003-09-02 12:50:55',0,'How about \"Positives and negatives attract\" as a solution to number four?',7600,0);
INSERT INTO comment VALUES (7603,1186,1575,'DJ','re(3): Some solutions','2003-09-02 12:56:45',0,'Or, the more common \"opposites attract.\" Good one!',7602,0);
INSERT INTO comment VALUES (7604,610,3329,'krishna tadimeti','solution','2003-09-02 12:57:02',0,'total 7 birds, 2 were non yellow',NULL,0);
INSERT INTO comment VALUES (7605,1186,2839,'FatBoy','some answers','2003-09-02 13:00:48',2,'1)\r\n2) going under cover\r\n3) too Hot for TV\r\n4)\r\n5) heart at home (home is where the heart is??)\r\n6)\r\n',NULL,0);
INSERT INTO comment VALUES (7606,1058,1920,'Brian Smith','re: Better than 50% - details','2003-09-02 14:19:40',3,'With a genuine coin for reference:\r\nChoose 2 coins from the set of 10. If either coin does not match the genuine coin, that coin is a fake. Otherwise both are genuine so choose one of the 8 remaining coins. The probability of not finding a fake is ((6*5)/(10*9))*(4/8) = 1/6. The success rate of finding a fake is then 5/6.\r\n\r\n\r\nWithout a genuine coin for reference:\r\nChoose 3 coins at random. Call the first coin A, the second coin B and the third coin C. Weigh A vs B and A vs C.\r\n\r\nIf both weighings are equal (prob 120/720) then A, B and C are all genuine. Take one of the other 7 coins (4 of 7 are fake).\r\n\r\nIf one weighing is equal and the other is not equal (prob 304/720) take the coin which appears only in the unequal weighing (prob fake 64/76). Example: if A=B and A>C take C.\r\n\r\nIf the weighing results are {A>B,A>C} or {B>A,C>A} (prob 248/720) then take A (prob fake 112/124).\r\n\r\nIf the weighing results are {B>A,A>C} or {C>A,A>B} (prob 48/720) then B and C are both fake with one heavier and one lighter. Take either B or C.\r\n\r\nTotal success rate = (120/720)*(4/7) + (304/720)*(64/76) + (248/720)*(112/124) + 48/720 = 29/35.',7596,0);
INSERT INTO comment VALUES (7607,1200,1919,'Lewis','re(2): Ig2e (I give) - missing words','2003-09-02 14:36:44',0,'I am English Fwaff but I thought as a majority of people would use f6e and c3r rather than how we would normally spell it, so it would make more sense to use the American spellings (I would have wrote that in Crypto but you probably would have to take ages working it out ;)',7593,0);
INSERT INTO comment VALUES (7608,611,3172,'SilverKnight','Solution (spoiler)','2003-09-02 14:50:16',3,'A: A\'s coat, B\'s hat, C\'s gloves, D\'s cane\r\nB: B\'s coat, D\'s hat, A\'s gloves, C\'s cane\r\nC: D\'s coat, C\'s hat, B\'s gloves, A\'s cane\r\nD: C\'s coat, A\'s hat, D\'s gloves, B\'s cane',NULL,0);
INSERT INTO comment VALUES (7609,611,1301,'Charlie','solution','2003-09-02 15:02:20',3,'As each man had one item from each of the men, that includes having exactly one of his own. In the cases of C and D that was his own hat and his own gloves respectively. A and B, on the other hand, each had his own coat. That means Messrs. A,B,C,D had the coats of A,B,D,C respectively--that is C\'s and D\'s coats were interchanged.\r\n\r\nAs C had his own hat, and none of A,B or D had his own, those three must have had one of the two possible derangements of their three hats: A,B,D had the respective hats of either B,D,A or D,A,B.\r\n\r\nLikewise, as D had his own gloves, and none of A,B or C had his own, those three must have had one of the two possible derangements of their gloves: A,B,C had the respective gloves of either B,C,A or C,A,B.\r\n\r\nThus there are only four possibilities for the three items: coats, hats and gloves. Each then determines the fourth item: the cane. But we can see the results:\r\n\r\n\r\nMan: ABCD ABCD ABCD ABCD\r\ncoat: ABDC ABDC ABDC ABDC\r\nhat: BDCA BDCA DACB DACB (the two possibilities)\r\ngloves: BCAD CABD BCAD CABD (in combination with these two possibilities)\r\ncane: ---- DCAB CDBA ---- (based on fact of one item from each of the four)\r\n
\r\n-------------\r\nThe hyphens in two of the columns represent the fact that in those columns there was already a duplication, in the fact of one of the men having more than one item from the same man.\r\n\r\nSince A did not end up with C\'s cane, A,B,C,D had in the given order, the coats of A,B,D,C; the hats of B,D,C,A; the gloves of C,A,B,D and the canes of D,C,A,B.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (7610,611,3172,'SilverKnight','method of solving (also a spoiler)','2003-09-02 15:23:28',2,'For those who want a hint on how to solve it... It\'s possibly easiest if you set up a 4x4 grid (such as ABCD along the side of the grid, and \"coat\", \"hat\", \"glove\", and \"cane\" along the top).
\r\nThen, fill in the LETTER of the person\'s item that each person took. So... based on the \"given\" rules that the problem stated. Write in A in {A, coat}, B in {B, coat}, C in {C, hat}, and D in {D, gloves}
\r\nNext, note that C and D each already have one of their own items, therefore neither has their own Coat. The only remaining solution (for coats) is that C has D\'s coat, and D has C\'s coat, so... fill in D for {C, coat} and C for {D, coat}.
\r\nNext, note that this means that the two remaining \"holes\" in C\'s row must be filled by \'A\' & \'B\'. Similarly, the remaining \"holes in D\'s row must also be filled by \'A\' & \'B\'. Both rows include the CANE column. Okay, so this means that C has A or B\'s cane, D has A or B\'s cane, and the GIVEN rules imply that A has A, B, or D\'s cane. Since, if A has EITHER A or B\'s cane, then only the OTHER is free for C and D, we have an impossibility. Therefore, A has D\'s cane--fill in D for {A, cane}. Also, since A and B\'s canes are taken by C and D, B must have C\'s cane--fill in C for {B, cane}.
\r\nB\'s row has only hats and gloves \"open\". And he\'s already got something from B and from C, so his hat and gloves must come from A and D. But D has his own gloves.... so B must have A\'s Gloves and that leaves B having D\'s hat. Fill in A for {B, gloves} and D for {B, hat}.
\r\nDo the same for A\'s row: A already has A\'s Coat, and D\'s cane, therefore his hat and glove belowng to B and C.... since C already has his own hat, A must have B\'s hat... and that mean A has C\'s gloves. Fill in B for {A, hat} and C for {A, gloves}.
\r\nD is the only one missing a hat, and A\'s is the only one not taken, so fill in A for {D, hat}. Similarly, C is the only one missing gloves, and B\'s are the only ones not taken, so fill in B for {C, gloves}.
\r\nAnd finally, C needs something from A, and D needs something from B and the canes are free... so fill in A for {C, cane} and B for {D, cane}.
\r\nYour whole grid should now be filled in with the appropriate information.
\r\nCheers!',7608,0);
INSERT INTO comment VALUES (7611,611,3248,'Kelsey','Solution','2003-09-02 16:06:16',3,'A: B\'s hat, A\'s coat, D\'s cane, C\'s gloves\r\nB: D\'s hat, B\'s coat, C\'s cane, A\'s gloves\r\nC: C\'s hat, D\'s coat, A\'s cane, B\'s gloves\r\nD: A\'s hat, C\'s coat, B\'s cane, D\'s gloves',NULL,0);
INSERT INTO comment VALUES (7612,611,2130,'ethan','Solution','2003-09-02 16:24:18',3,'A has his own coat, B\'s cane, D\'s hat, and C\'s gloves.\r\n\r\nB has his own coat, C\'s cane, D\'s hat, A\'s hat, and D\'s gloves.\r\n\r\nC has D\'s coat, A\'s cane, his own hat, and B\'s gloves.\r\n\r\nD has C\'s coat, his own cane, B\'s hat, and A\'s gloves.',NULL,0);
INSERT INTO comment VALUES (7613,341,3206,'Lawrence','Solution','2003-09-02 16:32:34',3,'8 and 1 have to go in the middle for this to work. So F:8, C:1. Obviously 2 and 7 must now go in H and A respectively. then it\'s simply a matter of triangulation. 3 and 4 are the vertices of the triangle with respect to 2, i.e. E:4, G:3. and 5 and 6 with respect to 8, so D:5, B:6. You could mirror these as well, switching 1 & 8 and moving things accordingly. And/Or the 5,6 can switch as long as you also switch the 4,3 at the same time.\r\n\r\n A:2\r\nB:6 C:8 D:5\r\nE:4 F:1 G:3\r\n H:7\r\n\r\nThe solution above saves properly with A and H centered, but then when I look at the comment, the A is over B and H over 7. That is NOT part of my solution. It\'s just the way this things handles white space, I suppose.\r\nEdited on September 2, 2003, 4:33 pm\n\nEdited on September 2, 2003, 4:35 pm',NULL,0);
INSERT INTO comment VALUES (7614,611,1575,'DJ','','2003-09-02 18:34:26',3,'I\'ll assume a cane is also considered an article of clothing...\r\n\r\nJust draw a grid of which things each took home, with the four people on one axis and the \'clothing\' on the other. Fill each blank with an A, B, C, or D to represent the rightful owner of that particular item, and each letter can appear only once in each row or column.\r\n\r\nHere\'s what we are given:\r\n A B C D\r\ncoat| A B · ·\r\nhat | · · C ·\r\nglvs| · · · D\r\ncane|
\r\nWe are told what correct article each person has, and that A does not have C\'s cane.\r\n\r\nA cannot have his own cane, since he has his own coat, and we are told that he does not have C\'s cane. Therefore, he has B\'s cane or D\'s cane.\r\n\r\nIf he has B\'s cane, he must have D\'s hat and C\'s gloves. Then, however, B must have A\'s hat (D and C\'s hats are taken, and B already has his own coat). Then, B has one article from A and of his own, but C and D\'s gloves are already taken, so that cannot work.\r\nC · · · A B C D\r\ncoat| A B · ·\r\nhat | D A C ·\r\nglvs| C ? · D\r\ncane| B · · ·
\r\nNothing can go in the ? spot without a contradiction.\r\n\r\nTherefore, A must have D\'s cane. He must also, then, have C\'s gloves (C has his own hat already) and B\'s hat.\r\n A B C D\r\ncoat| A B · ·\r\nhat | B · C ·\r\nglvs| C · · D\r\ncane| D · · ·
\r\nNow, look at what B has.\r\n\r\nB must have C\'s cane, A\'s gloves, and D\'s hat (the other articles for each person are already all taken.\r\n A B C D\r\ncoat| A B · ·\r\nhat | B D C ·\r\nglvs| C A · D\r\ncane| D C · ·
\r\nAll the pairs of gloves are taken but one..\r\n\r\nC must have B\'s gloves, the only ones left. He also took A\'s cane (D\'s is gone by now), and D\'s coat.\r\n A B C D\r\ncoat| A B D ·\r\nhat | B D C ·\r\nglvs| C A B D\r\ncane| D C A ·
\r\nFinally, by elimination, D has C\'s coat, A\'s hat, and B\'s cane.\r\n A B C D\r\ncoat| A B D C\r\nhat | B D C A\r\nglvs| C A B D\r\ncane| D C A B
',NULL,0);
INSERT INTO comment VALUES (7615,1186,3202,'Jill','...','2003-09-02 20:11:30',0,'I got all of them but number 4 on my own, however after seeing the fwaff\'s comment, opposites attract (I would phrase this way too DJ) makes perfect sense.',NULL,0);
INSERT INTO comment VALUES (7616,611,3202,'Jill','','2003-09-02 20:19:38',0,'A- A\'s coat, B\'s hat, C\'s gloves, D\'s cane\r\nB- B\'s coat, A\'s gloves, C\'s cane, D\'s hat\r\nC- C\'s hat, D\'s coat, A\'s cane, B\'s gloves\r\nD- D\'s gloves, A\'s hat, B\'s cane, C\'s coat\r\n\r\nI did this one a little different then I normally would have (using a grid) and instead simply made four rows labeled A, B, C, D and wrote the given info in the row. I then wrote for example for A: A coat, B D hat, B C D cane. I then just crossed off choices as they were eliminated. This just seemed faster to me for this problem.',NULL,0);
INSERT INTO comment VALUES (7617,1200,3202,'Jill','Solution of sorts...','2003-09-02 20:25:41',0,'A1yp3aa1dm0yf6ec4sa1eg3na1dp4e.',NULL,0);
INSERT INTO comment VALUES (7618,611,693,'Jun','Solution','2003-09-02 21:36:54',0,' Hat Coat Gloves Cane\r\nA: B A C D \r\nB: D B A C\r\nC: C D B A\r\nD: A C D B',NULL,0);
INSERT INTO comment VALUES (7619,607,3327,'Richard Briscoe','The solution','2003-09-03 04:09:33',0,'The numbers are 1 to 33, except for 19\r\nI.e., N=33, and 19 is the missing number',NULL,0);
INSERT INTO comment VALUES (7620,1148,3274,'Dacre','re(2):(fundamental symols)2','2003-09-03 04:56:06',0,'I like the problem, it\'s good - I guess feel \'cheated\' as spent ages trying to only use \'basic\' symbols. Felt ! brought in too many options, and would be more than one more solution. \r\nDon\'t mean to diss problem. Like this sort, simple operations, lots of possibilities. Another variation of Countdown is always good. (Do you get a version of that in the US?)',7522,0);
INSERT INTO comment VALUES (7621,789,3182,'Antonio','Solution','2003-09-03 07:41:33',3,'The figure that forms is an equilateral triangle with arc segments from vertex to vertex of radius equal to the triangle´s side. First we obtain the area of the equilateral triangle (A1), then we use an area-angle linear relation on one of the circles, that is, if an equilateral triangle has its tree angles equal to 60 degrees, then the area of a circle segment with an aperture of 60 degrees is the sixth part of the circle´s area (A2). If we subtract A2-A1 we get a third area of a circle´s arc section (A3), adding 3 times A3 with A1 we get the final area of the figure formed by the intersecting circles.\r\nA1=√3*R²/4, A2=Pi*R²/6, A3=A2-A1=R²*(2*Pi-3*√3)/12\r\nTotal area = 3*A3+A1=R²*(Pi-√3)/2\r\n',NULL,0);
INSERT INTO comment VALUES (7622,14,3327,'Richard Briscoe','Simpler solution','2003-09-03 08:37:46',0,'The solution is correct, but over-complicated.\r\n\r\nConsider a plane with only two seats.\r\nIt is clear that the probability that passenger 2 gets his own seat in this case is 50%.\r\nEither the mad passenger picks his own seat, and all is well, or he picks seat 2, and the second passenger is unlucky.\r\n\r\nFor a plane with any more than 2 seats remaining, there are really ony three cases to consider.\r\n1.The mad passenger picks his own seat [1/N]\r\n2.The mad passenger picks seat N [1/N]\r\n3.The mad passenger picks any other seat [(N-2)/N}]\r\n\r\nWhenever case 3 occurs, seating proceeds in an orderly manner, until the \'stolen\' seat is reached.\r\nAt this point, the situation is identical, save only that N is smaller.\r\n\r\nThe process repeats until either case 1 or case 2 occurs, and the probabilities of these are always equal. One or other will occur eventually, if only when N=2.\r\nCase 3 may recurr several times, but this cannot affect the outcome. \r\n\r\nAn equivalent problem is this.\r\nPut one black ball, one white ball, and 98 red balls in a bag.\r\nPick a ball at random.\r\nIf the ball is red, remove a random number, 1 to N, of red balls from the bag, where N is the number of red balls remaining (initially 98).\r\nRepeat until either the black ball or the white ball is picked.\r\nWhat is the probability that the white ball is picked before the black ?',NULL,0);
INSERT INTO comment VALUES (7623,611,2839,'FatBoy','Solution','2003-09-03 09:15:32',0,' Coat hat gloves cane\r\nMrA a b c d\r\nMrB b d a c\r\nMrC d c b a\r\nMrD c a d b',NULL,0);
INSERT INTO comment VALUES (7624,700,3182,'Antonio','Solution','2003-09-03 09:34:09',3,'To obtain the X point on the x-axis, we realize that it has to be between -1 and 9. Therefore, making a right-angle triangle of sides x, 4 and L (where L is the equidistant point from X to point A and X to point B), we obtain L²=X²+16 using the Pitagorian theorem. Then we make another right-angle triangle but with sides (10-X), 6 and L. Again using the Pitagorian theorem, we obtain L²=(10-X)²+36=X²-20*X+136. So, L²=L²=X²+16=X²-20*X+136, this gives X=120/20=6. \r\nThe X point in the x-axis is (5,0), based from the origin.\r\nNow, for the Y point on the y-axis, imagine an isoceles triangle of sides M, M and the distance between points AB (where the distande AB=√104). In an isoceles triangle, two angles are equal an the the third is the subtraction of 180 minus those two equal angles. The angle of aperture between the distance AB and the y-axis is ArcTan[(9+1)/(6-4)]=ArcTan[5]=78.690067526 degrees, so the angle between M and M should be 180-2*78.690067526=22.619864948 degrees. Using the law of cosines, we formulate an equation 104=√(M²+M²-2*M*M*Cos(22.619864948)), this equation results in M=√(52/(1-cos(22.619864948)))=26\r\nThe Y point in the y-axis is (0,30), based from the origin.',NULL,0);
INSERT INTO comment VALUES (7625,75,2839,'FatBoy','solution','2003-09-03 10:19:19',0,'23 times a day',NULL,0);
INSERT INTO comment VALUES (7626,700,3182,'Antonio','Sorry, my last Y point was wrong...','2003-09-03 10:24:00',3,'In my last solution comment, I posted a wrong distance in Y in order to find an equidistant point in the y-axis. From the y-axis, form two right angle triangles, one with sides 1, Y and an hypotenusa of M, the other right angle triangle with sides Y, 9 and an hipoteniusa of M. We get an equation M²=M²=1+4+4*Y*Y²=Y²+81. This will give us Y=19. We sum 4+2+19=25.\r\nSo from the origin in the y-axis the point would be in (0,25)',NULL,0);
INSERT INTO comment VALUES (7627,1260,2839,'FatBoy','solution','2003-09-03 10:39:05',0,'that people coming toward you are being requested to go SLOW which upsidea down looks like MO75 (in some fonts',NULL,0);
INSERT INTO comment VALUES (7628,1118,2839,'FatBoy','I\'ll take a shot','2003-09-03 10:54:07',3,'HOT\r\nhit\r\nhid\r\naid\r\nAIR\r\naid\r\nbid\r\nbig\r\nBAG',NULL,0);
INSERT INTO comment VALUES (7629,173,3182,'Antonio','Solution','2003-09-03 12:37:36',3,'We make a right triangle of sides 90cm, 120cm, and the hypotenusa represents the string. Using Pitagoras theorem the string is √(90²+120²)=150cm\r\nThe string is 150cm long',NULL,0);
INSERT INTO comment VALUES (7630,1265,1575,'DJ','Clueless?','2003-09-03 13:28:44',1,'Wow, no one has commented yet.. probably because they have as much clue to this one as I do.\r\nI\'ll just start out with some word associations:\r\nspy: glass, industrial, international, agent, ring\r\nbabe: baby, ruth, pig, bottom\r\ntree: house, wood, farm, oak, maple, pine (etc)\r\nwavy: hair, ocean, swirly\r\nskate: board, ice, figure, rink\r\nloyal: dog, honor, faithful, dedicated\r\nsteep: tea, slope, angle\r\nponder: think, mull, pinky, brain\r\n\r\nOkay, nothing so far. The words range in length from 3 to 6 letters, and are listed in ascending order, perhaps coincidentally.\r\nThe letters used are: A, B, D, E, K, L, N, O, P, R, S, T, V, W, Y. Nothing seemingly interesting there.\r\nLetters from the beginning and end of the alphabet are used in most of the words, so anything related to the sum of the alphanumeric value of the letters (as we have talked about in other puzzles) would appear to be a consideration here. Also, the letters of each are neither in strictly ascending or descending order, alpabetically.\r\n\r\nSo, while throwing out random ideas sometimes leads to something useful, what I have so far doesn\'t appear to be very helpful.\r\n\r\nWhat does everyone else think (or at least, what have you tried)?',NULL,0);
INSERT INTO comment VALUES (7631,1260,1920,'Brian Smith','Honk that horn!','2003-09-03 14:33:10',0,'The M07S is SLOW inverted, so, I am probably looking forward to an accident since I am going the wrong way down a lane of traffic.',NULL,0);
INSERT INTO comment VALUES (7632,221,3182,'Antonio','Solution','2003-09-03 15:38:11',3,'Well, 1 byte is 1024 bits, and 1 YB is 2^80 bytes, so 1 YB = 1.23794003928x10^27 bits, divided by 124,000 bpi is 9.98338741355x10^21 inches long of tape. Analysing the growth of the perimeter in every loop, the sum of all the loops must be equal to the total lenght of tape already calculated (9.98338741355x10^21 inches)2*Pi*R1+2*Pi*R2+2*Pi*R3+2*Pi*R4......2*Pi*Rn = 2*Pi*(R1+R2+R3+R4.....Rn) = 9.98338741355x10^21 inches. We can see that R1=.5, R2=.5+8.9x10^-6, R3=.5+2*8.9x10-6, etc. We can observe that .5 is added n times and 8.9x10^-6 is added n*(n-1)/2 times. From 9.98338741355x10^21=2*Pi*(.5*n+(8.9x10^-6)*n*(n-1)/2) we get the equation n ²+((1-8.9x10-6)/8.9x10-6)*n-(9.98338741355x10^21/(Pi*8.9x10-6))=0, we find the roots of the 2nd degree equation and neglect any negative root. This gives n=1.88959626281x10^13, we finally calculate de radius of the roll of tape R=.5+(8.9x10^-6)*n=168174067.89in\r\nThe total diameter is 336348135.78in= 5,308.52487027mi',NULL,0);
INSERT INTO comment VALUES (7633,813,1403,'John Smith','re: solution to B','2003-09-03 16:00:26',0,'I think you can look at it this way.\r\nFor each weighing, there are 3 possible outcomes, i.e. balanced, heavier or lighter. Thus, for X weighings, the total number of unique results would be 3^X out of which one is balance-balance-balance, which occurs when we exclude the coin totally frmo our weighings. Thus, removing this case would give a total of 3^X-1 possibilities.\r\n\r\nNow, since there are N coins, and each of them could be either heavier or lighter, thus, the total number of different cases is 2N that need to be mapped to these 3^X-1 possibilities. \r\n\r\nThus, this gives us the inequality 2N <= 3^X-1 or rather, \r\nN<= (3^X-1)/2\r\n\r\nFor the case where we know whether the coin is heavier or lighter, there are only N cases as opposed to 2N. Thus, the inequality would become \r\n\r\n N <= 3^X \r\n\r\nsince, in this case, even a balance-balance-balance result would tell us which coin is it and thus excluding it totally from our weighings is alright.\r\n',5032,0);
INSERT INTO comment VALUES (7634,1265,3202,'Jill','re: Clueless?','2003-09-03 16:21:58',0,'ok...well, I just read this one myself but I\'m just as clueless.\r\n\r\nI tried the usual stuff first, but got nothing. So then I tried looking for hidden words within the words or adding letters to make new words...and anagrams (though with a word like spy I didn\'t expect much).\r\n\r\nAnagrams:\r\nspy - \r\nbabe - abbe\r\ntree - \r\nwavy - \r\nskate - keats, stake, steak, takes, teaks\r\nloyal - alloy\r\nsteep - \r\nponder - ',7630,0);
INSERT INTO comment VALUES (7635,1265,3172,'SilverKnight','This is easy!','2003-09-03 16:42:22',3,'They all have two vowels!\r\n\r\nExcept spy...\r\nAnd wavy unless you count the \'y\' as a vowel...\r\nAnd loyal ... of course, now you can\'t count the y as a vowel...\r\n\r\nsee.... piece of cake!',NULL,0);
INSERT INTO comment VALUES (7636,1265,2899,'Brian Wainscott','One possible solution','2003-09-03 16:53:02',0,'The one thing these words have in common is that.....they all appear in this puzzle!\r\n\r\n\r\n(I never was good at these kinds of puzzles anyway...)\r\n\r\nSeriously, the only thing I\'ve been able to think of is \"line\" as in\r\n\r\ntree line (timberline)\r\nwavy lines\r\ninline skates\r\nloyal = \"tow the line\"\r\nsteep = incline\r\n\r\nbut even stretching things that far I can\'t get anywhere with spy, babe, or ponder....',NULL,0);
INSERT INTO comment VALUES (7637,165,3182,'Antonio','Solution','2003-09-03 17:05:31',3,'Any line that intersects in two points a circle, is always perpendicular to the circle\'s center. In this case, there are two parallel lines crossing the circle, so they both have to be perpendicular to the center, this is why I decided to represent the problem using half of each length of roads (25m and 56m) aligned horizontally or parallel to the x-axis with the origin in the 25m road. The two roads in this arrangement give out a difference of 31m (56m-25m=31m). The hypotenusa would be √9425. This hypotenusa is also perpendicular to the center of the circle, so we find the inclination respect to the x-axis of the perpendicular line that pases trough the middle of the hypotenusa and touches the x-axis. It results that the angle of aperture between the described perpendicular line respect to the x-axis is 18.621579793665 degrees. We use this angle to find the distance between the vertex where the 25m road part intersects with the circle and the point where the perpendicular line calculated previously touches the x-axis. This distance would be √9425/(2*sin(18.621579793665))=152.016129032m. We add 25m to 152.016129032m and we get 177.016129032m from the point of intersection of the perpendicular line from the origin. We find the intersection of perpendiculars were the center should be and is at a height of 177.016129032*tan(18.621579793665)=59.6467391303m from the origin. Finally we make a right triangle with sides of 59.6467391303m, 25m and an hypotenusa equal to the radius of such circular playground. The radius would be 64.6740557633m thus the diameter is 129.348111527m ',NULL,0);
INSERT INTO comment VALUES (7638,1188,2899,'Brian Wainscott','Solution','2003-09-03 17:30:19',3,'Take the right fork to get to Truth Town, and C is the girl.\r\n\r\nFirst, D cannot be a Knight. If he were, then C wouuld be a Knight, and B,C, and D would all be girls, which we know is false.\r\n\r\nTherefore either B or C is a Knight (since D is a liar, his statement is false and so B and C cannot both be liars).\r\n\r\nIf B were a Knight, then D must be girl. Since there is only one girl, it is not B (since D is), and hence C is a liar (and therefore a girl). Too many girls, so B is a liar.\r\n\r\nTherefore C is a Knight. Hence C is a girl. Furthermore, since there is only 1 girl there is only one Knight, so A is a liar.\r\n\r\nThus the right fork goes to Truth Town, which is presumably inhabited by Knights. And all Knights are girls, so I see why you might find it an interesting place to visit....',NULL,0);
INSERT INTO comment VALUES (7639,1188,1575,'DJ','A Solution','2003-09-03 18:01:13',3,'There are three statements beginning with \"All;\" B, C, and D.\r\n\r\nStatement D says that these statements are either all true or all false. If that is the case, then D is true, hence they all must be true.\r\n\r\nHowever, there is a contradiction in statements B and C, so that cannot be the case; D must be false.\r\n\r\nIf all three of statements B, C, and D were false, that would make statement D true (we\'ll assume D is referring to their small group), so one of B or C must be true, and the other false.\r\n\r\nIf B is true, then there can be only one false statement, since there is only one girl, and all liars are girls.\r\n\r\nWe already know that D is false, and this assumption would make statement C false as well, so that cannot be the case either.\r\n\r\nTherefore, C is true, B is false, and C is the only girl (and the only knight).\r\n\r\nFinally, we know that A, a guy, must be lying, and you should take the right fork to get to Truth Town.',NULL,0);
INSERT INTO comment VALUES (7640,1188,3202,'Jill','Ho hum...same solution, same logic...','2003-09-03 21:05:06',0,'Hang a right to get to Truth Town. C is the girl knight.\r\n\r\nIf D is true than B and C would both have to be true also, which is impossible as they contradict. Therefore D is false and either B or C is false. B must be false as we know we have at least two liars and only one girl (given info).\r\nSo C is telling the truth meaning that there is only one knight and three liars, so you\'d better take a right instead of listening to gentleman A.',NULL,0);
INSERT INTO comment VALUES (7641,254,3182,'Antonio','Solution','2003-09-04 04:25:55',3,'Imagine a circle with an inscribed square in it, when the circle rotates on a planar surface, the center never moves, but the vertex of the square are rotating and at the same time moving in an x-axis direction. The sine function relates one point in the circunference rotating and moving in X direction. In this case, we have to use all angle measurement in radians in order to relate rotation and distance. As the square rotates and moves, one vertex of the equare respect to the floor, moves in a way like a curve, in order to obtain the behavior of this curve, we first relate the distance of the center of the square to one of it\'s sides L. We make an isoceles triangle of two sides √2L/2 and the other would be L, in this triangle we make a random line that touches the center of the square and one random point in it\'s opposite side L (this new line would be M). This relation is proportional with the rotation of the square, so the angle of aperture between side √2L/2 and the line randomly drawed (M) is X radians. With this relationship we use the law of sines and the angles inside the new triangle in order to leave M in therms of X radians. This relation would give M=√2*L*sin(Pi/4)/(2*sin((3*Pi/4)-X)). M represents the distance that the mentioned curve would have from the center of the square to the curve, so to get the height of such curve from the x-axis to any point in the curve we subtract M from √2*L/2. This subtraction would be the amplitude A of a new sine equation that we must find in order to know the behavior of the curve. Simplifying the amplitude A gives A=√2*L*(2*sin((3*Pi-4*X)/4)-√2)/(4*sin((3*Pi-4*X)/4)-√2)). With the amplitude A we finally observe that the curve that describes the movement of the side L rotating like a wheel is a sine ecuation of amplitude A, but with the diference that in every cycle of the original square, the curve formed in the floor makes two cycles (that is 2*X) only in positive values (the curve is never negative in the y-axis). With this observation, the new equation must be evaluated in absolute values (always positive), so the solution to the problem would be Surface=Y=ABSOLUTE[A*sin(2*X)]=ABSOLUTE[(√2*L*(2*sin((3*Pi-4*X)/4)-√2)/(4*sin((3*Pi-4*X)/4)-√2)))*sin(2*X)]. It would plot a series of bump-like curves that is only a sine function showing always absolute or positive values. ',NULL,0);
INSERT INTO comment VALUES (7642,254,3182,'Antonio','re: Googled','2003-09-04 04:43:46',1,'Well TomM, that information that you found is great, but let me remind you that a catenary is the hyperbolic cosine of a distance X (cosh(X)), and also the hyperbolic cosine of X is ((e^X)/2)+((e^-X)/2), and if you would remember, any sine function or cosine function may be expresed in therms of Euler\'s constant e elevated at some value iX, jY. Of course that the solution to the problem in some form would be in therms of a hyperbolic cosine (catenary), but that is just another form of representing the surface. Thanks for showing another form of resolving this problem TomM. ',1648,0);
INSERT INTO comment VALUES (7643,117,3182,'Antonio','Solution','2003-09-04 06:15:00',3,'Open the compass at a random aperture, a small aperture would be fine. From the vertex of such angle, mark the lines of the angle sides 3 times, first from the vertex to the line, second from the point of intersection of first circle mark another circle of same radius, third mark another circle of same radius inntersecting the same line. Now open the compass from the angle\'s vertex to the first intersection of the line and mark the two lines, then open the compass from the vertex to the second point of intersection marked in the line and mark the two lines, finally open the compass from the vertex to the third point of intersection and mark the two lines. This process will make 3 lines perpendicular to the vertex and each one is bigger by 1 (the second line is twice the first and the third line is tree times the first). Now use the technique to find a perpendicular line in both points of the first line perpendicular to the vertex, and those perpendicular lines extend them on to the third line that is 3 times the first one. The last line that is perpendicular to the vertex, the one that is 3 times the first one, will be perfectly divided by 3, in those points of intersection just draw a line from the vertex to the two intersections in the line divided by 3 and you will get 3 equal angles of A/3. All of this shows the linear relation between the radius and any line perpendicular to the vertex that is opposite to the angle A',NULL,0);
INSERT INTO comment VALUES (7644,117,3182,'Antonio','My past solution does not apply...','2003-09-04 06:55:02',1,'Well, the radius grows proportional to the commented lines but not with the angle, for that, the arc of the aperture has to be divided by 3 not the perpendicular line opposite to the angle A',7643,0);
INSERT INTO comment VALUES (7645,136,3182,'Antonio','Solution','2003-09-04 07:28:26',3,'To tell you the truth, this problem was very easy. Using CD+BD=2*CD=2*BD=12, CD=BD=6. 11-CD=11-6=5=MD. AM²2=100-MD²=100-25=75. AC²=11²+AM²=121+75=196, so AC=√196=14',NULL,0);
INSERT INTO comment VALUES (7646,1184,2839,'FatBoy','SilverKnight, do not read this post......','2003-09-04 08:39:46',3,'Since teacher says the number is not greater than a thousand is must either be 1000 or be less. Q2 indicates that the sum of the digits must be greater than 10 (at least) so the answer can\'t be 1000 therefore the maximum number of possible digits in the number is 3.\r\n\r\nQ6 indicates that if you remove teh first digit the remaining digits are divisible by one of two two digits numbers (19 and 20) all numbers divisible by 2 digit numbers must have at least two digits therefore the minimum number of digits in our response must be three \r\nTHEREFORE we are looking for a three digit number.\r\n\r\nQ6 also indicates that the last two digits must be divisible by 19 or 20. They, however, can not be divisible by 20 because any number ending in a figure divisible by 20 would also be divisible by 20 and therefore divisible by both 2 and 5 but Q3 can only have 1 answer. Therefore the last two digits must be divisible by 19\r\n\r\nOf the 5 possible 2 digit numbers divisible by 19 (19,38,57,76,95), we can eliminate 19 and 95 as there exists no first digit to give such a number digits that are strictly increrasing or strictly decreasing as required by Q4.\r\n\r\nSimilarly we can eliminate 76 as it (when spelled out) contains both x and v which would leave Q7 with two correct answers. In the same manner we can eliminate 38 as the two possible numbers ending in 38 with strictly ascending digits (138 and 238) would leave question 7 with no answer at all.\r\n\r\nThis leaves us with a 3 digit number ending in 57. No number ending in 57 can be divisible by either 2 or 5 so Q3 indicates tht it must be divisible by 3. The only 3 digit number with strictly increasing digits that ends in 57 and is divisible by 3 is 357\r\n\r\nTherefore 357 is the answer',NULL,0);
INSERT INTO comment VALUES (7647,1200,1941,'shaun','m0ya4r','2003-09-04 08:51:03',0,'L3r,f2ab3sa1dan2ec5i,r1do7y',NULL,0);
INSERT INTO comment VALUES (7648,1184,2839,'FatBoy','kudos to Gamer','2003-09-04 09:06:06',0,'Not trying to give Gamer a big head but this was a way cool puzzle',NULL,0);
INSERT INTO comment VALUES (7649,611,3341,'joe gallagher','solution','2003-09-04 09:22:45',3,'gent.A: coat A; hat B; gloves C; cane D\r\ngent.B: \'\' B; \'\' D; \'\' A; \'\' C\r\ngent.C: \'\' D; \'\' C; \'\' B; \'\' A\r\ngent.D: \'\' C; \'\' A; \'\' D; \'\' B',NULL,0);
INSERT INTO comment VALUES (7650,111,3182,'Antonio','Solution','2003-09-04 09:51:01',3,'Try relating the angle A using the characteristics of an isoceles triangle, where two angles are the same and the other must be 180 minus the two already counted as the same. I managed to solve the problem using intersecting linear ecuations along with a series of angle relations that as I said in the begining, is pure isoceles relation. I put the coordinate origin in the vertex A and the x-axis pointing towards one of the isoceles vertex. I found a distance X that marks the intersection of one side of the isoceles and the line inside the triangle, I amr refering to the intersection in E perpendicular to AB. Such distance X is (I called L to any AD, De, EC, BC) L*tan(2*A)/(Tan(2*A)-Tan(A)). The side AE=X/cos(A)=L*tan(2*A)/(Tan(2*A)-Tan(A))/cos(A). With AE in therms of A and L, we use the law of cosines and get L²=(AE²+L)²+(AE²+L)²-2*(AE²+L)*(AE²+L)*cos(A). Replaceing AE and simplifying this ecuation we finally get 2*(1-cos(A))=(cos(A)/(cos(A)+(tan(2*A)/(tan(2*A)-tan(A)))))². We solve this equation to find A. A=20 degrees\r\n\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (7651,1187,3172,'SilverKnight','one solution...','2003-09-04 10:19:37',3,'GAMER\r\nGAMES\r\nGALES\r\nRALES\r\nRULES\r\n\r\nGAMER\r\nTAMER\r\nTIMER\r\nTIMED\r\nTIRED\r\n\r\nOkay.... not so rare... but first!',NULL,0);
INSERT INTO comment VALUES (7652,1187,2839,'FatBoy','partial answer','2003-09-04 10:19:40',2,'teh second one is fairly easy.\r\nGAMER\r\ntamer\r\ntamed\r\ntimed\r\nTIRED',NULL,0);
INSERT INTO comment VALUES (7653,1187,2839,'FatBoy','Curse you Silver Knight','2003-09-04 10:21:02',0,'3 seconds before me.\r\nOh well, I have yet to read your answer\r\nI will continue to add to mine',NULL,0);
INSERT INTO comment VALUES (7654,1187,3172,'SilverKnight','re: Curse you Silver Knight','2003-09-04 10:23:11',0,'That\'s because.... I\'m sittin\' RIGHT BEHIND YOU!\r\n\r\nMuhahaha\r\nMuhahahahahah',7653,0);
INSERT INTO comment VALUES (7655,1187,2839,'FatBoy','one (admittedly weak) shot at the other half','2003-09-04 10:24:27',2,'RULES\r\nroles\r\npoles\r\npales\r\ngales\r\ngames\r\nGAMER',NULL,0);
INSERT INTO comment VALUES (7656,1187,2839,'FatBoy','re: one solution...','2003-09-04 10:28:42',0,'S.K.\r\n\r\nI tried this option for gamer .. rules\r\nbut I eliminated it because I was not sure RALES was a word. Do you know something I don\'t?\r\n\r\nthe corpulant one',7651,0);
INSERT INTO comment VALUES (7657,1187,3172,'SilverKnight','re(2): one solution...','2003-09-04 10:32:53',0,'Main Entry: rale \r\nPronunciation: \'ral, \'räl\r\nFunction: noun\r\nEtymology: French râle, from râler to make a rattling sound in the throat\r\nDate: 1828\r\n: an abnormal sound heard accompanying the normal respiratory sounds on auscultation of the chest ',7656,0);
INSERT INTO comment VALUES (7658,1187,2839,'FatBoy','re(3): one solution...','2003-09-04 10:34:09',0,'oops, I didn\'t look hard enough',7657,0);
INSERT INTO comment VALUES (7659,113,1920,'Brian Smith','Solution: Part 1','2003-09-04 11:15:27',3,'First, express x and z in terms of y.\r\n\r\nLet s and t be sign variables (equal to 1 or -1), since square roots can be positive or negative.\r\n\r\nx = (-y/2) + s*sqrt[3 - (3*y^2/4)]\r\nz = (-y/2) + t*sqrt[16 - (3*y^2/4)]\r\n\r\nNow A can be expressed in terms of y and some sign variables.\r\n\r\nA = ((-y/2) + s*sqrt[3 - (3*y^2/4)])*((-y/2) + t*sqrt[16 - (3*y^2/4)]) + y*((-y/2) + s*sqrt[3 - (3*y^2/4)]) + y*((-y/2) + t*sqrt[16 - (3*y^2/4)])\r\n\r\nAfter some algebra:\r\n\r\nA = (1/4)*(-3*y^2 + y*s*sqrt[12 - 3*y^2] + y*t*sqrt[64 - 3*y^2] + s*t*sqrt[12 - 3*y^2]*sqrt[64 - 3*y^2])\r\n\r\nThe function A is defined as long as the square roots are real which means 12 - 3*y^2 >= 0 and 64 - 3*y^2 >= 0. From this, A is defined for 2 >= y >= -2.\r\n\r\nThe maximum value of A occurs at y = 2, y = -2, or some local maximum. Now its time for some calculus.\r\n\r\ndA/dy = (1/4)*( -6*y + s*sqrt[12 - 3*y^2] + t*sqrt[64 - 3*y^2] + y*(-6*s*y)/(2*sqrt[12 - 3*y^2]) + y*(-6*t*y)/(2*sqrt[64 - 3*y^2]) + s*sqrt[12 - 3*y^2]*(-6*t*y)/(2*sqrt[64 - 3*y^2]) + t*sqrt[64 - 3*y^2]*(-6*s*y)/(2*sqrt[12 - 3*y^2]) ) = 0',NULL,0);
INSERT INTO comment VALUES (7660,1187,1301,'Charlie','The RULES part','2003-09-04 11:32:28',3,'With the goal being common words rather than rare words, a 4-step solution to the RULES portion is ruled out as it would require RALES or GULES (the latter being a tincture red in heraldry); this portion requires a 5-step solution:\r\n\r\ngamer\r\ngames\r\ngales\r\nmales\r\nmules\r\nrules',NULL,0);
INSERT INTO comment VALUES (7661,113,1920,'Brian Smith','Solution: Part 2','2003-09-04 11:46:19',3,'From Part 1:\r\n\r\n(1/4)*( -6*y + s*sqrt[12 - 3*y^2] + t*sqrt[64 - 3*y^2] + y*(-6*s*y)/(2*sqrt[12 - 3*y^2]) + y*(-6*t*y)/(2*sqrt[64 - 3*y^2]) + s*sqrt[12 - 3*y^2]*(-6*t*y)/(2*sqrt[64 - 3*y^2]) + t*sqrt[64 - 3*y^2]*(-6*s*y)/(2*sqrt[12 - 3*y^2]) ) = 0 \r\n\r\nNow to solve this messy equation.\r\nFirst multiply each side by 4*s*sqrt[12 - 3*y^2]*t*sqrt[64 - 3*y^2]\r\nNote: s*s = 1 and t*t = 1\r\n\r\n0 = -6*y*s*t*sqrt[12 - 3*y^2]*sqrt[64 - 3*y^2] + (12 - 3*y^2)*t*sqrt[64 - 3*y^2] + (64 - 3*y^2)*s*sqrt[12 - 3*y^2] + -3*y^2*s*sqrt[12 - 3*y^2] + -3*y^2*t*sqrt[64 - 3*y^2] + -3*y*(12 - 3*y^2) + -3*y*(64 - 3*y^2)\r\n\r\nAfter some algebra and rearranging some terms:\r\n\r\n6*y*s*t*sqrt[12 - 3*y^2]*sqrt[64 - 3*y^2] + 228*y + -18*y^3 = (12 - 6*y^2)*t*sqrt[64 - 3*y^2] + (64 - 6*y^2)*s*sqrt[12 - 3*y^2]\r\n\r\nAfter squaring each side:\r\n\r\n(228*y - 18*y^3)^2 + 2*(228*y - 18*y^3)*(6*y*s*t*sqrt[12 - 3*y^2]*sqrt[64 - 3*y^2]) + 36*y^2*(12 - 3*y^2)*(64 - 3*y^2) = (12 - 6*y^2)^2*(64 - 3*y^2) + (64 - 6*y^2)^2*(12 - 3*y^2) + 2*(12 - 6*y^2)*(64 - 6*y^2)*s*t*sqrt[12 - 3*y^2]*sqrt[64 - 3*y^2]\r\n\r\nAfter even more algebra and removing a common multiple: (It seems most calculus is 80% algebra)\r\n\r\n9*y^6 - 228*y^4 + 1154*y^2 - 608 = (3*y^4 - 38*y^2 + 16)*s*t*sqrt[12 - 3*y^2]*sqrt[64 - 3*y^2]\r\n\r\nAfter squaring again and still more algebra, a final equation is formed (the higher exponents dropped out):\r\n\r\n217*y^4 - 608*y^2 + 256 = 0',7659,0);
INSERT INTO comment VALUES (7662,113,1920,'Brian Smith','Solution: Part 3','2003-09-04 12:01:53',3,'From Part 2:\r\n\r\n217*y^4 - 608*y^2 + 256 = 0\r\n\r\nSolving this equation yields y = 4/sqrt 31, y = -4/sqrt 31, y = 4/sqrt 7, and y = -4/sqrt 7 as possible values of y which yield a maximum value of A.\r\n\r\nSince all the sign variables dropped out, each y has two possible x\'s and two possible z\'s\r\n\r\nIf y = 4/sqrt 31, then x = -11/sqrt 31 or 7/sqrt 31 and z = 20/sqrt 31 or -24/sqrt 31\r\n\r\nIf y = -4/sqrt 31, then x = 11/sqrt 31 or -7/sqrt 31 and z = -20/sqrt 31 or 24/sqrt 31\r\n\r\nIf y = 4/sqrt 7, then x = 1/sqrt 7 or -5/sqrt 7 and z = 8/sqrt 7 or -12/sqrt 7\r\n\r\nIf y = -4/sqrt 7, then x = -1/sqrt 7 or 5/sqrt 7 and z = -8/sqrt 7 or 12/sqrt 7\r\n\r\nFrom Part 1: y = 2 and y = -2 are possible values for a maximum.\r\n\r\nIf y = 2, then x = -1 and z = -1+sqrt 13 or -1-sqrt 13\r\n\r\nIf y = -2, then x = 1 and z = 1+sqrt 13 or 1-sqrt 13\r\n\r\nIn all there are 20 candidate points to test. The two which create the highest value A=8 are (y=4/sqrt 31, x=7/sqrt 31, z=20/sqrt 31) and (y=-4/sqrt 31, x=-7/sqrt 31, z=-20/sqrt 31).',7661,0);
INSERT INTO comment VALUES (7663,1187,3206,'Lawrence','Solution','2003-09-04 13:54:21',0,'GAMER GAMER\r\nGAMES TAMER\r\nGALES TAMED\r\nMALES TIMED\r\nMULES TIRED',NULL,0);
INSERT INTO comment VALUES (7664,1184,3172,'SilverKnight','re: SilverKnight, do not read this post......','2003-09-04 13:54:31',0,'Just for the record, \"Your Buddy\" is *me* too.... I just changed my moniker to SilverKnight (which I prefer). ;-)
\r\nP.S. You can verify this, by clicking on the moniker, in the post.',7646,0);
INSERT INTO comment VALUES (7665,1150,1301,'Charlie','solution','2003-09-04 14:47:24',3,'If we denote the other digits of the number (than the initial or trailing 6) as \"string\", we seek a number 6string = 4 x string6. That is string6 = 6string / 4.\r\n\r\nSimilar to one of the the solutions of Move the 2, Double the Number, we start the long division:\r\n\r\n 1\r\n4)6\r\n
\r\nand note\r\nthat we can bring down the digit 1 in the quotient to be the digit after the 6 in the dividend, and continue the long division:\r\n\r\n 15\r\n4)61\r\n 4\r\n 21\r\n
\r\nThen we can bring down the 5 the same way\r\nand continue:\r\n\r\n 153846\r\n4)615384\r\n 4\r\n 21\r\n 20\r\n 15\r\n 12\r\n 33\r\n 32\r\n 18\r\n 16\r\n 24\r\n 24\r\n 0\r\n
\r\nThat\'s the first point where we can stop, as the remainder is zero.\r\n\r\nBut we also could choose to continue, and if we do we must bring down the 6 to be the next digit after the 4, and thus it starts again as from the beginning. So any such number must be the string 153846, either once or repeated any number of times.\r\n\r\nSo the first (smallest) such number is 153,846 and the second is 153,846,153,846 and the tenth is 153,846,153,846,153,846,153,846,153,846,\r\n153,846,153,846,153,846,153,846,153,846.',NULL,0);
INSERT INTO comment VALUES (7666,1187,1626,'Gamer','re: The RULES part','2003-09-04 19:07:24',0,'I actually considered a 6 step solution as I didn\'t know if gales was too common, but this works. I thought someone would mention something like RALES, that\'s why I put in \"less obscure rule\"',7660,0);
INSERT INTO comment VALUES (7667,85,3347,'Jake','huh?','2003-09-04 19:58:06',4,'why can\'t the green guy be wearing the yellow tie?',NULL,0);
INSERT INTO comment VALUES (7668,1150,3351,'Eric','solution','2003-09-05 00:27:27',0,'the nth smallest number is 153846*1000001^(n-1), making the solutions 153,846\r\n153,846,153,846\r\nand of course 153,846,153,846,153,846,153,846,153,846,153,846,153,846,153,846,153,846,153,846\r\n',NULL,0);
INSERT INTO comment VALUES (7669,1116,3335,'AJ','Recursive','2003-09-05 01:02:47',3,'This was done in VBA\r\nFunction Spiral(i As Integer, j As Integer, n As Integer) As Integer\r\n If n = 1 Or n = 0 Then\r\n Spiral = 0\r\n ElseIf i = 1 Then\r\n Spiral = 4 * n - 4 - j + Spiral(1, 1, n - 2) - (n > 2)\r\n ElseIf j = n Then\r\n Spiral = 3 * n - 3 - i + Spiral(1, 1, n - 2) - (n > 2)\r\n ElseIf i = n Then\r\n Spiral = n - 3 + j + Spiral(1, 1, n - 2) - (n > 2)\r\n ElseIf j = 1 Then\r\n Spiral = i - 2 + Spiral(1, 1, n - 2) - (n > 2)\r\n Else\r\n Spiral = Spiral(i - 1, j - 1, n - 2)\r\n End If\r\nEnd Function',NULL,0);
INSERT INTO comment VALUES (7670,611,3127,'lesa','solution','2003-09-05 01:02:58',0,'A had his own coat, B\'s hat, C\'s gloves and D\'s cane\r\nB had his own coat, A\'s gloves, C\'s cane and D\'s hat\r\nC had his own hat, A\'s cane, B\'s gloves and D\'s coat\r\nD had his own gloves, A\'s hat, B\'s cane and C\'s coat',NULL,0);
INSERT INTO comment VALUES (7671,781,3127,'lesa','???','2003-09-05 01:36:21',0,'According to the solution, the water was traveling at 6 miles per hour. Therefore, it would take the hat 10 minutes to travel back to the campsite. If Bob continued traveling for five minutes and then turned around, 10 minutes after dropping the hat, he would still be a mile away from the campsite. The problem states he \"catches up with\" the hat, not retreived it from the bank.\r\n\r\n\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (7672,1114,3351,'Eric','solution','2003-09-05 02:17:34',0,'My analysis reveals a great number of solutions for example: \r\n\r\n1, 5, 4,10 3, 5, 4,12 1, 5, 1, 7 1, 5, 7,13\r\n2, 3, 7,12 2, 1, 7,10 1,19, 5,25 1,19, 4,24\r\n1,15,19,35 1,15,19,35 13, 9, 3,25 3,14, 3,20\r\n4,23,30,57 6,21,30,57 15,33, 9,57 5,38,14,57\r\n\r\nMany more solutions can be generated by rearranging the numbers in the AFK diagonal (1,3,19 - the factors of 57), and building equations and inequalities from the remaining variables (C,G,E,I,and J). The two major equations evolve from EJ=C+G+K(1,3,or 19) and 5G=I+J+K. The major inequalities are built from the fact that all variables are between 1 and 57.',NULL,0);
INSERT INTO comment VALUES (7673,611,3335,'AJ','solution','2003-09-05 03:01:23',3,' A B C D\r\n ====================\r\nCoat == A B D C\r\nHat == B D C A\r\nGloves== C A B D\r\nCanes == D C A B',NULL,0);
INSERT INTO comment VALUES (7674,288,3354,'amy','well???','2003-09-05 05:49:35',1,'with this problem it is a good problem but it does not have a very good solution? But i don\'t think i could think of a better one.',NULL,0);
INSERT INTO comment VALUES (7675,1150,2839,'FatBoy','Not for SIlver Knight\'s Eyes','2003-09-05 07:44:25',3,'define the number we are looking for as x\r\n\r\nthe ones digit of x is six (specified by the problem)\r\nThe tens digit of x will be the ones digit in 4x so it must be equla to the ones digit of the four times the ones digit of x (six as noted above) so the tens digit must be 4\r\nThe one hundreds digit of x is the tens digit of 4x and so must be teh ones digit of four times the tens digit of x plus the tens digit of four times the ones digit of x (to accout for the \"carried\" tens) and is therefore 8 {(4*4)+2 = 18}\r\n\r\nUsing this technique we continue until we find a value of 4x with a leftmost digit that is 6.\r\nthe values we come up with are\r\nx = 153846\r\n4x = 615384\r\n\r\nthis is the smallest value of x\r\nthe second smallest value is this string repeated twice (153846153846)\r\nand teh 10th amllest value would be the string repeated 10 times.\r\n ',NULL,0);
INSERT INTO comment VALUES (7676,1260,2840,'Becky','Well, Gee','2003-09-05 08:19:39',0,'I would infer that I am driving the wrong way on a highway or road and the word slow is up-side-down OR the word slow is up-side-down on the opposit side of the road, but also in front of me.',NULL,0);
INSERT INTO comment VALUES (7677,1202,1183,'fwaff','H2T1E3 L3N8O7U4S1I6T5O2','2003-09-05 08:34:05',3,'V3E4I2F1',NULL,0);
INSERT INTO comment VALUES (7678,1202,2839,'FatBoy','A4I2L6F1N3Y7L5 O4E2E6F3B1R5 K2S1','2003-09-05 09:27:20',3,'E4I2V3F1, F2O1 U3O2E6R4S5C1',NULL,0);
INSERT INTO comment VALUES (7679,1202,1183,'fwaff','re: A4I2L6F1N3Y7L5 O4E2E6F3B1R5 K2S1','2003-09-05 10:30:32',0,'T3B1U2 O2T3N1 O4E2E6F3B1R5 A3W2F5F4F1 -2)3;1',7678,0);
INSERT INTO comment VALUES (7680,84,3342,'Jenny','Paradox','2003-09-05 10:30:58',3,'If you overtake the last person (infering you are behind them) that means you were the last person and you cannot overtake yourself, but if you managed to do that you would still be in last place. ',NULL,0);
INSERT INTO comment VALUES (7681,1260,3342,'Jenny','Soultion','2003-09-05 10:38:00',3,'\"MO7S\" is the backwards version of SLOW so one might infer that one is going the wrong way on the road and needs to slow down. OR...one is dyslexic and still needs to slow down. Or...the one who painted it on the road painted it backwards on the right way of the road.',NULL,0);
INSERT INTO comment VALUES (7682,1265,1575,'DJ','hint?','2003-09-05 11:54:03',4,'Bryan.. how about a little more context or something to help us out.. I don\'t think anyone is even close as of yet..',NULL,0);
INSERT INTO comment VALUES (7683,1202,2899,'Brian Wainscott','T4N2O3H5R7E6A1 U4S1L3N8T5I6O2O7','2003-09-05 12:44:50',0,'R2O1 V4L2N6E3E1E5 E4A2B1S3 O2F1R4U3\r\nI1 A2H1D3 O2T1 S1Y3A2 E4S1M3G9O2T5I7H6N8\r\nS4H2T1I3 S2I1 M1Y2 I2S4F1R3T5 T5C1Y3P4R2O6 S3P1T4O2',NULL,0);
INSERT INTO comment VALUES (7684,1073,3274,'Dacre','Yet another solution','2003-09-05 12:52:07',3,'Measure out 8 units using the 4 unit jug, and throw them away. \r\nFill the 4 unit jug up. You now have 4 units left in the 16 glass. Then pour away from the 4 glass until it\'s at the same height of water as the 16. \r\nSince the 16 glass is 4 times the size but the same height, this is a quarter of the amount left in there, so one unit.\r\nYou now how 5 units in total.\r\n',NULL,0);
INSERT INTO comment VALUES (7685,1202,2839,'FatBoy','re(2): A4I2L6F1N3Y7L5 O4E2E6F3B1R5 K2S1','2003-09-05 13:07:52',0,'E5A2M1B4Y3, A6E4O2M3Y7D5S1, F2I1 I1 Y3T1R2 A3E2L4R1 A2D4H1R3 .3.1.2',7679,0);
INSERT INTO comment VALUES (7686,1202,2839,'FatBoy','re: T4N2O3H5R7E6A1 U4S1L3N8T5I6O2O7','2003-09-05 13:17:38',0,'E4A2K3M1 O2S4L1T3 F2O1 E3H2M4T1.\r\nS302P1T4 U3Y1R4O2 E5A1R6S7S3N2W4 E1E3V2N4 F2I1\r\nE4O1H3T2S6R5 A1A5E4Y7D6L2R3 E4A2V3H1, T2I1 N3N2Y5O4S6A1 I9I2E5H11N8K7L3S1T12R6V4G10',7683,0);
INSERT INTO comment VALUES (7687,1184,2839,'FatBoy','re(2): SilverKnight, do not read this post......','2003-09-05 13:27:44',0,'CURSES, foiled again',7664,0);
INSERT INTO comment VALUES (7688,1202,3172,'SilverKnight','re(2): T4N2O3H5R7E6A1 U4S1L3N8T5I6O2O7','2003-09-05 13:45:54',0,'It\'s just a waste of bandwidth with you guys (and your own time ;-) How many people need to show that they figured out this incredibly difficult code (particularly after someone already said \'five\')?
\r\nAnd what\'s more... FatBoy, you clearly saw fwaff\'s post BEFORE you posted... so no risk of being different than his ;-) (x2) What\'s the silly reason for posting THIS time? (no... I\'m not annoyed... well... not VERY annoyed... lol)',7686,0);
INSERT INTO comment VALUES (7689,1267,1301,'Charlie','solution','2003-09-05 14:41:39',3,'If F were a knight then A would also be a knight; but then F would have to be a liar. So F is not a knight, but is a liar.\r\n\r\nTherefore either D is a knight or A is a liar. But if D is a knight then it\'s still true that A is a liar. So A is indeed a liar.\r\n\r\nSo either C or F must be a knight, and since it isn\'t F, it must be C that\'s a knight.\r\n\r\nThus B is a liar and E is a knight, by C\'s statements.\r\n\r\nSince E is a knight both C and D are knights. We already knew about C, but now we know also that D is a knight.\r\n\r\nSo C, D and E are knights and A, B and F are liars.',NULL,0);
INSERT INTO comment VALUES (7690,1202,1919,'Lewis','re(3): T4N2O3H5R7E6A1 U4S1L3N8T5I6O2O7','2003-09-05 15:19:24',0,'At least he posted a solution, not some worthless moaning....',7688,0);
INSERT INTO comment VALUES (7691,1267,1575,'DJ','Solution','2003-09-05 15:28:15',3,'Suppose A is a knight.\r\n\r\nThen, C and F are both liars, and at least one of the statements made by each must be false.\r\n\r\nF said that A is a knight, which we have alerady assumed to be true, so the other part of his statement must be false, and Derek is a knight.\r\n\r\nHowever, Derek says that A is a liar, so we have a contradiction, and our original assumption must be false.\r\n\r\nTherefore, A is a liar, and at least one of his statements must be false (either C or F is a knight).\r\n\r\nF cannot be a knight, since he says A (a liar) is a knight.\r\n\r\nC must be a knight.\r\n\r\nC says that B is a liar and E is a knight, which must both be true.\r\n\r\nFinally, E (a knight) says that C and D are knights, and we now know what each person is:\r\nA - liar\r\nB - liar\r\nC - knight\r\nD - knight\r\nE - knight\r\nF - liar
Going through the remaining statements shows no contradictions.',NULL,0);
INSERT INTO comment VALUES (7692,1260,3358,'Brent','heartland answer','2003-09-05 15:43:26',0,'Missouri Highway 7 South\r\n ',NULL,0);
INSERT INTO comment VALUES (7693,1202,3172,'SilverKnight','re(4): T4N2O3H5R7E6A1 U4S1L3N8T5I6O2O7','2003-09-05 15:48:12',0,'moaning? worthless? hardly...\r\n\r\nAnd you didn\'t address my questions... (not that I expect you will... ;-)',7690,0);
INSERT INTO comment VALUES (7694,937,3358,'Brent','what did you say?','2003-09-05 15:54:07',0,'EAR',NULL,0);
INSERT INTO comment VALUES (7695,1260,3359,'chris','Answer','2003-09-05 17:32:20',0,'SLOW',NULL,0);
INSERT INTO comment VALUES (7696,610,3360,'Nathan','solution','2003-09-05 17:44:41',0,'there are seven none yellow birds and nine yellow birds',NULL,0);
INSERT INTO comment VALUES (7697,7,3360,'Nathan','weak','2003-09-05 17:47:18',0,'There is a 50% chance of it being heads and a 50% chance of it being tails',NULL,0);
INSERT INTO comment VALUES (7698,1187,3360,'Nathan','','2003-09-05 18:07:00',4,'gamer gamer\r\ngames tamer\r\ngales timer\r\ngules timed\r\nrules tired\r\n\r\nI switch letters 1 by 1\r\nI hope its right but i\'m not sure',NULL,0);
INSERT INTO comment VALUES (7699,1062,3360,'Nathan','solution','2003-09-05 18:17:00',3,'1x3=3\r\n\r\n3x4=12\r\n\r\n12x5=60\r\n\r\n60x6=360\r\n\r\n360x7=2520\r\n\r\n2520x8=20160\r\n\r\n20160x9=181440\r\n\r\n181440x10=1814400\r\n\r\nThat is my solution',NULL,0);
INSERT INTO comment VALUES (7700,1202,1626,'Gamer','K4A2T1L3 Y3T5O6R2C1P4','2003-09-05 18:20:54',0,'E3H2T1 T5O3I2N4P1 S2I1 O2T1 T1K4A1L2 N2I1 Y3P4O6T5R2C1... U3Y1O2 L4L3W1I2 E2B1 F1R3T5S4I2 A6E4O2M3Y7D5S1 B4O5A2T3F1Y6! D2:1',7693,0);
INSERT INTO comment VALUES (7701,1267,3206,'Lawrence','And the winner is ...','2003-09-05 22:21:39',0,'Or should I say the winner is \"and.\" That\'s the big deal here, the \"and.\" The best way to solve this is to assume someone is a knight and follow the logic. Once you run into a liar, at least one half of the \"and\" is false, could be both, but that really tells you little. \r\n\r\nSo the most logical place to start the assumptions turns out to be the answer. E makes a statement that C & D are knights. Assume that to be true and follow the logic through. If it blows up, you know E is a liar, and you can go from there.\r\n\r\nIf E is telling the truth, then C\'s statement is true and we learn B is a Liar. If B is a liar and E is a knight, then F is a liar. If F is a liar ... well, here we are stuck because if E is telling the truth, the \"D is a liar bit\" already makes the statement false so we learn nothing. Dead end, but not contradiction, so go to D is a knight.\r\n\r\nD states A & B are liars, which is the complete truth. A says C and F are liars, but C is not, so that one is already a lie -- still ok. C states that A and B are liars, which we\'ve quite established.\r\n\r\nNothing blows up ... E is a knight, so are C and D; the others, A,B,F are liars. You need go through no further iterations.',NULL,0);
INSERT INTO comment VALUES (7702,145,3206,'Lawrence','HEY!','2003-09-05 22:31:00',0,'By definition, a circle is all the points equidistant fromt he center. 25% of the interior is shaded green. The other 75% is shaded blue. So 100% of the circle\'s interior is shaded. BUT the circle itself is the set of points in black, so you could say 100% of the circle is shaded in black, or if you were a tricky bastard you could say that none of it is shaded because black isn\'t considered a shade, i.e. it\'s considered neutral. That\'s as good an answer as I can give. In any case you are a tricky, vague bastard, qball -- not that there\'s anything wrong with that.\r\n\r\nL',NULL,0);
INSERT INTO comment VALUES (7703,288,3224,'Lee','pangram','2003-09-06 03:13:20',0,'It\'s called a pangram if anyone\'s bothered. The shorter ones are more desireable hence\r\n\'jumpS over the lazy dog\'\r\nwould be \'better\' in pangrammatical terms (at 35 letters).\r\nI read once a chinese pangram that contained only 26 letters (the \'best\'?). It was about 100 words long when translated! ',NULL,0);
INSERT INTO comment VALUES (7704,1151,3372,'sam','Solution','2003-09-06 15:05:43',3,'I\'m pretty sure this is right...:\r\n\r\nMonica Baker, 1, Puzzle\r\nKevin Farrell, 2, Crayons\r\nDarren Forbes, 3, Teddy\r\nHolly Lorenz, 4, Blocks\r\nMark Mckenna, 5, Picture Book\r\nJanet Collins, 6, Fire Engin',NULL,0);
INSERT INTO comment VALUES (7705,973,3372,'sam','re: Well','2003-09-06 15:35:36',4,'Wait, so what was the answer? Trevor\'s answer is clever (\"Wrong\" house), but doesn\'t explain why you then say \"Once again his call didn\'t go through,\" since he would have actually reached Bob the first time.',6130,0);
INSERT INTO comment VALUES (7706,27,3372,'sam','re: not true','2003-09-06 15:46:56',0,'No, you misunderstand the logic. Once Friday has been knocked off, it is permenently out. Simply because, even if we then go on to eliminate Thursday, if the students get to Thursday and they haven\'t had the exam, it must be on Friday. So our week is now shortened to Monday through Thursday, and we do the same thing all the way up through Monday. However, as other people have said, the puzzle does not end here. Let us suppose that the Students get to Thursday without having the exam. Then they will be certain that the professor cannot give it to them on the Friday. Therefore the professor can give it to them without breaking his word (and could give it on any other day by the same logic).',7497,0);
INSERT INTO comment VALUES (7707,31,3372,'sam','','2003-09-06 15:54:13',3,'This puzzle is the same as Thomson\'s lamp, where he turns it on at one second, off half a second later, on a quater of a second later, and so on. Is it on or off at two seconds.\r\n\r\nThe answer is that the question is meaningless in the bounds of the question, because the instructions for what he, or the bee, does are given up to the very end, but not at the very end. The sequence 1 + 0.5 + 0.25 *tends* to 2, and in calculus is equal to 2, but you cannot say what happens *at* 2.\r\nThis paradox is basically similar to asking if the \"last\" integer is even or odd - the question doesn\'t make sense.',NULL,0);
INSERT INTO comment VALUES (7708,66,3372,'sam','NOT a paradox! IMPORTANT distinction!','2003-09-06 16:02:21',3,'It\'s not actually a paradox, it\'s a contradiction (as humpty dumpty tells Alice eloquently in... through the looking glass?).\r\n\r\nIf I were to say, here\'s a great paradox: I met a man who was 4 foot tall AND 6 foot tall, what do you think of that?!? \r\n\r\nIt\'s perfectly obvious that that wouldn\'t be a paradox, because there simply couldn\'t be such a man. Likewise, such a barber could never exist. This isn\'t a meanigless statement, the distinction between paradoxes and contradictions is very important. After all, it\'s certainly true that I can utter the statement \"This statement is a lie,\" and so we then have to puzzle around at the boundaries of logic to work out what\'s wrong.\r\n\r\nIn this case, however, the puzzle is saying \"In a certain town there is a barber that neither shaves himself nor does not shave himself, which is akin to saying \"In a certain town there is a man who is six foot tall and four foot tall.\"\r\n\r\nNot that it\'s a bad puzzle though... :)',NULL,0);
INSERT INTO comment VALUES (7709,48,3143,'Vito','umm','2003-09-06 16:12:04',0,'This is one of the easier ones on the net. No mathematical computations necessary, if the chances are equal and we are on a 100% scale. 50% chance it\'ll be a boy and 50% chance it will be a girl. The ratio is, therefore, 1 to 1.',NULL,0);
INSERT INTO comment VALUES (7710,250,3372,'sam','re: fuzzy logic','2003-09-06 16:15:51',0,'You what?? Fuzzy logic is something else altogether, based on finding answers using imprecise or vague solutions, which, almost a paradox in itself, is extremely precise. \"Maybe\" is never a truth value to a logical statment. If it were, and all paradoxes could be answered by \"maybe,\" people would have stopped bothering with them long ago...\r\n\r\n:)',7498,0);
INSERT INTO comment VALUES (7711,1012,3143,'Vito','ahh very clever','2003-09-06 16:20:19',0,'Before...meaning in front of his father, killed his mom during childbirth (that was easy)...then (this one took me the longest) he must have been a priest/pastor in order to marry his sister. Marry meaning to have authority over the marriage and marry his sister with another after blessing them and giving their vows.',NULL,0);
INSERT INTO comment VALUES (7712,1151,1301,'Charlie','re: Solution','2003-09-06 16:54:41',0,'In this solution, the Lorenz child\'s box number is lower than Mark\'s. The Forbes child has an odd numbered box (I assume what\'s meant is box number in the puzzle, even though two boxes apparently are on each level(shelf).).',7704,0);
INSERT INTO comment VALUES (7713,1151,693,'Jun','re: Solution','2003-09-06 21:13:46',0,'In the problem, it\'s stated that, \'The shelf belonging to the Forbes child and the one which holds a box of crayons are both even-numbered shelves.\' However, you have placed Forbes in shelf no. 3 (odd number).\r\n\r\n\r\nAlso, just checking if the shelves are numbered in this way...\r\n\r\n 1 4\r\n 2 5\r\n 3 6',7704,0);
INSERT INTO comment VALUES (7714,1151,3195,'John Reid','Correct (?) Solution','2003-09-06 21:48:48',3,'In trying to solve this problem, the first difficulty was in trying to work out how the 6 shelves/compartments were arranged in the bookcase, and more to the point how the compartments were to be numbered. I ended up assuming that the system was that given by Jun in the previous comment, ie\r\n\r\n1 4\r\n2 5\r\n3 6\r\n\r\n(this seems to comply with the given info that the compartments are \'numbered top to bottom, then left to right\', as well as the information in the problem referring to \'the two top shelves\' - although it wasn\'t fully clear to me that the numbering couldn\'t have been\r\n\r\n1 2\r\n3 4\r\n5 6)\r\n\r\nAfter making this first step, the problem did come out fairly easily. In fact the solution posted by sam in the first comment is correct, except for the compartment numbers.\r\n\r\nHere is the answer:\r\n\r\nCompartment 1 (top left)\r\nMonica Baker\r\nPuzzle\r\n\r\nCompartment 2 (center left)\r\nDarren Forbes\r\nTeddy Bear\r\n\r\nCompartment 3 (lower left)\r\nMark McKenna\r\nPicture Book\r\n\r\nCompartment 4 (top right)\r\nKevin Farrell\r\nBox of Crayons\r\n\r\nCompartment 5 (center right)\r\nHolly Lorenz\r\nSet of Blocks\r\n\r\nCompartment 6 (lower right)\r\nJanet Collins\r\nFire Engine\r\n\r\n(Incidentally, the solution I had arrived at before reading the previous comments was flawed - I had switched Mark and Janet and had come up with Janet McKenna in #3 with the Picture Book and Mark Collins in #6 with the Fire Engine. Reading the other comments made me realize my error. So, perhaps we can call this solution a joint effort!)\r\n\r\nThanks for another fun puzzle DJ :)',NULL,0);
INSERT INTO comment VALUES (7715,157,3351,'Eric','re: A solution','2003-09-07 10:01:59',0,'Nick, just a minor correction: I believe that the area of each of the right angled triangles is half that: or (er * Sin a)/2. Other than that you have a very tight proof. Mine was full of messy Arctangents - yuk.',821,0);
INSERT INTO comment VALUES (7716,1203,3351,'Eric','Holy Hula Hoops!','2003-09-07 10:12:37',0,'In this classic tower of Babel problem, the clue to controlling the final position of the hoops is noticing the odd and even hoops. That is to say, begin by numbering the hoops from smallest to largest. If you want to move the tower of hoops to pole three you must begin by moving hoop #1 to pole three. Thereafter all even numbered hoops will first be moved to pole two, covered with their succesively smaller hoops until pole three is empty and available for the next larger odd numbered hoop. This, of course, applies to all tower sizes.',NULL,0);
INSERT INTO comment VALUES (7717,1203,3202,'Jill','Number of moves','2003-09-07 10:35:31',0,'It took me 35 moves to get them in order from largest on bottom to smallest on top on pole 3 moving 1 at a time.\r\n\r\nI did the following steps.\r\nxs to 2\r\ns to 3\r\nxs to 3\r\nm to 2\r\nxs to 2\r\ns to 1\r\nxs to 1\r\nm to 3\r\nxs to 2\r\ns to 3\r\nxs to 3\r\nl to 2\r\nxs to 2\r\ns to 1\r\nxs to 1\r\nm to 2\r\nxs to 3\r\ns to 2\r\nxs to 2\r\nxl to 3\r\nxs to 1\r\ns to 3\r\nxs to 3\r\nm to 1\r\nxs to 2\r\ns to 1\r\nxs to 1\r\nl to 3\r\nxs to 3\r\ns to 2\r\nxs to 2\r\nm to 3\r\nxs to 1\r\ns to 3\r\nxs to 3\r\n',NULL,0);
INSERT INTO comment VALUES (7718,1203,693,'Jun','Steps to follow (not for the impatient)','2003-09-07 10:41:04',0,'Well, I solved this in 31 steps (maybe there are shorter methods), label the hoops a,b,c,d,e (from smallest to biggest).\r\n\r\n1. a to pole 3\r\n2. b to pole 2\r\n3. a to pole 2\r\n4. c to pole 3\r\n5. a to pole 1\r\n6. b to pole 3\r\n7. a to pole 3\r\n8. d to pole 2\r\n9. a to pole 2\r\n10. b to pole 1\r\n11. a to pole 1\r\n12. c to pole 2\r\n13. a to pole 3\r\n14. b to pole 2\r\n15. a to pole 2\r\n16. e to pole 3\r\n17. a to pole 1\r\n18. b to pole 3\r\n19. a to pole 3\r\n20. c to pole 1\r\n21. a to pole 2\r\n22. b to pole 1\r\n23. a to pole 1\r\n24. d to pole 3\r\n25. a to pole 3\r\n26. b to pole 2\r\n27. a to pole 2\r\n28. c to pole 3\r\n29. a to pole 1\r\n30. b to pole 3\r\n31. a to pole 3\r\n\r\nThere you have it, hopefully you guys haven\'t fallen asleep...\r\n\r\nNote: You guys could create 5 folders in any directory on your com and follow my procedure by moving your folders around to see for urselves!!',NULL,0);
INSERT INTO comment VALUES (7719,1203,1301,'Charlie','re: Holy Hula Hoops!','2003-09-07 11:14:04',0,'If the smallest is always designated 1, and you always start moving that (and the other odd numbers) to pole 3 (the target pole), and start off the even ones to pole 2, then, in the case of an even starting number of hoops, they will wind up on the wrong hoop.\r\n\r\nTake the simplest even case: two hoops. Moving hoop 1 to pole 3, then hoop 2 to pole 2 then hoop 1 to pole 2 has moved them to the wrong pole.\r\n\r\nIf we want to say that even numbered hoops should start out toward pole 2 then the numbering should be from the bottom (largest) hoop. Then it works out correctly: if there are an even number of hoops the top hoop will have an even number; if there are an odd number of hoops the top hoop will have an odd number.\r\n',7716,0);
INSERT INTO comment VALUES (7720,1203,1301,'Charlie','strategy','2003-09-07 11:23:12',0,'The strategy for moving n hoops to pole 3 is first to move n-1 hoops to pole 2, then move the nth hoop to pole 3 and then move the other n-1 hoops onto pole 3. Defining the problem this way is known as recursion. Eventually you have broken it down into the problem of moving just 1 hoop. It\'s apparent that the target of the bottom (nth) hoop is to be pole 3; the target of hoop n-1 is to be pole 2; etc, alternating.\r\n\r\nFrom this description, the number of moves necessary for n hoops is one more than twice the number required for n-1 hoops, as n-1 must be moved to the non-target pole, the nth moved to the target pole and then the n-1 must be moved again to the target pole. \r\n\r\nSo the sequence showing the number of required moves is:\r\n1,3,7,15,31,63,127,...\r\n\r\nEdited on September 7, 2003, 11:24 am\n\nEdited on September 7, 2003, 3:48 pm',NULL,0);
INSERT INTO comment VALUES (7721,1265,1567,'Bryan','A hint','2003-09-07 12:57:49',2,'If you change one letter in each word, ...',NULL,0);
INSERT INTO comment VALUES (7722,1203,1626,'Gamer','re: strategy','2003-09-07 14:15:48',0,'I don\'t think your numbers at the bottom are correct. I think they should be powers of 2 minus 1 By induction (which I am not so good with), the n(1) = 1, and the n(x+1)=2(n(x))+1, but this can be expressed this way as well:\r\n\r\nn(1) equals 2^1-1,\r\nn(2) equals 2(2^1-1)+1 = 2(2^1)-1 =2^2-1\r\nn(3) equals 2(2^2 - 1) + 1 = 2^3 - 1\r\nSo if (n(x) equals 2^x - 1, then n(x+1)=n(x)+1 = 2(2^x -1) +1 = 2^(x+1)-1',7720,0);
INSERT INTO comment VALUES (7723,1203,1626,'Gamer','Recursion challenge','2003-09-07 14:19:04',4,'I am still trying induction so if I made a mistake in that last post, just tell me please! :)\r\n\r\nI have another challenge: How could you use recursion in a program to print out a list of hoops when given the number x of how many hoops they are? (Refer to the hoops as A, B, C and so on to reduce counting the X before a S or L)\r\n\r\nSample out put when x=3:\r\n\r\nMove A from 1 to 3\r\nMove B from 1 to 2\r\nMove A from 3 to 2\r\nMove C from 1 to 3\r\nMove A from 2 to 1\r\nMove B from 2 to 3\r\nMove A from 1 to 3\n\nEdited on September 7, 2003, 2:47 pm',NULL,0);
INSERT INTO comment VALUES (7724,1265,1626,'Gamer','re: A hint','2003-09-07 14:26:48',0,'I was looking for what the words all have in common when you change one letter... I don\'t see the connection yet.',7721,0);
INSERT INTO comment VALUES (7725,1203,3386,'Victor Zapana','solution in 19 moves','2003-09-07 15:13:01',0,'I did it in 19 moves, so here goes.\r\n1.) XS to pole 2\r\n2.) S to pole 4\r\n3.) M to pole 5\r\n4.) S to pole 5\r\n5.) XS to pole 5\r\n6.) L to pole 2\r\n7.) XS to pole 4\r\n8.) S to pole 1 (S is still smaller than XL)\r\n9.) M to pole 2\r\n10.) S to pole 2\r\n11.) XS to pole 2\r\n12.) XL to pole 3\r\n13.) XS to pole 1\r\n14.) S to pole 4\r\n15.) M to pole 5\r\n16.) L to pole 3\r\n17.) M to pole 3\r\n18.) S to pole 3\r\n19.) XS to pole 3\r\n\r\nThere.',NULL,0);
INSERT INTO comment VALUES (7726,1203,1626,'Gamer','re: solution in 11 moves with 5 poles','2003-09-07 15:40:06',0,'It might be an interesting twist to have more than 3 poles, but all the problem seems to allow is 5 poles... Did you mean for some of the 4s and 5s to be 1s 2s and 3s? Here\'s the solution for 5 poles (It might be harder with more than 5 rings/discs when we have 5 poles)\r\n\r\n1) XS from pole 1 to pole 2\r\n2) S from pole 1 to pole 5\r\n3) XS from pole 2 to pole 5\r\n4) M from pole 1 to pole 4\r\n5) L from pole 1 to pole 2\r\n6) XL from pole 1 to pole 3\r\n7) L from pole 2 to pole 3\r\n8) M from pole 4 to pole 3\r\n9) XS from pole 5 to pole 4\r\n10) S from pole 5 to pole 3\r\n11) XS from pole 4 to pole 3',7725,0);
INSERT INTO comment VALUES (7727,1203,1301,'Charlie','re(2): strategy','2003-09-07 15:48:01',0,'You are right. I added two rather than one at one point. I will correct that post, now that we have that ability.',7722,0);
INSERT INTO comment VALUES (7728,1265,3386,'Victor Zapana','grr','2003-09-07 15:51:20',0,'grr.. if tree and loyal weren\'t the there, the connection could have been that if you change the 2nd consonant in every word with the letter \"l\" would make a another sensible word. unless of course u can count tlee and lolal as words :P',NULL,0);
INSERT INTO comment VALUES (7729,1203,1301,'Charlie','re: Recursion challenge','2003-09-07 16:12:32',0,'DECLARE SUB transfer (n!, source!, dest!)\r\nINPUT \"Number of hoops:\", n\r\ntransfer n, 1, 3\r\n\r\nSUB transfer (n, source, dest)\r\n IF n = 1 THEN\r\n PRINT \"Move A from\"; source; \"to\"; dest\r\n ELSE\r\n transfer n - 1, source, 6 - source - dest\r\n PRINT \"Move \"; CHR$(ASC(\"A\") + n - 1); \" from\"; source; \"to\"; dest\r\n transfer n - 1, 6 - source - dest, dest\r\n END IF\r\nEND SUB\r\n\r\nwith sample runs:\r\nNumber of hoops:3\r\nMove A from 1 to 3\r\nMove B from 1 to 2\r\nMove A from 3 to 2\r\nMove C from 1 to 3\r\nMove A from 2 to 1\r\nMove B from 2 to 3\r\nMove A from 1 to 3\r\n\r\nNumber of hoops:4\r\nMove A from 1 to 2\r\nMove B from 1 to 3\r\nMove A from 2 to 3\r\nMove C from 1 to 2\r\nMove A from 3 to 1\r\nMove B from 3 to 2\r\nMove A from 1 to 2\r\nMove D from 1 to 3\r\nMove A from 2 to 3\r\nMove B from 2 to 1\r\nMove A from 3 to 1\r\nMove C from 2 to 3\r\nMove A from 1 to 2\r\nMove B from 1 to 3\r\nMove A from 2 to 3',7723,0);
INSERT INTO comment VALUES (7730,31,3387,'luke','don\'t believe the given solution is correct','2003-09-07 16:44:42',0,'Could be wrong but I don\'t believe the bee in this problem would make an infinite number of turns. The bee flies from the biker to the house and back and forth. The biker approaches the house at a steady rate and will eventually reach the house. Another way of saying this is that the distance between the biker and the house will be zero. When this occurs the bee will have no where to fly. The bee flies for a time and then ceases to fly.\r\n\r\nIf the bee finishes its route it cannot have been comprised of an infinite number of turns. Had the biker approached the house in some kind of exponentially decaying pattern then yes the bee would fly and turn infinitely but as the problem is constructed there is only a certain time the bee has to turn in.',NULL,0);
INSERT INTO comment VALUES (7731,1151,3372,'sam','re: Correct (?) Solution','2003-09-07 20:28:29',0,'Rats. I knew there was something wrong with my results, but I couldn\'t work out what. My problem was in the order of the shelves. I could have sworn the puzzle said \"numbered left to right, then top to bottom,\" so I had them\r\n\r\n12\r\n34\r\n56\r\n\r\nwhich then messed everything else up... Good job John for catching that.',7714,0);
INSERT INTO comment VALUES (7732,1265,3351,'Eric','thinking out loud','2003-09-07 20:29:14',0,'I am just going to think out loud in hopes someone gets a light bulb. \r\nBeginning with spy and changing one letter I can only think of shy, sly, and spa. Also, I think there are very few words that \"skate\" can be transformed into (slate is the only one I know, but some of you seem to have super dictionaries). If there are other, more obscure words I am going to disregard them because I am willing to bet that all the words we end up with will be relatively common - either that or this puzzle will simply be dismissed as bizarre.\r\n\r\nso either we are thinking that we change the same numbered letter in each word, or change one of the letters to the same letter, or change the letters by some pattern (e.g. spy became sly because \"l\" is 4 letters before \"p\"). I would like to pursue the possibility that we change different letters to different things but end up with related meaning of the eight words transformed. (I like this one the best because it would be the most fun)\r\n\r\nshy, sly, spa, bare, base, bake, baby, bane, bale, bate, free, thee, tyee, true, trek, wary, navy, wave, slate, royal, local, steer, sleep, sheep, steed, wonder, yonder - y\'s seem very powerful spy-spa, babe-baby, tree-tyee(or trey?), wavy-wave, skate-skaye??, loyal-local, steep-@#$%, ponder-yonder.\r\n\r\nI have heard of a Royal Navy, but they aren\'t local, let alone free. I am sure they are slated to steer over yonder. I\'ll go bake in the spa?\r\n\r\nI am also considering that Bryan might mean change one letter into a group of letters but I can\'t nail that down either.\r\n\r\nI hope this helps.',7728,0);
INSERT INTO comment VALUES (7733,1188,3372,'sam','Confusion','2003-09-07 21:20:57',0,'Hmmm, I was confused by the line \"all four are either knights or liars,\" which I took to mean that all four are knights or all four are liars.The solution works out the same, but it becomes impossible to tell who is the girl. (Note, they can all be liars, and D statement can still be a lie, since he seems to be referring to all people, not just those in the puzzle.',NULL,0);
INSERT INTO comment VALUES (7734,1033,3195,'John Reid','JM','2003-09-07 22:25:09',0,'I know I\'m getting a bit off topic here but...\r\n\r\nJM = John Major?\r\n\r\n(This was the only one in Helen\'s list that I struggled with, too, Travis!)',6437,0);
INSERT INTO comment VALUES (7735,1265,1575,'DJ','hmm','2003-09-08 01:06:27',0,'Here are all the possible words that can be made from each of these words, by changing a single letter into another single letter (and the letters used):\r\nspy:\r\n?py: - -\r\ns?y: say shy sky sly soy sty a h k l o\r\nsp?: spa a\r\n\r\n\r\nbabe:\r\n?abe - -\r\nb?be - -\r\nba?e bade bake bale bane bare base bate d k l n r s t\r\nbab? babu baby u y\r\n\r\ntree:\r\n?ree bree dree free gree pree b d f g p\r\nt?ee thee h\r\ntr?e true u\r\ntre? tref trek trey f k y\r\n\r\nwavy:\r\n?avy cavy navy c n\r\nw?vy - -\r\nwa?y wany wary waxy n r x\r\nwav? wave e\r\n\r\nskate:\r\n?kate - -\r\ns?ate slate spate state l p t\r\nsk?te - -\r\nska?e - -\r\nskat? - -\r\n\r\nloyal:\r\n?oyal royal r\r\nl?yal - -\r\nlo?al local loral c r\r\nloy?l - -\r\nloya? - -\r\n\r\nsteep:\r\n?teep - -\r\ns?eep sheep sleep sweep h l w\r\nst?ep strep r\r\nste?p - -\r\nstee? steed steek steel steer d k l r\r\n\r\nponder:\r\n?onder bonder fonder wonder yonder b f w y\r\np?nder pander a\r\npo?der polder powder l w\r\npon?er - -\r\npond?r - -\r\nponde? - -
\r\n\r\n.. Nothing is still apparent, there is no single letter that could be used in all of the words in any spot, let alone in the same position. So, I haven\'t looked at anything else, but I\'m still clueless..',NULL,0);
INSERT INTO comment VALUES (7736,1203,3196,'Dan','You blew it, Lewis !!!!!','2003-09-08 01:22:33',0,'You forgot to say \"And you cannot move a hoop from the middle or the bottom of the hoops on a pole, by slipping it OVER the smaller hoop(s) above it\"....\r\n \r\nSo then, you simply:\r\n Move XL from pole 1 to pole 3\r\n Move L from pole 1 to the top of XL on pole 3\r\n Move M from pole 1 to the top of L on pole 3\r\n Move S from pole 1 to the top of M on pole 3\r\n Move XS from pole 1 to the top of S on pole 3\r\n \r\nWell, we didn\'t need pole 2 at all. LOL !!! (Lewis, are you about to suggest what I can do with that pole ??????)\r\n\r\nEdited on September 8, 2003, 1:47 am\n\nEdited on September 8, 2003, 1:47 am',NULL,0);
INSERT INTO comment VALUES (7737,1265,3351,'Eric','GOT IT!','2003-09-08 01:42:03',3,'sky blue baby blue true blue navy blue slate blue royal blue steel blue powder blue',NULL,0);
INSERT INTO comment VALUES (7738,1203,3391,'Ryan','follow this order','2003-09-08 02:28:36',0,'Follow this order:\r\n\r\nplace the XS ring on pole 3\r\nplace the S ring on pole 2\r\nplace the XS ring on top of the S ring\r\nplace the M ring on pole 3\r\nplace the XS ring on pole 1\r\nplace the S ring on top of the M ring\r\nplace the XS ring on top of the S ring\r\nplace the L ring on pole 2\r\nplace the XS ring on pole 2\r\nplace the S ring on pole 1\r\nplace the XS ring on pole 1\r\nplace the M ring on pole 2\r\nplace the XS ring on pole 3\r\nplace the S ring on pole 2\r\nplace the XS ring on pole 2\r\nplace the XL ring on pole 3\r\nplace the XS ring on pole 1\r\nplace the S ring on pole 3\r\nplace the XS ring on pole 3\r\nplace the M ring on pole 1\r\nplace the XS ring on pole 2\r\nplace the S ring on pole 1\r\nplace the XS ring on pole 1\r\nplace the L ring on pole 3\r\nplace the XS ring on pole 3\r\nplace the S ring on pole 2 \r\nplace the XS ring on pole 2\r\nplace the M ring on pole 3\r\nplace the XS ring on pole 1\r\nplace the S ring on pole 3\r\nplace the XS ring on pole 3\r\n\r\nThat places the rings in order on pole 3',NULL,0);
INSERT INTO comment VALUES (7739,1152,3136,'Popstar Dave','A few ideas...','2003-09-08 09:34:15',1,'I\'ve only solved number 2:\r\n(-1, +2) \r\nTwo, One, Four, Three, Six, Five, Eight, Seven, Ten, Nine, Twelve, Eleven.\r\n\r\nBut a few ideas for solving them... \r\nWhat the letters can represent (<100)\r\nO - 1\r\nT - 2, 3, 10, 12, 13, 20s, 30s\r\nF - 4, 5, 14, 15, 40s, 50s\r\nS - 6, 7, 16, 17, 60s, 70s\r\nE - 8, 18, 80s\r\nN - 9, 19, 90s\r\nI know that this isn\'t amazing, out of the box thinking, but it might help somone!',NULL,0);
INSERT INTO comment VALUES (7740,75,3136,'Popstar Dave','re: solution','2003-09-08 09:42:35',0,'Actually, it passes 11 times in every 12 hour period as Ender specitied in his initial comment. As a result, it will only pass 22 time in each 24 hour period. (Quite simple actually if you think that the hour hand has gone around two times.) The 23rd time will be at 12am (assuming that you started counting at midnight) the following morning. So 22 times in 24 hours.',7625,0);
INSERT INTO comment VALUES (7741,1152,1183,'fwaff','Solutions to 1 & 5','2003-09-08 10:11:59',3,'1. 1, 3, 6, 10, 15, 21, 36, 45, 55\r\n(+2, +3, +4, +5, ......)\r\n\r\n5. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29\r\n(prime numbers)\r\n\r\nFWIW I also got the same answer as Popstar Dave for series 2\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (7742,1152,3327,'Richard Briscoe','Solution to 3','2003-09-08 11:05:18',0,'Number three is descending powers of two\r\n512, 256, 128, 64, 32, 16, 8, 4, 2, 1\r\n\r\nThe series defined in (1), for any that don\'t know and might possibly be interested, is called the triangular numbers. They are all the numbers of objects that may be arranged in a triangle (think of 10-pin bowling, snooker and pool balls, etc).',NULL,0);
INSERT INTO comment VALUES (7743,1203,1575,'DJ','C++ function','2003-09-08 12:29:22',1,'Here\'s a simple program in C++ to do the recursion, similar to Charlie\'s but it takes an input for each of the three poles (so you could call them A, B, and C or whatever) instead of hardcoding the numbering. Also, I made the output a separate function, so that if you wanted to diplay the output as the current state of the poles/hoops, perhaps using stacks to \'push\' and \'pop\' the hoops, you could do that. Mine right now just does the simple output anyway.\r\n#include <iostream>\r\nusing namespace std;\r\n\r\nvoid hanoi(int n, char src, char dst, char xtr);\r\nvoid showMove(int n, char src, char dst);\r\n\r\nvoid main() {\r\n int n;\r\n cout << \\\"Number of hoops: \\\";\r\n cin >> n;\r\n hanoi(n, \'A\', \'B\', \'C\');\r\n}\r\n\r\nvoid hanoi(int n, char src, char dst, char xtr) {\r\n // when there\'s just one left, put it where you want it\r\n if (n==1) {\r\n move(n,src,dst);\r\n return;\r\n }\r\n // if there are more than 1, move all but last hoop to extra pole\r\n hanoi(n-1, src, xtr, dst);\r\n showMove(n,src,dst);\r\n // after moving last hoop, put extra hoops back onto it\r\n hanoi(n-1, xtr, dst, src);\r\n\r\n}\r\n\r\nvoid showMove(int n, char src, char dst) {\r\n cout << \\\"Move \\\" << n << \\\" from \\\" << src << \\\" to \\\" << dst << endl;\r\n}\r\n\r\n#include <iostream> \r\n#include <stack> \r\nusing namespace std; \r\n\r\nvoid hanoi(int n, int src, int dst, int xtr); \r\nvoid move(int src, int dst); \r\nvoid display(); \r\n\r\nstack <char> p1, p2, p3;\r\nstack <char> *poles[3]={&p1, &p2, &p3};\r\nint num;\r\n\r\nvoid main() { \r\n cout << \"Number of hoops: \"; \r\n cin >> num; \r\n for (int h=num; h>0; h--) { \r\n char c=h+64;\r\n (*poles[0]).push(c);\r\n }\r\n cout << endl;\r\n display();\r\n cout << \"Starting position\\n\\n\";\r\n hanoi(num, 0, 2, 1);\r\n} \r\n\r\nvoid hanoi(int n, int src, int dst, int xtr) {\r\n if (n==1) {\r\n move(src, dst); \r\n return;\r\n }\r\n hanoi(n-1, src, xtr, dst);\r\n move(src, dst);\r\n hanoi(n-1, xtr, dst, src);\r\n}\r\n\r\nvoid move(int src, int dst) {\r\n char x;\r\n x=(*poles[src]).top();\r\n (*poles[src]).pop();\r\n (*poles[dst]).push(x);\r\n display();\r\n cout << \"Move hoop \" << x << \" from pole \" << ++src\r\n cout << \" to pole \" << ++dst << \"\\n\\n\";\r\n} \r\n\r\nvoid display() {\r\n stack <char> t1=*poles[0], t2=*poles[1], t3=*poles[2];\r\n stack <char> *temp[3]={&t1, &t2, &t3};\r\n for (int row=num; row>0; row--) {\r\n for (int p=0; p<3; p++) {\r\n cout << \" \";\r\n if ((*temp[p]).size()<row)\r\n cout << \"|\";\r\n else {\r\n cout << (*temp[p]).top();\r\n (*temp[p]).pop();\r\n }\r\n }\r\n cout << endl;\r\n }\r\n}\r\n
\r\nThe set of marbles you put in... is {1, 2, 3, 4, ....} all the way to infinity.
\r\nThe set of marbles you take out is {1, 2, 3, 4, ....} all the way to infinity.
\r\nThey are equal, therefore there are no marbles left.
_____________
\r\nNow... for (A):
\r\nThe set of marbles added is {1, 2, 3, 4, ...},
But the set you remove is {10, 20, 30, 40, ....}
While the sets are both EQUAL IN SIZE, many particular marbles have not been removed, so there are still an infinite number of marbles remaining at the end of the minute.
\r\n',NULL,0);
INSERT INTO comment VALUES (7748,1341,2899,'Brian Wainscott','Solution','2003-09-08 15:16:16',3,'A: There are an infinite number of marbles in the container. If there were only a finite number of marbles in the container, then there is some number M for which every marble in the container is numbered less than M. But at the end of the Mth interval, there are 9M marbles lef in the container, and none of these will ever be removed.\r\n\r\nB: The container is empty. If it were not empty, then you could pull a marble out. Suppose you did, and the marble was numbered M. But in the Mth interval, you took out the marble numbered M, which is a contradiction. Hence you cannot take out any marbles, and the container is empty.',NULL,0);
INSERT INTO comment VALUES (7749,1341,1626,'Gamer','My ideas','2003-09-08 15:50:53',3,'A. Well, how many marbles aren\'t removed? 9 out of every 10, so it\'s infinity times 9 divided by 10... Wait, we can\'t divide or multiply infinity, so I am confused\r\n\r\nB. Well, this is easy the way I think of it... this is an algorithm to remove all the marbles, so the answer is none.',NULL,0);
INSERT INTO comment VALUES (7750,1151,3398,'Marti Burkettt','Solution','2003-09-08 16:34:01',3,'Shelf 1 Monica Baker, puzzle\r\n 2 Darren Forbes, teddy bear\r\n 3 Janet McKenna, fire engine\r\n 4 Kevin Farrell, box of crayons\r\n 5 Holly Lorenz, set of blocks\r\n 6 Mark Collins, picture book\r\n',NULL,0);
INSERT INTO comment VALUES (7751,1341,3372,'sam','Interestingly','2003-09-08 22:24:34',0,'I think all those below solutions are correct, so I won\'t repeat, but interestingly in A you have exactly the same number of marbles inside the jar as outside, since you can make an exact one-to-one match with each pair of marbles -\r\n1 -> 10\r\n2 -> 20\r\nand so on. This is the case even though at first glance it looks like you have nine times as many marbles in the jar as out.\r\n\n\nEdited on September 8, 2003, 10:26 pm',NULL,0);
INSERT INTO comment VALUES (7752,1341,1575,'DJ','re: Interestingly','2003-09-08 22:58:25',1,'Actually, the interesting thing in case A is that the number of marbles outside the container is a greater infinity than the number of marbles inside. That is because, while there is exactly one marble outside the jar for every marble inside (1=>10, 2=>20, etc), the converse is not true. Every power of ten is outside the jar, and none of them but ten itself have a corresponding value n/10 inside the jar (100, 1000, 10000, ...).',7751,0);
INSERT INTO comment VALUES (7753,12,3372,'Sam','re: answet','2003-09-08 23:00:02',0,'Nearly! You forget that, not only is the first page on the right, but that the last page is on the left...',149,0);
INSERT INTO comment VALUES (7754,1341,3351,'Eric','I lost my marbles','2003-09-08 23:34:58',0,'With all due respect I think we are giving comparative infinity problems a bad name here. While it is valuable and significant to understand that some sequences approach infinity at different rates or ways (e.g. the sum of positive powers of two approaches infinity rapidly, while say the sum of natural reciprocals approches at a snail\'s pace). This problem leads us to reject hypothetical infinity scenarios altogether. \r\n\r\nSince this problem has no real basis with which to work from it is possible to abstract it in any way we wish. I would choose to disregard the numbering of the marbles altogether and choose to imagine that for each iteration of the process I have put 9 marbles in the container and thrown one away. At the end of the minute - even if I have somehow managed to \"process\" all the marbles - I still have nine times as many in the container as I do in the trash can.\r\n\r\nI remember a problem which involved equal amounts of water into two glasses and pouring the water in one of the glasses equally into two other glasses etc. etc. ad infinitum. Until someone brought up the point that eventually you are left with one water molecule which you cannot split (or if you could you wouldn\'t have water anymore). The point is that our mathematical models must still reflect (at least to some degree) the bounds of reality. And if we think that we can put ten marbles in a container and then go digging around for the one numbered 21 and throw that one away all within a two-millionth of a second - then someone should go check on the dilithilum crystals.',NULL,0);
INSERT INTO comment VALUES (7755,1152,3351,'Eric','Solution to 2','2003-09-09 00:15:19',0,'alternating evens and odds \r\n2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11 etc.',NULL,0);
INSERT INTO comment VALUES (7756,1341,2899,'Brian Wainscott','re(2): Interestingly','2003-09-09 00:24:07',1,'Excuse me, but no.\r\n\r\nBoth the number inside and outside are of the same cardinality. Just because the particular map you chose from one set to the other is not onto, does not mean there is no such map. Every integer is a rational number, but not conversely. However, it is well known (and not hard to show) that there are exactly as many rational numbers as integers. \r\n\r\nAs Eric posted, trying to deal with orders of infinity in \"real world\" situations can lead to seemingly silly results. This is of course why this problem is in the \"Paradoxes\" category.\r\n\r\nI find it particularly interesting that in both (A) and (B) there are 9 times as many marbles in the container as have been discarded AT EACH STEP OF THE PROCESS. But the end results are quite different....',7752,0);
INSERT INTO comment VALUES (7757,1151,3398,'Marti Burkettt','Solution','2003-09-09 01:03:08',3,'Monica Baker puzzle shelf 1\r\nDarren Forbes teddy bear shelf 2\r\nMark McKenna book shelf 3\r\nKevin Farrell crayons shelf 4\r\nHolly Lorenz blocks shelf 5\r\nJanet Collins fire engine shelf 6',NULL,0);
INSERT INTO comment VALUES (7758,602,1768,'Lorne Hrynkiw','Number of roots','2003-09-09 03:35:27',0,'There are always two roots, if the discriminent is zero than they have the same value.',NULL,0);
INSERT INTO comment VALUES (7759,1341,1920,'Brian Smith','Defining Infinity','2003-09-09 09:59:51',0,'Consider a system of infinite numbers. Call the base unit of infinity w. Unlike other definitions of infinity, w is different from w+1 and 2*w. In particular 2*w>w+1>w. Also w is defined to be a multiple of every finite integer, but some infinities like w-1 and w+1 are relatively prime to every finite integer.
The process is said to be reapeated an infinite number of times. We can define this instance of infinity as w. Since 10 marbles are introduced in each iteration, there are a total of 10*w marbles. The set of marbles can then be numbered {1,2,3,4,...,w-2,w-1,w,w+1,...,2*w-1,2*w,2*w+1,......,10*w-1,10*w}.
In case A, every multiple of 10 is removed, one in each iteration. In particular the set of marbles {10,20,30,40,...,w-20,w-10,w,w+10,...,2*w-10,2*w,2*w+10,......,10*w-10,10*w} is removed. This leaves 9*w marbles. All the finite numbered marbles which are not multiples of 10 and all the infinite numbered marbles which are not multiples of 10 remain.
In case B, every marble 1 through w are removed, leaving 9*w marbles the smallest of which is w+1. Every finite marble and some infinite marbles were removed, but even larger infinite marbles are left.',NULL,0);
INSERT INTO comment VALUES (7760,1203,1920,'Brian Smith','Parity','2003-09-09 10:06:49',0,'If the hoops are colored with alternating colors (XS, M, XL are one color and S, L are a second), then every move either places a hoop on an empty stack or on a hoop of the opposite color.',NULL,0);
INSERT INTO comment VALUES (7761,1341,3172,'SilverKnight','re: Defining Infinity','2003-09-09 10:47:06',0,'Brian, you said:
\r\n\"Call the base unit of infinity w.\"
\r\n\"We can define this instance of infinity as w.\"
\r\n*** Two different definitions of infinity. This is a problem
\r\nAlso, you DEFINE \"2*w>w+1>w\".... this ALSO is a problem. You seem to be thinking of w as an integer. But I\'m not certain about what\'s going on in your head. Infinity is not an integer, nor is it a real number.... Generally, infinities (at least in common, not -\"Brian Smith defined infinities\") are dealt with as the size of sets.
\r\nIf you can create a one-to-one mapping (ANY one-to-one mapping) from one infinity to another, then they have the same size. This does NOT mean that they are equal. But it DOES mean they are equal in size. (A simple example is... are there more points on the line segment from (0,1) or from (2,4), both on a one dimensional axis). Since I can create a (trivial) mapping from one to the other, they have the same size (cardinality).',7759,0);
INSERT INTO comment VALUES (7762,1341,3372,'Sam','Theoretical possibilities','2003-09-09 10:47:18',0,'I don\'t think that the bounds of actual reality are relevent in these puzzles. A huge number of senerios that are extremely intereting to discuss are based on exactly these sorts of premises.\r\n\r\nJust wondering, however, how this puzzle fares in theoretical reality:\r\nFor any marble, n, that you remove, you must remove marble n + 1.\r\nSuppose the last marble you remove is even (n is even). Then you must also remove the next marble, and so the last marble you remove cannot be even.\r\nDitto for odd.\r\nSo the last marble you remove may be neither even nor odd.\r\nSo you can\'t remove a last marble.\r\nSo the puzzle never ends.\r\n\r\nI don\'t think that this is a silly result. In the case of Achillis and the tortoise, both the time and the distance reduced by half each time, so it was possible to show that, by calculus, Achillis does indeed reach, and then pass, the tortoise. In this case, however, the size of your task does not reduce by half each time. Zeno was trying to use as a premise that you cannot perform an infinite number of tasks in a finite amount of time. This was shown not to be true in the case of the race, but still holds true is the tasks are discrete. So my feeling is tha the apparent paradox (same task leads to different results) is not actually a paradox after all but a result of the impossible premises set out in the question.\r\n\r\nAny thoughts?\r\n\r\nAnd where can get some of these dilithium crystals Eric mentioned...? ',7754,0);
INSERT INTO comment VALUES (7763,1195,1183,'fwaff','Possible solution???','2003-09-09 10:54:40',3,'Let x = the top right ?\r\nLet y = the bottom left ?\r\n\r\nThe sum of the top row is 3+9+2+x = 14+x\r\nThe sum of the right side is 3+4+7+x = 14+x\r\nThe sum of the bottom row is 8+1+7+y = 16+y\r\nThe sum of the left row is 3+6+7+y = 16+y\r\n\r\nSo if x=y+2 then all the rows have the same sum.\r\n\r\nThe middle two rows contain four numbers: 6,3,7,4. Of these numbers two of them appear as corner values (3&7). The other two (6&4) have a difference of 2, so if x=6 and y=4 then all the rows have the same values and the corner values are the same as those that appear in the middle two rows.\r\n\r\nThis makes the finished square...\r\n\r\n3926\r\n6__3\r\n7__4\r\n4817',NULL,0);
INSERT INTO comment VALUES (7764,1195,3172,'SilverKnight','re: Possible solution???','2003-09-09 11:00:12',3,'I like fwaff\'s solution... I came to the same solution in a different way:
\r\n3926
\r\n6__3
\r\n7__4
\r\n4817
\r\nSame logic to get the difference of 2 (so that the columns and rows add up), but my thought was... these are the only two numbers I could find to avoid REPEATING the same number in a column or row.
\r\n',7763,0);
INSERT INTO comment VALUES (7765,1341,2839,'FatBoy','Respectfully, I disagree with all (save perhaps eric)','2003-09-09 11:05:26',0,'You theorhetical math guys are a bit over my head, so forgive a poor holder of just an engineering degree. If these observations are cliched, please ignore.\r\n\r\nAs I understand infinity it is used to describe a set size that is infinite. But this problem indicates that you stop processing marbles at the end of a minute. At that time the number of marbles in the jar (and those discarded) ceases to be infinite. You put them in the jar and in 1/10 the cases taken them back out. Once you stop doing so you have limited the set of marbles. therefore it is not infinite.\r\n\r\nThere is a finite number x which is the number of times you went through the process of putting in and taking out. (don\'t tell me that you did it an infinite number of times) once you stop, which you did at the end of the minute you have limited the number of interation and it is no longer infinite.\r\n\r\nso, the answer to questions A and B are both 9x where x is defined as the number of iteration you performed.',NULL,0);
INSERT INTO comment VALUES (7766,1341,3172,'SilverKnight','re: Respectfully, I disagree with all (save perhaps eric)','2003-09-09 11:23:43',0,'I respectfully disagree with you too....\r\nWhy do you say: \"At that time the number of marbles in the jar (and those discarded) ceases to be infinite.\"
\r\nIt doesn\'t follow.
\r\nYou then say later, \"once you stop, which you did at the end of the minute you have limited the number of interation and it is no longer infinite\". Similarly, I don\'t follow your line of reasoning. Why is it no longer infinite?
\r\nIf I draw a circle in one minute, and then stop. Does the ratio of its circumference to its diameter (π) stop having infinite digits (in base 10 representation)? Of course not, and my premise, of course, is silly....\r\n\r\n--- SK',7765,0);
INSERT INTO comment VALUES (7767,1151,2839,'FatBoy','Please ignore','2003-09-09 11:25:43',3,'shelf\r\n1 Monica Baker puzzle\r\n2 Darren FOrbes teddy bear\r\n3 Mark McKena picture book\r\n4 Kevin Farrel crayons\r\n5 Holly Lorenz blocks\r\n6 Janet Collins puzzle',NULL,0);
INSERT INTO comment VALUES (7768,1195,3327,'Richard Briscoe','Solution','2003-09-09 11:28:58',0,'The complete sqare is as follows :\r\n3921\r\n6 3\r\n7 4\r\n9817\r\nReading clockwise, each number is simply the sum of the previous two, modulus 10. E.g. 1 + 3 gices 4, 7 + 6 gives 3 (from 13, ignoring the initial 1).\r\nIt is interesting to note that opposite digits always sum to 10. The missing digits comply with this rule - though it is of no use in deducing them.',NULL,0);
INSERT INTO comment VALUES (7769,1341,2899,'Brian Wainscott','Respectifully I disagree with most (save perhaps SK and Sam)','2003-09-09 11:32:58',0,'Defining Infinity: Regarding Brian Smith\'s comments, I have no comment\r\nexcept to say that Silver Knight made a good reply.\r\n\r\nSilver Knight: your one to one mappings have to be ONTO, which I\'m sure\r\nwas just a minor oversight on your part. As you point out, if you can\r\nfind any such mapping (one to one and onto) then the sets are of the same\r\nsize (cardinality). The fact that some mappings can be found that are\r\none to one and not onto (as DJ seemed to be having a problem with) is not\r\nrelevant.\r\n\r\nSam: The puzzle does end, because each step takes only half as long as the\r\nother. But I agree that the apparent paradox is a result of physically\r\nimpossible premises set out in the problem. But if mathematicians (or\r\nphilosophers) had to restrict themselves to physical reality, their jobs\r\nwould be so much more boring. And there is a lot of useful mathematics\r\nthat would never have been discovered (calculus, complex numbers, etc).\r\n\r\nFat Boy: the problem is clearly impossible in the real world, but is\r\na conceptual/theoretical problem. Since there is no marble that is\r\nnot processed within the minute, you do in fact process them all. That\r\nis the point of halving the time each iteration: there are an infinite\r\nnumber of steps, but they get completed within the minute.\r\n',NULL,0);
INSERT INTO comment VALUES (7770,1195,3172,'SilverKnight','re: Solution','2003-09-09 11:36:10',0,'Nice... I\'m sure you\'re right. Interestingly, I think the notion of \"square\" is what threw me and fwaff off... If it were phrased in a circle, I think it more likely that we might have seen that pattern. BTW, you should mark your comment with the \'Full Solution\' icon...
\r\nCheers!',7768,0);
INSERT INTO comment VALUES (7771,1195,1183,'fwaff','re(2): Possible solution???','2003-09-09 11:39:47',0,'Another \'interesting\' point to note is that opposite pairs add up to 10. (3,7), (9,1), (2,8), (6,4), (3,7), (4,6)',7764,0);
INSERT INTO comment VALUES (7772,1195,3172,'SilverKnight','re(3): Possible solution???','2003-09-09 11:40:57',0,'Methinks Richard Briscoe MENTIONED that in his post !',7771,0);
INSERT INTO comment VALUES (7773,1195,1183,'fwaff','re(4): Possible solution???','2003-09-09 11:47:50',0,'So he did. Well done Richard and apologies to you, SK, for wasting your precious bandwidth with a superfluous posting. I hadn\'t seen Richard\'s post when I replied to yours.',7772,0);
INSERT INTO comment VALUES (7774,1341,2839,'FatBoy','re(2): Respectfully, I disagree with all (save perhaps eric)','2003-09-09 11:52:42',0,'as you pick up each marble and put it into the jar, and (in 1/10 of the cases) take it back out. you define it as being part of a group (those you put in the jar).\r\nyou cuold have (if you had chosen to) counted them as you did so. (yes this would be taxing but if you can move marbles in an infinitessimally short time then you certainly can incrimite a number in your head). At the end of a minute you stop. You have coutned all the marbles you put in the jar, therfore they are no longer infinite. You have defined it (made it finite).\r\nEven if you do not choose to count them in your head the action of moving them into and out of the jar defines the number of them and the action of ceasing to move them limites the number.\r\n\r\nAs for you circle analogy, it is not apt. drawing a circle in no way defines the number of digits to the right of the ratio of its circumfernece to its diameter.\r\n\r\nThe number of digits is equivilant to the initial infinite set of marbles at teh beginning of the puzzle. \r\nA more apt analogy is if you were to calculate that ratio infinitly quickly, writing down the result as you go. at the end of a minute you have a number of digits on the (presumably huge) page. the number of digits is unimaginable huge but it is not infinite. the moment you stopped writing numbers you defined the number of those digits and made it finite.\r\njust as when you stop putting marbles into (and taking them out of the) the jar you have defined the number of marbles in the set.',7766,0);
INSERT INTO comment VALUES (7775,1195,3172,'SilverKnight','re(5): Possible solution???','2003-09-09 12:00:13',0,'lol... in my country... it costs me almost a nickel for each word I post, and almost 2 cents for each word I read. So, it\'s appreciated that you are concerned with my bandwidth!
\r\nCheers!',7773,0);
INSERT INTO comment VALUES (7776,1341,3172,'SilverKnight','re(3): Respectfully, I disagree with all (save perhaps eric)','2003-09-09 12:07:40',0,'FatBoy,
\r\nI will cede one of your points... your analogy of writing it down (perhaps the first digit at 30 seconds, the second digit at 45 seconds, the third digit at 52.5 seconds, ad infinitum) is a more apt analogy.
\r\nThat being said, and assuming that each digit was roughly the same size, and that I had an inifinite-sized piece of paper, and an infinite amount of ink, I would have an INFINITE number of digits at the end of the minute.
\r\nI *still* don\'t follow why you write \"the moment you stopped writing numbers you defined the number of those digits and made it finite\". That is a non sequitur.
\r\nYou also wrote \"You have coutned all the marbles you put in the jar, therfore they are no longer infinite. You have defined it (made it finite).\" Again, another non sequitur.',7774,0);
INSERT INTO comment VALUES (7777,1341,2839,'FatBoy','re(4): Respectfully, I disagree with all (save perhaps eric)','2003-09-09 12:23:49',0,'As I said at the beginning, you theorhetical math guys seem to be operating a level I have not attained but I do not see these as non-sequitors. \r\n \r\nI am aware that we are suspending the limits of the ral world and I do not have a problem with that. It does not however change my point.\r\n\r\nOnce something is counted it is finite, not infinite.\r\n\r\nRight up until the very last infinitessimally small unit of time before the end of the minute the set of marbles remains infinte. The act of ceasing to move marbles (or ceasing to write digits) places a limit on the set and makes it finite. ',7776,0);
INSERT INTO comment VALUES (7778,1341,2899,'Brian Wainscott','re(5): Respectfully, I disagree with all (save perhaps eric)','2003-09-09 13:18:29',0,'OK, suppose you are correct. Then the final number of marbles you process is finite.\r\n\r\nIf it is finite, then there is a last marble you processed. What is the number on this marble? Call it M. It must have been processed in step M/10. But there was a step M/10+1 during which you processed marbles with numbers greater than M! So M can\'t have been the last marble processed.\r\n\r\nThe point is, there can\'t have been a \"last\" marble, since there are an infinite number of processing steps, and the set is in fact infinite.\r\n\r\nThere are an infinite number of integers. Theoretically, you CAN line them all up and count them. The only problem is that you have to do it infinitely fast, or else never stop.\r\n\r\nIn this problem, right up to the last infinitessimally small unit of time, you have hardly started. Almost all the marbles are processed at the very last instant, but in that last instant they are ALL, infinitely many of them, processed.',7777,0);
INSERT INTO comment VALUES (7779,1152,1575,'DJ','Two more','2003-09-09 13:51:55',0,'Those are all the correct (intended) patterns.. but what about numbers 4 and 6?',NULL,0);
INSERT INTO comment VALUES (7780,1203,1301,'Charlie','re: Stacks--Basic version','2003-09-09 14:07:51',0,'DECLARE SUB display ()\r\nDECLARE SUB transfer (n!, source!, dest!)\r\nDIM SHARED pole$(3), n\r\nINPUT \"Number of hoops:\", n\r\nFOR i = 1 TO n\r\n pole$(1) = CHR$(64 + i) + pole$(1)\r\nNEXT\r\ntransfer n, 1, 3\r\n\r\nSUB display\r\n FOR i = n TO 1 STEP -1\r\n FOR p = 1 TO 3\r\n IF LEN(pole$(p)) < i THEN\r\n PRINT \\\" | \\\";\r\n ELSE\r\n PRINT \\\" \\\"; MID$(pole$(p), i, 1); \\\" \\\";\r\n END IF\r\n NEXT\r\n PRINT\r\n NEXT\r\nEND SUB\r\n\r\nSUB transfer (n, source, dest)\r\n IF n = 1 THEN\r\n PRINT \\\"Move A from\\\"; source; \\\"to\\\"; dest\r\n pole$(dest) = pole$(dest) + RIGHT$(pole$(source), 1)\r\n pole$(source) = LEFT$(pole$(source), LEN(pole$(source)) - 1)\r\n display\r\n ELSE\r\n transfer n - 1, source, 6 - source - dest\r\n PRINT \\\"Move \\\"; CHR$(ASC(\\\"A\\\") + n - 1); \\\" from\\\"; source; \\\"to\\\"; dest\r\n pole$(dest) = pole$(dest) + RIGHT$(pole$(source), 1)\r\n pole$(source) = LEFT$(pole$(source), LEN(pole$(source)) - 1)\r\n display\r\n transfer n - 1, 6 - source - dest, dest\r\n END IF\r\nEND SUB\r\n\r\nWith results:\r\n
\r\nNo one\'s trying to make this personal. We were explaining \"the basics of this kind of problem\" only because you seem(ed) to be unfamiliar with it.
\r\nNow... that aside... you continue to make statements that ARE non sequiturs. You say, \"The simple fact is... all of that thought does not apply.\" But... it does!
\r\n(And I think Bryan and I imagine that some other people around here might be silently reading this thread and might want to see it come to a logical, coherent resolution.)
\r\n_________________
\r\nYou are correct that at the end of the minute, we stop moving marbles around. At this point in time, we have a set of marbles that have been placed in the jar and a set that have been in and have come back out.
\r\nNow... the whole problem revolves around identifying the difference between the contents of those two sets. (BTW, I\'ve not limited the set in any way. The sets are what they are after the minute has expired.)
\r\nThe content of either set is not necessarily finite, though you continue to claim it is (for a reason that continues to escape me). But I agree, that it will not change (for we are no longer performing operations that affect the contents of either set).
\r\nAs stated previously, in case (A), the contents of the two sets are not the same, and leaves an infinite number of marbles in the bag. And in case (B), the contents of the two sets are the same, and therefore each marble that has been placed in the bag has been removed, so the bag is empty.
\r\n____________
\r\nLastly, you are correct, in that you cannot COUNT the integers (by your implied definition of counting). But you CAN map them to another set of the same Cardinality.
\r\nCheers
\r\n --- SK
\r\nP.S. I hope we can continue to keep the discussion related to the topic at hand. :-)\n\nEdited on September 9, 2003, 3:01 pm',7783,0);
INSERT INTO comment VALUES (7785,1195,1626,'Gamer','re: Solution','2003-09-09 15:51:37',0,'I think your solution and my solution are almost exactly the same... :)\r\n\r\nThe sequence is repeating, so that\'s why it\'s in a square format.\r\n\r\nA way to extend this problem (Did you hear that SilverKnight? The problem\'s not dead) is why are the numbers apart from each other able to add up to 10? I have been wondering this and am unable to come up with a solution.',7768,0);
INSERT INTO comment VALUES (7786,77,3372,'Sam','re(2): A more paradoxical version.','2003-09-09 16:08:50',0,'I disagree. If the person said that the taxi was green, and witnesses are right 80% of the time, then the probability that it was green has to be at least 80%. If the witnesses are straight out wrong the other 20%, then the probability is exactly 80%. If, as friedlinguini suggested, they say random things 20% of the time, then there is 80% + (20% * 15%) = 83% chance.\n\nEdited on September 9, 2003, 4:09 pm',3650,0);
INSERT INTO comment VALUES (7787,1341,3372,'Sam','Respectfully, I disagree with someone. Maybe.','2003-09-09 16:29:34',0,'In a sense I actually agree with what FatBoy is trying to say, though not because of any of this stuff about infinite sets becoming finite sets. Or maybe because of that. He is claiming that, if you could stop, you would have a finite set (likewise, if you could stop the last marble would be either even or odd). What I think he is doing wrong is to say that, since you do stop, you then do have a finite set. I think, rather, that since you cannot end with a finite set (it is absurd, as people have said), you cannot stop.\r\n\r\nI think I mentioned Thomson\'s lamp in some other question. If you turn on a lamp at 30 seconds, turn it off at 45 seconds, on at 52.5 seconds and so on, is the lamp on or off at the end of the time? We can\'t answer this question. However, it is strictly not a paradox: it\'s based on a premise which is logically incoherant, that he has to perform an infinite number of descrete tasks in a finite amount of time. Ditton for the marbles. *Not* ditto, however, for any of Zeno\'s paradoxes, as the tasks are not descrete.\r\n\r\nAn argument that starts from impossible premises and leads to an apparent paradox is not difficult to create: All brown haired people are six foot tall, all brown eyed people are four foot tall, I am brown haired and brown eyed. How tall am I?\r\n\r\nThe point was not to bring this off topic (appologies), but to show that saying that premises are logically incoherent is not running away from the question, but can be an equally valid answer.',7784,0);
INSERT INTO comment VALUES (7788,977,3407,'Troy Bull','Do it with 1 invocation of random as follows','2003-09-09 18:13:26',1,'my $number = 99999999\r\nmy $r = random(900000000)\r\n\r\nmy $randomString = $number + $r',NULL,0);
INSERT INTO comment VALUES (7789,1341,1626,'Gamer','My ideas?','2003-09-09 18:16:02',0,'Did anyone disagree with my idea, that dividing by infinity is illegal, or that you remove all the marbles?\r\n\r\nI think this is the solution, but maybe I missed someone saying that it wasn\'t.',NULL,0);
INSERT INTO comment VALUES (7790,1341,2899,'Brian Wainscott','re: My ideas?','2003-09-09 18:27:10',0,'Gamer,\r\n\r\nI don\'t know that anyone addressed your comments about part (A). Here is one way to think about it: after N steps there are 9N marbles in the bag and none of them ever get removed. So as N -> infinity, there must remain an infinite number of marbles in the bag. \r\n\r\nYour comment about (B) is quite clear, and correct.',7789,0);
INSERT INTO comment VALUES (7791,912,1220,'abc','re: 20 checkers to level 4','2003-09-09 20:27:25',0,'But you are only allowed to use the first two rows.\r\nYou use four in your example. That\'s not valid.',7597,0);
INSERT INTO comment VALUES (7792,619,3172,'SilverKnight','First thoughts...','2003-09-09 20:53:17',2,'
\r\nAgreed.
\r\nBut while this problem doesn\'t describe something that is physically possible, it is not logically incoherent. (Unless you consider calculus and limits of Riemann sums also logically incoherent.)
\r\nSo... stating that this problem\'s premises are logically incoherent is not \"running away from the question\", but it *is* wrong.\r\n__________
\r\nAs for what happens \"if you could stop, you would have a finite set\"... , well heck yeah. If you stopped after any particular iteration, we could specify exactly which marbles are in, and which are not in the container. But that is a completely different problem.
\r\n--- SK',7787,0);
INSERT INTO comment VALUES (7794,912,1220,'abc','problem with lvl 4','2003-09-09 21:11:23',0,'In order to reach level 4 I think there must be one row more like Brian did it. \r\nSome thoughts here...\r\n\r\nReaching the 3rd level:\r\n\r\n--*00\r\n11*\r\n\r\nThe asterisks are the \"ladder\" to climb the levels. The checkers with numbers are the stepping stones needed to build that ladder. The lines are checkers which are simply used to move the stepping stones up two levels.\r\nTo get another checker up to 3 you need again 8 checkers, leaving 4 to get one up to level 2. \r\nI can see no possible way to achieve that using only two rows of initials.\r\n\r\nIt seems the jumping around opens up another opportunity I can\'t grasp.\r\n\r\nBtw: Is there an edit function on these boards?\r\n',NULL,0);
INSERT INTO comment VALUES (7795,1341,3172,'SilverKnight','re: My ideas?','2003-09-09 21:13:01',0,'Well... to be specific, I think you said that you can\'t multiply or divide infinity (not dividing BY infinity).
\r\nI\'m not sure what dividing by infinity means, unless you\'re implying dividing by a variable as the variable grows towards infinity. In which case, you are talking about the \"normal\" limit described by calculus.\r\n_____________
\r\nYou said in your first post \"so it\'s infinity times 9 divided by 10... Wait, we can\'t divide or multiply infinity\".\r\nI don\'t see why not. But an infinity multiplied by, divided by, added to, or lessened by a constant is the same infinity.
\r\nAgain, I would refer you to studies about what infinities mean and that they are normally dealt with as sets of elements and operations (often mappings) ON those sets.
\r\n--- SK',7789,0);
INSERT INTO comment VALUES (7796,1195,3172,'SilverKnight','re(2): Solution','2003-09-09 21:15:04',0,'\"Did you hear that SilverKnight? The problem\'s not dead\"\r\n\r\ntouché !',7785,0);
INSERT INTO comment VALUES (7797,279,1220,'abc','re(4): did it - aka spoiler','2003-09-09 21:57:59',0,'I wonder that nobody told you during this long time, but you clearly violate the first rule with this method:\r\nno other digits should appear anywhere in the equation\r\n\r\nThe parameter in the bottom of the summation is a digit. But nice trick! ;)',1662,0);
INSERT INTO comment VALUES (7798,279,1220,'abc','re(5): did it - aka spoiler','2003-09-09 22:04:55',0,'Argh...sorry!\r\nI got it all wrong. And I can\'t delete it. \r\nBut there are still too many variables. Bending the rules at least.\r\n',7797,0);
INSERT INTO comment VALUES (7799,1341,1626,'Gamer','re(2): My ideas?','2003-09-09 22:26:21',0,'I will say we may not have to come to a complete stop when we multiply by infinity, but we can\'t simply further than 9/10 infinity.',7795,0);
INSERT INTO comment VALUES (7800,1341,3172,'SilverKnight','re(3): My ideas?','2003-09-09 22:33:35',0,'Gamer wrote: \"I will say we may not have to come to a complete stop when we multiply by infinity, but we can\'t simply further than 9/10 infinity.\"\r\n__________\r\nHuh?!?',7799,0);
INSERT INTO comment VALUES (7801,990,3410,'neil','solution','2003-09-09 22:37:12',0,'team lost in extra innings when different pitcher was brought in',NULL,0);
INSERT INTO comment VALUES (7802,619,1575,'DJ','Second thought','2003-09-09 22:39:20',1,'I don\'t have a proof for it yet, but I think that x=3 (x²+8=17, x³+16=43) is the only number that fits these criteria at all. Can anyone find another (or a way to corroborate this)?',NULL,0);
INSERT INTO comment VALUES (7803,1195,3172,'SilverKnight','re(3): Solution (further analysis)','2003-09-09 23:25:45',1,'And in Gamer\'s vein, let\'s take a look at his observation and see what we find...
\r\nNote that... you can start with any two digit number (from 00-99), and generate one of these patterns. It *will* cycle (eventually). Here are the cycles:\r\n\r\nPeriod 1:\r\n0
\r\nPeriod 3:\r\n550\r\n550 (can\'t divide the period in half, showing it a 2nd time)
\r\nPeriod 4:\r\n26\r\n84
\r\nPeriod 12:\r\n392134\r\n718976
\r\nPeriod 20:\r\n4606628088\r\n6404482022
\r\nPeriod 60:\r\n325729101123583145943707741561\r\n785381909987527965167303369549\r\n________
\r\n
\r\nOkay enough analysis on this puzzle for a while... who\'s taking it from here?\r\n',7796,0);
INSERT INTO comment VALUES (7804,977,3172,'SilverKnight','re: Do it with 1 invocation of random as follows','2003-09-09 23:29:28',0,'Troy wrote:\r\nmy $number = 99999999 \r\nmy $r = random(900000000) \r\n\r\nmy $randomString = $number + $r
\r\nSorry, but this doesn\'t guarantee that each digit is used once.',7788,0);
INSERT INTO comment VALUES (7805,619,3172,'SilverKnight','re: Second thought','2003-09-10 00:04:37',0,'I\'m tempted to agree... I wrote a quick program (but it\'s late... and I may have made a mistake in it...), and I couldn\'t find any number that satisfies this... below 1,000,000 (apart from 3).\r\n\r\nhmmmm\r\n\r\n--- SK',7802,0);
INSERT INTO comment VALUES (7806,619,3172,'SilverKnight','re(2): Second thought','2003-09-10 00:19:16',0,'More to the point... I think that if x is prime, x²+8 can not be prime for any x other than 3.
\r\nTherefore, the formula x³+16 is a red herring.... and the statement would be JUST as true if I wrote the third part as x³+14 or x³+2 or x²+2 (or any other formula based on x=3 that results in a prime number).
\r\nMy head hurts.... anyone wanna corroborate this?',7805,0);
INSERT INTO comment VALUES (7807,619,3172,'SilverKnight','re(3): Second thought','2003-09-10 00:44:23',3,'I think I\'ve got it!\r\n\r\nWhen x is a prime number, it is (by definition) not divisible by 3 (except when x = 3). Now, note that in every sequence of 3 consecutive integers ONE of them IS divisible by 3. Therefore, for any given prime number x (other than 3), either (x-1) is divisible by 3 or (x+1) is divisible by 3.\r\n\r\nso... x²+8 = (x²-1) + 9\r\n= (x-1)(x+1) + 9\r\nSince either (x-1) or (x+1) is divisible by 3 when x is prime, (x-1)(x+1) is ALSO divisible by 3. And if we then add nine to it, it remains divisible by 3.
\r\nTherefore, if x is prime then x²+8 cannot be prime unless x=3.\r\nSince x must be 3, and 3³+16 (which happens to be 43) is prime, the initial hypothesis is true.\r\n\r\n--- SK :-) (okay... now my head hurts more)',7806,0);
INSERT INTO comment VALUES (7808,619,3172,'SilverKnight','Solution (spoiler)','2003-09-10 01:40:51',3,'(Explained more clearly than in my earlier comment).\r\n
\r\nNow, given that x is a prime, not equal to 3:\r\nx²+8 = (x²-1) + 9\r\n= (x-1)(x+1) + 9\r\nSince either (x-1) or (x+1) is divisible by 3, (x-1)(x+1) is ALSO divisible by 3. And if we then add nine to it, the result remains divisible by 3.\r\nRestated: If x is a prime other than 3, then x²+8 is divisible by 3.\r\nTherefore, the only occasion that x and (x² + 8) are BOTH prime is when x=3.
\r\nSince (3³ + 16) = 43 which is prime, we\'ve proved the initial supposition!\n\nEdited on September 10, 2003, 1:41 am',NULL,0);
INSERT INTO comment VALUES (7809,1341,2839,'FatBoy','re: Respectfully, I disagree with someone. Maybe.','2003-09-10 07:54:39',0,'Sam,\r\nThanks, as I said from square one I am not a throretical math guy. This appears to mean I lack some vocabualary.\r\nThe problem says taht you continue to process marbles until the minute is over and then asks haow many marbles you had at the end of the minute.\r\nI took this to be asking how many marbles you had after you stopped processing. As you said, if you stop, you have a finite set. That states simply was I was awkwardly trying to say.\r\n\r\nSince it seems to be agreed that once you stop (if you could stop) then there is a finite number (however large) of marbles that have been processed.\r\n\r\nSorry for having wasted eveyones time. \r\n\r\nIT does raise the interesting quetion of what are you doing in the 62nd second? The minute is over, according to math theory you\'ve processed \"all\" of your infinite set of marbles before the 61st second. But you never stopped processing them.\r\n\r\nI\'m sure that this has been explored before so if someone could post me the stock solution I\'ll be fine.\r\n\r\nspecial to SK. Don\'t worry, I do not take it personally. I know that you and others are not being nasty. I\'m really not THAT thin skinned (hence my name)',7787,0);
INSERT INTO comment VALUES (7810,1151,3414,'alumination design','solution','2003-09-10 08:15:15',0,'kevin farrell has puzzle compartment 1\r\nholly forbes has blocks compartment 2\r\nmark collins has fire engine compartment3\r\nmonica baker has crayons compartmet 4\r\ndarren lorenz has teddy bear compartment 5\r\njanet mckenna has picture book compartment 6\r\nwill some one check this?',NULL,0);
INSERT INTO comment VALUES (7811,1151,3416,'holli wiedrick','The Answer','2003-09-10 09:29:21',0,'1 4\r\n2 5\r\n3 6\r\n1. Kevin Farrell- Puzzle\r\n2. Holly Forbes - Blocks\r\n3. Mark Collins - Fire Truck\r\n4. Monica Baker - Crayons\r\n5. Darren Lorenz- Teddy Bear\r\n6. Janet Mckenna- Picture book',NULL,0);
INSERT INTO comment VALUES (7812,1205,3372,'Sam','Some thoughts','2003-09-10 10:22:21',0,'Rats, got to run, so don\'t have time to work out a full solution. Obviously the trick is to start by having two timers starting together, one ot normal speed and one at double speed. Then you can start third timer after half an hour, and set it to go fast after another half hour. Otherwise you are always stuck with increments of half an hour.\r\nThe third timer will go off 15 minutes after the first. If a fourth timer was started when the second one was, and set to fast when the third one goes off, it will go off 7.5 minutes after the third, and 22.5 minutes after the first.\r\n\r\nThat\'s all I\'ve got for now, I expect this will all be solved next time I look.',NULL,0);
INSERT INTO comment VALUES (7813,1205,1920,'Brian Smith','Thoughts','2003-09-10 11:26:06',0,'As far as I can tell, the only \"constructable\" intervals of time are of the form 60*n/2^k (eg. 30min:n=1,k=1 26.25min:n=7,k=4). Unfortunately, 25 min is not in that form.',NULL,0);
INSERT INTO comment VALUES (7814,1205,1301,'Charlie','thoughts','2003-09-10 11:26:48',1,'I can see only ways of producing powers of 2 fractions of an hour. That would mean being able to produce time intervals that are expressed as a terminating binary fraction. However, 25/60 is a non-terminating binary fraction: 0.0110101010101.... This represents\r\n1/4+1/8+1/32+1/128+1/512+1/2048+...\r\n\r\nIt would seem, depending on how close to 25 minutes you want, there would be ever more complex timings that could be done, but none would give exactly 25 minutes.',NULL,0);
INSERT INTO comment VALUES (7815,1205,2899,'Brian Wainscott','re: thoughts','2003-09-10 12:10:26',1,'Interesting. I don\'t have a lot of time to look at this now either, but I expect you are correct that no finite number of clocks will work. But he did say we have a infinite number to work with.\r\n\r\n(I can see the whole \"Marbles Bonanza\" thread starting up again....)\r\n\r\nSo I expect the answer he has in mind is that you can do it if you use an infinite number of timers.\r\n\r\nThe interesting part is going to be \"what is the quickest time\" ie, what is the actual method used.',7814,0);
INSERT INTO comment VALUES (7816,1341,2899,'Brian Wainscott','How about this variation?','2003-09-10 12:27:25',4,'How would you have thought differently about the problem if all the marbles had started in the container? Then the problem would look like this:\r\n\r\nYou have a container holding an infinite number of marbles, numbered 1 to infinity. At the start of the minute, you remove one marble. You do this again after 30 seconds, then again in 15 seconds. You continuously repeat this process, each time after half as long an interval as the time before, until the minute is over.\r\n\r\nHow many marbles are in the container at the end of the minute if for every repetition (numbered N)\r\n\r\nA) you remove the marble numbered (10*N)\r\n\r\nB) you remove the marble numbered (N)\r\n\r\n\r\nDo you think this problem is different? If so, why? If not, why not?',NULL,0);
INSERT INTO comment VALUES (7817,1205,3372,'Sam','re(2): thoughts','2003-09-10 12:36:06',0,'Indeed, I was confused when I was trying it earlier in a hurry the way that I kept on just stepping over 25, getting closer but never quite hitting it. Indeed, I still can\'t see the exact algorithm to use, but intuitivley I\'m sure you\'re right, the time we will be measuring will tend towards 25 minutes, never hitting it with a finite number of clocks. \r\nHowever, I\'m almost certain that it can be done in a finite amount of time, because most of the clocks will be starting at the same time, I think. We\'ll have to see.',7815,0);
INSERT INTO comment VALUES (7818,1205,2839,'FatBoy','re(2): thoughts','2003-09-10 12:42:38',0,'(I can see the whole \"Marbles Bonanza\" thread starting up again....) \r\n\r\nno..... never again..... I promise....... I swear... \r\nplease...sweet merciful heavens...... don\'t come at me with that slide rule...........aaaaaaaaaaaaaaaahhhhhhhhhhhhhhhhhh',7815,0);
INSERT INTO comment VALUES (7819,1205,1301,'Charlie','a start','2003-09-10 14:15:01',1,'Given we need infinitely many clocks, the question is how do we use them. Getting 1/4 hour + 1/8 hour is the easy start, with three timers started simultaneously with the first one on immediate double speed, doubling the second timer when the first expires, and doubling the third when the second expires. Starting the timed interval at the half-hour mark, when the first timer expires, gives us the 1/4 + 1/8 when the third timer expires.\r\n\r\nThe problem is that an interval of 1/32, rather than 1/16, must begin immediately after the 1/4+1/8. Can anyone see how?\n\nEdited on September 10, 2003, 2:15 pm',NULL,0);
INSERT INTO comment VALUES (7820,1157,2592,'ben young','solution to 1','2003-09-10 15:09:31',0,'This is an interesting problem.\r\n\r\nThe answer to question 1 must be a number when, spelled out, has the same amount of letters as the digit it represents. The only such number is 4, since \"four\" has four letters.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (7821,1157,2592,'ben young','solution to 2, 3, and (sort of) 4','2003-09-10 15:25:51',0,'Following the logic from previous comment, the answer to question 2 must be a number whose value is one greater than the amount of letters to spell it. In this case, the answer would be \"five\".\r\n\r\nTherefore, the answer to question 3 is \"seven\".\r\n\r\nFor number 4, assuming n is a positive integer(although everyone knows what happens when you assume), by going up the number line we see that there is no number whose value is exactly 18 greater than the amount of letters that spell it. twenty-six is 17 greater (9 letters), and twenty-nine is 19 greater (10 letters), making the lowest number 18.\r\n\r\nI\'ll leave question 5 for the real brainiacs; I\'m just a rookie on this team.\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (7822,1157,2561,'Aaron','Alternate Approach','2003-09-10 15:49:20',3,'\r\n
',NULL,0);
INSERT INTO comment VALUES (7823,1157,1301,'Charlie','solution','2003-09-10 16:04:20',3,'Question 1 has several interpretations, so the answers fall into different categories:\r\n\r\n1. 0\r\nThis answer indeed has zero letters--only a digit.\r\n\r\n2. Four.\r\nThis answer indeed has four letters.\r\n\r\n3. The answer is 11.\r\nThe totality of this answer, as a sentence indeed has 11 letters.\r\n\r\n4. Wording similar to option 3, but somewhat different, with various numbers being correct depending on how many letters there are in the verbiage, such as \"The answer has 19 letters.\"\r\n\r\n5. The answer has twenty-nine letters.\r\nThis is also extensible with various wordings, and it ties into the subsequent questions on the list, as here we needed a number name that had a value 19 more than the number of letters in that number name. Again, variations are such as \"The answer is nineteen.\"\r\n\r\nQuestion 2 again has variations.\r\n\r\n1. 1\r\n\r\n2. Five.\r\n\r\n3. The answer is 12.\r\n\r\n4. Variations in wording on 3.\r\n\r\n5. The answer is twenty-one, and its variations in verbiage.\r\n\r\nQuestion 3 has the usual variations as above, including the one that is unique to it: \"seven\".\r\n\r\nIn answering question 4, let\'s first consider this straightforward single-word-number-oriented intepretation (four, five, seven, ...). There is no similar answer like this for n=4. That\'s because there are two answers for n=3 (\"six\" and \"eight\") and three such answers for n=5 (\"nine\", \"eleven\" and \"thirteen\"). While n can increase in general with the numbers, there are some that are repeated while others do not appear, and the first of these is n=4.\r\n\r\nOf course nothing precludes something like \"That\'s 9.\" or \"It\'s ten.\" as answers for n=4, and similar verbiages that can be used as work-arounds for any value of n.\r\n\r\nOf use in coming up with such answers is a table, ordered by the difference between the signification and the length, of the number words. The following table shows that difference, the signified number, the length of the number name and the name itself:\r\n\r\n 0 4 4 four\r\n 1 5 4 five\r\n 2 7 5 seven\r\n 3 6 3 six\r\n 3 8 5 eight\r\n 5 9 4 nine\r\n 5 11 6 eleven\r\n 5 13 8 thirteen\r\n 6 12 6 twelve\r\n 6 14 8 fourteen\r\n 7 10 3 ten\r\n 8 15 7 fifteen\r\n 8 17 9 seventeen\r\n 9 16 7 sixteen\r\n10 18 8 eighteen\r\n11 19 8 nineteen\r\n12 21 9 twenty-one\r\n12 23 11 twenty-three\r\n13 22 9 twenty-two\r\n14 20 6 twenty\r\n14 24 10 twenty-four\r\n15 25 10 twenty-five\r\n16 27 11 twenty-seven\r\n17 26 9 twenty-six\r\n17 28 11 twenty-eight\r\n19 29 10 twenty-nine\r\n22 31 9 thirty-one\r\n22 33 11 thirty-three\r\n23 32 9 thirty-two\r\n24 30 6 thirty\r\n24 34 10 thirty-four\r\n25 35 10 thirty-five\r\n26 37 11 thirty-seven\r\n27 36 9 thirty-six\r\n27 38 11 thirty-eight\r\n29 39 10 thirty-nine\r\n33 41 8 forty-one\r\n33 43 10 forty-three\r\n34 42 8 forty-two\r\n35 40 5 forty\r\n35 44 9 forty-four\r\n36 45 9 forty-five\r\n37 47 10 forty-seven\r\n38 46 8 forty-six\r\n38 48 10 forty-eight\r\n
\r\n--------\r\nThis table was produced by a computer program whose output was then sorted by the first column. Three negative values were discarded (-1 for \"two\" and -2 for \"one\" and \"three\").\r\n\r\nDECLARE SUB ProcPiece (piece$, MajorPower!)\r\nDATA one,two,three,four,five,six,seven,eight,nine\r\nDATA ten,eleven,twelve,thirteen,fourteen,fifteen,sixteen,seventeen\r\nDATA eighteen,nineteen\r\nDATA twenty,thirty,forty,fifty,sixty,seventy,eighty,ninety\r\nDATA thousand,million,billion,trillion,quadrillion,quintillion,sextillion\r\nDIM SHARED unit$(19), ten$(10), major$(7)\r\nFOR i = 1 TO 19\r\n READ unit$(i)\r\nNEXT\r\nFOR i = 2 TO 9\r\n READ ten$(i)\r\nNEXT\r\nFOR i = 1 TO 7\r\n READ major$(i)\r\nNEXT\r\nDIM SHARED name$, num$\r\nOPEN \"reptqest.txt\" FOR OUTPUT AS #1\r\nFOR n = 1 TO 100\r\n num$ = LTRIM$(STR$(n))\r\n IF num$ = \"0\" THEN\r\n name$ = \"zero\"\r\n ELSE\r\n name$ = \"\"\r\n MajorPower = 0\r\n DO\r\n l = LEN(num$): IF l > 3 THEN l = 3\r\n piece$ = RIGHT$(num$, l)\r\n num$ = LEFT$(num$, LEN(num$) - l)\r\n CALL ProcPiece(piece$, MajorPower)\r\n MajorPower = MajorPower + 1\r\n LOOP WHILE LEN(num$) > 0\r\n END IF\r\n numLets = 0\r\n FOR i = 1 TO LEN(name$)\r\n IF INSTR(\"abcdefghijklmnopqrstuvwxyz\", LCASE$(MID$(name$, i, 1))) > 0 THEN\r\n numLets = numLets + 1\r\n END IF\r\n NEXT\r\n PRINT #1, USING \"### ### ### &\"; n - numLets; n; numLets; name$\r\nNEXT\r\nCLOSE\r\n\r\nSUB ProcPiece (piece$, MajorPower)\r\n piece = VAL(piece$)\r\n n$ = \"\"\r\n IF piece > 99 THEN\r\n n$ = unit$(piece \\ 100) + \" hundred \"\r\n piece = piece MOD 100\r\n END IF\r\n IF piece > 19 THEN\r\n n$ = n$ + ten$(piece \\ 10)\r\n piece = piece MOD 10\r\n IF piece > 0 THEN n$ = n$ + \"-\": ELSE n$ = n$ + \" \"\r\n END IF\r\n IF piece > 0 THEN n$ = n$ + unit$(piece) + \" \"\r\n IF n$ > \"\" THEN name$ = n$ + major$(MajorPower) + \" \" + name$\r\nEND SUB\r\n\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (7824,1157,1220,'abc','last solutions for 1-3','2003-09-10 20:50:25',0,'1. 30 \r\n2. 31\r\n3. 32\r\n\r\n8)',NULL,0);
INSERT INTO comment VALUES (7825,865,2121,'Chaz','S O L U T I O N','2003-09-10 21:20:36',0,'I found a way to get around. You have to say \"That is incorrect. No is not hte answer to this question\".',NULL,0);
INSERT INTO comment VALUES (7826,1205,2899,'Brian Wainscott','re: a start','2003-09-10 21:20:41',1,'We know how to get time intervals of 1/2, 3/4, 7/8, 15/16 etc hours. So I\'ll\r\ntake that as given. To add 1/32 on the end of Charlie\'s 3/8, the only thing\r\nI can see to do is this:\r\n\r\nStart the necessary clocks (4) to measure 15/16 hours. When they hit\r\n7/8 (and still running), start the necessary clocks (5) for 31/32 hours.\r\nAt time 15/16 (when the first set runs out), start Charlie\'s 3 clocks.\r\nStart counting time 1/2 hour later. Then Charlie\'s 3 clocks have 1/4+1/8\r\nleft to run. When they expire, the (5) clocks still have 1/32 left to run.\r\n(They started 1/16 sooner, and run 3/32 longer). Total time to measure\r\n13/32 hours is 59/32 hours\r\n\r\nI can see how to extend this to any finite decimal expansion of 5/12 hours.\r\nThe problem is, each stretch of 0\'s in the decimal expansion will require\r\nadding at least 1/2 hour (more like an hour) to the total time.',7819,0);
INSERT INTO comment VALUES (7827,1195,1220,'abc','','2003-09-10 22:11:34',0,'Amazing!\r\nThe power of numbers. Wow.\r\n\r\nSome more analysis (I won\'t even try to find an explanation for this):\r\n\r\n* Period 4 and 20 contain only even digits (and numbers), but Period 12 contains 0 as well\r\n* Period 4 contains each even number once\r\n* Period 20 contains each even number and the zero 4 times\r\n* Period 12 contains all digits except 0 and 5 (which are on their own in Period 3). Each odd number occurs twice, each even only once. Between two equal odd numbers are either 3 or 7 (depends in which direction you count) different numbers. In such a row of 3 there is an even number in the middle, in a row 7 there are even numbers behind the odd from which you are counting, before the next equal odd and another one in the middle of that 7-digits-row. (Yeah, I know, that\'s nothing unusual.)\r\n* Every digit inside Period 20 appears 4 times. With exception of the 0 (which is logically vertically paired twice)each digit is once horizontally paired and once diagonally paired.\r\n* Period 60 contains all the digits, but mostly odds. Each odd digit (except 5, again vertically paired by force) is once horizontally paired and once diagonally paired.\r\n\r\n* All digits from Period 1 and 4 combined appear in Period 20. All digits from Period 3 and 12 combined appear in Period 60. \r\n* With the exceptiom of Period 1 and 3 you could create a square with all of them.\r\n\r\nMore useless facts for you.\r\n\r\nSomething is wrong with the board. I replied to SK but I was logged off and now it shows up as no subject.\r\nEdited on September 10, 2003, 10:12 pm\n\nEdited on September 10, 2003, 10:14 pm',7803,0);
INSERT INTO comment VALUES (7828,189,1626,'Gamer','re: This was easy','2003-09-10 22:39:48',3,'I\'m sorry, that\'s not the right answer. Your answer clearly consists of more than four letters. The correct answer would be one hundred seventeen.\n\nEdited on October 15, 2003, 5:41 pm',7417,0);
INSERT INTO comment VALUES (7829,1157,3372,'Sam','*The* correct answer?','2003-09-10 23:59:44',0,'Hmmm, going for Aaron\'s approach, which was also what I had in mind, you can do several more less obvious answers, such as:\r\n\r\n1: Thirty-three\r\n\r\nGiven that the sentence \"This solution has thirty-three letters\" is a correct solution, the answer above must also be correct.\r\n\r\nI guess using this approach in finding answers to 4 & 5 would be futile, though...',NULL,0);
INSERT INTO comment VALUES (7830,189,3372,'Sam','Haiku','2003-09-11 00:18:53',0,'An elegant answer is\r\nmade up from just\r\nfifty-one letters alone',NULL,0);
INSERT INTO comment VALUES (7831,1195,3172,'SilverKnight','re: (blank post)','2003-09-11 00:58:15',0,'abc, you probably spent so much time typing this out... that it logged you off... and Levik probably (unintentionally) allows you to post if you POST to the correct URL (by pushing the \"POST\" button). But again, the site has logged you off, so it zeroes out some fields....\r\n\r\n(Just my HTTP thoughts running rampant...)\r\n\r\n --- SK',7827,0);
INSERT INTO comment VALUES (7832,1195,3172,'SilverKnight','re(4): Solution (further analysis)','2003-09-11 01:05:21',1,'\r\nStarting with the lesser number| 1467\r\nAdd a 9 on each time until the | 1476\r\none\'s place is the digit you | 1485\r\nwant, which is the highest | 1494\r\nnumber that uses those digits | 1503\r\nNote that the numbers go up or | 1512\r\ndown when we subtract 9s | 1521\r\n\r\nTo the tens place. Subtracting | 1521\r\non 9x10 is the same idea, only | 1431\r\nmodified for the ten\'s place | 1341\r\n\r\nFor the hundred\'s place we need| 1341\r\nto add on 900s so we get the | 2241\r\nnumber on the hundred\'s place | 3141\r\nthat we want. Since we can\'t | 4041\r\nsubtract 900s (the quicker way)| 4941\r\nbecause we are going up instead| 5841\r\nof going down, we must use more| 6741\r\nnumbers and add on more 900s. | 7641
\r\nWe end with 7641, the number we wanted.\r\nSince we added on 9s each time using this process, the difference between the two numbers must be a multiple of 9. Since this process can be used for any number of 9s, this is a proof for all of them.',7863,0);
INSERT INTO comment VALUES (7877,1190,3195,'John Reid','Another way of thinking about this','2003-09-12 18:01:11',3,'I agree with the solution previously posted by SilverKnight. Here is a way to solve the problem algebraically.\r\n\r\nAs mentioned by SK, the given constraints boil down to the equation\r\n\r\nxy = 2x + 2y\r\n\r\nSolving for y, we get\r\n\r\ny = 2x/(x-2)\r\n\r\nNow modify this a little:\r\n\r\ny = 2x/(x-2)\r\n = (2x-4+4)/(x-2)\r\n = [2(x-2)+4]/(x-2)\r\n = 2 + 4/(x-2)\r\n\r\nWe know that we are looking for integer values of y; hence the 4/(x-2) term must take an integer value. Well, what values of x could possibly make this term an integer? Remember that x also must be an integer, hence x-2 is also an integer. So, 4 divided by some integer gives us another integer. The only positive integral factors of 4 are 1, 2 and 4; this means that x-2 must equal one of these 3 values. Therefore x must equal 3, 4 or 6, and these values for x correspond to the 3 rectangles given as examples in the problem. Hence indeed there are no other solutions to find.\r\n\r\nIt\'s always nice to have different ways of looking at the same problem. I hope this method is clear to the reader and that some of you will find it interesting.\r\n\r\nThanks for the puzzle Gamer, it was fun!\r\n\r\n-John',7871,0);
INSERT INTO comment VALUES (7878,1190,3172,'SilverKnight','re: Another way of thinking about this','2003-09-12 18:10:04',0,'Well John,\r\n\r\nI, for one, find your solution interesting (and very clear), and in some ways more elegant than what I offered.\r\n\r\nI hope other people are encouraged to propose alternative solutions as well.\r\n\r\nThanks,\r\n\r\n--- SK',7877,0);
INSERT INTO comment VALUES (7879,1190,1626,'Gamer','re: Another way of thinking about this','2003-09-12 19:17:37',0,'I had fun solving it, and I think your method of solving it makes more sense than mine. (which was much like SK\'s) ',7877,0);
INSERT INTO comment VALUES (7880,1190,1220,'abc',' solution without proof','2003-09-12 19:57:51',0,'I could have said that there is no other pair quite soon after trying a couple values.\r\nNone of the sides can be smaller than 3, because 2*y = 2(2+y) <=> 2y = 4+2y -> 0 = 4\r\nwhich is false.\r\nAfter trying values larger than 3 you notice very soon that the function (if you had drawn a graph) blows up. The area becomes too large for the perimeter to keep up with. \r\nIt\'s a solution without elegance, but there are at least some useful thoughts in the beginning. ;)',NULL,0);
INSERT INTO comment VALUES (7881,1279,1220,'abc','re(10): solution','2003-09-12 20:12:28',0,'What makes this puzzle unique is that the letters are pronounced like in the Old MacDonald Song! Hey, it\'s quite funny, isn\'t? The solution is not that obvious. But it\'s definitely not extremely difficult. It doesn\'t belong in this category.\r\n\r\nI\'ve got a question:\r\nI don\'t fully understand the concept of submitting puzzles on this site. I wonder why Scholars are allowed to work on puzzles before others can see it. This doesn\'t seem fair to me at all. I mean, scholars are the highest rank around here and I assume that those persons are exceptionally good in puzzle solving and submitting. They find solutions quicker than most of the others. \r\nAnd now, they can begin solving a puzzle long before anybody else can which makes the rest feeling inferior.\r\n\r\nI understand it can\'t work any different. Scholars need to see the problems because they must vote them live. First see, first solve. ',7875,0);
INSERT INTO comment VALUES (7882,507,1220,'abc','re(2): divisible by 9 proof :)','2003-09-12 20:38:23',0,'Yes, it\'s the proof via backwards-thinking. ;)\r\n\r\nIt\' still amazing that the positioning of the previous-to-last digit automatically sets the last digit right according to the rules.\r\nWe still have a hard time to find an explanation for this.',7876,0);
INSERT INTO comment VALUES (7883,1279,1626,'Gamer','re(11): solution','2003-09-12 20:40:26',0,'They don\'t! That\'s all I am going to say on the scholar issue. You can look in the forums under \"Flooding problem revisited\" for more information about why the scholar\'s and journeymen don\'t get this extra advantage.\r\n\r\nI also thought it wasn\'t too hard after I saw it, but only after I saw it. Maybe we could make it 4/5? I don\'t know...',7881,0);
INSERT INTO comment VALUES (7884,1195,3444,'greg','re(2): Solution','2003-09-13 00:16:07',0,'Noticing the same thing, that the numbers apart from each other add to 10, I started to delve into why. Let me know what you think...\r\n\r\nThe primary reason for this is the fact that the last digit of each sum is the only one entered. It\'s not that they add to 10 but that every other number added together is divisible by 5. If you add all the numbers in the puzzle together and divide by amount of numbers there are (60/12), then you get 5. I decided to see if the same would hold true no matter how big the square is and it works (even if the sequence doesn\'t loop again and again as in this one).',7785,0);
INSERT INTO comment VALUES (7885,946,3447,'Kumanan','Simple I guess','2003-09-13 03:21:55',0,'On the D-Day, just pick one of the papers and gobble it up. The left over paper will anyway say Death so it is sure that what you took was life. Long live..',NULL,0);
INSERT INTO comment VALUES (7886,621,1301,'Charlie','solution','2003-09-13 13:31:48',3,'The situation at the point at which the smaller sphere is most constricted is that at which the centers of the two spheres and their points of contact with the wall and floor all lie on one plane.\r\n\r\nAt that moment, the given plane contains the largest cross section of each sphere, with circles equal in diameter to those of the spheres. \r\n\r\nConstruct a square on that plane with corners at the center of the larger circle (and sphere), the corner where the wall meets the floor and the points of tangency of the larger sphere with the wall and with the floor. The edge of this square is 50 cm. Its diagonal is therefore 50 √(2).\r\n\r\nConstruct the same type of square with the smaller circle, making one corner the center of that sphere (and circle). Let the smaller circle\'s radius be called r, which is also the length of one side of the new square.\r\n\r\nThe smaller square\'s diagonal lies along the larger square\'s diagonal, and we can find the length of the the smaller one by subtracting lengths that we know from that of the larger.\r\n\r\nFrom the center of the larger circle (the beginning of the larger diagonal) to the point of tangency with the smaller circle is the 50-cm radius of the larger circle. From there to the center of the smaller circle (where the smaller diagonal begins) is r cm.\r\n\r\nThe ratio of the side of the smaller square to its diagonal is still 1/√(2), so\r\n\r\nr/(50(√2) - 50 - r) = 1/√(2)\r\n\r\nr√(2) = 50(√2) - 50 - r\r\n\r\nr((√2)+1) = 50 ((√2) - 1)\r\n\r\nr = 50((√2)-1)/((√2)+1)\r\n\r\nso the diameter is \r\n\r\n100((√2)-1)/((√2)+1) cm or about 17.157 cm.',NULL,0);
INSERT INTO comment VALUES (7887,621,1220,'abc','What I came up with','2003-09-13 15:51:16',3,'My solution only works on the assumption that it doesn\'t matter whether we have a sphere or a circle in this problem. I\'m not sure if this is correct. I\'m not good at geometry. ;)\r\n\r\nThe radius of the sphere is 50cm.\r\nThe distance from the centre C of the sphere to the point where the wall and the floor meet is the diagonal of a 50*50cm square (radius of the sphere) with C as one corner, the points of tangency of the sphere with the floor and the wall (I borrowed that explanation from Charlie, I hope he doesn\'t mind) plus the point at which wall and floor meet as the other 3 corners.\r\nThe diagonal of a square is 1.41*side, in this case it gives 70.7107cm.\r\n\r\nThis means that the difference between the radius of the sphere and the diagonal of the square is the diameter of the second sphere which is 20.7107cm.\r\n\r\nAt least this is the solution if there were 2 circles in the problem. 8)\n\nEdited on September 13, 2003, 4:00 pm',NULL,0);
INSERT INTO comment VALUES (7888,621,1301,'Charlie','re: What I came up with','2003-09-13 16:37:59',0,'Regarding your statement [with my clarification],\r\n\r\n\"This means that the difference between the radius of the [larger] sphere and the diagonal of the square is the diameter of the second sphere which is 20.7107cm. \"\r\n\r\nBut that measure is all the way from the point of tangency of the two spheres to the corner where the wall meets the floor, which includes a gap between the smaller sphere and that point, and so is larger than the diameter of the smaller sphere.',7887,0);
INSERT INTO comment VALUES (7889,621,1220,'abc','re(2): What I came up with','2003-09-13 19:21:51',0,'Yes, I\'m sorry, I completely forgot that the perimeter of the smaller circle doesn\'t touch the corner of wall and floor!\r\n\r\nWell, I thought I can still solve it, but as I don\'t know how long the sides of the smaller square are, it\'s not possible to determine the diameter of the smaller circle.\r\nMust be your solution then, Charlie. I agree.\r\n\r\nIt\'s still funny I made that stupid mistake. 8)\r\nAnd now my grammar becomes sloppy. *sigh*\r\n\r\nEdited on September 13, 2003, 7:23 pm\r\n\r\nEdited on September 13, 2003, 7:23 pm\n\nEdited on September 13, 2003, 7:28 pm',7888,0);
INSERT INTO comment VALUES (7890,830,3387,'luke','Problem must specify:','2003-09-13 21:53:24',0,'If the containers are covered as the problems suggests they may be the problem is entirely impossible. In a covered container the hot water that boils off will hit the cover, condense, and return to the liquid water. This ensures that the mass of the water will not decrease as the solution calls for. I do not know whether it is possible anyhow, but with covered containers there is no way.',NULL,0);
INSERT INTO comment VALUES (7891,817,3197,'gabbo','Alternate','2003-09-14 01:57:53',0,'How about this she wears a size 14 dress (or something) then next year she knows she\'s gunna get bigger.',NULL,0);
INSERT INTO comment VALUES (7892,532,3197,'gabbo','My solution','2003-09-14 01:59:25',0,'Adam and Eve were the only ones wearing fig leaves.... :)',NULL,0);
INSERT INTO comment VALUES (7893,840,3197,'gabbo','My solution','2003-09-14 02:03:50',0,'This is a really lame solution but here it goes, some guy is lifting something and he can barely hold on and he drops it. Meanwhile someone is taping him, forward (play) this looks like he\'s haveing a hard time picking it up, but in reverse it looks like it quickly swoops up into his hands...',NULL,0);
INSERT INTO comment VALUES (7894,501,3197,'gabbo','','2003-09-14 02:10:38',0,'I say the light from the lamps on street lights.',NULL,0);
INSERT INTO comment VALUES (7895,686,3197,'gabbo','my solution','2003-09-14 02:14:02',0,'He lives in a country were people are murdered all the time but no one dares to say anything, or he was in the middle of a hitchcock film.',NULL,0);
INSERT INTO comment VALUES (7896,621,3197,'gabbo','My solution','2003-09-14 02:31:03',0,'I got this\r\n17.15728752538099023966225515806... cm\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (7897,621,3197,'gabbo','Anyone','2003-09-14 02:36:11',0,'Does anyone think that their should be a time limit before \'comments\' and the \'solution\' can be shown to everyone. This is just for those who either are too easily tempted to cheat. (not that I would ever do such a thing :P).',NULL,0);
INSERT INTO comment VALUES (7898,1341,3197,'gabbo','The solution','2003-09-14 02:53:11',1,'The answer is you would have everything in the container, with that many marbles you would create a mass so large it would make a mega-black hole. \r\n\r\nAlso, you could make a killing in the computer business, get the guy who writes the the numbers on all the marbles to print circuit-boards or something. \r\nNot to mention the what you could do with the guy who processes an infinite amount of marbles in under a minute ( I wonder what his typing speed is)\r\n',NULL,0);
INSERT INTO comment VALUES (7899,865,3197,'gabbo','Solution','2003-09-14 02:56:00',0,'It isn\'t.',NULL,0);
INSERT INTO comment VALUES (7900,1260,3197,'gabbo','The one and only solution','2003-09-14 02:59:05',0,'umop apisdn\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (7901,621,3172,'SilverKnight','re: Anyone','2003-09-14 03:02:38',0,'I don\'t think there should be a \"hard and fast\" time limit... I think once someone has posted a solution in the comments, then the solution should be posted. It\'s not like it\'s now giving anything away.... And sometimes it\'s a more formal dealing of the problem.\r\n\r\nHowever, if no one can come up with a solution, I think the solution should not quickly be presented. Perhaps a hint or two would be appropriate (as I\'ve seen done on numerous occasions already).\r\n\r\n --- SK',7897,0);
INSERT INTO comment VALUES (7902,621,3444,'greg','just a thought','2003-09-14 10:42:04',1,'We know that the two ealls are perfectly straight, but said nothing if they are perfectly perpendicular. You can have the two lines meeting at an angel greater or less than 90 degrees and then the answer would change with each degree changed.',NULL,0);
INSERT INTO comment VALUES (7903,1161,3444,'greg','partial solution','2003-09-14 10:48:11',0,'BOOST\r\nBOAST\r\nBEAST\r\nLEAST\r\nLEASE\r\nLEAVE',NULL,0);
INSERT INTO comment VALUES (7904,1161,1220,'abc','','2003-09-14 13:20:08',0,'1.\r\nboost\r\nboAst\r\nbLast\r\nPlast (slightly uncommon)\r\nplaNt\r\nplanE/planK/planS\r\n\r\n2.\r\ncinch\r\ncOnch (uncommon, mollusk and mollusk\'s shell)\r\ncoUch\r\ncouGh\r\nRough\r\nrougE\r\n\r\nAnother (which uses the same word with different spelling):\r\ncinch\r\nSinch (the same as \"cinch\")\r\nsincE\r\nsinGe\r\nsiEge\r\nsTege (medical term -> internal pillar of Corti\'s organ)',NULL,0);
INSERT INTO comment VALUES (7905,1190,1768,'Lorne Hrynkiw','additional solution - questionable','2003-09-14 20:16:44',0,'There is an additional solution (0,0); this is both trvial and questionable. Zero is, in some cases, considered an integer and either positive or negative as required.\r\n ',NULL,0);
INSERT INTO comment VALUES (7906,70,3464,'Julie','Answer','2003-09-14 22:57:38',0,'Answer: Bob is Tim\'s father.\r\n\r\nReasoning: \"more than their respective sons\" respective is the keyword in that statement. It means that when the names of the sons were given, they were given in the same order as their fathers, since Tim\'s name was second, Bob is his fatehr because Bob\'s name comes second too.',NULL,0);
INSERT INTO comment VALUES (7907,70,3224,'Lee','none','2003-09-15 02:44:35',3,'Peter buys n books for n^2 shillings.\r\nAlex buys (n+5) books for (n+5)^2 shillings\r\nIf Alex is Peters father then\r\n(n+5)^2 =n^2+21 for some n\r\ncancelling gives\r\nn=-4/10\r\nClearly Alex is not Peters father and is therefore Tims',NULL,0);
INSERT INTO comment VALUES (7908,621,3224,'Lee','nothing new','2003-09-15 03:00:54',3,'The\'gap\' created between a sphere of 2 units diameter and a perpendicular wall/floor can be easily found as root2 -1\r\nSo a sphere of 2 units can pass through a \'gap\' of 2 + root2 -1 units\r\nor root2 + 1\r\nThe sphere/gap ratio is therefore 2/r2 +1.\r\nThe maximum diameter sphere that can pass through a \'gap\',X is\r\n2X/r2+1\r\nHere X is 50(r2-1) (50 times bigger than the 2 unit example)\r\nSo the answer is 100(r2-1)/r2 +1 = 17.157.....',NULL,0);
INSERT INTO comment VALUES (7909,1161,3444,'greg','re:','2003-09-15 07:42:49',0,'abc...even though I agree with your answers, I thought the rules had stated to use common words.',7904,0);
INSERT INTO comment VALUES (7910,1161,1301,'Charlie','re(2):','2003-09-15 08:55:50',3,'abc\'s first listed solution for CINCH is the best one possible, as one cannot avoid CONCH, which is not too unusual a word. Other solutions for CINCH involve rarer words (in addition to CONCH) such as COUTH and ROUTH, or COACT:\r\n\r\ncinch conch couch cough rough rouge\r\ncinch conch couch couth routh route\r\ncinch conch couch couth routh routs\r\ncinch conch coach coact coast boast\r\ncinch conch coach coact coast roast\r\ncinch conch coach coact coast toast\r\n\r\nBut of course greg\'s partial solution if better for BOOST. That and some others, are:\r\n\r\nboost boast beast least leapt leaps\r\nboost boast beast least lease leave\r\nboost boast beast least leash leach\r\nboost boast blast blase blade glade\r\nboost boast blast blase blame flame\r\nboost boast blast blase blare flare\r\nboost boast blast blase blare glare\r\nboost boast blast blase blaze glaze\r\n\r\nOthers involve rarer words like COAPT, FEASE, BOART or CLAST.\r\n\r\n\r\n',7909,0);
INSERT INTO comment VALUES (7911,622,3172,'SilverKnight','Solution (spoiler)','2003-09-15 09:07:00',3,'Let\'s call the men A, B, C, D, and E, and let\'s call the dogs owned by the respective men a, b, c, d, e, with the \'smart\' dog being a.\r\n\r\n(I hope this notation is clear)\r\n\r\n ---- AaBbCcDdEe\r\nabc {--- ABCDdEe\r\nbc ---} AaBCDdEe\r\nabcd {--- ABCDEe\r\nbcd ---} AaBCDEe\r\nBbCcDd {--- AaEe\r\nBbCc ---} AaDdEe\r\nAaBbCc {--- DdEe\r\nAaBb ---} CcDdEe\r\nAaBbCDE {--- cde\r\nABbCDE ---} acde\r\nAaBbCcDdE {--- e\r\nABbCcDdE ---} ae\r\nAaBbCcDdEe {---\r\n\r\nPre tags don\'t seem to be working\n\nEdited on September 15, 2003, 9:12 am',NULL,0);
INSERT INTO comment VALUES (7912,1341,775,'Cory Taylor','more','2003-09-15 11:38:44',0,'after this problem has been put ot bed (apparently), I\'d like to add my two cents worth. So far it has been a very interesting read...\r\n\r\nThe problem as stated in a and b are identical. There is a lot of places where we confuse the actual math of a situation by implying a local nomenclature that is irrelevant to the actual mathematics, but helps us process the information just the same. As with Fatboy, I am a mere Engineer, so the theoretical vocabulary may pose a problem for me, but the idea is that a marble is a marble, regardless of the number it has written on it. The way that the majority of people here are thinking, having the exact same process performed on the exact same marbles would have a different result if the numbers painted on them were in a different order. Clearly this is not the case. As an example, (and hopefully this will make sense, as its derived from an anaolgy my math teacher used to explain the chain rule in calculus), if we have twice as many apples as oranges, then we - in the math world - can define apples as \"x\" and oranges as \"y\" and then say that 2x=y. Now we want to find the relationship between the rate of change between these \"variables\". It is equally correct to ask for d(x)/d(y) as it is to ask for d(apples)/d(oranges) - with a properly set up naming system, these are equivalent.\r\nWhat this problem has done is forced upon you a nomenclature, which certainly seems legitimate, but obviously leads astray as both parts of the question, which identical except for the nomenclature, do not produce the same mathematical result.\r\n\r\nFinally for the case of the amended question posted about 7-8 comments ago. The rewording of the question has removed the problem of the nomenclature and allow a different mathematical result.\r\n\r\nAnd just to clarify, I see how the math works for the answer you are all supporting (to leave no marbles in the bag for part b), I am trying to show the mis-step in the process. The only way that you can end up with no marbles is to remove as many as you\'ve put in, and since in no interval do you remove more than you put in, if you ever have more than zero marbles you always will. Its very clear that the math produced is flawed.',NULL,0);
INSERT INTO comment VALUES (7913,1341,2899,'Brian Wainscott','re: more','2003-09-15 12:08:16',0,'Consider this: Given the problem as posted and consider part (B). If you say there are marbles in the container after the minute has expired, pull one out. What number will be written on it? N you say? But that marble was thrown out in step N of the process......\r\n\r\nThe point is, there is no marble that you can point to that was not thrown out before the minute was over. You cannot pull a marble from the bag. So the bag is empty.\r\n\r\nAnd there is one major difference between (A) and (B) that you missed. In A, the marble thrown out is always one of the last 10 you put in. So the other 9 will always remain in the bag. In (B), the marble thrown out (after the first step) is always from a previous step. So no marble is ever safe: each of the 10 you just put in will get removed at some specific later step. That is the difference between (A) and (B). It is not just a matter of labels....',7912,0);
INSERT INTO comment VALUES (7914,1341,3172,'SilverKnight','re: more','2003-09-15 12:14:24',0,'Cory,\r\n\r\nLike FatBoy, you are making at least a couple of (invalid and unstated) assumptions. In your case, you are likening normal arithmetic operations that work on real numbers to those that apply to infinities. But they do not.\r\n\r\nTo deal with two infinities of the same Cardinality, you MUST deal with the members of the set. And members of a set ARE named or referred to in some manner.\r\n\r\nI understand why you wish to dismiss the \"naming\" of the elements in a particular set. I am an engineer too, and I agree that it can help to understand problems by assigning numbers/labels.\r\n\r\nBut it does not change matters.\r\n\r\nWhat if I take an infinite set (the set of all integers), and I remove an infinite set of integers from that (the odd integers). I am left with an infinite set (the even integers). However, if, instead, I remove (the set of all integers), I am left with an empty set. Either way I remove a set of the same size. But that doesn\'t mean the sets are equivalent.\r\n\r\nBy this, I think it obvious that the LABELING (or more accurately, which members of the set I remove) DOES in fact make a difference.\r\n\r\nSo, to paraphrase your statement.... It\'s very clear that the math you produced is flawed.\r\n\r\n--- SK',7912,0);
INSERT INTO comment VALUES (7915,1341,775,'Cory Taylor','re(2): more','2003-09-15 12:27:55',0,'but my point exactly was that a marble is a marble is a marble... It is the labels themselves that cause the problem. Reading carefully you\'ve put all the marbles into the bag, and then you take one out. I can see your argument in the case where for each iteration you put in the 9 smallest numnered marbles remaining in your stock that have a remainder when divided by ten, but throw out the lowest numbered remaining marble that is divisible by ten, but this is fundamentally different than what is happening. Each iteration results in 10 balls in and then one ball out. An infinite number of iterations will not allow you to reduce the number of marbles to zero. The mathematics that supports this (and it is valid once the nomenclature has been derived) is flawed because of a numbering scheme that we have imposed on the situation - the actual sitation does not support the solution.\r\n\r\nYou may ask what possible naming convention could be derived to sidestep this discrepancy and that would be an excellent question for which I certainly dont have an answer (there may not be any such convention), but that doesn\'t mean that you can ignore the flaw.\r\n\r\nThe basic problem is that you\'re considering all infinities to be equal, which is not the case. Infinity minus infinity is not zero - it is some undefined quantity that can only be derived by knowing where the infinities came from in the first place. In this case the knowledge of where the infinities comes from leads to a simple mathematical solution to the problem, not some philosophical debate.\r\n\r\nAs an example, consider the process of normailizing number (if you\'re familiar with it). Physicist use this slution method quite frequently to remove infinities form equations - they do so by dividing equations by infinity. When they do so, they must choose their used infinity VERY cartefuly so that they produce an answer with relevance - simply dividing by the first infinity that comes along will only multiply their problems.\r\n\r\nLastly, as counter to the argument you\'ve given of picking a marble \"n\", well what if I pick the marble infinity? The core of the problem - which infinity did I pick? You\'ve limited your set size by forcing me to pick from within a limited set of numbers, and it is this exact limiting which is clouding your solution.',7913,0);
INSERT INTO comment VALUES (7916,608,3449,'dennis wenne','Solution','2003-09-15 12:31:01',0,'There are 10 numbers with only 1 digit. followed by 90 numbers with two digits. Thus it follows:\r\n10 (1)\r\n90 (2)\r\n900 (3)\r\n9000 (4) \r\n90.000 (5) etc\r\n10*1+90*2+900*3+9000*4= 38,890 (<40,000)\r\nThus we have to deal with 5 digit numbers to answer the question. WE need 40,000-38,890=110 more digits. Since the numbers contain 5 digits from now on, we have will have to look at the last number in the 110/5=22 th-5digit number. \r\nThus 10,022... will give us a 2.\r\n\r\nComments?? \r\n',NULL,0);
INSERT INTO comment VALUES (7917,622,1575,'DJ','Solution','2003-09-15 13:35:34',3,'Call the man A, B, C, D, and E, and their dogs a, b, c, d, and e. Assume that dog a is the one that knows how to row the boat.\r\n\r\nThe dogs are okay by themselves, so put some of them across first, then their owners, then bring some dogs back to put all the owners on the \'right\' side, and then just use the one \'smart\' dog to bring all the dogs back across.\r\n\r\nThat\'s the basic method used, and here is the list of crossings (including each intermediate state):\r\n\r\n\r\nABCDEabcde\r\nABCDEde abc →\r\nABCDEde abc\r\nABCDEde ← a bc\r\nABCDEade bc\r\nABCDEe ad → bc\r\nABCDEe abcd\r\nABCDEe ← a bcd\r\nABCDEae bcd\r\nAEae BCD → bcd\r\nAEae BCDbcd\r\nAEae ← Bb CDcd\r\nABEabe CDcd\r\nBEbe Aa → CDcd\r\nBEbe ACDacd\r\nBEbe ← Cc ADad\r\nBCEbce ADad\r\nbce BCE → ADad\r\nbce ABCDEad\r\nbce ← a ABCDEd\r\nabce ABCDEd\r\ne abc → ABCDEd\r\ne ABCDEabcd\r\ne ← a ABCDEbcd\r\nae ABCDEbcd\r\n ae → ABCDEbcd\r\n ABCDEabcde',NULL,0);
INSERT INTO comment VALUES (7918,1341,775,'Cory Taylor','a functional equivalent','2003-09-15 13:38:34',0,'within each iteration, you are adding nine marbles (adding ten and removing one). Don\'t even consider the label - that is something that is purely added to create the paradox. The sum of an infinite number of nines can\'t be zero - if the error isn\'t in the nomenclature that\'s fine - but its there somewhere. Possibly you\'re trying to justify that any marble \"n\" would\'ve been taken out on the n\'th iteration and then assuming that means that you take out all the marbles. Or maybe that once you\'ve taken out all the marbles that there aren\'t still more left. I don\'t know where the misleading assumption is, but it is definitely there somewhere.',NULL,0);
INSERT INTO comment VALUES (7919,1341,3172,'SilverKnight','re: a functional equivalent','2003-09-15 13:42:59',0,'Cory,\r\n\r\nPlease read and respond to my last post in this thread. Perhaps this will illuminate the issue.\r\n\r\nIt\'s really all about set membership.\r\n\r\n --- SK',7918,0);
INSERT INTO comment VALUES (7920,1341,775,'Cory Taylor','re(2): more','2003-09-15 14:49:05',0,'You\'re implicating here that the \"value\" of infinity is static. This couldn\'t be more untrue. If infinity minus infinity were zero and infinity divided by infinity was one, then we wouldn\'t even have calculus in the first place, and this question would be gibberish.\r\n\r\nThe set of all odd, positive integers is indeed of infinite size, as is the set of all positive integers. However, they are not the \"same\" size. In one case, the value of infinity is twice that for the other case. This is precisely what were boiling down to here in the marbles problem. Sure I\'ll concede that for evey value n, the nth marble has been removed, however, there is another, completely independant infinity of marbles (which happens to be 9 times as large as the first infinity) which never gets counted. The only alternative to this is that infinitely adding 9 to a number will produce a result of zero. Forget the math and realize the situation. I am good at math, but certainly no expert - I\'m not going to debate with you the intricacies of the equations or the definitions of limits. Just look at what the results are incrementally, and the expand these infinitely - this must produce the same results as a valid mathematical model. In this case, the two are very much at odds, and unless you can convince me that there is a flaw in the basic reasoning (not the math) ive produced, theres really no argument. An infinite number of nines summed cannot equal 0.\r\n',7914,0);
INSERT INTO comment VALUES (7921,1341,3172,'SilverKnight','re(3): more','2003-09-15 15:34:46',0,'Here are your statements with responses:\r\n\r\n... the \"value\" of infinity is static\r\nI\'m not at all sure what that means. (And I\'d love for you to explain it.) But, if by that you mean that the members of the set REPRESENTING a particular infinity is static, then YES.... It is static. e.g., The members of the set containing all even integers is static. It is not growing, it is not declining, it remains constant (over time?)... :-)\r\n_______________\r\n\r\nthe value of [the set of integers] is twice that for [the set of positive integers]...\r\nAt least that\'s what I *think* you meant by your sentence. Again, I\'m not sure what you mean, but I *think* you are saying the number of members is twice the size in one set as the other. However, I don\'t understand that line of reasoning at all. It is trivial to show a one-to-one mapping from one set ONTO the other set. And by your own (faulty) argument, if we can add one marble and remove a corresponding marble for EACH iteration, maintaining the empty status, then \"at the end\" it must remain empty. Well... I don\'t agree with your line of reasoning, but if you follow it, your reasoning produces inconsistencies.\r\n______________\r\n\r\nI\'m not going to debate with you the intricacies of the equations or the definitions of limits\r\nWell, that\'s your prerogative, but then why do you post on this thread? And isn\'t this exactly what we\'re all doing?\r\n_______________\r\n\r\nAn infinite number of nines summed cannot equal 0.\r\nUmmm... I think I agree.... but we didn\'t sum an infinite number of nines.\r\nCory, I beg of you... *please* read what I and Brian posted earlier, because I\'m getting the sense you didn\'t read them.\r\n\r\nYou are confusing TWO different issues about infinity. There is the SIZE of the set and the MEMBERSHIP of the set.\r\n\r\nAnd you\'re not being consistent about your use of \"value\" (as in your comment about the \"value\" of infinity being static).\r\n\r\nNow, I\'m sure you\'ll agree that given the two sets {1, 2, 3} and {2, 4, 6}, that the two sets do not have the same elements (and therefore, they do not have the same value). But they ARE of the same size.\r\n\r\nBy extension, {1, 2, 3, 4, 5} and {2, 4, 6, 8, 10} are of the same size. And if we look at what the results are incrementally, and then expand these infinitely as you so wish to do.... then we see that the positive integers have THE SAME SIZE, the SAME number of elements, as the positive EVEN integers. And at the SAME TIME, all the elements of one are in the other but not vice versa. This is not a logical inconsistency (as you would have us believe). (By the way, the size of both of these infinities is called aleph null.)\r\n\r\nNow, if you don\'t agree with this last line of reasoning, please explain where you find the problem.\r\n\r\n --- SK\n\nEdited on September 15, 2003, 3:38 pm',7920,0);
INSERT INTO comment VALUES (7922,608,1220,'abc','re: Solution','2003-09-15 18:55:27',0,'3 mistakes you made:\r\n\r\n1. There are 9 1-digit-numbers which are relevant for this problem cause 0 is left out. Which means that we have 38889 digits in front of the first 5-digit-number.\r\n\r\n2. 40,000-38889 = 1111\r\n\r\n3. Thus we need the first digit after the 222nd 5-digit-number like the other solutions tell you. Your last mistake was that 10,022 is not the 22nd 5-digit-number. It\'s the 23rd.\r\nBut we need the 223rd which is 10,222 and the first digit is 1.\n\nEdited on September 15, 2003, 7:11 pm',7916,0);
INSERT INTO comment VALUES (7923,1341,775,'Cory Taylor','re(4): more','2003-09-15 23:11:20',0,'my definitions;\r\nby saying that the value of infinity is not static, I mean that while adding one to a particular \"instance\" of infinity results in the same infinity (i.e. if you were allowed to represent infinity as a variable, then x+1=x), that infinity is not at all related to a different infinity (x<>x).\r\n\r\ncomments referring to the \"value\" of infinity referred to the number of elements. Yes this was fuzzy - I apologize. Now - while both the sets in question had an infinite size, it is not true that the subtraction of the two sets left null. This was the point of that comment, and right to the heart of my argument. We are dealing with completely different infinities with the addition of the ten marbles than we are with the subtraction of the marbles. When you quantize (which of course you can\'t do, but remember, we\'ve suspended disbelief) the adding marbles infinity minus the subtracting marbles infinity you do not end with the empty set., hence the jar isn\'t empty...\r\n\r\nThe reason that I\'ve mentioned that im not going to debate the intricacies or definitions of math is simply because I\'m not familiar with them. I have no understanding of cardinality (if thats the term) nor can I give you the definition of a set. This does not mean than my approach is invalid - by all means if the reasoning is flawed im happy to leave it at that.\r\n\r\nYour final comment about the sum of infinite 9\'s is a reference to the functional aspect of this problem. Reading the problem, it boils down to infinite iterations of a process. Each discreet iteration produces a net increase of 9 marbles in the jar. Without respect to labels, 10 go in and 1 comes out, resulting in my magical 9. This result is independent of the iteration number, and so the expression derived for the total number of marbles in the jar after any number of iterations is 9*n. As n approaches (and we\'ve conceded, reached) infinity this number approaches 9*infinity. This expression greatly disputes the claim that there are no marbles left in the jar. Either one or the other must be wrong. I\'m not here to tell you where the error lies in your method (I\'ve stated that i don\'t have the proper background), simply that there is one.\r\n\r\nTo hazard a guess, I would say that the problem itself has asked the results of an impossible situation, which, of course, is why the problem is listed in paradoxes. We have all seen MANY \"proofs\" that 1=0, or some other similar fallacious statement. Very often I can find the place where the proof becomes invalid, and if not then I generally have an idea. In those rare cases where I can\'t, does that mean that the math is in fact valid? Obviously no. This is the case here - your math is flawed, as it produces a flawed result. From the first iteration, the number of marbles is positive, and it only increases. When you start with a positive value (after any iteration of your choice, the number of marbles in the jar is positive) and increase it for an infinite period of time this CANNOT produce a null value.\n\nEdited on September 16, 2003, 4:15 am',7921,0);
INSERT INTO comment VALUES (7924,1210,1,'levik','Hint?','2003-09-16 00:31:50',4,'I think it may be time for a hint, Gamer :)',NULL,0);
INSERT INTO comment VALUES (7925,1210,1626,'Gamer','Hint','2003-09-16 07:37:09',0,'Remember the title, and read the newspaper headlines as follows\r\n\r\nYOU_RUB_IT_SHEEP_DUELED_WAR_STEPS_AGING_BORED_TO_NUT_PRAYED_FOSSIL_WINS_A_QUIT_AND_OIL_IT',NULL,0);
INSERT INTO comment VALUES (7926,1162,3172,'SilverKnight','solution?','2003-09-16 08:57:38',3,'die one:\r\n4, 5, 6\r\n\r\ndie two:\r\n6, 2, 4',NULL,0);
INSERT INTO comment VALUES (7927,1341,3172,'SilverKnight','re(5): more','2003-09-16 09:13:29',0,'I\'m sorry Cory.\r\n\r\nAs n approaches (and we\'ve conceded, reached) infinity... \r\nNo Cory, no one has conceded that any iterative process REACHES infinity. You simply want to justify your point.\r\n\r\nYou cannot say your math is flawed without showing what the flaw is (at least not and still be taken seriously). There is no flaw in the reasoning behind the solution to this problem. And you continue to be unable to show what it is.\r\n\r\nThere is nothing in this solution that is \"out of reach\" of your facilities, and I\'m sure you are familiar with set notation (though you seem eager to avoid discussing it).\r\n\r\nWhat\'s more, one most certainly can demonstrate that the SIZE of some infinities is definitely larger than others (size of real numbers > size of rational numbers), whereas the SIZE of some infinities is equal to some others (size of rational numbers = size of integers).\r\n\r\nI will FOR A THIRD TIME suggest that you address the issue as membership in a set, and mappings from one set onto another. And you will, more than likely, continue to avoid this way of analyzing the problem, because it supports the solution.',7923,0);
INSERT INTO comment VALUES (7928,1210,1,'levik','re: Hint','2003-09-16 09:28:25',0,'> Remember the title, and read the newspaper headlines as follows \r\n\r\nDammit, quit stretching my site! :)',7925,0);
INSERT INTO comment VALUES (7929,1205,1920,'Brian Smith','Closer and closer','2003-09-16 10:01:39',0,'I have a method to come arbitrarily close to 25 minutes using a finite number of timers.\r\n\r\nFirst, how to construct 1-(1/(2^n)) of an hour. Start with n timers all started simultaneously with timer #1 set to double speed. When #1 beeps (1/2 hr later) start #2, When #2 beeps (1/4 hr later) start #3, etc ... When the last timer beeps 1-(1/(2^n)) hours have passed.\r\n\r\n5/12 of an hour can be expressed as 1/4 + 1/8 + 1/32 + 1/128 + 1/512 + ....\r\nOr as (1-3/4) + (1-7/8) + (1-31/32) + (1-127/128) + (1-511/512) + ...\r\n\r\nAn approximation of 5/12 can then be given as n - (3/4 + 7/8 + 31/32 + 127/128 + ... + (2^(2n-1)-1)/(2^(2n-1)))\r\n\r\nUsing the latter expression, we can come arbitrarily close to 5/12 using a finite number of timers. For n terms of precision, we need n hours and n^2+n+1 timers.\r\n\r\nPut n timers in group A (n hrs). Put 2 timers in group B1 (3/4 hr), 3 in B2 (7/8), 5 in B3 (31/32), 7 in B4 (127/128), etc ...\r\n\r\nGroup A counts the hours, when one timer is finished in group A, start the next timer.\r\nGroups B1, B2, etc countdown 3/4 + 7/8 + 31/32 + ... hours.\r\n\r\nStart group A and group B1, when B1 is finished start group B2, when B2 is finished start group B3, etc.\r\n\r\nWhen group Bn (the last B group) finishes, 3/4 + 7/8 + 31/32 + ... + (2^(2n-1)-1)/(2^(2n-1)) hours have passed. From that point, there is 1/4 + 1/8 + 1/32 + ... + 1/(2^(2n-1)) hours remaining until the last (nth) timer in group A finishes. \r\n\r\n(3/4 + 7/8 + 31/32 + ... + (2^(2n-1)-1)/(2^(2n-1))) + (1/4 + 1/8 + 1/32 + ... + 1/(2^(2n-1)))\r\n = (1/4 + 3/4) + (1/8 + 7/8)+ ... + (1/(2^(2n-1)) + (2^(2n-1)-1)/(2^(2n-1)))\r\n = n\n\nEdited on September 16, 2003, 10:05 am',NULL,0);
INSERT INTO comment VALUES (7930,1162,1920,'Brian Smith','','2003-09-16 10:16:48',0,'The absolute minimum which the faces of the dice total is 12 (1+2+3+1+2+3). The absolute maximum is 30 (4+5+6+4+5+6). The only perfect cube in this range is 27. The pips seen can be are 6,5, and 4 on one die and 6,4, and 2 on the other.',NULL,0);
INSERT INTO comment VALUES (7931,1162,1301,'Charlie','solution','2003-09-16 10:24:16',3,'Opposite faces on a die add up to 7. Therefore, when three faces of a die are visible, exactly one number from each of the following three pairs is visible:\r\n1,6\r\n2,5\r\n3,4\r\n\r\nThe eight possible combinations correspond to the eight vertices of the cube where three faces meet.\r\n\r\nThe lowest total for 1 die is therefore 6 and the highest is 15. So for two dice the lowest total is 12 and the highest is 30.\r\n\r\nThe only perfect cube in the range of 12-30 is 27. This is three short of the maximum of 30.\r\n\r\nThe only way to lose 3 points compared to showing 4, 5 and 6 on both dice is to have one of them show a 2 instead of a 5. (Any showing a 1 instead of a 6 would be too much lost; a showing of 3 instead of 4 would have to be accompanied by a loss of 2 somewhere, which is not possible.)\r\n\r\nSo one die shows 4, 5 and 6 while the other shows 4, 2 and 6.',NULL,0);
INSERT INTO comment VALUES (7932,1162,1567,'Bryan','re: solution?','2003-09-16 10:42:54',0,'SK: in the future, please show your work :P',7926,0);
INSERT INTO comment VALUES (7933,1162,1220,'abc','alternative solution','2003-09-16 10:51:54',3,'The problem tells us that we can see three sides. However, it doesn\'t tell us if by \"visible\" it\'s meant that we look at all three sides at once. If you redefine it, you could say that we see three sides of a cube while we are allowed to look at it from all sides. One side is resting on the surface on which the cube lies, the other two sides could be covered by tape for example.\r\n\r\nIn this setup there is another solution.\r\nThe only cube to which the sides of the two dices can add up, is 27.\r\nEither it\'s 15+12 like in the previous solutions or it\'s 13+14.\r\nAfter redefinition of the problem, one dice can show 6,4 and 3 (if the dice sits on the 1 and 2 and 5 are covered and therefore not visible). The other dice shows 6,5 and 3.',NULL,0);
INSERT INTO comment VALUES (7934,1162,3172,'SilverKnight','re(2): solution?','2003-09-16 10:55:08',0,'lol.... but this was apparent... :-)\r\nSo, I left it as an exercise to the reader.\r\n\r\nBesides, Charlie jumped in and did an admirable job. (I knew he would!)',7932,0);
INSERT INTO comment VALUES (7935,320,3481,'Justine Dawson','Heard b/4','2003-09-16 13:38:28',3,'Easy, 2 barbers - must do each others hair - so the one with good hair, must of had it done by the one with the bad hair n vice-versa',NULL,0);
INSERT INTO comment VALUES (7936,1210,1626,'Gamer','re(2): Hint','2003-09-16 17:00:32',0,'Oops... sorry about that! :)\r\n\r\nAlso, think of what \"Third Base\" means, and remember that there are 26 letters in the alphabet, and between the words comes 1 space.\r\n\r\nIf you (levik) see any good hints after looking at the solution (given of course that you don\'t want to solve the problem!) you can too post them too... I am unsure of any other good hints that wouldn\'t give away the solution.',7928,0);
INSERT INTO comment VALUES (7937,1332,122,'Happy','AHA!','2003-09-16 17:31:02',3,'They\'re all synonyms for palindromes.\r\n\r\njoke = gag\r\nburst = pop\r\nallude = refer\r\nfather = dad\r\nmidday = noon\r\nobserves = sees\r\nhorizontal = level\r\n\r\n(midday was the one that gave it away for me)',NULL,0);
INSERT INTO comment VALUES (7938,1341,2899,'Brian Wainscott','re: a functional equivalent','2003-09-16 17:36:41',0,'I have two other attempts to clarify things:\r\n\r\n1 - OK, forget the labels. Restate the parts as follows. In each step you put in 10 marbles (one at a time). Then for part (A), always take out the last marble you put in. But in (B) always take out the marble that has been in the bag the longest. No labels now, but the same answer. The fundamental difference between (A) and (B) is that in (A), \"old\" marbles are left in the bag forever. In (B) all the marbles you put in will be removed at some later step. No marble currently in the bag will ever remain there. THAT is what makes them different.\r\n\r\n2 - OK, don\'t like that? Here is one I mentioned before. Start with all the marbles in the container. Thinking in terms of integers, the problems then become: in (A) you throw out all the integers that are multiples of 10. In (B) you throw out all the integers that are multiples of 1.\r\n\r\nAt each step, I agree that there are an infinite number that have not been thrown out. But after the minute is over (an infinite number of steps), (A) leaves you with lots of integers, and (B) with none.\r\n\r\nI\'m starting to repeat myself, so I guess I\'d best leave this thread....',7918,0);
INSERT INTO comment VALUES (7939,1341,775,'Cory Taylor','circles','2003-09-16 18:46:11',0,'To SK and BW;\r\nI have not attempted to find the hole in your reasoning or math because, I don\'t have the background. Why is it so hard to accept that I\'ve never taken anything on set theory? My math classes were sooo long ago that I really don\'t recall a lot of the intricacies required to have a debate of a definitional nature. Does that mean that that other methods I conceive are necessarily faulted - no. Because I can\'t personally find the flaw in your math does that make it correct - no.\r\n\r\nI really believe that the discrepancy lies in the question itself. You simply can\'t label marbles from 1 to infinity. Further, having stopped processing your marbles, there must have been a last iteration (Both of these important points are being ignored by your math. This is the very part of the problem I\'m referring to as the suspension of disbelief (its in the earlier posts - look for yourself). Is this a hard concept to grasp - definitely. But until you can show how my reworking of the problems mechanics is flawed, then clearly there is an error. Might it be in my version - sure. But you\'ve made no attempts to ever dispute the reasoning I’ve come up with (the sum of an infinite number of nines cannot equal zero), so further defense of your methods are pointless. I\'ve made no alterations to any meanings nor have I altered the process involved – indeed this seems to me to mean that I am working on a problem that has an identical solution. I have not violated or misused the term infinity in my method. Each discreet step produces a easily quantified increase in the number of marbles in the jar. An infinte sum of discreet values is no contradiction. Sometimes it may even end up as a finite number, but certainly not in the case where (both) no successive member of the set is valued less than its predecessor and any term is positive.\r\n\r\nI understand your reasoning. I see the math. I don\'t dispute that I can\'t number a marble that is still in the jar. It is a struggle to grasp how that results in a situation where there are any marbles left there at all, but lo and behold, there must be, or else at some point we\'ve begun taking more marbles away than we have addded, which isn\'t stated as a process and therefore violates the situation.\r\n\r\nYou have considered that infinity is a number that can be worked with. Not so. Infinity is not a number, it is an idea. There are plenty of numbers larger than infinity. Its just that they are also called infinity. And unlike in the case of finite number where x=x, 4=4 and pi=pi, infinity does not (necessarily) equal infinity. There are an infinite numbers in fact, both greater than and less than infinity, and wouldn\'t you know it - there all called infinity. So the last marble taken out is indeed the infiniti-eth one, but there are still an infinite number more marbles in the jar.\r\n\r\nMathematics is simply a toll the humans use to gain more concrete understanding of the world around them. Many times there have been very good mathematical models that adequately explain certain processes in our world but are later discovered to be incorrect. What do we do when this happens? We either discard the existing theory and replace it with one that doesn’t produce inconsistencies, or we adapt the theory so it includes the new situational data. We do not attempt to change the world to match our model, nor do we ignore that these inconsistencies exist. And sometimes when this happens, it takes the smartest people in the world millions of dollars and tens of years to do, but that doesn’t make the inconsistent method any more correct in the mean time. Aside from what has previously been stated, I simply cannot flaw your arguments. Unfortunately, that doesn’t take the inconsistency away.\r\n\r\nTo answer the question when there is an infinte number of marbles initially in the bag which are removed one at a time – this is in fact a different problem, and I’ll happily agree that after an infinite time you can remove all the marbles. Lets leave the semantics of removing an infinte number of items out of this, or else really this problem becomes a paradox as well (removing the last implies that there was never an infinite number to begin with...). The reason that these problems are different is direct to the point that infinity does not equal infinity. The way this problem has been remade, the origin of the infinity is different, and not linked to the number of marbles entering the jar, while originally it was quite dependant on the it.\r\n\r\nSo then, I request of you no further defences of the all marbles removed argument. If you wish to convince me, then find the hole in my reasoning.\r\n\r\nFinally, just to appease you, (which shall continue in the next post as this has become too long) I have come up with several possibilities for the inconsistency were experiencing. I’ll state right out that these may be in left field, these are just some thoughts so you can continue to think I’m not mathematically educated enough to disprove a result.',NULL,0);
INSERT INTO comment VALUES (7940,1341,775,'Cory Taylor','re: circles','2003-09-16 18:47:01',0,'Saying that you’re labeling marbles one to infinity (which would then include infinity, as marbles 1 to 5 include the marble 5) defies the definition of the term infinity.\r\n\r\nYou cannot simultaneously say hat you\'ve processed all the marbles and that there are still marbles being processed. If you finish, there is a last. If there is a last, there was never an infinity.\r\n\r\nThere are an infinite number of numbers greater than infinity.\r\n\r\nTwo sets with infinite size do not necessarily have the same size.\r\n\r\n:)',7939,0);
INSERT INTO comment VALUES (7941,1190,1626,'Gamer','re: additional solution - questionable','2003-09-16 19:06:15',0,'I don\'t think this would work because 0 would mean that the polygon wouldn\'t be a quadrilateral as it would only have 1 \"side\", and thus couldn\'t be a rectangle.',7905,0);
INSERT INTO comment VALUES (7942,500,3487,'Charlie','answer','2003-09-16 21:21:08',0,'ofcourse the answer is suicide because anything else you go to jail or get a ticket. but if it is a assisted suicide, the helper is charged with 2nd or 3rd degree murder.\r\n',NULL,0);
INSERT INTO comment VALUES (7943,568,3454,'Bart freeman','water absorbed cork','2003-09-16 23:27:43',0,'if i wanted to accomplish this i would take a cork that was a bit smaller than the bottle neck and soak it in water for a few days thus making it large enough to fit into the neck ,once the cork dries it would get smaller again and simply drop into the bottle enabling me to retrieve my coin ',NULL,0);
INSERT INTO comment VALUES (7944,1332,3372,'Sam','re: AHA!','2003-09-17 00:42:00',0,'Well done! I wasn\'t seeing this at all...',7937,0);
INSERT INTO comment VALUES (7945,1210,3372,'Sam','Hmmm','2003-09-17 02:08:06',0,'I\'m working on the assumption that the newspaper title must be the keyword to the code, and so when we plug in the correct title, all the headlines will (continue to) make sense. However, so far I\'m getting nowhere, and my little en/decryption program I had written isn\'t yet powerful enough to do more than and and subtract the letters...\r\nHmmm...',NULL,0);
INSERT INTO comment VALUES (7946,1332,3172,'SilverKnight','re: AHA!','2003-09-17 03:46:25',0,'(great job Happy!)\r\n\r\nOH MY GOSH!!! And yet another winner gets three TU... wow... I just KNOW you guys are doin\' this to yank my chain ;-)',7937,0);
INSERT INTO comment VALUES (7947,1341,3172,'SilverKnight','re(2): circles','2003-09-17 04:42:04',0,'Cory,\r\n\r\nLet me quote you again, with responses:\r\n\r\n\"Further, having stopped processing your marbles, there must have been a last iteration\"\r\nNo, your statement is a non-sequitor. You must differentiate between \"stopped processing\" and \"no longer processing\". The first implies there was a last. There is no last. And the flaw in your reasoning is that you assume there is/was.\r\n\r\n\"you\'ve made no attempts to ever dispute the reasoning I’ve come up with \"\r\nI certainly have, right here where I explain what I see as flaws in your logic...\r\nand so has Brian Wainscott right here where he points to things you have said and explains what he sees as flaws.\r\n\r\n\r\n\"I have not violated or misused the term infinity in my method.\"\r\nYes, you have. here you wrote that two particular infinities are not the same size (when they are), and here you refer, again, to the last element of a set of infinite elements.\r\nThis is somewhat analogous as saying \"a mile north of the north pole...\" In either case, the terminology applied in this situation simply implies a misunderstanding of the issue. North of the north pole has no meaning. The \"highest integer\" also has no meaning (which is essentially what you\'re saying).\r\n\r\n\r\n\"You have considered that infinity is a number that can be worked with. Not so. Infinity is not a number, it is an idea.\"\r\nNeither Brian, nor I, nor did Levik (in the solution) suggest that infinity is a real number (see definition of a real number). But you are correct in that it is an idea. What\'s more it is an idea that is useful in mathematics. And is generally dealt with by utilizing set theory and mappings--more about this later.\r\n\r\n\r\n\"There are an infinite numbers in fact, both greater than and less than infinity, and wouldn\'t you know it - there all called infinity.\"\r\nBut there are different cardinalities of infinities. Now, if you so choose not to learn about them... well fine.\r\n\r\n\r\n\"If you wish to convince me, then find the hole in my reasoning.\"\r\nI believe I have. You are misapplying terms (such as \"last marble\") and concepts (such as requiring an infinite time to deal with infinite marbles, when we don\'t need infinite time, we only need infinite iterations), and of course, if we are allowed to misapply concepts we can show anything we wish. If you wish to talk about infinities that apply the \"legal operations\" and proper terminology in discussing them.\r\n\r\n\r\n\"Saying that you’re labeling marbles one to infinity (which would then include infinity, as marbles 1 to 5 include the marble 5) defies the definition of the term infinity.\"\r\nBy \"labeling\" them, we attempt to simply the problem (wow... imagine that :-). I agree that Levik could have used a more rigourous statement than that, but I think it is clear that what is meant by the statement is: Each marble has a unique positive integer on it and every integer is represented. If this restatement pleases you, then please use this instead, and analyze the problem again.\r\n\r\n\r\n\"If you finish, there is a last. If there is a last, there was never an infinity. \"\r\nNo... another non-sequitor. Again, I agree that Levik could have used more rigorous language, but I think the meaning is clear.... the nth iteration took place 1/n minutes before the end of the minute. Period. There IS NO LAST. If you wish to ask about any given iteration, I can tell you when it occurred. And yes, of course, we could not really do this in practice.\r\n______________________\r\n\r\nAfter all this (and I think I have DEFINITELY addressed your major points), it seems clear that the only useful way to talk about infinity is to UNDERSTAND what infinity is.\r\n\r\nAs you point out... it is NOT a real number. So, let\'s STOP talking about the LAST marble.\r\n\r\nAs I\'ve pointed out it is generally dealt with by referring to elements. That is how we\'ve answered the problem, and set theory and operations is a natural way to describe that. You use inapplicable language and concepts. If you CHOOSE not to use applicable language to describe the situation, then what more can I say? Perhaps the best thing I can suggest is that you read up on the subject to better understand what the problem is asking.\r\n\r\n --- SK\r\n\r\nP.S. You\'re right... there ARE an infinite number of infinities greater than Aleph Null (the lowest infinity).\n\nEdited on September 17, 2003, 4:46 am',7940,0);
INSERT INTO comment VALUES (7948,1231,3495,'Andrew','A Solution','2003-09-17 07:57:46',0,'I think (not only because i am greek, but in general) that the name of the horse, is VOUKEFALAS.\r\nHe was the Great Alexanders\' horse.\r\nAm i correct???',NULL,0);
INSERT INTO comment VALUES (7949,1231,1220,'abc','','2003-09-17 08:40:43',0,'The horse\'s name was \"who had great fame\".',NULL,0);
INSERT INTO comment VALUES (7950,1231,1301,'Charlie','solution','2003-09-17 08:45:21',3,'Although proper capitalization would have given the answer away, to rephrase one of the sentences on the inscription, \r\n\r\nThe horse\'s name was What Do You Think.\r\n\r\n... and Who\'s on first, and What\'s on second.',NULL,0);
INSERT INTO comment VALUES (7951,1231,1183,'fwaff','re: solution','2003-09-17 09:50:56',0,'...and I Don\'t Know\'s on third\r\n\r\nClassic comedy at its finest!\r\n\r\nhttp://paul.merton.ox.ac.uk/filmtv/abbott-costello.html',7950,0);
INSERT INTO comment VALUES (7952,1160,3172,'SilverKnight','Solution','2003-09-17 12:21:05',3,'For the purposes of this argument, I am going to assume a crack has zero width, but is noticeable anyway.\r\n\r\nSince the solution repeats, we realize that the initial \'1\' and the \'1\' following each boing should be equidistant from the crack which caused the \'boing\'.\r\n\r\nSo, we see, that there are 7 slabs before we get back to the beginning of the cycle.\r\n\r\nWe can also count the steps between cycles, and we see there are 19 steps between each cycle.\r\n\r\n19 steps (x 35 inches/step) = 665 inches for a complete cycle\r\n\r\nAnd again, there are 7 slabs for each cycle, so 665 inches / 7 slabs = 95 inches/slab.\r\n\r\nSo, the cracks are 95 inches apart.\r\n\r\n\n\nEdited on September 17, 2003, 12:21 pm',NULL,0);
INSERT INTO comment VALUES (7953,1231,1220,'abc','re: solution','2003-09-17 13:25:38',0,'I see that you solution is correct, because the question mark is missing in the second sentence. \r\nIf there was one, my earlier solution would be valid.',7950,0);
INSERT INTO comment VALUES (7954,1210,1920,'Brian Smith','I think Im onto something ....','2003-09-17 14:13:36',1,'I think I finally figured out what the title means. Third Base could be a reference to base 3 notation. 26 letters plus a space can be easily represented with 27 3-digit base 3 numbers (000 to 222).',NULL,0);
INSERT INTO comment VALUES (7955,1160,1220,'abc','re: Solution','2003-09-17 14:31:17',0,'I think this sounds too easy. Do you account for the 9 inches of the sole? \r\nI agree that the person taking the steps must have stood on a crack, but I\'m not sure that you can say that the cracks are exactly 95 inches away from each other.\r\nCount the steps like this, with each crack in brackets:\r\n\r\n0 -> 35 -> 70 -> (95) 105 -> 140 -> 175 -> (190) 210 -> 245 -> 280 -> (285) 315 -> 350 -> (380) 385 -> 420 -> 455 -> (475) 490 -> 525 -> 560 -> (570) 595 -> 630 -> (665) 665\r\n\r\nWith a 9-inch-long sole it\'s possible that he stepped on the crack 380 inches away from the start. It\'s only 5 inches less than his 11th step took him. He could have touched it with the lower part of his sole.\r\n\r\nPerhaps I missed something, but I think we must be more precise.',7952,0);
INSERT INTO comment VALUES (7956,1160,3172,'SilverKnight','re(2): Solution','2003-09-17 15:21:00',3,'Actually, it *is* this easy. You bring up a good point, though.\r\n\r\nIf we assume there is a solution, then what I described earlier suffices. However, as we are trained to be skeptical (as you are), we should assume that perhaps what DJ is looking for is \"it\'s not possible!\".\r\n\r\nFair enough... no one suggested that we must start at 0 (as you did in the example). So, let\'s start at a \"convenient location\". After doing a little analysis, you may come up with beginning at 30... so... to continue with your description (where the cracks are described in parenthesis).\r\n30 -> 65 -> (95) 100 -> 135 -> 170 -> (190) 205 -> 240 -> 275 -> (285) 310 -> 345 -> (380) 380 -> 415 -> 450 -> (475) 485 -> 520 -> 555 -> (570) 590 -> 625 -> *BOING*\r\n\r\nNow, if you are troubled by the 380 (as you may be), then simply add 0.5 inches to every number not in parenthesis, and we have a clear solution.\r\n\r\n --- SK',7955,0);
INSERT INTO comment VALUES (7957,1160,3172,'SilverKnight','more thoughts (update to problem)','2003-09-17 15:38:01',0,'All.... I submit to you that this problem ISN\'T possible if the fellow wasn\'t quite so short in foot. If his foot is even an inch longer (at least 10 inches), then this problem is impossible.\r\n\r\nSince, I am proposing this, I will refrain from attempting to prove/show this. ;-)\r\n\r\nAnyone else wish to step up?\n\nEdited on September 17, 2003, 3:38 pm',7956,0);
INSERT INTO comment VALUES (7958,1160,2899,'Brian Wainscott','re: more thoughts (update to problem)','2003-09-17 18:10:32',3,'I\'ll take a run at it....\r\n\r\nClearly. SilverKnight\'s original analysis is correct. If in fact the pattern given by DJ repeats forever (long sidewalk there...can he ever reach the end? Maybe if he runs faster and faster....always covering twice the distance in the same time... Oh, sorry).\r\n\r\nAnyway, if it does repeat forever, then the distance between cracks must be EXACTLY 95 inches. Otherwise the discrepancy will accumulate, ruining the pattern.\r\n\r\nIgnore the size of the foot, and consider only where the heel lands. To simplify things, I\'m going to do everything modulo the slab distance (as if he were walking on a treadmill with a belt 95 inches long).\r\n\r\nStarting at 0 and going on for 19 steps, we have the heel landing at these distances:\r\n\r\n0 35 70 10 45 80 20 55 90 30 65 5 40 75 15 50 85 25 60\r\n\r\nSorting these, we arrive at these locations within a slab, where his heel will land:\r\n\r\n0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90\r\n\r\nNow, if his foot is > 5 inches long, he will obviously cover every point on the slab, and hence hit a crack, somewhere in his 19 steps. Since he completely covers the slab, in fact it does not matter WHERE he starts -- the above covering can be shifted by any amount, and it will still cover the slab.\r\n\r\nIn the original sequence, 60 is the last landing point for his heel. If we want him to miss the crack on the first 18 steps, we can offset his starting point by 30 inches, and the series becomes:\r\n\r\n30 65 5 40 75 15 50 85 25 60 0 35 70 10 45 80 20 55 90\r\n\r\nIf we consider 0 as a \"miss\", then in this case, with a foot >5 inches long, he will hit the crack on the 19th step. (Or offset by 30.00001 inches if you\'d rather).\r\n\r\nNow, to answer SilverKnight\'s question. Suppose his foot is >= 10 inches long? Going back to the original sequence, we find that he will hit every point on the slab within 18 steps. His last step, covering 60-70, was fully covered by steps 8 (55-65) and 11 (65-75).\r\n\r\nSo no matter where he starts, he covers the whole slab in less than 19 steps, which violates DJ\'s pattern.',7957,0);
INSERT INTO comment VALUES (7959,1210,1626,'Gamer','FOSSIL should be FOSSILL','2003-09-17 18:11:19',2,'Upon noticing that the number of letters isn\'t divisible by 3, I noticed I \"misspelled\" fossill. :D',NULL,0);
INSERT INTO comment VALUES (7960,1160,3172,'SilverKnight','re(2): more thoughts (update to problem)','2003-09-17 18:21:36',0,'Give the man a see-gar... and while you\'re there... I nominate him to get an automatic upgrade to apprentice!',7958,0);
INSERT INTO comment VALUES (7961,1231,3512,'Jeff','re(2): solution','2003-09-17 20:05:15',0,'Also, if proper grammar were to be taken into consideration, the \"do you think\" would be enclosed by 2 commas if the second sentence were a question and not a statement.',7953,0);
INSERT INTO comment VALUES (7962,1210,1575,'DJ','re: FOSSIL should be FOSSILL','2003-09-17 21:03:46',1,'Hmm.. I was thinking the other way, 26 letters plus a space is 27 characters, representing the full set of three-digit base 3 numbers (as Brian Smith noted). If the total number of letters has to be a multiple of three, then, perhaps it\'s the other way around?\r\n\r\nIf there were some mapping of the characters onto 0, 1, and 2, then YOU could be the first letter, _RU is the second letter, B_I is the third letter, and so on.\r\n\r\nAt least, that\'s what I think now, thanks to the inadvertent clue Gamer just dropped.',7959,0);
INSERT INTO comment VALUES (7963,1210,1575,'DJ','Solution, perhaps??','2003-09-17 21:25:59',3,'WARRITIRE\r\n\r\nFirst, here is the set of base-3 representations of the 26 letters and the _ (to represent a space or comma), following the usual convention of putting the space before the letters alphabetically:\r\n\r\n000 _001 A\r\n002 B\r\n010 C\r\n011 D\r\n012 E\r\n020 F\r\n021 G\r\n022 H\r\n100 I\r\n101 J\r\n102 K\r\n110 L\r\n111 M\r\n112 N\r\n120 O\r\n121 P\r\n122 Q\r\n200 R\r\n201 S\r\n202 T\r\n210 U\r\n211 V\r\n212 W\r\n220 X\r\n221 Y\r\n222 Z\r\n\r\nThen, using the same ordering, just let the first third go to 0, the middle third go to 1, and the third third go to 2:\r\n\r\n0: _ABCDEFGH\r\n1: IJKLMNOPQ\r\n2: RSTUVWXYZ\r\n\r\nThen, since Gamer alluded in the last \'hint\' that the total number of letters (and spaces/commas) must be a multiple of three, we can group them in threes, and the message can be translated into ternary:\r\n\r\nYOU _RU B_I T_S HEE P_D UEL ED_ WAR _ST EPS _AG ING _BO RED\r\n212 022 001 202 000 100 201 000 202 022 012 000 110 001 200\r\n\r\n_TO _NU T_P RAY ED_ FOS SIL L_W INS _A_ QUI T_A ND_ OIL _IT\r\n021 012 201 202 000 012 211 102 112 000 121 200 100 111 012\r\n\r\nAnd then, convert each ternary triplet into a character (by the first chart):\r\n\r\nWHAT_IS_THE_LARGEST_EVEN_PRIME\r\n\r\nWe find that this makes a coherent sentence! Translating each of the newspaper names by the same method (I\'ll do both steps at once this time) we get:\r\n\r\nWAR RIT IRE\r\n202 212 120\r\nT W O\r\n\r\nAT_ IT_ SPA RED\r\n020 120 210 200\r\nF O U R\r\n\r\nTAN K_C URE\r\n201 100 220\r\nS I X\r\n\r\nThe correct answer to the first question is TWO (the largest and only even prime), so the solution to the problem must be WARRITIRE.\n\nEdited on October 6, 2003, 12:15 pm',NULL,0);
INSERT INTO comment VALUES (7964,1160,3372,'Sam','Just a thought','2003-09-17 22:36:42',0,'Is it not possible that the slabs are 19 steps x 35 inches/step = 665 inches long? Unlikely I realise, and I know your answer is the one being looked for, but what is it that\'s keeping us to 7 slabs a cycle?',NULL,0);
INSERT INTO comment VALUES (7965,1341,775,'Cory Taylor','','2003-09-17 22:54:54',0,'ok, when Ive asked you to dispute my reasoning, you have misunderstood my request, and disputed my disputes, not my completely separate solution. I will make this easy. Your solution determines that there are no marbles in the jar. Fine.\r\n\r\nMy solution is as follows: At any point, the total number of marbles in the jar is equal to 9*n, where n is the problem defined repetition number. The only time that, assuming this is correct, that there are no marbles in the jar is before you\'ve started.\r\n\r\nDispute this, or agree that we\'ve proven that zero=infinity.\r\n\r\nAs I have attempted to explain before to you, and will try from yet another angle, this is not true. Math is a tool that we use to simplify things and thereby better understand them. All branches of math serve this purpose. One of the greatest things, and the most basic reason that I like math is that the process of working through a problem is irrelevant. If one makes no false assumptions, errors or ommisions, then then \"answer\" to a problem is unique (note that there are problems that some would say have multiple solutions as in \'what are the roots of an equation\', but in these cases the \"correct\" solution is only when you\'ve included all the correct answers.. but this is another discussion). There are plenty of calculus problems that have multiple {forms} to their solution, a simple example being that when one evaluation method produces 1 and a different evaluation method produces sin2 + cos2. I\'m certain you know these are in fact equal, and what this process has done is in fact proven that they are equal. I\'m afraid that that is exactly what we\'ve accomplished here - your method, allowing for the inconsistncies you\'re still trying to explain away concludes an answer of zero. My method, allowing for any inconsistencies it contains (of which I am not aware or we wouldn\'t still be debating this) produces an answer of infinity. If neither method is flawed then we\'ve found a rigid proof that 0=infinity. Hopefully I\'ll get no argument from you that this proof cannot be, so therefore, by deduction, one method must be incorrect.\r\n\r\nTo strengthen my approach, I can use another method. Proof by contradiction (in this case more appropriately disproof by contradiction, but we\'ll get to that some other time). Assume that at time 61 seconds there are no marbles in the jar. Clearly at time 40 seconds there are 9 marbles in the jar. As marbles are a discreet, not a continuos variable, at some point, to end with zero marbles then, the last marble must have been removed (we won\'t even discuss that there never was a last, or wait is that your point...). However, with each iteration, before a single marble is removed, ten are added, negating the possibility that the last is removed.\r\n\r\nAnd, I will restate that I do see why you\'re struggling here. All of the marbles, by the definition of the set they come from have been removed. Clear as can be. Yet, even clearer is that fact that we cannot have it both ways.',NULL,0);
INSERT INTO comment VALUES (7966,1160,3172,'SilverKnight','re: Just a thought','2003-09-17 23:25:13',0,'because he started counting at 1 repeatedly (7 times in fact, per cycle)',7964,0);
INSERT INTO comment VALUES (7967,1162,3197,'gabbo','mic','2003-09-17 23:48:28',0,'246 456\r\n',NULL,0);
INSERT INTO comment VALUES (7968,1231,1626,'Gamer','re(3): solution','2003-09-17 23:50:09',0,'Technically there aren\'t commas in the horses name... ;) If no commas tipped you off as well, then that\'s good too.',7961,0);
INSERT INTO comment VALUES (7969,1210,1626,'Gamer','re: Solution, perhaps??','2003-09-17 23:55:09',0,'Apparently it should be WARRITIRE... I don\'t know how that got past me though.',7963,0);
INSERT INTO comment VALUES (7970,1341,3172,'SilverKnight','re:','2003-09-18 00:08:17',0,'Okay... here is my rebuttal to your solution (both versions, as expressed in your last message).\r\n\r\nYou wrote:\r\nAt any point, the total number of marbles in the jar is equal to 9*n, where n is the problem defined repetition number.\r\nNo.... not any any point. Only after any finite number of iterations. And I wish to also stress... not at any point in time (only up to the end of the minute). At any given point up to the end of the minute, I can determine at which iteration we are at. Whereas AT or AFTER the minute is over, it is meaningless to ask which iteration we are at, and it is also meaningless to refer to the last iteration we performed, or the last marble we processed. And, don\'t forget, the problem asked for what happened at the end of the minute.\r\n\r\nSo, as I mentioned in my last message (and I quote), \"you are misapplying terms... and concepts...\"\r\n\r\nThe only inconsistency that you have shown is that your answer and our answer do not agree. But your solution is based on misapplication of concepts, so I\'m not surprised that the results are not equal.\r\n\r\nYou wrote:\r\n\", the last marble must have been removed (we won\'t even discuss that there never was a last, or wait is that your point...).\"\r\nYes, that is my point. You are applying a finite concept to an infinite set.',7965,0);
INSERT INTO comment VALUES (8398,622,1575,'DJ','re: Man\'s Best Friend','2003-10-06 12:19:51',0,'That would almost work, but when the clever dog and its owner are taking another dog, the other dog\'s owner is not around; and will attack the owner of the clever dog.',8075,0);
INSERT INTO comment VALUES (7971,1232,1183,'fwaff','Solution','2003-09-18 08:18:31',3,'From my limited understanding of probability calculations the way to approach this is by calculating the chance of failure. The only way to fail is by picking 4 consecutive yellows, so\r\n\r\nP(fail) = 0.9^4 = 0.6561\r\n\r\nwhich means that.\r\n\r\nP(win) = 1 - P(fail) = 0.3439\r\n\r\nThe cost of failing is $1, the benefit of winning is $2 ($3 winnings minus $1 to play).\r\n\r\nSo the net gain/loss is:\r\n\r\nGain/loss = P(win)x2 - P(fail)x1 = 0.3439x2 - 0.6561 = 0.0309\r\n\r\nThis is positive, which implies I should expect a net gain if I play for long enough.\r\n\r\nHowever, it\'s a game at a carnival therefore I would expect to make a net loss irrespective of what the probabilities may show! My guess is that either I\'ve missed the trick somewhere or my knowledge of probability calculations is even worse than I thought.',NULL,0);
INSERT INTO comment VALUES (7972,1341,775,'Cory Taylor','finally','2003-09-18 11:07:00',0,'Thank you for finally getting of your track. What I\'ve really been trying to do is show you that the math is irrelevant here - it is the interpretation of the problem itself from where the paradox is derived (note the problem is in the category \"paradoxes\", not \"math\"). The problem, boiled down, becomes simply a mathematical way of asking the same question as is asked in \"the guilty demon\". You have chosen to ignore the implications of such. I have chosen (by re-working the problem) to ignore different constraints. These different sets of assumptions are in fact both faulty. It is the problem itself that is faulty, and in fact there is no answer to this question.\r\n\r\nPS, I don\'t agree that I can\'t create an infinite sum by infinitly adding a constant term. This is a basic tenet of calculus.\r\n\r\nAlso on a side note, and I\'ll happily reiterate that I have no experience in set theory, so this might be a silly question (and its just out of curiousity, not as any form of attack on your math etc.), you mentioned that this aleph null is defined as the smallest infinity - what heppens to this if you take away one? Is this simply another definition that must be taken for granted or is there some reasoning involved?\r\n\r\nIt\'s been interesting.',NULL,0);
INSERT INTO comment VALUES (7973,1205,3520,'Norfolk-n-Good','Got it - but you gotta be fast!!!','2003-09-18 11:09:56',0,'As some of you have described already - you\'ve got to start a load of timers at once. Have one at double speed - 30 sec, when this runs out there are 30 seconds left, hit the next timer at doule speed - it will run for 15 sec, when it runs out - hit doule on the next etc etc etc etc -\r\nyou need to do this for 49 sequential clocks. When you hit double speed on the 49th it will run for 2.13 x10(-13) seconds - that was the easy bit- now we need to get 1.17 x10(16) of them to run consecutively. Does this sound a bit complex? Is it more logical than this? Do you want me to go on or am I barking up the wrong tree??',NULL,0);
INSERT INTO comment VALUES (7974,1232,1567,'Bryan','re: Solution','2003-09-18 11:24:18',0,'I would expect to lose money on this proposition, and you should, too.\r\n 10 100\r\n 100000 28133 71867 1419.564 242.7117\r\n 10 1000\r\n 1000 275 725 29941.54 343.24\r\n 1 100\r\n 100000 3288 96712 1425.148 24.40842\r\n
\r\n-----------\r\nRANDOMIZE TIMER\r\nres0 = 1\r\ngoal = 100\r\nFOR trial = 1 TO 100000\r\n res1 = res0\r\n tot = 0\r\n DO\r\n IF RND(1) < .3439 THEN\r\n res1 = res1 + 2\r\n ELSE\r\n res1 = res1 - 1\r\n END IF\r\n tot = tot + 1\r\n LOOP UNTIL res1 < 1 OR res1 >= goal\r\n IF res1 < 1 THEN\r\n loss = loss + 1:\r\n ltot = ltot + tot\r\n ELSE\r\n win = win + 1\r\n wtot = wtot + tot\r\n END IF\r\nNEXT trial\r\nPRINT res0, goal\r\nPRINT trial - 1, win, loss, wtot / win, ltot / loss\r\n\r\n\r\n',7995,0);
INSERT INTO comment VALUES (7987,1353,3172,'SilverKnight','solution?!?','2003-09-18 15:13:48',3,'Charlie, I kinda wish you asked a more objective (clear?) question. Only because it seems that you asked this only to get some discussion on the subject.\r\n\r\nSo, given that I think you are looking for some basic facts/discussion:\r\nThe apparent brightness of an object would be directly related to the intrinsic luminosity of an object and inversely related to the square of the distance between the object and the observer.\r\n\r\nF = L / (4ð x d²)\r\n\r\nWhere:\r\nF is the apparent brightness\r\nL is the intrinsic Luminosity, and\r\nd is the distance between the object and the observer\r\n\r\nIf we say that there are 90 years * 365.25 days/year * 24 hours/day * 60 minute/hour, then we see that the star in question is ~47.3 million light-minutes away from us.\r\n\r\nThis is ~5.917 million times further from us than the sun is....\r\n\r\nTherefore, it would by ~(5.917 million)² times dimmer than our sun (from our perspective).\r\n\r\nI hope that addresses your question.\r\n\r\n--- SK\r\n\n\nEdited on September 18, 2003, 3:15 pm',NULL,0);
INSERT INTO comment VALUES (7988,1353,2899,'Brian Wainscott','Correct me if I\'m wrong','2003-09-18 15:14:02',3,'I\'m not an astronomer, but this is what I\'ve computed, given the data in the problem:\r\n\r\n90 light years = 90 x 365.25 x 24 x 60 = 47336400 light seconds.\r\n\r\nThis is 5917050 times the distance from the earth to the sun.\r\n\r\nBrightness goes down as the square of distance, so this star is dimmer than the\r\nsun by a factor of 3.50x10^13. Logarithms give this as 100^6.772\r\n\r\nSo if 5 orders of magnitude represents a factor of 100, 6.772*5=33.86 would be afactor of 100^6.772. Since the sun is given as magnitude -27, this star would have a magnitude of about 6.86, or just below the limit of what the naked eye can see.',NULL,0);
INSERT INTO comment VALUES (7989,1353,3172,'SilverKnight','re: Correct me if I\'m wrong','2003-09-18 15:19:04',0,'Brian, you wrote:\r\n90 light years = 90 x 365.25 x 24 x 60 = 47336400 light seconds. This is 5917050 times the distance from the earth to the sun.\r\n\r\nI think you missed a 60 in there (to represent 60 minutes/hour or 60 seconds/minute)... since you seem to be looking for light seconds. Either way, I suppose the result worked out :-)\r\n\r\n --- SK',7988,0);
INSERT INTO comment VALUES (7990,1353,2899,'Brian Wainscott','re(2): Correct me if I\'m wrong','2003-09-18 15:20:43',0,'My mistake -- the calculations are what I intended, but I should have said \"light minutes\"',7989,0);
INSERT INTO comment VALUES (7991,1353,1301,'Charlie','re: solution?!?','2003-09-18 15:26:44',0,'As Brian Wainscott proceeded, the idea was to use the magnitude system to show that the star is not quite bright enough to be seen with the unaided eye, or if the numbers turned out differently, how bright relative to other nighttime stars and planets.',7987,0);
INSERT INTO comment VALUES (7992,1353,3172,'SilverKnight','re(2): solution?!?','2003-09-18 15:28:07',0,'ahhhh... gotcha... kudos to Brian!',7991,0);
INSERT INTO comment VALUES (7993,1205,1301,'Charlie','re(2): Got it - but you gotta be fast!!!','2003-09-18 16:14:02',0,'I\'d call it an infinite non-repeating binary expansion, since it\'s the binary numbering system.',7982,0);
INSERT INTO comment VALUES (7994,1231,3512,'Jeff','re(2): WRONG, Gamer !!!!!!!!','2003-09-18 16:15:18',0,'word',7985,0);
INSERT INTO comment VALUES (7995,1232,2899,'Brian Wainscott','re(4): Solution','2003-09-18 16:49:37',4,'Uh, Charlie, I think you got an inequality backwards. Shouldn\'t line 7 of your program read:\r\n\r\nIF RND(1) > .3439\r\n\r\n??\r\n\r\nSince the chance of losing the first round is 65.61%, there is no way that, starting with $1, you will win up to $100 almost 65% of the time.',7986,0);
INSERT INTO comment VALUES (7998,1151,3529,'Senthil Kumar','Solution','2003-09-18 17:49:29',3,'1. Kevin-Farell-Puzzle\r\n2. Monica-Baker-Crayons\r\n3. Holly-Forbes-Blocks\r\n4. Darren-Lorenz-Teddy Bear\r\n5. Mark-Collins-Fire Engine\r\n6. Janet-McKenna-Picture Book',NULL,0);
INSERT INTO comment VALUES (7999,1231,1626,'Gamer','re: WRONG, Gamer !!!!!!!!','2003-09-18 17:59:40',0,'I agree with Brian Smith that you are taking this too seriously, but I can disprove you this way... (remember he started it, and I don\'t have the God existance forum to unload my debating on.)\r\n\r\nI believe much of the Bible was written a long time ago, and I don\'t think it was originally written in English. And as for your Why anyone would go out in this weather is beyond me... is INTERPRETED as a question, but it really isn\'t one. The subject (Why anyone would go out in this weather) uses a verb (is) for (the horse\'s name).\r\n\r\nAlso, notice that the question you are answering is NOT what do you think... because that is only an inscription... The real question is What was it?\r\n\r\nFinally, in the distant planet of Horsople which I alone have contact to, there is a horse named \"What do you think\" and he isn\'t too happy for you to say that he doesn\'t exist.',7979,0);
INSERT INTO comment VALUES (8000,1232,3529,'Senthil Kumar','Solution','2003-09-18 18:37:10',3,'I would expect to make a net profit, if I play long enough.\r\n\r\nProbabilty of Pulling a Red ball = 1/10\r\ni.e if you play 10 times you might win once.\r\nSo if you play 20 times, you will have the chance of winning twice (win $6). But you will have to spend only $5 for 20 chances. So the net profit is $1.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (8001,1232,2899,'Brian Wainscott','re: Solution','2003-09-18 19:00:20',0,'Senthil,\r\n\r\nYou are misunderstanding the problem. When you pay $1, you get to try 4 times to pull out the red ball. But if you pull it out on the first try, you get $3 and the game is over. You don\'t get 3 more tries, you are done.\r\n\r\nYou analysis is equivalent to saying you pay 25 cents for each chance to pull out the red ball, and each time you pull it out you win $3. This is not the same thing. In this case, indeed, your expected winnings would be 5 cents per draw. But in the game as stated (1 game = 4 draws, you win $3 if any of the draws gives you a red ball), the expected winnings are about 3 cents per game, as fwaff showed. This is much lower than your 20 cents per four draws.',8000,0);
INSERT INTO comment VALUES (8002,1232,1220,'abc','re: Solution','2003-09-18 19:02:40',0,'No, the probability of winning a game can\'t be 1/10 because you have 4 tries. Better calculate the chance of failure ((9/10)^4) and substract it from 1 like in the previous solutions. \r\n\r\nEdit: You are too fast for me, Brian! ;)\n\nEdited on September 18, 2003, 7:03 pm',8000,0);
INSERT INTO comment VALUES (8003,1205,2899,'Brian Wainscott','re(3): Closer and closer','2003-09-18 19:23:53',0,'Agreed. I\'m just wondering if anyone can come up with a way to get N digits in F(N) time, where F(N) is bounded as N goes to infinity. Depending on the method, I\'m not sure that it even makes sense to talk about convergence. But that is about the best I could hope for. I think your answer is as good as it is going to get',7984,0);
INSERT INTO comment VALUES (8004,1231,3196,'Dan','re(2): WRONG, Gamer !!!!!!!!','2003-09-18 19:25:02',0,'Gamer wrote: \"Finally, in the distant planet of Horsople which I alone have contact to, there is a horse named \'What do you think\' and he isn\'t too happy for you to say that he doesn\'t exist.\" \r\n \r\nHahahahahahaha.... Good one, Gamer !!!! I stand corrected !! You are a creative GENIUS !! \r\n',7999,0);
INSERT INTO comment VALUES (8005,1232,3372,'Sam','re: Corrected Simulation Results','2003-09-18 19:51:03',0,'\"And when starting out with a measly $1, trying to leave with $100, she won not much more than 3% of the time (but of course gaining $100) and took an average of about 24 plays for a loss or 1400 plays for a win.\"\r\n\r\nThis is my point, and is why I would play. If there was a lottery that cost $1 to play, paid $100 and paid out 3% of the time, most rational people would play it. In the long run, it\'s quite obvious, as people have mentioned: If I play this lottery 100 times, I would expect to have paid $100 and won $300.\r\nIf I had a lottery that paid $1000000 for your buck, and paid out 33% of the time, would you play it? In the short term you might lose, but you should play it even if you had a single buck, because your expected returns are higher than your costs. In the carnival example, the expected returns are higher than the cost, so one should play (and the house is stupid because it is losing money).',7997,0);
INSERT INTO comment VALUES (8006,1232,3454,'Bart freeman','solution','2003-09-18 20:06:22',0,'you have a 90%chance of losing ,although some might think otherwise , you can only consider the present draw for if you pick the proper ball on that there is no need praw again , since you only have a 10%on your current draw the chances of losing is 90% ',NULL,0);
INSERT INTO comment VALUES (8007,622,3196,'Dan','It\'s a dog\'s life down on the riverbank....','2003-09-18 20:08:52',0,'You wrote \"Unfortunately, the dogs were edgy and could not be near another PERSON (not even momentarily) unless its owner was present.\" So it is possible for a dog to be near another DOG without its owner being present. A ha !!!!! Your little oversight allows an easy solution.....\r\n \r\nLet\'s call the men Melvin, Ichabod, Lucius, Mortimer, and Murray, who own, respectively, the dogs Rover, Fido, King, RinTinTin and Spot. Spot is the canine boat-operating genius. Murray owns Spot. \r\n \r\n(1) Spot sails across with Rover and Fido. On the other shore, Spot carefully leads Rover and Fido to separate areas, isolated from each other. Then Spot returns.\r\n(2) Spot sails across with King and RinTinTin. He then leads King and RinTinTin to separate areas, isolated from each other and from Rover and Fido. Then Spot returns.\r\n(3) Spot sails across with Melvin (the owner of Rover) and Murray. Melvin gets out and joins Rover. Spot and Murray sail back to the other shore.\r\n(4) Spot sails across with Ichabod (the owner of Fido) and Murray. Ichabod gets out and joins Fido. Spot and Murray sail back to the other shore.\r\n(5) Spot sails across with Lucius (the owner of King) and Murray. Lucius gets out and joins King. Spot and Murray sail back to the other shore.\r\n(6) Spot sails across with Mortimer (the owner of RinTinTin) and Murray. Mortimer gets out and joins RinTinTin. Spot and Murray also get out.\r\n(7) The five men and five dogs now join together on the opposite shore.\r\nQED\r\n\n\nEdited on September 18, 2003, 8:23 pm',NULL,0);
INSERT INTO comment VALUES (8008,297,3532,'Claire','re(2): Solution','2003-09-18 23:15:53',0,'actually, it says 5 queens and 3 pawns. not vice versa.',7559,0);
INSERT INTO comment VALUES (8009,1341,775,'Cory Taylor','whee','2003-09-19 02:36:07',0,'Sat here many hours debating whether to continue this thread.\r\n\r\nEven went to the point of conferring with peers who\'ve expertise in this subject (set theory).\r\n\r\nNone (well, neither) have found error with the method I\'ve produced (sum of nines).\r\n\r\nOne faults the question as being imprecise enough to allow the interpretational deviations experienced, while the other outright denies the analysis of a zero result as being wrong by being incomplete and defiant to the particulars of the situation.\r\n\r\nI don\'t mean to create any sort of stir here, nor do I do this as a result of mathematical ego as I have none (I work in road construction). I am just being thorough (as an engineer should be).\r\n\r\nI apologize that I simply cannot accept your statement that my method is un-allowed without a plausible explanation (and both experts I\'ve consulted have agreed with my interpretation - and they\'ve both seen the question originally - not any adaptation I\'ve made).\r\n\r\nI will concede that the second aforementioned expert, while certain the math was flawed, couldn\'t specifically flaw your argument any better than I (he mentioned that there are numbers, and therefore marbles, greater than the infinity referred to in the \"removal\" process) he was going to double check his theories to be sure. But as a basis, he was able to confirm, in a way, that the process is identical to increasing the set size by nine infinitely (his particular method was to graph the set size versus the repetition number, which of course results in a straight line not passing through zero any point but the origin (and you\'d better not tell me that the x-axis has a finite boundary)).\r\n\r\nI will apologize for my lack of future response. For a time, I considered that this problem was not worth the effort it apparently required to convince of you of the error, and thereby wasted possibly one or two returns. As it happens, I am set to return to work tomorrow (I\'ve just finished 5 days off) and won\'t return to internet capability for 4 (possibly, but more likely 2) weeks (check my forum posts or my personal description to verify this). I will say though, that I have great confidence in my experts, and its certainly going to take one heck-uv-an argument from you to refute them. By all means feel free to email me (though put \"to cory\" or some such in the subject or it\'ll just get deleted), or continue on as you see fit, but I\'m now gone till seasons end (typically mid-October).\r\n\r\nAnd I now wonder what monster I\'ve created.\r\n\r\n\r\nEdited on September 19, 2003, 2:37 am\n\nEdited on September 19, 2003, 2:39 am',NULL,0);
INSERT INTO comment VALUES (8010,1341,3172,'SilverKnight','re: whee','2003-09-19 03:06:10',0,'You\'ve basically just said,\r\n\"na n\'nah n\'naaah naaahhh...\r\nI don\'t believe you, and I\'m not listening to you anymore.... and I\'m not gonna talk to you anymore about this.\"\r\n\r\nvery amusing\r\n\r\n:-)\r\n\r\nP.S. I have two experts buddies on the subject too... and they say that the answers given in the solution are correct ;-) (If only it were that easy in a court of law.)',8009,0);
INSERT INTO comment VALUES (8011,272,3196,'Dan','This one was so easy !!!!','2003-09-19 03:34:41',0,'J + G = 14\r\n10J + G = 10G + J + 36\r\nJ=9, G=5\r\nI was so shocked at the brazen simplicity of this \"brain\" teaser, that I had heart palpitations, and was forced to take digitalis !!!! ',NULL,0);
INSERT INTO comment VALUES (8012,1232,3196,'Dan','This one took balls !!!!!!','2003-09-19 03:47:41',0,'Another tricky one from Gamer !! If he had asked \"Assuming the person running the game is telling the truth, and the balls only differ in color, WOULD you make a net profit or a net loss on this game?\" then the correct answer is that you would make a slight profit. It stands to reason. You would expect to pull out a red ball every 10th time. And since it only costs a dollar to try 4 times, you would only spend 5 dollars to try 20 times. And in 20 attempts, you would probably draw the red ball twice - you would win 6 dollars. BUT....that is NOT the question that the devious and subtle Gamer asked !! He asked \"would you EXPECT to make a net profit or a net loss on this game?\" The answer is that you would EXPECT (wrongly) to make a net loss, since the ever fallible human intuition invariably comes to the wrong conclusion about this, and thinks that you would lose money. Why do you think Gamer deliberately placed this game in a CARNIVAL ????? As I said, IT TOOK REAL BALLS TO PUT THIS RIDDLE OUT HERE !!!!!!!!!!!! \r\n\r\nEdited on September 19, 2003, 3:49 am\r\n\r\nEdited on September 19, 2003, 3:49 am\r\n\r\nEdited on September 19, 2003, 3:51 am\r\n\r\nEdited on September 19, 2003, 3:57 am\n\nEdited on September 19, 2003, 4:02 am',NULL,0);
INSERT INTO comment VALUES (8013,338,3196,'Dan','Pretty obvious','2003-09-19 04:07:44',0,'The five airy creatures are the five vowels.',NULL,0);
INSERT INTO comment VALUES (8014,1012,3196,'Dan','I am this man !!!!!','2003-09-19 04:18:35',3,'I am this man !! I was born \"before\" my father (that is, in front of my father in the delivery room, as in \"the play was performed before an English audience.\") I \"killed\" my mother, by telling her a funny joke!! (One of the meanings of \"kill\" is to cause to convulse with laughter, as in \"oh, these jokes are killing me !!\") And I \"married\" my sister (that is, as a lay minister, I officiated at her wedding, as in \"the bride and grrom were married by Reverend Smith\"). QED ',NULL,0);
INSERT INTO comment VALUES (8015,946,3536,'rola','escape cleverly','2003-09-19 05:53:09',0,'since every person in such situation must be allowed a final wish before being sentenced to death, yours in this case would be that the authorities execut not what\'s written on the paper u pick, but the opposite.. so if the paper u pick is the one written on it \"death\", u ll be set free, and if it\'s the one with \"life\" on it, they can carry on with the death sentence.. but u are smart and u know that both papers are \"death\" ones.. so u are saved anyway ! nice isn\'t it?',NULL,0);
INSERT INTO comment VALUES (8016,1162,3541,'Graham Starling','Solution','2003-09-19 10:32:47',3,'The largest numbers shown on three sides of any die would be 4, 5 and 6 giving a maximum number of 15 or 30 for the 2 dice.\r\nPerfect cubes less than or equal to 30 are 1, 8 and 27. Since it\'s impossible to have 3 faces of two dice adding up to less than 12, the perfect cube has to be 27.\r\nIf we\'re assuming these are normal dice, then no two faces will be the same, and opposite faces will add up to 7 (again we\'re assuming that we\'re in an ordinary universe and we no 2 of visible faces are opposites).\r\n27 is only 3 less than the maximum, so we get to take away 3 pips somewhere. The only way this can work is if we set one die to show 6, 5 and 4 and the other to show 6, 4 and 2.\r\n\r\nThere are a number of solutions already posted for this question. Why isn\'t it marked as solved??',NULL,0);
INSERT INTO comment VALUES (8017,1352,1220,'abc','solution?','2003-09-19 10:51:50',3,'You say that both the title and the category are clues.\r\n\r\nThe title \"not so triggy\" makes me think that the \'cos\' in question is not related to trigonometry. \r\nI suppose that \'cos\' in this case refers to the slang abbreviation of \'because\'. It\'s unique because there\'s no other word that transforms the \'au\' into an \'o\'.\r\n\r\nI fear that\'s not twisted enough, is it?',NULL,0);
INSERT INTO comment VALUES (8018,1232,1220,'abc','re: solution','2003-09-19 11:03:07',0,'No, that\'s not correct. The chance of failure is 90% in the first try, but not for the whole game. \r\nThe probability of an event is calculated by the summation of ALL possibilities that lead to a success. Draw a tree graph and you will see four different branches. \r\nYour method would only account for the first draw, in other words the first branch of that tree. ',8006,0);
INSERT INTO comment VALUES (8019,1162,1220,'abc','re: Solution','2003-09-19 11:09:28',0,'It takes a while for a problem to be officially solved. At least a week, I think. \r\nIf you see that someone has posted the solution to a problem, don\'t post it again if your solution is not different from the other one or you present it in a different way. It\'s just a waste of time.',8016,0);
INSERT INTO comment VALUES (8020,1017,3545,'joshua','proving dj wrong','2003-09-19 12:21:03',0,'that was a good try i almost believe it at first but then i started working it ok the factors of 1 is 1 so 1+1=2 the factors of 2 are 1 or 2 so 2+1=3 and the factors of three are 1 or 3 and since this number is also prime we will use 1 and look we ran into a problem 3+1 doesnt =5 it was a good try had me thinking thanks for the challange i think i almost have the correct way figured out so when i do i will post it for everyone to see. have a great day everyone\r\n\r\nJoshua',NULL,0);
INSERT INTO comment VALUES (8021,1352,3430,'pat','math/lang','2003-09-19 12:25:39',0,'perhaps math and language are foreign',NULL,0);
INSERT INTO comment VALUES (8022,1210,3430,'pat','anagrams','2003-09-19 12:27:45',0,'tougher anagrams than usual?',NULL,0);
INSERT INTO comment VALUES (8023,1232,3546,'RoyCook','An Ambiguity','2003-09-19 13:20:22',0,'Much of the reasoning given previously is correct- given a single play of the game, which involves UP TO 4 draws, you have a 34.39 percent chance of winning 2 dollars (3 dollar prize minus 1 dollar entry fee) and a 65.61 percent chance of losing 1 dollar. What this means for the problem, however, depends on how we disambiguate the wording of the question. On the one hand, if the question is meant to be read as:\r\n\r\n[1] On a single play of the game (i.e. up to 4 draws), would you expect to make a profit?\r\n\r\nthen the answer is of course no, since the chances of winning (regardless of how much you might win or lose) is quite a bit less than 50 percent. However, if the question is meant to be read as:\r\n\r\n[2] At the limit, i.e. on average, should one expect to make a profit from this game if one plays long enough?\r\n\r\nor even better:\r\n\r\n[3] Should the carnival, in setting up this game, expect to report a loss regarding it on their tax forms at the end of the year (assuming no tax fraud)? \r\n\r\nthen the answer is yes, since on average the game will pay out more than it collects (the 2 dollar prize being won 34.39 percent of the time outweighing the 1 dollar fee being taken 65.61 percent of the time, for reasons cited by others earlier).',NULL,0);
INSERT INTO comment VALUES (8024,1163,3172,'SilverKnight','SOLUTION','2003-09-19 13:22:34',3,'in DOS or Windows, create a file (you can use notepad) called test.bat\r\n\r\nThe contents of the file should be\r\ntype test.bat\r\n\r\nthen go to a command prompt and go to the current directory (containing the file) and type \'test\'\r\n\r\nIt should echo to the screen \'type test.bat\'\r\n\r\n--- SK',NULL,0);
INSERT INTO comment VALUES (8025,1089,3546,'RoyCook','re: Solution following Jason\'s','2003-09-19 13:44:28',3,'The geometric analogy in Ferran\'s solution doesn\'t quite do it (since it does not cover negative cases), but his computation allows another quick means. If (n+1)^3 + 8 must be a perfect cube, then this means we require for a solution two perfect cubes that differ by 8. There are only two possibilities: -8 and 0, and 0 and 8. So (n+1)^3 must equal either -8 or 0, so n must equal either -2 or 0. In the first case (-2), n^2 + 3 = 7 is not a perfect cube, in the second case (0), neither n + 3 = 3 nor n^2 + 3 = 3 is a perfect cube.',7286,0);
INSERT INTO comment VALUES (8026,1163,3172,'SilverKnight','SOLUTION (2) - Not Mine','2003-09-19 13:45:13',3,'main(){char*a=\"main(){char*a=%c%s%c;printf(a,34,a,34);}\";printf(a,34,a,34);}\r\n\r\nThis is pretty cute too... and probably more to the spirit of what DJ is looking for.\r\n(Although scripting languages that can easily deal with the file containing the source make the problem trivial, as my previous solution demonstrates).\r\n\r\nI found this solution at:\r\nhttp://www.its.caltech.edu/~boozer/symbols/programs.html\r\n\r\n--- SK',NULL,0);
INSERT INTO comment VALUES (8027,1160,3547,'brandi','solution(possibly)','2003-09-19 13:51:02',0,'2,835inches',NULL,0);
INSERT INTO comment VALUES (8028,1163,1920,'Brian Smith','On a C64 ....','2003-09-19 13:58:29',0,'I used to have a Commodore 64 with BASIC as its core language. The command LIST would print out the full program to the screen. LIST could be embedded in a program, so my self-printing program (to screen):\r\n\r\n10 LIST',NULL,0);
INSERT INTO comment VALUES (8029,1163,3172,'SilverKnight','re: On a C64 ....','2003-09-19 14:07:07',0,'Hey I had a TRS-80 COCO model 3....\r\n\r\nThat woulda worked there too! heheh... brings back memories. :-)',8028,0);
INSERT INTO comment VALUES (8030,621,3546,'RoyCook','Silly error','2003-09-19 14:15:54',0,'Just thought I would share with everyone so that if you do the same you won\'t spend a stupid amount of time wondering what went wrong, like I did - I worked this one out in a way similar to everyone else and got 100(√2 - 1)^2 instead of (100(√2 - 1))/(√2+1). It took me a half hour to realise that these are the same!',NULL,0);
INSERT INTO comment VALUES (8031,1163,1220,'abc','solution','2003-09-19 15:16:02',0,'main(){cout << \"itself\";}\r\n\r\nI\'m sorry.',NULL,0);
INSERT INTO comment VALUES (8032,1160,1220,'abc','re: solution(possibly)','2003-09-19 15:22:18',0,'???\r\nCan you make 3 steps which go that far?\r\nOr anyone else?',8027,0);
INSERT INTO comment VALUES (8033,1232,3454,'Bart freeman','re(2): solution','2003-09-19 15:45:18',0,'abc i believe you are mistaken becasue when you reach in the second time again you have a 90% failure rate and the same is ture of the third draw ',8018,0);
INSERT INTO comment VALUES (8034,1232,1626,'Gamer','re(3): solution','2003-09-19 17:38:20',0,'The whole idea is that if you get a red ball at any time in those first 4 draws you can count it as success for that trial, where as your method only takes one drawing into consideration, so if you get the ball wrong the first time you don\'t have 3 more draws to do; the trial has ended in failure.',8033,0);
INSERT INTO comment VALUES (8035,1352,122,'Happy','','2003-09-19 17:38:25',0,'Umm... it\'s the only 3-letter sequence using c, o, and s, in that exact order. How\'s THAT for twisted logic?\n\nEdited on September 19, 2003, 5:40 pm',NULL,0);
INSERT INTO comment VALUES (8036,1163,3196,'Dan','Too easy !!','2003-09-19 18:37:36',0,'\"Write a program that prints itself\"\r\n\r\nI took me less than a minute to do this in COBOL. The operative commands in my program were:\r\n \r\nMOVE \"ITSELF\" TO PRINTLINE\r\nPUT PRINTLINE',NULL,0);
INSERT INTO comment VALUES (8037,1163,3196,'Dan','re: solution','2003-09-19 18:39:21',0,'Damn !!!! You beat me to it !!!!!!!!!!!!!!',8031,0);
INSERT INTO comment VALUES (8038,865,3196,'Dan','I won\'t take NO for an answer !!!!!','2003-09-19 19:00:46',0,'Well, the answer to this chesnut finally dawned on me. One of the meanings of \"No\" is \"classic Japanese dance-drama having a heroic theme, a chorus, and highly stylized action, costuming, and scenery.\" So of course NO is not the correct answer to this question, since one cannot solve a riddle, or any other problem in life, through such idle escapism as attending a Japanese NO play. No, no, no !!!!! \r\n ',NULL,0);
INSERT INTO comment VALUES (8039,513,3196,'Dan','Huh ?????','2003-09-19 19:10:22',0,'\"We know that the First statement is False and so now can we conclude that the Second statement is True ?\" \r\n \r\nNo we cannot. They are not the same sentence. The first statement contains five words, and the second statement contains seven words; and because it really does contain seven words, it is false. I fail to see what the paradox is here.\r\n\r\n\n\nEdited on September 19, 2003, 7:11 pm',NULL,0);
INSERT INTO comment VALUES (8040,1163,1626,'Gamer','re(2): solution','2003-09-19 19:17:27',0,'You knwo what the problem intended, and DJ\'s use of my idea \"print twice\" (which he used for clarification purposes to make this problem better), shows you exactly what he means if you wanted to find the less mature way... :)\r\n\r\nI would imagine abc was submitting that solution as a joke, but it doesn\'t seem like you are doing the same.',8037,0);
INSERT INTO comment VALUES (8041,826,3196,'Dan','Calling the k9 corps !!!!!!!','2003-09-19 19:20:11',0,'\"k dogs\" ???? hahaha.... This one is SO EASY to shoot down !!!!! You wrote \"Now consider a subroup of A of k dogs, with x in the subgroup.\" You meant a PROPER SUBGROUP of k, and if k=1, there is no PROPER SUBGROUP of k. So the logical leap from k dogs to k+1 dogs ONLY WORKS if k is GREATER than 1. It\'s obvious that if we could somehow prove that every group of 2 dogs is the same color, then we could prove that ALL dogs are the same color. But we cannot. All we can prove is that every group of 1 dogs is the same color, and we are hounded by the dogged impossibility of going logically from 1 dog to a pack of dogs. I must say that this particular paradox was definitely a horse of a different color !!!! ',NULL,0);
INSERT INTO comment VALUES (8042,1163,1301,'Charlie','re: SOLUTION (2) - Not Mine -- Basic version','2003-09-19 21:42:00',0,'Translated into QuickBasic from C that becomes:\r\na$ = \"a$ = &&&: PRINT USING a$; CHR$(34); a$; CHR$(34):\": PRINT USING a$; CHR$(34); a$; CHR$(34):\r\nwhich does print out\r\na$ = \"a$ = &&&: PRINT USING a$; CHR$(34); a$; CHR$(34):\": PRINT USING a$; CHR$(34); a$; CHR$(34):\r\n\r\n\n\nEdited on September 19, 2003, 9:46 pm',8026,0);
INSERT INTO comment VALUES (8043,1352,1301,'Charlie','re:','2003-09-19 21:51:37',0,'That\'s what I was going to say. Since there\'s no such thing as degrees of uniqueness, every word is unique.',8035,0);
INSERT INTO comment VALUES (8044,1352,3512,'Jeff','solution?','2003-09-20 00:08:36',0,'Why is it unique?....Cos it just is.',NULL,0);
INSERT INTO comment VALUES (8045,1163,2682,'exoticorn','Ruby solution','2003-09-20 05:35:40',3,'www.ruby-lang.org\r\n\r\ns=\"s=%s;printf s, s.dump\";printf s, s.dump',NULL,0);
INSERT INTO comment VALUES (8046,695,3196,'Dan','Shuffle off to Buffalo','2003-09-20 07:17:41',0,'There are 52! (52*51*50*49*48*...*3*2*1) ways for the cards of any deck of 52 cards to be ordered. The \"shuffling\" was a red herring. There is 1 out of 52! chances that the second deck will be in the same order as the first deck, regardless of whether any shuffling has occurred. ',NULL,0);
INSERT INTO comment VALUES (8047,1352,3196,'Dan','I love Cos !!!!!','2003-09-20 07:22:41',0,'Cos is unique for two very good reasons: first, his concern and interest in the welfare of kids in very praiseworthy; and second, his television show \"The Cosby Show\", broke many racial barriers and stereotypes. So Bill Cosby (aka Cos) is one of the few truly unique performers. ',NULL,0);
INSERT INTO comment VALUES (8048,1359,1301,'Charlie','solution','2003-09-20 10:53:44',3,'By the transition from (3) to (4) either 7 or 0 is present while 6 or 9 is absent.\r\n\r\nFrom (1) to (4), 3 or 2 is present.\r\n\r\nFrom (1) and (2), either 0 or 9 is present, but not both (to make the fourth present digit, from the 3 accounted for in these two lines). But from the transition from (3) to (4) it must be the 0 that\'s present, not the 9.\r\n\r\nIf 0 and 7 were both present then neither 1 nor 4 would be (by (3)), and so the absence of 9 would mean that 6 would have to be present to satisfy (4). But then with 6 and 7 both present, (2) would not be correct. Therefore, since 0 is present, 7 is absent.\r\n\r\nThen, by (3) either 1 or 4 is present.\r\n\r\nBy (4), then, 6 is absent.\r\n\r\nThen, by (2), either 5 or 8 is present but not both.\r\n\r\nSummary so far:\r\n0 is present\r\n2 or 3 is present\r\n5 or 8 is present\r\n1 or 4 is present\r\n\r\nAs this accounts for all four, all the \"or\"s are exclusive.\r\n\r\nEither the 1 occupies the 3rd position or the 4 occupies the fourth, by the X in (4).\r\n\r\nSo in (3) neither of these can be the one in the correct position, so it must be the 0 in the 4th position.\r\n\r\nThat means the 4 can\'t be in the 4th position, so it must be the 1 in the 3rd position that\'s correct in (4).\r\n\r\nThen, by (1), the 1 is the one that\'s in the incorrect position, and since the 2 cannot be in the 3rd position, already assigned to 1, it must be the 3 in the 2nd position that\'s correct.\r\n\r\nThe only remaining position to be filled is the 1st. But (2) has 5 in the first position and the only correct number there is in the wrong position, so it must be the 8 that belongs in the 1st position.\r\n\r\nSo in sum the answer becomes:\r\n\r\n8310\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (8049,1359,3558,'Tristan','Solution','2003-09-20 12:04:59',3,'This is a messy proof, but it works in the end.\r\n\r\nSince guess 3 has no correct numbers in the right places and guess 4 has no correct numbers in the wrong places, the folowing digits can\'t have the following numbers:\r\n1: 9,1,4,5\r\n2:6,1,4\r\n3:6,9,4,7\r\n4:6,9,1,8\r\nFor guess 1 to have a number in the correct digit, digit 2=3 or digit 3=2. From guess 3, we can similarly deduce that digit 1=7 or digit 4=0\r\n\r\nIf digit 1=7, 9,1,or 4 must exist, according to guess 4. If 1 or 4 exist, the digits 3 or 2, 7, and 1 or 4 satisfy all guesses with only 3 digits, but the master number has 4 digits. Therefore, if digit 1=7, digit 2=9, digit 3=2, and both 3 and 0 would exist so as to satisfy guess 1 and 3 without including digits 1 and 4. There would be 5 digits, which is not possible. Therefore, digit 1 does not equal 7, and digit 4=0 instead.\r\nSince digit 4=0, the number 4 has no places to be and therefore does not exist.\r\n\r\nIf digit 3=2, 3 or 1 must exist too, according to guess 1. For 1 to exist, it must be digit 3, which is already equal to number 2. For 3 to exist, the number 1 doesn\'t, and so the only number left to satisfy guess 3 is number 7, which must be digit 2. Therefore, to satisfy guess 4, it must be 6720, which doesn\'t work with guess 2. Therefore, digit 3 doesn\'t equal 2, and instead, digit 2=3.\r\nSo far the number is ?3?0\r\n\r\nAccording to guess 4, 6 or 1 exist (only one), and for guess 1, 1 or 2 exist. For 6 and 2 exist, both of them must be in digit 1. Therefore, only number 1 exists, in digit 3\r\nSo far, ?310\r\n\r\nThe last digit must be from guess 2, the last guess to be satisfied. Only 8 works. \r\n\r\nThe number is 8310!',NULL,0);
INSERT INTO comment VALUES (8050,1103,3454,'Bart freeman','correct me if i\'m wrong','2003-09-20 13:14:46',0,'the number of different combinations is 777600000 i would then think that they would crack the code about half way through (although they could very well crack it on the first try or the last try) the codes thus it would still be a loss is this thinking correct ?',NULL,0);
INSERT INTO comment VALUES (8051,1103,3454,'Bart freeman','my solution is redundant','2003-09-20 13:24:48',0,'sorry didnt\' read the comments before posting ',NULL,0);
INSERT INTO comment VALUES (8052,1359,1575,'DJ','Solution & Method','2003-09-20 16:11:23',3,'8310.\r\n\r\nTo state the obvious, the first two guesses show us three things:\r\nExactly two digits from 1-4 are present.\r\nExactly one digit from 5-8 is present.\r\nExactly one of 9 or 0 is present.\r\n\r\nAssume that 9 is in the number, and 0 is not.\r\nThe fourth guess tells us that 1, 4, and 6 are not in the number.\r\nHowever, that leaves only one correct digit in guess 3 (0, 1, and 4 have been rules out), but we are told that there are two.\r\n\r\nTherefore, 0 is in the number, and 9 is not.\r\nFor guess three, then, exactly one of 1, 4, and 7 is present in the correct number.\r\n\r\nIf it is one, then 4 is not, and either 2 or 3 is in the number (from #1). Also, 7 is not, nor is 6 (#4), and one of either 5 or 8 is in the number.\r\nFurther, the X in #4 tells us that 1 would be the third digit, and the X in #3 tells us that 0 is the last digit.\r\nThere is an X and an O in #1; the O must correspond to the 1 (since we already know that it is the third digit), and the 2 or 3 will be in the correct position. It can\'t be the 2 in the third spot, so 3 must be the second digit.\r\nBy elimination, the 5 or the 8 must be the first digit.\r\nIf it were the 5, the response to #2 would be an X, but it\'s not, so it must be the incorrectly placed 8.\r\nTherefore, 8310 is a solution that works.\r\n\r\nWe are told that this is unique, but since the solution is based on an assumption, we will rule out the other possibilities.\r\n\r\nIf we assume that a 4 is in the number, and 1 and 7 are not, then from clue 4, the digit 4 must be in position 4 (kinda nice how that works). However, since the 4 in guess three is in a different spot, the O corresponds to that, and the X represents the 0 that we already know is in the number. However, that means that both 4 and 0 occupy the fourth spot; this is not possible, so the assumption is false.\r\n\r\nFinally, if we assume that 7 is in the number, and 1 and 4 are not, then a 6 must be in the number from guess #4 (1, 4, and 9 are eliminated already). However, that leaves us with 6 and 7 in the number, which by clue two we know cannot be the case. Again, we have a contradiction and know that the assumption is false.\r\n\r\nTherefore, 8310 is the only number that works.',NULL,0);
INSERT INTO comment VALUES (8053,1232,153,'TomM','Simplified example (re: Bart\'s solution)','2003-09-20 21:10:23',0,'Bart: In order to help you see the difference between your solution and the solution most of the others have come up with, I am going to simplify the conditions so that all possible outcomes can be listed, and the probability shown directly.\r\n\r\nAssume that there are only two balls, one red and one yellow, and that you have two chances to find the red. By your reasoning, you have a 50% chance of winning. By Fwaff\'s and the others\' reasoning you have a 1-(50%)² = 75% chance of winning.\r\n\r\nNow during the first draw, there are two possibilities with equal chance of happening: You can draw the red ball, or you can draw the yellow ball. On your second draw, you have the same two possibilities with equal chances.\r\nRR = win (25%)\r\nRY = win (25%)\r\nYR = win (25%)\r\nYY = lose (25%).\r\n\r\nI think where you went wrong, is that you forgot that you paid for two (or in the original problem, four) chances to draw. The fact that after a victory is assured you do not take your remaining draws does not change the odds. They could be restated: \r\nRx = win (50%)\r\nYR = win (25%)\r\nYY = lose (25%).',8006,0);
INSERT INTO comment VALUES (8054,937,3563,'Julie','An aid sometimes helps.','2003-09-20 22:46:50',0,'Ear-refutably easy. ',NULL,0);
INSERT INTO comment VALUES (8055,1117,3564,'aln','re(2): 5-point proof - to DJ','2003-09-20 23:12:44',4,'Comment for:\r\n\"Take any two points that are of different colors; let\'s say that they are blue and orange.\"\r\nI do not think that it is supposed in the problem that you can actually chose 2 points of different colors... what about 3 points of the same color?\r\nSo, if you just chose randomly 2 points and it will happen to have the same color -->> what is your solution then?',NULL,0);
INSERT INTO comment VALUES (8056,447,3567,'Jesse','possible sol.','2003-09-21 05:37:52',0,'14 x 14 = 196\r\n31 x 31 = 961',NULL,0);
INSERT INTO comment VALUES (8057,25,3567,'Jesse','solution','2003-09-21 05:52:08',0,'A bell sounds every 6 sec. So for noon it would take 11 x 6 for 66 sec.',NULL,0);
INSERT INTO comment VALUES (8058,1359,3568,'Stephanie','Solution','2003-09-21 06:48:38',0,'7924',NULL,0);
INSERT INTO comment VALUES (8059,1359,1301,'Charlie','re: Solution','2003-09-21 10:07:21',0,'7924 would have two X\'s in the last row instead of one.',8058,0);
INSERT INTO comment VALUES (8060,1164,1775,'Christian Perfect','solution','2003-09-21 10:12:19',0,'thanks to some computer hackery, n=9, giving the following possible combinations:\r\ny=3 t=4 k=1\r\ny=3 t=7 k=2\r\ny=6 t=5 k=1\r\ny=6 t=8 k=2\r\n\r\nif I do some actual thinking there\'s probably a reason for this...',NULL,0);
INSERT INTO comment VALUES (8061,1352,3558,'Tristan','definition','2003-09-21 11:02:01',0,'cos means, besides cosine, Kos, which is an island southwest of Turkey. Kos certainly isn\'t geographically unique, there are plenty of islands in the area. Is Kos the only island with only three letters in its name? I doubt it. I think I need a hint.',NULL,0);
INSERT INTO comment VALUES (8062,1164,3558,'Tristan','re: solution','2003-09-21 11:39:53',0,'It looks like you assumed that the letter O equals the number zero. I could prove that if n is odd, letter 0 equals zero. I\'ll spell zero if I refer to the number\r\n\r\nFor O times 3 to have a last digit of O, O must either be zero, or exactly half of n. Since O must be an integer, n must be divisible by 2 for O two be half of n. Since n is not even, O must be zero.\r\n\r\nYour assumption was correct, but you may have overlooked some solutions. Or you may not have. I think I might try to find other possible solutions. I wonder if n has to be less than or equal to ten...',8060,0);
INSERT INTO comment VALUES (8063,1164,1626,'Gamer','Solution','2003-09-21 13:37:09',3,'O must be 0 in this equation because 3O=O can\'t carry anything. If it did, then O would carry 1 (it can\'t carry anything more than 2, because if C is what you carry and B is the base (n here) 3O=O+CB, 2O=CB, and since O needs to be less than B, 2 must be greater than B)\r\n\r\nThen 3O=O+B, 2O=B, B/2=0. Remember this for later... 3O=K, and since 3O=O without any carried digit added in, K must be greater than O. 3K=T, but if O=B/2 (as stated above), 1.5B+number=T, and T doesn\'t exist in base B. This is a contradiction, so O must equal 0.\r\n\r\nNow you get the following equations: 3T=Y, 3Y=CB (since 0+some number can\'t possibly carry) C+3K=T (C is the same number in these two equations)\r\n\r\nFrom this you can conclude n=9... (more to come later)\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (8064,1164,3572,'Eradicator','Proof of solution','2003-09-21 14:22:14',0,'Right to left. First digit on right implies (2*o) mod n = 0. This consequently implies only one of o=0 or o=n/2. Second obviously cannot hold because from middle digit k>o and thus k>n/2, but left digit yields 3k<=t<=n-1 which implies 3k
\r\n--which returns a collection containing all words that have the same number of letters and differs by only one letter. If this requires disk access (also trivial), so be it.
\r\n\r\nA tree collection that allows n branches at each node, and provides a GetRootPathMembers method to return a collection of objects from the current node to the root ordered from the root to the current node.
\r\n_______________________\r\n\r\nCalculateWordLadder(StartWord, EndWord, MaxSteps)\r\n{\r\n CurrentWord = \"\"\r\n WordLadderTree.AddNode(NULL,StartWord) // add start as the root of the tree\r\n\r\n Repeat FOREVER\r\n {\r\n For Each Element X in WordLadderTree at Maximum TreeDepth\r\n {\r\n BOOLEAN NewWordsFound = FALSE\r\n\r\n WordCollection = FindAdjacentWords(Element)\r\n\r\n For Each Element Y in WordCollection\r\n {\r\n If ( Y NOT IN GetRootPathMembers(X) ) Then\r\n // we don\'t want to cycle nor do we want to include\r\n // a word that we\'ve already found in another branch\r\n {\r\n NewWordsFound = TRUE\r\n WordLadderTree.AddNode(X,Y) // add the new word to the tree; child of the current element X\r\n If ( Y == EndWord)\r\n {\r\n PRINT \"Problem solved:\"\r\n PRINT GetRootPathMembers(Y)\r\n END PROGRAM\r\n }\r\n }\r\n }\r\n\r\n If (NewWordsFound == FALSE ) Then\r\n {\r\n PRINT \"Search ended, no solution found\"\r\n END PROGRAM\r\n }\r\n\r\n If (WordLadderTree.MaximumTreeDepth = MaxSteps) Then\r\n {\r\n PRINT \"Search ended, maxsteps reached\"\r\n END PROGRAM\r\n }\r\n }\r\n }\r\n}\r\n\n\nEdited on September 24, 2003, 3:15 pm',NULL,0);
INSERT INTO comment VALUES (8177,1266,2899,'Brian Wainscott','re: solution','2003-09-24 15:02:04',0,'Good job. I\'m getting tired of finding complete solutions already posted, and felt I ought to contribute something once in a while, so here it goes.\r\n\r\nI don\'t dispute the correctness of your solution, but it isn\'t obvious that your final equation\r\n\r\nw = (4a^2 - 30a)/(30-3a)\r\n\r\nhas only 9 as a possible value for a. I did my algebra a bit differently.\r\nUsing your notation and starting from here:\r\n\r\n(w+2a)^2 - w^2 - wa = 30 (w+a)\r\n\r\nI got:\r\n\r\nw^2+4wa+4a^2-w^2-wa =30 (w+a)\r\na(3w+4a)/(w+a) = 30\r\n\r\nNow, since w and a are both positive integers,\r\n\r\n3(w+a) < 3w+4a < 4(w+a)\r\n\r\nso 3a < 30 < 4a\r\n\r\nThe only integer possibilities are then 8 and 9. 8 gives a non-integral value\r\nfor w, as you know. The end result is of course the same, but your final leap was not obvious to me at all.',8151,0);
INSERT INTO comment VALUES (8178,176,3454,'Bart freeman','easy','2003-09-24 15:20:41',0,'it is an elementary school , the kids were playing cops and robbers, this is why they didn\'t go to jail and why they didn\'t die',NULL,0);
INSERT INTO comment VALUES (8179,176,1920,'Brian Smith','re: easy','2003-09-24 15:25:19',0,'Did you notice in the puzzle it said \"This is not a game between children\"',8178,0);
INSERT INTO comment VALUES (8180,1354,1626,'Gamer','Defining','2003-09-24 15:47:58',0,'It\'s always good to define them unless it says explicitly in the problem that you have them in my opinion.',NULL,0);
INSERT INTO comment VALUES (8181,1354,3172,'SilverKnight','re: Defining','2003-09-24 16:06:39',0,'Gamer,\r\n\r\nI assume you are referring to my assumption of FindAdjacentWords, and the notion of having a tree template class (or equivalent, which exists in most mature programming libraries).\r\n\r\nIf so, then you are arguing about a matter of degree....\r\n\r\nCharlie didn\'t explicitly say I have a PRINT command, nor an END PROGRAM command, nor collection objects, nor iterators (to move through the collection, perhaps in order), nor loop control operators (REPEAT, FOR EACH).\r\n\r\nI must assume a modicum of basic understanding and familiarity with a computer language, and Charlie asked for an algorithm. I trust that what I proposed is sufficiently clear to actually write code in a language of your choosing.\r\n\r\nAgain, feel free to ask questions if this is in any way unclear.\r\n\r\n--- SK\r\n\r\nP.S.\r\n\r\nHowever, all that being said....\r\nTree is straightforward enough... (if you\'ve taken a basic computer algorithms class).\r\n\r\nThe FindAdjacentWords function could be implemented algorithmically as follows:\r\n\r\nFindAdjacentWords(InitialWord)\r\n{\r\n FILE fWords;\r\n ORDEREDCOLLECTION RetVal\r\n\r\n fWords.Open(\"WORDS\" + CurrentWord.Length + \".TXT\")\r\n\r\n while not fWords.EOF() // EOF = end of file\r\n {\r\n WORD Word = fWords.GetNextWord()\r\n\r\n If ( IsAdjacent(InitialWord, Word) == TRUE) Then\r\n {\r\n RetVal.AddMember(Word)\r\n }\r\n }\r\n return (RetVal)\r\n}\r\n____________________\r\n\r\nHelper Function\r\nIsAdjacent(Word1, Word2)\r\n{\r\n INT cDifference=0\r\n\r\n For Each Letter X in Word1\r\n {\r\n If (X is different than corresponding letter in Word2) Then\r\n {\r\n cDifference = cDifference + 1\r\n if (cDifference == 2) then\r\n {\r\n return (FALSE)\r\n }\r\n }\r\n }\r\n if (cDifference == 0) then\r\n {\r\n return(FALSE)\r\n }\r\n\r\n return (TRUE)\r\n}\n\nEdited on September 24, 2003, 4:59 pm',8180,0);
INSERT INTO comment VALUES (8182,1367,3605,'Daniel B.','(Quite Simple) solution...','2003-09-24 16:31:29',0,' The solution lies in the trick here. As any veteran paperfolder knows, simply knotting the paper and pressing the knot flat produces a pentagon, and held up to the light the creases inside the figure form a pentagram. use the pencil and straightedge to trace the outlines of the figures. ^^',NULL,0);
INSERT INTO comment VALUES (8183,59,1171,'nikki','re: hats','2003-09-24 17:23:55',0,'[in case you didnt know they are all wearing white hats for the very reasons given in the first two comments]\r\n\r\nI disagree. All we can tell for certain is color of the had of the front man. All of the following situations are possible (FMB means Front Middle Back)\r\n\r\nFMB\r\n\r\nWBB\r\nWBW\r\nWWB\r\nWWW\r\n\r\nlater!\r\n',152,0);
INSERT INTO comment VALUES (8184,587,1626,'Gamer','re: the easy solution','2003-09-24 17:57:39',0,'Unfortunately, that\'s not what it says in the problem.\r\n\r\n\"However, the wine and barrels must be split so that each son has the same number of full barrels, the same number of half-full barrels, and the same number of empty barrels.\"',7063,0);
INSERT INTO comment VALUES (8185,1205,3607,'kravix','Answer','2003-09-24 18:58:20',0,'12 Timers.\r\n\r\nSet 2 timers T1 at normal speed and T2 at double. When T2 beeps 30 mins has elapsed. Set T1 to double at the beep and start T3, T1 will run for 15 mins and beep(a total of 45 mins ).When T1 beeps set T3 to double and start T4. T3 will then run another 22.5 mins(a total of 37.5 mins). When T3 beeps set T4 to double and start T5 at normal....etc.. ect.. The time elapsed from the beep of T11 till the beep of T12 is 25 mins exactly with no seconds left over or under.',NULL,0);
INSERT INTO comment VALUES (8186,1266,2707,'Gordon Steel','A Very Challenging Problem','2003-09-24 19:42:12',0,'I like this problem very much, as it is simple to state but challenging to solve. It is not difficult to show that the geometric factor must be less than 2. With a little experimentation, one can derive a set on numbers that meets the problem\'s requirements. These are 18, 27, 36 and 48. The first three are arithmetic with a delta of 9. The last three are geometric with a factor of 3/2 times the previous term. The last temr is 30 more than the first. Gordon S.',NULL,0);
INSERT INTO comment VALUES (8187,1205,2899,'Brian Wainscott','re: Answer','2003-09-24 19:48:42',4,'I\'m confused. If I understand you correctly, the times you get will converge to 20 minutes, not 25. Also, the error only goes down by half each time, so even after N clocks (N = any finite number) there will still be some error (5/2^N minutes, +/- 1 on the N here, I\'d have to check)\r\n\r\nIn any case, you get neither 25 minutes, nor an EXACT measure of 20 minutes.\r\n\r\nOr did I completely misunderstand what you are saying?',8185,0);
INSERT INTO comment VALUES (8188,1266,1301,'Charlie','re(2): solution','2003-09-24 22:02:47',0,'Yes, that final leap was actually trial and error, aided by a computer.',8177,0);
INSERT INTO comment VALUES (8189,1354,3172,'SilverKnight','re(2): Defining - optimal solution?','2003-09-25 06:24:46',4,'One who has much experience programming will (I hope) note that the algorithm I proposed is not optimal.
\r\nOne possible efficiency issue is that FindAdjacentWords() searches through the whole collection of words each time it is called.
\r\nAs a related question (which I won\'t answer since I\'m posing it), how might you change the algorithm to speed up this function? (Speed measured in Big-O notation, of course. Yes, disk caching would speed things up... but it doesn\'t change the Big-O speed.)
\r\nHow might you change the algorithm and what kind of preprocessing might you perform if you can set up any kind of collection/files before you begin your problem?
\r\nWhat other optimizations to my proposed algorithm might you suggest? (Preferably show enhancements that reduce the Big-O time.)\r\n\r\n--- SK',8181,0);
INSERT INTO comment VALUES (8190,1151,3616,'Whitney','School Shelves Solution','2003-09-25 11:21:33',0,'Monica Baker has a puzzle in shelf one\r\nDarren Forbes has a teddy bear in shelf two\r\nMark McKenna has a picture book in shelf three\r\nKevin Farrell has crayons in shelf four\r\nHolly Lorenz has blocks in shelf five\r\nand Janet Collins has a fire engine in shelf six',NULL,0);
INSERT INTO comment VALUES (8191,568,3197,'gabbo','re: water absorbed cork','2003-09-25 14:30:15',0,'....or just get a cork that already fits loosely and just push it in.\r\n\r\n\r\nOr melt the bottle, melting isn\'t breaking so...\r\n\r\n',7943,0);
INSERT INTO comment VALUES (8192,1165,1920,'Brian Smith','Trivial solution','2003-09-25 14:31:14',0,'√10 - 3 = √10 - 3 + 1',NULL,0);
INSERT INTO comment VALUES (8193,1165,2707,'Gordon Steel','SImultaneous Equations','2003-09-25 15:02:03',0,'One solution for the three lines is the less than or equal sign and then 1. Therefore, the equation would read &10 - 3 <- 1. Gordon S.',NULL,0);
INSERT INTO comment VALUES (8194,1165,1301,'Charlie','re: Trivial solution','2003-09-25 15:21:31',0,'But the right side is now larger by 1 than the left.',8192,0);
INSERT INTO comment VALUES (8195,1165,1920,'Brian Smith','The Solution','2003-09-25 15:22:48',0,'Three lines: a line to change the minus into a plus, a line for a fraction bar, and a line for a 1.\r\n\r\n 1\r\n----------- = sqrt 10 - 3\r\nsqrt 10 + 3\r\n
\n\nEdited on September 29, 2003, 11:13 am',NULL,0);
INSERT INTO comment VALUES (8196,1165,1920,'Brian Smith','re(2): Trivial solution','2003-09-25 15:23:33',0,'It should have been √10 - 3 = √10 - 3 x 1',8194,0);
INSERT INTO comment VALUES (8197,393,3620,'Frederic Ouellet','Re: Solution','2003-09-25 19:23:10',0,'Well the pH of distillated water stands between 5 and 6 meaning that it is not very acid,HCO3 being a weak acid, it can explain the 2 pH unit difference. ',NULL,0);
INSERT INTO comment VALUES (8198,1165,3621,'Angelavender','','2003-09-25 19:40:07',0,'ã10 - 3 = ã10 - 3 x 1\r\n',NULL,0);
INSERT INTO comment VALUES (8199,1165,3621,'Angelavender','re:','2003-09-25 19:42:38',0,'√ 10 - 3 = √ 1 - 3 x 1',8198,0);
INSERT INTO comment VALUES (8200,1165,3558,'Tristan','Solution','2003-09-25 19:51:17',3,'I think it might be a little confusing to use the <√> sign because it could mean the square root of (10-3). But that\'s just in general, not particularly here...\r\n\r\nAnyway, the solution is to draw an x and a 1 to multiply by one',NULL,0);
INSERT INTO comment VALUES (8201,511,2121,'Chaz','Read this and be DAZZLED!','2003-09-25 20:16:24',0,'could god microwave a burrito so hot that even he could not eat it?',NULL,0);
INSERT INTO comment VALUES (8202,1165,3623,'jaypee','adding three lines','2003-09-25 21:59:07',0,'it could be in - 3 x 1\r\nwhere the multiply sign makes up two lines and the one makes up the third line\r\nanother possible solution is\r\nsqrt 10 - absolute value of a -3\r\ntwo lines for the absolute value designation\r\n(one vertical line goes on each side of the -3)\r\nand the third line would be the minus sign itself\r\nin -3',NULL,0);
INSERT INTO comment VALUES (8203,1165,3626,'matt white','this COULD work','2003-09-26 02:48:18',0,'ã10 - 3 = 1 ã10 + -3\r\nif you would assume the 1 in front of the... thingy would mulptiply it. ',NULL,0);
INSERT INTO comment VALUES (8204,1151,3629,'amy','answer','2003-09-26 04:50:20',0,'1. monica baker puzzle; 4. kevin farrell crayons\r\n2. darrin forbes bear; 5. holly lorenz blocks\r\n3. mark mckinna book; 6. janet collins fire engine',NULL,0);
INSERT INTO comment VALUES (8205,990,3629,'amy','innings.','2003-09-26 05:16:21',0,'extra innings. what a boring game it must have been thru the first 9 innings.',NULL,0);
INSERT INTO comment VALUES (8206,1354,3631,'Bruce','Been there, done that','2003-09-26 08:42:04',0,'This problem is the interview question for my company. So far we have solutions in a range of languages although my personal favourites are in Perl and Tcl.\r\n\r\nThe offered solution by SilverKnight employs a depth-first search - which is the most common \'good\' answer - but you can speed the search up by doing a double-headed search, ie, start at both the start -and- end words and check for either tree adding a node that already exists in the other search tree.\r\n\r\nIf you intend to run many word ladder problems against your program, you could always go for a long preperation time (and thereafter a short solution time) by building a graph of words of length N that differ by one character and storing it to disc. That way, all you\'ve got to do is a shortest-path solution over a graph (Dijkstra\'s Algorithm).',NULL,0);
INSERT INTO comment VALUES (8207,1354,3631,'Bruce','re: Been there, done that','2003-09-26 09:05:06',0,'I meant breadth-first not depth-first.',8206,0);
INSERT INTO comment VALUES (8208,1406,3631,'Bruce','','2003-09-26 09:23:31',3,'Its area is shared by 2x4.\r\nIts perimeter is shared by 2x7, 3x6 and 4x5\r\nIts diagonal is shared by 4x7.\r\n\r\nYou\'ve cut yourself a 1x8 slice.\r\n',NULL,0);
INSERT INTO comment VALUES (8209,1354,3631,'Bruce','Finding adjacent words','2003-09-26 09:56:59',2,'One useful footnote that we discovered setting this problem was that it is considerably faster to generate the 25N \'adjacent\' words (for an N-letter word) and then eliminate all the non-words in this list than it was to search the N-letter word list for words with a single letter difference.',NULL,0);
INSERT INTO comment VALUES (8210,1406,3631,'Bruce','\'No Subject\' should be \'Solution\'','2003-09-26 09:58:41',0,'..but I can\'t edit the comment to fix it :)',NULL,0);
INSERT INTO comment VALUES (8211,1406,1301,'Charlie','the Solution','2003-09-26 10:03:32',3,'The way I did this was to run a small program to find all the possible diagonals from cut rectangles:\r\n\r\nDEFDBL A-Z\r\nOPEN \"cutchess.txt\" FOR OUTPUT AS #1\r\nFOR i = 1 TO 8\r\n FOR j = i TO 8\r\n PRINT #1, SQR(i * i + j * j), i, j\r\n NEXT\r\nNEXT\r\nCLOSE\r\n\r\nThe output was then sorted by diagonal length, and it was found that only 7.07106 and 8.062257 were shared by more than one pair of dimensions: the former by 1x7 and 5x5 and the latter by 1x8 and 4x7.\r\n\r\nAll of these have non-unique perimeters, so perimeter doesn\'t narrow it down any further.\r\n\r\nBut 1x7 has a unique area as 7 is prime. Likewise 5 is prime, so the only other way to get 25 would be 1x25 and the chessboard is not that big. The 28 area from 4x7 is also unique, as the only alternatives, 1x28 and 2x14 are too big for the chessboard.\r\n\r\nThat leaves 1x8 as having the only ambiguous area as area 8 can also be 2x4.\r\n\r\nSo the answer is 1x8.',NULL,0);
INSERT INTO comment VALUES (8212,1406,3631,'Bruce','re: the Solution','2003-09-26 10:06:52',0,'Typically, I made perl do the work for me.',8211,0);
INSERT INTO comment VALUES (8213,1406,2899,'Brian Wainscott','General Comment','2003-09-26 11:09:57',0,'Since the area is not unique, one of the sides must be a composite number. This cuts the number of cases down a lot. In this case, it was enough that I could just look at the list of edge squares (1,4,9,...,64) and pretty quickly find that 1x8 works. ',NULL,0);
INSERT INTO comment VALUES (8214,1354,3172,'SilverKnight','re: Finding adjacent words','2003-09-26 11:43:00',1,'Bruce,\r\n\r\nThis is a useful footnote, and makes much sense, provided we have a sorted list of adjacent words. (You loosely answered my earlier question regarding what one might do in preprocessing, and I take for granted that we would have sorted all this ahead of time.)\r\n_________________\r\n\r\nAs for the \"double-headed\" algorithm you describe, I\'m not certain that I understand what you\'re suggesting. Namely, it doesn\'t seem to reduce the BIG-O speed, and now you not only have to search for adjacent words in two trees... you must do a search (log n, I\'m sure) in the other tree to see if it exists there.\r\n\r\nSo... I see the benefit of doing more in memory, reducing disk access in a practical sense, but I don\'t see how this speeds the algorithm up (from an algorithmic point of view).\r\n\r\nPerhaps you can clarify for me.\r\n\r\nThanks,\r\n\r\n --- SK',8209,0);
INSERT INTO comment VALUES (8215,1354,1301,'Charlie','re(2): Finding adjacent words','2003-09-26 11:51:23',0,'Reading Bruce\'s comment, it does seem that it refers to how to implement what you describe as \"the trivial function and class: FindAdjacentWords(GivenWord)\", in that to implement this, one should not search the word list and check to see if each word is adjacent to the latest on your tree, but rather to find all 25N letter combinations that are adjacent, and check to see if they are words or not.\r\n\r\nHe\'s not referring to a pre-prepared list of adjacencies, but rather merely that the list of words themselves be sorted so as to be available for a binary search.\r\n\r\nIn fact, I\'ve added this modified version to the solution that will be posted eventually, and it does speed the processing.\r\n\n\nEdited on September 26, 2003, 11:53 am',8214,0);
INSERT INTO comment VALUES (8216,1354,3172,'SilverKnight','re(3): Finding adjacent words','2003-09-26 12:16:52',0,'I most certainly agree with you (and him) regarding that. It would be much faster, provided we have a sorted list, prepared ahead of time.\r\n\r\nWhat I was last asking about is... is the \"double headed\" aspect a significant gain, in terms of \"relevant transactions\". For instance... perhaps we have to do only half as many \'cycles\' through the list, but now we have to do twice as much during each cycle (because of two trees). And now, we\'re ALSO doing a check between the two trees, so that we can determine if we\'ve \"met in the middle\", so to speak.',8215,0);
INSERT INTO comment VALUES (8217,1232,3430,'pat','$$$','2003-09-26 13:14:33',0,'kinda like playing red or black in roulette but with no zeros or double zeros',NULL,0);
INSERT INTO comment VALUES (8218,1170,3172,'SilverKnight','Solution','2003-09-26 14:17:10',3,'For all pairs of x, y where both are greater than or equal to e (2.71828...), the question is equivalent to taking the natural log (ln) of both sides and determining the inequality relationship there.\r\n\r\nTaking the log of both sides, the question becomes:\r\nwhich is greater pi * ln (e) --or-- e * ln(pi)?\r\n\r\nThe expression has two factors.... the first factor is a number, and the second factor is modified by taking the natural log of a number.\r\n\r\nThe unmodified factor will go up faster (as a function) than the natural log will go up, for numbers greater than or equal to e.\r\n\r\nTherefore, to maximize the result, we would want to use the LARGER number (in this case pi) as the unmodified factor.\r\n\r\nThe unmodified factor corresponds to the exponent in the original equation.\r\n\r\nTherefore e^pi must be greater than pi^e.\r\n\r\n(And, in fact, it is.)\r\n\n\nEdited on September 26, 2003, 2:24 pm',NULL,0);
INSERT INTO comment VALUES (8219,1170,1920,'Brian Smith','Solution','2003-09-26 14:30:43',0,'Consider the value e^pi - pi^e. If positive, e^pi is greater, and if negative, pi^e is greater.\r\n\r\nConsider the function f(x)=e^x-x^e\r\n\r\nThe function is defined on the interval [0,infinity) and is smooth along the interval (0,infinity). Since there are no singularities, the lowest value must occur at one of x=0, lim x to infinity, or at one of the local extrema.\r\n\r\nf\'(x) = e^x - e*x^(e-1)\r\nf\'(x) = 0 only if x=1 or x=e.\r\n\r\nf(0) = 1, f(1) = e-1, f(e) = 0, and lim x to infinity of f(x) = infinity. The lowest of these values is f(e)=0, therefore for all x>0, the function is nonnegative. It follows e^pi-pi^e>0. \r\n\r\nTherefore e^pi > pi^e.\n\nEdited on September 26, 2003, 2:32 pm',NULL,0);
INSERT INTO comment VALUES (8220,1170,3172,'SilverKnight','re: Solution','2003-09-26 14:32:23',0,'By the way:\r\n\r\nI wrote, in my solution, that:\r\n\"...the question is equivalent to taking the natural log (ln) of both sides and determining the inequality relationship there.\"\r\n\r\nThis is true, because if I have two functions F and G which have an inequality relationship (such as F < G ), I can perform an operation (such as taking the natural log of both) that keeps the sign (positive) and is monotonically increasing (to maintain the inequality).',8218,0);
INSERT INTO comment VALUES (8221,1165,3512,'Jeff','alternate solution','2003-09-26 19:13:50',3,'ok, since I don\'t know how to put absolute value signs on the computer, i will use [] instead. but realize that in real life, abs value is indicate by a straight line. \r\n\r\n√10 - 3 = √10 - [-3]\r\n\r\nThe additions I made were two abs value signs and one negative sign.',NULL,0);
INSERT INTO comment VALUES (8222,1010,2271,'mullen','easy peasy lemon squeezy','2003-09-26 19:39:38',3,'okay, i just lost all my intellectual prowess with the subject title i know but the answer really wasn\'t hard, it\'s soul',NULL,0);
INSERT INTO comment VALUES (8223,921,2271,'mullen','nope, noway no-how','2003-09-26 19:48:29',0,'nevermind never taking a bet where you have no chance of coming out on top...i say never take a bet where your drink gets drank by someone other than you',NULL,0);
INSERT INTO comment VALUES (8224,1165,3623,'jaypee','re: alternate solution','2003-09-26 20:48:19',0,'I already came up with that solution',8221,0);
INSERT INTO comment VALUES (8225,238,3512,'Jeff','','2003-09-26 22:32:57',0,'Ahhh....good ol\' diehard. Who can deny that Bruce Willis is the man?',NULL,0);
INSERT INTO comment VALUES (8226,1165,3512,'Jeff','re(2): alternate solution','2003-09-26 22:36:15',0,'dag yo, It\'s obivously not against the rules to post a solution that has already been posted. I mean, I did come up with it on my own, and it\'s not like anyone\'s dishing out points here or anything.',8224,0);
INSERT INTO comment VALUES (8227,1407,3351,'Eric','Solution','2003-09-27 13:07:39',3,'The Devil with ye!\r\n\r\nThe correct pattern is to arrange the trees in a pentagon within a pentagram within a pentagram with a lone tree in the center of it all. This will of course make the inner trees very close together and the outer trees far apart and make me seriously doubt the artistry of our landscape architect, but we will certainly have fifteen rows of four!',NULL,0);
INSERT INTO comment VALUES (8228,624,3351,'Eric','now we are learning','2003-09-27 13:24:10',0,'And 6009 - 2003 is 4006 which, I think, is more relevant.',NULL,0);
INSERT INTO comment VALUES (8229,1151,3640,'Susan','solution to compartments','2003-09-27 15:25:11',0,'Kevin Farrell has a puzzle in compartment 1.\r\nHolly Forbes has a set of blocks in compartment2.\r\nMark Collins has a picture book in compartment 3.\r\nMonica Baker has a box of crayons in compartment 4.\r\nDarren Lorenz has a teddy bear in compartment 5.\r\nJanet Mckenna has a fire engine in compartment 6.',NULL,0);
INSERT INTO comment VALUES (8230,525,3641,'Ashira','Hey','2003-09-27 15:55:25',0,'Solution: 1 person, you',NULL,0);
INSERT INTO comment VALUES (8231,500,3641,'Ashira','hey','2003-09-27 15:56:39',0,'Solution: Suicide',NULL,0);
INSERT INTO comment VALUES (8232,499,3641,'Ashira','Hey','2003-09-27 15:58:47',0,'Solution: Some sort of eating contest',NULL,0);
INSERT INTO comment VALUES (8233,467,3641,'Ashira','Soooooo Easy','2003-09-27 16:00:34',0,'This is an old one: Man. When a baby, he crawls on all fours. When an adult, walks on two legs. When an old man, walks with help of a cane.',NULL,0);
INSERT INTO comment VALUES (8234,360,3641,'Ashira','Easy','2003-09-27 16:01:49',0,'Easy: Nothing',NULL,0);
INSERT INTO comment VALUES (8235,315,3641,'Ashira','Answer','2003-09-27 16:02:50',0,'It\'s his son!',NULL,0);
INSERT INTO comment VALUES (8236,315,3641,'Ashira','re: The solution is wrong!','2003-09-27 16:05:17',0,'Actually...the word \'this\' precedes the word \'my.\' so actually, it IS right. it\'s like saying my mother is my grandma\'s daughter.',4838,0);
INSERT INTO comment VALUES (8237,543,3641,'Ashira','Answer','2003-09-27 16:08:15',0,'Any Tolkien fan knows this: an egg',NULL,0);
INSERT INTO comment VALUES (8238,190,3642,'matthew','First time','2003-09-27 19:16:00',0,'there are 6 different ways to make 100,correct?',NULL,0);
INSERT INTO comment VALUES (8239,1407,3623,'jaypee','re: Solution','2003-09-27 20:19:13',0,'there is a problem with your solution. The five rows making up \r\nthe outer pentagon will have only 2 trees in each row.',8227,0);
INSERT INTO comment VALUES (8240,1407,1626,'Gamer','re(2): Solution','2003-09-27 22:55:46',3,'\r\n O\r\nO O O O\r\n O O\r\n O\r\n O O\r\n
Here is a pentagram,\r\n\r\nNoting the pentagon in the middle,\r\n\r\n\r\n O\r\n\r\nO O O O\r\n O\r\n O O O O O\r\n O O\r\n O\r\n\r\n\r\n\r\n O O\r\n
\r\nPutting a pentagram with a tree inside another pentagram is the key to this problem.\r\n\r\nDue to the improper spacing, some rows aren\'t linear, but these would be if the diagram was drawn correctly. This diagram just shows the basic idea of where verything is.',8239,0);
INSERT INTO comment VALUES (8241,1407,3623,'jaypee','re(3): Solution','2003-09-28 00:00:28',0,'The sides of the inside pentagon is created by the lines (rows) of the pentagram. That only means there are five rows \r\nthat constitute the inner pentagram. So the sides of the\r\ninside pentagon are only segments of the five rows making up\r\nthe inner pentagram so can\'t be counted as five additional rows. Adding the five rows from the outer pentagram to the five rows of the inner pentagram adds up to only 10 rows.\r\nThe other five rows are created by connecting the outer most\r\npoints of the outside pentagram, creating an outside hexagon. These five rows, though, will have only 2 trees each.\r\nCould you check me out on that?\r\n',8240,0);
INSERT INTO comment VALUES (8242,1407,3623,'jaypee','error in re:3','2003-09-28 00:05:11',0,'where I mentioned an outside hexagon, I meant \r\noutside pentagon ',NULL,0);
INSERT INTO comment VALUES (8243,1407,1575,'DJ','Solution','2003-09-28 02:24:19',3,'To position the trees, draw a star, placing ten trees on each point and corner.\r\nThen, draw a star inside that, using the inside 5 corners as the second star\'s outside points, and place five more trees on the inside corners of the smaller star. Place the final tree in the center.\r\n\r\nThe outside star provides five lines:\r\n\r\n\r\n · \r\n\r\n\r\n\r\n\r\n\r\n\r\n * * * *\r\n\r\n ·\r\n\r\n · ·\r\n ·\r\n\r\n · · · ·\r\n \r\n \r\n \r\n ·\r\n\r\n\r\n\r\n · ·\r\n\r\n\r\n----------------------------------------------------\r\n\r\n\r\n * \r\n\r\n\r\n\r\n\r\n\r\n\r\n · * · ·\r\n\r\n ·\r\n\r\n · ·\r\n ·\r\n\r\n * · · ·\r\n \r\n \r\n \r\n ·\r\n\r\n\r\n\r\n * ·\r\n\r\n\r\n----------------------------------------------------\r\n\r\n\r\n * \r\n\r\n\r\n\r\n\r\n\r\n\r\n · · * ·\r\n\r\n ·\r\n\r\n · ·\r\n ·\r\n\r\n · · · *\r\n \r\n \r\n \r\n ·\r\n\r\n\r\n\r\n · *\r\n\r\n\r\n----------------------------------------------------\r\n\r\n\r\n · \r\n\r\n\r\n\r\n\r\n\r\n\r\n * · · ·\r\n\r\n ·\r\n\r\n · ·\r\n ·\r\n\r\n * · · ·\r\n \r\n \r\n \r\n *\r\n\r\n\r\n\r\n · *\r\n\r\n\r\n----------------------------------------------------\r\n\r\n\r\n · \r\n\r\n\r\n\r\n\r\n\r\n\r\n · · · *\r\n\r\n ·\r\n\r\n · ·\r\n ·\r\n\r\n · · · *\r\n \r\n \r\n \r\n *\r\n\r\n\r\n\r\n * ·\r\n\r\n\r\n
\r\n\r\nSimilarly, the edges of the smaller star make up five more lines:\r\n\r\n\r\n\r\n\r\n · \r\n\r\n\r\n\r\n\r\n\r\n\r\n · * · ·\r\n\r\n ·\r\n\r\n * ·\r\n ·\r\n\r\n · * · ·\r\n \r\n \r\n \r\n *\r\n\r\n\r\n\r\n · ·\r\n\r\n\r\n----------------------------------------------------\r\n\r\n\r\n · \r\n\r\n\r\n\r\n\r\n\r\n\r\n · · * ·\r\n\r\n ·\r\n\r\n · *\r\n ·\r\n\r\n · · * ·\r\n \r\n \r\n \r\n *\r\n\r\n\r\n\r\n · ·\r\n\r\n\r\n----------------------------------------------------\r\n\r\n\r\n · \r\n\r\n\r\n\r\n\r\n\r\n\r\n · · · ·\r\n\r\n ·\r\n\r\n · ·\r\n ·\r\n\r\n * * * *\r\n \r\n \r\n \r\n ·\r\n\r\n\r\n\r\n · ·\r\n\r\n\r\n----------------------------------------------------\r\n\r\n\r\n · \r\n\r\n\r\n\r\n\r\n\r\n\r\n · · * ·\r\n\r\n *\r\n\r\n * ·\r\n ·\r\n\r\n * · · ·\r\n \r\n \r\n \r\n ·\r\n\r\n\r\n\r\n · ·\r\n\r\n\r\n----------------------------------------------------\r\n\r\n\r\n · \r\n\r\n\r\n\r\n\r\n\r\n\r\n · * · ·\r\n\r\n *\r\n\r\n · *\r\n ·\r\n\r\n · · · *\r\n \r\n \r\n \r\n ·\r\n\r\n\r\n\r\n · ·\r\n\r\n\r\n
\r\n\r\nThat\'s ten out of the fifteen.\r\nUp to this point we haven\'t used the center tree yet. The last five rows each utilize the center tree along with one tree from each of the four concentric pentagons we have formed. The trees are not evenly spaced, but they are in a straight line (don\'t trust my drawing, but they are):\r\n\r\n\r\n\r\n · \r\n\r\n\r\n\r\n\r\n\r\n\r\n * · · ·\r\n\r\n ·\r\n\r\n * ·\r\n *\r\n\r\n · · · *\r\n \r\n \r\n \r\n ·\r\n\r\n\r\n\r\n · ·\r\n\r\n\r\n----------------------------------------------------\r\n\r\n\r\n · \r\n\r\n\r\n\r\n\r\n\r\n\r\n · · · *\r\n\r\n ·\r\n\r\n · *\r\n *\r\n\r\n * · · ·\r\n \r\n \r\n \r\n ·\r\n\r\n\r\n\r\n · ·\r\n\r\n\r\n----------------------------------------------------\r\n\r\n\r\n * \r\n\r\n\r\n\r\n\r\n\r\n\r\n · · · ·\r\n\r\n *\r\n\r\n · ·\r\n *\r\n\r\n · · · ·\r\n \r\n \r\n \r\n *\r\n\r\n\r\n\r\n · ·\r\n\r\n\r\n----------------------------------------------------\r\n\r\n\r\n · \r\n\r\n\r\n\r\n\r\n\r\n\r\n · · * ·\r\n\r\n ·\r\n\r\n · ·\r\n *\r\n\r\n · * · ·\r\n \r\n \r\n \r\n ·\r\n\r\n\r\n\r\n * ·\r\n\r\n\r\n----------------------------------------------------\r\n\r\n\r\n · \r\n\r\n\r\n\r\n\r\n\r\n\r\n · * · ·\r\n\r\n ·\r\n\r\n · ·\r\n *\r\n\r\n · · * ·\r\n \r\n \r\n \r\n ·\r\n\r\n\r\n\r\n · *\r\n\r\n
\r\n\r\nSo, that\'s it, 15 rows from 16 trees.\n\nEdited on September 28, 2003, 2:32 am',NULL,0);
INSERT INTO comment VALUES (8244,1403,1220,'abc','solution','2003-09-28 10:13:41',3,'Each of them forms another common English word if an \"e\" is added to the end.',NULL,0);
INSERT INTO comment VALUES (8245,1403,3646,'Brandon','','2003-09-28 10:42:20',0,'None of them have the letter u.',NULL,0);
INSERT INTO comment VALUES (8246,314,3558,'Tristan','Solution','2003-09-28 13:05:20',0,'This problem is kind of old, but I found the solution after reading the first comment.\r\n4344199=4444\r\nThe number of digits is equal to the first digit. You read the next digits, with the number you read equal to the first digit. For each digit you read take the nth digit and put it into the answer. n equals the digit you read.\r\nEx: 34215=143\r\nYou have three digits and the digits in order are the 4th, 2nd, and 1st digits of the original number',NULL,0);
INSERT INTO comment VALUES (8247,603,3655,'jonnyw76','easy explanation','2003-09-28 20:53:12',0,'x+x+x+x+....+x(\'x\' times)= x squared which is the same as saying x*x=x squared.\r\n\r\nyou then substitute x with 1 in only a portion of the problem when you differentiate. This is mathematically wrong. If you replace x with 1, you must do so with all x\'s in the problem. It would then become:\r\n\r\n1+1+1+1...+1 (1 time)=1²\r\n\r\nif you add 1, 1 time, you get 1. so the problem would become:\r\n\r\n1=1² which is true. Thank you.\r\n',NULL,0);
INSERT INTO comment VALUES (8248,486,3454,'Bart freeman','','2003-09-29 03:05:52',0,'although the mathmatic figure might be 22 , i\'ve read that if you take 40 people at random chances are 2 people will share a birthday',NULL,0);
INSERT INTO comment VALUES (8249,1117,3467,'B M','','2003-09-29 04:46:38',0,'This problem is the motivation for Ramsay numbers.5 is the smallest such Ramsay number.',NULL,0);
INSERT INTO comment VALUES (8250,1198,1171,'nikki','Solution','2003-09-29 08:55:21',3,'61 F and 16 C\r\n82 F and 28 C\r\n\r\nLater!',NULL,0);
INSERT INTO comment VALUES (8251,1198,3660,'Riaan','Solution','2003-09-29 09:04:36',0,'morning\r\n16 C 61 F\r\n\r\nafternoon\r\n28 C 82 F',NULL,0);
INSERT INTO comment VALUES (8252,1198,1220,'abc','proof','2003-09-29 10:36:22',3,'This solution requires a bit trial and error.\r\n\r\nFahrenheit: 10a + b\r\nCelsius: (10a + b - 32)*5/9 = 10b + a\r\n\r\nWe can solve this further:\r\n50/9a + 5/9b - 160/9 = 10b + a\r\n<=> 41a - 160 = 85b\r\n\r\nNow you have to try values for a:\r\na=9 -> b ~ 2.46\r\na=8 -> b ~ 1.98\r\na=7 -> b ~ 1.49\r\na=6 -> b ~ 1.01\r\na=5 -> b ~ 0.53\r\na=4 -> b ~ 0.05\r\na=3 -> b ~ -0.44 (we can stop here)\r\n\r\nNow you take the values for which b is closest to an integer.\r\nThose are:\r\na=8 and b=2 -> 82F and 28C°\r\na=6 and b=1 -> 61F and 16C°\r\na=4 and b=0 -> 40F and 04C° (which is not valid if we assume that there is no 0 for first digit)\r\n\r\nThe two first are correct solutions.\r\nProof:\r\n(82-32)*5/9 = 27 7/9 (28 nearest integer)\r\n(61-32)*5/9 = 16 1/9 (16 nearest integer) ',NULL,0);
INSERT INTO comment VALUES (8253,1151,3660,'ratsnstuff','Try this one','2003-09-29 10:39:58',0,'1 Monica Baker - puzzle\r\n2 Daren Forbes - teddy\r\n3 Mark McKenna - picture book\r\n4 Kevin Farrel - crayons\r\n5 Holly Lorenz - blocks\r\n6 Janet Collins - fire engine',NULL,0);
INSERT INTO comment VALUES (8254,1198,1301,'Charlie','computer solution','2003-09-29 11:00:07',3,'FOR f = 10 TO 99\r\n c1 = INT((f - 32.5) * 5 / 9 + .5)\r\n c2 = INT((f - 31.5) * 5 / 9 + .5)\r\n f$ = LTRIM$(STR$(f))\r\n c1$ = LTRIM$(STR$(c1))\r\n c2$ = LTRIM$(STR$(c2))\r\n IF RIGHT$(f$, 1) = LEFT$(c1$, 1) AND RIGHT$(c1$, 1) = LEFT$(f$, 1) THEN\r\n PRINT f, c1\r\n END IF\r\n IF RIGHT$(f$, 1) = LEFT$(c2$, 1) AND RIGHT$(c2$, 1) = LEFT$(f$, 1) THEN\r\n PRINT f, c2\r\n END IF\r\nNEXT\r\n\r\ndoes come out with the same \r\n\r\n61 16\r\n61 16\r\n82 28\r\n82 28\r\n
\r\n----------\r\n(listed twice each due to checking lower and upper limits of the Fahrenheit possibilities for each degree)\r\n\r\nSeeing abc\'s comment, I note that if 44 F were equivalent to 4 C (which it\'s not), the program would have found this as a match, as lengths weren\'t checked.',NULL,0);
INSERT INTO comment VALUES (8255,1151,3501,'r. allison','question--','2003-09-29 12:08:54',0,'how are you supposed to raise your rank from novice on up?? im new to the site. i guess if someone can tell me email me at ssdalocka@yahoo.com thanx\r\nthe solution is monica baker in 1 with a puzzle; darren forbes in 2 with the teddy bear; mark mckenna in 3 with the book; kevin farell in 4 with the crayons; holly lorenz in 5 with the blocks; and janet collins in 6 with the fire engine.',NULL,0);
INSERT INTO comment VALUES (8256,532,3501,'r. allison','different soultion--ribs','2003-09-29 13:33:46',0,'adam and eve are the only people in heaven with one rib.',NULL,0);
INSERT INTO comment VALUES (8257,1198,1220,'abc','re: computer solution','2003-09-29 15:14:59',0,'40F (not 44 like you typed) is equivalent to 4C°, by rounding down to the next integer.\r\n',8254,0);
INSERT INTO comment VALUES (8258,1276,1220,'abc','solution','2003-09-29 15:51:34',3,'The following notations don\'t represent the correct placement of the persons on photo #1. The color of clothing is given in the order of shirt/tie/suspenders.\r\n\r\nFrom picture 1 we have the placement:\r\n?/red/? - black/?/? - ?/?/white - white/?/? - ?/?/?\r\nI will refer to them as 1-2-3-4-5 in that order.\r\n\r\nPicture 3 tells us that the persons wearing a red shirt, a green shirt and white suspenders are three different persons. Combining this with the information of picture 1 shows that neither one of them can be person 2 or 4 and 3 is the one with the white suspenders. This leaves 1 and 5 for the red and the blue shirt. Person #1 cannot wear another red thing and therefore must wear the green shirt. Person #5 wears the red shirt and only the blue shirt is left for #3.\r\n\r\nThe description of picture 7 distinguishes the person wearing the black shirt (#2) from the one wearing the red suspenders. Only #3 and #4 are left for the red suspenders and because #3 is already wearing white suspenders, it must be #4.\r\n\r\nCurrently we have:\r\ngreen/red/? - black/?/? - blue/?/white - white/?/red - red/?/?\r\n\r\nFrom picture 1,3 and 7 we know that #2 can only wear the black suspenders.\r\n\r\nIn picture 6 we see that the person wearing the green shirt (#1) and the blue suspenders is not one and the same, thus #1 wears green suspenders and #5 the blue ones.\r\n\r\nNow only the ties are left to be distributed.\r\n\r\nFrom all that we know up to this point, picture 5 shows persons 1,3, 4 and the one with the black tie. Picture 6 shows persons 1,3,5 and the one with the black tie. This must mean that the person with the black tie isn\'t either 1,3,4 or 5 and therefore must be #2. \r\nThis solves the first part of the problem. Person #2 is wearing all black clothing.\r\n\r\nPicture 2 shows the person wearing a white tie in front of the three people wearing red things (1,4,5). This means either #2 or #3 is wearing a white tie. #2 already wears the black tie, ergo it\'s #3. This leaves the blue and the green tie for #4 and #5. From picture 4 we know that the person wearing the red shirt (#5) is not the one wearing a green tie. Thus #4 wears a green and #5 a blue tie.\r\n\r\nFinal solution:\r\ngreen/red/green - black/black/black - blue/white/white - white/green/red - red/blue/blue ',NULL,0);
INSERT INTO comment VALUES (8259,1198,3558,'Tristan','short solution','2003-09-29 18:24:23',3,'I figured out this problem by taking the two digits and making a two variable equation.\r\n(10x+y-32)5/9=10y+x\r\nAfter a lot of simplification, I got something close to 1/2*x-2=y. So I tested a few inputs of x that would give integers, and 61F and 82F came close to being their reflections in C. So it was 61F on the way to work and 82F back.',NULL,0);
INSERT INTO comment VALUES (8260,1198,1301,'Charlie','re(2): computer solution','2003-09-29 20:13:17',0,'That\'s why I said \"IF 44 F were equivalent to 4 C (which it\'s not),\" (new emphasis), this having to do with what would have triggered a bug in the program.',8257,0);
INSERT INTO comment VALUES (8261,486,1301,'Charlie','re:','2003-09-29 20:17:37',0,'Of course, the more people there are in the room the more likely it is to have a match. While 23 (not 22) is the least that will give a larger probability of a match than not, 40 gives even better odds of finding a match. There\'s no contradiction there.',8248,0);
INSERT INTO comment VALUES (8262,460,3667,'Michael','Another Solution','2003-09-30 01:04:58',0,'B +H+k\r\nh+ B +\r\n+r+ + \r\n + +r+\r\n+ Q + \r\n\r\n',NULL,0);
INSERT INTO comment VALUES (8263,1229,3172,'SilverKnight','solution','2003-09-30 09:50:57',3,'assuming that I understood exactly the rules, and that I faithfully reproduced them on a spreadsheet:\r\n\r\na) On your 15th birthday,\r\nGrandfather gives you: £16384\r\nGrandmother gives you: £10832 + £5 = £10837\r\n\r\nb) Grandfather gives you the most after 27 years:\r\nhe gives £134,217,727 (2^27-1)\r\ngrandmother gives £88,756,884 on the 27th birthday\n\nEdited on September 30, 2003, 9:53 am',NULL,0);
INSERT INTO comment VALUES (8264,1229,2899,'Brian Wainscott','re: solution','2003-09-30 11:10:38',0,'You got to this before I did, and got the same answer, so my only contribution is to be nit-picky:\r\n\r\nI believe that in your last sentence you mean \"grandmoter gives a total of £88,756,884 after 27 years.\"\r\n\r\nON the 27th birthday, grandmother \"only\" gives £44,378,442.\r\n',8263,0);
INSERT INTO comment VALUES (8265,1229,3172,'SilverKnight','re(2): solution','2003-09-30 11:20:51',0,'Indeed Brian...\r\n\r\nYou win the award for biggest picker of nits! :-)\r\n\r\nThe question I was addressing (namely the amount given after 27 years) is, I think, correctly answered by my answer of £88,756,884.\r\n\r\nI could have better phrased my statement by using \"by the 27th birthday\", rather than \"on the 27th birthday\".\r\n\r\n--- SK',8264,0);
INSERT INTO comment VALUES (8266,1166,2707,'Gordon Steel','A Solution (I think!)','2003-09-30 12:06:49',0,'Designate a rectangle as ABCD where AC and BD are the diagonals. Bring corner A into coincidence with corner C, creating a crease of XY where X lies on line AB and Y on line CD. AX must equal CX (since the length is a constant). We can also prove that XC = AX = CY = AY by virtue of being similar triangles. Thus diagonal AC is perpendicular to and bisects XY at a point we may label Z. Since triangles AZX and ABC are similar, we know that XZ/BC = AZ/AB. And, since XY = 2XZ, we can rewrite this as 2 x (AZ) x (BC)/AB. But this is the same as (W/L) x Square root of (L squared + Y squared). Gordon S.',NULL,0);
INSERT INTO comment VALUES (8267,1166,2707,'Gordon Steel','A Correction on the Solution','2003-09-30 12:18:42',0,'After posting the soltuion to the origamic problem, I noticed (naturally) that I had a typographical error in my last sentence. I had written the solution as (W/L) x square root of (L squared + Y squared). What I meant to write (and should have written) is the length of the crease is given as (W/L) x the square root of (L squared + W squared). I apologize for the error. Gordon S.',8266,0);
INSERT INTO comment VALUES (8268,27,3670,'Bruno','re: not true','2003-09-30 12:23:22',0,'Exactly what I thought. The only way for this to be a paradox is for the teacher to conduct the test on Friday, since no one expects him to give it on that day. As for the other days, he can conduct the test and, for at least one student, it will be a surprise.\r\n\r\nThe recursive process used to eliminate the other days of the week is not mutually exclusive; in other words, we eliminated friday DUE TO THE FACT that the teacher didn´t conduct the test on the other days. But we can´t eliminate the other days using the same process.\r\n\r\n:)',7497,0);
INSERT INTO comment VALUES (8269,31,3670,'Bruno','re: don\'t believe the given solution is correct','2003-09-30 12:27:10',0,'And we can´t forget that the bee ISN´T a point, but has a considerable dimension when the distance between the bike and house is small. So, the bee would be facing a direction when the bike reaches the house - just impossible to know.\r\n\r\n:)',7730,0);
INSERT INTO comment VALUES (8270,1352,3430,'pat','sos','2003-09-30 12:44:49',0,'i tried trig and words take shape easier',NULL,0);
INSERT INTO comment VALUES (8271,27,3172,'SilverKnight','re(2): not true','2003-09-30 13:17:49',0,'Not quite Bruno:\r\n\r\nWe eliminated Friday DUE TO THE FACTS that there are\r\n\r\nHeight of grid:21\r\nWidth of grid:15\r\n+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+\r\n| | | | | | | | | | | | | | | |\r\n+ + + + + + + + + + + + + + + +\r\n| | | | | | | | |\r\n+--+ + +--+ +--+--+ +--+ + +--+ + +--+\r\n| | | | | | | | |\r\n+ + + +--+ +--+ +--+--+ + + + +--+--+\r\n| | | | | | | | | | |\r\n+--+--+ +--+ + + + +--+ + + +--+--+ +\r\n| | | | | |\r\n+--+--+ + +--+ + +--+ + +--+ +--+--+--+\r\n| | | | |\r\n+--+--+--+--+--+ +--+--+--+ +--+--+ +--+--+\r\n| | | | | | |\r\n+--+ +--+--+--+ + + +--+ +--+--+--+--+--+\r\n| | | |\r\n+--+ +--+ +--+--+ +--+--+ +--+--+--+ +--+\r\n| | | | | | | | |\r\n+ + + + +--+ + +--+ +--+--+--+--+--+--+\r\n| | | | |\r\n+--+--+--+--+--+--+--+--+ + +--+--+ +--+--+\r\n| | | | |\r\n+--+ +--+--+--+--+ +--+--+--+--+ + +--+ +\r\n| | |\r\n+--+--+--+--+--+ +--+--+ +--+--+--+--+--+--+\r\n| | | | | | |\r\n+--+ +--+ + + +--+ +--+--+ +--+ +--+ +\r\n| | | | | | |\r\n+--+--+--+--+ + +--+--+--+ + +--+--+ +--+\r\n| | | | | |\r\n+--+--+--+ +--+ + + + + + + +--+ +--+\r\n| | | | | | | | |\r\n+--+ +--+ + + + + +--+--+ +--+--+ + +\r\n| | | | | | | | |\r\n+--+--+--+ +--+ +--+ + + + +--+--+--+ +\r\n| | | | | | | |\r\n+ +--+--+--+--+--+ +--+ + +--+--+ +--+--+\r\n| | | | | |\r\n+--+--+--+ + + + + + + + +--+--+ + +\r\n| | | | | | | | | | | |\r\n+ + + +--+ + + + + + + + + +--+--+\r\n| | | | | | | | | | | |\r\n+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+\r\nEnter for more; Esc to end.\r\n
\r\n-------------\r\nHopefully this maze will appear correctly above, given the appropriate pre and /pre value within angle brackets.',NULL,0);
INSERT INTO comment VALUES (8339,1216,1183,'fwaff','re: fiziks...here goes','2003-10-03 04:22:47',3,'You almost had the right answer, but dismissed the wrong value of t. At t=1.667s George is busy sliding through the junction (forwards). At t=3.333s George is at a standstill. Continuing to apply a deceleration of -30f/s/s means that at t=5 he is travelling backwards through the junction.\r\n\r\nLooking at the problem with simple sums (ie no calculus)...\r\n\r\nGeorge\'s car comes to a halt at 3.333s (=100/30)\r\nOver those 3.333s George\'s average velocity was 50f/s (=100/2), which means that he travelled 166.667 ft ie over 40 ft past the junction.\r\nAfter 3.333s Bill has travelled 100ft, so he still has 50ft to travel before he gets to the junction.\r\nEven allowing for the lengths and widths of the cars there is no collision before or at 3.333s. There is also no collision at any time after 3.333s since George is at a standstill sufficiently far through the junction that Bill doesn\'t hit him.\r\n',8336,0);
INSERT INTO comment VALUES (8340,624,3716,'Carolyn','What Happened?','2003-10-03 04:49:56',0,'The year 1961 was unique in that if you flipped it over it was still 1961. Carolyn_27587',NULL,0);
INSERT INTO comment VALUES (8341,638,3172,'SilverKnight','solution','2003-10-03 08:20:11',0,'16\r\n61\r\n106\r\n\r\nthe car is travelling at 45 miles/hour',NULL,0);
INSERT INTO comment VALUES (8342,638,1183,'fwaff','Solution - no brute force','2003-10-03 08:42:30',3,'Let \'ab\' represent the number on the first milestone - ie the first digit is \'a\' and the second digit is \'b\'.\r\nThen \'ba\' represents the number on the second milestone.\r\nAnd \'a0b\' represents the number on the third milestone\r\n\r\nSince the speed is uniform we know that a0b-ba=ba-ab\r\n\r\nba-ab<90, hence a0b-ba<90 hence a=1\r\n(if a>1 then a0b-ba>100)\r\n\r\nAbove we had the equation a0b-ba=ba-ab. Since we now know that the numbers are 1b, b1 and 10b, this can be re-written as:\r\n\r\nb1 + b1 = 10b + 1b\r\n\r\nb1 = (10b + 1b) / 2\r\n\r\nThe min value of (10b + 1b)/2 is 56 (when b=1)\r\nThe max value of (10b + 1b)/2 is 64 (when b=9)\r\n\r\nTherefore 56 <= b1 <= 64\r\n\r\nSo b1 = 61\r\n\r\nThus the three milestones showed 16, 61 and 106, which means that the car was travelling at 45 mph.',NULL,0);
INSERT INTO comment VALUES (8343,344,2839,'FatBoy','please ignore','2003-10-03 08:45:37',3,'a hole\r\nor a gas that is lighter than air',NULL,0);
INSERT INTO comment VALUES (8344,1277,2839,'FatBoy','please ignore','2003-10-03 09:13:46',3,'Azdam went with Forgam who wore white suspenders a blue tie and a green shirt\r\nBastam went with Holdram who wore blue suspenders a white tie and a red shirt\r\nCagram went with Golkam who wore green suspenders a red tie and a white shirt\r\nDartam went with Epotram who wore red suspenders a green tie and a blue shirt',NULL,0);
INSERT INTO comment VALUES (8345,1432,1920,'Brian Smith','Going in Circles','2003-10-03 09:29:32',0,'As I see it, the algorithm will keep adding walls to the maze until EVERY loop is broken. The algorithm will also never cut the maze into two sub-mazes. There are a total of x*(y-1)+y*(x-1)=2*x*y-x-y places to construct walls. Since there are x*y cells, there must be at least x*y-1 passages between cells for all the cells to be connected (with x*y-x-y+1 walls erected). If there are more than x*y-1 passages, then somewhere in the maze there is a loop, which means a wall can be added. So there must be exactly x*y-1 passages and exactly x*y-x-y+1 walls when the algorithm terminates.',NULL,0);
INSERT INTO comment VALUES (8346,638,3172,'SilverKnight','re: Solution - no brute force','2003-10-03 09:51:30',0,'I didn\'t brute force either! :-)\r\n\r\n(Of course, I didn\'t really explain it, to be fair)\r\n\r\nBut basically, very easy thought process:\r\nif the first two milestones are two digit, and the third is three digit... the third must be in the 100-199 range... (in fact we can narrow it down further, but...) the point is the first digit must be 1.\r\n\r\nso we have:\r\n\r\n1b\r\nb1\r\n10b\r\n\r\nclearly the b must be in the center (between 1 and 10)... so possible cases must be 5 or 6 (or thereabouts)...\r\n\r\nvery straightforward... all in the head.... no brute force... ;-)\r\n',8342,0);
INSERT INTO comment VALUES (8347,638,2839,'FatBoy','please ignore','2003-10-03 10:12:57',3,'You know, I\'m no big math stud, but I saw from teh titles that fwaff had come up with a \"no btute force colution\" I was going to read it as those solutions are so muchmor elegant than the old \"i punched it into a spread sheet and here\'s what came out answers but then I decided to see if I could do it. Here is what I came up with, I hope its as good as whatever fwaff had:\r\n\r\nfirst define the first milemarker number as AB where A and B are just digits with no mathmatical operations intended bejond the old ones place, tens place thing.\r\n\r\nSince the car is going a uniform speed and the first to milesones mentioned are two digit numbers the car must be travelling less than 100 miles per hour. therefore the difference between the second two milestones must be less than 100 therefore the third milestone number (defined in this case a A0B) must be less than 200 so A must equal 1.\r\n\r\nthis being the case we can write the mubmers of the three stones thusly:\r\n\"1B\"\r\n\"B1\"\r\n\"10B\"\r\n\r\n(with everything still representing digits and no additional operations implied)\r\n\r\nThis means however we can write the numbers mathematically as follows\r\n\"1B\" = 10+B\r\n\"B1\" = (10*B)+1\r\n\"10B\" = 100 + B\r\n\r\nsince we know the speed was constant the difference between teh first two must be the same as the difference between the second two \r\ntherefore\r\n[(10*B)+1] - (B+10) = (100+B) - [(10*B)+1]\r\nthrough my remaining HS Algebra I therfore concluded that B = 6\r\n\r\nthis means the three stones read 16, 61 and 106 \r\nThe car was going 45mph\r\n\r\nnot elegant, I admit and it probably would have been more studly to set it up with both A and B as variables in math equations and hash it out from there but I like my way anyway. ',NULL,0);
INSERT INTO comment VALUES (8348,1165,2839,'FatBoy','re(3): alternate solution','2003-10-03 10:24:50',0,'Jeff,\r\nLook out, there is a faction on this site who get cranky at those of us who have the audacity to actually work problems out and post answers without first reading everyone elses comments.\r\nBest bet is to just ignore them.\r\n',8226,0);
INSERT INTO comment VALUES (8349,1277,2839,'FatBoy','re: Explanation?','2003-10-03 10:41:07',4,'Do you mean you worked it out without a diagram?\r\nI could probably write out longhand an explanation of why each person ahd to be wearing what by listing oout how I worked my grid but I suspect you must have something else in mind as doing that would be too dull and pointless (even for me)\n\nEdited on October 3, 2003, 10:41 am',8333,0);
INSERT INTO comment VALUES (8350,638,1183,'fwaff','re: please ignore','2003-10-03 10:55:39',0,'FB: It\'s pretty much the same as I came up with, except I used lower case a & b ;-)\r\n\r\nSK: I wasn\'t implying you did use brute force, I was just differentiating my answer from whatever program Charlie posts. I hope that one day when I\'m all grown up I can be as clever as you and work things like this out in my head.',8347,0);
INSERT INTO comment VALUES (8351,638,3224,'Lee','solution','2003-10-03 11:20:15',0,'(let the milestones be at ab, ba, a0b)\r\nThe distance by inspection is 90a (diff\' between 1st and 3rd)\r\nSo average speed = 90a/2 mph\r\nba-ab=45a (halfway point) [ba = 10b + a, also, ab = 10a + b]\r\n9(b-a)=45a\r\nb=6a\r\nonly a=1, b=6 work\r\nAv. speed = 45mph\r\n(milestones at 16 61 106)',NULL,0);
INSERT INTO comment VALUES (8352,638,1301,'Charlie','Well, since fwaff was expecting one.','2003-10-03 11:21:10',0,'There being an analytic solution already, I wasn\'t going to post the brute force program, but it looks like fwaff expects one so I shan\'t disappoint:\r\nFOR a = 12 TO 89\r\n a$ = LTRIM$(STR$(a))\r\n b$ = RIGHT$(a$, 1) + LEFT$(a$, 1)\r\n b = VAL(b$)\r\n c = 2 * b - a\r\n c$ = LTRIM$(STR$(c))\r\n IF LEFT$(c$, 1) = LEFT$(a$, 1) AND RIGHT$(c$, 1) = RIGHT$(a$, 1) AND MID$(c$, 2, 1) = \"0\" THEN\r\n PRINT a, b, c\r\n END IF\r\nNEXT\r\n\r\nThe only pre-analysis that went in is that the three-digit milestone came after the two-digit ones, so the miles were going up rather than down, giving the limits for the first milestone as 12 to 89.',8350,0);
INSERT INTO comment VALUES (8353,1277,1183,'fwaff','','2003-10-03 11:21:17',1,'I guess this is another of those English English vs US English things, but for an island monkey like me the thought of blokes going out to dinner dressed in shirts, ties and suspenders conjours up some very bizarre images.',NULL,0);
INSERT INTO comment VALUES (8354,638,3172,'SilverKnight','re: Well, since fwaff was expecting one.','2003-10-03 11:22:38',0,'lol',8352,0);
INSERT INTO comment VALUES (8355,638,3172,'SilverKnight','re(2): please ignore','2003-10-03 11:27:05',0,'I think the (perhaps unintentional) implication of the prior solution being brute force was there, due to your title... but no matter... :-) \r\n\r\nI hope I never reach \"all grown up\" !\r\n\r\nAnd it\'s always good to be able to work things out in one\'s head... IMHO... kinda like those \'math tricks\' that they like to teach people to do....\r\n\r\ne.g., what\'s 48 x 52...? Well... gee I don\'t know... but it\'s 2² less than 50² so... 2500 - 4 = 2496.... cool...\n\nEdited on October 3, 2003, 11:27 am',8350,0);
INSERT INTO comment VALUES (8356,638,1183,'fwaff','re: Well, since fwaff was expecting one.','2003-10-03 11:33:06',0,'Thanks Charlie, I knew I could rely on you!',8352,0);
INSERT INTO comment VALUES (8357,1277,2839,'FatBoy','Oh, I\'m not so sure','2003-10-03 11:52:11',0,'fwaff,\r\nI\'ve partied with ex-pats from the UK in various thrid world countries (Hashers and such), and after having witnessed the \"dance of the flaming a**holes (or a***holes since we are discussing UK english)\" I find that there is very little that a bloke could do that I would find bizarre.\r\n\r\nNB I\'m sure you know but just in case, when we Yanks say suspenders we mean braces',8353,0);
INSERT INTO comment VALUES (8358,72,2839,'FatBoy','please ignore','2003-10-03 12:02:11',3,'B and C made the same statement so they must have the same inclination (both liars or both KNights)\r\n\r\nthe puzzle specifies that there is at least one of each type so A must be the opposite\r\n\r\nIf A were telling the truth then all the statements would be true so A must be a liar therefore B and C must be Knights\r\n\r\nSince a is a liar he does not have the key\r\nsince B is a knight he does not have the key\r\nso C has the key\n\nEdited on October 3, 2003, 12:05 pm',NULL,0);
INSERT INTO comment VALUES (8359,1277,1171,'nikki','Full explanation','2003-10-03 12:29:05',3,'\r\nFirst, let’s refer to Zablon’s statements as 1-6.\r\n\r\nEpotram is wearing red suspenders (5), and so he must be wearing a green tie (2). Since neither Forgam or Golkam will wear the red or blue shirt (4), that means that Epotram and Holdram have to wear them. But Epotram can’t wear the red shirt since he is wearing red suspenders (1). This means Epotram must be wearing the blue shirt and Holdram is wearing the red shirt.\r\n\r\nSince Epotram is wearing red, not white, suspenders he can’t be taking Azdam. Since he is wearing a green tie he can’t be taking Bastam (3). And since he is wearing a blue shirt, he can’t be taking Cagram (3). This means Epotram must be taking Dartam.\r\n\r\nSo we have successfully matched Dartam with Epotram and his red suspenders, green tie, and blue shirt. Here is what we are left with:\r\n\r\nWhite, green, blue suspenders\r\nWhite, red, blue tie\r\nWhite, red, green shirt \r\n\r\nSince Azdam’s date is wearing white suspenders, Bastam and Cagram must be going with the boys wearing green and blue suspenders. Due to their preferences, this must mean that Bastam’s date is wearing blue suspenders and Cagram’s date is wearing green suspenders (3).\r\n\r\nCagram’s date can’t be wearing a green shirt (1), and Cagram isn’t going out with Holdram (5) who is wearing a red shirt. This means that Cagram’s date must be wearing the white shirt along with his green suspenders.\r\n\r\nAzdam’s date can’t wear the white tie, nor can Cagram’s (1), so Bastam’s date must be wearing the white tie along with his blue suspenders. Bastam’s date can’t wear the white shirt now (1) and Bastam wouldn’t go with him if he were wearing green(3), so he must be wearing the red shirt. And Holdram happens to be wearing the red shirt.\r\n\r\nNow we have successfully matched Bastam with Holdram and his blue suspenders, white tie, and red shirt. Here is what we are left with:\r\n\r\nWhite, green suspenders\r\nRed, blue tie\r\nWhite, green shirt\r\n\r\nSince Cagram wouldn’t go with someone wearing blue(3), her date must be wearing the red tie. Golkam must be wearing the red tie since he won’t wear blue ties (4), so he is Cagram’s date.\r\n\r\nSo we have matched Cagram with Golkam and his green suspenders, red tie, and white shirt. This leaves the last match of Azdam with Forgram and his white suspenders, blue tie, and green shirt.\r\n\r\nLater!\r\n',NULL,0);
INSERT INTO comment VALUES (8360,638,3721,'tim','','2003-10-03 14:22:04',0,'45 mph',NULL,0);
INSERT INTO comment VALUES (8361,638,3172,'SilverKnight','re: No Subject','2003-10-03 14:26:48',0,'44.9999.... repeating mph',8360,0);
INSERT INTO comment VALUES (8362,1315,3558,'Tristan','Line Drive','2003-10-03 17:39:36',1,'I can\'t really find a pattern. Do the two share a pattern? Is this a pattern that you only need know the first line and the pattern to figure it out? Does it involve manipulating the dashes or the upright lines? Is it a one way pattern? Would two lines cancel to a dot? Does it in any way relate to the binary system? \r\n\r\nI\'m just giving other people ideas to discuss. Gamer doesn\'t need to answer.',NULL,0);
INSERT INTO comment VALUES (8363,1315,2899,'Brian Wainscott','re: Line Drive','2003-10-03 18:38:56',0,'I have no real ideas either, but in the spirit of throwing out ideas, perhaps Morse code is pertinent?',8362,0);
INSERT INTO comment VALUES (8364,1315,1626,'Gamer','Two seperate problems','2003-10-03 19:14:54',2,'Each sequence is seperate enough that they could be in two seperate problems. I just wanted to consolidate problems. :)',NULL,0);
INSERT INTO comment VALUES (8365,1315,3726,'JedC','Possible Solution to first sequence','2003-10-04 01:12:58',3,'||-|||--|-\r\n-||--|-|||\r\n|-|-|||--|\r\n||||--|-|-\r\n\r\n---|-||||| would be the next row in the sequence. Is this your answer?',NULL,0);
INSERT INTO comment VALUES (8366,1315,3558,'Tristan','re: Possible Solution to first sequence','2003-10-04 10:18:52',3,'It is best if you post how you got your answer instead of just the answer. There aren\'t any rules or anything, but I wouldn\'t really consider this a solution, just an answer.\r\n\r\nI did manage to figure out what you did anyway. From each row to the next, a \"|\" appears in the next if the one above it and the one above and to the right are different. The rightmost symbol is determined by the one above and the leftmost one in the row above. I\'m having a little trouble explaining it. I hope it\'s clear.',8365,0);
INSERT INTO comment VALUES (8367,1217,1301,'Charlie','Two solutions to the chemist\'s problem.','2003-10-04 13:45:17',0,'You could get a dummy sample to make a total of six, and distribute them in every other slot.\r\n\r\nOr you could do three samples in say slots 1, 5 and 9. After they\'re done, you could do the two others in two opposing slots.\r\n\r\nSince this is a question in \"Shapes\", perhaps these pragmatic solutions are not what is/are sought, but they\'d help the biochemist anyway.',NULL,0);
INSERT INTO comment VALUES (8368,1217,3195,'John Reid','Proposed solution','2003-10-04 13:59:40',3,'I believe we CAN run 5 samples!\r\n\r\nIf we think of the slots on the centrifuge being numbered as the face of a clock (with 12 at the top), we can use slots 12, 1, 5, 6 and 9.\r\n\r\nDraw yourself a diagram of a clock face with radius 1 centered at the origin of the x-y plane and consider these 5 points on it. Obviously they will have equal weighting in the y-direction, as 9 is on the x-axis (so has no weighting), and the other points balance out in pairs (12 with 6, 1 with 5). Now in the x-direction, the points at 12 and 6 have no weighting, and the point at 9 balances the two points at 1 and 5. This is because the points at 1 and 5 are at a 60 degree angle from the x-axis, and hence using trigonometry their distance d in the x-direction is 1/2.\r\n\r\n[cos 60 = d/1\r\nd = 1/2]\r\n\r\nSo each of these two points is 1/2 unit to the right of the origin, and this balances perfectly with the point at 9 which is 1 unit to the left.\r\n\r\nInterestingly, this means that we could also run a set of 7 samples, simply by using the opposite slots of the centrifuge (ie 2,3,4,7,8,10 and 11).\r\n\r\nI wonder if there are any other patterns that would work (not counting rotational copies of the same pattern of course)\r\n\r\nThanks DJ - another fun problem!\r\n\r\n-John',NULL,0);
INSERT INTO comment VALUES (8369,1217,3735,'Nick Hobson','Proposed solution','2003-10-04 17:38:47',0,'One way to arrive a solution is to note that if two configurations are balanced, so is their sum.\r\n\r\nTaking care to avoid an overlap, we can use the following two configurations, which are balanced by symmetry:\r\nConfiguration a: {3, 9},\r\nConfiguration b: {12, 4, 8}.\r\n\r\nTherefore the sum: {12, 3, 4, 8, 9} is balanced.',NULL,0);
INSERT INTO comment VALUES (8370,511,3736,'davey d','re: The ture answer','2003-10-04 19:41:52',0,'your answer is illogical because it contradicts the meaning of omnipotence, whihc in effect the question itslef does. god is said to be omnipotent, so he can do anything, --the paradox formed, is that he can create a stone, and he is omnipotent lettign hiom lift it, but if there is a stone he creates he cannot lift, it means he is not omnipotent, therefore the paradox stay at a standstill...gods \"will\" has nothing to do with it. the fact i do not believe in god has no effect on this',NULL,0);
INSERT INTO comment VALUES (8371,1217,153,'TomM','That\'s interesting.','2003-10-04 21:23:18',0,'My first thoughts were for the \"practical\" solutions that Charlie suggests, but I find it quite interesting that Nick found an easy solution by combining both runs of Charlie\'s second solution (provided there is no overlap). \r\n\r\nExamining John\'s question (whether there are, after accounting for rotations and reflections, more than one way to balance the five samples):\r\n\r\nFirst place three samples in (say) 12, 4, and 8\r\n\r\nSince there are three positions between any two samples, either the fourth sample will go next to one of the first three (e.g. position 11 or 1), which leads to John\'s and Nick\'s solutions and their reflections/rotations, or the fourth sample goes half-way between two of the first three (e.g. position 6). But if it is placed half-way between two, then it is opposite the third, and the fifth sample, which needs to go opposite the fourth, cannot be placed.\r\n\r\nSo, except for rotations and reflections, there is only one correct solution.\r\n\r\n ',NULL,0);
INSERT INTO comment VALUES (8372,638,2978,'Freddy Grants','solution','2003-10-05 01:35:12',0,'the car goes 45 miles per hour, the first sign is 16, the second sign is 61, 61-16=45, the third sign is 106, 106-61=45.',NULL,0);
INSERT INTO comment VALUES (8373,1315,1220,'abc','re(2): Possible Solution to first sequence','2003-10-05 08:45:51',0,'Unfortunately this doesn\'t work for the first line in the second row of the second problem. This one is different.\r\nAnd it\'s not the opposite. \r\n\n\nEdited on October 5, 2003, 8:47 am',8366,0);
INSERT INTO comment VALUES (8374,1423,1301,'Charlie','clarification','2003-10-05 11:22:39',0,'When the author says \"...starting with the most significant number\", I\'m sure she means the most significant digit of the answer.',NULL,0);
INSERT INTO comment VALUES (8375,1423,1626,'Gamer','Another Clarification','2003-10-05 12:27:18',0,'I am unsure how this got off the queue without adjustments, but it could be restated as follows:\r\n\r\n\"If you tell me a 3 digit number, I can tell you what 1667 times it is in my head, usually in less than 10 seconds. I will even start with the most significant digit in the number. How can I do that?\"\r\n\r\nI am assuming Charlie\'s idea is right, and that 1000 is being excluded. (because 1667 x 1000 is easy to do)',NULL,0);
INSERT INTO comment VALUES (8376,1423,3546,'RoyCook','solution','2003-10-05 12:58:01',3,'First off, I think the use of \"singnificant number\", or even \"significant digit\" (as in the comments) is incorrect, since such usage normally involves rounding errors.\r\n\r\nThe key to the problem is that 1667 is quite near to 1000 * (1 2/3), and in fact is exactly (1000 * (5/3)) + 1/3.\r\n\r\nOnce we have everything in fractions, since any number of the form nnn is divisible by 3 (nice fact- if a number\'s digits add up to a multiple of 3, then the number itself is a multiple of 3), it is easy to construct an algorithm which takes advantage of this in order to keep things at a managable level of complexity.\r\n\r\nAnyway, the formula (which is easily computed in the head) that will give you the correct number is:\r\n\r\n(nnn/3) * 5 * 1000 + nnn/3\r\n\r\nAgain, all numbers of the form nnn (i.e. 111, 222, 333... 888, 999) are divisible by three. Thus, for 555, we get:\r\n\r\n555/3 = 185\r\n185*5 = 925\r\n925*1000 = 925000\r\n925000 + 555/3 = 925000 + 185 = 925185.\r\n\r\nWith some concentration, this could easily be done in the head in under 10 seconds.\r\n\r\n[Presumably the author meant by \"significant number\", the fact that we can give the 925 part first. If not, then this will presumably only count as a partial solution.]',NULL,0);
INSERT INTO comment VALUES (8377,1423,3224,'Lee','solution','2003-10-05 14:09:50',0,'First, in \'normal\' multiplication you work out the result right to left - finishing with \"the most significant\" (the biggest). I think the poster is simply saying they quote the answer in full (left to right). The \'impressive\' part, I assume, is that the whole answer appears to have been worked out by some method other than the \'standard\' method. Anyway that\'s my interpretation.\r\nAlso I assume nnn is any 3 digit number (not just 111,222,333...)\r\n\r\nThis method still requires mental skill, but with practise should become fairly straightforward (under 10 sec)\r\n\r\n1. Divide nnn by 3 to give xxx (include leading 0 if nnn<300)\r\n2. Remember the remainder (0,1/3, 2/3)\r\n3. If the remainder is 1/3 work out xxx+667\r\n4. If the remainder is 2/3 work out xxx+334\r\n5. These are you last 3 digits\r\n6. Now divide xxx (and any remainder) by 2 \r\n7. The first 3 digits are the first 3 digits of the result (if nnn<600). If nnn =600 or greater use the first 4 digits\r\n\r\nExample 634 * 1667\r\n1. 634/3 = 211 (and a third)\r\n2. 211 + 667 = 878 (the last 3 digits of the result)\r\n3. (211 1/3)/2 = 105.6666666\r\n4. Result 1056 878 ',NULL,0);
INSERT INTO comment VALUES (8378,1423,3224,'Lee','also','2003-10-05 14:23:41',0,'If it isn\'t clear in my previous post ,\r\nIf nnn is divisible by 3 then nnn/3 are the last 3 digits\r\nAlso if nnn is divisible by 6 you\'ll need to include the 0000\'s following the decimal point.\r\neg 768 * 1667\r\n1. 768/3 = 256\r\n2. 256/2 = 128.00000\r\nresult 1280 256',NULL,0);
INSERT INTO comment VALUES (8379,1423,1301,'Charlie','another path?','2003-10-05 14:36:43',1,'Wouldn\'t the fact that 1667 is close to 10,000/6 make for an easier method? I haven\'t worked out the details, but it might be more straightforward than the division by 3 method, at least for the first few digits.',NULL,0);
INSERT INTO comment VALUES (8380,1423,3224,'Lee','re. another path?','2003-10-05 14:54:06',0,'That\'s where I started.\r\n1667 =10002/6\r\nIt\'s the 2 that makes it awkward I think.\r\nnnn * 10002/6 = nnn * [10000/6 + 2/6]\r\n\r\nnnn * 2/6 is where I divide by 3 (step1)\r\nDividing this result by 2 gives me the digits involved in 10000/6 element.\r\nThe awkward part is when nnn is not divisible by 3 (and therefore not 6). You can\'t just stick the numbers together. (hence my messy \"if the remainder = 1/3....\" stage)\r\nI tried this on about six or seven examples and by the end was getting much quicker!(but not 10 seconds)',NULL,0);
INSERT INTO comment VALUES (8381,1423,1626,'Gamer','re: another path?','2003-10-05 14:57:13',3,'I was thinking along the same lines as Charlie. All you would need to do this way is to figure out what the number is when divided by 6, and what the remainder is.\r\n\r\nTo do this, take the number divided by 6. These are the first two digits. The next is the decimal equivelant of the remainder, plus twice the first two digits, plus one.\r\n\r\nFor example, 263/6 = 43 with a remainder of 5. So 263 times 1667 is 438,421 because that equals 43 followed by the decimal representation of 5/6 or 8333 plus 2x43 plus 1.\r\n\r\nAlthough this may sound harder, it would be easier to do for me.',8379,0);
INSERT INTO comment VALUES (8382,1315,3558,'Tristan','more ideas','2003-10-05 15:23:12',1,'I found a few more ideas on the second sequence.\r\nIt may have something to do with dividing the rows of dashes and lines, like ----|---|| would become 4- 2| 3- 2|, and then go somewhere from there.\r\nThe last step or first step of changing one row to the next might be reversing the order, shifting to the left or right, or switching the | and -.\r\nThe last | might automatically shift so it\'s always on the very right.\r\nI also think the second one may deal with dashes.',NULL,0);
INSERT INTO comment VALUES (8383,1036,3746,'matt','what about this','2003-10-05 19:35:54',0,'this is kinda a compatition type of thing, but what is the word with the highest point value? ',NULL,0);
INSERT INTO comment VALUES (8384,1277,3740,'Teresa White','my solution','2003-10-05 20:24:00',0,'OK, this is what I came up with:\r\n\r\nEpotram is wearing red suspenders, a green tie, a blue shirt and is taking Dartam.\r\n\r\nForgam is wearing white suspenders, a blue tie, a green shirt and is taking Azdam.\r\n\r\nGolkram is wearing green suspenders, a red tie, a white shirt and is taking Cagram.\r\n\r\nHoldram is wearing blue suspenders, a white tie, a red shirt and id taking Bastam.',NULL,0);
INSERT INTO comment VALUES (8385,1315,1575,'DJ','Thoughts..','2003-10-05 20:50:27',1,'It might be helpful to change each - to a 0 and each | to a 1.\r\n\r\nThe first sequence becomes:\r\n\r\n1101110010\r\n0110010111\r\n1010111001\r\n1111001010\r\n\r\nwhere each bit is the binary sum of the two bits above it and to the right (with a carryover of the leftmost bit to be used in calculating the rightmost).\r\nIn binary addition, 0+0=0, 0+1=1, 1+0=1, and 1+1=0. So, the result will be 0 if the bits above it are the same, and 1 if they are different, as someone noted earlier.\r\nSo, this isn\'t exactly a binary addition, but a twisted variation of a bitwise addition.\r\nIf this is the case, then the next few rows are:\r\n\r\n0001011111\r\n0011100001\r\n0100100011\r\n\r\nHowever, if that is the case, then the first row must have been selected arbitrarily, so it\'s possible that something else may have been intended altogether.\r\n1101110010 in binary becomes 652 in decimal; I don\'t see anything significant about that number. The other three rows are binary representations of 407, 697, and 970, respectively. Nothing interesting there, either.\r\nPerhaps we\'ve solved it; perhaps there is something more to consider.\r\n\r\nThe second pattern, when changed, looks like:\r\n\r\n00000011111\r\n00001100011\r\n00110100111\r\n11011001101\r\n\r\nA few general observations can be made about this series; each row has first 6, then 4, then 2, then no zeroes at the beginning. Then come at least two ones, with some intermittent zeroes and ones, and at least one 1 at the end. Perhaps, if each row depends on the previous one, the ones propagate down from row to row. How this may work is not immediately apparent, so I\'ll just throw that idea out there.\r\nThe binary rows, when represented in decimal, are 31, 99, 423, and 1741. I don\'t see much relating these numbers, except for the fact that they are all odd (a result of the last bit being a 1).\r\nAny other ideas?',NULL,0);
INSERT INTO comment VALUES (8386,1217,2716,'Federico Kereki','Simple way','2003-10-05 21:15:18',3,'Distribute three samples at equal intervals (say, at places 4, 8 and 12) and the other two samples in opposite empty places (for example, 1 and 7) -- that should be balanced.',NULL,0);
INSERT INTO comment VALUES (8387,1416,2716,'Federico Kereki','re(3): Solution','2003-10-05 21:29:15',1,'In this case, there is no ambiguity: since liars tell lies all the time, both \"I am lying\" and \"I tell lies\" imply that the speaker is a liar. Anyway, I meant the second interpretation.',8304,0);
INSERT INTO comment VALUES (8388,1151,3740,'Teresa White','my solution','2003-10-05 23:19:08',0,'This is what I came up with:\r\n\r\nMonica Baker, Puzzle, position #1\r\n\r\nDarren Forbes, Teddy Bear, position #2\r\n\r\nMark McKenna, Picture Book, position #3\r\n\r\nKevin Farrell, Crayons, position #4\r\n\r\nHolly Lorenz, Blocks, position #5\r\n\r\nJanet Collins, Fire Engine, position #6',NULL,0);
INSERT INTO comment VALUES (8389,355,1112,'Greg','What\'s the last thing...?','2003-10-06 00:00:33',0,'So, what\'s the last thing that goes through the fly\'s mind as he hits the car?\r\n\r\nHis butt of course!',7200,0);
INSERT INTO comment VALUES (8390,1423,3750,'mohan','a possible solution?','2003-10-06 01:32:25',0,'1667=10002/6. so 1667*abc where abc=a*100+b*10+c\r\ngives us the number (abcABCD)/6 where ABCD are the four digits of the number equal to 2*abc. if you can divide by 6 in 10 seconds (after multiplying the given number by 2 and placing it next to the given number in a 4 digit format, of course), you have your answer, starting from the left to the right (possibly what the problem-poser means by the words \"most significant number\").\r\nfor e.g. 1667*101=101[0202]/6 ....where 0202=2*101\r\n =1010202/6 \r\n = 168367!\r\nand 1667*999=999[1998]/6....where 1998=2*999\r\n =9991998/6\r\n =1665333!\r\n-mohan.\r\n',NULL,0);
INSERT INTO comment VALUES (8391,1423,3750,'mohan','re: solution','2003-10-06 01:42:22',0,'i think when the author gives the number in the form nnn, she still includes 3 dissimilar digits abc such as 101 which is not divisible by 3. (?)',8376,0);
INSERT INTO comment VALUES (8392,638,3750,'mohan','re: solution','2003-10-06 02:46:15',0,'elegant solution!\r\n-mohan.',8351,0);
INSERT INTO comment VALUES (8393,1315,3750,'mohan','probably not a solution','2003-10-06 04:24:21',0,'i looked for patterns and came up with something i\'m not really convinced with (the patterns didn\'t make much sense): //-/-/-/// for the 1st sequence\r\n and\r\n -//-////-// for the 2nd sequence.\r\n\r\n(in the first solution above, for instance, one of the patterns i found was that the characters # 3 through 7 are identical to those at #6 through 10 in the row above; etc.)\r\n-mohan.',NULL,0);
INSERT INTO comment VALUES (8394,638,3753,'priyank','Ans ...','2003-10-06 08:49:57',0,'The speed of the 45 Km per Hr.\r\n( First Milstone 16 \r\nSecond is 61 \r\nThird is 106)',NULL,0);
INSERT INTO comment VALUES (8395,637,1183,'fwaff','Answer','2003-10-06 09:28:24',3,'We know that the total value of the sales is $x^2 and that there are an odd number of $10 notes. \r\n\r\nWhenever the 10s value of a square number is odd, the units value is always 6. Which means that the first brother must write a cheque for $2 to even things up.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (8396,637,1171,'nikki','Solution','2003-10-06 10:07:28',3,'\r\nThe check was for 2 dollars.\r\n\r\nSince the x sheep were sold for x dollars, they received x^2 dollars. Since the brother who drew first also drew last, we know that the 10’s place of their sheep-money is odd. Let’s first see what would happen if they sold 1-10 sheep. The possible sheep-money they received is 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. Now, I know that the first three items aren’t really possible for this problem statement (since the first brother is supposed to make out with more money than the second), but bear with me here =)\r\n\r\nTechnically, the 10’s place of all of those numbers is even, except for 16 and 36. This looks promising, since we have more than one possibility for how much sheep-money they received, but the 1\'s place is the same for each. However, we should prove that there aren’t any more numbers that could fit the bill.\r\n\r\nLet’s say x = (n*10 + m) where n is an element of [0, 1, 2, 3, 4, 5…} and m is an element of [1, 2, 3, … 8, 9, 10]. Then x^2 = (n*10 + m)*(n*10 + m) = 100*n^2 + 20*n*m + m^2.\r\n\r\nRemember, we only care about if the 10’s place is odd, and then what the corresponding 1’s place is. Let’s look at each term. No matter what value n is, 100*n^2 will always have zero in its 10’s place. And if we consider 20*n*m, this term will always have an even value for it’s 10’s place. So the only term that can have an odd 10’s place (and thus make x^2 have an odd 10’s place) is m^2.\r\n\r\nAnd we have already shown that only happens when m is a 4 or a 6. So, x must end in a 4 or a 6, and x^2 will always end in a 6. So the difference between the extra 10 that the first brother gets, and all 6 ones that the second brother gets is 4. So if the first brother writes a check for $2, that means he loses $2 while his brother gains $2, thus closing the $4 gap that was between them.\r\n\r\nLater!',NULL,0);
INSERT INTO comment VALUES (8397,1036,1301,'Charlie','re: what about this','2003-10-06 10:31:20',0,'The maximum value found in the file I use is for \"reinstitutionalizations\", with a value of 319.',8383,0);
INSERT INTO comment VALUES (8399,622,1575,'DJ','re: It\'s a dog\'s life down on the riverbank....','2003-10-06 12:25:44',0,'After your third step, Melvin is then on the opposite shore with Rover and Fido, without Fido\'s owner. If the problem allowed for isolated \'separated areas,\' it becomes completely trivial.\r\nMy solution uses the fact that dogs can be near other dogs without their owners. Your oversight is that anyone on the same side of the river is considered to be \'near\' each other; justification for that could be that if Fido could walk to his little separate area, he could just as easily walk back and attack Melvin, since Ichabod has been left helplessly on the far bank.',8007,0);
INSERT INTO comment VALUES (8400,714,3430,'pat','familiar','2003-10-06 12:35:17',0,'your solutions are tough. I feel like a number or a groundhog... keep up the work...',NULL,0);
INSERT INTO comment VALUES (8401,31,3546,'RoyCook','re:','2003-10-06 13:18:56',0,'Actually, Sam is both correct and incorrect. The Bee puzzle given here is, to all intents and purposes, equivalent to the Thompson\'s lamp example, but that does not mean that such puzzles must necessarily fail to have an answer. The problem is that the particular description of the puzzle is incomplete, and as a result we cannot tell what would happen at the limit. Compare Sam\'s description of Thomson\'s lamp (...where he turns it on at one second, off half a second later, on a quater of a second later, and so on. Is it on or off at two seconds?), which does not allow a solution, with the following more detailed account: Imagine we have a lamp (whose bulbs, wires, etc. are idealized so that they can take the strain of infinitely many changes in current, etc.), a wire leading from the lamp, through a power source (i.e. a battery, also idealized) and connected up to a switch (also idealized) that allows current to flow (and the light to thus glow) when the switch is depressed (pressed down, not sad) but allows no current to pass through when it is not depressed. Now find a rubber ball such that, when dropped from a certain height, will hit the switch and remain on it for a half-second, then bounce into the air for a half second, then sit on the switch for a quarter second, then bounce into the air for a quarter second, then sit on the switch for an eighth of a second, then bounce into the air for an eighth of a second, etc... (We can think of the time the ball \'sits\' on the switch as the time that the ball, after first contacting the switch, is compressed by the impact and then regains its shape). Clearly, the ball will have bounced (and the light will have switched on and off) infinitely many times after 2 minutes, yet it is equally obvious in this case that the ball will, after its infinitely many bounces, be sitting on the switch at the end, so the light will be on. The moral is that certain puzzles involving infinity are only insoluble because the situation has not been described in enough detail and, given a sufficiently fine-grained description of what is going on, the answer is usually straightforward.',7707,0);
INSERT INTO comment VALUES (8402,1315,1575,'DJ','re: probably not a solution (you never know!)','2003-10-06 13:28:10',1,'Acutally, I think that observation leads to a solution for the first set, along with the fact that each row contains the same number of -s and |s. If you map the values 0-9 to each row, the next row is a simple rearrangement.\r\n\r\n0123456789 in one row maps to\r\n2056789341 in the next row.\r\n\r\nTo be more precise, the first character in each row is the third digit in the previous row, the second digit in each row is the first digit of the previous row, the third digit is the sixth digit of the row above it, and so on.\r\n\r\nI was unable to determine a similar 1:1 mapping for the second series, and Gamer\'s comments seem to imply that each set has different properties.\r\n\r\nThis solution works just as well as the one I came up with before, for the small sample we have, but both still have the problem that the symbols in the first row appear to be completely arbitrary.\n\nEdited on October 6, 2003, 1:30 pm',8393,0);
INSERT INTO comment VALUES (8403,1315,3558,'Tristan','re(2): probably not a solution (you never know!)','2003-10-06 13:35:21',0,'That\'s pretty curious, how there are two patterns for this relatively complex sequence. And they both end up with different answers. I don\'t think this solution is as elegant, but it still could be the one gamer was expecting (and since they both work, they both can be called correct).\r\n\r\nOn the second sequence, maybe switching the 1s and 0s might help (possibly).',8402,0);
INSERT INTO comment VALUES (8404,66,3546,'RoyCook','','2003-10-06 13:39:13',3,'There is another possible solution (based on a time-honoured approach to similar paradoxes such as the Liar and Russell\'s). We can give up what is known as Bivalence- i.e. the claim that every sentence is either determinately true or determinately false. So sentences, and in particular, the crucial sentence \"Bill shaves himself\" can come out either true, false, or neither (think of neither, intutively, as \"is a borderline case\" or \"sorta\"- there is a very well worked out area of mathematical logic dealing with such middle possibilities.) Anyway, imagine now that Bill shaves the left side of his face every morning, but does nothing to the right side and lets the beard there grow long. Then we might say that the sentence \"Bill shaves himself\" is neither true nor false, it gets the middle value, and as a result, the sentence \"Bill shaves himself if and only if it is not the case that Bill shaves himself\" can turn out true, since it is an \"if and only if\" sentence where both sides have the same truth value (i.e. \"Neither\" or \"sorta\").\r\n\r\nInteresting fact: I once attended a party at a university philosophy department where costumes were encouraged. One of the philosophers shaved half his beard and claimed he was dressed as the Barber who shaves only those who fail to shave themselves.\r\n\r\nOne interesting aspect of this sort of solution is that it is open to what are called \'revenge\' problems. So, even assuming that we accept that some people shave themselves, other people do not shave themselves, and still other people neither shave themselves nor do not shave themselves, we can get a new paradox by assuming that Bill has a cousin in a neighbouring town who decides to shave exactly those people who either do not shave themselves, or who neither shave themselves nor do not shave themselves. ',NULL,0);
INSERT INTO comment VALUES (8405,637,3558,'Tristan','Solution','2003-10-06 13:49:56',3,'Since the first brother to draw also drew last, there is and odd number of $10 bills. Since they sell x sheep for $x dollars each, the amount of money they have is a perfect square.\r\n\r\nThe squares with an odd number in the tens place are 16 and 36. No square I\'ve found after that would have an odd number of $10s. I\'m not sure why that is.\r\n\r\nWhether it is 16 or 36, there will be 6 $1 bills. To balance this, the brother must write a $2 check.',NULL,0);
INSERT INTO comment VALUES (8406,504,3546,'RoyCook','The Real Solution','2003-10-06 13:53:43',3,'The posted solution is incorrect, at least if we are sticklers about grammar and punctuation.\r\n\r\nQuotes, such as those used around the words \"False\" and \"True\" in the puzzle, serve three main purposes:\r\n\r\n[1] scare quotes, used to indicate that one should take the use of the word with a grain of salt, or that the word is not being used in a perfectly literal sense.\r\n\r\n[2] for quoting something said, written, etc. by another speaker, author, etc.\r\n\r\n[3] for the purposes of mentioning a word, instead of using it.\r\n\r\nNow, given the context (a logic puzzle, or paradox), we can rule out the use of scare quotes, since it is unclear what the intention of the question would then be, and presumably the present context is one in which precision is wanted (and, being charitable, we can assume that the question should be interpreted in a precise way). Second, we can immediately rule out the possibility that the puzzle writer meant to be quoting someone else\'s use of \"true\" and \"false\". As a result, the only coherent way in which to intepret the use of the quotation marks is that of signifying that the words in question are being mentioned, not used. \r\n\r\nA bit of clarification: One uses a word when one wants to speak, write, etc. about what the word refers to, while one mentions a word (and uses quotes) when one wants to talk about the word itself. A word without quotation marks is understood always to be used, while (in some instances, see above) a word in quotes is being mentioned. So for example:\r\n\r\nRed is a colour.\r\n\r\n\"Red\" has three letters.\r\n\r\nare true while:\r\n\r\nRed has three letters.\r\n\r\n\"Red\" is a colour.\r\n\r\nare false (the first would imply that there is some colour that has three letters, while the second would imply that there is some object that is simultaneously a word and a colour). Thus, realizing that the sentence involved in the puzzle are mentioning the words \"False\" and \"True\", we can now see that they are equivalent, respectively, to:\r\n\r\nThe next statement is identical to the word \"False\".\r\n\r\nThe previous statement is identical to the word \"True\".\r\n\r\nUpon inspection, we can see that both statements are false, since neither statement consists of a single word (much less one or the other of the particular words \"True\" or \"False\").',NULL,0);
INSERT INTO comment VALUES (8407,1151,3759,'Howard Bandy','solution','2003-10-06 13:56:23',0,'Regarding: Logic School Shelves\r\n\r\nAssuming that the top two shelves are numbers 1 and 4, the middle two are 2 and 5, and the bottom two are 3 and 6. (The text describing the numbering could be clearer -- a drawing would help.)\r\n\r\nShelf 1 -- Top Left -- Monica Baker and Puzzle\r\nShelf 2 -- Middle Left -- Daren Forbes and Teddy Bear\r\nShelf 3 -- Bottom Left -- Mark McKenna and Picture Book\r\nShelf 4 -- Top Right -- Kevin Farrell and Crayons\r\nShelf 5 -- Middle Right -- Holly Lorenz and Blocks\r\nShelf 6 -- Bottom Right -- Janet Collins and Fire Engine\r\n\r\nThis also assumes that Shelf 5 has a higher number than Shelf 3. Otherwise, it is Janet McKenna on Shelf 3 and Mark Collins on Shelf 6.\r\n\r\nThanks,\r\nHoward',NULL,0);
INSERT INTO comment VALUES (8408,1205,1920,'Brian Smith','Tick Tock goes the clock ... (Solution)','2003-10-06 14:30:02',3,'It is impossible to time exactly 5/12 hours (25 minutes) in a finite amount of time.\r\n\r\nSince there is no reason to start a timer at a random time, there are exactly two conditions when a timer is turned on. One is at the very beginning and the other is when another timer beeps.\r\n\r\nASSUME that there is some possible method to time exactly 5/12 hours in a finite amount of time. Then there must be two timers A and B such that the amount of time from A\'s beep to B\'s beep is 5/12 hours.\r\n\r\nTimer A was turned on when timer A1 beeped. Timer A1 was turned on when A2 beeped. Timer A2 was turned on when A3 beeped. Etc... Since every timer has to run at least 30 minutes, then there are a finite number of timer beeps between A and the start, which means the amount of time from the start to A\'s beep is of the form a/(2^k) hours.\r\n\r\nThe same argument shows the time from the start to timer B\'s beep is also of the form b/(2^k) hours.\r\n\r\nThe amount of time from A\'s beep to B\'s beep is then (b/(2^k) - a/(2^k)) hours. BUT the amount of time was assumed to be exactly 5/12 hours and 5/12 CANNOT be expressed in the form b/(2^k) - a/(2^k). Therefore it is impossible to time exactly 5/12 hours in a finite amount of time.',NULL,0);
INSERT INTO comment VALUES (8409,1315,3172,'SilverKnight','re(3): probably not a solution (you never know!)','2003-10-06 14:37:01',1,'Tristan and DJ,\r\n\r\nKudos to the two of you, for you both have far more patience than I. (Of course... my being such an impatient individual... oh well).\r\n\r\nPerhaps Gamer will extend both sequences by an extra two (or so) rows, to help differentiate/eliminate \"multiple, viable solutions\".\r\n\r\n --- SK',8403,0);
INSERT INTO comment VALUES (8410,638,3760,'Ruxi','solution','2003-10-06 15:00:05',0,'\r\nIn one hour, the driver travels ba-ab miles with the speed v : v*1=ba-ab <=> v*1=10*b+a-10*a-b <=> v=9*b-9*a (1) ;\r\nThen after another hour, the driver travels a0b-ba miles with the same speed v: v*1=aob-ba <=> v=100*a+b-10*b-a <=> v=99*a-9*b (2);\r\nIn total, in 2 hours, the driver travels a0b-ab miles with the same speed v: a0b-ab=v*2 <=> 2*v= 100*a+b-10*a-b <=>v=45*a => a=v/45 (3) ;\r\nIn 9*b-9*a=v (1) we have a=v/45 (3) =>b=(6*v)/45=6*a\r\nSo, a=v/45 and b=6*a; We know that a and b are numbers from 1 to 9 so, the only posibility is a=1 and b=6 (for a>1 => b>10 which is not possible); a=v/45=1 => v=45 miles/hour;',8372,0);
INSERT INTO comment VALUES (8411,1217,3760,'Ruxi','solution','2003-10-06 15:07:03',0,'We have 5 samples which we devide in 2 groups: the first group contains 2 stamples and the second contains 3 stamples.Now, we think how to balance the elements of one group (if the elements of one group balance each other, then all 5 stamples will be balanced).\r\nFor example: 1)stamples placed in slots 1 and 7 are balanced and stamples placed in slots 2,6 and 10 are balanced. So, we place the stamples in slots 1,2,6,7 and 10 to balanced the centrifuge.\r\n2)2,3,7,8,11;\r\n3)3,4,8,9,12;\r\n4)4,5,9,10,1;\r\n5)5,6,10,11,2;\r\n6)6,7,11,12,3;\r\n7)7,8,12,1,4;\r\n8)8,9,1,2,5;\r\n9)9,10,2,3,6;\r\n10)10,11,3,4,7;\r\n11)11,12,4,5,8;\r\n12)12,1,5,6,9;\r\n(all the solutions form 2 to 12 are obtained by rotating the solution 1)',NULL,0);
INSERT INTO comment VALUES (8412,1256,3765,'Alfred','Pretty sure','2003-10-06 23:30:01',3,'Im pretty sure i know, since i\'m an air cadet, i think the next street name is Hotel Street, and the street before is Foxtrot, why? beacause when communicating on the radio, instead of using letters, pilots say the alphabet in a special way, like this, alpha bravo charlie delta echo FOXTROT GOLF HOTEL and so on, i hope i get this right :)',NULL,0);
INSERT INTO comment VALUES (8413,1277,3767,'Kyle Winking','Solution','2003-10-07 00:18:01',3,'Azdam is going with Forgam, who is wearing his white suspenders, a green shirt, and a blue tie.\r\n\r\nBastam is going with Holdram, who is wearing a red shirt, a white tie, and blue suspenders.\r\n\r\nCagram is going with Golkam, who is wearing a white shirt, a red tie, and green suspenders.\r\n\r\nDartam is going with Epotram, who is a blue shirt, a green tie, and red suspenders.',NULL,0);
INSERT INTO comment VALUES (8414,511,3660,'ratsnstuff','If it was me...','2003-10-07 02:23:48',0,'I am not a religious person, but I do not rule out the existance of an omnipotent god (which this question rules out by the way). But here is what I think. \r\n\r\nAt first sight this looks like a yes or no question, but we all know by now it isn\'t. Its a paradox as has been explained by previous comments. To say yes or no to this question will not work.\r\n\r\nIf I was omnipotent, I would create such a stone, and probably lift it also :-) Don\'t ask me how, I am not omnipotent. So I will answer this question with another question:\r\n\r\nCan an omnipotent god answer this question correctly? Of course he/she can! Thus making the answer to the first question \"yes\". He/she can create such a stone. And \"no\". He/she can lift anything. As for making sense of this? Ask the One making the stone and lifting it...',NULL,0);
INSERT INTO comment VALUES (8415,637,3660,'ratsnstuff','Possible solution','2003-10-07 02:45:58',0,'I am assuming that x in this question is a constant. In other words, each sheep is sold for an amount of dollars equal to the amount of sheep in the flock. I am also assuming that all of the sheep were sold. They must then get a nice turnover of x*x (square of x)\r\n\r\nTo work out the size of the check:\r\ny = remainder of sqr(x)/10 or y = sqr(x) mod 10\r\n\r\ncheck = (10 - y)/2\r\n\r\nThen there\'s also that weird all end on six thing in Nikki\'s answer, which is great.\r\n\r\nEdited on October 7, 2003, 3:01 am\n\nEdited on October 7, 2003, 3:02 am',NULL,0);
INSERT INTO comment VALUES (8416,428,3750,'mohan','2 other solutions!','2003-10-07 02:51:55',0,'she did not know what the second man wanted. she guessed (correctly, as it turned out) that the second man probably wanted Guinness too, and put down half a pint of Guinness in front of the second stranger. if her guess was wrong, all she would have to do upon the second customer\'s turning the Guinness down, is to give the same half pint of Guinness to the first stranger whom she had not yet served! she could then serve the second one his Worthington. i read the query carefully and the query did not affirmatively indicate that the first stranger had been served his half pint of Guinness yet, and instructed me to \"think crooked\", so there! \r\n:-)\r\n-mohan.\r\np.s. it is even possible that the bartender was only trying to serve the first one his Guinness and the author (and possibly the second man) simply misunderstood the situation and thought that the bartender had somehow divined what the second man wanted! second one\'s gotta wait until the first one\'s been served his Guinness, if you ask me! and maybe, afterward, the (slow) fair lady will turn her attention to you, mister! :-)',NULL,0);
INSERT INTO comment VALUES (8417,637,3660,'ratsnstuff','re: Solution','2003-10-07 02:56:46',0,'I don\'t totally agree, because there are more squares with uneven 10$ bills. Look at: 14 => 196 and 16 => 256 which has 19 10$ bills and 25 10$ bills respectively. There are many more where those came from, but the really weird part is that ALL of the ones I have seen have a 6 as the least significant digit, so the check would be 2$ \r\n\r\nFor the case where the brothers have 8866 sheep in their flock this still remains. I don\'t think I should even check higher because who could sell more than 8866 sheep in one day, even if there\'s two of them? Who is going to get 78 million dollars for a bunch of sheep anyway?',8405,0);
INSERT INTO comment VALUES (8418,637,3750,'mohan','re: Solution','2003-10-07 04:42:17',0,'nikki, beautiful! i got the solution too but by inspection, and was stumped as to why all my units place numbers were 6 for (x*x) with an odd tens place number...but you just proved it. and a smart way to prove it too!\r\n-mohan.',8396,0);
INSERT INTO comment VALUES (8419,637,3224,'Lee','re: Solution','2003-10-07 07:58:24',0,'(In reply to Solution by nikki)\r\n yes mohan, nice isn\'t it.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (8420,1165,3546,'RoyCook','New Alternate Solution','2003-10-07 10:51:05',3,'I don\'t know how to format it so it will look right, but the idea is simple: Just add three \"1\"\'s as exponents, either have one attached to \"√10\" and two attached to \"3\", or two attached to \"√10\" and one to \"3\", or all three attached to \"√10\", or all three attached to \"3\". Consider the first possibility. We can eliminate the need for parentheses by writing the second \"1\" attached to \"√10\" higher than the first one. Then, in words, the right-hand side would read \"The square root of ten, raised to the power one, raised to the power one (again), minus three raised to the power one. Similar comments apply to the other three possibilities.',NULL,0);
INSERT INTO comment VALUES (8421,1152,1920,'Brian Smith','Sequence Four','2003-10-07 10:55:51',0,'Sequence Four is a modular arithmetic sequence.\r\nx(n) = (x(n-1) + 5) mod 12\r\n\r\n6 = (1 + 5) mod 12\r\n11 = (6 + 5) mod 12\r\n4 = (11 + 5) mod 12\r\netc',NULL,0);
INSERT INTO comment VALUES (8422,1165,3546,'RoyCook','Along the Same Lines','2003-10-07 11:03:47',0,'We could also rewrite \"√10\" as \"√10\" divided by: \"1\" raised to the power \"1\", or rewrite \"3\" as \"3\" divided by: \"1\" raised to the power \"1\", or reqrite the entire \"√10 - 3\" as \"√10 - 3\" divided by: \"1\" raised to the power \"1\". So that\'s three more solutions.\r\n
(again, I don\'t know how to do superscripting, but hopefully you get the idea.)
|√10| minus: 3 raised to the power 1,
√10 minus: |3| raised to the power 1, etc.
\r\nSo, already only ACB or BAC are even possible
\r\nIf reporter 2 finishes his sentence with \"...bronze\"\r\nHe is saying\r\n
\r\n_A_ or\r\n_ _C\r\n\r\nThis \'statement\' contradicts our possible positions (ACB since neither\'s right, - BAC since both are)\r\nThe reporter did not say bronze.\r\n\r\nIf the reporter finished with silver, then he is saying,\r\n_A_ or\r\n_C_\r\n\r\nNow, both of our \'possible podiums\' are satisfied by only one of these statements - so we can\'t deduce which is correct.\r\n\r\nThe sentence must have finished with \"....gold\" by elimination - but we\'ll check.\r\n\r\n_A_ or (but not both)\r\nC__\r\n\r\nWith this ACB is ruled out since neither are in the right position , but BAC is consistent. Argentine must therefore have won silver, Chile didn\'t win gold or silver and therefore bronze, and Brazil won the gold.\r\n\r\nFinal order \r\nBrazil\r\nArgentine\r\nChile\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (8437,1218,3172,'SilverKnight','solution','2003-10-07 15:48:12',3,'P V W C S I\r\nL E N Z H M\r\nO D R K G F\r\nT J Y A U B\r\n\r\nAfter doing this manually, I have too much chicken scratch (and not enough patience) to write out my formal solution. I did this logically, but I kinda wish I had done this by brute force.\r\n\r\nI\'ll hopefully get back to this later.\n\nEdited on October 7, 2003, 3:49 pm',NULL,0);
INSERT INTO comment VALUES (8438,27,1626,'Gamer','re(3): not true','2003-10-07 18:16:57',0,'I don\'t believe you did it indirectly. You merely stated what has been said by others in comments below.',8271,0);
INSERT INTO comment VALUES (8439,1449,2231,'Trevor Leitch','re(5):solution','2003-10-07 18:36:31',0,'Silverknight is right insofar as he states that I forgot about the option \"Chile won bronze, or both\". I did mean silver when I wrote silver, though, I just forgot about the third possibility.\r\nIn any case, we all agree on the right answer. Kudos to us.',8430,0);
INSERT INTO comment VALUES (8440,27,3172,'SilverKnight','re(4): not true','2003-10-07 19:54:00',0,'By \"indirectly\" do you mean \"recursively\"?\r\n\r\nIf you mean recursively, then yes. I did it recursively... (whether you believe it or not).\r\n\r\nIf you mean something else, I don\'t understand you.\r\n\r\nGamer, please be more precise in your comments.\r\n\r\nAnd yes, some of what I restated is what others said earlier. I was trying to make more clear (to Bruno) what they had already said. Perhaps I didn\'t succeed to Bruno\'s or your satisfaction.',8438,0);
INSERT INTO comment VALUES (8441,325,3660,'ratsnstuff','Approach','2003-10-08 03:31:54',0,'I don\'t know how everybody else aproach these type of problems, but I used a nifty little grid, that compares all attributes with all other attributes. It works quite well. This is what popped out of it:\r\n\r\nUncle Pat chips Broncos\r\nSister Chris Cookies Cowboys\r\nCousin PJ Popcorn Dolphins\r\nBrother Stacey Carrots Raiders\r\nMother Bobbi Pizza Packers',NULL,0);
INSERT INTO comment VALUES (8442,1449,3660,'ratsnstuff','Possible Solution','2003-10-08 04:01:39',0,'From the first statement the order can only have two possibilities. If Brazil got gold, Chile must have bronze. If Chile had silver, Brazil must have had bronze, thus, from the first statement we se that it must be either of these two orders:\r\n\r\nBrazil - gold | Argentine - gold\r\nArgentine - silver | Chile - silver\r\nChile - bronze | Brazil - bronze\r\n\r\nThe second statement started, stating that Argentine got silver, and would probably have ended with \"...but not both.\" That is what I assume anyway. The first part is pointing at the first possible order. The seocond part would either be Chile got gold, silver or bronze. If he said Chile got gold, Brazil would have Bronze. This is not one of the possible solutions. If he said bronze, Argentine must have got gold (since they could not get silver or bronze) and brazil got silver - again not one of the possible solutions. If he said silver, we have a problem, because then both the possible solutions are included. However, the last part of the question states that the last reporter heard the last word and was able to deduce the correct order, therefore Argentine got silver and the first possible order is the correct one:\r\n\r\nBrazil - gold\r\nArgentine - silver\r\nChile - bronze',NULL,0);
INSERT INTO comment VALUES (8443,1449,1301,'Charlie','Of course one thing is assumed.','2003-10-08 09:28:31',0,'In all of these solutions, the press reporter is assumed to know that in fact Argentina, Brazil and Chile all won medals, which is not actually stated in the puzzle.\r\n\r\nBoth the TV and Radio announcers\' statements could be satisfied by Brazil getting gold, Argentina getting silver, and, say, Peru getting bronze, regardless of the completion of the sentence. The only way the press reporter could have deduced the order of medals is to know that the medals were restricted to these three countries mentioned.',NULL,0);
INSERT INTO comment VALUES (8444,643,1301,'Charlie','solution','2003-10-08 10:25:35',3,'Let G be the number of girls originally in the nursery.\r\n\r\nThe probability that the newest born was a girl given that a random selection of the latest population chose a boy is the probability that the newest born was a girl and that a boy would be chosen, divided by the probability that a boy would be chosen regardless of which sex the latest born was. This comes out to:\r\n\r\n(1/2)(2/(2+G+1)) / ((1/2)(2/(2+G+1)) + (1/2)(3/(3+G)))\r\n\r\nOf course 2+G+1=3+G, the new baby population of the nursery, with the former representation emphasizing the original 2 boys would still be the only 2 boys, and the latter representation showing the new 3-boy component.\r\n\r\nBut the equality of the two allows multiplying the numerator and denominator by this value. At the same time we can divide the numerator and denominator by the (1/2) factor that they share.\r\n\r\nThe result is 2/5. That\'s the probability that the latest born was a girl given that a random selection of the new population resulted in a boy being selected.\r\n\r\nThis assumes a priori that the probability was 1/2 of any given baby being a girl.',NULL,0);
INSERT INTO comment VALUES (8445,643,2839,'FatBoy','I have not read Charlie\'s post yet','2003-10-08 13:04:41',3,'I\'m probably all wet on this but it seems to me that teh baby chose at random AFTER a baby was added would have no influence on the probabilities associated with that baby so the probabality that the added baby was a girl is a little better than 50% because there are slightly more females than males born.',NULL,0);
INSERT INTO comment VALUES (8446,643,3172,'SilverKnight','Who else hasn\'t read Charlie\'s post yet?','2003-10-08 13:18:36',4,'... because I\'m just dying of curiousity to find out.',NULL,0);
INSERT INTO comment VALUES (8447,643,3626,'matt white','does the lightbulb mean they\'re right?','2003-10-08 13:35:35',0,'then why does it still say no solution yet on teh thing???? \r\n\r\nSomething that gets me is that you say a baby was added to the nursery, yet you talk about boys and girls... you automatically assume that they\'re babies. so I agree that it\'s one half, but simply because there\'s a chance it\'s either a boy or a girl, and there\'s just the one baby. \r\n',NULL,0);
INSERT INTO comment VALUES (8448,643,2839,'FatBoy','re: does the lightbulb mean they\'re right?','2003-10-08 13:41:47',0,'Matt,\r\nThe lightbulb just shows that you slected the little box below your comment that siad \"full solution\"\r\n\r\nNo matter ow many people post comments taht they claim are solutions (even if they are right. The puzzle wil stil say \"no solution posted until the folks who run the site pot the official solution.\r\n\r\nBTW welcome to Flooble',8447,0);
INSERT INTO comment VALUES (8449,1232,3626,'matt white','re: Solution','2003-10-08 13:42:53',0,'according to your final number, it means that 309 out of 10,000 people will win. Sounds like a carnival game to me!',7971,0);
INSERT INTO comment VALUES (8450,1232,3172,'SilverKnight','re(2): Solution','2003-10-08 13:47:29',0,'No Matt,\r\n\r\nAccording to fwaff\'s final number (.0309), you should expect to MAKE .0309 dollars for every dollar you wager... in the long run.\r\n\r\nSo, if you start with $10000, then after playing this game 10000 times, you can expect to find yourself with $10309 dollars.\r\n\r\n--- SK',8449,0);
INSERT INTO comment VALUES (8451,643,3172,'SilverKnight','re: does the lightbulb mean they\'re right?','2003-10-08 13:52:11',0,'I\'m afraid it doesn\'t mean that Matt.\r\n\r\nAs one might notice after reading the postings, two differing (and mutually exclusive) \"solutions\" both have the lightbulb on. So clearly, at least one would be wrong.\r\n\r\nI would encourage you to post if you can offer new information to fellow flooblers!',8447,0);
INSERT INTO comment VALUES (8452,643,1301,'Charlie','re: I have not read Charlie\'s post yet','2003-10-08 15:46:02',0,'Consider this: you have a box with one red ball and one white ball. Someone adds a ball of one or the other color, but you can\'t see which. You try a ball at random and see that it\'s red. Doesn\'t that increase the probability, in your estimation, that the ball that was added had been red?\r\n\r\nEach time you pull out a red ball in your random trials, it makes it more likely that the ball placed in there had been in fact red.',8445,0);
INSERT INTO comment VALUES (8453,643,3172,'SilverKnight','re: solution - different manner of looking at this','2003-10-08 16:26:52',3,'I\'m not sure I follow what Charlie is doing. But I come up with the same answer. Perhaps Charlie or someone else can relate these two as being the same. \r\n\r\nLet\'s continue with the assumption that the probability of any given baby being a girl is 1/2.\r\n\r\n\r\nG = the number of girls already there.\r\nRegardless of the number of girls already there then there are two cases with equal chance of occurrence.\r\n\r\ncase 1:\r\nthe added baby is a girl.\r\nin which case there are 2 boys (leaves on the event tree that could have led to the result), and G + 1 girls (leaves on the event tree that don\'t lead to the result).\r\n\r\ncase 2:\r\nthe added baby is a boy.\r\nin which case there are 3 boys (leaves on the event tree that could have led to the result), and G girls (leaves on the event tree that don\'t lead to the result.)\r\n\r\nEvery leaf on this event tree is equally likely to occur, and the problem states \"The selected baby is a boy\", limiting it to these 5 leaves.\r\n\r\nOf these 5 leaves, 3 of them are on a branch (case 2) where the boy was added, and 2 of them are on a branch (case 1) where the girl was added.\r\n\r\nAgain, all the leaves are equally likely to occur.\r\n\r\nSo, given that we selected a boy, in 2 of the 5 equally likely cases, a girl had been added. Therefore, 2/5.\r\n\r\nG, the number of girls, doesn\'t enter into the picture.',8444,0);
INSERT INTO comment VALUES (8454,1218,1171,'nikki','Explanation','2003-10-08 17:34:07',3,'Ok, here goes =)\r\n\r\nFirst note that Q and X are the two letters not used.\r\nFrom SAFE and FLAW you know that L and W must be on the same cubes as E and S. So we could either have E&L on a cube with S&W on another cube, or E&W with S&L. But from DEWY we know that E and W cannot be on the same cube, so it must be E&L with S&W.\r\n\r\nBy going through all the words that have an E or an L in them, we can eliminate many letter that we know can\'t be on the same cube with them. Luckily we eliminate so many that we see only H,M,N and Z are left, so they must be on the same cube as E and L. Good, one cube done =)\r\n\r\nNow let\'s look at JOVE and VOTE. These share E,O and V, which means T&J must be on the same cube. From TOWN we see that T and W can\'t be on the same cube. So, just to capture where we are, here is a table of what we know:\r\n\r\nCube 1: E H L M N Z\r\nCube 2: S W\r\nCube 3: T J\r\nCube 4: ?\r\n\r\nFrom TOWN we know that O must be on Cube 4.\r\nFrom PLOT we know that P must be on Cube 2.\r\nFrom VOTE we know that V must be on Cube 2.\r\n\r\nFrom DEWY we know that D and Y must be Cubes 3 and 4. But from COZY we see that Y cannot be on Cube 4. So Y must be on Cube 3 and D must be on Cube 4. And, again from COZY, we see that C must be on Cube 2.\r\n\r\nThe letters that are unplaced so far are ABFGIKRU. From all the words that SWPVC are in, we can eliminate all of those except for I. Now Cube 2 is done and we have:\r\n\r\nCube 1: E H L M N Z\r\nCube 2: S W P V C I\r\nCube 3: T J Y\r\nCube 4: O D\r\n\r\nA cannot be on the same cube as FGKR. Since there are only two cubes with open spaces, this means that FGKR must all be on the same cube. The only one with 4 open spots left is Cube 4.\r\n\r\nSo the Solution is:\r\n\r\nCube 1: E H L M N Z\r\nCube 2: S W P V C I\r\nCube 3: T J Y A B U\r\nCube 4: O D F G R K\r\n\r\nLater!\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (8455,1317,1575,'DJ','First Stabs','2003-10-08 18:32:20',1,'I don\'t know what to make of this, but I thought it might be helpful to look at in a fixed-width font:\r\n\r\n/\\\\\r\n/-\\\\\r\n/\\\\\\\\-/\r\n/\\\\-\\\\/\r\n/-\\\\/\\\\/\\\\\r\n/\\\\\\\\-//-\\\\/-\\\\\r\n/\\\\-\\\\-/-\\\\-/\r\n/-\\\\\\\\/\\\\/\\\\/\\\\/\r\n\\\\/-\\\\/\\\\/\\\\//\\\\\r\n\r\nThe first thing I noticed here is that all the backslashes (\\) appear in pairs. So, maybe that\'s just a red herring, and similar to the first slash and dash problem, I\'ll try replacing the / with ( and \\\\ with ), and the - with 1, just for kicks.\r\n\r\n()\r\n(1)\r\n())1(\r\n()1)(\r\n(1)()()\r\n())1((1)(1)\r\n()1)1(1)1(\r\n(1))()()()(\r\n)(1)()()(()\r\n\r\nThat seems to be a little better, but still all of the ( ) pairs don\'t \'close\' properly, even between rows. Also, the rows are not steadily increasing in length, as I had thought they might.\r\n\r\nMaybe I\'ll take a step back and use the original form, only replacing \\\\ with \\:\r\n\r\n/\\\r\n/-\\\r\n/\\\\-/\r\n/\\-\\/\r\n/-\\/\\/\\\r\n/\\\\-//-\\/-\\\r\n/\\-\\-/-\\-/\r\n/-\\\\/\\/\\/\\/\r\n\\/-\\/\\/\\//\\\r\n\r\nA nice little argyle piece, but still not very useful. Another thing I notice is that are an even number of \\s and /s in each row, and they are paired in order (if you ignore the -s for now):\r\n\r\n/\\\r\n/-\\\r\n/\\ \\-/\r\n/\\ - \\/\r\n/-\\ /\\ /\\\r\n/\\ \\-/ /-\\ /-\\\r\n/\\ - \\-/ - \\-/\r\n/-\\ \\/ \\/ \\/ \\/\r\n\\/ - \\/ \\/ \\/ /\\\r\n\r\nAlso, now, the rows have some kind of increasing order; if you consider /\\, \\/, /-\\, \\-/, and - to be separate entities, each row has at least as many of these pieces as the row before it.\r\n\r\nI\'m assuming the sequence is some representation of a fairly common sequence such as the counting numbers, odd numbers, prime numbers, something like that.\r\n\r\nThat\'s as far as I have gotten, though..',NULL,0);
INSERT INTO comment VALUES (8456,1218,1220,'abc','re: different Explanation','2003-10-08 20:00:33',0,'Argh...I left this lying around and couldn\'t submit it earlier. Now nikki beat me to it, but I put it on anyway. 8)\r\nIt\'s a different approach (I think nikki\'s is the better and less complicated one).\r\n\r\nLet\'s start:\r\nJOVE and VOTE are the only two words which have three letters in common (E,O,V). Therefore J and T must be on the same cube. \r\n\r\nVOTE, PLOT and TOWN all have T and O in them.\r\nE/V, L/P and N/W are each on one of the other two dices. \r\nNow we have to find words which have one letter from any two of these pairs in them. Those must then be on separate die as well. Here they are:\r\nDEWY - E and W\r\nFLAW - L and W\r\nGAPE - E and P\r\nJOVE - E and V (like VOTE)\r\nNow we know:\r\nE, V, P and W are on separate die, thus E, L and N are on one and V, P and W on the other die.\r\n\r\nSo far we have (numbered for later reference):\r\n1) J - T\r\n2) E - L - N\r\n3) P - V - W\r\n4) O\r\n\r\nWe can now proceed with the same words we just used, because they each share two of the above letters and have two unknowns. These are:\r\nDEWY - D and Y on #1 and #4\r\nFLAW - F and A on #1 and #4\r\nGAPE - G and A on #1 and #4\r\nWe immediately see that F and G are on the same die, but we don\'t know about D and Y as there is no word that shares one of them plus another letter we know the position of .\r\n\r\nWe must figure out the die with letter A, that will help a lot. As we have many words with that letter, let\'s pick those and see what we can find. We see that there are not only many words with A, but 3 with both A and S in them. Best we use these like we did with those above. While A and S are on two different die, the other two letters in each word are on the remaining two, thus we get 3 pairs:\r\nMASK - M/K\r\nRASH - R/H\r\nSAFE - F/E (we already know that)\r\nFinding words which share letters we get:\r\nBECK - E and K are separate -> E and M are on one dice with L and N/F and K are on one dice -> we still have to find out R/H\r\nCurrently we know that A,D,F,G,K and Y are on die #1 or #4. Checking up with MASK this means that M and S are on #2 and #3, we already know that M is on #2, thus we can put S on #3.\r\n\r\nNext we take words sharing A and R:\r\nLAIR - I/L\r\nRASH - H/S\r\nBecause a is on either #1 or #4 and S is on #3, one of R and H must be on #2. It cannot be R, because of LAIR, therefore it is H and R is on either #1 or #4. Since we know that A and R are on #1 and #4 and L is on #2, the letter I must be on #3.\r\n\r\nLet\'s check back quickly what we know:\r\n1) J - T - A/FGKR - D/Y\r\n2) E - H - L -M - N \r\n3) P - V - W - S - I\r\n4) O - A/FGKR - D/Y\r\n\r\nAs you can see the sequence [FGKR] cannot be on #1 as this one has already three letters, so it must be on #4 and A is on #1.\r\nCOZY has both O and Y and this means that Y cannot be #4 and must be #1 and D is #4. C and Z are on #2 and #3. \r\nBecause of BECK the letter C cannot be on #2 (E is on this one), thus we put that on #3 and Z on #2. Only #1 is left for B. The only letter left is U and must be placed on #1.\r\n\r\nSolution:\r\n1) A - B - J - T - U - Y\r\n2) E - H - L - M - N - Z\r\n3) C - I - P - S - V - W\r\n4) D - F - G - K - O - R\r\n\r\n\n\nEdited on October 8, 2003, 8:02 pm',8454,0);
INSERT INTO comment VALUES (8457,1317,1626,'Gamer','re: First Stabs','2003-10-08 20:32:21',2,'I will say that you will need to \"convert\" the numbers as you see them here to another more readilly used set.\r\n\r\nYour last ideas are good! Now you just have to figure out how to get those into the numbers, then \"convert\" them.\r\n\r\nNotice the last \"part\" in each row. This may give a clue as to what\'s happening. I think the last \"part\" in each row would continue in this pattern if continued.',8455,0);
INSERT INTO comment VALUES (8458,1317,3778,'Hipnox','Well...','2003-10-08 20:44:45',0,'There are the same numbers of / and \\\\ in each line.\r\n1º 1/ 1\\\\\r\n2º 1/ 1\\\\\r\n3º 2/ 2\\\\\r\n4º 2/ 2\\\\\r\n5º 3/ 3\\\\\r\n6º 4/ 4\\\\\r\n7º 3/ 3\\\\\r\n8º 5/ 5\\\\\r\n9º 5/ 5\\\\\r\n\r\nI think that in line 10 there will be 6/ and 6\\\\',NULL,0);
INSERT INTO comment VALUES (8459,1317,1626,'Gamer','re: Well...','2003-10-08 21:17:06',0,'That wouldn\'t qualify as a solution, mainly because you aren\'t giving the next few rows, only the number of / in \\\\ in each line.\r\n\r\nEven so, your prediction about line 10 is wrong. :)',8458,0);
INSERT INTO comment VALUES (8460,1317,3558,'Tristan','A trend','2003-10-08 21:18:22',0,'As DJ last interpreted it, I found some trends in the beginning and end.\r\n\r\nThe end goes like this for the whole pattern:\r\n/\\\r\n/-\\\r\n\\-/\r\n\\/\r\nAnd it repeats again and again.\r\n\r\nIn the beginning of each row, the following trend shows.\r\n/\\\r\n/-\\\r\n/\\\r\nAnd it continues until the ninth row, where a \\/ appears. I\'m not sure what\'s special about nine, except that it\'s 3^2, but then 4 is 2^2 and 1 is 1^2, and I don\'t see exceptions in those rows.\r\n\r\nAs for the middle, I found nothing',NULL,0);
INSERT INTO comment VALUES (8461,1315,1626,'Gamer','Hints on the second sequence','2003-10-08 21:21:18',0,'But I can\'t extend the second sequence! That would be impossible!\r\n\r\nBinary is the key for the last sequence, but don\'t think across. :)',NULL,0);
INSERT INTO comment VALUES (8462,1315,1626,'Gamer','Combining problems','2003-10-08 21:23:08',0,'For the second sequence, just ignore the first sequence. It doesn\'t need to be there... I just wanted to combine my problems.\r\n\r\n(The second sequence was what I was talking about last post; you have already got the first sequence)',NULL,0);
INSERT INTO comment VALUES (8463,1315,3558,'Tristan','partial solution to second sequence','2003-10-08 21:38:09',0,'Gamer gave me the idea to think in columns, not rows. I converted each column to binary, then to base ten, and got this:\r\n\r\n1, 1, 2, 3, 5, 6, 8, 9, 11, 14, 15\r\n\r\nI can\'t make anything of it. I do think that maybe, since he\'s asking for the next row, he actually means one on top. That means that these numbers are not the complete numbers in the sequence. For example. maybe 6 actually turns out to be 16 + 6=22.',NULL,0);
INSERT INTO comment VALUES (8464,643,1301,'Charlie','re(2): solution - different manner of looking at this','2003-10-08 22:16:23',0,'The method I used was based on Baye\'s theorem, the inference of a probability of a cause from an effect. If p(A|B) represents the probability of A given that B is true, then p(A&B) = p(B)p(A|B), or p(A&B) = p(A)p(B|A).\r\n\r\nBut this is useful in considering that p(A|B) = p(A&B)/p(B). A Venn diagram is useful in seeing this, and I think relates to your leaves.\r\n\r\nIn Baye\'s theorem, p(A|B)=p(A&B)/p(B) = p(B|A)p(A)/p(B).\r\n\r\nIn this instance A is the birth having been that of a girl, while B is the observation of having randomly selected a boy. Further, the denominator, p(B) was broken down into two parts: p(B) = p(B|A)p(A) + p(B|~A)p(~A). Here A and ~A are each 1/2. (~ represents \"not\")',8453,0);
INSERT INTO comment VALUES (8465,1315,1575,'DJ','Wha..','2003-10-08 23:07:41',4,'If it is impossible to extend the second sequence, why are you asking for the next row? Am I interpreting that incorrectly?',NULL,0);
INSERT INTO comment VALUES (8466,1315,3558,'Tristan','Aha!','2003-10-08 23:27:41',3,'-||||||||||\r\n\r\nEach column is a prime in the binary system. This last row is the missing row to complete the prime numbers. It goes 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 from left to right. There are no more rows after this one, which is why Gamer couldn\'t give a few more rows!',NULL,0);
INSERT INTO comment VALUES (8467,1416,3766,'Drew','Simple','2003-10-08 23:50:47',3,'Ok let\'s speculate:\r\nBecause A\'s and B\'s exclaimations agree with each other then,\r\nIf both knights: They would conflict because they cannot possibly tell truth about them being liars.\r\nIf both liars: Statements agree and no conflict occurs.\r\n\r\nThey are both liars',NULL,0);
INSERT INTO comment VALUES (8468,1317,1575,'DJ','re(2): First Stabs','2003-10-08 23:57:51',1,'Based on those comments, I\'ve aligned everything to the right, and put them into groups of four:\r\n\r\n / \\\r\n\r\n /-\\\r\n\r\n / \\ \\-/\r\n\r\n / \\ - \\ /\r\n\r\n\r\n /-\\ / \\ / \\\r\n\r\n / \\ \\-/ /-\\ /-\\\r\n\r\n / \\ - \\-/ - \\-/\r\n\r\n /-\\ \\ / \\ / \\ / \\ /\r\n\r\n\r\n\\ / - \\ / \\ / \\ / / \\\r\n\r\n . . . /-\\\r\n\r\n . . . \\-/\r\n\r\n . . . \\ /\r\n
\r\nThe last part is a repeating series: / \\, /-\\, \\-/, \\ /.\r\n
(2) DFS
(3) SFD
(4) SDF
(5) FDS
(6) FSD
\r\nDenmark won bronze, and/or France won silver.
\r\nDenmark won bronze, and/or France won bronze. \r\n 1001\r\n 1001 \r\n 1002001\r\n\r\n 1001\r\n 1001\r\n 1001 \r\n 1002002001
\r\nThat\'s about it.',8549,0);
INSERT INTO comment VALUES (8553,1242,1626,'Gamer','Another note:','2003-10-10 17:13:09',0,'First of all, you get no rank increase by submitting a solution, even one that\'s right.\r\n\r\nSecond of all the solutions aren\'t 6 and -10, they are 6 and -10/3.',NULL,0);
INSERT INTO comment VALUES (8554,1319,3172,'SilverKnight','re(3): Divisibility','2003-10-10 17:18:01',0,'I wasn\'t talking to you. I WAS TALKING TO NICK!!!\r\n\r\n:-) j/k\r\n\r\nHowever, I\'m not sure what you\'re saying....\r\n1001³ = 1001 x 1002001, but does not equal 1002002001.',8552,0);
INSERT INTO comment VALUES (8555,1317,1626,'Gamer','A final big hint','2003-10-10 19:36:27',2,'Group dash or no dash first, then direction. You are very close!',8524,0);
INSERT INTO comment VALUES (8556,488,1626,'Gamer','re: Solution','2003-10-10 19:39:19',0,'The last 2 lines don\'t really follow a rythmic pattern as well as the first 4 lines (as well as Finis isn\'t really a fair sentence) which is why they were excluded.\r\n\r\nIt is a riddle if you see the manipulating the Solution does. :) You just misinterpreted what I was.',8521,0);
INSERT INTO comment VALUES (8557,824,3821,'Madison','re: Surely drives fast','2003-10-10 19:40:05',0,'Yeah. He must. Hehe. I love these things. :)',5381,0);
INSERT INTO comment VALUES (8558,243,1626,'Gamer','re(2): duh','2003-10-10 19:41:57',0,'If you mean multiplicative inverses (a/b and b/a) they actually aren\'t. Even if they were, the two numbers are being ADDED, not multiplied. By no means are two multiplicitave inverses always able to add up to 1. (Of course if Average of Reciprocals was shown you would know that, but of course that\'s not important) :D ',8520,0);
INSERT INTO comment VALUES (8559,1012,3821,'Madison','Solution','2003-10-10 19:44:01',0,'Confused me for a while, but I get it. He was born in front of his dad, killed his mom in child birth, and was a priest and wed his sister to another man. :) ',7711,0);
INSERT INTO comment VALUES (8560,1051,3821,'Madison','re(3): could it be....','2003-10-10 19:47:04',0,'No. It\'s tail is round. And it\'s gray, so it DOES fit.....',6923,0);
INSERT INTO comment VALUES (8561,994,3821,'Madison','Uh..','2003-10-10 19:50:23',0,'I\'m really confused..:(',6292,0);
INSERT INTO comment VALUES (8562,1317,3778,'Hipnox','Progess','2003-10-10 20:41:09',0,'Converting the symbols to number I got this and putting there in the way dj did i got this:\r\n\r\n 1\r\n 2\r\n 13\r\n 104\r\n 211\r\n 1322\r\n 10303\r\n 24444\r\n404441\r\n\r\nSo I orginazed it in other way\r\n 4\r\n 120\r\n 1044\r\n 123344\r\n 1012044\r\n123412341\r\n\r\nThe last line we have already figure it out. But look at the line 5. 101, 204, 4...\r\nI think now will come a 408\r\n',NULL,0);
INSERT INTO comment VALUES (8563,1150,3735,'Nick Hobson','Solution','2003-10-10 21:28:37',3,'
\r\n
\r\nn: H(n)
\r\n-----
\r\n1: 0
\r\n2: 1
\r\n3: 2
\r\n4: 9
\r\n5: 44
\r\n6: 265
\r\n7: 1854
\r\n8: 14853
\r\n
\r\nMultiply the H(n-1) by the n people, then add 1 if n is odd and subtract 1 if n is even to get H(n)\r\n',NULL,0);
INSERT INTO comment VALUES (8567,648,1301,'Charlie','solution','2003-10-11 10:15:30',3,'This is the same as having two lists of names and one of them is shuffled to a random permutation. Some of the permutations will result in one or more names finding itself in its initial position and therefore matching at that/those spots, the unshuffled list; other permutations will result in no such matches. Such permutations, resulting in no matches, are called derangements.\r\n\r\nCall the number of derangements of n things d(n). The number of permutations of n things is n! (n factorial--all the integers from 1 to n multiplied together). The probability of no match, the answer to this question, is d(n)/n!.\r\n\r\nThere is a recursive formula for d(n): d(n)=(n-1)(d(n-1)+d(n-2)). This is derived as follows:\r\n\r\nA derangement of n objects can be obtained from a derangement of n-1 objects by swapping the nth (last) object to be added with any one of the n-1 objects in the older derangement. But this results in only one subset of the derangements of the new set of n object: that is, those derangements in which the last position is occupied by the object other than the one originally in the spot now occupied by piece number n as it is based on a strict derangement of the n-1 objects. The other derangements of n objects can be obtained by doing the swap with the already ordered list of n-1 objects (therefore there are still n-1 ways of doing this) and then deranging the remaining n-2 (not the last position as we want that to have the object from the position currently occupied by piece number n, and not object n itself). Thus it\'s (n-1)(d(n-1)) + (n-1)(d(n-2)), or more simply (n-1)(d(n-1)+d(n-2)).\r\n\r\nThis is the series mentioned in the Sequences puzzle Next in Line.\r\n\r\nThis sequence of numbers, 0,1,2,9,44,265,... (for n=1,2,3...) can be obtained non-recursively based on the fact that it quickly approaches n!/e where e is 2.71828..., the base of the natural logarithms. Each one in fact is n!/e rounded to the nearest integer, or in mathematical terms [n!/e + 1/2] where the square brackets indicate the floor function; the addition of 1/2 turns it into the normal rounding function.\r\n\r\nSo the final probability can be given by [n!/e + 1/2] / n!. As the number of participants gets into the teens it quickly approaches 1/e.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (8568,432,2716,'Federico Kereki','A simple solution','2003-10-11 10:42:32',3,'Since Barry and Carl disagree, one of them is a Knight and the other a Liar, but in any case Alan is a Liar, so he is guilty.',NULL,0);
INSERT INTO comment VALUES (8569,1319,2716,'Federico Kereki','Simple solution, with no words!','2003-10-11 10:44:15',3,'1001001001...001001001 x 1001 = \r\n\r\n1001001001...001001001000 \r\n++ 1001001...001001001001 =\r\n-------------------------\r\n1002002002...002002002001\r\n\n\nEdited on October 11, 2003, 10:46 am',NULL,0);
INSERT INTO comment VALUES (8570,1317,3778,'Hipnox','re(3): base 5?','2003-10-11 10:49:09',0,'I tried other numbers and I got\r\n\r\n 1\r\n 2\r\n 14\r\n 153\r\n 211\r\n 1422\r\n 15454\r\n 23333\r\n353331\r\n....52 ---maybe',8564,0);
INSERT INTO comment VALUES (8571,421,3735,'Nick Hobson','Feynman\'s answer','2003-10-11 14:03:03',1,'An interesting perspective.',NULL,0);
INSERT INTO comment VALUES (8572,1319,3827,'bharath','simple','2003-10-11 14:21:00',0,'each number is divisible by 11!',NULL,0);
INSERT INTO comment VALUES (8573,1242,3827,'bharath','simple','2003-10-11 14:24:19',0,'let cd =x then ab,af,fe,ed=x/2 and bc=x\r\narea of fig =(x^2)-1/4(x^2)=3x^2/4\r\nperimeter =4x\r\nthus 3x^2-16x=60*4\r\ntherefore x=56.\r\nalso adc is an equilateral triangle threfore ac=56',NULL,0);
INSERT INTO comment VALUES (8574,186,1626,'Gamer','Simple Solution','2003-10-11 17:11:29',3,'Here\'s the way I figured it.\r\n\r\nIn the three consecutive numbers (the one divisible by 6 and the two primes), there must be at least one number divisible by 2 and one number divisible by 3. Since neither of the primes can be divisible by 2 or 3, the middle one must be.',NULL,0);
INSERT INTO comment VALUES (8575,648,1301,'Charlie','example','2003-10-11 21:47:56',0,'An example of all 44 derangements of 5 letters is as follows:\r\n\r\nFirst those 4 x 9 = 36 in which the last letter is swapped with one of the other letters after all the other letters have been deranged, so that the original letter of the position in which the last letter (e in this instance) is not now in the last position:\r\n\r\neabcd\r\necabd\r\nedbac\r\nedacb\r\neadbc\r\necdab\r\necbad\r\nedabc\r\neadcb\r\ndebca\r\ndeabc\r\ncebad\r\nbeacd\r\ncedba\r\nbedac\r\ndebac\r\nceabd\r\nbedca\r\ndaecb\r\ndceba\r\ncdeab\r\nbdeca\r\ncaebd\r\nbcead\r\ndceab\r\ncdeba\r\nbaecd\r\ndabec\r\ndcaeb\r\ncdbea\r\nbdaec\r\ncadeb\r\nbcdea\r\ndcbea\r\ncdaeb\r\nbadec\r\n\r\nAnd then the 4 x 2 = 16 in which the last letter is swapped with one of the other letters while (or after or before; it doesn\'t matter), while the non-swapped letters are deranged:\r\n\r\nedbca\r\necdba\r\ndeacb\r\ncedab\r\ndaebc\r\nbdeac\r\ncabed\r\nbcaed\r\n\r\nThey were produced by the following program, which separates the two above groups with a blank line (debugging variable how$ is included and the line that prints it out is commented out with an apostrophe):\r\nDECLARE SUB derange (noSubst)\r\nDIM SHARED exempt(26), subPos(26), subPos2(26), xtra$(26), how$(26)\r\nDIM SHARED noExempt, basStr$\r\n\r\nINPUT \"Size:\", sz\r\nbasStr$ = LEFT$(\"abcdefghijklmnopqrstuvwxyz\", sz)\r\n\r\nderange 0 \' no substitutions yet\r\n\r\nEND\r\n\r\nSUB derange (noSubst)\r\n FOR i = LEN(basStr$) TO 1 STEP -1\r\n IF exempt(i) = 0 THEN rtmost = i: EXIT FOR\r\n NEXT\r\n IF noExempt < LEN(basStr$) - 1 THEN\r\n FOR i = 1 TO rtmost - 1\r\n IF exempt(i) = 0 THEN\r\n noS2 = noSubst + 1\r\n subPos(noS2) = i\r\n exempt(rtmost) = 1\r\n subPos2(noS2) = rtmost\r\n noExempt = noExempt + 1\r\n how$(noS2) = \"A\"\r\n derange noS2\r\n exempt(rtmost) = 0\r\n noExempt = noExempt - 1\r\n END IF\r\n NEXT\r\n IF noExempt < LEN(basStr$) - 2 THEN\r\n FOR i = 1 TO rtmost - 1\r\n IF exempt(i) = 0 THEN\r\n noS2 = noSubst + 1\r\n subPos(noS2) = i\r\n exempt(i) = 1\r\n noExempt = noExempt + 1\r\n exempt(rtmost) = 1\r\n subPos2(noS2) = rtmost\r\n noExempt = noExempt + 1\r\n how$(noS2) = \"X\"\r\n derange noS2 \' does not derange position i before swap\r\n exempt(rtmost) = 0\r\n exempt(i) = 0\r\n noExempt = noExempt - 1\r\n noExempt = noExempt - 1\r\n END IF\r\n NEXT\r\n END IF\r\n ELSE\r\n IF noExempt = LEN(basStr$) - 1 THEN\r\n p$ = basStr$\r\n FOR i = noSubst TO 1 STEP -1\r\n h$ = MID$(p$, subPos(i), 1)\r\n MID$(p$, subPos(i), 1) = MID$(p$, subPos2(i), 1)\r\n MID$(p$, subPos2(i), 1) = h$\r\n \'PRINT subPos(i), subPos2(i), how$(i)\r\n NEXT\r\n PRINT p$\r\n \'\r\n END IF\r\n END IF\r\nEND SUB\r\n\r\n\r\n\r\n\n\nEdited on October 11, 2003, 9:50 pm',NULL,0);
INSERT INTO comment VALUES (8576,824,3818,'A','very old riddle','2003-10-11 22:18:41',0,'i\'ve heard this about a million times....\r\nthe guy climbed on a stack of ice to reach the rope, hung himself, the the ice melted, creating a puddle',NULL,0);
INSERT INTO comment VALUES (8577,1217,3818,'A','possible solution','2003-10-11 22:23:39',0,'well, from my experience in the laboratory, u could technically place a sample in every other slot....this should leave one open....i was always taught that when faced with this situation, to just place a sample of water with the same mass as the sample across from it.',NULL,0);
INSERT INTO comment VALUES (8578,643,3818,'A','assumption','2003-10-11 22:30:37',0,'r we assuming that when the boy was picked out of the group it was following the majority? cause it could just be pure dumb luck that a boy was picked',NULL,0);
INSERT INTO comment VALUES (8579,643,1301,'Charlie','re: assumption','2003-10-11 23:01:58',0,'No, no assumption was made that the boy was picked out of the group following the majority. Remembering that this is independent of the number of girls originally present, let\'s just take the example of the case where 4 girl babies were originally present. The following table shows on each line the original 2 boys and 4 girls followed by either boy or girl (in equal number, representing the possible newborn), and the 7 possible choices of baby to select, and whether that particular baby is a boy or a girl.\r\n\r\nYou can see that even when girls are in the majority as in this instance, out of the five times that a boy was chosen under these circumstances, two of the times it was after a girl had been born and three after a boy had been born, although in no instance would a boy have been in the majority.\r\n\r\nboy boy girl girl girl girl; girl & chose baby 1 which is a boy\r\nboy boy girl girl girl girl; girl & chose baby 2 which is a boy\r\nboy boy girl girl girl girl; girl & chose baby 3 which is a girl\r\nboy boy girl girl girl girl; girl & chose baby 4 which is a girl\r\nboy boy girl girl girl girl; girl & chose baby 5 which is a girl\r\nboy boy girl girl girl girl; girl & chose baby 6 which is a girl\r\nboy boy girl girl girl girl; girl & chose baby 7 which is a girl\r\nboy boy girl girl girl girl; boy & chose baby 1 which is a boy\r\nboy boy girl girl girl girl; boy & chose baby 2 which is a boy\r\nboy boy girl girl girl girl; boy & chose baby 3 which is a girl\r\nboy boy girl girl girl girl; boy & chose baby 4 which is a girl\r\nboy boy girl girl girl girl; boy & chose baby 5 which is a girl\r\nboy boy girl girl girl girl; boy & chose baby 6 which is a girl\r\nboy boy girl girl girl girl; boy & chose baby 7 which is a boy\r\n\r\n',8578,0);
INSERT INTO comment VALUES (8580,648,1301,'Charlie','re: solution -- numerically','2003-10-12 09:49:02',0,'Numerically this comes out to the following for various values of n:\r\n\r\n1 0\r\n2 .5\r\n3 .3333333333333333\r\n4 .3749999999999999\r\n5 .3666666666666668\r\n6 .3680555555555558\r\n7 .3678571428571427\r\n8 .3678819444444442\r\n9 .3678791887125222\r\n10 .3678794642857141\r\n11 .3678794392336056\r\n12 .3678794413212808\r\n13 .3678794411606918\r\n14 .3678794411721625\r\n15 .3678794411713976\r\n16 .3678794411714453\r\n17 .3678794411714414\r\n18 .3678794411714417\r\n19 .3678794411714417\r\n20 .3678794411714417',8567,0);
INSERT INTO comment VALUES (8581,1423,2489,'nellie','re(2): solution','2003-10-12 11:26:22',0,'If I, as the author, can chip in. \r\n\r\nYes I did mean any 3 digit number between 100 and 1000, not just 111 or 222 etc.\r\n\r\nI also mean that I declare my answer starting with the most significant digit, ie the left hand digit first.\r\n\r\nI am enjoying your various approaches, since although I know how to do it, I have never known why my method works.\r\n\r\nKeep going.\r\n\r\n ',8391,0);
INSERT INTO comment VALUES (8582,151,2489,'nellie','another possible answer','2003-10-12 12:08:20',0,'All the comments suggest one answer.\r\nWould someone please explain why 8100000000 is not a correct answer as well. Thanks.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (8583,1436,2489,'nellie','JD plus','2003-10-12 13:23:10',0,'develop the routine a stage further to convert dates into so many weeks and so many days since the base date. All the Thursdays will have the same day remainder. ',NULL,0);
INSERT INTO comment VALUES (8584,648,3840,'Hal9000','Solution','2003-10-12 14:10:12',0,'Define n choose k as the number of distinct combinations of n elements taken k at a time. Denote n choose k as (n k) = n!/k!(n-k)! There are n! possible outcomes, now how many outcomes are such that no one draws there own name? Start with n! subtract from that the number of drawings such that one person draws there name. However we now are counting twice the situation where two people draw there own names so we must add this back in. Ups... We added back in those outcomes where three people match, get the idea, alternate until you hit n... Thus prob is the series Sum(k=0 to k=n) of (-1)^(k)*(n-k)!*(n k)/n! = Sum(k=0 to k=n) (-1)^k/k! and of course via taylor lim n-> infinity = e^(-1)',NULL,0);
INSERT INTO comment VALUES (8585,504,2716,'Federico Kereki','Oh, those quotes...','2003-10-12 14:19:14',3,'The first sentence is obviously false, since the second is not \"False\" but a rather longer one starting with \"The previous statement...\".\r\n\r\nSimilarly, the second sentence is also false, as the first one is not \"True\" but \"The next statement...\".\r\n\r\nYou should be careful with quotes!\r\n\r\nPS. I was taught how (not) to use quotes this way: would you like reading in the paper that you were seen entering a \"hotel\" with your \"wife\", a \"young\", \"healthy\", \"female\"?',NULL,0);
INSERT INTO comment VALUES (8586,1219,3196,'Dan','ATTENTION SPORTS FAN gave it away','2003-10-12 18:04:52',0,'When I read the heading \"Attention Sports Fans\", I thought at once of the 2003 Australia/New Zealand (ANZ) Golf Championships, and of Australian golfer Shannon Jones. In the first round at the New South Wales Golf Course, Mr. Jones got the following totals on the first ten holes: 0, -1, -1, -1, 1, 3, 2, 4, 4, 6\r\nSo \"6\" replaces \"?\" in the riddle. \"6\" is the answer. (DJ, you really have to try to come up with tougher riddles !!! This one was really par for the course. :-)',NULL,0);
INSERT INTO comment VALUES (8587,1219,1626,'Gamer','re: ATTENTION SPORTS FAN gave it away','2003-10-12 18:23:58',0,'Of course I didn\'t watch this golf championship, so I would be clueless about such things. :)',8586,0);
INSERT INTO comment VALUES (8588,1219,1575,'DJ','re: ATTENTION SPORTS FAN gave it away','2003-10-12 20:40:37',0,'While the score for that particular half round of golf is an interesting coincidence, I should hope it is obvious that the intended answer is less specific, more concrete, and certainly more satisfying than the absolute value of one obscure golfer\'s cumulative score..',8586,0);
INSERT INTO comment VALUES (8589,1219,3196,'Dan','re(2): ATTENTION SPORTS FAN gave it away','2003-10-12 21:29:27',0,'DJ: \"..I should hope...the intended answer is less specific, more concrete, and certainly more satisfying than the absolute value of one obscure golfer\'s cumulative score..\" \r\n \r\nYou mean that wasn\'t the right answer ?? LOL !!!!\r\nhttp://sportsillustrated.cnn.com/golf/pga/holebyhole/2003/euro_ANZ/hbh18221.html \n\nEdited on October 12, 2003, 9:46 pm',8588,0);
INSERT INTO comment VALUES (8590,1219,3801,'Callum','answer','2003-10-13 03:33:10',0,'the answer is 5',NULL,0);
INSERT INTO comment VALUES (8591,1423,3750,'mohan','','2003-10-13 04:42:39',1,'\n\nEdited on October 13, 2003, 4:48 am',NULL,0);
INSERT INTO comment VALUES (8593,96,3660,'ratsnstuff','re: Law of signs','2003-10-13 06:29:54',0,'This is also how I did it (Law of sines). :)\r\n\r\nWhy is there so many solutions with diameters less than 6cm. Thats not possible, since the longest possible chord on a circle is the diameter... Anyway... Nobody\'s probably even going to read this. This is an old problem, so, forget it...',5985,0);
INSERT INTO comment VALUES (8594,1450,3851,'Nishant','re: Solution','2003-10-13 06:48:33',0,'Obiously, that is the answer. Spain does win gold, France silver and the bronze goes to Denmark.\r\n\r\n',8486,0);
INSERT INTO comment VALUES (8595,946,3660,'ratsnstuff','The BIG hat','2003-10-13 06:49:27',2,'Assuming that the prisoner is all human sized like we all are. How is he going to swallow the \"life\" or \"death\" paper if it is poster sized and drawn from a BIG hat. It will probably take hime hours in which time he will have to keep everyone from seeing whats on his poster. Could be quite funny...',NULL,0);
INSERT INTO comment VALUES (8596,11,3660,'ratsnstuff','Solution','2003-10-13 07:02:19',3,'The cyclist and bee travel at constant ~speeds~ (we need the distance not displacement - scalars) Anyway. The Cyclist travels at 5mph, taking him 2 hrs to get home, right? \r\n\r\nThe question is thus simplified by: \"How far does a bee fly at 15mph in 2 hrs?\" Which is 30 miles.\r\n\r\nOne could even say that since the bee travels at thrice the speed of the cyclist, he will travel three times as far (30 miles).',NULL,0);
INSERT INTO comment VALUES (8597,980,3802,'Sheets','','2003-10-13 07:42:54',2,'The key piece of information you need is that noone is ever going to call themselves a Liar. Knights will always say they are a Knight and Liars will also say they are a Knight because they always lie.',NULL,0);
INSERT INTO comment VALUES (8598,828,3802,'Sheets','','2003-10-13 07:51:20',0,'The key piece of information you need is that noone is ever going to call themselves a Liar. Knights will always say they are a Knight and Liars will also say they are a Knight because they always lie.\r\n\r\nthe native must In this case a knave because the answer to the question must have been liar ',NULL,0);
INSERT INTO comment VALUES (8592,1423,3750,'mohan','solution','2003-10-13 04:45:20',3,'i posted this solution several days ago...maybe it is not clear, so here i go again.\r\n /\\\r\n / \\\r\n / \\\r\n / \\\r\n / \\\r\n / \\\r\n ½/ \\½\r\n / \\\r\n / \\\r\n / \\\r\n / \\\r\n A B\r\n /\\ /\\\r\n / \\ / \\\r\n ¼/ \\¾ ¾/ \\¼\r\n / \\ / \\\r\n / \\ / \\\r\n W B W B\r\n /\\ /\\ /\\ /\\\r\n ¼/ \\¾ ¼/ \\¾ ¾/ \\¼ ¾/ \\¼\r\n W B W B W B W B\r\n1/32 3/32 3/32 9/32 9/32 3/32 3/32 1/32\r\n
\r\nThe tree is deterministic.\r\nEach fraction along a segment represents the conditional probability of that branch given the previous step.\r\nThe last numbers are the probability of each [mutally exclusive] chain of events.\r\n\r\nThus, the probability that the first marble was black is the sum of those events, namely:\r\n3/32 + 9/32 + 3/32 + 1/32 = 16/32 = 1/2.\r\n\r\nThe probability that two black marbles were selected is the sum of those two events, or:\r\n9/32 + 1/32 = 10/32 = 5/16.\r\n\r\nThe probability of getting two black marbles, given that the first marble is black, is just the ratio of those probabilities:\r\n(10/32)/(16/32) = 10/16 = 5/8.',NULL,0);
INSERT INTO comment VALUES (8621,1220,2707,'Gordon Steel','A Different Approach on Chords','2003-10-13 15:55:28',0,'Start with circle with center C and chord AB where A and B are random points on a circle. Draw radii, R, from C to A and from C to B. Designate angle ACB as alpha. Bisect angle alpha with a line from C to D, the midpoint of AB. Therefore, Sin(alpha/2) = AD/AC = AD/R. Or, Rsin(alpha/2) = AD. Since AD = AB/2, we now have 2Rsin(alpha/2)= AB. So the question is how often does 2Rsin(alpah/2)exceed R. Space is short so I will continue on the following sheet. ',NULL,0);
INSERT INTO comment VALUES (8622,649,1575,'DJ','re: Could be wrong','2003-10-13 16:00:08',2,'You are right in saying that your \"version of the problem ignores that we know for certain that a black marble was pulled the first time.\" What you have calculated is the probability of getting two black marbles from all possible outcomes.\r\n\r\nHowever, since we are told that the first martble was black, the outcomes for which the first marble was white are eliminated, and we need to find the fraction of outcomes just from the cases where the first draw was black.\r\n\r\nAs it turns out, there is a 50/50 chance that the first marble was either black or white, and with replacement, the two pulls are independent of each other, so your answer is exactly half of what we are looking for.',8619,0);
INSERT INTO comment VALUES (8623,1220,2707,'Gordon Steel','Different Approach (Continued)','2003-10-13 16:03:32',0,'This is carried over from the immediately prior comment. We have shown that 2Rsin(alpha/2)must be >R. Dividing both sides by R, we obtain sin(alpha/)>1/2. Taking the sine function for every degree from 0 to 179, this occurs 119 times out of 180, or some 66.1%. Gordon S.',NULL,0);
INSERT INTO comment VALUES (8624,1450,1171,'nikki','re: Solution','2003-10-13 17:07:33',0,'I don\'t think RoyCook made a type-o at all. \"The press reporter must have heard\" is the same as \"the TV reporter must have said\" since the press reporter heard what the TV reporter said.',8498,0);
INSERT INTO comment VALUES (8625,1451,3862,'megan','At the Olympic Games 3','2003-10-13 17:41:42',0,'holland won the gold. if italy won the gold, holland is not better than italy. but if it is not true that holland was better than italy than greece winning the gold assumed, but this cannot be true that both italy and greece win the gold. ',NULL,0);
INSERT INTO comment VALUES (8626,1242,1171,'nikki','re: Another note:','2003-10-13 17:58:14',0,'Actually, if Callum had already ranked at least one problem, and posted two other comments, then this comment would move him from being a Novice to a Student, wouldn\'t it?',8553,0);
INSERT INTO comment VALUES (8627,532,2925,'Danny','re: different soultion--ribs','2003-10-13 18:01:05',0,'haha that is tru but how would he know unless he went up to every person and starting feeling on them ah haha ^_^',8256,0);
INSERT INTO comment VALUES (8628,1012,2925,'Danny','re: looking at every angle?!#%$&&**.','2003-10-13 18:05:53',0,'yea but if he had no mother than how could he kill her? ',6769,0);
INSERT INTO comment VALUES (8629,1205,3864,'TJ','\"double speed\"','2003-10-13 19:09:20',0,'Does this mean that a clock\'s speed can be doubled ad nauseam - i.e. taking the original clock - pressing double speed twice implies that beep will go off in 15 mins? 3 presses and 7.5 minutes?',NULL,0);
INSERT INTO comment VALUES (8630,1220,1920,'Brian Smith','re: Different Approach (Continued)','2003-10-13 19:34:14',0,'Your statement \"Taking the sine function for every degree from 0 to 179, this occurs 119 times out of 180, or some 66.1%\" implies that a finite number of chords are examined.',8623,0);
INSERT INTO comment VALUES (8631,1205,1920,'Brian Smith','re: double speed','2003-10-13 19:36:49',0,'I took the problem to mean it could be doubled only once.',8629,0);
INSERT INTO comment VALUES (8632,649,3196,'Dan','Have you lost your marbles ?','2003-10-13 20:43:39',0,'If the bag you picked was the one with three white marbles and one black marble, there is zero probability of drawing another black marble. If the bag is the one which originally had three black marbles and one white marble, it now has two black marbles and one white marble, and you have a 2-in-3 (66%) chance of drawing another black marble. There is a 50% chance of drawing either bag. So the probability of drawing the black marble as a second marble is 50% of 66%, or 33%.',NULL,0);
INSERT INTO comment VALUES (8633,649,1920,'Brian Smith','re: Have you lost your marbles ?','2003-10-13 21:04:14',0,'The puzzle stated You then put it back and draw another marble ...',8632,0);
INSERT INTO comment VALUES (8634,649,3196,'Dan','re(2): Have you lost your marbles ?','2003-10-13 21:15:50',0,'Whoops....Take 2. (Thanks for the correction, Mr. Smith).\r\n\r\nLet\'s say you do this marbleous experiment repeatedly, and draw the initial black marble 200 times. In 100 of those times, on average, you will have a bag with three white marbles and one black marble, and wil pull the second black marble approximately 25 times. In the other 100 times, with the bag with three black marbles and one white marble, you will draw the second black marble 75 times, on average. So out of 200 tries, you will draw the second black marble 25 + 75 times, or 100 times. 50% probability ???? That can\'t be right....Maybe I should have checked with golfer Shannon Jones before I tried this one..... :-) \n\nEdited on October 13, 2003, 9:47 pm',8633,0);
INSERT INTO comment VALUES (8635,649,1575,'DJ','re(3): Have you lost your marbles ?','2003-10-13 22:57:12',1,'What you\'re forgetting this time is that, if you picked a black marble on your first try, either bag is not equally likely; there is a 75% chance that you have picked one of the three black marbles in the second bag, rather than the one black marble in the first bag.\r\nLook at it this way: say you have two bags of four marbles, and all eight marbles are the same color. Any individual marble is just as likely as any other.\r\nBy the same reasoning, there is a 50/50 chance that you will pick a black marble or a white marble with a single trial. Three times out of four (not half the time), that one black marble will come out of the bag with three black marbles, and one time out of four the black marble will be the one with three white neighbors.\r\n\r\nSo, to give the same kind of analysis, out of 400 trials in which you picked the black marble, 300 of those times you will be holding the bag with three black marbles and one white marble, and you will pull a second black marble 225 times. The other 100 trials, you have the bag with one black and three white marbles, and get the black marble again 25 times on average.\r\nAll in all, that\'s an expected 250 out of 400, which does indeed reduce to 5/8, the same answer arrived at previously.',8634,0);
INSERT INTO comment VALUES (8636,649,3196,'Dan','re(4): Have you lost your marbles ?','2003-10-14 00:47:26',0,'DJ writes: \"What you\'re forgetting this time is that, if you picked a black marble on your first try, either bag is not equally likely...out of 400 trials in which you picked the black marble, 300 of those times you will be holding the bag with three black marbles and one white marble, and you will pull a second black marble 225 times....\"\r\n\r\nExcellent point, DJ. Good insight into the problem. You are correct. I did overlook that point. Maybe I\'ll give the flooble website a rest for a while, and stick to brain surgery......nahhhhhhh.... :-)',8635,0);
INSERT INTO comment VALUES (8637,1051,3868,'tyrone Etpison','re(4): could it be....','2003-10-14 01:02:43',3,'I live in Palau. It is found in the Pacific near Guam... which is in between the Philippines and Hawaii.. anyways.. in Palau there are a lot of Manatees.. or sea cows. it gotta be a sea cow. \r\nDid I get it?',8560,0);
INSERT INTO comment VALUES (8638,649,3224,'Lee','marble madness','2003-10-14 01:40:40',0,'If there were a million-and-one marbles in each bag (1m black only 1 white and vice versa) and your first draw was black you would be pretty convinced (probability 1000000/1000001) you\'d picked the black-heavy bag and the next one out was probably going to be black. Since these bags are also unevenly filled, the colour of your first draw gives the best indication of the colour of the majority of the bag (which indicates the final probability will be higher than 1/2)\r\nHere the fact your first marble is black gives you a 3/4 probability you have the bag with three blacks and 3/4 probability the next one will be.\r\n3/4*3/4 = 9/16\r\nYou could, however, have got \'lucky\' and picked the first black marble from a white-heavy bag. It\'s less likely, 1/4, but it could be the case. If so, your chances of picking the lone black marble again are 1/4.\r\n1/4*1/4 = 1/16\r\nThe total probability is therefore 9/16 + 1/16 =10/16 \r\n=5/8',NULL,0);
INSERT INTO comment VALUES (8639,649,3196,'Dan','Marble not at this......','2003-10-14 03:02:45',0,'With apologies to DJ and Brian Smith and Shannon Jones and Jesus Christ......\r\n \r\nAs someone (was it Jesus ?) astutely pointed out, when you draw a black ball, it was probably from the bag with three black balls and one white ball. Let\'s say you draw a ball of either color from a random bag 1600 times. If it is truly random, there will be roughly 800 picks from the 3-white-1-black-marble bag and 800 from the 3-black-1-white-marble bag. From the group of 800 from the 3-white-1-black bag, about 200 of these initial picks will be a black marble, and the subsequent draw, after that black marble is returned, will yield another (the same) black marble about 50 times (out of 200). From the 800 initial picks from the 3-black-1-white-marble bag, about 600 will be black; subsequent picks after the black marble is returned will yield approximately 450 black marbles (out of 600) on the second try. So after 800 (200 + 600) initial black marbles are picked from the two bags, 500 (50 + 450) black marbles are subsequently picked. So the probability of picking a black ball, after initially picking a black ball, is 5/8. (This is the same result that fell out of DJ\'s strange tree). \r\n \r\nThat may be wrong, but that is the analysis given in the latest edition of Marble Comics.... :-) ',NULL,0);
INSERT INTO comment VALUES (8640,1423,3750,'mohan','re: none','2003-10-14 03:25:01',0,'well, lee, maybe there is another way that the poster is seeking. but for me,\r\ndivision by 6 is easy if i focus on the 7-digit number in my mind\'s \r\neye...\'cos from that point onward, i only think of two digits at a time \r\n(as you illustrated) and i am able to rattle off the answer. is it \r\npossible to make a mistake once in a while? sure...but i can\'t think \r\nof another way of coming up with the answer from left to right \r\nwithout a long division being involved somewhere. i guess we\'ll \r\nfind out soon enough, though. :-)\r\n-mohan.\r\n\r\nEdited on October 14, 2003, 3:38 am\n\nEdited on October 14, 2003, 3:52 am',8609,0);
INSERT INTO comment VALUES (8641,219,3660,'ratsnstuff','The house','2003-10-14 05:30:05',1,'Well, if you look at it from the \'house\' point of view: The chance for the player to get anything more than 2$ is less than 50% In fact, the chance of winning x$ is 1/x. If the house can clearly stipulate rules such as, only 10 flips for instance, giving a jackpot of 1024$ Stating then that you can play the game for any amount more than 2$ (no, make that just a bit more) and less than 1024$ is a matter of market research. For instance, setting the buy in price to 10$ would require more than 3 consecutive successful flips (1/16 chance of winning anything) Thus the house will definately make money in the end... It would just require that magic number that would make the player say \"Wow, I can pay 10$ for this game, but I can win 1024$ !!\" The upper limit could obviously be lifted, to get a higher payout, but that would just be unfair... ',NULL,0);
INSERT INTO comment VALUES (8642,1423,2489,'nellie','Mental Arithmetic','2003-10-14 06:33:32',0,'mohan says you will be given my answer soon enough, but I\'m not certain how this site operates and who puts in my answer that I included with the question.\r\n\r\nMy screen of the question has a bottom line \"this is your question. Add/Edit solution.\" Would someone advise what I am next supposed to do and when does my answer become visible to others.',NULL,0);
INSERT INTO comment VALUES (8643,352,3660,'ratsnstuff','One solution','2003-10-14 06:54:55',3,'Below is a sequence, and below that is the sums between each number:\r\n\r\n08 01 15 10 06 03 13 12 04 05 11 14 02 07 09\r\n_09 16 25 16 09 16 25 16 09 16 25 16 09 16\r\n\r\nNotice how every second sum is 16... That is how I started...',NULL,0);
INSERT INTO comment VALUES (8644,649,2489,'nellie','no expert','2003-10-14 07:05:04',0,'I don\'t understand probablity. Since the first ball picked is then replaced, does it have any relevance what colour it was? Are you not back at square one, with the question just coming down to what are the odds of drawing a black ball from one of the bags. Ill leave it to someone else to give the odds for this.\r\n ',NULL,0);
INSERT INTO comment VALUES (8645,649,2231,'Trevor Leitch','Extension to the problem','2003-10-14 07:16:15',4,'Ok, since I think we\'ve cleared it up that the answer is 5/8, can I ask a further question: suppose that, as before, you select a bag at random and pull a black marble from it. You then replace it, and pull a second black marble, replacing that as well. What is the odds of picking a third black marble? What is the general formula of pulling a black marble on the nth try if the first (n-1) marbles pulled were all black? And what is the limit as n approaches infinite?',NULL,0);
INSERT INTO comment VALUES (8646,650,2839,'FatBoy','a start?','2003-10-14 10:00:05',0,'I haven\'t worked out the details but I bet it has something to do with selecting a certain number of coins and turning half od them over....',NULL,0);
INSERT INTO comment VALUES (8647,649,1301,'Charlie','re: Extension to the problem','2003-10-14 10:37:33',0,'The probability you have the majority-black box, by Bayes\' rule is:\r\n\r\n(1/2)(3/4)^(n-1) / ((1/2)(3/4)^(n-1) + (1/2)(1/4)^(n-1))\r\n\r\nwhich reduces to 3^(n-1)/(3^(n-1)+1)\r\n\r\nSo the probability of getting the nth ball as black would be\r\n\r\n3^(n-1)/(3^(n-1)+1) (3/4) + (1 - 3^(n-1)/(3^(n-1)+1)) (1/4)\r\n\r\nAs n gets larger, this approaches 3/4, as it becomes a near certainty you have the first bag.\r\n\r\n2 0.750000 0.250000 0.625000\r\n3 0.900000 0.100000 0.700000\r\n4 0.964286 0.035714 0.732143\r\n5 0.987805 0.012195 0.743902\r\n6 0.995902 0.004098 0.747951\r\n7 0.998630 0.001370 0.749315\r\n8 0.999543 0.000457 0.749771\r\n9 0.999848 0.000152 0.749924\r\n10 0.999949 0.000051 0.749975\r\n11 0.999983 0.000017 0.749992\r\n12 0.999994 0.000006 0.749997\r\n13 0.999998 0.000002 0.749999\r\n14 0.999999 0.000001 0.750000\r\n15 1.000000 0.000000 0.750000\r\n
\r\n----------\r\nThe above from a spreadsheet, showing the probability that you have bag 1, the probability you have bag 2 and the probability that the next ball is black.',8645,0);
INSERT INTO comment VALUES (8648,649,1301,'Charlie','re: no expert','2003-10-14 10:42:40',0,'The fact that you got a black ball increases the likelihood that it was a black-majority bag. \r\n\r\nSuppose there were a thousand black balls and 1 white ball in one bag and a thousand white balls plus 1 black in the other. In this instance the inference would be even stronger that initially drawing out a black ball makes it more likely that the next will be black also.\r\n\r\nThe case with only 4 balls in each bag is similar but to a less pronounced extent.',8644,0);
INSERT INTO comment VALUES (8649,650,3172,'SilverKnight','solution','2003-10-14 10:49:41',3,'Separate out 128 pennies from the large group (call these 128 group A, and the remainder group B)\r\n\r\nTurn all of Group A over, one by one. Then you have the same number of heads-up-pennies in both groups.\r\n\r\nProof:\r\nWhen you separate group A, you have from 0 to 128 heads-up-pennies there, lets call the number X.\r\n\r\nTherefore, you have 128-x heads-up-pennies in group B.\r\n\r\nIf you flip over all the pennies in Group A, you now have 128-x heads-up pennies in Group A as well.\r\n\r\n(e.g. If you had 5 heads-up-pennies in group A when you first separated the groups, then you must have had 123 tails-up in group A, and 123 heads-up in Group B. When you flip over *ALL* in group A, you will have 123 heads-up in Group A as well.... this satisfies the problem.)',NULL,0);
INSERT INTO comment VALUES (8650,650,1575,'DJ','re: solution','2003-10-14 12:44:24',0,'If you are only supposed to find two groups at some point in time (\"keep trying until you get it right\"), I don\'t like this problem very much.\r\n\r\nSince the problem doesn\'t say that the two subgroups involved have to include the entire set of pennies, just take two. If they\'re both heads or both tails, you\'re done; if not, just flip one over.\r\n\r\nI hope there is a more satisfactory solution, although I don\'t see how, right now...',8649,0);
INSERT INTO comment VALUES (8651,650,3172,'SilverKnight','re(2): solution','2003-10-14 12:52:29',0,'huh?\r\n\r\nYou are blindfolded... so you don\'t know (after taking two) whether or not they\'re both heads.\r\n\r\nThe point is... to be able to solve the problem WITHOUT looking, and without being told when you\'re right... rather to KNOW that you\'ve succeeded without outside intervention.\r\n\r\nAnd I think my solution does that.',8650,0);
INSERT INTO comment VALUES (8652,1221,3172,'SilverKnight','solution','2003-10-14 13:01:16',3,'The answer is n³\r\n\r\nProof:\r\nThe first element in the nth row is given by:\r\nfirst element = n² - n + 1\r\n\r\nsince each row is an arithmetic sequence (with a gap of 2), and each row has n elements, the \'middle\' element is equal to the first element + (n-1)\r\n\r\nThis is:\r\n[ (n² - n + 1) + (n - 1) ] = n²\r\n\r\nThen, the sum of the whole row is equal to the middle value, multiplied by the number of elements (n)... n² * n = n³',NULL,0);
INSERT INTO comment VALUES (8653,621,3875,'Lug','the resting sphere','2003-10-14 14:00:44',0,'The distance from the center of the sphere to the corner where the walls meet (assuming they\'re perpendicular) is 50√2. Draw the square whose diagonal is the distance from the closest point on the sphere to the corner. The length of this diagonal is 50√2 - 50. The diameter of the sphere that will fit in this little space is not the DIAGONAL of that square, but the side, no? This is (50√2 - 50)/√2. Which is about 14.64.',NULL,0);
INSERT INTO comment VALUES (8654,650,1301,'Charlie','re(3): solution','2003-10-14 14:13:59',0,'Am I missing something here? SilverKnight\'s original solution, while specifying that the pennies be turned over one by one, actually produces the desired state at the end of all the turnings over, not at some unspecified time when only some have been turned over. So, I\'m not quite sure what DJ\'s objection is, but also SilverKnight hasn\'t seemed to respond to that misunderstanding. Perhaps SK hasn\'t noticed DJ\'s misconstrual of the solution.',8651,0);
INSERT INTO comment VALUES (8655,1221,1301,'Charlie','re: solution','2003-10-14 14:17:41',0,'Don\'t we need to prove that the first element in each row is indeed n² - n + 1?\r\n\r\n',8652,0);
INSERT INTO comment VALUES (8656,650,3172,'SilverKnight','re(4): solution','2003-10-14 14:22:51',0,'misconstrual?!? is that a word? :-)\r\n\r\nI think you\'re missing something here. My solution, I think, works. I also don\'t understand what DJ\'s objection is. Perhaps he is misconstruing the orginal problem.\r\n\r\nI also don\'t understand what Charlie wants me to respond to. Charlie, if you understand what DJ meant, please feel free to elaborate.\n\nEdited on October 14, 2003, 2:23 pm',8654,0);
INSERT INTO comment VALUES (8657,1221,3172,'SilverKnight','re(2): solution','2003-10-14 14:35:35',3,'DARNIT... yeah Charlie, you\'re right. It\'s a common one though... and so I figured I could gloss over it...\r\n\r\nSo, in the interest of completeness, here you are:\r\n\r\nLike many other similar sequences... we can use the calculus of differences.\r\nThe sequence we are trying to generate is:\r\n1, 3, 7, 13, 21, ...\r\nIf we show the DIFFERENCES (of each number to the next) in the next row we have:\r\n2, 4, 6, 8, ... \r\nDo it once more... and we have:\r\n2, 2, 2, ....\r\n\r\nAha.... it is in the second row that we found a constant number. Well, we all know (don\'t we?), that this means that the sequence can be generated by a second order equation. (An² + Bn + C)\r\n\r\nso, let\'s solve for A, B, and C.\r\nLet\'s use n=1, 2, 3 to set up the equations:\r\n(1) A + B + C = 1\r\n(2) 4A + 2B + C = 3\r\n(3) 9A + 3B + C = 7\r\n\r\nSubtract (1) from (2) and we have:\r\n3A + B = 2 let\'s call this (4)\r\n\r\nSubtract (2) from (3) and we have:\r\n5A + B = 4 let\'s call this (5)\r\n\r\nsubtract (4) from (5) and we have:\r\n2A = 2\r\nTherefore, A = 1\r\nIf A = 1, then B = -1\r\nIf A = 1 and B = -1, then C = 1\r\n\r\nSo.... putting these constants back into the original generating function, we have:\r\n\r\n1n² + -1n + 1\r\n\r\nAnd this is what we wanted to show.',8655,0);
INSERT INTO comment VALUES (8658,1220,2707,'Gordon Steel','re(2): Different Approach (Continued)','2003-10-14 15:45:22',0,'Brian, Thanks for your comment. I realize that I used a finite number of chords for determining the probability of a randomly drawn chord exceeding the radius in lenght. I thought at the time that intervals of 1 degree should be reasonably precise. After reading your comment, I refined the measurment by using one-tenth of one degree for the intervals. As you probably suspect, the total was slightly greater but by only very little (less than 1%). Accordingly, I concluded that my answer was \"reasonably close\". Best regards, Gordon S.',8630,0);
INSERT INTO comment VALUES (8659,1221,2130,'ethan','Solution','2003-10-14 16:27:24',3,'n²*n. n² will always get you the mean of the row. The mean of a set times the number of elements in the set gets the sum of all the numbers in the set. Take the fourth row. 4² is 16. 13+15+17+19=4²*4=64. If you check any other row, this solution will work.',NULL,0);
INSERT INTO comment VALUES (8660,1221,2130,'ethan','re: Solution','2003-10-14 16:29:21',0,'Duh! that my first comment was pretty stupid of me. Here I am, trying to think of the perfect way to word my solution, and I end up forgetting to simplify n²*n to n³',8659,0);
INSERT INTO comment VALUES (8661,1242,3878,'sean','re: simply put','2003-10-14 16:43:52',0,'is it ab=5...bc=10...area is 100, perimeter 40.\r\nsq root(absq+bcsq)=ac....sq root of 75 is 8.66 blah...it late but it sounds right...dont burn me if its wrong :-(',8533,0);
INSERT INTO comment VALUES (8662,650,1626,'Gamer','Clarification:','2003-10-14 17:01:04',0,'What you need to do is subdivide ALL of the pennies into two groups, (and do other stuff), then say \"I\'m done\", which at that point each pile will contain the same number of heads.\r\n\r\nI don\'t think there is anything wrong with SK\'s solution... :)',NULL,0);
INSERT INTO comment VALUES (8663,1423,1626,'Gamer','re: Mental Arithmetic','2003-10-14 17:23:54',0,'You found the comments, and that\'s fine. :) Anyway, I think linking to other peoples solutions would be a good idea. Would we be allowed to add links to your solution to demonstrate other solutions (not neccesarily better)?',8642,0);
INSERT INTO comment VALUES (8664,650,1575,'DJ','re: Clarification:','2003-10-14 18:03:14',0,'Yeah.. I looked at SK\'s solution much too quickly when on my lunch break at school. Saying to turn over every penny \"one by one\" implied that at some point, the two groups would have the same number of heads. It would have been more clear just to say, take 128 of the pennies and turn each one over, after which both groups will have the same number of heads.\r\nSo, his solution is fine, of course, the wording just muddled up for me at first glance.',8662,0);
INSERT INTO comment VALUES (8665,1242,1626,'Gamer','re: simple... except you\'re wrong','2003-10-14 18:07:57',0,'First of all, according to my calculations, 12 and -20/3 are the solutions to your equation, not 56.\r\n\r\nSecond of all, the hypoteneuse of a right triangle is never equal to one of its legs! ',8573,0);
INSERT INTO comment VALUES (8666,649,3196,'Dan','re: no expert','2003-10-14 19:40:29',0,'In reply to Nellie, who wrote \"I don\'t understand probablity. Since the first ball picked is then replaced, does it have any relevance what colour it was?\" \r\n\r\nThe relevance of the color of the first ball, is that it indicates that it was probably drawn from the bag where marbles of that color predominate. ',8644,0);
INSERT INTO comment VALUES (8667,10,3883,'Krysta Harty','Not that long','2003-10-14 19:53:32',0,'19 Mins\r\n\r\nA+B CROSS = 2 MINS\r\nA RETURNS = 1 MIN\r\nA+C CROSS = 5 MINS\r\nA RETURNS = 1 MIN\r\nA+D CROSS = 10 MINS\r\n TOTAL 19 MINS\r\n',NULL,0);
INSERT INTO comment VALUES (8668,1451,3196,'Dan','','2003-10-14 21:08:38',0,'In this riddle, I decided to make two assumptons:\r\n\r\n(1) Holland, Greece and Italy, in some order, won gold, silver and bronze.\r\n(2) The \"either/or\" part of the announcer\'s statement is exclusive. Both statements \"Holland was better than Italy\" and \"Greece won gold\" cannot be true. One of them is true and one is false. \r\n \r\nEveryone, including the Dutch and Italian reporters, knew that Italy did not win gold, since if Italy had won gold, both statements \"Holland was better than Italy\" and \"Greece won gold\" would be false. \r\n \r\nIf Greece had won gold, \"Greece won gold\" is true, so \"Holland was better than Italy\" must be false. Greece would have won the gold, Italy the silver and Holland the bronze. The Dutch reporter would have known that, since he knew Holland\'s standing, and would have known that \"Holland was better than Italy\" is false, and \"Greece won gold\" is therefore true. Then he would have known that Greece won gold, Italy silver and Holland bronze. Therefore Greece did not win the gold, since the Dutch reporter could not figure out the standings. \r\n \r\nSo Holland must have won gold. Both reporters knew their own countries\' standings, and they knew that \"Holland was better than Italy\" and \"Greece won gold\" are mutually exclusive. If Italy had won bronze, the Italian reporter would have known that \"Holland was better than Italy\" is true, and that therefore \"Greece won gold\" is false. So he would have known that Greece must have won silver and Holland gold and Italy bronze - he would have known the final standings. Since he didn\'t, Italy must have won silver and Greece bronze.\r\n \r\nThe final standings:\r\n Holland - gold\r\n Italy - silver \r\n Greece - bronze \r\n',NULL,0);
INSERT INTO comment VALUES (8669,1451,3196,'Dan','re: solution','2003-10-14 21:19:13',0,'If Greece had won gold, \"Greece won gold\" is true, so \"Holland was better than Italy\" must be false. (You have to assume that those statements cannot both be true, or this riddle makes no sense). Greece would have won the gold, Italy the silver and Holland the bronze. The Dutch reporter would have known that, since he knew Holland\'s standing, and would have known that \"Holland was better than Italy\" is false, and \"Greece won gold\" is therefore true. Then he would have known that Greece won gold, Italy silver and Holland bronze. Therefore Greece did not win the gold, since the Dutch reporter could not figure out the standings. ',8611,0);
INSERT INTO comment VALUES (8670,1166,2707,'Gordon Steel','A Slight Improvement on My Last Posting','2003-10-14 21:35:24',0,'This is not an easy problem to solve or to discuss an answer lucidly. I am making minor text modifications to my last posting to hopefully improve clarity. With rectangle ABCD where AC and BD are diagonals bring corner A into coincidence with C, creating a crease from X on line AB to Y on line DC. AX must equal CX since the length being folded is constant. It can also be proved that AX = AY = CY by virtue of being similar triangles. Then, diagonal AC must bisect and be perpendicular to XY at a point we can lable Z. Since triangles AZX and ABC are similar we know XZ/BC = AZ/AB. Since XZ = 1/2 x (XY), we know that XY/2 = (AZ)(BC)/(AB) so XY = 2(AZ)(BC)/(AB). But 2AZ is equal to the diagonal, BC equal to the rectangle width and AB equal to the rectangle length. Therefore the length of the line is the square root of (Width squared + Length squared)x Width over Length. For a standard 8 by 11 inch paper this crease would be approx 9.2 inches. I feel better now. Gordon S.',NULL,0);
INSERT INTO comment VALUES (8671,650,3196,'Dan','Heads I win, tails you lose.','2003-10-15 04:07:22',0,'Let Z be the original mass of coins, consisting of 128 heads and x tails. Select 128 coins arbitrarily (by feeling, since you are blindfolded). Call this group A. A consists of m heads and n tails. m + n = 128. Z is now reduced to 128 - m heads and x - n tails. Now flip all the coins in A. A will then consist of n heads and m tails. But since m + n = 128, it follows that 128 - m = n. So the selected group A and the revised original pile Z now contain the same number of heads. ',NULL,0);
INSERT INTO comment VALUES (8672,392,3660,'ratsnstuff','re: solution','2003-10-15 04:57:09',0,'Can\'t see how this helps...',6199,0);
INSERT INTO comment VALUES (8673,1229,3660,'ratsnstuff','Nitting a scarf','2003-10-15 05:29:07',0,'There\'s so much polite niting and picking going on here, it makes me dizzy...\r\n\r\nHowever, I am not so dizzy that I can\'t say this.\r\n\r\nON 15th B-day:\r\n\r\nGramps: 16384\r\nGrams : 10837\r\n In total after 27th B-day:\r\n\r\nGramps: 134217727\r\nGrams : 88756884\r\n\r\nThis is of course solved through brute force on a spreadsheet, just like everybody else :)',NULL,0);
INSERT INTO comment VALUES (8674,1221,2716,'Federico Kereki','Triangular numbers everywhere','2003-10-15 09:20:23',3,'The first number of the n-th row is twice the (n-1)th triangular number, plus one. The last number of the same row is twice the n-th triangular number, minus one. There are n numbers in the n-th row.a 500-1000\r\nb 1000-1500\r\nc 1500-2000\r\nd 2000-2500\r\ne 2500-3000\r\n\r\n
\r\nThese are all the possible values in the puzzle.\r\nPrize 1 has possible values of a, b, or c; prize 2 has possible values of b, c, or d; and prize 3 has possible values of c, d, or e.\r\n\r\nThis gives 3³=27 possible results, as far as into which ranges each price could potentially fall into, and 3!=6 possible orderings of prizes 1, 2, and 3.\r\n\r\nFor each of the 27 sets of range assignments, there are certain possibilities for the prize rankings; for example, if prize 1 was in range c, prize 2 was in range b, and prize 3 was in range e, there is only one possible ordering, 2 is the least expensive, then 1, and then 3. On the other hand, if prize 1 was in range b, prize 2 was in range d, and prize 3 was in range d, there are two possibilities: the prizes are, in ascending order, either 123 or 132. That particular arrangement is not deterministic, but both outcomes are equally likely.\r\n\r\nThat being said, we can list all 27 outcomes for the ranges, and then determine the possible outcomes for the prize ranks in order. As it turns out, 14 of these are deterministic, 12 have two possible values, and one (all three prices fall into range c) has 6 equally likely outcomes.\r\n\r\nHere is the list:\r\nabc 123\r\nabd 123\r\nabe 123\r\nacc 123(1/2) 132(1/2)\r\nacd 123\r\nace 123\r\nadc 132\r\nadd 123(1/2) 132(1/2)\r\nade 123\r\nbbc 123(1/2) 213(1/2)\r\nbbd 123(1/2) 213(1/2)\r\nbbe 123(1/2) 213(1/2)\r\nbcc 123(1/2) 132(1/2)\r\nbcd 123\r\nbce 123\r\nbdc 132\r\nbdd 123(1/2) 132(1/2)\r\nbde 123\r\ncbc 213(1/2) 231(1/2)\r\ncbd 213\r\ncbe 213\r\nccc 123(1/6) 132(1/6) 213(1/6) 231(1/6) 312(1/6) 321(1/6)\r\nccd 123(1/2) 213(1/2)\r\ncce 123(1/2) 213(1/2)\r\ncdc 132(1/2) 312(1/2)\r\ncdd 123(1/2) 132(1/2)\r\ncde 123\r\n\r\n
\r\nRemember that each outcome has an overall probability of 1/27.\r\n\r\nBased on that, we can find out how likely each of the six rankings are:\r\n\r\nP(123) = (1/27)(10 + 10(1/2) + 1/6) = 91/162\r\nP(132) = (1/27)(2 + 6(1/2) + 1/6) = 31/162\r\nP(213) = (1/27)(2 + 6(1/2) + 1/6) = 31/162\r\nP(231) = (1/27)(1/2 + 1/6) = 4/162\r\nP(312) = (1/27)(1/2 + 1/6) = 4/162\r\nP(321) = (1/27)(1/6) = 1/162\r\n\r\n\r\nAs could be expected from the problem, the order 1, 2, 3 is by far the most likely result, occuring a little more than half of the time.\n\nEdited on October 15, 2003, 4:29 pm',NULL,0);
INSERT INTO comment VALUES (8687,1220,2707,'Gordon Steel','re(3): Different Approach (Continued)','2003-10-15 17:30:19',0,'DJ. I admit that restricting my sample to discrete degrees resulted in a slight understatement, but I take some solace that my response was approx. 99.5% of yours. I\'m not certain I understand Aaron\'s statement. It is true that the sine function changes as the degree of the angle changes, but that is not what we have here. We are asking if the number of chords within one segment of a circle is idential to the number withing an identical segment within a different portion of the circle. The answer is yes, there is no difference. The chords that can be drawn from 0 degrees to 5 degrees are precisely the same as those that can be drawn in any other 5 degree sector of the circle. The proof I think is straight-forward. Incidentally, are you the same person who proposed the Origami question (computing the length of a fold in a rectangle?). That was challenging! I spent a significant amount of time on it (admittedly struggling as to how to explain my \"solution\" clearly). Assuming you are the same person, please let me know, when convenient, if my proposed answer is correct. I posted it a few days ago. I believe the length of the fold is equal to the square root of the diagonal of the rectangle multiplied by the width over the length, or W/L x square root of (W squared + L squared).\r\n\r\nThanks for providing the mental challenges.\r\n\r\nBest regards,\r\nGordon S.',8680,0);
INSERT INTO comment VALUES (8688,1220,3172,'SilverKnight','re(4): Different Approach (Continued)','2003-10-15 17:57:08',0,'Gordon,\r\n\r\nYour response is approximate. No one is arguing with that fact. But that is exactly the point. We\'re looking for an exact answer. Ideally, we always want an exact answer, and rely on approximations only when an exact answer is impossible or too difficult to achieve.\r\n___________\r\n\r\nWhat surprises me most is.... the number of people who seem to be missing the point. Namely: that one can\'t answer this problem without first specifying what random method one uses to determine the chords. This is the key. There is no \'right\' answer, unless we refer to a particular method. And once we specify a particular method, we should be able to achieve an exact answer.\r\n___________________\r\n\r\nAs for your question about the Origami... please keep comments about that problem in the same problem\'s comment list. The solution will be posted shortly, no doubt. But in the meantime, I suggest you READ the other comments (such as this one or this one), which suggest ways of determining the answer, and in fact, specify the answer. You can verify that way, whether or not you came up with the same answer.\r\n\r\nCheers!\r\n\r\nSK\n\nEdited on October 15, 2003, 5:59 pm',8687,0);
INSERT INTO comment VALUES (8689,1458,3558,'Tristan','re(4): Possible?','2003-10-15 18:39:57',0,'If I recall, photons don\'t count as matter, and therefore must not count as any kind of object. Photons don\'t have any mass, and more than one of them can occupy the same space. I wonder why this is difficulty 5 though.',8684,0);
INSERT INTO comment VALUES (8690,1449,3895,'PWP','Got it','2003-10-15 18:46:04',3,'1st. Brazil\r\n2nd. Argentina\r\n3rd. Chile',NULL,0);
INSERT INTO comment VALUES (8691,1423,1626,'Gamer','re: gamer\'s reply','2003-10-15 19:51:52',0,'You can post it here. The people who have reached the rank of Journeymen (see the <a href=\\\"http://perplexus.info/faq.php\\\"FAQEdited on October 19, 2003, 11:56 am',NULL,0);
INSERT INTO comment VALUES (8695,66,3896,'iggyb387','yuo, no solution','2003-10-15 21:04:59',0,'I was \"taught\" this in a math class. He would not be able to shave himself because ha cannot shve people who shave themselves, and if he shaved himself then the barber would be shaving someone who shaves himself which is against the rule. He cannot not shave himself as well. If he did\'t shave himself then he would HAVE to shave himself, but he would be shaving someone who shaves himself which is against the rule. This contradicts the TAUTOLOGY p or not P so it must be a paradox.',NULL,0);
INSERT INTO comment VALUES (8696,66,3896,'iggyb387','re: yuo, no solution, sry i meant yup','2003-10-15 21:06:02',0,'see title',8695,0);
INSERT INTO comment VALUES (8697,1322,1301,'Charlie','Different distribution(s)','2003-10-15 22:18:06',0,'The probabilities will depend on the probability distributions within the three ranges specified. The preceding solutions assumed a uniform distribution within these ranges. Other possibilities exist. An example would be if the median of each range were not the arithmetic mean of the endpoints but rather the geometric mean. This would occur if the logarithm of the value were distributed uniformly rather than the value itself. This has the advantage that, for example, 500-2000 is described as probably 1000 but possibly off by a factor of 2.\r\n\r\nIn that instance the probability of winning increases to about .609962587. This is computed by the following program:\r\nDEFDBL A-Z\r\nFOR i = 1 TO 6\r\n cp(i) = LOG(500 * i)\r\nNEXT\r\n\r\nFOR k = 6 TO 4 STEP -1\r\n maxJ = 5: IF k < 5 THEN maxJ = k\r\n FOR j = maxJ TO 3 STEP -1\r\n maxI = 4: IF j < 4 THEN maxI = j\r\n FOR i = maxI TO 2 STEP -1\r\n PRINT k, j, i,\r\n p1 = (cp(k) - cp(k - 1)) / (cp(6) - cp(3))\r\n p2 = (cp(j) - cp(j - 1)) / (cp(5) - cp(2))\r\n p3 = (cp(i) - cp(i - 1)) / (cp(4) - cp(1))\r\n totP = p1 * p2 * p3\r\n IF j = k THEN\r\n totP = totP / 2\r\n IF i = k THEN\r\n totP = totP / 3\r\n END IF\r\n ELSE\r\n IF i = j THEN totP = totP / 2\r\n END IF\r\n totPr = totPr + totP\r\n PRINT USING \"#.#######\"; totP\r\n NEXT\r\n NEXT\r\nNEXT\r\nPRINT totPr\r\n\r\nIt relies on the fact that since, within the same band (of the six bands discussed) given that any two or three are in the same band the probability distribution of each is the same, so each ordering possibility still has 1/2 or 1/6 probability of being the case.\r\n\r\nMore complicated, but more likely, distributions would require numerical integrations. Particularly more likely distributions would concentrate probability near the center of the ranges, and trail off at the edges of each of the three ranges. They would presumably make success even more probable, as in the extreme case, pinpointing the prices would guarantee success.',NULL,0);
INSERT INTO comment VALUES (8698,1423,3750,'mohan','a solution?','2003-10-16 01:17:00',0,'nellie, i understood your comment to mean you have posted the solution \r\nsomewhere. if so, could you please post your solution as a comment so i \r\ncan find out what it is? (it has been a lo..o..ong time.) thanks.\r\n-mohan. ',NULL,0);
INSERT INTO comment VALUES (8699,1458,3660,'ratsnstuff','re(3): Possible? (well gee sorry...)','2003-10-16 02:24:01',0,'Sorry about the plasma statement then, didn\'t mean to offend anybody. I looked it up, and yes, it is apparent that a flame is NOT plasma. Thanks for bringing it to my attention. \r\n\r\nPlasma is a fourth state of matter. Here is a quote from\r\nhttp://www.plasmas.org/rot-plasmas.htm\r\n\r\nPlasma consists of a collection of free-moving electrons and ions - atoms that have lost electrons. Energy is needed to strip electrons from atoms to make plasma. The energy can be of various origins: thermal, electrical, or light (ultraviolet light or intense visible light from a laser). With insufficient sustaining power, plasmas recombine into neutral gas. \r\n\r\nTake this information as you like. If you are interrested in the topic, just google for plasma. And with that said, I resign from trying to comment on this problem and surrender to saying that the magnifying glass is the best option indeed, as it does not violate the rules of the problem (given of course there is enough sunlight... Also given that while trying to find a strong enough laser that is cheap enough, someone already swiped the ciggy) ',8681,0);
INSERT INTO comment VALUES (8700,1458,3660,'ratsnstuff','re(3): Possible?','2003-10-16 02:25:15',0,'Of course the butt burns! Well they do, here in South Africa...',8682,0);
INSERT INTO comment VALUES (8701,1221,3660,'ratsnstuff','re(3): solution (Well done)','2003-10-16 02:43:07',0,'From SK\'s solution:\r\n\r\nLike many other similar sequences... we can use the calculus of differences. \r\n\r\nI love the way you approached this. I never thought of it. You are differentiating the \'function\' until you get a straight line. This is done by calculating the slope between known points: (y1-y2)/(x1-x2). Since you know that (x1-x2) = 1, you just look at the difference in the values you\'ve got. Thus enabling you to find the order of the function... Briliant!',8657,0);
INSERT INTO comment VALUES (8702,482,3660,'ratsnstuff','Like in Afrikaans','2003-10-16 04:53:02',0,'Corn on the cob probably, or like we say in Afrikaans:\r\n\r\n\"Mielie so van die stronk af\"',NULL,0);
INSERT INTO comment VALUES (8703,1221,3900,'anand','here is a solution','2003-10-16 04:54:24',0,'obviously the sum of the numbers in row n is given by n^3.\r\n\r\nProof:\r\n\r\nthe first number in the nth row is given by\r\n\r\nn*(n-1)+1\r\n\r\nThis is cos till the end of the n-1th row, the number of odd numbers that would have been used up is given by 1+2+3+4....n-1 i.e n(n-1)/2 .. if that many odd numbers are used up, the last number in the n-1th row is \r\n\r\n(n(n-1)/2 *2 -1) ..so the first number of the nth row is n(n-1)/2 *2 -1 +2 = n(n-1)+1\r\n\r\nThere are n odd numbers in row n starting with \r\n\r\nn(n-1)+1, n(n-1)+1+2, n(n-1)1+4 ..n(n-1)+1+2(n-1)\r\n\r\nThe sum can be restated as \r\n\r\nn*(n(n-1)+1))+2*(1+2+3+4.....n-1)\r\n\r\n= n(n(n-1)+1)+2*(n(n-1)/2\r\n\r\n= n(n(n-1)+1)+n(n-1)\r\n\r\n= n^2(n-1)+n+n(n-1)\r\n\r\n= n^3-n^2+n+n^2-n = n^3 q.e.d',NULL,0);
INSERT INTO comment VALUES (8704,1221,3900,'anand','u dont need a hammer to crack a nut','2003-10-16 04:56:04',0,'i think we can solve this problem using a simple formula for sum of numbers from 1 to n ... dont think u need to use calculus ..i have posted the above solution.',NULL,0);
INSERT INTO comment VALUES (8705,1221,3275,'retiarius','Solution','2003-10-16 05:13:03',0,'In a series of m odd numbers the last number is 2m - 1 and the sum of the numbers is (2m - 1 + 1)m/2 = m^2\r\n\r\nIn a pyramid of odd numbers of n rows there are (n + 1)n/2 numbers. The sum of the numbers is (n + 1)^2(n^2)/4 = (n^4 + 2n^3 + n^2)/4.\r\n\r\nIn a pyramid of odd numbers of (n - 1) rows there are n(n - 1)/2 numbers. The sum of the numbers is n^2(n - 1)^2/4 = (n^4 - 2n^3 + n^2)/4.\r\n\r\nTherefore, the sum of the numbers in the nth row is 4n^3/4 = n^3\r\n',NULL,0);
INSERT INTO comment VALUES (8706,1322,3196,'Dan','The Price Is Right','2003-10-16 08:24:27',0,'The first prize is equally likely to lie in each of the price ranges 500-999, 1000-1499, and 1500-2000. The second prize is equally likely to be in the price ranges 1000-1499, 1500-1999, and 2000-2500. The third prize will fall with equal probability in the price ranges 1500-1999, 2000-2499, and 2500-3000.\r\n \r\nHere is the complete combination table, listing the 1st prize price range, the 2nd prize price range, the 3rd prize price range, and the resulting ascending price order of the prizes, is:\r\n \r\n0500-0999 1000-1499 1500-1999 123\r\n0500-0999 1000-1499 2000-2499 123\r\n0500-0999 1000-1499 2500-3000 123\r\n0500-0999 1500-1999 1500-1999 123 or 132 \r\n0500-0999 1500-1999 2000-2499 123\r\n0500-0999 1500-1999 2500-3000 123\r\n0500-0999 2000-2500 1500-1999 132\r\n0500-0999 2000-2500 2000-2499 123 or 132\r\n0500-0999 2000-2500 2500-3000 123\r\n1000-1499 1000-1499 1500-1999 123 or 213\r\n1000-1499 1000-1499 2000-2499 123 or 213 \r\n1000-1499 1000-1499 2500-3000 123 or 213\r\n1000-1499 1500-1999 1500-1999 123 or 132\r\n1000-1499 1500-1999 2000-2499 123\r\n1000-1499 1500-1999 2500-3000 123\r\n1000-1499 2000-2500 1500-1999 132\r\n1000-1499 2000-2500 2000-2499 123 or 132\r\n1000-1499 2000-2500 2500-3000 123 \r\n1500-2000 1000-1499 1500-1999 213 or 231\r\n1500-2000 1000-1499 2000-2499 213\r\n1500-2000 1000-1499 2500-3000 213\r\n1500-2000 1500-1999 1500-1999 any order \r\n1500-2000 1500-1999 2000-2499 123 or 213\r\n1500-2000 1500-1999 2500-3000 123 or 213\r\n1500-2000 2000-2500 1500-1999 132 or 312\r\n1500-2000 2000-2500 2000-2499 123 or 132\r\n1500-2000 2000-2500 2500-3000 123\r\n \r\n123 occurs 21 times\r\n132 occurs 9 times\r\n213 occurs 9 times\r\n231 occurs 2 times\r\n312 occurs 2 times\r\n321 occurs 1 time\r\n \r\nIf you order the prizes in 123 order, you will win 47% of the time (the highest probablility).\r\nIf you order the prizes in 132 order, you will win 21% of the time.\r\nIf you order the prizes in 213 order, you will win 21% of the time.\r\nIf you order the prizes in 231 order, you will win 4% of the time.\r\nIf you order the prizes in 312 order, you will win 4% of the time.\r\nIf you order the prizes in 321 order, you will win 3% of the time. \r\n\n\nEdited on October 16, 2003, 8:25 am',NULL,0);
INSERT INTO comment VALUES (8707,1322,1301,'Charlie','re: The Price Is Right','2003-10-16 08:52:08',0,'The problem is that not all the ways shown are equally likely. For example, the line\r\n\r\n1500-2000 1500-1999 2000-2499 123 or 213 \r\n\r\nshould be in total as likely as say\r\n\r\n1500-2000 1000-1499 2500-3000 213 \r\n\r\nand as\r\n\r\n1500-2000 1500-1999 1500-1999 any order \r\n\r\nso in the case of the splits between two orders, each is entitled to only half a \"way\", and in the case of \"any order\" each of those is entitled to only 1/6 of a way. Alternatively multiply each of the individual lines as counting as 6 ways, each possible order in double lines as 3 ways and each of the 6 sharers in \"any order\" as 1 way.',8706,0);
INSERT INTO comment VALUES (8708,1221,3172,'SilverKnight','re(4): solution (Well done)','2003-10-16 09:33:10',0,'I\'m flattered ratsnstuff,\r\n\r\n(If only I could take credit for this approach :-)\r\n\r\n\"...for I am standing on the shoulders of giants.\" --- Newton',8701,0);
INSERT INTO comment VALUES (8709,1322,1301,'Charlie','Simulation of differing distribution','2003-10-16 09:33:12',0,'On the possibility that the distribution of probable prices is more centralized than a uniform distribution between the lowest possible price and highest possible price in each of the three price ranges, I simulated a more central distribution by using a program:\r\n\r\nRANDOMIZE TIMER\r\nFOR trial = 1 TO 1000000\r\n FOR item = 1 TO 3\r\n amt = 500 * item\r\n FOR i = 1 TO 3\r\n amt = amt + 500 * RND(1)\r\n NEXT\r\n amount(item) = amt\r\n bin = INT(amt / 500)\r\n totCt(item, bin) = totCt(item, bin) + 1\r\n NEXT\r\n ct = ct + 1\r\n IF amount(3) > amount(2) AND amount(2) > amount(1) THEN winCt = winCt + 1\r\nNEXT\r\nFOR item = 1 TO 3\r\n FOR bin = 1 TO 5\r\n PRINT USING \"########\"; totCt(item, bin);\r\n NEXT\r\n PRINT\r\nNEXT\r\nPRINT\r\navg = winCt / ct\r\nPRINT USING \"######### #.##### #.#####\"; ct; avg; SQR(ct * avg * (1 - avg)) / ct\r\n\r\nAs this program uses three uniform distributions with a range of 500, added together to produce a number from 0 to 1500 to add to the lowest value in each range, and the variance of a uniform distribution is r²/12, the variance of each price is 3(500²/12)=62500, making the s.d. 250. The results of one run are:\r\n\r\n166601 666750 166649 0 0\r\n 0 166565 666642 166793 0\r\n 0 0 167612 666078 166310\r\n\r\n1000000 0.83892 0.00037\r\n
\r\n-----------\r\nshowing how many of each prize were in each bin of prices. In this instance, no longer is the probability of each of 2 or 3 orders within matching bins either 1/2 or 1/6.\r\n\r\nThe average shows as 83.8% or 83.9% (the standard error of the mean showing as .00037), so the centralized tendency does help raise the odds of a win.',NULL,0);
INSERT INTO comment VALUES (8710,651,1920,'Brian Smith','By inspection...','2003-10-16 09:38:41',2,'Just by plugging in some primes, I would say the answer is p-1, but I dont have a proof yet.',NULL,0);
INSERT INTO comment VALUES (8711,651,1301,'Charlie','re: By inspection...','2003-10-16 09:52:36',2,'Indeed it works for the first 35 primes as the following output shows:\r\n\r\nlist\r\n 5 for I=1 to 35\r\n 10 P=nxtprm(P)\r\n 20 print p, (!(P)-1)@P\r\n 30 next\r\nrun\r\n 2 1\r\n 3 2\r\n 5 4\r\n 7 6\r\n 11 10\r\n 13 12\r\n 17 16\r\n 19 18\r\n 23 22\r\n 29 28\r\n 31 30\r\n 37 36\r\n 41 40\r\n 43 42\r\n 47 46\r\n 53 52\r\n 59 58\r\n 61 60\r\n 67 66\r\n 71 70\r\n 73 72\r\n 79 78\r\n 83 82\r\n 89 88\r\n 97 96\r\n 101 100\r\n 103 102\r\n 107 106\r\n 109 108\r\n 113 112\r\n 127 126\r\n 131 130\r\n 137 136\r\n 139 138\r\n 149 148\r\nOK\r\n
\r\n----------\r\nThe above is a UBASIC program, that language having the built-in nxtprm function and factorial function.',8710,0);
INSERT INTO comment VALUES (8712,651,3172,'SilverKnight','a big hint','2003-10-16 09:58:22',2,'A restatement of this problem is:\r\n\r\nGiven:\r\n(p-1)! = p * q + m\r\n\r\nwhere:\r\np is a prime number,\r\nq is some integer, and\r\nm is some integer between 0 and p-1 (the remainder)\r\n\r\nWhat is m? And yes, by inspection, m = p-1. Prove it.',NULL,0);
INSERT INTO comment VALUES (8713,651,3172,'SilverKnight','full solution','2003-10-16 11:23:06',3,'Another restatement of the problem is:\r\nGiven: \r\n(p-1)! ≡ m (mod p)\r\n\r\nwhere:
\r\nWhat is m?\r\n______________\r\n\r\nThis is a restatement of Wilson\'s theorem. The answer (as stated three times before) is p-1, which of course is ≡ -1 (mod p).\r\n\r\nAnd a proof is available at:\r\nhttp://en.wikipedia.org/wiki/Wilson\'s_theorem\r\nhttp://modular.fas.harvard.edu/edu/Fall2001/124/lectures/lecture6/html/node1.html\r\n- and- \r\nhttp://www.utm.edu/research/primes/notes/proofs/Wilsons.html\r\nas well as at many other sources on the net (just look up \"Wilson\'s Theorem\").\r\n\r\nI will refrain from duplicating these proofs here.\r\n\r\n--- SK\n\nEdited on October 16, 2003, 4:50 pm',NULL,0);
INSERT INTO comment VALUES (8714,914,3136,'Popstar Dave','Looking for lookings sake','2003-10-16 11:38:08',1,'Some times I look around with nothing in mind as to what I\'m looking for. In that case nothing is ever in the last place I look, coz I never actually find anything, coz I\'m not looking for anything. \r\nI\'m not sure why I do this. Maybe it\'s just coz you posted this problem.',NULL,0);
INSERT INTO comment VALUES (8715,912,1920,'Brian Smith','Level 5 Solution','2003-10-16 12:18:26',3,'It is impossible to get to level 5 using any number of checkers.\r\n\r\nConsider a checkerboard with infinite rows and columns. Half of the checkerboard is filled so that a half infinite plane is filled.\r\n\r\n* = empty space\r\nX = filled space\r\n$ = goal (empty)\r\n\r\nrow 5 * * * * $ * * * *\r\nrow 4 * * * * * * * * *\r\nrow 3 * * * * * * * * *\r\nrow 2 * * * * * * * * *\r\nrow 1 * * * * * * * * *\r\nrow 0 X X X X X X X X X\r\nrow -1 X X X X X X X X X\r\nrow -2 X X X X X X X X X\r\nrow -3 X X X X X X X X X\r\nrow -4 X X X X X X X X X\r\nrow -5 X X X X X X X X X\r\n
-\r\n\r\nEach checker contributes some value to the goal. A checker which is closer contributes more than one that is farther away. A checker in row x is one magnitude more valuable than a checker in row x+1. A checker closer to the center column by one row is one magnitude more valuable that the further away checker. Applying this order of magnitude to the grid yeilds:\r\n\r\n\r\ncol#s-> -4 -3 -2 -1 0 1 2 3 4\r\nrow 5 * * * * (t^5) * * * *\r\nrow 4 * * * * (t^4) * * * *\r\nrow 3 * * * * (t^3) * * * *\r\nrow 2 * * * * (t^2) * * * *\r\nrow 1 * * * * (t) * * * *\r\nrow 0 t^-4 t^-3 t^-2 t^-1 1 t^-1 t^-2 t^-3 t^-4\r\nrow -1 t^-5 t^-4 t^-3 t^-2 t^-1 t^-2 t^-3 t^-4 t^-5\r\nrow -2 t^-6 t^-5 t^-4 t^-3 t^-2 t^-3 t^-4 t^-5 t^-6\r\nrow -3 t^-7 t^-6 t^-5 t^-4 t^-3 t^-4 t^-5 t^-6 t^-7\r\nrow -4 t^-8 t^-7 t^-6 t^-5 t^-4 t^-5 t^-6 t^-7 t^-8\r\nrow -5 t^-9 t^-8 t^-7 t^-6 t^-5 t^-6 t^-7 t^-8 t^-9\r\n
-\r\n\r\nIf reaching a specific level is possible, then the sum of the checkers in the initial configuration is equal to the value of the final checker\'s position.\r\n\r\nFor level one: \r\n\r\nrow 1 (t)\r\nrow 0 1\r\nrow -1 t^-1\r\n
-\r\n\r\n1 + t^-1 = t. This implies t=(1+sqrt5)/2\r\n\r\n\r\nFor level two:\r\n\r\nrow 2 * * (t^2)\r\nrow 1 * * *\r\nrow 0 t^-2 t^-1 1\r\nrow -1 t^-1\r\n
-\r\n\r\n1 + 2(t^-1) + t^-2 = t^2 agrees with t=(1+sqrt5)/2\r\n\r\n\r\nFor level 3:\r\n\r\nrow 3 * * (t^3) * *\r\nrow 2 * * * * *\r\nrow 1 * * * * *\r\nrow 0 t^-2 t^-1 1 t^-1 t^-2\r\nrow -1 t^-3 t^-2 t^-1\r\n
-\r\n\r\n1 + 3(t^-1) + 3(t^-2) + t^-3 = t^3 agrees with t=(1+sqrt5)/2\r\n\r\n\r\nFor level 4:\r\n\r\nrow 4 * * * * (t^4) * *\r\nrow 3 * * * * * * *\r\nrow 2 * * * * * * *\r\nrow 1 * * * * * * *\r\nrow 0 t^-4 t^-3 t^-2 t^-1 1 t^-1 t^-2\r\nrow -1 t^-3 t^-2 t^-1 t^-2 t^-3\r\nrow -2 t^-5 t^-4 t^-3 t^-2 t^-3 t^-4\r\nrow -3 t^-4 t^-3\r\n
-\r\n\r\n1 + 3(t^-1) + 5(t^-2) + 6(t^-3) + 4(t^-4) + t^-5 = t^4 agrees with t=(1+sqrt5)/2\r\n\r\n\r\nFor level 5:\r\n\r\nAdd up the entire half infinite plane of checkers. Each column is an infinite geometric series with ratio t^-1.\r\n\r\nColumn 0 = 1/(1 - t^-1)\r\nColumns 1, -1 each equal (t^-1)/(1 - t^-1)\r\nColumns n, -n each equal (t^-n)/(1 - t^-1)\r\n\r\nThe sum of the half infinite plane is the sum of the columns:\r\n\r\n1/(1 - t^-1) + 2*(t^-1)/(1 - t^-1) + 2*(t^-2)/(1 - t^-1) + 2*(t^-3)/(1 - t^-1) + 2*(t^-4)/(1 - t^-1) + 2*(t^-5)/(1 - t^-1) + ...\r\n\r\nAside from the first term, this is geometric with a ratio of t^-1. Sum of half infinite plane = 1/(1 - t^-1) + (2*(t^-1)/(1 - t^-1))/(1 - t^-1) = (t^2 + t)/(t - 1)^2. Since t=(1+sqrt5)/2, the sum of the half infinite plane is (5*sqrt5 + 11)/2. But t^5 is also (5*sqrt5 + 11)/2. This means that no finite number of checkers can ever reach level 5.\n\nEdited on October 16, 2003, 12:20 pm',NULL,0);
INSERT INTO comment VALUES (8716,1458,3903,'scott olson','might it be?','2003-10-16 13:26:18',0,'I thought maybe sonic energy could knock off it\'s butt. Maybe a big hefty Aretha Franklin yell in it\'s near vacinity?\r\n\r\nScott',NULL,0);
INSERT INTO comment VALUES (8717,185,3172,'SilverKnight','re(2): Solution - Ender & Levik !!!','2003-10-16 14:36:44',4,'Guys,\r\n\r\nI understand your solution, but what I don\'t understand is Ender\'s statement:\r\nThe best you can do is 533 batteries, with 1 unused battery left sitting on the road. (...even allowing for the extra 1/3)\r\n\r\nTo restate, I understand that this gets 533+ all the way to the end... And I believe this is the max that can be achieved.... but I don\'t think you\'ve shown/proven that this is the maximum that can be attained.\r\n\r\nAm I missing something here?\r\n\r\n --- SK\n\nEdited on October 16, 2003, 2:45 pm',1076,0);
INSERT INTO comment VALUES (8718,1470,3172,'SilverKnight','full solution','2003-10-16 15:15:38',3,'take away the third letter in each word, and they all are real words:\r\n\r\ntaper\r\nsped\r\nmiter\r\ndeal\r\nastray\r\nunformed\r\nsnaky\r\nreined',NULL,0);
INSERT INTO comment VALUES (8720,1470,1567,'Bryan','re: full solution','2003-10-16 15:46:45',0,'That\'s a very good start, SilverKnight, but it is not a \"full solution\".',8718,0);
INSERT INTO comment VALUES (8721,1470,3172,'SilverKnight','re(2): full solution','2003-10-16 15:53:55',0,'It\'s full as far as I\'m concerned. (I\'m not going to spend significant amounts of time on trivial \"word problems\".) Now, if there were some critical thought involved here... then I might actually spend hours trying to find a solution.\r\n\r\nIn any case, you\'re more than welcome to come up with some other trivial commonalities between these words... to make it \"fuller\".\r\n\r\nCheers!',8720,0);
INSERT INTO comment VALUES (8722,692,3904,'steve','parabola','2003-10-16 16:51:54',0,'all u need to do is use the equation -b/2a \r\nuse the equation for the height of an object which is h(t)= -g(t)+ V,(t) + h,\r\nsorry dont know how to type equations so \r\n`=squared h=height\r\n,=initial t=time\r\nV=velocity g=gravitational constant\r\nuh also use the equation for a parabola \r\n x=ax` +bx +c\r\nso the ten is b and -9.8 is a\r\nso the answer is -10/(2)(-9.8)\r\ni probably could have explained this a lot easier ... oh well',NULL,0);
INSERT INTO comment VALUES (8723,1221,3172,'SilverKnight','re: u dont need a hammer to crack a nut','2003-10-16 17:08:32',0,'Anand,\r\n\r\nIf you read my solution (and yours) you realize that you stated a formula for the last number in row n-1. Whereas I generated a formula for the first number in row n. As you pointed out, my formula is just your formula +2.\r\n\r\nNow, you simply STATED what your formula is. So did I, at first... but then Charlie called me on it... and I generated the formula (using the calculus of differences, not the same thing as integral calculus).\r\n\r\nIf you wish to avoid using your hammer to crack this nut, then you need to show WHY your formula works. You did not do this.\r\n\r\n--- SK',8704,0);
INSERT INTO comment VALUES (8724,501,3904,'steve','city','2003-10-16 17:24:46',0,'i live in NY so there are never any stars cuz of ambiant lights and such',NULL,0);
INSERT INTO comment VALUES (8725,428,3904,'steve','stupid british','2003-10-16 17:32:44',0,'stupid british how is anyone supposed to know how much that a pint of worthingtion costs',NULL,0);
INSERT INTO comment VALUES (8726,342,3904,'steve','','2003-10-16 17:44:34',0,'use the bat to beat down the door\r\nlol',NULL,0);
INSERT INTO comment VALUES (8727,1470,1626,'Gamer','More complete solution','2003-10-16 17:48:30',3,'You should find the full solution or the problem... :)\r\n\r\nThe deleted letters spell MISCHIEF\r\n\r\ntaMper\r\nspIed\r\nmiSter\r\ndeCal\r\nasHtray\r\nunIformed\r\nsnEaky\r\nreFined',NULL,0);
INSERT INTO comment VALUES (8728,1470,3172,'SilverKnight','re: More complete solution','2003-10-16 18:00:24',0,'Not to be too nitpicky, but...\r\n\r\nThe fact that the deleted letters spells a word is a nifty fact, but is not something in common with those words. It is an artifact of the problem, and the ordering of those particular words.\r\n\r\nNevertheless, kudos to you for observing the fact.',8727,0);
INSERT INTO comment VALUES (8729,1458,3558,'Tristan','re: might it be?','2003-10-16 18:22:05',0,'I\'m not so sure that this solution is valid. The sonic energy is just a wave causing the air to knock it over. The air counts as a gas and an object.',8716,0);
INSERT INTO comment VALUES (8730,1205,3905,'Alain','Tic Toc','2003-10-16 19:36:27',0,'Let us assume the solution consist in building a system that is made of many clocks.\r\nIn order to get 25 min, we would use a 15min clock, a 7.5 min clock. Next, a 3.75 clock cannot be used, because it would exceed 25min. Thus we would use a 1.875 and so, each time either using the next shortest ONLY IF it does not exceed 25 min.\r\n\r\nAfter an hour, we can obtain the shortest time clock, which is virtually zero and wich will be used as the last clock used in the system.\r\n\r\nHence, for this system we need a infinite number of timers. But does that necessarily mean we need an infinite ammount of time to build our system?\r\n\r\nNo, because in 45 minutes we can build the first timer (a 15 min clock), and using the others as they get available. As said before, in one hour every needed timer is available, so the minimum time is 45 min + 25 min = 70 minutes.\r\n\r\nHowever, the system cannot be achieved in 110 minutes, because after 15 + 7.5 minutes, the next timer to be used is not ready yet (the 3,75min is ready but it cannot be used), so we have to wait some extra time before the 1,875 timer gets available.\r\n\r\nBut we do know that after an hour, all timers are available so we need a maximum of 60 + 25 = 85 minutes.\r\n\r\nThe solution would consist in using an infinite number of timers but it would require 70 to 85 minutes to build the system and run it while only 60 minutes to build it.\r\n\r\nI hope I didn\'t waste your time with my solution (because if so, I lose a lot more in writing all this ;)',NULL,0);
INSERT INTO comment VALUES (8731,129,3896,'iggyb387','the solution is basically right, but logic is terrible','2003-10-16 21:32:58',0,'first of, i\'m not sure about this, but the formula is probably wrong in some way. Also, the amount of substance is NOT 355 mL, it would have to be in grams (the mass, ml is the volume which is not correct, unless you have the density), which would make the whole 140 cal from nutrients thing obsolete, since the mass would be of the entire drink including the nutrients. asically, the Cal to cal covers it, but the rest of the solution is flawed...',NULL,0);
INSERT INTO comment VALUES (8732,921,3908,'Paul','Duh','2003-10-16 22:24:58',0,'This is a bet you should definatly take',NULL,0);
INSERT INTO comment VALUES (8733,544,3908,'Paul','','2003-10-16 22:27:19',0,'cards',NULL,0);
INSERT INTO comment VALUES (8734,824,3908,'Paul','hi','2003-10-16 22:35:56',0,'he stood on a block of ice the ice melted to create a puddle',NULL,0);
INSERT INTO comment VALUES (8735,263,3660,'ratsnstuff','What!? The tortoise...','2003-10-17 03:02:45',0,'What?! The tortoise actually reached point a? How did he do that, since he would have had to cross 1/2 the distance to point a first... .... .... .... ....',NULL,0);
INSERT INTO comment VALUES (8736,1205,2899,'Brian Wainscott','re: Tic Toc','2003-10-17 03:10:06',0,'While it is true that any of your timers can be built in less than an hour, how do you guarantee they all become available at the correct moment?\r\n\r\nFor example, to time X minutes, it is not just enough to construct two timers of duration A and B where A+B=X, you also have to build them in such a way that one of them expires at the precise instant that the other begins. One thing you CANNOT do is pause the clocks -- so you can\'t build a timer then pause it until you want to use it.\r\n\r\nI think several things are clear:\r\n\r\n1 - It can\'t be done with a finite number of timers. As many have pointed out, 5/12 isn\'t a finite fraction in binary decimal, so an infinite number of timers must be used, and you have to use some kind of limit process.\r\n\r\n2 - Constructing each of the intervals (60 minutes/2^k) for each k is straight forward.\r\n\r\n3 - getting all these intervals lined up is going to be the hard part, if it can be done at all in finite time.\r\n\r\nI think Brian Smith has the nicest solutions so far: it can\'t be done, but you can come infinitely close if you are willing to work at it (total time required is about 60 minutes times the number of terms in the binary expansion of 5/12, and I like his approach in \"Closer and closer\")',8730,0);
INSERT INTO comment VALUES (8737,1221,3900,'anand','re my solution','2003-10-17 04:21:07',0,'hi sk .. i thought that i had proved it when i stated my solution..to clarify, my formula for the last number in row n-1 and by extension the first number in row n was based on the fact that by the end of row n-1, the number of odd numbers that would have been used up was 1+2+3+4....n-1\r\nwhich is given by n(n-1)/2 ..therefore, the last number on row n-1 would be 2*(n(n-1)/2-1 since the generic formula for the xth odd number is given by 2*x-1 ... the rest of the solution is as i had already posted ... as a non-mathematician, my solution seemed simpler ...this is not to denigrate ur solution in any way',NULL,0);
INSERT INTO comment VALUES (8738,1458,2899,'Brian Wainscott','An idea','2003-10-17 05:28:56',0,'Does using a vacuum cleaner count? If I put a straw/vacuum cleaner near it and create a partial vacuum near one side, the in rush of air will knock it over. But I didn\'t FORCE the air to rush in to fill the vacuum, it did that on its own.....\r\n\r\nOr is this disallowed also? Then what WOULD be allowed. Some force must act on it, and if I cause that force to occur then is that necessarily disallowed? What forces don\'t involve direct object interaction? I think photons count as objects -- they do have mass.\r\n\r\nMass....gravity? It wouuld take a pretty massive object placed very near the cigarette to pull it over by force of gravity, so that is probably out.\r\n\r\nBeing a \"bar bet\" makes me suspect a trick of some kind is involved....',NULL,0);
INSERT INTO comment VALUES (8739,1274,1575,'DJ','','2003-10-17 08:06:31',3,'Well, since each step can either add a letter or change a letter, this will take at least five steps. There are a few ways to do it in the minimum number of moves. Here\'s one:\r\nRED\r\nREAD (add A)\r\nTARE (D → T)\r\nCRATE (add C)\r\nREACTS (add S)\r\nSCARLET (add L)\r\n\r\n
',NULL,0);
INSERT INTO comment VALUES (8740,1274,2839,'FatBoy','','2003-10-17 08:22:09',0,'RED\r\nREAD\r\nREAL\r\nCLEAR\r\nCLEARS\r\nSCARLET',NULL,0);
INSERT INTO comment VALUES (8741,1274,1941,'shaun','ANOTHER WAY','2003-10-17 08:43:30',3,'RED\r\nare d becomes a\r\ncare add c\r\ntrace add s\r\ncartel add l\r\nSCARLET',NULL,0);
INSERT INTO comment VALUES (8742,1221,3172,'SilverKnight','re: re my solution','2003-10-17 09:31:58',0,'Anand,\r\n\r\nI don\'t feel like you denigrated anything (me or my solution). :-)\r\n\r\nSimply put: You mentioned a \"generic formula\". But you didn\'t show WHY the generic formula works. I also mentioned an equivalent formula. But after Charlie\'s prodding, I then demonstrated why the formula works. You didn\'t.\r\n\r\nI suppose that if you showed why your \"generic formula\" works (rather than simply relying on it), you would find that you used your \"proverbial hammer\".\r\n\r\n--- SK',8737,0);
INSERT INTO comment VALUES (8743,1458,3916,'Kelly','Solution???','2003-10-17 10:00:59',0,'The problem never said that the cigarette couldn\'t be lit in the first place. Since you can\'t do anything to it while it\'s there do it before it is placed.',NULL,0);
INSERT INTO comment VALUES (8744,1274,1301,'Charlie','11,929 solutions','2003-10-17 11:47:18',3,'The following lists horizontally solutions to the puzzle, leaving out the words RED and SCARLET themselves. The number at the end of each line is the number of solutions altogether that that line represents, counting exchanging one or more words with anagrams. The anagrams for the various words that appear are listed at the bottom, with the word used in the solutions at the top shown in bold face. Some uncommon words have been excluded.\r\n\r\nEAR CARE SCARE TRACES 252\r\nEAR CARE SCARE CLEARS 36\r\nEAR CARE TRACE TRACES 315\r\nEAR CARE TRACE RECTAL 135\r\nEAR CARE CLEAR RECTAL 27\r\nEAR CARE CLEAR CLEARS 9\r\nEAR EARS SCARE TRACES 336\r\nEAR EARS SCARE CLEARS 48\r\nEAR EARS STARE ALERTS 144\r\nEAR EARS STARE TRACES 336\r\nEAR EARS LASER ALERTS 72\r\nEAR EARS LASER CLEARS 24\r\nEAR REAL LATER ALERTS 54\r\nEAR REAL LATER RECTAL 54\r\nEAR REAL CLEAR RECTAL 18\r\nEAR REAL CLEAR CLEARS 6\r\nEAR REAL LASER ALERTS 36\r\nEAR REAL LASER CLEARS 12\r\nEAR TEAR LATER ALERTS 54\r\nEAR TEAR LATER RECTAL 54\r\nEAR TEAR STARE ALERTS 72\r\nEAR TEAR STARE TRACES 168\r\nEAR TEAR TRACE TRACES 210\r\nEAR TEAR TRACE RECTAL 90\r\nDEAR CARE SCARE TRACES 252\r\nDEAR CARE SCARE CLEARS 36\r\nDEAR CARE TRACE TRACES 315\r\nDEAR CARE TRACE RECTAL 135\r\nDEAR CARE CLEAR RECTAL 27\r\nDEAR CARE CLEAR CLEARS 9\r\nDEAR EARS SCARE TRACES 336\r\nDEAR EARS SCARE CLEARS 48\r\nDEAR EARS STARE ALERTS 144\r\nDEAR EARS STARE TRACES 336\r\nDEAR EARS LASER ALERTS 72\r\nDEAR EARS LASER CLEARS 24\r\nDEAR REAL LATER ALERTS 54\r\nDEAR REAL LATER RECTAL 54\r\nDEAR REAL CLEAR RECTAL 18\r\nDEAR REAL CLEAR CLEARS 6\r\nDEAR REAL LASER ALERTS 36\r\nDEAR REAL LASER CLEARS 12\r\nDEAR TEAR LATER ALERTS 54\r\nDEAR TEAR LATER RECTAL 54\r\nDEAR TEAR STARE ALERTS 72\r\nDEAR TEAR STARE TRACES 168\r\nDEAR TEAR TRACE TRACES 210\r\nDEAR TEAR TRACE RECTAL 90\r\nDEAR CARED SCARE TRACES 420\r\nDEAR CARED SCARE CLEARS 60\r\nDEAR CARED TRACE TRACES 525\r\nDEAR CARED TRACE RECTAL 225\r\nDEAR CARED CLEAR RECTAL 45\r\nDEAR CARED CLEAR CLEARS 15\r\nDEAR CARED SCARED TRACES 420\r\nDEAR CARED SCARED CLEARS 60\r\nDEAR CARED SCARED CRADLES 60\r\nDEAR CARED TRACED TRACES 315\r\nDEAR CARED TRACED RECTAL 135\r\nDEAR CARED CRADLE RECTAL 90\r\nDEAR CARED CRADLE CLEARS 30\r\nDEAR CARED CRADLE CRADLES 30\r\nDEAR READS SCARE TRACES 252\r\nDEAR READS SCARE CLEARS 36\r\nDEAR READS STARE ALERTS 108\r\nDEAR READS STARE TRACES 252\r\nDEAR READS LASER ALERTS 54\r\nDEAR READS LASER CLEARS 18\r\nDEAR READS SCARED TRACES 252\r\nDEAR READS SCARED CLEARS 36\r\nDEAR READS SCARED CRADLES 36\r\nDEAR READS STARED ALERTS 108\r\nDEAR READS STARED TRACES 252\r\nDEAR TRADE LATER ALERTS 108\r\nDEAR TRADE LATER RECTAL 108\r\nDEAR TRADE STARE ALERTS 144\r\nDEAR TRADE STARE TRACES 336\r\nDEAR TRADE TRACE TRACES 420\r\nDEAR TRADE TRACE RECTAL 180\r\nDEAR TRADE TRACED TRACES 252\r\nDEAR TRADE TRACED RECTAL 108\r\nDEAR TRADE STARED ALERTS 144\r\nDEAR TRADE STARED TRACES 336\r\nREDS EARS SCARE TRACES 112\r\nREDS EARS SCARE CLEARS 16\r\nREDS EARS STARE ALERTS 48\r\nREDS EARS STARE TRACES 112\r\nREDS EARS LASER ALERTS 24\r\nREDS EARS LASER CLEARS 8\r\nREDS REST STARE ALERTS 12\r\nREDS REST STARE TRACES 28\r\nREDS REST CREST TRACES 7\r\nREDS READS SCARE TRACES 84\r\nREDS READS SCARE CLEARS 12\r\nREDS READS STARE ALERTS 36\r\nREDS READS STARE TRACES 84\r\nREDS READS LASER ALERTS 18\r\nREDS READS LASER CLEARS 6\r\nREDS READS SCARED TRACES 84\r\nREDS READS SCARED CLEARS 12\r\nREDS READS SCARED CRADLES 12\r\nREDS READS STARED ALERTS 36\r\nREDS READS STARED TRACES 84\r\n\r\nThe numbers of ways, based on anagrams, totals 11,929.\r\n\r\nThe anagrams which can be substituted are (per line), alphabetically by bold-faced word (the words used in the above solutions) (non-anagrammed words appear by themselves):\r\n\r\nALERTS ALTERS STALER\r\nACRE CARE RACE\r\nARCED CADRE CARED CEDAR RACED\r\nCLEAR\r\nCLEARS\r\nCRADLE RECLAD\r\nCRADLES\r\nCREST\r\nDARE DEAR READ\r\nARE EAR ERA\r\nARSE EARS ERAS SEAR\r\nEARLS LASER\r\nALERT ALTER LATER\r\nDARES DEARS READS\r\nEARL REAL\r\nCARTEL CLARET RECTAL\r\nREDS\r\nREST\r\nACRES CARES RACES SCARE\r\nCADRES CEDARS SACRED SCARED\r\nDATERS STARED TRADES TREADS\r\nRATE TEAR\r\nASTER RATES STARE TEARS\r\nCARET CATER CRATE REACT TRACE\r\nCARTED CRATED TRACED\r\nCARETS CASTER CATERS CRATES REACTS RECAST TRACES\r\nDATER RATED TRADE TREAD\r\n',NULL,0);
INSERT INTO comment VALUES (8745,1242,3902,'J Miesch','My solution','2003-10-17 11:48:53',0,'The answer is: the square root of 180 (approximately 13.416).\r\n\r\nSteps:\r\n\r\n1. The equation for the length of each full side:\r\n ((x ^2) * 0.75) - (4x) = 60\r\n\r\n The solution to this is 12\r\n\r\n2. Therefore, the length of AB is 6 and BC is 12\r\n\r\n3. Therefore, according to Pythagorean theorem, ((6 ^ 2) + (12 ^ 2)) ^ 0.5 = square root of 180, or 13.416 (approx.)',NULL,0);
INSERT INTO comment VALUES (8746,1274,3172,'SilverKnight','re: 11,929 solutions','2003-10-17 11:51:04',0,'Charlie,\r\n\r\nI actually laughed out loud when I read this.\r\n\r\nYou rock, dude! :-D\r\n\r\n--- SK',8744,0);
INSERT INTO comment VALUES (8747,1470,3902,'J Miesch','Another solution???','2003-10-17 12:08:31',0,'The first word has an even number of values and an even number consonants. The next word has an even number of one (either consonants or vowels), and an odd number of the other. This pattern continues throughout the list.\r\n\r\nHere\'s to thinking outside the box ;) hehe\r\nNot the best solution, but it makes sense to my strange mind...',NULL,0);
INSERT INTO comment VALUES (8748,1470,3902,'J Miesch','re: Another solution???','2003-10-17 12:11:10',0,'Whoops, I meant a number of VOWELS at the beginning, not values. The corrected answer would read:\r\n\r\nThe first word has an even number of vowels and an even number of consonants. The next word has an even number of one (either consonants or vowels), and an odd number of the other. This pattern continues throughout the list. \r\n',8747,0);
INSERT INTO comment VALUES (8749,650,3895,'PWP','Got it...','2003-10-17 12:49:35',3,'First, make a subgroup of 128 pennies, dun matter which ones really. Flip all of them over. All of the pennies should now have equal face up and face down. \r\n\r\nThe ones that have heads will be flip to tail. The tails will be flip to head so even amount. So have a number of pennies in group A. Take 128 pennies from it to form group B. Now you have some number of heads (call it H). So group A has 128 - H heads. By flipping the pennies in group B you will get 128 - H heads as well. Ex: 10 pennies, 4 heads. Take 4 pennies and have 1 head and 3 tails in group B. Group A now has 3 heads. Flip pennies in group B and get 3 heads now. So same number.\r\n',NULL,0);
INSERT INTO comment VALUES (8750,533,2716,'Federico Kereki','Solution','2003-10-17 13:02:58',3,'If we add 1 to the number, divided by 2...10 it will leave no remainder, so the number is one less than the LCM of 2...10, which is 2520.\r\n\r\nActually, the problem should read \"the smallest POSITIVE number\"; otherwise, -1 could also be considered to qualify, and so would -2521, -5041, and so on.',NULL,0);
INSERT INTO comment VALUES (8751,1458,3919,'Jim','SOUND¿','2003-10-17 13:24:32',0,'Sound. its not an object, nor is it physicaly touching the cig. crank up some bassy sound to vibrate it. kinda like when you stick you head by a big speaker and your hair pulses with the beat. Seems to me this would work under the guidelines.',NULL,0);
INSERT INTO comment VALUES (8752,1470,3917,'Bill Bailey','Brian\'s Problem','2003-10-17 13:32:13',0,'The solution to this problem is that sequentially combining the third letter of each word makes the word \"mischief\".',NULL,0);
INSERT INTO comment VALUES (8753,1470,3917,'Bill Bailey','Answer to Words In Common 8','2003-10-17 13:56:41',0,'For the solution see \"Brian\'s Problem\" by Bill Bailey on 10/17.',NULL,0);
INSERT INTO comment VALUES (8754,1221,3900,'anand','sk, i dnt understand quite what u r getting at','2003-10-17 14:31:01',0,'i m at a bit of a loss here.. how does one prove that the nth odd number is given by 2n-1 .. it is how odd and even numbers are defined .. the nth even number is given by 2n and the nth odd one is given by 2n-1 ',NULL,0);
INSERT INTO comment VALUES (8755,649,3900,'anand','the solution','2003-10-17 14:38:05',0,'the answer is fifty percent ... basically the first marble drawn being black is irrelevant in determining the probablity of the second one being black since we are replacing the marbles... this is exactly the same probability tree that ws suggested earlier except that 5/8 was the probability of drawing two black marbles but what we are asked is the probability that the second one would be black...',NULL,0);
INSERT INTO comment VALUES (8756,1319,3919,'Jim','solution','2003-10-17 14:45:12',0,'1002001\r\n1002002001,\r\n1002002002001,\r\n1002002002002001,\r\n1002002002002002001',NULL,0);
INSERT INTO comment VALUES (8757,1222,3172,'SilverKnight','full solution','2003-10-17 14:48:15',3,'Let\'s define\r\nFor a given integer a,\r\nrelation R(x) as (a#x), and\r\nrelation S(x) as (x#a), and\r\n\r\nAlso, given (by the original problem): S is the inverse of R such that applying R, then S will return the original value.\r\n_________________\r\n\r\nThe original problem is (a#b)#a=b.\r\n\r\nThis can now be rewritten (by substitution) as:\r\n\r\n(a#b)#a = b\r\n(R(b))#a = b\r\nS(R(b)) = b\r\n\r\nThe key to this problem is that if R is the inverse of S, then S is the inverse of R (definition of inverse).\r\n\r\nTherefore, R(S(b)) = b as well !\r\nAnd this can be rewritten (again by substitution) as:\r\nR(S(b)) = b\r\na#(S(b)) = b\r\na#(b#a) = b (which is what we wanted to show!)\r\n',NULL,0);
INSERT INTO comment VALUES (8758,1451,3919,'Jim','re: Solution...Really','2003-10-17 14:50:49',0,'i with yall.',8614,0);
INSERT INTO comment VALUES (8759,1221,3172,'SilverKnight','re: sk, i dnt understand quite what u r getting at','2003-10-17 14:52:43',0,'Anand,\r\n\r\nYou wrote:\r\n, the number of odd numbers that would have been used up is given by 1+2+3+4....n-1 i.e n(n-1)/2 .. \r\n__________\r\n\r\nYou used the generic formula n(n-1)/2. This is true... but you didn\'t prove it. Neither did I initially. Charlie called me on it, so I did.',8754,0);
INSERT INTO comment VALUES (8760,1222,3172,'SilverKnight','point of interest','2003-10-17 14:58:38',1,'If memory serves... XOR would be one such operator (matching the description of this problem).\r\n\r\n--- Oren',NULL,0);
INSERT INTO comment VALUES (8761,1222,1301,'Charlie','another way to describe it','2003-10-17 15:07:18',3,'Without using a different notation, we can substitute (a#b) for the old a and a for the old b:\r\n\r\n((a#b)#a)#(a#b) = a\r\n\r\nNow, replacing the (a#b)#a within this expression with b, as we are still entitled to do, we get\r\n\r\nb#(a#b)=a\r\n\r\nNow, renaming b as a and a as b:\r\n\r\na#(b#a)=b',NULL,0);
INSERT INTO comment VALUES (8762,1051,3920,'abby','re: farm animal ?','2003-10-17 15:33:08',3,'hey! a manatee...u kno..a sea cow?',NULL,0);
INSERT INTO comment VALUES (8763,1242,3878,'sean','Its been solved....','2003-10-17 16:31:30',0,'I have had several third parties who have thought this one through... after i gave them the print out of the puzzle and they all came to the same answer as i did (on my second send)...are you saying this is still unsolved? Let me know one way or the other!',NULL,0);
INSERT INTO comment VALUES (8764,1274,1626,'Gamer','re: 11,929 solutions','2003-10-17 17:05:46',0,'Great Job Charlie! You set an excellent example for someone who says \"this puzzle is finished :(\", where as you can take the problem further than just what is suggested there.',8744,0);
INSERT INTO comment VALUES (8765,1458,3922,'Paul','Energy..','2003-10-17 19:06:00',0,'Some other forms of \"invisible\" energy that could somehow be used.. (but I\'m no scientist)\r\nMagnetism or static electricity (or electricity in general).. \r\nI know that a cigarette isn\'t magnetized, but given enough magnetism and a frog will hover. So maybe an electro magnet will allow the cigarette to fall.\r\n',NULL,0);
INSERT INTO comment VALUES (8766,1458,1626,'Gamer','re: SOUND¿','2003-10-17 19:28:30',0,'You would be touching it with the air around it. Isn\'t sound just vibrations?',8751,0);
INSERT INTO comment VALUES (8767,1222,3896,'iggyb387','re: full solution','2003-10-17 20:55:06',0,'i\'m probably wrong, but this is basically the commutative property ',8757,0);
INSERT INTO comment VALUES (8768,1416,3920,'abby','knights&liars','2003-10-17 23:11:34',0,'A was telling the truth....B was telling a lie',NULL,0);
INSERT INTO comment VALUES (8769,921,3920,'abby','10 for 5?','2003-10-17 23:33:05',2,'ok....y would u stand there lettin him drink your 10 dollar drink when its only a 10$ wager?>',NULL,0);
INSERT INTO comment VALUES (8770,1458,3924,'Fernando Baibich','Magnetism','2003-10-18 19:25:13',0,'Since the cigarette has lead, cadmium and mercury in it, a REALLY powerful magnet should do the job!',NULL,0);
INSERT INTO comment VALUES (8771,1242,3934,'Adrian Aisemberg','Here\'s the answer ...','2003-10-19 09:21:32',0,'the small line is x so the large one is 2x.\r\nso we got 3x²-8x=60\r\n-> x=6\r\nso AC=√180=13.416',NULL,0);
INSERT INTO comment VALUES (8772,1221,3914,'Abhishek','Solution','2003-10-19 09:30:00',3,'The answer as per me in the cube of the row number thats n, thus n³ as in 1 for 1³ , 8 for 2³ and so on... should be the answer',NULL,0);
INSERT INTO comment VALUES (8773,1222,3936,'Angela','A simple solution','2003-10-19 11:15:50',3,'Given (a*b)*a = b and given a*b is closed, then a*b = b*a under the commutative property of real numbers. Thus,(a*b)*a = (b*a)*a. \r\n\r\nWe can then say (b*a)*a = a*(b*a) under the commutative property. By substitution (or transitive property), (a*b)*a = a*(b*a).\r\n\r\nUsing the substitution (or transitive) property it follows that if (a*b)*a = b and (a*b)*a = a*(b*a) than a*(b*a) = b.',NULL,0);
INSERT INTO comment VALUES (8774,1472,3937,'Dave','humble guess','2003-10-19 11:40:51',3,'everything depends on the direction of travel. Your chances of staying within is 50/50',NULL,0);
INSERT INTO comment VALUES (8775,1221,3807,'DrBob','Probably not that original','2003-10-19 12:04:53',0,'There are n elements in the nth row. The total number of elements in the previous n-1 rows is\r\nn(n-1)/2; the first element in row n is the next odd number, given by 2(n(n-1)/2 +1)-1\r\ni.e. n^2-n+1\r\nEach odd number in the row increases by 2, giving a total of\r\nn(n^2-n+1)+2(n(n-1)/2 = n^3-n^2-n+n^2-n = n^3\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (8776,1222,3172,'SilverKnight','re: A simple solution','2003-10-19 13:22:39',0,'In reply to Angela, and to Iggyb387. This is not the commutative property (although, the relation *might* be commutative).\r\n\r\nCommutative means that (a#b)#c = a#(b#c). This is not a given in the original problem. Therefore, we cannot use the commutative property.\r\n\r\nAnd if the relation has the transitive property, this means that if a#b and b#c, then a#c. Again, this is not guaranteed by original problem.\r\n\r\n--- SK',8773,0);
INSERT INTO comment VALUES (8777,1222,1301,'Charlie','re(2): A simple solution','2003-10-19 13:25:13',0,'You say \"Commutative means that (a#b)#c = a#(b#c).\" That is the associative property. The commutative property is that a#b = b#a.',8776,0);
INSERT INTO comment VALUES (8778,1472,1301,'Charlie','solution','2003-10-19 13:26:40',3,'When a point is selected at random, and then a direction in which to travel .5 units, one is selecting a randomly oriented line segment, one of whose ends is at a random position in the square. It is easier to consider the probability distribution (uniform) of the angular orientation of the .5-unit line segment first.\r\n\r\nFirst we must find the probability that the line will extend to the right of the right edge of the square (extended infinitely up and down). The probability that it extends to the left of the left edge will be equal to this, and as they are mutually exclusive, the two can be added together (or the one doubled) to get the probability that the line will extend outside the square to the left or right. By symmetry this will also be the probability that the line will extend either above or below the top or bottom of the square. As we are considering the sides extended indefinitely, the possibility exists that the distal end of the line will be outside the square in both ways, say to the up and right from the upper right corner of the square. So if the probability of being outside the square horizontally is called P(H) and vertically P(V), then the probability of being outside the square altogether must be P(H)+P(V)-P(H and V), as we would have counted the \"outside the corners\" areas twice by adding the horizontal and vertical probabilities together.\r\n\r\nThe two probabilities P(H) and P(V) are not independent, as a line which extends outside to the left or right would be more likely to be more horizontal and therefore less likely to extend above or below also, so P(H and V) is not equal to P(H)P(V), the product of the two probabilities.\r\n\r\nAs the probability of extending to the left is the same as that of extending to the right, let\'s just consider the latter:\r\n\r\nThe probability is the same whether the line is sloped up or down, and of course must be to the right. So we can find the average by taking the integral\r\n\r\n∫{0 to pi/2} .5 cos θ dθ\r\n\r\nand dividing by pi to get the average \"danger band\" on the right. The reason we divide by pi, rather than pi/2 is that the direction could fully swing out to the left as well, where there is no danger at all of falling off the right edge. Again, the average is the same on the lower semicircle as on this upper, i.e., over -pi to 0 or 0 to pi, and consequently as this is an average, over 0 to 2pi. As the height and the area of the square are both 1, this quotient also serves as the probability, and it comes out to .5/pi. \r\n\r\nThat\'s the probability of falling off the right. The probability of falling off the left is equal to that, and they are mutually exclusive so the probability of falling off either left or right is 1/pi, the total of the two.\r\n\r\n(The problem so far resembles the Buffon\'s Needle method of estimating pi--dropping a needle on a lined surface, where the lines run in just one direction--all parallel, and counting how many cross a line, and comparing to the theoretical value.)\r\n\r\nThe probability of spilling over the top or below the bottom is also 1/pi by the symmetry of the situation.\r\n\r\nNow we have to find the probability that the distal end spills over the top or bottom and also falls off to the right or left (in a corner \"tic-tac-toe\" or \"naughts-and-crosses\" type extension of the square). As mentioned before, the left-right and top-bottom probabilities are not independent, so we can\'t just muliply them to get the combined probability.\r\n\r\nHowever we can similarly compute the area of the rectangle in, say the upper right corner of the square, where the initial point would have to fall for the average angle to result in placing it in that upper-right tic-tac-toe area relative to the central square under consideration. That rectangle has a width of .5 cos θ just as mentioned above for the width of the full strip on the right. Its height is .5 sin θ, so the integral over θ is\r\n\r\n∫{0 to pi/2} .5 cos θ .5 sin θ dθ\r\n\r\nwhich is also\r\n\r\n∫{0 to pi/2} sin(2 θ) / 8 dθ\r\n\r\nwhich comes out to 1/8.\r\n\r\nTo get the average this time, we must divide by 2 pi, as the whole circle has to be considered this time, as only 1/4 of it has any danger of falling off the corner at all. But of course we still have to multiply by 4 to account for the fact that there are four corners from which to fall out. So (1/8)/(2 pi) multiplied by 4 comes out to (1/4)/pi.\r\n\r\nSo the overall probability that the endpoint will come outside the square is\r\n\r\nP(V)+P(H)-P(V and H)\r\n\r\n= 1/pi + 1/pi - (1/4)/pi = 1.75 / pi or approximately .5570423008216342.\r\n\r\nA simulation verifies this, using the program:\r\n\r\nDEFDBL A-Z\r\npi = 4 * ATN(1)\r\nFOR i = 1 TO 1000000\r\n x = RND(1)\r\n y = RND(1)\r\n angle = 2 * pi * RND(1)\r\n x = x + .5 * COS(angle)\r\n y = y + .5 * SIN(angle)\r\n ct = ct + 1\r\n IF x < 0 OR x > 1 OR y < 0 OR y > 1 THEN\r\n outside = outside + 1\r\n END IF\r\nNEXT\r\nPRINT USING \"####### ####### #.##### #.#####\"; outside; ct; outside / ct; SQR(ct * outside / ct * (1 - outside / ct)) / ct\r\n\r\nresulting in the statistics:\r\n\r\n 556944 1000000 0.55694 0.00050\r\nshowing the average as .55694 with std. error of the mean .00050, after a million trials.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (8779,1458,3938,'Jebus','Plasma','2003-10-19 13:44:59',0,'Use some type of Plasma to knock it down',NULL,0);
INSERT INTO comment VALUES (8780,1458,3940,'Mag','Solution.','2003-10-19 16:08:23',3,'Do not touch the sucker, No problem.\r\nThe butt of a cigarette is a filter.\r\nThe filter has humectants which is basically a moisturizing agent for prolonged shelf life. If that was to dry up the physical strenght of the filter would diminish. By raising the heat in the room and using a dehumidifyer (extracts water from the air) you have created an atomsphere that will weaken the structure of the cigarette. the base will shrivel and the cigarette will fall. of course there is a flaw in this solution, what if the base shrivels up equally on all sides. yea yea yea.. whatever. You know the probability of that happening.',NULL,0);
INSERT INTO comment VALUES (8781,1472,3940,'Mag','Solution using graphical logic','2003-10-19 16:48:19',3,'1. The target square is 1u²\r\n2. The distance of available travel is 0.5u in any direction. (circle with radius of 0.5u)\r\n\r\nThe maximum distance of the ending position is 0.5u. Thus we can represent this by an extended perimiter of 0.5u circling the 1u² box. This creates a square with round edges.\r\n\r\nThe probility of the target being inside the square is basically the area of the square / the area of the square with the round edges.\r\n\r\nArea of the Target Square\r\n=l*w\r\n=1*1\r\n=1u²\r\n\r\nArea of the Round edge Square\r\nor Area of large square - area of 4 rounded corners\r\n=l * w - 4[(w- Pi*r*²)/4]\r\n=2*2 - 4[(1 - Pi*0.5²)/4]\r\n=4 - (1-Pi*0.25)\r\n=3 + 1/4 Pi (aprox 3.7854u²)\r\n\r\nProbility of the ending position in Square\r\n=1u² / (3 + 1/4 Pi u²)\r\n=0.2642 (aprox)\r\n\r\nThe probility of the ending position is within the square is 26.42%',NULL,0);
INSERT INTO comment VALUES (8782,1472,1301,'Charlie','re: solution','2003-10-19 19:22:41',0,'Of course the idea was to come up with the probability that you are still within the square, not that you are outside the square, so the answer is 1 - .5570423008216342, or .4429576991783658, that is, 1 - 1.75/pi.\r\n\r\n',8778,0);
INSERT INTO comment VALUES (8783,1472,3558,'Tristan','re: Solution using graphical logic','2003-10-19 19:29:02',0,'The only problem is that the chance for ending up in every spot in the round edge square is not the same. It is very unlikely, for example, to end up at the edge of the round edge square, because the exact right spot on the square must be chosen and the exact right direction must be chosen.',8781,0);
INSERT INTO comment VALUES (8784,1322,1626,'Gamer','Solution provisions','2003-10-19 21:40:27',4,'Do the solutions take into account that none of the prizes will have the same price; you will be able to win with some method of arranging?\r\n\r\nI think it\'s fine if the solutions use a different interpretations, but that was one idea I had in mind for this problem.',NULL,0);
INSERT INTO comment VALUES (8785,1222,1575,'DJ','re(3): A simple solution','2003-10-19 22:08:41',0,'Commutativity is a property of an operation, not of the set of real numbers, as someone suggested. The point of the problem is that you can\'t assume anything about the given operation other than what\'s stated in the problem, so arguments about commutativity, associativity, inverses, anything that applies to \'normal\' operations do not necessarily apply here.\r\nCharlie\'s first suggestion shows the only valid way to prove this.',8777,0);
INSERT INTO comment VALUES (8786,31,1626,'Gamer','Basic idea','2003-10-19 22:09:23',0,'The basic paradox here is divide by zero. How many turns the bee makes is some number divided by zero, which creates the paradox',NULL,0);
INSERT INTO comment VALUES (8787,1222,3172,'SilverKnight','re(3): A simple solution','2003-10-20 01:05:22',0,'Yes, you are correct. I misspoke. And that, too, cannot be assumed about the problem.\r\n\r\nThanks, Charlie.',8777,0);
INSERT INTO comment VALUES (8788,1222,3172,'SilverKnight','re(4): A simple solution','2003-10-20 01:14:35',0,'I beg your pardon DJ.\r\n\r\nArguments about inverses certainly DO apply if the original problem provides the necessary basis for it.\r\n\r\nYour \"given\" is equivalent to one operation \"undoing\" (for all integers) the other operation. Because, for any given \'a\', for all integers \'b\', we can break your equation down into the operation of two operators. It is very much analagous to Charlie\'s substitution.\r\n\r\nIn other words, the assumption GIVEN in the problem is equivalent to saying that if\r\nF(x) = a#x, and\r\nG(x) = x#a, then \r\nG is the inverse of X.\r\n\r\nBecause the problem DID write G(F(x)) = x. (If we substitute the functions, we restate the problem.)\r\n\r\nThis is EXACTLY the definition of inverse. And this is EXACTLY what the problem tells us to assume.',8785,0);
INSERT INTO comment VALUES (8789,1222,1575,'DJ','re(5): A simple solution','2003-10-20 02:18:01',0,'The problem does not say to assume that if F(G(x))=x, then G(F(x)) must also equal x. It\'s true, of course .. because that\'s what the problem is asking you to prove.',8788,0);
INSERT INTO comment VALUES (8790,1458,1183,'fwaff','re: Energy..','2003-10-20 03:26:18',0,'\"given enough magnetism and a frog will hover\"\r\n\r\nReally???\r\n\r\nNow there\'s an experiment I\'d like to see.\r\n\r\nDoes it work with cows as well?',8765,0);
INSERT INTO comment VALUES (8791,1222,3172,'SilverKnight','re(6): A simple solution','2003-10-20 03:48:46',0,'The problem DOES say thet G(F(x)) = x (for all x). Alternatively, the problem says that if F(x) = a#b, then there *is* an inverse to this relation.\r\n\r\nThat F(G(x)) = x as well... is not given by the problem, but is given by the definition of inverse relations. (That you limit the domain to the set of integers makes this no less true.)\r\n\r\nAnd the fact that G is the inverse of F implies F is the inverse of G as well.\r\n\r\nI refer you to:\r\nhttp://www.math.csusb.edu/notes/func/node3.html\r\n\r\n\n\nEdited on October 20, 2003, 4:29 am',8789,0);
INSERT INTO comment VALUES (8792,1223,3546,'RoyCook','Solution','2003-10-20 08:39:04',3,'The song goes:\r\n\r\nn bottles of beer on the wall, n bottles of beer, take one down, pass it around, n-1 bottles of beer on the wall.\r\n\r\nThere are two solutions, depending on whether we treat the occurrence of \"one\" as a number or as a pronoun. If the former, as I suspect was intended, then the solution is the summation, with n ranging from 1 to 99, of n+n+n-1, which can easily be computed, and is 14850. If we ignore the occurrence of \"one\", then the answer would be: 14751.',NULL,0);
INSERT INTO comment VALUES (8793,1223,1183,'fwaff','re: Solution 2nd part','2003-10-20 09:15:17',3,'Assuming that \'one\' is a number rather than a pronoun then in the general case the sum is...\r\n\r\n(1+...+n) + (1+....+n) + (1+...+1) + (0+....(n-1))\r\n\r\nwhich is equal to\r\n\r\n3 x (1+....+n)\r\n\r\n= 3 x n x (n+1) / 2\r\n\r\nIn the traditional song this gives...\r\n\r\n3 x 99 x 100 / 2 = 14850 as per Roy\'s answer',8792,0);
INSERT INTO comment VALUES (8794,1322,1301,'Charlie','re: Solution provisions','2003-10-20 11:41:08',0,'The solutions actually consider a continuous range of prices and therefore probability zero that two are the same, which is the same as your statement that none have the same price.\r\n\r\nWhen two prices are in the same band, most of these solutions assume one or the other is equally likely to be the larger. When three are in the same band, it\'s considered equally likely to be in any of the 6 possible orders, without consideration of the possibility that two are the same price. The same goes for the one of my solutions that does not make them equally likely, but still assumes that they are from a continuous distribution and therefore have zero likelihood of matching prices.',8784,0);
INSERT INTO comment VALUES (8795,1222,1575,'DJ','re(7): A simple solution','2003-10-20 11:59:28',0,'I know what the property of inverses states. My point is, you can\'t assume it, because it\'s what you are proving.',8791,0);
INSERT INTO comment VALUES (8796,1223,3224,'Lee','solution','2003-10-20 12:16:04',0,'If you only mentioned the number once per \'verse\' the answer would simply be the triangular number of n - given by (n^2+n)/2.\r\nI\'ve only heard the song in movies, but I think it goes something like,\r\n\r\nn bottles of beer on the wall\r\nn bottles of beer, if\r\n1 of those bottles should happen to fall there\'d be\r\n(n-1) bottles of beer on the wall.\r\n\r\nfor a total of 3n bottles mentioned per \'verse\'.\r\nThe answer is therefore 3 x the triangular number of the bottles you start with on the wall.\r\nTriangular number when n=99\r\n(99^2 + 99)/2 = 4950\r\nmultiplied by 3 = 14850\r\n\r\nThe general formula is therefore 3(n^2+n)/2',NULL,0);
INSERT INTO comment VALUES (8797,1222,3172,'SilverKnight','re(8): A simple solution','2003-10-20 12:33:51',0,'I beg to differ. I showed that a#(b#a)=b (which is what the problem asks us to prove).\r\n\r\nThis is related to, but not equivalent to, that property of inverses. That I invoked that property, which I found useful in the solution is appropriate.',8795,0);
INSERT INTO comment VALUES (8798,1463,3922,'Paul','AARRGG..','2003-10-20 14:04:23',1,'Ok this one is still mind boggling me..\r\n\r\nI\'ve tried to find a relation between the gaps of the numbers, but keep coming up short mainly because of the last two numbers. I\'ve also tried to see if it was in base 8 or 9 instead of base 10. So far I\'m out of luck. Next option is to see if there is any relation of what the numbers represent. ie: Do they represent population of cities in alphabetical order, Do they correspond to the chemical chart in any way. \r\n\r\nSo far those are my current thoughts..',NULL,0);
INSERT INTO comment VALUES (8799,1458,3951,'Riddly One','Here\'s the solution','2003-10-20 14:08:06',0,'Use a magnifying glass or even a laser to compromise the base of the cigarette.',NULL,0);
INSERT INTO comment VALUES (8800,1458,3951,'Riddly One','I apologize','2003-10-20 14:09:56',0,'I\'ll try not to post without reading the other stuff first...',NULL,0);
INSERT INTO comment VALUES (8801,1463,1920,'Brian Smith','re: AARRGG..','2003-10-20 15:21:35',0,'You\'re not alone. I also tried consucutive differences, other bases, etc and have gotten nowhere. This sequence even stumped the Sloane Integer Encyclopedia.',8798,0);
INSERT INTO comment VALUES (8802,1463,3924,'Fernando Baibich','re(2): AARRGG..','2003-10-20 15:28:27',0,'I\'ve also tried converting them to Hex and binary, but it didn\'t seem to help...',8801,0);
INSERT INTO comment VALUES (8803,1463,3172,'SilverKnight','solution? maybe not what he had in mind....','2003-10-20 15:32:35',0,'Once, in 5th grade, I wrote a pretty long essay. And these numbers, exactly correspond to the number of words in the first seven paragraphs of my eight paragraph essay.\r\n\r\nThe last paragraph had 83 words. So, clearly, the next number in the sequence is 83. Wow! Tough one... very good Freddy.',8802,0);
INSERT INTO comment VALUES (8804,1223,2130,'ethan','Solution','2003-10-20 16:52:35',0,'The sum would be 14,751.\r\nA solution to get the sum of the numbers when you start on n would be: 1.5*n*(n-1)+2n',NULL,0);
INSERT INTO comment VALUES (8805,1473,3172,'SilverKnight','solution','2003-10-20 18:23:10',3,'Let\'s place this on a Cartesian graph, sitting on the x-axis, and centered on the y-axis.\r\n\r\nR is the radius of the big (middle circle).\r\n\r\nLet\'s introduce point A as the center of the top circle, point B as the center of the big (middle) circle, point C as the point of tangency between the two bottom circles, and point D as the center of the right, bottom circle.\r\n\r\nPoint C sits at (0,1) since it is on the y-axis, and is at the same height (y value) as the center of the two lower circles\r\n\r\nPoint D is at (1,1) since it is at the center of the the right, bottom circle\r\n\r\nDraw right triangle BCD. The length of BD (the hypotenuse) is R+1. The length of CD is 1. Let the length of CB = x.\r\nx² + 1² = (R+1)²\r\nx = √(R² + 2R)\r\n\r\nTherefore, point B sits at (0, 1 + √(R² + 2R) )\r\n\r\nPoint A is R + 1 (the sum of the two radii) higher than point B, therefore it is at (0, R + 2 + √(R² + 2R) ).\r\nAnd of course, the length of AC is therefore R + 1 + √(R² + 2R).\r\n\r\nLet\'s introduce point E, the point of tangency of the middle circle and the right side of the triangle.\r\n\r\nIntroduce line segment AD which connects the centers of two 1 unit circles. This line segment is parallel to the side of the right triangle (both circles have radius 1).\r\n\r\nIntroduce line segment BE which is perpendicular to the line segment AD and to the side of the triangle. Call the intersection of BE and AD, point F.\r\n\r\nNote that length of BE = R, FE = 1, and BF = R-1.\r\n\r\nDraw triangle ABF and DBF. Note that these two are similar right triangles (having hypotenuse = R+1, one leg = R-1, and therefore, the other leg must be 2√R).\r\n\r\nTherefore, the length of AD = 2 * 2√R = 4√R.\r\n\r\nThis is the hypotenuse of right triangle ACD.\r\n\r\nAC = has already been determined above: R + 1 + √(R² + 2R)\r\nand CD = 1\r\n\r\nSo, let\'s set up the pythagorean theorem and solve for R:\r\n\r\n( 4√R. )² = ( R + 1 + √(R² + 2R) )² + (1)²\r\n\r\nThis can be simplified to:\r\n2R² - 12R + (2R+2)(√(R²+2R)) + 2 = 0\r\n\r\nIf we solve this, numerically for R, we get\r\nR is approximately equal to 1.51067547264602\r\n\r\nI probably made an error along the way, please check my work.\n\nEdited on October 20, 2003, 6:24 pm',NULL,0);
INSERT INTO comment VALUES (8806,1229,3954,'Benjamin Marsh','I think I have the solution','2003-10-20 20:06:45',0,'a) The amount of money that the grandfather gives can be modeled by the summation series ∑(2^k-1) with index 1 and upper limit 15. The summation is 32,767. The amount of money that the grandmother gives can be represented by the series ∑(2^k-2) with index 2 and upper limit of 17. The summation is 65,554 (my arithmetic may be incorrect).\r\n\r\nb) In the end, the grandfather pays the most money. Please correct my if I am wrong on any of this.',NULL,0);
INSERT INTO comment VALUES (8807,651,3954,'Benjamin Marsh','is this is?','2003-10-20 20:22:58',0,'is the answer (p-1)/p ?',NULL,0);
INSERT INTO comment VALUES (8808,651,3954,'Benjamin Marsh','re: is this is?','2003-10-20 20:29:46',0,'please ignore my previous post....i am an idiot\r\n',8807,0);
INSERT INTO comment VALUES (8809,1473,3558,'Tristan','re: solution','2003-10-20 22:22:33',0,'First, I like your proof. It\'s a really nice proof. Second, I checked everything except the final calculation of R and it seems to have no errors. Except that triangles ABF and DBF are congruent, not similar.',8805,0);
INSERT INTO comment VALUES (8810,288,3958,'hi','of course','2003-10-20 22:23:42',0,'it has every letter of the alphabet',NULL,0);
INSERT INTO comment VALUES (8811,1473,3172,'SilverKnight','re(2): solution','2003-10-20 22:54:07',0,'DANG DANG DANG!!!!!\r\n\r\nYou\'re right, of course... that\'s what I meant... congruent. :-)',8809,0);
INSERT INTO comment VALUES (8812,840,3785,'Ashlee','Sloution','2003-10-21 05:07:50',3,'I\'ve been told this one last year I think.\r\n\r\nton',NULL,0);
INSERT INTO comment VALUES (8813,1473,3785,'Ashlee','My solution','2003-10-21 05:18:23',0,'Well I thought that if you got a ruler and measured the actual sizes like that it would be easier.\r\n\r\nThe little circles had a radius of .7cms and the big one had a radius of 1cm.\r\n\r\nSo if the small ones are 1cm and the big circle is .3cms bigger,\r\n\r\n1 + .3cms \r\n\r\n= 1.3cms <---my answer (I think I got it wrong)',NULL,0);
INSERT INTO comment VALUES (8814,1222,3785,'Ashlee','My solution','2003-10-21 05:32:09',0,'First one...(a#b)#a=b\r\nit\'s just changed around\r\nsee.........a#(b#a)=b a# is at the front\r\n............(a#b)#a=b a# is at the back\r\n \r\n (b#a) b is before a\r\n (a#b) a is before b\r\n\r\nthere is no difference!!\r\n\r\na#(b#a)=b = (a#b)#a=b ',NULL,0);
INSERT INTO comment VALUES (8815,1473,1920,'Brian Smith','re: solution','2003-10-21 09:30:20',0,'Your equation 2*R^2 - 12*R + (2*R+2)(sqrt(R^2+2*R)) + 2 = 0 \r\nreduces to cubic equation 16*R^3 - 33*R^2 + 14*R - 1 = 0.\r\n\r\nThat equation has three positive roots: R=1.51067547264, R=0.462340147657, and R=0.0894843796967, but since the radius must be large enough to touch the triangle, the only solution is R=1.51067547264.\n\nEdited on October 21, 2003, 9:32 am',8805,0);
INSERT INTO comment VALUES (8816,1463,3196,'Dan','This one was tuff !!','2003-10-21 10:15:42',0,'A \"DIFFICULT\" sequence... DIFFICULT = DIICL + FFUT. FFUT is the reverse spelling of TUFF, a common slang spelling of TOUGH, a synonym for DIFFICULT. If you remove TUFF from DIFFICULT, the sequence becomes much less tuff. DIFFICULT minus TUFF leaves Roman Numerals DIICL. (D=500, C=100, L=50, I=1). DIICL = DCLII= 652 = 21 + 45 + 66 + 102 + 115 + 171 + 132. So the next number in the sequence is 132. (Lame ? Yes, but I managed to find Silver Knight\'s essay after rummaging through my papers last night, and his third paragraph actually contains 67 words, not 66. So mine is the only \"valid\" solution so far.) ',NULL,0);
INSERT INTO comment VALUES (8817,1473,1301,'Charlie','Spreadsheet solution','2003-10-21 10:35:16',3,'The tangent line along one side from the single 1-unit-radius circle to the radius-r circle makes an angle with the central line of arcsin((r-1)/(r+1)), as the tangent line itself, plus perpendiculars along the radii for a length of 1 unit, touches the center of the unit circle and leaves (r-1) to go along the r-radius circle, and the angle that one side of the rectangle makes with the center line is the same as the other. The hypotenuse of the triangle is length r+1, so the sine of the angle at the center of the single 1-unit circle is (r-1)/(r+1).\r\n\r\nThe distance from the center of the radius-r circle to where the two 1-unit circles are tangent to the center line is sqrt((1+r)^2-1), so the angle from the center if the solitary unit circle to the center of one of the pair of unit circles has tan equal to 1/(sqrt((1+r)^2-1)+r+1)\r\n\r\nSetting cells A1 through F1 to\r\n1.1, =SQRT((1+A1)^2-1), =(A1-1)/(A1+1), =1/(B1+A1+1), =D1/SQRT(1+D1^2), =E1-C1, they represent the initial guess for r, the distance from the center of the radius-r circle to the tangent point of the unit circle pair, the sine of the first angle, the tangent of the second angle and the sine of the second angle, and finally the difference between the two sines.\r\n\r\nThe two angles must equal in order for this to be one exterior triangle. We use Excel\'s solver to vary cell A1 to make F1 be zero. Being careful to set the accuracy high enough, we get cell A1 to be 1.51067547264613, being the value of r to produce the triangle.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (8818,1222,1920,'Brian Smith','re: My solution','2003-10-21 11:05:20',0,'Your solution assumes the commutative property is true. You cannot assume that from what the problem tells you.',8814,0);
INSERT INTO comment VALUES (8819,1463,3172,'SilverKnight','re: This one was tuff !!','2003-10-21 11:11:38',0,'Gee Dan,\r\n\r\nI hate to nit pick... but the hypenated word \"thinga-mabob\", in the third paragraph of my 5th grade essay, should only count as one word. I understand that it is an unusual spelling. But as I was directly quoting a famous author, I was forced to include his admittedly peculiar choice of spelling.\n\nEdited on October 21, 2003, 11:11 am',8816,0);
INSERT INTO comment VALUES (8820,655,1920,'Brian Smith','A solution','2003-10-21 11:31:01',0,'24=7*(3+3/7)',NULL,0);
INSERT INTO comment VALUES (8821,1274,3430,'pat','sorry lewis','2003-10-21 12:33:14',0,'sometimes the comments are more fun than the puzzle.... sorry lewis',NULL,0);
INSERT INTO comment VALUES (8822,1463,1920,'Brian Smith','An alternate approach','2003-10-21 13:22:16',0,'It is possible that this sequence is two sequences intertwined. Consider every other term: 21, 66, 115, X. The short sequence 21, 66, 115 can be interpreted as a quadratic sequence, which makes the next term 168. Similarly the term after 168 is 252. 252 comes from treating 45, 102, 171 as a quadratic sequence.\n\nEdited on October 21, 2003, 1:53 pm',NULL,0);
INSERT INTO comment VALUES (8823,1463,3172,'SilverKnight','re: An alternate approach','2003-10-21 13:31:52',0,'Brian,\r\n\r\nYou wrote \"21, 66, 171, X\". I think you meant \"21, 66, 115, X\". The rest of your argument is straightforward... but I sincerely hope that this is not what Freddy had in mind.',8822,0);
INSERT INTO comment VALUES (8824,1463,1920,'Brian Smith','re(2): An alternate approach','2003-10-21 13:53:37',0,'Thanks for catching that error.',8823,0);
INSERT INTO comment VALUES (8825,1275,3964,'B','A solution','2003-10-21 15:22:40',1,'1/2,2,9,48,300,2160,17640\r\n\r\nwhere x=[1+n+[1/(n-1)]]*[x-1]',NULL,0);
INSERT INTO comment VALUES (8826,1275,3970,'sandy','solution','2003-10-21 15:25:03',0,'then next two numbers are 2160, 17640...',NULL,0);
INSERT INTO comment VALUES (8827,1275,1920,'Brian Smith','Nth term','2003-10-21 15:44:24',0,'The nth term of this sequence is n*(n!)/2',NULL,0);
INSERT INTO comment VALUES (8828,1275,1626,'Gamer','re: Nth term','2003-10-21 15:49:36',0,'I was thinking the difficulty was going to get changed to something less difficult before it would get posted.',8827,0);
INSERT INTO comment VALUES (8829,1152,1626,'Gamer','Sequence 6?','2003-10-21 17:36:38',0,'I think sequence 6 was a bit hard... Is anyone going to do it or should the solution be published?',NULL,0);
INSERT INTO comment VALUES (8830,1275,3922,'Paul','re: Nth term','2003-10-21 18:24:28',0,'What was your thought process to find out the formula? ',8827,0);
INSERT INTO comment VALUES (8831,1275,1575,'DJ','','2003-10-22 00:51:19',3,'I came up with xn = xn-1(n²/(n-1)), where x1 is 1/2.\r\n\r\nI got this by looking at what you would have to multiply each term by to get the next. To get 2 from 1/2, you multiply by 4; to get 9 from two you multiply by 9/2; to get 48 from 9 you multiply by 48/9, which reduces to 16/3 .. you are multiplying each time by n²/(n-1).\r\n\r\nI see that this is equivlent to Brian\'s answer, which almost certainly the intended response, since it also accounts for the first term. If you have that xn-1 = [(n-1)!(n-1)]/2 , then mutliplying that by n²/(n-1) will yield:\r\n\r\nxn = (1/2)[(n-1)!(n-1)][n²/(n-1)]\r\n\r\n = (1/2)[(n-1)/(n-1)][(n-1)!n²]\r\n\r\n = (1/2)(1)[n(n-1)!n]\r\n\r\n = n(n!)/2\r\n\r\nWhich, given my formula, serves as a sort of useless proof by induction that Brian\'s answer is the same thing.',NULL,0);
INSERT INTO comment VALUES (8832,1475,1183,'fwaff','Possible solution','2003-10-22 08:51:05',3,'Looking at the map it appears that the northernmost and westernmost points of the USA are both in Alaska, the easternmost point is in Maine and the Southernmost point is in Florida.\r\n\r\nSo start in Alaska by visiting the N\'most and W\'most points. Travel across Canada to Maine to vist the E\'most. Finally sail down the east coast of the USA to the tip of Florida.\r\n\r\nAs far as I can see this meets the criteria of not crossing landborders and only leaving US territory once.',NULL,0);
INSERT INTO comment VALUES (8833,1475,1301,'Charlie','re: Possible solution','2003-10-22 09:00:09',0,'But Hawaii (in the tropics) is further south than Florida.',8832,0);
INSERT INTO comment VALUES (8834,1475,3196,'Dan','Are you sure what these geographic points are ?','2003-10-22 09:07:33',0,'Mr. FB, are you sure you are clear on what these geographic points actually are ? The northernmost point of the USA is Point Barrow, Alaska. The westernmost point is Cape Wrangell, Alaska (Attu Island). The easternmost point is West Quoddy Head, Maine. The southernmost point is Ka Lae (South Cape), Hawaii. Ted must have left U.S. controlled territory at least twice to accomplish this feat. To get from Alaska to Hawaii, or from Hawaii to Maine, or from Alaska to Maine, would be the first required absence; to get from Hawaii to Maine, from Maine to Alaska, or from Maine to Hawaii would be the second. You can make all those transitions without crossing landborders between states, but unless I\'m missing some obvious trick (Ted made his trip in 1776, before Alaska and Hawaii were part of the U.S.? Ted is in the Space Shuttle the whole time ??), you cannot leave U.S. controlled territory \"just once\" and do it. \r\n\n\nEdited on October 22, 2003, 9:34 am',NULL,0);
INSERT INTO comment VALUES (8835,1458,2992,'Chan Wah','Clarification','2003-10-22 09:14:08',0,'You are not permitted to physically change the cigarette. You will have all the \'equipment\' you need with you. This is not a trick question.\r\n\r\nSorry for not being clearer. This is my first problem and English is not my first language.',8800,0);
INSERT INTO comment VALUES (8836,1475,1301,'Charlie','re: Are you sure what these geographic points are ?','2003-10-22 09:38:19',0,'The longitude of Attu Island is about 173 degrees East. Semisopochnoi Island is even further east at over 179 degrees East. It is Amatignak Island that is about as far west as you can go, at about 179 degrees West.\r\n\r\nThis is a riddle after all.',8834,0);
INSERT INTO comment VALUES (8837,1475,1920,'Brian Smith','re(2): Are you sure what these geographic points are ?','2003-10-22 10:19:37',0,'I think I got it. East and west can be measured relative to the prime meridian. The eastern most point and western most point are then the two spots mentioned in your post. With the eastern, western and northern most points all in Alaska, it is easy to accomplish the task by visiting all three points and then leaving for Hawaii.',8836,0);
INSERT INTO comment VALUES (8838,1225,1920,'Brian Smith','A start','2003-10-22 12:38:27',0,'The value \'6\' should never be allowed to come up on the other die. A roll of 5,6 never harms the shooter.',NULL,0);
INSERT INTO comment VALUES (8839,1225,3172,'SilverKnight','some thoughts','2003-10-22 12:50:40',1,'Well, we can\'t make him lose on the first roll (because we can\'t generate 2, 3, or 12 by using one \'5\').\r\n\r\nSo, we wish to maximize the chances that he doesn\'t get a 7 or 11 on the first roll AND he gets a seven on a later roll.\r\n\r\nSo, it is necessary to allow for a \'2\' to show up (to make the 7 on a later roll).\r\n\r\nI think we want to eliminate the probability of rolling a six (this way, rolling an 11 on the first throw can\'t occur).\r\n\r\nSo, at least at first glance, it seems that we have to identify x, the probability of rolling a 2. And then we can divide the remaining probabilities among the remaining numbers (1, 3, 4, and 5), and assign (1-x)/4 as the probability to each of those numbers.\r\n\r\nIf this is all true, then we need to solve for x such that it minimizes your adversary\'s chances of winning.\r\n\r\n--- SK',8838,0);
INSERT INTO comment VALUES (8840,643,3977,'Bill','Could be easy.','2003-10-22 13:19:04',0,'I find that no matter how you slice it, The nursery is %100 full of babies after the addition, 2 boys are in the mix. Confusion is that there could be 1 or many Girls. If there were xGirls and 2Boys, we will call the last addition \"a\" (a is equal to \"1\" because only one was added to the mix then (xG-B+1=n)\r\nProbability is: (n/xG)+1\r\nExample if 50Girls, 2 are Boys + 1 Addition.\r\nn=49 so 49/50 or 98%.',NULL,0);
INSERT INTO comment VALUES (8841,1225,1301,'Charlie','re: some thoughts','2003-10-22 13:40:12',3,'If we make x be the probability that we assign to rolling a 2 on the second die, make the probability of a 6 zero, and apportion the probability of any of the other four possibilities equally (so as to minimize the likelihood of getting the same point again), then the probability of the shooter\'s winning, which is to be minimized, is:\r\n\r\nx+(1-x)*((1-x)/4)/(x+(1-x)/4)\r\n\r\nwhose terms represent the probability, x, of winning on the first throw, and 1-x of not winning on the first throw, (then multiply by the conditional probability of getting whatever point comes up before getting a seven).\r\n\r\nPutting this into Excel, as =B2+(1-B2)*((1-B2)/4)/(B2+(1-B2)/4), where an initial guess of .2 or .3 (or anything reasonable) is placed into cell B2, and then using Solver to minimize this formula by changing B2, we get a minimum when x is 1/3. At that point the probability of a win is 5/9 (that is, the evaluation of this formula).',8839,0);
INSERT INTO comment VALUES (8842,1220,3979,'Jonathan shao','re(3): Different Approach (Continued)','2003-10-22 14:56:35',0,'when we are dealing with infinite something (chords, points etc.), normal rules just don\'t hold true any more. Here is a good example : given two fragments AB and CD (say length of AB larger than CD) , comparing the number of points on AB and CD . Now we know the total points number on AB and CD are both infinte, there seems no way to compare two infinte numbers. But an intuitive answer will be N ab is more than N cd because AB is longer than CD. But is that right? The answer is no. Now I will prove the number of points on AB is exact same as that on CD.\r\n\r\n a ---------------------------b\r\n A \\ | C\r\n \\ |\r\n \\ |\r\n B \\ | D\r\n c--------------------------d\r\n \r\nTo prove this, we might think about a reasoning first: If we can prove for any points on AB, we can found a counter part on CD, vice verser.then we can say the number of points on AB is exactly the same as that on CD. Now put these two fragments between two pararel lines,ab and cd ( see the picture above) , pick a random points on A, we call it E, make a parallel line start from E and cross CD at F, then F is the 1to1 correspondent point for E. Using the same way we will find that for all the points on AB (infinite) , we can find a counter part on CD, vice verser. So we can conclude the number of points on AB is same as to that on CD, although AB is longer than CD, and the numbers are infinite.\r\n\r\nFinally, using this theory , we can prove that the chance of chord longer than \r\nradius is 50%. If you are using other methods that can only apply to finite numbers, you will generate different answers depend on which method you use. But I think the truth is unique! hehe. good question, good luck guys ',8680,0);
INSERT INTO comment VALUES (8843,1220,3979,'Jonathan shao','','2003-10-22 15:03:36',0,'sorry guys, the picture in my last post was messed up, so just read the text',NULL,0);
INSERT INTO comment VALUES (8844,1463,3924,'Fernando Baibich','Strange','2003-10-22 15:07:46',0,'\r\n Ok, this can\'t be the solution! :)\r\n\r\n Looking at the numbers, we can see they somehow follow the order T - F - S:\r\n \r\nTwenty one\r\nForty five\r\nSixty six\r\nOne hundred and two\r\nOne hundred and fifteen\r\nOne hundred and seventy one\r\n\r\n If we do not count the hundreds as part of the story, the number in the sequence would begin with an unused T, leaving us with 212. \r\n\r\n Or 250 if we count the T of the TWO hundred.\r\n\r\n Whatever.',NULL,0);
INSERT INTO comment VALUES (8845,1220,3979,'Jonathan shao','','2003-10-22 15:16:13',0,'sorry guys, the picture in my last post was messed up, so just read the text',NULL,0);
INSERT INTO comment VALUES (8846,1220,3979,'Jonathan shao','','2003-10-22 15:42:31',0,'sorry guys, the picture in my last post was messed up, so just read the text',NULL,0);
INSERT INTO comment VALUES (8847,1242,3878,'sean','','2003-10-22 15:43:12',0,'Good man, i missed the fact that the area is only 3/4 of the square...well done mate!',NULL,0);
INSERT INTO comment VALUES (8848,1220,3979,'Jonathan shao','re(3): Different Approach (Continued)','2003-10-22 15:43:33',0,'when we are dealing with infinite something (chords, points etc.), normal rules just don\'t hold true any more. Here is a good example : given two fragments AB and CD (say length of AB larger than CD) , comparing the number of points on AB and CD . Now we know the total points number on AB and CD are both infinte, there seems no way to compare two infinte numbers. But an intuitive answer will be N ab is more than N cd because AB is longer than CD. But is that right? The answer is no. Now I will prove the number of points on AB is exact same as that on CD.\r\n\r\n a ---------------------------b\r\n A \\ | C\r\n \\ |\r\n \\ |\r\n B \\ | D\r\n c--------------------------d\r\n \r\nTo prove this, we might think about a reasoning first: If we can prove for any points on AB, we can found a counter part on CD, vice verser.then we can say the number of points on AB is exactly the same as that on CD. Now put these two fragments between two pararel lines,ab and cd ( see the picture above) , pick a random points on A, we call it E, make a parallel line start from E and cross CD at F, then F is the 1to1 correspondent point for E. Using the same way we will find that for all the points on AB (infinite) , we can find a counter part on CD, vice verser. So we can conclude the number of points on AB is same as to that on CD, although AB is longer than CD, and the numbers are infinite.\r\n\r\nFinally, using this theory , we can prove that the chance of chord longer than \r\nradius is 50%. If you are using other methods that can only apply to finite numbers, you will generate different answers depend on which method you use. But I think the truth is unique! hehe. good question, good luck guys ',8680,0);
INSERT INTO comment VALUES (8849,1225,2899,'Brian Wainscott','some thoughts...and a question','2003-10-22 17:18:51',0,'I guess I need to learn a bit about conditional probabilities -- they seem to show up around here a lot.\r\n\r\nAssuming Charlie\'s formula is correct, differentiating it and setting it to 0 results in a quadratic, with x=1/3 as a solution, which Charlie gave. The other solution is x = -1. Obviously, this makes no sense as a probability. I\'m just curious if anyone has any speculation on what if anything this other root might mean.\r\n\r\nOn another note -- why not just weight the die so that 2 ALWAYS comes up. Then after about the 3rd time he rolls a 7, someone will catch on and they\'ll pound him to a pulp for cheating....',8841,0);
INSERT INTO comment VALUES (8850,1475,3981,'Panther','Riddle solution','2003-10-22 17:28:25',3,'Easy --\r\nTed is travelling from Alaska to Hawaii.\r\n\r\nAlaska is the northern most state, the western most state, and the eastern most state all in one. It\'s simple to get to Hawaii, our southern most state without ever crossing over a landborder and only leaving the U.S. by going over the Pacific.',NULL,0);
INSERT INTO comment VALUES (8851,1225,3172,'SilverKnight','re: some thoughts...and a question','2003-10-22 19:33:05',0,'Actually, I don\'t think Charlie is correct in that it is conditional probability. (Although I think his calculation is correct.)\r\n\r\nThe remainder of his calculation, ((1-x)/4)/(x+(1-x)/4), is not conditional... it is simply the likelihood of getting 1, 3, 4, or 5 (1-x)/4) divided by (the likelihood of getting a 2 (x) plus the likelihood of getting the same number again (1-x)/4 ).\r\n\r\nCharlie, you are welcome to correct me if I misunderstood what you wrote.\r\n________________________\r\n\r\nAs for what conditional probability is... it is the probability of an even happening given that another event has already occurred.\r\n\r\n(Let\'s not deal with the trivial case when the former event has no effect on the latter case, such as... what is the likelihood of heads coming up on a fair coin toss, given that it previously came up tails).\r\n\r\nBut, what\'s the likelihood that a blue die and a red die add up to a number greater than 8, given that the blue die has already been rolled and shows six. Well... normally, the odds that two (normal) dice add up to a number greater than 8 is 5/18.\r\n\r\nBut since we know the blue die is 6, we can calculate the likelihood of them adding up to greater than 8 as 2/3.\r\n\r\nMore formally, this probability can be written as:\r\nP(B|A) (which is read as \"the probability of event B given event A\")\r\n\r\nP(B|A) = P(A and B) / P(A)\r\n\r\nSo, to apply this to our die problem:\r\nEvent B = P(red die and blue die totalling greater than 8)\r\nEvent A = P(blue die shows 6)\r\n\r\nP(A and B) is 1/9 (out of 36 possible red/blue combinations, only {3,6} {4,6} {5,6} and {6,6} will work)\r\n\r\nand of course P(A) = 1/6\r\n\r\nso... P(B|A) = (1/9) / (1/6) = 2/3.\r\n____________________\r\n\r\nAnd yes, in this relatively trivial example, we could have calculated the probability directly rather than using conditional probability.\r\n\r\nBut I hope this helps.\n\nEdited on October 22, 2003, 8:24 pm',8849,0);
INSERT INTO comment VALUES (8852,1463,3922,'Paul','Odd/Even..','2003-10-22 19:40:14',0,'Guarenteed it is based on only a 50% chance (either it is odd or even).. the sequence seems to be odd, odd, even, even, odd, odd, ?? Which would mean the next is even.',NULL,0);
INSERT INTO comment VALUES (8853,12,3351,'Eric','Voila!','2003-10-22 21:24:50',3,'Ordinarily a two volume book set is set on a shelf with the first volume on the left meaning that page one is on the right side of the left volume and that the last page of the second volume is on the left side of the right volume. That means simply has to eat through the front cover of the first volume and the back cover of the second volume. Since each of these is a millimeter thick, and the worm eats at 2 mm per hour, the answer is just 1 hour!',NULL,0);
INSERT INTO comment VALUES (8854,1475,3985,'sammy','just guessing','2003-10-22 22:48:38',0,'it said LANDborder so i think this guy crossed over a bridge or a river ',NULL,0);
INSERT INTO comment VALUES (8855,1256,3985,'sammy','too confuzing','2003-10-22 22:58:43',0,'that is way too freakishly confuzing, i mean how an i supposed to know all that crap about the military/gov. alphabet road sign junk? i don\'t work for the gov.',NULL,0);
INSERT INTO comment VALUES (8856,1051,3985,'sammy','is it...','2003-10-22 23:03:21',0,'is it some deformed cow that was injected w/ toxic waste? ',NULL,0);
INSERT INTO comment VALUES (8857,579,3985,'sammy','just guessing','2003-10-22 23:07:24',0,'i dont really know how i got this but i think it is 121 ~just a guess~',NULL,0);
INSERT INTO comment VALUES (8858,1045,3985,'sammy','just maybe','2003-10-22 23:19:43',0,'378',NULL,0);
INSERT INTO comment VALUES (8859,576,3985,'sammy','i got it!!!','2003-10-22 23:27:39',0,'i filaly got one! this was pretty easy i saw it almost right away, if u start w/ the 8th letter in the 3rd row and go down diagonaly to the right\r\nMUAH HA HA!!! ',NULL,0);
INSERT INTO comment VALUES (8860,1043,3985,'sammy','got it!','2003-10-22 23:37:39',0,'it is 21:39 (the clock is on army time)',NULL,0);
INSERT INTO comment VALUES (8861,1463,3965,'Manguexa','Another approach','2003-10-23 00:05:55',0,'By regression I get the next number to be 600.',NULL,0);
INSERT INTO comment VALUES (8862,1225,1301,'Charlie','re(2): some thoughts...and a question','2003-10-23 08:12:46',0,'I was thinking of the probabilities of getting one\'s point conditional upon not having gotten a 7 to begin with.',8851,0);
INSERT INTO comment VALUES (8863,1323,3172,'SilverKnight','2/3 of a solution','2003-10-23 09:16:37',3,'Well... for 3 and 5 terms (from brute force searching):\r\n\r\n3: 3, 5, 7\r\nfirst term: 3,\r\nconstant difference: 2\r\n\r\n5: 5, 11, 17, 23, 29\r\nfirst term: 5.\r\nconstant difference: 6\r\n\r\nI\'ll continue searching for 8 terms.',NULL,0);
INSERT INTO comment VALUES (8864,1323,3172,'SilverKnight','remaining 1/3 of the solution','2003-10-23 09:24:34',3,'The first example I\'ve found for 8 terms begin at:\r\n199 and had a constant difference of 210:\r\n\r\n199, 409, 619, 829, 1039, 1249, 1459, 1669',8863,0);
INSERT INTO comment VALUES (8865,1323,1920,'Brian Smith','22 terms','2003-10-23 10:55:45',0,'The longest arithmetic sequence of positive prime integers contains 22 integers:\r\n11,410,337,850,553 + 4,609,098,694,200*k for k=0 to 21\r\n\r\nSource: mathworld.wolfram.com\n\nEdited on October 23, 2003, 10:56 am',NULL,0);
INSERT INTO comment VALUES (8866,27,3274,'Dacre','On Sunday evening','2003-10-23 11:03:59',0,'It\'s sunday evening, assuming the prof is telling the truth, and IS giving a surprise test this week, are you 100% sure (ie willing to bet your life, money, pet goldfish etc) that he will give the test on Monday?\r\nSurely not!\r\nMonday evening - no? etc.\r\nOnly Thur evening do you KNOW it has to be on Friday - on Tue evening, it could still be on 3 days.\r\n\r\nYou can\'t rule out Thursday as a possible date until Wed evening.\r\n\r\n(Alright, it\'s a paradox and unsolvable - but I like thinking of myself in bed the previous day wondering what will happen)\r\n',NULL,0);
INSERT INTO comment VALUES (8867,397,2839,'FatBoy','re(2): Another...','2003-10-23 11:10:56',0,'Maybe up north where you yankees are, but down south Iron is a one syllable word just like tire, fire and school',4628,0);
INSERT INTO comment VALUES (8868,655,3992,'Jane Doe','re: A solution','2003-10-23 11:16:33',0,'\r\n7*(3+3/7) gives 24, but I am not sure if it meets the given criteria. (3+3/7) would account for a third use of the number 7 in the problem wouldn\'t it ? \r\n\r\nThe only other close possibility that I can see is 7/3 + (7*3) which gives 23.33 ',8820,0);
INSERT INTO comment VALUES (8869,655,1920,'Brian Smith','re(2): A solution','2003-10-23 11:24:54',0,'I dont see a problem with 7*(3+3/7). I used two 3\'s, two 7\'s, addition, multiplication, and division to create 24 as the problem stated. The only thing that could possibly be wrong is the use of (). If that is a problem, I can use postfix form: \'7*(3+3/7)\' changes to \'3 7 / 3 + 7 *\'\n\nEdited on October 23, 2003, 11:25 am',8868,0);
INSERT INTO comment VALUES (8870,1458,1171,'nikki','Hmmmm','2003-10-23 11:37:48',1,'Well, if we can\'t physically change the cigarette, then I guess burning it in some way is out of the question.\r\n\r\nIn that case, I guess the high-power magnet, or the massive object (high gravitational force) are the other options.',NULL,0);
INSERT INTO comment VALUES (8871,397,3172,'SilverKnight','re(3): Another...','2003-10-23 11:39:26',0,'I agree with FatBoy... (school? who thinks school has anything other than one syllable?)\r\n\r\n\'Iron\' has one syllable.\r\n\r\nMerriam-Webster agrees as well.\r\n\r\nHowever, Dictionary.com seems to think it has two syllables.\r\n\r\n(Both systems place a bullet between syllables.)\n\nEdited on October 23, 2003, 11:40 am',8867,0);
INSERT INTO comment VALUES (8872,1323,3172,'SilverKnight','re: remaining 1/3 of the solution','2003-10-23 13:08:00',2,'and this continues for two more terms... so it will work for 9 and 10 terms as well:\r\n\r\n199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089',8864,0);
INSERT INTO comment VALUES (8873,1458,2899,'Brian Wainscott','What is the foundation?','2003-10-23 14:25:17',0,'What is it sitting ON? If it is sitting on an ice cube, then it will almost certainly fall all by itself as the cube melts. I\'ve been assuming it is sitting on the bar top, but perhaps not....',NULL,0);
INSERT INTO comment VALUES (8874,650,3994,'Tabitha','Duh!!!','2003-10-23 14:43:50',0,'If your given is 128 pennies head up. Then count out 128 pennies and then the rest will be heads down. you don\'t have to see to count. count out 128 pennies, then count the rest. you may not have the right ones heads up tales up but the math WILL be right.!!',NULL,0);
INSERT INTO comment VALUES (8875,1323,1301,'Charlie','re: 22 terms','2003-10-23 14:45:16',0,'That same web site also shows that there is an 8-term sequence of primes that begins at just 11. However the difference between successive members is 1,210,230.',8865,0);
INSERT INTO comment VALUES (8876,1323,2899,'Brian Wainscott','More brute force','2003-10-23 14:46:58',0,'I wrote a short program to look for such sequences (sorry about the indenting -- one of these days I\'ll get around to figuring out how to do HTML in this window):\r\n\r\n\r\n#include <stdio.h>\r\n#include <stdlib.h>\r\n#include <math.h>\r\n#define MAX_PRIME 1000000\r\nmain()\r\n{\r\n char *isprime;\r\n int i,j,k,step,count,best;\r\n\r\n isprime = (char *) malloc((MAX_PRIME+2)*sizeof(char));\r\n memset(isprime,1,(MAX_PRIME+2)*sizeof(char));\r\n isprime[0] = isprime[1] = 0;\r\n fprintf(stderr,\"memory initialized\\n\");\r\n for(i=2; i<MAX_PRIME; i++) {\r\n if(!isprime[i]) continue;\r\n for(j=2*i; j
\r\n\"Put them together\" Carefully build one 3x3 layer at a time, gluing them together, except don\'t glue the middle one.
\r\n\"Remove the cube in the middle\" Since all the cubes are wire frames, use some long narrow tweazers to reach in, collapse the middle one, then pull it out (kinda like that old kids game, DOCTOR).
\r\nLooking forward to seeing the real solution.',NULL,0);
INSERT INTO comment VALUES (8912,476,4004,'Andrei','A nicer more universal solution','2003-10-24 19:27:33',3,'Another solution is:\r\n\r\nI\'m telling a lie.\r\n\r\nYou can\'t be saying the truth, because you\'d be saying a lie, and the other way around.',NULL,0);
INSERT INTO comment VALUES (8913,1324,3922,'Paul','Magnets?','2003-10-24 19:35:38',0,'What if you make the middle cube, smaller than the rest and metal. Then have the top middle cube slightly larger than the rest, making it rest on the edges of those underneith it. Also make this top cube have a hole through the middle. Now get a magnet and pull the middle cube out, very carefully so you don\'t touch any of the other cubes. \r\n\r\n',NULL,0);
INSERT INTO comment VALUES (8914,1324,1732,'Helen','probably wrong, but worth a try','2003-10-24 19:42:00',0,'What if you drew 27 cubes in a Computer Aided Design program, stacked them together in the same program, then simply deleted the centre one?',NULL,0);
INSERT INTO comment VALUES (8915,1324,1626,'Gamer','re: Magnets?','2003-10-24 19:43:05',0,'Remember that the 27 small cubes you start out with are equivalent. All the cubes you put together to make one larger cube are equivalent.',8913,0);
INSERT INTO comment VALUES (8916,1324,1253,'brianjn','Properties','2003-10-24 20:14:02',0,'Gamer, in Hints, you say \"that all the small cubes mentioned in the beginning of this problem are equivalent, but not equivalent to the cube in the middle you take away\".\r\n\r\nI am imagining 26 cubes which are like wire mesh structures, ie, their edges are the only concrete substance, and can be interlocked, so that a cube, say made of paper can be collapsed, withdrawn through the \'body\' of one of the middle side cubes, an reconstructed.',NULL,0);
INSERT INTO comment VALUES (8917,1324,3818,'A','other possiblity','2003-10-24 21:11:43',0,'nothing said how far apart the cubes on the outside were spaced, they could be miles apart as long as they are in cubic proportions soo....as long as the outer cubes are spaced far enough apart, it is possible to just pick up the inner cube and remove it.',NULL,0);
INSERT INTO comment VALUES (8918,1324,1626,'Gamer','re: other possiblity','2003-10-24 21:57:36',0,'I can say that my solution means that all the cubes put together at the beginning werere equivalent and the cube in the middle that you want to remove was surrounded.\r\n\r\nMy solution is very different than the ones presented here.',8917,0);
INSERT INTO comment VALUES (8919,1220,4005,'SacklanMacMannis','My Stab','2003-10-24 22:08:40',0,'I\'m repeating alot here, but anyways...\r\n\r\nWe pick a random point, and draw a radius to that point. Now we pick another random point, draw a chord and another radius to the second point. We now have a triangle, with the chord, two radii, and angle A between the two radii.\r\n\r\nNow we solve for angle A at which the chord is equal to the radii. This would be an equilateral triangle, with all three sides equal (chord=radius=radius) and all three angles equalling 60 degrees. For all angles A greater than 60 degrees, the chord is longer than the radii, for all A less than 60 degrees, the chord is shorter than the radii.\r\n\r\nNow to calculate the probablity that the chord is greater than the radii, we calculate the probality that A is greater than 60 degrees (pi/3 radians). Because an equivalent chord could be drawn from the same starting point to the other side of the circle, we will divide the circle in two halves, each with 180 degrees. The probablity that A is greater than 60 is (180-60)/180=120/180=2/3. \r\n\r\nI saw someone saying we dont know how the chords are distributed according to angle. I didnt really follow that but this might help. We can assume there are an equal number of infinite points over any two equal proportions of the circumfrence. If you think of angle A in radians rather than degrees, it might help. Radians measure the amount of the cicumfrence encompassed by the angle, so any two equal angles A will have an equal number of infinite points and an equal number of infinite possible chords.\r\n\r\nI dont know if I explained this very clearly, I usually reach peak lucidity after 4 beers, and am presently dead sober, however I think this makes sense and it all adds up to 2/3.',8688,0);
INSERT INTO comment VALUES (8920,656,3623,'jaypee','sophie germain primes','2003-10-24 22:38:28',0,'check out web address:\r\n\r\nhttp://mathworld.wolfram.com/SophieGermainPrime.html\n\nEdited on October 24, 2003, 10:39 pm',NULL,0);
INSERT INTO comment VALUES (8921,1324,3623,'jaypee','re: Slow solution','2003-10-24 23:03:54',0,'I agree with Nikki but to insure that the wooden cubes do not move upon assembly, coat the surfaces of each wooden cube with some sort of bonding agent that would adhere all the wooden cubes together. ',8900,0);
INSERT INTO comment VALUES (8922,1225,2674,'mike','could be','2003-10-24 23:13:41',1,'the dice probabilities should be as follows:\r\n 1- 13/60, 2- 6/60, 3- 13/60,4- 13/60, 5-- 13/60, 6-0/60. \r\nthat would be a probability of 6/60 (1/10) of rolling a winning combination of 7. \r\non the second roll there is a 13/60 chance of rolling the same number combined with the 13/60 chance of rolling that number in the first place which is a 13/120 chance. on the 3rd roll there is a 13/90 chance of rolling the same combination as your initial roll(with all combined chances of the three rolls).Unfortunately for you his chances of rolling that same number grow with each roll. But fortunately so will the chances of not only the othere numbers but also the small cance of rolling a 2 increases. \r\nI understand this isnt a completely correct answer but with a little tweaking it could become one. ',NULL,0);
INSERT INTO comment VALUES (8923,1324,3558,'Tristan','don\'t touch the sides','2003-10-24 23:47:30',0,'On a cube, there are no sides, only faces. Just take the cubes off, remove the middle, and put the remaining 26 back. This could be the solution Gamer was looking for, but maybe not.',NULL,0);
INSERT INTO comment VALUES (8924,1324,3558,'Tristan','re: don\'t touch the sides','2003-10-24 23:50:02',0,'Wait, never mind... I just remembered that it also says not to touch the outer cubes. As you can see, I\'m trying to solve this by finding word trickery, but this is all I got.',8923,0);
INSERT INTO comment VALUES (8925,1324,4008,'darlene','','2003-10-25 01:07:38',0,'-- why is there a question mark after 26? \r\n\r\n\"Without touching the sides of the larger cube, remove the cube in the middle to leave 26?\"\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (8926,1458,2992,'Chan Wah','re: What is the foundation?','2003-10-25 04:56:08',0,'The cigarette is sitting on a normal bar/table top. As I said you should already possess the tools necessary to perform the job. No need for any high power magnet.',8873,0);
INSERT INTO comment VALUES (8927,1324,1626,'Gamer','re:','2003-10-25 08:59:09',0,'This isn\'t the trick, I accidently changed the problem and left the question mark in here.\r\n\r\nThe answer isn\'t anything word trickery. It\'s not that sort of trick. ',8925,0);
INSERT INTO comment VALUES (8928,1323,1626,'Gamer','A forgotten part','2003-10-25 09:03:46',0,'Actually what I meant to say here was \"every term is over 3\" for 3 terms, \"every term is over 5\" for 5 terms and \"every term is over 8\" for 8 terms.\r\n\r\nI wrote the solution to reflect these parts, is that OK?',NULL,0);
INSERT INTO comment VALUES (8929,1463,2978,'Freddy Grants','Hint','2003-10-25 10:13:03',0,'I admit, this problem is very difficult, hence difficult sequence. I dont know if this is much of a hint, but it will lead you in the right direction, it does not have anything to do with roman numerals, chemistry tables, or words in an elementary essay, you can figure this out without any research. The numbers have no more meaning then the number itself, they represent nothing but part of a formula.',NULL,0);
INSERT INTO comment VALUES (8930,1358,1575,'DJ','Solution','2003-10-25 10:45:50',3,'zero.\r\n\r\nIf the mother has b boys and g girls, then each boy would have b-1 brothers and g sisters, while each girl would have g-1 sisters and b brothers.\r\n\r\nThe only thing that can be deduced from the mother\'s statement is that her children, if they exist, are either all boys or all girls.\r\n\r\nThat way, each of b boys would have b-1 brothers and 0 sisters, or each of g girls would have g-1 sisters and 0 brothers.\r\n\r\nThe final possibility is that there are no boys or girls at all, and the mother\'s statement (while meaningless) is vacuously true.\r\n\r\nSince the friend knew the number of daughters beforehand, but not the number of sons; and she knew the number of sons after, that implies that the mother has some nonzero number of daughters, and the friend realized that she could not have any sons at all.\r\n\r\nThe answer is zero.',NULL,0);
INSERT INTO comment VALUES (8931,1358,3623,'jaypee','may be a solution','2003-10-25 13:26:46',1,'let x = number of boys\r\n\r\nlet n = number of girls\r\n\r\nfor each girl she has (n - 1) sisters + x brothers\r\n\r\nfor each boy he has n sisters and (x - 1) brothers\r\n\r\nif each boy has the same number of brothers and \r\n\r\nsisters as each girl then that means that\r\n\r\n(n - 1) girls + x boys = n girls + (x - 1) boys\r\n\r\nfor there to be an equal number of brothers for\r\n\r\neach sibling then x needs to be equal to x - 1\r\n\r\nwhich is not possible.\r\n\r\nalso for there to be an equal number of sisters \r\n\r\nfor each sibling then n needs to be equal to n - 1\r\n\r\nwhich also is not possible.\r\n\r\nif you had just girls then each sibling would have\r\n\r\nn - 1 sisters and 0 brothers, which IS possible.\r\n\r\nso the number of sons is 0.\r\n\r\n ',NULL,0);
INSERT INTO comment VALUES (8932,1358,4017,'Lisa','Solution','2003-10-25 14:42:11',3,'She has one son, no daughters.\r\n\r\nSons = s\r\ndaughters = d\r\n\r\ns-1=d\r\n1-1=0',NULL,0);
INSERT INTO comment VALUES (8933,1358,1575,'DJ','re: Solution','2003-10-25 15:27:36',0,'What if she had ten sons and no daughters? You can\'t tell from the problem.\r\n\r\nThe key is that the friend didn\'t know how many sons she had before, and she did know how many after the mother made the statement.',8932,0);
INSERT INTO comment VALUES (8934,1324,1626,'Gamer','Solution post?','2003-10-25 16:16:52',0,'I am unsure if I can post the solution, but if I can, would it be OK with everyone if I did it later today or tommorrow? I think this has had enough exposure already.',NULL,0);
INSERT INTO comment VALUES (8935,90,4023,'Romulo','Great','2003-10-26 00:08:19',0,'I think this one is really good.',NULL,0);
INSERT INTO comment VALUES (8936,1324,3372,'Sam','Ha!','2003-10-26 00:20:50',0,'After seeing the solution, I\'m very impressed, and don\'t feel cheated in any way. Very good puzzle.',NULL,0);
INSERT INTO comment VALUES (8937,1358,3818,'A','re: Solution','2003-10-26 00:25:21',0,'the mother could have had zero sons or zero daughters\r\nthis is because knowing a number of sumthing does not force that number to be a nonzero integer.\r\nfor instance: i know that i have no cans of soda in the refridgerator......i kno the number of cans, and that number happens to be 0',8930,0);
INSERT INTO comment VALUES (8938,1358,3818,'A','mathematical solution','2003-10-26 00:44:24',0,'x=sons\r\ny=daughters\r\n\r\nif all siblings have same number of brothers and sisters as the others then:\r\n x-1=y-1 --> x=y\r\n\r\nin order to solve for x and y there needs to be and equation to compare it to, in this case we have three\r\n1)x<y or x>y which does not work because the = sign canot be compared to a < or > sign. how can sumthing be equal to yet greater than or less than at the same time? i\'ll tell u, it can\'t\r\n2)x=0 and y=0 which may work mathematically, but technically how can she be a mother w/o having any kids? if u think she still is a mother even tho she has no kids, then this does indeed work, but that\'s ur call\r\n3)x=0 or y=0 this is the correct answer because it is the only one that works mathematically and logically.\r\n\r\nthe mother either has no sons or no daughters',NULL,0);
INSERT INTO comment VALUES (8939,381,3435,'Brittany','An Obvious solution','2003-10-26 01:00:38',0,'Siamese twins joined at the hip or butt or torso',NULL,0);
INSERT INTO comment VALUES (8940,1357,3558,'Tristan','similar sequence','2003-10-26 10:20:44',1,'This reminds me of a similar sequence, where each number is the number of letters in the previous number. That sequence always ends up repeating 4 though.\r\n\r\nSo, I think that every number, no matter where it is, will always be followed by a specific number. 4 is always followed by 3, 3 is followed by 2, and 2 is followed by 2. If you notice, both 20 and 12 are always followed by sixes. Both 10 and 6 are followed by 4, and 3 and 5 are always followed by 2. This leads me to believe that this sequence does not follow a mathematical function.',NULL,0);
INSERT INTO comment VALUES (8941,90,3026,'Drew Skau','Nothing to do with time.','2003-10-26 13:09:15',3,'There were two sets of twins born, she was part of one set, he was part of another.',NULL,0);
INSERT INTO comment VALUES (8942,1358,4030,'sandra','I think I got it','2003-10-26 14:11:00',0,'she has 1 daughter and 1 son!!!! ',NULL,0);
INSERT INTO comment VALUES (8943,1357,2231,'Trevor Leitch','re: similar sequence','2003-10-26 14:58:47',3,'Each successive number is the number of factors in the preceding number:\r\n\r\n60 has 12: 1,2,3,4,5,10,12,15,20,30,60\r\n20 has 6: 1,2,4,5,10,20\r\n16 has 5: 1,2,4,8,16\r\n12 has 6: 1,2,3,4,6,12\r\n10 has 4: 1,2,5,10\r\n6 has 4: 1,2,3,6\r\n5 has 2: 1,5\r\n4 has 3: 1,2,4\r\n3 has 2: 1,3\r\n2 has 2: 1,2\r\n\r\nI imagine that unless the randomly chosen first number is 1, the sequence will always collapse into an infinite sequence of 2\'s, starting right after the first prime number is reached.\r\n',8940,0);
INSERT INTO comment VALUES (8944,1702,3172,'SilverKnight','full solution','2003-10-26 16:42:55',3,'I bet the *pre* tags don\'t work right here... so Levik, please fix them:\r\n\r\n<PRE>\r\n8 = 6 + 2\r\n6 - 5 = 1\r\n2 = 2 + 0\r\n1 + 8 = 9\r\n<PRE>\r\n\r\nIf it isn\'t clear these represent the ordering of the columns:\r\n4th - rightside up\r\n2nd - rightside up\r\n3rd - upside down\r\n1st - upside down\r\n5th - rightside up\r\n_____\r\n\r\nSince there (should/can) be only one equal sign in any given row, one of the two first columns must be flipped, and they must be the 2nd and 4th column.\r\n\r\nSo, we have the remaining strips which can be placed in only the 1st, 3rd, and 5th positions. \r\n\r\nIt doesn\'t leave too many combinations (there\'s only one 1 on the end... so we need an 8, 1, 9 relation and a 2, 6, 8 relation... and they both use a +... so, there are not many possibilities to sort through.\r\n',NULL,0);
INSERT INTO comment VALUES (8945,1324,1171,'nikki','yeah, but...','2003-10-26 18:59:25',0,'I have read the solution. I get it, makes sense. But here\'s one thing - in the problem statement you said:\r\n\r\n(Note: No one may touch the outer cubes or in any way do anything that would move or change them)\r\n\r\nIn your solution, the \"outer cubes\" are 2 and 6. But those aren\'t perfect cubes.\r\n\r\nJust being a nit-picky devil\'s advocate =) No justification needed. It is a neat solution!',NULL,0);
INSERT INTO comment VALUES (8946,655,4040,'melissa','Solution','2003-10-26 20:03:11',3,'7 times 3 equals 21. Then subtract 3 which is 17 then add 7 which is 24.',NULL,0);
INSERT INTO comment VALUES (8947,145,4040,'melissa','Answer','2003-10-26 20:24:52',3,'25% because the square forms a 90 degree angle and 360/90=4 and if you treat 360 as 100%, 25 goes into 100 4 times, and 90 goes into 360(which is a full circle) four times, thus the answer being 25%',NULL,0);
INSERT INTO comment VALUES (8948,6,4040,'melissa','another way?','2003-10-26 20:35:01',1,'make a square with four of the matches and then make an X with the other two in the middle.',NULL,0);
INSERT INTO comment VALUES (8949,655,3172,'SilverKnight','re: Solution','2003-10-26 20:43:12',4,'I think I may have been drinking too much tonight....\r\n\r\nDid I understand you to say that 21 - 3 = 17 ?',8946,0);
INSERT INTO comment VALUES (8950,1358,4031,'Julia','re: I think I got it','2003-10-26 20:49:41',0,'cant be cuz ten the daughter has one brother and no sisters and the son has one sister and no brothers, which is DIFFERENT',8942,0);
INSERT INTO comment VALUES (8951,1357,4031,'Julia','idea','2003-10-26 21:08:28',0,'factors of the previous number? that could be possiblem since:\r\nFactors\r\n20: 1, 2, 4, 5, 10, 20 Total:6\r\n2 and 3 are prime numbers, so the number after is OBVIOUSLY 2...that is why it is Etc. after the 2',NULL,0);
INSERT INTO comment VALUES (8952,53,1626,'Gamer','re: response to Jason','2003-10-26 21:16:31',0,'Well done jim, I could \"learn\" from you!\r\n\r\nAll I would be able to say is point out the obvious things like what he is saying is completely illogical, and the fact that he uses caps and profanity expresses his inability to be logical. ',111,0);
INSERT INTO comment VALUES (8953,1324,1626,'Gamer','re: yeah, but...','2003-10-26 21:22:26',0,'That is a good point... I was trying to write such that it would make sense anyway.',8945,0);
INSERT INTO comment VALUES (8954,1475,4045,'john robinson','Solution','2003-10-27 04:20:51',3,'The most distant points of Alaska are simultaneously the most Eastern AND most Northern points; Hawaii is most Western and most Southern. Therefore he flew from one to the other.\r\n\r\nI think!',NULL,0);
INSERT INTO comment VALUES (8955,1226,3172,'SilverKnight','Full solution?!?','2003-10-27 08:45:54',3,'Didja ever get the feeling that you\'ve seen a problem somewhere before?',NULL,0);
INSERT INTO comment VALUES (8956,1226,3172,'SilverKnight','full solution','2003-10-27 09:01:27',3,'(In case there\'s a problem with the link in the previous comment...)\r\n____________________________\r\n8 = 6 + 2 \r\n6 - 5 = 1 \r\n2 = 2 + 0 \r\n1 + 8 = 9
\r\n\r\nIf it isn\'t clear these represent the ordering of the columns: \r\n4th - rightside up \r\n2nd - rightside up \r\n3rd - upside down \r\n1st - upside down \r\n5th - rightside up \r\n_____ \r\n\r\nSince there (should/can) be only one equal sign in any given row, one of the two first columns must be flipped, and they must be the 2nd and 4th column. \r\n\r\nSo, we have the remaining strips which can be placed in only the 1st, 3rd, and 5th positions. \r\n\r\nIt doesn\'t leave too many combinations (there\'s only one 1 on the end... so we need an 8, 1, 9 relation and a 2, 6, 8 relation... and they both use a +... so, there are not many possibilities to sort through. ',NULL,0);
INSERT INTO comment VALUES (8962,59,2716,'Federico Kereki','re: hats','2003-10-27 12:43:54',1,'I disagree: the only one who must be wearing a white hat, is the first one; the other two may wear any color.',152,0);
INSERT INTO comment VALUES (8957,1226,1301,'Charlie','To be specific','2003-10-27 09:13:58',3,'To avoid more than one equal sign in a given row and to give each row an equal sign, one or the other of the operation/relation strips must be upside down. They can\'t be at the end, and they can\'t be together (to avoid such things as +=, though =+ would be ok if there were enough zeros, as in 02=+2, but, in any case, there are not).\r\n\r\nThe first (top) row can consist only of 8\'s, 6\'s, 2, and/or 1. Out of that, we can get only 6+2=8 or a variation. Since it is on the top and the only minus sign is not on an end, it can\'t be 8-2=6. The only strip with a 2 at an end is 2109 (read top to bottom); the only one remaining with a six on the end is 6528 (the 8256 inverted), leaving 8621.\r\n\r\nThe 2 must be next to the 6 with a + between them. As the next line has a 1, 5 and 6 and the = comes between the 1 and the 5, it\'s the minus sign that comes between the 5 and the 6, and that means the 6 must come before the 5 in the second row, so the first row is 8=6+2. So we get\r\n\r\n8=6+2\r\n6-5=1\r\n2=2+0\r\n1+8=9\r\n
\r\n---------\r\nNote that for the pre to work in these comments, it requires at least one paragraph after its close with a /pre. If such a paragraph is present it should work. The first paragraph after the close of the pre does not wrap and after a certain point you can\'t see it. That\'s why I put a short line of hyphens after the close of the pre.',NULL,0);
INSERT INTO comment VALUES (8958,1226,1301,'Charlie','re: full solution','2003-10-27 09:16:00',0,'We also can\'t figure out how this problem got posted yesterday as the earliest problem on the site, but with yesterday\'s date (i.e., no \"previous\" puzzle). It was still on the queue also, until this morning.\r\n',8956,0);
INSERT INTO comment VALUES (8959,1226,3172,'SilverKnight','re(2): full solution','2003-10-27 09:27:08',0,'Perhaps the high pid number (on the earlier version) will provide a clue to Levik. Maybe a bug....',8958,0);
INSERT INTO comment VALUES (8960,1463,1920,'Brian Smith','re: An alternate approach - I think I got it','2003-10-27 10:46:37',0,'The nth term can be expressed as a function by finding the formulas for the two subsequences.\r\nf(n) for odd n = (1/2)*n^2 + (41/2)*n\r\nf(n) for even n = (3/2)*n^2 + (39/2)*n\r\n\r\nThese two sequences can be combined, utilizing (-1)^n:\r\nf(n) = n^2 + 20*n + ((-1)^n)*((1/2)*n^2-(1/2)*n)\r\n\r\nIn other words, to calculate the nth term find n^2 + 20*n and the (n-1)th triangular number. If n is even then take the sum and if n is odd then take the difference.',8822,0);
INSERT INTO comment VALUES (8961,6,1920,'Brian Smith','re: another way?','2003-10-27 10:51:08',0,'The four triangles created that way are not equilateral.',8948,0);
INSERT INTO comment VALUES (8963,59,2716,'Federico Kereki','Simple & short','2003-10-27 12:46:50',0,'If the first and second wore black, the third would have known his hat was white; as he didn\'t know his color, he didn\'t see two black hats.\r\n
If the first wore black, the second would have known his hat was white (as if it had been black, the third would have known his own color); as the second didn\'t know his color, he didn\'t see a black hat... and thus the first one knows his color.',NULL,0);
INSERT INTO comment VALUES (8964,917,2716,'Federico Kereki','Solution','2003-10-27 13:03:57',3,'If A told the truth, then F stole it, and hears well; since F says he is deaf, then he lies, and therefore B was the thief -- we\'d have two thieves!
\r\nThus, A lies, so F is deaf and innocent. F says he is deaf, so he tells the truth, and thus B is innocent as well.
\r\nD said A lies, so D tells the truth, and is thus innocent.
\r\nC said A told the truth, so he lies, and thus E is also innocent.
\r\nE said he wasn\'t guilty, so he tells the truth, and so C isn\'t guilty either.
\r\nB said C lied, so he tells the truth, and so A is also innocent!
\r\nIn conclusion, nobody stole the wallet!',NULL,0);
INSERT INTO comment VALUES (8965,775,2716,'Federico Kereki','Sweet and short','2003-10-27 13:10:18',0,'If Drew was a knight, Mohammed would have to be one, and thus wouldn\'t disagree with Drew; he thus lies, and then Mohammed must tell the truth.',NULL,0);
INSERT INTO comment VALUES (8966,660,3172,'SilverKnight','full solution','2003-10-27 15:20:20',3,'To maximize the number of pieces, you want the nth line to cross as many regions as possible. Another way of putting this is to cross as many previous lines as possible.\r\n\r\nIn general it will cross one more region than the number of previous lines it crosses. And every region it crosses (divides), adds an additional piece.\r\n\r\nWith zero lines, there is one piece.\r\nThe first line crosses zero other lines, and one region, so it creates 2 pieces.\r\nThe second line crosses one other line, and two regions, so it adds 2 for a total of 4 pieces.\r\nThe third line crosses two other lines, and three regions, so it adds 3 for a total.\r\n\r\nIn general, the nth line will add n pieces:\r\n\r\nSo:\r\n<PRE>\r\nlines pieces\r\n0 1\r\n1 2\r\n2 4\r\n3 7\r\n4 11\r\n5 16\r\n6 22\r\n7 29\r\n<PRE>\r\n
',8983,0);
INSERT INTO comment VALUES (8985,1227,1920,'Brian Smith','Take me out to the ball game ....','2003-10-28 10:57:35',0,'One. The pitcher is a relief pitcher coming out in the 9th inning with two outs. One pitch is made, the batter hits it and the ball is caught in the air for the last out.',NULL,0);
INSERT INTO comment VALUES (8986,1225,4059,'Saso','solution','2003-10-28 11:05:11',3,'Key idea is to minimize the chance of rolling 2 or 6 in te initial roll while maximizing the chance of rolling 2 (and avoiding rolling the same number as in initial roll) in next rolls.\r\n\r\nObviously, we can ascribe probability 0 to rolling 6, because we will lose in first roll and it does not help in next rolls, either.\r\n \r\nProbability of rolling 1,3,4,5 should be the same as it is indifferent whether we roll 1 initially and try to get 2 in next roll or we roll 3 (or 4, or 5) in first roll and try to get 2 in next roll. \r\n\r\nQuestion is, what is the desired probability of rolling 2? We will find this by maximizing our winning probability. Formula for winning probability is this: (1-p)*(p/((1-p)/4+p)), where p is probability of rolling 2. Explanation: we dont want to roll 2 in first roll, thus (1-p) for first roll. In next rolls, probability of winning is p (if we roll 2), probability of losing is (1-p)/4 if rolling the same number as in initial roll (probabilities of rolling 1,3,4,5 are the same, therefore (1-p)/4 is probability of rolling one of these numbers). Every game must end by winning or losing (even if the game continues to infinity) so probability of winning is p/((1-p)/4+p). Multiplying the winning probability for initial roll and next rolls we get (1-p)*(p/((1-p)/4+p)). We find the \'maximizing\' p by first derivation of this formula equalling 0, which gives p=1/3.\r\n\r\nThe answer is then: we should load probability of 1/3 to face 2, probability of 0 to face 6 and probability of 1/6 to faces 1,3,4,5 of the other die. Our chance of winning will be then 4/9, which is still not worth the effort :)',NULL,0);
INSERT INTO comment VALUES (8987,1227,3964,'B','','2003-10-28 11:16:56',0,'The Visiting pitcher would need to pitch 3 pitches per the first 8 innings. He could skip the bottom of the nineth only if his team is losing. Therefore, he\'d have to give up a home run somewhere using an additional 1 pitch. So, it\'d be:\r\n8*3+1=25\r\n',NULL,0);
INSERT INTO comment VALUES (8988,1227,4060,'daniel trosdahl','re: Take me out to the ball game ....','2003-10-28 11:41:20',0,'That would not be a complete game. A Complete Game is defined (roughly) as a pitcher who starts and finishes an entire game.',8985,0);
INSERT INTO comment VALUES (8989,1227,4060,'daniel trosdahl','re(3): SilverKnight','2003-10-28 11:49:36',0,'Yes, the reason a balk is called is because the pitcher isn\'t allowed to stop his pitching motion to throw at a runner. Therefore, if there are no runners on base, there is no reason to call a balk.\r\n',8984,0);
INSERT INTO comment VALUES (8990,1227,4060,'daniel trosdahl','not likely','2003-10-28 11:55:34',0,'Using the same thought process that SilverKnight came up with, there is another way to get nine. A few years ago MLB came up with a delay of game rule. If the pitcher doesn\'t deliver a pitch within so many seconds the batter is awarded a ball. Theoretically(sp) this could be done eight times to walk two batters without throwing a pitch. Then the third batter of the inning could hit into a triple play. This would have to happen nine times.\r\n\r\nObviously the probability of this happening is about the same as me laying a golden egg, but is possible.',NULL,0);
INSERT INTO comment VALUES (8991,1364,3992,'Jane Doe','some guesses','2003-10-28 16:06:25',1,'I could be totally off but here\'s what I think.....\r\n\r\nBlarg = liar\r\nGrot = knight\r\nCloysta = knave\r\n\r\nJeswin is a knight\r\nParker is a knave\r\nCrasbo is either a knave or a liar (but I think he\'s a knave) \r\n',NULL,0);
INSERT INTO comment VALUES (8992,1364,2899,'Brian Wainscott','Solution','2003-10-28 16:55:07',3,'I got lucky, and starting by trying Jeswin as a Knight. This makes \"Grot\"=Knight. Next, I decided to try \"Cloysta\"=Liar (lucky again!). This makes Parker a liar. He claims to be a Knave, and claims Crasbo is a Knave. Crasbo is therefore NOT a Knave. Crasbo claims Jeswin is a Liar, and hence is a Liar. It all works out. I checked another case or two and got contradictions. So unless there is more than one \"solution\" (ie, the true solution may be that you cannot tell, there is not enough information). I\'m not really up to checking all the other cases, so IF there is enough information, the solution is:\r\n\r\nJeswin is a Knight\r\nParker is a Liar.\r\nCrasbo is a Liar.\r\nGrot = Knight\r\nCloysta = Liar\r\nBlarg = Knave',NULL,0);
INSERT INTO comment VALUES (8993,1364,1301,'Charlie','re: some guesses','2003-10-28 17:04:26',0,'A Blarg can\'t be a liar, since Parker claims to be a Blarg, and no one would claim to be a liar.',8991,0);
INSERT INTO comment VALUES (8994,1364,1301,'Charlie','re: Solution','2003-10-28 17:11:05',0,'Sounds like there is not enough information, as the following also works:\r\nremains the same:\r\nGrot = Knight \r\nCloysta = Liar (this is for sure, as no one claims to be a Cloysta)\r\nBlarg = Knave\r\n\r\nJeswin is a Cloysta (liar)\r\nParker is a Blarg (knave) and is saying true then false\r\nCrasbo is a Grot (knight)\r\n\r\n\r\n',8992,0);
INSERT INTO comment VALUES (8995,1364,3172,'SilverKnight','re(2): some guesses','2003-10-28 17:11:18',0,'If Parker were a Knave, he could claim to be a liar... as long as his second statement were true.',8993,0);
INSERT INTO comment VALUES (8996,1364,1171,'nikki','Clarification please','2003-10-28 17:21:54',4,'I know you said \"you know that they are either liars, knights, or knaves,\" but do we necessarily need to have one of each? Or can we have two knaves and one knight, for example?',NULL,0);
INSERT INTO comment VALUES (8997,351,3818,'A','solution','2003-10-28 18:03:11',0,'uses all vowels in alphabetical order',NULL,0);
INSERT INTO comment VALUES (8998,1364,1171,'nikki','Brute force','2003-10-28 18:23:08',1,'First, let me start with a disclaimer. Even though I tried to write it all out clearly and redundantly for myself, I got confused at times, so I am admitting up front that I could have goofed up =)\r\n\r\nWell, I went through all 6 possible combinations of what Grot, Cloysta and Blarg could mean.\r\n\r\nI was able to completely eliminate three of those combinations because they lead to contradictions no matter what the people were. Those combinations that I eliminated are [Grot, Cloysta, Blarg] = [Liar, Knight, Knave], [Liar, Knave, Knight], and [Knave, Liar, Knight]. I\'d explain how I eliminated those, but that would take too long.\r\n\r\nWith the other 3 possible combinations of Grot, Cloysta and Blarg, I got 6 possible situations! If we are allowed to assume that there is exactly one knave, one knight, and one liar in this group, then I can eliminate 4 of those situations. But this still leaves me with two possible solutions:\r\n\r\nGrot - Knight\r\nCloysta - Liar\r\nBlarg - Knave\r\nJeswin - Liar\r\nParker - Knave\r\nCrasbo - Knight\r\n\r\nor\r\n\r\nGrot - Knight\r\nCloysta - Knave\r\nBlarg - Liar\r\nJeswin - Knight\r\nParker - Knave\r\nCrasbo - Liar\r\n\r\nI was hoping that out of all the possible solutions, there would only be one where all of the people were different types, but unless I goofed it looks like there are two solutions. The wording of the problem makes it sound like we should see only one situation is possible. Frustration!',NULL,0);
INSERT INTO comment VALUES (8999,1364,3558,'Tristan','re: Brute force','2003-10-28 18:57:33',0,'I would say that you never, ever assume that each person is a different type, but in this case, it seems as if there are two solutions even when you do assume it... I think that it MUST be stated if they wanted you to assume it. Otherwise, how would you differentiate between puzzles where you\'re supposed to assume it and where you\'re not? I haven\'t carefully read the previous comments, so I apologize if someone already proved that they must be different types or something like that.',8998,0);
INSERT INTO comment VALUES (9000,1364,3172,'SilverKnight','Really Full Solution','2003-10-28 19:29:09',3,'If we look at the meanings of the three words, there are only six combinations:
\r\nGrot, Cloysta, and Blard mean one of the following six items:\r\n
\r\nCase (1)
\r\nJeswin calls himself a Liar and calls Parker a Knight. Since Jeswin calls himself a liar, he can be neither a liar, nor a knight, therefore he is a Knave, and his first statement is false. Therefore his second statement is true. He calls Parker a Knight, but Parker\'s first statement calls himself a Knave. Since a knight couldn\'t do this, case (1) isn\'t possible.
\r\nCase (2)
\r\nJeswin calls himself a Liar and calls Parker a Knave. Since, again, Jeswin calls himself a liar, he can be neither a liar, nor a knight, therefore he is a Knave, and his first statement is false. Therefore his second statement is true. Jeswin called Parker a Knave, and Parker\'s first statement calls himself a Knight, so Parker is a knight and his first statement is false. Therefore his second statement is true. And he calls Crasbo a Knight. But Crasbo\'s first statement is that he is a liar, and a knight can\'t say this, therefore, this case (2) is impossible.
\r\nCase (3)
\r\nParker calls himself a Knave, therefore he is either a Liar or a Knave.
\r\nCase 3.1: If he is a Knave, then his first statement is true, and his second statement is false, and he calls Crasbo a Knave. Crasbo therefore is a Liar or a Knight.
\r\n Case 3.11: If Crasbo is a Knight, then his first statement checks out. And his second statement means that Jeswin is a Liar. If so, the Jeswin\'s first statement checks out, and his second statement means that Parker is either a Knight or a Knave. This checks out.
\r\n Case 3.12: If Crasbo is a Liar, then his first statement is ok, and his second statement means that Jeswin is a Knight or a Knave, but Jeswin is not a Knight because Jeswin calls Parker a liar which he\'s not, so Jeswin is a Knave, and his first statement is false. Therefore his second statement must be true, but it isn\'t. So this is not possible.
\r\nCase 3.2: If he is a Liar, then his second statement means that Crasbo is either a Knight or a Liar. Either way his first statement is okay, but...
\r\n Case 3.21: If Crasbo is a Knight then (same as 3.11) he calls Jeswin a Liar. If Jeswin is a liar, and he calls Parker a Liar, but this it true! So 3.21 can\'t be the case.
\r\n Case 3.22: If Crasbo is a Liar then Jeswin is either a Knight or a Knave.
\r\n Case 3.221: If Jeswin is a Knight, then this checks out.
\r\n Case 3.222: If Jeswin is a Knave, then his first statement is false, and his second statement is true. This checks out.
\r\nCase (4)
\r\nParker calls himself Liar. Therefore he is a Knave, and his first statement is false. Therefore, his second statement is true, and Crasbo is a Liar. Crasbo\'s first statement is that he is a knight (which is okay), and his second statement is that Jeswin is a Knave which must be false. Therefore Jeswin is either a Knight or a Liar.
\r\nCase 4.1: If Jeswin is a Liar, then his first statement that he is a knight is okay... but his second statement would be true (that Parker is a liar), so this can\'t be the case.
\r\nCase 4.2: If Jeswin is a Knight, then his first statement is true, and his second statement is also true. So 4.2 is consistent.
\r\nCase (5)
\r\nParker calls himself a Liar. Therefore he is a Knave, and his first statement is false. Therefore his second statement is true, and Crasbo is a Liar. Crasbo\'s first statement is ok, and hist second statement means that Jeswin is a Knave or a Liar.
\r\nCase 5.1: If Jeswin is a Liar, then his statements check out, and this is possible.
\r\nCase 5.2: If Jeswin is a Knave, then his first statement is true, and his second statement is false. This is consistent
\r\nCase (6)
\r\nJeswin calls himself a Knave. Therefore he is either a Knave or a Liar.
\r\nCase 6.1: If Jeswin is a Knave, then his first statement is true, and his second statement is false, and he calls Parker a Liar. This means Parker is either a Knave or a Knight.
\r\n Case 6.11: If Parker is a Knave, then his first statement is false, and his second statement is true, so Crasbo is a knight, but Crasbo calls himself a Knave, so this is inconsistent.
\r\n Case 6.12: If Parker is a Knight, then his second statement (that Crasbo is a Knight can\'t be correct, because Crasbo calls himself a Knave). Therefore, this is inconsistent.
\r\nCase 6.2: If Jeswin is a Liar, then Parker is either a Knave or a Knight.
\r\n Case 6.21: If Parker is a Knave, then his first statement is false, and his second statement is true. Then Crasbo is a Knight, but he can\'t be (since he calls himself a Knave), so this is inconsistent.
\r\n Case 6.22: If Parker is a Knight, then his second statement is true and the same inconsistency as above holds true.
\r\n
\r\nSo... from this analysis, to recap, we have the following SIX solutions:\r\n3.11 - Jeswin (Liar), Parker (Knave), Crasbo (Knight)
\r\n3.221 - Jeswin (Knight), Parker (Liar), Crasbo (Liar)
\r\n3.222 - Jeswin (Knave), Parker (Liar), Crasbo (Liar)
\r\n4.2 - Jeswin (Knight), Parker (Knave), Crasbo (Liar)
\r\n5.1 - Jeswin (Liar), Parker (Knave), Crasbo (Liar)
\r\n5.2 - Jeswin (Knave), Parker (Knave), Crasbo (Liar)
\r\nOnly in two cases are the three of them all different (which was not a requirement of the problem)\r\n3.11, 4.2
\r\n\r\nIn 3.xx, GROT=Knight, CLOYSTA=Liar, BLARG=Knave
\r\nIn 4.xx, GROT=Knight, CLOYSTA=Knave, BLARG=Liar
\r\nIn 5.xx, GROT=Knave, CLOYSTA=Knight, BLARG=Liar
\n\nEdited on October 28, 2003, 7:44 pm',NULL,0);
INSERT INTO comment VALUES (9001,1364,3172,'SilverKnight','re: Really Full Solution','2003-10-28 19:41:36',1,'I must agree with Nikki and with Tristan about the ridiculousness of this problem.
\r\nHow does this escape the scrutiny of the journeymen and scholars? I would hope that at least someone would not only look at the answer, but actually work through the problem, and ensure that the solution is correct and unique (or if not unique, at least word the problem such, to indicate that the puzzlers should find any and all solutions).\r\n______________
\r\nMore than that, perhaps we should revisit *this* forum topic.\r\n\n\nEdited on October 28, 2003, 7:58 pm',9000,0);
INSERT INTO comment VALUES (9002,1227,4068,'Bruno Pelletier','Short but sweet','2003-10-28 21:33:55',0,'About the complete game in baseball, I\'d say 25 pitches is the minimum for a complete game.\r\n \r\nIf the local team wins 1-0, the other pitcher will have to throw 8 complete innings, (24 pitches) plus another throw for let\'s say a home run, or an error, etc..\r\n \r\nAm I right???\r\n \r\nAnd now, what\'s the maximum stikeouts a pitcher can have in one inning?\r\n',NULL,0);
INSERT INTO comment VALUES (9003,1227,3386,'Victor Zapana','re: Short but sweet','2003-10-28 21:56:36',0,'This sound oddly reasonable and simple. I agree with it, coz if u do the away pitcher strikes everyone out and in the bottom of the 9th pitches once and it was a home run, this ends the game 1-0, and that does equal 25.',9002,0);
INSERT INTO comment VALUES (9004,660,1575,'DJ','re(3): full solution','2003-10-28 22:26:29',0,'As far as that goes, the problem doesn\'t say anything about straight cuts. Even if you\'re restricted to two dimensions, and say a cut cannot cross itself, the first cut will yield two pieces, and the second can cross the first one any number of times.\r\nSo, I say the number of cuts is:\r\n2^n - 1, 0 ≤ n ≤ 1\r\n∞, n > 1\r\n(n ∈ Z)',8978,0);
INSERT INTO comment VALUES (9005,865,3136,'Popstar Dave','Deffinative Solution','2003-10-28 22:56:27',0,'Yes, erm... No. Hmmm, hang on. Maybe, but.. yes...No.\r\nARGHHHHHHHHHHH!!!',NULL,0);
INSERT INTO comment VALUES (9006,1227,4070,'Tim','solution','2003-10-28 23:37:36',0,'Zero... a pitcher in the dugout who does not throw a pitch is still counted as a player on the team. As soon as the game is complete... he goes home.',NULL,0);
INSERT INTO comment VALUES (9007,1364,4073,'JennaBanenna','Solution!','2003-10-29 00:19:55',3,'Jeswin : I am a Grot (knight). Parker is a Cloysta (liar). \r\nParker : I am a Blarg (knave). Crasbo is a Blarg (knave). \r\nCrasbo : I am a Grot (knight). Jeswin is a Cloysta (liar). \r\nBlarg=knave\r\nGrot=knight\r\nCloysta=liar\r\nJeswin=liar\r\nParker=knave\r\nCrasbo=knight\r\n\r\nUmmm, guess and check. Nyahaha',NULL,0);
INSERT INTO comment VALUES (9008,19,4073,'JennaBanenna','*just read the solution*','2003-10-29 00:48:02',4,'Okay, lets just say that Bob is like any ordinary friend of yours. And you go up to him, and ask him \"Is Bob a liar\" and he says no. How are you supposed to know if he\'s telling the truth or not? My question would be more like something that I knew, like \"Are you Bob?\"',NULL,0);
INSERT INTO comment VALUES (9009,19,4073,'JennaBanenna','re: *just read the solution*','2003-10-29 00:51:29',0,'OOOH, nvm ^^ just realised that all he\'s trying to do is specify who is who! Okay...nvm then',9008,0);
INSERT INTO comment VALUES (9010,1364,4076,'c','Solution','2003-10-29 02:52:11',3,'Answer is \r\nBlarg is Knave\r\nGrot is a Knight\r\nCloysta is a Liar\r\n\r\nJeswin is a Liar\r\nParker is a Knave\r\nCrasbo is a Knight\r\n\r\nIs this correct?',NULL,0);
INSERT INTO comment VALUES (9011,1335,1686,'DuCk','solution','2003-10-29 07:32:31',0,'a=speed of A\r\nb=speed of B = 2a\r\nx=distance between houses\r\nt=time\r\n\r\na*t=x-(2/3) --> t=(x/a)-(2/3a)\r\nand\r\n2a*t=x+(2/3) --> t=(x/2a)+(1/3a)\r\n\r\nand t=t so...\r\n\r\n(x/a)-(2/3a)=(x/2a)+(1/3a)\r\n\r\nSolving for x gives x=2miles',NULL,0);
INSERT INTO comment VALUES (9012,1335,3275,'retiarius','Solution','2003-10-29 09:18:43',3,'When B leaves his house the second time A is at the same place he was when B left his house the first time. Therefore, B is 1 mile behind A, travelling at twice the speed, and will arrive at the same time. The houses are 2 miles apart.',NULL,0);
INSERT INTO comment VALUES (9013,1227,4064,'rerun141','complete game','2003-10-29 10:08:22',0,'cant be 0. he needs to pitch a complete game...',NULL,0);
INSERT INTO comment VALUES (9014,1222,3386,'Victor Zapana','freaky solution','2003-10-29 10:33:39',0,'I made an \"opposite\" of that operation (like u subtraction is the \"opposite\" of adding, multiplying is the opposite of dividing, squaring is the opposite of square rooting, etc.) Let\'s say the opposite of # is @, so...\r\n\r\n(A # B) # A = B (@ A to both sides) -->\r\nA # B = B @ A (@ B to both sides) -->\r\nA = (B @ A) @ B (# B to both sides) -->\r\nB # A = B @ A (# A to both sides) -->\r\nA # (B # A) = B',NULL,0);
INSERT INTO comment VALUES (9015,656,3386,'Victor Zapana','solution','2003-10-29 10:37:52',0,'so.. to sum it up \r\nthe next numbers 83 then 89, due to the Sophie German Prime principal where, these are the \"first few S. G. P.\'s\" (\"Sophie German Prime\"). fr further info look at previous post by jaypee',NULL,0);
INSERT INTO comment VALUES (9016,660,1920,'Brian Smith','re(4): full solution','2003-10-29 11:41:03',0,'Well then how about using fractal cuts. Make a straight cut along any line, then make a fractal cut based off of that line. In two cuts an infinite number of pieces are formed.',9004,0);
INSERT INTO comment VALUES (9017,1222,1920,'Brian Smith','re: freaky solution','2003-10-29 13:12:08',0,'Your proof has a serious problem. Given only the information in the problem, it is not guaranteed that an inverse operator (your @) even exists.\r\n\r\nAlso, when you apply # B to each side (from line 3 to 4 in your proof), you assumed the commutative property was true and put B on the left.',9014,0);
INSERT INTO comment VALUES (9018,661,3172,'SilverKnight','umm...','2003-10-29 15:48:59',4,'... is it safe to assume that the \'man\' is \'you\'?\r\n\r\nAnd if not, is the tiger minimizing the distance between the tiger and the man, or the tiger and you (or you and the man, somehow)?',NULL,0);
INSERT INTO comment VALUES (9019,661,3172,'SilverKnight','first thought','2003-10-29 15:56:41',1,'If the man were to swim directly to a point diametrically opposite the tiger\'s initial position, he travels distance, 1 unit. The tiger must travel all the way around the lake, distance PI units. This is less than 4 times the man\'s distance, and therefore, the tiger would beat him there.\r\n\r\nHowever, if the man swims in a spiral... he could keep the tiger running around the lake, chasing a \'moving closest point\'. So, I think a \'loose\' enough spiral path would be a solution to this, and the man could get to shore a bit ahead of the tiger.\r\n\r\nNow... a remaining question is... once to shore, can the man RUN at least as fast as the tiger...?',NULL,0);
INSERT INTO comment VALUES (9020,1227,4082,'wonshot','time delay, solution?','2003-10-29 16:07:39',0,'1) There is a rule that a ball will be awarded if not pitched within ten seconds, however it cannnot be used in order to intentionally walk a batter, which would be the case here. At most maybe one batter could be walked this way before the umpire takes greater action against the pitcher (ejection).\r\n2) One rule that may permit a batter to get on base without recording a pitch could be catcher\'s interfierence, which takes place when the batter\'s swung bat hits the catcher\'s mit and the offensive team choose to take the free base as opposed to the outcome of the play. At this rate every batter could reach base and then procede to be picked off, until the last inning where one could score by similar means, thus ending the game. So, if this rule allows the batter first base without recording a pitch, no pitches are necessary to record a complete game.\r\n\r\nThis could have been said in less words but oh well.',NULL,0);
INSERT INTO comment VALUES (9021,661,1072,'Alan','Heres a thought','2003-10-29 16:08:45',0,'Well since this in the category general and not in just math I\'ll try thinking outside of the box. Fist the man jumps in and swims underwater so the tiger can\'t see him. If he gets far enough then its a matter of the tiger getting to the point opposite of where he is standing by the time you reach there.',NULL,0);
INSERT INTO comment VALUES (9022,661,1301,'Charlie','Specifically...','2003-10-29 16:09:12',3,'So long as the man is less than 1/4 of the radius of the circle from the center (the ratio of the speeds) he can keep the tiger opposite himself with regard to the lake and still have a component of motion left over to go outward from the center. Once he reaches 1/4 the radius out, he can no longer do this, but at that point with only 3/4 the radius to go, the tiger has to travel pi times the radius to get to the nearest point. The tiger\'s speed being 4 times the man\'s, this is covered in pi/4 times the time it takes the man to go one radius of distance, which is more than the 3/4 that the man takes.\r\n\r\nI don\'t know if it would help if the man applied some component of his motion non-radially once the 1/4 point was reached, or if he should just head straight for shore at that point and depend on the (pi-3)/4 time unit advantage.',NULL,0);
INSERT INTO comment VALUES (9023,661,3172,'SilverKnight','re: Specifically...','2003-10-29 16:20:36',1,'Well stated, Charlie.\r\n\r\nI was playing with some numbers/equations, and the calculus was getting too complicated for me to do this over a break at work, but I think here\'s a \'smooth\' path for the man to follow, that I believe will get him there ahead of the tiger.\r\n\r\nFirst the man gets on the \'East\' side of the rock (let\'s say where theta, the radian angle = 0 or 2ð), then let the man traverse the path that is described by:\r\n\r\nfor:\r\n7/8 * π ≤ theta ≤ 11/8 * π,\r\nlet r = (4 / π²) * (theta - (7/8)*π)²\r\n\r\nwhere r is the distance from the center of the lake, and theta is the angle from East in radians.\r\n\r\nWould anyone like to verify this?\n\nEdited on October 29, 2003, 4:26 pm',9022,0);
INSERT INTO comment VALUES (9024,661,4083,'jim','solved','2003-10-29 16:37:03',0,'Looks to me like Charlie solved this problem, provided that once ashore the man can maintain or increase the pi-3 distance between himself and the tiger.',NULL,0);
INSERT INTO comment VALUES (9025,656,4085,'jen','','2003-10-29 17:44:25',0,'107, 215\r\n\r\n2+3=5 \r\n5+6=11\r\n11+12=23\r\n\r\nand so on',NULL,0);
INSERT INTO comment VALUES (9026,1335,4085,'jen','','2003-10-29 17:51:56',0,'1 and a third of a mile',NULL,0);
INSERT INTO comment VALUES (9027,1358,4085,'jen','0 how hard is that','2003-10-29 17:58:31',0,'its 0',NULL,0);
INSERT INTO comment VALUES (9028,1229,4068,'Bruno Pelletier','Let\'s make a deal !!!','2003-10-29 18:03:20',0,'The deal was made with my parents.\r\n\r\nSo my grandparents won\'t give me anything for my 15th birthday, and after 27 years, both nothing!',NULL,0);
INSERT INTO comment VALUES (9029,65,4085,'jen','idea','2003-10-29 18:11:04',0,'not fair because the bottom of the card is the same as the top seeing they are both on the same side so he takes ur money anyway',NULL,0);
INSERT INTO comment VALUES (9030,295,4083,'jim','solution','2003-10-29 18:14:24',0,'The possible hat configurations areas follows (each occurs with equal probability 1/8)\r\n\r\nrrr\r\nrrb\r\nrbr\r\nrbb\r\nbrr\r\nbrb\r\nbbr\r\nbbb\r\n\r\nIn six of these 8 cases, 1 player will see two hats of color opposite to his. In these six cases, the other 2 players will see two different colored hats. If the players agree to the rule that they will pass if they see different hats, and guess the opposite color if they see the same color hats, then they will win in these 6 cases. In the other 2 cases they lose.\r\n\r\nOverall, they win 6 out of 8 times with this strategy. (I offer no proof, just this example strategy - proof by jawboning?)',NULL,0);
INSERT INTO comment VALUES (9031,661,3558,'Tristan','re: Specifically...','2003-10-29 19:44:34',0,'Well, down here in my high school, I haven\'t taken calculus yet, so I wouldn\'t be able to figure out a specific path. Since this is a puzzle, and it only asks for a safe swim for shore, I\'m not going to worry about the events afterwards.\r\n\r\nJust thinking about it (no evidence) I\'d say that to get to 1/4 out of the lake would take an infinite amount of swimming in circles. The spiral would approach 3/4 as you swim for an infinite amount of time, I think. I say that you only have to get (4-π)/4 out of the lake. Then, you have enough advantage to swim straight to shore. Of course, this only shortens the swim, if we want to try to find that too.',9022,0);
INSERT INTO comment VALUES (9032,1223,3386,'Victor Zapana','hmm...','2003-10-29 20:12:23',0,'Well, the verse goes\r\n\r\n\"99 bottles of beer on the wall, 99 bottles of beer, take 1 down, pass it around, 98 bottles of beer on the wall.\"\r\n\r\nLet\'s say 99= n.\r\n\r\n\"n bottles of beer on the wall, n bottles of beer, take 1 down, pass it around, (n-1) bottles of beer on the wall.\"\r\n\r\nThus, in one round 3n is the sum of numbers said ( n + n + (n-1) + 1 [from \"take 1 down\"]). This 3(the number of that round) will continue all the way to 0. So.. the general formula would be...\r\n3 (n + (n - 1) + (n - 2) + (n - 3) + ... + 2 + 1). Thus, with \"99 bottles of beer on the wall,\" the sum would be 3 x 4950 = 14850',NULL,0);
INSERT INTO comment VALUES (9033,1227,4053,'Sali Saved','Solution','2003-10-29 20:21:20',0,'The pitcher throws a COMPLETE game, so they pitch all 9 (kind of) innings. So the least number of pitches per inning would be 3 (each person was thrown one pitch and popped out). The other team doesn\'t score any points. This would lead to 9 innings of 3 pitches each so 27 pitches. But this is not the right answer because if the team plays on the bottom of the 9th, then they don\'t have to play the 9th inning if they are ahead).\r\n\r\nTherefore the least amount of pitches would be 8 innings of 3 pitches each or 24 pitches. An amazing no hitter!',NULL,0);
INSERT INTO comment VALUES (9034,1227,4053,'Sali Saved','Correction on Solution','2003-10-29 20:31:29',0,'A little clarification. The other team doesn\'t score, but your team must do a little hitting and get at least one run on their time up for the game to end after the bottom of the ninth.',9033,0);
INSERT INTO comment VALUES (9035,1227,4070,'Tim','re: Solution','2003-10-29 21:54:50',0,'The other team would still be up to bat for the ninth inning regardless. So it would still be 27 pitches... I am curious though. Is there a major league rule that states a certain number of point differencial to call the game (i.e. team A has 3 runs, Team B has 18 runs... so they call the game)',9033,0);
INSERT INTO comment VALUES (9036,1364,4070,'Tim','possible solution (one of many)','2003-10-29 22:03:19',0,'Jeswin=Cloyser=liar: I am a Grot(lie), Parker is a Cloysta (lie)\r\nParker=Blarg=Knave: I am a Blarg (true), Crasbo is a Blarg (lie)\r\nCrasbo=Grot=Knight: I am a Knight (true), Jeswing is a Cloysta (true)',NULL,0);
INSERT INTO comment VALUES (9037,1335,4064,'rerun141','re:','2003-10-29 22:18:01',0,'no retarius and duck are right 2 miles. they meet 2/3 fom house B. B returns home in the time it takes A to reach 1 mile from B\'s house. B walks 2 miles in the times it takes A to do the remaining 1. ',9026,0);
INSERT INTO comment VALUES (9038,1227,4057,'Jason','re(2): Solution','2003-10-29 22:27:14',0,'Sali is right. If one team is winning by any margin of score, let\'s say 2-0, and the team that is winning is fielding and shut out the batters of the losing team, then there is no possible way for the team down by two points to win. Therefore there is no point in playing the bottom of the ninth inning, so it is skipped. The correct answer is 24 pitches. And no, to my knowledge there is no mercy rule for calling games in major league baseball.',9035,0);
INSERT INTO comment VALUES (9039,1335,4090,'canonsburg','?','2003-10-29 22:49:06',0,'the houses are 3/2 miles away?',NULL,0);
INSERT INTO comment VALUES (9040,1335,4088,'ben','it is a try','2003-10-29 22:53:02',0,'being a mile away from B\'s, they both start back to thier respective houses at the same time. everyone else thinks A waits until B gets back to his house to start towards his house. let\'s say A\'s house is west and B\'s house is east.\r\n\r\nB walks east 1 mile to get back to his house.While that is happening, A walked half a mile to the west. then B walked back west to the meeting place (a mile away) in the time it took A to go another half-mile west. seperated by a mile now, just continue halving the distance between the two and adding it together until you come to the point where they meet.\r\n\r\nanswer:A\'s house is 3 miles away from B\'s house.',NULL,0);
INSERT INTO comment VALUES (9041,1475,4057,'Jason','Half Solution','2003-10-29 23:03:25',0,'Northernmost : Point Burrow, Alaska--------(71°23\'N 156°29\'W)\r\nSouthernmost : Ka Lae, Hawaii---------------(18°55\'N 155°41\'W)\r\nEasternmost : West Quoddy Head, Maine-----(44°49\'N 66°57\'W)\r\nWesternmost : Cape Wrangell, Alaska-------(52°55\'N 172°27\'E)\r\n \r\nI\'m not really sure how to get from Alaska to Hawaii to Maine with only leaving US territory once. Maybe there is a path from Alaska to Hawaii that remains in US territory or from Hawaii to the contential US? ',8977,0);
INSERT INTO comment VALUES (9042,655,4057,'Jason',' Solution','2003-10-29 23:29:13',0,'Brian has it right. 7(3+3/7)=24 To make it clearer you can just distribute the 7 to get: 7(3) + 7(3/7) This yeilds: 21 + 3 = 24. Its simple.',8974,0);
INSERT INTO comment VALUES (9043,1358,4091,'Tanya','','2003-10-30 00:28:41',0,'Hi\r\nI just visited this site in search for sum good logic prob and read this one.\r\nI think the mother can have 1)all daughters and no son \r\nor 2)all sons and no daughter.\r\nSo that in the first case if X is the no. of daughters then each one of them would hv (X-1) sisters ans zero brothers.In the second case each one of them would hv (X-1) brothers.\r\n',NULL,0);
INSERT INTO comment VALUES (9044,661,1768,'Lorne Hrynkiw','Minimum Swim','2003-10-30 05:09:56',0,'It has been a lonngg time since I had to use calculus and I\'m not going to try to refresh my memory at this time of the night. That said, always swim directly away from the tiger; the tiger will always be PI away from where you could land; your path will be a logarithmic spiral.',NULL,0);
INSERT INTO comment VALUES (9045,178,3136,'Popstar Dave','re: I beg to differ','2003-10-30 07:20:24',0,'The experiment that has been described here has been performed in many states, to opose those who say that it only applies to children and people dealing with token units of transfer. It was recently performed (I forget who actually performed the study) in Indonesia with amounts of currency equivalent to approximately two to three months wages for the two participants. In this case (as with any in this game) theory suggests that the decision maker should give the other participant only one unit, as they will accept, being better off than the zero unit non-decision, threat point. But, as with the children described previously, the non-decision making participant was less than 50% likely to accept any split less than 70:30, even though this 30% proportion may have been equivalent to one months wages. \r\n\r\nI guess it all goes to show that we\'re not all game theoreticians!',1736,0);
INSERT INTO comment VALUES (9046,20,3136,'Popstar Dave','Solution (Mathematical)','2003-10-30 07:49:12',3,'If we have a point, M, that is the midpoint of FD then we know that the distancee AM is the same as MG. We can calculate the distance AM (and therefore MG) with some simple use of pythagoras\' theorem. If we use x as the side length of the cube:\r\nAM = √(x² + (x/2)²)\r\nAM = (√(5)x)/2\r\nTherefore:\r\nAG = 2AM\r\nAG = √(5)x\r\n\r\nThis can be compared to Karen\'s proposal of A->F->G, where:\r\nAF = √(2)x\r\nand\r\nFG = x\r\ntherefore:\r\nAFG = √(2)x + x\r\nWhich is greater than √(5)x for all positive values of x.\r\n\r\nI know that this is not a definitive mathematical solution, but I hope this helps.\r\n\r\nCheers,\r\nDave',NULL,0);
INSERT INTO comment VALUES (9047,1227,4060,'daniel trosdahl','re: time delay, solution?','2003-10-30 09:23:18',0,'The only problem I see with this is that after to or three cather interference calls the umpire again would take exception, or the catcher\'s own manager.\r\n\r\nImaginary conversation between Catcher and Manager.\r\nJoe Torre: Posada, scoot your @ss back three inches. Your glove is hanging over the plate.\r\n\r\nJorge Posada: Sorry coach, I was jus\' tryin\' to save Roger Clemens from making any pitches. He\'s getting old you know.\r\n\r\nJoe Torre: Knock that crap off.\r\n',9020,0);
INSERT INTO comment VALUES (9048,541,4097,'george','face','2003-10-30 10:20:56',0,'Daisies are not green',NULL,0);
INSERT INTO comment VALUES (9049,1335,1171,'nikki','re: it is a try','2003-10-30 11:24:53',0,'That\'s what I thought at first too, until I re-read the problem. They don\'t meet 1 mile from B\'s house. It\'s that when A is 1 mile from B\'s house, that\'s when B just leaves his house. They meet somewhere in between and then both start walking. When A gets BACK to the 1 mile mark, B just arrived back at his home before turning around to go to A\'s house.',9040,0);
INSERT INTO comment VALUES (9050,661,1920,'Brian Smith','re(2): Specifically...','2003-10-30 12:09:48',0,'I agree with your analysis. Trying to minimize the distance out (4-pi)/4 will get you out the fastest, but with the narrowest margin against the tiger. Approaching 1/4 gets you out the slowest, but gives a better lead against the tiger.\r\n\r\nThe best path probably is 1: swim out (4-pi)/4, 2: swim in a spiral which reaches 1/4 radius exactly when the tiger is directly opposite of you, 3: head straight for shore.',9031,0);
INSERT INTO comment VALUES (9051,1475,4098,'kevin coyne','summer vacation','2003-10-30 12:16:32',0,'He starts off from haiwaii (most western and southern) he flies to Alaska (most northerly) and then across Canadian airspace (leaving U.S. controlled airspace) and lands in calais Maine (most easterly)',NULL,0);
INSERT INTO comment VALUES (9052,292,4055,'S','A modification to the official solution','2003-10-30 12:17:50',0,'\"To maximise your probability (as someone suggested in the comments) roll a \"d20\" - a 20 sided die - and only send the letter if you roll a 20. A probability calculation shows that this yields the best odds, with a surprising 37.7% chance that only one of you will roll a 20 and send a letter. Better odds than predicting post office behaviour, surely!\"\r\n\r\nOnce the die has been rolled, you could then wait a random (long) period of time before sending your letter. If another person thinks the same, it is likely that his/her chosen time will be different and the possibility exists that the letter will be received and the prize distributed before a second person submits a letter. This would increase the odds of receiving a prize.\r\n',NULL,0);
INSERT INTO comment VALUES (9053,1227,4055,'S','Solution','2003-10-30 12:28:10',0,'8 pitches. A balk is not considered a pitch. The pitcher could balk twice, putting two people on base. He could then force a triple play. As mentioned in previous posts, if the pitcher is for the away side, he would not have to pitch the bottom of the ninth if his team were winning.',NULL,0);
INSERT INTO comment VALUES (9054,1479,3224,'Lee','solution','2003-10-30 13:33:44',0,'Ian Fleming is the connection.\r\nPeter Sellers, David Niven and Woody Allen all starred in the Bond \'spoof\' Casino Royale (based on Fleming\'s books).\r\nLikewise Sean Connery played the spy.\r\nDick Van Dyke starred in one of Fleming\'s slightly lesser known tales - \'Chitty Chitty Bang Bang\'\r\nI know an awful lot of people will know this but it\'s the first opportunity I\'ve had to post first.\r\nFinally!',NULL,0);
INSERT INTO comment VALUES (9055,1227,4060,'daniel trosdahl','re: Solution','2003-10-30 14:36:03',0,'A balk does not put players on base. It only moves up runners on base.',9053,0);
INSERT INTO comment VALUES (9056,1458,4101,'sheryl','Solution?','2003-10-30 14:47:20',0,'Use a magnifying glass to light it and, as it burns, the ashes will fall to the table (or foundation).\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (9057,1458,4101,'sheryl','sorry chan','2003-10-30 14:50:51',0,'I apologize...hadn\'t read the posts before I posted. ',NULL,0);
INSERT INTO comment VALUES (9058,1331,1171,'nikki','Maybe I\'m missing something...','2003-10-30 16:02:08',3,'but wouldn\'t the paths still be in a star (pentagram) shape? Then you place the trees just inside, instead of ON, the vertices.\r\n\r\nThen all of the trees would be on the inside. So you would only have a problem if some squirrels started out somewhere inside the pentagram.\r\n\r\nAnother way to describe this is draw a regular pentagram. Draw another one that is slightly smaller than the first, with no rotation, and the \"centers\" should be at the same point.\r\n\r\nThe outer pentagram is the human path, and plant the trees on the vertices of the inner pentagram (this just helps illustrate that the trees are still placed with 5 rows of 4).',NULL,0);
INSERT INTO comment VALUES (9059,1227,1171,'nikki','re(2): Solution','2003-10-30 16:12:42',0,'I think that\'s why S said 8 pitches (and to only balk twice). You pitch once to get someone on base. Then you balk, and the second person gets on base. You balk again, and the third person gets on base. Then you make an amazing triple play and you finished an inning with only one pitch.\r\n\r\nI do think there has been some confusion about pitching during the 9th inning, though, in several posts (not just the one by S). If the team that bats during the top of the innings is losing, then the team that bats during the bottom of the inning doesn\'t need to play the bottom of the 9th because they are already winning.\r\n\r\nSo for this special pitcher to avoid pitching during the 9th inning, he must pitch on the bottoms of the innings. This means his team bats during the tops of the innings, which means his team must be LOSING (not winning) after the top of the 9th.\r\n\r\nSo, for those who approve of the solution that includes some balking, during at least one of those innings, you will have balk at least 3 times in order to let someone score. You still will have only made one pitch per inning, so the answer of 8 pitches for the game still holds.\r\n\r\nFor those who don\'t approve of solutions including balking, and think the answer is 24, that is not enough. Someone already explained how it would actually need to be 25. During one inning you would need to let someone score - otherwise your team is not losing and you would have to pitch the 9th inning. So let\'s say you pitched twice, and got both of those runners out. But you can\'t let the 3rd runner score AND get him out. So you have to pitch to him, let him score, pitch a 4th time and get the third out.\n\nEdited on October 30, 2003, 4:37 pm',9055,0);
INSERT INTO comment VALUES (9060,1331,1626,'Gamer','re: Maybe I\'m missing something...','2003-10-30 16:15:39',0,'This is just a story for \"Do the same as before, but put some trees on the inside this time.',9058,0);
INSERT INTO comment VALUES (9061,1331,3172,'SilverKnight','re(2): Maybe I\'m missing something...','2003-10-30 16:17:56',4,'So, Gamer, are you confirming that she is correct?',9060,0);
INSERT INTO comment VALUES (9062,1364,4103,'kevin','Solutions','2003-10-30 17:12:35',3,'Anytime a liar refers to himself, he cannot call himself a liar, so Grot and Blarg cannot mean liar. Then if you assume Blarg means Knight, and do the tables, you realize there is no solution, so Grot must be Knight, and Blarg must be Knave.\r\n\r\nBlarg = Knave\r\nGrot = Knight\r\nCloysta = Liar\r\n\r\nWith that, there are three solutions:\r\nSolution 1:\r\nIf Jeswin is a knight, that means Parker is a liar, which means Crasbo can\'t be a Knave. Crasbo can\'t be a knight,since he calls jeswin a liar, so he has to be a liar as well.\r\nJeswin = Knight.\r\nParker = Liar.\r\nCrasbo = Liar.\r\n\r\nSolution 2:\r\nIf Jeswin is a Knave, then his first statement is a lie, so Parker must be a liar. Parker lies calling himself a knave, and lies calling crasbo a knave. Crasbo also can\'t be a knight, since he calls Jeswin a Liar, when in fact he is a Knave, so Crasbo must be a liar as well.\r\n\r\nJeswin = Knave\r\nParker = Liar\r\nCrasbo = Liar.\r\n\r\n\r\nSolution 3:\r\nif Jeswin is a Liar, then Parker can\'t be a Liar. If Parker were a knight, he would be lying when calling Crasbo a knight, so Parker is a Knave, and he lied calling Crasbo a Knave.\r\nCrasbo can\'t be a knave, and he can\'t be a liar, as his second statement is a truth, so he must be a Knight.\r\n\r\nJeswin = Liar\r\nParker = Knave\r\nCrasbo = Knight.\r\n\r\n\r\nIf all three have to be different, then solution 3 is the answer, but if not, then any of the three will work.',NULL,0);
INSERT INTO comment VALUES (9063,1364,1171,'nikki','re: Solutions','2003-10-30 17:27:10',0,'\"Anytime a liar refers to himself, he cannot call himself a liar, so Grot and Blarg cannot mean liar.\"\r\n\r\nOnly part of this is true. IF a person is a liar, he cannot say he is a liar. But saying that Grot and Blarg cannot mean liar means you concluded that NO ONE can say they are a liar, which is not correct.\r\n\r\nAs SilverKnight mentioned in a previous comment (#5), a Knave can still say he is a liar, and his second statement would have to be true.',9062,0);
INSERT INTO comment VALUES (9064,1331,4057,'Jason','Solution','2003-10-30 17:55:38',0,'This is easy. If you draw a star, and place a tree at each of the points where lines intersect, you have 5 rows of 4 with some on the inside as well as the outside. Quite simple.',NULL,0);
INSERT INTO comment VALUES (9065,1331,1626,'Gamer','Not so simple','2003-10-30 18:06:20',0,'No, just put your diagram down, and draw the lines where there are 5 lines of 4. Now, if the lines are ignored that go through tree X, tree X is on the inside if there are lines that go all around it.\r\n\r\nI am a little confused about why people would write down the exact same solution as in another problem, especially when I link to it. It\'s not that difficult to figure out that THAT\'S not the solution I am looking for!',NULL,0);
INSERT INTO comment VALUES (9066,1331,1626,'Gamer','Also:','2003-10-30 18:08:09',0,'If you still want to place it in a star pattern, I will say that they aren\'t in an exact straight line, they are in a curved line, which doesn\'t count.',NULL,0);
INSERT INTO comment VALUES (9067,1331,4064,'rerun141','AND some on the inside','2003-10-30 18:10:51',0,'Theres 4 trees on each path and some on the inside. In the pentagram pattern thre are 4 trees on each path.(it must be a different problem or gamer A) wouldn\'t have posted it and B) would have confirmed we had the solution when he posted his comment) so we have to repeat the problem with eualt to or less then 9 trees and but the left over trees in the middle.\r\n',NULL,0);
INSERT INTO comment VALUES (9068,1331,4064,'rerun141','oops','2003-10-30 18:13:07',0,'read gamers post after finishing mine. but different then even I thought.',NULL,0);
INSERT INTO comment VALUES (9069,1331,1171,'nikki','re: Not so simple','2003-10-30 18:50:27',0,'1) Gamer, you are not the only one who is confused. I was confused at the beginning because I truly believe that a slightly modified version of the solution to the 10 trees problem is A solution to this one.\r\n\r\n2) I couldn\'t tell what you meant by \"Now, if the lines are ignored that go through tree X, tree X is on the inside if there are lines that go all around it.\" I\'ll probably feel dumb for not getting it, but please clarify.\r\n\r\n3) It\'s not difficult to figure out that the repeat-solution is not what you were looking for. But that doesn\'t change the fact that it is still a solution.\r\n\r\n4) I don\'t see how my solution has the trees in a curved line. I was considering a realistic 3D park, where you have a path that has width and the trees that are \"on\" the path might actually be a foot or so off the path. Perhaps this was an incorrect theory.\r\n',9065,0);
INSERT INTO comment VALUES (9070,1331,1171,'nikki','After thought','2003-10-30 18:57:49',4,'Ok, so would this be an appropriate way of rewording the problem?\r\n\r\nMake 5 straight rows of 4 trees. These lines are 1D and trees exist ON (not next to) these lines and are 0D.\r\n\r\nIf a tree is on an outer edge of whatever shape you made, it is vulnerable to these vicious squirrels. The tree is not vulnerable if it is on an inner edge (not adjacent to the \"outside\" world).\r\n\r\nIf this is the case, I see how my solution doesn\'t work.',NULL,0);
INSERT INTO comment VALUES (9071,1331,4064,'rerun141','It seems to me','2003-10-30 19:19:24',0,'it seems to me that the question is asking you to use 9 or fewer trees to make 5 lines of 4. The other tree(s) will be placed within these paths. ',NULL,0);
INSERT INTO comment VALUES (9072,1331,1626,'Gamer','re: It seems to me','2003-10-30 19:24:57',0,'Stick with nikki\'s wording. I think her wording is better than mine. :)\r\n\r\nI am not saying that any solution that is in previous problems is excluded, just that people were like \"Duh! Use the old solution!\", when there was a debate about whether I allowed solutions like that or not.',9071,0);
INSERT INTO comment VALUES (9073,1331,4064,'rerun141','ok. so...','2003-10-30 19:46:39',4,'so would the trees on the inner vertices (the ones on two lines) in the original problem be legal?',NULL,0);
INSERT INTO comment VALUES (9074,1227,4057,'Jason','Confused','2003-10-30 20:01:41',0,'Excuse me ignorance on the subject, but what is balking? This is what you get for growing up in Europe.',NULL,0);
INSERT INTO comment VALUES (9075,1475,4057,'Jason','re: summer vacation','2003-10-30 20:06:27',0,'What about when he leaves Hawaii? Did the U.S. purchase the Pacific Ocean without my knowing? Also the most western point is in Alaska not Hawaii.',9051,0);
INSERT INTO comment VALUES (9076,1331,3386,'Victor Zapana','It seems to me.. i have a solution','2003-10-30 20:07:28',0,'i may have a solution. b4 i tell ill give u the overall shape.. its arrowhead like. now fr the really bad description of it. Ok. First, make an equilateral triangle (lets say triangle ABC) on ur paper extend AC a little more and end the line segment with point D (now you should a line segment AD). now add a point E on line AC, so that AE is about 1/3 of AC and CE is about 2/3 of AC. Now, add 2 points, point F and G, on line AB so that point F is closer to A and point G is closer to B line segments AF, FG, and BG are about equal (thus, each line segment shud be about 1/3 of the line) Now make a line from point F to point D. Next, make another line from point B to point E. Now, make another line from point C to point G. If done correctly, you should now have 3 points of intersection inside the original equilateral triangle (do NOT count any points of intersection you have made that intersected the base of the triangle, BC. there should be only one of these). Darken these points and any points I talked about above (points a-g). Then erase line BC, because this is not needed. Now, you should have 5 rows of 4 using 10 trees, and u have one of the points surrounded by the others, in the shape of an arrowhead. \r\nSorry if these directions are a lil confusing but thats what you should get.\r\n \n\nEdited on October 30, 2003, 8:08 pm',NULL,0);
INSERT INTO comment VALUES (9077,1331,4064,'rerun141','re: It seems to me.. i have a solution','2003-10-30 20:27:49',0,'lol there\'s gotta a much easier way to explain that budy. but anyway i belaive points A,B, abd D are exposed to squirel attack. sorry\r\n ',9076,0);
INSERT INTO comment VALUES (9078,661,3820,'Joseph ODonnell','A Suggested Solution','2003-10-30 20:31:49',3,'My brother Mathews sent me the following which I now offer as a possible solution to today\'s dilemma:\r\n\r\nI think you can swim to shore. I didn\'t do the arithmetic right earlier. Since I\'m doing absolutely nothing at the moment, let me outline the solution. If no one else has this tomorrow, feel free to post.\r\n\r\n1. Get into the water on the opposite side of the\r\nisland from the tiger. We\'ll assume that the unit of distance is one mile, the radius of the lake.\r\n\r\n2. Swim towards the shore AND in the same lateral\r\ndirection as the tiger is moving, keeping the \r\nisland between you and the tiger. i.e. if the tiger begins walking clockwise to get near you, swim clockwise as well, keeping as close to the \r\nimaginary diameter line that has the tiger as an end point. This line will move, much like the second hand on a clock and as you swim towards it your path will form a spiral.\r\n\r\n3. At one quarter speed of the tiger, you can \r\ncover a longer arc, in terms of degrees per unit time, until you are 1/4 mile from the island. At 1/4 mile, the circumference of your swimming circle is 1/4 that of the lake shore so both you and the tiger can complete a circle in the same \r\nunit of time. You can keep the tiger exactly opposite the island from you by swimming parallel to the shore, but you will no longer make any progress towards shore AND keep the tiger opposite you and the island.\r\n\r\n4. Take a deep breath.\r\n\r\n5. Turn and swim directly toward shore as fast as \r\nyou can. You have to cover 3/4mile to get to the shore. The tiger needs to cover half the circumference of the circle, or pi*1 mile = 3.1417 miles. The tiger runs 4 times faster than you can swim, so in the time it takes you to cover 3/4 mile, he can cover 3 miles. That leaves him somewhat less than .15 miles away when you reach shore. \r\n\r\n6. At this point, you\'re on your own.\r\n',NULL,0);
INSERT INTO comment VALUES (9079,1331,3386,'Victor Zapana','re(2): It seems to me.. i have a solution','2003-10-30 20:34:23',0,'well... it dint say ALL of the points have to inside, so poitns a b d can be destroyed by the squirells lol... wait thats not even possible to all be \"inside.\' also the point that is covered inside is the point of intersection btwn line CE and BF, so that is enuf to fill the requirement of the problem..\r\nalso another thing... i no my directions were mega confusing sry lol\n\nEdited on October 30, 2003, 8:35 pm',9077,0);
INSERT INTO comment VALUES (9080,176,4057,'Jason','re(2): easy','2003-10-30 20:40:07',0,'It could be played between adults who are young at heart.',8179,0);
INSERT INTO comment VALUES (9081,1479,4057,'Jason','re: solution','2003-10-30 20:50:26',0,'Very Nice :)',9054,0);
INSERT INTO comment VALUES (9082,442,2674,'mike','','2003-10-30 21:00:23',0,'shes 72. the first prime numbers tht pop into my head are 7 and 2. and the rest was history.\n\nEdited on October 30, 2003, 9:03 pm',NULL,0);
INSERT INTO comment VALUES (9083,442,2674,'mike','re: solution','2003-10-30 21:08:13',0,'that was over solved. it took me three seconds to sole this as im sure it did a lot of other people. there are only 5 prime single digit numbers 1,2,3,5 and 7. shes a grandma shes probably old you think first digit is 7. i usually use formulas and not guess and check but in this case with such a small number of numbers to work with why waste time making a formula. I didn\'t thik of thaat though andi aplaud you ',3008,0);
INSERT INTO comment VALUES (9084,661,3172,'SilverKnight','re: A Suggested Solution','2003-10-30 21:18:25',0,'That\'s absolutely amazing! Why didn\'t someone write this before...?\r\n\r\nOh wait... someone DID write this before!\r\n\r\nWell... whadaya know.',9078,0);
INSERT INTO comment VALUES (9085,1227,3172,'SilverKnight','re: Confused','2003-10-30 21:20:19',0,'To balk means to moon the umpire.',9074,0);
INSERT INTO comment VALUES (9086,661,4068,'Bruno Pelletier','Be Kind Tiger','2003-10-30 22:20:17',0,'I\'d say that you wait \'til the night.\r\n\r\nSo the tiger won\'t see you swimming in the darkness, and I suppose tigers sleep at night.',NULL,0);
INSERT INTO comment VALUES (9087,1227,4068,'Bruno Pelletier','Strike 2???','2003-10-30 22:38:41',0,'Since I had a strike with my first attempt, here\'s a second try that will probably be my strike #2:\r\n\r\nIf he only throws let\'s say fastballs, that can be consider as one kind of pitch, I guess...\r\n\r\nSo 1 is the fewest number of pitches a pitcher can throw and come away with a complete game.\r\n\r\nStrike 2 ???',NULL,0);
INSERT INTO comment VALUES (9088,1227,4055,'S','re: Confused','2003-10-30 22:57:45',0,'A balk is where a pitcher begins to pitch but stops before releasing the ball. The penalty (as found on www.baseball-almanac.com) is: ...each runner shall advance one base without liability to be put out...\r\n\r\nThis implies that I was incorrect in believing that a balk would place a batter on base.',9074,0);
INSERT INTO comment VALUES (9089,1331,3172,'SilverKnight','Full Solution','2003-10-30 23:13:26',3,'Here\'s one solution:\r\n\r\nTo describe the points... let\'s use a cartesian graph.\r\n\r\nThe 10 points are:\r\n\r\n01) (0,4)\r\n02) (-2,2)\r\n03) (2,2)\r\n04) (0,1)\r\n05) (-4,0)\r\n06) (-2,0)\r\n07) (2,0)\r\n08) (4,0)\r\n09) (-6,-2)\r\n10) (6,-2)\r\n\r\nThe 5 lines that they fall on (each line having 4 points) are:\r\n\r\ny=0 (containing points 5, 6, 7, and 8)\r\ny=(1/2)x + 1 (containing points 3, 4, 6, and 9)\r\ny=(-1/2)x + 1 (containing points 2, 4, 7, and 10)\r\ny=x + 4 (containing points 1, 2, 5, and 9)\r\ny=-x + 4 (containing points 1, 3, 8, 10)\r\n\r\nAnd of course... the lone tree in the middle is at point 4 (0,1).\r\n',NULL,0);
INSERT INTO comment VALUES (9090,65,4055,'S','I agree with the solution','2003-10-30 23:24:03',0,'I agree with the \"official\" solution: 1/3 odds of winning.',NULL,0);
INSERT INTO comment VALUES (9091,1331,4064,'rerun141','re: Full Solution','2003-10-30 23:49:10',0,'dats da same solution as Vicor only a bit more symetrical. I need some clarification from gamer but i think points 1) (0,4), 9 (-6,-2), and 10 (6,-2) are vulnerablr to squirrel attack!',9089,0);
INSERT INTO comment VALUES (9092,1331,3172,'SilverKnight','re(2): Full Solution','2003-10-31 00:06:57',0,'As I mentioned, there is a LONE tree in the center... point (4). All the others, including 1, 9, and 10 would be vulnerable to squirrels.\r\n\r\nAfter I posted my solution, I briefly tried to follow Vicor\'s thoughts.... well.. he says \"arrowhead like\", but the rest, I didn\'t follow.',9091,0);
INSERT INTO comment VALUES (9093,970,4055,'S','re: A binary solution','2003-10-31 00:22:11',0,'The RANDOM_1_TO_7 function can return 0 + 2*0 + 4*0 = 0. Therefore, this solution does not meet the criteria.',6458,0);
INSERT INTO comment VALUES (9094,1475,4098,'kevin coyne','poss solution','2003-10-31 08:57:03',0,'how about, he takes a ship (I think on the high seas a ship counts as US controlled territory)\r\nfrom hawaii to alaska (covering south, west and north) Then flies to over Canada (outside US control) to Maine easternmost.',NULL,0);
INSERT INTO comment VALUES (9095,1496,3275,'retiarius','Charlie loses','2003-10-31 09:35:52',0,'The barmen are loosing. Alan should have taken his 10 dollar bill (Canadian) across the border and exchanged it for 11.11 dollars (US). Bob should have done likewise and changed his 10 dollar bill (US) for 11.11 dollars (Canadian). If each country was serious about the exchange rate, they would honour the currency transaction. (One of them might actually honor it).\r\n\r\nCharlie might have enjoyed a few free drinks, but he would have been better off staying sober and playing the currency market. He should have taken his US dollars to a US bank and bought Canadian dollars. The he should have taken those to a Canadian bank and bought US dollars. He should then have continued in this manner before ending up in each bar and buying everybody a celebratory drink. Charlie was a loser.\r\n\n\nEdited on October 31, 2003, 9:56 am',NULL,0);
INSERT INTO comment VALUES (9096,1496,1301,'Charlie','solution','2003-10-31 09:50:53',3,'If the barmen in question, Alan and Bob, had received their respective foreign currencies, that they are using to make change, before the devaluations, then they are the losers, in the ordinary sense of holding money that has been devalued.\r\n\r\nBut as time goes on, the only way Alan and Bob will have such opposite-country currency is by more people from over the border spending their money there. When this happens, those Canadians spending their hard-earned Canadian dollars in Al\'s bar lose out 10% of their value, as Al considers their $10 bill to be worth only $9 worth of drinks. Those customers would get full value if they stayed at home. Likewise Americans using money earned in the U.S. at full scale, spending their money at Bob\'s lose out.\r\n\r\nSo the answer: the first few such transactions are the loss of Al and Bob, but an ongoing basis, the barkeep\'s supply of foreign currency is replenished by people from the other country, who lose out by crossing the border to drink using their native currency.',NULL,0);
INSERT INTO comment VALUES (9097,1496,4064,'rerun141','bars lose nothing','2003-10-31 10:07:29',0,'lets say before the dollar decrease there was $100 (U.S.) and $100 (canadian) in Alan cash register. Afterwars the $100 candian is only worth $90 U.S., Alan\'s total is $190 U.S. carlie pays one dollar., but gives a ten U.S. for a 10 canadian. alan now has 11 U.S. bills and 9 canadian. A total of $191 minus one for the drink is 190. The bars lose nothing... ',NULL,0);
INSERT INTO comment VALUES (9098,1331,3386,'Victor Zapana','re(3): Full Solution','2003-10-31 10:21:52',0,'u dun have to really follow the rest silver knight . coz basically what you wrote is like what i wrote only dramatically easier to comprehend lol',9092,0);
INSERT INTO comment VALUES (9099,1496,4064,'rerun141','solution','2003-10-31 10:42:24',0,'no ones losing out on this transaction. At the time of de-valuing the bars lost 10% of the value of their faoreign money. Charlie \"found it\" by minipulating the exchange rate.',NULL,0);
INSERT INTO comment VALUES (9100,1496,4107,'Marc Meyer','Who loses.','2003-10-31 11:35:25',3,'The governments of both countries pay for the drinks.\r\nafter 1 transaction the canadian barman will have \r\n10 CANADIAN, and be out 10 US and 1 drink. In order to serve our drinker again, he needs to go to the bank, give them 9 CAN and get 10 US back.\r\nThe bank can get its supply of US from either tourists/commercial transactions, or from a governmental source. No tourists/commercial (or few) will be available, because the bank is offering 9 CAN for 10 US, while in the States 11 CAN can be had for the 10 US. So the govt central bank needs to supply the US currency, at 10US = 9 CAN, but it needs to replenish that supply from Stateside sources at a rate of 10US=11CAN, losing 22% on each transaction (to people like Charlie!)\r\nSimilarly, when in the States, the US Govt pays for Charlie\'s drinks.',NULL,0);
INSERT INTO comment VALUES (9101,1496,1575,'DJ','Loser.','2003-10-31 12:03:07',1,'I don\'t know, but the northern New York in which I live, five minutes from the Canadian border, charges ($3 CD, $2.50 USD) every time you cross.\r\n\r\nIn the situation described, I\'ll assume the border accepts both currencies at par. Even still, Charlie (unless he is a very strong swimmer) is paying a good deal more for the trips over the border than it is worth for the drinks he is recieving.\r\n\r\nEven if you neglect border fees, Charlie is performing work in going back and forth. He is obviously traveling on foot (and avoiding bridge fees), due to New York\'s strictly enforced Zero Tolerance DUI laws (especially so at border crossings because of the difference in the countries\' drinking ages), so walking even a few miles from one bar to the other is probably not worth the dollar he is saving in expediting the premature death of a good number of brain cells on his binge.',NULL,0);
INSERT INTO comment VALUES (9102,27,4107,'Marc Meyer','martin gardner\'s write-up','2003-10-31 12:13:25',0,'Chapter 43, The Unexpected Hanging, The Colossal Book of Mathematics, Martin Gardner, Norton Press, 2001. This is considered a real paradox and his writeup and history, along with the rest of the \"colossal\" book, is fascinating!',NULL,0);
INSERT INTO comment VALUES (9103,1331,1626,'Gamer','Solution notes:','2003-10-31 12:43:10',0,'I don\'t believe anyone would really understand Victor\'s method, but some might.\r\n\r\nI think Silver Knight had the solution I was looking at, only flipped over.',NULL,0);
INSERT INTO comment VALUES (9104,662,3172,'SilverKnight','solution','2003-10-31 12:56:50',3,'7 round coins (worth $15/11 each) + 1 square coin (worth $16/11 each) should do it...\r\n\r\n7 x (15/11) = 105/11\r\n1 x (16/11) = 16/11\r\n\r\ntogether: 105/11 + 16/11 = 121/11 = $11',NULL,0);
INSERT INTO comment VALUES (9105,1331,1920,'Brian Smith','re: Full Solution - Another solution','2003-10-31 13:02:02',0,'This solution can be modified to create a solution with two trees in the middle.\r\nChange the line y=0 to y=1.5',9089,0);
INSERT INTO comment VALUES (9106,1227,4060,'daniel trosdahl','re: Strike 2???','2003-10-31 13:02:15',0,'Sttrrriiike two!\r\n\r\nType of pitch has nothing to do whatsoever with pitch count.\r\n\r\nThat\'s like saying there\'s only one planet orbiting around the sun because they are all round.',9087,0);
INSERT INTO comment VALUES (9107,1227,4060,'daniel trosdahl','re(2): Confused','2003-10-31 13:05:59',0,'Knight has it. When I play softball I generally balk the umpire two, maybe three times a game.',9085,0);
INSERT INTO comment VALUES (9108,1479,4098,'lovejoy','re: solution','2003-10-31 13:50:11',0,'I\'m sorry to rain on ytour parade, but chitty was written by roald dahl. Nice try though.',9054,0);
INSERT INTO comment VALUES (9109,1479,3172,'SilverKnight','re(2): solution','2003-10-31 13:57:37',0,'I think Lee is correct... check out:\r\nhttp://www.ianflemingcentre.com/index.cfm?page=chitty, or\r\nhttp://www.bookcrossing.com/journal/163486',9108,0);
INSERT INTO comment VALUES (9110,1479,4098,'lovejoy','re(3): solution','2003-10-31 14:10:30',0,'Looks like your\'r right siver and lee, I took the info from halliwells film guide and they give roald dahl, first time I\'ve ever known them be wrong.',9109,0);
INSERT INTO comment VALUES (9111,1479,4098,'lovejoy','re(3): solution','2003-10-31 14:15:56',0,'take a look at this odd\r\n\r\nhttp://us.imdb.com/title/tt0062803/',9109,0);
INSERT INTO comment VALUES (9112,1479,4098,'lovejoy','re(4): solution','2003-10-31 14:23:11',0,'mmmm I didn\'t know you couldn\'t copy and paste url here,and when I tried to type it in the page is not available',9111,0);
INSERT INTO comment VALUES (9113,1479,3172,'SilverKnight','re(4): solution','2003-10-31 14:24:14',0,'Lovejoy, What\'s odd about it...?\r\n\r\nThe movie (like the Bond movies) is based on a book by Ian Flemming.\r\n\r\nNow... Roald Dahl is great, unto himself... he worked on the unforgettable Willy Wonka and the Chocolate Factory which starred Gene Wilder as Willy Wonka and Peter Ostrum as Charlie.\r\n\r\n(I\'m a little unnerved by them trying to remake it in 2005 with Charlie and the Chocolate Factory, starring Johnny Depp as Willy Wonka.)',9111,0);
INSERT INTO comment VALUES (9114,1458,2231,'Trevor Leitch','can we have the solution now?','2003-10-31 15:21:31',0,'Chan, I\'m dying to find out how to do this so I can win cash from friends at the bar... ',9057,0);
INSERT INTO comment VALUES (9115,1331,1626,'Gamer','Solution with 2 in the middle.','2003-10-31 15:48:56',3,'I just checked where I got the answer from and you are right. There are 2 trees on the inside:\r\n\r\nA: -12, -7\r\nB: -5,0\r\nC: -4,1\r\nD: -2, 0\r\nE: 0,-1\r\nF: 0,5\r\nG: 2,0\r\nH: 4,1\r\nI: 5,0\r\nJ: 12,-7',NULL,0);
INSERT INTO comment VALUES (9116,1224,3807,'DrBob','Fairly straightforward','2003-10-31 16:16:51',0,'For the sum & product of two numbers to be the same, if the first is x the second is of the form x/(x-1) or 1+1/(x-1). This is easily proved.\r\nIn this case, x is a 2 digit number (AB) & C=1\r\n1/(x-1) = y/100 (where y is a one or two digit number). This means that (x-1) divides 100. Since (x-1) cannot have more than two digits it does not equal 100. Check out the other possibilities\r\nx has 2 digits so (x-1) cannot be 2,4 or 5 \r\n(x-1)=50 implies that x=51 (oops: B=1=C)\r\n(x-1)=20 - same problem: B=1=C\r\nThis leaves x-1 = 25; so x=26 & 1/(x-1) = 0.04\r\nSo: A=2; B=6; C=1; D=0; E=4',NULL,0);
INSERT INTO comment VALUES (9117,662,3558,'Tristan','','2003-10-31 16:42:41',3,'Well, this is my solution.\r\n\r\nSince 11 round coins equal $15, each coin is $15/11. Likewise, the square coins are $16/11, and the triangular coins are $17/11. The amount we\'re trying to get is 11 dollars, or 121/11.\r\n\r\nTo get the number 121 from all these numbers, I divided by 16. 121=8*16-7=7*16+9. So, to get 121, we can use coins of lesser or greater value to compensate for the remainders. Therefore, only combination that works is 7 round coins and a square coin. You cannot change 9 of the coins to triangular coins because there are only seven coins using that combination.',NULL,0);
INSERT INTO comment VALUES (9118,1331,3386,'Victor Zapana','re: Solution notes: (in reply to Gamer)','2003-10-31 19:37:42',0,'lol ok my method is Silver Knight\'s exactly, only that\'s his description is so much better than mine lol',9103,0);
INSERT INTO comment VALUES (9119,1335,4112,'Sniper59','','2003-10-31 20:25:45',3,'Okay, I started out by finding where A and B met for the first time. We know since they meet between n=0 and n=1 where n is the distance from B\'s house (since B starts out at 0 and A starts at 1), the distance traveled by A and B (henceforth repesented by a and b, respectively)is equal to one. We know in t Time, B can travel 2 times as much distance as A, so therefore b/t=2a/t or b=2a. Since they travel 1 mile in total, b+a=1, and substituting 2a for b, 3a=1 so a=1/3 and b=2(1/3)=2/3.\r\n\r\nWhere d is the total distance to travel between A\'s house and B\'s house, B will travel 2/3+d mi to get to A\'s house, as B starts out at 2/3 mi away from his house and therefore travels 2/3 mi to get to his house then d distance to get to A\'s house. A, on the other hand, will travel d-2/3 mi to get to his house, as A is 2/3 mi away from B\'s house. \r\n\r\nSo, assume it takes them x time to get to A\'s house. We know (d+2/3)/x is equal to b and (d-2/3)/x is equal to a. Since we know b=2a, substituting the values for a and b we get (d+2/3)/x=(2d-4/3)/x. Multiplying both sides by x we get d+2/3=2d-4/3. Subtract d from both sides and we get 2/3=d-4/3. Add 4/3 to both sides and the result is 6/3=d. Since 6/3 is equal to 2, the total distance traveled between the two houses is equal to 2 miles. \r\n\r\nThis result is arrived at by assuming A and B have to travel in a straight line. If, however, they do not travel in a straight line, without further data it is impossible to determine the absolute distance between the two houses. The best we can do is essentially \"taxi distance\".\r\n\r\nSo, in case you\'d rather not read all that, my answer is 2 if they travel in a straight line and no solution if they do not.\r\n',NULL,0);
INSERT INTO comment VALUES (9120,493,4112,'Sniper59','So...','2003-10-31 20:40:45',0,'I know it\'s kind of a lazy, but why not just say... 24*1^0*1^0*1^0*1^0, or 24*1*1*1*1 = 24. Since it says ONLY 4 zeros and any mathematical operators/symbols... you could consider 24 as a symbol for 2*10^1+4*10^0 and since I added the 4 \"1^0\"\'s, I used 4 0\'s and 1 mathematical symbol.\r\n\r\nHow\'s about that?',NULL,0);
INSERT INTO comment VALUES (9121,174,4112,'Sniper59','Reducto ad absurdum?','2003-10-31 23:16:25',0,'Wouldn\'t it be possible to use the common mathematical process of Reducto ad Absurdum on this?\r\n\r\nWe start out by assuming B is true, meaning there is no solution. However, in providing the solution (b), we have provided a solution to the problem, meaning that there is a solution to a problem, which is a direct contradiction to b. So ergo, because by assuming B is true we run into a contradiction, there must be a solution. Therefore, a.\r\n\r\nWe can also try to prove a is false with Reducto ad Absurdum: Assume a is true. Since a is true, there is a solution. Since a is a solution there is a solution. This means there is no contradiction, and Reducto ad Absurdum fails. \r\n\r\nBy analyzing the problem itself, and supposing \"s\" represents that the problem has a solution, we get...\r\nIf: a or b then s\r\nIf: b then not s\r\n\r\nIn doing so, we say that if: b then s and not s, which is a direct contradiction, hence the answer is a.\r\n\r\nI\'m sure there\'s a hole in my logic somewhere, but I can\'t see it right now, as it\'s kind of late. Feel free to point it out to me, if it\'s there, of course.',NULL,0);
INSERT INTO comment VALUES (9122,1458,4068,'Bruno','re(2): What is the foundation?','2003-11-01 00:32:19',0,'Since we already have the tools with us to make it drop, and since normal bar tables are rather fragile, I\'d say that we jump on the floor to create a vibration. So the cigarette will drop without having to toch the cigarette and the foundation.\r\n\r\nAnother possibility would have been an earthquake, but I don\'t have the strength to create one !',8926,0);
INSERT INTO comment VALUES (9123,1458,4114,'Rochelle','cigarette on bar---I HAVE IT!!','2003-11-01 01:26:51',3,'Drop a very heavy object on the floor near the bar. The vibration will shake both bar and cigarette. Soundwaves are not gas, solid or liquid.',NULL,0);
INSERT INTO comment VALUES (9124,493,1626,'Gamer','re: So...','2003-11-01 09:13:58',0,'You can\'t perform any functions on symbols. For example, I can\'t multiply plus by minus...',9120,0);
INSERT INTO comment VALUES (9125,662,3759,'Howard Bandy','Solution','2003-11-01 10:14:50',0,'He should pay 7 round plus 1 square coins.\r\n\r\nHoward',NULL,0);
INSERT INTO comment VALUES (9126,1335,3759,'Howard Bandy','Solution','2003-11-01 10:31:48',0,'They live 2 miles apart.\r\n\r\nA walks distance W until he is 1 mile from B\'s house. Then A and B walk toward each other, B walking twice as fast. So they meet when A has traveled an additional 1/3 mile and B has traveled 2/3 mile. A is (W + 1/3) miles from his house, B is 2/3 mile from his house.\r\n\r\nA returns to his house -- (W + 1/3) miles. \r\nB returns to his house, then to A\'s -- (2/3 + 1 + W) miles.\r\n\r\nTheir times are equal, and B\'s rate is twice A\'s. Distance equals rate times time, so time equals distance divided by rate (D/R). \r\n\r\nA\'s D/R is (W + 1/3) / 1.\r\nB\'s D/R is (W + 5/3) / 2.\r\n\r\nSolving, W = 1 mile.\r\nSo they live two miles apart.\r\n\r\nHoward',NULL,0);
INSERT INTO comment VALUES (9127,660,3759,'Howard Bandy','Solution if I may do this','2003-11-01 10:34:38',0,'If I may cut, then stack the pieces, each cut doubles the number of pieces, so n cuts makes 2 raised to the n power pieces.\r\n\r\nHoward',NULL,0);
INSERT INTO comment VALUES (9128,638,3759,'Howard Bandy','Solution','2003-11-01 11:07:14',0,'Assume the first post is AB, then the second is BA, and the third is A0B. Since the drivers speed is constant and the posts are seen at the same interval, the distance between the posts is the same.\r\n\r\nSo, A0B - BA == BA -AB\r\n\r\nThat is, 100A + B - 10B - A = 10B + A - 10A -B\r\nor 108A = 18B\r\nor B = 108A / 18\r\n\r\nIf A = 1, then B = 6.\r\nThere are no other solutions where A and B are single digits.\r\n\r\nSo the posts show 16, 61, and 106.\r\n\r\nHoward',NULL,0);
INSERT INTO comment VALUES (9129,638,3759,'Howard Bandy','re: Solution','2003-11-01 11:08:38',0,'I forgot the important line. The speed is 45 miles per hour.\r\n\r\nHoward',9128,0);
INSERT INTO comment VALUES (9130,1496,3136,'Popstar Dave','Arbitrage','2003-11-01 11:25:47',1,'This kind of arbitrage (risk-free profit; see below for a full definition) opportunity could never exist for long in a world with a free market for currency. Many people would take advantage of this inequality and the relative prices of each currency (the exchange rates) would rise until the currency market was back in equilibrium. For currency markets the size of USA and Canada, this would happen in a matter of minutes; hardly time for Charlie to get many drinks at all!\r\n\r\n\r\nArbitrage involves the simultaneous purchase of a security in one market and the sale of it or a derivative product in another market to profit from price differentials between the two markets.',NULL,0);
INSERT INTO comment VALUES (9131,1482,3386,'Victor Zapana','1st thoughts','2003-11-01 12:28:00',0,'hmm.. well coz i think this is math related i\'ll give what the position of each them is in the alphabet\r\n\r\nB- 2,\r\nC- 3,\r\nF- 6,\r\nH- 8,\r\nI- 9,\r\nK- 11,\r\nN- 14,\r\nO- 15,\r\nP- 16,\r\nS- 19,\r\nU- 21,\r\nV- 22,\r\nW- 23,\r\nY- 25\n\nEdited on November 1, 2003, 12:32 pm',NULL,0);
INSERT INTO comment VALUES (9132,1482,3386,'Victor Zapana','more thoughts','2003-11-01 12:38:42',0,'now.. ill consider the letters (and their position on the alphabet is below them in respective order) not included and see if theres a relationship btwn them\r\n\r\nA, D, E, G, J, L, M, Q, R, T, X, Z\r\n1, 4, 5, 7,10,12,13,17,18,20,24,26\n\nEdited on November 1, 2003, 12:39 pm',NULL,0);
INSERT INTO comment VALUES (9133,1364,4119,'Maria','Gotta be this or that','2003-11-01 15:59:01',0,'Beginning with the fact that no Liar would call himself as such, then Grot could not mean Liar in any case. Then:\r\n1. If Jeswin is a Grot (Knight), Parker is a Cloysta (Liar).\r\nThen Parker is not a Blarg (Knive), and Crasbo is not a Blarg either. \r\nThen Crasbo has to be also a Cloysta, then Jeswin could be a Grot.\r\nThat give us this result:\r\nJeswin = Grot (Knight)\r\nParker = Cloysta (Liar)\r\nCrasbo = Cloysta (Liar)\r\nBut if Parker is a Cloysta (Liar), Crasbo could be also a Grot (Knight), then he is telling the truth, so Jeswin would be a Cloysta... So:\r\n2. If Jeswin is not a Grot (a Knight), Parker is not a Cloysta (Liar).\r\nThen Parker could be either Grot or Blarg (Knave). If he is a Grot then Crasbo is a Blarg; but if Parker is a Blarg, then Crasbo could be either Grot or Blarg. If Crasbo is a Grot, Jeswin is a Cloysta; but if Crasbo is a Blarg, then Jeswin could be either Cloysta or Grot... and we start again.\r\nSo another result could be:\r\nJeswin = Cloysta (Liar)\r\nParker = Grot (Knight)\r\nCrasbo = Blarg (Knave)\r\n',NULL,0);
INSERT INTO comment VALUES (9134,662,4120,'Ness','hMmm','2003-11-01 16:38:58',2,'set it up as a matrix equation:\r\n[11 0 0]-1 [15]\r\n[0 11 0] (*) [16]\r\n[0 0 11] [17]\r\n\r\nput in calculator (TI 83) under matrix a and matrix b:\r\n\r\nfind the inverse of matrix a and multiply it by matrix b and you\'ll get your answer! enjoy! ',NULL,0);
INSERT INTO comment VALUES (9135,1482,3196,'Dan','This has to be the answer','2003-11-02 01:11:39',3,'In the periodic table of elements, these are the only chemical symbols that consist of a single letter:\r\n \r\nB (boron) \r\nC (carbon) \r\nF (fluorine) \r\nH (hydrogen) \r\nI (iodine) \r\nK (potassium...is there a K in potassium ???) \r\nN (nitrogen) \r\nO (oxygen) \r\nP (phosphorous) \r\nS (sulfur) \r\nU (uranium) \r\nV (vanadium) \r\nW (tungsten...so where is the W in tungsten, dude?) \r\nY (yttrium)\r\n \r\n\r\nEdited on November 2, 2003, 1:22 am\n\nEdited on November 2, 2003, 1:23 am',NULL,0);
INSERT INTO comment VALUES (9136,1227,4125,'Tom','Solution ?','2003-11-02 01:58:28',0,'I believe the solution is ZERO pitches.\r\n\r\nIf a pitcher touches his fingers to his mouth while on the mound, a Ball is called. After 4 times (4 Balls) the batter walks. Without throwing a pitch, the runner is picked off first base. This continues for 9 innings...0 pitches!\r\n\r\nImprobable, but possible',NULL,0);
INSERT INTO comment VALUES (9137,1482,4112,'Sniper59','re: This has to be the answer','2003-11-02 01:59:31',0,'Obviously, there is no K in potassium and no W in Tungsten. Both come from the Latin words for these elements, kalium and wolframium (respectively). \r\n\r\nOther such elements include Tin (Sn, latin Stannus), Lead (Pb, latin Plumbum), Mercury (Hg, latin Hydrargyrus), Copper (Cu, latin Cuprum), Silver (Ag, latin Argentum), Gold (Au, latin Aurum), Iron (Fe, latin Ferrum), Chromium (Cr, greek Color), Sodium (Na, egyptian Natron).\r\n\r\nSo, yeah. There is a K in potassium, sort of.',9135,0);
INSERT INTO comment VALUES (9138,662,3196,'Dan','No kitten would be that cheap !!','2003-11-02 02:25:35',3,'How many of each coinage should the customer pay? He should pay x round coins, y square coins, and z triangular coins. (Wasn\'t that easy?) Each round coin is 15/11 of a dollar. Each square coin is 16/11 of a dollar. Each triangular coin is 17/11 of a dollar. \r\n \r\n15x/11 + 16y/11 + 17z/11 = 11. \r\n\r\n15x + 16y + 17z = 121 \r\n\r\nx=7 y=1 z=0\r\n\r\nHe should pay 7 round coins and 1 square coin. ',NULL,0);
INSERT INTO comment VALUES (9139,1482,3196,'Dan','re(2): This has to be the answer','2003-11-02 02:33:45',0,'Sniper59 writes: \"Obviously, there is no K in potassium and no W in Tungsten. Both come from the Latin words for these elements, kalium and wolframium (respectively).\"\r\n\r\nOf course. I was being facetious. You forgot to mention Britney Spears\' favorite element, holmium (ho), and Elton John\'s favorite element, bismuth (bi). \r\n\n\nEdited on November 2, 2003, 2:34 am',9137,0);
INSERT INTO comment VALUES (9140,1496,3196,'Dan','4 losers, 2 winners, bar none.','2003-11-02 04:06:41',1,'\"WHO (if anyone) is losing out on these transactions?\"\r\n\r\nOne clear loser was, as you say, WHO (World Health Organization), whose anti-alcohol campaign had fallen on deaf ears. Beyond that, after 50 visits from Charlie, Alan had given up 50 Canadian dollars ($45 in America) and gotten 50 US dollars. He was ahead $5 in US currency. Bob had given up 50 US dollars ($45 in Canada) and gotten 50 Canadian dollars. He was ahead by $5 in Canadian currency.\r\n \r\nSo the 4 losers were:\r\n(1) WHO (World Health Organizaton)\r\n(2) Charlie. He lost social prestige, his wife left him, he got brain and liver damage, and he received 20 years in prison for double vehicular homicide.\r\n(3) Alan. As he was on his way to the bank, after hours, to deposit his $5 profit, a besotted Charlie (by now too drunk to walk) plowed into him in his SUV, killing him instantly.\r\n(4) Bob. He was Charlie\'s other victim.\r\n\r\nThe 2 winners:\r\nFlora and Fauna,the barmaids of Alan and Bob, respectively. They inherited the two alehouses. \n\nEdited on November 2, 2003, 10:03 pm',NULL,0);
INSERT INTO comment VALUES (9141,1479,3196,'Dan','There\'s another possibility.....','2003-11-02 04:59:37',0,'\"What do these five famous actors have in common?\r\nDick Van Dyke, Peter Sellers, Sean Connery, \r\nDavid Niven and Woody Allen.\"\r\n \r\nEach would have been able to defend himself against Liza Minnelli ?\r\n',NULL,0);
INSERT INTO comment VALUES (9142,511,3196,'Dan','This is an old conundrum','2003-11-02 05:09:07',0,'This question was settled a long time ago, by Augustine, who wrote an esay detailing all the things God cannot do. These include:\r\n\r\nGod cannot create such a rock.\r\nGod cannot commit suicide.\r\nGod cannot create a being more powerful than Himself.\r\nGod cannot sin.\r\nGod cannot be tempted by evil.\r\nGod cannot cause the Cubs to win the World series.',NULL,0);
INSERT INTO comment VALUES (9143,1344,3386,'Victor Zapana','question to gamer','2003-11-02 08:57:31',0,'if u flip a light right next to an already lit light, will that make the already lit light turn off? or will the already lit light stay on?',NULL,0);
INSERT INTO comment VALUES (9144,1344,3386,'Victor Zapana','re: question to gamer','2003-11-02 09:00:38',0,'n/m im stupid lol',9143,0);
INSERT INTO comment VALUES (9145,1344,3386,'Victor Zapana','stuck lol','2003-11-02 09:14:54',0,'I\'ma stuck. I can get all the lights to light except for 2 ( I did that in 11 steps), but afterward every possibility I try to do ends up in 2, over and over again. gah help lol',NULL,0);
INSERT INTO comment VALUES (9146,1482,3386,'Victor Zapana','re: This has to be the answer','2003-11-02 09:16:31',0,'gj',9135,0);
INSERT INTO comment VALUES (9147,656,3386,'Victor Zapana','re:','2003-11-02 09:22:04',0,'a flaw in ur proof.\r\n\r\nu said 2+3 = 5, then 5+6= 11, u frgt 3+4 in between. and that would equal 7, which is not part of the sequence. If you dont include 3+4, ur proof dun work at all.',9025,0);
INSERT INTO comment VALUES (9148,1344,4064,'rerun141','re: stuck lol','2003-11-02 10:48:03',0,'lol you didnt read the problem, you must turn all lights off, not on!',9145,0);
INSERT INTO comment VALUES (9149,1344,1626,'Gamer','Solution or impossible','2003-11-02 11:00:45',0,'The point of this problem is to either give a way that its possible, or prove that it\'s impossible. I don\'t have a solution to this, but I have been wondering and thought it would be a good problem for others.\r\n\r\nThe answer it to turn them all off, not on. :)',NULL,0);
INSERT INTO comment VALUES (9150,692,4129,'dl','¤','2003-11-02 13:33:39',0,'m=7kg ; v=10m/s ; g=9.8m/s²\r\nEp=m*g*h ; Ek=(m*v²)/2\r\nEp=Ek\r\n7kg*9.8m/s²*h=(7kg*10m/s²)/2\r\n68.6h=350\r\nh=5.1',NULL,0);
INSERT INTO comment VALUES (9151,1344,3386,'Victor Zapana','re: Solution or impossible','2003-11-02 13:42:26',0,'woops lol',9149,0);
INSERT INTO comment VALUES (9152,355,4129,'dl','¤','2003-11-02 13:59:24',0,'Difference in mass\r\n',NULL,0);
INSERT INTO comment VALUES (9153,1344,3386,'Victor Zapana','possibly impossible','2003-11-02 14:05:48',0,'i\'m pretty sure now thats impossible (tho i cant prove it), coz im getting stuck again with 2 lit lights in 21 steps, and in all possibilities ive tried it always ends up at 2 , over and over. so if anyone can now prove me wrong or right, itll be helpful. (also, now i think it\'s only possible to have 1 lit light minimum with 0 steps).\n\nEdited on November 2, 2003, 2:06 pm',NULL,0);
INSERT INTO comment VALUES (9154,253,4129,'dl','¤','2003-11-02 14:33:00',0,'H2O; There are two H and one O atoms.\r\nH isn`t stabile becouse it has a tendency to give away the only electron it has and become proton, and O needs two electrons to become as stabile as Ne, which means that those two are very unstabile, reactive and combustible. Two H atoms give away their electrons to O atom and everybody become satisfied and that is the reason why H2O is not reactive (explosive).',NULL,0);
INSERT INTO comment VALUES (9155,1463,3196,'Dan','re(2): An alternate approach - I think I got it','2003-11-02 14:51:22',0,'Good work ! The only problem with your solution is that the problem title is \"Difficult Sequence (single)\", not \"Difficult Sequences (plural).\" So there has to be just one sequence, not two. But that\'s nitpicking.......',8960,0);
INSERT INTO comment VALUES (9156,1358,4130,'Jenna','i no it really','2003-11-02 14:53:58',0,'the answer is 3 boys n 4 grls... ok we did this in science class as a brain teaser.. ok i dont no how to explain but i think thats wat the answer is',NULL,0);
INSERT INTO comment VALUES (9157,1344,3558,'Tristan','First steps to proof','2003-11-02 15:56:24',1,'After trying myself, this puzzle seems impossible so far. So, I need to find a way to prove it. \r\n\r\nI think that to go about proving this, we have to keep in mind how many lights switch each time we flip a switch. Depending on which switch is flipped, 3,4, or 5 lights switch. We need to switch just one light total, in the middle. \r\n\r\nIt is crucial to recognize the fact that the possibilities of light combinations do not depend on the order that the switches are flipped. So, there are 2^25 possible combinations. This may match the number of total combinations, but some of the possibilities are probably the same.\r\n\r\nThe corner lights are important because only three switches change each of them. And we can only use two of the switches that switch the corner lights, or none at all. The lights on the side of the grid have only 4 corresponding switches. So, we can either use 4,2, or none of these switches. Similarly, with the rest of the lights that are off, 4,2,or none of the adjacent/same switches must be flipped. The middle light must have an odd number of changes.\r\n\r\nIf a combination of switches follows these rules, then this puzzle is possible. We must disprove (or prove) such a combination. I hope everyone is following me.',NULL,0);
INSERT INTO comment VALUES (9158,1458,4131,'Steven','solution, maybe?','2003-11-02 16:04:52',0,'Couldn\'t you increase the temperature in the room, causing it to combust and burn to ash, which would naturally drop? Or even increases the pressure to where it can no longer hold itself up? \r\n\r\nforgive my nievete if i\'m incredibly wrong - first post.',NULL,0);
INSERT INTO comment VALUES (9159,1458,4131,'Steven','re: solution, maybe?','2003-11-02 16:11:15',0,'yeah well now that i\'ve realized there are more solution ideas down below i saw that my idea wasn\'t the first of its type. But the pressure thing is different, so perhaps that?\r\nanyway, sorry for the repeated part.',9158,0);
INSERT INTO comment VALUES (9160,1496,3558,'Tristan','Loser','2003-11-02 16:11:16',3,'I agree with Charlie (not the Charlie in the puzzle). The bars lost the minute the U.S. government and Canadian government devalued each other\'s money. Each bar had currency from the other company, or else they wouldn\'t be able to give Charlie his change in the foreign currency. Of course, I can\'t assume; the bars might have gotten the money after it was devalued. Then, whoever decided to pay them in foreign currency is the loser. Charlie used this this devaluation to his advantage and gained what the bars lost.',NULL,0);
INSERT INTO comment VALUES (9161,1344,3386,'Victor Zapana','re: First steps to proof','2003-11-02 16:16:31',1,'another thing to point at (mebe useless dunno) is that a 1x1 grid will work, a 2x2 grid will work, a 3x3 grid will work, but everything beyond that doesnt see to work.\n\nEdited on November 2, 2003, 4:17 pm',9157,0);
INSERT INTO comment VALUES (9162,1344,4064,'rerun141','re(2): First steps to proof','2003-11-02 16:36:36',4,'how does a 2*2 solution work?',9161,0);
INSERT INTO comment VALUES (9163,1344,3386,'Victor Zapana','re(3): First steps to proof','2003-11-02 17:16:50',0,'hmm... oh yeah. for the 2 by 2 square i just put the x to the top left. There, you can flip that switch on to make it \r\n 0 0 0 1 1\r\n 0 0 1 0 0\r\n 0 1 1 0 1\r\n 1 0 0 0 1\r\n 1 0 1 1 0\r\n\r\n 0 1 1 0 1\r\n 1 0 0 0 1\r\n 1 0 1 1 0\r\n 0 0 1 0 0\r\n 1 1 0 0 0\r\n\r\n 1 0 1 1 0\r\n 1 0 0 0 1\r\n 0 1 1 0 1\r\n 0 0 1 0 0\r\n 0 0 0 1 1\r\n\r\n 1 1 0 0 0\r\n 0 0 1 0 0\r\n 1 0 1 1 0\r\n 1 0 0 0 1\r\n 0 1 1 0 1\r\n
\r\n---------\r\nNote that the center bulb has three neighbors flipped (counting itself and orthogonal neighbors but not diagonal), while each of the other bulbs has an even number (zero or two) counted the same way.\r\n\r\nThe program which found these is:\r\nDECLARE SUB vary (r%, c%)\r\nDEFINT A-Z\r\nCLEAR , , 4000\r\nDIM SHARED flip(6, 6)\r\nDIM SHARED lit(6, 6)\r\n\r\nlit(3, 3) = 1\r\n\r\nvary 1, 1\r\n\r\nEND\r\n\r\nSUB vary (r, c)\r\n IF r = 5 AND c = 5 THEN\r\n GOSUB checkIt\r\n ELSE\r\n IF c = 5 THEN r1 = r + 1: c1 = 1: ELSE c1 = c + 1: r1 = r\r\n vary r1, c1\r\n END IF\r\n flip(r, c) = 1 - flip(r, c)\r\n lit(r, c) = 1 - lit(r, c)\r\n lit(r - 1, c) = 1 - lit(r - 1, c)\r\n lit(r, c - 1) = 1 - lit(r, c - 1)\r\n lit(r + 1, c) = 1 - lit(r + 1, c)\r\n lit(r, c + 1) = 1 - lit(r, c + 1)\r\n IF r = 5 AND c = 5 THEN\r\n GOSUB checkIt\r\n ELSE\r\n IF c = 5 THEN r1 = r + 1: c1 = 1: ELSE c1 = c + 1: r1 = r\r\n vary r1, c1\r\n END IF\r\n flip(r, c) = 1 - flip(r, c)\r\n lit(r, c) = 1 - lit(r, c)\r\n lit(r - 1, c) = 1 - lit(r - 1, c)\r\n lit(r, c - 1) = 1 - lit(r, c - 1)\r\n lit(r + 1, c) = 1 - lit(r + 1, c)\r\n lit(r, c + 1) = 1 - lit(r, c + 1)\r\n EXIT SUB\r\n\r\ncheckIt:\r\n bad = 0\r\n FOR row = 1 TO 5\r\n FOR col = 1 TO 5\r\n IF lit(row, col) THEN bad = 1: EXIT FOR\r\n NEXT\r\n IF bad THEN EXIT FOR\r\n NEXT\r\n IF bad = 0 THEN\r\n FOR i = 1 TO 5\r\n FOR j = 1 TO 5\r\n PRINT flip(i, j);\r\n NEXT\r\n PRINT\r\n NEXT\r\n PRINT\r\n END IF\r\n RETURN\r\n\r\nEND SUB\r\n\r\n\n\nEdited on November 2, 2003, 8:22 pm',NULL,0);
INSERT INTO comment VALUES (9168,1344,1301,'Charlie','re: Brute Force','2003-11-02 20:29:10',3,'Oh, yes, that\'s eleven switch flips to accomplish the task. I forgot that was part of the question.',9164,0);
INSERT INTO comment VALUES (9169,662,2716,'Federico Kereki','Quick solution','2003-11-02 20:34:21',3,'8 round coins @ $15/11 = $120/11, so you are $1/11 short; if you change a round coin for a square one you\'ll get $121/11=$11.',NULL,0);
INSERT INTO comment VALUES (9170,1496,4068,'Bruno','re: 4 losers, 2 winners, bar none.','2003-11-02 21:37:13',0,'Brilliant answer!\r\n\r\nYou deserve a 11.11/10 for it !\r\n\r\n(If 10 is worth 9, then 11.11 is worth 10, right???)',9140,0);
INSERT INTO comment VALUES (9165,1227,4133,'DENNIS MARSHALL','re: Solution ?','2003-11-02 18:14:18',0,'I BELIEVE YOU ARE RIGHT, BUT MORE THAN IMPROBABLE, IT WOULD BE ABSURD. I THINK A BETTER ANSWER WOULD BE 25. THE PITCHER COULD THROW 1 PITCH PER BATTER TO THE HOME TEAM, INDUCING GROUND BALL OR FLY BALL OUTS EACH TIME UNTIL THE BOTTOM OF THE 9TH. THE 1ST BATTER COULD HIT A WALK-OFF HOMERUN. IN THIS SCENARIO HE MAY HAVE HIT A BATTER OR 2 & GOTTEN A SUBSEQUENT DOUBLE OR TRIPLE PLAY TO STAY WITHIN THE MINIMUM AMT OF PITCHES.',9136,0);
INSERT INTO comment VALUES (9166,1344,4064,'rerun141','re: Brute Force','2003-11-02 19:49:19',0,'gj charlie... why did you call the topic brute force?',9164,0);
INSERT INTO comment VALUES (9167,1344,1301,'Charlie','re(2): Brute Force','2003-11-02 20:19:59',0,'It wasn\'t deductive logic. It just examined every possible arrangement of fliped and non-flipped switches. That\'s what we call brute force.',9166,0);
INSERT INTO comment VALUES (9171,718,4138,'zurheld','re: What\'s wrong','2003-11-02 22:10:06',0,'Wouldn\'t this be a smaller number? sin is smaller than tan.\r\n\r\nsin(.1°)^32!\r\n\r\nAlso, some of the answers posted seem to use the () symbols more than once, which I wouldn\'t think is legal.',7217,0);
INSERT INTO comment VALUES (9172,718,4138,'zurheld','re(2): What\'s wrong','2003-11-02 22:33:56',0,'oops, should have read the thread more carefully since better than this had already been posted.\r\n\r\ntan[sin(.1°)]^{2e3}!\r\n',9171,0);
INSERT INTO comment VALUES (9173,1344,3224,'Lee','','2003-11-02 23:28:45',0,'',NULL,0);
INSERT INTO comment VALUES (9174,1344,3224,'Lee','real-world method','2003-11-02 23:32:30',2,'I\'ll try again ......,\r\nThis wierd wiring feature described in Gamer\'s puzzle made for some happy guys down at Tiger Electronics after the succes of their \'lights out\' game a few years ago. I played it once in a toy store. It\'s quite frustrating.\r\nI don\'t think you could set your own puzzle/starting position, but Gamer\'s put us in the spot of finding a solution if only the center light is lit at the outset.\r\nNot all starting positions are possible - but the original game I believe only gives you possible \'winners\' (I presume so that if you\'re stuck the computer can show off by solving it for you - smart a@$e).\r\nThe situation Gamer descrines is, of course, possible (as Charlie\'s shown) so I just thought I\'d post this method of solving the real game (and quickly) so that you could show off to any annoying nephew who hands you his game. I take no credit for this method whatsoever. Please don\'t ask any questions as to how it might work. I don\'t know.\r\nIf you\'re going to practise this method go to one of the many \'lights out\' emulators on the net. This puzzle is next to impossible to keep up with armed with your trusty pencil and paper.\r\nAnyways,\r\n\r\nStep 1\r\nRemember, or have reference to this table\r\n\r\nx---x............cc---\r\n-x-x-............c--c-\r\nxxx--............-c---\r\n--xxx............---c-\r\nx-xx-............----c\r\n-xx-x............c----\r\nxx-xx............--c--\r\n\r\nx\'s are lit lights c\'s are \'clicks\' and the .....are just to seperate.\r\n\r\nStep 2\r\nStarting from the top \"Chase the lights down\" this means switching the lights immediately below lit ones(to put them out).Start switching on row 2(to turn off the light in row 1)and carry on down until you hit row 5.\r\n\r\nStep 3\r\nIf the puzzle is not solved look at the bottom row (the only one with any lights lit). Refer to the left hand portion of the above table to find the matching configuration of x\'s.\r\n\r\nStep 4\r\nClick on the corresponding c\'s in the top row (Row 1)\r\n\r\nStep 5 \r\n\"chase the lights down\' again and this time \r\nyou\'ll get all the lights out.\r\n\r\nWith Gamer\'s problem we only need to chase the lights down from row 4 and we end up with a final configuration of\r\nx---x\r\nso now we click/switch on the first 2 in row 1,\r\ncc---\r\n\r\nwhich gives us a board layout thus,\r\n\r\n--x--\r\nxx---\r\n-----\r\n-----\r\nx---x\r\n\r\nchasing these lights down will knock them all out.\r\n(note; you\'ll need a trusty pencil and paper to note which ones you\'ve switched to answer Gamer\'s poser)\r\nHope someone finds this interesting. I\'m a terrible typester and this has just taken ages.',NULL,0);
INSERT INTO comment VALUES (9175,1344,4145,'Choop','ANSWER HERE.','2003-11-03 01:12:10',0,'4 clicks.\r\n0=off, 1=on.\r\n\r\nstart:\r\n00000\r\n00000\r\n00100\r\n00000\r\n00000\r\n\r\nclick at pos.1:\r\n11000\r\n11000\r\n00100\r\n00000\r\n00000\r\n\r\nClick pos. 6;\r\n00000\r\n00000\r\n11100\r\n00000\r\n00000\r\n\r\nClick pos. 17:\r\n00000\r\n00000\r\n00000\r\n11100\r\n11100\r\n\r\nClick pos. 22:\r\n00000\r\n00000\r\n00000\r\n00000\r\n00000\r\n\r\n\r\nThere\'s four clicks that solve the problem. No programming necessary, just some pen & paper. If I \'m supposed to come up w/ some sort of formula, I\'ll fail miserable around here. I\'m just good at puzzling.',NULL,0);
INSERT INTO comment VALUES (9176,1344,4145,'Choop','Oh hell nevermind.','2003-11-03 01:17:29',0,'I was counting on diagonals as well. I\'ll post a different theory in a few minutes.',NULL,0);
INSERT INTO comment VALUES (9177,661,4145,'Choop','Support and denial.','2003-11-03 01:49:36',0,'Sorry, Brian, but tigers don\'t sleep at night: that\'s when they hunt. Swim at dawn, after the hunt but before the awakening. Now: I like the idea of swimming underwater, but you\'ll have to remember we ain\'t in Cleveland if we have a rock in a body of water with a radius (period...) of 1.\r\n\r\nThe lack of distance measures shouldn\'t bother me, though it does. Mathematically, if Tiger moves at 4x Man speed, there\'s no big bother about units. Still and all, there\'s a major difference between 1 inch and 1 mile.\r\n\r\nLet\'s go with 1 Km. (x) as the distance to the shore. The average human swims probably at 2/3 the speed of the fastest human (at 2.29 m/s:see http://hypertextbook.com/facts/2000/NoahKalkstein.shtml), which would yield about 1.53 m/s. It would then take 7min. for an average human to swim one Km (called x/y). The body of water (now BOW) will be (pi)x around. Derivatively, the tiger covers about 6.12 m/s, and would be across the lake 52.8 seconds before the human gets there. The logarithmic spiral proposed by several earlier seems to be the best answer.',NULL,0);
INSERT INTO comment VALUES (9178,576,4145,'Choop','audacity of posters','2003-11-03 02:03:49',0,'i can\'t believe there are such as those who would so discriminate against the dislexic, insomniac, agnostic, or amnesiac.\r\n\r\nObviously there is a Dog, and it wishes to grant few paryers, as it doesn\'t believe in itse..zzzzzzz',NULL,0);
INSERT INTO comment VALUES (9179,663,2839,'FatBoy','not sure if this counts','2003-11-03 08:25:16',2,'if you consider 1 to be the square of one than the puzzle works if Jack has 25 marbles and Jill has 24\r\n25 = 5*5\r\n25-24=1=1*1\r\n25+24=49=7*7',NULL,0);
INSERT INTO comment VALUES (9180,663,4146,'Kitty Saturn','re: not sure if this counts','2003-11-03 09:06:15',0,'If Jill has to have more than zero marbles, then the above solution should be multiplied by 4 to give an even square after taking away Jill\'s marbles.\r\n\r\n100 marbles / 96 marbles\r\n100 = 10\r\n100 + 96 = 14²\r\n100 - 96 = 2² which is even',9179,0);
INSERT INTO comment VALUES (9181,663,3172,'SilverKnight','solution','2003-11-03 10:06:42',3,'If we call the number of marbles Jack has x, and the number of marbles Jill has y...\r\n\r\nthen the problem says that:\r\n\r\n
\r\ny - x must be positive (because it leaves \"an even square\"), and therefore Jill has more marbles than Jack.\r\n\r\nJack having zero marbles, and Jill having four marbles will satisfy these requirements.\r\n\r\nBut if Jack must have non-zero marbles, then his having 16 marbles and Jill having 20 marbles will also satisfy these requirements.\n\nEdited on November 3, 2003, 10:08 am',NULL,0);
INSERT INTO comment VALUES (9182,663,3196,'Dan','This is terrible.....','2003-11-03 10:32:22',0,'\"What is the fewest number of marbles Jack could have?\"\r\n \r\nJack could have zero marbles. (That is, if a \"marble collection\" can consist of zero marbles. Perhaps when he fell down and broke his crown, he lost his marbles.) \r\n\r\n',NULL,0);
INSERT INTO comment VALUES (9183,663,1301,'Charlie','re: solution','2003-11-03 10:54:27',0,'But according to Jill\'s reply, Jack would give her a number of marbles equal to what she had already, so Jill is the one with fewer marbles, and in your letter assignments it is x - y that needs to be an even square.',9181,0);
INSERT INTO comment VALUES (9184,663,3172,'SilverKnight','re(2): solution','2003-11-03 10:59:55',0,'You are correct... I read the problem (incorrectly) as if Jack said the second sentence as well....\n\nEdited on November 3, 2003, 11:03 am',9183,0);
INSERT INTO comment VALUES (9185,663,3172,'SilverKnight','re(3): solution','2003-11-03 11:12:07',0,'I have to agree with Kitty\'s solution.\r\n\r\nFour for Jack and Zero for Jill... but if Jill should be non-zero... then\r\n100 for Jack and 96 for Jill.',9184,0);
INSERT INTO comment VALUES (9186,662,4106,'Sandeep','Another angle','2003-11-03 11:31:16',0,'If no. of round,square and triangular coins are x,y and z then we have simple equation to solve.\r\n\r\n 15x+16y+17z=121\r\n\r\nWe can then make an exhaustive search using a simple C program.',NULL,0);
INSERT INTO comment VALUES (9187,637,4106,'Sandeep','Complete exhaustive solution','2003-11-03 11:33:44',0,'check was of Rs. 2. \r\n\r\nlet us consider x to be any number \r\n\r\nx=10y+z ----- (1) \r\n\r\nsqauring eqn. (1) \r\n\r\nx^2=100y^2+z^2+20yz ------------- (2) \r\n\r\neqn. (2) represents the total amount after selling all the sheeps. \r\n\r\nnow, \r\n\r\neqn(2) % 10 = no. of one rupee note \r\neqn(2) / 10 = no. of ten rupee note \r\n\r\nnow, \r\n\r\neqn(2) % 10 = z^2 % 10 -------(3) \r\n/* others terms being divisible by 10 */ \r\n\r\neqn(2) / 10 = 10y^2 + 2yz + (z^2)/10 \r\n\r\nsince we can observe that total no. of 10 rupee note will be a odd number- \r\n\r\nwe conclude, \r\n\r\n(z^2)/10 is a odd number.--------(4) \r\n\r\npossible value of z = 1,2,3,4,5,6,7,8,9 \r\n\r\neqn (4) is true only for z=4,6. \r\n\r\neqn (3) gives 6 as result for z=4 and 6 \r\n\r\nhence, 6 one rupee notes are there.. \r\n\r\nso Rs. 2 transfer from Big B to choota bhai will divide the money equally.. \r\nAND THEY CAN LIVE HAPPILY THERE AFTER .......... \r\n\r\n',NULL,0);
INSERT INTO comment VALUES (9188,661,4106,'Sandeep','Calculus angle','2003-11-03 11:53:42',0,'Well have you all heard of that calculus problem involving three motocyclist.Well here it is.\r\n\r\nThere are 3 motor cyclist each at the vertex of an equilateral triangle.A moves towards B,B towards C and C towards A.They all are at equal speeds.Where shall they meet?\r\n\r\nMost of you would say that they would never meet, but they would and meet at the centriod.This solution is according to calculus.I think similar ideas work in this problem.\r\n\r\nThe start moving in a direction opposite to the tiger.The tiger too starts running towards the man.After swimming for time t(infinitely small) he changes his direction and swims oppsite to the tigers current postion.\r\n\r\nThus his path would be an arc.This is my solution.\r\n\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (9189,661,4106,'Sandeep','Calculus angle','2003-11-03 11:54:17',0,'Well have you all heard of that calculus problem involving three motocyclist.Well here it is.\r\n\r\nThere are 3 motor cyclist each at the vertex of an equilateral triangle.A moves towards B,B towards C and C towards A.They all are at equal speeds.Where shall they meet?\r\n\r\nMost of you would say that they would never meet, but they would and meet at the centriod.This solution is according to calculus.I think similar ideas work in this problem.\r\n\r\nThe start moving in a direction opposite to the tiger.The tiger too starts running towards the man.After swimming for time t(infinitely small) he changes his direction and swims oppsite to the tigers current postion.\r\n\r\nThus his path would be an arc.This is my solution.\r\nIf u have any doubt Then mail me at\r\n sandeep_bansal@da-iict.org\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (9190,663,1575,'DJ','Lost their marbles (full solution)','2003-11-03 12:37:34',3,'I\'ll use the notation already suggested; Jack has x marbles and Jill has y. Then, x is a perfect square, x+y is a perfect square, and x-y is a perfect square.\r\n\r\nThe simplest solution is that Jill has zero marbles (y=0), then Jack could have any square number. Even more simply, maybe Jack doesn\'t have any at all either. Or he has just one, or four.. whatever.\r\n\r\nAssume, then, Jill\'s collection actually contains some marbles.\r\n\r\nThe number in Jack\'s collection, is the square of some number, let\'s say n (n² = x).\r\nThe difference of the numbers in their respective collections is the square of some other number, say m (m² = x-y).\r\nThe sum, similarly, is the square of another number p (p² = x+y).\r\n\r\nWe know y is a positive integer. Thus, m<n, so we can say m=n-a for some a>0. Also, p>n, so p=n+b for some p>0.\r\n\r\nThen, some algebra:\r\nx-y = m² = (n-a)²\r\nx-y = n² - 2na + a²\r\nx-y = x - 2na + a²\r\ny = 2na - a²\r\n\r\nx+y = p² = (n+b)²\r\nx+y = n² + 2nb + b²\r\nx+y = x + 2nb + b²\r\ny = 2nb + b²\r\n\r\n
\r\nThen:\r\n2nb + b² = 2na - a²\r\n2na - 2nb = b² + a²\r\nn = (b² + a²)/2(a-b)\r\n\r\n
\r\nTherefore,\r\n0 < b < a (as could be intuitively determined from fact that the squares of n-a and n+b are in arithmetic progression).\r\n\r\nAny values of a and b will work in this equation, as long as n works out to an integer. Since the denominator contains a two, the numerator of the fraction must be even to yield an integral value of a. That is, the sum of a² and b² must be even, so a² and b² are both even or both odd. In either of these cases, their difference will be even as well, so the denominator will be the product of two even numbers, and the numerator must be a multiple of four. Therefore, a and b must both be even for n to work out to an integer. The simplest case for this (0 < b < a, given a and b both even)occurs when b=2 and a = 4.\r\nThus:\r\ny = 2nb + b² = 2na - a²\r\ny = 2(5)2 + 2² = 2(5)4 - 4²\r\ny = 20 + 4 = 40 - 16\r\ny = 24\r\n\r\n
\r\nAnd to check:\r\n25 - 24 = 1 is the square of 5-4=1\r\nand\r\n25 + 24 = 49 is the square of 5+2=7.\n\nEdited on November 3, 2003, 12:42 pm',NULL,0);
INSERT INTO comment VALUES (9191,663,3172,'SilverKnight','re: Lost their marbles (full solution)','2003-11-03 12:54:39',0,'DJ, I think your full solution has 25-24 = 1, but \'1\' isn\'t an even square as the problem requires.',9190,0);
INSERT INTO comment VALUES (9192,663,1575,'DJ','re(2): Lost their marbles (full solution)','2003-11-03 13:36:30',0,'Why isn\'t 1 an even square? An even square is the square of an integer (you can figure out which ones work).',9191,0);
INSERT INTO comment VALUES (9193,663,3172,'SilverKnight','re(3): Lost their marbles (full solution)','2003-11-03 13:39:24',0,'um... I think you\'re trying to be difficult... or at best, you are stretching the intent of the problem. \'Even\' means evenly divisible by \'2\'.\r\n\r\nExamples of \'even squares\' are 0, 4, 16, 36, etc...\r\nExamples of \'odd squares\' are 1, 9, 25, 49, etc...',9192,0);
INSERT INTO comment VALUES (9194,663,1575,'DJ','re(4): Lost their marbles (full solution)','2003-11-03 13:45:04',0,'I don\'t think the problem means the square of an odd number. We are originally told only that the number of Jack\'s marbles is a square, and that x+y is still a square, and x-y is still an even (perfect) square. If you take the problem to mean only 0, 4, 16.., using the word \'still\' is out of a proverbial left field. \'Even\' in this case, I still think, is only intended to mean a perfect square.',9193,0);
INSERT INTO comment VALUES (9195,663,3172,'SilverKnight','re(5): Lost their marbles (full solution)','2003-11-03 13:48:01',0,'DJ, if Ravi intended to mean PERFECT, Ravi would have said perfect. What\'s more, Ravi would have included the word \'perfect\' (or \'even\') in the OTHER two references to a square number in the problem.\r\n\r\nAlso, EVERY number is a square (of something :-)\r\n\r\nThe reason he wrote \'even\' was to imply divisible by two.\n\nEdited on November 3, 2003, 1:49 pm',9194,0);
INSERT INTO comment VALUES (9196,663,1171,'nikki','Dead Horse','2003-11-03 15:09:02',0,'I\'m not trying to beat a dead horse, nor am I trying to spur on a debate, but I just wanted to say that when I first read this problem I took \"even square\" to mean \"perfect square\" just like DJ did.\r\n\r\nLater!',NULL,0);
INSERT INTO comment VALUES (9197,663,3172,'SilverKnight','re: Dead Horse','2003-11-03 15:24:42',0,'I agree that it could have been better worded, and I misunderstood the intent when I first read it too (as you can read in the comment listing)...\r\n\r\nbut (since you raised your head)... now that you\'ve had time to reread it... do you think \'even\' means \'opposed to odd\' or \'perfect\'?',9196,0);
INSERT INTO comment VALUES (9198,1234,3172,'SilverKnight','solution (first take)','2003-11-03 15:54:00',3,'Here\'s one solution... (but I doubt it\'s what DJ\'s looking for)\r\n\r\nAll the words can be transformed by replacing one of ANY of the three letters.\r\n\r\nFAT SAT FIT FAR\r\nOAK YAK ORK OAR\r\nLAX PAX LOX LAB\r\nSAT RAT SIT SAW\r\nDEN HEN DIN DEW\r\nSEA TEA SPA SET\r\nPIT NIT POT PIN\r\nLIT SIT LOT LIP',NULL,0);
INSERT INTO comment VALUES (9199,1234,4150,'c','Solution','2003-11-03 16:03:58',0,'They are airport codes',NULL,0);
INSERT INTO comment VALUES (9200,663,1575,'DJ','re(6): Lost their marbles (full solution)','2003-11-03 17:07:08',0,'That\'s a rather presumptuous statement, and I\'m still pretty sure that simply a perfect square was intended, whether it was intended or not. It is rather common to see usage such as an \'even integer,\' an \'even factor,\' or an \'even square\' intended not to mean divisible by two, but exact or precise.\r\n\r\nAs you put it so well, \"every number is a square (of something)\" and saying an \'even square\' in this case clarifies that a perfect square is what we are looking for.\r\n\r\nBased on the context, if Jack started with any square, and after giving Jill marbles he still had an even square, to say that it is still divisible by two would not make sense, since that wasn\'t a condition in the first place.\r\nBy your own logic, if he intended \'even\' to mean divisible by two, he would have included the word \'even\' in the OTHER two references to a square number in the problem.\r\nPerhaps, then, \'even\' isn\'t the best word to have used, but I think it was perfectly clear to everyone else what was intended.\r\n\r\nAnyway, I\'m done discussing it; Ravi can tell us what he meant, as opposed to your prematurely bold declaraion of what he did mean and would have said, since you would of course know his exact thoughts when writing the problem.',9195,0);
INSERT INTO comment VALUES (9201,663,3172,'SilverKnight','re(7): Lost their marbles (full solution)','2003-11-03 17:16:21',0,'Wow! DJ... don\'t take it so personally... And there was nothing presumptuous about it.\r\n\r\nIf Jack pics a number, of COURSE he started with a square.... Every number is a square :-). (But we already went through that.)\r\n\r\nAnd you simply didn\'t address the issue of why Ravi would have mentioned a \'perfect\' (or an \'even\') square only once in the three times he referenced a square. (This is my logic, not what you implied.)\r\n\r\nClearly... there is something different about the third time he referenced a square. You (presumptuously) assumed that the other two times he meant a square as well.... Why?!? Answer: because you presumptuously understood that \'a square\' meant a perfect square (as we all did).\r\n\r\nAgain, the difference of using \'even\' in the third reference meant something special. It limited it... not not being \'the lowest\' solution otherwise.\r\n\r\nBut no hard feelings here DJ... And I hope you\'re right, and Ravi intended even to mean \'integral\'.\r\n\r\nCheers!',9200,0);
INSERT INTO comment VALUES (9202,532,4153,'Sarah','a dissenting view','2003-11-03 18:07:13',0,'The belly button solution assumes that God does not have a navel, and that belly buttons came into existance only later on, when children were carried in utero. To my mind, there is no evidence to support this assumption. How do we know that God and, by extension, Adam and Eve, did not have navels? \r\n\r\nAnd that when Eve conceived her first child, the navel became the most convenient place for the umbilical cord to attach? \r\n\r\nPerhaps navels have their own purpose, independent of and predating the one they serve in utero. Certainly navels are pretty cute. At least, mine is. I recommend that we all gaze at ours and see if we can discern their true purpose. \r\n\r\nAll the paintings of Adam and Eve have navels.\r\n\r\nI, for one, refuse to accept this solution. I think the navel is divine. ',NULL,0);
INSERT INTO comment VALUES (9203,1234,3386,'Victor Zapana','re: Solution','2003-11-03 18:12:44',4,'elaborate plz im not airport language literate lol.',9199,0);
INSERT INTO comment VALUES (9204,1234,3172,'SilverKnight','re(2): Solution','2003-11-03 18:24:47',0,'I\'m sure \'c\' is correct....\r\n\r\nVictor, check out http://www.mapping.com/airportcodes.html',9203,0);
INSERT INTO comment VALUES (9205,663,1575,'DJ','Fuller Solution','2003-11-03 18:52:02',3,'First, I\'ll just restate what I determined in my previous post. Call the number of marbles Jack has x, and the number of Jill has is y. Since x is a square, let n be the square root of x. Also, x-y and x+y are perfect squares, so (n-a)² = x-y and (n+b)² = x+y for some integers a and b.\r\nWith some algebraic manipulation, I came up with two equations:\r\n\r\ny = 2na - a² = 2nb + b²\r\n\r\nand\r\n\r\nn = (a² + b²)/2(a-b)\r\n\r\nand of course,\r\n\r\nx = n²\r\n\r\nWhenever the values for a and b give an integer n, the resulting values of x and y are a solution to the problem. I also showed that a and b must both be even and 0 < b < a. It is not necessary that b < a < n, but whenever a is greater than n, you have a repeated solution (for example, a=4, b=2 and a=6, b=2 give the same result, with n=2 and n=-2 respectively).\r\n\r\nAll that being said, I wrote the following small javascript to find all valid solutions. I checked all values 0 < b < a < 30, and eliminated repeated values (there were six altogether) by specifying that n>a. The smallest answer is the one that I previously said was the simplest.\r\nFor the sake of argument, the smallest \'even\' (divisible by two) result is just double the simplest result (Jack and Jill each have four times as many marbles).\r\n\r\nHere\'s the program:\r\nfunction isInt(x) {\r\n return (x == Math.round(x));\r\n}\r\n\r\nfor (var b=1; b<30; b++) {\r\n for (var a=b+1; a<30; a++) {\r\n var n = (a*a+b*b)/(2*a-2*b);\r\n var x = n*n;\r\n var y = 2*n*a - a*a; // = 2*n*b + b*b;\r\n if (isInt(n) && n>a) {\r\n document.write(\"x = \" + x + \" = \" +n + \"²<br>\");\r\n document.write(\"y = \" + y + \"<br>\");\r\n document.write(\"x - y = \" + (x-y) + \" = \" + (n-a) + \"²<br>\");\r\n document.write(\"x + y = \" + (x+y) + \" = \" + (n+b) + \"²<br>\");\r\n document.write(\"[ a=\" + a + \"; b=\" + b + \"; n=\" + n + \" ]<p>\");\r\n }\r\n }\r\n}\r\n\r\n\r\nAnd the output:\r\n\r\nx = 25 = 5²\r\ny = 24\r\nx - y = 1 = 1²\r\nx + y = 49 = 7²\r\n[ a=4; b=2; n=5 ]\r\n\r\nx = 169 = 13²\r\ny = 120\r\nx - y = 49 = 7²\r\nx + y = 289 = 17²\r\n[ a=6; b=4; n=13 ]\r\n\r\nx = 100 = 10²\r\ny = 96\r\nx - y = 4 = 2²\r\nx + y = 196 = 14²\r\n[ a=8; b=4; n=10 ]\r\n\r\nx = 625 = 25²\r\ny = 336\r\nx - y = 289 = 17²\r\nx + y = 961 = 31²\r\n[ a=8; b=6; n=25 ]\r\n\r\nx = 289 = 17²\r\ny = 240\r\nx - y = 49 = 7²\r\nx + y = 529 = 23²\r\n[ a=10; b=6; n=17 ]\r\n\r\nx = 225 = 15²\r\ny = 216\r\nx - y = 9 = 3²\r\nx + y = 441 = 21²\r\n[ a=12; b=6; n=15 ]\r\n\r\nx = 1681 = 41²\r\ny = 720\r\nx - y = 961 = 31²\r\nx + y = 2401 = 49²\r\n[ a=10; b=8; n=41 ]\r\n\r\nx = 676 = 26²\r\ny = 480\r\nx - y = 196 = 14²\r\nx + y = 1156 = 34²\r\n[ a=12; b=8; n=26 ]\r\n\r\nx = 400 = 20²\r\ny = 384\r\nx - y = 16 = 4²\r\nx + y = 784 = 28²\r\n[ a=16; b=8; n=20 ]\r\n\r\nx = 3721 = 61²\r\ny = 1320\r\nx - y = 2401 = 49²\r\nx + y = 5041 = 71²\r\n[ a=12; b=10; n=61 ]\r\n\r\nx = 1369 = 37²\r\ny = 840\r\nx - y = 529 = 23²\r\nx + y = 2209 = 47²\r\n[ a=14; b=10; n=37 ]\r\n\r\nx = 625 = 25²\r\ny = 600\r\nx - y = 25 = 5²\r\nx + y = 1225 = 35²\r\n[ a=20; b=10; n=25 ]\r\n\r\nx = 7225 = 85²\r\ny = 2184\r\nx - y = 5041 = 71²\r\nx + y = 9409 = 97²\r\n[ a=14; b=12; n=85 ]\r\n\r\nx = 2500 = 50²\r\ny = 1344\r\nx - y = 1156 = 34²\r\nx + y = 3844 = 62²\r\n[ a=16; b=12; n=50 ]\r\n\r\nx = 1521 = 39²\r\ny = 1080\r\nx - y = 441 = 21²\r\nx + y = 2601 = 51²\r\n[ a=18; b=12; n=39 ]\r\n\r\nx = 1156 = 34²\r\ny = 960\r\nx - y = 196 = 14²\r\nx + y = 2116 = 46²\r\n[ a=20; b=12; n=34 ]\r\n\r\nx = 900 = 30²\r\ny = 864\r\nx - y = 36 = 6²\r\nx + y = 1764 = 42²\r\n[ a=24; b=12; n=30 ]\r\n\r\nx = 841 = 29²\r\ny = 840\r\nx - y = 1 = 1²\r\nx + y = 1681 = 41²\r\n[ a=28; b=12; n=29 ]\r\n\r\nx = 12769 = 113²\r\ny = 3360\r\nx - y = 9409 = 97²\r\nx + y = 16129 = 127²\r\n[ a=16; b=14; n=113 ]\r\n\r\nx = 4225 = 65²\r\ny = 2016\r\nx - y = 2209 = 47²\r\nx + y = 6241 = 79²\r\n[ a=18; b=14; n=65 ]\r\n\r\nx = 1225 = 35²\r\ny = 1176\r\nx - y = 49 = 7²\r\nx + y = 2401 = 49²\r\n[ a=28; b=14; n=35 ]\r\n\r\nx = 21025 = 145²\r\ny = 4896\r\nx - y = 16129 = 127²\r\nx + y = 25921 = 161²\r\n[ a=18; b=16; n=145 ]\r\n\r\nx = 6724 = 82²\r\ny = 2880\r\nx - y = 3844 = 62²\r\nx + y = 9604 = 98²\r\n[ a=20; b=16; n=82 ]\r\n\r\nx = 2704 = 52²\r\ny = 1920\r\nx - y = 784 = 28²\r\nx + y = 4624 = 68²\r\n[ a=24; b=16; n=52 ]\r\n\r\nx = 32761 = 181²\r\ny = 6840\r\nx - y = 25921 = 161²\r\nx + y = 39601 = 199²\r\n[ a=20; b=18; n=181 ]\r\n\r\nx = 10201 = 101²\r\ny = 3960\r\nx - y = 6241 = 79²\r\nx + y = 14161 = 119²\r\n[ a=22; b=18; n=101 ]\r\n\r\nx = 5625 = 75²\r\ny = 3024\r\nx - y = 2601 = 51²\r\nx + y = 8649 = 93²\r\n[ a=24; b=18; n=75 ]\r\n\r\nx = 48841 = 221²\r\ny = 9240\r\nx - y = 39601 = 199²\r\nx + y = 58081 = 241²\r\n[ a=22; b=20; n=221 ]\r\n\r\nx = 14884 = 122²\r\ny = 5280\r\nx - y = 9604 = 98²\r\nx + y = 20164 = 142²\r\n[ a=24; b=20; n=122 ]\r\n\r\nx = 5476 = 74²\r\ny = 3360\r\nx - y = 2116 = 46²\r\nx + y = 8836 = 94²\r\n[ a=28; b=20; n=74 ]\r\n\r\nx = 70225 = 265²\r\ny = 12144\r\nx - y = 58081 = 241²\r\nx + y = 82369 = 287²\r\n[ a=24; b=22; n=265 ]\r\n\r\nx = 21025 = 145²\r\ny = 6864\r\nx - y = 14161 = 119²\r\nx + y = 27889 = 167²\r\n[ a=26; b=22; n=145 ]\r\n\r\nx = 97969 = 313²\r\ny = 15600\r\nx - y = 82369 = 287²\r\nx + y = 113569 = 337²\r\n[ a=26; b=24; n=313 ]\r\n\r\nx = 28900 = 170²\r\ny = 8736\r\nx - y = 20164 = 142²\r\nx + y = 37636 = 194²\r\n[ a=28; b=24; n=170 ]\r\n\r\nx = 133225 = 365²\r\ny = 19656\r\nx - y = 113569 = 337²\r\nx + y = 152881 = 391²\r\n[ a=28; b=26; n=365 ]\r\n\r\n\r\nJust for kicks, changing the n>a to n<=a gives the negative values:\r\n\r\n\r\n1 25 49 24\r\n4 100 196 96\r\n49 169 289 120\r\n9 225 441 216\r\n49 289 529 240\r\n16 400 784 384\r\n289 625 961 336\r\n25 625 1225 600\r\n196 676 1156 480\r\n1 841 1681 840\r\n36 900 1764 864\r\n196 1156 2116 960\r\n49 1225 2401 1176\r\n529 1369 2209 840\r\n441 1521 2601 1080\r\n64 1600 3136 1536\r\n961 1681 2401 720\r\n81 2025 3969 1944\r\n1156 2500 3844 1344\r\n100 2500 4900 2400\r\n441 2601 4761 2160\r\n784 2704 4624 1920\r\n289 2809 5329 2520\r\n121 3025 5929 2904\r\n4 3364 6724 3360\r\n144 3600 7056 3456\r\n2401 3721 5041 1320\r\n2209 4225 6241 2016\r\n1225 4225 7225 3000\r\n529 4225 7921 3696\r\n169 4225 8281 4056\r\n784 4624 8464 3840\r\n196 4900 9604 4704\r\n49 5329 10609 5280\r\n2116 5476 8836 3360\r\n2601 5625 8649 3024\r\n225 5625 11025 5400\r\n1764 6084 10404 4320\r\n256 6400 12544 6144\r\n3844 6724 9604 2880\r\n5041 7225 9409 2184\r\n1681 7225 12769 5544\r\n1225 7225 13225 6000\r\n289 7225 14161 6936\r\n9 7569 15129 7560\r\n1681 7921 14161 6240\r\n324 8100 15876 7776\r\n2401 8281 14161 5880\r\n361 9025 17689 8664\r\n49 9409 18769 9360\r\n4624 10000 15376 5376\r\n400 10000 19600 9600\r\n6241 10201 14161 3960\r\n1764 10404 19044 8640\r\n3136 10816 18496 7680\r\n441 11025 21609 10584\r\n1156 11236 21316 10080\r\n961 11881 22801 10920\r\n484 12100 23716 11616\r\n4761 12321 19881 7560\r\n9409 12769 16129 3360\r\n529 13225 25921 12696\r\n16 13456 26896 13440\r\n3969 13689 23409 9720\r\n2401 14161 25921 11760\r\n576 14400 28224 13824\r\n9604 14884 20164 5280\r\n8649 15129 21609 6480\r\n7225 15625 24025 8400\r\n5329 15625 25921 10296\r\n625 15625 30625 15000\r\n8836 16900 24964 8064\r\n4900 16900 28900 12000\r\n2116 16900 31684 14784\r\n676 16900 33124 16224\r\n729 18225 35721 17496\r\n3136 18496 33856 15360\r\n289 18769 37249 18480\r\n784 19600 38416 18816\r\n5929 20449 34969 14520\r\n16129 21025 25921 4896\r\n14161 21025 27889 6864\r\n841 21025 41209 20184\r\n25 21025 42025 21000\r\n196 21316 42436 21120\r\n8464 21904 35344 13440\r\n7921 22201 36481 14280\r\n10404 22500 34596 12096\r\n900 22500 44100 21600\r\n3969 23409 42849 19440\r\n961 24025 47089 23064\r\n7056 24336 41616 17280\r\n2209 24649 47089 22440\r\n2601 25281 47961 22680\r\n1024 25600 50176 24576\r\n15376 26896 38416 11520\r\n1089 27225 53361 26136\r\n8281 28561 48841 20280\r\n1 28561 57121 28560\r\n20164 28900 37636 8736\r\n6724 28900 51076 22176\r\n4900 28900 52900 24000\r\n1156 28900 56644 27744\r\n12769 29929 47089 17160\r\n36 30276 60516 30240\r\n14161 30625 47089 16464\r\n1225 30625 60025 29400\r\n6724 31684 56644 24960\r\n1296 32400 63504 31104\r\n25921 32761 39601 6840\r\n9604 33124 56644 23520\r\n21609 33489 45369 11880\r\n14161 34225 54289 20064\r\n13225 34225 55225 21000\r\n2401 34225 66049 31824\r\n1369 34225 67081 32856\r\n5929 34969 64009 29040\r\n1444 36100 70756 34656\r\n5329 37249 69169 31920\r\n196 37636 75076 37440\r\n
\r\n........\r\nThe program:\r\nDEFDBL A-Z\r\nDO\r\n n = n + 1\r\n nsq = n * n\r\n FOR i = 1 TO nsq\r\n tr = nsq - i\r\n trl = INT(SQR(tr) + .5)\r\n IF trl * trl = tr THEN\r\n tr = nsq + i\r\n trl = INT(SQR(tr) + .5)\r\n IF trl * trl = tr THEN\r\n PRINT nsq - i, nsq, nsq + i, i\r\n ct = ct + 1\r\n IF ct MOD 40 = 0 THEN DO: LOOP UNTIL INKEY$ > \"\"\r\n END IF\r\n END IF\r\n NEXT\r\nLOOP\r\n\r\n\r\n',9205,0);
INSERT INTO comment VALUES (9214,1344,1301,'Charlie','re(2): Brute Force','2003-11-03 23:18:07',0,'I\'d say probably 3/4 of all lit configurations are impossible. To test a given configuration, go through the \"Chase the lights down\" technique given by Lee in the \"real-world method\" comment. Then, if the bottom row does not match one of the configurations on the left of the diagram:\r\n\r\n\r\nx---x............cc--- \r\n-x-x-............c--c- \r\nxxx--............-c--- \r\n--xxx............---c- \r\nx-xx-............----c \r\n-xx-x............c---- \r\nxx-xx............--c-- \r\n
\r\nthen the layout is impossible to solve.\r\n\r\nIf it is one of those, then as Lee says, click as shown in the pattern on the right, on the top row, and again chase the lights down.\r\n\r\nNote that 8 of the possible bottom rows are accounted for: the 7 shown plus the all out configuration which is already solved without further punching, that\'s 8 out of the 2^5=32 possibilities, or 25%.\r\n',9206,0);
INSERT INTO comment VALUES (9215,1344,1301,'Charlie','re(3): Brute Force','2003-11-04 00:39:10',0,'Looked at another way, any configuration that has a solution also has a solution based on exclusively ORing it with any one of three null configurations of clicks.\r\n\r\nThe following are shown in part of the solution description, off of the main URL for this puzzle . Clicking on any of these three sets has no net effect on the lights:\r\n\r\n\r\nc-c-c....cc-cc....-ccc-\r\nc-c-c....-----....c-c-c\r\n-----....cc-cc....cc-cc\r\nc-c-c....-----....c-c-c\r\nc-c-c....cc-cc....-ccc-\r\n
\r\nNote that each is the exclusive OR of the other two.\r\n\r\nSo for example, the first (leftmost) transformation shown above, applied to the first solution in my Brute Force post, produces the third solution shown in that post. The second (middle) transformation turns my first solution into my fourth solution, and the last (rightmost) transformation converts my first into my second solution. (By exclusively oring and considering the c\'s as 1\'s)\r\n\r\nThese null transformations will convert any set of clicks into an equivalent but different set, so indeed only 1/4 of the states are attainable.',9214,0);
INSERT INTO comment VALUES (9216,663,3224,'Lee','Ravi Triples','2003-11-04 00:53:02',0,'Jack\'s marbles , x, is a square a^2 (for some a)\r\nJacks + Jill\'s marbles , (x+y), is a square b2 (for some b)\r\nJack\'s less Jill\'s marbles , (x-y), is a square c^2 (for some c)\r\nSo Jack\'s marbles is the average of the two extremes\r\nb^2 + c^2 = 2.a^2.\r\nWe require integers a,b,c that satisfy this equation (although in this specific problem there is the concensus that c^2 needs to be even)\r\n...................................................\r\nNow, consider a Pythagorean triple (ascending)\r\n(x, y, z)..........such that x^2 + y^2 = z^2\r\nsince x, y, z all integers then (y+x) is an integer and (y-x) is an integer\r\nlet (y+x) = a\r\nand (y-x) = b\r\nMultiply Pytha\' triple through by 2\r\n2.x^2 + 2.y^2 = 2.z^2\r\nRecognize the LHS can be written (y+x)^2 + (y-x)^2\r\n(y+x)^2 + (y-x)^2 = 2.z^2\r\nsubstitute a,b\r\na^2 + b^2 = 2.z^2 (a,b,z all integers)\r\nSo to generate a Ravi Triple (from a pythagorean);\r\nPythagorean triple (x y z)\r\nRavi triple ((y-x) (y+x) z)\r\nSo, for the smallest non trivial, unique Pyth\' triple,\r\n(3,4,5)\r\nwe get the corresponding unique Ravi triple \r\n(1,7,5)\r\nand Jack originally has 5^2 (25) marbles.\r\nObviously multiples of ravi triples also work so if the smallest square needs to be even we get\r\n(2,14,10)\r\nand Jack originally has 10^2 (100) marbles.\r\nI\'m not going to show how to generate Pythogorean triples. Suffice it to say they can be generated without trial and error and generators are all over the web like a rash. I just thought the link between the two types of equations was of interest.\r\n ',NULL,0);
INSERT INTO comment VALUES (9217,1458,4161,'Scott G','solution maybe--> light','2003-11-04 02:15:35',0,'A focused beam of light(lazer or magnifying glass and sunlight) aimed at the base where the filter touches the foundation, burn a small portion away and gravity topples it(took me about 6 minutes to do it) assuming this object is not located in a vacum, but if it is just increase the intensity of the beam and it will fall.',NULL,0);
INSERT INTO comment VALUES (9218,334,4163,'didi','This is ezee','2003-11-04 06:33:36',0,'it\'s ( s ) :)',NULL,0);
INSERT INTO comment VALUES (9219,288,3136,'Popstar Dave','Better question.','2003-11-04 07:31:09',0,'Here\'s one that features each letter, only once!\r\n\r\nNew job: fix Mr. Gluck\'s hazy TV, PDQ!',NULL,0);
INSERT INTO comment VALUES (9220,1234,3136,'Popstar Dave','re(3): Solution','2003-11-04 07:36:41',0,'Wow... that\'s impressive, but I\'m kinda confused. It doesn\'t have all the big, capital city airports (excecpt for Perth). There\'s no: Sydney, Melbourne, Brisbane, Adelaide, Hobart, Darwin and Canberra. Hmmmm...',9211,0);
INSERT INTO comment VALUES (9221,1234,1301,'Charlie','re(4): Solution','2003-11-04 10:31:44',0,'Of the codes for these cities:\r\nADL ADELAIDE Australia\r\nBNE BRISBANE INTL Australia\r\nCBR CANBERRA Australia\r\nDRW DARWIN Australia\r\nHBA HOBART Australia\r\nKAH MELBOURNE CITY HLPT Australia\r\nLBH SYDNEY PALM BEACH Australia\r\nMEB MELBOURNE ESSENDON Australia\r\nMEL MELBOURNE TULAMARINE Australia\r\nRSE SYDNEY ROSE BAY Australia\r\nSYD SYDNEY KINGSFORD Australia\r\nTAN TANGALOOMA BRISBANE Australia\r\n\r\nonly the last is an english language word. That last was on the list previously given.',9220,0);
INSERT INTO comment VALUES (9222,1343,3172,'SilverKnight','solution','2003-11-04 10:35:53',3,'B) A bomb in a bull\r\n\r\nand\r\n\r\nD) No bull\r\n\r\nCute :-)\n\nEdited on November 4, 2003, 10:36 am',NULL,0);
INSERT INTO comment VALUES (9223,1343,3386,'Victor Zapana','re: solution','2003-11-04 10:45:55',0,'I believe what SilverKnight is right. but lemme give u my \"out of the box\" answers.
\r\nThis is a system of three equations with three unknowns:\r\nLet f be the father, s be the son, g be the grandson.\r\nf+g+s=100\r\n7g=s\r\n12g=f',NULL,0);
INSERT INTO comment VALUES (9232,1496,2121,'Chaz','re: Loser','2003-11-04 19:05:59',0,'I agree with charlie from flowers for algernon',9160,0);
INSERT INTO comment VALUES (9233,1341,2121,'Chaz','Infinite - infinite','2003-11-04 19:17:00',0,'This is actually a number of paradoxes. If you did it an infite amount of times, but removed inf./10 each time, then I guess it would be infinite.',NULL,0);
INSERT INTO comment VALUES (9234,1489,2121,'Chaz','Anomolie?','2003-11-04 19:22:21',0,'I like poop.',NULL,0);
INSERT INTO comment VALUES (9235,1479,1413,'dave domingo','Solution?','2003-11-04 21:34:04',0,'All have appeared in movies based on Ian Fleming stories: Van Dyke in \"Chitty Chitty Bang Bang,\" Connery in the James Bond series, and Niven, Sellers and Allen in \"Casino Royale,\" based VERY loosely on one of the James Bond novels. It is accurate to say that four of the five have played James Bond. In \"Casino Royale,\" Niven is the real Bond, Sellers is an expert gambler recruited to take on the identity of Bond, and Allen is Bond\'s nephew Jimmy Bond.',NULL,0);
INSERT INTO comment VALUES (9236,1489,3623,'jaypee','how many days in a month','2003-11-04 21:39:26',0,'how many days are you talking about in a month.\r\nIf you are talking both days and months for the \r\ngrandsons age, then there must be a specific number of days in a month in mind.',NULL,0);
INSERT INTO comment VALUES (9237,1489,3224,'Lee','Solution','2003-11-05 00:05:41',0,'\"My son is as many weeks as my grandson is in days\"\r\nor, The son is seven times older than the grandson\r\n\"My grandson is as many months old as I am in years\"\r\nor, The (grand)Father is twelve times older than the grandson.\r\nLet the age of the grandon be x\r\nSon is 7x\r\nFather is 12x\r\nTotal age is 100 years\r\n12x + 7x + x = 100\r\nx=5\r\nGrandson is 5\r\nSon is 35\r\n(grand)Father is 60',NULL,0);
INSERT INTO comment VALUES (9238,643,3224,'Lee','my take','2003-11-05 00:57:52',0,'Let the probability of a boy being picked when a girl is added to the nursery as x.\r\nAdding a boy to the nursery increases the chance of a boy being picked by 50% (from 2 in whatever, to 3 in whatever) hence \r\nThe probability of a boy being picked when a boy is added is 3x/2.\r\nA boy was picked - that\'s a certainty - so the probabilities sum to 1,\r\n\r\nx + 3x/2 = 1\r\nx=2/5\r\n\r\nIt follows that in general, the probability,x, a girl was added to a nursey, given a random selection is a boy can be found with\r\n(n+1)/n = (1-x)/x\r\nwhere n is the original number of boys. \r\n',NULL,0);
INSERT INTO comment VALUES (9239,1343,3196,'Dan','Wordplay','2003-11-05 02:15:10',0,'\"What word would best describe the situation now?\"\r\nB) Abominable (\"a bomb in a bull\")\r\n\r\nWhat word would best describe the situation after the bomb has gone off?\r\nD) Noble (\"no bull\")\r\n\r\n \r\n',NULL,0);
INSERT INTO comment VALUES (9240,1343,1183,'fwaff','re(2): solution','2003-11-05 02:56:19',0,'On the same theme, the message to the bomb disposal squad said.....\r\n\r\nComfortable\r\n\r\nbut alas they were too late.',9224,0);
INSERT INTO comment VALUES (9241,1335,3196,'Dan','Lets do lunch','2003-11-05 04:00:37',3,'Let X be the distance in miles between the houses of A and B. After A walks X-1 miles, B starts out. At this time they are a mile apart. Since B walks twice as fast as A, they meet when they are 2/3 mile from B\'s house. A now begins a journey of X-2/3 miles back to her house, and B walks 2/3 mile to his house, picks up his food very quickly, and commences to walk X miles to A\'s house, a total distancce of X+2/3 miles. (Let\'s say the time required for A to \"pick up his food\" is negligible). Since B walks twice as fast as A, and A and B arrive at A\'s house simultaneously, it must be true that B was required to walk twice as far as A on this last leg. \r\n2*(X-2/3)=X+2/3\r\nX=2 miles\r\nThey live two miles apart. ',NULL,0);
INSERT INTO comment VALUES (9242,649,4178,'Prab','Solution','2003-11-05 09:07:55',0,'Let A be the event that the first marble drawn is black, B denote the event that the second marble drawn is black. Also let C denote the event that the bag chosen for the drawing is the one with 3 black and 1 white marbles and D denote the event that the bag chosen is the other one with 1 black and 3 white marbles.\r\n\r\nWe need to find the conditional probability of B given A, denoted P(B|A) which is P(A and B)/P(A).\r\n\r\nNow P(A and B)= P(A and B and C) + P(A and B and D) since C and D are exclusive and exhaustive.\r\n\r\nP(A and B and C) = P(A and B | C).P(C) = (3/4).(3/4).(1/2) = 9/32.\r\n\r\nP(A and B and D) = P(A and B | D).P(D) = (1/4).(1/4).(1/2) = 1/32\r\n\r\nSo P(A and B) = (9/32)+(1/32)=(10/32)=(5/16)\r\n\r\nSimiliarly, P(A) = P(A and C) + P(A and D)\r\nP(A and C) = P(A | C).P(C)=(3/4).(1/2)=(3/8)\r\nP(A and D) = P(A | D).P(D)=(1/4).(1/2)=(1/8)\r\n\r\nSO P(A)=(3/8)+(1/8)=(4/8)=(1/2).\r\n\r\nThus, the required probability\r\n\r\nP(B|A) =(5/16)/(1/2)=(5/16).(2)=(5/8)\r\n',NULL,0);
INSERT INTO comment VALUES (9243,658,3172,'SilverKnight','first thoughts','2003-11-05 09:40:44',1,'Well... as long as it\'s a power of two, we can do a \'binary search\' by doing half at a time.\r\n\r\nIn other words, if it were up to 128 (2^7), then we can test 64, then 32 (in which group has the poison), then 16 (in which group has the poison), etc.... and identify the poison in 7 tests.\r\n\r\nBut if we have 129 or more (up to 2^8=256), then it may take up to 8 tests.\r\n\r\nSo, it occurs to me, that we don\'t change the maximum, if that is the number of glasses of wine.\r\n______________\r\n\r\nBut if there were more than 129, then you would want to be more useful that checking just one (you\'d check n-128)... since then you have to potentially binary search either group\r\n\r\nSo, to ensure that you\'re not going past the maximum, the number of glasses must be 129.\n\nEdited on November 5, 2003, 9:41 am',NULL,0);
INSERT INTO comment VALUES (9244,658,3224,'Lee','darn you SK','2003-11-05 09:47:22',0,'I read the puzzle (0 comments).\r\nI scribble on paper.\r\nI go to post my answer (1 comment)\r\nTell me it\'s not true!!....\r\n\'SilverKnight\'',NULL,0);
INSERT INTO comment VALUES (9245,658,3275,'retiarius','Solution','2003-11-05 09:53:28',0,'I agree.\r\n\r\nBetween 100 and 128 glasses could take 7 tests.\r\nBetween 129 and 200 glasses could take 8 tests.\r\nBewteen 130 and 200 glasses could still take 8 tests after 1 has been tested.\r\n129 is the answer.',NULL,0);
INSERT INTO comment VALUES (9246,658,3136,'Popstar Dave','What REALLY happened.','2003-11-05 09:55:09',1,'\"The POLICE COMMISSIONER desired...\"\r\n\r\nWe don\'t know what the mathematician wanted to do.\r\n\r\nAs a gambling man, I think the mathematician wanted to find out what glass had the poison in it, chuck it out, invite three of his friends \'round to drink the 128 glasses of wine that were left and play poker. \r\n\r\nFor the record, I got the same solution as SK, but he beat me to posting it by a few mintues. So I decided to post what I thought might REALLY happen!',NULL,0);
INSERT INTO comment VALUES (9247,658,3196,'Dan','I will drink to this solution','2003-11-05 12:50:45',3,'There were 129 glasses.\r\n \r\nThe logical way to proceed in a case like this is a binary test, and that will be minimized if the number of glasses is a power of 2: progressively dividing the glasses into 2 groups and testing one of the groups. The only power of 2 between 100 and 200 is 128. So there must have been 129 glasses, so that testing one glass at random would leave 128 glasses - a power of 2, which would minimize the tests.',NULL,0);
INSERT INTO comment VALUES (9248,1458,4176,'Joe C','hmm or','2003-11-05 13:50:39',0,'put it on a trap door',NULL,0);
INSERT INTO comment VALUES (9249,1227,4176,'Joe C','um','2003-11-05 13:54:08',0,'hmm\r\nyou said complete game\r\nnvm i was just thinking it a winning game',NULL,0);
INSERT INTO comment VALUES (9250,42,4176,'Joe C','hmm','2003-11-05 14:13:39',1,'i would have said buy all the packs to make sure∞',NULL,0);
INSERT INTO comment VALUES (9251,1341,4176,'Joe C','solution','2003-11-05 14:29:22',3,'0 marbles\r\n30 + 15 + 7.5 + 3.25 + 1.625 + .8125 + .40625 + .203125 + .1015625 = less than a minute\r\nand you alrady took 1 out',NULL,0);
INSERT INTO comment VALUES (9252,1228,3372,'Sam','Quick partial answer','2003-11-05 14:40:43',1,'Well, in the first case the only way you could form a triangle would be to pick the 2, 3 and 4 inch sticks. The probability of this is \r\n(3/5) * (2/4) * (1/3) = 0.1\r\n\r\nThe next part... well let me think about it for a couple minutes.',NULL,0);
INSERT INTO comment VALUES (9253,1228,1301,'Charlie','re: Quick partial answer','2003-11-05 14:45:12',0,'There is also 2, 4 and 5 as well as 3, 4 and 5. Out of the 10 ways that three sticks could be picked, that leaves a probability of 3/10 = .3.',9252,0);
INSERT INTO comment VALUES (9254,1228,3172,'SilverKnight','re(2): Quick partial answer','2003-11-05 14:52:49',0,'2, 3, and 4\r\n2, 3, and 5\r\n3, 4, and 5\r\n\r\nall produce triangles...\r\n\r\nThere are 5x4x3 = 60 different Ordered possibilities. \r\nTaken 3 at a time (6 orderings each...) leaves 10 distinct possibilities\r\n\r\nFor completion, the 7 distinct orderings that DON\'T produce triangles are:\r\n1, 2, 3\r\n1, 2, 4\r\n1, 2, 5\r\n1, 3, 4\r\n1, 3, 5\r\n1, 4, 5\r\n2, 3, 5\r\n\r\nSo, Charlie is correct 3/10 = .3',9253,0);
INSERT INTO comment VALUES (9255,1228,1301,'Charlie','Second Part','2003-11-05 15:30:46',3,'The following program produces two answers (one not asked): the probability that any triangle would be formed from a random selection from 20 sticks, and the probability that a right triangle would be formed (as asked):\r\n\r\nn = 20\r\nPRINT\r\nFOR i = 1 TO n - 2\r\n FOR j = i + 1 TO n - 1\r\n FOR k = j + 1 TO n\r\n tot = tot + 1\r\n IF k < i + j THEN\r\n suc = suc + 1\r\n IF i * i + j * j = k * k THEN\r\n suc2 = suc2 + 1\r\n PRINT STR$(i) + STR$(j) + STR$(k)\r\n END IF\r\n END IF\r\n NEXT\r\n NEXT\r\nNEXT\r\nPRINT\r\n\r\nPRINT USING \\\"### ### #### #.####### #.#######\\\"; suc; suc2; tot; suc / tot; suc2 / tot\r\n\r\nIts output,\r\n 3 4 5\r\n 5 12 13\r\n 6 8 10\r\n 8 15 17\r\n 9 12 15\r\n 12 16 20\r\n\r\n525 6 1140 0.4605263 0.0052632\r\n\r\nshows the 6 possibilities for forming a right triangle, out of the 1140 possible combinations of sticks that could be produced, giving a probability of .0052632 that a right triangle could be formed.\r\n\r\nAs for the unasked question, 525 out of the 1140 combinations could form \r\n 0 0 0 0 0\r\n 1 1 1 1 1\r\n 1 0 0 0 1\r\n 1 1 1 1 1\r\n 0 0 0 0 0\r\n\r\n 0 1 1 1 0\r\n 0 1 0 1 0\r\n 0 1 0 1 0\r\n 0 1 0 1 0\r\n 0 1 1 1 0\r\n\r\n 1 0 1 0 1\r\n 0 1 0 1 0\r\n 1 0 0 0 1\r\n 0 1 0 1 0\r\n 1 0 1 0 1\r\n\r\n 1 1 0 1 1\r\n 1 1 1 1 1\r\n 0 1 0 1 0\r\n 1 1 1 1 1\r\n 1 1 0 1 1\r\n
\r\n-----------\r\nwhere a 1 means to flip the switch and a zero means not to.\r\n\r\nThese results can also be produced by the program listed in Brute Force modified to start with all the lights lit except the center, rather than the negative of that.\r\n',9284,0);
INSERT INTO comment VALUES (9292,1496,4189,'John','re: W00t','2003-11-06 17:59:32',0,'You are incorrect about Alan and Bob losing money. The bar owners can take the $10 local currency and go change it in at the banks for $11.11 in foreign currency. They are only giving back $10 foreign in change, meaning they are \"keeping\" $1.11 foreign (which =$1 local) for each beverage. The bar owners break even, period.\r\n\r\nIt is then the banks (i.e. the governments who guarantee the banks\' solvency) who end up holding the bag because they have assigned an artificial (i.e. non-market) value to the other country\'s currency.',9275,0);
INSERT INTO comment VALUES (9293,1488,3558,'Tristan','re: solution','2003-11-06 18:29:06',0,'Eschew obfuscation',9278,0);
INSERT INTO comment VALUES (9294,1345,1626,'Gamer','Hint:','2003-11-06 19:36:33',2,'Since nobody has even attempted a solution, I will give a hint as to the answer here:\r\n\r\nAs with another such logic problem, The White Suspenders, the first clue is a big one. There is only one set of \"Cost pairs\" that fits this clue. You won\'t know who spent what (except for Diane), but you will be able to use these cost pairs eventually to narrow down who bought what.',NULL,0);
INSERT INTO comment VALUES (9295,1496,1301,'Charlie','re(2): W00t','2003-11-06 19:41:35',0,'But Alan and Bob had originally given a full $10 worth of drinks in order to get the bills that they are now using as mere $9 worth of change, if they were already in their possession at the time of the rate changes.',9292,0);
INSERT INTO comment VALUES (9296,1345,3558,'Tristan','re: Hint:','2003-11-06 20:00:09',1,'Well, I\'m trying to figure out the only cost pair that works and this is what I got. The lowest amount spent possible is 50 because no one got the same two colors and two people tied. I am assuming that no one got two of the same color, thought it is not completely clear in the wording. 60 is also possible for 2 people, as well as 70. 80 and 90 are not, but Diane could possibly have spent that much. This still leaves plenty possibilities.\r\n\r\nTo try to narrow it down, I take into account number 3. Diane\'s possible combinations so far are:\r\n50+40\r\n50+30\r\n50+20\r\n40+30\r\nIn the last two, the other four people are forced to have the following:\r\n10+40\r\n20+30\r\n10+50\r\n20+40\r\nIt looks like this doesn\'t really narrow down the possibilities, even considering that Carol, someone besides Emily, bought a 40 dollar shirt. If Diane spent 80 or 90, there would be even more possibilities for the other four.\r\n\r\nI\'m still failing to figure out this problem, but I was sort of doing all this work while I typed, so maybe I just need to think on it more.',9294,0);
INSERT INTO comment VALUES (9297,1345,3386,'Victor Zapana','Solution with no proof lol','2003-11-06 20:05:33',0,'Someone prove this coz im too lazy to right out mine :P \r\nrgybo\r\ngrrbg\r\nboboy\r\n 60 60 50 90 50 \r\n\r\nrygbo\r\nrryby\r\nbobog\r\n 50 60 60 90 50 \r\n\r\nrygbo\r\nyrrby\r\nbobog\r\n 60 60 50 90 50 \r\n\r\nyorbg\r\nyoory\r\nbrbbg\r\n 50 50 60 70 60 \r\n\r\nyrgbo\r\ngrybr\r\nbobog\r\n 70 70 50 90 50 \r\n\r\nyrobg\r\nyrroy\r\nbobbg\r\n 50 50 60 70 60 \r\n\r\nyrobg\r\nyryor\r\ngobgb\r\n 60 50 50 80 60 \r\n\r\nyrobg\r\nrryoy\r\nbobbg\r\n 60 50 50 70 60 \r\n\r\ngorby\r\ngoorg\r\nbrbby\r\n 50 50 60 70 60 \r\n\r\ngrbyo\r\ngrbyr\r\nyoyob\r\n 50 70 70 90 50 \r\n\r\ngrbyo\r\nrrbbg\r\nboyoy\r\n 50 70 70 80 50 \r\n\r\ngroby\r\ngrrog\r\nbobby\r\n 50 50 60 70 60 \r\n\r\ngrybo\r\ngrybr\r\nboboy\r\n 50 70 70 90 50 \r\n\r\ngrybo\r\nrryyg\r\nyobob\r\n 50 70 70 80 50 \r\n\r\nogybr\r\ngoobg\r\nbrbry\r\n 60 60 50 90 50 \r\n\r\nogybr\r\nygobg\r\nbrbry\r\n 70 70 50 90 50 \r\n\r\norgby\r\ngrobr\r\nbybyg\r\n 70 70 50 90 50 \r\n\r\norybg\r\nyrobr\r\nbgbgy\r\n 70 70 50 90 50 \r\n\r\noygbr\r\nyooby\r\nbrbrg\r\n 60 60 50 90 50 \r\n\r\noygbr\r\ngyoby\r\nbrbrg\r\n 70 70 50 90 50 \r\n\r\nrbgyo\r\nrrbyb\r\nyoyog\r\n 50 60 60 90 50 \r\n
\r\n---------\r\nwhere the first line of each group indicates the colors in order of increasing price, from $10 to $50. The second line shows each girls less expensive shirt (Alice to Emily order) and the third line shows each girls more expensive shirt (same order). The bottom line shows the total each girl spent (Alice to Emily again).\r\n\r\nSpot checking, I don\'t see any discrepancies with the clues.',NULL,0);
INSERT INTO comment VALUES (9322,658,3807,'DrBob','','2003-11-07 15:47:06',0,'',NULL,0);
INSERT INTO comment VALUES (9323,1345,4119,'Maria','Perhaps...','2003-11-07 15:56:20',0,'I cannot find (yet) another possible combination than this:\r\nDiane: yellow (40) + organge (50) = $90\r\nEmily: green (30) + blue (20) = $50\r\nCarol: blue + yellow = $60\r\nBetty: red (10) + orange = $60\r\nAlice: red + yellow = $50',NULL,0);
INSERT INTO comment VALUES (9324,658,3807,'DrBob','Re No Comment','2003-11-07 15:58:13',0,'Hmm! Interesting. I\'m sure I had a comment all lined up - but it has disappeared.\r\nI wanted to comment on the expression \'minimise the maximum\', which must be a feature of the method used. I agree that the binary approach gives the smallest maximum number of samples. If there are 128 glasses this number is exactly 7; if 129-256 it a maximum of 8. As has already been shown, the only way taking a single sample can fit in with the binary approach is if there are only 129 glasses.\r\n\r\nI have a gripe though. The question says that the detective is concerned about wasting a test. True, taking a single sample might solve the problem in 1 - but that is very unlikely; and after that 7 further tests are needed. By dividing the sample 65/64 it is probable that only 7 tests in all would be needed. The maximum might not change, but a test is likely to have been saved. And it could be argued that this is the more pragmatic approach. However, it would not have given rise to the problem. Might this suggest that mathematicians are more concerned about interesting problems than pragmatic solutions? I do hope so.\r\n\r\nAnd now in the hope that this makes it through the ether ... here goes',NULL,0);
INSERT INTO comment VALUES (9325,1345,1301,'Charlie','re: Perhaps...','2003-11-07 16:25:31',0,'That\'s the last of the 21 solutions on my post of 21 solutions found by brute force.\r\n',9323,0);
INSERT INTO comment VALUES (9326,1345,1301,'Charlie','re: Solution (maybe)','2003-11-07 16:33:42',0,'Jun\'s solution is #10 on the list of 21 I posted.',9303,0);
INSERT INTO comment VALUES (9327,1345,4210,'kas','...','2003-11-07 16:47:06',0,'shouldn\'t these logic things have only one answer?? here\'s mine anyway.\r\nyellow is 10\r\nred is 20\r\ngreen is 30\r\nblue 40\r\norange 50\r\n\r\nalice- blue+yellow\r\ncarol- blue+green\r\nbetty- red+orange\r\ndiane- orange+blue\r\nemily-green+red',NULL,0);
INSERT INTO comment VALUES (9328,1358,4210,'kas','re: i no it really','2003-11-07 17:04:04',0,'it cant be 3 boys and 4 girls. in that case each guy would have 2 bros and 4 sisters and each girl will have 3 bros and 3 sisters. obviously 2 and 3 are not the same digit as well as the case with 2 and 4. there are 3 answers:\r\na) no kids\r\nb) all boys no girls\r\nc)all girls no boys',9156,0);
INSERT INTO comment VALUES (9329,1205,4206,'Eric','short and sweet','2003-11-07 17:57:49',0,'It is impossible. 25 min = 60*(5/12), and all possible fractions that result in the manipulation of the timers are of the form 60*(x/2^k) – where both x and k are positive integers – thus any addition of the fractions will always give a denominator that is a power of 2, thereby eliminating the possibility of having a 5/12 fraction of an hour.',NULL,0);
INSERT INTO comment VALUES (9330,1345,3529,'Senthil Kumar','','2003-11-07 18:17:55',0,'Yellow $10\r\nRed $20 \r\nOrange $30 \r\nBlue $40\r\nGreen $50\r\n\r\nDiane Green/Orange $90\r\nEmily Red/Blue $60\r\nAlice Green/Yellow $60\r\nBetty Red/Orange $50\r\nCarol Blue/Yellow $50\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (9331,1345,1626,'Gamer','Each shirt purchased twice','2003-11-07 18:24:02',2,'Actually I think what I meant was each shirt was purchased twice, though I don\'t think I have actually put that in there.\r\n\r\nSenthil\'s solution is the one I had, and I believe is the only one that\'s correct. It\'s number 7 on Charlie\'s list.',NULL,0);
INSERT INTO comment VALUES (9332,1345,1301,'Charlie','re: Each shirt purchased twice','2003-11-07 21:18:54',0,'With the added rule, the solution set is indeed reduced to one. The revised program is:\r\n\r\nDECLARE SUB varyGirl (which!)\r\nDECLARE SUB permute (a$)\r\nCLS\r\nDIM SHARED colr$, gs$(2, 5), total(5)\r\ncolr$ = \"rgbyo\"\r\nOPEN \"shirts.txt\" FOR OUTPUT AS #2\r\nFOR costs = 1 TO 120\r\n varyGirl 1\r\n permute colr$\r\nNEXT\r\n\r\nCLOSE\r\n\r\nSUB permute (a$)\r\nDEFINT A-Z\r\n x$ = \"\"\r\n FOR i = LEN(a$) TO 1 STEP -1\r\n l$ = x$\r\n x$ = MID$(a$, i, 1)\r\n IF x$ < l$ THEN EXIT FOR\r\n NEXT\r\n\r\n IF i = 0 THEN\r\n FOR j = 1 TO LEN(a$) \\ 2\r\n x$ = MID$(a$, j, 1)\r\n MID$(a$, j, 1) = MID$(a$, LEN(a$) - j + 1, 1)\r\n MID$(a$, LEN(a$) - j + 1, 1) = x$\r\n NEXT\r\n ELSE\r\n FOR j = LEN(a$) TO i + 1 STEP -1\r\n IF MID$(a$, j, 1) > x$ THEN EXIT FOR\r\n NEXT\r\n MID$(a$, i, 1) = MID$(a$, j, 1)\r\n MID$(a$, j, 1) = x$\r\n FOR j = 1 TO (LEN(a$) - i) \\ 2\r\n x$ = MID$(a$, i + j, 1)\r\n MID$(a$, i + j, 1) = MID$(a$, LEN(a$) - j + 1, 1)\r\n MID$(a$, LEN(a$) - j + 1, 1) = x$\r\n NEXT\r\n END IF\r\nEND SUB\r\n\r\nDEFSNG A-Z\r\nSUB varyGirl (which)\r\n DIM t(5)\r\n DIM colrCt(5)\r\n FOR shirt1 = 1 TO 4\r\n gs$(1, which) = MID$(colr$, shirt1, 1)\r\n FOR shirt2 = shirt1 + 1 TO 5\r\n gs$(2, which) = MID$(colr$, shirt2, 1)\r\n total(which) = shirt1 + shirt2\r\n SELECT CASE which\r\n CASE 1\r\n IF gs$(1, which) = \"o\" OR gs$(2, which) = \"o\" THEN GOTO notThis\r\n CASE 2\r\n IF gs$(1, which) <> \"r\" AND gs$(2, which) <> \"r\" THEN GOTO notThis\r\n CASE 3\r\n IF gs$(1, which) <> \"b\" AND gs$(2, which) <> \"b\" THEN GOTO notThis\r\n IF gs$(1, which) = \"b\" AND shirt1 = 1 OR gs$(2, which) = \"b\" AND shirt2 = 1 THEN GOTO notThis\r\n IF gs$(1, which) = \"g\" OR gs$(2, which) = \"g\" THEN GOTO notThis\r\n IF gs$(1, which) <> gs$(1, 1) AND gs$(1, which) <> gs$(2, 1) AND gs$(2, which) <> gs$(1, 1) AND gs$(2, which) <> gs$(2, 1) THEN GOTO notThis\r\n IF gs$(1, which) = gs$(1, 1) OR gs$(1, which) = gs$(2, 1) THEN\r\n IF shirt1 = 2 THEN GOTO notThis\r\n ELSE\r\n IF shirt2 = 2 THEN GOTO notThis\r\n END IF\r\n IF shirt1 <> 4 AND shirt2 <> 4 THEN GOTO notThis\r\n CASE 5\r\n IF gs$(1, which) = \"o\" OR gs$(2, which) = \"o\" THEN GOTO notThis\r\n END SELECT\r\n FOR j = 1 TO which - 1\r\n IF gs$(1, j) = gs$(1, which) AND gs$(2, j) = gs$(2, which) THEN GOTO notThis\r\n NEXT\r\n IF which < 5 THEN\r\n varyGirl which + 1\r\n ELSE\r\n GOSUB evaluate\r\n END IF\r\nnotThis:\r\n NEXT\r\n NEXT\r\n EXIT SUB\r\n\r\nevaluate:\r\n IF total(4) > total(1) AND total(4) > total(2) AND total(4) > total(3) AND total(4) > total(5) THEN\r\n t(1) = total(1): t(2) = total(2): t(3) = total(3): t(4) = total(5)\r\n DO\r\n fl = 0\r\n FOR i = 1 TO 3\r\n IF t(i) > t(i + 1) THEN SWAP t(i), t(i + 1): fl = 1\r\n NEXT\r\n LOOP UNTIL fl = 0\r\n gs1$ = gs$(1, 1) + gs$(1, 2) + gs$(1, 3) + gs$(1, 4) + gs$(1, 5)\r\n gs2$ = gs$(2, 1) + gs$(2, 2) + gs$(2, 3) + gs$(2, 4) + gs$(2, 5)\r\n IF t(3) = t(4) AND t(1) = t(2) THEN\r\n IF gs$(1, 4) <> gs$(1, 5) AND gs$(1, 4) <> gs$(2, 5) AND gs$(2, 4) <> gs$(1, 5) AND gs$(2, 4) <> gs$(2, 5) THEN\r\n bad = 0\r\n FOR i = 1 TO 2\r\n FOR j = 1 TO 5\r\n ix = INSTR(colr$, gs$(i, j))\r\n colrCt(ix) = colrCt(ix) + 1\r\n IF colrCt(ix) > 2 THEN bad = 1\r\n NEXT\r\n NEXT\r\n IF bad = 0 THEN\r\n PRINT\r\n PRINT colr$\r\n PRINT gs1$\r\n PRINT gs2$\r\n FOR g = 1 TO 5\r\n PRINT 10 * total(g);\r\n NEXT\r\n PRINT\r\n END IF\r\n END IF\r\n END IF\r\n END IF\r\n RETURN\r\nEND SUB\r\n\r\nand it finds the one solution\r\nyrobg (order of colors from $10 to $50 value)\r\n\r\nyryor (girls\' less expensive shirts: Alice to Emily)\r\ngobgb (girls\' more expensive shirts: Alice to Emily)\r\n 60 50 50 80 60 (amounts spent: Alice to Emily)\r\n\r\n',9331,0);
INSERT INTO comment VALUES (9333,1475,3487,'Charlie','Possible Answer','2003-11-07 21:44:11',3,'I think that what he did was go to Alaska because it is the Northern most, Eastern most, and Western most state because if you look at a map, the 180 degree latatude line runs through the \"Aleutian Islands\" and then he went to Hawaii which is the Southern most state. There, I\'m so smart.',NULL,0);
INSERT INTO comment VALUES (9334,1358,3487,'Charlie','','2003-11-07 22:19:36',4,'I disagree with the solution because there are only 2 possible solutions. 1 daughter or 0 daughters.\r\n',NULL,0);
INSERT INTO comment VALUES (9335,1358,3487,'Charlie','re:','2003-11-07 22:21:01',0,'Never mind. I see that even if she had 10 daughters, they would all have 9 sisters and 0 brothers.\r\n',9334,0);
INSERT INTO comment VALUES (9336,1345,3487,'Charlie','Ugh...','2003-11-07 22:23:31',0,'Somebody beter post a comment before i go insane and distroy my computer through frustration.\r\n',NULL,0);
INSERT INTO comment VALUES (9337,1227,3487,'Charlie','','2003-11-07 22:29:40',3,'I think the answer is 0 because they come away with a complete game and yet he didnt throw a single ball.\r\n',NULL,0);
INSERT INTO comment VALUES (9338,1458,3487,'Charlie','re: cigarette on bar---I HAVE IT!!','2003-11-07 22:40:51',0,'the question said you cant touch the base or the cigarette with a solid, liquid, or gass. Thuss rendering your answer impossible.\r\n',9123,0);
INSERT INTO comment VALUES (9339,690,3487,'Charlie','Duh...','2003-11-07 22:48:10',3,'Ofcourse it is going to be the oil because if it was the ice-water, it wouldn\'t be a very good riddle now would it?\r\n√²³<>≤≥∞±∑π',NULL,0);
INSERT INTO comment VALUES (9340,690,4068,'Bruno','A TEST PLEASE !!!','2003-11-08 00:20:20',0,'Can anybody make a test and clear up this confusion???\r\n\r\nIf I\'d have the fever, I\'d jump into the ice-water bucket...\n\nEdited on November 8, 2003, 4:19 pm',NULL,0);
INSERT INTO comment VALUES (9341,1424,3136,'Popstar Dave','What happened?','2003-11-08 08:48:32',4,'What\'s the story, Lew?\r\nAfternoon problem and only one comment (well, two now!)...\r\nI think it\'s about time we had a good, long chat to the people of Perplexus-land and told them to get in gear!',NULL,0);
INSERT INTO comment VALUES (9342,1345,1301,'Charlie','re: Each shirt purchased twice','2003-11-08 09:30:42',0,'Until the official solution is posted, you should still be able to edit the puzzle (and solution) itself. This proviso can be added, so that in the future people seeing the puzzle for the first time will get the full intended set of clues.',9331,0);
INSERT INTO comment VALUES (9343,1491,1171,'nikki','Silly Guess =)','2003-11-08 10:46:03',3,'Well, this is in Tricks, so maybe it\'s not so silly. What if he bought a banner that had a picture of six human feet, but the banner was, say, seven feet long?\r\n\r\nThen he can hold up his fishing rod next to the banner and show that his fishing rod is shorter than six feet.\r\n\r\nMy other guess is he bought a fish, hooked it on the end of his fishing line. Then when he stood the fishing pole up, the weight of the fish will bend the end of the pole over. Hopefully it will bend 3 inches.\r\n\r\nThat\'s it, I\'m out of guesses =)',NULL,0);
INSERT INTO comment VALUES (9344,1491,153,'TomM','re: Silly Guess (Actual Solution)','2003-11-08 11:18:16',3,'No, it\'s even simpler than that.\r\n\r\nHe put the pole in a box that was 6 ft or shorter long and wide enogh so that the diagonal was more than 6 ft 3 in\r\n\r\nThe fishing pole fits in perfectly well diagonally, and yet the box is less than 6 ft long',9343,0);
INSERT INTO comment VALUES (9345,1345,1626,'Gamer','Solution:','2003-11-08 12:03:35',0,'I will petition Levik to add this to the problem. :)\r\n\r\nI have the problem worked out, but to get the reasoning behind the problem and explain it in words rather than a filled in grid might be hard.',NULL,0);
INSERT INTO comment VALUES (9346,1345,3558,'Tristan','logic','2003-11-08 12:45:36',3,'Looking at my previous post, I see that letting only two people buy each color does indeed narrow it down to the following cost pair:\r\nDiane: 50+30\r\n40+20\r\n50+10\r\n40+10\r\n30+20\r\n\r\nAnd using the grid, I can get the answer Gamer expected, which I am too lazy to restate here.',NULL,0);
INSERT INTO comment VALUES (9347,1345,1301,'Charlie','re: Solution:','2003-11-08 14:18:00',0,'It should still be available under \"Your Problems\", for your editing, until the \"official\" solution is posted. This may be applicable only to scholars, but you\'re a scholar.',9345,0);
INSERT INTO comment VALUES (9348,690,4068,'Bruno','Skeptic...','2003-11-08 16:28:56',0,'Another reason why I disagree with the answer is because the bucket of oil is AT ROOM TEMPERATURE, usually about 20 C.\r\n\r\nSo, as soon as he\'d dump his steel into the bucket of oil, oil\'s temperature would be HIGHER than air\'s temperature. So steel would cool SLOWER in oil than simply cooling it with air.\r\n\r\nSo, the 2 best choices are air or ice-water. And at near 0 C, ice-water is the obvious choice.\n\nEdited on November 8, 2003, 4:29 pm',NULL,0);
INSERT INTO comment VALUES (9349,1235,3196,'Dan','Ducks Unlimited','2003-11-09 01:34:55',3,'The problem states:\r\n \r\n\" \'Today I shot more ducks than two days ago, but fewer than a week ago.\' For how many days can the baron say this?\"\r\n \r\nIt does NOT state \"For how many CONSECUTIVE days can the baron say this?\" \r\n \r\nSo if he shot 100 ducks on Tuesday, 7/25/2000, and zero ducks on 7/26/2000 - 7/31/2000, he can make his fowl assertion on 99 consecutive Tuesdays, by shooting zero ducks on every Sunday, Monday, Wednesday, Thursday, Friday, and Saturday following 7/25/2000, and shooting 99 ducks on Tuesday, 8/1/2000, 98 ducks on Tuesday, 8/8/2000, 97 ducks on Tuesday, 8/15/2000, etc.\r\n \r\n(All my family members tell me I missed my calling: I should have been a lawyer).\n\nEdited on November 9, 2003, 1:45 am',NULL,0);
INSERT INTO comment VALUES (9350,1424,3807,'DrBob','Re: Solution','2003-11-09 02:18:28',0,'I agree with the solution - one three digit number 420. Rather than a programmed method I narrowed down the possibilities & then tested the last half dozen or so.\r\nThe first or second digits cannot be zero - if the first is zero, squaring the number formed by the last two is greater than the whole. If the second is zero, squaring the individual digits will give a number larger than the number formed from the last two digits.\r\nAlso, the number formed from the last two digits is less than 33 - otherwise squaring it gives a 4 digit number.\r\nThis has the additional implication that no digit of the three can be greater than 5.\r\nWe have now substantially reduced the number of possible cases (to 11). These can be checked against the condition that the sum of the digits, squared have to equal the number formed by the last two. 32,31,30 don\'t work. 24 does - it could be 224 - but then two digits are the same, so no. 23 - no; 21 works - 421 would do - but 21^2+14+4 is not 421. 20 works too - 420 satisfies all the conditions. The next possibility is 13 - doesn\'t work; nor does 12; 10 could give 310 - but also fails at the last 10^2+9+3 is not 310. So the only possibility is 420. ',NULL,0);
INSERT INTO comment VALUES (9351,1491,3372,'Sam','re(2): Silly Guess (Actual Solution)','2003-11-09 02:35:02',3,'Indeed, I don\'t think that, mathematically at least, there is any limit to the size of the fishing pole you can bring.\r\n\r\nA box measuring 6^3 feet will take a pole measuring over ten feet (the diagonal is Sqrt(6^2 + 6^2 + 6^2)). In a four dimensional box you could carry a pole measuring twelve feet, and all the while no side of the box would measure over six feet.\r\n\r\nOf course, I think you might raise eyebrows on the bus when you try to take your 60-foot long fishing pole on board in a box wrapped up in ten dimensions...\n\nEdited on November 9, 2003, 2:36 am',9344,0);
INSERT INTO comment VALUES (9352,666,3386,'Victor Zapana','a thought','2003-11-09 08:53:55',1,'A has to be 0, 1, or 2, due to the sum can\'t be more than 5 digits. A thus can\'t be 1 either because nothing 0-9 x 4= a number with 1 as a one\'s digit. Also, A cannot be 0 because 0x4=0 and 0 can\'t be E. thus A=2=P
',9383,0);
INSERT INTO comment VALUES (9385,1350,3196,'Dan','re: solution','2003-11-10 18:51:53',0,'I got essentially the same answer as SilverKnight, except that (surprise, surprise !!) his solution is more intelligent than mine..... \r\n\r\nThey roll A,B,C,A,B,C,A,B,C,........ It is mathematically certain beyond a negligible doubt that there will be a winner in the first 16 rolls of the dice, so only those rolls need be considered.\r\n\r\nRoll 1: A has 0 chance to win\r\nRoll 2: B has 1/6 chance to win \r\nRoll 3: C has (5/6)*(1/6) chance \r\nRoll 4: A has [(5/6)^2]*(1/6) chance (^ means \"raised to the power of\") \r\nRoll 5: B has [(5/6)^3]*(1/6) chance\r\n....etc..... \r\nRoll 16: A has [(5/6)^14]*(1/6) chance \r\n \r\nA\'s total chance in the first 16 rolls is 26%\r\nB\'s is 38%\r\nC\'s is 36%\r\n\r\n\r\n\n\nEdited on November 11, 2003, 1:33 am',9380,0);
INSERT INTO comment VALUES (9387,1488,3430,'pat','wisdom','2003-11-10 20:16:51',0,'hurray for the obscured obvious...',NULL,0);
INSERT INTO comment VALUES (9388,1488,3430,'pat','yeehah','2003-11-10 20:18:29',0,'the expansion is superflous',NULL,0);
INSERT INTO comment VALUES (9389,219,4250,'Sara','','2003-11-10 20:18:31',0,'I wouldn\'t play the game for $100, but I think it\'s fair to play for about $32. I don\'t have any fancy logic but I don\'t think you\'ll get heads more than 5 times.',NULL,0);
INSERT INTO comment VALUES (9386,643,4250,'Sara','It really does seem too easy.','2003-11-10 19:17:32',0,'If there were a box of babies and 3 were boys and four were girls, the probability would be 4/7 (Right? Make a fool of me if that\'s wrong) but it says nothing about where the baby being added came from or how many babies there were of each gender, so it\'s really 50:50. The probability is 1/2',NULL,0);
INSERT INTO comment VALUES (9390,1236,3196,'Dan','re(2): A footnote to this problem','2003-11-10 20:30:57',0,'LOL !! Nice thought, Popstar Dave !! The humanitarian spirit is alive and well on perplexus.\r\n \r\nAnd how about this alternate game, in the interests of life and peace ?\r\n \r\n\"Two men are playing Irish roulette using a pistol with six chambers. A single, harmless blank cartridge is used and the chamber is spun after every turn. What is the probability that the first man will lose his bet and have to pay the other guy a dollar?\"\r\n\r\nThen the answer is:\r\n\r\n\"As the chamber is spun after every turn the probability of losing a dollar by hearing the harmless sound of a blank going off on any turn is (1/6); the probability of a silent miss is (5/6). Player 1 could lose a dollar on the first turn. This has a probability of (1/6). If not, he could lose his dollar missing on the first turn, then the second player also misses, then the first player loses his dollar when the blank goes off harmlessly on their second turn. This has a probability of (5/6)²(1/6). If this still doesn\'t happen then they could lose their small dollar bill by both players missing on their first two turns, then player one hearing the little blank go off on their third turn. This has a probability of (5/6)^4(1/6). As this pattern continues indefinetely, the probability of player one hearing an innocuous bang and losing a dollar is the total of the infinite series: \r\n(1/6) + (5/6)^2(1/6) + (5/6)^4(1/6) + ... + (5/6)^n(1/6). \r\nThis equates to 6/11 or a 54.545% chance of the first player being embarrassed by the exploding blank and feeling the chagrin of losing a dollar.\"\r\n \r\nThere we go, no dead people! :-)\r\n \r\n \r\n\n\nEdited on November 10, 2003, 8:31 pm',9384,0);
INSERT INTO comment VALUES (9391,529,3196,'Dan','The official solution of this problem is in error','2003-11-11 02:06:56',3,'\"An archaeologist claims he found some gold coins dated 64 B.C. Before Christ was born, nobody knew when exactly He would be born, so there was no way specify what year it was B.C.\"\r\n \r\nNot so fast. The archaeologist was telling the truth !! It was quite common in the earliest Chrstian kingdoms such as Armenia (converted to the Faith by St. Bartholomew before 200 A.D.) to rededicate monuments, statues, coins, etc., in honor of their new religion. This is typically seen in the conversion of various pagan festivals to Christian use (e.g. Christmas and Easter), and to the adoption and adaptation of heathen symbols as well (e.g. the Christmas tree). So that if it were known by the ruler of second century A.D. Armenia that certain coins had been minted, say, 64 years before they believed that Christ had been born, these early believers could have rededicated the pagan coins by removing from them the images of the old gods, effacing the old date (which may have read \"in the 30th year of the reign of King So-And-So\"), and stamping on them the post-dated \"64 B.C.\" and perhaps a venerating picture of the Madonna and Child. \n\nEdited on November 11, 2003, 2:13 am',NULL,0);
INSERT INTO comment VALUES (9392,1236,3136,'Popstar Dave','re(3): A footnote to this problem','2003-11-11 07:11:29',0,'Hehehe... Brilliant! \r\nMuch better.',9390,0);
INSERT INTO comment VALUES (9393,658,4257,'Jack McBarn','Hard','2003-11-11 09:07:25',1,'This is way too hard!',NULL,0);
INSERT INTO comment VALUES (9394,658,4257,'Jack McBarn','re: Solution','2003-11-11 09:08:06',2,'Wow!',9245,0);
INSERT INTO comment VALUES (9395,1236,2716,'Federico Kereki','re(3): A footnote to this problem','2003-11-11 09:32:33',1,'Blanks aren\'t a trivial matter either; actor Jon-Erik Hexum died because of an accident with a gun loaded with blanks. \r\n\r\nIf I have to go for a PC problem, I\'d keep with the \"gold coin in box\" variation.',9390,0);
INSERT INTO comment VALUES (9396,1490,3964,'B','Solution','2003-11-11 09:38:26',0,'This one\'s (over) easy.\r\n\r\n7 Eggs\r\n1st order = 7-(.5*7+.5)=3\r\n2nd order = 3-(.5*3+.5)=1\r\n3rd order = 1-(.5*1+.5)=0\r\nNo More Eggs!',NULL,0);
INSERT INTO comment VALUES (9397,1350,4059,'Saso','solution - not so nice as that of SK','2003-11-11 09:45:20',3,'If we inspect the probabilities of winning on 1st move, we get A=0, B=1/6, C=5/6^2. In 2nd move we get A=5^2/6^3, B=5^3/6^4 and C=5^4/6^5. Final probabilities for A, B, C will be sum of partial probabilities in 1st, 2nd...infinite roll for A, B and C respectively. These probabilities are infinite geometrical sequences with quocient of 5^3/6^3 but with different first sequence members (1/6 for B, 5/6^2 for C and 5^2/6^3 for A). Then from formula for sum of infinite geometrical sequence sum= a/(1-q), where a is first member and q is quocient we get A=25/91, B=36/91, C=30/91.',NULL,0);
INSERT INTO comment VALUES (9398,202,4257,'Jack McBarn','re: Solution','2003-11-11 10:08:22',0,'Funny at the end!',1180,0);
INSERT INTO comment VALUES (9399,1490,1301,'Charlie','That was the answer; this is the solution','2003-11-11 10:25:43',0,'The last purchase of half the eggs plus half an egg resulted in zero left, so half the eggs was 1/2 an egg, so it started out as 1, leaving zero.\r\n\r\nThe next-to-last purchase left 1, so half the eggs was 1.5, so all the eggs were 3, and two were bought.\r\n\r\nThe third-to-last (or first) purchase was of half the eggs+1/2, so half the eggs was 3.5, and all the eggs to begin with was 7 and 4 were initially bought.',9396,0);
INSERT INTO comment VALUES (9400,1490,4241,'Vinod','The Methodology','2003-11-11 10:54:54',0,'Well, the fact that no eggs were broken in the process tells us that we have to begin with an odd number[half of an odd number is a number short of .5 to become a natural number, which in turn is the required condition -- no breakage of eggs]. \r\n Since our salesman was left with no eggs at the end of his transaction, our working equation becomes (.5)*(x)-(.5) == 0\r\nwhich yields the soln. for x as 1, where x represents the remainder from the previous transaction. \r\n Thus the general equation is (.5)*(x) - (.5) == y\r\nwhere x --> no. of eggs the salesman had before the transaction; and\r\n y--> no.of eggs the salesman has after the transaction.\r\nstarting off with y = 0; and noting that x of a given transaction equals the y for the previous transaction, we arrive at the right answer.',9399,0);
INSERT INTO comment VALUES (9401,569,4257,'Jack McBarn','re: No problem','2003-11-11 11:01:06',0,'Stop this\r\n≤How your friend opens the box is a different question and is not the question that is asked.≥\r\nstuff',6540,0);
INSERT INTO comment VALUES (9402,1163,4257,'Jack McBarn','Solution','2003-11-11 11:33:02',3,'Here is SELFPRT.BAS, a QBasic program:\r\n\r\nLET NUMLINES%=10 \'10 lines\r\nDIM PRT$(NUMLINES%) \'Declare size\r\nOPEN \"SELFPRT.BAS\" FOR INPUT AS #1 \'Open self\r\nFOR I=1 TO NUMLINES% \'Do this til the end of the file\r\nINPUT #1, PRT$(I) \'Add it to the contents\r\nNEXT I \'Do it again\r\nCLOSE \'Close self\r\nFOR J=1 TO I \'Start outputing file\r\nPRINT PRT$(I) \'Output file\r\nNEXT \'Do it again\n\nEdited on February 9, 2004, 1:32 pm',NULL,0);
INSERT INTO comment VALUES (9403,1163,1920,'Brian Smith','re: Solution','2003-11-11 13:10:12',0,'A true quine (self-printing program) does NOT access its source code file.',9402,0);
INSERT INTO comment VALUES (9404,1490,3196,'Dan','The yoke is on the previous posters','2003-11-11 13:14:46',3,'7 CANNOT BE THE CORRECT ANSWER, because it is so obvious that it would be unworthy of the flooble/perplexus website. The correct answer is 2.75 eggs.\r\n \r\nThe saleman started out with 2 eggs.\r\n1st customer bought 1 + 0.5 eggs. To fill this order, the salesman broke one of the eggs. (\"But the problem stated he didn\'t break an egg all day !!\" That\'s not a problem. He wasn\'t selling these eggs during the day. These transactions occurred at night.) \r\nNow there were 0.5 eggs left.\r\nThe 2nd customer bought 0.5*(0.5) + 0.5 = 0.25 + 0.5 = 0.75 eggs. Since the salesman only had an inventory of 0.5 egg at this point, he sold the customer his 0.5 egg and placed a future order of 0.25 egg. \r\nNow the salesman had a zero inventory and one future order for 0.25 egg.\r\nThe 3rd customer ordered 0.5*(0) + 0.5 = 0.5 egg.\r\nThe salesman now placed another future order for 0.5 egg.\r\nHis future orders now total 0.25 + 0.5 = 0.75 egg.\r\n \r\nSo all the conditions of the problem are met. He sold all two eggs (along with placing two future orders totalling 0.75 egg) and he \"didn\'t break an egg all day\" since the selling occurred at night. \r\n\r\n\r\n\r\n\n\nEdited on November 11, 2003, 1:19 pm',NULL,0);
INSERT INTO comment VALUES (9405,1428,3172,'SilverKnight','Full Solution','2003-11-11 13:42:45',3,'Rod 1\r\n1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31\r\n\r\nRod 2\r\n2, 3, 6, 7, 10, 11, 14, 15, 18,19, 22, 23, 26,27, 30, 31\r\n\r\nRod 3\r\n4, 5, 6, 7, 12, 13, 14, 15, 20, 21, 22, 23, 28, 29, 30, 31\r\n\r\nRod 4\r\n8, 9, 10, 11, 12, 13, 14, 15, 24, 25, 26, 27, 28, 29, 30, 31\r\n\r\nRod 5\r\n16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31\r\n\r\nThe top numbers should be the FIRST one in each list...\r\n\r\nThe first number is 2^(x-1) (where x is the number of the rod), and all the numbers on each rod contain that first numbered bit when expressed in base 2 (binary).\r\n\r\n\n\nEdited on November 11, 2003, 1:44 pm',NULL,0);
INSERT INTO comment VALUES (9406,1428,3172,'SilverKnight','re: Full Solution','2003-11-11 13:45:34',0,'Further explanation, if that wasn\'t clear... take 26 (for example)...\r\n26 written in base 2 is:\r\n11010 (16 + 8 + 2), and it is on Rods 2, 4, and 5, corresponding to those bits.\r\n\r\nAnd to solve the \"missing number\", you simply add up the first number in the list... (the person tells you it\'s on the rod starting with 2, with 8, and with 16, and you simply add those numbers together!).\r\n\r\nHope that\'s clear.\n\nEdited on November 11, 2003, 1:49 pm',9405,0);
INSERT INTO comment VALUES (9407,1236,3840,'Hal9000','Inconclusive','2003-11-11 14:36:21',0,'Inconclusive, if they are not perfectly blindfolded it is possible one and or both of them noticed which chamber the bullet was loaded into. Then depending on their relative skills they could significantly reduce or increase their change of \"losing\". Moreover, to better answer the question I would have to examine the gun, bullet and environmental conditions to calculate the probability of potential misfires. Also, I would need to know the rules (variation) of this particular game of Russian Roulette, and also consider that it is theoretically possible to survive any gunshot wound from point blank range. Whether or not this qualifies as losing depends on the game of Roulette played. I guess what I\'m trying to say is I don\'t like your question so I will not answer. Let\'s watch a little less tv, a little less \'Deer Hunter\', get a little less violent, and rephrase the question into a game of casino roulette.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (9408,1236,3172,'SilverKnight','re: Inconclusive :-)','2003-11-11 14:45:04',0,'Wow!!! :-)\r\n\r\nI suppose that, clearly, DJ having referenced the \'game\' of Russian Roulette, is evidence of his desire to promote suicides, homicides, and violence in general.\r\n\r\nDJ, what childhood trauma did you go through, that causes you to encourage violent behavior?\r\n\r\n(Or should I ask Hal, what childhood trauma (s)he endured that causes such an unwarranted reaction to a HYPOTHETICAL SITUATION, that most people are already familiar with, used to do nothing more than exemplify a probability riddle?)\r\n\r\nCheers!',9407,0);
INSERT INTO comment VALUES (9409,1236,3840,'Hal9000','re(2): Inconclusive :-)','2003-11-11 15:00:03',0,'I suppose there\'s no harm in merely mentioning something. http://www.snopes.com/movies/films/deerhunt.htm',9408,0);
INSERT INTO comment VALUES (9410,1428,3224,'Lee','ever so slight improvement','2003-11-11 15:03:54',1,'Smart, SK did it just \'hit\' you or seem obvious or had you seen something like this before?\r\nMe I was nowhere - I misread \'whatever rods\' as \'whatever rod\' and couldn\'t hold out - I just had to look.\r\nAnyhows, although the question\r\n\"What numbers should be on each of the five rods?\"\r\nhas, of course, been answered I would just like to add that if you mixed the numbers up un each stick, so the top numbers were\r\n1...........1\r\n2...........22\r\n3...........14\r\n4...........18\r\n5...........16\r\nyou could simply add the end digits on the rods, unless you see the \'magical\' 16 where you add the full 16.\r\nSame result of course, just a bit more showmanship and longevity (most kids would soon realise you\'ve just added the numbers together)\r\nThere are probably more \'codes\' but this seems quite easy.\r\nI know it doesn\'t add much, or answer anything asked but I just pictured my nephew\'s expression should I perform such a trick on him twice.\r\nIt isn\'t one of awe.\r\n',NULL,0);
INSERT INTO comment VALUES (9411,1236,3172,'SilverKnight','re(3): Inconclusive :-)','2003-11-11 15:08:15',0,'No harm in it... but Hal... how is it that you managed to avoid the almost unavoidable results after having been made aware of this film?\n\nEdited on November 11, 2003, 3:10 pm',9409,0);
INSERT INTO comment VALUES (9412,1236,3172,'SilverKnight','re(4): Inconclusive :-)','2003-11-11 15:22:37',0,'I suppose there\'s no harm in merely mentioning something else:\r\nhttp://www.darwinawards.com/',9411,0);
INSERT INTO comment VALUES (9413,1428,1301,'Charlie','The top number?','2003-11-11 15:40:32',3,'If by \"the top number\" is meant the highest number, the following set will do, albeit with a little more mental activity on the part of the magician:\r\n\r\nrod 1:\r\n 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30\r\nrod 2:\r\n 1, 4, 5, 8, 9, 12, 13, 16, 17, 20, 21, 24, 25, 28, 29\r\nrod 3:\r\n 1, 2, 3, 8, 9, 10, 11, 16, 17, 18, 19, 24, 25, 26, 27\r\nrod 4:\r\n 1, 2, 3, 4, 5, 6, 7, 16, 17, 18, 19, 20, 21, 22, 23\r\nrod 5:\r\n 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15\r\n\r\nThese are the numbers that have a zero, rather than a one, in their corresponding binary positions. To use them, the magician must subtract each of the top numbers from 31, then add up those differences and subtract from 31. For example, 12 is on rods whose highest number is 30, 29 and 15. Subtracting each from 31 is 1,2 and 16; add these to get 19 and subtract that from 31 to get 12.\r\n\r\nIf the person tells you it\'s on no rods, it\'s 31, as the total is zero to be subtracted from 31.',NULL,0);
INSERT INTO comment VALUES (9414,1428,4055,'S','Clue','2003-11-11 15:45:16',0,'What makes this problem easier is realizing that 2^5 is 32. Right away, this makes me think of binary and as SilverKnight has used in his solution.',NULL,0);
INSERT INTO comment VALUES (9415,1490,1567,'Bryan','re: The yoke is on the previous posters','2003-11-11 15:47:26',0,'Dan, your solution is so obvious, I\'m surprised no one else thought of it first!',9404,0);
INSERT INTO comment VALUES (9416,1428,3172,'SilverKnight','re: The top number?','2003-11-11 15:55:29',0,'Charlie, I follow your solution....\r\n\r\nI certainly hope that your interpretation is not what Lewis intended... because then IMHO he should have been much more explicit and not used \'top\', but rather the GREATEST or HIGHEST-VALUED number on each rod.\r\n\r\nAmbiguity sux. :-)',9413,0);
INSERT INTO comment VALUES (9417,1236,3840,'Hal9000','re(4): Inconclusive :-)','2003-11-11 16:05:07',0,'The answer is 5/11, jk. It is apparent you & I are of two philosophies on the subject. Let us examine these two things as individual cases. Firstly, if the point of this problem is an examination of probabilities, doubtless, you will agree with me the question could have been posed in another manner. Surely you could understand I do not come to this website to be confronted with the mention/implications of senseless violence and social ills. Mathematics is one of the few savory things left these days (granted we often use to develop deadly weapons) but let us not UNCESSARILY defile it with such revolting applications. The film medium should be afforded a certain degree of artistic freedom, and individuals are ultimately responsible for their own actions, I will concede this point to you. What annoys me is the arrogance/ingnorance demonstrated by those do not examine the consequence of their actions. Let us consider the greater social good rather than indulging the attrocities and desenitizing ourselves to them. ',9411,0);
INSERT INTO comment VALUES (9418,1236,3840,'Hal9000','','2003-11-11 16:17:39',0,'Please appreciate it is my personal experiences and love of mathematics that lead me to question the ethics of this posting. Of course, the moderators of this site are the ones who decided whether it is appropriate. I will abide and respect whatever decision they choose to make about this problem. I simply felt so strongly I had to post my opinion, you are certainly entitled to yours.',NULL,0);
INSERT INTO comment VALUES (9419,1491,3512,'Jeff','re(3): Silly Guess (Actual Solution)','2003-11-11 17:35:17',0,'A 4-dimensional box eh? I\'d like to see that......',9351,0);
INSERT INTO comment VALUES (9420,1228,4265,'Yevgen','A simpler formula','2003-11-11 17:44:21',0,'Found a simpler formula for the probability of forming a triangle with non-zero area with 3 sticks randomly picked out of n:\r\np=(2n-5)/(4(n-1))\r\nFor even n this formula is exact, for odd n a correction term (-1/(8C)) must be added where C is the total number of combinations of 3 sticks (C=n(n-1)(n-2)/6). \r\nThe correction term however becomes negligible very rapidly as n grows (<0.01% for n>20), so the formula for even n can be used universally if n is sufficiently large.\r\n',NULL,0);
INSERT INTO comment VALUES (9421,1490,1626,'Gamer','The yoke is on YOU!','2003-11-11 17:53:19',0,'Unfortunately, the first line of the problem says \"how many he had sold that day\"... indicating that he did sell them during the day.\r\n\r\nThe fact that you think this puzzle demands a different solution since it is here is directly wrong. The fact that this isn\'t in tricks explains that any doubtful trickery isn\'t included here.',NULL,0);
INSERT INTO comment VALUES (9422,826,4266,'michelle','don\'t get it','2003-11-11 18:17:03',0,'This makes absolutely no sense to me. It sounds like you\'re saying that if you have multiple groups of one dog each, all dogs in each group would be the same color, which is obvious. But k dogs? Is k a variable? You can\'t just suppose that it\'s true for any random number of dogs just because it\'s true for one dog.\r\nThen, when you get the a group A of k+1 dogs you\'ve lost me completely =/',NULL,0);
INSERT INTO comment VALUES (9423,263,4266,'michelle','re: It Can\'t','2003-11-11 18:30:42',0,'I agree with Matthew in that it can\'t be. First of all, it was stated that the tortoise is much slower than the swift Achilles. Well, if he\'s slower, there is so way that just because he had a head start he would always be able to keep the same distance between himself and Achilles.',1689,0);
INSERT INTO comment VALUES (9424,227,4266,'michelle','re(2): if I were his student','2003-11-11 18:41:20',0,'I am very confused by the meaning of \"first case\" in this paradox.\r\nWhen it says \"...which states that they do not have to pay him until they have won their first case,\" it seems to be implying the logical meaning, being the first case the student WINS.\r\nHowever, it then says \"If the student loses their first case, then they don\'t have to pay Protagoras at all.\" Here it seems to say that the payment is all dependant on the first case he TRIES.\r\nIf it is dependant on the first tried case, the student should have just gone to court and lost a cose before the teacher felt the need to sue him. Then again, if it got to the point of suing, he should not have represented himself.',5122,0);
INSERT INTO comment VALUES (9425,1345,4256,'gary','','2003-11-11 18:46:46',0,'Tristan thank you for that post ... I could get what others say is the answer but with that post my answer works perfectly.\r\n\r\nDo not know how to post the grid\r\n\r\n\r\nAlice green yellow 50 \r\nBetty red orange 60 \r\nCarol red blue 50 \r\nDiane yellow orange 80 \r\nEmily green blue 60 \r\nred 10 \r\ngreen 20 \r\nyellow 30 \r\nblue 40 \r\norange 50 \r\n',NULL,0);
INSERT INTO comment VALUES (9426,189,4266,'michelle','Is it...?','2003-11-11 18:56:36',0,'four',NULL,0);
INSERT INTO comment VALUES (9427,1428,3558,'Tristan','solution','2003-11-11 18:59:48',3,'Ah yes, that old binary system trick...\r\n\r\nThink of the binary system. All the numbers ending in 1 in the binary system go on the first rod. All the numbers with a 1 in the 10\'s digit go on the second rod. Then all those with a 1 in the 100\'s digit on the third, and so on. The top numbers should be 1,2,4,8, and 16. Then, simply add the numbers to get the number the person thought of.\r\n\r\nI\'m probably repeating something, but I hope I brought in at least one new idea.',NULL,0);
INSERT INTO comment VALUES (9428,228,4266,'michelle','I thought I had it','2003-11-11 19:01:44',0,'I was going to say that \"is\" should be \"are\", \"three\" should be \"two\", and \"thise\" should be \"this\", but then there are three errors and you can\'t change the three to two! =)',NULL,0);
INSERT INTO comment VALUES (9429,1490,3386,'Victor Zapana','re: The yoke is on YOU!','2003-11-11 19:26:54',0,'I agree with Gamer. Also, some terribly easy riddles have been posted on Perplexus before.
\r\n26 gangstas wit dey cribs and hos\r\nall showing colors, some wit’out clothes\r\nits all real quiet, not a lotta sound,\r\nbut once they get started, folks goin’ down\r\n ',NULL,0);
INSERT INTO comment VALUES (9445,1345,4290,'magee','Solution??','2003-11-12 12:49:01',3,'Diane spent $80 total for a green($50) and orange($30)\r\nAlice spent $60 total for a Red ($10) and Green($50)\r\nEmily spent $60 total for a Blue($40) and a Yellow($20)\r\nBetty spent $50 total for a Yellow($20) and an Orange(#30)\r\nand \r\nCarol spent $50 total for a Red($10) and a blue ($40)',NULL,0);
INSERT INTO comment VALUES (9446,1234,3430,'pat','here and there','2003-11-12 13:06:31',0,'hey, give the guy a break...i rated it a 3.. but I\'ve only been to a few cities....-',NULL,0);
INSERT INTO comment VALUES (9447,1493,3172,'SilverKnight','re: with apologies to the Popstar','2003-11-12 13:32:57',0,'lol!\r\n\r\n(I\'m enjoying FatBoy\'s postings a lot lately.... Now if we can only get him to stop PRE-APOLOGIZING to maintain \"P.C.-ness\")',9444,0);
INSERT INTO comment VALUES (9448,382,4257,'Jack McBarn','Ravi Raji, read this','2003-11-12 14:07:24',2,'It\'s an, not a, hourglass.',NULL,0);
INSERT INTO comment VALUES (9449,382,4257,'Jack McBarn','re: Not sure','2003-11-12 14:11:51',0,'You\'re right, levik.',2483,0);
INSERT INTO comment VALUES (9450,1238,3172,'SilverKnight','','2003-11-12 14:43:13',3,'The situation can be re-described thusly:\r\n\r\nTake a circle and draw the horizontal diameter.\r\n\r\nThen stick at the center of the circle... stick a post and tether the dog to it.\r\n\r\nFrom the end points of the diameter, draw line segments to ANY point in the top half of the circle. These two line segments and the diameter will form a right triangle, and if we scale it up to the size of one acre, we describe the farmer\'s pasture. The circle represents the range of the dog.\r\n\r\nNow, you will note the the COMPLETE triangle (tract of land) is within range of the dog. So, the sheep must content themselves to their respective circles OUTSIDE the larger (dog\'s circle).\r\n______________________\r\n\r\nSince I will assume that this is the same answer regardless of whether or not the respective legs are equal to each other... I will assume (for simplicity) that the two legs are √2 in length (and the diameter is 2 units in length).... then the area of the triangle tract is 1/2 * √2 * √2 (1/2 x base x height) = 1 acre.\r\n______________________\r\n\r\nOne sheep\'s respective semicircle is 1/2 x π x (√2/2)² = π/4.\r\n\r\nBut we must subtract the area OF THE SHEEP\'S SEMICIRCLE that the dog can reach... which is a quarter of the dog\'s circle less half the triangular tract.\r\n\r\nOne quarter of the dog\'s region is: π/4. And half the triangular area is 1/2.\r\nso... the region of interest is π/4 - 1/2.\r\n\r\nSubtracting the region of interest from the sheep\'s semicircle is:\r\nπ/4 - (π/4 - 1/2)\r\n\r\n= 1/2 acre\r\n\r\nSince both sheep can get to its own 1/2 acre... the total is twice that...\r\n\r\n= 1 acre.',NULL,0);
INSERT INTO comment VALUES (9451,1238,3172,'SilverKnight','Solution - shoulda labeled it as such','2003-11-12 14:43:37',3,'The situation can be re-described thusly:\r\n\r\nTake a circle and draw the horizontal diameter.\r\n\r\nThen stick at the center of the circle... stick a post and tether the dog to it.\r\n\r\nFrom the end points of the diameter, draw line segments to ANY point in the top half of the circle. These two line segments and the diameter will form a right triangle, and if we scale it up to the size of one acre, we describe the farmer\'s pasture. The circle represents the range of the dog.\r\n\r\nNow, you will note the the COMPLETE triangle (tract of land) is within range of the dog. So, the sheep must content themselves to their respective circles OUTSIDE the larger (dog\'s circle).\r\n______________________\r\n\r\nSince I will assume that this is the same answer regardless of whether or not the respective legs are equal to each other... I will assume (for simplicity) that the two legs are √2 in length (and the diameter is 2 units in length).... then the area of the triangle tract is 1/2 * √2 * √2 (1/2 x base x height) = 1 acre.\r\n______________________\r\n\r\nOne sheep\'s respective semicircle is 1/2 x π x (√2/2)² = π/4.\r\n\r\nBut we must subtract the area OF THE SHEEP\'S SEMICIRCLE that the dog can reach... which is a quarter of the dog\'s circle less half the triangular tract.\r\n\r\nOne quarter of the dog\'s region is: π/4. And half the triangular area is 1/2.\r\nso... the region of interest is π/4 - 1/2.\r\n\r\nSubtracting the region of interest from the sheep\'s semicircle is:\r\nπ/4 - (π/4 - 1/2)\r\n\r\n= 1/2 acre\r\n\r\nSince both sheep can get to its own 1/2 acre... the total is twice that...\r\n\r\n= 1 acre.',NULL,0);
INSERT INTO comment VALUES (9452,1238,775,'Cory Taylor','not quite complete','2003-11-12 14:58:36',0,'SK, while you have correctly shown the answer to a specific case (and I\'ll agree this answers the question), the assumption you\'ve made about the orientation of the triangle (while true) is not justified. If you could not assume that the triangle was isosolese (sp!) then it is a much more involved problem...',NULL,0);
INSERT INTO comment VALUES (9453,1238,3172,'SilverKnight','re: not quite complete','2003-11-12 15:06:22',0,'Cory,\r\n\r\nI only object to your \"not quite complete\" description.\r\n\r\nAs you\'ve agreed, my solution DOES answer the question.\r\n___________\r\n\r\nFor anyone who wants to continue the tedium :-), you need only show that the two sheep\'s respective circles grow/shrink in size in proportion to the square of the growth/shrinking of the respective legs (from equality).\r\n\r\nAnd similarly, the dog\'s portion of those circles grow/shrink accordingly.\r\n\r\nI will leave it as an excersise to the reader (to the floobler?) to set up those equations and bring closure to any outstanding issues.\r\n_____________\r\n\r\nLastly, contrary to any impression I may have given above, I think this problem is definitely flooble-worthy, and I would rate it a 4 or a 5.\r\n\r\nCheers!',9452,0);
INSERT INTO comment VALUES (9454,1238,1301,'Charlie','In generality--not assuming one case','2003-11-12 15:12:18',3,'The dog\'s circle will indeed intersect the right angled vertex as well as the other two vertices and thus the endpoints of the sheep\'s two lines will lie on the circle.\r\n\r\nBy the pythagorean theorem, the sum of the squares on the two sides will equal the square on the hypotenuse. As the areas of any two similar shapes are proportional to the square of a corresponding side, this applies to semicircles erected on the outside of each side of the triangle.\r\n\r\nThe inner semicircle of the dog\'s circle is of course equal to the outer semicircle, and further, encompasses the triangle plus a two small areas, one cut out of each of the sheep\'s outer semicircle.\r\n\r\nLet t be the area of the triangle; let s be the area of the outer semicircle on the hypotenuse, which is equal to the inner semicircle on the hypotenuse as well as the sum of the two outer semicircles on the legs; let o be the area of overlap between the dog\'s (hypotenuse\'s) inner semicircle and the combined pair of outer semicircles on the legs (the sheep\'s semicircles). As the sheep\'s inner semicircles are completely covered by the dog\'s circle, only the outer semicircles count. Then:\r\n\r\ns = t + o (considering s as the area of the dog\'s semicircle)\r\n\r\nso \r\n\r\ns-o = t\r\n\r\nBut s, being the total of the sheep\'s outer semicircles, minus the area of those semicircles\' overlap with the dog\'s semicircle, is the area the sheep have free of the dog, so that is t, which in this case is 1 acre.',NULL,0);
INSERT INTO comment VALUES (9455,1350,4082,'wonshot','late jump solution','2003-11-12 15:56:41',0,'Ok so I used Excell after comming up with equations, is that cheating. Anyway.\r\n\r\nP(B) = SUM (5/6)^(3n-3)*(1/6) = 36/91\r\nP(C) = SUM (5/6)^(3n-2)*(1/6) = 30/91\r\nP(A) = SUM (5/6)^(3n-1)*(1/6) = 25/91\r\n\r\n(1/6) is the prob of matching any given role, thereby winning.\r\n(5/6)^(3n-3) is the probabilty that no one will have won by B\'s turn in round \'n\'. For every round each player roles die once, if no one wins first.\r\n\r\nB has the best chance of winning because he is the first one to role with a chance of winning (i.e after A roles).\r\n',NULL,0);
INSERT INTO comment VALUES (9456,1458,4292,'Archon','Bet this is it','2003-11-12 16:59:18',3,'cigarette standing on its butt.Butt=filter.Burn filter.Direct contact with any object of \"material\" nature prohibited. Use concentrated light rays. photons are somewhere inbetween radiation and material.',NULL,0);
INSERT INTO comment VALUES (9457,1458,4292,'Archon','haha got it','2003-11-12 17:06:24',0,'you can\'t touch it. but you can untouch it.just use a straw and suck near the tip.hahaha\r\n',NULL,0);
INSERT INTO comment VALUES (9458,1238,1171,'nikki','Mathematical / Graphical Solution','2003-11-12 17:33:15',3,'Let\'s call one leg of the triangle B (for Base), the other leg of the triangle L, and the hypotenuse H.\r\n\r\nAnd let\'s call the area of the Dog\'s semi-circle D, the area of one sheep\'s semi-circle S1, the area of the other sheep\'s semi-circle S2, and the area of the triangular field T.\r\n\r\nSince we know the field is a right triangle, we know that B^2 + L^2 = H^2\r\n\r\nThe dog\'s semi-circle intersects with all three vertices of the triangle (I\'ll prove this later on, I don\'t want to bog down the solution so soon). This is very important because otherwise the math won\'t work out nicely.\r\n\r\nSo now we can define the area of freedom for the sheep as:\r\nA = T + S1 + S2 - D\r\nA = T + pi/2*(B/2)^2 + pi/2*(L/2)^2 - pi/2*(H/2)^2\r\nA = T + pi/8*(B^2 + L^2 - H^2)\r\nA = T + pi/8*0\r\nA = T = 1 acre\r\n\r\nTo prove that the Dog\'s semi-circle intersects with all three vertices, I can approach this one of two ways. First, there is some geometric proof that if you have a circle and draw it\'s diameter, then pick any point on the circumference (other than the end points of the diameter, of course) you will always get a right triangle with the diameter being the hypotenuse. Since the dog\'s post would be located at the center of the circle, and the circle represents the boundary of the dog\'s reach, we see that the vertex of the right angle will always be on this boundary.\r\n\r\nThe other approach is more graphical. On a cartesian plane, place the right angle vertex at (0,0), another vertex at (B,0) and the last vertex at (0,L) to represent the triangle. Clearly the posts of the sheep will be at (B/2,0) and (0,L/2). The coordinates of the midpoint of the hypotenuse is found by averaging the coordinates of the endpoints of the hypotenuse. So the X coordinate is the average of B and 0, which is B/2, and the Y coordinate is the average of 0 and L, which is L/2. This means the dog\'s post is exactly horizontal and exactly vertical to the other two posts. Well, draw a triangle with vertices at (0,0), (B/2,0), and (B/2,L/2). This is a right triangle, and the hypotenuse is sqrt[(B/2)^2 + (L/2)^2] = sqrt[(B^2 + L^2)/4] = sqrt(H^2/4) = H/2 which is exactly the length of the dog\'s tether. So again, the right angle vertex is just exactly on boundary of the dog\'s reach.\n\nEdited on November 12, 2003, 5:34 pm',NULL,0);
INSERT INTO comment VALUES (9459,1491,3558,'Tristan','re: uhh...','2003-11-12 19:09:26',0,'Then maybe he just bought some candy while returning the fishing rod or something and ate it. This fits all the given information, but is not the solution. \"Why can\'t there be multiple solutions?\" one might ask. Well the solution I\'m referring to is the one Popstar Dave expected or something even more satisfying.',9431,0);
INSERT INTO comment VALUES (9460,27,3558,'Tristan','re: That cannot be.','2003-11-12 19:20:34',0,'That may have been the case in the way it was told to you, but here it specifically states, \"sometime next week.\"\r\nThe idea behind the answer here is that the students cannot be sure of the professors honesty. In fact, by logic, it is impossible for him to have told the truth (that doesn\'t mean he lied).',9435,0);
INSERT INTO comment VALUES (9462,1238,4300,'Minion123','solution','2003-11-13 00:12:47',0,'i got 0',NULL,0);
INSERT INTO comment VALUES (9463,1472,4300,'Minion123','guess','2003-11-13 00:16:51',0,'50/50',NULL,0);
INSERT INTO comment VALUES (9464,1223,4300,'Minion123','dont know','2003-11-13 00:20:24',0,'number to big for my claculator',NULL,0);
INSERT INTO comment VALUES (9465,1490,4235,'casper','solution','2003-11-13 04:14:17',0,'the answer is 7.\r\nthe 1st person bought 1/2 the total which is 3.5 eggs and 1/2 an egg more which makes the total 4. \r\n7 - 4 = 3 so now he has 3 eggs left.\r\nthe second person buys 1/2 the total remaining which is 1.5 eggs and 1/2 an egg more which makes their total 2.\r\n3 - 2 = 1so now he has 1 egg left.\r\nthe last customer buys 1/2 the total remaining which is 1/2 an egg and 1/2 an egg more which equals 1.\r\n1 - 1 = 0\r\nso as you see he has no eggs left and never had to break egg one.',NULL,0);
INSERT INTO comment VALUES (9466,352,1178,'Medicherla','explanation for the arrangement of numbers 1 to 15','2003-11-13 06:11:00',3,'As some people have already mentioned(comments) \r\nthat 8 and 9 can not take other positions than \r\nthe ends, is good and agreed upon. 8 and 9 each\r\nhas only one partner(1, 7) to make perfect square.\r\n\r\nWhen we fix them at the ends(for example,\r\nposition 1 for 8 and 15 for 9). Then obviously \r\nposition 2 should be UNIQUELY taken by 1 and\r\npos. 14 by 7. \r\n\r\nIf we start working from pos. 14, it is easy to \r\ncomplete the series uniquely. As 7 can take only 2 \r\nand 2 can take only 14 and 14 can take only 11 etc. \r\n\r\nso, the solution I gave long back is the unique\r\nsolution. Any how as the addition has commutative \r\nproperty(a+b=b+a), inverting the above solution is \r\nalso a solution. \r\n\r\n',NULL,0);
INSERT INTO comment VALUES (9467,1351,1686,'DuCk','Solution','2003-11-13 06:55:22',0,'you you are not not looking over over this slowly and and spotting the flaw...\r\n\r\n\n\nEdited on November 13, 2003, 6:58 am',NULL,0);
INSERT INTO comment VALUES (9468,1351,3196,'Dan','re: Solution','2003-11-13 07:28:01',1,'Wow, Gamer, this was a great one, worthy of the Psychology Department of a major testing University !! ',9467,0);
INSERT INTO comment VALUES (9469,1236,3196,'Dan','re(2): A footnote to this problem','2003-11-13 09:54:00',0,'Popstar Dave: \"I don\'t like the idea of people shooting themselves, so here\'s my version of the problem: Two men are trying to find a gold coin in a container that contains the gold coin and five other coins of the same weight.... There we go, no dead people!\"\r\n \r\nAnd then one of the guys pulls out the gold coin. This enrages the other guy, and he pulls a Samurai sword out of his pocket and lops the fellows head off !\r\n \r\nWhoops....a dead person !! \r\n\r\n:0(\r\n',9384,0);
INSERT INTO comment VALUES (9470,1351,4241,'Vinod','re(2): Solution','2003-11-13 11:15:20',0,'Well, one anamoly here is that first the para. claims that you will not notice an error if you are reading through it hastily, then, later claims that it will surprise you while you are reading it hastily.',9468,0);
INSERT INTO comment VALUES (9471,1351,3430,'pat','alpha omega','2003-11-13 12:26:01',0,'alpha omega',NULL,0);
INSERT INTO comment VALUES (9472,1351,1920,'Brian Smith','Keep off the grass','2003-11-13 12:54:26',0,'The first time I encountered this trick was with a sign:\r\n\r\nPLEASE DONT\r\nWALK ON THE\r\n THE GRASS',NULL,0);
INSERT INTO comment VALUES (9473,1351,2839,'FatBoy','Check out the \"newest problems\" listing','2003-11-13 14:16:40',0,'Gamer,\r\nSorry to say, when the problem is listed in teh \"newest problems\' listing it has a slightly different spacing which completely ruis the trick.\r\n',NULL,0);
INSERT INTO comment VALUES (9474,669,3172,'SilverKnight','Full Solution','2003-11-13 14:43:06',3,'1800 yards\r\n\r\nSet up the problem:\r\n\r\nt = the amount of time to first meeting\r\nu = the amount of time to second meeting\r\nw = width of river\r\nx is rate of the boat 1\r\ny is rate of the boat 2\r\n\r\n(at their first meeting, they have traversed the width together, once)\r\nxt + yt = w\r\nxt = 700 (similarly yt = w -700\r\n\r\n(at their second meeting, they have traversed the width together, three times)\r\nxu + yu = 3w\r\n\r\nand the other boat (speed y) has come to within 300 yards of the other side so:\r\nyu = 2w - 300\r\n\r\nAnd since they\'ve traversed the river 3 times at constant speeds, this takes 3 times the original time so\r\nu=3t.\r\n__________________\r\n\r\nCombine equations\r\n\r\nxu + 2w - 300 = 3w\r\nxu - 300 = w\r\n3xt - 300 = w\r\n2100 - 300 = w\r\n\r\nw = 1800 yards',NULL,0);
INSERT INTO comment VALUES (9475,669,1301,'Charlie','solution','2003-11-13 14:53:18',3,'Units of time are arbitrary, so set the speed of one boat as 1 and the other as s (which is then just the ratio of their speeds). Let the speed of 1 apply to the boat that has traveled 700 yards less than the river\'s width at the first meeting, and the speed of s apply to the one that has traveled 700 yards at that time. Call the width x, which will be our final answer.\r\n\r\nAt the first time:\r\n(x-700)/1 = 700/s\r\nAt the second time:\r\n(2x-300)/1 = (x+300)/s\r\n\r\nDividing one equation by the other, and cross-multiplying (or just cross multiplying to begin with):\r\nx²-400x-210000=1400x-210000\r\nor\r\nx²-1800x=0\r\n\r\nIgnoring the x=0 solution, we get x=1800 yards.\r\n\r\nThe ratio of the speeds, by the way, is 7/11.',NULL,0);
INSERT INTO comment VALUES (9476,669,2707,'Gordon Steel',' Solution Without Almost No Equations','2003-11-13 15:16:49',0,'Since the boats pass twice, the combined distance of both boats is precisely three times the width of the river. The total distance travelled by the boat that on its first segment went 700 yards from shore is therefore 3 x 700 = 2100. Since he ends up 300 miles short of returning to home shore, the width of the river is 2100 - 300 = 1800. Gordon S.',NULL,0);
INSERT INTO comment VALUES (9477,1351,4188,'GimmeKat','Solution','2003-11-13 15:57:45',0,'at the end of every line and at the beginning of of every line is the same word like this: duh\r\nduh',NULL,0);
INSERT INTO comment VALUES (9478,669,3172,'SilverKnight','re: Solution Without Almost No Equations','2003-11-13 16:05:53',0,'Actually, Gordon... the boat that went 700 the first time they passed is the slower boat.\r\n\r\nAt the time of the 2nd passing. The boat in question didn\'t end up 300 yards short of returning home. It only passed the far side by 300 yards.... He is actually 1500 yards short of returning to the home shore.\r\n\r\nBut yes... 2100 is 300 yards past one width of the river, and 2100 - 300 = 1800.\r\n____________________\r\n\r\nUnfortunately, it is not obvious (at least to me) without setting up the equations, which boat is near which side at the respective meetings.',9476,0);
INSERT INTO comment VALUES (9479,666,4311,'todd','this one is easy','2003-11-13 18:41:06',0,'as long as one of the letters stands for 0 they will multiply out to equal 9 \r\ne.g. 0*1*2*3*9*4=0\r\nand\r\n9*3*2*1*0=0\r\n\r\nthe problem is solved',NULL,0);
INSERT INTO comment VALUES (9480,669,2707,'Gordon Steel','In Defense of Limited Equations','2003-11-13 19:50:07',0,'Silverknight, thanks for your comments. I stand by my conclusion that we do not need to calculate the speed of either boat to determine the river width. We do know that one boat has traveled 700 yards at the first meeting, at which time the combined distance traveled by both boats is equal to the river width. We also know that both boats proceed to their respective far shores and then are in the process of returning to their home shores when they meet again. At this second meeting, the combined distance traveled by both boats is equal to three x the river width. Since the problem states that both boats travel at constant speed, the selected boat has traveled 700 yards x 3 = 2,100 yards. Since the problem states the boat at this time is returning to the shore from which it departed and is some 300 yards from the opposite shore, the width of the river must be 2,100 - 300 = 1,800 yards. Gordon S. ',NULL,0);
INSERT INTO comment VALUES (9481,669,3196,'Dan','Current Events','2003-11-13 20:07:08',0,'Let X be the width of the river in yards. The boat coming from the east bank is A, from the west bank is B. The first rendevous point is 700 miles from the east bank. The second is 300 miles from the west bank. \r\n\r\nIn time interval t1, A sails 700 yards west and B sails \r\nX-700 yards east. In time interval t2, A sails X-700 yards west, then X-300 yards east, for a total of 2X-1000 yards, while B sails 700 yards east and 300 yards west, for a total of 1000. \r\n \r\nSince the two boats\' relative speeds remain constant, the ratio of the distances they sail in t1 should be equal to the ratio of the distances they sail in t2.\r\n \r\n700/(X-700) = (2X-1000)/1000\r\n350/(X-700) = (X-500)/1000\r\n350000 = (X-700)*(X-500)\r\nX^2 - 700X - 500X + 350000 = 350000\r\nX^2 -1200X = 0 \r\nX(X-1200) = 0\r\nX=1200\r\n \r\nThe river is 1200 yards wide.\r\n\r\n\n\nEdited on November 13, 2003, 9:04 pm',NULL,0);
INSERT INTO comment VALUES (9482,669,3172,'SilverKnight','re: In Defense of Limited Equations','2003-11-13 20:12:08',0,'Gordon, you\'re welcome to stand by anything you want to.\r\n\r\nAnd, contrary to what you suggested, I didn\'t calculate the speed of either boat (until you made the erroneous comment \"he ends up 300 miles short of returning to home shore\"), and I did so only to refute said comment.',9480,0);
INSERT INTO comment VALUES (9483,669,3196,'Dan','Can someone please tell me where I went wrong ?','2003-11-13 20:53:05',4,'I am the only one who got 1200 yards as the answer. Can you please check \"Current Events\" in this comment list and point out what I am too blind to see? (I knew I shouldn\'t have fallen behind on my brain bill !!) Thanks.',NULL,0);
INSERT INTO comment VALUES (9484,669,3172,'SilverKnight','re: Can someone please tell me where I went wrong ?','2003-11-13 21:11:38',0,'Sure Dan,\r\n\r\nYou were mistaken about what happens in time interval t2.\r\n\r\nYou wrote:\r\n\"In time interval t2, A sails X-700 yards west, then X-300 yards east, for a total of 2X-1000 yards, while B sails 700 yards east and 300 yards west, for a total of 1000.\r\n\r\nYou should have written:\r\nIn time interval t2, A sails X-700 yards West, then 300 yards East, for a total of X-400 yards, while B sails 700 yards East and X-300 yards West, for a total of X+400 yards\r\n________________________________-\r\n\r\nThen when you set up your equations you would have done:\r\n\r\n700/(X-700) = (X-400)/(X+400)\r\n... cross multiply ...\r\n700X + 280000 = X² - 1100X + 280000\r\n700X = X² - 1100X\r\n0 = X² - 1800X\r\n0 = X(X-1800)\r\n\r\nX = 1800 (throwing away the zero)\r\n\r\n(and this is somewhat similar to what Charlie did)',9483,0);
INSERT INTO comment VALUES (9485,1351,4057,'Jason','Problem','2003-11-13 21:18:16',0,'Its messed up because of the spacing, its too obvious. Maybe next time, type more carefully.',NULL,0);
INSERT INTO comment VALUES (9486,1351,4057,'Jason','Flaws','2003-11-13 21:20:21',0,'Forgot to indent, and possibly an antecedant confusion. Depends on how you look at it',NULL,0);
INSERT INTO comment VALUES (9487,1493,4057,'Jason','hehehe','2003-11-13 21:27:27',0,'VERY nice with the \'urban vernacular\', Fatboy. LOL!',NULL,0);
INSERT INTO comment VALUES (9488,1238,4057,'Jason','re: solution','2003-11-13 21:31:36',0,'Justify.',9462,0);
INSERT INTO comment VALUES (9489,1488,4057,'Jason','','2003-11-13 21:35:54',0,'1) Don\'t look a gift horse in the mouth\r\n2) BRAIN SHUT DOWN\r\n3) Don\'t put all your eggs in one basket\r\n4) Birds of a feather, stick together\r\n5) BRAIN SHUT DOWN',NULL,0);
INSERT INTO comment VALUES (9490,669,3196,'Dan','re(2): Can someone please tell me where I went wrong ?','2003-11-13 21:42:19',0,'Thank you so much, SilverKnight !! Now that you\'ve pointed it out, it\'s so obvious !! I guess now I understand why, whenever I go to the mind reader, she always offers me a big discount. I just put a big sign on my bathroom mirror that reads: \"Warning. Objects in this mirror are dumber than they appear.\"\r\n \r\nBut thanks again !!!!!\r\n \r\nCheers, \r\n \r\nDan ',9484,0);
INSERT INTO comment VALUES (9491,1235,4300,'Minion123','my solution','2003-11-14 01:30:12',0,'he can say it till August 8 2000',NULL,0);
INSERT INTO comment VALUES (9492,1239,1183,'fwaff','Solutions','2003-11-14 08:08:35',3,'One solution\r\n1A = Roman\r\n3A = Tiler\r\n1D = Right\r\n2D = Nadir\r\n\r\nAnother Solution\r\n1A = Salad\r\n3A = Mason\r\n1D = Sperm\r\n2D = Drain\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (9493,1239,1301,'Charlie','re: Solutions--another possibility','2003-11-14 09:10:32',0,'My solution was the same as fwaff\'s except instead of Roman I had reign. Roman is probably better, as that particular Roman was Caesar, while the particular reign was Caesar\'s and there is not \"\'s\" in the clue.',9492,0);
INSERT INTO comment VALUES (9494,1239,3196,'Dan','Another possibility, in addition to the previous ones','2003-11-14 11:59:59',0,'If \"grout and mortar\" is \"plaster\", and \"getting plastered\" means getting drunk (i.e. being a \"toper\") then...\r\n1A = Roman, 3A = Toper, 1D = Right, 2D = Nadir\r\nAlso, someone who works with grout and mortar is also a \"maker\". And if \"dinar\" is accepted as an anagram for \"dinar\" (by transposing zero letters...GROAN....) that yields:\r\n1A = Salad, 3A = Maker, 1D = Sperm, 2D = Dinar \r\n\n\nEdited on November 14, 2003, 1:20 pm',NULL,0);
INSERT INTO comment VALUES (9495,669,3529,'Senthil Kumar','Solution','2003-11-14 13:39:23',0,'Frist time when they meet the speed ratio is:\r\n 700 : X \r\n 1400 : 2X -> (1)\r\n\r\nFrom Second time:\r\n X+300 : (1400+X-300)\r\n X+300 : 1100 + X -> (2)\r\n\r\nSubstitute (1) in (2) gives:\r\n X = 1100\r\nSo Total yards T = 700 + X = 1800.\r\n \r\n\r\n',NULL,0);
INSERT INTO comment VALUES (9496,1497,3172,'SilverKnight','solution','2003-11-14 15:24:11',3,'Any right triangle can be placed on a Cartesian coordinate system such that the vertex between the two legs (opposite the hypotenuse) is at the origin.\r\n\r\nThen the two other vertices can fall on (0,Y) and (X,0) respectively.\r\n\r\nClearly at the midpoint of the hypotenuse (which occurs at (X/2, Y/2) ) , the distance is exactly half way between (X,0) and (0,Y)...\r\n\r\nAnd, if I draw the line segment from (X/2, Y/2) to the origin, then I have either of two iscocoles triangles, which shows that it is the same distance as to either other vertex.\r\n_______\r\n\r\nSo, all vertices are equidistant (equal radius) from the midpoint of the hypotenuse.\n\nEdited on November 14, 2003, 3:25 pm',NULL,0);
INSERT INTO comment VALUES (9497,1239,3196,'Dan','Here\'s an creative solution.....','2003-11-14 15:24:29',0,'The term \"grout and mortar guy\" could be metaphorically used to describe a particularly florid writer. (e.g.\"In his latest novel, he really lays it on with a trowel!! He\'s a real grout and mortar guy\") So..... \r\n\r\nAcross\r\n1. Joker (e.g. Sid Caesar) \r\n3. Onnad (Danno Onnad, noted writer) \r\nDown:\r\n1. Jumbo (synonym for whale)\r\n2. Ranid (a kind of frog) \r\n\r\nEdited on November 14, 2003, 3:30 pm\n\nEdited on November 14, 2003, 3:50 pm',NULL,0);
INSERT INTO comment VALUES (9498,1497,3172,'SilverKnight','re: solution','2003-11-14 15:42:08',0,'This is probably redundant, but in case it isn\'t clear what isosceles triangles I\'m referring to in the previous comment....\r\n\r\nOne triangle is made up of:\r\nhypotenuse midpoint (X/2, Y/2),\r\none vertex (X,0), and\r\nthe origin (0,0)\r\nwith both equal sides (X/2, Y/2)-(0,0) AND (X/2, Y/2)-(X,0)\r\n\r\nThe other triangle is made up of:\r\nhypotenuse midpoint (X/2, Y/2),\r\none vertex (0,Y), and\r\nthe origin (0,0)\r\nwith both equal sides (X/2, Y/2)-(0,0) AND (X/2, Y/2)-(0,Y)\r\n',9496,0);
INSERT INTO comment VALUES (9499,1497,1301,'Charlie','another way','2003-11-14 15:55:04',3,'Place the center of the hypotenuse at the origin of cartesion coordinates, and make the legs parallel to the coordinate axes. The equation of a circle with origin at the center will be x²+y²=r² where r is half the length of the hypotenuse. By symmetry the coordinates of the vertices that do not match, will be the negative of each other and also on this circle, where the squaring removes the effect of the sign.',NULL,0);
INSERT INTO comment VALUES (9500,1351,4315,'Edward E. Kang','Very Simple Solution.','2003-11-14 17:46:50',3,' Although this question is off-topic, but the paragraph is not indented. Also the third sentence is a run-on sentence.',NULL,0);
INSERT INTO comment VALUES (9501,1358,4256,'gary','Logical answer','2003-11-14 18:12:33',0,'Answer: if the mother had 1 son then there would be 0 brother 0 sister and if 1 daughter then she would have 1 brother so that is the key … the mother is childless or has 1 son because ALL children have the same amount of sisters and brothers.',NULL,0);
INSERT INTO comment VALUES (9502,666,3386,'Victor Zapana','re: this one is easy','2003-11-14 18:29:07',0,'hmm.... i think what ravi meant for this problem is that ABCDE is a 5-digit integer, but i can see how u can make a case otherwise. so gud job',9479,0);
INSERT INTO comment VALUES (9503,650,4256,'gary','everyone missing something','2003-11-14 18:50:46',0,'Answer: Considering you are blindfolded and not allowed to see what you are doing ... you feel or run your finger nail in crossing motion over the surface of each penny. If smooth and no rough vibration that is the heads up side and if you get a rough surface like a ladder or rail road track those are tails up. Once you have the smooth surface separated then you count the number of tails up and subtract the smaller amount from the lager amount. Example Only: 128 smooth side up (Heads) and 114 rough side up (tails) then you bring 7 smooth side up to the rough side up and then flip the rest of the rough side over one at a time. thus you would have two groups of 121 coins to the smooth side up.\r\n\r\nAgain the Key: when you scratch cross ways on a tail up penny you feel the same effect as a tire on a ripple median on the highway breakdown lane which is there to wake up a nodding driver.\r\n\r\nGary\r\n',NULL,0);
INSERT INTO comment VALUES (9504,1497,3196,'Dan','re: solution','2003-11-14 19:27:26',0,'I\'m afraid your solution fails to take into account things like wind resistance and the current of the river. (It said we shouldn\'t do that in the boat/river puzzle, but it didn\'t say we shouldn\'t do that in this one.)\r\n \r\n:-) ',9496,0);
INSERT INTO comment VALUES (9505,1451,4256,'gary','solution','2003-11-14 20:28:37',0,'“Either Holland was better than Italy, or Greece won gold.” At this point Greece is in the lead for the gold with Italy second for the Silver and Holland third place. If Holland beat Italy Holland would be tied for the gold with Greece and Italy would get the silver or the bronz depending on if Holland scored high enough to beat out Greece \r\n\r\nAn Italian reporter heard that, and commented that even knowing his own country’s final place, he wasn’t able to deduce the other places. Thus Italy would be in third place leaving Greece and Holland at odds for First and second place depending on how much Holland beat Italy. \r\n\r\nCuriously, a Dutch reporter who knew Holland’s final place, and who hadn’t heard the other reporter, made exactly the same remark. With Holland tied for 1st place with Greece that leaves Italy in second place. Unless Holland beat Greece putting Greece in second place.\r\nRemember a tie for the gold goes down just that way.\r\n',NULL,0);
INSERT INTO comment VALUES (9506,1351,3558,'Tristan','re: Very Simple Solution.','2003-11-14 21:57:13',0,'The third sentence is not a run-on, but it has other mistakes besides the intended one (see lower comments). \"It\'s not too hard to spot,\" need not be followed by a comma, since it is only a compound predicate. It\'s just a rather complex and awkward sentence that could be written better. But we all make mistakes; you yourself wrote a grammatically incorrect sentence in your comment.',9500,0);
INSERT INTO comment VALUES (9507,1493,4256,'gary','Too Easy','2003-11-14 22:35:06',0,'Chess Match',NULL,0);
INSERT INTO comment VALUES (9508,1238,4323,'Benjamin J. Ladd','Solution','2003-11-15 07:03:18',0,'The answer is 0. As the hypotenuse forms the diameter of the semicircle the dog is alotted to roam in, regardless of the dimensions of the right triangle, that right triangle will always be completely inscribed within that semicircle. Moreover, the point where the legs meet on the triangle will always lie on the circumference of the circle. A more detailed proof (Euclidean) can be obtained if required--but I hope this will be sufficient.',NULL,0);
INSERT INTO comment VALUES (9509,86,1626,'Gamer','Ideas','2003-11-15 07:42:07',0,'I think I could say 3.999 doesn\'t really exist. You will never find a number that has such a repeating decimal and terminates. (Of course!) So we really are infringing on infinity here, and the proofs that 1=2 because multiplying both sides by 0 is an identity.\r\n\r\nAlso, my example and yours are the same idea. If you put an infinite tower of blocks together, such that nothing is between them, could you say that the top block is the same as the one below it?',NULL,0);
INSERT INTO comment VALUES (9510,86,3558,'Tristan','re: Ideas','2003-11-15 10:29:59',0,'I disagree. I think you\'re using analogies in the wrong way.',9509,0);
INSERT INTO comment VALUES (9511,1236,3840,'Hal9000','re(3): A footnote to this problem','2003-11-15 10:58:40',0,'That sounds more like comic violence, I find that easier to digest.',9469,0);
INSERT INTO comment VALUES (9512,670,4064,'rerun141','first thoughts','2003-11-15 11:06:34',0,'doubt this will help but the sum of the digits of multiples of thirteen (and the sum of those digits if their 2 digit numbers) goes in a patern:\r\n4,8,3,7,2,4,1,5,9. Therefore, sice 3 and 6 arent present in the patern, we can rule out 2 and 8.\r\n49*1+2=51. 5+1=6.\r\n49*1+8=57. 5+7=12. 1+2=3.\r\n ',NULL,0);
INSERT INTO comment VALUES (9513,670,1301,'Charlie','solution','2003-11-15 11:32:16',3,'The powers of 10 mod 13 repeat in a cycle of 6:\r\n 0 1\r\n 1 10\r\n 2 9\r\n 3 12\r\n 4 3\r\n 5 4\r\nThe next power (10^6) is again 1 mod 13 and the cycle starts again.\r\n\r\nThese total 39, which is 0 mod 13\r\n\r\nFifty ones is the sum of the powers of 10 from 0 to 49, which is [50/6]=8 times through the cycle plus the first two remainder. So the string of fifty ones is (1+10) mod 13 or 11. We need to add two more mod 13 to get to zero mod 13 so that it would be divisible.\r\n\r\nThe 26th digit in the fifty-digit number is the 25th from the right, representing 10^24. Representing the exponent mod 6 since there is a cycle of six in the mod-13 values, that\'s 10^0, or 1. We need to add just 2 in that position, making that position a 3, which is the answer.',NULL,0);
INSERT INTO comment VALUES (9514,670,1301,'Charlie','Less thinking using extended precision','2003-11-15 11:46:40',3,'The mod-13 values could be found directly via extended precision provided by UBASIC:\r\n\r\nlist\r\n 10 point 15\r\n 20 for I=0 to 49\r\n 30 N=N+10^I\r\n 40 next\r\n 50 print N@13\r\n 60 print (10^24)@13\r\nOK\r\nrun\r\n 11\r\n 1\r\nOK\r\n\r\ntelling us the original mod value and the mod value\r\nfor each additional point in the 26th position, then:\r\n\r\n? 11111111111111111111111113111111111111111111111111 @ 13\r\n 0\r\nOK\r\n
\r\n---------\r\nWith the latter immediate-mode print command (the ?) being a check on the answer.\r\n',9513,0);
INSERT INTO comment VALUES (9515,687,1732,'Helen','don\'t force it','2003-11-15 17:27:10',0,'When the bucket is stationary, the only forces acting on the cork are its weight, and the buoyancy force. The buoyancy force is proportional to the weight of liquid displaced.\r\n\r\nWhen freefalling, it is as if the cork and the liquid both have no weight. Therefore the situation is equivalent to no forces acting on the cork, so it will stay where it is in relation to the bucket - at the bottom.\r\n',NULL,0);
INSERT INTO comment VALUES (9516,1351,2707,'Gordon Steel','Solution to Not Another One.','2003-11-15 17:47:46',0,'If carefully, read, the paragraph shows three instances of having a word at the end of one line and then using the same word as the start of the next line. The three words are \"you\" (lines 1 and 2). \"not\" (lines 2 and 3) and \"over\" (lines 3 and 4). Gordon S.',NULL,0);
INSERT INTO comment VALUES (9517,1238,1301,'Charlie','re: Solution','2003-11-15 22:09:39',0,'The triangular one-acre tract is not the whole pasture. Both the dog and the sheep are free to travel through their whole circles, not just the semicircles that are within the triangle. At least, that\'s the reading of the people who come up with non-zero answers.',9508,0);
INSERT INTO comment VALUES (9518,151,3351,'Eric','re: another possible answer','2003-11-16 00:55:12',0,'Nellie 8100000000 is not a solution because there is an 8 in the number making H greater than 0',8582,0);
INSERT INTO comment VALUES (9519,151,3351,'Eric','re: 6210001000','2003-11-16 00:56:03',0,'Tim, could you please refrain from putting the solution in the subject line. \r\n\r\nThank you',3461,0);
INSERT INTO comment VALUES (9520,670,3351,'Eric','a little more straightforward','2003-11-16 01:07:26',3,'note that 111111 is divisible by 13. (13*8547)\r\n\r\nlikewise every group of six consecutive ones in the 50 digit number is divisible by sixteen. \r\n\r\nRemoving the first and last 24 (4*6) digits of our 50 digit number leaves us with only the 25th and 26th digit. \r\n\r\nthe 25th digit is 1 and therefore the 26th must be 3 since 13 is divisible by itself.\r\n\r\nThat said, I very much appreciate the elegance of Charlie\'s solutions.',NULL,0);
INSERT INTO comment VALUES (9521,1497,3351,'Eric','re(2): solution','2003-11-16 01:23:03',1,'That is an excellent point Dan,\r\n\r\nIn fact I believe that we have neglected these variables in quite a few of our solutions. Perhaps a \"flooble-wide neglected variable audit\" is in order. I propose we go back into the archives and reconsider any more poorly tested solutions that we find. Should we find this problem to be as rampant as we might suspect, we could extend this audit to the vast expanse of the internet in its entirety. Who knows how many innocent problem solvers across the planet have been horribly disillusioned by overly-simplified solutions.\r\n\r\nNow is the time Dan, we have the power to begin the revolution. Never underestimate the ability of a small group of concerned citizens to change the world, indeed it is the only thing that ever has!',9504,0);
INSERT INTO comment VALUES (9522,1497,3109,'Roger','re: solution','2003-11-16 08:12:52',0,'Now that we have established that the midpoint is at (X/2, Y/2) we can then break it down\r\n\r\nPythagorean theorem states that X² + Y² = H²\r\n\r\nTherefor the radius of the circle is (√(X² + Y²))/2\r\n\r\nWe also know that the secondary hypoteneuse from midpoint to vertex of right angle will have a distance of √((X/2)² + (Y/2)²)\r\n\r\nThrough equating these two above equations results in a true statement, we know that a cicle will pass through all vertexes.',9496,0);
INSERT INTO comment VALUES (9523,1447,153,'TomM','Solution','2003-11-16 09:13:58',3,'\r\nTakaetshemoenecytothreswientgingbrmidgeethseothsersidaeoftgowen.\r\n\r\ntakAetShemoEneCytothReswiEnTgingbrMidgeEthSeothSersidAeoftGowEn.\r\n\r\ntak et hemo ne ytoth eswi n gingbr idge th eoth ersid eoft ow n.
A S E C R E T M E S S A G E\r\n\r\nTake the money to the swinging bridge the other side of town.\r\nA SECRET MESSAGE',NULL,0);
INSERT INTO comment VALUES (9524,1447,4256,'gary','Solution','2003-11-16 09:34:44',0,'Take the money to the swinging bridge the other side of town\r\n a secret message ',NULL,0);
INSERT INTO comment VALUES (9525,1345,4340,'and silvis','hmmmmmmm','2003-11-16 09:50:38',1,'Could taxes have an effect?',NULL,0);
INSERT INTO comment VALUES (9526,1447,1301,'Charlie','which one or both?','2003-11-16 10:46:17',4,'Now, which of those two messages is the secret message?\r\n\r\nAnd is there a pattern to where the letters of the shorter one are placed in the longer one?',NULL,0);
INSERT INTO comment VALUES (9527,1220,4323,'Benjamin J. Ladd','I\'m no mathemetician:','2003-11-16 12:04:21',3,'I don\'t know if this is the solution, but I did arrive at a different answer than everyone else. My approach was to take the chord of radius r, draw the two radii to the center of the circle, and then calculate the distance of the line segment bisecting the chord (found here using the same method as (1/2r)*√3 that a few people used. I then used that point of bisection and drew a circle of radius (1/2r)*√3 and calculated the probability of the arc falling in the central circle (where the chord taken at random would have to be greater than the radius) compared to the area of the whole circle. The pi*r²\'s cancel and you are finally left with 3/4 or 75%.',NULL,0);
INSERT INTO comment VALUES (9528,1220,4323,'Benjamin J. Ladd','re: I\'m no mathemetician:','2003-11-16 12:31:20',1,'I actually (after thinking about it) think that this is a safe way of determining the probability. If you take a point at random in the circle you can always form a chord out of that line such that the radius runs perpendicular through the point. Because every chord formed in a circle can be represented in such fashion by such points (only one point necessary), the area that was presented in my proof should account for the infinite amount of chords (and chords) that can be taken at random.',9527,0);
INSERT INTO comment VALUES (9529,1447,3196,'Dan','This is my kind of problem !!','2003-11-16 12:47:44',3,'Takaetshemoenecytothreswientgingbrmidgeethseothsersidaeoftgowen = \r\na secret message\r\n+\r\nTake the money to the swinging bridge the other side of town.\r\n \r\nThe secret message is \"a secret message\". \n\nEdited on November 16, 2003, 1:02 pm',NULL,0);
INSERT INTO comment VALUES (9530,1447,3386,'Victor Zapana','re: which one or both?','2003-11-16 12:52:48',0,'like what dan sed, it is indeed \"a secret message,\" for if you take it out, the other message makes coherent sense. Also, by looking at it, there isn\'t really any pattern. It\'s probably just randomly put in.',9526,0);
INSERT INTO comment VALUES (9531,670,3386,'Victor Zapana','re: a little more straightforward','2003-11-16 12:57:06',0,'finally a solution i understand lol. gj',9520,0);
INSERT INTO comment VALUES (9532,86,3172,'SilverKnight','re(2): Ideas','2003-11-16 13:03:20',0,'I must agree with Tristan.... Gamer, your analogies don\'t apply.\r\n\r\nWhat\'s more... you wrote:\r\n\"...I could say 3.999 [sic] doesn\'t really exist.\r\n\r\nIf you mean 3.999..., then generally, that is denoted with 3.9 with the 9 having a bar over it, indicating a repeating decimal. It exists simply because we write it in our nomenclature, and algebra has means to deal with such numbers.',9510,0);
INSERT INTO comment VALUES (9533,1220,4323,'Benjamin J. Ladd','A revised solution:','2003-11-16 13:10:01',3,'Every chord can be represented by only it\'s midpoint (the radius always perpendicularly bisects a chord). If we take any chord whose length is equal to that of the radius and use its midpoint to draw an inner circle, we will have divided the areas of the circle into possible places for chords to fall. If a chord is selected at random, it\'s midpoint will either lie in the region whose chord is larger than, smaller to, or equal to the radius.\r\n\r\nFor a circle of radius r, the radius of the inner circle will be 1/2r√3. To compare the probability of all chords produced that are greater than the radius, we can divide the area of the inner circle by the area of the entire circle. The equation for this is:\r\n\r\npi*(1/2*r*√3)²/pir²\r\n\r\nAnd the final result after the pi*r² is cancelled is 3/4. Therefore there is a 75% chance that a randomly drawn chord will be longer than the radius of the circle.',9527,0);
INSERT INTO comment VALUES (9534,1447,3196,'Dan','Here is an improved version of this puzzle','2003-11-16 13:28:01',0,'The following string of letters contains a secret message. Once you have found it, the rest of it is very easy to figure out.\r\n\r\ntuoerueggiafsosteymstaeerycreesva\r\n\r\nAnswer:\r\n\r\ntuoerueggiafsosteymstaeerycreesva\r\n\r\n= egassemtercesa + tuorugifotysaeyrev\r\n\r\n= \"a secret message\" + \"very easy to figure out\"\n\nEdited on November 16, 2003, 1:29 pm',NULL,0);
INSERT INTO comment VALUES (9535,1447,1626,'Gamer','Not really :)','2003-11-16 13:59:51',0,'I think the way Lewis did it is fine. First of all, you can actually solve it. Second of all, the letters aren\'t scrambled. :)',NULL,0);
INSERT INTO comment VALUES (9536,1089,4344,'Kevin Foster','re: A preliminary thought for half of a solution','2003-11-16 14:04:44',0,'hey... I\'ve been trying to get ahold of you... :/\r\nyou\'re very difficult to find. Hope you get this and can get in contact with me.',7192,0);
INSERT INTO comment VALUES (9537,1447,3196,'Dan','re: Not really :)','2003-11-16 14:44:33',0,'The letters aren\'t scrambled in the improved version either. The two strings are in perfect reverse order once you disentangle them from each other. Besides, these puzzles are supposed to be difficult. Lewis\' version was too easy. :0) \n\nEdited on November 16, 2003, 2:46 pm',9535,0);
INSERT INTO comment VALUES (9538,86,3558,'Tristan','more thoughts','2003-11-16 15:47:57',1,'Gamer, you apparently aren\'t convinced. Here\'s yet another proof for you:\r\n\r\nImagine the function f(x)=4-1/(10^x).\r\nThe line would be 3.9999..., where x is the number of 9s, right? Well, as x approaches infinite, f(x) approaches 4. So 3.999... with infinite nines is 4. You\'ll probably disagree with this still, and I myself admit there might be a problem somewhere.\r\n\r\nTo adress your other doubts, the fact that two different numbers have more numbers inbetween on the number plane I think is a postulate. If you want to go questioning postulates, than maybe the reflexive property is false as well, and 4 doesn\'t equal 4.\r\n\r\nOn dividing by 0 or infinite, I think those count as postulates as well. I think you know why people think we can\'t divide by zero. You might say we actually can. If you graph all the points where x/0=y is true (not really a function), then you will get the y-axis. x/0 can equal anything, then. But this has its limits, or you would be able to prove 1=0, and 3.9=4. As for infinite, ∞+1=∞. Infinite is the highest you can go by definition.\r\n\r\nIf you\'re actually just trying to make us think or something to that effect, well good job then. Keep it up and I\'ll have to make up a dozen more proofs.\r\n\r\nEdited on November 16, 2003, 3:49 pm\n\nEdited on November 16, 2003, 3:51 pm',NULL,0);
INSERT INTO comment VALUES (9539,1447,4346,'MILLIE','SOLUTON','2003-11-16 16:12:45',0,'TAKE THE MONEY TO THE SWINGING BRIDGE THE OTHER SIDE OF TOWN-\r\n\r\nTHE REMAINING LETTERS WRITE: A SECRET MESSAGE',NULL,0);
INSERT INTO comment VALUES (9540,1447,4347,'Sandi','I am confused','2003-11-16 16:51:05',0,'This is my first puzzle, but I am sort of confused. I found \"A secret message\" but the rest is not a sentence..Take the money to the swinging bridge the other side of town. I could not find a pattern...or maybe there wasn\'t one??',NULL,0);
INSERT INTO comment VALUES (9541,360,4256,'gary','too easy','2003-11-16 17:10:11',0,'nothing is the answer',NULL,0);
INSERT INTO comment VALUES (9542,1447,3196,'Dan','re: I am confused','2003-11-16 17:52:25',0,'Sandi writes: \"..I am sort of confused...the rest is not a sentence..Take the money to the swinging bridge the other side of town. I could not find a pattern...or maybe there wasn\'t one??\"\r\n \r\nWelcome to flooble, Sandi. There\'s no shame in being confused. I am often confused for Brad Pitt. As for your question, \"Take the money to the swinging bridge the other side of town\" is an elliptical sentence. (An ellipsis is the omission of one or more words that are obviously understood but that must be supplied to make a construction grammatically complete). For instance, when someone says \"Coming !!\" they really mean \"I am coming !!\". In \"\"Take the money to the swinging bridge the other side of town\", the word \"on\" is missing but is understood, as in \"Take the money to the swinging bridge on the other side of town\". \r\n\r\n:-)',9540,0);
INSERT INTO comment VALUES (9543,1447,1626,'Gamer','re(2): I am confused','2003-11-16 18:26:57',0,'Yex, I mentioned this in the queue. But I didn\'t change it because it could be thought to be a sentence. It is like an elliptical sentence, I would call it a parenthetical sentence the way I saw it. Take the money to the swinging bridge (the other side of town)',9542,0);
INSERT INTO comment VALUES (9544,1447,3372,'Sam','re(2): I am confused','2003-11-16 19:58:49',0,'\"Take the money to the swinging bridge the other side of town\" is an elliptical sentence.\r\nSo you say. Me, I think it\'s more likely that the spy (or Lewis) just missed out a word. It happens even to the best of us when we\'re trying to encrypt a sentence :)
\r\nI\'m wondering if DJ was not looking for either a different pattern or a different name to fit it.',NULL,0);
INSERT INTO comment VALUES (9632,671,2716,'Federico Kereki','Short','2003-11-19 11:58:44',3,'If the mean was 1.8 higher, the sum of the numbers was 18 higher, which means the interchanged numbers had a difference of 18/9 = 2. (This is an old trick used by accounting people to find mistyped numbers.)',NULL,0);
INSERT INTO comment VALUES (9633,671,4082,'wonshot','solution','2003-11-19 12:30:30',0,'(X + Y)/10 - (X + Z)/10 = 1.8\r\n\r\nX = sum of the 9 positive integers with 2 digits\r\nY = ba\r\nZ = ab\r\n\r\nY - Z = 18 \r\nTherefore, \r\n(y,z) = (31,13) ; (42,24); . . .;(97,79)\r\nIn each case (b - a) = (-2).',NULL,0);
INSERT INTO comment VALUES (9634,1497,885,'np_rt','Solution without Analytic Geometry','2003-11-19 13:08:47',0,'Consider the right triangle ABC with angle C as the right angle. Let D be the midpoint of the hypotenuse. Draw the circle with center D and radius equal to one-half of the hypotenuse. By definition, this circle contains points A and B. So the proof is to show that C is on the circle.\r\n\r\nFirst of all, measure of any inscribed angle of a circle is half the measure of the arc. If C were on the circle, it would have a measure of one-half of the arc AB. Since AB is a diameter, arc AB has a measure of 180, so angle C would have to be a right angle if it were on the circle.\r\n\r\nTo prove the converse, we use an indirect proof. Assuming that C is not on the circle. We could find a point P on the line formed by AC (or BC) that intersects the circle. Then angle APB must be a right angle by the above. However, you can only draw ONE unique perpendicular through one point (point B in this case) to a given line (AC in this case). Hence, this is a contradiction, which means that C must be on the circle.\r\n\r\nSince A, B, and C are on the circle, they are all equidistant from the midpoint of the hypotenuse. Therefore, drawing any circle with the center on the midpoint of the hypotenuse and containing at least one of the vertices will contain all three.\r\n\r\nQED',NULL,0);
INSERT INTO comment VALUES (9635,1351,4176,'Joe C','w00t','2003-11-19 14:28:09',0,'it is repeating words \"you\" \"not\", \"over\", and \"and\"',NULL,0);
INSERT INTO comment VALUES (9636,279,2716,'Federico Kereki','Easy solution','2003-11-19 15:26:05',3,'You can write\r\n\r\nlim (x*x*x*x....x)\' = N\r\n x-->2^0 + 0*3 \r\n\r\nand there should be N \"x\" in the product.',NULL,0);
INSERT INTO comment VALUES (9637,1240,1301,'Charlie','the words','2003-11-19 15:30:16',1,'When the Random House Unabridged Dictionary CD is asked for all the 8-letter words ending in ther, it gives aweather, breather, ingather, regather, sheather, smoother, Strother, together, untether, upgather and wreather.',NULL,0);
INSERT INTO comment VALUES (9638,1474,3172,'SilverKnight','interesting problem...','2003-11-19 15:51:52',1,'I think it\'s difficult to analyze directly, because the conditional probabilities quickly grow quite complex... kind of like trying to analyze the game of black jack.\r\n\r\nMy thoughts would be to run this through computer simulations (this is a relatively easy problem to simulate) and analyze the results of performing one million trials of this.\r\n\r\nThen we could determine the mean, median, mode, of the number of cards drawn.\r\n\r\nBTW, it is not clear what this question is asking....\r\n\r\nFor instance, it may be that we can expect to get three of a kind (I\'m making these figures up) before reaching the 22nd card (say... 50.0034% occur on or before the 22nd card), but it may be the most likely card to be the third of three-of-a-kind might be the 19th card pulled.\r\n\r\nFor which of these questions is Lewis after the answer? (Although if one performs the simulation, it should be trivial to answer both).\r\n_______________________________\r\n\r\nLastly, a couple of observations...\r\n\r\n\r\n 3 2353 0.0023529 0.0023529\r\n 4 6915 0.0069148 0.0092677\r\n 5 13541 0.0135414 0.0228091\r\n 6 22028 0.0220275 0.0448367\r\n 7 32059 0.0320592 0.0768958\r\n 8 43179 0.0431794 0.1200752\r\n 9 54772 0.0547716 0.1748468\r\n10 66065 0.0660651 0.2409119\r\n11 76172 0.0761724 0.3170843\r\n12 84160 0.0841603 0.4012447\r\n13 89155 0.0891549 0.4903995\r\n14 90472 0.0904717 0.5808713\r\n15 87752 0.0877525 0.6686237\r\n16 81077 0.0810771 0.7497008\r\n17 71020 0.0710195 0.8207203\r\n18 58613 0.0586129 0.8793333\r\n19 45210 0.0452103 0.9245436\r\n20 32252 0.0322518 0.9567953\r\n21 20987 0.0209866 0.9777819\r\n22 12227 0.0122267 0.9900086\r\n23 6213 0.0062133 0.9962220\r\n24 2650 0.0026498 0.9988717\r\n25 891 0.0008912 0.9997630\r\n26 211 0.0002107 0.9999737\r\n27 26 0.0000263 1.0000000\r\n28 0 0.0000000 1.0000000\r\nMedian is 13.10611589574091\r\nMean is 13.55606605519886\r\n
\r\n-------\r\nWhere the second column shows the probability of that run length multiplied by 1,000,000 to facilitate comparison to the previous simulation results; the third column shows the probability as calculated; the fourth shows the cumulative probability, which does reach 1 at the number of draws equal to 27.\r\n\r\nIf the decks variable is changed to 2 and the program run, it produces:\r\n\r\n 3 3998 0.0039977 0.0039977\r\n 4 11399 0.0113994 0.0153971\r\n 5 21659 0.0216589 0.0370561\r\n 6 34114 0.0341138 0.0711699\r\n 7 47909 0.0479086 0.1190785\r\n 8 61979 0.0619789 0.1810574\r\n 9 75096 0.0750961 0.2561534\r\n10 85972 0.0859715 0.3421249\r\n11 93411 0.0934109 0.4355359\r\n12 96498 0.0964977 0.5320336\r\n13 94770 0.0947703 0.6268038\r\n14 88347 0.0883470 0.7151509\r\n15 77958 0.0779581 0.7931090\r\n16 64854 0.0648540 0.8579630\r\n17 50596 0.0505958 0.9085587\r\n18 36765 0.0367655 0.9453242\r\n19 24670 0.0246696 0.9699939\r\n20 15118 0.0151177 0.9851115\r\n21 8340 0.0083402 0.9934517\r\n22 4064 0.0040637 0.9975154\r\n23 1703 0.0017029 0.9992182\r\n24 590 0.0005902 0.9998085\r\n25 159 0.0001590 0.9999675\r\n26 30 0.0000297 0.9999971\r\n27 3 0.0000029 1.0000000\r\n28 0 0.0000000 1.0000000\r\nMedian is 11.66803791319374\r\nMean is 12.21442208680124\r\n
\r\n--------\r\nThese numbers, including the medians and the means, compare well with the simulation results.\r\n',NULL,0);
INSERT INTO comment VALUES (9726,1383,4424,'kimberly','we got this','2003-11-21 00:24:21',0,'1763',NULL,0);
INSERT INTO comment VALUES (9743,1474,1301,'Charlie','Notes on the solution','2003-11-21 16:04:16',0,'The computation of each term is somewhat of a hybrid of combinations and permutations, as one select card is in the final position, with all 52 possibilities considered there, but only the combinations are considered for the first n-1 positions without regard to the order they are drawn.\r\n\r\nThe same computation was done also using UBASIC for the added precision and the builtin COMBI function. The results were the same, but the program looks nicer in QuickBasic, without the line numbers. UBASIC helped in the debugging as the need for the restriction on p+s being less than or equal to 12 was found by the argument checking that UBASIC does on the COMBI function, that I did not build into the subroutines in the QuickBasic program.',9742,0);
INSERT INTO comment VALUES (9744,670,4408,'Kirk','re(2): solution','2003-11-21 16:33:21',0,'It\'s all very well you doing these complicated methods, but you have to remember that average people are reading this and won\'t understand what you say! I\'m a 17 year old Maths and Further Maths student and have never come across \"mod\" numers (modulo i believe)...I think that\'s university level! I think Eric\'s solution to the 13 problem and my solution to the 11 problem are the most user friendly. They may not be as elegant mathematically - but a darn more people understand what\'s going on!',9718,0);
INSERT INTO comment VALUES (9745,1506,4189,'John','5s and 2s legal?','2003-11-21 16:42:57',4,'Ok, so we\'ve established that 1, 0, 6, 8, and 9 are still legible upside down. Obviously 3, 4, and 7 are out. What about 5 and 2? Are they legal? Do we read them like an LCD alarm clock? \r\n\r\n(P.S. Preliminarily, my answer to this one is \"no\", I probably can\'t do it. But that doesn\'t mean it can\'t be done!) =)',NULL,0);
INSERT INTO comment VALUES (9746,670,4374,'Richard','re(3): solution','2003-11-21 17:48:09',0,'Sorry, Kirk. I did not mean to intimidate you. Modular arithmetic should be pre-university, but maybe it isn\'t. It wasn\'t back in 1959 when I first went to college, but those were primitive times! Anyway, the idea is simply that given a fixed whole number m greater than 1 (called the modulus) we can do an interesting brand of arithmetic by only considering the remainders after dividing by m. When we do this, we say we are calculating modulo m, or for short, mod m. Two numbers are \"the same\" mod m (or \"congruent\" modulo m) if they leave the same remainder when divided by m. If we introduce the operator % (as in the C programming language) used to indicate remaindering, so that a%m means the remainder when a is divided by m, and use / to denote the quotient operation (or \"integer divide\") we have a=m*(a/m) + a%m=m*q+r. It is quite easy to show that (a+b)%m= (a%m+b%m)%m and (ab)%m= ((a%m)*(b%m))%m, which means we can remainder first before adding or multiplying without affecting the remainder of the result. It is this that makes casting out nines work as a checksum. Since (10^n)%9=1, 176923%9 =(1+7+6+9+2+3)%9=1. The same idea can be applied to digit problems using any value for m, although m=9 is the nicest for decimals, and m=11 is second nicest (since (10^n)%11=(-1)^n). \r\n\r\nWorking mod m is very basic in puzzle math. For example, working mod 7, it can be shown with a bit of work that every year must have at least one Friday the 13th (leap years must be treated separately). \r\n\r\nI hope this clears up the concept of \"mod m\" for you and enables you to begin to use it in solving problems. \r\n\r\n~Richard ',9744,0);
INSERT INTO comment VALUES (9747,1506,3386,'Victor Zapana','solution','2003-11-21 17:53:48',0,'96 11 89 68
This is a math kinds place and it sounds like you are ready to leap into the glorious math pantheon of Levik, Charlie et al. I thnk you will find their frank discussion (as well as that of DJ, fwaff and all the rest) quite stimulating.
\r\nIf I might make a suggestion, how about laying off teh criticism of other people\'s submissions? you ahve posted 7 comments on three problems and two of them have been complaints. IF you do not like a problme, give it a low rating (thats what the ratings are for.) Any regular flooblers will be surprised to read me defending silverknight but, you know, he found an interesting problem that folks seem to like. WHo cares if it was somewhere else first? After all most puzzles probably are, as mathematicians have had a darn long time to think them up.
\r\nAs for yor clever problem by including it in a comment, why not jsut post it the proper way? SK waited a darn long time to get his problems on, and he did so quite patiently with nary a complaint. Why can\'t you wait in line just like everyone else.\r\nI\'m done, thats my grip for the day',9942,0);
INSERT INTO comment VALUES (9946,1270,2839,'FatBoy','re(2): This is deja vu all over again','2003-11-28 17:02:18',0,'What do you know? \r\nI guess I wasn\'t really done after all.\r\nYou know, maybe the problem was childishly easy, but that is why it was posted early in the day. You see Flooble likes to give the mental midgits like myself a chance to stop drooling in our sippy cups and actually work a puzzle we enjoy. We realize it must be annoying to you, but chill out, take a moment to shine up your Nobel prize in Math.
Be patient. We won\'t clutter up your vision for too long and then we will fade back into our trogldyte obscurity.
\r\nI know, why don\'t you take a moment to prove Herons whatamacallit only using arithmatic, and a Captain Crunch decoder ring. When you do, post the results in teh forum. Someone is looking for it over there. ',9945,0);
INSERT INTO comment VALUES (9947,1270,4507,'Penny','re(2): This is deja vu all over again','2003-11-28 17:23:36',0,'Dear Fatboy:\r\n\r\nWho was it who once said that sarcasm is wasted on the young?\r\n\r\nI was not \"posting a problem without waiting in line like everybody else.\" I was being sarcastic!! That birthday riddle was so ridiculously easy that any idiot could figure it out in a few seconds. There are only so many combinations of single digit primes that are also prime numbers. The only reasonable ones for my boyfriend Sylvester and his Grandfather Garfield are 73 and 23. If Garfield was born in 1873, then he turned 73 in the year 1946. If Sylvester was born in 1923 (hey, I like older men !!) he turned 23 in 1946. \r\n \r\nSeecondly, I am sorry I was picking on SilverKnight. I know he\'s been having a rough time lately, as he is suffering a bout of anxiety. I understand that he recently said to his wife: \"Darling, I want to be completely honest with you. I am seeing a therapist.\" She replied \"Oh, that\'s nothing, sweetheart. I am currently seeing two therapists, three hockey players, four lumberjacks and a bartender.\"\r\n \r\nLastly, I couldn\'t help but notice the folllowing misspelled words in your post: vary, thnk, teh, ahve, problme, yor, jsut, and grip. If you can\'t afford a spellchecker, dude, I\'ll be happy to e-mail you the money.\r\n \r\nI\'m done, that\'s my gripe for the day.\r\n \r\n:-) ',9945,0);
INSERT INTO comment VALUES (9948,1270,1626,'Gamer','re(3): This is deja vu all over again','2003-11-28 18:13:55',0,'I am perfectly sure FatBoy doesn\'t know how to spell teh or ahve even though they are common words, and I am positive that you don\'t know what he means at all. You haven\'t been able to see the chatterbox, so of course you don\'t know where I am coming from from here. You also couldn\'t have read the forums where another such event happened, where someone used sarcasm less well so that nobody knew that person was joking.\r\n\r\nYou also get the right to criticize a few things that none of us others do. First of all, your less than perfect sarcastic skills, and the fact that you are proposing a puzzle then saying that \"any idiot could figure it out in a few seconds\".\r\n\r\n\r\nDoes this sound silly? I hope so... I had recently learned the limits of sarcasm; it\'s not terrible, but it\'s not the best approach. If we could post comments like FatBoy did, trying to have patience when people insult problems and when people try to explain problems that would get posted on the site with difficulty 1, Flooble would be a nicer place. If we could ignore some problems that might seem \"childishly easy. You just draw a few tables, eliminate possibilites, etc. No real insight or higher intelligence is required.\" and leave them for the people who prefer challenging puzzles lesser puzzles, it would be better.',9947,0);
INSERT INTO comment VALUES (9949,1511,4064,'rerun141','A\'s observations','2003-11-28 18:23:53',0,'A observes the bullet moving 1000 mph, whether the pistol is pointed forward or backward, obviously.\r\nThough obviously not the answer, B can\'t see the bullet, its moving far to fast for the brain to register...\r\nmore conclusive answer on b in a minute...',NULL,0);
INSERT INTO comment VALUES (9950,1396,4507,'Penny','re: Change:','2003-11-28 18:46:44',2,'Back to the drawing board, dude. You\'re in serious need of some hamburger helper !! Your \"improvement\" still allows for at least two valid solutions:\r\n\r\nA (Knave) wants ketchup,onions,relish,tomato. \r\nB (Knight) wants ketchup,tomato,cheese,lettuce. \r\nC (Knave) wants mustard,cheese,ketchup,onions. \r\n\r\nA (Knave) wants ketchup,onions,relish,tomato. \r\nB (Knight) wants ketchup,tomato,cheese,lettuce. \r\nC (Knave) wants mustard,cheese,onions,relish. \r\n\r\n',9936,0);
INSERT INTO comment VALUES (9951,1511,3351,'Eric','What a doppler effect!','2003-11-28 19:06:26',1,'Let us consider all this happening in a one dimensional x - axis number line sort of thing where B stands at the origin and A begins at say x = -1 light hours at t = 0 hours. One light-hour is about 600 million miles. At t =1 hour the very first wave of light will hit B\'s eyes, but by this time A will already be physically 10 miles away. So in the following 1/60 millionth of an hour B will witness A\'s entire 600 million mile arrival. Bullets aside, A will physically arrive at point x = 1 light-hour a hair after t = 2 hours. It wont be until t = 3 (plus another 1/60 millionth of an hour) for B to finally see A cover the same distance away from him/her.\r\n\r\n Since all these times are from B\'s point of view we must now introduce the most significantly relevant element of the theory of relativity. When mass is accellerated close to the speed of light, that mass\' energy becomes devoted to the travel itself. This occurs in such a way that for a passenger on a near-light speed craft, the trip seems to be near instantaneous. \r\n Theoretically, if A were actually travelling the speed of light, his/her trip would be completely instantaneous giving him/her no time to even pull the trigger. \r\n But A is travelling 10 mph less than light speed so let us say that the bullet leaves the gun precisely when A passes B (ignoring the acceleration of the bullet within the chamber) The bullet will then appear to be travelling (10mph*1000mph/600millionmph) = 1/60thousandths mph relative to A. The apparent speed of the bullet fired in the other direction would I believe be the same - although I\'ll return with some equations.',9949,0);
INSERT INTO comment VALUES (9952,1511,4064,'rerun141','re: What a doppler effect!','2003-11-28 19:18:06',0,'no, A has a right to his own frame of reference (according to his observation, nothing is moving, everything is realtive to him except the godd ol\' speed of light). A will see the same thing as he did on earth, a bullet moving 1000 mph.',9951,0);
INSERT INTO comment VALUES (9953,1511,1301,'Charlie','solution','2003-11-28 19:37:18',3,'The formula for the speed of an object when that object is moving at speed s1 with respect to another object that is already moving at speed s2 in the same direction is (s1+s2)/(1+s1*s2/c^2), where c is the speed of light.\r\n\r\nThe speed of light is 670616629.384395 mi/hr, so A\'s ship is moving at 670616619.384395 mi/hr relative to B\'s.\r\n\r\nSo the bullet, relative to B is travelling at\r\n\r\n(1000+670616619.384395) / (1+1000*670616619.384395/(670616629.384395^2))\r\n\r\n= 670616619.384424 mi/hr, or just .000029 mi/hr more than A\'s ship itself.\r\n\r\nThe alternative version, with A shooting rearward, just reverses the sign of the 1000 mi/hr:\r\n\r\n(-1000+670616619.384395) / (1-1000*670616619.384395/(670616629.384395^2))\r\n\r\n= 670616619.384365 mi/hr, or just .000030 mi/hr less than A\'s ship itself.\r\n\r\nOf course, relative to A, the bullet travels at 1000 mi/hr, regardless of the direction.\r\n',NULL,0);
INSERT INTO comment VALUES (9954,1396,1301,'Charlie','re(2): Change:','2003-11-28 19:42:26',0,'The first of those two solutions has all three wanting ketchup, while the new rule specifies not all three can have any of the same topping.',9950,0);
INSERT INTO comment VALUES (9955,1396,4507,'Penny','re(3): Change:','2003-11-28 20:08:45',0,'Good point, Charlie. I only missed that one because my boyfriend, Sylvester, was fooling around with two jars, 50 red marbles and 50 blue marbles. He told me he was about to pick one of the jars at random, and then pick a marble from the jar. He challenged me to place all the marbles in the jars (a maximum of 50 marbles will fit in each jar) so as to maximize the chances of a red marble being picked. I did so at once, and gave him the exact odds of getting a red marble as a result of my genius. Aren\'t you proud of me?',9954,0);
INSERT INTO comment VALUES (9956,1396,1626,'Gamer','re(4): Change:','2003-11-28 20:23:17',0,'No, not really. I feel that problem \"was so ridiculously easy that any idiot could figure it out in a few seconds.\" (This would go back into the \"non-uniqueness\" way of solving a such problem)\r\n\r\nI think it would be easier if you just said \"Sorry, I didn\'t realize that! as I did when I realized I had made a mistake, rather than go into super detail about why. I also am confused as to why you were typing while solving another problem involving jars. You seem smart enough not to insult another person while working on a puzzle. :)',9955,0);
INSERT INTO comment VALUES (9957,1511,3351,'Eric','re: What a doppler effect!','2003-11-28 21:59:53',0,'Okay, \r\n \r\n I recognize that there will be a difference in apparent speed of the bullet should the gun be fired in the negative x direction rather than the positive by the mini-doppler effect of the bullet itself. Now we will be working with REALLY small speeds. Since the bullet fired in the negative x direction is leaving B apparently slower than A is leaving B the doppler effect will detract from A\'s apparent speed more than it will detract from the bullet\'s apparent speed. More clearly, at time t = 2 (or so) A will be at x = 1 light-hour (or so) and the bullet will be at 1 light-hour - 1/60 thousandth of a mile (about 1 inch closer to B than A is). When B sees this inch seperation though, B will be seeing A before the bullet had spanned the inch making the bullet seem to be travelling even slower relative to A but not as slow as it would seem were the bullet fired away from B. Either way we are looking at speed differences way too small for me to figure. I hope someone else has fun with this one.',9951,0);
INSERT INTO comment VALUES (9958,1511,4507,'Penny','We actually tried this experiment','2003-11-28 22:28:59',0,'Sylvester (my boyfriend) and I just got back from trying this experiment in the new car he bought me last week. It was a failed experiment when we realized we\'d never be able to approach the speed of light, plus at Sylvester\'s age, his gun fires blanks. This new car came with five tires, including the spare. Each tire can sustain for a maximum of 1200 miles. If all the tires are used equally, how far can the car travel? \r\n ',NULL,0);
INSERT INTO comment VALUES (9959,1270,4548,'Diane','re: solution','2003-11-28 22:41:21',0,'Hi,\r\nThat\'s what I got, too.\r\nBut I\'m new & didn\'t know how to post a solution.',9937,0);
INSERT INTO comment VALUES (9960,1511,3351,'Eric','re(2): What a doppler effect!','2003-11-28 22:46:36',0,'You are absolutely right and so is Charlie. I don\'t suggest that A doesn\'t have a normal frame of reference where the bullet would appear to travel 1000mph in either direction the gun is fired. The point of near light speed travel is that your entire spaceship\'s internal clock slows to a crawl relative to the outside universe. Lets say you were travelling between planets which were 1 light year apart at the aforementioned 10 mph less than the speed of light. To an external observer this trip would appear to take just over 1 year. But for someone aboard the ship the trip would seem to take less than a second.\r\n\r\nI am basing this on Charlie\'s numbers since I have no tool to manipulate that quantity of significant digits. But basically if the bullet appears to be travelling .00030 mph relative to A from B\'s point of view, then over the course of the year the bullet will have gone .2628 miles (.000030*365*24) relative to A - which from A\'s frame of reference only takes (.2628 miles/1000 mph = .0002628 hours = .0002628hrs*3600sec/hr=.94 seconds).\r\n\r\nThe classic NASA wonderbyte is that Niel Armstrong, Buzz Aldrin and the like are younger than anyone else born at the same time as them because they have experienced \"relativistic speeds\".\r\n\r\nOh, and Penny, you rock!',9952,0);
INSERT INTO comment VALUES (9961,195,2716,'Federico Kereki','re(2): Win, starting anywhere','2003-11-28 23:33:22',1,'Mea culpa, mea maxima culpa... I stand corrected: I forgot the part about not overlapping; I just assumed the new coin had to cover some uncovered space.',9871,0);
INSERT INTO comment VALUES (9962,86,2716,'Federico Kereki','re(3): solution is wrong','2003-11-28 23:45:27',0,'Nope; by the same kind of proof used to show that 3.999...=4, you can show that 0.000...01 is zero, if there are infinite zeroes, but if you don\'t accept this, there is another way of looking at it.
\r\nYou usually say that two numbers a and b are different, if there exists a certain d such that b lies outside the interval (a-d,a+d). In this case, if you take a=0 and b=0.00...1, you can never find any such d, which leads to accept that a=b.
\r\n(The previous is the same as saying that if a and b are different, there exists a number c between them. In this case, for these a and b, you cannot find such a c.)
\r\nThe classic explanation is that our every day finite experiences do not allow to predict the result of infinite experiments, but don\'t worry: the same happened to an old philosopher called Zeno...',9933,0);
INSERT INTO comment VALUES (9963,105,4550,'vanetria ross','re: easy...','2003-11-29 00:19:25',0,'some people don\'t drink so why want you think of a better math question\r\n',1567,0);
INSERT INTO comment VALUES (9964,1509,4551,'chris','Real Solution','2003-11-29 00:55:54',0,'Is it:\r\n\r\nApril 8th, 1996',NULL,0);
INSERT INTO comment VALUES (9965,1511,153,'TomM','My stilborn dream','2003-11-29 03:24:58',0,'Although I used a different framing story (based on the \"twin paradox\"), I have been working on this puzzle off and on for about 30 years. I have gotten as far as Charlie\'s answer:\r\n \r\n s1 + s2 \r\n 1 + [(s1)(s2)/c²]\r\n\r\nThat is as far as the basics of Special Relativity could take me. \r\n\r\nMy particular framing story did make it clear, however, that there is a velocity difference that is conceptually related to the Doppler shift effect. Since Relativity has not yet been reconciled with Quantum Mechanics, I had harbored hopes that showing that particles can obey what is considered to be a rule for waves I could open the way toward such a reconciliation. But alas, I have never been able to translate the Doppler shift into a velocity difference for particles travelling at less than the speed of light.*\r\n\r\nBTW, SK, the math would have been a lot easier if you\'d expressed the speeds as fractions of c (for example, the ship travelling at .95c and the bullet at .01c relative to the ship). Or was that deliberate, to make the problem \"trickier\"?\r\n\r\n*I even tried considering a \"meta-velocity\" of which the velocity which is measured in Special Relativity is the hyperbolic tangent, since tanh(a + b) = [tanh(a) + tanh(b)]/[1 + tanh(a)tanh(b)], but it didn\'t help. ',9953,0);
INSERT INTO comment VALUES (9966,1511,3172,'SilverKnight','re: My stilborn dream','2003-11-29 03:29:57',0,'To answer TomM\'s question to me:\r\n\r\nI wished to ensure that the Newtonian addition of velocities (speed of A relative to B + speed of the bullet) would be greater than c, the speed of light.\r\n\r\nTo do that I would have had to use many more nines/zeroes than are in (.999c) or in (c - .001c). That seemed more putting off.\n\nEdited on November 29, 2003, 3:41 am',9965,0);
INSERT INTO comment VALUES (9967,1270,3351,'Eric','re(2): solution','2003-11-29 03:44:34',0,'Yeah, but isn\'t toast bread? I make toast out of bread. Sometimes I forget about it and the little internal switch mechanism in the toaster doesn\'t release and I start a fire and spend a week trying to get the smell out of the walls. Some people say they like burnt toast. I don\'t really believe them, I just think they are too proud to admit that they left it in the toaster too long so they pretend to enjoy it. It takes a lot of courage to admit you made a mistake. Especially when it means some people won\'t respect you anymore. No one ever said life was going to be easy though.\r\n\r\nMy girlfriend (ex-girlfriend actually, but we still - you know) weighs about a hundred pounds. If I throw her into a river whose current is 6 miles per hour, will I have time to finish my toast before she drowns?',9959,0);
INSERT INTO comment VALUES (9968,1511,153,'TomM','re(2): My stilborn dream','2003-11-29 10:16:16',0,'I see. Still, 1%c and 99.5%c would have served. \r\n\r\nIn my framing story, there were two ships and a planet. Ship A was travelling at .75c relative to the planet, and ship B was travelling at .75c relative to ship A.\r\n\r\nRelative to the planet, it would be traveling at .75c + .75c = 1.5c (Newtonian), or 1.5c/(1 + .5625) = 1.5c/1.5625 = .96c (Relativistic).\r\n\r\n\n\nEdited on November 29, 2003, 10:20 am',9966,0);
INSERT INTO comment VALUES (9969,1513,4507,'Penny','A synonym for \"FLAWLESS\" is.......','2003-11-29 13:15:26',3,'\"PERFECT\" !!!\r\n \r\nList of Perfect Numbers\r\n\r\nDate: 24 Mar 1995 03:37:47 -0500\r\nFrom: Jirachai Chuchat\r\nSubject: Perfect Numbers\r\n\r\nDo you know any Perfect Numbers besides, 6, 28, and 496. Do you know \r\nwhere I can get a list of Perfect Numbers\r\n\r\nThanks.\r\nChris\r\n\r\nDate: 24 Mar 1995 21:13:05 -0500\r\nFrom: Dr. Sydney\r\nSubject: Re: Perfect Numbers\r\n \r\nThanks for writing Dr. Math! Perfect numbers are pretty interesting! It turns out that perfect numbers are involved in several unsolved \r\nproblems of mathematics. Euclid showed that the number \r\n \r\n (*) n = [2^(m-1)](2^m - 1) \r\n \r\nis perfect if 2^m - 1 is a prime number.\r\n \r\nPrime numbers of the form 2^m - 1 are called Mersenne primes, and it is not known whether there are a finite or infinite number of Mersenne \r\nprimes. \r\n \r\nWe also don\'t know if there are any odd perfect numbers. It has been shown that there are no odd perfect numbers in the interval from 1 to \r\n10^50. We do know that all even perfect numbers end in 6 or 8. \r\n \r\nYou wanted a list of perfect numbers. Well, as of 1990 (that is the date of my source), there were 30 known perfect numbers, beginning \r\nwith 6, 28, 496, 8128, 33550336, and so on. The numbers get huge, so it is easier to write them in the notation (*) above. The 30 known \r\nperfect numbers correspond to the following values of m: 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, \r\n4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 132049, and 216091.\r\n \r\nSome books you might want to look up on perfect numbers are:\r\n\r\nDickson, L.E.: _History of the Theory of Numbers_, 1, Chelsea, \r\nreprint, 1952.\r\n\r\nNankar, M.L.: \"History of perfect numbers,\" Ganita Bharati 1, \r\nno. 1-2 (1979), 7-8.\r\n\r\nHagis, P.: \"A Lower Bound for the set of odd Perfect Prime Numbers\", \r\nMath. Comp. 27, (1973), 951-953.\r\n\r\nRiele, H.J.J. \"Perfect Numbers and Aliquot Sequences\" in H.W. Lenstra \r\nand R. Tijdeman (eds.): _Computational Methods in Number Theory_, \r\nVol. 154, Amsterdam, 1982, pp. 141-157.\r\n \r\nRiesel, H. _Prime Numbers and Computer Methods for Factorisation_,\r\nBirkhauser, 1985. \r\n \r\nHope this helps! Write back with any more problems.\r\n \r\n--Sydney \"Dr. Math\"\r\n',NULL,0);
INSERT INTO comment VALUES (9970,1513,4507,'Penny','And a synonym for this posting is......','2003-11-29 14:17:35',4,'And a kind synonym for SK\'s posting is UNORIGINAL. But I\'m an original girl, and this, my discussion of SK\'s posting, is HIGHLY original. This is an unusual paragraph. At first it looks and sounds ordinary, until you match it to almost all paragraphs this long. Can you find out what is so unusual about this paragraph? Try to ! Good luck, and don\'t blow your cool !! ',9969,0);
INSERT INTO comment VALUES (9981,1513,3172,'SilverKnight','Penny\'s thoughts... not worth her name...','2003-11-29 20:28:57',0,'SK: \"...provide an answer to the problem (and demonstrate the reasoning behind such interesting facts as the association between perfect numbers and Mersenne primes). All that said, I doubt it will be Penny.\"\r\n\r\nPenny: \"Any number of the form... blah blah blah... plug in some numbers... blah blah blah... Therefore the next three numbers in your puzzle are...\"\r\n\r\nHmmm... interesting that Penny who ACTUALLY INTRODUCED into this thread the notion that Mersene primes are the manner to demonstrated what the next few numbers would be... doesn\'t seem to be able to do any more than CUT AND PASTE an answer... or plug some numbers into a formula.\r\n__________________________\r\n\r\nPenny... put up or shut up... \r\nEither (1) do what you claim to be able to do... or (2) stop your ranting about what you think you can do, but aren\'t able to.\r\n\r\nI suggest that you either demonstrate WHY that formula might work, or better yet, show the answer (and how you got it) without relying on Mersene primes. But, *sigh*, again, I doubt Penny will be up to the task.\r\n______________________________\r\n\r\nAs for answering your new problem(s), you\'ll just have to submit them, and wait your turn. ;-)',9978,0);
INSERT INTO comment VALUES (9971,1511,3558,'Tristan','relativity','2003-11-29 14:55:36',0,'I don\'t remember much about relativity and I never knew much about the math involved, but I have more or less of an idea of how it works. I hope I\'m not repeating something.\r\n\r\nFrom what I remember, from B\'s reference point, the bullet would probably have a speed very close to A\'s ship, 10 mph short of light speed. How does this work? A\'s ship, from B\'s reference point, would appear very short, so even if the bullet zips accros the ship, it hasn\'t gone very far at all. I don\'t think changing directions changes anything.',NULL,0);
INSERT INTO comment VALUES (9972,1513,1626,'Gamer','re: And a synonym for this posting is......','2003-11-29 15:04:56',0,'You aren\'t as original as you think. Even if your boyfriend is bugging you, you still should refrain from putting problems in your post, even if \"any idiot could figure it out in a few seconds\" just as a matter of practice.\r\n\r\nAlso, please don\'t start sentences with coordinating conjunctions, and makE surE that whEn you \"rEply to a synonym for flawlEss\" you pay morE attEntion to thE dEtails. ',9970,0);
INSERT INTO comment VALUES (9973,1509,1626,'Gamer','re: Comments','2003-11-29 16:02:37',0,'It\'s a time for celebration! You didn\'t manage to slip some problem in here hoping that nobody will notice! *gasp*\r\n\r\nThis is probably due to something I saw (or rather didn\'t see) in your user profile\r\n\r\nLevel: Novice (What does this mean?) \r\nEmail: [hidden] \r\nHomepage: \r\nComments Posted: 13 (List) \r\nRatings: 1 votes, averaging 1.0000 \r\n\r\nNo pending problems? Wow, that leaves you lots of room to talk.\r\n\r\nAlso I noticed a few other things:\r\n\r\nNovice means you don\'t know the site very well. In other words, you are ignorant enough not to know that we also include old problems like this if they aren\'t already on the site.\r\n\r\n13 comments, most of them in a rather negative tone.\r\n\r\nAlso 1 rating averaging 1. So the one problem you did see, you hated.\r\n\r\nFinally, I get to slip in a problem too. Based on these three statistics, what logical conclusion can you draw?\r\n',9911,0);
INSERT INTO comment VALUES (9974,1513,4507,'Penny','re(2): And a synonym for this posting is......','2003-11-29 16:04:09',0,'Gamer: \"You aren\'t as original as you think.\" \r\n\r\nPerhaps not, but I wouldn\'t have listed three well known \"perfect numbers\", and then expected my \"brain-teaser\" to actually tease anyone\'s brain. What I would have done is, first define what a perfect number is, and then asked the flooblers to either provide the smallest ODD perfect number, or prove that there is no odd number !! I would then have been challenging them to go beyond current mathematical knowledge. \r\n\r\nGamer: \"Also, please don\'t start sentences with coordinating conjunctions....\"\r\n\r\nI\'d say I\'m in pretty good company in that literary practice. \"And God said, \'Let there be light\', and there was light.\" (Genesis 1:3) Perhaps when you meet Her, you can reprimand God on Her sloppy grammar. \r\n ',9972,0);
INSERT INTO comment VALUES (9975,1513,1626,'Gamer','re(3): And a synonym for this posting is......','2003-11-29 17:04:59',0,'Anyone includes more than just you. It includes people who prefer a less hard puzzle. It also includes people who actually submit problems. So don\'t go insulting others\' puzzles when they weren\'t meant to be super hard anyway; that\'s why there\'s a 3/5 difficulty on this.\r\n\r\nUnfortunately in your haste to correct me, you noted the old practice of starting sentences with And... I don\'t believe Genesis was written recently, but I am not smart about biblical matters. I do know, that \"Let there be light\" contains no \"and\" at all, and that is the only thing that follows the word \"said\"',9974,0);
INSERT INTO comment VALUES (9976,1510,3840,'Hal9000','Golden Proportion','2003-11-29 17:43:19',0,'The golden ration is the value of x>0 that satifies the proportion 1/x = x/x+1. This is the solution of x²-x=1 or (x²-x+1/4)=1+1/4 so (x-1/2)²=5/4. (x-1/2)=√5/2, thus x=(1+√5)/2, or approx 1.62.',NULL,0);
INSERT INTO comment VALUES (9977,1513,3172,'SilverKnight','re: A synonym for','2003-11-29 17:52:08',0,'It\'s been a while since I\'ve seen someone write so much and say so little... thanks!\r\n__________________________________\r\n\r\nAnyway... while you did a very good job of cutting and pasting a bunch of stuff from the internet, you didn\'t actually answer the question, nor show any understanding beyond the ability to search on keywords and cut and paste.\r\n\r\nBut, you did those things very well.\r\n\r\nHopefully, someone will actually provide an answer to the problem (and demonstrate the reasoning behind such interesting facts as the association between perfect numbers and Mersenne primes). All that said, I doubt it will be Penny.',9969,0);
INSERT INTO comment VALUES (9978,1513,4507,'Penny','SK and Gamer, a Penny for your thoughts...','2003-11-29 18:54:01',0,'SK: \"...you didn\'t actually answer the question, nor show any understanding beyond the ability to search on keywords and cut and paste.\"\r\n \r\n(Obviously I copy/pasted. You can\'t cut/paste from a read-only document. You can\'t even get your insults right!) Any number of the form \r\n[2^(m-1)](2^m - 1)] is a perfect number if \r\n2^m - 1 is a prime number. Therefore the next three numbers in your puzzle are: 33554432, 8589934592, and 137438691328.\r\n \r\nGamer: \"Also, please don\'t start sentences with coordinating conjunctions.\"\r\n\r\nYou mean I shouldn\'t begin a sentence with a conjunction, words such as \"And\" and \"So\" ?\r\n\r\nGamer: \"So don\'t go insulting others\' puzzles...but I am not smart....\" \r\n\r\nNow, Gamer and SilverKnight, I said it before and I say it again: either tell me what the smallest odd perfect number is, or prove to me that there aren\'t any odd perfect numbers. Doing that will keep you two so busy that you won\'t have time to post another snide attack on me in this thread. You are well advised not to continue this battle with me. In a battle of wits, I hate to contend with unarmed opponents. It would be as one-sided as a fistfight between you two and my boyfriend would be. ',NULL,0);
INSERT INTO comment VALUES (9979,263,4317,'C.B.','no paradox','2003-11-29 19:32:13',0,'1/2 + 1/4 + 1/8 ... = 1, a finite number. An infinite sum can be finite with the right parameters. In this case, the sum is finite, so Achilles can overtake the tortoise at that point as long as neither speeds up nor slows down.',NULL,0);
INSERT INTO comment VALUES (9980,1513,1626,'Gamer','re: Thanks for your thoughts!...','2003-11-29 19:41:42',0,'Because I don\'t think you heard me, I will say don\'t start a sentence with a coordinating conjunction. Since you didn\'t read carefully enough, I will say that doesn\'t include all conjunctions.\r\n\r\nI said it before and I will say it again. I don\'t care for solving the problem you posted here. If you were smart enough, you would realize that what you said \"I am not smart\" was on biblical matters, so you are lying about what I said. I think it\'s good to just summarize what you read. It makes it easier on everyone else.\r\n\r\nI am as well angered by unwise people, so I would advise you to stay here and learn a thing or two about how problems are submitted. It would be nice if you went a comment without mentioning a problem or your boyfriend, or even both like you did now.\n\nEdited on November 29, 2003, 7:44 pm',9978,0);
INSERT INTO comment VALUES (9982,394,3351,'Eric','re: guess','2003-11-29 22:47:34',3,'More likely sweat. Sweat is pH crazy (that\'s why Secret is pH balanced for a woman.) Someone just playing basketball on a hot day would be dripping all over the litmus strip as they tested the water.',5192,0);
INSERT INTO comment VALUES (9983,1270,4566,'thatsright','tada','2003-11-29 23:01:26',0,'brewer-4-sparrow-bread\r\nchandler-10-cardinal-toast\r\nemery-8-robin-suet\r\ndennis-2-blackbird-cake crumbs\r\nallison-6-thrush-birdseed',NULL,0);
INSERT INTO comment VALUES (9984,1513,4507,'Penny','A good Penny always returns....','2003-11-30 03:16:15',0,'SilverKnight, I bet I could have you and Gamer working feverishly for at least 48 hours if I handed you pieces of paper that had \"turn over\" written on both sides.\r\n\r\nSilverKnight: \"Penny... put up or shut up... Either (1) do what you claim to be able to do... or (2) stop your ranting about what you think you can do, but aren\'t able to.\"\r\n\r\nAnd what exactly did I claim to be able to do ? (Besides deflate your massive ego? \"Flawless Series\" collapsed faster under my laser-like scrutiny than any other lame conundrum in the history of the brainteaser). BTW, the actual values for the next three numbers in the series are 33550336, 8589869056, and 137438691328. Two of the three values I gave previously were deliberately erroneous. I just wanted to see if you would check my numbers. You didn\'t.\r\n \r\nYou have a great deal of technical knowledge, SilverKnight. You also have all the originality and creativity of a fax machine. Let\'s see...\"Golden Ratio\" - that\'s been around since Ancient Egypt... \"Lovelorn Snail\" -- that one was old when Reagan was in diapers.... \"Relativistic bullet\" -- Einstein beat you to the punch in the 1930s.... and now \"perfect numbers\" -- the ancient Greek, Euclid, \"anticipated\" you on that one. Can\'t you come up with anything new, SilverKnight? Is it asking too much for you to use your brain for something more than keeping your hat in place? Even Gamer\'s inane hamburger riddle was at least original. \r\n\r\nWell, that\'s all I have to say for now. My boyfriend, Sylvester, read all my posts and all of your and Gamer\'s ripostes, and he just shook his head and said \"Darling, you went through those two egomaniacs like ex-lax !!\" ',NULL,0);
INSERT INTO comment VALUES (9985,1513,3172,'SilverKnight','re: (unfortunately...) Penny always returns','2003-11-30 03:35:16',0,'Penny: \"And what exactly did I claim to be able to do ?\"\r\n\r\nYou (falsely) claimed to have solved and answered the problem....\r\n\r\nSo not only did you contradict your own answer (and then sloppily try to cover it up with your \"Two of the three values I gave previously were deliberately erroneous.\"), but you have still failed to explain how one determines these numbers (excepting citing an equation and mindlessly plugging numbers into it).\r\n______________________________\r\n\r\nI\'ve been told it has been amusing to others (and it most certainly amuses me...), so I\'ll (repeat myself and) let you face the continuing truth:\r\n\r\nPenny... put up or shut up...\r\nEither (1) do what you claim to be able to do... or (2) stop your ranting about what you think you can do, but aren\'t able to.\r\n\r\nI suggest that you either demonstrate WHY that formula might work, or better yet, show the answer (and how you got it) without relying on Mersene primes. But, *sigh*, again [now a third time], I doubt Penny will be up to the task.',9984,0);
INSERT INTO comment VALUES (9986,1396,4568,'Scott','Please help me here....','2003-11-30 03:40:13',0,'Please correct me if I am wrong because I believe that I am somehow reading the last statement wrong. \r\n\r\n\"Note: I placed commas and periods to remind that each item/statement separated by COMMAS IS a separate statement.\" (Emphasis added) \r\n\r\nIf this is indeed the case then the problem is unsolvable. Why I say that is for this reason: \r\n\r\n1. Each person lists at least four items (four statements)\r\n\r\n2. If one them is a liar and ALWAYS lies then that person lied about all four items which only leaves 3 items that he really wants.\r\n\r\n3. Therefore, he can\'t have wanted four items on his burger...\r\n\r\nRight or Wrong??? ',NULL,0);
INSERT INTO comment VALUES (9987,1396,3172,'SilverKnight','re: Please help me here....','2003-11-30 03:53:15',0,'You wrote: \"If one them is a liar...\"\r\n\r\nYour analysis is correct except for the above assumption. As your analysis points out, none can be a liar. (Perhaps two are knaves and one is a knight.)',9986,0);
INSERT INTO comment VALUES (9988,1510,1768,'Lorne Hrynkiw','Fibonacci series','2003-11-30 03:59:00',0,'Just as an aside - the ratio of the last two terms in a Fibonacci series will approach this ratio by oscillating above and below this value as we increase the number of terms. ',NULL,0);
INSERT INTO comment VALUES (9989,965,4568,'§çåpëstër','Deduction','2003-11-30 04:23:02',0,'This was a nice problem and very easy to work out. I simply made the True/False list that follows then tested A for each of the personalities. Attached is the final solution that I worked out. (Caps are the correct answers)\r\n\r\nA. t/F - Liar\r\nB. T/f t/F \r\nC. T/f T/f\r\nA. t/F t/F - Liar\r\nC. T/f\r\nB. T/f\r\n\r\nA. Ajax is the Lair\r\nB. Balthzar is the Knave\r\nC. Cicero is the Knight\r\n\r\nFrom there we know that Balthzar did not arrive second as statement 5 and 6 show and since Cicero was telling the truth in statement 3 that he came first then Balthzar came in last and the puts Ajax in second place.\r\n\r\nCicero - Spare bunk\r\nAjax - Stable\r\nBalthzar - pighouse\r\n\r\nYes, this may be some screwed up logic, but it works for me... \r\n',NULL,0);
INSERT INTO comment VALUES (9990,1509,4569,'Anthony','solution','2003-11-30 06:05:57',0,'march 15th, 1996',NULL,0);
INSERT INTO comment VALUES (9991,1513,1626,'Gamer','re: Penny: Too cheap to not be copper.','2003-11-30 07:30:29',0,'I would thank you on your compliment, although that problem is \"in serious need of some hamburger helper\"\r\n\r\nAnd let\'s count the number of problems you have submitted. Any problem would be better no problem because then we know you are contributing to the site. 1... umm.... 1.... *looks around* I don\'t see any. So not only are YOU not making any original ones, you aren\'t making any non-original ones EITHER!\r\n\r\nI would wonder where\'s the justification for you statement. You seem to talk and not really say anything, except wrong values, cut-and-pasted answers solution, and old insults. I appreciate your vast consumation of ex-lax as a health point, but I appreciate it even more that you didn\'t mention a problem here! Well... you did mention your boyfriend in this post (and named him, again, even though everyone who\'s currently talking to you has read ALL of your insults.) but it\'s a start! \n\nEdited on November 30, 2003, 12:15 pm',9984,0);
INSERT INTO comment VALUES (9995,1513,1626,'Gamer','re(3): Penny: Smart enough to stay silent','2003-11-30 12:22:42',0,'Personally I would prefer to make sure we are of an understanding on the issue; I think I was wrong in answering to Penny\'s insults with my own. I don\'t think Penny couldn\'t reply, it\'s just she realised we aren\'t going to get anywhere by arguing sooner than I did.\r\n\r\nI indeed have editted both my posts for any smacking I might have done. I feel like I need to address the issues like Penny\'s insulting our problems when she hasn\'t submitted any at all, and the fact that had she included a problem with every post. (not a problem recently, but I DID talk about that) Also a minor problem wasn\'t saying what the actual answer was, but rather requiring someone to look through the post to find it, and rather submitting wrong answers and not admitting to it.\r\n\r\nThe Subjects are more of a joke, rather than an insult (at least from me); Pennies were indeed made of copper instead of being made like the dimes, nickels and quarters because when pennies weren\'t made of copper, people would just melt the pennies down and sell that; in other words 100 pennies had more than a dollar\'s worth of metal in it!',9994,0);
INSERT INTO comment VALUES (9992,1510,153,'TomM','re: Fibonacci series','2003-11-30 11:14:25',0,'Because of this, a rectangle with sides which are consecutive Fibonacci numbers is close to being a golden rectangle, and since it is easier to measure, is often used instead. For example cards are often in Fibonacci ratios: 2x3, 3x5, 5x8. ',9988,0);
INSERT INTO comment VALUES (9993,1513,1301,'Charlie','In fact... (another solution)','2003-11-30 11:16:54',3,'The relation to the Mersenne primes brings to mind that the first four terms of this sequence do not fully identify it. The sequence does in fact show 2^(p-1)*(2^p-1) for the first four primes. It just happens that for these four primes, 2^p-1 is also prime. However, if we choose to continue the series without regard to whether 2^p-1 is prime, we get a different continuation:\r\n\r\n 2 6\r\n 3 28\r\n 5 496\r\n 7 8128\r\n 11 2096128\r\n 13 33550336\r\n 17 8589869056\r\n 19 137438691328\r\n 23 35184367894528\r\n 29 144115187807420416\r\nOK\r\n
\r\nas produced by the following program:\r\nlist\r\n 10 P=1\r\n 20 for J=1 to 10\r\n 30 P=nxtprm(P)\r\n 40 print P,2^(P-1)*(2^P-1)\r\n 50 next\r\n\r\nso the next three numbers would be 2096128, 33550336, 8589869056, the first of which is imperfect as it does not involve a Mersenne prime.\r\n',NULL,0);
INSERT INTO comment VALUES (9994,1513,3386,'Victor Zapana','re(2): Penny: Too cheap to not be copper.','2003-11-30 11:25:19',0,'lol you both made Penny silent. that\'s what i think is the funniest part of all. \r\ntemplate <ptr>\r\neraseElement(ptr p) {\r\n **p = *((*p).next);\r\n (*p).next = ((*p).next).next;\r\n delete p.next;\r\n}\r\n\r\nThat should work, I think.\r\nI didn\'t actually implement a singly-linked list and test it, but if you have a pointer to a node, and next is a member variable of a node that is a pointer to the next node, that should work, conceptually.\r\n\r\nProblems arise here if, say, you have a pointer elsewhere in your program to the node after the one you want to delete, and then you try to use that pointer; so while this is more efficient, it\'s preferable to traverse the list from the head (in O(n) time) and delete the physical node in question. Given the problem, though, I\'m assuming that\'s what he had in mind.',NULL,0);
INSERT INTO comment VALUES (10064,1309,3172,'SilverKnight','This is a cool problem...','2003-12-01 13:40:05',0,'(like the title says)',NULL,0);
INSERT INTO comment VALUES (10065,1309,1301,'Charlie','thoughts','2003-12-01 13:58:24',1,'There are many more irrationals than rationals. So this may be possible.\r\n \r\nHow, I\'ll have to think about.\r\n\n\nEdited on December 1, 2003, 2:00 pm',NULL,0);
INSERT INTO comment VALUES (10066,1309,1920,'Brian Smith','Three points','2003-12-01 14:28:30',0,'I dont have time for a proof, but three points which will work are (0,0), (0,1), and (0,pi).',NULL,0);
INSERT INTO comment VALUES (10067,1389,1626,'Gamer','re: Solution','2003-12-01 14:53:22',0,'The other letter doesn\'t enter into the code either. I think that\'s because they both aren\'t used very often. Anyway, the version I had seen has that letter instead of 37 for the third letter of the name, so I had to adjust it. I actually had the first two words of that next line as the title until DJ stole them :P',10061,0);
INSERT INTO comment VALUES (10068,1517,2130,'ethan','Solution','2003-12-01 16:41:38',0,'hes selling numbers (that would go on top a door to mark house numbers). 1 would cost 10 cents, 1 and a five would cost 20 cents, and a 1 and a 1 and a 0 would cost 30 cents.',NULL,0);
INSERT INTO comment VALUES (10069,1389,4450,'drew','what solution?','2003-12-01 18:05:25',0,'so whats the solution?',NULL,0);
INSERT INTO comment VALUES (10070,1270,4595,'Carolyn','my solution','2003-12-01 19:29:42',3,'Allison - #6 - Thrush - Birdseed\r\nBrewer - #4 - Sparrow - Toast\r\nChandler - #10 - Robin - Suet\r\nDennis - #2 - Blackbird - Cake Crumbs\r\nEmery - #8 - Cardinal - Bread',NULL,0);
INSERT INTO comment VALUES (10071,1389,1626,'Gamer','re: what solution?','2003-12-01 19:53:24',0,'I am pretty sure that Sam knows it, but is graciously keeping it back so others like you can solve it. :) I think that\'s a good way to solve problems like this.',10069,0);
INSERT INTO comment VALUES (10072,1389,3372,'Sam','re(2): what solution?','2003-12-01 22:44:57',0,'It\'s a children\'s rhyme. The last \"word\" of the encrypted line I gave might help.',10071,0);
INSERT INTO comment VALUES (10073,1309,4323,'Benjamin J. Ladd','','2003-12-01 22:49:08',3,'The real problem for me in approaching this problem has been in thinking of the circumference of circles intuitively as having depth and area (which they obviously don\'t), and not in considering them as symbolic representations of a fixed point and extended radius. If we take however, the differing circumferences of concentric circles, we will be able to examine such areas in terms of the line segment seperating them along the same radial line. Or, in other words, if we make a point anywhere on the paper and draw a radius coming out of that point such that it\'s full length extends to the outermosts edges, we can carefully look at the properties of segments of that radius that would yield either stampable or unstampable areas.\r\n\r\nIn fact, if we take such a segment there can only be (5) conceivable types, only two of which are possible. These are:\r\n\r\nCase (1):\r\nCase (1) would exist such that between the two points on this given segment, there stands an unbroken continuity of irrational numbers that would constitute an area that is inkable.\r\n\r\nCase (2):\r\nCase (2) is similar to case (1) in that between the two points on this given segment, there stands an unbroken continuity of rational numbers that would constitute an area that is uninkable.\r\n\r\nCase (3):\r\nCase (3) would exist such that between lengths along this given segment of unbroken irrational continuity there exists only singular points of rational numbers breaking up the otherwise continuous stream of irrational numbers (still inkable as shown below).\r\n\r\nCase (4):\r\nCase (4) would exist such that between lengths along this given segment of unbroken rational continuity there exists only singular points of irrational numbers breaking up the otherwise continuous stream of rational numbers (still uninkable as shown below).\r\n\r\nCase (5):\r\nAnd case (5) would contain composites of all of the above.\r\n\r\nIf case (1) exists, the area is inkable. Although it is mentally possible to form such a construct of length almost infinitesimally small whose entire construct is formed of entirely irrational numbers, this isn\'t at all feasible. However, if we consider that all rational points that interfere with this continuity are to be easily disposed of insofar as they do not form a continuous chain of unbroken rational numbers (and represent an area that is uninkable), we can treat case number (3) and case number (1) as identical. (As stated above, these points (whose circles are actually formed from the radius thus described) lack any depth and can be readily discarded.) If it can be determined that case (2) and case (4) are absolute impossibilities (and hence no uninkable portion can exist), even the existence of case (5) (the most probable outcome of randomly selecting a line segment) wouldn\'t matter, it would be shown to only exist as a type of case (1) or (3).\r\n\r\n(Note: I can\'t go into the number theory, so I would gladly solicit some help at this point from better mathemeticians out there than myself.)\r\n\r\nI say only hesitantly, therefore, that it is impossible to form a length of line that can only be composed of unbroken rational integers. If we take a point p/q there seems to me to exist an infinite amount of irrational numbers arbitrarily close (from either direction) that no rational number can get closer to this p/q. Again, I\'m stating this somewhat axiomatically, and if someone can offer the formal proof of this here, I would be greatly at their disposal. This seems intuitively the case considering the number of transcendental numbers is far, far greater than the number of rational numbers. With this in mind, we can therefore disregard all possibilities of areas that are uninkable, (i.e. cases (2), (4), and (5) where the composites contain cases (2) and (4)), and arrive at the following answer:\r\n\r\nFor any given point on a sheet of paper, this unique stamp will ink the entire surface.\r\n\r\nWell, these are my thoughts and I hope the proof will hold. In any case, I\'m eager to hear your thoughts and comments on it, all. Great problem, DJ.\n\nEdited on December 1, 2003, 11:48 pm',NULL,0);
INSERT INTO comment VALUES (10074,1513,4300,'Minion123','m-e-h','2003-12-01 22:50:41',3,'please both of you just chill and relax. If either of you feel an urge to insult the other, don\'t give in just say meh. \r\n\r\nThe Simpsons is there anything they can\'t solve or at least complicate even further into thirty minutes of great comedy.\r\n\r\nEdited on December 1, 2003, 10:51 pm\n\nEdited on December 1, 2003, 10:51 pm',NULL,0);
INSERT INTO comment VALUES (10075,1309,1575,'DJ','re:','2003-12-01 23:34:51',1,'I think you\'re reverting to the idea that an ink line will have depth and area, in which case this problem makes no sense to even address.\r\n\r\n\"For any given point on a sheet of paper, this unique stamp will ink the entire surface.\"\r\n\r\nNo, if i center the stamp at exactly (0, 0) on a Cartesian plane, I know that the point (0, 3) is a rational distance (exactly three units) away, and will not be inked by that single stamp.\r\n\r\nActually, looking at a single radius from a single point, the distances must actually alternate rational and irrational points. You can prove that there exists an irrational number between any two unequal rational numbers, and that there exists a rational number between any two unequal irrational numbers.\r\n\r\nTo prove the first one, assume two rational numbers a and b. Let x = a + (b-a)(√2)/2. Thus, x is irrational, and a < x < b.\r\n\r\nTo prove the second, assume two irrational numbers x and y. Conceptually, if you write x and y out in decimal form, if they are not equal, the first digit that is different must exist at some countable location in the number, where you can just pick a rational (terminating) number that fits between them.\r\nMore formally:\r\nif (y-x < 1), n = ceil(-log(y-x))\r\nif (y-x ≤ 1), n = 0\r\nthen, let a = x(10^(n+1)) and b = y(10^(n+1))\r\nb - a ≥ 10, so:\r\na < ceil(a) < floor(b) < b\r\na = x/(10^(n+1)) < ceil(x)/(10^(n+1)) < floor(y)/(10^(n+1)) = b\r\nThen, let z = floor(b)/(10^(n+1)), so z is rational, and\r\nx < z < y.\r\n\r\nIn any case, the answer is \r\n 10 P=1\r\n 20 while 1=1\r\n 30 P=nxtprm(P):P2=P+10\r\n 40 if nxtprm(P2-1)=P2 then\r\n 50 :DigSum=0:T=P2\r\n 60 :while T>0\r\n 70 :Dig=T@10:T=T\\10\r\n 80 :DigSum=DigSum+Dig*Dig\r\n 90 :wend\r\n 100 :if P=DigSum then print P,P2:endif\r\n 150 :DigSum=0:T=P\r\n 160 :while T>0\r\n 170 :Dig=T@10:T=T\\10\r\n 180 :DigSum=DigSum+Dig*Dig\r\n 190 :wend\r\n 200 :if P2=DigSum then print P,P2:endif\r\n 210 wend\r\n
\r\n---------\r\nWhen the program was run with p2=p+20 instead of p2=p2+10, there were no results found. The program is manually stopped, and p in the millions when stopped.',NULL,0);
INSERT INTO comment VALUES (10087,1309,1567,'Bryan','re(3):','2003-12-02 10:59:43',0,'Hey guys, are there any sites you can recommend that discuss irrational numbers? Everything Charlie said I\'ve heard before, but my mind still boggles at the concept that, while there is a rational number between any two irrational numbers (and vice versa), there are still more irrationals than rationals!',10083,0);
INSERT INTO comment VALUES (10089,1309,775,'Cory Taylor','alternation implies 1-1','2003-12-02 12:20:25',0,'I\'m confused how you could say that between any two unequal irrational numbers there is a rational number and vice versa without also showing that the numbers alternate between rational and irrational. If the numbers didn\'t alternate then either;\r\n1) there is a third type of number which is neither rational nor irrational (which I don\'t agree with), or,\r\n2) there are/is (as least one case of) cases/a case where two irrational numbers are adjacent, i.e. with no rational value between them. I believe that this is what you\'re saying.\r\n\r\nPoorly worded-ness aside - My question is how you can have a rational value between ~any~ two irrational values, while having consecutive irrational values? Now I understand that this can be associated with the idea that \"there is no smallest positive number\" (i.e. you can infinitely subdivide any region of the number line), but I don\'t see how this would imply either a majority of irrationals or conversely a majority of rationals - it just means they are arbitrarily close to one another in value. \r\n\r\nNow let me say that I didn\'t verify either DJ\'s equations to show that this is the case nor Charlies assertion that there are Aleph-1 irrationals and Aleph-null rationals, so I don\'t really have a position on this. If I had to, I\'d agree that there are more irrational, not that there are equal numbers, but my lack of understanding of infinity is unfortunately well documented...',10083,0);
INSERT INTO comment VALUES (10090,1309,3172,'SilverKnight','re: alternation implies 1-1','2003-12-02 12:35:34',0,'Perhaps it would be better to say there\'s an infinite number of rationals between any two different irrationals (and vice versa). (Does that clear anything up? :-) This way, you don\'t think of alternating points?\r\n\r\nAnother problem with thinking of \"alternating\" points... is this notion of adjacency. No point is adjacent to another point (unless, perhaps, you\'re naming the same point).\r\n\r\nEither way, the notion of one being larger than the other is generally represented by sets. One can construct the (infinite) set of the rationals and the (infinite) set of irrationals, and then demonstrate that one can provide a mapping function from one to the other (but not vice versa).\r\n\r\nSince we can\'t get a corresponding rational for every irrational, the set of irrationals is larger.\r\n\r\nMethinks the proof of this is beyond the scope of flooble. :-)\r\n_________________\r\n\r\nDid any of that help?',10089,0);
INSERT INTO comment VALUES (10091,1517,4507,'Penny','re: Solution','2003-12-02 12:37:54',0,'I considered your solution, but rejected it, because no hardware shop owner could afford to sell something like that for as little as 10 cents. That would not cover the cost of stocking it.\r\n \r\nThe guy was selling copies on his copying machine. \n\nEdited on December 2, 2003, 12:41 pm',10068,0);
INSERT INTO comment VALUES (10092,1517,3172,'SilverKnight','re(2): Solution','2003-12-02 12:43:20',0,'What if he were stocking it to draw people to come (a loss leader) in the hopes that the customer will buy additional (profitable) items?\r\n\r\nOr perhaps, he just hopes that the customer will buy lots of them?\r\n\r\nOr what if it were many years ago (and 10 cents was worth more)?',10091,0);
INSERT INTO comment VALUES (10093,82,2716,'Federico Kereki','Impossible!','2003-12-02 12:43:22',1,'As posed, Zeus would have needed infinite time to give his orders...',NULL,0);
INSERT INTO comment VALUES (10094,697,3224,'Lee','solution','2003-12-02 12:55:20',0,'At first I believed there was 20 between the houses. After a while of checking and re-checking I just had to look at Charlie’s solution and surprised to find there was no solution. Does anyone live where houses aren’t separated by 2?\r\nAnyhows my approach was (quite) easily modified to accommodate a difference of 10.\r\n\r\n1 digit case\r\nIf Y lives at house, # a\r\nX must live at #a^2\r\na^2>a (for all a in H)\r\nso a^2-a = 10\r\nwhich clearly can’t work for a to be a whole house number\r\n\r\n2 digit case\r\nY lives at # ab\r\nX lives at a^2 + b^2\r\nSo either\r\ni) (a^2 + b^2) –ab = 10 (Mr X’s number is bigger)\r\nii) ab – (a^2 + b^2) = 10 (Mr Y’s number is bigger)\r\n\r\n\r\ni) Mr X’s number is bigger: (a^2 + b^2) – ab = 10\r\nrearranged,(a^2 – 10a) + (b^2-b) = 10\r\nb can’t be even (would make ab non-prime)\r\nhence \r\n(b^2-b) = 6 (b=3)\r\n 20 (b=5)\r\n 42(b=7)\r\n 72(b=9)\r\nso, (a^2 – 10a) = 4, -10, -32, -62\r\nbut (a^2 – 10a) has a minimum value of 25 (when a=5) and is always negative hence\r\n(a^2 – 10a) = -10\r\nand this doesn’t hold for any a\r\n\r\nii) Mr Y’s number is bigger: ab - (a^2 + b^2) = 10\r\nrearranged ,(10a – a^2) + (b – b^2) = 10\r\nagain, b is odd so,\r\n(b – b^2) = - 6 (b=3)\r\n -20 (b=5)\r\n -42(b=7)\r\n -72(b=9)\r\nso, (10a – a^2) = 16, 30, 52, 82\r\nbut (10a – a^2) has a maximum value of 25 (when a=5) \r\nso (10a – a^2) = 16 (and this occurs when b=3)\r\nthis is true for a = 8 and a = 2\r\nHence valid house numbers for Y are\r\n83 (Mr X living at 73)\r\n23(Mr X living at 13)\r\nBoth these sets of figures work as Charlie pointed out.\r\n\r\nAny more?\r\n3 digit case\r\nMr Y living at # abc\r\nMr X living at # a^2 + b^2 + c^2\r\nBy inspection a=1\r\nSo,\r\ni) Mr Y’s number is bigger\r\nabc – (a^2 + b^2 + c^2) = 10\r\nsince a=1\r\n100 + 10b + c – (1 + b^2 + c^2) = 10\r\n10b + c – (b^2 + c^2) = -89\r\nor, (10b – b^2) + (c – c^2) = -89\r\n(10b – b^2) has a minimum value of 9 so,\r\n(c – c^2)<-98\r\nwhich it can’t be\r\n\r\nii) Mr X’s number is bigger\r\n(a^2 + b^2 + c^2) – abc =10\r\nrearranging again,\r\n(1 + b^2 + c^2) – (100 + 10b + c) =10\r\n(b^2 + c^2) – (10b + c) =109\r\n(b^2-10b) + (c^2 – c) = 109\r\n(b^2-10b) is always negative hence\r\n(c^2 – c) must be a three figure number, which clearly it can’t be.\r\n\r\nMore than three digits?\r\nClearly the sum of the squares of the digits can only increase by 81 per new digit introduced hence for more than three digits the possibilities of solutions are non-existent.\r\n\r\nExcuse this post if it\'s a bit messy - flooble wouldn\'t let me preview it.',NULL,0);
INSERT INTO comment VALUES (10095,697,4605,'Vadi D','The answer is ...','2003-12-02 13:58:16',3,'X = 13 and Y = 23\r\nX = 2^2 + 3^3 = 13',NULL,0);
INSERT INTO comment VALUES (10096,1309,775,'Cory Taylor','re(2): alternation implies 1-1','2003-12-02 13:58:59',0,'Unfortunately no...\r\n\r\nWhile the idea of alternation wasn\'t mine, it makes conceptual sense to me. Unfortunately the math in the case is not conceptual...\r\n\r\nThe reason that these explanations do not help my understanding is that they both work back to the comment I made regarding no smallest number, which I am clear on. But really this is a moot point, as I didn\'t believe it (the alteration of rationals and irrationals) to begin...\r\n\r\nAnd darn you SK for bringing set theory into the game! :)\r\n\r\nby the way, it appears that DJ missed a \"not\" in the last line of his post.\r\n',10090,0);
INSERT INTO comment VALUES (10097,1517,4507,'Penny','re(3): Solution','2003-12-02 14:11:02',0,'This is refreshing, SilverKnight. A post from you which is civil, and contains no personal attacks. This is a step in the right direction for both of us.\r\n\r\nSK: \"What if he were stocking it to draw people to come (a loss leader) in the hopes that the customer will buy additional (profitable) items?\"\r\n\r\nA loss leader is defined as something sold at a loss to attract customers. It must be something that will actually draw in more than one or two customers, but that is not sold at high volume to individual customers. It utterly defeats the purpose of a loss leader if few people are interested in buying it (a clothing store using tee-shirts with \"My name is Penny\" emblazoned on them as a loss leader), or people tend to buy a lot of it at one time (a gas station using gasoline as a loss leader in order to boost the sales of cigarettes). Anyone buying numerals to put on house doors, would of course probably be either a new home owner, someone whose old house number had been damaged, or a construction guy who now has a lot of new houses ready for market. By definition, there would not be many such people at any point in time. This is not a good loss leader candidate. \r\n\r\nSK: \"Or perhaps, he just hopes that the customer will buy lots of them?\"\r\n\r\nThen such a person has just bought lots of houses, or owns lots of houses that have just been struck by vandals or natural catastrophes, or is a construction guy with lots of new houses on the market. That in unlikely. Even if that were the case, then if the store owner loses x amount of money on one such transaction, he will lose n*x amount of money on n of them. \"I\'ll make it up on volume\" is a common misconception. \r\n\r\nSK: \"Or what if it were many years ago (and 10 cents was worth more)?\"\r\n \r\nThe puzzle states \"A hardware shop owner IS setting up his store...\", not \"A hardware shop owner WAS setting up his store...\" \r\n\n\nEdited on December 2, 2003, 2:47 pm',10092,0);
INSERT INTO comment VALUES (10098,1269,4605,'Vadi D','Answer is...','2003-12-02 14:14:54',0,'C for MARCH\r\nN for EDEN\r\nA for CANDY\r\nW for WORTH\r\nR for TIMBER\r\nE for DENSE\r\nT for TAUNT\r\nR for ENROL\r\nF for FAST\r\nG for BEGAN\r\nR for MIRED\r\nP for MAPLE\r\nZ for DIZZY\r\nR for STORE\r\nT for CONNECT\r\nC for TRANCE\r\nB for PROBE\r\nF for DIFFER\r\nO for BLOOM\r\nT for SPOT\r\nF for FUDGE\r\nU for MURMUR\r\nB for RABBIT\r\nK for TOKEN\r\nL for HELPER\r\nM for FAMOUS\r\n',NULL,0);
INSERT INTO comment VALUES (10099,1309,3172,'SilverKnight','re(3): alternation implies 1-1','2003-12-02 14:15:28',0,'I\'m sorry that it wasn\'t helpful.\r\n_______________________\r\n\r\nI think some are misreading what DJ wrote. He said:\r\n\"...looking at a single radius from a single point, the distances must actually alternate rational and irrational points.\"\r\n\r\nI don\'t want to put words in his mouth (or in anyone\'s who read this post), but it seems to imply that one point (along the radius) is rational, and the next point is irrational.... the next point is rational, and so on.\r\n\r\nBut that\'s not what that statement means.\r\n\r\nWhat would the \"next point\" mean? If I center at the origin, what\'s the next point after (1,0)?\r\n\r\nPoints are not adjacent.\r\n\r\nCory, if you are clear on the issue of \"no smallest positive number\", then why don\'t you think that applies to this situation (namely, that there must be a rational number between any two irrationals and vice versa).\r\n_________________\r\n\r\nBTW, I don\'t see it... where would you put this \"missing\" not of yours?',10096,0);
INSERT INTO comment VALUES (10100,1269,3172,'SilverKnight','re: Answer is...','2003-12-02 14:19:14',0,'EDEN and SPOT have four letters',10098,0);
INSERT INTO comment VALUES (10101,1269,1575,'DJ','re: Answer is... (sorry)','2003-12-02 14:21:37',0,'The difficulty in this problem is in choosing a different (see the instructions) letter to fill each blank. Most of the lines have multiple letter choices that will form a word.',10098,0);
INSERT INTO comment VALUES (10102,1269,4605,'Vadi D','re: Answer is...','2003-12-02 14:22:43',3,'Did not earlier note the word length was 5 or more!\r\nC for MARCH \r\nN for DENOTE \r\nA for CANDY \r\nW for WORTH \r\nR for TIMBER \r\nE for DENSE \r\nT for TAUNT \r\nR for ENROL \r\nI for SOFIA \r\nG for BEGAN \r\nR for MIRED \r\nP for MAPLE \r\nZ for DIZZY \r\nR for STORE \r\nT for CONNECT \r\nC for TRANCE \r\nB for PROBE \r\nF for DIFFER \r\nO for BLOOM \r\nS for SUITE \r\nF for FUDGE \r\nU for MURMUR \r\nB for RABBIT \r\nK for TOKEN \r\nL for HELPER \r\nM for FAMOUS \r\n',10098,0);
INSERT INTO comment VALUES (10103,1389,4450,'drew','screw it','2003-12-02 14:24:29',0,'i dont feel like trying to solve this problem so just forget about it when the awnser comes out i will see it.',NULL,0);
INSERT INTO comment VALUES (10104,1269,3172,'SilverKnight','re(2): Answer is...','2003-12-02 14:26:25',0,'you\'ve still used the same letter repeatedly (like C, T, and R)',10102,0);
INSERT INTO comment VALUES (10105,1269,3172,'SilverKnight','DON\'T look at this answer','2003-12-02 14:29:14',3,'Pretty sneaky to give us MARCH as the first one...\r\n\r\n\r\nT R A M A R S H E G O U S \r\nD E L E D E P O T E C A R \r\nG L O T A C A N D Y U N T \r\nR I N C E L N O R T H A D \r\nE T I M B E R C L O F I C \r\nL E W I N D Y N S E N C H \r\nM A C I E R H A U N T E R \r\nC A P P E N D O L A B E S \r\nF R A S O F E A S T U R M \r\nA L T E B E G A N N E S E \r\nH I N A M I X E D B R I C \r\nB L A N M A I L E D N E L \r\nI N C E D I Z Z Y E C T S \r\nN E R S T O W E D A N T O \r\nC O N N E C T A S P L I C \r\nK A T R A N C E R O I C L \r\nO T I P R O V E R A O U S \r\nP L A D I F F E R M A C H \r\nJ O L A B L O O M S G E R \r\nT R A S P O Q U I T E A N \r\nE N C R E S J U D G E V E \r\nR A T U L M U R M U R T E \r\nS P I R A B B I T H O L L \r\nM U S A T O K E N R E S P \r\nD A N O H E L P E R P E N \r\nA C R U F A M O U S N A T\r\n
',NULL,0);
INSERT INTO comment VALUES (10106,1309,775,'Cory Taylor','re(4): alternation implies 1-1','2003-12-02 14:36:29',0,'Well, it wasn\'t helpful because I already agree with all of your points, not because it didn\'t make sense. I never agreed that points could be adjacent to each other, I was simply replying to Charlies comment insofar as he could accept that the points could alternate, but not that they were 1-1. To me this was the same issue.\r\n\r\nAnd in DJ\'s post, his final comment is meant to rebut the earlier claim that a single stamp will mark the entire plane. In fact he even disproves this very comment as part of his post. I have reposted his final remark, with the not I believe he intended included.\r\n\r\nIn any case, the answer is ~not~ that a single stamp will cover an entire plane.',10099,0);
INSERT INTO comment VALUES (10107,1517,3172,'SilverKnight','re(4): Solution','2003-12-02 14:41:13',0,'\"I\'ll make it up on volume\" is a common misconception. \r\n\r\nNo it is fact--fixed costs versus variable costs. (This is what \"breakeven analysis\" is all about.) I hope I can refrain from teaching fundamental economics here.\r\n\r\nAs for the others two points, you are taking the wording too literally.',10097,0);
INSERT INTO comment VALUES (10108,1309,3172,'SilverKnight','re(5): alternation implies 1-1','2003-12-02 14:43:51',0,'ahhh, my bad.',10106,0);
INSERT INTO comment VALUES (10109,1269,3224,'Lee','An answer','2003-12-02 14:50:34',0,'where did all thes comments come from!\r\nAnyways, here\'s an answer (one of many variations I presume)\r\nM A R C H \r\nD E N O T E \r\nC A N D Y \r\nW O R T H \r\nT I M B E R \r\nW I N D Y \r\nS A U N T E R \r\nA P P E N D \r\nF E A S T \r\nB E G A N \r\nM I X E D \r\nM A I L E D \r\nD I Z Z Y \r\nS T O V E \r\nC O N N E C T \r\nH E R O I C \r\nO P E R A \r\nD I F F E R \r\nB L O O M S \r\nQ U I T E \r\nJ U D G E \r\nM U R M U R \r\nR A B B I T \r\nT O K E N \r\nH E L P E R \r\nF A M O U S \r\n',NULL,0);
INSERT INTO comment VALUES (10116,1270,4595,'Carolyn','re: & my solution','2003-12-02 17:20:00',0,'That\'s what I got too! after a second try ;)',10081,0);
INSERT INTO comment VALUES (10117,1517,4608,'Crystal Lynn','','2003-12-02 19:55:01',0,'The answer would be numbers, as in house numbers. \r\nEach number cost 10 cents.',NULL,0);
INSERT INTO comment VALUES (10112,1269,1301,'Charlie','And another couple of solutions + variants','2003-12-02 15:16:52',3,'\r\nTRAMAR_HEGOUS 1 C MARCH\r\n\r\nDELEDE_OTECAR 2 N DENOTE\r\n\r\nGLOTAC_NDYUNT 3 A CANDY\r\n\r\nRINCEL_ORTHAD 4 W WORTH\r\n\r\nETIMBE_CLOFIC 5 R TIMBER\r\n\r\nLEWIND_NSENCH 6 Y WINDY\r\n\r\nMACIER_AUNTER 7 V VAUNT\r\n\r\nCAPPEN_OLABES 8 D APPEND\r\n\r\nFRASOF_ASTURM 9 E FEAST\r\n\r\nALTEBE_ANNESE 10 G BEGAN\r\n\r\nHINAMI_EDBRIC 11 X MIXED\r\n\r\nBLANMA_LEDNEL 12 I AILED\r\nBLANMA_LEDNEL 12 I MAILED\r\n\r\nINCEDI_ZYECTS 13 Z DIZZY\r\n\r\nNERSTO_EDANTO 14 S SEDAN\r\n\r\nCONNEC_ASPLIC 15 T CONNECT\r\n\r\nKATRAN_EROICL 16 H HEROIC\r\n\r\nOTIPRO_ERAOUS 17 P OPERA\r\nOTIPRO_ERAOUS 17 P PROPER\r\n\r\nPLADIF_ERMACH 18 F DIFFER\r\n\r\nJOLABL_OMSGER 19 O ABLOOM\r\nJOLABL_OMSGER 19 O BLOOM\r\nJOLABL_OMSGER 19 O BLOOMS\r\nJOLABL_OMSGER 19 O LOOMS\r\n\r\nTRASPO_UITEAN 20 Q QUITE\r\n\r\nENCRES_UDGEVE 21 J JUDGE\r\n\r\nRATULM_RMURTE 22 U MURMUR\r\n\r\nSPIRAB_ITHOLL 23 B RABBI\r\nSPIRAB_ITHOLL 23 B RABBIT\r\n\r\nMUSATO_ENRESP 24 K TOKEN\r\n\r\nDANOHE_PERPEN 25 L HELPER\r\n\r\nACRUFA_OUSNAT 26 M FAMOUS\r\n
\r\n\r\nor, swapping P and S\r\n\r\nTRAMAR_HEGOUS 1 C MARCH\r\n\r\nDELEDE_OTECAR 2 N DENOTE\r\n\r\nGLOTAC_NDYUNT 3 A CANDY\r\n\r\nRINCEL_ORTHAD 4 W WORTH\r\n\r\nETIMBE_CLOFIC 5 R TIMBER\r\n\r\nLEWIND_NSENCH 6 Y WINDY\r\n\r\nMACIER_AUNTER 7 V VAUNT\r\n\r\nCAPPEN_OLABES 8 D APPEND\r\n\r\nFRASOF_ASTURM 9 E FEAST\r\n\r\nALTEBE_ANNESE 10 G BEGAN\r\n\r\nHINAMI_EDBRIC 11 X MIXED\r\n\r\nBLANMA_LEDNEL 12 I AILED\r\nBLANMA_LEDNEL 12 I MAILED\r\n\r\nINCEDI_ZYECTS 13 Z DIZZY\r\n\r\nNERSTO_EDANTO 14 P PEDANT\r\nNERSTO_EDANTO 14 P TOPED\r\n\r\nCONNEC_ASPLIC 15 T CONNECT\r\n\r\nKATRAN_EROICL 16 H HEROIC\r\n\r\nOTIPRO_ERAOUS 17 S PROSE\r\n\r\nPLADIF_ERMACH 18 F DIFFER\r\n\r\nJOLABL_OMSGER 19 O ABLOOM\r\nJOLABL_OMSGER 19 O BLOOM\r\nJOLABL_OMSGER 19 O BLOOMS\r\nJOLABL_OMSGER 19 O LOOMS\r\n\r\nTRASPO_UITEAN 20 Q QUITE\r\n\r\nENCRES_UDGEVE 21 J JUDGE\r\n\r\nRATULM_RMURTE 22 U MURMUR\r\n\r\nSPIRAB_ITHOLL 23 B RABBI\r\nSPIRAB_ITHOLL 23 B RABBIT\r\n\r\nMUSATO_ENRESP 24 K TOKEN\r\n\r\nDANOHE_PERPEN 25 L HELPER\r\n\r\nACRUFA_OUSNAT 26 M FAMOUS\r\n\r\n
\r\n----------\r\nboth using the given MARCH in the first row. (The variants above are the different words for the same letter in a given row, shown single-spaced.)',NULL,0);
INSERT INTO comment VALUES (10118,1517,4610,'plextor','Answer is obvious','2003-12-02 21:14:45',0,'Correct me if I am wrong, but E=MC²\r\ntherefore if this is the owner of a hardware shop then he is selling ...\r\n\r\nHARDWARE !',NULL,0);
INSERT INTO comment VALUES (10119,1517,3172,'SilverKnight','re: Answer is obvious','2003-12-02 21:21:26',0,'lol... that was kinda funny!',10118,0);
INSERT INTO comment VALUES (10120,1517,4507,'Penny','re: Answer is obvious','2003-12-02 22:05:21',0,'plextor: \"Correct me if I am wrong...if this is the owner of a hardware shop then he is selling ...\r\nHARDWARE !\"\r\n \r\nYou are wrong. Do gas stations sell cigarettes? Yes. And cigarettes are not gas. Do hospitals sell turkey sandwiches? I had one in a hospital last week. And sandwiches are not medicine. Do grocery stores sell stamps? Yes. And while you can lick stamps, they are not food. Do hardware stores sell the use of copying machines? They certainly do. The copying machines themselves are hardware, but that which is being sold - the making of paper copies, is not.\r\n\r\nNow some folks will tell you that the store owner is selling numerals at 10 cents apiece, to be placed on houses to address them, and that by using them as \"loss leaders\" to lure in six or seven extra customers each year, he will eventually open the floodgates of capitalistic profit and wealth beyond the dreams of avarice. Such people have no concept of what a loss leader is. To be a loss leader, a product must (a) be desired strongly by enough people that it will entice significantly larger numbers of them to visit the store who otherwise would not have done so; and (b) people need to replenish their supplies of it by repurchasing it frequently. Milk is a good loss leader for convenience stores, because people will make an extra trip to the store at 2 in the morning when they\'re out of it, but no one buys huge supplies of milk when they do buy it; instead they return to buy it again and again. Numerals for house addresses are a perfectly laughable loss leader, bcause no one is going to go out at 2 in the morning to seek to buy them; having bought a few of them, they are not likely to need to replenish their supply even infrequently; and very few people have the need for them anyway. When was the last time you went out to buy address numerals for your house? I have done so once in my entire life. \r\n \r\nThe store owner is selling time on his copying machine. \r\n\r\n\r\n\n\nEdited on December 2, 2003, 11:03 pm',10118,0);
INSERT INTO comment VALUES (10114,1269,3172,'SilverKnight','re: And another couple of solutions + variants','2003-12-02 15:21:18',0,'\"both using the given MARCH in the first row\"\r\n\r\n:-P\r\nshowoff!',10112,0);
INSERT INTO comment VALUES (10115,1269,1301,'Charlie','re: And another couple of solutions + variants','2003-12-02 15:37:27',0,'Yes, there was computer assistance. For the record, after finding words matching the rows, a matrix was built, to be examined manually, showing the number of words using given fill-in letters for each row:\r\n\r\n A B C D E F G H I J K L M N O P Q R S T U V W X Y Z\r\n 1 . . 1 . . . . . . . . . . . . . . . 1 . . . . . . .\r\n 2 . . . . . . . . . . . . 2 1 . 1 . . . . . 1 . . . .\r\n 3 1 . . . . . . . . . . . . . . . . . . . . . . . . .\r\n 4 . . . . . 1 . . . . . 1 . 1 . . . . . . . . 1 . . .\r\n 5 . . . 1 . . . . . . . . . . . . . 1 . . . . . . . .\r\n 6 . . . . 1 . . . . . . . . . . . . . 1 . . . . . 1 .\r\n 7 . . . 1 . . 2 2 . 1 . . . . . . . . 1 2 . 1 . . . .\r\n 8 . . . 1 . . . . . . . . . . . . . . . . . . . . . .\r\n 9 . . . . 1 . . . 1 . . . . . . . . . . . . . . . . .\r\n10 . . . . . . 1 . . . . . . . . . . . . . . . . . . .\r\n11 . . . 1 . . . . . . . . 1 1 . . . 1 . . . . . 1 . .\r\n12 . . . . . . . . 2 . . . . . . 1 . . . . 1 . . . . .\r\n13 . . . . . . . . . . . . . . . . . . . . . . . . . 1\r\n14 . . . . . . . . . . 3 1 . 3 . 2 . 2 1 1 . 1 2 . 1 .\r\n15 . . . . . . . . . . . 1 . . . . . . . 1 . . . . . .\r\n16 . . 1 . 1 . 3 1 . . . . . . . . . . 1 1 . . . . . .\r\n17 . 2 . . . . 1 . . . . . . 1 . 2 . . 1 . . 3 1 . . .\r\n18 . . . 1 . 1 . . . . . . . . . . . . . . . . . . . .\r\n19 . . . . . . . . . . . . . . 4 . . . . . . . . . . .\r\n20 . . . . . . . . . . . . . . . . 1 . 1 . . . . . . .\r\n21 . 1 . . . 1 . . . 1 . 1 1 1 . . . . 1 1 . . . . . .\r\n22 . . . . . . . . . . . . . . . . . . . . 1 . . . . .\r\n23 . 2 . . . . . . . . . . . . . . . . . . . . . . . .\r\n24 . . . . . . 2 . . . 1 . . 1 . . . . . . . . . . . .\r\n25 . . . . . . . . . . . 1 . . . . . . . . . . . . . .\r\n26 . . . . . . . . . . . . 1 . . . . . . . . . . . . .\r\n
\r\n----------\r\nwhere, immediately rows 3, 8, 10, 13, 19, 20, 22, 23, 25 and 26 have only 1 possibility and F and X have unique possible rows (aside from those letters unique in both ways-- A on 3, O on 19, Q on 20, Z on 13).\r\n\r\nSecondarily, when these are chosen, and other possibilities in their respective rows and columns are removed, R can be on row 5 only and T on 15 only.\r\n\r\nAfter that it\'s manual trial and error.',10112,0);
INSERT INTO comment VALUES (10121,1309,1575,'DJ','re(3): alteration','2003-12-02 22:36:09',0,'You are correct. Alteration was a poor word choice; I meant only to address Benjamin\'s claim that there can exist an unbroken continuity of either rational or irrational numbers. SK said it better; between any two given unequal irrational points, there are an infinite number of both rational and irrational points; likewise between any two unequal rational points.\r\n\r\nOf course, there is not a one-to-one correspondence between rational and irrational numbers, which would imply the same cardinality. The limit of the ratio of irrational to rational numbers in an interval as the infinitesimal size of that interval approaches zero, which would intuitively be 1, is not (I think that ratio will be Ν1/Ν0, the ratio of the cardinalities of the sets, but I am not sure). \'Alteration\' in this case does not imply a one-to-one ratio because we cannot delimit every possible point on an infinite segment or within a finite interval.\r\n\r\nAlso, I did type the word \'not\' in the last sentence of my previous post, but for some reason the <i> </i> tags made the word disappear altogether (I will not bother editing the post, but the curious can look at the source of that page to confirm). But yes, that should read, \"the answer is not that a single stamp will cover an entire plane\" (I will not risk the use of italics this time).',10083,0);
INSERT INTO comment VALUES (10122,1517,3558,'Tristan','re(2): Answer is obvious','2003-12-02 23:16:18',0,'The intended solution is obviously numerals. Would they really charge those amounts for time on a copying machine? Would they, in this puzzle, charge those amounts for time on a copying machine? The answer to the first question is perhaps, and the answer to the second is no.\r\n\r\nStill, it\'s always nice to hear the creative solutions people come up with. And if they start ranting for dozens of posts about their solution, I suppose I don\'t really have to read them. No, I\'m not referring to you in particular.',10120,0);
INSERT INTO comment VALUES (10123,697,3224,'Lee','slightly simpler? (or maybe it isn\'t)','2003-12-02 23:38:06',3,'Mr Y lives at a, ab or abc (cannot live in a 4-digit house since the sum of the squares of the digits is 3 figures maximum)\r\nSo Mr X lives at a^2, (a^2 + b^2), (a^2 + b^2 + c^2)\r\na^2 can never be prime so the 1 digit case fails.\r\n\r\n2 digit case (Mr Y at ab)\r\nab is prime –> odd –> b is odd\r\n(a^2 + b^2) is prime -> odd, b we know is odd, so b^2 is odd, making a^2 (and therefore a) even.\r\na…a^2…b…b^2\r\n2…..4….3…..9\r\n4….16…5…..25\r\n6….36…7…..49\r\n8….64…9…..81\r\n\r\nOnly prime choices for ab (Mr Y) are\r\n23, 43, 47, 67, 83, 89\r\nDisregard 89 (since 8^2+9^2 is three figures)\r\nSo Mr X lives at one of these;\r\n33, 53, 57, 77, 93, (if he lives up the street by 10)\r\n13, 33, 37, 57, 73, (if he lives down the street by 10)\r\nAnd Mr Y at\r\n23, 43, 47, 83\r\nFinally since Mr X lives at (a^2 + b^2), he lives at\r\n13, 25, 65, 73\r\nand only 13 and 73 are prime (which means he lives down the street with Mr Y at 23 or 83)\r\n\r\n3 digit case (fails quickly)\r\nMr Y at abc\r\nMr X at (a^2 + b^2 + c^2)\r\na is clearly 1 (since (a^2 + b^2 + c^2)<244 and (a^2 + b^2 + c^2)<200 if a=2)\r\nabc is prime, therefore c is odd\r\nfor (1+ b^2 + c^2), with c odd, b must be odd.\r\nMax for (1+ b^2 + c^2) = 163 (b,c, both 9)\r\nSo b<6\r\nb>3 (since (1+ 9 + c^2)<100)\r\nSo b = 5 and c must equal 9 to have (1+ 25 + c^2) >100\r\nBut (1+ 5^2 + 9^2) does not equal 159\r\n\r\nMr Y lives at 83 with Mr X at 73\r\nor\r\nMr Y lives at 23 with Mr X at 13\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (10124,1517,1575,'DJ','re(2): Answer is obvious','2003-12-03 00:12:32',0,'\"You are wrong. Do gas stations sell cigarettes?\"\r\n\r\nDo you mean to say that if I said, \"Gas stations sell gas,\" I would be wrong because they sell things other than gas? I hope not.\r\n\r\nTo say that a grocer sells groceries, a pharmacist sells pharmaceuticals, or that a hardware shop owner sells hardware seems a pretty airtight statement to me.',10120,0);
INSERT INTO comment VALUES (10125,492,4300,'Minion123','what i got','2003-12-03 00:29:16',3,'i used a piece of paper and pencil to make a table in order to find a solution.\r\nStarting from the front\r\n\r\nPrancer \r\nCupid \r\nRudolph\r\nDasher\r\nBlitzen\r\nVixen\r\nComet\r\nDonder\r\nDancer',NULL,0);
INSERT INTO comment VALUES (10126,1517,3224,'Lee','some thoughts and an alternative solution','2003-12-03 00:40:47',0,'A normal photocopier has a negligable set-up time. The majority of the time is spent scanning the page, which it does so on every copy. A normal copier has a ‘click’ charge (if you lease the copier as most do) which will cover toner replacement and servicing. If you own the machine this ‘click’ charge obviously drops but monies will need to set aside to cover maintenance yourself.\r\nMost high volume/dependant users lease.\r\nThe click charge is around .7p (data from 8 years ago), or 1 cent (I have no reason to believe this figure will have dropped greatly)\r\nFrom 15 to 110 copies the store owner collects a paltry 10 cents for the 95 copies – about a 10th of the charge to himself\r\nThere exists, copiers that have a greatly reduced ‘click’ charge and do require a set up time and cost (around 10 cents?). These are more like low-run printing machines, with the machine making a ‘plate’ that is then used to produce bulk copies. You could argue that the ink costs for this machine would be low enough to justify 10c for 95 copies (ink is cheaper than toner) but your enemy now is paper costs.\r\n53 cents a ream – gimme some!\r\nI’ll take 50 reams please!\r\nIt is clearly more profitable, time-wise, to charge your clients the same for the paper as you would to copy (saving you the hassle) but at 53 cents a ream you would have the whole world and his dog at your store clearing you out of paper.\r\nFactor in the floor space the machine takes up (space you can’t fill with profitable products) and you don’t have a loss leader you have deadwood.\r\nThe hardware store isn’t selling photocopies at this price. Although I admire Penny’s tenacity (suspiciously like Dan but more eloquent)\r\nIt’s selling numerals (not necessarily house numerals – what about letraset?). The sign in the window is a marketing device – who (who doesn’t know this classic puzzle) would not be tempted to go in the store to find out what this great deal was for? Who would not think ‘ah, that’s clever/neat!’ (again who doesn’t know this classic puzzle)\r\nThe chip shop near my girlfriend Tweetie’s house has a chalkboard they scribble puzzles on to think over while waiting. It’s not the nearest chip shop, but it’s the one I always use – the sign is just a hook to get you in the shop.\r\nIf you want an alternative solution here’s mine;\r\n“Words of hardware advice.”\r\nWhat ampage fuse do I want for a kettle?\r\n‘Thirteen’ (10 cents)\r\nWhat’s the best way to put up a picture?\r\n‘First, drill a hole, pop in this plug, screw in this (offers) and hang your picture’ (20 cents)\r\n',NULL,0);
INSERT INTO comment VALUES (10127,1475,4615,'John','A guess','2003-12-03 04:22:35',3,'I\'ll take everyone\'s word for it that Alaska is the furthest north, east, and west, but I think Florida has the southern most point.',NULL,0);
INSERT INTO comment VALUES (10128,1475,4615,'John','re: A guess','2003-12-03 04:46:20',0,'Ya, I just checked, Key West, Florida is the southernmost point in the US. Here\'s a link to a picture of it:\r\nhttp://www.milemarkerzero.com/gallery/pages/000.html',10127,0);
INSERT INTO comment VALUES (10129,1269,4507,'Penny','A solution differing a bit from prior posts. NO COMPUTER PGM USED.','2003-12-03 04:51:27',0,'I knew the fact that I almost got a perfect score on the college verbal SAT would come in handy someday. I found this one to be very easy.\r\n\r\nI don\'t use any proper nouns like SOFIA and EDEN (the latter also is less than 5 letters). Proper nouns are not forbidden by the wording of the puzzle, but clearly their use makes it much too easy to solve, when you have an unabridged Atlas to supply strange letter combinations. I did not use a computer program. (Use of computer programs takes all the challenge out of it. That\'s why competing athletes in Olympic cross country skiing are not allowed to use snowmobiles). All my words are common words except for \"CRESS\", a crucifer with pungent leaves, and \"PROKE\", an old form of the word \"poke\". I used CRESS in preference to the obvious JUDGE, and PROKE in preference to the obvious PROVE, in an attempt to be a little more creative than a computer program would have been. (That PROKE is a valid word can be verified here: http://www.thefreedictionary.com/Proke)\r\n\r\nT R A M A R **C** H E G O U S = MARCH \r\nD E L E D E **P** O T E C A R = DEPOT \r\nG L O T A C **A** N D Y U N T = CANDY \r\nR I N C E L **W** O R T H A D = WORTH \r\nE T I M B E **R** C L O F I C = TIMBER \r\nL E W I N D **Y** N S E N C H = WINDY \r\nM A C I E R **J** A U N T E R = JAUNT \r\nC A P P E N **D** O L A B E S = APPEND \r\nF R A S O F **E** A S T U R M = FEAST \r\nA L T E B E **G** A N N E S E = BEGAN \r\nH I N A M I **X** E D B R I C = MIXED \r\nB L A N M A **I** L E D N E L = MAILED \r\nI N C E D I **Z** Z Y E C T S = DIZZY \r\nN E R S T O **V** E D A N T O = STOVE \r\nC O N N E C **T** A S P L I C = CONNECT\r\nK A T R A N **H** E R O I C L = HEROIC \r\nO T I P R O **K** E R A O U S = PROKE\r\nP L A D I F **F** E R M A C H = DIFFER \r\nJ O L A B L **O** O M S G E R = BLOOM \r\nT R A S P O **Q** U I T E A N = QUITE \r\nE N C R E S **S** U D G E V E = CRESS \r\nR A T U L M **U** R M U R T E = MURMUR \r\nS P I R A B *B** I T H O L L = RABBIT \r\nM U S A T O *N** E N R E S P = ATONE \r\nD A N O H E **L** P E R P E N = HELPER \r\nA C R U F A **M** O U S N A T = FAMOUS \r\n\r\n\r\n\r\n\r\n\r\n\r\n\n\nEdited on December 3, 2003, 5:38 am',NULL,0);
INSERT INTO comment VALUES (10130,1389,4507,'Penny','FULL SOLUTION (No computer program used)','2003-12-03 07:16:03',3,'First of all, the pattern strongly suggests that it is made up of letters represented by two-digit codes. The apostrophe limits the values \"37\" to S,M, and D. The real key to solving this puzzle is to concentrate on \"18281422361218\", a seven letter word with 1st and last letters matching, and no other letters matching. This word occurs three times. It is preceded by \"12\", a single letter word. \"12\" is a vowel, so \"18\" must be a consonant. \"18\" is the first letter of the two letter word \"1836\". All the possible two letter words beginnning with a consonant are: be, by, do, go, me, my, no, so, to, we. All the possible one letter words are:\r\na,i. So we are looking for a seven letter word of this form:\r\n\r\nno matching letters except for the 1st and 7th letters\r\n1st letter = 7th letter = N,B,T,D,M,G,S or W \r\n5th letter: O (if 1st letter = N,G,D,T,S) \r\n5th letter = E or Y if 1st letter = B,M,or W. \r\n6th letter = A or I\r\n\r\nNow the puzzle becomes easy, due to the fact that there is ONLY ONE WORD like that in the English language: TUGBOAT. (You don\'t need a computer program to figure that out. All you need is a methodical approach, and one of the Internet \"crossword puzzle guides\" that list all the seven-letter words). \r\n\r\nSo we plug in: 18=T, 28=U, 14=G, 22=B, 36=O, 12=A. Then you just look at the result, make a succession of intelligent guesses, figure out the remaining substitutions, and (although this sure doen\'t sound like a \"children\'s rhyme\" to me...):\r\n \r\nMISS SUSY HAD A TUGBOAT,\r\nTHE TUGBOAT HAD A BELL,\r\nMISS SUSY WENT TO HEAVEN,\r\nHER TUGBOAT WENT TO...\r\nWELL, THAT\'S ENOUGH SINGING FOR NOW..\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\n\nEdited on December 3, 2003, 2:53 pm',NULL,0);
INSERT INTO comment VALUES (10131,865,4618,'taoist','DUH!','2003-12-03 07:31:54',3,'You can put any answer because it doesn\'t have to be a yes or no answer... for example I would answer it with a \'maybe\'. = )',NULL,0);
INSERT INTO comment VALUES (10132,1309,1301,'Charlie','re(5): alternation implies 1-1','2003-12-03 08:46:51',4,'Hmmm...\r\n\"I was simply replying to Charlies comment insofar as he could accept that the points could alternate, but not that they were 1-1. To me this was the same issue.\"\r\n\r\nWhat I had said was:\r\n\"The idea of alternation would imply equal numbers in the sense of 1-to-1 correspondence. But there are many more irrational numbers on the radius than rational. There are Aleph-1 of the former, but only Aleph-null of the latter. The numbers are intimately mixed, but not alternating.\"\r\n\r\nI don\'t see that I accepted that the types alternate; rather I was stating what you state: it\'s the same as a 1-to-1 correspondence.\r\n\r\nBTW, does anyone know of an HTML code for an Aleph?\r\n\r\n\r\n',10106,0);
INSERT INTO comment VALUES (10133,1389,1301,'Charlie','re: FULL SOLUTION (No computer program used)','2003-12-03 08:53:37',3,'You didn\'t decrypt the title, which is PHONE FUN, and explain why that title is a propos.',10130,0);
INSERT INTO comment VALUES (10134,1309,1301,'Charlie','re(4): alteration','2003-12-03 09:00:09',0,'Looking at the source for that disappearing not: it seems the site translated the closing greater than symbol of the i that opens the italics, into ampersand-gt; as if you had wanted a greater than sign to appear. Apparently these things happen sporadically, like the backslashes that sometimes get placed before quotes.\n\nEdited on December 3, 2003, 9:00 am',10121,0);
INSERT INTO comment VALUES (10135,1389,2839,'FatBoy','re: FULL SOLUTION (No computer program used)','2003-12-03 09:07:58',0,'Wow, good analysis.\r\nA couple questions, \r\n1) in \"1st letter = 7th letter = N,B,T,D,M,G, or W\" you left out \"s\" was this just a typo or had you eliminated \"s\" in some other step?\r\n2) Did you find any underlying Mathmatical corelation letters to numbers? \r\nYours is the only response that I\'ve read so I am not sure if anyone else has found such a link.\r\nI really like the Crypto puzzles but am poor at them so I like to pick te brains of those who complete them. ',10130,0);
INSERT INTO comment VALUES (10136,1517,2839,'FatBoy','there might be trouble in Floobleland','2003-12-03 09:18:56',0,'Seems Lees gal adn Penny\'s guy ahve a history...',NULL,0);
INSERT INTO comment VALUES (10137,1517,2839,'FatBoy','there might be trouble in Floobleland','2003-12-03 09:19:35',0,'Seems Lees gal adn Penny\'s guy ahve a history...',NULL,0);
INSERT INTO comment VALUES (10138,1517,2839,'FatBoy','sorry folks','2003-12-03 09:21:48',0,'That was barely witty enough to post once, I certainly did not mean to post it twice',NULL,0);
INSERT INTO comment VALUES (10139,1389,4507,'Penny','re(2): FULL SOLUTION (No computer program used)','2003-12-03 09:52:47',0,'Charlie: \"You didn\'t decrypt the title, which is PHONE FUN, and explain why that title is a propos\"\r\n \r\nPHONE is short for PHONETIC. I had to leave something for you to work on. ',10133,0);
INSERT INTO comment VALUES (10140,1309,775,'Cory Taylor','a solution??','2003-12-03 10:03:58',0,'after all the discussion of the rational/irrational set sizes, the problem has kinda been overlooked. I like the approach that Eric started with, and I think it shows ~conceptually~ that there is a solution, but it is not really complete...',NULL,0);
INSERT INTO comment VALUES (10141,1389,4507,'Penny','re(2): FULL SOLUTION (No computer program used)','2003-12-03 10:18:05',0,'FatBoy: \"A couple questions, \r\n1) in \"1st letter = 7th letter = N,B,T,D,M,G, or W\" you left out \"s\" was this just a typo or had you eliminated \"s\" in some other step? \r\n2) Did you find any underlying Mathmatical corelation letters to numbers?\"\r\n \r\n1) Typo !! I went back and corrected the post. Thanks.\r\n2) I wasn\'t looking for anything like that. This puzzle didn\'t come from Pythagoras.\n\nEdited on December 3, 2003, 2:41 pm',10135,0);
INSERT INTO comment VALUES (10142,1507,1301,'Charlie','Multiple solutions.','2003-12-03 10:27:56',3,'There are several relationships involved. In addition to the given equations, these three, derived from those given, are useful:\r\nB-H=C-I\r\nD-C=H-F\r\nF-B=I-D\r\n\r\nThat means that the contents of A,B,C,D and G determine all the rest:\r\nH=A+B+C-G-D\r\nF=H+C-D\r\nI=C+H-B\r\nJ=A+B+C-F-I\r\nand E is whatever is left over.\r\n\r\nTrying all possibilities of A,B,C,D and G is easier than trying all possible permutations.\r\n\r\nThe following program goes through the possibilities, and then it prints out only those solutions where A>G>J, so that reflections and rotations are not considered as different:\r\n\r\nCLS\r\nFOR a = 0 TO 9\r\n taken(a) = 1\r\n FOR b = 0 TO 9\r\n IF taken(b) = 0 THEN\r\n taken(b) = 1\r\n FOR c = 0 TO 9\r\n IF taken(c) = 0 THEN\r\n taken(c) = 1\r\n FOR d = 0 TO 9\r\n IF taken(d) = 0 THEN\r\n taken(d) = 1\r\n FOR g = 0 TO 9\r\n IF taken(g) = 0 THEN\r\n h = a + b + c - g - d\r\n IF h >= 0 AND h <= 9 THEN\r\n IF taken(h) = 0 THEN\r\n taken(h) = 1\r\n f = h + c - d\r\n IF f >= 0 AND f <= 9 THEN\r\n IF taken(f) = 0 THEN\r\n taken(f) = 1\r\n i = c + h - b\r\n IF i >= 0 AND i <= 9 THEN\r\n IF taken(i) = 0 THEN\r\n taken(i) = 1\r\n j = a + b + c - f - i\r\n IF j >= 0 AND j <= 9 THEN\r\n IF taken(j) = 0 THEN\r\n taken(j) = 1\r\n IF g + h + i = a + c + f AND c + f + j = b + d + g THEN\r\n IF a > g AND g > j THEN\r\n FOR e = 0 TO 9\r\n IF taken(e) = 0 THEN EXIT FOR\r\n NEXT\r\n r0 = 5 * (ct \\ 5): c0 = 10 * (ct MOD 5)\r\n LOCATE r0 + 1, c0 + 5: PRINT STR$(a)\r\n LOCATE r0 + 2, c0 + 4: PRINT STR$(b); STR$(c)\r\n LOCATE r0 + 3, c0 + 3: PRINT STR$(d); STR$(e); STR$(f)\r\n LOCATE r0 + 4, c0 + 2: PRINT STR$(g); STR$(h); STR$(i); STR$(j)\r\n\r\n ct = ct + 1\r\n END IF\r\n END IF\r\n taken(j) = 0\r\n END IF\r\n END IF\r\n taken(i) = 0\r\n END IF\r\n END IF\r\n taken(f) = 0\r\n END IF\r\n END IF\r\n taken(h) = 0\r\n END IF\r\n END IF\r\n END IF\r\n NEXT\r\n taken(d) = 0\r\n END IF\r\n NEXT\r\n taken(c) = 0\r\n END IF\r\n NEXT\r\n taken(b) = 0\r\n END IF\r\n NEXT\r\n taken(a) = 0\r\nNEXT\r\nPRINT ct\r\n\r\nThe program finds:\r\n\r\n 5 5 6 7 7\r\n 1 7 6 2 0 4 1 3 1 5\r\n 6 2 4 1 3 9 5 8 2 2 8 5 6 0 3\r\n 4 3 9 0 4 8 4 0 2 3 7 1 5 4 6 0 3 4 8 2\r\n\r\n 7 8 8 8 8\r\n 6 0 0 5 2 3 2 4 2 4\r\n 1 4 8 6 2 3 1 4 7 3 0 6 6 1 5\r\n 3 9 3 2 3 4 9 1 7 5 6 0 6 5 7 1 1 7 9 0\r\n\r\n 8 8 8 9 9\r\n 2 6 2 6 4 3 0 4 0 6\r\n 4 1 7 7 0 4 1 2 9 2 6 5 5 1 3\r\n 7 5 9 0 4 5 9 3 7 7 6 0 8 3 7 1 8 2 8 4\r\n\r\n 9 9 9 9 9\r\n 1 3 1 4 2 4 3 0 3 1\r\n 2 4 6 3 2 6 3 1 7 1 5 6 0 5 7\r\n 6 5 7 0 6 5 8 0 6 6 8 0 4 7 4 2 7 6 4 2\r\n\r\n 9 9 9 9 9\r\n 3 2 3 2 3 4 3 5 5 1\r\n 0 4 8 1 4 8 2 0 8 4 0 7 0 2 8\r\n 8 6 5 1 6 7 6 0 8 6 7 1 7 6 8 2 8 7 3 4\r\n
\r\n--------\r\nThus there are 25 basic solutions, not counting rotations and reflections.',NULL,0);
INSERT INTO comment VALUES (10143,1507,4082,'wonshot','re: Multiple solutions.','2003-12-03 10:36:03',0,'I think there is a slight problem with this, there seems to be duplicate numbers.',10142,0);
INSERT INTO comment VALUES (10144,1389,1301,'Charlie','re(3): FULL SOLUTION (No computer program used)','2003-12-03 10:47:14',3,'RE:\r\n\"PHONE is short for PHONETIC. I had to leave something for you to work on.\"\r\n\r\nThanks for your graciousness. Since no one has said it before:\r\n\r\nThe second digit of each 2-digit code is the number on a telephone keypad and the first digit is the ordinal number of the letter on that key.',10139,0);
INSERT INTO comment VALUES (10145,1507,2716,'Federico Kereki','Full solution','2003-12-03 10:54:12',3,'There are a dozen solutions:\r\n\r\nABCDEFGHIJ\r\n0594378261\r\n0957341628\r\n1574639028\r\n1672398450\r\n1753648209\r\n1769320548\r\n8230679451\r\n8246351790\r\n8327601549\r\n8425360971\r\n9042658371\r\n9405621738\r\n\r\nThey were produced by the following awk program:\r\n\r\nBEGIN {\r\n for (A=0; A<=9; A++)\r\n { for (B=0; B<=9; B++) if (B!=A)\r\n { for (C=0; C<=9; C++) if ((C!=A) && (C!=B))\r\n { for (D=0; D<=9; D++) if ((D!=A) && (D!=B) && (D!=C))\r\n { for (E=0; E<=9; E++) if ((E!=A) && (E!=B) && (E!=C) && (E!=D))\r\n { for (F=0; F<=9; F++) if ((F!=A) && (F!=B) && (F!=C) && (F!=D) && (F!=E))\r\n { for (G=0; G<=9; G++) if ((G!=A) && (G!=B) && (G!=C) && (G!=D) && (G!=E) && (G!=F))\r\n { for (H=0; H<=9; H++) if ((H!=A) && (H!=B) && (H!=C) && (H!=D) && (H!=E) && (H!=F) && (H!=G))\r\n { for (I=0; I<=9; I++) if ((I!=A) && (I!=B) && (I!=C) && (I!=D) && (I!=E) && (I!=F) && (I!=G) && (I!=H))\r\n { J = 45 - (A+B+C+D+E+F+G+H+I)\r\n if ((J!=A) && (J!=B) && (J!=C) && (J!=D) && (J!=E) && (J!=F) && (J!=G) && (J!=H) && (J!=I))\r\n { if ((A+B+D+G==G+H+I+J) && (A+B+D+G==A+C+F+J) && (A+B+C==D+G+H) && (D+G+H==F+I+J))\r\n { print A B C D E F G H I J\r\n }\r\n }\r\n }\r\n }\r\n }\r\n }\r\n }\r\n }\r\n }\r\n }\r\n }\r\n}\r\nEdited on December 3, 2003, 11:25 am P\r\n /|\\_\r\n / \\ \\_\r\n u/ \\ \\__\r\n / |v w\\_\r\n / \\ \\_\r\n / T \\ \\\r\n---A---------B---------C---\r\n x x\r\n
\r\nBy the law of cosines:\r\nu^2 = v^2 + x^2 - 2vx*cos(T)\r\nw^2 = v^2 + x^2 - 2vx*cos(pi-T)\r\n\r\nSince cos(pi-x) = -cos(x), the second equation can be written as\r\nw^2 = v^2 + x^2 + 2vx*cos(T)\r\n\r\nAdding the two equations together yeilds\r\nu^2 + w^2 = 2v^2 + 2x^2\r\n\r\nIf we assume u, v, and w are all rational, then a contradiction is formed because if both u and w are rational then v^2 = (u^2 + w^2 - 2x^2)/2 is irrational which means v must be irrational.\r\n\r\nSo points A, B, and C are three points which allow the stamp to cover the entire plane.\n\nEdited on December 9, 2003, 10:08 am',NULL,0);
INSERT INTO comment VALUES (10149,1507,775,'Cory Taylor','wording change','2003-12-03 11:31:00',0,'I seem to remember that the three number sums were originally different when this problem was waiting in the queue - possibly when it was re-formatted the intent was altered? I could easily be wrong of course, but the three number equivalent sums were originally;\r\n\r\nD+E+F = B+E+I = C+E+H\r\n\r\nI also don\'t know if this would reduce the redundancies, as I never worked through this one.',NULL,0);
INSERT INTO comment VALUES (10150,1507,1920,'Brian Smith','re: wording change','2003-12-03 11:45:15',0,'I am fairly sure this problem is equivalent.',10149,0);
INSERT INTO comment VALUES (10151,1309,775,'Cory Taylor','re: Solution','2003-12-03 12:19:56',0,'{Let x be any positive irrational number. \r\nLet AC be a line segment with length 2x. \r\nLet B be the midpoint of AC. \r\nLet P be any point in the plane. \r\nLet u be the length of PA. \r\nLet v be the length of PB \r\nLet w be the length of PC. \r\nLet T be the measure of angle ABP.}\r\n\r\nFurther refinement is required unless I\'ve missed a constraint of your solution.\r\n\r\nLet x=any positive irrational number (okay x=root3)\r\nLet p=any point on the plane (okay choose p so that t=90 degrees and v=1)\r\n\r\nGeomety works the following lengths;\r\n u=w=2\r\n v=1\r\n t=90,pi\r\n\r\nThis causes your equation to produce no contradiction, ie.,\r\nv^2 = (u^2 + w^2 - 2x^2)/2\r\n1^2 = (2^2 + 2^2 - 2(√3)^2)/2\r\n1 = (4 + 4 - 6) /2\r\n1=1\r\n\r\nall with x->irrational and u,v,w -> rational',10148,0);
INSERT INTO comment VALUES (10152,1507,2716,'Federico Kereki','re: wording change','2003-12-03 13:11:19',0,'As the problem stands, E is useless, for it doesn\'t appear in any of the sums; its only function is to use up a number.',10149,0);
INSERT INTO comment VALUES (10153,1507,1301,'Charlie','re(2): Multiple solutions.--down to two','2003-12-03 14:12:03',3,'A bug in my original program (failure to set taken(g)), resulted in those duplicate digits. Correcting that, we\'re left with 2 solutions:\r\n\r\n 8 9\r\n 2 4 0 4\r\n 6 3 5 2 6 5\r\n 1 7 9 0 8 3 7 1\r\n
\r\n---------\r\nNote that the 3\'s across the center do add up to a constant in each solution: 14 and 13 respectively, the same as the corner triangles.\r\n\r\nThese solutions, when rotated and reflected, produce the same twelve as found by Federico Kereki.\n\nEdited on December 3, 2003, 2:18 pm',10143,0);
INSERT INTO comment VALUES (10154,7,4430,'Eberhard','re(2): Solution Using Real Prob/Stats','2003-12-03 14:20:58',0,'ell- first let me say i did read the solution, what i think you might be missing is that HT and TH are functionally equivilant, meaning that there are 2 not 3 outcomes even in art\'s solution - i.e. 1/2 not 1/3 but anyway...\r\n\r\nOn Independence-\r\n\r\nIn this particular example the probability of a particular outcome (which we will call flip one or F1), that is to say H or T, does not change the probability of the outcome of F2 (flip 2). \r\ni.e. when P(F1)>0, P(F1|F2) = P(F2)\r\nindicating independence\r\nFurthermore- the multiplication rule here become\r\n \r\nP(F1 intersect F2)=P(F1)P(F2|F1)=P(F1)P(F2)\r\nWhich implies that when P(F2)>0, then\r\n\r\nP(F1|F2)= (P(F1 intersect F2)/P(F2)) = (P(F1)P(F2))/P(F2)= P(F1)\r\n\r\n\r\nNow- I am going to stop here before i get to far into a Statistics Class, if you want me to follow up and complete this explanation let me know what you made of this begining so I know where you are coming from on a mathematics level-',9875,0);
INSERT INTO comment VALUES (10155,1309,1301,'Charlie','re(2): Solution','2003-12-03 14:32:02',0,'As a result of what Cory Taylor has said, it seems Brian Smith\'s proof (excellent, by the way) needs only add the constraint that not only must x be irrational, but also x². There are still many, many, such sets of points that can be found.',10151,0);
INSERT INTO comment VALUES (10156,1475,2839,'FatBoy','re(2): A guess','2003-12-03 14:43:46',0,'nice try John, Key West is the Southernmost point in the CONTINENTAL United States. But Hawaii is located at 16 degree north Lattitude a full eigth degrees south of Key West\'s 24 degrees North Latitude',10128,0);
INSERT INTO comment VALUES (10157,7,3172,'SilverKnight','re(3): Solution Using Real Prob/Stats','2003-12-03 15:43:16',0,'HT and TH are \"functionally equivalent\" (as you put it) only if the function is \"one coin is heads and one coin is tails\".\r\n\r\nIf I flip two fair coins together a bunch of times, I will expect to get one of three outcomes:\r\n(1) two heads, 1/4 of the time\r\n(2) one head and one tail, 1/2 of the time, and\r\n(3) two tails, 1/4 of the time\r\n\r\n(I assume you agree with this so far.)\r\n_______________________________\r\n\r\nThe problem states:\r\n\"at least one of the coins is showing up as \'tails\'.\"\r\n\r\nThis rules out outcome (1).\r\nOutcomes (2) and (3) are still possible.\r\n\r\nThe probability of those two outcomes have a 1/2 : 1/4 ratio, and the question asked what is the chance the outcome is (3).\r\n\r\n(1/4) / [ (1/2) + (1/4) ] = (1/4) / (3/4) = 1/3\r\n_______________________________\r\n\r\nPlease continue with your statistics class.',10154,0);
INSERT INTO comment VALUES (10158,7,3172,'SilverKnight','re(4): Solution Using Real Prob/Stats','2003-12-03 16:10:30',0,'BTW, Eberhard, your math is correct:\r\n\r\nEberhard wrote:\r\nOn Independence-\r\n\r\nIn this particular example the probability of a particular outcome (which we will call flip one or F1), that is to say H or T, does not change the probability of the outcome of F2 (flip 2).\r\ni.e. when P(F1)>0, P(F1|F2) = P(F2)\r\nindicating independence\r\nFurthermore- the multiplication rule here become\r\n\r\nP(F1 intersect F2)=P(F1)P(F2|F1)=P(F1)P(F2)\r\nWhich implies that when P(F2)>0, then\r\n\r\nP(F1|F2)= (P(F1 intersect F2)/P(F2)) = (P(F1)P(F2))/P(F2)= P(F1) \r\n_______________________\r\n\r\nWhat is not correct is your understanding of the problem.\r\n\r\nThe problem did not say, \"I tell you that the FIRST coin flipped is a tails, what is the probability that the OTHER coin flipped is tails\" (in which case your mathematics would apply and the answer would be 1/2).\r\n\r\nThe problem can be restated as \"I tell you that one of the following is true: either the FIRST coin flipped is tails and the SECOND is heads -- or -- the SECOND coin flipped is tails and the FIRST is heads -- or -- both coins are tails. What is the chance that both coins are tails?\"\r\n\r\nGiven this equivalent restatement, the mathematics is different and leads to 1/3.',10157,0);
INSERT INTO comment VALUES (10159,1404,3386,'Victor Zapana','reason for my 5','2003-12-03 17:28:50',0,'the reason why i voted this one 5 coz this completely stumps me... lol things that i have no idea to start impresses me greatly. so thats for my 5.',NULL,0);
INSERT INTO comment VALUES (10160,1404,3172,'SilverKnight','reason for my 1','2003-12-03 17:31:40',0,'The reason I voted 1 is because this completely stumps me, and I don\'t like problems that I don\'t get \'right off the bat\'.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\nj/k - I didn\'t vote on it... :-P',NULL,0);
INSERT INTO comment VALUES (10161,1404,3386,'Victor Zapana','re: reason for my 1','2003-12-03 17:32:33',0,'lol sk the feeling is mutual. i see no start and no end in this cryptogram',10160,0);
INSERT INTO comment VALUES (10162,1404,3386,'Victor Zapana','mebe?','2003-12-03 17:34:42',1,'well something i have noticed is that all most all the words are 4 or 6 letter words, EXCEPT for the last word of each line, which are 5. mebe Faded, Sides, Royal, and Hides is important?',NULL,0);
INSERT INTO comment VALUES (10163,1404,3386,'Victor Zapana','re: mebe?','2003-12-03 17:37:06',1,'another thought is that the title might be clue. the middle words in this riddle are: Then, Band, Late, Pedals, Muzzle, Want. mebe they\'re important too?',10162,0);
INSERT INTO comment VALUES (10164,1404,3386,'Victor Zapana','help sk','2003-12-03 17:41:37',0,'help sk ur the only other one whos responding to this problem lol.',NULL,0);
INSERT INTO comment VALUES (10165,1404,4360,'Gus','Answer','2003-12-03 17:52:19',0,'The answer is: Emily Dickinson\r\n:)\r\n',NULL,0);
INSERT INTO comment VALUES (10166,1404,3386,'Victor Zapana','re: Answer','2003-12-03 18:07:49',0,'hmm.. for those who are lost in this problem can u explain how u got to that answer.',10165,0);
INSERT INTO comment VALUES (10167,1404,4360,'Gus','re(2): Answer - Explanation','2003-12-03 18:19:06',3,'Take the middle letter(s) of each word and concatenate them to form a phrase.\r\n\r\nThe first paragraph:\r\n\r\nTask Slip Lights Catnip Wind Hogtie Vote Then Itches Will Midrib Bend Team Losers Faded\r\n\r\n... actually is: \"As lightning to the children eased\"\r\n\r\nThis phrase is a fragment of a poem by Emily Dickinson.\r\n\r\nCool problem :)\r\n\r\n\n\nEdited on December 3, 2003, 6:21 pm',10166,0);
INSERT INTO comment VALUES (10168,1404,1626,'Gamer','re(3): Answer - Explanation','2003-12-03 18:24:31',0,'If you read the rest of it, it\'s the same. (I hope!)\r\n\r\nI checked this one twice so I am pretty sure it\'s right :)\r\n\r\nI knew you had it when you said Emily Dickenson :)',10167,0);
INSERT INTO comment VALUES (10169,27,4627,'donnmike','the solution is wrong','2003-12-03 19:07:23',0,'to say it can be given on any day because we have deduced it cannot be given on any day is wrong. that a surprise can still occur is totally unrelated to our logic. the statement by the teacher that the test will be a surprise is nonsensical and must be ignored (you can\'t tell someone when you will surprise them). now we are only left with the information that there will be a test the following week. it may still be a surprise (if it happens mon-thur), or it might not be a surprise (if it happens on friday). and if, instead, the teacher tells the students there will be a \"surprise test\" (instead of conveying the information in two parts) then the whole statement must be disregarded. so now it is just as if the teacher told us nothing, so any test given will be a surprise (even if it occurs friday). \r\n\r\nwe have now decided that there may still be a surprise test the following week, but that is the null assumption (there may always be a surprise test the following week no matter what a teacher might tell you) and that conclusion was not derived from anything the teacher told us.',NULL,0);
INSERT INTO comment VALUES (10170,68,4628,'steven','','2003-12-03 19:37:01',0,'that was fun to do thanks',NULL,0);
INSERT INTO comment VALUES (10171,1517,4628,'steven','','2003-12-03 19:38:29',0,'Dang this is really a brain teaser\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (10172,1478,4628,'steven','praise','2003-12-03 19:44:50',0,'good job jadeite',NULL,0);
INSERT INTO comment VALUES (10173,777,4628,'steven','','2003-12-03 19:47:01',0,'this one was tough',NULL,0);
INSERT INTO comment VALUES (10174,1509,4629,'chris Knight','answer','2003-12-03 19:47:38',3,'March 13th 1996',NULL,0);
INSERT INTO comment VALUES (10175,1404,4507,'Penny','Wild alternative solution','2003-12-03 19:50:57',0,'Of course we all revere Emily Dickinson. She was not only a great poet, but she was also a great actress in the TV series \"Policewoman\". \r\n \r\nBut here is an alternative solution to this riddle. If you interpret \"The answer is a female\'s first and last name\" as wanting a single name which is both a first and last name of a famous woman, then the answer is Reece (or Reese), as in Reese Witherspoon (\"Legally Blonde\"), and also superstar athlete Gabrielle Reece, the co-author of \"Big Girl in the Middle\", which chronicles her struggles and achivements as a top female pro athlete. In this case, all the clue words in this puzzle suddenly make sense. They are common expressions in various sports:\r\n\r\n\"That pitcher has the TASK of stopping three powerful sluggers.\"\r\n\"The running back has managed to SLIP through two linebackers.\"\r\n\"A quick left hook by Ali turned out his opponent\'s LIGHTS in short order.\"\r\n\"Those hockey players are pursuing the puck like cats after CATNIP!!\"\r\n\"He is about to WIND up and deliver!!\" \r\n\"The wrestler has his opponent HOGTIED.\"\r\n\"Johnny Unitas got into the Hall of Fame with many a VOTE to spare.\"\r\n\"What a difference between this Superbowl and the last one -that was THEN, this is now.\"\r\n\"Here is a competitor who clearly ITCHES for the city-wide title.\"\r\n\"The underdogs\' victory proves that where there\'s a WILL, there\'s a way.\"\r\n\"A punishing jab acught him in MIDRIB.\"\r\n\"Notre Dame\'s victory has electrified all of South BEND.\"\r\n\"There is no place on this TEAM for LOSERS.\"\r\n\"The Steelers hopes to repeat have FADED badly in the fourth quarter\".\r\n\"No one today can SWIM with the power and skill of Mark Spitz.\"\r\n\"Linebacker Brian Bosworth is going for the GOTHIC look.\"\r\n\"Arnold Schwarzenegger FLEXED his muscles convincingly to win Mr. Universe.\"\r\n\"The Toronto MAPLES\' fabled dynasty continues.\"\r\n\"A college marching BAND is a delight to watch in the Fall.\"\r\n\"It\'s LATE in the ninth inning, and time is running out for the Yankees.\"\r\n\"Alex Karras was a Detroit LION many years ago.\"\r\n\"Denny McLain pulled a \'TANKER\' in the third game of the series.\"\r\n\"Tiger Woods will try to SINK a long birdie to win the tournament.\"\r\n\"Venus Williams can hit convincingly down both SIDES of the court.\"\r\n\"The Oakland Raiders are putting on an offensive display certain to WITHER the opposing team.\"\r\n\"All BETS are off if the Rams score on this drive.\"\r\n\"That pitcher has now STRUCK out the side.\"\r\n\"Bobby Knight is in a real LATHER over that call.\" \r\n\"It never fails to BEMUSE me when I see the offcials make such incompetent calls.\"\r\n\"The middle linebacker is LISTED at 6\'3\" and 240 lbs.\"\r\n\"Joe Frasier back PEDALS as George Foreman continues to attack aggressively.\"\r\n\"Pitches like that will MUZZLE even the best batters.\"\r\n\"It\'s hard to believe the Cardinals actually BLEW a four touchdown lead.\"\r\n\"Charles Barklay is the OGRE to the opposing team\'s fans.\" \r\n\"He has now MADE every out in the last three innings.\"\r\n\"Yogi Berra filled the DUAL roles of slugger and philosopher.\"\r\n\"No Kansas City ROYAL is on this year\'s All Star Team.\"\r\n\"The CORE of the Giants\' lineup is due up.\"\r\n\"This starting ELEVEN is hard to match.\"\r\n\"\'Mean Joe Green\' - hey, that RHYMES!\"\r\n\"The Seattle Seahawks clearly WANT a defensive struggle today.\"\r\n\"His racquetball style defies LABELS.\"\r\n\"The game is officially RAINED out.\"\r\n\"He\'s the kind of competitor who HIDES when the going gets tough.\" \r\n\r\n\r\n\r\n\n\nEdited on December 4, 2003, 8:26 am',NULL,0);
INSERT INTO comment VALUES (10176,1507,4629,'chris Knight','check it out','2003-12-03 20:01:49',3,' 0\r\n 1 2 \r\n 5 3 \r\n7 8\r\n\r\n0,1,5,7 =13\r\n0,2,3,8 =13\r\n',NULL,0);
INSERT INTO comment VALUES (10177,1507,4629,'chris Knight','re: check it out','2003-12-03 20:04:27',0,'nevermind, i jumped the gun.',10176,0);
INSERT INTO comment VALUES (10178,1428,4631,'David Hanna','My solution','2003-12-03 20:59:41',0,'With 5 rods you can represent 0 - 31 different numbers. Break each number down in to it\'s binary equivalent and on those rods write down the number. At the top of each rod, write the number 1 - 5 representing the least to most significant bits. \r\n\r\nFor example, take the number 19. In binary\r\n\r\n10011\r\n\r\nSo, 19 would be written on the first, second and fifth rod.',NULL,0);
INSERT INTO comment VALUES (10179,1517,4631,'David Hanna','My solution','2003-12-03 21:01:41',0,'He\'s selling the individual numbers. Each number is 10 cents',NULL,0);
INSERT INTO comment VALUES (10180,1508,4631,'David Hanna','My solution','2003-12-03 21:10:15',0,'Node *temp = current->next;\r\ncurrent->val = current->next->val;\r\ncurrent->next = current->next->next;\r\nfree(temp->val);\r\nfree(temp);\r\n\r\nOr something like that. Been a while for C.\r\n\r\nThe idea is that you move the next node\'s values into the current node, then have the current node point to the node following the next node, then you can delete the next node.\r\n',NULL,0);
INSERT INTO comment VALUES (10181,1364,4612,'Magick321','i dunno if someone else gottit yet... -.-\'','2003-12-03 21:45:20',3,'Given their statements we can determine:\r\n\r\nJeswin : Grot (or Knight)\r\nParker : Cloysta (or Knave)\r\nCrasbo : Blarg (or liar)\r\n\r\nBoth a Knight and a Liar will say that they themselves are the truthteller, but the Knave is free to call himself whatever he chooses. So, naturally the one who calls himself something other than the rest would (Knight) must be the Knave. In this case, he is calling self a \'Blarg\', or a liar. Then, knowing that the Knave alternates truth and lies per sentence, we know that Crasbo is the real \'Blarg\', so Jeswin must be the true \'Grot\', or Knight.\r\n\r\nTo check our findings, we can see that Jeswin confirms that Parker is the Cloysta, or Knave, and Crasbo lies as to what Jeswin is.\r\n\r\n∞ Magick is not to be taken lightly...',NULL,0);
INSERT INTO comment VALUES (10182,1225,4612,'Magick321','o.o\' *feels brain fluids draining away*','2003-12-03 21:52:34',1,'couldnt you just load 2 to always come up...?\r\n\r\n∞ Magick is not to be taken lightly...',NULL,0);
INSERT INTO comment VALUES (10183,7,1301,'Charlie','re(4): Solution Using Real Prob/Stats','2003-12-03 22:00:28',0,'SK, I don\'t know if you\'ve had a chance to look over the full set of comments on this, but this problem is a particular bugaboo of mine. The salient point is the full quote from the problem--not \"at least one of the coins is showing up as \'tails\'.\" but \"I [the narrator, who has just tossed the coins] then tell you that at least one of the coins is showing up as \'tails\'.\" \r\n\r\nSuppose the narrator has done this 4 times--no, make that 8 times-- and it has come out, strangely enough, exactly the number predicted theoretically:\r\n\r\nHH and the narrator reports at least one head.\r\nHH and the narrator reports at least one head.\r\nHT and the narrator reports at least one head.\r\nTH and the narrator reports at least one head.\r\nHT and the narrator reports at least one tail.\r\nTH and the narrator reports at least one tail.\r\nTT and the narrator reports at least one tail.\r\nTT and the narrator reports at least one tail.\r\n\r\nOut of the 4 times that the narrator chose to say at least one is a tail, in 2 cases (or half the time) both are tails.\r\n\r\nWhile the narrator is not saying a particular coin in the sense of \"the first one\" or \"the one that\'s a nickel\", etc., he is in effect saying, \"the one about which I choose to report.\" By putting in the form of a narrative story, rather than a puzzle statement, the dynamics change to what I have mentioned here.',10157,0);
INSERT INTO comment VALUES (10184,1517,4634,'stephany','HERE\'S THE SOLUTION','2003-12-03 22:19:10',0,'He\'s selling house numbers....... ',NULL,0);
INSERT INTO comment VALUES (10185,1478,4612,'Magick321','These kind of puzzles are always interesting to do... ^-^','2003-12-03 22:26:25',0,'1st : Ben Jones : Fruit Cake\r\n2nd : James Best : Chocolate Cake\r\n3rd : Nigel Stevens : Sponge Cake\r\n4th : Vicky Andrews : Cheese Cake\r\n\r\n(No elaboration on proces thank you o.o\')\r\n\r\n∞ Magick is not to be taken lightly...',NULL,0);
INSERT INTO comment VALUES (10186,1389,4612,'Magick321','LMAO','2003-12-03 22:40:33',0,'LMAO -- I remember singing that a while back...\r\n\r\n∞ Magick is not to be taken lightly...',NULL,0);
INSERT INTO comment VALUES (10187,678,4612,'Magick321','Easier than it sounds...','2003-12-03 22:53:38',3,'The fly (as well as any other fly that passes through before the spider is fed) has a 50% chance of survival... the previous flies cannot and will not affect the sixth\'s chances...\r\n\r\n\r\n∞ Magick is not to be taken lightly...',NULL,0);
INSERT INTO comment VALUES (10188,7,3224,'Lee','devil\'s advocate','2003-12-03 23:50:28',0,'It’s 1/3\r\nOr maybe 50-50\r\nLike ‘Charlie says’ (British ad-joke) if you ask the flipper ‘is one of them tails?’ and he responds in the affirmative then you’ve ruled out the HH option and most likely the other coin shows heads.\r\nThe way the question is posed implies either\r\ni) (How most have interpreted). It’s a one-time deal. The flipper has casually flipped two coins and one of them is a tail. That out of the way, ‘what is the probability the other is a tails?’\r\nii) The flipper only reports ‘at least one Tail’ (outcome HH means no report)\r\niii) The flipper only reports ‘at least one Tail’ (unless the outcome is HH in which case he reports ‘at least one Head’)\r\niv) The flipper randomly reports ‘at least one Head/Tail’ (ruling out the opposite double HH or TT)\r\nv) The flipper can choose when and what to report\r\n\r\nFor case;\r\ni) This could have happened in one of three ways, all equally likely. Probability of the other being a Tail is only one of those three options (prob(T) = 1/3)\r\nii) Like above, the other coin is clearly twice as likely to be Heads for the reason described in most of the points here (prob(T)=1/3)\r\niii) A report of Heads makes it a certainty the other is a Head (prob(T) =0). The other ¾ of the time (when he reports Tails) the other coin is twice as likely to be a Head (prob(T) = 1/2 [3/4*2/3])\r\niv) Half the time the coins will be different. Half of these times the flipper will report Heads (prob(T) = 2/3) and half of these times report Tails (prob(T) = 1/3)\r\nTotal probability = (1/4*2/3 + 1/4*1/3) = 1/4\r\nThe other half of the time the coins will show the same the flipper is forced to report the side they show and whether you choose the same or different,\r\nFor HH flipper forced to report one is Heads (prob(T) = 0*1/4 = 0)\r\nFor TT flipper forced to report one is Tails (prob(T) = 1*1/4 = 1/4)\r\nTotal probability the other coin is Tails = 1/4+1/4 = 1/2\r\nv) The flipper knows the other coin is more likely to be Heads if ‘at least one is Tails’ and so only reports one is Tails if both are (prob(T) =1) in order to catch you out.\r\n\r\nI agree the question’s more likely to be interpreted as case i), simply a casual coin-flipping exercise. My problem with it is it is very dull to think someone has flipped two coins – and with no thought for profit, interest or amusement reported one is a Tail and went about their business whilst you’ve pondered on the probability the other was a Tail. If this is the case then prob(T) is certainly a 1/3 but where there is human input there is motive and this is undoubtably a zero sum ‘game’ . Cases i) and ii) are biased in favour of the ‘player’ – iii) and iv) are fair and v) seems like a game of wits - but boils down to a fair game if you as a guesser simply pick H or T at random yourself.\r\nI find it difficult to believe it’s either of the first two cases.\r\nIn a game environment, because of the human input, I feel, on a one-off trial, the flipper has reported ‘at least one Tail’ only when both are (knowing the player will believe the other to be Heads as twice as likely). \r\nOf course as a guesser, you are aware of this.\r\nOf course as a flipper, you are aware the guesser is aware\r\nOf course as a guesser, you are aware the flipper is aware, the guesser is aware…………..\r\n',NULL,0);
INSERT INTO comment VALUES (10189,678,3224,'Lee','re: Easier than it sounds...','2003-12-03 23:57:12',0,'\'the previous flies cannot and will not affect the sixth\'s chances... \'\r\nThey do.\r\nYou\'re wrong.',10187,0);
INSERT INTO comment VALUES (10190,7,3172,'SilverKnight','re: devil\'s advocate','2003-12-04 07:18:32',0,'Lee, very nice post.',10188,0);
INSERT INTO comment VALUES (10191,7,3172,'SilverKnight','re(5): Solution Using Real Prob/Stats','2003-12-04 07:23:49',0,'Charlie, you have a valid point here (and Lee, I think, has encapsulated it very well a couple of comments back).\r\n\r\n(And I have read the full set of comments), but the issue that you are talking about is definitely not the issue that Eberhard and I were talking about. (Which translates to Lee\'s case (i) and maybe (ii)).\r\n\r\nAs evidence of what Eberhard was discussing, I will quote his earlier postings:\r\n...the real answer and why are as follows: The first know that each toss is concidered a seperate event by probability (known as independence)- meaning that the probability of either coin showing a particular side is always one half 1/2. Second know that when trying to determine if both will be the same side the probabilities are multiplied, i.e. 1/4 (this can be thought of as an ordered sequence).\r\n-- and --\r\n...what i think you might be missing is that HT and TH are functionally equivilant, meaning that there are 2 not 3 outcomes even in art\'s solution...\r\n\n\nEdited on December 4, 2003, 7:44 am',10183,0);
INSERT INTO comment VALUES (10192,1404,2839,'FatBoy','1 last question for gamer','2003-12-04 07:53:21',0,'Just curious, was the number of letters (all 4 or 6 except for last word which was 5) an intentional red herring (in which case it was a doozy as I spent an hour trying to find so arrangement in those 4s adn 6s) or was it just an unintional biproduct of coming up with words that lad obvious center letters?',NULL,0);
INSERT INTO comment VALUES (10193,1309,4507,'Penny','Lateral thinking solution','2003-12-04 07:54:17',0,'Wait until the flight attendant is distracted, then sneak up to the \"plane lighting and illumination\" button, and use the stamp to press down on the off button. The entire plane will go black. :-)',NULL,0);
INSERT INTO comment VALUES (10194,1511,4554,'Edward','Solution','2003-12-04 08:17:24',3,'Here is an Australian newbie giving it a shot:\r\n\r\n(a)\r\nObserver A will always observe the bullet going forwards (or backwards) at 10 mph.\r\n\r\n(b)\r\nFrom observer B’s point of view, the velocities will have to add relativistically. If they did not, then the bullet – a massive object – would be travelling at c, and this isn’t allowed. In order to add the velocities, we take the Lorentz transformation (which is a compact way of writing what B observers in terms of what A sees):\r\n\r\ndx’ = ã(dx + v.dt), dt’ = ã(dt + v.dx/c²)\r\n\r\n(The dashes refer to what B sees; ã is the Lorentz factor, and v is the relative velocity between A and B)\r\n\r\nDivide the two gives\r\n (dx + v.dt)\r\ndx\'/dt\' = --------------\r\n (dt + v.dx/c²)\r\n\r\n u + v\r\nSo that u\' = -------\r\n u.v\r\n 1 + ---\r\n c²\r\n\r\n(where u\' = dx\'/dt\', and u = dx/dt).\r\n\r\nNow, for spaceship A travelling at v = c - 10 mph, and the bullet travelling at u = 10 mph = 16 km h^-1, we get:\r\n\r\n 16 km/h + c - 16 km/h\r\nSo that u\' = -------------------------\r\n 1 + (1.48e-8)(0.99999994)\r\n\r\n c\r\nu\' = --------------\r\n 1.000000014799\r\n\r\n(Two points: (1) The c’s in the denominator cancel, (2) I am unable to work with anything besides metric.)\r\n\r\nThus, u\' = 0.999999985c. That is, the bullet is travelling slightly faster, but the difference is less than 10 mph (or 16 km h^-1)\r\n\r\n(c)\r\nIf the bullet is being shot backwards, we just change its sign in the equation above:\r\n\r\n - 16 km/h + c - 16 km/h\r\nu\' = ------------------------- = \r\n 1 - (1.48e-8)(0.99999994) \r\n\r\n 0.99999988\r\nu\' = ----------- .c\r\n 0.999999985\r\n\r\nThis gives u\' = 0.99999989c = 0.99999990 c. That is, B sees the bullet as travelling slower than A, but not by as much as 16 km h^-1.\r\n\r\nTa da! This is the work of a newbie, so apologies if it stinks (I haven\'t been able to see if the positioning of the fonts work).',NULL,0);
INSERT INTO comment VALUES (10195,1310,2716,'Federico Kereki','Three cuts','2003-12-04 08:45:57',3,'Make the third cut horizontally, and you\'ll get 8 equal pieces. (However, the ones who get the lower pieces may object they get less frosting.)',NULL,0);
INSERT INTO comment VALUES (10196,1310,1301,'Charlie','re: Three cuts','2003-12-04 08:50:24',0,'But is it possible to make three straight cuts vertically so that each piece has the same surface area on top and therefore the same volume as well?\r\n\r\n(to get 7 equal-sized pieces, of course)\n\nEdited on December 4, 2003, 8:53 am',10195,0);
INSERT INTO comment VALUES (10197,1511,3172,'SilverKnight','re: Solution','2003-12-04 09:05:55',0,'Perhaps it\'s a typo... but did you mean that A (the one who shoots the bullet), watches the bullet go away from him (in either direction) at only 10 mph?',10194,0);
INSERT INTO comment VALUES (10198,1310,1301,'Charlie','Thoughts','2003-12-04 09:07:02',1,'Consider this as a 2-D problem to make 7 equal-sized pieces:\r\n\r\nThe first cut (a chord of the circular top of the cake) is going to have to cut the circle into a ratio of areas of 3:4. That\'s easy enough, and there\'s a unique distance from the center that will do this. Rotationally it doesn\'t matter where you do this, so you can\'t mess up here.\r\n\r\nThe next cut has to cut that smaller previous piece in a 1:2 ratio and the larger previous piece in a 2:2 ratio (i.e., in half--left unreduced to emphasize the double-size nature of the pieces left). That should also be possible, given that there are two degrees of freedom in placing that second chord, though it will be a little tricky figuring out where.\r\n\r\nBut then the third cut must divide each of three double-sized pieces in half. Unless the pieces are fortunately placed (and I doubt that they would be from the constraints imposed by the previous step), you wouldn\'t be able to divide all three remaining pieces in half. That would be accomplishing 3 things with just the 2 degrees of freedom in choosing the chord.\r\n\r\nEdited on December 4, 2003, 9:07 am\n\nEdited on December 4, 2003, 9:09 am',NULL,0);
INSERT INTO comment VALUES (10199,1404,3172,'SilverKnight','re: 1 last question for gamer','2003-12-04 09:07:51',0,'or perhaps was it that the line had an odd number of letters... so if you put in a 4 or 6 letter word, you\'d have an extra letter in there?',10192,0);
INSERT INTO comment VALUES (10200,1310,1301,'Charlie','re: Thoughts','2003-12-04 09:16:40',0,'If my logic was correct in stating that a 7-piece solution is impossible (considered as a 2-D problem with vertical cuts), then what remains, to answer the question, is the 6-piece solution, which there are various ways of accomplishing, such as a radially symmetric asterisk-like set of cuts, or dividing in half and then making two cuts perpendicular to the original diameter cut, with appropriate distances figured out.',10198,0);
INSERT INTO comment VALUES (10201,15,2716,'Federico Kereki','The continued fraction way','2003-12-04 09:49:37',3,'We are looking for a number abcde...z2.
\r\n10^3-6^3=784=28^2
\r\n10^2-6^2=64=4^3',NULL,0);
INSERT INTO comment VALUES (10253,698,1301,'Charlie','And after that there\'s...','2003-12-06 11:22:41',3,'After 6 and 10 come 384 and 640.',NULL,0);
INSERT INTO comment VALUES (10254,1311,1626,'Gamer','Ideas','2003-12-06 12:05:18',0,'There are many such texts, but I was thinking it was the same as Penny\'s thoughts; which is why I thought the first word was we when I saw it in the queue. I didn\'t count the words or anything since I didn\'t want to do anything to solve it while still in the queue.',NULL,0);
INSERT INTO comment VALUES (10255,1310,3558,'Tristan','define...','2003-12-06 12:23:58',4,'...\"equal\"\r\nEqual surface area? Equal icing (the walls and top being iced)? Equal surface area on top? Equal volume? Equal shape? Equal in every respect? It\'s just a bit ambiguous.',NULL,0);
INSERT INTO comment VALUES (10256,698,3386,'Victor Zapana','re: And after that there\'s...','2003-12-06 12:24:37',0,'then most like 384x64 and 640x64 works, then 384x64x64 and 640x64x64 works and so on... but that wont be the answer of course coz they ask smallest/ but just as a heads up',10253,0);
INSERT INTO comment VALUES (10257,698,3386,'Victor Zapana','','2003-12-06 12:25:24',0,'and i believe that 6 and 10 are the answer not 1 and 1, coz the question infers 2 different postivive whole numbers tho i cud be wrong.',NULL,0);
INSERT INTO comment VALUES (10258,698,4670,'Eduardo Guerrero','re: Different?','2003-12-06 12:31:42',0,'It certainly doesn\'t ask for different numbers.',10257,0);
INSERT INTO comment VALUES (10259,698,3386,'Victor Zapana','re(2): Different?','2003-12-06 12:47:42',0,'but like the 2 smallest positive whole numbers. it sounds like 1 is not 2 smallest positive whole numbers, its just 1.',10258,0);
INSERT INTO comment VALUES (10260,698,4374,'Richard','Nontrivial Implied','2003-12-06 12:57:37',0,'This was clearly not intended as a trick question with a trivial answer. Somebody, though, needs to actually show that the notrivial answer is the smallest -- \"my computer program says so\" is the very least such, and we would then need to see the program to make sure that there is no hole in it.',NULL,0);
INSERT INTO comment VALUES (10261,698,1301,'Charlie','re: Nontrivial Implied','2003-12-06 13:52:06',0,'The program in two versions: Quick Basic and UBASIC:\r\nDEFDBL A-Z\r\nsum = 3\r\nDO\r\n FOR a = 1 TO (sum + 1) / 2 - 1\r\n b = sum - a\r\n diffSq = b * b - a * a\r\n diffCu = b * b * b - a * a * a\r\n cuRt = INT(diffSq ^ (1 / 3) + .5)\r\n sqRt = INT(SQR(diffCu) + .5)\r\n IF sqRt * sqRt = diffCu AND cuRt * cuRt * cuRt = diffSq THEN\r\n PRINT a, b\r\n ct = ct + 1: IF ct > 40 THEN END\r\n END IF\r\n NEXT\r\n sum = sum + 1\r\nLOOP\r\n\r\n\r\n 10 for Sum=3 to 30000000\r\n 15 Max=int((Sum+1)/2-1)\r\n 20 for A=1 to Max\r\n 30 B=Sum-A\r\n 40 DiffSq=B*B-A*A\r\n 50 DiffCu=B*B*B-A*A*A\r\n 60 CuRt=int(DiffSq^(1/3)+0.5)\r\n 70 SqRt=int(sqrt(DiffCu)+0.5)\r\n 80 if SqRt*SqRt=DiffCu and CuRt*CuRt*CuRt=DiffSq then\r\n 90 :print A,B\r\n 100 next\r\n 110 next\r\n
\r\n--------\r\nUBASIC has additional precision available. It was stopped when sum was in the 5000+ range, and found only the two answers I posted. At these high numbers the cubing would get to the murky boundaries of the precision available to QuickBasic.',10260,0);
INSERT INTO comment VALUES (10262,698,4374,'Richard','re(2): Nontrivial Implied','2003-12-06 16:32:26',0,'Thank you. It seems very unlikely to me that this one can be solved without a program. However, please see the next comment -- I don\'t think we are done yet.\r\n\n\nEdited on December 6, 2003, 9:47 pm',10261,0);
INSERT INTO comment VALUES (10263,1509,4443,'rhoelle','answer maybe','2003-12-06 19:14:28',0,'I think he got out March 14th 1996. because: 1 foot every 24 hours. it is a thirty foot well. so 30x24= 720hours or 30 days. so it would take about a month. valentines day is the 14th, plus 30 is february 44th or..march 14th.',NULL,0);
INSERT INTO comment VALUES (10264,698,4374,'Richard','re: And after that there\'s...','2003-12-06 21:44:54',0,'\"After 6 and 10 come 384 and 640.\" Here 6 and 10 are smaller than 384 and 640. But the problem asks for \"the two smallest positive whole numbers\" and assuming nontriviality of the solution, how do we know that such actually exist? For example, could there be a y such that 2 and y are a nontrivial solution? If 6 and 10 are indeed the two smallest, then we need to somehow show that every other solution x,y with y > x has x > 6 and y > 10. I don\'t think this can be done with a computer program.',10253,0);
INSERT INTO comment VALUES (10265,698,1301,'Charlie','re(2): And after that there\'s...','2003-12-06 22:46:42',0,'Yes, 24576 and 40960 work, as well as 1572864 and 2621440.',10256,0);
INSERT INTO comment VALUES (10266,698,3558,'Tristan','re(3): And after that there\'s...','2003-12-06 23:35:57',0,'I think the reason that multiplying both numbers by 64 renders more solutions is that 64=2^6 (though you probably already thought of that). Maybe multiplying both by 3^6 would work too. Maybe I can prove it for all u^6.\r\n\r\nAll of the following variables represent integers.\r\nSo, if x²-y²=z³ and x³-y³=t²,\r\nwould (x*u^6)²-(y*u^6)²= a perfect cube?\r\n= x²*u^12-y²*u^12\r\n= (x²-y²)*u^12\r\n= a perfect cube!\r\nAlso, would (x*u^6)³-(y*u^6)³= a perfect square?\r\n= (x³-y³)*u^18\r\n= a perfect square!\r\n\r\nSo I was right. Why u^6 instead of u^5 or something else? Because 6 is a factor of both 2 and 3. I guess I was a little off topic there... it\'s not relevant to the puzzle.\r\n\r\nWhen it says \"the two smallest positive whole numbers,\" I think that that means we want to minimize the sum of the two numbers, though it could be interpreted in other ways. If you interpret as the smallest minimum of the two numbers, you could plausibly get a different answer.',10265,0);
INSERT INTO comment VALUES (10267,698,1253,'brianjn','re(2): And after that there\'s...','2003-12-07 00:31:47',0,'Without inviting a \'3 ring circus\' .....\r\n\r\n*** If 6 and 10 are indeed the two smallest, then we need to somehow show .... ***\r\n\r\n ..... I wonder if a maxima/minima calculus would provide this. I DO NOTE however that there is no onus within the problem to provide either proof or understanding, but it might prove a \'fun\' exercise to set for secondary school maths class.\r\n',10264,0);
INSERT INTO comment VALUES (10268,1270,4680,'Mark','JinCo\'s Solution','2003-12-07 03:21:47',3,'2,Chandler,toast,blackbird----\r\n4,Dennis,bread,sparrow----\r\n6,Allison,birdseed,thrush----\r\n8,Emery,cake crumbs,cardinal----\r\n10,Brewer,suet,robin----',NULL,0);
INSERT INTO comment VALUES (10269,1511,4554,'Edward','re(2): Solution - Yes. I have erred.','2003-12-07 06:18:51',0,'Oops. Thanks for pointing that out: yes. My solutions seem to consider the average bullet to travel at 10 mph, instead the slightly more sane 1000 mph.\r\n\r\nSo, to restate the answer, when A fires the bullet at 1000 mph - in either direction - he will see it travelling at 1000 mph. B will see it, relative to A, travelling at a speed much less than 1000 mph. And the relevant quantitative answers are given by the \"relativistic velocity addition formula.\"\r\n\r\nCheers.',10197,0);
INSERT INTO comment VALUES (10270,1270,4686,'Robert','Solution:','2003-12-07 14:01:37',0,'No2: Mrs Chandler, Toast, Blackbird\r\nNo4: Mrs Dennis, Bread, Sparrow\r\nNo6: Mrs Allison, Birdseed, Thrush\r\nNo8: Mrs Emery, Cake Crumbs, Cardinal\r\nNo10: Mrs Brewer, Suet, Robin',NULL,0);
INSERT INTO comment VALUES (10271,1514,1301,'Charlie','solution','2003-12-07 14:42:19',3,'Let the stick in each case be 1 unit long.\r\n\r\n1. Let x and y be the two random unformly distributed points from 0 to 1. First take the case where x is the smaller. The three pieces have lengths x, y-x and 1-y. In order to form a triangle, the sum of any two piece lengths must be greater than the length of the third piece. In this case\r\n\r\nx+y-x>1-y which is the same as y > 1/2\r\nx+1-y>y-x which is the same as y<x+1/2\r\n1-y+y-x>x which is the same as x<1/2\r\n\r\nSo within the bounds of a unit square from x=0 to x=1 and y=0 to y=1, further limited to the part above y=x, the above three inequalities fall within a triangle of area 1/8, for a probability of (1/8)/(1/2) = 1/4 that the triangle can be formed given that x<y. By symmetry the conditional probability given that y is the smaller, is the same. Thus the probability is 1/4 overall.\r\n\r\nThen, let\'s do case 3 next, because it will provide a conditional probability that will be used in solving case 2:\r\n\r\n\r\nlist\r\n 5 T=0\r\n 10 for X=1 to 4999\r\n 20 Term=(2*X+1)/(10000-X)\r\n 30 T=T+Term\r\n 40 next\r\n 50 print T/9999\r\nOK\r\nrun\r\n 0.3863022960678033686\r\n
\r\n------\r\nNote that the last term within parentheses within the square brackets is in fact 9999/5001.\r\n\r\nI don\'t know how it is intended to evaluate the series without a computer.\r\n\r\nAnd, while approximation was good enough for Archimedes, he did not have the advantage of standing on Newton\'s and Leibnitz\'s shoulders.\r\n\r\nOf course we also could have left the answer to case 3 as 2 ln(2) - 1, and be in the same quandary as to its numerical value, but it helps to see the numbers.\r\n\r\n',10282,0);
INSERT INTO comment VALUES (10288,1309,4698,'Larry Settle','Brian\'s solution','2003-12-08 10:26:42',0,'I\'ve been waiting patiently for someone to make a tiny correction to Brian\'s solution. Any three randomly selected distinct points will ink the entire plane with probability one. Brian\'s A,B,C works just fine if he selects x to be transcendental.',NULL,0);
INSERT INTO comment VALUES (10289,1419,3136,'Popstar Dave','Solution','2003-12-08 10:31:07',3,'With 54 as the first number and 93 as the second; this will give us 39 as the third, then -54, -93 and -39. These six numbers will continuously cycle. Therefore taking the sum of the first 6n terms (where n is any positive integer) will give a sum of 0. As 6000 = 6*1000 and 1000 is certainly a positive integer, the answer in this case is 0.',NULL,0);
INSERT INTO comment VALUES (10290,1419,3136,'Popstar Dave','re: Solution','2003-12-08 10:36:05',0,'I forget to mention that this answer stands for any two inital values. \r\nFor any two starting values a and b, the six term, repeating pattern will be:\r\na, b, (b-a), -a, -b, (a-b).\r\nTherefore the sum of any sequential, multiple of six terms will be zero.',10289,0);
INSERT INTO comment VALUES (10291,1419,3224,'Lee','In general','2003-12-08 10:39:10',3,'Of course it doesn\'t matter what the numbers are\r\nThe series cancels to give\r\na, b, (b-a),-a, -b, (-b+a), a, b, (b-a)........\r\nThe sum of the first 6 terms are 0 and from then it repeats - so the sum of the first n terms is 0 if n/6 is an integer.\r\nPenny will be pleased to hear this theory is verified for the first 6 000 000 000 000 000 000 terms. I\'ve just had my friend at NASA run through it at work and he informs me it does, indeed, sum to zero',NULL,0);
INSERT INTO comment VALUES (10292,1309,3172,'SilverKnight','re: Brian\'s solution','2003-12-08 10:44:48',0,'Larry,\r\n\r\nIt is possible that the three random points turn out to be something like... (0,1) (0,2) and (0,3) (or any three points with rational distance to the origin, I can think of at least four more :-) ).\r\n\r\nThen, clearly this doesn\'t cover the origin.\r\n\r\nSo, \"Any three randomly selected distinct points will ink the entire plane with probability one.\" seems to be faulty.\r\n\r\nYour continuation of \"Brian\'s A,B,C works just fine if he selects x to be transcendental.\" is not sufficient. (π+1,0) (π+2,0) and (π+3,0) will not cover point (π,0).\r\n\r\nWhat\'s more, if he selects the x then this violates your earlier notion of randomly selecting distinct points.\r\n',10288,0);
INSERT INTO comment VALUES (10293,1419,3172,'SilverKnight','re: In general','2003-12-08 10:48:34',0,'roflmao !',10291,0);
INSERT INTO comment VALUES (10294,144,4699,'Barry Knapp','re: Forced March','2003-12-08 10:49:42',3,'Actually this answer isn\'t completely correct as the rate of the messenger is actually (25 + 2d)t because his rate has to include the time he is marching back to his position in line or he will only get to the point where he meets the officer. If we make 2 linear equations representing the distance each marcher has marched from the officers initial position at t=0 \r\nwe get\r\n\r\nofficer: D = 25t\r\nmessenger: D = (25 + 2d)t - 25\r\n\r\n-25 represents the fact that the messenger starts 25 miles behind the officer\r\n\r\nNow we know that the Messenger will catch the officer at\r\n0 = (25 + 2d)t - 25 - 25t\r\n\r\nsolving for d we get:\r\nd = 25/(2t) \r\n\r\nsubstituting in for d into rate of the messenger we get and using Distance = Rate * Time\r\n\r\nDistance = (25 + 2(25/(2t))t\r\nDistance = 25t + 25 \r\nt = 1 at end of day so\r\nDistance = 50\r\n\r\nThe messenger actually marches 50 miles.',725,0);
INSERT INTO comment VALUES (10295,672,4257,'Jack McBarn','Both can coexist','2003-12-08 10:53:07',2,'The sword slices through, but does not destroy the shield, as it cannot be destroyed but the sword can slice through anything.',NULL,0);
INSERT INTO comment VALUES (10296,1514,4507,'Penny','re(5): help me! correction','2003-12-08 11:03:39',0,'Charlie writes: \"As Lee has pointed out, the 2500th term would be 5001/7500...If you continued on to the 4999th term....the answer...would come out to 0.3863022960678033686....your series does not approximate 1/4. It is about 0.3863, as mentioned, which is close to the actual answer found by calculus...And, while approximation was good enough for Archimedes, he did not have the advantage of standing on Newton\'s and Leibnitz\'s shoulders.\"\r\n \r\nYeah, I was pretty tired when I specified the last term in that series, and that the sum approximated 1/4. I had the right idea, though, in seeking an approximation with a 10,000 meter stick whose breaks occur at even meter points. Had I done that correctly, I would definitely have come up with an answer so close to the actual value that there would have been no need to look further. (BTW, I was NOT comparing myself to Archimedes. I am obviously a lot brighter than he was...)\r\n \r\n\n\nEdited on December 8, 2003, 11:05 am',10287,0);
INSERT INTO comment VALUES (10297,1514,3172,'SilverKnight','re(6): help me! correction','2003-12-08 11:20:01',0,'I think the reason why Charlie brought up Newton and Leibnitz was because he invoked Calculus in his solution.\r\n\r\nCharlie did not (as your previous comment title implies) use a computer program in his solution. Charlie only used the computer to verify his solution to a more complicated aspect of the problem.\r\n\r\nAn aspect of Chalie\'s solution is that your approximation to the answer is unnecessary, and almost requires a computer to solve it....\r\n\r\nI noticed that you first approximated the solution with a 10 meter stick and fixed the points along 1 meter intervals. And you came up with an answer of 29%. Then, I suppose after looking at others\' answers, you decided (and accurately so), that if you approximate with higher gradation you will get closer to the actual answer. So you updated your post to make it 10000 meters long.\r\n\r\nUnfortunately, it ends up being a very long \"by-hand\" calculation... and you wrote:\r\n\" ...and (1/9999)*[(3/9999) + (5/9998) + (7/9997) + (9/9996) + ... + (5001/5001)] does appear to be approximately 1/4.\"\r\n\r\nWhen as Charlie pointed out,\r\n\"I don\'t know which case you were addressing in your original post, but your series does not approximate 1/4. It is about 0.3863, as mentioned, which is close to the actual answer found by calculus (not computer...\"\r\n\r\nThe point of all of this, of course, is that it is possible to get an arbitrarily precise numerical answer without resorting to approximating a smooth probability function.',10296,0);
INSERT INTO comment VALUES (10298,1419,4507,'Penny','Solution (No computer program used)','2003-12-08 11:31:45',3,'The first 6 terms in the series are:\r\n54 \r\n93 \r\n93-54 \r\n93-54-93\r\n93-93-93\r\n93-93-93+54\r\n\r\nand then the terms begin to repeat....54, 93, etc..\r\n\r\nThe sum of the first 6,000 terms is: \r\n\r\n1000*(54+93+93-54+93-54-93+93-93-93+93-93-93+54)\r\n= 1000*(0)\r\n= ZERO ',NULL,0);
INSERT INTO comment VALUES (10299,1309,775,'Cory Taylor','re(2): Brian\'s solution','2003-12-08 12:09:11',0,'SK, Not that I\'m agreeing with Larry but,\r\n\r\nBrians ABC does work if x is chosen as transcendental - your example uses x=1. Where the three equidistant colinear points are centered is irrelevant, it is the distance between them that is labelled \"x\"\r\n\r\nand\r\n\r\nIf you calculate the probability of choosing (0,1),(0,2) and (0,3) by choosing points from the entire plane at random, is this not zero (1/an infinite number of three point selections)?\r\n\r\nOf course there are many sets of three points that will not work, so I am not happy with Larrys continuation either...',10292,0);
INSERT INTO comment VALUES (10300,1311,1575,'DJ','Solution','2003-12-08 12:12:50',2,'In any case, I did not miscount; since the letters are arranged in groups of 5, it\'s fairly easy to confirm that there are indeed 270 letters. The original message also contains 270 letters, \"with meaningless filler characters at the end\" just to make the letter blocks come out even. The point is that the method of encryption demands that there are the same number of letters in the encrypted message as in the original.\r\n\r\nI will confirm that the passage in question is the Preamble to the Constitution, and the first three words are indeed \"We the people.\" The fact that the first three blocks of letters in the encrypted message have W, T, and P as their initial letters is a mild coincidence.\r\n\r\nActually, the very first letter will always be the same as that of the original message, but every letter after that could turn out to be any. That may be enough of a hint to point someone in the right direction.\r\n\r\nIf not, try converting each letter to its alphanumeric value. Since you now know the encrypted message as well as the original one, the pattern may be easier to find...',10286,0);
INSERT INTO comment VALUES (10301,1309,3172,'SilverKnight','re(3): Brian\'s solution','2003-12-08 12:20:44',0,'Cory,\r\n\r\nPlease reread my post.\r\n\r\nThe first example I gave is NOT where x is transcendental.\r\nThe second example I gave is.\r\n\r\nThe points (in both examples) I gave ARE colinear, but they\'re not equidistant (i.e., on a circle) from anything, so I\'m not sure what you\'re talking about.\r\n\r\nAgain, in my second example, x is indeed transcendental in all three points, and the stamp will not cover the plane.\r\n____________________\r\n\r\nIf I understand what you wrote, you are saying that as long as the distance between successive points is constant (and transcendental), and they are colinear, then the three stamps will cover the plane.\r\n\r\nWithout analysis, I\'m not certain whether or not that is correct. But, either way, I did not get that notion from what Larry wrote. Larry didn\'t mention anything about distance between points, so I interpret his \'x\' as the horizontal coordinate (standard on the Cartesian plane).\n\nEdited on December 8, 2003, 12:30 pm',10299,0);
INSERT INTO comment VALUES (10302,1509,4700,'MARIE','possibly','2003-12-08 13:11:18',0,'he\'d get out on March 16 1996, i think.',NULL,0);
INSERT INTO comment VALUES (10303,1311,4507,'Penny','re: Solution','2003-12-08 13:46:36',0,'DJ: \"I will confirm that the passage in question is the Preamble to the Constitution, and the first three words are indeed \'We the people.\' \"\r\n \r\nI guessed the right answer, in a puzzle so difficult (rated a 2 !!) that even Victor Zapana was stumped? Cool...Of course I don\'t know the encryption method, but as you say, it shouldn\'t be hard to figure out. Besides, my brilliant insight was to bypass the encryption method altogether, and to use Zen-like enlightenment to achieve the result. (\"When a rope is cut, the knife is forgotten.\") My IQ actually approaches triple digits, and it really shows, doesn\'t it? ',10300,0);
INSERT INTO comment VALUES (10304,1309,4698,'Larry Settle','re(4): Brian\'s solution','2003-12-08 14:29:15',0,'The first use of the stamp leaves uninked, concentric circles at rational radii. The second use of the stamp leaves uninked, intersection points of the two sets of concentric circles. Each concentric circle has a countable number of intersections (since the rationals are countable) and there are a countable number of circles(same reason). Therefore, the total number of uninked points is of the order of countable squared and is also countable. The probability(slightly tongue in cheek) that a third use of the stamp from a random point will not cover all the remaining points is the proportion of rationals in the continuum(i.e. 0).\r\n Brian gets the credit because the problem only called for a specific solution and x=transcendental in his diagram is a solution.\r\n His solution is easily generalizable by writing similar equations for non co-linear points. The central argument will be that the distance between two of the random points will be expressed as the solution of an algebraic equation with rational co-efficients which is a contradiction.',10301,0);
INSERT INTO comment VALUES (10305,1309,775,'Cory Taylor','re(4): Brian\'s solution','2003-12-08 14:30:46',0,'Im gonna try something new (to me). Whee. Im gonna try to link to a previous post. Very exciting (again, for me!!!)\r\n\r\nBrian Smith\'s solution hereEdited on December 8, 2003, 4:39 pm',NULL,0);
INSERT INTO comment VALUES (10311,1314,2130,'ethan','Solution','2003-12-08 16:38:47',0,'1*6*11=66\r\n13+20+33=66\r\n40/20*33=66',NULL,0);
INSERT INTO comment VALUES (10312,1309,3172,'SilverKnight','re(5): Brian\'s solution','2003-12-08 17:28:25',0,'I beg to differ Larry.\r\n\r\nBy your argument, if I have a stamp that covers the whole plane except the centered point, and I stamped it on the origin, I would cover the whole plane (--since the probability that a random point is the origin, definitely countable, would be zero).\r\n\r\nBut the probability is not at issue. The \"point\" is: there exists a point that is not covered. So, while I believe Brian has a correct ANSWER (I think)... Brian has not give a true SOLUTION.\r\n',10304,0);
INSERT INTO comment VALUES (10313,1311,3558,'Tristan','re(3): Solution','2003-12-08 17:30:38',0,'Heh heh...\r\n\r\nI bet the title translates to \"Preamble to the Constitution.\" Not that I\'ve cracked the code.\n\nEdited on December 9, 2003, 7:54 pm',10309,0);
INSERT INTO comment VALUES (10314,1314,4507,'Penny','This one was really hard....','2003-12-08 18:54:31',1,'...and as I was about to give up on it, my boyfriend Sylvester said \"Wait ! I\'ve got an idea !!\" Then he \"hacked\" into the CalTech nuclear physics systems and ran it on one of their Cray Supercomputers. Just 6 hours later, it produced the answer. Dude, you have to start putting simpler puzzles out here. As an example of a really easy one, here\'s something that Sylvester was doodling on his napkin this morning over coffee:\r\n \r\n\"Five friends went mountain climbing this monsoon, but not together. They climbed different mountains. Sanjiv climbed higher than 1000 meters, but not on Panchgani. Sanjay climbed higher than both Subhash and the one who climbed Murud. Lohgadh is shorter than the mountain climbed by Subhash, but heigher than the one climbed by Sujay. The tallest mountain was not climbed by Suvdeep. Murud is not the tallest but taller than Panchgani. The mountain which is 2500 meters tall is not Tikona or Panchgani. Visapur is taller than Panchgani, which is taller than the mountains climbed by Sanjiv and Sujay.\r\nCan you figure out who climbed which mountain?\" \r\n ',NULL,0);
INSERT INTO comment VALUES (10315,1309,2899,'Brian Wainscott','re(6): Brian\'s solution','2003-12-08 19:10:21',0,'I agree with Larry.\r\n\r\nInstead of picking 3 points in the plane, pick a single point in R^6 (the cartesian product of the plane 3 times). For every point (a,b,c,d,e,f) in R^6, color it either white or black: black if stamping the points (a,b), (c,d), (e,f) results in covering the whole plane, and white otherwise.\r\n\r\nWhat Larry has done is argue that the \"white\" set in R^6 has measure 0. That doesn\'t mean there aren\'t a lot of points in it, only that they are relatively rare compared to black points. It is like saying \"the odds of a random number being rational is 0\" which is true.',10312,0);
INSERT INTO comment VALUES (10316,1309,3172,'SilverKnight','re(7): Brian\'s solution','2003-12-08 19:43:52',0,'I agree with Larry too... it just doesn\'t address the problem.\r\n\r\nThere ARE many more irrational than rational points.\r\n\r\nBut this isn\'t about the odds of finding a particular point (or a set of points). It is about the existence of a point (or a set of points) that satisfy or refute the problem.\r\n_________________________\r\n\r\nWhat if I paint the WHOLE plane black, except for a small circle of radius .00000001 centered on the origin, which I paint white?\r\n\r\nWhat are the odds that if I take a random point, the point will be white...?\r\n\r\nThe problem with this argument (which is analogous to Brian\'s, Brian\'s, and Larry\'s) is that the probability isn\'t the issue.\r\n\r\nExistence of a white point is the issue. And, in this case, the whole plane is not black.',10315,0);
INSERT INTO comment VALUES (10317,1314,3386,'Victor Zapana','re: This one was really hard....','2003-12-08 20:58:51',0,'hmm mebe ill do the problem if it gets publicized by the site (not if its posted on a post) tch tch dun criticize. easy and hard questions all are welcomed in this site. Wow, do Sylvester and you come up with problems to give each other every day?',10314,0);
INSERT INTO comment VALUES (10318,1314,2500,'ken','a wild stab','2003-12-08 21:56:15',0,'1*6*11=66\r\n13+20+33=66\r\n33*40/20=66',NULL,0);
INSERT INTO comment VALUES (10319,1270,4709,'Virginia','solution','2003-12-08 21:58:21',0,'#2 Mrs. Chandler, Blackbird, Toast\r\n#4 Mrs. Dennis, Sparrow, Bread\r\n#6 Mrs. Allison, Thrush, Birdseed\r\n#8 Mrs. Emery, Cardinal, Cake\r\n#10 Mrs. Brewer, Robin, Suet',NULL,0);
INSERT INTO comment VALUES (10320,1314,1626,'Gamer','Please don\'t:','2003-12-08 22:04:09',0,'Post problems in the chat. Even easy ones. This means all problems.\r\n\r\nPlease don\'t insult others\' problems\r\n\r\nFinally, I would prefer if you kept your illegal events to yourself, as they don\'t add any color to the site, and stop mentioning your boyfriend. Random fact: People who lie assert a fact much more than people who tell the truth. ',NULL,0);
INSERT INTO comment VALUES (10321,1323,1626,'Gamer','re: Solution to 2 extra parts...','2003-12-08 22:18:43',0,'This may work, and was actually the solution I had in mind. I think others have shown that this isn\'t the SMALLEST one. If I misread your post tell me. :)',10307,0);
INSERT INTO comment VALUES (10322,1514,4507,'Penny','re: Lee','2003-12-08 23:34:35',0,'Lee: \"Penny: \'...and (1/9999)*[(3/9999) + (5/9998) + (7/9997) + (9/9996) + ... + (5001/5001)] does appear to be approximately 1/4.\' Your bracketed term has a numerator that increases by 2 per term and a denominator that decreases by one - you would never have the term 5001/5001; the 2500th term would be 5001/7500 wouldn\'t it? The final term would be 20001/1\"\r\n \r\nSilverKnight and Charlie said that you don\'t really need either my laborious approximation, or computer assistance. All you need is a little calculus. But just to set the record straight, the series I used is made up of 4999 terms of the form (2x+1)/(10000-x), for values 1 through 4999 of x (the original break, on a meter boundary, of a 10,000 meter stick), the only values of x that will make a triangle possible. The last value in the series is 9999/5001. I have corrected my original post, based on the criticisms. \r\n \r\nBut it is academic, after SilverKnight\'s and Charlie\'s comments.\r\n',10283,0);
INSERT INTO comment VALUES (10323,1314,4300,'Minion123','Don\'t start that again','2003-12-09 01:29:00',0,'Don\'t start arguing again',NULL,0);
INSERT INTO comment VALUES (10324,1478,4709,'Virginia','solution','2003-12-09 08:48:50',0,'1st place: Ben Jones, fruit cake\r\n2nd place: James Best, chocolate cake\r\n3rd place: Nigel Stevens, sponge cake\r\n4th place: Vicky Andrews, cheese cake',NULL,0);
INSERT INTO comment VALUES (10325,1478,4709,'Virginia','solution','2003-12-09 08:49:18',0,'1st place: Ben Jones, fruit cake\r\n2nd place: James Best, chocolate cake\r\n3rd place: Nigel Stevens, sponge cake\r\n4th place: Vicky Andrews, cheese cake',NULL,0);
INSERT INTO comment VALUES (10326,698,1920,'Brian Smith','Any other primitive solutions?','2003-12-09 10:35:35',0,'So far the only nontrivial primitive solution found is 10,6. Are there any other primitive solutions?',NULL,0);
INSERT INTO comment VALUES (10327,1522,3172,'SilverKnight','solution','2003-12-09 10:45:33',3,'4.086599978 feet from the wall\r\n__________________________________\r\n\r\nLet\'s draw a picture...\r\n\r\n\r\n|\\\r\n| \\\r\n| \\\r\n|___\\\r\n| |\\\r\n|___|_\\\r\n\r\n\r\nLet the square on the bottom be 3ft x 3ft.\r\n\r\nThe height of the big triangle be 3+y ft.\r\nThe base of the big triangle be 3+x ft.\r\n\r\nLet the hypotenuse of the lower right triangle be z, so the hypotenuse of the upper left triangle is 12-z.\r\n\r\nNow, by similar triangles, we see that\r\n3/x = y/3 ==> xy = 9 ==> y = 9/x equation (1)\r\n\r\nBy Pythagorean theorem:\r\nx² + 3² = z² ==> x² = z² - 9 equation (2)\r\n-- and --\r\ny² + 3² = (12-z)² equation (3)\r\n\r\nNow we have three equations and three unknowns\r\n\r\nsubstitute equation (1) into equation (3) (to eliminate y):\r\n(9/x)² + 3² = (12-z)²\r\n\r\n81/x² + 3² = (12-z)²\r\n\r\nnow substitute equation (2) to eliminate x:\r\n81/(z²-9) + 9 = (12-z)²\r\n\r\n81/(z²-9) = (12-z)² - 9\r\n-- difference of perfect squares --\r\n81/[ (z-3)(z+3) ] = [ (12-z) + 3 ] [ (12-z) - 3 ]\r\n\r\n81 = (15-z)(9-z)(z-3)(z+3)\r\n0 = (15-z)(9-z)(z-3)(z+3) - 81\r\nNow we have one equation, and one unknown.\r\n\r\nShould be easy enough to solve numerically... (sure enough I just used Excel solver to set this equal to zero), and I find:\r\nz = 3.190720845, or\r\nz = 8.809279155 (fortunately, they add up to 12, the length of the ladder)\r\n\r\nwe are looking for x + 3, so plug back into equation (2):\r\nx² = z² - 9 = (3.190720845)² - 9\r\nx = 1.086599978\r\n\r\nTherefore, the base of the ladder is 3 + x or\r\n4.086599978 feet from the wall',NULL,0);
INSERT INTO comment VALUES (10328,1522,4507,'Penny','re: solution','2003-12-09 10:58:28',0,'Please reread the words of this puzzle. It says that the ladder \"LEANS against the wall such that it TOUCHES the top edge of the box.\" If the base of the ladder is only 4.086599978 feet from the wall, there is no way the top of the ladder will be touching the wall, unless we go for a trick solution and bend the ladder into a curve.\r\n \r\n(Also, let\'s dismiss all the trick solutions that have the box sitting against the wall in any other manner than flat on the ground with one of its faces flush against the wall....I know your solution didn\'t have that feature).\r\n\r\nIt seems that there is only one way for the ladder to touch all three: the ground, the top of the box, and the wall. The minimum and maximum height will be the same. Let x be the distance from the base of the ladder to the wall. Then obviously the distance from the ground to the point where the top of the ladder touches the wall is also x.\r\n\r\nx^2 + x^2 = 12^2\r\n2x^2 = 144\r\nx^2=72\r\nx=8.4852813742\r\n\r\nThe foot of the ladder can only be 8.4852813742 feet from the wall.\r\n',10327,0);
INSERT INTO comment VALUES (10329,1522,3224,'Lee','re(2): solution','2003-12-09 11:21:26',0,'Dan, sorry, Penny, if the ladder was set up in this fashion it would only touch the top edge of the box if the box a cube with sides (srqt 72)/2 = 4.24264\'\r\nThe question specifically states it\'s a 3\' cube.\r\nOr are you just trying to wind SK up?',10328,0);
INSERT INTO comment VALUES (10330,1522,4507,'Penny','re(3): solution','2003-12-09 11:31:03',1,'Lee: \"Dan, sorry, Penny...The question specifically states it\'s a 3\' cube. Or are you just trying to wind SK up?\"\r\n \r\nLee: You, \"Dan\" and SilverKnight need to upgrade your Excel software with the latest Microsoft \"common sense\" module. If the ladder is leaning against the ground, the box and the wall in any way, touching all three, and you try to improve the height by sliding the foot of the ladder closer to the wall, you will be pulling the top of the ladder away from the wall.\r\n \r\nThe fact that the box is a PERFECT CUBE, indicates that IF IT IS EVEN POSSIBLE for the ladder of length 12\' to be leaning so as to touch all three, then the ladder, the ground and the wall must form a triangle with hypotenuse 12 and base=height. 2x^2=144. x=sqrt(72)=8.4852813742\r\n ',10329,0);
INSERT INTO comment VALUES (10331,1522,1301,'Charlie','re(2): solution','2003-12-09 11:44:03',0,'Penny, draw a 3-inch square on a paper, and extend the bottom to the right to represent the floor. Extend the left side upward to represent the wall. Then get a 12-inch ruler. See that if you make the ruler be at a 45-degree angle, touching the wall and the floor at the ends of one of its edges, that it will not touch the 3-inch square at all. You have to bring the base in, while raising the end on the wall, so as to allow the ruler just to touch the top right vertex of the box.\r\n\r\n(or you could bring the top down while the bottom goes right, but that would not maximize the height.)\r\n\r\nAnd Penny, you\'d better get some sleep if you are this exhausted.',10328,0);
INSERT INTO comment VALUES (10332,1522,1301,'Charlie','re: solution','2003-12-09 11:48:29',0,'So long as we eventually use Excel anyway, we might as well make it easy:\r\nLet cell A2 start at 4, representing x.\r\nin B2: =3*A2/(A2-3) representing y, based on the similarity of the bottom little triangle to the large triangle.\r\nin C2: =A2^2+B2^2\r\nThen set solver to making C2 be 144 by changing A2. You still get 4.086599979\r\n(well, there\'s rounding at the end...)',10327,0);
INSERT INTO comment VALUES (10333,1522,3224,'Lee','re(4): solution','2003-12-09 11:52:45',0,'Penny, I\'m sure if I went to a mind-reader she would give me change or something, but I don\'t understand your point. It doesn\'t matter what length of ladder you have, or how you set it up, there is ALWAYS a cube you could \'squeeze\' in the trangle formed, so that the cube \'touches\' the ladder without disturbing it. This quetion, however, gives you the cube size and ladder length and asks how you set it up.\r\nYour answer is the specific case where the cube is precicely sqrt(L^2/8) - L being the ladder length',10330,0);
INSERT INTO comment VALUES (10334,1522,1920,'Brian Smith','Solution','2003-12-09 11:59:02',3,'\r\n A+\r\n |\\\r\n | \\\r\n | \\\r\n | \\\r\n | \\\r\n | \\\r\n | \\\r\n | \\ E\r\n C+--------\\\r\n | |\\\r\n | | \\\r\n | | \\\r\n | | \\\r\n +--------+----+\r\n O D B\r\n
\r\nThe length of the ladder is 12: AB = 12\r\nThe edge length of the box is 3: CE = DE = OD = OC = 3\r\nThe distance the foot of the ladder is from the wall is OB: OB=x\r\nThe distance the top of the ladder is from the ground is OA: OA=y\r\n\r\nAC = OA - OC = y-3\r\nBD = OB - OD = x-3\r\nACE and EDB are similar triangles, so AC/CE = ED/DB: (y-3)/3 = 3/(x-3)\r\nAOB is a right triangle, so AO^2 + BO^2 = AB^2: y^2 + x^2 = 12^2\r\n\r\nx and y can be found by solving the system:\r\nEqn 1: (y-3)/3 = 3/(x-3)\r\nEqn 2: y^2 + x^2 = 12^2\r\n\r\nFrom Eqn 1: y = 3 + 9/(x-3)\r\nSubstitute into eqn 2: (3 + 9/(x-3))^2 + x^2 = 144\r\n\r\n9 + 54/(x-3) + 81/(x-3)^2 + x^2 = 144\r\n\r\n9(x-3)^2 + 54(x-3) + 81 + x^2*(x-3)^2 - 144(x-3)^2 = 0\r\n\r\nx^4 - 6x^3 - 126x^2 + 864x - 1296 = 0\r\n\r\nUsing a numeric solver gives:\r\nx = 11.2827168988, x = 4.08659997799, x = 2.39022497512, x = -11.7595418519\r\nas roots of the polynomial.\r\n\r\nTwo roots are in the range [3,12]: x = 11.2827168988, and x = 4.08659997799\r\n\r\nIf x = 11.2827168988 then y = 3 + 9/(11.2827168988-3) = 4.08659997799\r\n\r\nIf x = 4.08659997799 then y = 3 + 9/(4.08659997799-3) = 11.2827168988\r\n\r\nThese two solutions represent the only two positions the ladder can be in to satisfy the physical constraints of the problem. The two solutions are actually reflections of each other over the line x=y.\r\n\r\nThe problem is looking to achieve the greater height so the solution is the foot of the ladder is 4.08659997799 feet from the wall.',NULL,0);
INSERT INTO comment VALUES (10335,1522,1575,'DJ','Solution','2003-12-09 11:59:36',3,'There are two possible ways that the situation described could occur, but they are reflections of each other.\r\n\r\nLet the distance from the edge of the box to the foot of the ladder be x, and the distance from the top of the box to the top of the ladder be y.\r\n|\\\r\n| \\\r\n|y \\\r\n|___\\\r\n| 3 |\\\r\n| | \\\r\n x\r\n
\r\nWe also know that each edge of this square is three feet long.\r\n\r\nAlso, because all the angles are the same, the two triangles formed are similar.\r\nThus,\r\ny/3 = 3/x\r\ny = 9/x\r\n\r\nWe also know by the large triangle and the Pythagorean theorem that\r\n(x+3)² + (y+3)² = 12²\r\nSubstituting 9/x for y, we get\r\n(x+3)² + (9/x)² = 144\r\n\r\nI\'m not sure how to solve this order of equation, but putting it into Maple gives a value of 1.0865999806791402. Thus, the length from the wall to the foot of the ladder (x+3) is 4.0865999806791402\', or about 4\'1\".\r\n\r\nIn this scenario, y+3 is √(12² - 4.0865..²), about 11.828499482999559, or close to 11\'10\". So, by moving the bottom of the ladder four feet, the top of the ladder only goes down two inches! I found that pretty interesting.',NULL,0);
INSERT INTO comment VALUES (10336,1522,4507,'Penny','re(5): solution','2003-12-09 12:03:09',0,'Perhaps (make that certainly) Lee, Charlie and SilverKnight are correct. I was so \"rung-out\" that I was taking this one too \"ladder-ally\". I was right about one thing: the puzzler was guilty of sloppy language when he talked about \"\"maximizing\" the height. There is no minimum and maximum height. The ladder can only lie one way to meet the conditions of the puzzle.\r\n\r\nLee: \"Penny, I\'m sure if I went to a mind-reader she would give me change or something...\" THAT\'S NOT THE JOKE !! We all get change back if we overpay the mind-reader. The joke is \"Whenever you go to the mind-reader, she gives you half price.\"\r\n\r\n',10333,0);
INSERT INTO comment VALUES (10337,1522,1920,'Brian Smith','re(6): solution','2003-12-09 12:08:02',0,'Actually there are TWO ways to place the ladder to meet the physical constraints of the problem. If the first is {x feet away and y feet up} then the second is {y feet away and x feet up}. The distances get swapped.',10336,0);
INSERT INTO comment VALUES (10338,1419,4505,'Bob Genisot','2 ways to solve','2003-12-09 12:35:22',0,'VERSION 1 - \r\nIt\'s already been stated, but the sequence repeats itself every 6 terms, i.e.\r\n1 - 54\r\n2 - 93\r\n3 - 93-54=39\r\n4 - 39-93=-54\r\n5 - -54-39=-93\r\n6 - -93-(-54)=-39\r\n7 - -39-(-93)=54\r\n8 - 54-(-39)=93\r\nWhich brings us right back to where we started. The sum of the first 6 terms 54+93+39+(-54)+(-93)+(-39) = 0, thus since the sequence repeats every 6 terms the sum of any 6n terms, where n is a natural number is 0. For this problem let n=1000, so the sum of the first 6000 terms is 0.\r\n\r\nVERSION 2 - \r\nThe sum of the first n terms-\r\nn=1 sum=a\r\nn=2 sum=a+b\r\nn=3 sum= a+b+(b-a) = 2b\r\nn=4 sum=2b+(c-b) = b+c\r\nn=5 sum=b+c+(d-c) = b+d\r\nn=6 sum=b+d+(e-d) = b+e\r\nAnd so on. The 2nd term and the n-1 term remain after each successive addition. From part 1, the 2nd term is 93, and the n-1 term, with n=6000 is -93 (term 5). So the sum = 93+(-93) = 0.',NULL,0);
INSERT INTO comment VALUES (10339,1309,2899,'Brian Wainscott','re(8): Brian\'s solution','2003-12-09 12:36:11',0,'I was thinking about this a bit this morning. While my comments about Larry\'s solution aren\'t rigorous, they can be made so. I CAN prove (and will if you want) that the set I called \"white\" in R^6 has measure 0.\r\n\r\nDJ\'s problem is equivalent to proving there exists a \"black\" point in R^6.\r\n\r\nIt seems to me that this does address the problem, since all non-white points are black.',10316,0);
INSERT INTO comment VALUES (10340,1522,3224,'Lee','re(6): solution - the joke','2003-12-09 12:40:44',0,'Dan was a big fan of that mind-reader gag.\r\nTop man Dan',10336,0);
INSERT INTO comment VALUES (10341,1309,3172,'SilverKnight','re(9): Brian\'s solution','2003-12-09 12:55:07',0,'Measure 0 doesn\'t mean non-existant.\r\n\r\nYou must prove that there are no white points (not that they are measure zero, i.e., countable).\r\n____________________\r\n\r\nAnd of course this stuff is provable... that\'s one of the reasons why DJ submitted it in the first place... again... a COOL problem. (It just doesn\'t involve probabilities... :-)',10339,0);
INSERT INTO comment VALUES (10342,1522,4507,'Penny','Real, Lee ?','2003-12-09 13:22:41',0,'Lee: \"Dan was a big fan of that mind-reader gag. \r\nTop man Dan\". \r\n \r\nThen \"Dan\" must have heard it on the David Letterman show, which is where I and 70 million other people heard it. So you have narrowed down the possibilities for the identity of \"Dan\" to 70,000,002 people. You have a keen grasp of logic, sir. No wonder you did so well on that \"PGKKW XIMAF TNEGA NFYGZ TMUIV\" cryptography puzzle.... \r\n\n\nEdited on December 9, 2003, 1:27 pm',10340,0);
INSERT INTO comment VALUES (10343,1458,4257,'Jack McBarn','re(2): cigarette on bar---I HAVE IT!!','2003-12-09 14:03:00',1,'But he didn\'t. Sound waves aren\'t solids, liquids or gases.\r\nThink again.',9338,0);
INSERT INTO comment VALUES (10344,1458,4257,'Jack McBarn','re: Getting \'round the wording.','2003-12-09 14:04:56',4,'What do you think?\r\nNO.',9308,0);
INSERT INTO comment VALUES (10345,1458,4257,'Jack McBarn','re(2): Another answer that works','2003-12-09 14:06:04',0,'Fire is plasma.',9805,0);
INSERT INTO comment VALUES (10346,1458,4257,'Jack McBarn','re: A few possible solutions','2003-12-09 14:07:45',1,'Solution 2:\r\nNot in a million years.',9620,0);
INSERT INTO comment VALUES (10347,1458,4257,'Jack McBarn','re(2): SOUND¿','2003-12-09 14:08:28',0,'No you wouldn\'t.',8766,0);
INSERT INTO comment VALUES (10348,1505,4257,'Jack McBarn','re: program','2003-12-09 14:17:47',0,'I do. Just send it to me.',9777,0);
INSERT INTO comment VALUES (10349,66,4718,'Jack Squat','not a contradiction?','2003-12-09 14:34:51',0,'Maybe it\'s just me, but the way I\'m interpreting this problem, there is a definite solution. I see three subgroups of people in the town: \r\n1) people who don\'t need to shave ever (most ladies and some guys)\r\n2) people who have chosen never to shave (bearded guys and maybe bearded ladies if the town has a permanent freak show)\r\n3) people who choose to shave. \r\n\r\nIf you are in group 3, your choices for shavers are either yourself or Bill. For Bill, the choice is only himself. \r\n\r\nThe fact the problem is told in the present tense means Bill is applying his rule starting now. This is key to the problem having a solution. If the problem is told in the past tense, then the contradiction holds.\r\n\r\nIf Bill is in group 3, he shaves himself. Therefore according to his rule, going forward he cannot shave himself anymore. Because there are no more options, he must stop shaving all together, and he moves into group 2 permanently and doesn\'t shave himself.\r\n\r\nIf Bill is in group 2 he will either stay in group 2 forever and not shave, or he will at some point decide he wants to get rid of his beard. However he can\'t, since the instant he starts shaving himself he\'ll have to stop or he\'ll contradict the rule. So he stays in group 2.\r\n\r\nIf Bill is in group 1, he\'ll either stay in 1 forever, or he\'ll start having the need to shave later on, at which point he moves either moves into 2 and then has to never shave, or tries to go into 3. But again, the instant he tries he has to stop, so he goes into 2 whether he wants to or not.\r\n\r\nSo the answer to the question \"Will he shave himself\" is no. Again, if the problem was told in the past tense, and the question was \"DOES he shave himself\", well then we have issues.',NULL,0);
INSERT INTO comment VALUES (10350,1239,1575,'DJ','re: question','2003-12-09 14:46:01',0,'What \'existing letters\' are you referring to?',9877,0);
INSERT INTO comment VALUES (10351,82,4718,'Jack Squat','classics 101','2003-12-09 14:52:13',0,'I thought Prometheus was chained to a rock and had his liver eaten everyday by a vulture only to have it grow back and continue on to eternity. Did Zeus put out two contract hits?',NULL,0);
INSERT INTO comment VALUES (10352,1309,2899,'Brian Wainscott','','2003-12-09 15:02:55',0,' Sounds like a miscommunication. Sorry, my fault. In my original post I used the terms \"white\" and \"black\" to describe subsets of R^6 and I should have used different terms. Here is a somewhat different restatement, which I think captures Larry\'s point, and answers both you and DJ:\r\n\r\nClaim: Let S(A,B) [A and B in the plane] be the set of points C in the plane such that placing DJ\'s stamp at A,B, and C will leave a white point somewhere in the plane. Then if A and B are distinct, S(A,B) has measure 0.\r\n\r\nLemma: Let x be any point in the plane, and Px be the set of points where DJ\'s stamp can be placed and leave x white. Then Px has measure 0.\r\n\r\nProof of lemma: Px is clearly the set of circles, centered at x, with rational radii. This is a countable collection of sets of measure 0 (circles have measure 0 in the plane), and hence has measure 0.\r\n\r\nProof of claim: Choose A, B distinct. As Larry showed, after stamping at A and B there are only countably many points still white. Call this set X. S(A,B) = {Union of all Px: x is in X}. By the lemma, each Px has measure 0. So again we have a countable collection of sets of measure 0, so S(A,B) has measure 0. End of proof of claim.\r\n\r\nSo, since S(A,B) has measure 0, it has a non-empty complement. Any point D chosen from the complement of S(A,B) will give you three points (A,B,D) where you can stamp and cover the plane. Since A and B were arbitrary (provided they are distinct), and S(A,B) has measure 0, then Larry was correct in his assertion that picking three points at random from the plane, the odds of covering all the points int the plane is 1.\r\n\r\n\n\nEdited on December 9, 2003, 3:05 pm',10341,0);
INSERT INTO comment VALUES (10353,1517,4670,'Eduardo Guerrero','Quotes needed','2003-12-09 15:10:08',3,'He is selling brass numbers, and missed including some quotes in his sign -- \"1\" for 10 cents, \"15\" for 20 cents, and \"110\" for 30 cents.',NULL,0);
INSERT INTO comment VALUES (10354,1309,3172,'SilverKnight','re:','2003-12-09 15:16:50',0,'Brian,\r\n\r\nYou wrote:\r\n\"...Larry was correct in his assertion that picking three points at random from the plane, the odds of covering all the points int the plane is 1. \"\r\n\r\nExamples of three distinct points have already been shown that do not cover the plane. Those three points are POSSIBLE to be chosen at random.\r\n\r\nThe fact that even one set (of three distinct points that having stamps centered on them) exists, that will not cover the plane, is sufficent to say you can\'t take any three points at random.\r\n___________________________\r\n\r\nAs for your proof:\r\n\r\nThe conclusion may be correct, but the proof is lacking... you wrote:\r\n\"Any point D chosen from the complement of S(A,B) will give you three points (A,B,D) where you can stamp and cover the plane.\"\r\n\r\nThat is an assertion and you have not (yet) justified, explained, or otherwise proven it.',10352,0);
INSERT INTO comment VALUES (10355,1522,4719,'Scott','different approach','2003-12-09 15:27:34',3,'Depending on what the question means by \"leans against the wall\" one could argue that the foot of the ladder should be 0\' 0\" away from the wall. All you need to do is put the ladder vertically on the side of the cube perpendicular to the wall. One edge of the ladder is touching (if not leaning on) the wall and the height of ladder on the wall is 12\'.',NULL,0);
INSERT INTO comment VALUES (10356,1309,2899,'Brian Wainscott','re(2):my proof','2003-12-09 15:33:18',0,'True, points CAN be chosen, but there are relatively few such. Given a random real number in [0,1] it MIGHT be rational, but the odds are it won\'t be. There are relatively few rationals (compared to the irrationals) in [0,1].\r\n\r\nAs for my proof, which part is a problem? I proved that S(A,B) has measure 0 in the plane. So not only does it have a non-empty complement from which D can be chosen, amost every point in the plane is in the complement. The assertion is an immediate result of the proof of the claim. I\'m confused about what else you are expecting.',10354,0);
INSERT INTO comment VALUES (10357,672,4718,'Jack Squat','Zero effect','2003-12-09 15:38:54',0,'This problem is similar to a tango between two fundamental math rules.\r\n1) Any number times zero is zero\r\n2) And number divided by zero is infinity\r\n\r\nSo what happens when you take zero divided by zero? Well that depends on what form of zero you are using. 0/0 is impossible to solve for, however (X-2)/(X^2-4) where X=2 is not.\r\n\r\nSo in the sword and shield context, there are four possible answers:\r\n1) the sword cuts the shield\r\n2) the shield blocks the sword\r\n3) any combination of the sword and shield both taking damage (or not taking damage).\r\n4) a paradox\r\n\r\nWe don\'t have enough info to know the right answer, but I don\'t think we should say a universe that contains both can\'t exist, since ours is doing just fine!',NULL,0);
INSERT INTO comment VALUES (10358,1521,1920,'Brian Smith','f(x) = x+1','2003-12-09 15:43:35',0,'Using only two 2\'s:\r\n\r\nsec (arctan (sqrt x)) = sqrt (x + 1) is true for all positive values of x, so starting at x=2:\r\n\r\n(sec (arctan (sqrt 2)))^2 = 3 \r\n\r\n(sec (arctan (sec (arctan (sqrt 2)))))^2 = 4 \r\n\r\n(sec (arctan (sec (arctan (sec (arctan (sqrt 2)))))))^2 = 5 \r\n\r\n(sec (arctan (sec (arctan (sec (arctan (sec (arctan (sqrt 2)))))))))^2 = 6\r\n\r\nUsing only two 3\'s:\r\n\r\nThe exponent 2 can be written as (sec (arctan (sqrt 3))) = 2, so starting at x=3:\r\n\r\n(sec (arctan (sqrt 3)))^(sec (arctan (sqrt 3))) = 4\r\n\r\n(sec (arctan (sec (arctan (sqrt 3)))))^(sec (arctan (sqrt 3))) = 5\r\n\r\n(sec (arctan (sec (arctan (sec (arctan (sqrt 3)))))))^(sec (arctan (sqrt 3))) = 6\r\n\r\n(sec (arctan (sec (arctan (sec (arctan (sec (arctan (sqrt 3)))))))))^(sec (arctan (sqrt 3))) = 7\n\nEdited on December 10, 2003, 11:19 am',NULL,0);
INSERT INTO comment VALUES (10359,1309,3172,'SilverKnight','re(3):my proof','2003-12-09 15:46:00',0,'Brian, the assertion is not an immediate result of anything.\r\n\r\nYou wrote:\r\n\" Given a random real number in [0,1] it MIGHT be rational, but the odds are it won\'t be.\"\r\nOnce again, the odds are not the issue. Existence is the issue.\r\n\r\nYou wrote:\r\n\"So not only does it have a non-empty complement from which D can be chosen, amost every point in the plane is in the complement.\"\r\n\r\nYour assertion (that \"Any point D chosen from the complement of S(A,B) will give you three points (A,B,D) where you can stamp and cover the plane.\") is not an immediate result of the claim.\r\n\r\n\"Almost every...\" doesn\'t cut it.\r\n\r\nTo, hopefully clear up your confusion, here\'s what I am expecting from your proof:\r\n\r\nYou must demonstrate that, in the non-empty complement, there exists a point that, if stamped, will ensure that the set of non-black points (are not only countable, but) equals the NULL SET.\r\n\r\nEqualling the NULL set means, of course, there does not exist even one non-black point.',10356,0);
INSERT INTO comment VALUES (10360,865,4718,'Jack Squat','pi rho sigma taoist','2003-12-09 15:51:43',0,'To clarify taoist\'s answer, you can put any response, as long as you don\'t put any answer that implies yes. You also can\'t put a straight \"no\", but that\'s obvious. \r\n\r\nSo \"uh-huh\" wouldn\'t fly, but \"of course not you buffoon\" would.\r\n',NULL,0);
INSERT INTO comment VALUES (10361,1309,2899,'Brian Wainscott','re(4):my proof','2003-12-09 16:08:50',0,'You wrote:\r\nYour assertion (that \"Any point D chosen from the complement of S(A,B) will give you three points (A,B,D) where you can stamp and cover the plane.\") is not an immediate result of the claim.\r\n\r\nBut it is! The definition of S(A,B) includes all points C such that stamping at C will yield at least one white point. So if D is in the complement, it yields no white points.\r\n\r\nYou wrote:\r\n You must demonstrate that, in the non-empty complement, there exists a point that, if stamped, will ensure that the set of non-black points (are not only countable, but) equals the NULL SET\r\n\r\nThat is what S(A,B) means: S(A,B) is the set of points where you get ANY white points at all. If D is in the complement of S(A,B) then stamping at A, B, and D will yield NO white points.\r\n\r\nThe question of measures came in at the size of S. I showed that nearly any choice of D will give you NO white points remaining.',10359,0);
INSERT INTO comment VALUES (10362,1309,3172,'SilverKnight','re(5):my proof - I stand corrected!','2003-12-09 16:21:46',0,'!@$#^%\r\n\r\nokay... here it is: *head bowed in shame*\r\n\r\nI stand corrected!!!\r\n\r\nI retract my misgivings about his proof. I misunderstood what he wrote earlier, but I now follow his line of thought.\r\n\r\n(I\'ll buy ya a beer or something :-)\r\n_________________________\r\n\r\nP.S. Hey Levik, would you please erase this whole thread?',10361,0);
INSERT INTO comment VALUES (10363,1522,4374,'Richard','Solution: Equation in One Unknown','2003-12-09 16:26:15',3,' Let the overall triangle have sides U and V (and hypontenuse 12) so that U=12cosT, V=12sinT. Then by similar triangles, (U-3)/3=3/(V-3) or UV-3U-3V=0 or 4sinT=1+tanT. Squaring both sides and multiplying by (cosT)^2 gives 16(sinTcosT)^2=1+2sinTcosT or 4(sin2T)^2=1+sin2T. Solving the quadratic gives sin2T=(1+sqrt17)/8 so that 2T=39.82077293 degrees. Thus U=12cosT=11.2827169 and V=12sinT=4.086599978.\n\nEdited on December 9, 2003, 4:30 pm',10334,0);
INSERT INTO comment VALUES (10364,1458,3558,'Tristan','re(3): SOUND¿','2003-12-09 19:11:21',0,'Couldn\'t you put all your replies into a single post, even if it takes a little more effort?\r\n\r\nThe problem with sound and other waves is in order for them to contact the cigarette and make it fall, they would have to go through some medium. The medium would have to be a solid, liquid or gas, and so by making a wave, you\'re making this medium touch the cigarette.',10347,0);
INSERT INTO comment VALUES (10365,1311,3558,'Tristan','the actual decryption','2003-12-09 20:19:57',1,'Even though I know what the first part of the message is (I haven\'t memorized the constitution), I still don\'t know how to get to this message. On inspecting the message and code, it seems that there are many letters in common.\r\n\r\nPGKKW XIMAF TNEGA NFYGZ TMUIV\r\nPREAM BLETO THECO NSTIT UTION\r\n\r\nWATAE TXLAL PDIBI MGTBU YBTMM\r\nWETHE PEOPL EOFTH EUNIT EDSTA\r\n\r\nOut of those 50 letters I compared, 8 were the same in both lines. That\'s more than it should be if it were left up to chance. \r\n\r\nAlso, if you look at the fourth word of the decrypted title and the decrypted message, they both end in \"IT.\" Even though \"IT\" is in the same place for the two codes, it is encrypted to \"GZ\" in the title and \"BU\" in the message. This proves (unless I have the title wrong) that the letter and position are not the only factors in decrypting.\r\n\r\nI hope that some one else comes in and shows me how obvious it is and that it was right in front of me.',NULL,0);
INSERT INTO comment VALUES (10366,1311,3172,'SilverKnight','re: the actual decryption','2003-12-09 20:45:51',3,'Thanks Tristan... kudos for pointing that out!\r\n\r\nThat gave it to me...\r\n\r\nThe first has no predecessor and predecessor is all we need to encode the next letter.\r\n\r\nFirst, each letter has a number associated with it A=0 through Z=25.\r\n\r\nEncoding...\r\nWETHEPEOPL\r\n22 4 19 7 4 15 4 14 15 11\r\n\r\njust add the value of the previously encoded letter and then mod 26 (subtract 26 if it is above 25).\r\n\r\nSo... encoded:\r\nthe first letter is 22 + previous letter (0) = 22, encoded = \'W\'\r\nthe second letter is E=4, + 22 =26, MOD 26 = 0, ENCODED = \'A\'\r\nthe third letter is T=19 + 0 =19, MOD 26 = 19, ENCODED = \'T\'\r\nthe fourth letter is H=7 + 19 = 26, MOD 26 = 0, ENCODED = \'A\'\r\nthe fifth letter is E=4, + 0 = 4, MOD 26 = 4, ENCODED = \'E\'\r\nthe sixth letter is P=15, + 4 = 19, MOD 26 = 19, ENCODED = \'T\'\r\nthe seventh letter is E=4, + 19 = 23, MOD 26 = 23, ENCODED = \'X\'\r\nthe eight letter is O=14, + 23 = 37, MOD 26 = 11, ENCODED = \'L\'\r\n\r\n... and so on ...\r\n\r\nI leave it as an exercise to the reader to reverse the process.\r\n\r\nThanks again, Tristan!',10365,0);
INSERT INTO comment VALUES (10367,1514,4708,'puzzlesrfun','I think this is a solution','2003-12-09 21:09:45',0,'We have a stick of finite length L. We break it into three pieces a, b, and c, such that a+b+c=L.\r\n\r\nWe can graph the function a+b+c=L on a three-dimensional axes. Since a, b, and c are all positive, we are confined to the \r\nfirst octant. We find that the solution space is a finite equilateral triangular plane, with vertices at (L,0,0), (0,L,0), and (0,0,L), and sides of length sqrt(2)*L. Total area of plane = sqrt(3)/4*(sqrt(2)*L)^2=sqrt(3)/2*(L^2).\r\n\r\nThe components of every point on the solution space add to L, but the components of every point do not constitute the requirements to form a triangle.\r\n\r\nThe fraction of the area of the solution space that have coordinates that can be made into triangles corresponds to the probablity that three segments taken at random will form a triangle.\r\n\r\nIt can be seen that a triangle cannot be made if two of the sides sum to less than half the total length of the stick. \r\n\r\nUsing our three dimensional graph, we can find the projection onto the solution space in which a+b < (1/2)*L, b+c < (1/2)*L, a+c < (1/2)*L. Those are the areas in which the solution points do not constitute the neccessary conditions for a triangle. \r\n\r\nThe remaining area will encompass the points where triangles can be formed.\r\n\r\nRelative to our triangular solution space, we find that the vertices get cut out, that is, there are smaller triangles at the vertices, inside which area the points taken will not form triangles, because two of the three components sum to less than (1/2)*L.\r\n\r\nThe sides of these smaller triangles are given by sqrt(2)*(1/4)*L. The 1/4 follows from the fact that two of the components are less than or equal to (1/4)*L, and therefore must sum to less than (1/2)*L. Again using the formula for the area of an equilateral triangle we get sqrt(3)/4*(sqrt(2)*1/4*L)^2=sqrt(3)/32*L^2 for the smaller areas. There are three of these areas so the total area that contains points that will not make triangles is 3*sqrt(3)/32*L^2.\r\n\r\nFinally, the probability that a point picked at random does not fall on this space is\r\n\r\n sqrt(3)/2*(L^2) - 3*sqrt(3)/32*L^2\r\n_____________________________________\r\n \r\n sqrt(3)/2*(L^2)\r\n\r\n\r\n\r\nwhich reduces to 1-(3/16)=13/16. So you have a 13/16 probability that three random lengths will have the right properties that they can form a triangle.',NULL,0);
INSERT INTO comment VALUES (10368,1474,4708,'puzzlesrfun','This might be a solution','2003-12-09 21:14:21',0,'A binomial random variable X represents the number of successes that occur in k trials for a given experiment that can result in either a \"success\" or a \"failure\". The expected number of successes in k trials, with success having probablility p, is given by E[X]=kp.\r\nIn our case, a \"success\" occurs in the event that, having chosen n cards, at least one and no more than one of the \"n choose 3\" ( =n!/[(n-3)!*3!] ) subsets of three cards contains a three of a kind. The probablity of success for any given 3 card subset is given by (3/51)*(2/50)=3/1275, since, given the first card, there is a 3/51 chance that the second card is the same rank, and given the first two cards, there is a 2/50 chance that the third card is the same rank as the first two.\r\nSo, for this problem, the number of trials k is given by \"n choose three\", where n is the number of cards we have chosen so far. p is as already given above, 3/1275. We wish to equate this such that kp=1, that is, the expected number of 3 of a kinds just equals one.\r\nSo we have\r\n\r\nn!/[(n-3)!*3!] * 3/1275 = 1\r\n\r\nn(n-1)(n-2)/2550=1\r\n\r\nn^3-3n^2+2n-2550=0.\r\n\r\nSolving the above for n yields a number between 14 and 15, 14 yielding an expected number of three of a kinds less than 1, and 15 yielding a number greater than 1. So we will say that 15 cards is the expected number for at least one three of a kind.\r\n\r\nIf we increase the number of decks to two decks, then p, the chance of a success, will change. It will now be given by 7/103*6/102 = 7/1751.\r\n\r\nnow we have\r\n\r\nn!/[(n-3)!*3!] * 7/1751 = 1\r\n\r\nThis results in a value between 12 and 13. So now 13 is the expected answer.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (10369,1311,1301,'Charlie','re(2): the actual decryption -- except','2003-12-10 09:02:17',0,'The following program prints the encoded title; decodes the title; encodes the expected title; and decodes the body as presented:\r\n\r\nDATA PGKKWXIMAFTNEGANFYGZTMUIV\r\nDATA PREAMBLEOFOURCONSTITUTION\r\nDATA WATAETXLALPDIBIMGTBUYBTMMFJBJWKBEIZSGLZQCCOCTXMQHMQSLFS\r\nDATA AOBFXQQRCKCJSMEXFHLTGYSJNQEQUMFNPIZZMCWEPXQODUIDLOSXLCV\r\nDATA CGIWIUIVYCHLYAETKYKYRVOVZFJWARRCYCNSSJNNADVZBBMQJQUVGKC\r\nDATA UCPVNBGRZAEVOMFTHBSKOZUYQQDGUOFUIATXOWPNQESJMMUHHUXBTMM\r\nDATA NYGYFYFNFHVIATBUOHPDQVJATAEYLTMQTLEEXBTHMMYCTBDDAX\r\nCLS\r\n\r\n\'decode title\r\nREAD l$\r\nPRINT l$\r\np$ = \"A\"\r\nFOR i = 1 TO LEN(l$)\r\n let$ = MID$(l$, i, 1)\r\n ltr = ASC(let$) - ASC(p$) + ASC(\"A\")\r\n p$ = let$\r\n IF ltr < ASC(\\\"A\\\") THEN ltr = ltr + 26\r\n PRINT CHR$(ltr);\r\nNEXT\r\nPRINT\r\n\r\n\'encode title\r\nREAD l$\r\np$ = \\\"A\\\"\r\nFOR i = 1 TO LEN(l$)\r\n let$ = MID$(l$, i, 1)\r\n ltr = ASC(let$) + ASC(p$) - ASC(\\\"A\\\")\r\n IF ltr > ASC(\"Z\") THEN ltr = ltr - 26\r\n p$ = CHR$(ltr)\r\n PRINT CHR$(ltr);\r\nNEXT\r\nPRINT\r\n\r\n\'decode body\r\np$ = \"A\"\r\nDO\r\n READ l$\r\n FOR i = 1 TO LEN(l$)\r\n let$ = MID$(l$, i, 1)\r\n ltr = ASC(let$) - ASC(p$) + ASC(\"A\")\r\n p$ = let$\r\n IF ltr < ASC(\\\"A\\\") THEN ltr = ltr + 26\r\n PRINT CHR$(ltr);\r\n NEXT\r\n PRINT\r\nLOOP\r\n\r\nThe result is\r\n\r\n
\r\n\r\nand we\'ve got tests of no more than 5 problems.\r\n________________________________\r\n\r\n(2)\r\nIf the point is to get the highest of any given grade (100, 89, 79, 69, and 59) and minimize the number of problems on the tests then, by inspection:\r\n\r\n\r\n
\r\n\r\nYes, these are brute forced, but certainly a short brute force that can be done by hand (or hand held calculator).',NULL,0);
INSERT INTO comment VALUES (10416,1409,4374,'Richard','Continued Fractions?','2003-12-11 16:55:24',4,'69/100=1/(1+(1/(2+(1/(4+(1/(2+(1/3)))))))) and truncating at successive + signs gives 1,2/3,9/13,20/29 each of which approximates 69/100 better than its predecessor. The first one times 100 that is close enough to round to 69 is 9/13. There is a theory about this. See the book \"Introduction to Diophantine Approximations\" by Serge Lang, for example.',NULL,0);
INSERT INTO comment VALUES (10417,1341,2899,'Brian Wainscott','re: question','2003-12-11 17:01:55',0,'No, each interval you add 10 marbles and remove 1.',10404,0);
INSERT INTO comment VALUES (10418,144,4718,'Jack Squat','re(2): Forced March','2003-12-11 17:17:56',3,'Sorry Barry, it is you that is incorrect. TomM defines little \"t\" as the time until they meet, not the time for the whole day (where t=1)so you don\'t want to include the extra \"d\" in the rate. Your solution is solving the question \"How far does the messenger march if at the end of the day he meets the officer\". Work it out, at 50 miles per day, he\'ll only reach the officer at the very end of the day.\r\n\r\nThe problem is a little easier to get your head around if you think of the column as standing still, and just adjust the messenger\'s speed relative to the column. Call the messenger\'s ACTUAL speed \"x\". Heading to the front of the line, the messenger\'s RELATIVE speed compared to the column is x - 25. His relative speed heading to the back of the line is x + 25. The distance both ways is 25 miles (the column is standing still). So the time to get to the front is distance over speed, or 25/(x-25) and the time to the back is 25/(x+25). The two times added together equal 1 (the whole process takes him 1 day). So you are left with the equation:\r\n\r\n25/(x+25) + 25/(x-25) = 1\r\n\r\nUsing algebra you get this to:\r\n\r\n0 = x² - 50x - 625\r\n\r\nUse the quadratic and you get:\r\n\r\nx = (50 + √5000)/2 (the negative answer, much like TomM\'s negative answer of t = - 1/√2 is ignored)\r\n\r\nSimplify and you get:\r\n\r\nx = 25 + 25 * √2 or x = 25 * (1 + √2)\r\n\r\nThis is his ACTUAL speed per day. How far does he travel in one day? His speed! 25 * (1 + √2)',10294,0);
INSERT INTO comment VALUES (10419,1312,4750,'Kat','answer','2003-12-11 17:26:49',3,'alicia got all 5',NULL,0);
INSERT INTO comment VALUES (10420,1312,3529,'Senthil Kumar','Solution','2003-12-11 17:54:40',3,'Paul\'s test: 4 correct answers\r\nTodd\'s test: 3 correct answers\r\nJason\'s test: 2 correct answers\r\nAlicia\'s test: 5 correct answers\r\nBebe\'s test: 1 correct answer\r\n\r\nSo, it is Alicia.',NULL,0);
INSERT INTO comment VALUES (10421,1312,4507,'Penny','re: answer','2003-12-11 18:01:08',0,'Kat is correct. It is very simple to case this one out. Incidentally, the quiz that the teacher gave to Paul, Todd, Jason, Alicia and Bebe consisted of a single question: \"Name five things that could really mess up the planned Australian honeymoon of Jennifer Lopez and Ben Affleck. Answer: eggs, evaporation, Alligator, a kangaroo, \r\nteeth.\" (btw, why is Alligator capitalized but kangaroo is not? Does DJ have something against marsupial bipeds?)\n\nEdited on December 11, 2003, 6:04 pm',10419,0);
INSERT INTO comment VALUES (10422,1409,3529,'Senthil Kumar','Solution','2003-12-11 18:08:40',3,'For A 1/1 - 100\r\n B 8/9 - 89 (88.89)\r\n C 11/14 - 79 (78.57)\r\n D 9/13 - 69 (69.23)\r\n F 10/17 - 59 (58.82)\r\n',NULL,0);
INSERT INTO comment VALUES (10423,144,3172,'SilverKnight','re(3): Forced March','2003-12-11 18:17:11',0,'Jack,\r\n\r\nNicely worded/explained.\r\n\r\n- SK',10418,0);
INSERT INTO comment VALUES (10424,865,4739,'ben','HERES ONE FOR YOU','2003-12-11 20:11:35',4,'is there an answer to this question?\r\n\r\ni just thought of that....most likely it has already been done but i genuinly thought of it myself.',NULL,0);
INSERT INTO comment VALUES (10425,865,3558,'Tristan','re: HERES ONE FOR YOU','2003-12-11 20:59:54',0,'I\'m not answering your question because you\'re not supposed to post puzzles in the comments. lol',10424,0);
INSERT INTO comment VALUES (10426,1312,3351,'Eric','Solution','2003-12-11 21:25:33',0,'Paul\'s answers differ entirely from Bebe, therefore neither of them could be all right or the other would have to be all wrong.\r\n\r\nIf Todd had correctly answered each of the questions, it would follow that both Jason and Paul would have each answered two correctly.\r\n\r\nIf Jason had been the ace, both Alicia and Todd would have ended up with the same score.\r\n\r\nTherefore the only possible perfect scorer could have been Alicia. And as it happens, the rest follows without paradox.',NULL,0);
INSERT INTO comment VALUES (10427,1513,4507,'Penny','New Mersenne prime discovered','2003-12-11 22:17:23',0,'DETROIT, Michigan, 12/11/2003 (AP) -- More than 200,000 computers spent years looking for the largest known prime number. It turned up on Michigan State University graduate student Michael Shafer\'s off-the-shelf PC. \"It was just a matter of time,\" Shafer said. The number is 6,320,430 digits long and would need 1,400 to 1,500 pages to write out. It is more than 2 million digits larger than the previous largest known prime number. Shafer, 26, helped find the number as a volunteer on an eight-year-old project called the Great Internet Mersenne Prime Search. Tens of thousands of people volunteered the use of their PCs in a worldwide project that harnessed the power of 211,000 computers, in effect creating a supercomputer capable of performing 9 trillion calculations per second. Participants could run the mathematical analysis program on their computers in the background, as they worked on other tasks. Shafer ran an ordinary Dell computer in his office for 19 days until November 17, when he glanced at the screen and saw \"New Mersenne prime found.\" A prime number is a positive number divisible only by itself and one: 2, 3, 5, 7 and so on. Mersenne primes are a special category, expressed as 2 to the \"p\" power minus 1, where \"p\" also is a prime number. In the case of Shafer\'s discovery, it was 2 to the 20,996,011th power minus 1. The find was independently verified by other participants in the project. Mersenne primes are rare but are critical to the branch of mathematics called number theory. That said, what is the practical significance of Shafer\'s number? \"People are going to make posters of it to hang up on the wall,\" said Shafer, who is pursuing a doctorate in chemical engineering. \"It\'s a neat accomplishment, but it really doesn\'t have any applicability.\" As for his own standing in the world of mathematics, \"I don\'t think I\'m going to be recognized as I go down the street or anything like that.\" He said the method by which the number was found -- harnessing many computers together -- is more important than the number itself. \"Somebody else could have found the number,\" he said. \"You install the program on the computer and it takes care of itself.\" But \"I get the credit, along with the people that developed the software.\" \r\n\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (10428,1309,4698,'Larry Settle','General solution','2003-12-11 22:32:00',0,' Given three points in the plane that define a triangle with distinct sides of lenght S1,S2,and S3 and obey the following restrictions on the lengths;\r\n1. S1 is irrational of the form R1(2^1/2) where R1 is rational.\r\n2. S2 is irrational of the form R2(2^1/2) where R2 is rational.\r\n3. S3 is transcendental.\r\n Then,the stamp when applied to the three points will ink the plane.\r\n\r\nProof: Let P be an uninked point. Then the straight line distances from P to the three points are all rational.There are three cases;\r\n1. P is in the exterior of the triangle and the angles formed by the connections to the three points of the triangle can be labeled alpha,beta, and (alpha+beta).\r\n2. P is on the perimeter of the triangle which leads to an immediate contradiction since every point on the perimeter is an irrational distance from at least one triangle point by the above restrictions.\r\n3. P is in the interior of the triangle and the angles formed can be labeled alpha,beta,and (360-alpha+beta). This case can be mapped into case one for the purpose of this proof without any loss of generality.\r\nIn case one there are three equations from the law of cosines. The first two are of the form;\r\nside^2=rational^2+rational^2-2(rational)(rational)cos(alpha or beta). The third equation is of the form;\r\nside^2=rational^2+rational^2-2(rational)(rational)cos(alpha+beta).\r\nThe third equation can be put in terms of cos(alpha) and cos(beta) by the following steps;\r\n1.cos(alpha+beta)=cos(alpha)cos(beta)-sin(alpha)sin(beta)\r\n2. Collect sin(alpha)sin(beta) alone on one side of equation three and square both sides.\r\n3. Replace sin^2(alpha) with 1-cos^2(alpha) and sin^2(beta) with 1-cos^2(beta).\r\nFinally solve equations one and two for cos(alpha) and cos(beta) and substitutee in equation three.\r\nThe resulting equation has only rational terms and powers of S3. Note that S1^2 and S2^2 are rational. Therefore our third equation is algebraic in S3 with rational coefficients which is a contradiction.\r\nQED\r\n \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (10429,1513,4300,'Minion123','?','2003-12-11 23:12:02',0,'k?',10427,0);
INSERT INTO comment VALUES (10430,1312,4755,'drew','Solution','2003-12-11 23:25:24',0,'Is this where I put the Answer?\r\n\r\nAlicia',NULL,0);
INSERT INTO comment VALUES (10431,1312,3224,'Lee','algorithm','2003-12-12 00:15:03',3,'Draw 5 \'nodes\', or boxes, 1 for each of the pupils.\r\nConnect all of them to each other (with lines)\r\nOn each line write the number of answers the two \'nodes\'/boxes/pupils share.\r\nThe one who got them all right is the only one who connects to the other four with a 4,3,2,1\r\nThis conveniently gives the information as to who got what on the test.\r\nI know it\'s not particularly insightful - I just like the fact that when I drew it out in this fashion (expecting it to be harder) the question of who got what is instantly answered. In fact, this post took longer to type (I\'ve got to stop doing that)',NULL,0);
INSERT INTO comment VALUES (10432,1528,1686,'DuCk','???','2003-12-12 07:09:10',0,'I\'m guessing that I really don\'t understand the question, but....\r\n\r\n8\r\n18\r\n7\r\n40\r\n16',NULL,0);
INSERT INTO comment VALUES (10433,1528,1920,'Brian Smith','Solution','2003-12-12 10:42:48',0,'Solid |{F, E, V}\r\n------------+------------\r\nTetrahedron |{4, 6, 4}\r\nCube |{6, 12, 8}\r\nOctahedron |{8, 12, 6}\r\nDodecahedron|{12, 30, 20}\r\nIcosahedron |{20, 30, 12}\r\n\r\nF=faces, E=edges, V=vertecies',NULL,0);
INSERT INTO comment VALUES (10434,1409,4505,'Bob Genisot','Additional Part','2003-12-12 11:58:10',0,'If the problem read that each quiz had to have the same number of questions, the results are as follows: \r\nSince it is possible to score exactly 100,89,79,69 and 59 on a 100-question quiz, the number of questions must be less than or equal to 100. Checking all possibilities by brute force results in:\r\n61/61 = 100%\r\n54/61 = 88.52% ~ 89%\r\n48/61 = 78.69% ~ 79%\r\n42/61 = 68.85% ~ 69%\r\n36/61 = 59.02% ~ 59%\r\n\r\nAll other denominators less than 61 do not give the desired result.',NULL,0);
INSERT INTO comment VALUES (10435,1528,1301,'Charlie','... and of course','2003-12-12 12:12:28',3,'By way of explanation, these are the regular (or Platonic) solids. There are of course irregular octahedra, dodecahedra and icosahedra (such as prisms with bases of (F-2) sides), and these are the figures for the regular ones.\r\n\r\nAlso, as the figures show, these solids have duals, the tetrahedron being its own dual, while the cube and octahedron are duals of each other as are the dodecahedron and icosahedron. The duals switch vertices for faces in each other. Thus the vertices column can be swapped with the faces column so long as the names of the cube and octahedron are switches as well as the dodecahedron and the icosahedron. Then the list is in order by number of vertices rather than number of faces--unusual only because of the naming conventions based on number of faces.',10433,0);
INSERT INTO comment VALUES (10436,1509,4764,'Christie','I\'m pretty sure i got it','2003-12-12 12:35:08',0,'it was march 14th. 1996 was a leap year and every day he basically gained one foot because if he climbed three and slid 2 feet in his sleep, it would take him 30 days because it was a thirty foot well.',NULL,0);
INSERT INTO comment VALUES (10437,1521,4670,'e.g.','Look Ma, no numbers!','2003-12-12 12:52:01',3,'You don\'t need any numbers if you write\r\nn= d/dx (x+x+x+...+x) and there are n x\'s in the sum.',NULL,0);
INSERT INTO comment VALUES (10438,1528,4507,'Penny','Ever hear of Occam\'s Razor?','2003-12-12 13:28:17',3,'There is a simpler (and, according to Occam\'s Razor, therefore superior) solution. The third number in each ordered triplet is the smaller of the first two:\r\n \r\n{4, 6, 4}\r\n{6, 12, 6}\r\n{8, 6, 6}\r\n{20, 30, 20}\r\n{20, 12, 12}\r\n\r\nThis answer does not require us to go back to 347 BC and borrow ideas from Plato\'s dialogue \"Timaeus\", which first propounded the doctrine of the Platonic Solids. As for the title of this puzzle being \"shapely figures\", that could have been a reference to this meaning of the word \"shape\": \"a mode of existence or form of being having identifying features\". One of the \"identifying features\" of any two positive integers, is the fact that unless they are identical, one of the two will be smaller.\r\n\r\n\r\n\r\n\n\nEdited on December 12, 2003, 1:52 pm',NULL,0);
INSERT INTO comment VALUES (10439,150,4718,'Jack Squat','re: Problem with Solution','2003-12-12 14:02:32',0,'You are right Gamer, a 1x1 grid does not apply, but it doesn\'t have to be a 1x1 grid for A and B to be the same person. Consider the following grid of people (numbers are the heights, in an arbitrary unit):\r\n\r\n10 11 12 13\r\n14 15 16 17\r\n18 19 20 21\r\n\r\nThe tallest of each row are 13, 17, 21. A is the shortest, 13.\r\n\r\nThe shortest of each column are 10, 11, 12, 13. B is the tallest, lucky number 13.\r\n\r\nThere is an infinite number of grids this works for.',4133,0);
INSERT INTO comment VALUES (10440,1528,1626,'Gamer','Only 5','2003-12-12 15:40:03',0,'You should go as if these 5 are the only ones that follow that rule. I don\'t know if this is what Silver Knight wanted because he didn\'t listen to me in the queue when I asked him to either not have a ? in all terms or instead to say these 5 are the only ones that fit the rule.\r\n\r\nSecond of all, is that the best answer? In most tests, the one that fits closest is the correct one. You have a very loose connection to shape, much more questionable than a definition given by the others when they solved this problem. Think about this in all the problems you solve. Although without the title, you solution is correct (because of some things that were left out), the title lets us know which one is correct.',NULL,0);
INSERT INTO comment VALUES (10441,1528,4769,'stern','re: Ever hear of Occam\'s Razor?','2003-12-12 16:08:25',0,'What a pathetic attempt to stroke your own ego! Everyone who thinks Penny\'s solution is \"superior\", raise your hand.',10438,0);
INSERT INTO comment VALUES (10442,327,4718,'Jack Squat','Im not going hiking with pleasance!','2003-12-12 17:04:45',0,'The solution assumes there is an outflow to this lake, which isn\'t always the case. The lake outflow can dry up in the fall, if it even HAS an outflow. Pleasance\'s solution could have both people walking around the lake for eternity (if they are unlucky enough to walk in the same direction).',NULL,0);
INSERT INTO comment VALUES (10443,1538,3172,'SilverKnight','Full RESPONSE (answer continues to be hidden)','2003-12-12 17:31:56',3,'\"Fortunately, it\'s not... and I don\'t like to push those things either!\"\r\n\r\n:-)',NULL,0);
INSERT INTO comment VALUES (10444,1538,3558,'Tristan','Nice...','2003-12-12 18:05:23',0,'Nice response SK. It puzzled me and got me interested now.\r\n\r\nHmmmm... there aren\'t any 8\'s or 0\'s. There are two 1541 words. Looks like a simple substitution, but there aren\'t enough numbers to represent all the letters, especially without the 8 or 0. It can\'t be that 2 numbers represent each letter. I can\'t figure it out on first look (like SK seems to have done), but I\'m betting it\'s more obvious than it looks.',NULL,0);
INSERT INTO comment VALUES (10445,1528,4507,'Penny','A stern rebuke !!!!!','2003-12-12 18:42:35',0,'Why does stern feel the need to fiddle with the answers of others? But since stern has already posted over 100 brilliant answers to puzzles on this website, I should not be criticizing such a genius.....\n\nEdited on December 12, 2003, 6:46 pm',NULL,0);
INSERT INTO comment VALUES (10446,1312,4742,'Judith Moore','re: Solution','2003-12-12 19:14:15',0,'Eric\r\nI have the same result - I have also posted solutions to other problems - in the \'comment\' sections - and it has not shown up as \'solved\'?? Is this the correct place to post solutions?? this page is not set up very \'user-friendly\' for this purpose.\r\nJudith',10426,0);
INSERT INTO comment VALUES (10447,1528,4507,'Penny','re: Only 5','2003-12-12 19:28:15',0,'Gamer: \"You have a very loose connection to shape, much more questionable than a definition given by the others when they solved this problem...Although without the title, you solution is correct (because of some things that were left out), the title lets us know which one is correct.\"\r\n \r\nBut the title can be unrelated to the correct solution. Case in point: \"Flawless Series?\", in which the author of that puzzle seemed to be referring to perfect numbers (\"flawless\"=\"perfect\") and Mersenne primes. The puzzle listed the first few perfect numbers, and asked the flooblers to list the next few. Later, to save face, he had the brazen audacity to deny that perfect numbers were at all related to the puzzle. \r\n\r\n\r\n\r\n\r\n\n\nEdited on December 12, 2003, 7:33 pm',10440,0);
INSERT INTO comment VALUES (10448,1538,1626,'Gamer','Ideas:','2003-12-12 20:17:38',2,'Here are my prime factorizations:\r\n\r\n23-23\r\n923-13x71\r\n29279-19x23x67\r\n1541-23x67\r\n53-53\r\n122-2x61\r\n21574-2x7x23x67\r\n20999-11x23x83\r\n1541-23x67\r\n437-19x23\r\n19-19\r\n14-2x7\r\n74-2x37\r\n166-2x83\r\n43-43\r\n159941-41x47x83\r\n671-11x61',NULL,0);
INSERT INTO comment VALUES (10449,1528,1626,'Gamer','re: A stern rebuke !!!!!','2003-12-12 20:27:01',0,'Namely you Penny. That\'s why you have been insulting us! :)\r\n\r\nI was unaware that SK said that. Can you show me where. I thought he thought that \"These are the first few elements of the perfect numbers. Perfect numbers are those positive integers that equal the sum of all their factors (not including themselves).\"\r\n\r\nAnyway, I think you will find the title either is blunt (like Word Meld 6, A riddle, Strawberries!) and offers no insight on the solution, or is a key to solving it, like tricky and Third Base.\r\n\r\nIf I don\'t reply, it is not because I am avoiding you, but because I am too tired to carry on some of our previous conversations.',10445,0);
INSERT INTO comment VALUES (10450,150,4699,'Barry Knapp','Question.','2003-12-12 21:12:08',1,'I\'m not sure how to prove it but I am speculating that the A = B always. But I guess the reason would be the fact that the tallest of the short people are columns and the shortest of the tall people are rows which means that they can infact and always will be the same person.',NULL,0);
INSERT INTO comment VALUES (10451,1538,4507,'Penny','re: Ideas:','2003-12-12 22:03:31',2,'\"Nothing but flowers\" is a song by the group \"The Talking Heads\". Someone named exoticorn might be into them. ',10448,0);
INSERT INTO comment VALUES (10452,1312,3558,'Tristan','re(2): Solution','2003-12-13 00:14:33',0,'Read the FAQ. They\'re above the chatterbox.',10446,0);
INSERT INTO comment VALUES (10453,1310,3558,'Tristan','re(3): define...-not so simple','2003-12-13 00:58:27',1,'I found a problem with my solution.\r\n\r\nlet X equal the chords\' distances from the center and R equal the radius of the cake.\r\n\r\nX=R * √π / 2 / 3^(1/4)\r\nSo X is about .6733868435*R\r\nThe distance from the center to the corners of the pyramid\'s base should be twice that: about 1.346773687*R. The problem here is that the pyramid extends beyond the cake! This does not mean that there is no solution in the shape I described, but it means that the exact measurements of it are much harder to calculate and beyond my ability. If anyone actually understood my messily explained solution idea, I invite him/her to find the numbers that would make it work.',10414,0);
INSERT INTO comment VALUES (10454,1538,3372,'Sam','re: Ideas:','2003-12-13 02:13:49',0,'Yes, the prime factors looks like a very good place to start. Obviously this isn\'t a straight substitution, because the things separated by hyphens aren\'t words created by the digits (though may be words created by the factors or something), and if each hyphen-separated number was a letter the puzzle would be unsolvable.\r\n\r\nHmmm, so does\r\n\r\n23-13 71-19 23 67-23 67-53-2 61-2 7 23 67-11 23 83-23 67-19 23-19-2 7-2 37-2 83-43-41 47 83-11 61 \r\n\r\nmean anything? Probably not, but it looks a little nicer, perhaps. At least we have some repitition. Must think.\r\n\r\nI\'m not sure I quite understood SK\'s comment, though..',10448,0);
INSERT INTO comment VALUES (10455,1543,4507,'Penny','Welcome to Logic 101','2003-12-13 08:58:51',3,'Here is what is wrong with your proof, Sam. You say \"If S if [sic] false, then any statement that starts with \'If S is true...\' is true\" Yes, but you are obviously confusing two things: whether S is true, as opposed to whether or not the consequent of S is true. A conditional statement is false if and only if the antecedent (the IF part) is true and the consequent (the THEN part) is false. (\"If George Bush is President, then the U.S. is at peace\" is a false statement). It is true if both antecedent and consequent are true. (\"If the Pope is Polish, then the moon is smaller then the earth\" is a true statement.) It is also true if the antecedent is false and the consequent is true. (\"If Ireland is more populous than India, then Tokyo is the capitol of Japan\" is a true statement.) It is even true if both antecedent and consequent are false. (\"If smoking cigarettes is good for your health, then drinking beer improves your driving skills\" is, believe it or not, a true statement !!) Consider the statement S: \"If S is true then God exists.\" The antecedent is \"If S is true\", and the consequent is \"then God exists.\" As I have just demonstrated, S may be true when it asserts that it is true, while the consequent of S (\"then God exists\") is false. To say that S is true, is NOT, repeat NOT, to assert that the consequent of S is true !! (Btw, you gotta feel sorry for a guy like Sam. Normally he is a man of great sobriety, but when he does drink, he becomes very confused, as when he posted this paradox. Once, while touring the CNN studio in New York, Sam imbibed a little too much, and he woke up the next morning wearing Larry King\'s suspenders.) \r\n\n\nEdited on December 13, 2003, 9:16 am',NULL,0);
INSERT INTO comment VALUES (10456,1543,1626,'Gamer','re: Welcome to Logic 101','2003-12-13 10:48:04',0,'\"A conditional statement is false if and only if the antecedent (the IF part) is true and the consequent (the THEN part) is false. (\"If George Bush is President, then the U.S. is at peace\" is a false statement). It is true if both antecedent and consequent are true. (\"If the Pope is Polish, then the moon is smaller then the earth\" is a true statement.) It is also true if the antecedent is false and the consequent is true. (\"If Ireland is more populous than India, then Tokyo is the capitol of Japan\" is a true statement.) It is even true if both antecedent and consequent are false. (\"If smoking cigarettes is good for your health, then drinking beer improves your driving skills\" is, believe it or not, a true statement !!) \"\r\n\r\nWe already know this. That\'s what the note says.\r\n\r\nThe way this proof works, is it says the statement is true, and then says the antecedent is true. Obviously in order to prove a statement, you need to actually prove it.\r\n\r\nThe part that you read is correct. We don\'t care about the consequent until the very end except for saying the original statement is true. This is possible by doing what is listed in the proof.',10455,0);
INSERT INTO comment VALUES (10457,1229,4068,'Bruno','Rich grandparent$','2003-12-13 11:34:10',0,'Here\'s my answers:\r\n\r\nOn the 15th birthday:\r\n\r\nGrandpa gives 16 384\r\nGrandma gives 13 397\r\n\r\nAfter 27 years:\r\n\r\nGrandpa has given 134 217 727\r\nGrandma has given 109 728 404\r\n',NULL,0);
INSERT INTO comment VALUES (10458,1509,4783,'ting','i guess is this...','2003-12-13 11:43:35',0,'15 march 1996',NULL,0);
INSERT INTO comment VALUES (10459,1543,3386,'Victor Zapana','hm..','2003-12-13 12:24:00',0,'well lets see.. let\'s go into context. If S is a tautology then this proof does work. If S is a always false statement (forgot the term for this), then this is an indeterminate paradox. so depending on the statement S, God can exist or no conclusion can be made.',NULL,0);
INSERT INTO comment VALUES (10460,1543,4507,'Penny','re(2): Welcome to Logic 101','2003-12-13 12:29:47',0,'Where the proof is wrong, is that it contains a self-referencing proposition. The statement S is essentially \"If this statement S that I am now making is true, then God exists.\" S says something about the truth of S. (See \"Is NO the correct answer to this question?\") Self-referencing statements in logic are exactly like dividing by zero in mathematics. They are totally bogus. They lead to all kinds of paradoxes, and are disallowed. That is what is wrong with Sam\'s proof. \r\n\r\n(I once read a \"proof\" that 1+1=2, that involved division by zero).\r\n \r\nNow why don\'t you stop debating with me about this, and go make some progress on that \"Nothing but flowers\" cryptography? \r\n\r\n\r\n\r\n\n\nEdited on December 13, 2003, 1:23 pm',10456,0);
INSERT INTO comment VALUES (10461,1389,3372,'Sam','re(5): FULL SOLUTION (No computer program used)','2003-12-13 13:45:27',0,'re: sheesh....How the heck were people who still have rotary phones supposed to realize that? ..... \r\n\r\n\r\nwell, when I had worked it out I didn\'t actually realise that the numbers were based on phone keys, but it was very easy to see how they related to each other in a pattern.\r\n\r\nHad you written them out, you would have seen\r\n\r\nA 12\r\nB 22\r\nC 32\r\nD 13\r\nE 23\r\nF 33\r\n\r\nand so on. That\'s how I was able to fill in the missing numbers to give the next line:\r\n\"Hello operator, please give me number nine\"\r\neven though letters like \"p\" weren\'t in the original.\r\n\r\nps: \"phone\" is short for \"phonetic\"??? Where did you learn Greek?\r\n\n\nEdited on December 13, 2003, 1:51 pm',10147,0);
INSERT INTO comment VALUES (10462,1509,4785,'strawbaryfields','solution','2003-12-13 14:16:42',0,'Herb gets out on March 14, 1996 because he climbs one foot a day which takes 30 days and 1996 was a leap year so thiry days after the 14th of feb is march fourteenth.',NULL,0);
INSERT INTO comment VALUES (10463,1543,4507,'Penny','Untying the Gordian Knot','2003-12-13 15:32:40',3,'They say that as Alexander The Great was in the early days of his conquest of Persia, he was shown an intricately tied knot, known to history as the Gordian Knot, because a legendary hero named Gordius had tied it long before. A prophecy stated that whoever untied the knot would conquer Asia. Alexander was an educated man, having been tutored by Aristotle, and he saw at once that it would be a complete waste of time to try to untie this knot. So he said \"Thus do I untie it!\" and sliced through it with his sword.\r\n \r\nThis paradox \"Proof of Anything\" is such a Gordian knot. It contains a self-referencing statement: a statement that says something about itself. The terminally naive (I wouldn\'t want to mention any names...) will spend (waste) hours pondering it, trying to figure it out. But the real student of philosophy will at once recognize it for the bogus nonsense that it is, the logical equivalent of dividing by zero in mathematics or exceeding the speed of light in physics, and will \"point and drag it\" to the recycle bin of his mind. Thus will he or she untie it. The moral of the story is: Don\'t waste time trying to rationalize paradoxes based on self-referencing statements. \r\n ',NULL,0);
INSERT INTO comment VALUES (10464,1543,4786,'winnie','proof of anything','2003-12-13 15:58:06',0,'the problem seems retorical because you would be proving something true and false with the same logic.',NULL,0);
INSERT INTO comment VALUES (10465,783,4786,'winnie','','2003-12-13 16:16:17',0,'i dont get it',NULL,0);
INSERT INTO comment VALUES (10466,1227,4786,'winnie','short but sweet','2003-12-13 17:12:34',0,'really i never knew that ',NULL,0);
INSERT INTO comment VALUES (10467,1359,4786,'winnie','master number','2003-12-13 17:19:15',0,'all these stuff are so hard',NULL,0);
INSERT INTO comment VALUES (10468,1543,153,'TomM','Penny, you missed a chance to impress us...','2003-12-13 18:08:35',0,'...with your ability to copy what the \"Dr. Math\" site has to say about Gödel\'s Theorem and post it here.',NULL,0);
INSERT INTO comment VALUES (10469,1543,3372,'Sam','re: Welcome to Logic 101','2003-12-13 18:09:09',0,'\"Self-referencing statements in logic are exactly like dividing by zero in mathematics. They are totally bogus. They lead to all kinds of paradoxes, and are disallowed. That is what is wrong with Sam\'s proof.\"\r\n\r\nI\'m confused as to where you came up with this idea. Did you invent it yourself? Can you show me where they are \"disallowed\"? I\'m actually quite interested, because I must have completely forgotten to teach my students this when I was a TA for Logic 101 (a true, but completely coincedental reference to the title above), so I guess it\'s lucky none of them failed!\r\n\r\nWhich of these statements are \"bogus\":\r\n\r\n-This statement has five words\r\n-This statment has four words\r\n-This statement starts with \"this\"\r\n-S: Statement S starts with \"statment\"\r\n-This statement would be included in the set of all statments that refer to themselves\r\nThis statement would not be included in the set of all statments that refer to themselves\r\n-S: S is not a letter\r\n-S: \"S\" is not a letter\r\n-The referent of this statement is not what it appears to be\r\n\r\nNow some of those statements are true, and some are false (and that last one looks a little confusing), but I don\'t remember being able to assign \"bogus\" to a statement. My professor must not have gotten around to that.\r\n\r\nSelf-reference is actually quite vital. Godel\'s proof, which many would consider to be the most important mathematical proof ever written, relies on it most explicitly:\r\nS: S cannot be proven true under system F\r\n\r\nPossibly some people wrote him letters where they said \"come now, statement S is neither provable not disprobvable, it\'s just bogus\" but these people were neither mathematicians nor logicians, who realized the importance of the proof.\r\n\r\nSo do tell me, where are these logical laws that you refer to?\n\nEdited on December 13, 2003, 6:14 pm',10460,0);
INSERT INTO comment VALUES (10470,1269,4752,'B.A.','Solution','2003-12-13 18:32:17',0,'march, denote, candy, worth, timber, windy, saunter, append, feast, began, mixed, mailed, dizzy, stove, connect, heroic, proper, differ, bloom, quite, judge, murmur, rabbit, token, helper, famous',NULL,0);
INSERT INTO comment VALUES (10471,1269,4752,'B.A.','re: A solution differing a bit from prior posts. NO COMPUTER PGM USED.','2003-12-13 18:39:06',0,'What does proke mean?',10129,0);
INSERT INTO comment VALUES (10472,1543,1626,'Gamer','Penny was right?!?!??!','2003-12-13 21:45:51',0,'Sorry Sam, but I am going to do the unthinkable and agree with what a certain person said earler. (I am unable to reply to anything that person said, so I don\'t know who that person would be.)\r\n\r\nThe problem arises when you group a self referring sentence with another sentence by using a binary operator (like OR, or AND) Although problems can arise from a certain unary statement (This statement is false) we can prove that a statement can\'t refer to itself because the recursion never ends.\r\n\r\nS = S=>X (X is the consequent that you explain after step 9)\r\n\r\nS = S=>X\r\n\r\nReplace S in S=>X with S=>X, and keep doing this.\r\n\r\n...S=>S=>S=>S=>S=>S=>S=>S=>X\r\n\r\nThis obviously doesn\'t make sense, which is why it can\'t be proven true.\r\n\r\nI will post another way to show this is false if I find it is fine. Otherwise I am still confused. I just remember you can\'t use the word in it\'s definition. Logic: Something of Logical nature.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (10473,1543,4507,'Penny','Poor Sam...Trying to be a philosopher while ignoring the Ancient Greeks !!!!','2003-12-13 21:54:10',3,'This puzzle shows again how dangerous it is to attempt to be original in philosophy while ignoring the Ancient Greeks !!\r\n\r\nParadoxes based on self-referential statements have been discussed continually in philosophy since the Ancient Greeks in the middle of the 4th century BCE. The most ancient attribution is to Eubulides of Miletus. He said, \"A man says that he is lying. Is what he says true or false?\" An ancient gravestone on the Greek Island of Cos was reported by Athenaeus to contain this poem about the paradox:\r\n\r\nO Stranger: Philetas of Cos am I,\r\n\'Twas the Liar who made me die,\r\nAnd the bad nights caused thereby.\r\n \r\nTheophrastus, Aristotle\'s successor, wrote three papyrus rolls about the Liar Paradox, and the Stoic philosopher Chrysippus wrote six, but their contents are lost in the sands of time. In the New Testament of the Bible, Saint Paul warned, \"One of themselves, even a prophet of their own, said the Cretans are always liars.\" Paul, however, gave no indication he recognized anything paradoxical about the Cretan\'s remark, but it would be paradoxical if no other Cretan utters a truth and if \'liar\' means utterer only of falsehoods.\r\n\r\nIn the late medieval period, Buridan put the Liar Paradox to devious use with the following proof of the existence of God. It uses the pair of sentences:\r\n\r\nGod exists.\r\nNone of the sentences in this pair is true.\r\n \r\nThe only consistent way to assign truth values, that is, to have these two sentence be either true or false, requires making \"God exists\" be true. So, Buridan has \'proved\' that God does exist. \r\n\r\nThere are many other versions of the Paradox. Some liar paradoxes begin with a chain of sentences:\r\n\r\nThe following sentence is true.\r\nThe following sentence is true.\r\nThe following sentence is true.\r\nThe first sentence in this list is false.\r\n \r\nThe Strengthened Liar Paradox begins with the Strengthened Liar Sentence\r\n\r\nThis sentence is not true.\r\n \r\nThis version is called \"Strengthened\" because some promising solutions to (1) fail completely when faced with the Strengthened Liar. So, finding one\'s way out of the Strengthened Liar is the acid test of a successful solution. \r\n\r\nThere are also Contingent Liars which depend upon what occurs in the empirical world. Suppose that the last sentence in today\'s edition of The New York Times newspaper is:\r\n\r\nThe last sentence in tomorrow\'s edition of The New York Times newspaper is true.\r\n \r\nWas that sentence grammatical? Was it meaningful? Was it true or false, even if we don\'t know which at the moment? The common sense answers are \"yes\" to all these questions. Perhaps we should not retain those intuitive answers tomorrow when the Times\'s presses print a newspaper whose last sentence is\r\n\r\nThe last sentence in yesterday\'s edition of The New York Times newspaper is not true.\r\n \r\nIf we adopt the metaphor of a paradox as being an argument which starts from the home of seemingly true assumptions and which travels down the garden path of seemingly valid steps into the den of a contradiction, then a solution to the paradox has to find something wrong with the home, find something wrong with the garden path, or find a way to live within the den. Less metaphorically, the main kinds of ways out of the Paradox are the following: Forget it; we can live with the problem. The Liar Sentence isn\'t grammatical. The Liar Sentence isn\'t meaningful. The Liar Sentence is grammatical and meaningful but isn\'t true or false. There is some other error in one of the steps of the argument that leads to the contradiction. The Liar Sentence is both true and false. Two philosophers might take one of these ways out but for very different reasons, and they might offer different changes in our naive system of beliefs and concepts in order to take this way out.\r\n\r\nTo put the Paradox in perspective, it is essential to appreciate why such an apparently trivial problem in fact is a deep problem. Suppose we ask the larger question: What is truth? As a question about what are the significant paths of life to be followed or the significant things to know in order to have the best grasp on reality, the question is just too difficult, and also too vague, to be a center of attention for the analytical philosophers of the present age. However, as a question asking simply for general characteristics of all true sentences, the question is more amenable to solution. Nevertheless, it is still a very difficult one. For instance, in the attempt to generally characterize the grounds of validity of a true sentence, that is, in the attempt to characterize why a true sentence is true, philosophers have created several ingenious, and alluring theories of truth: the correspondence theory of truth, the coherence theory of truth, and the pragmatic theory of truth, among others. Yet none of these has produced any detailed theory. At best, each is still at the stage of being a suggestive, but uncompelling, metaphor. [Tarski\'s Semantic Theory is a detailed theory, but it is not designed to characterize why a true sentence is true.]\r\n\r\nMore progress on answering the question \"What is truth?\" will be had by concentrating not on why a sentence is true, but on what other sentences are true when a sentence is true. By concentrating this way on truth\'s logical liaisons, Aristotle offered what many philosophers consider to be a partially correct answer to our question about truth. Stripped of its overtones suggesting a correspondence theory of truth, Aristotle proposed what is essentially sentence (T):\r\n\r\n(T) A declarative sentence is true if and only if what it says is so.\r\n \r\nIf pairs of quotation marks serve to name a sentence, then (T) requires that \"It is snowing\" be true just in case it is snowing. Similarly, if the sentence about snow were named with the numeral 88 inside a pair of parentheses, then (88) would be true just in case it is snowing. What could be less controversial? Unfortunately, this seemingly correct, but trivial response to our question \"What is truth?\" is neither obviously correct nor trivial; and the resolution of the difficulty is still an open problem in philosophical logic. Why is that? The brief answer is that (T) can be used to produce the Liar Paradox. The longer answer refers to Tarski\'s Undefinability Theorem of 1936.\r\n\r\nWe began this discussion with a mere sketch of the Liar argument using sentence (1). To appreciate the various proposed solutions to the paradox, and the central role of (T), we need to examine more than just a sketch of the argument. The argument requires the following assumptions:\r\n\r\n(2) Any declarative sentence \"S\" says that S. \r\n(3) The Liar Sentence, (1), is a legitimate declarative sentence, i.e., it is well formed.\r\n\r\n(4) A legitimate declarative sentence is either true or else false.\r\n\r\n(5) The usual naming convention holds so that\r\n\r\nthe phrase \"This sentence\" in (1) refers to (1), and \r\n(1) = \"This sentence is false\".\r\n\r\nTarski added precision to convention (T) and to these other assumptions by focussing not on English directly but on a classical formal language capable of expressing arithmetic. Here the difficulties produced by the Liar argument became much clearer; and, very surprisingly, he was able to prove that the assumptions lead to semantic incoherence. Tarski pointed out that the crucial assumption is (3). For there to be a legitimate Liar Sentence in the language, there must be a definable notion of \"is true\" which holds for the true sentences and fails to hold for the other sentences. If there were such a \'global truth predicate,\' then the predicate \"is a false sentence\" would also be definable and [here is where we need the power of arithmetic] a Liar Sentence would exist. Then one could deduce a contradiction.\r\n\r\nThis deduction of Tarski\'s is a formal analog of the informal Liar Argument. The contradictory result tells us that the argument began with a false assumption. Because (T), (2), (4), and (5) are essential to what we call a \"classical formal language,\" the mistaken assumption is (3), and the only possible problem here is the assumption that the global truth predicate \"is a true sentence\" can be defined. So, Tarski has proved that truth is not definable in a classical language--thus the name \"Undefinability Theorem.\" Tarski\'s theorem establishes that classically interpreted languages capable of expressing arithmetic cannot contain a global truth predicate. A language containing its own global truth predicate is said to be semantically closed. Tarski\'s Theorem implies that classical formal languages with the power to express arithmetic cannot be semantically closed. This suggests that English itself may not be semantically closed, or, if English is closed, then it is self-contradictory. This shocking result indicates to some that our thought about our thoughts is incoherent. That\'s the conclusion Tarski himself reached, so he quit trying to find the coherent structure underlying natural languages and concentrated on developing systems of formal languages that did not allow the deduction of the contradiction. Many other philosophers of logic have not drawn Tarski\'s pessimiistic conclusion from his theorem.\r\n\r\nFor these optimists, there are four main detailed and coherent ways out.\r\n\r\n(1) The Liar Sentence is meaningless, so the Liar argument can\'t even get started because its main assumption (that the Liar Sentence exists or is meaningful) is faulty. Natural language is incoherent, and its underlying sensible structure is that of an infinite hierarchy of levels. Because the Liar Sentence would have to reside on more than one level simultaneously, it\'s not really a meaningful sentence. This way out of the paradox is taken by Russell in his ramified theory of types and, following Tarski, by Quine in his hierarchy of meta-languages. For Russell, the referential phrase \"This sentence\" in (1) is the culprit because the phrase is not allowed to refer to the sentence in which the phrase itself occurs. For Quine, instead, the culprit is the phrase \"is false\" in (1) because the phrase must be satisfied by sentences in a language lower in the hierarchy and not by the very sentence in which the phrase occurs.\r\n \r\n(2) Kripke, on the other hand, retains the intuition that the Liar Sentence is meaningful, but argues that it is neither true nor false. It lacks a classical truth value as does the odd sentence \"The present king of France is bald.\" Kripke trades infinite syntactic complexity for infinite semantic complexity. He rejects the infinite hierarchy of meta-languages underlying English in favor of one formal object language having an infinite hierarchy of partial interpretations. The truth predicate is the formal language\'s only basic partially-interpreted predicate. Each step in the semantic hierarchy is an interpretation of the language, and in these interpretations all the basic predicates except one must have their interpretations already fixed in the base level from which the first step is taken. This one exceptional predicate is intended to be the truth predicate for the previous level. It becomes a truth predicate for its own level when the inductive interpretation building reaches the so-called \'fixed point\'. Each step uses all the sentences which had their truth values fixed at the lower steps in order to help fix the truth values of semantically more complex sentences, e.g., to fix the truth value of sentences with even longer chains of nested truth predciates. The Liar sentence, even up at the infinite semantic height of the lowest fixed point, still isn\'t true or false. But at the fixed point, the language satisfies Tarski\'s Convention (T).\r\n\r\n(3) The third way out says the Liar Sentence is meaningful and is true or else false, but one step of the argument in the Liar Paradox is incorrect (the move from the falsehood of the Liar Sentence to its truth). Prior, following the informal suggestions of Buridan and Peirce, takes this way out and concludes that the Liar Sentence is simply false.\r\n\r\n(4) A fourth and more radical way out of the paradox is to argue that semantic incoherence is not necessarily caused by letting the Liar Sentence be both true and false. This solution embraces the contradiction, then tries to limit the damage that is ordinarily a consequence of that embrace. This way out of the paradox uses a paraconsistent logic.\r\n\r\nThere are many suggestions for how to deal with the Liar Paradox, but most are never developed to the point of giving a formal, symbolic theory. Some give philosophical arguments for why this or that conceptual reform is plausible as a way out of paradox, but then don\'t show that their ideas can be carried through in a rigorous way. Usually it appears that a formal treatment won\'t be successful. Other attempts at solutions will take the formal route and then require changes in standard formalisms so that a formal analog of the Liar Paradox\'s argument fails, but then the attempted solution offers no philosophical argument to back up these formal changes. A decent theory of truth showing the way out of the Liar Paradox requires both a coherent formalism (or at least a systematic theory of some sort) and a philosophical justification backing it up. The point of the philosophical justification is an unveiling of some hitherto unnoticed or unaccepted rule of language for all sentences of some category which has been violated by the argument of the paradox. \r\n\r\nIt is to the credit of Russell, Quine, and Kripke that they provide a philosophical justification for their solutions while also providing a formal treatment in symbolic logic that shows in detail both the character and implications of their proposed solution. Kripke\'s elegant and careful treatment of (1) stumbles on the Strengthened Liar and reveals why it deserves its name. The theories of Russell-Tarski-Quine do \'solve\' the Strengthened Liar. In the formal, symbolic tradition, other important researchers in the last quarter of the 20th century are Barwise, Burge, Etchemendy, Gupta, Herzberger, McGee, Routley, Skyrms, van Fraassen, and Yablo. Martin and Woodruff created the same solution as Kripke, though a few months earlier. Dowden and Priest first showed how to embrace contradiction.\r\n\r\nPrincipal solutions to the Liar Paradox all have a common approach, the \"systematic approach.\" The solutions agree that the Liar Paradox represents a serious challenge to our understanding the logic of natural language, and they agree that we must go back and systematically reform or clarify some of our original beliefs in order to solve the paradox. The solution must be presented systematically and be backed up by an argument about the general character of our language. In short, there must be both systematic evasion and systematic explanation. Also, when it comes to developing this systematic approach, the goal of establishing a logical basis for a consistent semantics of natural language is much more important than the goal of explaining the naive way most speakers use the terms \"true\" and \"not true.\" As Vann McGee expresses this point, \"The problem of giving voice to our preanalytic intuitions about truth is comparatively less important, just as understanding popular misconceptions about space and time is comparatively less important than understanding the actual geometry of space-time.\"\r\n\r\nThis \'systematic approach\' has been seriously challenged by Wittgenstein. He says one should try to overcome \'\'the superstitious fear and dread of mathematicians in the face of a contradiction.\" The proper way to respond to any paradox is by an ad hoc reaction and not by any systematic treatment designed to cure both it plus any future ills. Symptomatic relief is sufficient. It may appear legitimate, at first, to admit that the Liar Sentence is meaningful and also that it is true or false, but the Liar Paradox shows that one should retract this admission and either just not use the Liar Sentence in any arguments, or say it is not really a sentence, or at least say it is not one that is either true or false. Wittgenstein is not particularly concerned with which choice is made. And, whichever choice is made, it needn\'t be backed up by any theory that shows how to systematically incorporate the choice. He treats the whole situation cavalierly and unsystematically. After all, he says, the language can\'t really be incoherent because we\'ve been successfully using it all along, so why all this \"fear and dread\"?\r\n\r\nInfluenced by Wittgenstein, P. F. Strawson has argued that the proper way out of the Liar Paradox is to re-examine how the term \"truth\" is really used by speakers. When we say some proposition is true, we aren\'t making a statement about the proposition. We are not ascribing a property to the proposition--such as the property of correspondence, or coherence, or usefulness. When we call a proposition \"true\" we are approving it, or praising it, or admitting it, or condoning it. We are performing an action. Similarly, when we say to our sister, \"I promise to pay you fifty dollars,\" we aren\'t ascribing some property to the proposition, \"I pay you fifty dollars.\" Rather, we are performing the act of promising. For Strawson, when speakers utter the Liar Sentence, they aren\'t saying something true or false; they are attempting to praise something that isn\'t there, as if they were saying \"Ditto\" when no one has spoken. The person who utters the Liar Sentence is making a pointless utterance. The Sentence is grammatical but it\'s not a proposition and so is not something from which a contradiction can be derived.\r\n\r\nSome of the solutions to the Liar Paradox require a revision in classical logic, the formal logic in which sentences of a formal language have exactly two possible truth values (TRUE, FALSE), and in which the usual rules of inference allow one to deduce anything from an inconsistent set of assumptions. Kripke\'s revision uses a 3-valued logic with the truth values TRUE, FALSE and NEITHER. Some logicians argue that classical logic is not the incumbent which must remain in office unless an opponent can dislodge it, although this is gospel for other philosophers of logic (probably because of the remarkable success of two-valued logic in expressing most of modern mathematical inference). Instead, the office has always been vacant for natural language.\r\n\r\nOther philosophers object to revising classical logic merely to find a way out of the Paradox. They say that philosophers shouldn\'t build their theories by attending to the queer cases. There are more pressing problems in the philosophy of logic and language than finding a solution to the Paradox, so any treatment of it should wait until these problems have a solution. From the future resulting theory which solves those problems, one could hope to deduce a solution to the Liar Paradox. However, for those who believe the Paradox is not a minor problem but one deserving of immediate attention, there can be no waiting around until the other problems of language are solved. Perhaps the investigation of the Liar Paradox will even affect the solutions to these other problems.\r\n\r\n[The above material was quoted from the Internet Encyclopedia of Philosophy:\r\nhttp://www.iep.utm.edu/p/par-liar.htm ]\r\n \r\n\r\n\r\n\n\nEdited on December 13, 2003, 10:13 pm',10469,0);
INSERT INTO comment VALUES (10474,1543,3372,'Sam','re: Poor Sam...Trying to be a philosopher while ignoring the Ancient Greeks !!!!','2003-12-13 23:01:44',0,'Penny, I\'m not quite sure that you\'ve understood the point of these puzzles on Flooble. The point of my posting this is certainly not to say \"my paradox is right, I\'m so smart\" for two reasons: 1) I cannot lay claim to the paradox, much as I would like to, as it is a simple extension of Curry\'s paradox and Lob\'s theorem, and the liar\'s paradox before that, and 2) at the bottom of the post I say \"What, if anything, is wrong with this proof?\" Thus statements such as \"Poor Sam...Trying to be a philosopher while ignoring the Ancient Greeks !!!!\" really mean nothing.\r\n\r\nThat said, this discussion is becoming interesting, even though you as usual resort to your \"proof by cut-and-paste\" style of argument that we have all grown to love.\r\n\r\n\r\n\r\nGamer\'s comment about infinite loops is actually very interesting. Consider the statement\r\n\r\nS: Statement S has five words\r\n\r\nThis looks ok until we try to replace S with it\'s referent:\r\n\r\n\"Statement S has five words\" has five words\r\n\r\nlooks correct, while\r\n\r\nS: \"Statement S has five words\" has five words\r\n\r\ndoesn\'t look quite as nice, and the problem only magnifies when we start unpacking the statement further. \r\n\r\n[Edit: actually, it only starts to look really bad once we unpack it twice:\r\nS: \"\"Statement S has five words\" has five words\" has five words\r\nis quite definately false]\r\n\r\n(On a side note, Hofstadter had an interesting statement uttered by a djin who asked a favor from \"GOD,\" which stands for \"GOD Over Djin,\" and thus asked the favor from an infinite number of djins above him.\r\nAlso related, the statement might be considered analogous to the formal language <S: aSb>, which is of course non-terminating, and so not adequately described.)\r\n\r\n\r\nOn the other hand, are \r\nS: Statement S has five words, and \r\nS: \"Statement S has five words\" has five words\r\n\r\ntruely equivalent? Clearly they are refering to different *sentences*, if not to different statements. We know from Quine (or is it Kripke? I forget) that sometimes referents cannot be simply inserted, even in a normal statement. Consider:\r\n\r\n\r\nThe president might not have become the president\r\n\r\nvs\r\n\r\nGeorge Bush might not have become the president.\r\n\r\n\r\nThe second statement looks unabiguously true in modal logic, while the first less so.\r\n\r\n(or more formally in intensional logic, the distinction between 1) In all worlds it is necessary that the president is the president vs. 2) In all worlds it is necessary that George Bush is the president).\r\n\r\nTherefore, if it might be the case that we cannot equate \"Statement S has five words\" with \"\"Statement S has five words\" has five words\", must we assume that we can equate S: S=>T with S:(S=>T)=>T? \r\nBut even if we can, is it such a bad thing? Godel\'s proof is no less valid just becuase\r\n\r\nS: S cannot be proven under F \r\n\r\nis equivalent to\r\n\r\nS: \"S cannot be proven under F\" cannot be proven under F\r\n\r\nindeed, it is quite necessary!\r\n\r\n\r\n\r\nAnd speaking of which (to bring it back to the puzzle at hand), one can generalize the exact sentence above to get to Godel\'s second incompleteness theorem.\r\n \r\nLob\'s theorem states that:\r\n\r\nD: If D is provable, then D\r\n\r\nis always provable (and you can see that his statement has much the same structure as my original statement S above).\r\n\r\nFrom here we can reach Godel\'s second proof that, in any consistant system F, F\'s own consistancy cannot be proven from within that system (don\'t ask me to try to prove this right here). Godel\'s second theorem is usually simply presented as a corollary to his first, but Lob\'s theorem can be used to springboard right into it.\r\n\r\n...\r\n\r\nNone of this is supposed to be a final answer to anything people have written, it\'s all just food for thought, but I hope that it goes further than a mis-guided attempt at a competition. I for one am extremely interested in all the directions one can go from such paradoxes.\n\nEdited on December 14, 2003, 12:17 am',10473,0);
INSERT INTO comment VALUES (10475,150,4374,'Richard','The crux of the matter','2003-12-13 23:51:03',3,'In the grid, replace each person by a real number. Choose a row and a column. There is exactly one grid position that is both in the chosen row and in the chosen column, and the real number r in that position is no greater than the maximum element M in the chosen row and no less than the minimum element m in the chosen column. Hence m <= r <= M so that m <= M. This is the crux of the matter. Now if we happened to choose the row to contain a minimum M\' of the row maxima, and the column to contain a maximum m\' of the column minima, we would have m\' <= r <= M\'. If the real numbers that replace the people are the people\'s heights, then we have an answer to the problem as originally formulated: A is always at least as tall as B. It is possible for m\' = r = M\' to occur as with the grid\r\n6 5\r\n5 4\r\nand in this case A = B. In fact, if the heights are all different in the M\' row and in the m\' column, then clearly A = B whenever m\' = r = M\'. Since the problem statement seems to imply that there is a unique minimum of the row maxima and a unique maximum of the column minima, we conclude m\'=M\' if and only if A = B. Thus if interpret the problem statement in this way and also insist that A and B be two different people, A is always strictly taller.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n \n\nEdited on December 14, 2003, 1:01 am',NULL,0);
INSERT INTO comment VALUES (10476,1543,4507,'Penny','re(2): Poor Sam...Trying to be a philosopher while ignoring the Ancient Greeks !!!!','2003-12-14 00:37:42',0,'This post has been superceded by \"Has self-referential logic ever achieved anything?\" \n\nEdited on December 14, 2003, 2:43 am',10474,0);
INSERT INTO comment VALUES (10479,1538,2682,'exoticorn','','2003-12-14 05:50:49',0,'Congratulations SilverKnight, I see you have decyphered my numbers :)\r\n\r\nTo everyone else: Go on, you are on the right track...',NULL,0);
INSERT INTO comment VALUES (10478,1543,3351,'Eric','Self-referential logic saved my life.','2003-12-14 02:46:32',0,'But Penny, 1+1 is 2. Isn\'t it?',10477,0);
INSERT INTO comment VALUES (10477,1543,4507,'Penny','Has self-referential logic ever achieved anything?','2003-12-14 01:14:03',1,'Except, of course, for Kurt Godel\'s wonderful theorem, \"which many would consider to be the most important mathematical proof ever written...\" ROTFLMAO !!!! Ever hear of the Pythagorean Theorem? Without Pythagoras and his theorem, there would be no theorem of Kurt Godel (and no Kurt Godel either, that anyone would remember. Without his Greek predecessors, Kurt Godel would have spent his life herding sheep. Even Einstein admitted that, had it not been for the Ancient Greek pioneers, modern mathematics and science would not have been discovered.) But I digress...\r\n \r\nEven Kurt Godel\'s theorem...What diseases has it cured (besides insomnia)? What economic policy decisions have come from it? What planets have been discovered using it? Have any engineering feats resulted from it?\r\n \r\nAnd then there was Bertrand Russell\'s much too clever paradox: \"Is the set of all sets that are not members of themselves, a member of itself or not?\" That one really opened the floodgates of human empowerment, didn\'t it? It did, however, give historian Will Durant a good opportunity to satirize old Bertrand, though, so it wasn\'t a total loss. \r\n \r\nWe owe it too the Greeks, that they invented abstract analytical thinking. But the Greeks also invented sophistry, as in \"S: If S is true, then God exists\", and that is not to their credit. Socrates gave his life in an attempt to oppose sophistry, and the Greek-Roman historian Polybius wrote \"Such men [sophists] really bring all of philosophy into disrepute. They distract from the study of ethics and politics that really do benefit students of philosophy. They spend all their time trying to invent useless absurdities.\" \r\n\r\nThat may be unfair. I do know one thing, though. I will not be sending any money to the Rev. Jerry Falwell, or the Vatican, based on Sam\'s proof of the existence of God. \r\n \r\nI\'d like to continue this post, but I have to drive Sylvester to the barber. Sylvester\'s barber shaves all the men in our town, and only the men, who do not shave themselves. (Does this barber shave himself? Hmmmm.... Let\'s not get all lathered up about it!) \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\n\nEdited on December 14, 2003, 3:12 am',NULL,0);
INSERT INTO comment VALUES (10480,1333,4064,'rerun141','first soloution','2003-12-14 12:30:07',1,'state\r\nt a\r\ni r\r\nf l\r\nfairy\r\n',NULL,0);
INSERT INTO comment VALUES (10481,1333,3992,'Jane Doe','One solution (I think)','2003-12-14 12:40:09',2,'R I V E R\r\nI E\r\nG L\r\nI A \r\nD E C A Y',NULL,0);
INSERT INTO comment VALUES (10482,1333,3992,'Jane Doe','re: first soloution','2003-12-14 12:42:34',0,'This was a cute problem, and.... we did good :-)',10480,0);
INSERT INTO comment VALUES (10483,1478,4788,'corey','logically....','2003-12-14 14:11:08',0,'Ben Jones\' first place fruit cake\r\nJames Best\'s second place chocolate cake\r\nNigel Stevens third place sponge cake\r\nVicky Andrews\' fourth place cheese cake',NULL,0);
INSERT INTO comment VALUES (10484,1333,4788,'corey','my ideas','2003-12-14 14:22:33',0,'going clockwise:\r\nstate, early, fairy, stiff\r\nriver, relay, decay, rigid',NULL,0);
INSERT INTO comment VALUES (10485,1522,4788,'corey','re: different approach','2003-12-14 14:30:30',0,'I worked this using similar triangles and reached the answer of approximately 4.087 feet from the wall to give a max height of 11.283 feet, but I like Scott\'s solution better. I think his answer justifies the wording of the problem best.',10355,0);
INSERT INTO comment VALUES (10486,1543,1626,'Gamer','re: Self-referential logic saved my life.','2003-12-14 14:31:21',0,'Wow! What a great postulate! If we didn\'t know that, we wouldn\'t be able to add, subtract, multiply and divide! So isn\'t that the best?\r\n\r\nTo Someone: No, mainly because the barber is a girl.\r\n\r\nI think that\'s interesting Sam. I think that logic is too hard for me to understand. Without postulates I am stuck, so I can\'t really approach things that define themselves. Just ignore Someone (who has done very well by posting many posts until this recent one about Someone Else and in submitting problems that are already on the site) in these recent posts. :)\r\n\r\nIn one of my problems, I am defining a number in terms of itself with stuff done to it. (Called \"Power to the 2\" currently, with a pid of 1525) which is also interesting.',10478,0);
INSERT INTO comment VALUES (10487,1333,4797,'m','I think I have both solutions','2003-12-14 14:49:24',0,'Across Down\r\n1. river 1. rigid \r\n3. decay 2. relay\r\n\r\nAcross Down\r\n1. state 1. stiff \r\n3. fairy 2. early',NULL,0);
INSERT INTO comment VALUES (10488,1543,4507,'Penny','HEY, THEY JUST CAUGHT \"GAMER\" IN IRAQ !!','2003-12-14 15:16:07',0,'Barb removed by Penny.\n\nEdited on December 17, 2003, 9:29 pm',NULL,0);
INSERT INTO comment VALUES (10579,1543,4507,'Penny','Kripke solved it a long tome ago, Tristan.','2003-12-17 21:40:20',0,'(...long \"tome\" ago was a typo, but a funny one...)\r\n[btw, I just removed that nasty crack about Gamer and Iraq. Unfortunately I cannot remove the Subject line...]\r\n\r\nSam wrote: \"5. This is in contradiction with 1., so S cannot be false. 6. Therefore S is true.\"\r\n \r\nSam is using classical logic, the formal logic in which sentences of a formal language have exactly two possible truth values (TRUE, FALSE). On this basis he makes the dizzying leap from (5.) to (6.) Kripke\'s revision uses a 3-valued logic with the truth values TRUE, FALSE and NEITHER. It\'s obvious that Kripke\'s modern logic should be used here, not Sam\'s classical logic. Then we wouldn\'t get caught up in a paradox. \r\n\r\n\n\nEdited on December 17, 2003, 9:43 pm',10576,0);
INSERT INTO comment VALUES (10489,1543,2716,'Federico Kereki','The error','2003-12-14 19:35:24',3,'The error is in (6); if S isn\'t false, it doesn\'t follow that it must be true, and the classic example for this is \"THIS SENTENCE IS FALSE\".',NULL,0);
INSERT INTO comment VALUES (10490,698,4772,'Stephen Morris','Analytic General Solution','2003-12-14 21:37:55',3,'I am ignoring trivial solutions where the two numbers are equal, although strictly speaking they are allowed by the question.\r\n\r\nThe following gives all solutions, a little thought will show that 10, 6 is the smallest solution.\r\n\r\n\r\nChoose x, y, n positive integers where x and y have no common factors and y>x>0. The following algorithm gives a different solution for each choice of x, y and z. All solutions are given by this method so there¡¦s a one to one relationship between choices of x, y and z and solutions.\r\n\r\nI need to define a few bits of notation, although I only use some of them in the proof.\r\n\r\n x^y x raised to the power of y\r\n e.g. 2^3 = 8, 5^2 = 25\r\n\r\nx rem n the remainder when x is divided by n, \r\nE.g. 9 rem 2 = 1, 9 rem 5 = 4.\r\n\r\nx „k y mod n x and y give the same remainder when divided by n, \r\ni.e. (x rem n) = (y rem n)\r\nE.g. 9 „k 14 mod 5\r\n\r\n x | y x divides y exactly leaving no remainder\r\ni.e. y rem x = 0, x „k 0 mod y\r\n E.g. 5 | 10, 3| 9, 3 | 15\r\n\r\n x ~| y x does not divide y exactly\r\n i.e. not (x | y)\r\n E.g. 3 ~| 10\r\n\r\n x, y co-prime x and y have no common factors\r\n e.g. 3, 4 are co-prime, \r\n9, 15 are not co-prime because they are both divisible by 3\r\n\r\n\r\nPut z = 3y^2 ¡V x^2.\r\n\r\nNow for the hard bit, you need to factorise x, y and z into their prime factors. For each prime factor also calculate the index, that is the highest power that divides the number. For example 12 = 2^2 * 3 so the prime factors are 2 and 3 with indices 2 and 1 respectively.\r\n\r\nWe are going to calculate a multiplier, called H, which will turn x and y into the basis for a solution. \r\n\r\nStart with H = 1.\r\n\r\nFor each prime, p, that divides y with index I adjust H as follows. \r\n\r\n If p = 2 and 3 | I then \r\nmultiply H by 2^6\r\nelse \r\nmultiply H by 2^( 4I rem 6 )\r\n\r\n\r\nIf 3 divides x with index I, adjust H as follows. \r\n Multiply H by p^( 3(I rem 2) )\r\n\r\nFor each prime, p, that divides x with index I, adjust H as follows. \r\n Multiply H by p^( I rem 6)\r\n\r\nFor each prime, p, that divides z with index I, and does not dived x, adjust H as follows. \r\n Multiply H by p^( 3(I rem 2) )\r\n\r\n\r\nNow put \r\n a = (y + x) * H * n^6 / 2\r\n b = (y - x) * H * n^6 / 2\r\n\r\nYou will find that a^2 ¡V b^2 is a cube and a^3 ¡V b^3 is a square.\r\n\r\n\r\n\r\nExample 1:\r\n Choose y = 2, x = 1.\r\n\r\n z = 3 * 2^2 + 1^2 = 3*4 + 1 = 13\r\n\r\n 2 | y with py = 1 so choose ph = 4\r\n\r\n 13 | z and 13 ~| x with pz = 1 so choose ph = 3\r\n\r\n This gives h = 2^4 * 13^3\r\n\r\n a = h(y + x)/2 = 2^4 * 13^3 * (2 + 1)/2 = 2^3 * 3 * 13^3\r\n b = h(y - x)/2 = 2^4 * 13^3 * (2 - 1)/2 = 2^3 * 13^3\r\n\r\n a^2 ¡V b^2 = 2^6 * 13^6 * (9 ¡V 1) = 2^9 * 13 ^6 = (2^3 * 13^2)^3\r\n a^3 ¡V b^3 = 2^9 * 13^9 * (27 ¡V1) = 2^9 * 13^9 * 26 \r\n= 2^9 * 13^9 * 2 * 13 \r\n= 2^10 * 13^10 \r\n= (2^5 * 13^5)^2\r\n\r\nExample 2:\r\n Choose y = 4, x = 1\r\n\r\n z = 3 * 4^2 + 1 = 49 = 7^2\r\n\r\n 2 | y with py = 2 so choose ph = 2\r\n\r\n 7 | z and 7 ~| x with pz = 2 so choose ph = 0.\r\n\r\n This gives h = 2^2 = 4.\r\n\r\n a = h(y + x)/2 = 4( 4 + 1 )/2 = 10\r\n b = h(y ¡V x)/2 = 4( 4 ¡V 1 )/2 = 6\r\n\r\n 10^2 ¡V 6^2 = 64 = 4^3\r\n 10^3 ¡V 6^3 = 784 = 28^2\r\n\r\n\r\n\r\n\r\n\r\nProof\r\n\r\n\r\nIf a and b are a solution then we have \r\n\r\n1. a^2 ¡V b^2 = c^3\r\n2. a^3 ¡V b^3 = d^2\r\n\r\nPut \r\n3. h = hcf (a - b, a + b)\r\n4. x = (a ¡V b)/h\r\n5. y = (a + b)/h\r\n6. Z = 3y^2 + x^2\r\n\r\nReverse mapping is\r\n7. a = h(y + x)/2\r\n8. b = h(y - x)/2\r\n\r\nSo\r\n9. h^2 xy = c^3\r\n10. h^3 xZ = ( 2d )^2\r\n\r\nNote that multiplying x and y by a sixth power will give another solution, so we should just look for solutions where h is minimal. We can then multiply by n^6 to give other solutions. This will always give unique solutions because (hx/hy) = x/y is uniquely determined by x and y, remember x and y are co-prime.\r\n\r\nWe are now going to consider how many times a prime number, p, divides into each of the numbers in the equation.\r\n\r\nWe define px to be the number of times p divides into x, py to be the number of times p divides into y and pz to by the number of times p divides into z.\r\n\r\n9. => 3 | px + py for all primes, p, which divide x or y.\r\n\r\n\r\nConsidering 10. we know that h^3 xZ is a square. As we are going for a minimal solution we need only consider factors of x, y and Z.\r\n\r\np | y => 3ph = 2pd „Æ ph „k 0 mod 2\r\n 3 | 2ph + py „Æ ph „k py mod 3\r\n\r\n „Æ ph „k 4py mod 6\r\n\r\np | x and p <> 3\r\n => 3ph + px = 2pd „Æ ph „k px mod 2\r\n 3 | 2ph + px „Æ ph „k px mod 3 \r\n\r\n „Æ ph „k px mod 6\r\n\r\np | x and p = 3\r\n„à 3ph + 1 + px = 2pd „Æ ph „k px + 1 mod 2\r\n3 | 2ph + px „Æ ph „k px mod 3\r\n\r\n „Æ ph „k 3px mod 6\r\n\r\np | Z, p ~| x (p could divide x if p = 3)\r\n => 3ph + pZ = 2pd „Æ ph „k pZ mod 2 where Z = (3y^2 + x^2)/h^2\r\n 3 | 2ph „Æ ph „k 0 mod 3\r\n\r\n „Æ ph „k 3pZ mod 6\r\n\r\nThis ensures that h^ 3 xZ is a square. We have also to make sure it is an even square. This will be true if any of the following are true:\r\n\r\ni) x is even.\r\nii) x and y are both odd, which makes Z even.\r\n\r\nThis leaves the case where y is even and x is odd. x and Z will be odd so we must make sure that h is even. This is the first case where p = 2 and p | y. We have ph „k 4py mod 6. We must ensure ph is not zero. This can only be true if py is divisible by 3 which gives ph „k 0 mod 6. So in this case we must choose ph = 6, rather than zero.\r\n\r\nSo for any co-prime x and y we have a unique minimal way of choosing h as follows.\r\n\r\n If p | y then\r\n if p = 2 and 3 | py choose ph = 6\r\nelse choose ph = 4py rem 6\r\n\r\nIf p | x and p <> 3 choose ph = px rem 6\r\n\r\nIf p | x and p = 3 choose ph = 3px rem 6\r\n\r\nIf p | Z and p ~| x choose ph = 3pZ rem 6\r\n\r\n\r\nExample 1:\r\n Choose y = 2, x = 1.\r\n\r\n z = 3 * 2^2 + 1^2 = 3*4 + 1 = 13\r\n\r\n 2 | y with py = 1 so choose ph = 4\r\n\r\n 13 | z and 13 ~| x with pz = 1 so choose ph = 3\r\n\r\n This gives h = 2^4 * 13^3\r\n\r\n a = h(y + x)/2 = 2^4 * 13^3 * (2 + 1)/2 = 2^3 * 3 * 13^3\r\n b = h(y - x)/2 = 2^4 * 13^3 * (2 - 1)/2 = 2^3 * 13^3\r\n\r\n a^2 ¡V b^2 = 2^6 * 13^6 * (9 ¡V 1) = 2^9 * 13 ^6 = (2^3 * 13^2)^3\r\n a^3 ¡V b^3 = 2^9 * 13^9 * (27 ¡V1) = 2^9 * 13^9 * 26 \r\n= 2^9 * 13^9 * 2 * 13 \r\n= 2^10 * 13^10 \r\n= (2^5 * 13^5)^2\r\n\r\nExample 2:\r\n Choose y = 4, x = 1\r\n\r\n z = 3 * 4^2 + 1 = 49 = 7^2\r\n\r\n 2 | y with py = 2 so choose ph = 2\r\n\r\n 7 | z and 7 ~| x with pz = 2 so choose ph = 0.\r\n\r\n This gives h = 2^2 = 4.\r\n\r\n a = h(y + x)/2 = 4( 4 + 1 )/2 = 10\r\n b = h(y ¡V x)/2 = 4( 4 ¡V 1 )/2 = 6\r\n\r\n \r\n\r\nComments:\r\n\r\n1. I think this could possibly be simplified by putting h = hcf( a, b ) rather than hcf ( a + b, a ¡V b). They are the same except for a factor of 2. This could avoid the nasty treatment of 2 differently when it divides y.\r\n\r\n2. A little consideration will show that 10, 6 is the smallest non-trivial solution.\r\n\r\n3. This approach is a bit nasty as you have to factorise into prime factors, which is not exactly pretty from a mathematical viewpoint and is also slow from a computing viewpoint (if you care about that). There may well be a prettier solution, but I haven¡¦t found one yet.\r\n',NULL,0);
INSERT INTO comment VALUES (10491,698,4772,'Stephen Morris','re: Analytic General Solution','2003-12-14 21:42:23',0,'A couple of characters came out wrong.\r\n\r\n,,k should be the \'equivalent to\' symbol\r\n\r\niV should be the minus sign.',10490,0);
INSERT INTO comment VALUES (10492,1312,4804,'manuel','solution','2003-12-15 01:18:11',0,'alicia got perfect!!',NULL,0);
INSERT INTO comment VALUES (10493,599,4804,'manuel','let me try!','2003-12-15 01:27:02',0,'12 0 0\r\n4 8 0\r\n4 3 5\r\n9 3 0\r\n9 0 3\r\n1 8 3\r\n1 6 5\r\n6 6 0',NULL,0);
INSERT INTO comment VALUES (10494,1409,4804,'manuel','let me guess','2003-12-15 01:41:13',0,'I think 10 is the fewest number of questions possible on each quiz. ',NULL,0);
INSERT INTO comment VALUES (10495,1543,4627,'donnmike','my thoughts','2003-12-15 02:11:29',0,'i\'m a newbie to this site, and i don\'t know much about logic, but what i first thought about this problem is that the statement can\'t be contingent on itself. not that it can\'t refer to itself as others have commented. that\'s why saying \"this statement has five words\" is allowed. whether the statement has five words or not does not matter to the statement.',NULL,0);
INSERT INTO comment VALUES (10496,1163,4805,'Michael Biserov','Turbo Pascal','2003-12-15 02:44:47',3,'Hi,\r\nHere is a solution compiled with Turbo Pascal 7.1\r\n\r\nuses crt; var i: integer;\r\nconst str: array[0..8] of string=(\r\n\'uses crt; var i: integer;\',\r\n\'const str: array[0..8] of string=(\',\r\n\'begin clrscr;\',\r\n\'for i:=0 to 2 do writeln(str[i]);\',\r\n\'for i:=0 to 8 do\',\r\n\'if i<>8 then writeln(chr($27)+str[i]+chr($27)+chr($2C))\',\r\n\'else writeln(chr($27)+str[i]+chr($27)+chr($29)+chr($3B));\',\r\n\'for i:=3 to 8 do writeln(str[i]);\',\r\n\'readkey; end.\');\r\nbegin clrscr;\r\nfor i:=0 to 2 do writeln(str[i]);\r\nfor i:=0 to 8 do\r\nif i<>8 then writeln(chr($27)+str[i]+chr($27)+chr($2C))\r\nelse writeln(chr($27)+str[i]+chr($27)+chr($29)+chr($3B));\r\nfor i:=3 to 8 do writeln(str[i]);\r\nreadkey; end.',NULL,0);
INSERT INTO comment VALUES (10497,1543,4804,'manuel','assumption','2003-12-15 02:51:36',0,'looking at the statement 2-6, such were derived from the assumption that S is false( statement 1), however from statement 6-9, prior assumption (statement 1) was contradicted. \r\n\r\nStatement 7-9 were based solely from statement 6, contatry to the first assumption where all prior statements were derived in the first place. This is where the error is. ',NULL,0);
INSERT INTO comment VALUES (10498,1543,3372,'Sam','re: The error; re: assumption','2003-12-15 04:43:13',0,'Federico, while it is certainly true that the two paradoxes are related, one difference is that \"This statement if false\" can not only not be false but also not be true, by it\'s very nature. This proof, however, doesn\'t contain within it any internal contradictions, the paradoxicalness must be seen from the outside.\r\n\r\nManuel, I\'m not sure what you mean, but it is a common way of solving logical proofs to split an \'OR\', then show that one side leads to a contradiction, and therefore prove the other side. We could take Descarte\'s proof (modified) as an example: Either I am or I am not. Let\'s suppose that I am not. If so, I can\'t be pondering this question. Since I am pondering it, we have a contradiction. Therefore I am. \r\nIn the proof above, we start with \"either S is ture or it is false.\" It then goes on to show that you get a contradiction if S were false, and so proves that it must be true.\r\n\r\n\r\nIf it makes it any better for anyone, the proof can also be done in the reverse manner (but it can be a little more confusing):\r\n\r\nS: If S is true then God exists.\r\n\r\n1. Let us suppose that S is true (P1)\r\n\r\n2. By modus ponens, God would have to exist. (by premise P1)\r\n\r\n3. Therefore we can say that if S were true, God would have to exist. (with no premises)\r\n\r\n4. This is exactly what S says, so S is True, with no premises (so therefore we have now proved S, instead of merely supposing it. Ie, nothing relies on our having said \"let us suppose S\").\r\n\r\n5. S must be true so blah blah blah so God must exist.\r\n\r\n\r\nThat might be less intuitive to some, granted, but is actually equally valid in standard logic.\r\n\n\nEdited on December 15, 2003, 4:49 am',10497,0);
INSERT INTO comment VALUES (10499,1427,2839,'FatBoy','First Thoughts','2003-12-15 08:55:22',1,'Someone will probably solve this right away so I want to get my first thoughts so you folks won’t think I never contribute...\r\n\r\nAt least four of the six respondents must be liars. Here’s why. Since they all identify themselves as having been first there can be no more than one Knight. \r\nIf there is more than one Knave, their answers for every second questing would have to line up unless they were lying in different (ie one lies to the first third and fifth questions the other lies to the second fourth and sixth) no such matching pattern exists so there is either only one knave or two and one answered the first question truthfully which means there can not be a knight…\r\n',NULL,0);
INSERT INTO comment VALUES (10500,1427,3172,'SilverKnight','Full Solution','2003-12-15 09:19:54',3,'The answer is:\r\nA F D C B E\r\n\r\nA is a Knave, and all the others are liars\r\n____________________________________________\r\n\r\nSince SOMEONE must have won, only one of them can have gotten the first one correct.\r\n\r\nTherefore, there is either zero or one knights. Also, since one told the truth in the first position, they can\'t ALL be liars.\r\n\r\nCase (1): If there is one knight,\r\n then one of the six people have the actual order, and we merely try each in succession.\r\n case (1.1):\r\n if A is the knight, then B told the truth in only the 4th position. impossible\r\n case (1.2):\r\n if B is the knight, then A told the truth in only the 4th position. impossible\r\n case (1.3):\r\n if C is the knight, then B told the truth in only the 2nd position. impossible\r\n case (1.4):\r\n if D is the knight, then C told the truth in only the 5th position. impossible\r\n case (1.5):\r\n if E is the knight, then D told the truth in only the 6th position. impossible\r\n case (1.6):\r\n if F is the knight, then A told the truth in only the 2nd position. impossible\r\n\r\n Therefore Case (1) isn\'t the case. There is no knight, and at least one knave.\r\n\r\n\r\nCase (2):\r\n (let X be an unknown letter) there are only two possibilities in each case 2.x.x,\r\n because the other possible 4 combinations would let each person lie twice in six times.\r\n\r\n Case (2.1) If A is a knave and told the truth in the first position: A X D X B X\r\n Case (2.1.1) A E D F B C\r\n impossible \'cause then C told the truth in only 4th position.\r\n Case (2.1.2) A F D C B E\r\n POSSIBLE - A is a Knave and tells the truth first, the others are all liars.\r\n\r\n Case (2.2) If B is a knave and told the truth in the first position: B X F X C X\r\n Case (2.2.1) B E F A C D\r\n impossible \'cause then D told the truth in 2nd and 3rd position.\r\n Case (2.2.2) B A F D C E\r\n impossible \'cause then D told the truth in only 3rd position.\r\n\r\n Case (2.3) If C is a knave and told the truth in the first position: C X E X A X\r\n impossible can\'t be because D agrees in only one of the positions.\r\n\r\n Case (2.4) If D is a knave and told the truth in the first position: D X F X A X\r\n impossible can\'t be because C agrees in only one of the positions.\r\n\r\n Case (2.5) If E is a knave and told the truth in the first position: E X A X F X\r\n Case (2.5.1) E D A C F B\r\n impossible \'cause then C told the truth in only 6th position.\r\n Case (2.5.2) E C A B F D\r\n impossible \'cause then D told the truth in only the 4th position.\r\n\r\n Case (2.6) If F is a knave and told the truth in the first position: F X B X E X\r\n Case (2.6.1) F A B D E C\r\n impossible \'cause then D told the truth in only the 6th position.\r\n Case (2.6.2) F D B C E A\r\n impossible \'cause then B told the truth in 2nd and 6th position.\n\nEdited on December 15, 2003, 9:22 am',NULL,0);
INSERT INTO comment VALUES (10502,1427,1301,'Charlie','... and the computer way.','2003-12-15 09:28:25',0,'The answer is also provided by running:\r\nDECLARE FUNCTION eval$ (s1$, s2$)\r\nDATA ACDEBF\r\nDATA BDFECA\r\nDATA CDEFAB\r\nDATA DEFBAC\r\nDATA EBADFC\r\nDATA FCBAED\r\nCLS\r\nFOR i = 1 TO 6\r\n READ order$(i)\r\nNEXT\r\n\r\nFOR winner = 1 TO 6\r\n good = 1\r\n FOR speaker = 1 TO 6 \' evaluate if winner is knight\r\n id$ = eval$(order$(speaker), order$(winner))\r\n IF id$ = \"-\" THEN good = 0: EXIT FOR\r\n NEXT speaker\r\n IF good THEN PRINT order$(winner)\r\n \' evaluate if winner is knave\r\n var$ = MID$(order$(winner), 2, 1) + MID$(order$(winner), 4, 1) + MID$(order$(winner), 6, 1)\r\n winsays$ = order$(winner)\r\n FOR perm = 1 TO 2\r\n var$ = MID$(var$, 2) + LEFT$(var$, 1)\r\n FOR psn = 1 TO 3\r\n MID$(winsays$, 2 * psn, 1) = MID$(var$, psn, 1)\r\n NEXT psn\r\n good = 1\r\n FOR speaker = 1 TO 6\r\n id$ = eval$(order$(speaker), winsays$)\r\n IF id$ = \"-\" THEN good = 0: EXIT FOR\r\n NEXT speaker\r\n IF good THEN PRINT winsays$\r\n NEXT perm\r\nNEXT winner\r\n\r\nFUNCTION eval$ (s1$, s2$)\r\n e$ = \"-\": evenCt = 0: oddCt = 0\r\n FOR i = 1 TO 3\r\n IF MID$(s1$, 2 * i - 1, 1) = MID$(s2$, 2 * i - 1, 1) THEN oddCt = oddCt + 1\r\n IF MID$(s1$, 2 * i, 1) = MID$(s2$, 2 * i, 1) THEN evenCt = evenCt + 1\r\n NEXT i\r\n IF evenCt = 3 THEN\r\n IF oddCt = 3 THEN\r\n e$ = \"knight\"\r\n ELSEIF oddCt = 0 THEN\r\n e$ = \"knave\"\r\n END IF\r\n ELSEIF evenCt = 0 THEN\r\n IF oddCt = 3 THEN\r\n e$ = \"knave\"\r\n ELSEIF oddCt = 0 THEN\r\n e$ = \"liar\"\r\n END IF\r\n END IF\r\n eval$ = e$\r\nEND FUNCTION\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (10501,1427,1301,'Charlie','solution','2003-12-15 09:22:05',3,'The winner must be a knight or a knave as his first statement is true. Every odd numbered position he notes (counting first as #1) is true. The non-winners must be liars or knaves as their first statements are false. Every odd numbered position they note must be false.\r\n\r\nRunners B and D agree on position 3. Since both can\'t be true, both must be false, and neither B nor D won.\r\n\r\nRunners C and D agree on position 5. By the same logic, neither C nor D won.\r\n\r\nThat leaves 3 possible winners: A, E or F. The winner could be either a knight or a knave. If he\'s a knight, his ordering is correct. If he\'s a knave, there are two possible derangements (in this case, as it\'s 3 positions, cyclic permutations) of the three even positions, to falsify his even numbered statements. So there are three possible winners and three possible orders for each possible winner, so there are 9 possible orders to check out.\r\n\r\nThe 9 possible orders have to be checked out by seeing if the remaining speakers all can be evaluated as either liars or knaves.\r\n\r\nIf runner A is the winner and a knight then speaker B\'s only true statement would be about position 4, so runner A can\'t be a knight.\r\n\r\nIf runner A is the winner and a knave, the true order could be either AEDFBC or AFDCBE. In the former case, speaker C\'s only true statement would be about position 4 and so can be neither liar nor knave. However if the order is AFDCBE, then every other runner/speaker is a liar. So a solution is AFDCBE with A being a knave, and everyone else liars.\r\n\r\nAs far as uniqueness goes:\r\nIf E were the winner and a knight, the order would disagree with all speaker D\'s statements except the last. If E were a winner and the order was EDACFB, then speaker B\'s statements would be all wrong except the second position. If the order were ECABFD, then A\'s 2nd statement would be his only true one.\r\n\r\nIf the order were FCBAED, again speaker A\'s second statement would be his only true one. If the order were FABDEC, then speaker D\'s last statement would be his only true one, and if the order were FDBCEA, then speaker B\'s 2nd and 6th statements would be his only true ones.\r\n',NULL,0);
INSERT INTO comment VALUES (10503,1427,1183,'fwaff','Another solution','2003-12-15 10:50:51',3,'Looking at the previous solutions I pretty much used the same logic as FatBoy, SK and Charlie to work out the basics. ie.\r\n\r\n1. There are no knights\r\n2. There is one (and only one) knave of the form TFTFTF, which must be A, E or F\r\n3. There are no knaves of the form FTFTFT\r\n\r\nBut then I used a different (and simpler, therefore superior!!! ;-) ) approach to get the rest of the answer...\r\n\r\nThe above 3 basic statements mean that everybody lied about who came last - therefore by elimination E must have come last. Which means that neither E nor F can be the knave (since E appears in truth telling positions for both E & F). Thus A must be the knave.\r\n\r\nSo at this point we have A ? D ? B E\r\n\r\nWe also know that everybody lied about who came 4th - therefore by elimination C must have come 4th and F finished 2nd.\r\n\r\nSo the order is AFDCBE\r\n\r\nI can\'t wait to see what wonderful insight Dr Math can bring to the discussion. I\'d have a look myself, but I\'m not bright enough to use the search function.',NULL,0);
INSERT INTO comment VALUES (10504,1538,4360,'Gus','re: Full RESPONSE (answer continues to be hidden)','2003-12-15 11:00:04',3,'But, SK, it could be a good exercise...\r\n\r\nGoing back to the problem: If that was the case, I would \"eat the fruit and kiss the snake good night\" (\"Pretty Noose\" - Soundgarden).\r\n\r\n:)\r\n\r\n\r\nEdited on December 15, 2003, 12:21 pm\r\n\r\nEdited on December 15, 2003, 12:53 pm\n\nEdited on December 15, 2003, 1:53 pm',10443,0);
INSERT INTO comment VALUES (10505,1543,4627,'donnmike','statement 2','2003-12-15 12:24:14',0,'can you explain statement 2? why must S be true if it is false?',NULL,0);
INSERT INTO comment VALUES (10506,1333,4505,'Bob Genisot','Both Parts','2003-12-15 12:59:02',0,' R I V E R\r\n I _ _ _ E\r\n G _ _ _ L\r\n I _ _ _ A\r\n D E C A Y\r\n\r\nS T A T E\r\nO _ _ _ A\r\nL _ _ _ R \r\nI _ _ _ L\r\nD E C A Y',NULL,0);
INSERT INTO comment VALUES (10507,1542,4412,'krdmt5_000','Solution','2003-12-15 15:51:41',3,'1.) they all have vowels in them\r\n2.) none have the letter q (Q) in them\r\nand now time for some pointless java scripts.\r\n√³∞∑π∞>≤³∞≤∑π√²³≥≤∞±±><',NULL,0);
INSERT INTO comment VALUES (10508,1427,4412,'krdmt5_000','','2003-12-15 15:57:56',3,'dont ask why but im pretty sure the correct order is...\r\n\r\n B D F E A C\r\n\r\nnow time for some pointless java scripts\r\n¡î©÷©ø¡Ä¡Ã¡Â>¡¾¢²¥ð¡¾¡Ä¡Ã<>©ø©÷¡Â¡Ã¡Â¡¾¢²¥ð¡Ä\n\nEdited on December 15, 2003, 4:05 pm',NULL,0);
INSERT INTO comment VALUES (10509,469,4412,'krdmt5_000','','2003-12-15 16:19:11',0,'...In the afternoon the plumber called on me to collect his bill. As I had no other moey at home, I settled his account with the Hundred Rupee note that I had found... \r\n\r\nYou spelled money wrong.\r\n\r\nNow for some pointless java scripts√²∞≤≥±∑π∑±±∞≥>³<²³³<>≤≥≤∞∑π∞±',NULL,0);
INSERT INTO comment VALUES (10510,469,4412,'krdmt5_000','...solution','2003-12-15 16:23:17',3,'100 rupee notes by the old lady and that is the only person who lost MOEY.\r\n\r\nnow for pointless java scripts...again\r\n√²³²>≥±≤<²³±≤≥∞±π√³≥><∞±<∑≥∞>±∑≤',NULL,0);
INSERT INTO comment VALUES (10511,1542,4507,'Penny','The real solution (no computer program used)','2003-12-15 16:27:06',3,'Consider the following string of 52 letters (a-z repeated). \r\n\r\nabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz\r\n\r\n1. For each of the words win, won, nor, ..., fusion, replace each letter with the letter 6 places down. \"win\" becomes \"cot\". Now replace each letter in \"cot\" with the letter 20 places down in the string. Then \"cot\" becomes \"win\". It\'s a win-win proposition!! Similarly for all the other words....(\"fusion\" becomes \"layout\" (down 6), and \"layout\" becomes fusion (down 20).) \r\n\r\n2. Take each of the letters in the words be, ova, vex, ..., abjurer, find its first occurrence in the string, then replace it with the letter 13 places down in the string. Then do the same to the resulting word. \"be\" becomes \"or\" and \"or\" becomes \"be\" again. \"ova\" becomes \"bin\" and \"bin\" becomes \"ova\"....\"abjurer\" becomes \"nowhere\", and \"nowhere\" becomes \"abjurer\".\r\n\r\n\r\n\r\n\n\nEdited on December 15, 2003, 4:55 pm',NULL,0);
INSERT INTO comment VALUES (10512,1542,3386,'Victor Zapana','re: The real solution (no computer program used)','2003-12-15 18:56:02',0,'hmm this solution looks fine to me. tho the 20 places down things is a lil unnecessary, coz 20+6= 26, and the 26th position after a letter technically will be the same letter. like wise for 13+ 13. So i think u just need the 6 places down and the (only 1)13 places down. ',10511,0);
INSERT INTO comment VALUES (10513,1036,4798,'patricia janik','re: what about this','2003-12-15 19:39:33',0,'another work is PAYPHONE = 100 DO YOU HAVE ANY MORE\r\nPATSY J',8383,0);
INSERT INTO comment VALUES (10514,1036,4798,'patricia janik','$1.00 WORDS','2003-12-15 19:41:40',0,'i NEED WORDS NOT CODES, I DON\'T KNOW HOW TO PROGRAM THE CODES... PLEASE HELP',NULL,0);
INSERT INTO comment VALUES (10515,1543,3372,'Sam','re: statement 2','2003-12-15 20:03:01',0,'Hey Donmike,\r\n\r\nthis is a sometimes contriversial but quite standard rule in logic. Specifically, if you have an If...Then statement, the only way that it can be false is if the first part, the antecedent, is true and the concequence is false. Thsi means that the statement\r\n\"If it is sunny tomorrow I will play soccer\"\r\nwill only be false if it IS sunny tomorrow yet I DON\'T play soccer. Any other combination of events will result in the statement being called true (it is sunny and I play, it isn\'t sunny and I don\'t play, or it isn\'t sunny and I do play).\r\n\r\nA consequence of this is that if the first part of the conditional is false, the statement will always be true.\r\nTherefore, in the argument above, we said \"supposer S is false.\" This means that any conditional with \"S is true\" in the beginning will always be true (still asumming that S is false). We then find that we get a contradiction, so S must be true.',10505,0);
INSERT INTO comment VALUES (10516,1427,4507,'Penny','Two independent solutions (No computer assistance)','2003-12-15 20:46:54',3,'(1) All six are Liars. The race ended in a dead heat - a six-way tie. (Just kidding...But this puzzle would have been so much improved if that WERE the answer. Somehow make it so that every possible finishing order leads to a contradiction, so that only those imaginative enough to picture a 6-way tie would solve it. But as it is, solving this puzzle just involves mechanically eliminating the possibilities. It comes by its 2.6 rating honestly.)\r\n\r\n(2) Assuming ties are not possible, they finished A-F-D-C-B-E. A is a Knave and all the others are liars. There are no Knights, Silver or otherwise.\r\n \r\nExplanation: \r\nThey can\'t all be Knights, since they disagree. Since someone is telling the truth about the first place finisher, they can\'t all be Liars. There is at least one Knave. \r\n\r\nAs usual, we solve this problem by ignoring the boring Liars and the equally boring Knights, and concentrate on the interesting Knaves.\r\n\r\nThere are only 24 possible ways they could have finished, 4 each gotten by assuming that each of the 6 is a Knave. Of these, only one is possible, given the constraints of the puzzle. So the answer is: They finished A-F-D-C-B-E. A is a Knave and all the others are liars. \r\n\r\nHere are the other 23 possibilities: \r\n\r\nIf A-E-D-F-B-C, then C told 3 consecutive lies and then the truth. \r\n \r\nIf B-C-A-E-D-F, then B told the truth and then consecutive lies. \r\n \r\nIf D-C-B-E-A-F, then B told the truth followed by consecutive lies. \r\n \r\nIf B-A-F-D-C-E, then D told consecutive lies and then the truth. \r\n \r\nIf B-E-F-A-C-D, then D told a lie followed by consecutive truths. \r\n \r\nIf C-D-B-E-F-A, then A told consecutive lies and then the truth. \r\n \r\nIf F-D-C-E-B-A, then A told consecutive lies and then the truth. \r\n \r\nIf C-B-E-D-A-F, then A told consecutive lies followed by the truth. \r\n \r\nIf C-F-E-B-A-D. then D told consecutive lies followed by the truth. \r\n \r\nIf A-D-C-F-E-B, then A told the truth and then consecutive lies. \r\n \r\nIf E-D-A-F-C-B, then B told a lie, the truth, and then consecutive lies.\r\n \r\nIf D-C-F-E-A-B, then A told a lie, the truth, a lie, the truth, and two consecutive lies. \r\n \r\nIf D-B-F-C-A-E, then B two lies and then the truth. \r\n \r\nIf A-E-D-B-F-C, then A told the truth, a lie, the truth, and then consecutive lies.\r\n \r\nIf F-E-A-B-D-C, then E told two lies and then the truth.\r\n \r\nIf E-C-A-B-F-D, then A told a lie, the truth, and then consecutive lies. \r\n \r\nIf E-D-A-C-F-B, then B told a lie, the truth, and then consecutive lies. If F-B-E-D-A-C, then C told two lies and then the truth. \r\n \r\nIf A-B-F-D-E-C, then A told the truth and then consecutive lies. \r\n \r\nIf F-D-B-C-E-A, then B told a lie, the truth, and then consecutive lies. \r\n \r\nIf F-A-B-D-E-C, then D told consecutive lies, then the truth.\r\n \r\nIf E-C-F-A-B-D, then A told a lie, the truth and then consecutive lies. \r\n \r\nIf B-C-E-A-F-D, then A told a lie, the truth, and then consecutive lies. \r\n\r\n\r\n\r\n\r\n\r\n\n\nEdited on December 16, 2003, 12:53 am',NULL,0);
INSERT INTO comment VALUES (10517,1542,1301,'Charlie','Added question.','2003-12-15 20:54:38',4,'Of the words in the second group, which one has a unique characteristic that stands out?',NULL,0);
INSERT INTO comment VALUES (10518,1542,4507,'Penny','Added answers','2003-12-15 21:10:43',0,'\"be,ova,vex,nag,she,one,tang,rail,errs,ebbs, Pyrex,terra,Cheryl,abjurer\"\r\n \r\nWhich one stands out? Pyrex !!!! Pyrex, a trademark for \"material used for borosilicate glass and glassware resistant to heat, chemicals, and electricity\", is an important ingredient in the making of \"sexual toys\". It \"stands out\" (or should we say \"stands up\"?) in the same way Viagra does. Very funny !!! \r\n\r\nOther possibilities:\r\n\r\n\"be\" is the only 2-letter word\r\n\"abjurer\" is the only one with 3 vowels\r\n\"vex\" is the only one that describes the effect my quick solution of this puzzle had on Charlie\r\n\"ova\" is the only Latin plural word\r\n\"rail\" is the only one with the letter \"i\"\r\n\"abjurer\" is the only one with the letter \"j\"\r\n\"abjurer\" is the only one with the \"er\" ending\r\n\"she\" is the only gender-specific pronoun\r\n\"one\" is the only number\r\n\"one\" is the only non-gender-specific pronoun\r\n\"errs\" is the only one with more than one way to be pronounced\r\n\"tang\" is the only one that, when capitalized, is also the name of a Chinese Dynasty \r\n\"Cheryl\" is the only one not in the AOL (Merriam-Webster) online dictionary\r\n\"Cheryl\" is the only person\'s name\r\n\"Cheryl\" is the only 6 letter word\r\n\"Pyrex\" is the only trademark (\"tang\" is not capitalized, so it is not the breakfast drink beloved of astronauts)\r\n\"abjurer\" is the only 7 letter word \r\n \r\n...am I getting warmer ? \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\n\nEdited on December 15, 2003, 10:06 pm',10517,0);
INSERT INTO comment VALUES (10519,1428,4816,'Christopher Kostelec','Solution here','2003-12-15 23:01:10',0,'31. If you are asked to make a set of 5 rods, each rod has a set of numbers 1 to 31 on them. The top number is 31 due to you can only use up to 31. ',NULL,0);
INSERT INTO comment VALUES (10520,1543,4627,'donnmike','re(2): statement 2','2003-12-15 23:02:37',0,'are you sure? that isn\'t intuitive and seems wrong. i can see how the antecedent being false does not prove the statement false, but i don\'t see how it validates the statement. there\'s a difference between not proving something false, and proving something true. it would seem to me that both the antecedent and consequent need to be true for the statement to be true.\r\n\r\notherwise you could make the two statements:\r\nif it is above 80 degrees tomorrow it will be sunny\r\nif it is above 80 degrees tomorrow it will rain\r\n\r\nbut if it is below 80 degrees tomorrow then both statements would be true.',10515,0);
INSERT INTO comment VALUES (10521,1542,1301,'Charlie','re: Added answers','2003-12-15 23:07:13',0,'The specific uniqueness I have in mind has to do with the 13-letter-difference cypher scheme you had already found.',10518,0);
INSERT INTO comment VALUES (10522,1542,4507,'Penny','re(2): Added answers','2003-12-16 00:07:02',0,'\"vex\" is the only one that translates to a synonym of itself (\"irk\")\r\n\r\nHere they all are:\r\n\r\nbe=or; ova=bin; vex=irk; nag=ant; she=fur; one=bar; tang=gnat; rail=envy; errs=reef; ebbs=roof; Pyrex=Clerk; terra=green; Cheryl=Purell (a sanitizing gel); abjurer=nowhere.',10521,0);
INSERT INTO comment VALUES (10523,1543,4627,'donnmike','','2003-12-16 02:04:22',0,'',10520,0);
INSERT INTO comment VALUES (10524,1542,3136,'Popstar Dave','re(3): Added answers','2003-12-16 02:05:06',0,'\'Vex\' and \'irk\' the only synonyms?\r\nYou\'ve obviously never eaten a gnat before... very tangy!',10522,0);
INSERT INTO comment VALUES (10525,1543,4627,'donnmike','re(3): statement 2','2003-12-16 02:05:07',0,'and if the conclusion about the scenario that i described involving tomorrows weather is technically correct, that both statements are true, then clearly the problem with the original paradox about the existence of god is one of semantics. saying that the statement is \"logically true\" means something quite different than saying that the antecedent and consequent of the statement are factually true. so the argument fails at line #8 when the logical truthfulness of the statement is extended to the factual truthfulness of its parts.\r\n\r\nlike i mentioned, i don\'t know much about logic so i realize that what i just said might not make any sense, and might reveal my ignorance and make me sound arrogant, but i don\'t see a problem with it.\r\n\r\nalso, i\'m still sticking with my original comment that a statement can\'t be contingent on itself.',10520,0);
INSERT INTO comment VALUES (10526,1542,4507,'Penny','re(2): The real solution (no computer program used)','2003-12-16 03:47:53',0,'Of course you\'re right. I wasn\'t thinking. 6+20 and 13+13 will always get you back to the starting letter. ',10512,0);
INSERT INTO comment VALUES (10527,1529,2839,'FatBoy','answer','2003-12-16 08:34:03',3,'Woohoo,\r\nSK made one so easy even the Fatboy can do it:\r\n\r\nFor problem one,\r\nsetting x equal to the number of jars and y equal to the number of pencils we find:\r\n3x+1 = y and\r\n4(x-1) = y\r\ntwo equations, two unknowns x = 5jars and y equals 16 pencils\r\n\r\nfor number two:\r\n6x + 3 = y and\r\n9(x-2) = y\r\n\r\nso x = 7 jars and y = 45 pencils ...\r\n\r\nNow the rest of you can point out what I missed... there must be something\r\n',NULL,0);
INSERT INTO comment VALUES (10528,1529,3172,'SilverKnight','re: answer','2003-12-16 09:49:33',0,'NOOOO!!!!!!!\r\n\r\nFatBoy answered one of my submitted problems!!! It\'s gotta be one of the signs of the Apocalypse!',10527,0);
INSERT INTO comment VALUES (10529,1542,1301,'Charlie','re(3): Added answers','2003-12-16 09:56:17',0,'Cheryl -> Purely, not Purell',10522,0);
INSERT INTO comment VALUES (10530,1542,4507,'Penny','re(4): Added answers','2003-12-16 10:22:46',0,'I just wanted to see if you were awake, Charlie !!!!',10529,0);
INSERT INTO comment VALUES (10531,1529,4507,'Penny','Solution (MIT Supercomputer used)','2003-12-16 10:36:33',3,'x pencils, y jars\r\n \r\n(1) 4(y-1)=x, 3y+1=x\r\n x=16, y=5\r\n\r\n(2) 9(y-2)=x, 6y+3=x\r\n x=45, y=7 \n\nEdited on December 16, 2003, 10:38 am',NULL,0);
INSERT INTO comment VALUES (10532,66,4507,'Penny','This is a variant of a famous Bertrand Russell paradox','2003-12-16 11:03:04',3,'This is a dressing down in plain clothes of a famous Bertrand Russell paradox.\r\n \r\nA certain mathematician had devoted many years to producing an opus, his life\'s work, that was to explain all of reality based on set theory. As he was about to publish, along came a clever and malicious young Bertrand Russell. He said to him: \"Some sets are members of themselves - the set of all sets, for example. Some sets obviously are not members of themselves. Is the set of all sets that are not members of themselves, a member of itself or not?\" The mathematician was so discomfited by this, that he had to put a forward in his book that said in effect that the whole book was worthless.\r\n \r\nThe answer to Bertrand Russell\'s paradox is that we do not know whether the set of all sets that are not members of themselves, is a member of itself or not, since either choice involves a contradiction. The set of all sets that are not members of themselves, is therefore not well defined; therefore, it is not a set at all, since one of the ideas behind the primitive notion of a set is that it will always be possible to know whether a given object is a member of the set or not. That is the sine qua non of any set; you cannot have a set without that idea.\r\n \r\nApplying this logic to the barber riddle: if he shaves himself, there is a contradiction; if he does not shave himself, there is a contradiction; therefore his identification of himself as a barber who shaves all those, and only those, who do not shave themselves, is not well defined, and he cannot possibly be such a barber. The answer to the question \"If Bill follows this rule, will he shave himself or not?\" is that there is no \"if\". Bill cannot follow that rule. He must redefine himself as \"the barber who will shave all the town\'s residents who do not shave themselves, but not the ones who do, except for himself\". \r\n\n\nEdited on December 16, 2003, 11:09 am',NULL,0);
INSERT INTO comment VALUES (10533,1429,4317,'C.B.','Should be','2003-12-16 13:50:17',3,'The bottles line up like this (left to right):\r\n\r\nPoison, Wine, Poison, Forward potion, Poison, Wine, Backward potion\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (10534,1429,4505,'Bob Genisot','Process of Elimination','2003-12-16 14:14:09',0,'The big key is that the largest is second from the left, and the smallest is second from the right. Neither holds poison. The second from the left (largest) and second from the right are the same, meaning they are both wine or both poison. Since they can\'t be poison, they are both wine. Neither end bottle contains the forward potion, so the forward potion must be in the smallest bottle.\r\n\r\nIn order (from left to right)\r\nPoison,Wine,Poison,Forward,Poison,Wine,Backward',NULL,0);
INSERT INTO comment VALUES (10535,1429,1626,'Gamer','A Variation:','2003-12-16 15:13:43',0,'I was actually hoping to make changes to this before it got pushed, but evidently we were in a hurry. :) Here\'s another version of the problem.\r\n\r\nYou have entered a mysterious tunnel with your friend. As you get to the middle of the room, flames rise at both ends, disallowing you from exiting.\r\n\r\nOn a table you see a row of 7 bottles of potions,5 the same middle size, with one clearly smallest and another clearly largest. There also is a riddle.\r\n\r\n\"Danger lies before you, while safety lies behind,\r\nTwo of us will help you, whichever you would find.\r\nOne among us seven will let you move ahead,\r\nanother will transport the drinker back instead,\r\nTwo among our number hold only nettle wine,\r\nThree of us are killers, waiting hidden in line.\r\nChoose, unless you wish to stay here forevermore,\r\nTo help you in your choice, we give you these clues four\r\nFirst, however slyly the poison tries to hide\r\nYou will always find some on nettle wine\'s left side;\r\nSecond, different are those who stand at either end.\r\nBut if you would move onward, neither is your friend;\r\nThird as you see clearly, two are different size.\r\nNeither dwarf nor giant holds death in their insides;\r\nFourth, the second left and the second on the right\r\nAre twins once you taste them, though different at first sight.\r\n\r\nIf the smallest bottle is in the middle, which bottle will contain the potion to allow you to continue on in the tunnel, and which one will allow your friend to go backward in the tunnel? ',NULL,0);
INSERT INTO comment VALUES (10536,1529,1626,'Gamer','about it:','2003-12-16 15:27:27',0,'First of all, if anyone used a Supercomputer, it would be a very innefficient and bad idea to do so since this could be solved easily otherwise.\r\n\r\nIf you put 4 pencils in each jar, you will have 4 pencils too few.\r\nIf you put 3 pencils in each jar, you will have 1 pencil too many.\r\nA difference of 5 pencils for 1 pencil per jar. That means 5 jars and 16 pencils.',NULL,0);
INSERT INTO comment VALUES (10537,1429,4507,'Penny','Give em hell, Harry !!','2003-12-16 15:29:33',3,'Problems like these are best approached by stripping away the mumbo-jumbo and stating them symbolically.\r\n\r\nLet the bottles be, from left to right, a,b,c,d,e,f,g. \r\n\r\nAll are of different sizes. b is the largest. \r\nd is the smallest. Let T,U,V,W be their types. No bottle is of more than one type. One is type T. One is type U. Two are type V. Three are type W. Neither b nor d are type W. There will be one type W to the left of each type V. a and g are different types. a and g are not type T. b and f are of the same type. \r\n\r\nThe only assignment that is consistent with these statements is:\r\n\r\na(W) b(V) c(W) d(T) e(W) f(V) g(U)\r\n \r\nReplacing T with \"forward\", U with \"backwards\", \r\nV with \"wine\", and W with \"deadly\", the bottles are, from left to right:\r\n\r\ndeadly-wine-deadly-forward-deadly-wine-backwards\n\nEdited on December 16, 2003, 3:51 pm',NULL,0);
INSERT INTO comment VALUES (10540,1429,4505,'Bob Genisot','re: A Variation:','2003-12-16 15:53:00',0,'I believe the order remains the same (from left to right)\r\n\r\nPoison,Wine,Poison,Forward,Poison,Wine,Backward\r\n\r\nForward - Middle Bottle\r\nBackward - Bottle on Right Side',10535,0);
INSERT INTO comment VALUES (10538,1542,1567,'Bryan','re: Added question.','2003-12-16 15:34:46',0,'The one word in the second group that stands out IMHO is \"tang\", which when each letter is shifted 13 spaces, results in the reverse of itself letter for letter.',10517,0);
INSERT INTO comment VALUES (10539,1429,4788,'corey','i guess....','2003-12-16 15:38:17',0,'poison, nettle, poison, forward, poison, nettle, backward',NULL,0);
INSERT INTO comment VALUES (10541,1351,4412,'krdmt5_000','just one word...','2003-12-16 15:57:59',1,'THIS IS THE EASIEST QUESTION ON THIS ENTIRE WEB SITE.\r\nand now time for some pointless java scripts\r\n√²≥≤>±>³π∑∞∑∑±±≤≥³>∞>∑∑∑π',NULL,0);
INSERT INTO comment VALUES (10542,1542,4412,'krdmt5_000','re: The real solution (no computer program used)','2003-12-16 16:00:22',0,'mine works too...',10511,0);
INSERT INTO comment VALUES (10543,932,4412,'krdmt5_000','My solution','2003-12-16 16:06:26',3,'the smoke is moving south at 31 km/h because the direction and speed of the train dose not effact the smoke when there is an alternative force acting upon the smoke\r\nnow for some pointless java scripting:\r\n³<><≤≥≤≥±∞±∑\r\nNO THERE TRYING TO TAKE ME FROM THE KEYBOARD\r\n³<>≤≥≥≥...',NULL,0);
INSERT INTO comment VALUES (10544,973,4412,'krdmt5_000','solution?','2003-12-16 16:09:17',3,'Jim didnt dial from a phone...',NULL,0);
INSERT INTO comment VALUES (10545,1168,4412,'krdmt5_000','this is easy','2003-12-16 16:13:26',0,'1 2 3 4 5\r\n 6 7 8 9 10\r\n11 12 13 14 15\r\n16 17 18 19 20\r\n\r\nThe lettered route:\r\n\r\nA B A B A\r\nA B A B A\r\nB A B A B\r\nB A B A B\r\n\r\nIf a path were constructed that switched from A to B more than once, it would need to use either 8 or 13 as a cross over point for two reasons: First, there are only 2 cross over points from A to B that don\'t require 8 or 13 (12-9 and 14-7) and since 1 is an A and 10 is a B, you would need to cross over an odd number of times. Secondly, you would need to stop or start on 8 and 13 as part of the tour. In other words, you can\'t use 11-8-15 or 10-13-6 as part of your path because this would leave 5 or 16 unvisitable. This means that you can go from an A tile to a B tile or from a B tile to an A tile at most 4 times if there is any chance of a knight\'s tour to be constructed.\r\n\r\nSo the four cross overs are: 12-9, 14-7, (11 or 15)-8, (10 or 6)-13. If we wanted to cross over 3 times, and if both of the last two cross overs are used, then this leaves two possibilities; either 12-9 is used or 14-7 is used. \r\n\r\nSince 1-8 and 20-13 aren\'t used, then 1-12 and 9-20 must be used. 12-9 can\'t be used because then the sequence 1-12-9-20 would follow, and this would lead to a contradiction.\r\n\r\n14-7 can\'t be used as well if the last two crossovers are used because then the path must include (10 or 6)-13-16-7-14-5-8-(11 or 15) and then 4 and 17 will be unvisitable.\r\n\r\nNot being able to use either of the first two cross overs results in inability to use 3 cross overs, which is a contradiction. So, only one of the last two cross overs can be used, which means that both 12-9 and 14-7 need to be used. \r\n\r\nBut if 13-(10 or 6) isn\'t used, then the chain must contain (11 or 15)-8-5-14. 14-7 must be used because it\'s a cross over. 1-8 can\'t be used because 8 is already in the chain, so 1-12-9 must be the beginning of the chain since 12-9 is a crossover. 20-13-16-7 must be used because 1-8 can\'t be used. This leads to the chain of (11 or 15)-8-5-14-7-16-13-20. Again, 4 is isolated and can\'t be visited, leading to this situation as a contradiction.\r\n\r\nIf 13-(10 or 6) was used and (11 or 15)-8 wasn\'t used, then similar logic could be used because the grid is exactly the same when flipped such that 1 becomes 20, 5 becomes 16 and so on. In this situation 17 is the space that can\'t be visited.\r\n\r\nAll four situations where 3 of the 4 cross overs were used result in spaces unable to be visited, which means a knight\'s tour can\'t be accomplished with 3 cross overs. Since no more than 4 cross overs can be done, only an odd number of cross overs can happen since you need to start on A and end on B, and you can\'t cross over 3 times, you must visit all the As then go on to the Bs since you can only cross over once. \r\n\r\nThis allows the problem to be broken down further.\r\n\r\n\r\n1 3 5\r\n6 8 10\r\n 12 14\r\n 17 19\r\nRearranging this so knights moves are seen easier: \r\n /---8---\\\r\n / / \\ \\\r\n 1 | | 5\r\n | | | |\r\n 12-19 17-14\r\n | | | |\r\n | 10 6 |\r\n | \\ / |\r\n \\---3---/ \r\nThrough deduction it can be seen there are 7 half-routes:\r\n\r\n1 route for 1 to 12:\r\n1 8 5 14 17 6 3 10 12\r\n\r\n3 routes for 1 to 10:\r\n1 8 5 14 17 6 3 12 19 10\r\n1 12 19 8 5 14 17 6 3 10\r\n1 12 3 6 17 14 5 8 19 10\r\n\r\n1 route for 1 to 8:\r\n1 12 19 10 3 6 17 14 5 8\r\n\r\n2 routes for 1 to 6:\r\n1 12 3 10 19 8 5 14 17 6\r\n1 12 19 10 3 14 8 17 6\r\n\r\n1 route for 1 to 14:\r\n1 12 19 10 3 6 17 8 5 14\r\n\r\nThe other set of letters follows the same pattern, so these may be reflected over the horizontal middle of the board. Doing this shows that routes that end in 6 or 10 can match up with flipped-8 (13) and routes that end in flipped-6 (11) or flipped-10 (15) can match up with 8. Also, routes that end in 12 match up with flipped-14 (9) and routes that end in flipped-12 (7) match up with 14.\r\n\r\nSo this means the routes can be defined as 6-8 + 8-6 + 10-8 + 8-10 + 12-14 + 14-12, where a dash means the number of routs ending in one number times the number of routes ending in the other. This means the asnwer is (2*1)+(1*2)+(3*1)+(1*3)+(1*1)+(1*1) which equals 12. This means there are 12 knight\'s tours starting from 1 and ending in 20.\r\n\r\nim just kidding i stole this solution. HA HA HA ∑',NULL,0);
INSERT INTO comment VALUES (10546,1429,1626,'Gamer','re(2): A Variation:','2003-12-16 18:07:22',0,'Both are consistent with what is in the book (in case you cheated!), but how would you solve the second one?',10540,0);
INSERT INTO comment VALUES (10547,1543,4323,'Benjamin J. Ladd','God\'s existence:','2003-12-16 18:40:33',2,'The whole premise... \"if S is true (or even false)... then God exists\" has got to be one of the most humorous sentences that I think we (mankind) have ever uttered. I can only imagine God shaking His head from heaven (and probably chuckling softly)... And in fact, I shudder to think where we would all be without His grace.\r\n\r\nBut to continue on after that and go through steps 2-9 is just the punchline to a much deeper (and far dumber) joke. No insult to the real intellects (and my apologies to you all for this post) who really analyse such things, but here I must take leave from all of the logicians and respectfully defend my faith--albeit an unphilosophically simplistic one. And here it is, folks:\r\n\r\nGod exists.\r\n\r\nAs this statement is unconditionally true (and I believe entirely supportable by the preponderance of evidence that exists out there), to make it rely on any such conditional claims is absurd. In fact, even if no such evidence were given, the truth of God\'s existence would still remain an unconditional fact, unverifiable though it is.\r\n\r\nI hope you all have a Merry Christmas and happy holidays. Be kind to me in your replies. And remember: I\'m not a logician!\r\n\r\nGod bless,\r\nJordan',10525,0);
INSERT INTO comment VALUES (10548,1542,4507,'Penny','re(2): The real solution (no computer program used)','2003-12-16 18:45:24',1,'krdmt5_000: \"mine works too...\"\r\n \r\nYes it does. If our imaginations are active, we can often come up with multiple solutions to these puzzles. I am still fond of my solution to \"What\'s for sale?\", which was much more creative than the boring \"official solution\".\r\n \r\nHere is another solution to \"Words In Common 10\". This also works.\r\n\r\n1. None of the words words \"win, won, nor, fin, log, din, pun, ion, lug, boy, boa, bog, gun, fur, dug, bun, bus, mix, loam, quay, joey, foam, oafs, bomb, guff, hymn, buff, lion, wily, wolf, mocha, chain, munch, funny, bulls, mills, jimmy, fusion\" is found in the Preamble to the \r\nU.S. Constitution. \r\n\r\n2. Not one of the words \"be, ova,vex, nag, she, one, tang, rail, errs, ebbs, Pyrex, terra, Cheryl, abjurer\" was used in that \"Pencils and Jars\" puzzle.\r\n \r\n',10542,0);
INSERT INTO comment VALUES (10549,1543,4627,'donnmike','re: God\'s existence:','2003-12-16 21:03:57',0,'\"And remember: I\'m not a logician! \"\r\n\r\nobviously not. you have absolutely no clue! the problem has nothing to do with god\'s existence. the problem is about bad logic. it would make no difference if instead of saying \"if S is true then god exists\" it said \"if S is true then i am wearing underwear\". the same rules would apply and there would be a paradox, and we would be presented with the challenge of solving that paradox. \r\n\r\ni can\'t believe you took the time to write all that, and thought that much about the problem without realizing that it has nothing to do with god at all.',10547,0);
INSERT INTO comment VALUES (10550,1429,4825,'renuka','','2003-12-16 21:52:44',0,'my guess is (From left to right)\r\nbackward potion, wine, poison, forward potion, poison, wine, poison\r\nand just a thought- when they say nettle wine\'s left, shouldn\'t it be our right?',NULL,0);
INSERT INTO comment VALUES (10551,1429,1575,'DJ','re:','2003-12-16 22:40:53',0,'who\'s to say the bottles are facing us? i think they\'re facing away, so the bottles\' lefts and our lefts are the same...',10550,0);
INSERT INTO comment VALUES (10552,1429,4828,'Jennifer','re(2):','2003-12-17 00:10:26',0,'Well, really it doesn\'t matter which way is the bottles\' left. After all, the only bottle we care about is the one that lets us go forward, which is the center one in either case. If, however, Harry got a case of cold feet and wanted to go back then it would be critical to know which way was left in the clue. After all, he\'d either be drinking the backwards potion or the poison...',10551,0);
INSERT INTO comment VALUES (10553,569,4827,'Steve','This seems too easy, or is it?','2003-12-17 00:13:06',0,'First of all, the problem is not specific as to the number of locks the box may contain, it just states \"multiple\" meaning more than one. Then,assuming that you have several locks and their corresponding keys does not necessarily mean that all the locks you put on the box will require a key. So the logical answer would be to assign one of the multiple locks a combination in lieu of a key and the other locks will contain the keys inside of the locked box with the combination known only to the sender and the recipient. The only lock that is securing the box is that of the combination lock. Once the combination opens the box, the other keys can be removed. So, the only real security, unbeknownst to any mail carrier would be that of the combination lock since the remaining key locks could not be tested since the box could not be opened anyhow.',NULL,0);
INSERT INTO comment VALUES (10554,278,4827,'Steve','It\'s in the bag, baby...','2003-12-17 00:16:42',0,'Who says the teacher needs to keep the bag? Give the bag to the last kid with the orange in it!',NULL,0);
INSERT INTO comment VALUES (10555,1529,4828,'Jennifer','re: about it:','2003-12-17 00:17:55',0,'Or from a more formal mathematical presentation:\r\nlet j = #jars\r\nlet p = #pencils\r\nthen for problem 1 have 4(j-1) = p and 3j+1 = p. Solving for j have 4j-4 = 3j+1, or j=5. Then solving for p have 3(5)+1 = p = 16. Thus the answer shown above, 5 jars and 16 pencils.\r\n\r\nfor problem 2 have 9(j-2) = p and 6j+3 = p, so 9j-18=6j+3, so 3j=21, j=7. Then solving for p have 9(7-2) = p, 9(5) = p, so p=45. Thus the answer for problem 2 is seven jars and forty-five pencils.\r\n\r\nI agree that it would really be a waste of time to use a Supercomputer to solve this basic algebra problem.',10536,0);
INSERT INTO comment VALUES (10556,75,4507,'Penny','Achilles and the Tortoise !!!!!!!!!','2003-12-17 02:58:17',3,'As Sam has recently discovered (see \"Proof of Anything\"), those who try to be original thinkers while ignoring the Ancient Greeks, do so at their peril. Does this sound familiar?\r\n\r\n\"In a race in which the tortoise has a head start, the swifter-running Achilles can never overtake the tortoise. Before he comes up to the point at which the tortoise started, the tortoise will have got a little way, and so on ad infinitum.\" \r\n - Zeno of Elea, Ancient Greek philosopher, born 488 BC \r\n\r\nQuoting from the Internet Encyclopedia of Philosophy (http://www.utm.edu/research/iep/):\r\n \r\n\"Kant\'s, Hume\'s and Hegel\'s solutions to [Zeno\'s] paradoxes have been very stimulating to subsequent thinkers, but ultimately have not been accepted. There is now general agreement among mathematicians, physicists and philosophers of science on what revisions are necessary in order to escape the contradictions discovered by Zeno\'s fruitful paradoxes. The concepts of space, time, and motion have to be radically changed, and so do the mathematical concepts of line, number, measure, and sum of a series. Zeno\'s integers have to be replaced by the contemporary notion of real numbers. The new one-dimensional continuum, the standard model of the real numbers under their natural (less-than) order, is a radically different line than what Zeno was imagining. The new line is now the basis for the scientist\'s notion of distance in space and duration through time. The line is no longer a sum of points, as Zeno supposed, but a set-theoretic union of a non-denumerably infinite number of unit sets of points. Only in this way can we make sense of higher dimensional objects such as the one-dimensional line and the two-dimensional plane being composed of zero-dimensional points, for, as Zeno knew, a simple sum of even an infinity of zeros would never total more than zero. The points in a line are so densely packed that no point is next to any other point. Between any two there is a third, all the way \'down.\' The infinity of points in the line is much larger than any infinity Zeno could have imagined. The non-denumerable infinity of real numbers (and thus of points in space and of events in time) is much larger than the merely denumerable infinity of integers. Also, the sum of an infinite series of numbers can now have a finite sum, unlike in Zeno\'s day. With all these changes, mathematicians and scientists can say that all of Zeno\'s arguments are based on what are now false assumptions and that no Zeno-like paradoxes can be created within modern math and science. Achilles catches his tortoise, the flying arrow moves, and it\'s possible to go to an infinite number of places in a finite time, without contradiction.\" \r\n\r\n\r\n ',NULL,0);
INSERT INTO comment VALUES (10557,1529,4507,'Penny','Oh my God.......','2003-12-17 03:41:35',0,'Jennifer to Gamer: \"I agree that it would really be a waste of time to use a Supercomputer to solve this basic algebra problem.\"\r\n \r\nYou two didn\'t realize I was joking when I said I used a Supercomputer to solve this problem? That is scary !!\n\nEdited on December 17, 2003, 3:43 am',10555,0);
INSERT INTO comment VALUES (10558,648,4830,'Jils','Similar Result','2003-12-17 04:33:48',0,'We do a pressie dip each Christmas at our office and have had this problem on occasions. My solution is ((n-1)/n))^(n-1) as each person has a (n-1)/n chance of not picking their own except the last person who has 100% chance. The probability for each person remains the same as there is a chance that their name has already been removed by the earlier pickers. For high n this does come out close to the other solution. The case for n=3 is interesting as my answer gives 0.4444 - not 0.3333. I may sit with some bits of paper over Christmas to test this....',NULL,0);
INSERT INTO comment VALUES (10559,1543,2839,'FatBoy','re: God\'s existence:','2003-12-17 08:35:27',0,'Benjamin,
\r\nBe careful, you probably do not know what you are getting yourself into. I suggest that you check out the \"existence of God\" discussion in the General Discussion forum and also the comments on the puzzle \"Can or Can Not\" in Paradoxes.
\r\n\r\nThere are those among us who believe as you do and I recognize that there is no shame in wanting to share true faith (in fact I belieev the Bible enjoins a believer to do so). But remember there are also those among us who legitmaltly hold other beliefs.
I just wanted to let you know that you are setting yourself up for a lot of raised hackles, name calling and unhappiness.
\r\n\r\nI personally take accept your blessing gladly in the spirit in which it is meant and wish you the best in this holy season. May God shine his blessings upon you and keep you safe in the assurance of His love.',10547,0);
INSERT INTO comment VALUES (10560,1547,153,'TomM','Life is not all Sunshine and Lollipops','2003-12-17 09:27:31',3,'... but the answer to this classic riddle is\r\n S.mile.s',NULL,0);
INSERT INTO comment VALUES (10561,1547,4507,'Penny','Life can\'t be all Beer and Skittles','2003-12-17 12:34:27',3,'Don Vito Corleone would not have submitted this riddle if there were not a more original answer than \"smiles\", and there is !!\r\n \r\n\"short\", as a whole, is \"short\".\r\n\"lengthy\", in the middle, is \"g\".\r\n\"short\" + \"g\" = \"thorgs\" !!! \r\n\r\nA thorg is either:\r\n\r\n(a) a member of Denis Hebbelynck\'s organization for playing chess by e-mail. (http://users.skynet.be/THORG/)\r\n \r\nOR\r\n\r\n(b) a monster in a dungeons-and-dragons game\r\n(http://camelot.allakhazam.com/Mobs/search.html?cmob=4013)\r\n \r\nA good chess opponent will lift you up and help your day. A monster will do the opposite. So, sarcastically taken, thorgs can go either way.\r\n \r\nEnough of this foolishness... I have to get back to \"Cicak and Kancil\", an Indonesian play I was reading. Indonesian plays go well with your morning coffee, since there\'s nothing like a good cup of java when you\'re perusing a Java script...... ',NULL,0);
INSERT INTO comment VALUES (10562,1543,3172,'SilverKnight','re(2): God\'s existence:','2003-12-17 13:35:07',0,'FatBoy said it... soooo much more sensitively than I would have put it.\r\n\r\nAs donnmike put it... this problem \"has nothing to do with God\'s existence\". And it is apparently the \"blinders\" that you are wearing, that prevented you from seeing this.\r\n\r\nI may share some of your beliefs, Benjamin, but I don\'t share your desire to express them in inappropriate forums.',10559,0);
INSERT INTO comment VALUES (10563,1529,4835,'bex','answer','2003-12-17 13:38:03',0,'1)5jars and 16 pencils\r\n2)dunno the answer to this one but i think there are 7 jars',NULL,0);
INSERT INTO comment VALUES (10564,1334,4505,'Bob Genisot','First Thoughts','2003-12-17 14:21:36',0,'At first, it looks like a contradiction to the \"Four Color Map Problem\". Perhaps I need to read further.',NULL,0);
INSERT INTO comment VALUES (10565,1334,3172,'SilverKnight','solution','2003-12-17 14:23:36',3,'I don\'t have a proof of it... but I can come up with a 16-penny solution...\r\n\r\nMake a diamond with 4 of them... (like two equilateral triangles against each other), and use that as a base.\r\n\r\nThen put 4 diamonds together (for a total of 16) at the 4 compass points, oriented perpendicular to their direction.\r\n\r\nrough ascii art view:\r\n\r\n\r\n O\r\n O O\r\n O O O\r\n\r\nO O O O\r\n\r\n O O O\r\n O O\r\n O\r\n\n\nEdited on December 17, 2003, 2:33 pm',NULL,0);
INSERT INTO comment VALUES (10566,1547,1626,'Gamer','re: Life can\'t be all Beer and Skittles','2003-12-17 14:55:39',0,'I think this is an interesting solution. The only problem is it doesn\'t say \"the middle of lengthy\", but \"lengthy in the middle\", so we are looking for something with \"lenghty\" or something lengthy.\r\n\r\nAlso, you have to trust that a normal person would NOT know a member of a certain chess club, or a certain game. That would be too detailed for an answer to a riddle.',10561,0);
INSERT INTO comment VALUES (10567,692,4824,'sean','soln.','2003-12-17 15:37:40',0,'u=10m/s\r\nv=0m/s\r\na=-9.8m/s²\r\ns=?\r\n\r\nthen just use...\r\n\r\ns=(v²-u ²)/2a',NULL,0);
INSERT INTO comment VALUES (10568,830,4824,'sean','explanation of why original theory came about','2003-12-17 15:44:26',0,'water particles in hot water have greater kinetic energy than those in cold water. high energy compounds are more unstable and so lose energy more quickly, i.e. warm water will cool down more quickly (relatively speaking) than cold water. however, once the hot water has cooled down to such an extent that it is just as cold as the cold water was originally, it will then take the same amount of time to freeze from this temperature - and therefore, hot water - under any conditions - should take longer to freeze than cold water, according to the laws of thermodynamics and kinetic theory.',NULL,0);
INSERT INTO comment VALUES (10569,1334,4412,'krdmt5_000','Solution???','2003-12-17 16:05:47',3,'there must 1 and only one penny which touchs 3 others. see diagram below.\r\n*=peeny\r\n\r\n 3*others\r\n\r\nsee?\r\nnow for some pointless java scripts\r\n√²³>³²∞≤≥±³>∞≥√³π³>',NULL,0);
INSERT INTO comment VALUES (10570,1334,4507,'Penny','re: solution','2003-12-17 16:28:48',1,'I tried to verify SK\'s solution using actual pennies on an actual table, and it works beautifully. Intuitively it seems that 16 is the minimum number.',10565,0);
INSERT INTO comment VALUES (10571,1334,3172,'SilverKnight','re(2): solution','2003-12-17 16:34:23',0,'*gasp* cough cough... dang... I think something just went down the wrong pipe...',10570,0);
INSERT INTO comment VALUES (10572,1543,4323,'Benjamin J. Ladd','','2003-12-17 16:38:44',0,'The title of this puzzle is \"Proof of Anything.\" As the author has used the example of George Washington and the moon being made out of cheese, I gathered (this may be difficult for you to believe) that this problem wasn\'t merely about God\'s existence and was of a more general nature--\"...find the problem in the logical conclusion derived from these set of statements.\" Fine, that\'s easily accepted all good and well. Still, there they are--those words \"then God exists...\" glaring at me from the computer screen and begging me to reply to them...\r\n\r\nHere\'s my real fault with the problem and not at all from a religious standpoint--although it certainly does have its application. I believe that logic and reason must ultimately halt at fundamental statements that are either true or untrue and go no further. For example: God exists, I exist, I have brown hair. There we may conjecture some statement about reality if we assume that S is true or we may conjecture another statement if S is false. Faith, really then in the truth of one or the other of those statements is what enables us to make intelligible assumptions about this universe. As the faculties we employ in determining our faith in these fundamental assumptions are derived solely from our senses, our moral conscience, and our reason (others of varied faiths and occult practices would also include supersensual or spiritual revelation), it would seem pointless to begin at the statements themselves as any grounds for a proof. In fact, those assumptions that we hold dearest to us are still in fact unprovable assumptions and we\'ve decided by faith alone to accept their truth.\r\n\r\nMy point is this: logic and reason are subordinate to faith and at bottom logic is merely a tool employed by faith to determine the truth of this universe. That truth is of course by no means \"proven,\" it\'s entirely accepted by faith. By postulating sentences such as \"if x is true, then pink elephants float in space...\" and watching mystified at a two page discourse on a paradox arising from this inconsistency...\r\n\r\nWell, my good friends, give me my faith.\n\nEdited on December 17, 2003, 4:39 pm',NULL,0);
INSERT INTO comment VALUES (10573,1543,3172,'SilverKnight','re:','2003-12-17 16:49:26',0,'dangit Benjamin....\r\n\r\nYou\'re missing the reason why those words were included as the predicate of the problem. The reason is exactly that many, if not most, readers will view the predicate as a truth. And those who don\'t, will undoubtedly acknowledge that many others do, and have the association of truth applied to the predicate.\r\n\r\nAnd this notion, of the statement S being true or false when the predicate is true, ADDS to the problem itself. \r\n\r\nThis is NOT equivalent to saying that this problem is questioning (or stating) the truth of the predicate.\r\n\r\nYet, you have equated the two, and while Sam submitted a religiously/spiritually neutral problem, you have unnecessarily introduced your religion/spirituality into this.\r\n\r\nI would just as soon ask Levik to delete this thread as they have NO relevance to this problem apart from your applying your religious/spiritual views to it and sharing them with us.',10572,0);
INSERT INTO comment VALUES (10574,1543,4841,'stephen ocone','','2003-12-17 18:03:06',0,'ok, maybe this isn\'t the correct solution, but it seems to be that you make a mistake when you mistakenly place truth in the consequent of the statment \'If ~A then B\' yes this statment is true but \'B\' is not the true part, the statment itself is true but \'B\' is not true. to be specific when you say:\r\n 3. Specifically, the statement \"If S is true then God exists\" would be true\r\n but this is not true yet, the statment \'If ~S then S\' maybe true, but S is not true.',NULL,0);
INSERT INTO comment VALUES (10575,1429,3558,'Tristan','re(3): A Variation:','2003-12-17 18:58:13',0,'The variation is more sneaky, because you need to catch the hint \"second left and the second on the right [...] though different at first sight.\" This implies that one of these two is the largest. Either way, the pattern of potions is the same.',10546,0);
INSERT INTO comment VALUES (10576,1543,3558,'Tristan','Partial disproof','2003-12-17 19:27:29',1,'So has anyone actually solved the problem yet? I think we\'ve been too preoccupied with \"If ~A, then ...\" is true when A is true and other stuff. Self-referencing statements doesn\'t seem to be what Sam had in mind. So what is the problem really?\r\n\r\nSpeaking of the matter of antecedents, what if the antecedent is true only part of the time? For example, \"If my computer is on, then I\'m on Flooble\" is not true (though comes close). Even if my computer is off, the statement is still false, isn\'t it? Following this same logic, statement S might have only been true part of the time. The other times, it still has the opportunity to be false. Of course, the paradox is still there since you can prove anything was true at least at one time. That\'s why I call this a partial disproof, because it only replaces the paradox with another.',NULL,0);
INSERT INTO comment VALUES (10577,1543,3172,'SilverKnight','re: Partial disproof','2003-12-17 20:10:18',0,'Tristan, you wrote:\r\n\"For example, \"If my computer is on, then I\'m on Flooble\" is not true (though comes close). Even if my computer is off, the statement is still false, isn\'t it?\"\r\n\r\nNo, if your computer is off, then the statement is true (though the predicate is false--because you\'re not on Flooble).\r\n\r\n(This is, I think, the point the Sam is trying to make with his *Note at the end.)',10576,0);
INSERT INTO comment VALUES (10578,152,4844,'Linda Malone','Good one!','2003-12-17 20:27:04',0,'Sorry, I\'m new and that was my comment...',NULL,0);
INSERT INTO comment VALUES (10580,1543,4627,'donnmike','re:','2003-12-17 22:07:15',0,'You still don\'t get it. And the arrogance of your latest post is even more irritating than the first one. \r\n\r\nYou toss thousands of years of philosophy and reason aside and simply conclude that faith is somehow of greater meaning than logic. \r\n\r\nWell, if you understood logic at all, you would recognize that the problem being discussed is only a syllogism and that the paradox can be resolved using only logic. It seems that you still actually believe that it is possible to logically proove something with a statement alone, as the original poster claims. If that were so, this post would not have been made in a forum where the object is to find and elucidate logical flaws in what is stated.',10572,0);
INSERT INTO comment VALUES (10581,1334,4849,'sargon','Isn\'t this kind of easy?','2003-12-18 01:07:17',0,'Correct me if I\'m wrong, but isn\'t it 4? Just put the pennies in a square right? Like this:\r\n\r\noo\r\noo\r\n\r\nUmmm...',NULL,0);
INSERT INTO comment VALUES (10582,1334,4374,'Richard','re: solution','2003-12-18 01:24:20',0,'If we assume (or could prove) that any solution must be n of your tight diamonds put together, then we still need to show n=4 is minimal. With my pennies, it isn\'t utterly clear that n=3 won\'t work. The centers of the pennies of the diamond are vertices of a rhombus made up of two equilateral triangles that share a side. This rhombus can be scaled up to just circumscribe the pennies of the diamond. Maybe these observations will help to rule n=3 in or out. \r\n\r\n\n\nEdited on December 18, 2003, 3:48 pm',10565,0);
INSERT INTO comment VALUES (10583,1334,1301,'Charlie','re: Isn\'t this kind of easy?','2003-12-18 08:13:25',0,'That solution, with 4 pennies arranged in a square, has each penny touching only two other pennies. The diagonally opposite pennies are not touching.',10581,0);
INSERT INTO comment VALUES (10584,723,4850,'Rachel','a solution?','2003-12-18 08:59:48',0,'I\'m sure there\'s a better way to do this, but while I was looking at the problem, I noticed the lengths of the lines that are drawn from P to triangle vertices are proportionate. I then cheated like a madwoman and realized that 4 is the length needed for each segment to meet in the center of the triangle. I drew an imaginary line from the middle of one the sides of the triangle to P, and had a 30-60-90 triangle. Two times the langth of s times the square root of three should be the answer. 8[3^(1/2)]',NULL,0);
INSERT INTO comment VALUES (10585,723,1301,'Charlie','Excel solution','2003-12-18 09:09:41',3,'To set up an Excel solver for this, let x be considered the altitude of the point to the nearest side of the triangle, and thus lying between the length-3 distance and the length-4 distance points. Let this be the variable to be solved for and keep it in A2.\r\n\r\nThe side is then √(3^2-x^2 + 4^2-x^2); put this in B2 as =SQRT(9-A2^2)+SQRT(16-A2^2).\r\n\r\nThe angle at the distance-4 point in the right triangle with x as the opposite side is then arcsin(x/4); place this in C2 as =ASIN(A2/4).\r\n\r\nAdjacent to this angle in that corner of the triangle is another angle of 60 degrees minus this one. It\'s part of a triangle with sides of 4 and the side of the equilateral triangle adjacent to it and the length-5 distance as the opposite side. We can calculate the side that is supposed to be length 5 by the law of cosines as equal to √(4^2+side^2-2*4*side*cos(60-a)), where a is the angle we had originally found. We enter this into D2 as =SQRT(4^2+B2^2-2*4*B2*COS(PI()/3-C2)). Note Excel uses radian measure and 60 degrees is pi/3 radians.\r\n\r\nThen use solver to make D2 be equal to 5 by changing A2. Be sure to ask for sufficient precision. The length of the side that we seek will be in B2, and comes out to 6.766432568 cm.',NULL,0);
INSERT INTO comment VALUES (10586,723,1301,'Charlie','If ... (an alternate question)','2003-12-18 10:18:46',3,'In the queue someone brought up the possibility of the point lying outside the triangle rather than within it. That also has a solution:\r\n\r\nConsider a triangle formed by the point and the nearest two points on the equilateral triangle. Its distances from the nearest vertices are 3 and 4 cm. If one side of the original triangle (the remaining side of the new triangle) is length s, then we can find angle a, adjacent to the length-3 side by the law of cosines: 4^2 = 3^2 + s^2 -2*3*s*cos(a). If we assume s is in Excel cell A10, we can put angle a in B10 with the formula =ACOS((9+A10^2-16)/(6*A10)).\r\n\r\nThen the distance that should be 5 can be found via the law of cosines applied to the point in question and the points of the equilateral triangle that are 3 and (supposed to be) 5 cm away. The square of the side that is supposed to be length 5 is then 3^2 + s^2 - 2*3*s*cos(60+a), using degree measure. In Excel, in radian measure, we can place in cell C10 =SQRT(9+A10^2-6*A10*COS(PI()/3+B10)), and ask Solver that C10 be made into 5 by changing cell A10.\r\n\r\nThis results in a side length of 2.053141571 cm--the length the side would have if the point that is 3, 4 and 5 cm away from the points in the equilateral triangle had been specified to lie outside the triangle.\r\n\r\nThis methodology would also have been possible for the original question, where angle a would have been subtracted from 60 instead of added, and the calculation would have been simpler, as it was here, with one fewer steps.',10585,0);
INSERT INTO comment VALUES (10587,723,4830,'Jils','re: a solution?','2003-12-18 11:29:39',0,'Rachel, It looks like lines of length 4 should be close to meeting,but 8[3^1/2] is nearly 14 - do you mean 4[3^1/2] ?',10584,0);
INSERT INTO comment VALUES (10588,1545,3172,'SilverKnight','Full Solution','2003-12-18 14:09:01',2,'Ask Charlie to do it... :-)\r\n\r\nbig-O notation:\r\nO(1) = this is solved in constant time.',NULL,0);
INSERT INTO comment VALUES (10589,1429,4853,'chris duarte','Tunnel','2003-12-18 14:26:01',0,'Young apprentice, Brother Manning, declares that p3 and p4 transports away. P3 onward and p4 back again.',NULL,0);
INSERT INTO comment VALUES (10590,723,4788,'corey','by inspection','2003-12-18 14:39:16',0,'By drawing circles of radii 3, 4, and 5 and then moving them slowly along 30, 150, and 270 degree lines in AutoCAD until the three circles intersect and then measuring the distances between their centers, I came up with about 6.7524. Not very complex, but somewhat effective?',NULL,0);
INSERT INTO comment VALUES (10591,1545,4670,'e.g.','Racing around','2003-12-18 15:04:44',3,'\r\nlet P = first node; if P=NULL, exit\r\nlet Q = NEXT(P); if Q=NULL, exit\r\nloop\r\n P = NEXT(P)\r\n R = NEXT(Q); if R=NULL, exit\r\n Q = NEXT(R); if Q=NULL, exit\r\nuntil P=R OR P=Q\r\n\r\nThe idea is that Q races along the list at twice P\'s speed; if the list loops back, Q will eventually get behind P and catch it.',NULL,0);
INSERT INTO comment VALUES (10592,1545,4507,'Penny','I don\'t understand the definition of a \"looped\" list.','2003-12-18 15:41:48',4,'SilverKnight wrote: \"A \'looped\' list means that the linked list has a node that points to a PREVIOUS member (thereby creating a cycle).\" \r\n\r\nBy this definition, the following list is \"looped\":\r\n\r\n1(points to 2), 2(points to 3), 3(points to 5), \r\n4(points to 7), 5(points to 4), 6(points to 9), \r\n7(points to 12), 8(points to 11), 9(points to 12), \r\n10(points to 1), 11(points to 2), 12(pointer is NULL)\r\n \r\nHowever, we move through this list without any cycles:\r\n\r\n1--> 2 --> 3 --> 5 --> 4 --> 7 --> 12 --> NULL \r\n\r\nWhat am I missing ?\n\nEdited on December 18, 2003, 6:14 pm',NULL,0);
INSERT INTO comment VALUES (10593,1545,1301,'Charlie','a solution','2003-12-18 15:45:49',3,'We must compare each forward pointer we look at to a previous pointer to see if they are the same. Every once in a while we have to replace the one we\'re comparing against in case the loop comes back to a point after the one we had saved. But if we keep replacing the comparison pointer at fixed intervals we risk that the loop is larger than our interval of replacement, and we\'ll never recognize a loop. So start out replacing the comparison pointer every 2 (say) pointers that we look at, but then every time we replace the comparison pointer, double the interval at which the replacement is made the next time.\r\n\r\nIf there is no loop, then the time is obviously O(N). To see why the time is O(N) even when there is a loop, consider an approximate calculation based on a list of N elements with a terminal loop of x elements out of this. You must examine N - x elements before entering the loop. To that we have to add the expected number of elements that will be examined within the loop. In the following, I use log to represent the base-2 logarithm. We will have reset the replacement interval for the comparison pointer log(N-x) times. But each time we do that, we double the interval. So we expect the size of the interval to be 2^log(N-x), or just N-x. Compared to the size of the loop, x, this is (N-x)/x times as big, so we\'d expect to have to go through the loop (N-x)/x times (\"give or take\" (actually multipy or divide by) a factor not too far from 1), but since it contains x elements, that is gone through by examining ((N-x)/x)*x = N-x times. So we get N-x+N-x, which is O(N).\r\n\r\nThe below is a sample, written in PL/I. Some object-oriented languages may be able to do this without regard to the way the structure is laid out, but here I\'ve just put in a fictitious structure that contains a forward pointer. It\'s not tested, as I didn\'t wish to put together a driver program, and all that linkage work.\r\n\r\nISLOOPED: PROC (HEADPTR) RETURNS (BIT(1));\r\n DCL HEADPTR POINTER;\r\n DCL LOOKPTR POINTER;\r\n DCL CURRPTR POINTER;\r\n DCL SKIPAMT FIXED BIN(31) INIT(2);\r\n DCL NUM_SKIPPED FIXED BIN(31) INIT(0);\r\n DCL 1 MYSTRUCT BASED (CURRPTR),\r\n 2 STRUCT_STUFF CHAR(20),\r\n 2 FWD_PTR POINTER;\r\n\r\n CURRPTR=HEADPTR;\r\n LOOKPTR=HEADPTR;\r\n CURRPTR=MYSTRUCT.FWD_PTR;\r\n DO WHILE (CURRPTR ¬= LOOKPTR & CURRPTR¬=NULL);\r\n NUM_SKIPPED = NUM_SKIPPED + 1;\r\n IF NUM_SKIPPED = SKIPAMT THEN\r\n DO;\r\n SKIPAMT = 2 * SKIPAMT;\r\n NUM_SKIPPED = 0;\r\n LOOKPTR = CURRPTR;\r\n END;\r\n CURRPTR=MYSTRUCT.FWD_PTR;\r\n END; /* DO WHILE */\r\n IF CURRPTR = NULL THEN\r\n RETURN (\'0\'B); /* NOT LOOPED */\r\n ELSE\r\n RETURN (\'1\'B); /* IS LOOPED */\r\nEND ISLOOPED;\r\n\r\nTo test out the idea, I wrote a program in Quick Basic to simulate pointers with an array of numbers 1-N and shuffled them. Each is considered a pointer (subscript actually) to the next in the list. If it points to N (in this case 4000) it is considered terminated. Thus the N as a length of the list is actually less than the length of the array. The program marks, in the REDIMed array useCt which are actually used (the algorithm looks at every element that\'s really in the \"list\" at least once), and the populated entries in that array are counted to determine the actual N.\r\n\r\nThe maximum N is the size of the array, 4000. The ratio of number of elements looked at to number of elements, N, is tabulated for bins of 1000 (i.e., under 1000, 1000-2000, etc.) I haven\'t done a chi-squared analysis but it looks as if the ratio is about constant, so as to confirm O(N). The tabulation is done only for those which found a loop. There\'s no point in counting in those which it\'s obvious it is O(N). (What may be confusing in the program is that variable N is the size of the array, acting as a null pointer, while the variable called used contains the size of the \"list\", which we are calling N in the write-up.)\r\n\r\nThe statistics produced for the 1000-wide bins\' average ratio of examined nodes to nodes is:\r\n0 2.343126213126932\r\n1 2.360104875078315\r\n2 2.613321757777493\r\n3 2.238462445587248\r\nwhere the number at the left is the number of thousands starting the range.\r\n\r\nActually, the above ratios show up approximately, consistently. But a graphics version of the stat program, plotting individual results of examined nodes as the y axis and nodes as the x axis, indicates a stepped function, with steps breaking at powers of 2, and each step sloped at a value of 1. The steps are what increase the average slope to the approximate 2.4? value. \r\n\r\nThe program is:\r\n\r\nRANDOMIZE TIMER\r\nDEFDBL A-Z\r\nn = 4000\r\n\'SCREEN 12\r\nDIM array(n)\r\n\r\nDIM ctCtr(10)\r\nDIM usedCtr(10)\r\n\r\nFOR trial = 1 TO 2000\r\n\' OPEN \"looptrce.txt\" FOR OUTPUT AS #2\r\n REDIM useCt(n)\r\n FOR i = 1 TO n\r\n array(i) = i\r\n NEXT\r\n\r\n FOR i = 1 TO n\r\n r = INT(RND(1) * n + 1)\r\n IF i <> r THEN SWAP array(i), array(r)\r\n NEXT\r\n\r\n skipamt = 2\r\n numSkipped = 0\r\n\r\n ct = 1\r\n\r\n headptr = 1\r\n currptr = headptr\r\n useCt(currptr) = 1\r\n lookptr = headptr\r\n currptr = array(currptr)\r\n useCt(currptr) = 1\r\n DO WHILE (currptr <> lookptr AND currptr <> n)\r\n numSkipped = numSkipped + 1\r\n IF numSkipped = skipamt THEN\r\n skipamt = 2 * skipamt\r\n numSkipped = 0\r\n lookptr = currptr\r\n END IF\r\n currptr = array(currptr)\r\n useCt(currptr) = 1\r\n\' PRINT #2, skipamt; numSkipped; currptr\r\n ct = ct + 1\r\n LOOP\r\n\' CLOSE\r\n used = 0\r\n FOR i = 1 TO n\r\n IF useCt(i) THEN used = used + 1\r\n NEXT\r\n\r\n PRINT used, ct, currptr, ct / used\r\n subsc = INT(used / 1000)\r\n IF currptr < n THEN\r\n ctCtr(subsc) = ctCtr(subsc) + ct\r\n usedCtr(subsc) = usedCtr(subsc) + used\r\n END IF\r\n\' IF ct / used > 2 THEN END\r\n\' IF currptr = n THEN\r\n\' PSET (used * 630 / n, 400 - ct * 100 / n), 7\r\n\' ELSE\r\n\' PSET (used * 630 / n, 400 - ct * 100 / n), 14\r\n\' END IF\r\nNEXT\r\nFOR i = 0 TO 10\r\n IF usedCtr(i) > 0 THEN PRINT i, ctCtr(i) / usedCtr(i)\r\nNEXT\r\n\r\n\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (10594,1545,1301,'Charlie','re: I don\'t understand the definition of a','2003-12-18 15:55:10',0,'The node that has been labeled 5 is actually the fourth node. They are numbered by the order in which you get to them, so when it is said that you go back to a previous number, it is to one that you have previously visited. As in the Basic simulation that I posted, when the list is stored in an array, the subscripts are acting like memory locations in real lists, and they do not count in what their numerical value is; what counts is the sequence in which they are encountered.',10592,0);
INSERT INTO comment VALUES (10595,1545,2899,'Brian Wainscott','Solution','2003-12-18 16:03:52',3,'Description of algorithm:\r\n save a pointer to the current item on the list\r\n go down the list COUNT times, checking to see if you get back to the item you saved (or hit the end -- start COUNT at 1).\r\n double COUNT, save the current location instead, and continue\r\n\r\nIf the list has length N, with a loop of M items on the end, then the number\r\nof items checked will be on the order of N+M (actually, it will be bounded\r\nby 2*max(N,M)), so the runtime is O(N+M).\r\n\r\nHere is a C subroutine (sans indentation, as usual -- how do I fix that?):\r\n\r\nloopcheck(ITEM *head) {\r\n save=head;\r\n item=head->next;\r\n count=1;\r\n while(1) {\r\n for(i=0; i<count; i++) {\r\n if(item==save) goto is_looped;\r\n if(item==NULL) goto is_not_looped;\r\n item=item->next;\r\n }\r\n count=2*count;\r\n save=item;\r\n }\r\n is_looped:\r\n printf(\"Is looped\\n\");\r\n return(1)\r\n is_not_looped:\r\n printf(\"Is NOT looped\\n\");\r\n return(0)\r\n}\r\n',NULL,0);
INSERT INTO comment VALUES (10596,1545,3172,'SilverKnight','re: Solution - indention solution','2003-12-18 16:15:20',0,'How to address indention:\r\n\r\nI usually convert all tabs to spaces, and then use a simple editor and change (find/replace all) each space to an html non-breaking space.',10595,0);
INSERT INTO comment VALUES (10597,723,3386,'Victor Zapana','the simplified answer','2003-12-18 17:24:51',0,'well u see i absolutely hate decimals, so here\'s the clean answer. sqrt(25 + 12sqrt3)
\r\n(Before anybody else flames me, please note I wrote \"seems\" -- I didn\'t have the time to calculate the average or maximum number of \"node visits\" or something like that.)',10603,0);
INSERT INTO comment VALUES (10613,1439,4064,'rerun141','if x=3???','2003-12-19 12:38:22',0,'oh nvm. positive EVEN interger...\n\nEdited on December 19, 2003, 12:39 pm',NULL,0);
INSERT INTO comment VALUES (10614,1545,4450,'drew','GJ silver knight','2003-12-19 14:16:29',0,'I would like to say thanks to silver knight for explaining it i know we had a long conversation about explaining things.',NULL,0);
INSERT INTO comment VALUES (10615,1439,4507,'Penny','Solution (no computer assistance used)','2003-12-19 15:33:16',3,'Mathematical induction to the rescue !!!!!\r\n \r\nAssume, for positive even integer x (such as 6) with series coefficients ending with (3,1,1,1), that:\r\n \r\nx^2 + (x-1)^2 +3(x-2)^2 + (x-3)^2 + (x-4)^2 + (x-5)^2 +3(x-6)^2 + (x-7)^2 +...\r\n+ 3(4^2) + 3^2 +2^2 + 1^2 = (1/2)(x^3 + x^2 -x) \r\n\r\nThen x+4 will also be a positive even integer with coefficients (3,1,1,1).\r\n\r\nthe series for x+4 is:\r\n\r\n(x+4)^2 + (x+3)^2 +3(x+2)^2 + (x+1)^2 + (x)^2 + (x-1)^2 +3(x-2)^2 + (x-3)^2 +...\r\n+ 3(4^2) + 3^2 +2^2 + 1^2\r\n\r\nBut by our assumption for x, this becomes:\r\n\r\n= [(x+4)^2 + (x+3)^2 +3(x+2)^2 + (x+1)^2] + [(1/2)(x^3 + x^2 - x)]\r\n\r\n=(1/2)(x^3 + 13x^2 + 55x + 76) \r\n\r\n= (1/2)[x^3 + 8x^2 + 16x + 4x^2 + 32x + 64) + x^2 + 8x + 16 - x - 4]\r\n\r\n = (1/2)[(x+4)^3 + (x+4)^2 - (x+4)]\r\n\r\nSo we have proved that the theory is true for integers 6, 10, 14, 18, 22,....... \r\n\r\nThe proofs for positive even integers with series coefficients ending with (1,3,1,1), (1,1,3,1) and (1,1,1,3) are almost identical to the foregoing. I will omit those details.\r\n\r\n\n\nEdited on December 19, 2003, 4:02 pm',NULL,0);
INSERT INTO comment VALUES (10616,1439,1301,'Charlie','proof','2003-12-19 16:33:44',3,'This proof is similar to Penny\'s, but is based on the coefficient\'s starting at 1,1,3,1, which they always do (once x > 3), it need be done only one way:\r\n\r\nFirst, it is true for x=2, as 2^2+1^2=5 and (2^3+2^2-1)/2 = 5.\r\n\r\nIt is also true for x=4, as 4^2+3^2+3*2^2+1^2 = 38 and (4^3+4^2-4)/2 = 38.\r\n\r\nThen, assume it is true for x-4, so that the sum is\r\n\r\nx^2 + (x-1)^2 + 3(x-2)^2 + (x-3)^2 + ((x-4)^3 + (x-4)^2 - (x-4))/2\r\n\r\nThis expands to x^2 + x^2 - 2x + 1 + 3x^2 - 12x + 12 + x^2 - 6x + 9 + (x^3-12x^2+48x-64+x^2-8x+16-x+4)/2\r\n\r\nThis simplifies to\r\n\r\n6x^2 - 20x + 22 + (x^3 - 11x^2 + 39x - 44)/2\r\n\r\nwhich further simplifies to (x^3 + x^2 - x)/2\r\n',NULL,0);
INSERT INTO comment VALUES (10617,723,4317,'C.B.','re(2): the simplified answer','2003-12-19 17:12:18',0,'sqrt(25+12*sqrt(3)) = 6.77\r\nI don\'t know how he came up with this number. I have a solution in the form of three ugly equations with three unknowns, which is technically solvable but ugly. I did this by setting up vectors from each vertex to the center, then adding the vector from the center to point P (which is unknown, 2-dmensional, labeled D). Squaring these the equations gives 3 equations with 3 unknowns: the length of a side, and the two components of D.',NULL,0);
INSERT INTO comment VALUES (10618,1547,4865,'Heartberry','Possible Solution','2003-12-19 17:34:04',0,'Smiles?',NULL,0);
INSERT INTO comment VALUES (10619,1439,1626,'Gamer','re: proof','2003-12-19 18:27:34',0,'That is good. How about a way to do this without using induction? Is that just as easy?',10616,0);
INSERT INTO comment VALUES (10620,1545,2899,'Brian Wainscott','re(4): Racing around -- simulation','2003-12-19 18:45:38',0,'Fredrico,\r\n\r\nNo flame intended, but I figured it was worth looking at. Complete detailed analysis is a bit messy, due to the 2^N cutoffs, and the answers depend on the relative length of the list and the length of the looped part, if any. So I ran a simulation. Taking lists of random length up to 10000, and looping them back to a random point, I counted the number of times through the inner loop of e.g.\'s code and Charlie\'s code (which I\'m biased toward, since it is the same solution I had).\r\n\r\nThe \"inner loop\" in Charlie\'s case does one memory fetch, and some comparisons In e.g.\'s case it does 3 memory fetches and some comparisons. In the real world, the number of memory fetches is going to be the deciding factor. I ran 10000 trials, and took the average ratio of the number of times through the inner loop, and the average ratio of the number of memory fetches. In both cases I used e.g.\'s value / Charlie\'s value:\r\n\r\nloops: 1.973699\r\nfetches: 0.657914\r\n\r\nSo in real applications, Charlie\'s code would run in about 2/3 the time of e.g.\'s. This is about what I expected, since Charlie will generally check most items once, and e.g. will check most of them twice.\r\n\r\nHere is the test code I used: (I used my implementation of what I\'ve been calling \"Charlie\'s code\", and found a bug in my earlier posted code while doing this!):\r\n\r\n(Special thanks to SK, who told me about the non-breaking space trick!)\r\n\r\n#include <stdio.h>\r\n#include <stdlib.h>\r\n#define MAXLEN 100000\r\n#define END -1\r\n#define ROUNDS 10000\r\nmain()\r\n{\r\n int list[MAXLEN];\r\n int N,M,i,j;\r\n int eg_loops,eg_fetch;\r\n int charlie_loops,charlie_fetch;\r\n float rloop,rfetch;\r\n\r\n for(i=0; i\r\n 06264 , 22428 , 44846 , 66264 , 88682 \r\n 02884 , 24668 , 48226 , 62884 , 86442 \r\n 04244 , 28488 , 46866 , 64244 , 82622 \r\n 08824 , 26648 , 42286 , 68824 , 84462 \r\n
\r\n-----\r\n\r\nIt\'s best to consider the row numbers of this table 0, 1, 2 and 3 for the powers of 5 (mod 4) that they represent.\r\n\r\nIf a given number is expressed as the sum of multiples of powers of 5, that is to say in base-5 notation, we can start with the highest power of 5 (leftmost digit), to see what the last non-zero digit is.\r\n\r\nNow to the question at hand:\r\n\r\nFirst, UBASIC can be used to find that 20! itself is 2432902008176640000, and that number represented in base-5 is 130402040313000221204440000, a 27-digit number, so the highest power of 5 used is 26.\r\n\r\n26 = 2 mod 4, so we use row 2 (the third row in 1-based consideration). As our first consideration is the multiple of 5^26, and that multiple is just 1, we use the first digit after the zero in that row: 4. The last non-zero digit of (5^26)! is 4. The rest of the base-5 number is then used, as it represents, in base-5, how far past 5^26 our desired base-of-the-factorial number is. The preceding row of the table includes, of course, the higher power of 5, as the grouping beginning with 4, that is 48226. As the next base-5 digit of our number is 3, we have to go 3 positions beyond the initial 4, and we get a 2. So the last non-zero digit of (5^26 + 3*5^25)! is 2.\r\n\r\nWe continue in this fashion, remembering that above the top row is just a repetition of the bottom row, so we keep cycling through. This could be tedious and error-prone, so let a computer do the work, with the following UBASIC program:\r\n\r\n 10 data \"06264\",\"22428\",\"44846\",\"66264\",\"88682\"\r\n 20 data \"02884\",\"24668\",\"48226\",\"62884\",\"86442\"\r\n 30 data \"04244\",\"28488\",\"46866\",\"64244\",\"82622\"\r\n 40 data \"08824\",\"26648\",\"42286\",\"68824\",\"84462\"\r\n 50 dim Lu$(4,4)\r\n 51 dim Check(4,4,4)\r\n 60 for Row=0 to 3\r\n 65 for Col=0 to 4\r\n 70 read Lu$(Row,Col)\r\n 80 next\r\n 90 next\r\n 110 N=!(20):print N\r\n 120 Nsub=N\r\n 125 Base5$=\"\":H=-1\r\n 130 while Nsub>0\r\n 140 Dig=Nsub@5\r\n 150 Nsub=Nsub\\5\r\n 160 Base5$=mid(str(Dig),2)+Base5$\r\n 165 H=H+1\r\n 170 wend\r\n 180 print Base5$,H\r\n 205 Dig=0\r\n 210 Row=H@4\r\n 220 for D=H to 0 step -1\r\n 230 Col=Dig\\2\r\n 235 Psn=val(mid(Base5$,H-D+1,1))\r\n 240 Dig=val(mid(Lu$(Row,Col),Psn+1,1))\r\n 241 Check(Row,Col,Psn)=1\r\n 245 print Row,Col,Psn,Dig\r\n 250 Row=Row-1:if Row<0 then Row=Row+4\r\n 260 next\r\n 280 print Dig\r\n 390 end\r\n\r\nThe result is:\r\n\r\n 40 2\r\n 80 8\r\n 120 6\r\n 160 6\r\n 200 2\r\n 240 6\r\n 280 4\r\n 320 4\r\n 360 6\r\n 400 8\r\n 440 2\r\n 480 6\r\n 520 6\r\n 560 4\r\n 600 6\r\n 640 8\r\n 680 4\r\n 720 6\r\n 760 4\r\n 800 6\r\n 840 6\r\n 880 6\r\n 920 8\r\n 960 6\r\n 1000 2\r\n 1040 4\r\n 1080 6\r\n 1120 2\r\n 1160 8\r\n 1200 6\r\n 1240 8\r\n 1280 6\r\n 1320 6\r\n 1360 4\r\n 1400 4\r\n 1440 6\r\n 1480 8\r\n 1520 4\r\n 1560 6\r\n 1600 4\r\n
\r\n--------\r\nFor the first couple, \r\n\r\n40! = 815915283247897734345611269596115894272000000000\r\n80! = 71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000',10657,0);
INSERT INTO comment VALUES (10661,1338,4906,'stan','One Solution','2003-12-22 08:43:59',3,'\r\n1 8 = 2 x 9\r\n9 + 6 = 1 5\r\n5 = 1 0 / 2\r\n1 1 - 5 = 6\r\n\r\nSince the lines cannot begin or end with \"=\", the first line must begin and end with 1 and 9, the last line with 1 and 6. Then some trial and error gives the solution above. There may be others...\r\n ',NULL,0);
INSERT INTO comment VALUES (10662,706,1301,'Charlie','re(2): simple solution','2003-12-22 08:46:01',0,'By the way, with the only possibilities being 2, 4, 6 and 8, it\'s not too hard to get the right answer by an invalid method.',10660,0);
INSERT INTO comment VALUES (10663,706,4908,'don scheuer','Seems Simple','2003-12-22 13:34:44',0,'the last non-zero digit is 4',NULL,0);
INSERT INTO comment VALUES (10664,1509,4909,'Brian','lovelorn snail','2003-12-22 14:02:50',0,'1996 was a leap year, so the snail made it out on march 12 before he dropped that night.\r\n',NULL,0);
INSERT INTO comment VALUES (10665,1509,4909,'Brian','lovelorn snail','2003-12-22 14:03:22',0,'1996 was a leap year, so the snail made it out on march 12 before he dropped that night.\r\n',NULL,0);
INSERT INTO comment VALUES (10666,1509,4909,'Brian','re: solution','2003-12-22 14:06:32',0,'he goes 3 feet a day which takes 2 days off your solution\r\n',10462,0);
INSERT INTO comment VALUES (10667,1509,4909,'Brian','re: solution','2003-12-22 14:07:03',0,'he goes 3 feet a day which takes 2 days off your solution\r\n',10462,0);
INSERT INTO comment VALUES (10668,1509,4909,'Brian','get it?','2003-12-22 14:10:36',0,'1996 is a leap year, but it only take the snail 28 days to go 30 feet because he doesn\'t slip back down on the 28th day because he is OUT! therefore the date is march 12th. tyvm',10436,0);
INSERT INTO comment VALUES (10669,706,1301,'Charlie','re: Seems Simple','2003-12-22 14:25:13',0,'That\'s the last non-zero digit of 20! itself, but not of the factorial of that number.',10663,0);
INSERT INTO comment VALUES (10670,513,4909,'Brian','solution','2003-12-22 15:00:15',0,'this sentence doesn\'t contain seven words',8039,0);
INSERT INTO comment VALUES (10671,227,4909,'Brian','1st case','2003-12-22 15:24:12',0,'lose the first case and win succeeding cases and be free of all constrictions\r\n',NULL,0);
INSERT INTO comment VALUES (10672,1509,4902,'bridgette','poor herb','2003-12-22 18:03:25',0,'herb never will get out. if he climbs 3 feet in a day (24 hours) but only climbs 16 hours a day ( 2 feet) then he slides back the same two feet when he sleeps each night. so he never gets out. poor herb!',NULL,0);
INSERT INTO comment VALUES (10673,1551,4507,'Penny','Hint','2003-12-22 18:52:13',2,'If WEIUTIBSTBZWJEPBGNSFUKHR is a single word formed by straight letter substitution, then it is a 24-letter word of which the 1st and 12th letters are identical, as are the 2nd and 14th letters. Other than proper names, there are only five legitimate 24-letter words in the English language: \r\n\r\nformaldehydesulphoxylate \r\npathologicopsychological\r\nscientificophilosophical\r\ntetraiodophenolphthalein\r\nthyroparathyroidectomize\r\n\r\nNone of them have those two matching letter pairs. So maybe it\'s an anagram or a person\'s name or a place name?.....\r\n\r\n\n\nEdited on December 23, 2003, 1:34 am',NULL,0);
INSERT INTO comment VALUES (10674,1338,1301,'Charlie','re: One Solution -- verification of uniqueness','2003-12-22 18:52:44',0,'As stan noted, the two strips containing only numbers must come at one end or the other of the set of strips. Also, the strip with -19= must be flipped relative to the others to have the one equal sign and one operator in each row. Also, either or both of the numeric strips may be flipped independently. Additionally, the whole set may be flipped.\r\n\r\nTo find all the solutions (verify the uniqueness of the one stan found), the following program is run:\r\n\r\nDECLARE SUB permute (a$)\r\nDATA 8+=1,=61-,2=05,9526,*1/=,1561\r\nallFlipped:\r\nDATA 1=+8,-19=,50=2,9526,=/1*,1561\r\n\r\nCLS\r\n\r\nFOR i = 1 TO 6\r\n READ s$(i)\r\nNEXT\r\n\r\nGOSUB evalPerms\r\ns$(4) = \"9256\" \'reverse strip 4\r\nGOSUB evalPerms\r\ns$(6) = \"1951\" \'reverse strip 6\r\nGOSUB evalPerms\r\ns$(4) = \"9526\" \'reverse strip 4 back to original\r\nGOSUB evalPerms\r\n\r\nRESTORE allFlipped\r\nPRINT\r\nFOR i = 1 TO 6\r\n READ s$(i)\r\nNEXT\r\n\r\nGOSUB evalPerms\r\ns$(4) = \"9256\" \'reverse strip 4\r\nGOSUB evalPerms\r\ns$(6) = \"1951\" \'reverse strip 6\r\nGOSUB evalPerms\r\ns$(4) = \"9526\" \'reverse strip 4 back to original\r\nGOSUB evalPerms\r\n\r\nEND\r\n\r\nevalPerms:\r\n order$ = \"1235\"\r\n FOR ord = 1 TO 24\r\n o2$ = \"46\"\r\n FOR o1 = 1 TO 2\r\n order1$ = LEFT$(o2$, 1) + order$ + RIGHT$(o2$, 1)\r\n FOR row = 1 TO 4\r\n eq$ = \"\"\r\n good = 1: pCol = 0\r\n FOR col = 1 TO 6\r\n newCh$ = MID$(s$(VAL(MID$(order1$, col, 1))), row, 1)\r\n IF pCol = 1 AND INSTR(\"+-*/=\", newCh$) > 0 THEN good = 0: EXIT FOR\r\n IF INSTR(\"+-*/=\", newCh$) > 0 THEN pCol = 1: ELSE pCol = 0\r\n eq$ = eq$ + newCh$\r\n NEXT col\r\n eq$(row) = eq$\r\n IF good = 0 THEN EXIT FOR\r\n num1$ = \"\": p = 1\r\n DO\r\n num1$ = num1$ + MID$(eq$, p, 1)\r\n p = p + 1\r\n LOOP UNTIL INSTR(\"+-*/=\", MID$(eq$, p, 1))\r\n op1$ = MID$(eq$, p, 1): p = p + 1: num2$ = \"\"\r\n DO\r\n num2$ = num2$ + MID$(eq$, p, 1)\r\n p = p + 1\r\n LOOP UNTIL INSTR(\"+-*/=\", MID$(eq$, p, 1))\r\n op2$ = MID$(eq$, p, 1): p = p + 1\r\n num3$ = MID$(eq$, p)\r\n IF op1$ = \"=\" THEN \'standardize so num1 rel num2 = num3\r\n h$ = num1$\r\n num1$ = num2$: num2$ = num3$: num3$ = h$\r\n op1$ = op2$\r\n END IF\r\n SELECT CASE op1$\r\n CASE \"+\"\r\n IF VAL(num1$) + VAL(num2$) <> VAL(num3$) THEN good = 0: EXIT FOR\r\n CASE \"-\"\r\n IF VAL(num1$) - VAL(num2$) <> VAL(num3$) THEN good = 0: EXIT FOR\r\n CASE \"*\"\r\n IF VAL(num1$) * VAL(num2$) <> VAL(num3$) THEN good = 0: EXIT FOR\r\n CASE \"/\"\r\n IF VAL(num1$) / VAL(num2$) <> VAL(num3$) THEN good = 0: EXIT FOR\r\n END SELECT\r\n NEXT row\r\n IF good THEN\r\n PRINT\r\n FOR row = 1 TO 4\r\n PRINT eq$(row)\r\n NEXT\r\n END IF\r\n \r\n o2$ = RIGHT$(o2$, 1) + LEFT$(o2$, 1)\r\n NEXT o1\r\n permute order$\r\n NEXT ord\r\nRETURN\r\n\r\nSUB permute (a$)\r\nDEFINT A-Z\r\n x$ = \"\"\r\n FOR i = LEN(a$) TO 1 STEP -1\r\n l$ = x$\r\n x$ = MID$(a$, i, 1)\r\n IF x$ < l$ THEN EXIT FOR\r\n NEXT\r\n\r\n IF i = 0 THEN\r\n FOR j = 1 TO LEN(a$) \\ 2\r\n x$ = MID$(a$, j, 1)\r\n MID$(a$, j, 1) = MID$(a$, LEN(a$) - j + 1, 1)\r\n MID$(a$, LEN(a$) - j + 1, 1) = x$\r\n NEXT\r\n ELSE\r\n FOR j = LEN(a$) TO i + 1 STEP -1\r\n IF MID$(a$, j, 1) > x$ THEN EXIT FOR\r\n NEXT\r\n MID$(a$, i, 1) = MID$(a$, j, 1)\r\n MID$(a$, j, 1) = x$\r\n FOR j = 1 TO (LEN(a$) - i) \\ 2\r\n x$ = MID$(a$, i + j, 1)\r\n MID$(a$, i + j, 1) = MID$(a$, LEN(a$) - j + 1, 1)\r\n MID$(a$, LEN(a$) - j + 1, 1) = x$\r\n NEXT\r\n END IF\r\nEND SUB\r\n\r\nIt finds only\r\n18=2*9\r\n9+6=15\r\n5=10/2\r\n11-5=6\r\n\r\n',10661,0);
INSERT INTO comment VALUES (10675,1475,4913,'Dotto','I\'m not even American and I got this (I think)','2003-12-22 21:54:49',0,'Assuming he means the mainland:\r\n\r\nHe travelled to Maine and went to the most northerly point there and to the most easterly point there (these are also the most northerly and easterly points of the U.S.). He travelled down via boat to Florida to reach the most southerly point, keeping within U.S. waters. He then travelled around the world to reach the most westerly point (looking at the map, somewhere in California).\r\n\r\nI guess if he means Alaska and Hawaii as well I\'m stuck. But if it\'s just the mainland that\'d be right.',NULL,0);
INSERT INTO comment VALUES (10676,1509,4915,'Neil Prowd','persistent snail makes escape?','2003-12-23 01:31:33',0,'I calculate that the snail reaches his freedom at 10pm on the 12th March :)',NULL,0);
INSERT INTO comment VALUES (10677,1531,1183,'fwaff','Yes I can.','2003-12-23 09:35:04',3,'The four plots are all the same shape as the original with each side reduced by a half. The corners of each plot in standard (x,y) format are....\r\n\r\n1. (0,30), (0,60), (30,60), (30,45), (15,45), (15,30)\r\n\r\n2. (15,30), (15,45), (45,45), (45,15), (30,15), (30,30)\r\n\r\n3. (30,45), (30,60), (60,60), (60,30), (45,30), (45,45)\r\n\r\n4. (30,0), (30,15), (45,15), (45,30), (60,30), (60,0)',NULL,0);
INSERT INTO comment VALUES (10678,1531,4908,'don scheuer','Yes, I can help him','2003-12-23 09:39:22',0,'Connect (15,30) to (15,45) to (30,45) to (30,60). Then connect (30,45) to (45,45) to (45,30) to (60,30). Finally, connect (45,30) to (45,15) to (30,15).',NULL,0);
INSERT INTO comment VALUES (10679,1531,1575,'DJ','','2003-12-23 10:27:35',3,'You can make four pieces that are the same size, and not only identical in shape to each other, but to the original piece:\r\n\r\n ___________\r\n| | |\r\n| __|__ |\r\n| | | |\r\n|__|__ |__|\r\n | | |\r\n |__| |\r\n | |\r\n |_____|
\r\n\r\nI know other solutions have been posted, but I didn\'t feel like plotting all their little points to see if they have the same solution I do. Everyone likes a visual better anyway...',NULL,0);
INSERT INTO comment VALUES (10680,706,3558,'Tristan','re(3): simple solution','2003-12-23 12:53:20',0,'Yeah, you\'re right. I simply can\'t argue with those numbers. It\'s too bad my solution didn\'t work, because it was easy to understand.',10662,0);
INSERT INTO comment VALUES (10681,1458,4920,'James','What about . . .','2003-12-23 12:54:50',0,'Why can\'t the cigarette just be lit? It may burn evenly (I don\'t know, I don\'t smoke), but there\'s a good chance that the ashes won\'t be symmetrical when it burns, thus dropping it. What state of matter is a flame considered as anyway?\r\n',NULL,0);
INSERT INTO comment VALUES (10682,1551,3558,'Tristan','re: Hint','2003-12-23 13:02:43',0,'By that logic, none of the other letters can be identical. So none of those words work. It must be more than one word all run together. If it is simple substitution, there\'s likely to be a pattern to the substitution, or solving such a puzzle would be improbable.',10673,0);
INSERT INTO comment VALUES (10683,1509,4920,'James','Slow but steady','2003-12-23 13:06:45',0,'March 2, 1996. Everyday he climbs 3 feet during the day only to slide down two feet each night. On the morning of the 17th day he will be three feet from the top of the well. He\'ll climb that distance and crest the edge.',NULL,0);
INSERT INTO comment VALUES (10684,1531,4374,'Richard','Contiguous?','2003-12-23 13:26:18',0,'The solutions of the first three comments are all the same, but do they meet the \"contiguous\" requirement of the problem? Contiguous means \"sharing an edge or boundary; touching.\" The problem thus seems to require that each plot at least touch the other three, which is not the case with the solution of the first three comnments. Perhaps the proposer meant \"connected\" instead of \"contiguous,\" or maybe there is another solution such that each plot shares a boundary with the others. \n\nEdited on December 23, 2003, 4:17 pm',NULL,0);
INSERT INTO comment VALUES (10685,1531,1626,'Gamer','re: Contiguous?','2003-12-23 15:00:32',0,'A variation of this puzzle I have seen says they don\'t have to be contigous, but that a person could walk on all of his property without stepping foot in another\'s property, this counts properties touching diagonally as counting. I think this problem wanted to not count properties only touching by diagonals as counting.',10684,0);
INSERT INTO comment VALUES (10686,1531,1575,'DJ','re(2): Contiguous?','2003-12-23 17:06:31',0,'Yes, by contiguous I took the problem to mean just that each of the son\'s plots must be a single piece, as opposed to taking several disjoint sections and saying that they constitute one of the son\'s portions of land.',10685,0);
INSERT INTO comment VALUES (10687,1543,4925,'Jeff','This statement is false.','2003-12-23 19:46:02',0,'It seems to me the problem with this logic is the same as the problem with statement\r\n\r\nS: This statement is false.\r\n\r\nOf course, if the truth value of the above statement is true it contradicts itself. The same can be said if the truth value is false. Similiary, this problem arises when dealing with a set of inner-referring statements such as\r\n\r\nS: Statement T is true.\r\nT: Statement S is false.\r\n\r\nClassically speaking, there has been no definitive answer to this type of paradox.\r\n\r\n--Graatz',NULL,0);
INSERT INTO comment VALUES (10688,1312,4925,'Jeff','How I solved this (solution)','2003-12-23 20:12:03',0,'At quick glance, you notice that Paul and Bebe have 0 common answers thus neither Paul nor Bebe got all 5 correct. Todd shares 2 answers with both Paul and Jason thus Todd did not get all 5 correct. Jason shares 2 answers with both Todd and Alicia thus Jason did not get all 5 correct. This leaves Alicia as the student getting all 5 answers correct and as a check, if this is the case, Paul had 4/5, Todd had 3/5, Jason had 2/5, and Bebe had 1/5.\r\n\r\n--Graatz',NULL,0);
INSERT INTO comment VALUES (10689,826,4925,'Jeff','Misuse of induction','2003-12-23 20:42:46',0,'Induction assumes that there is a set S with a least element (Well Ordering Principle). Induction, in breif, generalizes that a set S is equivalent to N (natural numbers, of course) if and only if every element in S is generated by stepwise combinations of the least element.\r\n\r\nTo use induction in a formal proof, one must establish a set, a property p(n), and a least element of the set S (call it 1) such that p(1) is true. Then by assuming p(n-1) is true, it must follow that p(n) is true (or equivically, if p(m) is true for all m between 1 and n are true (left inclusive), then p(n) must be true).\r\n\r\nQuite clearly, this proof does not correctly use induction because there is no least element of the set in question. In other words, it is never esablished that a set of k dogs has a \"least\" dog from which the other dogs are generated.\r\n\r\n--Graatz',NULL,0);
INSERT INTO comment VALUES (10690,1429,3171,'snapp','i finnally got one','2003-12-23 20:54:38',0,'i just had to say it',NULL,0);
INSERT INTO comment VALUES (10691,263,4925,'Jeff','Think physics and limit theory (solution)!','2003-12-23 21:00:42',3,'Assume that Achilles gives the tortise a 1m head start (measure from the front of Achilles and the back of the tortise) and moves at 1m/s. Assume the torise moves at .5m/s. In 1 second the two bodies are .5m apart. (1/2 the original distance). In another .5 seconds, the two bodies are .25m apart (1/2 the new distance). Certainly time can be sliced infinitely small such that the distances keep decreasing by a factor of 1/2. But notice under these conditions, the summation of time this takes approaches 2s, never at or above. Logic allows us then to consider what happens at the instant of 2s (as does the simple calculation of the veolcity and distance). The distance between the 2 is 0m and thus Achilles wins (horray!)\r\n\r\n--Graatz',NULL,0);
INSERT INTO comment VALUES (10692,66,4925,'Jeff','Just a thought','2003-12-23 21:15:16',1,'This question essentially assumes that every object must be able to be classified exclusively as one thing or the other, when this is quite often not the case. To be a little more specific, why must we assume that the only possible categories for people in the town are people that the barber shaves or people that shave themselves? I have heard the problem stated \"Assume everyone in town is either shaved exculsively by the barber or by themselves\" Is this assumption even a logical one to make? It seems not, as for the paradox that follows it.\r\n\r\nI have also heard the question asked as defining a word that indicates an adjective that describes itself (such as tiny, polysyllabic, etc) and defining another word for the opposite (such as long, monosyllablic, etc). [I wish I could remember what these words were for clarity\'s sake] A paradox then arises when one tries to classify the adjective itself that is used to describe adjectives that do not describe themselves. (!!) On the outside, these seem non-related but again the essential question is: must every adjective fit exactly one of these catagories?\r\n\r\nBlah, now I\'m just rambling....\r\n--Graatz',NULL,0);
INSERT INTO comment VALUES (10693,1409,4925,'Jeff','Pondering (still haven\'t solved yet)','2003-12-23 21:44:56',4,'Of course, a 100% is possible with just a 1 question test (however rather cruel!) but must all other answers take the form n/p^m (prime p) where n < p <===this much is obvious]?\r\n\r\nThis also makes me wonder if there is a definitive way to produce answers for all possible grades (ie least # of question that can have a grade of 96; a grade of 34; etc). Will these also take on the form n/p^m ?\r\n\r\nAny response to this is greatly appreciated, as I don\'t feel like just brute-forcing this question.\r\n\r\n--Graatz',NULL,0);
INSERT INTO comment VALUES (10694,1458,4926,'John','Yippy kai yay','2003-12-23 22:09:45',0,'Simple ways are sometimes too obvious, but I say start a good old fashioned bar fight. It may be painful but that cigerette won\'t stand a chance.\r\n\r\nJust shoot it. You aren\'t touching the bullet so technically you didn\'t touch it with anything.\r\n\r\nMore seriously this reminds me of a brain teaser from when I was a kid except for not being able to touch the foundation. The answer for that one was to hit a penny with another penny to move the a third one.',NULL,0);
INSERT INTO comment VALUES (10695,690,4926,'John','intuition vs. science','2003-12-23 23:38:45',0,'Vinodhan explains this very well. This is something that is already well known by metalworkers. When your cool steel quickly it will become case hardened. I remember this from a course in manufacturing processes. The reason it won\'t burst into flames is because the flash point deals with the vapor, the temperature to ingite a liquid or solid is the ingition point. ',NULL,0);
INSERT INTO comment VALUES (10696,1440,3705,'zaphod','','2003-12-24 01:51:43',3,'We\'re evaluating Sum = (2x)²+(2x-1)²+...+(x+1)²-x²-(x-1)²-...-1²\r\nGrouping up the terms: Sum = [(2x)²-x²]+[(2x-1)²-(x-1)²]+...+[(x+1)²-1²]\r\nEach bracket [] contains a difference of squares, so: Sum = (2x+x)*(2x-x)+(2x-1+x-1)*(2x-1-x+1)+...+(x+1+1)*(x+1-1) = 3x*x+(3x-2)*x+...+(x+2)*x = x*[(x+2)+(x+4)+...+(3x-2)+3x]\r\nRe-grouping inside the brackets: Sum = x*[(x+x+...+x)+2+4+...+(2x-2)+2x] = x*[(x+x+...+x)+2(1+2+...+(x-1)+x)]\r\nThere are x x\'s in the first parentheses, and the sum inside the second parentheses is x*(x+1)/2. Thus: Sum = x*[x²+x(x+1)] = x²*(x+x+1) = x²(2x+1)\r\nFor the second result: x²(x+1)²-x^4 = x²(x²+2x+1)-x^4 = x^4+2x³+x²-x^4 = 2x³+x² = x²(2x+1)\r\nAnd that about does it :)',NULL,0);
INSERT INTO comment VALUES (10697,1340,1301,'Charlie','thoughts','2003-12-24 08:55:29',1,'There have to be at least three numbers to be added, as each number can have at most three dots, and we need to use up 8.\r\n\r\nRepeated single digits immediately after the decimal point are ninths (e.g., .7777... = 7/9). Repeated double digits immediately after the decimal point are 99ths, such as .67676767... = 67/99, etc.) \r\n\r\nIf they start repeating some place further on, they are divided by the appropriate power of 10, such as .00123123123123... = 123/99900, and then of course .65123123123123... = 123/99900 + 65/100, whatever that reduces to. The numbers are to be written in the dot fashion, of course, which is a little unwieldy for use here, but the point is, for example:\r\n\r\n\r\n . .\r\n.4 + .5 = 1\r\n
\r\n--------\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (10698,1340,775,'Cory Taylor','and the winner is...','2003-12-24 09:52:48',0,'someone else, surely, but I thought I\'d get the ball rolling. And at least for a little while, I\'m winning!!\r\n\r\nI\'ve got a solution that gets within 6/99 of the target, though I\'ve a dot left over. If it is permissible, I can waste the extra dot on a whole number, but not sure if this is allowed. So here goes...\r\n\r\n74+6+9/9+8/9+5/99=81+93/99, or,\r\n74 + + 6. + .9dot + .8dot + .0dot5dot',NULL,0);
INSERT INTO comment VALUES (10699,1531,4903,'naive','The Solution','2003-12-24 09:59:56',3,'We divide the given figure into 12 squares as shown in the fig.Let the brothers be named A,B,C and D.Now each one of them shoud get an area of \r\ncomprising of 3 squares.As can be seen from the figure, the allotment serves our both purposes ie the area alloted to each brother has the same shape as others and is contiguous.(Squares marked X have been used for formatting purposes)\r\n\r\n -- -- -- --\r\n|A |A |B |B |\r\n -- -- -- --\r\n|A |D |D |B |\r\n -- -- -- --\r\n|X |X |D |C |\r\n -- - -- --\r\n|X |X |C |C |\r\n -- -- -- --',NULL,0);
INSERT INTO comment VALUES (10700,1340,2370,'Dave','my answer','2003-12-24 11:55:40',0,'I got 82.2222... with the following equation:\r\n80 + .54(dots over 5, 4) + .9(dot) + .67 (dots over 6, 7)',NULL,0);
INSERT INTO comment VALUES (10701,1340,2370,'Dave','re: my answer (closer one)','2003-12-24 11:58:51',0,'80 + .4(dot) + .95(dots over 9,5) + .67 (dots over 6,7) yields\r\n82.0808080808...',10700,0);
INSERT INTO comment VALUES (10702,1544,1575,'DJ','None','2003-12-24 13:28:45',0,'There is no solution; it is a diverging series. The sum of the reciprocals of all the known primes only adds up to about 4, but the complete series adds up to an infinite number.\r\n\r\nI\'ll leave the proof up to someone else...',NULL,0);
INSERT INTO comment VALUES (10703,1544,4374,'Richard','re: None','2003-12-24 13:47:41',0,'A nice reference (with Euler\'s proof) is Hua\'s Introduction to Number Theory. See also Proofs from the Book.',10702,0);
INSERT INTO comment VALUES (10704,1340,3558,'Tristan','even closer...','2003-12-24 14:14:46',0,'\r\n . .. ..\r\n80.9+.46+.57=82+4/99\r\n\r\nI just brute forced it and as a result, I will be surpassed by other people even more. I bet Charlie could write a program for this.',NULL,0);
INSERT INTO comment VALUES (10705,1340,4374,'Richard','4/99 high','2003-12-24 14:18:41',0,'80 + .4\'7\' +.5\'6\' +.9\' = 81 + 103/99 = 80 + .4\'6\' +.5\'7\' +.9\' also.',NULL,0);
INSERT INTO comment VALUES (10706,1544,1301,'Charlie','informal indication','2003-12-24 15:54:34',0,'Even without rigorous proof it would seem that this series diverges. The informal reasoning is that the density of prime numbers in the vicinity of x is 1/ln(x). If we multiply this density function by the function 1/x, representing the values in the series itself, we get 1/(x ln x) to be integrated out to infinity. But ∫(1/(x ln x)) dx = ln(ln(x)), and this function increases without limit as x grows larger, albeit very slowly.',NULL,0);
INSERT INTO comment VALUES (10707,1340,1301,'Charlie','re: even closer...','2003-12-24 16:17:47',0,'\"I bet Charlie could write a program for this. \"\r\n\r\nBelieve me, I\'ve thought about it. But the 32,432,400 distinct permutations of 7 distinct digits and 8 dots gives one pause, especially considering that one has to throw in a few +\'s as well.\r\n\r\nJust considering the permutations of 7 different digits, 8 dots and 3 +signs gives 26,464,838,400 possibilities. Although some may be nonsensical, such as two plus signs in a row, or a repetition dot other than just before a +, there\'s also the possibility of just two +\'s, or of four +\'s.\r\n\r\nBut if anyone can think of an algorithm that could work this out in reasonable time, I\'d be interested.\r\n',10704,0);
INSERT INTO comment VALUES (10708,82,4926,'John','The morale is','2003-12-24 16:20:27',0,' As soon as the clock is started back up where ever Prometheus is became very crowded indeed. I think he was suffocated, and not killed by any particular demon. Imagine even a trillion demons in a tiny room all squashed instantly along with poor Prometheus. The moral is that you shouldn\'t make Zeus angry. ',NULL,0);
INSERT INTO comment VALUES (10709,1340,3558,'Tristan','Got it!','2003-12-24 17:38:41',3,'\r\n . .. ..\r\n80.7+.54+.69=82+2/99\r\n\r\nAgain I just brute forced it.\r\n\r\nEdit: I had another solution here with 0 difference, but I repeated a number, thus the title.\n\nEdited on December 24, 2003, 5:41 pm',NULL,0);
INSERT INTO comment VALUES (10710,1517,4925,'Jeff','THE solution :)','2003-12-24 17:42:00',0,'The solution is that the hardware shop owner is going out of business & is trying to clear out his inventory so everything in his store is buy one for $0.10, fifteen for $0.20 and one-hundred ten for $0.30\r\n\r\n--OR--\r\n\r\nThe hareware shop owner failed basic math and honestly feels he\'s getting the better end of this deal\r\n\r\n:)\r\n\r\n--Graatz',NULL,0);
INSERT INTO comment VALUES (10711,1340,3558,'Tristan','This time I really got it','2003-12-24 17:55:21',3,'\r\n . .. ..\r\n80.5+.64+.79=82\r\n\r\nI got zero difference by brute force after several attempts. But, to further describe my methods, I first made a few assumptions. I decided that if you started with 79 or lower, then you would not have enough. If you started with two numbers to add up to around 80, then you would be forced to use 4 numbers with only 2 dots. Therefore, I decided that starting with 80 would most likely have a solution. There had to be three other numbers using 3, 3, and 2 dots each. Brute force took me the rest of the way, and of course, I just put one of the decimals into the 80 to make the solution simpler.\r\n\r\nBTW, besides trivial permutations, you can also switch around the digits in the last two decimals for another solution.\n\nEdited on December 24, 2003, 6:03 pm',NULL,0);
INSERT INTO comment VALUES (10712,1334,3171,'snapp','I got it','2003-12-24 18:13:56',0,'it\'s seven, six pennies around one pennies. I think anything else would violate the rules.',NULL,0);
INSERT INTO comment VALUES (10713,1544,3351,'Eric','very slowly indeed','2003-12-24 19:08:07',0,'The recipricol of the 40th Mersenne prime is on the order of 10^-6320431, and as DJ said the sum of all known primes is only about 4.',10703,0);
INSERT INTO comment VALUES (10714,1341,4926,'John','re(2): solution','2003-12-24 19:29:11',0,'I believe you have the right of it, but since I also come from an engineering background I am also sure that the high priests of calculus will cast down us non-believers. \r\n\r\nI noticed many or your arguments were struck down by platitudes that you (we for that matter) don\'t understand the difference between \'stopped processing\' and \'no longer processing\'. While I admit they are not precisely the same for this purpose the difference seems to be of no consequence. It was dismissively labeled as non sequitur. However as you were neither affirming the consequent, or denying the antecedent, and it certainly logically follows that when you have \"processed\" ALL your marbles that you have indeed stopped. (ok, you could start over but that wouldn\'t change the fact that you had completed a cycle, and could now numerate the iterations) Ergo it is not non sequitur. Maybe they forgot to mention the magic quantum marble accelerator with Phantom Power (TM) :) ',9628,0);
INSERT INTO comment VALUES (10715,1310,4926,'John','simple may be best','2003-12-24 22:32:47',0,'I\'d go with the first solution. After all the complicated ones could mess up the icing and then you\'d have to deal with Stephanie.',NULL,0);
INSERT INTO comment VALUES (10716,1340,1301,'Charlie','re(2): even closer...','2003-12-25 01:37:02',3,'Well, by avoiding going through all those permutations, I got a program written, anticlimactically after the solution was found manually. \r\n\r\nThe program doesn\'t count the dots, but there are not that many solutions that add to 82, so the ones with 8 dots can be picked out manually. The output shows the ordinary decimal points, plus a dot before a repetition, and after a repetition of more than one digit. The total is shown, and sometimes due to internal rounding, it does not seem to be exactly 82, but it is:\r\n\r\n\r\n80.4.6 ..5 .9.7 82\r\n80..46. ..5 ..97. 82\r\n80.6.4 ..5 .7.9 82\r\n80..64. ..5 ..79. 82\r\n80.4.7 ..5 .9.6 82.00000000000001\r\n80..47. ..5 ..96. 82\r\n80.7.4 ..5 .6.9 82.00000000000001\r\n80..74. ..5 ..69. 82.00000000000001\r\n80..5 .4.6 .9.7 82\r\n80..5 ..46. ..97. 82\r\n80..5 .6.4 .7.9 82\r\n80..5 ..64. ..79. 82\r\n80..5 .4.7 .9.6 82\r\n80..5 ..47. ..96. 82\r\n80..5 .7.4 .6.9 82\r\n80..5 ..74. ..69. 82.00000000000001\r\n80.6.9 .7.4 ..5 81.99999999999999\r\n80..69. ..74. ..5 82.00000000000001\r\n80.9.6 .4.7 ..5 82\r\n80..96. ..47. ..5 82\r\n80.7.9 .6.4 ..5 82\r\n80..79. ..64. ..5 82\r\n80.9.7 .4.6 ..5 82.00000000000001\r\n80..97. ..46. ..5 82\r\n80 .4.6 ..5 .9.7 82\r\n80 ..46. ..5 ..97. 82\r\n80 .6.4 ..5 .7.9 82\r\n80 ..64. ..5 ..79. 82\r\n80 .4.7 ..5 .9.6 82\r\n80 ..47. ..5 ..96. 82\r\n80 .7.4 ..5 .6.9 82\r\n80 ..74. ..5 ..69. 82.00000000000001\r\n
\r\n-------\r\n\r\nThese are the same results Tristan got manually, with the fractions shuffled among the three addends. The ones with only 6 dots in fact merely have a single digit after the decimal and a single repeated digit after that.\r\n\r\n\r\nThe program:\r\nDECLARE SUB groupEm (avail$)\r\nDECLARE SUB buildOn (avail$)\r\nDECLARE SUB examine (g#)\r\nDECLARE SUB permute (a$)\r\nDEFDBL A-Z\r\n\r\nCLEAR , , 4000\r\ndig$ = \"0456789\"\r\nDIM SHARED grps AS INTEGER\r\nDIM SHARED grp$(10), hist$(10), valHist(10), perm(10)\r\nDIM SHARED minDots, maxDots, totValue\r\n\r\nOPEN \"dots.txt\" FOR OUTPUT AS #2\r\nperm(1) = 1\r\nFOR i = 2 TO 10\r\n perm(i) = i * perm(i - 1)\r\nNEXT\r\n\r\ngrps = 0: totValue = 0\r\ngroupEm dig$\r\nCLOSE\r\n\r\nEND\r\n\r\nSUB buildOn (avail$)\r\n STATIC ct\r\n IF avail$ = \"\" THEN\r\n ct = ct + 1\r\n PRINT ct; \" \";\r\n FOR i = 1 TO grps\r\n PRINT grp$(i); \" \";\r\n NEXT\r\n PRINT\r\n minDots = 0: maxDots = 0: totValue = 0\r\n examine 1\r\n\' IF ct / 40 = INT(ct / 40) THEN DO: LOOP UNTIL INKEY$ > \"\"\r\n ELSE\r\n groupEm avail$\r\n IF LEN(avail$) > 3 - grps THEN\r\n FOR i = 1 TO LEN(avail$)\r\n ch$ = MID$(avail$, i, 1)\r\n IF ch$ > RIGHT$(grp$(grps), 1) THEN\r\n grp$(grps) = grp$(grps) + ch$\r\n av2$ = LEFT$(avail$, i - 1) + MID$(avail$, i + 1)\r\n buildOn av2$\r\n grp$(grps) = LEFT$(grp$(grps), LEN(grp$(grps)) - 1)\r\n END IF\r\n NEXT\r\n END IF\r\n END IF\r\nEND SUB\r\n\r\nSUB examine (g)\r\n gr$ = grp$(g)\r\n l = LEN(gr$)\r\n FOR p = 1 TO perm(l)\r\n FOR decimal = 0 TO l\r\n FOR begrept = 0 TO decimal\r\n iPart$ = LEFT$(gr$, l - decimal)\r\n valHist(g) = VAL(iPart$)\r\n n1$ = \"\"\r\n n2$ = \"\"\r\n IF decimal > 0 THEN\r\n n1$ = MID$(gr$, l - decimal + 1, decimal - begrept)\r\n num1 = VAL(n1$)\r\n den1 = VAL(LEFT$(\"100000000\", decimal - begrept + 1))\r\n valHist(g) = valHist(g) + num1 / den1\r\n IF begrept > 0 THEN\r\n n2$ = MID$(gr$, l - begrept + 1)\r\n num2 = VAL(n2$)\r\n den2 = VAL(LEFT$(\"999999999\", begrept))\r\n valHist(g) = valHist(g) + num2 / (den2 * den1)\r\n END IF\r\n END IF\r\n hist$(g) = iPart$\r\n IF n1$ > \"\" OR n2$ > \"\" THEN hist$(g) = hist$(g) + \".\" + n1$\r\n IF n2$ > \"\" THEN hist$(g) = hist$(g) + \".\" + n2$\r\n IF LEN(n2$) > 1 THEN hist$(g) = hist$(g) + \". \"\r\n tValSave = totValue\r\n totValue = totValue + valHist(g)\r\n IF g < grps THEN\r\n IF totValue < 83 THEN\r\n examine g + 1\r\n END IF\r\n ELSE\r\n IF ABS(totValue - 82) < .001 THEN\r\n FOR i = 1 TO grps\r\n PRINT hist$(i); \\\" \\\";\r\n PRINT #2, hist$(i); \\\" \\\";\r\n NEXT\r\n PRINT \\\" \\\"; totValue\r\n PRINT #2, \\\" \\\"; totValue\r\n END IF\r\n END IF\r\n totValue = tValSave\r\n NEXT begrept\r\n NEXT decimal\r\n permute gr$\r\n NEXT p\r\nEND SUB\r\n\r\nSUB groupEm (avail$)\r\n grps = grps + 1\r\n grp$(grps) = LEFT$(avail$, 1)\r\n av2$ = MID$(avail$, 2)\r\n buildOn av2$\r\n grps = grps - 1\r\nEND SUB\r\n\r\nDEFSNG A-Z\r\nSUB permute (a$)\r\nDEFINT A-Z\r\n x$ = \\\"\\\"\r\n FOR i = LEN(a$) TO 1 STEP -1\r\n l$ = x$\r\n x$ = MID$(a$, i, 1)\r\n IF x$ < l$ THEN EXIT FOR\r\n NEXT\r\n\r\n IF i = 0 THEN\r\n FOR j = 1 TO LEN(a$) \\ 2\r\n x$ = MID$(a$, j, 1)\r\n MID$(a$, j, 1) = MID$(a$, LEN(a$) - j + 1, 1)\r\n MID$(a$, LEN(a$) - j + 1, 1) = x$\r\n NEXT\r\n ELSE\r\n FOR j = LEN(a$) TO i + 1 STEP -1\r\n IF MID$(a$, j, 1) > x$ THEN EXIT FOR\r\n NEXT\r\n MID$(a$, i, 1) = MID$(a$, j, 1)\r\n MID$(a$, j, 1) = x$\r\n FOR j = 1 TO (LEN(a$) - i) \\ 2\r\n x$ = MID$(a$, i + j, 1)\r\n MID$(a$, i + j, 1) = MID$(a$, LEN(a$) - j + 1, 1)\r\n MID$(a$, LEN(a$) - j + 1, 1) = x$\r\n NEXT\r\n END IF\r\n\r\nEND SUB\r\n\r\n',10707,0);
INSERT INTO comment VALUES (10717,1442,4936,'Mary Buckingham','A Pronounced Day','2003-12-25 10:35:30',0,'The wife would answer \"Monday\", since that\'s the second day of the week in America.',NULL,0);
INSERT INTO comment VALUES (10718,1531,2130,'ethan','Solution','2003-12-25 12:26:55',3,'Draw a line from (30,15) to (45,15).\r\nDraw a line from (45,15) to (45,45).\r\nDraw a line from (15,45) to (45,45).\r\nDraw a line from (15,45) to (15,30).\r\nFrom (30,45) to (30,60). \r\nFrom (45,30) to (60,30).',NULL,0);
INSERT INTO comment VALUES (10719,1475,3646,'Brandon','Solution','2003-12-25 22:22:56',0,'Ted first visits the northernmost and westernmost points in Alaska, then he travels to Hawaii for the southernmost point, finally he goes through the Panama Canal to reach Maine for the easternmost point.',NULL,0);
INSERT INTO comment VALUES (10720,66,4945,'hiwhi','Ahem! Flaw!','2003-12-26 00:20:37',0,'Yeah, um, what about the people who have beards? They do not have. Anyway, ill just go look at the answer...',NULL,0);
INSERT INTO comment VALUES (10721,1312,4944,'Natalia','Gues','2003-12-26 00:24:04',0,' I find that the answer is in the way you put the question: someone got \"four right\", you didn\'t use the word\"correct\" as on the others.\r\n In my vision Alicia\'s Test it\'s the \"fourth right\" ,with all the answers \"correct\" :)',NULL,0);
INSERT INTO comment VALUES (10722,1442,4627,'donnmike','nitpicking','2003-12-26 00:56:43',0,'how the wife would correctly answer is not necessarily how she would most likely answer. if the wife mistakes the 2nd day of the week for tuesday, the intent of the trick, then she would most likely answer \'tuesday\' or \'chuesday\'.',10717,0);
INSERT INTO comment VALUES (10723,1491,4627,'donnmike','solution is wrong','2003-12-26 01:16:22',0,'a side of the box may be 6\', but the diagonal would still be longer than 6\'. the bus driver did not say that he couldn\'t bring anything on the bus with a length greater than 6\', but that he couldn\'t bring anything on the bus longer than 6\'. there is a difference. ',NULL,0);
INSERT INTO comment VALUES (10724,1491,1626,'Gamer','re: solution is wrong','2003-12-26 08:57:48',0,'Not much of one. The box isn\'t LONGer than 6; we are talking about its length. Long = length. It isn\'t wider than 6 wide, and isn\'t higher than 6 high.',10723,0);
INSERT INTO comment VALUES (10725,727,1575,'DJ','Common Word','2003-12-26 11:26:18',3,'Probably the answer he is looking for is indivisibility, which of course contains six is and no other vowels.\r\n\r\nOf course, if you count the y as a vowel, which is how it is used in this word, then you have to keep looking...\n\nEdited on December 26, 2003, 11:31 am',NULL,0);
INSERT INTO comment VALUES (10726,727,1575,'DJ','Another Possibility','2003-12-26 11:30:42',1,'Another English word [matching these criteria] that appears in several dictionaries is tamarasalata, a Greek fish roe paste used in appetizers.',NULL,0);
INSERT INTO comment VALUES (10727,727,4507,'Penny','Ooooooh my !!!!','2003-12-26 11:45:37',0,'This was a tough one !!',NULL,0);
INSERT INTO comment VALUES (10728,727,1301,'Charlie','the computer finds','2003-12-26 12:02:59',3,'defenselessnesses',NULL,0);
INSERT INTO comment VALUES (10729,727,1575,'DJ','Still more...','2003-12-26 13:37:31',1,'I asked google what answers other people have found to the same question, and here are some other words it found (other than the ones already mentioned):\r\nTATHAGATAGARBHA\r\nRETELEMETERED\r\nDEGENERESCENCE\r\nCHRONONHOTONTHOLOGOS\r\n\r\nWords with only one vowel are called univocalics (according to Dmitri Borgmann in Language on Vacation). The longest such word is STRENGTHLESSNESSES, although it contains only 5 Es.',NULL,0);
INSERT INTO comment VALUES (10730,1360,950,'sarah','i think...','2003-12-26 14:18:09',0,'i think that the probability is:\r\n 0.5219 to 4 s.f \r\nhowever there may some error as i used the long winded method of a tree diagram and i expect there is an easier way.\r\n',NULL,0);
INSERT INTO comment VALUES (10731,1360,4068,'Bruno','Well well well','2003-12-26 14:19:04',0,'I\'d say 52,184185% to do well on the fifth quiz.',NULL,0);
INSERT INTO comment VALUES (10732,1442,950,'sarah','','2003-12-26 14:26:52',0,'If the wife was considering tuesday as the 2nd day rather than monday i think she would say \"chuesday\" as that is how most people say it as it is \"tu\"',NULL,0);
INSERT INTO comment VALUES (10733,1360,1301,'Charlie','Depends...','2003-12-26 14:49:56',3,'The first question to be answered is whether, in fact, the mere statistics that the teacher presented actually back up her claim that \"how well a student does on a particular quiz is affected by how well or poorly he or she did on the last quiz.\"\r\n\r\nWhat immediately comes to mind is the likelihood that different students, whether due to motivation levels, different aptitudes for the subject, and other factors, tend consistently to do better or worse than others on these tests. Then, rather than being evidence for a test-to-test correlation for a given student, the statistics merely reflect that good students usually do better and poorer students poorer on the tests, and the previous test is a barometer of the aptitudes of the students.\r\n\r\nIn that case, and if the scores on the tests are actually independent, the probability of doing well on the fifth quiz given a good score on the first, would be the same as the probability of doing well on the second test given a good score on the first: 80%. (That\'s 80%, in case the html bold indication makes the number disappear entirely.)\r\n\r\nA scenario which approximates the statistics given, and consistent with the independence hypothesis is the following:\r\n\r\nIf the students are grouped into five groups, labeled Bright to Low, they could have the following probabilities, each, of scoring well, so-so or poorly:\r\n\r\n Well Soso Poorly\r\nBright 1 0 0 0.16\r\n 0.74 0.18 0.08 0.19\r\nAvg 0.14 0.79 0.07 0.25\r\n 0 0.16 0.84 0.2\r\nLow 0 0.05 0.95 0.2\r\n
\r\n--------\r\nThe last column is the fraction of the class that is in each of the five groups.\r\n\r\nThose statistics indicate the following as the probabilities that a student is at a given performance level given that he or she has done well, so-so or poorly on a given test:\r\n\r\np(bright) 0.476758 0 0\r\n 0.418951 0.124954 0.038905\r\np(avg) 0.104291 0.721593 0.044791\r\n 0 0.116916 0.429997\r\np(low) 0 0.036536 0.486307\r\n
\r\n-------\r\nTo take one example of how this was figured: p(bright given well) = 1*.16 / (1*.16 + .74*.19 + .14*.19) = .476758.\r\n\r\nThen, the probability of doing well on some other test given doing well on the first test would be\r\n.476758*1 + .418951*.74 + .104291*.14 = .801383, which might be quoted, to the nearest percent as 80%. The full distribution would be:\r\n\r\n p(well) p(soso) p(poorly)\r\nhad done well 0.801383 0.157801 0.040816\r\n\r\nhad done soso 0.193489 0.613084 0.193427\r\n\r\nhad done poorly 0.03506 0.135503 0.829437\r\n
\r\n-----\r\nwhich is close to the observed statistics.\r\n\r\nThe Excel solver wasn\'t able to come up with a scenario exactly matching all the given statistics. Perhaps the independence hypothesis is not enough to completely account for the statistics, but it certainly could account for the major tenor of them. In fact there could be mixed motivations in the student body, some being buoyed by a good score and depressed by a bad score, while others take a good score as a reason for \"resting on their laurels\" and tend to slack off or see a poor score as a \"wake up call\" to \"get cracking\". The combined mixture of student types and abilities could account for the statistics shown.\r\n\r\nThe alternative, from the teacher\'s opinion:\r\n\r\nBut, to take the teacher\'s point of view that the statistics are completely the result of the psychologically buoying effects of a good score and the depressing effects of a poor score, and they affect only the next test:\r\n\r\nIf the probabilities are as given by the statistics, from one test to the next, then for each successive test, the probability of doing well equals the probability of having done well on the previous test times .8 plus the probability of having done soso times .15 plus the probability of having done poorly times .05. Similar conditional probabilities, as given by the statistics, applied to the previous test\'s probabilities give the new test\'s probabilities. In the first test, we know the probability of having done well is 1, as that has already happened. The following program goes through the 4 additional generations of tests:\r\n\r\nDEFDBL A-Z\r\nCLS\r\n\r\nwell2well = .8#\r\nwell2soso = .15#\r\nwell2poor = .05#\r\n\r\nsoso2well = .2#\r\nsoso2soso = .6#\r\nsoso2poor = .2#\r\n\r\npoor2well = .03#\r\npoor2soso = .15#\r\npoor2poor = .82#\r\n\r\nDIM results(5, 3)\r\nresults(1, 1) = 1\r\nFOR i = 2 TO 5\r\n results(i, 1) = results(i - 1, 1) * well2well + results(i - 1, 2) * soso2well + results(i - 1, 3) * poor2well\r\n results(i, 2) = results(i - 1, 1) * well2soso + results(i - 1, 2) * soso2soso + results(i - 1, 3) * poor2soso\r\n results(i, 3) = results(i - 1, 1) * well2poor + results(i - 1, 2) * soso2poor + results(i - 1, 3) * poor2poor\r\n PRINT USING \" #.########\"; results(i, 1); results(i, 2); results(i, 3)\r\nNEXT\r\n\r\nPRINT results(5, 1)\r\n\r\nThe results are\r\n\r\n 0.80000000 0.15000000 0.05000000\r\n 0.67150000 0.21750000 0.11100000\r\n 0.58403000 0.24787500 0.16809500\r\n 0.52184185 0.26154375 0.21661440\r\n .5218418500000002\r\n
\r\n-------\r\nwith internal rounding causing that excess 00000002.\r\n\r\nWith the teacher\'s assumptions in mind, the answer would be 52.18%. (That\'s 52.18% in case the html bold indication makes the number disappear altogether.)\r\n\r\nSo the answer is somewhere between 52.18% and 80%, depending on how much general aptitude actually played in the statistics observed by the teacher. Similarly to the probability of broken sticks forming triangles, or random chords being larger than a circle\'s radius, or other coin\'s matching a reported coin\'s tails status, the probability depends on how the observed statistics got there.',NULL,0);
INSERT INTO comment VALUES (10734,1360,1301,'Charlie','re: Depends...','2003-12-26 15:02:42',0,'By the way, in going through various scenarios in the independent-tests assumption, 7 of the desired statistics could be made to come out exactly, as in the following set of the three tables presented:\r\n\r\n\r\n Well Soso Poorly\r\nBright 0.888224 0.072408 0.039369 0.360933\r\nAvg 0.142968 0.727862 0.12917 0.301099\r\nLow 0 0.081176 0.918824 0.337969\r\n\r\np(bright) 0.88162 0.095825 0.039076\r\np(avg) 0.11838 0.80358 0.106956\r\np(low) 0 0.100595 0.853968\r\n\r\nhad done well 0.8 0.15 0.049999\r\nhad done soso 0.2 0.6 0.2\r\nhad done poor 0.049999 0.15 0.8\r\n
\r\n-------\r\nExcel consistently made the probability of doing poorly given having done well equal to the probability of doing well having done poorly, here 5%, in order to get exact matches on the others.\r\n\r\n(this was with a simpler, 3-ability-level, scenario than was previously given.)\n\nEdited on December 26, 2003, 3:03 pm',10733,0);
INSERT INTO comment VALUES (10735,1491,4627,'donnmike','re(2): solution is wrong','2003-12-26 17:16:55',0,'There is a difference. You make the mistake of only considering the box, but the bus driver said he can\'t take ANYTHING longer than 6\' on the bus. A diagonal of a box is a thing. ',10724,0);
INSERT INTO comment VALUES (10736,865,4925,'Jeff','SOLUTION','2003-12-26 20:33:15',0,'Answer: \"This is the answer to that question.\"\r\n\r\n=P\r\n--Graatz',NULL,0);
INSERT INTO comment VALUES (10737,1360,4507,'Penny','Solution (only a common calculator used)','2003-12-26 20:58:34',3,'Symbols: G (Good), M (Mediocre), B (Bad)\r\n\r\nIf any quiz is G, the odds for the next quiz are G(0.8), M (0.15), B (0.05); \r\nIf any quiz is M, the next one\'s odds are G(0.2), M (0.6), B (0.2)\r\nIf any quiz is B, the next one\'s odds are G(0.3), M (0.15), B (0.82)\r\n\r\nAssuming the first quiz is G (probability=1), here are all possibilities for the next 4 quizzes that result in the 5th quiz being G: \r\n\r\n GGGG (0.8)(0.8)(0.8)(0.8) = 0.4096 \r\n GGMG (0.8)(0.8)(0.15)(0.2) = 0.0192 \r\n GGBG (0.8)(0.8)(0.05)(0.3) = 0.0096 \r\n GMGG (0.8)(0.15)(0.2)(0.8) = 0.0192 \r\n GMMG (0.8)(0.15)(0.6)(0.2) = 0.0010368 \r\n GMBG (0.8)(0.15)(0.2)(0.3) = 0.0072 \r\n GBGG (0.8)(0.05)(0.3)(0.8) = 0.0096 \r\n GBMG (0.8)(0.05)(0.15)(0.2) = 0.0012 \r\n GBBG (0.8)(0.05)(0.82)(0.3) = 0.00984 \r\n MGGG (0.15)(0.2)(0.8)(0.8) = 0.0192 \r\n MGMG (0.15)(0.2)(0.15)(0.2) = 0.0009 \r\n MGBG (0.15)(0.2)(0.05)(0.3) = 0.0003 \r\n MMGG (0.15)(0.6)(0.2)(0.8) = 0.0144 \r\n MMMG (0.15)(0.6)(0.6)(0.2) = 0.0108 \r\n MMBG (0.15)(0.6)(0.2)(0.3) = 0.0054 \r\n MBGG (0.15)(0.2)(0.3)(0.8) = 0.0072 \r\n MBMG (0.15)(0.2)(0.15)(0.2) = 0.0009 \r\n MBBG (0.15)(0.2)(0.82)(0.3) = 0.00738 \r\n BGGG (0.05)(0.3)(0.8)(0.8) = 0.0096 \r\n BGMG (0.05)(0.3)(0.15)(0.2) = 0.00045 \r\n BGBG (0.05)(0.3)(0.05)(0.3) = 0.000225 \r\n BMGG (0.05)(0.15)(0.2)(0.8) = 0.0012 \r\n BMMG (0.05)(0.15)(0.6)(0.2) = 0.0009 \r\n BMBG (0.05)(0.15)(0.2)(0.3) = 0.00045 \r\n BBGG (0.05)(0.82)(0.3)(0.8) = 0.00984 \r\n BBMG (0.05)(0.82)(0.15)(0.2) = 0.00123\r\n BBBG (0.05)(0.82)(0.82)(0.3) = 0.00413526\r\n\r\nThe sum of these odds is: 0.59538706\r\n\r\nIf you did well on the first quiz, the probability that you will do well on the fifth quiz in the class is 60 %\r\n',NULL,0);
INSERT INTO comment VALUES (10738,1360,4068,'Bruno','re: Solution (only a common calculator used)','2003-12-26 22:35:40',0,'You did a mistake for the odds for \"Bad\" (B).\r\n\r\n3% should be written 0.03, not 0.3',10737,0);
INSERT INTO comment VALUES (10739,1360,1301,'Charlie','re: Solution (only a common calculator used)','2003-12-26 22:36:38',0,'The transition probability from B to G is 0.03--not 0.3. (1 - 0.15 - 0.82 = 0.03).\r\n\r\nGiven the use of the wrong probability, there are also some arithmentic mistakes:\r\n(0.8)(0.15)(0.6)(0.2) = 0.0144, not 0.0010368.\r\n(0.15)(0.2)(0.05)(0.3) = 0.00045, not 0.0003\r\n(0.05)(0.82)(0.82)(0.3) = 0.010086, not 0.00413526 \r\n\r\nThe array should (using the correct 0.03) look like\r\n\r\nGGGG .8 .8 .8 .8 0.409600\r\nGGMG .8 .8 .15 .2 0.019200\r\nGGBG .8 .8 .05 .03 0.000960\r\nGMGG .8 .15 .2 .8 0.019200\r\nGMMG .8 .15 .6 .2 0.014400\r\nGMBG .8 .15 .2 .03 0.000720\r\nGBGG .8 .05 .03 .8 0.000960\r\nGBMG .8 .05 .15 .2 0.001200\r\nGBBG .8 .05 .82 .03 0.000984\r\nMGGG .15 .2 .8 .8 0.019200\r\nMGMG .15 .2 .15 .2 0.000900\r\nMGBG .15 .2 .05 .03 0.000045\r\nMMGG .15 .6 .2 .8 0.014400\r\nMMMG .15 .6 .6 .2 0.010800\r\nMMBG .15 .6 .2 .03 0.000540\r\nMBGG .15 .2 .03 .8 0.000720\r\nMBMG .15 .2 .15 .2 0.000900\r\nMBBG .15 .2 .82 .03 0.000738\r\nBGGG .05 .03 .8 .8 0.000960\r\nBGMG .05 .03 .15 .2 0.000045\r\nBGBG .05 .03 .05 .03 0.000002\r\nBMGG .05 .15 .2 .8 0.001200\r\nBMMG .05 .15 .6 .2 0.000900\r\nBMBG .05 .15 .2 .03 0.000045\r\nBBGG .05 .82 .03 .8 0.000984\r\nBBMG .05 .82 .15 .2 0.001230\r\nBBBG .05 .82 .82 .03 0.001009\r\n
\r\n------\r\nTotalling .52184185.\r\n\r\nMaybe your calculator needs a repair for its intermittent problems.',10737,0);
INSERT INTO comment VALUES (10740,1360,4507,'Penny','re(2): Solution (only a common calculator used)','2003-12-26 22:56:32',0,'Charlie, does this mean there is a 3% chance I will do well on the next quiz, a 15% chance I will do so-so, and an 82% chance I will do poorly ?\r\n \r\n:-)\n\nEdited on December 26, 2003, 10:59 pm',10739,0);
INSERT INTO comment VALUES (10741,500,4953,'seth','pretty easy','2003-12-27 00:41:20',3,'suicide,if u attempt u dont die if committed u r dead',NULL,0);
INSERT INTO comment VALUES (10742,738,4953,'seth','easy','2003-12-27 00:46:26',3,'add 5 then either add subtract multiply or divide by 1',NULL,0);
INSERT INTO comment VALUES (10743,1360,2716,'Federico Kereki','Markov chains','2003-12-27 01:12:39',2,'This is a classic \"Markov chains\" problem, with a standard solution. If you write the status change matrix A\r\n [ 0.80 0.15 0.05 ]\r\nA = [ 0.20 0.60 0.20 ]\r\n [ 0.03 0.15 0.82 ]
\r\nthen the probability of doing well in the fifth quiz is the first element of the vector [1 0 0]T times A^5. (T stands for \"transpose\")',NULL,0);
INSERT INTO comment VALUES (10744,1334,4956,'Babu','is 4 not ok ??','2003-12-27 06:43:15',0,'I think four pennies would be sufficient so that each penny can touch three other pennies.\r\nam i wrong in understanding the problem ?',NULL,0);
INSERT INTO comment VALUES (10745,1360,1301,'Charlie','re: Markov chains','2003-12-27 09:32:25',0,'\"first element of the vector [1 0 0]T times A^5.\"\r\n\r\nSince you\'re going from the first to the fifth test, isn\'t it A^4? That is, multiplying by A^1 would get you to the second test, so A^4 would get you to the fifth.\r\n\r\n',10743,0);
INSERT INTO comment VALUES (10746,1334,1301,'Charlie','re: is 4 not ok ??','2003-12-27 09:33:53',0,'How would you arrange 4 pennies so that that happens: that each of them touches the other 3?',10744,0);
INSERT INTO comment VALUES (10747,1560,1575,'DJ','Solution?','2003-12-27 11:33:33',3,'C\r\n\r\nIf you read the title aloud, it sounds like \"An old joke with a new twist.\" The question becomes \"Why did a chicken cross the road?\" and the answer, of course, is C: \"To get to the other side.\"\r\n\r\nI\'m assuming that is correct. Some of the word choices seem a little odd, and what the words are supposed to mean are not as immediately obvious as they could be. Anyway, I don\'t know what the other three choices are supposed to say.\r\n\r\nThis type of phoenetic spellings was introduced in 1956 by Howard Chace in his book Anguish Languish (\"English Language\"). The entire text of the book, containing excerpts such as:\r\n\r\nMarry hatter ladle limb \r\nItch fleas worse widest snore. \r\nAn ever-wear debt Marry win \r\nDoor limb worse shorter gore.\r\n\r\ncan be found here.',NULL,0);
INSERT INTO comment VALUES (10748,1560,1626,'Gamer','re: Solution?','2003-12-27 11:52:02',0,'There was also the two phrases in the queue that I was unable to decipher as well. Can I see the solution for those two as well?\r\n\r\nB reads: That\'s for me to know and you to find out (or something close to that)',10747,0);
INSERT INTO comment VALUES (10749,1440,4698,'Larry Settle','Proof by Induction','2003-12-27 13:53:11',0,'Many of the sequence problems can be solved by Induction. This problem is a proposition P(x) on the integers.\r\nP(1)=2^2-1^2=3=1^2(2+1).\r\nAssume P(k) for all x<=k.\r\n Write P(k+1) in terms of P(k). There are two \r\n more terms and one term has the sign reversed.\r\nP(k+1)=P(k)+(2k+2)^2+(2k+1)^2-2(k+1)^2\r\n =k^2(2k+1)+(2k+2)^2+(2k+1)^2-2(k+1)^2\r\n =2k^3+7k^2+8k+3 after expansion and\r\n collection.\r\n Now compute P(k+1) by the formula.\r\nP(k+1)=(k+1)^2(2(k+1)+1)\r\n =(k+1)^2(2k+3)\r\n =2k^3+7k^2+8k+3 after expansion and\r\n collection. The two results are an identity.\r\n Therefore the assumption implies P(k+1).\r\nQED.',NULL,0);
INSERT INTO comment VALUES (10750,1560,3351,'Eric','re(2): Solution?','2003-12-27 14:09:36',0,'I think A reads \"There was rain.\" and D reads \"None of the above.\"',10748,0);
INSERT INTO comment VALUES (10751,1560,1301,'Charlie','re(2): Solution?','2003-12-27 15:37:16',0,'\"There was also the two phrases in the queue that I was unable to decipher as well. Can I see the solution for those two as well?\"\r\n\r\nI don\'t know if the one I put in was not decipherable, but it was something like \"Do flow my spot sat ray fickle height.\" To follow Ms. Potts at the traffic light, referring to another pending puzzle.\r\n',10748,0);
INSERT INTO comment VALUES (10752,1560,1626,'Gamer','re(3): Solution?','2003-12-27 17:42:16',0,'Zealot = There? That sounds a little farfetched. I think D is a closer translation :) But like I said before, Icy Theon sir, I\'d own taffy knee-in. Site a pout, Thea, Thurs!\r\n\r\nAnyway, Cory said \"Test but lick dime store?\"; I don\'tknow what that means either.',10751,0);
INSERT INTO comment VALUES (10753,1560,1626,'Gamer','re(3): Solution?','2003-12-27 17:46:03',0,'\n\nEdited on December 27, 2003, 7:51 pm',10751,0);
INSERT INTO comment VALUES (10756,1531,4964,'Abigail Mitchell','Solution...','2003-12-27 21:06:15',0,'The plot of land can be divided into four L-shaped pieces. I\'ll give the coordinates outlining one of them... then the rest are fairly easy to see.\r\n\r\n(15,30)\r\n(15,45)\r\n(45,45)\r\n(45,15)\r\n(30,15)\r\nand two sections of the plot boundary:\r\n(30,15) to (30,30)\r\n(30,30) to (15,30)\r\n\r\nAnybody know if this is unique? I strongly suspect so, but don\'t have a proof to offer.',NULL,0);
INSERT INTO comment VALUES (10754,500,4068,'Bruno','Death Penality ???','2003-12-27 18:33:54',0,'If we attempt suicide and fail, do we get death penalty ???\n\nEdited on December 28, 2003, 11:34 pm',NULL,0);
INSERT INTO comment VALUES (10755,1360,4963,'Finkle','re(2): Markov chains','2003-12-27 19:21:26',0,'Additional comments on the markov chain point of view:\r\n\r\nIf we introduce a \"state space\" with three states:\r\nS1: you did well on the previous quiz\r\nS2: you did so-so on the previous quiz\r\nS3: you did poorly on the previous quiz\r\n\r\nthen the matrix A=\r\n0.8 0.15 0.05\r\n0.2 0.6 0.2\r\n0.03 0.15 0.82\r\n\r\nwill be the transition matrix. That is, element A(1,1) (read: A(row,col)) is the probability that you\'ll remain in S1 if you started in S1, element A(1,2) the probability that you\'ll go to S2 if you started in S1, and so on (this matrix is usually denoted with \"P\" in standard textbooks on Markov chains, at least the ones I\'ve read).\r\n\r\nSince we know for certain that we start out in S1, the initial state probability vector will be I=\r\n1\r\n0\r\n0\r\n\r\nIn other words, it is certain that we did well on the last quiz (quiz number 1). The state probability vector after the second quiz will have propagated to A*I=\r\n4/5\r\n1/5\r\n3/100 \r\n\r\nIn the same way the state probability vector after quiz five will be A^4*I (as Charlie pointed out in the previous post)=\r\n10436837/20000000 \r\n1676387/5000000 \r\n2128893/12500000 \r\n\r\nI.e. the first element of the above vector is the probability of doing well on the fifth quiz (which is equivalent to ending up in S1 after the fifth quiz). An approximation of this fraction is:\r\n\r\n0.52184\r\n',10745,0);
INSERT INTO comment VALUES (10757,1550,4966,'CC','Answer is Calculus','2003-12-28 05:07:09',0,'in 2-D the area of a sphere is 4 * pi * r^2\r\nin 3-D the volume is just the integral of the area which is 4/3 * pi * r^3\r\nso in 4-D the \"hypervolume\" would be the integral again so it would be 1/3 * pi * r^4\r\n\r\nwaala, whats with these sequences, maybe the infinte sum of those equals to the equation just found.',NULL,0);
INSERT INTO comment VALUES (10758,726,4670,'e.g.','Solution','2003-12-28 09:34:17',3,'INLETS, but I found it using a program, which doesn\'t strike me as a very elegant method...',NULL,0);
INSERT INTO comment VALUES (10759,726,1301,'Charlie','re: Solution','2003-12-28 10:15:20',0,'I agree there are probably more elegant methods, but even with an inelegant method, a solution is more than just the answer. Here\'s my solution in the form of a program, which had taken me more time to write than the 8 minutes e.g. took.\r\n\r\nDECLARE SUB permute (a$)\r\nCLS\r\na1$ = \"nosier\"\r\na2$ = \"astral\"\r\ntr$ = \"nosieratl\"\r\nFOR perm = 1 TO 362880\r\n v1$ = a1$\r\n FOR i = 1 TO LEN(v1$)\r\n MID$(v1$, i, 1) = LTRIM$(STR$(INSTR(tr$, MID$(v1$, i, 1))))\r\n NEXT\r\n v2$ = a2$\r\n FOR i = 1 TO LEN(v2$)\r\n MID$(v2$, i, 1) = LTRIM$(STR$(INSTR(tr$, MID$(v2$, i, 1))))\r\n NEXT\r\n t = VAL(v1$) + VAL(v2$)\r\n IF t = 725613 THEN\r\n PRINT \"123456789\"\r\n PRINT tr$\r\n s1$ = \"\"\r\n FOR i = 1 TO LEN(\"725613\")\r\n s1$ = s1$ + MID$(tr$, VAL(MID$(\"725613\", i, 1)), 1)\r\n NEXT\r\n PRINT s1$\r\n PRINT\r\n END IF\r\n permute tr$\r\nNEXT\r\n\r\nSUB permute (a$)\r\nDEFINT A-Z\r\n x$ = \"\"\r\n FOR i = LEN(a$) TO 1 STEP -1\r\n l$ = x$\r\n x$ = MID$(a$, i, 1)\r\n IF x$ < l$ THEN EXIT FOR\r\n NEXT\r\n\r\n IF i = 0 THEN\r\n FOR j = 1 TO LEN(a$) \\ 2\r\n x$ = MID$(a$, j, 1)\r\n MID$(a$, j, 1) = MID$(a$, LEN(a$) - j + 1, 1)\r\n MID$(a$, LEN(a$) - j + 1, 1) = x$\r\n NEXT\r\n ELSE\r\n FOR j = LEN(a$) TO i + 1 STEP -1\r\n IF MID$(a$, j, 1) > x$ THEN EXIT FOR\r\n NEXT\r\n MID$(a$, i, 1) = MID$(a$, j, 1)\r\n MID$(a$, j, 1) = x$\r\n FOR j = 1 TO (LEN(a$) - i) \\ 2\r\n x$ = MID$(a$, i + j, 1)\r\n MID$(a$, i + j, 1) = MID$(a$, LEN(a$) - j + 1, 1)\r\n MID$(a$, LEN(a$) - j + 1, 1) = x$\r\n NEXT\r\n END IF\r\nEND SUB\r\n\r\nIt found\r\n\r\n123456789\r\ntnsaleiro\r\ninlets\r\n
\r\n-----\r\nthe first two lines being the full number-to-letter encoding.\n\nEdited on December 28, 2003, 10:16 am',10758,0);
INSERT INTO comment VALUES (10760,1550,1301,'Charlie','re: Answer is Calculus','2003-12-28 11:19:08',0,'Your first two examples are both for spheres. By analogy, the third, whatever it is, would be for a sphere, not a hypersphere. The proper \"series\" sequence is from circle to sphere to hypersphere. The area of a circle is pi*r^2. The volume of a sphere is (4/3) pi * r^3. In this progression, one is not the integral of the previous, but rather a composed integral of previous (lower dimension) values as given in the preceding posts.',10757,0);
INSERT INTO comment VALUES (10761,726,4670,'e.g.','re(2): Solution','2003-12-28 13:12:36',0,'My program was far simpler -- something like\r\n\r\nfor (a=1; a>=9; a++) {\r\nfor (s=1; s>=9; s++) if (s!=a) {\r\nfor (t=1; t>=9; t++) if (t!=a) && (t!=s) {\r\n...\r\n\r\nand so on; you get the idea. After getting the only solution, I worked out the answer by hand.\r\n 0 1 2 4 7 12 6 10 3 11 5 9 8 13 14\r\nABC 1 DEF 2 GHI 3 JKL 4 MNO 5\r\nCID 2 GLA 1 MFK 3 NEJ 4 HBO 6\r\nDKG 1 MJC 2 HAE 3 BLN 5 FIO 4\r\nGEM 2 HND 1 FCL 3 IJB 5 AKO 7\r\nMLH 1 FBG 3 ADJ 5 KNI 2 CEO 8\r\nHJF 3 AIM 4 CGN 6 EBK 1 DLO 9\r\nFNA 2 CKH 4 DMB 3 LIE 1 GJO 10\r\n\r\n 0 1 2 4 7 10 8 12 3 11 5 9 6 13 14\r\nABC 1 DEF 2 GHI 3 JKL 4 MNO 5\r\nCID 2 MLH 1 FAK 3 NEJ 4 GBO 6\r\nDKM 1 GJA 2 HCE 3 BLN 5 FIO 4\r\nMEG 2 FNC 3 ADL 1 IJB 5 HKO 7\r\nGLF 3 HBD 4 CMJ 2 KNI 1 AEO 8\r\nFJH 2 AIM 4 DGN 1 EBK 6 CLO 9\r\nHNA 3 CKG 4 MFB 6 LIE 2 DJO 1\r\n\r\n 0 1 2 6 9 12 4 8 13 11 5 7 3 10 14\r\nABC 1 DEF 2 GHI 3 JKL 4 MNO 5\r\nCMG 2 HJA 1 DNB 3 ILE 5 KFO 4\r\nGKD 1 NIC 2 HFM 3 BEJ 4 LAO 6\r\nDLH 2 FBG 1 NAK 3 MJI 5 ECO 7\r\nHEN 1 AMD 2 FCL 3 KIB 4 JGO 8\r\nNJF 3 CKH 4 AGE 6 LBM 1 IDO 9\r\nFIA 2 GLN 5 CDJ 3 EMK 4 BHO 1\r\n\r\n 0 1 2 8 11 4 12 3 6 13 7 9 5 10 14\r\nABC 1 DEF 2 GHI 3 JKL 4 MNO 5\r\nCHF 3 NJI 1 AMD 2 BLE 5 KGO 4\r\nFMI 2 GBD 1 CKN 3 HEJ 4 LAO 6\r\nIKD 4 AHN 1 FLG 5 MJB 2 ECO 3\r\nDLN 4 CMG 2 IEA 6 KBH 1 JFO 7\r\nNEG 3 FKA 1 DJC 5 LHM 2 BIO 8\r\nGJA 2 ILC 6 NBF 5 EMK 1 HDO 9\r\n
\r\n---------\r\nThe row of numbers at the top represent the position numbers for the vertices of the triangle, 0 through 13 on the outside; 14 in the center of the circle.\r\n\r\nHere\'s the program. Note that I did not check to make sure that the two points left to team up with the center point were of opposite parity, a necessity so that everyone gets to eat with the center person, but it seems to work out that way anyway.\r\n\r\nDEFINT A-Z\r\nDECLARE SUB place (size)\r\nCLEAR , , 4000\r\n\r\nDIM SHARED ct(13), hist(14, 2), solCt\r\n\r\n\r\nct(0) = 1: ct(1) = 1\r\nhist(1, 1) = 0: hist(1, 2) = 1\r\nCLS\r\nplace 2\r\nPRINT solCt\r\n\r\nEND\r\n\r\nSUB place (size)\r\n FOR ev = 0 TO 12 STEP 2\r\n IF size <= 7 OR size MOD 2 = 1 THEN i = ev: ELSE i = ev + 1\r\n j = (i + size) MOD 14\r\n IF ct(i) < 2 AND ct(j) < 2 THEN\r\n good = 1\r\n IF ct(i) AND ct(j) THEN\r\n FOR sb = 1 TO size - 1\r\n IF hist(sb, 1) = i THEN other1 = hist(sb, 2)\r\n IF hist(sb, 2) = i THEN other1 = hist(sb, 1)\r\n IF hist(sb, 1) = j THEN other2 = hist(sb, 2)\r\n IF hist(sb, 2) = j THEN other2 = hist(sb, 1)\r\n NEXT\r\n\r\n IF other1 <> other2 THEN\r\n good = 0\r\n ELSE\r\n \'\r\n END IF\r\n ELSEIF ct(i) OR ct(j) THEN\r\n FOR sb = 1 TO size - 1\r\n IF hist(sb, 1) = i AND ct(hist(sb, 2)) > 1 THEN\r\n good = 0\r\n END IF\r\n IF hist(sb, 2) = i AND ct(hist(sb, 1)) > 1 THEN\r\n good = 0\r\n END IF\r\n IF hist(sb, 1) = j AND ct(hist(sb, 2)) > 1 THEN\r\n good = 0\r\n END IF\r\n IF hist(sb, 2) = j AND ct(hist(sb, 1)) > 1 THEN\r\n good = 0\r\n END IF\r\n NEXT\r\n END IF\r\n IF good THEN\r\n ct(i) = ct(i) + 1: ct(j) = ct(j) + 1\r\n hist(size, 1) = i: hist(size, 2) = j\r\n IF size = 13 THEN\r\n oneCt = 0\r\n FOR sb = 0 TO 13\r\n IF ct(sb) = 1 THEN oneCt = oneCt + 1\r\n NEXT\r\n IF oneCt = 2 THEN\r\n REDIM marker(13), soln(5, 3)\r\n solUpto = 0\r\n FOR sb = 1 TO 12\r\n u1 = hist(sb, 1): u2 = hist(sb, 2)\r\n IF ct(u1) > 1 AND ct(u2) > 1 AND marker(u1) = 0 THEN\r\n marker(u1) = 1: marker(u2) = 1\r\n FOR sb2 = sb + 1 TO 13\r\n IF hist(sb2, 1) = u1 OR hist(sb2, 2) = u1 OR hist(sb2, 1) = u2 OR hist(sb2, 2) = u2 THEN\r\n IF hist(sb2, 1) <> u1 AND hist(sb2, 1) <> u2 THEN\r\n u3 = hist(sb2, 1): marker(u3) = 1\r\n ELSE\r\n u3 = hist(sb2, 2): marker(u3) = 1\r\n END IF\r\n END IF\r\n NEXT\r\n solUpto = solUpto + 1\r\n soln(solUpto, 1) = u1: soln(solUpto, 2) = u2: soln(solUpto, 3) = u3\r\n PRINT u1; u2; u3; \" \";\r\n END IF\r\n NEXT\r\n pcUpto = 0\r\n FOR sb = 0 TO 13\r\n IF ct(sb) = 1 THEN\r\n pcUpto = pcUpto + 1\r\n soln(5, pcUpto) = sb\r\n PRINT sb;\r\n END IF\r\n NEXT\r\n soln(5, 3) = 14\r\n PRINT 14\r\n solCt = solCt + 1\r\n GOSUB show1\r\n \'IF solCt / 40 = INT(solCt / 40) THEN DO: LOOP UNTIL INKEY$ > \"\"\r\n END IF\r\n ELSE\r\n place size + 1\r\n END IF\r\n ct(i) = ct(i) - 1: ct(j) = ct(j) - 1\r\n END IF\r\n END IF\r\n NEXT\r\n\r\nEXIT SUB\r\n\r\nshow1:\r\n REDIM lets$(14), tbl(14, 20)\r\n assnCt = 0\r\n FOR grp = 1 TO 5\r\n FOR memb = 1 TO 3\r\n lets$(soln(grp, memb)) = CHR$(65 + assnCt)\r\n assnCt = assnCt + 1\r\n NEXT\r\n NEXT\r\n FOR day = 0 TO 6\r\n REDIM tblDay(20)\r\n FOR grp = 1 TO 5\r\n tblTry = 1\r\n FOR memb = 1 TO 3\r\n IF grp = 5 AND memb = 3 THEN\r\n PRINT lets$(soln(5, 3));\r\n sb = soln(5, 3)\r\n ELSE\r\n sb = (soln(grp, memb) + 2 * day) MOD 14\r\n PRINT lets$((soln(grp, memb) + 2 * day) MOD 14);\r\n END IF\r\n DO WHILE tbl(sb, tblTry) > 0 OR tblDay(tblTry) > 0\r\n tblTry = tblTry + 1\r\n LOOP\r\n NEXT\r\n DO WHILE tbl(sb, tblTry) > 0 OR tblDay(tblTry) > 0\r\n tblTry = tblTry + 1\r\n LOOP\r\n tblDay(tblTry) = 1\r\n tbl(sb, tblTry) = 1\r\n PRINT tblTry; \" \";\r\n NEXT\r\n PRINT\r\n NEXT\r\n PRINT\r\n DO: LOOP UNTIL INKEY$ > \"\"\r\nRETURN\r\n\r\nEND SUB\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (10793,1441,1301,'Charlie','re: solution--computer used','2003-12-30 11:03:34',0,'I see that my table-assignment algorithm is not preventing some people from visiting the same table twice. I don\'t have time to correct that right now, but I\'ll work on it later.',10792,0);
INSERT INTO comment VALUES (10794,1441,1301,'Charlie','re(2): solution--computer used','2003-12-30 11:30:23',0,'That algorithm has been repaired so it no longer assigns the same person to the same table twice in the week, but now the minimum number of tables among the 84 solutions is 11, so I need a more efficient algorithm.',10793,0);
INSERT INTO comment VALUES (10795,1362,4993,'Chase Borman','is this the right way?','2003-12-30 12:54:47',3,'1/3 + 2/4 = 5/6',NULL,0);
INSERT INTO comment VALUES (10796,1441,4507,'Penny','This is how I solved it.','2003-12-30 13:26:36',1,'I don\'t know why this one went so long without an answer. Like so many other seemingly difficult flooble puzzles, it yielded rather easily to step-by-step logic.\r\n\r\nI began by arbitrarily assigning meetings to A. I could do this in any way, since the names A through O are arbitrary. (I knew that if the end result did not have the day 1 meetings specified in the puzzle, I could transpose letters to change it to match the puzzle.)\r\n\r\nDay1: ABC; Day2: ADE; Day3: AFG; Day4: AHI; Day5: AJK; Day6: ALM; Day7: ANO\r\n\r\nNow it was a simple matter to assign everybody else to the remaining meetings in such a way that everyone meets every other person exactly once. I started with B. I just had B neeting with A and C, so I arranged for her to meet with the remaining girls D through O: BDF, BEG, BHJ, BIK, BLN and BMO. Now it was C\'s turn. I already had her meeting with A and B, so I set her up with D through O: CDG, CEF, CHK, CIJ, CLO, CMN. Now for D, whom I now had meeting with A, B, C, E, F and G, I set up meetings with H through O: DHL, DIM, DJN, and DKO. I now had E meeting with A, B, C, D, F and G, so I assigned her the following meetings: EHM, EIL, EJO and EKN. Now F was meeting with A, B, C, D, E and G, so I set her up with the remaining girls: FHN, FIO, FJL, and FKM. So now G was meeting with A, B, C, D, E, and F, so I filled out her schedule with the following meetings: GHO, GIN, GJM and GKL.\r\n \r\nSo now I had a set of 35 meetings with everbody meeting everybody else exactly once:\r\n\r\nABC, ADE, AFG, AHI, AJK, ALM, ANO, BDF, BEG, BHJ, BIK, BLN, BMO, CDG, CEF, CHK, CIJ, CLO, CMN, DHL, DIM, DJN, DKO, EHM, EIL, EJO, EKN, FHN, FIO, FJL, FKM, GHO, GIN, GJM, and GKL\r\n\r\nThe next step was to assign the groupings by day, from 1 to 7. This involved some minor trial and error, and I didn\'t verify that this is the only arrangement:\r\n\r\nDay 1: ABC, DHL; EJO; FKM; GIN; \r\nDay 2: ADE; BHJ; CMN; FIO; GKL; \r\nDay 3: AFG; BIK; CLO; DJN; EHM; \r\nDay 4: AHI; BLN; CEF; DKO; GJM;\r\nDay 5: AJK; BMO; CDG; EIL; FHN; \r\nDay 6: ALM; BDF; CIJ; EKN; GHO; \r\nDay 7: ANO; BEG; CHK; DIM; FJL\r\n\r\nNow I had to assign tables. I guessed correctly that I should use all ten tables on the first two days:\r\n\r\nDay 1: ABC(1), DHL(2); EJO(3); FKM(4); GIN(5); \r\nDay 2: ADE(6); BHJ(7); CMN(8); FIO(9); GKL(10); \r\n\r\nThen it was not too hard to assign successive tables to successive groups of three people, based on avoiding all tables that any of the three had sat at previously.\r\n\r\nDay 1: ABC(1), DHL(2); EJO(3); FKM(4); GIN(5); \r\nDay 2: ADE(6); BHJ(7); CMN(8); FIO(9); GKL(10); \r\nDay 3: DJN(1); AFG(2); BIK(3); CLO(4); EHM(5); \r\nDay 4: AHI(4); DKO(5); BLN(6); CEF(7); GJM(9); \r\nDay 5: EIL(1); BMO(2); CDG(3); AJK(8); FHN(10); \r\nDay 6: GHO(1); EKN(2); ALM(3); CIJ(6); BDF(8); \r\nDay 7: BEG(4); FJL(5); ANO(7); CHK(9); DIM(10); \r\n\r\nNow all that remained was to transpose letters to arrive at the correct solution. By replacing H with E, L with F, E with G, J with H, O with I, F with J, M with L, G with M, I with N, and N with O, the result is the solution to the puzzle:\r\n\r\nDay 1: ABC(1), DEF(2); GHI(3); JKL(4); MNO(5); \r\nDay 2: ADG(6); BEH(7); CLO(8); JNI(9); MKF(10); \r\nDay 3: DHO(1); AJM(2); BNK(3); CFI(4); GEL(5); \r\nDay 4: AEN(4); DKI(5); BFO(6); CGJ(7); MHL(9); \r\nDay 5: GNF(1); BLI(2); CDM(3); AHK(8); JEO(10); \r\nDay 6: MEI(1); GKO(2); AFL(3); CNH(6); BDJ(8); \r\nDay 7: BGM(4); JHF(5); AOI(7); CEK(9); DNL(10) \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\n\nEdited on December 31, 2003, 2:44 am',10791,0);
INSERT INTO comment VALUES (10797,1554,4064,'rerun141','2 questions','2003-12-30 13:30:20',3,'first ask \"Who would your partner say is a liar?\"\r\nthe oposite of his answer will always be true.\r\nsecond ask \"Who would your partner say is answering this question?\" again the oposite will be true.\r\neg. where bert lies and answers second\r\nanswer to question one \"He would say that alex lies\"\r\nanswer to question 2 \"He would say Alex answered this question\"',NULL,0);
INSERT INTO comment VALUES (10798,1162,4718,'Jack Squat','Light on the particulars','2003-12-30 13:38:23',0,'If you want to get really technical, nowhere in this question does it mention a six-sided die, nor does it mention that the numbers are 1 to 6. \r\n\r\nThere are 5 solutions if you assume the above (1 being the solution posted where you can\'t see the back of any numbers). Can you find them?',NULL,0);
INSERT INTO comment VALUES (10799,1554,4627,'donnmike','re: 2 questions','2003-12-30 13:48:26',0,'the problem says they only answer yes or no questions. you asked them to give you a name and they cannot do that.\r\n\r\nthe correct solution:\r\n1) would your partner say that you tell the truth?\r\n2) is your name alex? (you can also ask \"is your name bert?\")',10797,0);
INSERT INTO comment VALUES (10800,1334,4718,'Jack Squat','Big table!','2003-12-30 13:57:58',0,'The building block of 080 where the loops of the 8 are pennies is the key here. SilverKnight\'s answer I think is correct, as you can\'t fit three of these building blocks together, but you can fit four.\n\nEdited on December 30, 2003, 2:08 pm',NULL,0);
INSERT INTO comment VALUES (10802,1554,4064,'rerun141','another try','2003-12-30 15:03:16',0,'in donmike\'s second question doesn\'t prove anything as you don\'t know whos answering\r\npennies question doesn\'t establish whos the liar and whs the knight....\r\nghanging my original answer to yes or no form you could ask:\r\n\"Would your partner say that you alex is the liar?\"\r\n\"Would your partner say that alex is answering this question?\" ',NULL,0);
INSERT INTO comment VALUES (10803,1362,1575,'DJ','re: is this the right way?','2003-12-30 15:25:37',0,'No.. you can only write those six digits down (the lines in the fractions aren\'t allowed) ...',10795,0);
INSERT INTO comment VALUES (10801,1554,4507,'Penny','One question','2003-12-30 14:01:59',0,'You only need to ask one question: \"If I were to ask you if your name is Alex, would you say yes?\"\r\n\r\nIf Alex answers and is a truthteller, he will say yes. If he is a liar, he will also say \"yes\", since he would say \"no\" if you were to ask him if his name is Alex. Similarly if Bert answers and is a truthtelller, he will say \"no\". If Bert is a liar, he will again say \"no\", since he would answer \"yes\" if asked if his name is Alex.\r\n\n\nEdited on December 30, 2003, 2:03 pm',NULL,0);
INSERT INTO comment VALUES (10804,1554,4507,'Penny','re: another try','2003-12-30 15:32:41',0,'rerun141: \"penny\'s question doesn\'t establish who\'s the liar and who\'s the knight....\"\r\n\r\nRight. Let me try again.... \r\n\r\nTwo questions:\r\n\r\nIf I were to ask you if you were Alex, would you say yes?\r\nIf I were to ask you if you were a liar, would you say yes?\r\n\r\nIf the answers are \"yes, yes\", liar Alex has answered.\r\nIf the answers are \"yes, no\", truthteller Alex has answered.\r\nIf the two answers are \"no, yes\", liar Bert has answered.\r\nIf the answers are \"no, no\", truthteller Bert has answered.',10802,0);
INSERT INTO comment VALUES (10805,1362,1301,'Charlie','solution','2003-12-30 15:35:27',3,'There are various ways of using exponentiation, which doesn\'t require an added symbol--just superscripting. Here, I\'ll use the caret (^), but written out it\'s just superscripting:\r\n\r\nMany ways involve wasting powers of 1, such as in\r\n\r\n1^236 + 4 = 5\r\nor\r\n1^2^4^3 + 5 = 6\r\nor\r\n1^545 + 2 = 3\r\nor\r\n2 + 3 = 5^1^46\r\nwhere it\'s understood the 1^46 is done before 5 to that power.\r\n\r\nMore satisfying is 2^5 + 4^1 = 36 or 5^1^6 + 4 = 3^2.\r\n\r\nThere\'s 1^2 + 4^3 = 65.\r\n\r\nThere are 240 variations the computer found (or 120 if you discount switching the order of the two addends).\r\n',NULL,0);
INSERT INTO comment VALUES (10806,1554,1626,'Gamer','re(2): another try','2003-12-30 17:15:11',0,'Does it say anywhere there is exactly one liar and one knight? Couldn\'t both be liars and both be knights?',10804,0);
INSERT INTO comment VALUES (10807,1554,4627,'donnmike','re: another try','2003-12-30 17:44:33',0,'\n\nEdited on December 30, 2003, 5:59 pm',10802,0);
INSERT INTO comment VALUES (10810,1554,4627,'donnmike','the solution','2003-12-30 18:28:56',0,'1: would your partner say that alex is a liar?\r\n2: would your partner say that bert is a liar?\r\n3: would your partner say that alex is answering this question?',NULL,0);
INSERT INTO comment VALUES (10811,1554,4064,'rerun141','number of liars and knights','2003-12-30 18:48:01',0,'never mind...\n\nEdited on December 31, 2003, 2:30 pm',10810,0);
INSERT INTO comment VALUES (10809,1554,4627,'donnmike','re: another try','2003-12-30 17:58:51',0,'my solution works if you understand the problem a certain way. when i read where it says \"only one of them will respond\" i thought it meant only one will respond to both questions, as if the other one doesn\'t want to talk to you.\n\nEdited on December 30, 2003, 6:16 pm',10802,0);
INSERT INTO comment VALUES (10808,1554,4064,'rerun141','re(3): another try','2003-12-30 17:46:28',0,'It actually never says whether either is a liar or a knight at all. Still we should try to find a solution that alows for 2 liars or 2 knights... ',10806,0);
INSERT INTO comment VALUES (10826,1554,4064,'rerun141','re(2): number of liars and knights','2003-12-31 14:51:16',0,'Your right of course\r\nthe first time i tried your solution I forgot to change answers for the different 1liar/1 knight sittuation.\r\ngood job.',10819,0);
INSERT INTO comment VALUES (10812,1554,3558,'Tristan','re: number of liars and knights','2003-12-30 19:42:43',1,'I\'m not exactly sure why you must double the questions half of the time (I probably haven\'t tried hard enough), but I think that you could fix this problem with another question. Ask this: \"What would you say if I asked you whether Alex and Bert are the same type?\" Then, depending on the answer, you could ask different questions. I\'ll assume that you only count the maximum possible questions for all the cases (just like I\'ll assume there are no knaves). I hope I\'m helping somehow, but I\'m too tired right now to do the real solving myself.',10811,0);
INSERT INTO comment VALUES (10813,1554,4064,'rerun141','re(2): number of liars and knights','2003-12-30 19:51:28',3,'thanks tristan\r\nheres a solution using 3 quetion\r\n1. what would you say if i asked if you were both the same type?\r\nif answer is no then\r\n2. would the othere say alex is a liar\r\n3 would the say alex just answered\r\nIf answer to 1 is yes then\r\n2. what would you say if i asked if you were a knight\r\n3. what would you say if i asked if alex is answering this quesion',10812,0);
INSERT INTO comment VALUES (10814,1554,3558,'Tristan','solution and proof','2003-12-30 19:58:03',3,'I was kind of tired, but after looking at the problem a little more, I found a quick solution.\r\n\r\nThe minimum number of questions is three, because each question must be a yes or no question, and therefore only have two possible answers. The number of possible combinations of results are 8:\r\n\r\nAlex=liar/knight; Bert=liar/knight; last speaker=Bert/Alex\r\n\r\nTherefore, you must ask at least three questions, because there must be at least 8 possible combinations of answers.\r\n\r\nOnce proven that three questions are needed, it is a simple matter to find them.\r\n\r\n1. What would you say if I asked you if Alex is a knight?\r\n2. What would you say if I asked you if Bert is a knitht?\r\n3. What would you say if I asked you if you were Alex?\r\n\r\nOf course there are many possible solutions.',NULL,0);
INSERT INTO comment VALUES (10815,1362,4999,'Lou','my solution','2003-12-30 20:41:22',0,'12 ways.\r\n\r\n1+2=3, 1+3=4, 1+4=5, 1+5=6, 2+3=5, 2+4=6,\r\n2+1=3, 3+1=4, 4+1=5, 5+1=6, 3+2=5, 4+2=6\r\n',NULL,0);
INSERT INTO comment VALUES (10816,1362,4064,'rerun141','re: my solution','2003-12-30 21:14:34',0,'you have to use all six numbers.\r\nthere are no solutions in the simple form of ab+cd=ef, theres some trick to it.',10815,0);
INSERT INTO comment VALUES (10817,1554,4507,'Penny','re: solution and proof','2003-12-30 21:26:51',3,'There is a better solution that uses just one question. \r\n\r\n\"If I were to tell you that I have wired my body with explosives, which I am about to detonate, blowing all three of us to bits, unless I find out who is who in the next five seconds, what would you say?\"\r\n \r\nBoth guys would tell the truth in a hurry.... Btw, I thought it was \"Bert and Enie\", not \"Alex and Bert\".',10814,0);
INSERT INTO comment VALUES (10818,1554,1626,'Gamer','The answer','2003-12-30 22:40:54',0,':) I think that\'s an interesting question!\r\n\r\nOf course, they could reply \"That\'s what you get for asking us all those questions and intruding on our privacy!\"',NULL,0);
INSERT INTO comment VALUES (10819,1554,4627,'donnmike','re: number of liars and knights','2003-12-31 01:59:17',0,'i don\'t know why you are saying you have to ask 6 questions half the time. and of course the answers are conditional, there are different answers for each scenario. do the work if you don\'t believe me. make a chart for each scenario and you will find that there is a different combination of yes/no answers to the questions i asked for each scenario.',10811,0);
INSERT INTO comment VALUES (10820,730,2716,'Federico Kereki','Almost (50%) there','2003-12-31 09:58:58',1,'It must be either 2 or 8, for all odd powers of 8 end with one of these numbers.',NULL,0);
INSERT INTO comment VALUES (10821,730,1301,'Charlie','solution','2003-12-31 10:35:24',3,'There is a 6 raised to a power. The result of that power must be even, as six is even.\r\n\r\n7, raised to an even power, always results in a number that is congruent to 1 mod 4.\r\n\r\nWhen 8 is raised to a power that is congruent to 1 mod 4, the last digit is 8.',NULL,0);
INSERT INTO comment VALUES (10822,730,4197,'luminita','','2003-12-31 10:41:34',3,'the last digit is 6.\r\n\r\nthe last digits of the 8 powers\' are: 8, 4, 2, 6 and so on. the final power is 7! = 5040\r\n5040 = 4 (mod 4) which means that 5040 is divisible by 4,\r\nso the last digit of the 8^5040 is the same as the last digit of 8^4, that is 6\r\n',NULL,0);
INSERT INTO comment VALUES (10823,730,1301,'Charlie','re:','2003-12-31 10:58:39',0,'The last digit would be 6 if the association were ((((((8^7)^6)^5)^4)^3)^2)^1, as that would be 8^(7!), where the exponent is a multiple of 4. However, the association (order of taking the powers) is right-to-left, not left-to-right.\n\nEdited on December 31, 2003, 11:00 am',10822,0);
INSERT INTO comment VALUES (10824,670,4197,'luminita','solution','2003-12-31 11:27:06',0,'my solution is 9\r\n\r\nthe digit is the solution of the following equation:\r\n(10^50 -1)/9 + (x-1)10^24 = 13k (K natural)\r\nusing Charlie\'s remarks regarding modulo 13 and the power series of 10,\r\n10^50 -1 + 9(x-1)10^24 = 0 (mod 13)\r\n9-1+12y=0 (mod 13), where y = x-1\r\ny=8, thus x=9\r\nsolution x=9\r\n',NULL,0);
INSERT INTO comment VALUES (10825,670,4374,'Richard','re: solution','2003-12-31 13:22:37',0,'Of course Charlie got x=3 because his x is the 26th digit from the left end. You and I got x=9 because our x is the 26th digit from the right end. If you look at the number Charlie shows in Comment 3, and count carefully, the 3 is in the 25th digit from the right end (26th from the left end):\r\n? 11111111111111111111111113111111111111111111111111 ',10824,0);
INSERT INTO comment VALUES (10827,730,4982,'Dan Blume','Solution','2003-12-31 15:10:16',3,'8\r\n\r\nThe first three numbers are the key.\r\n\r\nThe number 8 when raised to succeeding powers ends in numbers with the following pattern:\r\n\r\n8,4,2,6,8,4,2,6 . . . \r\n\r\nor generally, when 8 is raised to the \"x\" power, the final digit will be based on the Remainder of (x/4):\r\nRem\r\n 1 8\r\n 2 4\r\n 3 2\r\n 4 6\r\n\r\n\r\nSo if we can divide the result of (7^((()))) by 4, the remainder should tell us the final digit.\r\n\r\nIf we rewrite 7 as (8 - 1) then raise it to the second power, we get:\r\n\r\n(8 - 1)^2 = (64 - 16 + 1)\r\nSince the first two numbers are divisible by 4, the remainder for the expression when divided by 4 is 1\r\n\r\n(8 - 1)^3 = (512 - 128 + 8 - 64 + 16 - 1)\r\nSince every number except the last is divisible by 4, the remainder for the expression when divided by 4 becomes 3.\r\n\r\nThe final element of the expression flips from +1 to -1 and the remainder flips from 1 to 3 when 7 is raised to even and odd numbers respectively.\r\n\r\nFor (6^((()))) the number is always even, so the remainder for (7^((())))/4 is always 1. So the final digit for (8^((()))) will be \"8\"\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (10828,86,4718,'Jack Squat','...horseshoes and grenades','2003-12-31 15:12:11',0,'I don\'t think you can use Tristan\'s proof. If 3.999... equals 4, then 4.0000...001 must equal 4 as well. So 3.999... then equals 4.000...001. But these can\'t be the same since 4.0 is a number between these.\r\n\r\nI don\'t think you can actually prove 3.999... equals 4. Mathematically the posted solution is correct, but literarily 3.999... is equal to \"almost 4\". And almost only counts in...',NULL,0);
INSERT INTO comment VALUES (10829,460,1301,'Charlie','re: Another Solution','2003-12-31 15:29:01',0,'\r\nB +H+k \r\nh+ B + \r\n+r+ + \r\n + +r+ \r\n+ Q + \r\n
\r\n-------\r\nhas two bishops on the same-colored squares.',8262,0);
INSERT INTO comment VALUES (10830,1568,1301,'Charlie','solution','2003-12-31 15:33:08',3,'The process involves 6 steps, going successively to 11, 9, 7, 5, 3 and then 1 card remaining. At each step let n be the total number of cards at the start of the step, and let r be the ordinal value of a given card whose probabilities you want to follow into the next step, that is, it is card r out of n cards in ascending order of value.\r\n\r\nDuring each step, the card will go from being r out of n to either r-2, r-1 or r out of n-2, or it will be eliminated from the deck.\r\n\r\nThe cases:\r\nIt will go to position r-2 if all three chosen cards are lower in value than it. This has probability\r\n(r - 1) / n * (r - 2) / (n - 1) * (r - 3) / (n - 2)\r\n\r\nIt will go to position r-1 if either one or two of the three chosen cards is/are lower in value than it, and the highest chosen card is higher than it, or if the card in question is the middle-valued of the three chosen. The respective probabilities that two or one are below the given card and one above are:\r\n3 * (r - 1) / n * (r - 2) / (n - 1) * (n - r) / (n - 2)\r\nand\r\n3 * (r - 1) / n * (n - r) / (n - 1) * (n - r - 1) / (n - 2)\r\nand of being the middle-valued chosen card:\r\n6 / n * (r - 1) / (n - 1) * (n - r) / (n - 2)\r\n\r\nIt will remain at position r if all the drawn cards are higher in value, having probability\r\n(n - r) / n * (n - r - 1) / (n - 1) * (n - r - 2) / (n - 2)\r\n\r\nThe card will be eliminated from the deck if it is either the lowest or highest chosen card, with respective probabilities:\r\n3 / n * (n - r) / (n - 1) * (n - r - 1) / (n - 2)\r\nand\r\n3 / n * (r - 1) / (n - 1) * (r - 2) / (n - 2)\r\n\r\nA program which evaluates these successive probabilities for cards that start at the various positions and totals the probability of being eliminated (and then subtracts that total from 1, to get the probability of being the last card) is:\r\nCLS\r\nDEFDBL A-Z\r\nFOR stPos = 1 TO 13\r\n REDIM prob(13, 13)\r\n prob(0, stPos) = 1\r\n killed = 0\r\n FOR newRow = 2 TO 12 STEP 2\r\n oldRow = newRow - 2\r\n n = 13 - oldRow\r\n FOR r = 1 TO 13\r\n GOSUB transit\r\n IF r > 2 THEN prob(newRow, r - 2) = prob(newRow, r - 2) + allBelow * prob(oldRow, r)\r\n IF r > 1 THEN prob(newRow, r - 1) = prob(newRow, r - 1) + (oneBelow + twoBelow + middle) * prob(oldRow, r)\r\n prob(newRow, r) = prob(newRow, r) + allAbove * prob(oldRow, r)\r\n killed = killed + (lowest + highest) * prob(oldRow, r)\r\n NEXT r\r\n NEXT newRow\r\n PRINT USING \"## #.#######\"; stPos; 1 - killed\r\nNEXT stPos\r\nEND\r\n\r\n\r\ntransit:\r\nallBelow = (r - 1) / n * (r - 2) / (n - 1) * (r - 3) / (n - 2)\r\ntwoBelow = 3 * (r - 1) / n * (r - 2) / (n - 1) * (n - r) / (n - 2)\r\noneBelow = 3 * (r - 1) / n * (n - r) / (n - 1) * (n - r - 1) / (n - 2)\r\nallAbove = (n - r) / n * (n - r - 1) / (n - 1) * (n - r - 2) / (n - 2)\r\nlowest = 3 / n * (n - r) / (n - 1) * (n - r - 1) / (n - 2)\r\nhighest = 3 / n * (r - 1) / (n - 1) * (r - 2) / (n - 2)\r\nmiddle = 6 / n * (r - 1) / (n - 1) * (n - r) / (n - 2)\r\nRETURN\r\n\r\nThe results are:\r\n\r\n 1 0.0000000\r\n 2 0.0034965\r\n 3 0.0127146\r\n 4 0.0357067\r\n 5 0.0892845\r\n 6 0.1961927\r\n 7 0.3252101\r\n 8 0.1961927\r\n 9 0.0892845\r\n10 0.0357067\r\n11 0.0127146\r\n12 0.0034965\r\n13 0.0000000\r\n
\r\n-------\r\nA similar program written in UBASIC, using that language\'s rational number capability, gives the following exact probabilities:\r\n\r\n1 0\r\n2 1/286\r\n3 20/1573\r\n4 337/9438\r\n5 1264/14157\r\n6 505/2574\r\n7 4604/14157\r\n8 505/2574\r\n9 1264/14157\r\n10 337/9438\r\n11 20/1573\r\n12 1/286\r\n13 0\r\n\r\nor, with a common denominator:\r\n\r\n0 / 28314\r\n99 / 28314\r\n360 / 28314\r\n1011 / 28314\r\n2528 / 28314\r\n5555 / 28314\r\n9208 / 28314\r\n5555 / 28314\r\n2528 / 28314\r\n1011 / 28314\r\n360 / 28314\r\n99 / 28314\r\n0 / 28314\r\n
\r\n----\r\n(The slashes are doubled in UBASIC\'s indication of rational numbers. I\'ve changed them to single slashes to give the conventional notation.)\r\n',NULL,0);
INSERT INTO comment VALUES (10831,1568,4982,'Dan Blume','yikes!','2003-12-31 15:59:50',0,'I got 1 and 13 :)',NULL,0);
INSERT INTO comment VALUES (10832,1474,3171,'snapp','When is there gonna be a solution?','2003-12-31 16:01:50',0,'I just don\'t know if I can take the suspense anymore!!!!!!\r\n\r\nAnyway here is my $.02. Im very new at this.\r\n\r\nThe probability of getting three of a kind for n number of draw is:\r\n\r\nP(n)=((3*(n-1))/(52-(n-1))*((2*(n-1))/52-(n-1))\r\n\r\nFor n>2 and where n is the number of draws.\r\n\r\nUsing this formula I got that at 16th draw you have a 0.986 probility of getting three of a kind.\r\n\r\nin the case of 2 decks I came to a 0.986 probabiltiy of having three of a kind on 31 draws. (substitue 104 for 52)\r\n\r\n\r\n\r\n\n\nEdited on December 31, 2003, 4:52 pm',NULL,0);
INSERT INTO comment VALUES (10833,1362,4982,'Dan Blume','re: is this the right way?','2003-12-31 16:20:12',0,'I like your answer. With the numerators above the drawn lines, and the denominators below, it works. I see no other way.',10795,0);
INSERT INTO comment VALUES (10834,97,4718,'Jack Squat','','2003-12-31 17:51:30',0,'There are an infinite number of solutions in which this does not work either, as negative x\'s and y\'s do not work.\r\n\r\nI can think of two integer/special solutions. One is x=1, y=1 and the other is x=0, y=0. Plugging those into the equation (using any two powers that add to 43) will work. However this is sort of cheap.\r\n\r\nx=-1, y=-1 would be another integer solution, if 43 wasn\'t an odd number...',NULL,0);
INSERT INTO comment VALUES (10835,1443,3386,'Victor Zapana','Some Thoughts','2004-01-01 12:00:48',0,'Happy New Year everyone! Well, I havent been commented a lot in December coz I was in Washington for vacation, and now that I\'m back, I\'ll start commenting more frequently. Let\'s see... coz I don\'t like using computer programs, I would use the guess and check method. There are 24 different possibilities: T L K R, T L R K, T K L R, T K R L, ... Also, A and D\'s first statement involves B, but they both say different things about B, so one is telling the truth and the other isn\'t, or both aren\'t telling the truth with the B statement. Also, B and C both share a common statement, so possibly it is true, though I\'m not entirely sure at this moment. Also, D has a conflicting statement with B. Because D has 2 conflicting statement, I would say he is either a liar, or rebel, though there is a chance (though I find highly unlikely) that he is a knight... More stuff to come when I think of it.\r\n\r\n+--+--+--+--+--+--+--+--+--+--+--+\r\n| 1 1 1 1 1|80 80|79 79|78 78|\r\n+ + + + +\r\n| 1 1 1 1 1|80 80|79 79|78 78|\r\n+ +--+--+--+--+--+--+\r\n| 1 1 1 1 1|75 75|76 76|77 77|\r\n+ + + + +\r\n| 1 1 1 1 1|75 75|76 76|77 77|\r\n+ +--+--+--+--+--+--+\r\n| 1 1 1 1 1|74 74|73 73|72 72|\r\n+--+--+--+--+--+ + + +\r\n|47 47|62 62 62|74 74|73 73|72 72|\r\n+ + +--+--+--+--+--+--+\r\n|47 47|62 62 62|67 67 67|66 66 66|\r\n+--+--+ + + +\r\n|48 48|62 62 62|67 67 67|66 66 66|\r\n+ +--+--+--+ + +\r\n|48 48|61 61 61|67 67 67|66 66 66|\r\n+--+--+ +--+--+--+--+--+--+\r\n|49 49|61 61 61|65 65|64 64|63 63|\r\n+ + + + + +\r\n|49 49|61 61 61|65 65|64 64|63 63|\r\n+--+--+--+--+--+--+--+--+--+--+--+\r\n\r\n+--+--+--+--+--+--+--+--+--+--+--+\r\n| 1 1 1 1 1|80 80|79 79|78 78|\r\n+ + + + +\r\n| 1 1 1 1 1|80 80|79 79|78 78|\r\n+ +--+--+--+--+--+--+\r\n| 1 1 1 1 1|75 75|76 76|77 77|\r\n+ + + + +\r\n| 1 1 1 1 1|75 75|76 76|77 77|\r\n+ +--+--+--+--+--+--+\r\n| 1 1 1 1 1|74 74|73 73|72 72|\r\n+--+--+--+--+--+ + + +\r\n|47 47|62 62 62|74 74|73 73|72 72|\r\n+ + +--+--+--+--+--+--+\r\n|47 47|62 62 62|67 67 67|66 66 66|\r\n+--+--+ + + +\r\n|48 48|62 62 62|67 67 67|66 66 66|\r\n+ +--+--+--+ + +\r\n|48 48|61 61 61|67 67 67|66 66 66|\r\n+--+--+ +--+--+--+--+--+--+\r\n|49 49|61 61 61|65 65|64 64|63 63|\r\n+ + + + + +\r\n|49 49|61 61 61|65 65|64 64|63 63|\r\n+--+--+--+--+--+--+--+--+--+--+--+\r\n\r\n+--+--+--+--+--+--+--+--+--+--+--+\r\n| 1 1 1 1 1|70 70 70|69 69 69|\r\n+ + + +\r\n| 1 1 1 1 1|70 70 70|69 69 69|\r\n+ + + +\r\n| 1 1 1 1 1|70 70 70|69 69 69|\r\n+ +--+--+--+--+--+--+\r\n| 1 1 1 1 1|71 71 71|68 68 68|\r\n+ + + +\r\n| 1 1 1 1 1|71 71 71|68 68 68|\r\n+--+--+--+--+--+ + +\r\n|46 46|62 62 62|71 71 71|68 68 68|\r\n+ + +--+--+--+--+--+--+\r\n|46 46|62 62 62|67 67 67|66 66 66|\r\n+--+--+ + + +\r\n|56 56|62 62 62|67 67 67|66 66 66|\r\n+ +--+--+--+ + +\r\n|56 56|61 61 61|67 67 67|66 66 66|\r\n+--+--+ +--+--+--+--+--+--+\r\n|57 57|61 61 61|60 60|59 59|58 58|\r\n+ + + + + +\r\n|57 57|61 61 61|60 60|59 59|58 58|\r\n+--+--+--+--+--+--+--+--+--+--+--+\r\n\r\n+--+--+--+--+--+--+--+--+--+--+--+\r\n| 1 1 1 1 1|70 70 70|69 69 69|\r\n+ + + +\r\n| 1 1 1 1 1|70 70 70|69 69 69|\r\n+ + + +\r\n| 1 1 1 1 1|70 70 70|69 69 69|\r\n+ +--+--+--+--+--+--+\r\n| 1 1 1 1 1|71 71 71|68 68 68|\r\n+ + + +\r\n| 1 1 1 1 1|71 71 71|68 68 68|\r\n+--+--+--+--+--+ + +\r\n|46 46|44 44 44|71 71 71|68 68 68|\r\n+ + +--+--+--+--+--+--+\r\n|46 46|44 44 44|43 43 43|42 42 42|\r\n+--+--+ + + +\r\n|56 56|44 44 44|43 43 43|42 42 42|\r\n+ +--+--+--+ + +\r\n|56 56|53 53 53|43 43 43|42 42 42|\r\n+--+--+ +--+--+--+--+--+--+\r\n|57 57|53 53 53|60 60|59 59|58 58|\r\n+ + + + + +\r\n|57 57|53 53 53|60 60|59 59|58 58|\r\n+--+--+--+--+--+--+--+--+--+--+--+\r\n\r\n+--+--+--+--+--+--+--+--+--+--+--+\r\n| 1 1 1 1 1|70 70 70|69 69 69|\r\n+ + + +\r\n| 1 1 1 1 1|70 70 70|69 69 69|\r\n+ + + +\r\n| 1 1 1 1 1|70 70 70|69 69 69|\r\n+ +--+--+--+--+--+--+\r\n| 1 1 1 1 1|71 71 71|68 68 68|\r\n+ + + +\r\n| 1 1 1 1 1|71 71 71|68 68 68|\r\n+--+--+--+--+--+ + +\r\n|45 45|44 44 44|71 71 71|68 68 68|\r\n+ + +--+--+--+--+--+--+\r\n|45 45|44 44 44|43 43 43|42 42 42|\r\n+--+--+ + + +\r\n|55 55|44 44 44|43 43 43|42 42 42|\r\n+ +--+--+--+ + +\r\n|55 55|53 53 53|43 43 43|42 42 42|\r\n+--+--+ +--+--+--+--+--+--+\r\n|54 54|53 53 53|52 52|51 51|50 50|\r\n+ + + + + +\r\n|54 54|53 53 53|52 52|51 51|50 50|\r\n+--+--+--+--+--+--+--+--+--+--+--+\r\n\r\n+--+--+--+--+--+--+--+--+--+--+--+\r\n|39 39|40 40|41 41|25 25 25|28 28|\r\n+ + + + + +\r\n|39 39|40 40|41 41|25 25 25|28 28|\r\n+--+--+--+--+--+--+ +--+--+\r\n|38 38 38|37 37 37|25 25 25|27 27|\r\n+ + +--+--+--+ +\r\n|38 38 38|37 37 37|24 24 24|27 27|\r\n+ + + +--+--+\r\n|38 38 38|37 37 37|24 24 24|26 26|\r\n+--+--+--+--+--+--+ + +\r\n|45 45|44 44 44| 0|24 24 24|26 26|\r\n+ + +--+--+--+--+--+--+\r\n|45 45|44 44 44|43 43 43|42 42 42|\r\n+--+--+ + + +\r\n|55 55|44 44 44|43 43 43|42 42 42|\r\n+ +--+--+--+ + +\r\n|55 55|53 53 53|43 43 43|42 42 42|\r\n+--+--+ +--+--+--+--+--+--+\r\n|54 54|53 53 53|52 52|51 51|50 50|\r\n+ + + + + +\r\n|54 54|53 53 53|52 52|51 51|50 50|\r\n+--+--+--+--+--+--+--+--+--+--+--+\r\n\r\n+--+--+--+--+--+--+--+--+--+--+--+\r\n|39 39|40 40|41 41|25 25 25|28 28|\r\n+ + + + + +\r\n|39 39|40 40|41 41|25 25 25|28 28|\r\n+--+--+--+--+--+--+ +--+--+\r\n|38 38 38|37 37 37|25 25 25|27 27|\r\n+ + +--+--+--+ +\r\n|38 38 38|37 37 37|24 24 24|27 27|\r\n+ + + +--+--+\r\n|38 38 38|37 37 37|24 24 24|26 26|\r\n+--+--+--+--+--+--+ + +\r\n|15 15|14 14|13 13|24 24 24|26 26|\r\n+ + + +--+--+--+--+--+\r\n|15 15|14 14|13 13| 2 2 2 2 2|\r\n+--+--+--+--+--+--+ +\r\n|10 10|11 11|12 12| 2 2 2 2 2|\r\n+ + + + +\r\n|10 10|11 11|12 12| 2 2 2 2 2|\r\n+--+--+--+--+--+--+ +\r\n| 9 9| 8 8| 7 7| 2 2 2 2 2|\r\n+ + + + +\r\n| 9 9| 8 8| 7 7| 2 2 2 2 2|\r\n+--+--+--+--+--+--+--+--+--+--+--+\r\n\r\n+--+--+--+--+--+--+--+--+--+--+--+\r\n|36 36|35 35|34 34|25 25 25|23 23|\r\n+ + + + + +\r\n|36 36|35 35|34 34|25 25 25|23 23|\r\n+--+--+--+--+--+--+ +--+--+\r\n|38 38 38|37 37 37|25 25 25|22 22|\r\n+ + +--+--+--+ +\r\n|38 38 38|37 37 37|24 24 24|22 22|\r\n+ + + +--+--+\r\n|38 38 38|37 37 37|24 24 24|21 21|\r\n+--+--+--+--+--+--+ + +\r\n|15 15|14 14|13 13|24 24 24|21 21|\r\n+ + + +--+--+--+--+--+\r\n|15 15|14 14|13 13| 2 2 2 2 2|\r\n+--+--+--+--+--+--+ +\r\n|10 10|11 11|12 12| 2 2 2 2 2|\r\n+ + + + +\r\n|10 10|11 11|12 12| 2 2 2 2 2|\r\n+--+--+--+--+--+--+ +\r\n| 9 9| 8 8| 7 7| 2 2 2 2 2|\r\n+ + + + +\r\n| 9 9| 8 8| 7 7| 2 2 2 2 2|\r\n+--+--+--+--+--+--+--+--+--+--+--+\r\n\r\n+--+--+--+--+--+--+--+--+--+--+--+\r\n|36 36|35 35|34 34|20 20 20|23 23|\r\n+ + + + + +\r\n|36 36|35 35|34 34|20 20 20|23 23|\r\n+--+--+--+--+--+--+ +--+--+\r\n|30 30 30|29 29 29|20 20 20|22 22|\r\n+ + +--+--+--+ +\r\n|30 30 30|29 29 29|17 17 17|22 22|\r\n+ + + +--+--+\r\n|30 30 30|29 29 29|17 17 17|21 21|\r\n+--+--+--+--+--+--+ + +\r\n| 5 5 5| 6 6 6|17 17 17|21 21|\r\n+ + +--+--+--+--+--+\r\n| 5 5 5| 6 6 6| 2 2 2 2 2|\r\n+ + + +\r\n| 5 5 5| 6 6 6| 2 2 2 2 2|\r\n+--+--+--+--+--+--+ +\r\n| 4 4 4| 3 3 3| 2 2 2 2 2|\r\n+ + + +\r\n| 4 4 4| 3 3 3| 2 2 2 2 2|\r\n+ + + +\r\n| 4 4 4| 3 3 3| 2 2 2 2 2|\r\n+--+--+--+--+--+--+--+--+--+--+--+\r\n\r\n+--+--+--+--+--+--+--+--+--+--+--+\r\n|31 31|32 32|33 33|20 20 20|19 19|\r\n+ + + + + +\r\n|31 31|32 32|33 33|20 20 20|19 19|\r\n+--+--+--+--+--+--+ +--+--+\r\n|30 30 30|29 29 29|20 20 20|18 18|\r\n+ + +--+--+--+ +\r\n|30 30 30|29 29 29|17 17 17|18 18|\r\n+ + + +--+--+\r\n|30 30 30|29 29 29|17 17 17|16 16|\r\n+--+--+--+--+--+--+ + +\r\n| 5 5 5| 6 6 6|17 17 17|16 16|\r\n+ + +--+--+--+--+--+\r\n| 5 5 5| 6 6 6| 2 2 2 2 2|\r\n+ + + +\r\n| 5 5 5| 6 6 6| 2 2 2 2 2|\r\n+--+--+--+--+--+--+ +\r\n| 4 4 4| 3 3 3| 2 2 2 2 2|\r\n+ + + +\r\n| 4 4 4| 3 3 3| 2 2 2 2 2|\r\n+ + + +\r\n| 4 4 4| 3 3 3| 2 2 2 2 2|\r\n+--+--+--+--+--+--+--+--+--+--+--+\r\n\r\n+--+--+--+--+--+--+--+--+--+--+--+\r\n|31 31|32 32|33 33|20 20 20|19 19|\r\n+ + + + + +\r\n|31 31|32 32|33 33|20 20 20|19 19|\r\n+--+--+--+--+--+--+ +--+--+\r\n|30 30 30|29 29 29|20 20 20|18 18|\r\n+ + +--+--+--+ +\r\n|30 30 30|29 29 29|17 17 17|18 18|\r\n+ + + +--+--+\r\n|30 30 30|29 29 29|17 17 17|16 16|\r\n+--+--+--+--+--+--+ + +\r\n| 5 5 5| 6 6 6|17 17 17|16 16|\r\n+ + +--+--+--+--+--+\r\n| 5 5 5| 6 6 6| 2 2 2 2 2|\r\n+ + + +\r\n| 5 5 5| 6 6 6| 2 2 2 2 2|\r\n+--+--+--+--+--+--+ +\r\n| 4 4 4| 3 3 3| 2 2 2 2 2|\r\n+ + + +\r\n| 4 4 4| 3 3 3| 2 2 2 2 2|\r\n+ + + +\r\n| 4 4 4| 3 3 3| 2 2 2 2 2|\r\n+--+--+--+--+--+--+--+--+--+--+--+\r\n\r\n
\r\n-------\r\nSo, for example, on the base, 5-cm cube 2 lies at the lower right. A 6x6 area lies to the left of that and at this level is a set of 4 3-cm cubes (cubes 3 thru 6), and if you follow that area up, you\'ll see it\'s overlain by a layer of nine 2-cm cubes (cubes 7 - 15). At the top, cube 1 is the 5-cm cube and 72-80 take up the 6x6 area (arbitrarily the 2-cm cubes are on top and the 3-cm cubes 68-71 lie below them, rather than above).\r\n\r\nThe empty unit cube is labeled 0.',NULL,0);
INSERT INTO comment VALUES (10903,344,5033,'Captain Paradox','re: Alternative solution','2004-01-04 20:56:08',0,'I never would have thought of that. Nice word play, fwaff.',2259,0);
INSERT INTO comment VALUES (10904,1358,5033,'Captain Paradox','Sons or daughters','2004-01-04 21:05:44',0,'If the mother has no daughters, then the number of sons can be 0 to infinity, because each would have the same number of brothers. If the mother has daughters, however, she can\'t have any sons because every son would have 1 less brother than the sister and every daughter 1 less sister than the brothers.',NULL,0);
INSERT INTO comment VALUES (10905,227,5033,'Captain Paradox','re: Solution','2004-01-04 21:11:25',0,'Protagoras is suing, however, for the fee that he was not paid. If the court pays anything less than the tuition fee, he can argue that he is again being cheated.',1364,0);
INSERT INTO comment VALUES (10906,27,5033,'Captain Paradox','If I were the professor . . .','2004-01-04 21:15:35',1,'If I were the professor, I would tell my class that I MAY or MAY NOT give them a surprise quiz next week. Therefore, they would never be 100% sure until Friday when I told them whether or not there would be a surprise quiz.',NULL,0);
INSERT INTO comment VALUES (10907,1555,5047,'Stereo','Solution?','2004-01-05 00:43:04',0,'Using PBasic (A Language used in small processing chips) \r\na VAR Byte\r\nb VAR Byte\r\n\r\na = 123\r\nb = 456\r\nprint a,b\r\na = b\r\nIF a = 456 THEN swap\r\nSwap:\r\nb=123\r\nPrint a,b\r\n',NULL,0);
INSERT INTO comment VALUES (10908,40,5049,'Ali','you can do up to 27 with 3 times weighing','2004-01-05 01:57:49',0,'Hi all,\r\nfor the initial problem (So Easy)\r\ndevide 11 into 3 piles, 4,4,3 (and assuming the odd one is lighter)\r\n\r\n1. weigh the two piles of 4s, if one is lighter==> the odd one is in it, if the are equal==> the odd one is in the pile of 3.\r\n\r\n2. assuming the odd one is in the pile of 3, we devide the pile to 3 individual coins, the we weigh 2, if one is lighter ==> it is the one, if they are equal==> the one left is the lighter one.\r\n\r\n3. assuming the odd one is in the pile of 4, we devide them into piles of 2s, we weigh and the lighter one has the lighter coin. finally we weigh again the 2 to see which is lighter and that is the one.\r\n(same reasoning can be used if the odd coin is heavier)\r\n\r\n\r\nas for the open problem:\r\nup to 27 can be solved with the same reasoning.\r\n\r\n1. we devide 27 into piles of 9s and weigh 2, if one is lighter==> it is the one; if equal==> the remaining pile is the one.\r\n\r\n2. we devide the pile of 9 into 3 piles of 3s. we weigh 2 piles, if one is lighter==> it is the one; if equal==> the remaining pile is the one.\r\n\r\n3. we devide the pile of 3 into 3 individual coins. we weigh 2 coins, if one is lighter==> it is the one; if equal==> the remaining coin is the one.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (10909,1220,4197,'luminita','Bertrand problem - paradox','2004-01-05 03:58:47',3,'This problem is known as \"Bertrand problem\" and has 3 solutions:\r\n1. as Bryan said: p=2/3 in case the hazard refers to the angle of the chord\r\n2. as np_rt said: √3/2 in case the hazard refers to the distance between the chord and the center of the circle\r\n3. as Benjamin said: 3/4 in case the hazard refers to the positioning of the center of the chord in the circle.\r\nIt is correct to place this problem in \"paradox\".',NULL,0);
INSERT INTO comment VALUES (10910,1376,4197,'luminita','solution','2004-01-05 05:20:17',3,'L=211.8 m\r\n\r\nu = speed of the soldier\r\nv= speed of the dog\r\na=u/v (a<1)\r\nb= the distance to the new position (50m)\r\n\r\nThe 1-st and the 3-rd path is the length of the pursuit curve:\r\nL1=L3=b/(1-a²)\r\n\r\nL2=b/(1-a)\r\nL4=b/(1+a)\r\n\r\nthe equation of time for both dog and soldiers gives the value of \"a\":\r\n2/(1-a²)+1/(1-a)+1/(1+a)=1/a\r\na²+4a-1=0\r\na=√5-2\r\n\r\nL=L1+L2+L3+L4 = 2b/(1-a²)+b/(1-a)+b/(1+a)\r\nL=50(2+√5)=211.8m',NULL,0);
INSERT INTO comment VALUES (10911,1363,4542,'Katie','solution','2004-01-05 08:50:07',0,'This is really simple. I just totaled each line and figured what number combinations would leave me with 20.\r\n\r\n7x5x62\r\n81x65x\r\nx843x5\r\n468x2x\r\n1xx478\r\nx537x5',NULL,0);
INSERT INTO comment VALUES (10912,1556,1301,'Charlie','How many solutions?','2004-01-05 09:26:12',4,'Both solutions presented so far (Dan Blume\'s and mine) do follow a pattern with six 6x6x5 sub-blocks in each of which there is a layer of 4 3-cm cubes and a layer of 9 2-cm cubes. A question then exists: are there any solutions that do not follow this pattern?\r\n\r\nIf any solution must actually follow this pattern, then how many variants are there?\r\n\r\nThe answer to that depends on whether you are considering a particular orientation for the box, or consider a solution to be the same even if it is rotated.\r\n\r\nWhen orientation is considered, the first 5x5x5 cube can be placed in any of the four bottom corners of the box. The 6x6 area occupied by the lying-flat 6x6x5 sub-assembly must be adjacent to this (otherwise it would create a 1-cm-thick layer eventually), but either clockwise or counterclockwise from the 5x5x5 cube. From there, the pieces will fit in only one way. That\'s 4x2 choices so far.\r\n\r\nWithin each 6x6x5 subassembly, the 3-cm cubes can be either toward the outside (including bottom or top) of the box or toward the inside (leaving the 2-cm cubes to face the outside). As there are 6 of these subassemblies, that gives each of the 8 original choices 2^6 possibilities, so the number of solutions is 8*2^6 = 2^9 = 512 ways of packing the box.\r\n\r\nHowever if the orientation of the larger box is not to count, there would be fewer distinct packings. The diagonal formed by the two 5x5x5 cubes can be placed in a standard orientation. When considering the placement of the 6x6 flat on the surface, these can be either clockwise or counterclockwise at a given vertex with the 5x5x5 cube, but in any packing, one will be clockwise and the other counterclockwise, so there is no clockwise version vs. counterclockwise version.\r\n\r\nThe orientations of 3-cm out or 2-cm out for the 6x6 explosed flats, about the clockwise vertex can be (said regarding the 3-cm side): \r\n1) All outward\r\n2) all inward\r\n3) Two outward\r\n4) two inward.\r\n\r\nIn the case of \"all outward\" or \"all inward\", there are the same four possibilities at the other end of the diagonal axis, accounting for a total of 8 packings so far.\r\n\r\nIn the case of \"two outward\" or \"two inward\" the \"all outward\" or \"all inward\" at the other end constitute one way each, accounting for 4 more packings. But the \"two outward\" or \"two inward\" orientations at the other end also, could themselves be oriented 3 ways each with regard to where the odd one is in relation to the odd one at the other end, so 2x2x3=12 is added to the total. Thus the final total is 8+4+12 = 24 ways of packing the cubes, when orientation of the whole box is not considered.\r\n\r\nThe only remaining consideration is whether there are solutions which do not have the 6 identical 6x6x5 subassemblies.',NULL,0);
INSERT INTO comment VALUES (10913,1555,2716,'Federico Kereki','re: solution','2004-01-05 11:07:48',0,'That code might cause an overflow/underflow problem. (A+B could be too high/low.) If you have binary logic, you can rather write\r\nA=A XOR B\r\nB=A XOR B\r\nA=A XOR B
\r\nwhich doesn\'t cause any problems.',10848,0);
INSERT INTO comment VALUES (10914,1363,5054,'Becky','Solution','2004-01-05 12:57:21',3,'7 5 6 2\r\n8 1 6 5 \r\n 8 4 3 5\r\n4 6 8 2 \r\n1 4 7 8\r\n 5 3 7 5',NULL,0);
INSERT INTO comment VALUES (10915,1363,5054,'Becky','re: Solution','2004-01-05 13:02:17',3,'Redoing this because the alignment messed up.\r\n\r\n705062\r\n810650\r\n084305\r\n468020\r\n100478\r\n053705\r\n',10914,0);
INSERT INTO comment VALUES (10916,1363,5055,'Sujit','re(2): Solution','2004-01-05 13:22:43',3,'7-5-62 \r\n81-65- \r\n-843-5 \r\n468-2- \r\n1--478 \r\n-537-5 \r\n\r\n:>',10915,0);
INSERT INTO comment VALUES (10917,172,4718,'Jack Squat','Simplify a bit','2004-01-05 14:17:06',0,'The sum of 1+3+5+... is represented by ∑2n-1 where n runs from 1 to n. So the question is does this sum equal n², or\r\n\r\n∑2n-1 = n² ?\r\n\r\nTaking the 2 and the 1 out of the summation gives:\r\n\r\n2(∑n)-n = n²\r\n\r\nMoving the 2 and the -n to the other side gives:\r\n\r\n∑n = (n²-n)/2 = n(n+1)/2\r\n\r\nLook familiar?',NULL,0);
INSERT INTO comment VALUES (10918,1446,4982,'Dan Blume','Give it a try','2004-01-05 18:02:09',0,'Six',NULL,0);
INSERT INTO comment VALUES (10919,1509,5061,'Michelle','solution','2004-01-05 18:59:28',3,'march 15th',NULL,0);
INSERT INTO comment VALUES (10920,1443,5063,'Tnewt','solution','2004-01-05 19:59:17',0,'A is the liar, B is the rebel, C is the knave, and D is the knight. A came in first, B second, C third and D fourth. Victor- if the knave is C and the knight D as you have indeed ceded, then C\'s first statement, that D is the knave (when he is clearly the knight) must be false. Thus, as the knave alternates between true and false, the second statement, A won the race must be true. Thus D could not have come in first as you had suggested. ',NULL,0);
INSERT INTO comment VALUES (10921,1446,3558,'Tristan','possible tricks','2004-01-05 20:14:34',1,'I see a few spots where the trickery could be involved. \"five too many\" may refer to dollars or cents or coins. \"sixth\" may also refer to dollars, but only if \"dollar bill\" refers to a five dollar bill. Also, \"he remarked\" may refer to either the customer or the shopman. When I first read it, I interpreted as the customer speaking first, then the shopman, but it might be different.',NULL,0);
INSERT INTO comment VALUES (10922,1509,5062,'Steve','leap year','2004-01-05 20:15:48',0,'march 15th is an easy answer if you pay attention to why they put the year in the question. it isn\'t really required unless there is a trick to it.',NULL,0);
INSERT INTO comment VALUES (10923,1509,5062,'Steve','re: leap year','2004-01-05 20:21:07',0,'i am retracting that answer because by the 10 pm on the 27th day he will be at the 30 foot mark meaning he is out. therefore the answer would be on march 12th.',10922,0);
INSERT INTO comment VALUES (10924,1446,1626,'Gamer','In relation to that:','2004-01-05 20:38:10',0,'The \"he\" refers to the man at the beginning; that should have been reworded.\r\n\r\nThe bill the man gave is really just a dollar bill, worth only a dollar.\r\n\r\n\r\nI editted the problem to make sure these are what\'s intended. Tricks problems are the only problems where you can be picky about words.\n\nEdited on January 5, 2004, 8:41 pm',10921,0);
INSERT INTO comment VALUES (10925,1446,4374,'Richard','5 too many whats?','2004-01-05 22:16:06',0,'It seems plausible to me that the shopkeeper means 5 too many n-ths of a chestnut. Thus 5/n should be more than 0 and less than 1/2 since the buyer thinks he deserves 6 (due to rounding). Thus n > 10. I pick 12 because the shopkeeper thinks the buyer has a case, albeit a marginal one, for getting 6 instead of 5 and $60 presumably buys a whole number of chestnuts. Hence $60 should buy 60 x 5 7/12 = 335 chestnuts.\n\nEdited on January 5, 2004, 10:29 pm',NULL,0);
INSERT INTO comment VALUES (10926,429,4909,'Brian','that\'s an old one','2004-01-05 22:43:59',0,'just like a joke, there are many deliveries but only one answer. the poison was in the ice (it took a little while to melt into the punch)\r\n',NULL,0);
INSERT INTO comment VALUES (10927,429,4909,'Brian','that\'s an old one','2004-01-05 22:44:16',0,'just like a joke, there are many deliveries but only one answer. the poison was in the ice (it took a little while to melt into the punch)\r\n',NULL,0);
INSERT INTO comment VALUES (10928,429,4909,'Brian','that\'s an old one','2004-01-05 22:45:24',0,'just like a joke, there are many deliveries but only one answer. the poison was in the ice (it took a little while to melt into the punch)\r\n',NULL,0);
INSERT INTO comment VALUES (10929,344,4909,'Brian','another old one','2004-01-05 22:47:40',0,'a hole',NULL,0);
INSERT INTO comment VALUES (10930,344,4909,'Brian','another old one','2004-01-05 22:48:03',0,'a hole',NULL,0);
INSERT INTO comment VALUES (10931,344,4909,'Brian','another old one','2004-01-05 22:50:06',0,'a hole',NULL,0);
INSERT INTO comment VALUES (10932,1446,4507,'Penny','Solution','2004-01-06 00:09:00',3,'As soon as I read \"But you will have five too many chestnuts if I gave you one chestnut more [than five]\", I figured that this has to do with modulus 5 arithmetic, where 6 = 1. So my solution is based on that idea.\r\n\r\nAnswer: For 3 twenty dollar bills, the man should have gotten 15 chestnuts. (That doesn\'t sound very equitable, but hey, this is a \"nonsense puzzle\" !!)\r\n \r\nExplanation:\r\n\r\nWhenever a shopper hands the shopkeeper a bill which is the equivalent of N dollars (N=1 for a dollar bill, N=5 for a five dollar bill,...,N=20 for a twenty dollar bill, ...), the shopkeeper gives F[N] chesnuts to the shopper, where\r\n \r\n F[N] = 1 + [(N+4) mod 5]\r\n\r\nBut when the shopper in the puzzle came in, the shopkeeper accidentally typoed the function: \r\n\r\n G[N] = 5 + [(N+4) mod 5] \r\n\r\nSo the shopkeeper handed him \r\nG[1] = 5 + [(1+4) mod 5] = 5 chesnuts.\r\n\r\nRealizing that a mistake had been made, the shopper asked for an extra chestnut, for a total of 6. But the shopkeeper realized that the correct number should be F[1] = 1 + [(1+4)mod 5] = 1 chestnut, so he knew that 6 would be 5 too many. Hence his answer.\r\n\r\nNow F[20] = 1 + [24 mod 5] = 5\r\nSo each twenty dollar bill should get him 5 chestnuts. Three twenty dollar bills will therefore get him 15 chestnuts.',NULL,0);
INSERT INTO comment VALUES (10933,1446,5065,'Darryl','The answer is..............(----------------------------------','2004-01-06 00:50:40',0,'300',NULL,0);
INSERT INTO comment VALUES (10934,1446,3136,'Popstar Dave','solution','2004-01-06 01:38:42',3,'The trick in this question is that when the shopkeeper replies that the shopper would have \"five too many\" if he received an extra chestnut; the \'five\' refers to the \'sixth\' that the shopper mentioned in the previous sentence. Thus the shopkeeper was saying that the rate for chestnuts was 5 and 1/6 chestnuts for $1. Thus if the shopper received 6 chestnuts, he would have five (sixths) too many...\r\n\r\nAt the going rate of $1 for 5 and 1/6 chestnuts, the shopper should receive 310 (60*(5+1/6)) chestnuts for his $60.',NULL,0);
INSERT INTO comment VALUES (10935,1446,5068,'cory','answer','2004-01-06 01:46:37',0,'60 chestnuts',NULL,0);
INSERT INTO comment VALUES (10936,1446,5068,'cory','the real answer','2004-01-06 01:50:04',0,'360 chestnuts',NULL,0);
INSERT INTO comment VALUES (10937,1446,153,'TomM','re: solution -- Of Course!','2004-01-06 01:57:08',0,'As with so many \"trick\" questions, the answer is obvious once it\'s been pointed out. Still, 31 for $6 is a very odd sales amount. (unless it\'s by weight, [say $3 a lb, and each chestnut weighs approximately 1.032 oz.])',10934,0);
INSERT INTO comment VALUES (10938,1446,5068,'cory','maybe the answer','2004-01-06 02:01:21',0,'310 chestnuts',NULL,0);
INSERT INTO comment VALUES (10939,1547,5067,'randy','lifes a joke and all my friends are clowns','2004-01-06 02:06:51',0,'SMILES--makes people wonder what you\'ve been up to.',NULL,0);
INSERT INTO comment VALUES (10940,1446,1626,'Gamer','re: solution','2004-01-06 06:24:35',0,'Although Penny\'s strange formula may be right, it is definitely way too much of a stretch, and there isn\'t anything supplied in the formula for that. I think 310 chestnuts is right. :)',10934,0);
INSERT INTO comment VALUES (10941,759,1920,'Brian Smith','Solution','2004-01-06 10:56:19',0,'For any natural number x, (x^2+2x+3) mod 5 is congruent to 2, 3 or 4. This means the value of x^2+2x+3 can never be a multiple of 5. Then the answer to the problem is there are no natural numbers x which make x^2+2x+3 a multiple of 35.',NULL,0);
INSERT INTO comment VALUES (10942,730,5071,'Kerry Graham','Possible Solution','2004-01-06 11:00:28',0,'All you really care about is the last digit in each of the calculations:\r\n8^7 = 2097152\r\n2^6 = 64\r\n4^5 = 1024\r\n4^4 = 256\r\n6^3 = 216\r\n6^2 = 36\r\n6^1 = 6\r\nLast digit is 6.\r\nDid I understand the problem correctly?',NULL,0);
INSERT INTO comment VALUES (10943,759,4982,'Dan Blume','Semantics','2004-01-06 11:30:11',3,'Semantics.\r\nFor ALL natural numbers x, the expression (x² + 2x + 3) is divisible by 35. One just ends up with a fraction. ;^)\r\n\r\n(I\'m guessing that is not what you were looking for.)',NULL,0);
INSERT INTO comment VALUES (10944,1446,4507,'Penny','re: solution','2004-01-06 11:37:35',0,'Popstar Dave: \"Thus the shopkeeper was saying that the rate for chestnuts was 5 and 1/6 chestnuts for $1.\"\r\n \r\nWhy would someone want 1/6 of a chestnut? ',10934,0);
INSERT INTO comment VALUES (10945,759,3172,'SilverKnight','re: Solution','2004-01-06 11:38:28',0,'Brian, you wrote:\r\n\" For any natural number x, (x^2+2x+3) mod 5 is congruent to 2, 3 or 4.\"\r\n\r\nI\'m not arguing with the statement, but I think you should show why this is true, to constitute a full solution.\r\n\r\n-SK',10941,0);
INSERT INTO comment VALUES (10946,759,1301,'Charlie','re(2): Solution','2004-01-06 13:18:15',0,'Per Brian:\r\n\" For any natural number x, (x^2+2x+3) mod 5 is congruent to 2, 3 or 4.\" \r\n\r\nBut isn\'t it 1, 2 or 3?\r\n\r\nAs it is modular arithmetic, it need be checked only for values of x as 0 through 4, which give 3, 1, 1, 3, 2 respectively.',10945,0);
INSERT INTO comment VALUES (10947,1557,3172,'SilverKnight','solution','2004-01-06 13:57:02',3,'Don\'t have a proof of it... but, {3, 4, 6, 9, 12, 24} seems to work.\r\n_____________\r\n\r\nArithmetic:\r\n3, 6, 9, 12\r\n\r\nGeometric:\r\n3, 6, 12, 24\r\n\r\nHarmonic:\r\n3, 4, 6, 12\r\n\r\n(1/12, 1/6, 1/4, 1/3 make an arithmetic sequence)',NULL,0);
INSERT INTO comment VALUES (10948,1557,3172,'SilverKnight','re: solution','2004-01-06 14:09:13',2,'My thoughts behind this solution are:\r\n\r\nStart with the harmonic sequence.\r\n\r\nWe need to find reciprocals, which when expressed in lowest terms, have a numerator of 1.\r\n\r\nTo minimize the numbers in the original set, we want to minimize the denominator.... but we need a denominator which is evenly divisible by the numerator (so that it can reduce to one).\r\n\r\nThe lowest integer that has 4 factors that are adjacent is 12. (1, 2, 3, 4, 6, and 12).\r\n\r\nSo... let\'s look at 1/12, 2/12, 3/12, 4/12 (arithmetic sequence)... the reciprocals are 12, 6, 4, and 3 respectively.\r\n\r\nLet\'s assume that those four numbers are in the set of 6.\r\n\r\n3, 6, and 12 are already in arithmetic sequence if we add the missing \'9\'...\r\n\r\n3, 6, and 12 are already in geometric sequence if we add the missing \'24\'...\r\n\r\nSo... that\'s how I came up with these numbers.',10947,0);
INSERT INTO comment VALUES (10949,1557,4906,'stan','Solution','2004-01-06 14:55:14',1,'How about 1/2, 2/3, 1,2,3,4?\r\n\r\nArthimetric: 1,2,3,4\r\nGeometric: 1/2,1,2,4\r\nHarmonic: 1/2,2/3,1,2 (Reciprocals are 2,3/2,1,1/2)\r\n\r\nThis gives lower numbers than SilverKnight, but it may not be best!',NULL,0);
INSERT INTO comment VALUES (10950,1557,4906,'stan','re: Solution','2004-01-06 15:15:01',0,'Whoops, missed the part about all numbers being integers... I guess that makes SilverKnight\'s answer the best...',10949,0);
INSERT INTO comment VALUES (10951,1446,4197,'luminita','possible solution','2004-01-06 15:54:05',3,'Assumption: the price is 1$ for 1 chestnut and the Marketing VP decided a promotional campaign of 14 chestnuts for free at each 3$ spent.\r\n\r\nFor 1 $ the buyer expects 1+14/3 chestnuts (roundup), i.e. 1+5=6 (he applied the promotion at maximum).\r\n\r\nFor 1$ the seller considers the integer [1+14/3] i.e. 1+4 =5. The meaning of \"5 too many\" refers to the fact that the promotion is not applicable for 1$, but he was very generous giving a 4 free chestnuts.\r\n\r\nFinally, for 60$, the buyer will receive 60 chestnuts + 20X14 (promotion) = 340 chestnuts.\r\n\r\nHm, I hope my English was clear enough!',NULL,0);
INSERT INTO comment VALUES (10952,1557,1626,'Gamer','re(2): Solution','2004-01-06 16:07:56',0,'Actually that\'s a good place to start. Think if 1,2,3,4, then note 1,2,4, so add 1/2. Then note if you add 3/2 it\'s harmonic. THEN, multiply the whole sequence by 6. :)',10950,0);
INSERT INTO comment VALUES (10953,1012,4909,'Brian','i think i got it','2004-01-06 16:44:48',0,'he was born -in front- of his dad. his mother died giving birth to him. later he became a clergyman or a captian of a ship and performed a weding ceremony for his sister and her significant other.\r\n\r\nswish!',NULL,0);
INSERT INTO comment VALUES (10954,378,5075,'Pam','Solution','2004-01-06 18:43:36',0,'a coffin.',NULL,0);
INSERT INTO comment VALUES (10955,378,5075,'Pam','Another change?','2004-01-06 18:46:08',0,'At the last line, you make it obvious by putting \"neither see nor feel it.\" When I tell the riddle, I say \"Who uses it does not know it.\"',NULL,0);
INSERT INTO comment VALUES (10956,343,5075,'Pam','solution','2004-01-06 18:52:14',0,'train wreck',NULL,0);
INSERT INTO comment VALUES (10957,759,1626,'Gamer','re(3): Solution','2004-01-06 20:24:43',0,'Well, if you added 1 to each, you would end up with values of 1,2,3,4,5; 5 is the \"0\" value.\r\n\r\nWhat Charlie is saying is this: Replace x with 5y+z, where y and z are non-negative integers, with z less than 5. This gives 25y² +10yz + z² + 10y+ 2z + 3 or 5(5y²+2yz+2y) + z² + 2² + 3 . Then divide that by 5 to get what it is mod 5, which is easily seen to be what we started with, only with z to be 0 through 4. So using higher forms of the same number base 5 (3,8,13,18...) will be the same for each one.',10946,0);
INSERT INTO comment VALUES (10958,1446,1626,'Gamer','re(2): solution','2004-01-06 20:28:28',0,'Couldn\'t you use that for recipies where you don\'t need a whole one? You obviously can use half a melon, or half a pepper. Anyway, the sale could be just like gas; giving partials because nobody will buy just 1, they will buy 6 or 36, or something like that :)',10944,0);
INSERT INTO comment VALUES (10959,1557,3386,'Victor Zapana','question','2004-01-06 21:51:02',0,'What is meant by \"largest member of the set is a minimum\"? Does it mean, which I think it does, that the largest number is the smallest as well? Well, if thats the case, then probably all the numbers in the set are the same?',NULL,0);
INSERT INTO comment VALUES (10960,759,3705,'zaphod','a bit clearer','2004-01-07 03:19:36',3,'Just to make things clear, we can calculate the last digit of x²+2x+3 for any possible natural x.\r\nx can end in 0,1,2,3,4,5,6,7,8,9.\r\nx² will end in 0,1,4,9,6,5,6,9,4,1 respectively.\r\n2x will end in 0,2,4,6,8,0,2,4,6,8 (also respectively).\r\nAdding these together with 3 yields 3,6,1,8,7,8,1,6,3,2 as the whole expression\'s last digit.\r\nThis means that the expression cannot be divided by 5, much less by 35 ;)',NULL,0);
INSERT INTO comment VALUES (10961,1557,1301,'Charlie','re: question','2004-01-07 09:13:53',0,'Regarding \"What is meant by \"largest member of the set is a minimum\"? Does it mean, which I think it does, that the largest number is the smallest as well? Well, if thats the case, then probably all the numbers in the set are the same? \"\r\n\r\nI\'m sure it just means that the largest member of this set is smaller than the largest member of any other set that satisfies these properties.\r\n',10959,0);
INSERT INTO comment VALUES (10962,337,4909,'Brian','old one','2004-01-07 10:42:41',0,'12... the second of jan., feb., and so on',NULL,0);
INSERT INTO comment VALUES (10963,1378,153,'TomM','First Steps','2004-01-07 10:56:16',1,'What you have are the lengths of a chord and the subtended arc of a circle and you need to find the radius.\r\n\r\n1)Define a few variables:\r\nR = the unknown radius\r\nθ = the subtended angle (in radians)\r\nA = the arclength of the subtended arc = 5\r\nC = the length of the chord = 4\r\n\r\n2) Set up the equations:\r\nA = Rθ =5\r\nsin(θ/2) = (C/2)/R = 2/R\r\n\r\n3) Solve for θ:\r\nθ = 5/R = 2(arcsin[2/R])\r\n\r\n4) Solve for R\r\n',NULL,0);
INSERT INTO comment VALUES (10964,1378,1920,'Brian Smith','re: First Steps','2004-01-07 11:17:58',0,'A numeric solution for 5/R = 2(arcsin[2/R]) is R = 2.21023276908',10963,0);
INSERT INTO comment VALUES (10965,1443,5083,'Sam','Different Solution','2004-01-07 12:45:45',0,'I think I have it. I began by trying to figure out who the knight is. It has to be A, C, or D (B said C was the knight, so it can\'t be B). If A was the knight, B had to be the liar. D could not have been the knave because A contradicted both his second and third statements, so D was the rebel and C the knave. If C was the knave his first statment was false since he said D was the knave. So, his second statment (A was 1st)would have to be true, but it contradicts A\'s second statement (that C was 1st).\r\n\r\nSo the knight was C or D. If it were C, however, D would be the knave. His third statement would have to be false (it contradicts C\'s third statement), so the first must be false (therefore B couldn\'t be the rebel, so A is and B is the liar) and the second true. However, B\'s second statement was that C is the knight, which would have to be true, so this doesn\'t work.\r\n\r\nSo, D is the knight, and he says that B is the rebel. B\'s first statement is false (that C is the knight), and his second statement (that B was 4th) contradicts D\'s statement that B was third), so it has to be false. So, B\'s third statement (that C was 2nd) must be true, and we already knew it anyway because D said so. A cannot be the knave because D\'s second statement contradicts both A\'s 2nd and 3rd statements. So, A is the liar and C is the knave. We know from D the knight that C was 2nd and B was 3rd. Knave C\'s first statement (that D was the knave) was false, so the second (A was first) must be true. So A was first, B was third, C was second, and by process of elimination D was 4th.',NULL,0);
INSERT INTO comment VALUES (10966,1514,5086,'vikas','solution','2004-01-07 13:53:09',3,'firstly if 3 lengths are to form a triangle then they must satisfy a property stated as \" the sum of any two of the three must be greater than the third \"\r\n\r\nNow let us see the problem as a step procedure...\r\nto break the stick into 3 pieces we\'ll have to make 2 random cuts.\r\nThe probability of getting the first random cut exactly at the centre of the stick is very very low, say d (d<<1).\r\ntherefore the probability of getting the cut anywhere else on the stick is 1-d (which will be almost 1).\r\nso this cut will break the stick into two parts, which are:\r\n\r\na)EQUAL, if the cut is at centre (which is with \r\n probability d). And in this case making the \r\n second cut anywhere on the two pieces wont make\r\n a triangle possible.\r\n\r\nb)UNEAQUAL, if the cut is off the centre(with probability almost 1). Now its easy to see that triangle is only possible if the second cut is made on the piece which is the larger of the 2 pieces obtained after the first random cut.\r\nAnd here the longer piece can be selected with probability 1/2 from the two equally likely pieces (the position of the cut on this piece doesn\'t matter).\r\n\r\nSo, the triangle is only possible with probability (1-d)(1/2) which is almost equal to \r\n1/2.\r\n \r\n',NULL,0);
INSERT INTO comment VALUES (10967,1446,4670,'e.g.','Possibility','2004-01-07 13:58:42',3,'The shopper could mean \"a sixth OF A CHESTNUT\" (instead of \"a sixth chestnut\") and the shopkeeper could have meant that \"you will have five SIXTHS too many if I gave you one chestnut more\".\r\n 1 11 5 15\r\n14 10 6 2\r\n 9 3 13 7\r\n\r\n 1 13 3 15\r\n11 9 7 5\r\n12 2 14 4\r\n\r\n 4 14 2 12\r\n 5 7 9 11\r\n15 3 13 1\r\n\r\n 7 13 3 9\r\n 2 6 10 14\r\n15 5 11 1\r\n\r\n 9 3 13 7\r\n14 10 6 2\r\n 1 11 5 15\r\n\r\n12 2 14 4\r\n11 9 7 5\r\n 1 13 3 15\r\n\r\n15 3 13 1\r\n 5 7 9 11\r\n 4 14 2 12\r\n\r\n15 5 11 1\r\n 2 6 10 14\r\n 7 13 3 9\r\n
\n\nEdited on January 8, 2004, 8:22 pm',NULL,0);
INSERT INTO comment VALUES (10998,1445,1626,'Gamer','re(2): How about this? from Penny','2004-01-08 20:12:05',0,'I think Penny found her talent; answering riddles. Although with all of Penny\'s solutions, they are a little stretched, but she did find a semi-sensible answer for this one. :)\r\n\r\nYou will see that\'s not really the answer, but it could at least make sense if you didn\'t consider a few aspects of problem-creating. (which don\'t really count in assessing a solution\'s validity too much)',10990,0);
INSERT INTO comment VALUES (10999,1581,3705,'zaphod','Yep','2004-01-09 00:57:53',3,'I think James got to it. The chances of ANY of the three prisoners being pardoned cannot change due to any comments made by the warden.\r\nThe warden\'s information and any subsequent data exchange between him and the prisoners, or among the prisoners, are statistically independent from the selection process that only involved three slips and a hat (and this selection has not been altered in any way, while changes DO happen in the \'similar\' problem suggested).\r\nSo the chances for any of the prisoners to survive remain at 1/3.\r\nMade even simpler, let\'s say we know nothing of this and we just come across the result AFTER the two have been executed. The survivor\'s chances have NOT grown to 100% just because the outcome is now known to us (or him, for that matter). Even now, the process itself implies that he had 1/3 chances of being pardoned anyway.',NULL,0);
INSERT INTO comment VALUES (11000,1581,4197,'luminita','re: Yep','2004-01-09 06:48:35',0,'Absolutely right.\r\nBut I think that for the problem itself we assume \"the probabily the prisoners know the answer\" is what we are looking for. ',10999,0);
INSERT INTO comment VALUES (11001,1581,1183,'fwaff','re: Yep - er, nope','2004-01-09 08:49:04',0,'You are effectively saying that even though we know that Bob is definitely going to be executed (ie zero survival chance) he still has a 1 in 3 of surviving. Nonsense!\r\n\r\nThat\'s like saying that even though I was born a girl that there\'s still a 50:50 chance of me being a boy.\r\n\r\nBy providing more information the valid \'sample space\' has changed. Therefore the probabilities of the outcomes change.\r\n\r\nThink about it this way: I\'m feeling particularly generous and make a game where you receive £100 if a fair die lands on 1,2,3,4 or 5, but you must pay £1 if it lands on 6. Even more generously I even offer to roll the die and show you the outcome before you decide whether or not to play. Now suppose I roll a 6, would you play?',10999,0);
INSERT INTO comment VALUES (11002,1379,1920,'Brian Smith','Three words','2004-01-09 10:22:39',0,'1. mILLILIter\r\n3. bIQUAdratic\r\n4. sAWBlade',NULL,0);
INSERT INTO comment VALUES (11003,1379,1301,'Charlie','for 2','2004-01-09 10:29:17',0,'2. eighth',NULL,0);
INSERT INTO comment VALUES (11004,1379,5122,'Rich Dearing','More words','2004-01-09 10:40:37',0,'diphtheria; diphthong; ophthalmologist\r\n\r\npiquant\r\n\r\njawbreaker',NULL,0);
INSERT INTO comment VALUES (11005,1379,5122,'Rich Dearing','One more','2004-01-09 10:42:19',0,'antiquated',NULL,0);
INSERT INTO comment VALUES (11006,1379,3209,'Haley','word search','2004-01-09 11:20:15',3,'probably not the kind of answer you want, but this is what a word search found:\r\n\r\nMILLILITER\r\n\r\nAUTOCHTHON AUTOCHTHONES AUTOCHTHONISM AUTOCHTHONOUS AUTOCHTHONOUSLY AUTOCHTHONS AUTOCHTHONY CHTHONIAN CHTHONIC DIPHTHERIA DIPHTHERIAL DIPHTHERIAN DIPHTHERITIC DIPHTHONG DIPHTHONGAL DIPHTHONGIZATION DIPHTHONGIZE EIGHTH EIGHTHES EIGHTHS EXOPHTHALMIC EXOPHTHALMOS EXOPHTHALMUS HETEROCHTHONOUS ICHTHYOID ICHTHYOIDAL ICHTHYOLOGICAL ICHTHYOLOGICALLY ICHTHYOLOGIST ICHTHYOLOGY ICHTHYOPHAGOUS ICHTHYORNIS ICHTHYOSAUR ICHTHYOSAURIAN ICHTHYOSIS ICHTHYOTIC KNIGHTHOOD LIGHTHEARTED LIGHTHEARTEDLY LIGHTHEARTEDNESS LIGHTHOUSE LIGHTHOUSES MONOPHTHONG MONOPHTHONGAL NAPHTHA NAPHTHALENE NAPHTHALENIC NAPHTHENE NAPHTHENIC NAPHTHOL NIGHTHAWK OPHTHALMIA OPHTHALMIC OPHTHALMOLOGIC OPHTHALMOLOGICAL OPHTHALMOLOGICALLY \r\nOPHTHALMOLOGIST OPHTHALMOLOGY OPHTHALMOSCOPE OPHTHALMOSCOPIC OPHTHALMOSCOPICAL OPHTHALMOSCOPY PHENOLPHTHALEIN PHTHALEIN PHTHALOCYANINE PHTHIRIASIS PHTHISES PHTHISIC PHTHISICAL PHTHISICKY PHTHISIS TRIPHTHONG TRIPHTHONGAL XEROPHTHALMIA XEROPHTHALMIC\r\n\r\nANTIQUARIAN ANTIQUARIANISM ANTIQUARIANS ANTIQUARY \r\nANTIQUATE ANTIQUATED ANTIQUATION BIQUADRATIC DEMISEMIQUAVER HEMIDEMISEMIQUAVER LIQUATE LIQUATION PIQUANCY PIQUANT PIQUANTLY PIQUANTNESS RELIQUARY SEMIQUAVER\r\n\r\nBAWBEE DRAWBACK DRAWBACKS DRAWBAR DRAWBORE DRAWBRIDGE DRAWBRIDGES JAWBONE JAWBREAKER LAWBREAKER RAWBONED SAWBUCK STRAWBERRIES STRAWBERRY STRAWBOARD',NULL,0);
INSERT INTO comment VALUES (11007,1560,2376,'Jim C','hew azo baying tallow','2004-01-09 12:52:25',0,'a.) The light was green.\r\n\r\nThat was definitely the hardest of the bunch. I have to admit, though, that I didn\'t get the riddle until I got C.)',NULL,0);
INSERT INTO comment VALUES (11008,1581,3224,'Lee','Get a grip','2004-01-09 14:26:45',0,'It really tickles me when I read these ‘a coin has no memory’ advocates, or read cries of ‘what’s happened, has happened and no …’ \r\nWe’re on a puzzle site and things, more than often, have a tendency to require some thought.\r\nI don’t even understand why people even post\r\n ‘why, it’s gotta be 50:50, since it doesn’t matter…..’\r\nanswers – especially after numerous posts to the contrary have been, well, posted.\r\nWhat kind of self-confidence must you have to hear half a dozen people say something different to your thoughts, simply to cite a principle we all learnt aged 12 and then claim they’re all wrong?\r\nI’m not against speaking out or having conviction for your answer, but when the problem itself is fairly straightforward??? \r\n\r\nCharlie has the greater chance of the pardon.\r\nIt isn’t a puzzle if he doesn’t.\r\nWhy? There are several ways of looking at this.\r\n\r\nView 1 (I prefer this one)\r\nSince Alan never receives ‘Alan’ as an answer, he’s totally in the dark about the chances of himself being pardoned. The answer is irrelevant to Alan and his chances of a pardon remain 1/3. Since all probabilities (of survival) sum to 1 the remaining 2/3 must be in Charlie’s favour since Bob is going to be executed (prob’ survival =0)\r\n\r\nView 2 (the way the problem initially hit me)\r\nProbability of hearing ‘Bob’ if Charlie is to be pardoned =1 (given in the question)\r\nProbability of hearing ‘Bob’ if Alan is to be pardoned = 0.5 (given in the question – coin toss)\r\nIt’s right there – the probability of the warden saying Bob is to be executed is twice as likely if Charlie is to be pardoned.\r\n\r\nView 3\r\nImagine 1000 prisoners. Alan (prisoner # 1000) says “if it is prisoner 1, tell me 2-999 (the rest other than Alan) are going to be executed - if it is prisoner 2, tell me 1, 3-999 are going to be executed……..if it is me to be executed pick a prisoner at random and tell me they’re going to be executed”\r\nThere is only 1/1000 chance the warden will respond with news of the execution of a random prisoner – anything else Alan’s doomed.\r\nThis viewpoint might not seem intuitive but it’s the natural extension of the problem with more than 3 prisoners/options.\r\n\r\nView 4 (Similar to 1)\r\nImagine the scenario is played out 666 times.\r\n222 times Charlie is to be pardoned and the warden says “Bob is to be executed”\r\n222 times Bob is to be pardoned and the warden says “Charlie is to be executed”\r\n222 times Alan is to be pardoned and the warden says either,\r\n “Bob is to be executed” (111 times) or,\r\n “Charlie is to be executed” (111 times)\r\n\r\nOut of the 333 times the warden says \r\n“Bob is to be executed” – as he has done in the question,\r\n222 (2/3) of these are when Charlie is to be pardoned.\r\n\r\nCharlie’s expectation of survival initially, of course, is a third – but the fact that Alan has put Charlie in a situation (and here’s why it’s a puzzle) where you’re name has a 50% chance of zero or full survival (between Charlie and Bob) changes things entirely.\r\nOn one hand you surrender your 1/3 to Bob on the other you assume his1/3.\r\n\r\nThere’s been a few of this type of puzzle on this site (‘a something is somethinged and you are then told….’) and some debate as to the motives of the participants and what might happen over repeated ‘plays’. Silverknight has outlined the problem clearly in this case (unlike the one he’s linked to in the question) and there is no debate.\r\n\r\nSorry to go on – I’m a bit drunk.\r\n',NULL,0);
INSERT INTO comment VALUES (11009,1584,4982,'Dan Blume','Not a cryptologist but . . .','2004-01-09 16:46:14',1,'Not an answer but some thoughts. The numbers are heavily weighted toward ones and twos and lightly weighted toward zero. This appears to be some sort of direct/indirect substitution of numbers 1-26 for the letters of the alphabet. This leads me to believe that the words are of the following lengths: 4:2:3:7:2:5:12:8. Second line: 4:9:6:5:3:2:6:4\r\n\r\nThe last series of numbers in the first line is significantly different. It has no twos and only one \"1\" at the end.\r\n\r\nOther thoughts are that \"27\" and \"28\" appear often and \"13 15 17 19\" are the last numbers of the second line.\r\n\r\nDoes this help? Thought not! :)\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (11010,1584,3386,'Victor Zapana','More like a 5 difficulty.. and some thoughts','2004-01-09 16:56:37',0,'Well, the first line is 8 words long, according to the code, so possible first lines are:
\r\n\r\nIf anyone\'s interested, I used Excel and played around a little... there\'re only \"two degrees of freedom\" here...\r\n\r\nFor example, if you plug in values in the squares where the \'4\' and the \'33\' are... then all the rest of the values are determined.',NULL,0);
INSERT INTO comment VALUES (11054,701,4718,'Jack Squat','negatives','2004-01-13 14:21:26',0,'None of the solutions address the possibility of one or more of the numbers being negative.\r\n\r\nI\'ll save you the trouble, there are no negative solutions.',NULL,0);
INSERT INTO comment VALUES (11055,1587,5175,'Surender Taalla','re: Tessellation','2004-01-13 14:50:14',0,'Length of the Diagonal=√2+ 1+ diameter of red circle(x)+ 1+ √2\r\n\r\nso 4√2=2+2√2+x\r\n\r\nthen x=2√2-2 (diameter of red circle)\r\nso the red circle should be of radius √2-1',11044,0);
INSERT INTO comment VALUES (11056,1384,5175,'Surender Taalla','re(2): some more !','2004-01-13 14:59:17',0,'my mistake I was just finding valid words, of all combinations.',11052,0);
INSERT INTO comment VALUES (11057,1570,4507,'Penny','A solution without \"excellence\"','2004-01-13 17:35:09',3,'From 44 in the third row, the integer that begins the first row must be either 4 or 10.\r\n\r\nIf you try 4, then the number to the right of 39 must be 48. Therefore the number five places below 48 must be an even number larger than 78 (since it is 78 plus a multiple of 2) that differs from 48 by a multiple of 5. The smallest such number is 88. If you put 88 there, every other square is forced.\r\n \n\nEdited on January 13, 2004, 5:39 pm',NULL,0);
INSERT INTO comment VALUES (11058,1217,5178,'Dan Porter','other numbers of samples','2004-01-13 22:20:35',0,'1 or 11(12-1) are the only number of samples that need to be balanced with water. All sample sizes > 6 can be reached by inverting full for empty possitions of the paterns < 6.',NULL,0);
INSERT INTO comment VALUES (11059,1407,5178,'Dan Porter','more trees','2004-01-14 00:11:24',0,'I a novice so I can\'t post new puzzles. Besides this is just a modification.\r\n\r\nI thought 15/16 was a good ratio but I wondered if it could be 1 or higher. I found that 24 trees in 24 rows of 4 was possible. A ratio of 1!\r\n\r\nI\'m sure the ratio could be even higher with more trees per row. Can anyine beet a ratio of 1 for 4 trees per row?',NULL,0);
INSERT INTO comment VALUES (11060,1459,5188,'Perry','Did everyone wear three different colours?','2004-01-14 09:07:40',0,'First in was Green tie/Blue shirt/ Green suspenders. Second in was White tie/Green shirt/ White suspenders. Third was Blue tie/Red shirt/Red suspenders. Last in was Red tie/ White shirt/Blue suspenders.',NULL,0);
INSERT INTO comment VALUES (11061,1380,1301,'Charlie','solution','2004-01-14 09:15:28',3,'Point P is so high up that, even with the slightness of the inward leaning of line DB, that is still enough that line PD passes to the right of point B. Thus angle BDC is not equal to angle BDP plus angle PDC, but rather, angle PDC minus angle BDP.\r\n\r\nThe following spreadsheet results show how angle PBD, taken on the left side, is more than 180 degrees, as line QP is over 113 units long, under the assumption that AC=1, CD=2, DB=1 and angle CDB=89 degrees:\r\n
+----+----+----+----+----+
| | | | | |
| 4 | 7 | 10 | 13 | 16 |
| | | | | |
+----+----+----+----+----+----+----+
| |XXXX|XXXX|XXXX| | | |
| 13 |XXXX|XXXX|XXXX| 30 | 39 | 48 |
| |XXXX|XXXX|XXXX| | | |
+----+----+----+----+----+----+----+
| |XXXX|XXXX|XXXX| |XXXX| |
| 22 |XXXX|XXXX|XXXX| 44 |XXXX| 56 |
| |XXXX|XXXX|XXXX| |XXXX| |
+----+----+----+----+----+----+----+
| |XXXX|XXXX| | | | |
| 31 |XXXX|XXXX| 55 | 58 | 61 | 64 |
| |XXXX|XXXX| | | | |
+----+----+----+----+----+----+----+----+
| | | | | |XXXX|XXXX| |
| 33 | 40 | 47 | 54 | 61 |XXXX|XXXX| 72 |
| | | | | |XXXX|XXXX| |
+----+----+----+----+----+----+----+----+
| |XXXX|XXXX|XXXX| |XXXX|XXXX| |
| 35 |XXXX|XXXX|XXXX| 67 |XXXX|XXXX| 80 |
| |XXXX|XXXX|XXXX| |XXXX|XXXX| |
+----+----+----+----+----+----+----+----+
| |XXXX|XXXX|XXXX| | | | |
| 37 |XXXX|XXXX|XXXX| 73 | 78 | 83 | 88 |
| |XXXX|XXXX|XXXX| | | | |
+----+----+----+----+----+----+----+----+
| | | | | |
| 39 | 49 | 59 | 69 | 79 |
| | | | | |
+----+----+----+----+----+\r\nWhat Can You Prove?\r\nAssuming AC=1, CD=2, DB=1 Angle CDB 89\r\nDiagonal CB B3 2.220403201 (=SQRT(1+4-4*COS($E$2*PI()/180)))\r\nAngle BCD B4 26.76293713 (=ASIN(SIN($E$2*PI()/180)/B3)*180/PI())\r\nAB B5 1.982547599 (=SQRT(1+B3^2-2*B3*COS((90-B4)*PI()/180)))\r\nAngle BAC B6 89.99559838 (=ASIN(B3*SIN((90-B4)*PI()/180)/B5)*180/PI())\r\nA to line RP along AB B7 1.000000003 (=1/COS((90-B6)*PI()/180))\r\nQ to intersection of RP with AB 0.008726203 (=B7-B5/2)\r\nQP B9 113.5887264 (=B8*TAN(B6*PI()/180))\r\nAngle BPQ B10 0.500000003 (=ATAN(B5/2/B9)*180/PI())\r\nAngle PBQ B11 89.5 (=90-B10)\r\nAngle ABD B12 91.00440162 (=360-$E$2-90-B6)\r\nAngle PBD B13 180.5044016 (=B12+B11)\r\n
\r\n----\r\nThe formulas are shown to the right of the calculated cells. The 89 is in cell E2, and each calculated cell is in column B, starting at row 3 (I\'ve marked most of them for reference). The law of cosines and law of sines have been used.\r\n\r\nThe internal angle being over 180 degrees indicates that in fact line PD is outside the main figure (to the right of B).\r\n\n\nEdited on January 14, 2004, 9:17 am',NULL,0);
INSERT INTO comment VALUES (11062,1459,4507,'Penny','re: Did everyone wear three different colours?','2004-01-14 10:29:45',1,'They couldn\'t each have worn three different colors, \r\nbecause if they did, then the only possibilities for the shirt/tie/suspenders of the first arrival at the dance, are:\r\n \r\nRWB, RWG, RBW, RBG, RGW, RGB, WRB, WRG, WBR, WBG, WGR, WGB,\r\nBRW, BRG, BWR, BWG, BGR, BGW, GRW, GRB, GWR, GWB, GBR, GBW.\r\n\r\nEvery one of these possibilities quickly leads to a contradiction of the rules of the puzzle.\r\n \r\nI got the same answer you did. It must be right. ',11060,0);
INSERT INTO comment VALUES (11063,1459,4507,'Penny','Note that Perry and Penny are two different people.','2004-01-14 10:31:18',0,'n/m',11062,0);
INSERT INTO comment VALUES (11064,1284,1301,'Charlie','solution','2004-01-14 15:43:24',3,'For the purpose of counting available positions in the same diagonal, there are 10 possible types of position of the first chosen square. It could be on one of the two main diagonals, either in a corner or once, twice or three times removed from the corner (that\'s 4 so far). It could be on an edge, once, twice or three times removed from the corner (we\'re up to 7). It could be adjacent to an edge row and either near the center of that row or near the main diagonal, or it could be 2 rows removed from an edge row and adjacent to the center line.\r\n\r\nIt simplifies matters if we consider only one triangle of 10 squares and multiply each one\'s subsequent probabilities by the probability that the first square chosen would be of that type. The four types that are on a main diagonal have probability 4/64 each, as there are four corner squares, four squares that are on a main diagonal one removed from the corner, etc. The types that are not on a main diagonal have probability 8/64 each as there are duplicates, one on either side of the nearest main diagonal.\r\n\r\nIf we number the rows 1-8 (from top to bottom) and the columns 1-8 (left to right), let\'s consider the ten typical squares as those in which the column number is equal to or greater than the row number and less than or equal to 4. Those where the column number equals the row number are of course on a main diagonal, and the probability is 1/16 of our initially choosing a given such type of square. The others have a probability of 1/8 of being chosen as the initial square. We\'ll multiply the conditional probabilities given that type of initial square by these initial probabilities and add them up to get the overall probability.\r\n\r\nFor most squares, there are two possible diagonals to consider. The restricted triangle of squares we have chosen makes the formula simple for how many choices of other squares there are in each of these diagonals. The SW-NE (directionally speaking) diagonal will have c+r-2 squares besides the one at row r, column c (for example, the square at row 1, column 3, has 2 other squares in its SW-NE diagonal: row 2, column 2 and row 3, column 1). The NW-SE diagonal has 7+r-c other squares besides the one under consideration. (Again for example, the square at row 1, column 3, has 5 other squares sharing this diagonal, at r 2, c 4; r 3, c 5; r 4, c 6; r 5, c 7 and r 6, c 8.) So, for a given row and column, the probability of completing one diagonal is (c+r-2)/63 * (c+r-3)/62, and of completing the other diagonal is (7+r-c)/63 * (6+r-c)/62. These are mutually exclusive, so their probabilities can be added, before multiplying by the probability that the first one was of that type to begin with.\r\n\r\nTaking the ten types by row and column, we get:\r\n\r\nr 1 c 1 : 1/16 * (0/63 *-1/62 + 7/63 * 6/62) = 1/1488\r\nr 1 c 2 : 1/8 * (1/63 * 0/62 + 6/63 * 5/62) = 5/5208\r\nr 1 c 3 : 1/8 * (2/63 * 1/62 + 5/63 * 4/62) = 11/15624\r\nr 1 c 4 : 1/8 * (3/63 * 2/62 + 4/63 * 3/62) = 1/1736\r\nr 2 c 2 : 1/16 * (2/63 * 1/62 + 7/63 * 6/62) = 11/15624\r\nr 2 c 3 : 1/8 * (3/63 * 2/62 + 6/63 * 5/62) = 1/868\r\nr 2 c 4 : 1/8 * (4/63 * 3/62 + 5/63 * 4/62) = 2/1953\r\nr 3 c 3 : 1/16 * (4/63 * 3/62 + 7/63 * 6/62) = 3/3472\r\nr 3 c 4 : 1/8 * (5/63 * 4/62 + 6/63 * 5/62) = 25/15624\r\nr 4 c 4 : 1/16 * (6/63 * 5/62 + 7/63 * 6/62) = 1/868\r\n
\r\n----\r\nNote that the cases where there are no choices or only one choice do have the corresponding probability nulled out, as the formula introduces a zero in each of these two cases. \r\n\r\nThe probabilities add up to 7/744, or 1/106.285714... (the 285714 repeats).\r\n\r\nThe above was calculated by\r\n\r\n 10 Tot=0\r\n 20 for Row=1 to 4\r\n 30 for Col=Row to 4\r\n 40 if Row=Col then P=4//64:else P=8//64\r\n 50 W1=Col+Row-2\r\n 60 W2=7-Col+Row\r\n 65 print Row;Col;\":\";P;tab(14);\"* \";\r\n 70 P=P*(W1*(W1-1)+W2*(W2-1))//(63*62)\r\n 75 print str(W1);\"/63 *\";str(W1-1);\"/62 +\";str(W2);\"/63 *\";str(W2-1);\"/62 =\";P\r\n 80 Tot=Tot+P\r\n 90 next Col\r\n100 next Row\r\n110 print Tot,1/Tot\r\n
\r\n----\r\nwith its output cleaned up (putting the letters r and c, adding parentheses and eliminating the double / that UBASIC produces in its output of rational numbers).\n\nEdited on January 14, 2004, 3:57 pm',NULL,0);
INSERT INTO comment VALUES (11065,1284,3172,'SilverKnight','solution, simplification?','2004-01-14 15:59:22',3,'I got the same answer as Charlie, I used nothing more than a calculator for factorial. Perhaps this is a simpler way of looking at it, as it requires no conditional probabilities or programs.\r\n____________________________________\r\n\r\n392/41664 = .009408602 (or a little less than 1% chance)\r\n\r\nThere are [ (64 x 63 x 62) / (3 x 2 x 1) ] = 32 x 21 x 62 =\r\n41664 different combinations of choosing 3 squares at a time.\r\n\r\nAlong a NW - SE direction (on the chessboard), there are 15 diagonals, 4 of which have only 1 or 2 squares, leaving 11 diagonals that could potentially contain the 3 random squares.\r\n\r\nThose 11 diagonals contain:\r\n3, 4, 5, 6, 7, 8, 7, 6, 5, 4, and 3 squares to contain the 3 random squares.\r\n\r\nThose diagonals can each contain that many \"choose 3\" at a time possible combinations of the three random squares, so respectively:\r\n\r\n3!/(3!0!), 4!/(3!1!), 5!/(3!/2!), 6!/(3!3!), 7!/(3!4!), 8!/(3!5!), and then back down again... which gives us:\r\n1, 4, 10, 20, 35, 56, 35, 20, 10, 4, and 1\r\n\r\nThis totals (1 + 4 + 10 + 20 + 35 + 56 + 35 + 20 + 10 + 4 + 1) = 196.\r\n\r\nWe must also allow for the diagonals going from NE - SW, and they will also have 196 possible combinations.\r\n\r\nSo, there are 196 x 2 = 392 possible locations.\r\n\r\n392 possible locations that work / 41664 different combinations of placing 3 squares at a time =\r\n\r\n392/41664 = .009408602 (or a little less than 1% chance)',NULL,0);
INSERT INTO comment VALUES (11066,1284,4507,'Penny','Simple solution (no program used)','2004-01-14 16:23:13',0,'(The solution that follows is incorrect, since it overlooks the fact that most squares are on two diagonals, not one.) \r\n\r\nThere is only a slightly greater than 2% probability that three randomly chosen squares will be on the same diagonal.\r\n\r\nExplanation:\r\n\r\nWe can all thank Al Gore for inventing the method of solving problems by applying simple and methodical logic. Such methods are called \"algorithms\" (\"Al-Gore-ithms\") in his honor. \r\n\r\nThere are 28 out of 64 squares along the edge of the board, and each of these is on the same diagonal with 7 other squares. There are 20 out of 64 squares that are 1 square removed from the edge, and each is on the same diagonal as 9 other squares. There are 12 out of 64 squares that are exactly 3 squares removed from the edge of the board, and each is on the same diagonal as 11 other squares. That leaves 4 out of 64 squares that occupy the center of the chessboard, and each is on the same diagonal as 13 other squares.\r\n\r\nSo the odds that all three are on the same diagonal, are:\r\n\r\n(28/64)*(7/63)*(7/62) + (20/64)*(9/63)*(9/62) + (12/64)*(11/63)*(11/62) + (4/64)*(13/63)*(13/62)\r\n\r\n= 0.0204813108\r\n\r\n\r\n\r\n\n\nEdited on January 14, 2004, 7:02 pm',NULL,0);
INSERT INTO comment VALUES (11067,1284,3172,'SilverKnight','re: Simple solution (no program used)','2004-01-14 16:31:32',4,'Penny, you wrote:\r\n\"So the odds that all three are on the same diagonal, are:\r\n\r\n(28/64)*(7/63)*(7/62) + (20/64)*(9/63)*(9/62) + (12/64)*(11/63)*(11/62) + (4/64)*(13/63)*(13/62)\r\n\r\n= 0.0204813108\"\r\n\r\nI don\'t understand how you came up with these odds, but they seem incorrect.',11066,0);
INSERT INTO comment VALUES (11068,1284,4507,'Penny','Corrected solution','2004-01-14 19:00:46',3,'(My original entry had to be corrected after the criticism by SilverKnight. I had overlooked the fact that the first square could be on the same diagonal as the 2nd square and the 3rd square, but the 2nd and 3rd squares might not be on the same diagonal with respect to each other).\r\n\r\nThe correct answer: the probability that three randomly chosen squares on a chessboard are all on the same diagonal is less than 1%\r\n\r\nExplanation:\r\n\r\nEach corner square on the chessboard in on just one diagonal. Every other square is on two diagonals. I overlooked this in my original solution. \r\n\r\nIf we adopt the modern algebraic notation for the chessboard, where the lower left-hand square is a1 and the upper right-hand corner is h8, then, of the 64 squares on the chessboard:\r\n\r\na1, h1, a8 and h8 are each on one diagonal with 7 other squares. \r\nb1, g1, a2, h2, a7, h7, b8, and g8 are on diagonals with 1 and 6 other squares. \r\nc1, f1, a3, h3, a6, h6, c8, and f8 are on diagonals with 2 and 5 other squares. \r\nd1, e1, a4, h4, a5, h5, d8, and e8 are on diagonals with 3 and 4 other squares.\r\nb2, g2, b7, and g7 are on diagonals with 2 and 7 other squares.\r\nc2, f2, b3, g3, b6, g6, c7, and f7 are on diagonals with 3 and 6 other squares.\r\nd2, e2, b4, g4, b5, g5, d7, and e7 are on diagonals with 4 and 5 other squares.\r\nc3, f3, c6, and f6 are on diagonals with 4 and 7 other squares. \r\nd3, e3, c4, f4, c5, f5, d6, and e6 are on diagonals with 5 and 6 other squares.\r\ne4, f4, e5, and f5 are on diagonals with 6 and 7 other squares.\r\n\r\n\r\nSo the true odds are:\r\n\r\n(4/64)*(7/63)*(6/62) \r\n+ (8/64)*(6/63)*(5/62) \r\n+ (8/64)*(2/63)*(1/62) + (8/64)*(5/63)*(4/62) \r\n+ (8/64)*(3/63)*(2/62) + (8/64)*(4/63)*(3/62) \r\n+ (4/64)*(2/63)*(1/62) + (4/64)*(7/63)*(6/62)\r\n+ (8/64)*(3/63)*(2/62) + (8/64)*(6/63)*(5/62)\r\n+ (8/64)*(4/63)*(3/62) + (8/64)*(5/63)*(4/62)\r\n+ (4/64)*(4/63)*(3/62) + (4/64)*(7/63)*(6/62) \r\n+ (8/64)*(5/63)*(4/62) + (8/64)*(6/63)*(5/62)\r\n+ (4/64)*(6/63)*(5/62) + (4/64)*(7/63)*(6/62) \r\n\r\n0.0094086022\r\n\r\n\n\nEdited on January 14, 2004, 7:44 pm',NULL,0);
INSERT INTO comment VALUES (11069,1284,3172,'SilverKnight','re: Corrected solution','2004-01-14 19:05:18',4,'Penny, you wrote:\r\n\"So the true odds are:\r\n\r\n(4/64)*(7/63)\r\n+ (8/64)*(6/63)\r\n+ (8/64)*(2/63)*(1/62) + (8/64)*(5/63)*(4/62)\r\n+ (8/64)*(3/63)*(2/62) + (8/64)*(4/63)*(3/62)\r\n+ (4/64)*(2/63)*(1/62) + (4/64)*(7/63)*(6/62)\r\n+ (8/64)*(3/63)*(2/62) + (8/64)*(6/63)*(5/62)\r\n+ (8/64)*(4/63)*(3/62) + (8/64)*(5/63)*(4/62)\r\n+ (4/64)*(4/63)*(3/62) + (4/64)*(7/63)*(6/62)\r\n+ (8/64)*(5/63)*(4/62) + (8/64)*(6/63)*(5/62)\r\n+ (4/64)*(6/63)*(5/62) + (4/64)*(7/63)*(6/62)\r\n\r\n= 0.0076804916\"\r\n\r\nI don\'t understand how you are coming up with these probabilities, but they appear incorrect.\r\n______________________\r\n\r\nBTW, this Al-Gore-ithm thing... did this occur before or after Al invented the internet?',11068,0);
INSERT INTO comment VALUES (11070,1587,2184,'mark hartman','answer?','2004-01-14 19:48:30',0,'This one seems pretty easy, or am I missing something???\r\nThe radius of the inner circle is the difference between the diagonal of a unit square and 1. The radius of the inner circle is square root of two minus one',NULL,0);
INSERT INTO comment VALUES (11071,1284,4507,'Penny','re(2): Corrected solution','2004-01-14 19:59:55',0,'Touche !! My first two terms should have read \r\n(4/64)*(7/63)*(6/62) and (8/64)*(6/63)*(5/62). When these two corrections are made, I get exactly the same answer you do, so this must be right. For instance, my third line, \r\n(8/64)*(2/63)*(1/62) + (8/64)*(5/63)*(4/62),\r\nreflects the fact that the first randomly selected square has an 8/64 chance to be in the set \r\n{c1, f1, a3, h3, a6, h6, c8, f8}. Each of these is on one diaganol with 2 other squares, and one with 5 other squares. \r\n___________________________________________________________\r\n(I think Al Gore\'s invention of the \"Al-Gore-ithm\" is right up there with George Bush\'s originating the Code of Bushido). ',11069,0);
INSERT INTO comment VALUES (11072,834,5178,'Dan Porter','Comment','2004-01-14 23:10:36',0,'When I was in highschool I learned a version called Hexanim. Played with a rack of pool balls. You may remove one to five balls on each turn. The balls you remove must be touching each other and in a straight line. The player to pick up the last ball is the looser. \r\n\r\nIf you think of bowling pins, you could remove pins 2,5,9 as one move. You could not remove 2,3,6,10 because it is not a straight line and could not remove 3,8,12 because 5 has already been removed and 3 and 8 do not touch. \r\n\r\nI still play this game from time to time but it\'s hard to find a good opponant. You can play it on paper by drawing circles and then coloring them in durring play or if you have a golf tee puzzle with one extra tee that works great too.\r\n',NULL,0);
INSERT INTO comment VALUES (11073,834,5178,'Dan Porter','more hexanim boards','2004-01-14 23:42:59',0,'Here are some other boards to play on.\r\n\r\nHexanim 15 (standard)\r\n\r\n____O\r\n___O O\r\n__O O O\r\n_O O O O\r\nO O O O O\r\n\r\n\r\nHexanim 16\r\n\r\n___O\r\n__O O\r\n_O O O\r\nO O O O\r\n_O O O\r\n__O O\r\n___O\r\n\r\n\r\nHexanim 18\r\n\r\n_O O O O\r\nO O O O O\r\n_O O O O\r\n__O O O\r\n___O O\r\n\r\n\r\nHexanim 19\r\n\r\n__O O O\r\n_O O O O\r\nO O O O O\r\n_O O O O\r\n__O O O\r\n\r\n\r\nEdited on January 14, 2004, 11:45 pm\r\n\r\nEdited on January 14, 2004, 11:47 pm\r\n\r\nEdited on January 14, 2004, 11:47 pm\r\n\r\nEdited on January 14, 2004, 11:48 pm\r\n\r\nEdited on January 14, 2004, 11:49 pm\n\nEdited on January 14, 2004, 11:50 pm',NULL,0);
INSERT INTO comment VALUES (11074,1380,3372,'Sam','re: solution','2004-01-14 23:43:37',0,'That\'s what I was thinking, but I couldn\'t prove it formally. I kept trying to draw the picture the way it was in the problem, and it kept coming out with BD inside PD. Some sleight of hand in the artistry there...',11061,0);
INSERT INTO comment VALUES (11075,219,5178,'Dan Porter','How much you play','2004-01-15 02:49:15',0,'The key to the amount is how much you play. If you charge $100 doller, for instance, the odds will favor you coming out ahead if you play less than 200 games. At 200 the odds are equal for you to be ahead or behind. Remember though that in every game there is always a chance of loosing a staggering amount of money. Something like playing Russian roulette with a revolver that has 200 chambers and one bullet!',NULL,0);
INSERT INTO comment VALUES (11076,207,5178,'Dan Porter','another method','2004-01-15 04:45:03',0,'I started by looking for the number of winning games at the fith move.\r\n\r\nThere are 8 way to win. 3 vertical, 3 horizontal and 2 diaganal.\r\n\r\nThere are 6 ways to place 3 objexts in a row. 123, 132, 213, 231, 312, 321\r\n\r\n6*8=48 combonations for the first player.\r\n\r\nThe second player placed 2 objects in 6 possible locations for 6*5=30 combotaions.\r\n\r\nTotal winnig combos after 5 moves is 48*30=1440.\r\n\r\nThis by the way is the same as the actual count by Jim Lyon. I\'m guessing he coded correctly.\r\n\r\nBy removing just these winning combos you get a number less than 344242.\r\n\r\n(9*8*7*6*5-1440)*4*3*2+1440=329760\r\n \r\n\r\nEdited on January 15, 2004, 4:52 am\n\nEdited on January 15, 2004, 5:11 am',NULL,0);
INSERT INTO comment VALUES (11077,1270,5202,'mike','re(2): JinCo\'s Solution','2004-01-15 06:49:20',0,'ME too got the same. ',11017,0);
INSERT INTO comment VALUES (11078,1380,5178,'Dan Porter','','2004-01-15 06:53:16',0,'Oops!\n\nEdited on January 15, 2004, 11:51 am',NULL,0);
INSERT INTO comment VALUES (11079,1380,5178,'Dan Porter','solution','2004-01-15 06:53:51',0,'Having worked on tables with this problem I saw the solution at once. Table legs are nearly always bent at arbitrary angles. Never on the planes shared by the other legs. Therefore point B does not lie within plane ACD. The angle of plane ACD to ABD is what is missing from vertex D. Furthermor there are two solutions. One where B lies infront of plane ACD and one where it lies behind it.',NULL,0);
INSERT INTO comment VALUES (11080,21,5033,'Captain Paradox','One way to do it?','2004-01-15 08:23:53',1,'There is a stategy what works for most games like this: (t-1)/(c+1)where t = the total number of cards and c = the number of cards you can take on a turn.\r\nAs long as there is a remainder after this division takes place, you can go first and win the game. Just start by taking the remainder, and after that take 1 when they take 3, 2 when they take 2, and 3 when they take 1.\r\nIf there is a remainder, then try to trick them into going first. Otherwise, try to reduce the number to a multiple of 4, like levik said.',NULL,0);
INSERT INTO comment VALUES (11081,1459,5188,'Perry','re: Note that Perry and Penny are two different people.','2004-01-15 08:27:31',0,'Very different, I\'d day!',11063,0);
INSERT INTO comment VALUES (11082,1461,3275,'retiarius','Solution','2004-01-15 09:04:28',0,'A triangular number may be expressed according to its position, n, as (n+1)n/2 (ie. sum of consecutive numbers)\r\n8 times the triangular number plus 1 is therefore 4n(n + 1)+1 = 4n^2 + 4n + 1 = (2n + 1)^2\r\nwhich is a square of the number\'s place doubled plus 1.\r\n',NULL,0);
INSERT INTO comment VALUES (11083,32,4507,'Penny','Solution','2004-01-15 09:05:50',3,'There were 30 Knights and 15 Liars\r\n\r\nExplanation:\r\n\r\nIf there had been only 6 at the dinner, they could have been placed in seats 1-6 (where, it being a round table, seat 6 is to the left of seat 1) as follows:\r\n\r\nKKKLKL \r\n\r\nThen the Knights in 1 and 3 are telling the truth, the Knights in 2 and 5 are mistaken, and both Liars are lying.\r\n\r\nJust extend this pattern to the right by adding the pattern KKL 13 times.\r\n\r\nKKKLKLKKLKKLKKLKKLKKLKKLKKLKKLKKLKKLKKLKKLKKL \r\n\r\nThis must have been the way they were seated.',NULL,0);
INSERT INTO comment VALUES (11084,1461,4507,'Penny','Solution','2004-01-15 09:34:21',3,'If a triangle number is expressed as 1+2+3+...+N, then its place is N. (1 is the place of 1, 2 is the place of 1+2, 3 is the place of 6=1+2+3, 4 is the place of 1+2+3+4. etc.)\r\n\r\n1+2+3+...+N = N[(1+N)/2] \r\n\r\n8(1+2+3+...+N)+1 = 8(N[(1+N)/2])+1 \r\n= 4N^2 + 4N + 1\r\n= (2N+1)^2 ',NULL,0);
INSERT INTO comment VALUES (11085,1461,4670,'e.g.','Geometrically','2004-01-15 10:13:08',3,'The n-th triangular number can be represented as a triangle such as:
\r\nXX
\r\nXXX
\r\nXXXX
\r\n
\r\nand so on. Two such triangles can be joined to build a nx(n+1) rectangle. Four such rectangles can be joined to build a (2n+1)x(2n+1) square, with just the center cell missing. Thus, (2n+1) squared equals 8 times the n-th triangular number, plus 1.',NULL,0);
INSERT INTO comment VALUES (11086,1026,5178,'Dan Porter','182','2004-01-15 11:35:15',0,'\r\nOops!\n\nEdited on January 15, 2004, 11:47 am',NULL,0);
INSERT INTO comment VALUES (11087,1461,5208,'bharath','arithmaticely','2004-01-15 13:29:10',3,'each triangle number \"k\" is the sum of all natural nos from 1 to n. \r\nthis is the sum of an arithmatic progression from 1 to n with commen difference 1 \r\nk= n/2*(1*2+(n-1)1)=n(n+1)/2\r\n8*the square of n +1 = 4(n^2+n)+1\r\nwhich is a perfect square =(2n+1)^2\r\nwhich is the square of the numbers place n doubled plus 1.',NULL,0);
INSERT INTO comment VALUES (11088,1026,2899,'Brian Wainscott','re: 182','2004-01-15 14:04:26',0,'Please explain your method.',11086,0);
INSERT INTO comment VALUES (11089,497,4718,'Jack Squat','The 3 solutions','2004-01-15 15:24:02',3,'As previously stated by others, there could be 3 solutions to this. All 3 solutions use the same general method, setting up bird-speed equations and cancelling. I\'ll use Cory Taylor\'s notation rather than my own (I like his better!)\r\n\r\nThe first is where the Reno and LV birds cross, reach their destination, turn around and cross again. The bird-speed equations are:\r\n\r\nv(r) = (d-2x)/t(1) = (2d-x)/t(2) and\r\nv(lv) = 2x/t(1) = (d+x)/t(2)\r\n\r\nGet rid of the v\'s and simplify to get (d-2x)(d+x) = (2d-x)(2x). Solve and you get d=5x. So when the LV goes 2x, the Reno bird goes 3x. It\'s probably easier to just draw it out from here to get an answer, but one math route would be the following: At the third meeting point, the LV bird will have travelled a distance I\'ll call \'a\' from the second meeting point. So we get more equations:\r\n\r\nv(r) = (2d+x+a)/t(3) and v(lv) = (d+x+a)/t(3)\r\n\r\nDivide the two and use 3/2 for v(r)/v(lv) and you get (after simplification) d=x+a. Because d=5x, you get a=4x, which puts the two birds exactly in Las Vegas.\r\n\r\n\r\nThe second case is where the LV bird is a total slowpoke, and the Reno bird gets to LV, turns and catches the LV bird before it even gets to Reno. You now get the equations:\r\n\r\nv(r) = (d-2x)/t(1) = (2d-x)/t(2) and\r\nv(lv) = 2x/t(1) = (d-x)/t(2)\r\n\r\nGet rid of the v\'s and simplify to get (d-2x)(d-x) = (2d-x)(2x), which expanded out gives d²-7xd+4x²=0 (Here\'s where Cory Taylor went wrong, he missed a d in his equation). Solve with quadratic and get d=6.37x (rounded). So the new velocity ratio of the two birds is 4.37/2. \'a\' is defined the same way, and we get a new second set of equations:\r\n\r\nv(r) = (2d+x-a)/t(3) and v(lv) = (d-(x-a))/t(3)\r\n\r\nDivide the two and use the new ratio of 4.37/2 and you get .37d = 6.37x-6.37a. Use d=6.37x and you end up with x-a=0.37x which is the distance from Reno where they meet for the third time.\r\n\r\n\r\nThe final case is where the Reno bird is sucking wind and the LV bird gets to Reno and turns around and catches the Reno bird before it even gets to LV. New equations:\r\n\r\nv(r) = (d-2x)/t(1) = x/t(2) and\r\nv(lv) = 2x/t(1) = (d+x)/t(2)\r\n\r\nGet rid of the v\'s and simplify to get d²-xd-4x²=0. Use quadratic to get d=2.56x (rounded). Use \'a\' again and get two new equations:\r\n\r\nv(r) = (x+a)/t(3) and v(lv) = (d+x+a)/t(3)\r\n\r\nDivide the two and use the new ratio of .56/2 and you get 2.56(x+a)=1.68d. Put in d=2.56x and you get x+a=1.68x which is the distance from Reno where they meet for the third time (0.88x from LV)\r\n\r\nSummary:\r\n1) they meet in LV\r\n2) they meet 0.37x from Reno\r\n3) they meet 0.88x from LV\n\nEdited on January 15, 2004, 3:26 pm',NULL,0);
INSERT INTO comment VALUES (11090,1569,5175,'Surender Taalla','','2004-01-15 17:29:46',0,'',NULL,0);
INSERT INTO comment VALUES (11091,1569,5175,'Surender Taalla','can someone review this','2004-01-15 17:31:19',0,' 1.Start\r\n\r\n 2.Replace first letter with an alphabet A-Z excluding itself and any other alphabets already used. Check if the new word is in words.txt \r\n 3.NO for 2, goto 5\r\n 4.YES for 2, goto 8.\r\n\r\n 5.Check if all possible alphabets are used up replacing the first letter.\r\n 6.NO for 5, goto 2.\r\n 7.YES for 5, QUIT.\r\n\r\n 8.Replace the next letter with an alphabet A-Z excluding itself and any other alphabets already used. Check if the new word is in words.txt \r\n 9.NO for 8, goto 11.\r\n10.YES for 8, goto \r\n\r\n11.Check if all possible alphabets are used up.\r\n12.NO for 11, goto 14.\r\n13.YES for 11,QUIT.\r\n\r\n14.Replace the letter again with an alphabet A-Z excluding itself and any other alphabets already used.Check if the new word is in words.txt \r\n15.NO for 14, goto 11.\r\n16.YES for 14, goto 17.\r\n\r\n17.Check if any more letters are in the original word.\r\n18.NO for 17 DONE.\r\n19.YES for 17, goto 8.\r\n',NULL,0);
INSERT INTO comment VALUES (11092,1569,1301,'Charlie','re: can someone review this','2004-01-15 21:13:41',0,'The algorithm given changes the word from left to right. If there is no word that differs from the original word only in the first letter, the QUIT is taken in step 7. Thus ladders such as \"hard hand band bind bins\" would not be found, as the first change there is in the third letter.\r\n\r\nAlso, the algorithm stops upon reaching the end of the length of the word, in step 18, without looking for more ladders.\r\n\r\nIt\'s uncertain, though, what it will do as step 10\'s goto is not completed. Presumably it\'s 14.',11091,0);
INSERT INTO comment VALUES (11093,759,979,'Ravi Raja','re: Semantics','2004-01-16 02:45:36',0,'Yes you are right Dan. That is not what I am looking for. In fact your answer is not correct. Here divisible by 35 means that the quotient has to be a whole number and not a fraction.',10943,0);
INSERT INTO comment VALUES (11094,1569,4507,'Penny','I think this pseudocode will do it','2004-01-16 03:30:18',3,'(I assume it is possible for a program to consider one word of length L to be greater than or less than another word of length L, based on the normal ordering of letters from left to right:\r\ne.g. hard < sard, sard < sord, sold < sord, \r\nsold < solo) \r\n\r\nThis pseudocoded Al-Gore-ithm should do the job.\r\n\r\n*\r\n* Program initializations\r\n* \r\nM001: Read the input word.\r\nM002: Scan the input word and determine its length. Set variable L to this value.\r\nM003: Dynamically allocate and move blanks to workareas WORDLADDER (length L*(L+1)), PRIORWORD, LETTERORDER, (both of length L), and ORDERTABLE (length = L*(L!))\r\nM004: Build the contents of ORDERTABLE (L! elements of length L each) such that ORDERTABLE contains every possible ordering of the integers 1 through L.\r\nM005: Set J=1\r\nM006: Move the input word to the leftmost L positions in WORDLADDER.\r\n*\r\n* Find all the word ladders for a \r\n* particular ordering of integers 1-L. \r\n* (E.g. for the word hard and the \r\n* ordering 3124, find all the word ladders \r\n* formed by changing the third letter, then \r\n* the first letter, then the second letter, \r\n* and then the fourth letter: \r\n* (hard, hand, land, lend, lens), etc......\r\n*\r\nM007: Move the Jth element of ORDERTABLE to LETTERORDER. \r\nM008: Set N to 1.\r\nM009: Perform subroutine S001 thru S015.\r\nM010: If position (L+1) in WORDLADDER is blank, go to M016\r\nM011: Edit WORDLADDER into readable form, and PRINT it.\r\nM012: Move rightmost L positions of WORDLADDER to PRIORWORD \r\nM013: Blank out rightmost L positions of WORDLADDER\r\nM014: Set N=L\r\nM015: Go to M009\r\n*\r\n* Go to the next ordering.\r\n*\r\nM016: If J=L!, exit the program.\r\nM017: Set J=J+1\r\nM018: Go to M007.\r\n\r\nS001: Set variable K to the Nth position of LETTERORDER.\r\nS002: Read the first dictionary word of length L that is greater than PRIORWORD, but is exactly the same as the word in the rightmost nonblank L positions of WORDLADDER, except for the Kth letter. \r\nS003: If end-of-dictionary, go to S009\r\nS004: Move the dictionary word to the first leftmost blank L positions of WORDLADDER.\r\nS005: Move spaces to PRIORWORD.\r\nS006: Add 1 to N\r\nS007: If N>L, go to S009.\r\nS008: Go to S001.\r\nS009: If the last position in WORDLADDER is nonblank, go to S015.\r\nS010: If position (L+1) in WORDLADDER is blank, go to S015.\r\nS011: Move the rightmost nonblank L positions of WORDLADDER to PRIORWORD.\r\nS012: Move spaces to the rightmost nonblank L positions of WORDLADDER.\r\nS013: Set N down by 1.\r\nS014: Go to S001. \r\nS015: Exit this subroutine.\r\n\r\nI believe this program would produce the following results for input word \"hard\":\r\n \r\n(hard bard bird bind bine) \r\n(hard bard bird bind bins) \r\n(hard bard bird bind bint) \r\n(hard bard burd bund bung) \r\n(hard bard burd bund bunk) \r\n(hard bard burd bund bunn) \r\n(hard bard burd bund buns) \r\n(hard bard burd bund bunt) \r\n(hard card cord cold cola) \r\n(hard card cord cold cole) \r\n(hard card cord cold cols) \r\n(hard card cord cold colt) \r\n(hard card cord cold coly) \r\n(hard card curd cued cues) \r\n(hard fard ford fold folk) \r\n(hard fard ford fond fons) \r\n(hard fard ford fond font) \r\n(hard fard ford food fool) \r\n(hard fard ford food foot) \r\n(hard lard lord load loaf) \r\n(hard lard lord load loam) \r\n(hard lard lord load loan) \r\n(hard lard lord loud loup) \r\n(hard lard lord loud lour) \r\n(hard lard lord loud lout) \r\n(hard nard nerd need neem) \r\n(hard nard nerd need neep) \r\n(hard sard sord sold sola) \r\n(hard sard sord sold sole) \r\n(hard sard sord sold soli) \r\n(hard sard sord sold solo) \r\n(hard sard sord sold sols) \r\n(hard sard surd sudd suds) \r\n(hard sard surd sued suer) \r\n(hard sard surd sued sues) \r\n(hard sard surd sued suet) \r\n(hard ward word wold wolf) \r\n(hard ward word wood woof) \r\n(hard ward word wood wool) \r\n(hard ward word wood woos)\r\n.....ETC.....\r\n.....ETC.....\r\n.....ETC.....\r\n(hard hart hast hist cist) \r\n(hard hart hast hist fist) \r\n(hard hart hast hist gist)\r\n(hard hart hast hist kist) \r\n(hard hart hast hist list) \r\n(hard hart hast hist mist)\r\n(hard hart hast hist wist) \r\n(hard hart hast host cost) \r\n(hard hart hast host dost) \r\n(hard hart hast host lost) \r\n(hard hart hast host most) \r\n(hard hart hast host post) \r\n(hard hart hast host tost) \r\n(hard hart hast host wost)\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\n\nEdited on January 22, 2004, 12:55 pm',NULL,0);
INSERT INTO comment VALUES (11095,1509,4098,'lovejoy','think I got it','2004-01-16 08:25:45',0,'We agree that 1996 was a leap year so feb had 29 days, Herb started the 28th day at level 27feet, he climbed 3ft and was out, so 28 days onto 14th Feb is the 12th. How can this not be?',NULL,0);
INSERT INTO comment VALUES (11096,1285,1301,'Charlie','solution','2004-01-16 10:34:12',3,'Six students solved only B.\r\n\r\nIf we designate the number that got A alone as a, B alone as b, C alone as c; and that got A and B without C as d, that got B and C without A as e, that got C and A without B as f; and that got all three correct as g, then:\r\n\r\na+b+c+d+e+f+g = 25\r\nb+e=2(c+e)\r\na=f+g+d+1\r\na=b+c\r\n\r\nThen\r\n2b+2c+e+b+c-1=25\r\nor\r\n3b+3c+e = 26\r\n\r\nand since b=2c+e,\r\n\r\n4b+c=26\r\nor\r\nc=26-4b\r\n\r\nWe can work backwards to deduce from b what a, c and e are, and what remains for d+f+g:\r\n\r\n a b c e the rest\r\n 23 1 22 -43 22\r\n 20 2 18 -34 19\r\n 17 3 14 -25 16\r\n 14 4 10 -16 13\r\n 11 5 6 -7 10\r\n 8 6 2 2 7\r\n 5 7 -2 11 4\r\n 2 8 -6 20 1\r\n -1 9 -10 29 -2\r\n -4 10 -14 38 -5\r\n -7 11 -18 47 -8\r\n -10 12 -22 56 -11\r\n
\r\n----\r\nThe only line for which all the variables are positive is that on which b is 6.\r\n\r\nWe can also see that 8 people got A alone correct and 2 people got C alone correct. Two people got both B and C correct but not A, but we don\'t know how the remaining 7 split among the other possibilities.',NULL,0);
INSERT INTO comment VALUES (11097,1285,3172,'SilverKnight','solution','2004-01-16 10:51:05',3,'This solution is almost identical to Charlie\'s... barring that I narrowed it down to looking for a solution where V>X (rather than looking where all the variables are positive, as Charlie did).\r\n\r\nThey are equivalent.\r\n_____________________________\r\n\r\n6 students\r\n_____________________________\r\n\r\nProof:\r\n\r\nLet\'s identify all the possible \"regions\" of the problem space :\r\n\r\nLet:\r\nR = # of students that solved ONLY A\r\nS = # of students that solved ONLY A and B\r\nT = # of students that solved A, B, and C\r\nU = # of students that solved ONLY A and C\r\nV = # of students that solved ONLY B\r\nW = # of students that solved ONLY B and C\r\nX = # of students that solved ONLY C\r\n\r\nNote: CLEARLY, all of these must be non-negative integers less than 25! This is a key constraint.\r\n\r\n\"Among the contestants there were 25 who solved at least one problem each.\"\r\nR + S + T + U + V + W + X = 25 Eqn [1]\r\n\r\n\"Of all the contestants who did not solve problem A, the number who solved B was twice the number who solved C.\":\r\nV + W = 2 * (W + X) ==>\r\nW = V - 2X Eqn [2] ==>\r\nV = 2X + W Eqn [2.5]\r\n\r\n\"The number of participants who solved only problem A was one more than the number who solved problem A and at least one other problem.\":\r\nR = S + T + U + 1 Eqn [3]\r\n\r\n\"Of all students who solved just one problem, half did not solve problem A. \"\r\n2 * (V + X) = R + V + X ==>\r\nR = V + X Eqn [4]\r\n\r\n\"How many students solved only problem B?\"\r\nmeans: Solve for V.\r\n___________________________\r\n\r\n starting with equation [1]\r\nR + S + T + U + V + W + X = 25\r\n add one to both sides\r\nR + (S + T + U + 1) + V + W + X = 26\r\n substitute R (for S+T+U+1), using equation [3]\r\n2R + V + W + X = 26\r\n substitute for R, using equation [4]\r\n2(V + X) + V + W + X = 26\r\n simplify\r\n3V + W + 3X = 26\r\n substitue for W, using equation [2]\r\n3V + (V - 2X) + 3X = 26\r\n simplify\r\n4V + X = 26\r\n\r\nNow we have a key relationship between V and X\r\n\r\nSince BOTH must be non-negative integers, 4V must be between 0 and 25, meaning V must be a number from 0 to 6. Here are the possible pairings:\r\n\r\nFor V = 0, X = 26,\r\nFor V = 1, X = 22,\r\nFor V = 2, X = 18,\r\nFor V = 3, X = 14,\r\nFor V = 4, X = 10,\r\nFor V = 5, X = 6,\r\nFor V = 6, X = 2,\r\n\r\nRemember, equation [2.5]?\r\nV = 2X + W\r\n\r\nThis equation shows the V>=2X (since none of the values can be negative)\r\n\r\nThe last pairing is the ONLY one where V>X, so it must be the solution.\r\n\r\nTherefore V = 6.',NULL,0);
INSERT INTO comment VALUES (11098,1589,3172,'SilverKnight','Food for thought','2004-01-16 14:20:05',1,'Here\'s a thought to help get you started.\r\n\r\nI\'ll work through an example...\r\n______________________________________________________\r\n\r\nSay I start with a point very close to the left (0.01)\r\niteration 1 (regions: 0-1)\r\nadd .01\r\n.01 is in region 1(the only region)\r\nWORKS!\r\n\r\niteration 2 (regions: 0-.5, .5-1)\r\n* .01 is in region 1\r\nadd .99\r\n* .99 is in region 2\r\nWORKS!\r\n\r\niteration 3 (regions: 0-.333, .333-.667, .667-1)\r\n* .01 is in region 1\r\n* .99 is in region 3\r\nadd .34\r\n* .34 is in region 2\r\nWORKS!\r\n\r\niteration 4 (regions: 0-.25, .25-.5, .5-.75, .75-1)\r\n* .01 is in region 1\r\n* .99 is in region 4\r\n* .34 is in region 2\r\nadd .62\r\n* .62 is in region 3\r\nWORKS!\r\n\r\niteration 5 (regions: 0-.2, .2-.4, .4-.6, .6-.8, .8-1)\r\n* .01 is in region 1\r\n* .99 is in region 5\r\n* .34 is in region 2\r\n* .62 is in region 4\r\nadd .55\r\n* .55 is in region 3\r\nWORKS!\r\n\r\niteration 6 (regions: 0-.166, .166-.333, .333-.5, .5-.667, .667-.833, .833-1)\r\n* .01 is in region 1\r\n* .99 is in region 6\r\n* .34 is in region 3\r\n* .62 is in region 4\r\n* .55 is in region 4 OH NO!!!\r\nno new number to add... we have a conflict.\r\nTHIS DOESN\'T WORK, because .62 and .55 are both in the interval (3/6 - 4/6)\r\n\r\nSo, in this example, I was able to place only 5 numbers.',NULL,0);
INSERT INTO comment VALUES (11099,503,4718,'Jack Squat','Pull the trigger','2004-01-16 15:03:52',0,'I never thought to use graphing, that\'s pretty clever. I stumbled around with trig until I found this solution. \r\n\r\nConsider the triangle made underneath the two ladders. It has a base of 6 and a height h. The left corner (I anchored the 10 ladder in the left corner) has an angle of ~53.1 degrees (arctan(8/6)). The right corner has an angle of 60 degrees (arccos(6/12)).\r\n\r\nDrawing a line straight down from the intersection point to the ground splits this triangle into two. The length of this line is h. Call the distance from the left corner to the point on the ground where this line hits x (with the distance from the right corner being 6-x). Since we have the angles, we get two equations:\r\n\r\ntan(53.1 degrees) = h/x and\r\ntan(60 degrees) = h/(6-x)\r\n\r\nThe first equation gives you x = 0.75h. Putting that into the second equation gives you 1.73(6 - 0.75h) = h. Solve for h and you get 4.52.',NULL,0);
INSERT INTO comment VALUES (11100,1380,4197,'luminita','solution','2004-01-16 16:36:09',3,'If BDC is less than 90, the next correct sentence should be:\r\nQP is perpendicular bisector of AB and QZ the perpendicular bisector of CD.\r\nP coincide with Z if and only if BDC is 90.\r\n\r\nIn other words:\r\nQR is the line connecting the middle of the two opposite sides of ABCD. P coincides with Z if and only if QR is parallel to AB so QR parallel to CD, so BDC=90.\n\nEdited on January 16, 2004, 4:37 pm',NULL,0);
INSERT INTO comment VALUES (11101,1589,5219,'draistal','A possibility','2004-01-16 16:46:46',0,'Let\'s assume that all points on the interval are zero-dimensional. Then, one approach is to work backwards. For example, say you intend to place five points on the interval. Subdivide the interval into five equal intervals: \r\n.01-.19, .2-.39, .4-.59, .6-.79, .8-.99\r\n\r\nRound one, place the first point: .01\r\nRound two, place the second point: .8\r\nRound three, place the third point: .6\r\nRound four, place the fourth point: .4\r\nRound five, place the fifth point: .2\r\n\r\nNote the strategy used for placing the points. I began with placing the first point at the smallest possible value. I place the second point at the lowest value of the highest interval. In the scenario of five intervals, .8 is the lowest value in the interval with the highest overall values.\r\n\r\nAfter these first two points, I used the intervals as my guides by taking the lowest possible value in the highest group that covers the appropriate interval. For example, in round 3, I had three intervals from which to choose: .2-.39, .4-.59, and .6-.79. I choose .6 as my point since it is the lowest value in the interval with the highest values that satisfied the thirds requirement.\r\n\r\nThe only limit my theory has is your patience. Subdivide the interval as much as you like, and this theory should(?) hold. Since I have yet to test it at higher orders, I hesitate to make a definitive statement.\r\n\r\nI realize that this isn\'t a rigorous mathematical proof, so please feel free to amend or correct this.',NULL,0);
INSERT INTO comment VALUES (11102,1589,3172,'SilverKnight','re: A possibility','2004-01-16 17:09:36',0,'Those are good thoughts....\r\n\r\nTo confirm, all the points on the interval are zero-dimensional, but you shouldn\'t use .2 (or .4, .6, etc...) as one of your points, because it lies ON a boundary (when dividing the segment into 5 parts).\r\n\r\nI look forward to the listing of the n points in your answer.\r\n\r\n _/_/_/ _/ _/
',11101,0);
INSERT INTO comment VALUES (11103,1380,3172,'SilverKnight','re: solution','2004-01-16 17:12:45',4,'Luminita, you wrote:\r\n\"If BDC is less than 90, the next correct sentence should be:\r\nQP is perpendicular bisector of AB and QZ the perpendicular bisector of CD.\r\nP coincide with Z if and only if BDC is 90.\r\n\r\nIn other words:\r\nQR is the line connecting the middle of the two opposite sides of ABCD. P coincides with Z if and only if QR is parallel to AB so QR parallel to CD, so BDC=90.\"\r\n\r\nWhat the heck is Z?!?\r\n\r\nAnd are you suggesting that the two perpendicular bisectors won\'t intersect?\r\n\r\n
_/ _/ _/ _/
_/ _/ _/
_/_/_/ _/_/_/ _/_/
_/ _/ _/
_/ _/ _/ _/
_/_/_/ _/ _/
\r\n _/_/_/ _/ _/
',11100,0);
INSERT INTO comment VALUES (11104,1589,4507,'Penny','Solution (I think !)','2004-01-16 19:17:33',1,'Ah.....better rethink this one.....\r\n\r\n\n\nEdited on January 18, 2004, 5:26 am',NULL,0);
INSERT INTO comment VALUES (11105,1589,3172,'SilverKnight','re: Solution (I think !)','2004-01-17 02:21:45',1,'Penny wrote:\r\n\"Notice that this puzzle doesn\'t just ask how large can N be, for N points to be placed on the line so that they are all at least 1/N apart.\"\r\n\r\nThe problem states \"the first n points always occupy different 1/nth parts of the line\"... so my first three points could be...\r\n.32 (occupies the whole region)\r\n.74 (now .32 occupies the 1st half, and .74 occupies the 2nd half)\r\n.35 (now .32 occupies, the 1st third, .35 occupies the 2nd third, and .74 occupies the 3rd third...)\r\n\r\nNote that .32 and .35 are NOT 1/3 or more apart from each other, but this satisfies the problem...\r\n\r\nIt is NOT clear that you can place an infinite number of points in this manner (just try it!)',11104,0);
INSERT INTO comment VALUES (11106,1589,4507,'Penny','re(2): Solution (I think !)','2004-01-17 02:33:21',0,'Best rethink this one, Penny.....\n\nEdited on January 18, 2004, 5:27 am',11105,0);
INSERT INTO comment VALUES (11120,1574,1301,'Charlie','worst case & information theoretic','2004-01-18 12:34:11',1,'If you weigh two at a time, there are 6 pairs to weigh (six weighings) in the first round. If each of these weighings balance, then you have 6 pairs each of member of which is equal in weight to its partner. In the next three weighings weigh one representative of each against the representative of another. In at least one case there must be an unequal weighing, showing that in that pair which is the heavy and which is the light coin. In the third round, just weigh the heavy against a representative of one of the other two pairs: that determines which of those pairs has heavy coins (and in turn the groups of four from the original round).\r\n\r\nThis is 10 weighings.\r\n\r\nIf unequal weights come up earlier than in the above scenario, the number of unknown coins goes down by 2 for each such balance tipping, so you could get by with just 6 weighings, if each pair in the initial round weighed unequally.\r\n\r\nBy information theory, the minimum possible number of weighings (with no guarantee there\'s actually a way of doing it in this few), would be the base-3 log of 12C6.\r\n\r\n12C6 = 924 and its base-3 log is 6.2..., so even theoretically no solution could guarantee less than 7 weighings.\r\n\r\nOne thing that contributes to the excess over the information theoretic value is that certain combinations of results cannot happen, such as a single equal weighing followed by 5 straight unequal weighings in the remainder of the paired coins in the first round.\r\n\r\nOn second thought\r\nYou don\'t need the sixth weighing in the above worst-case scenario: If the first 5 weighings all are equal, then so will the 6th, so it is not needed. On the other hand, in the second round, the third of those three weighings can\'t be dispensed with, as you don\'t know which of the two is the heavier, even though you know one must be.\r\n\r\nThis reduces the worst case scenario to 9 weighings.\r\n\r\nThis also still leaves the way for more clever methods to reduce the worst case to 8 or 7 weighings, but I don\'t see how that can be done.',NULL,0);
INSERT INTO comment VALUES (11107,1589,153,'TomM','re: Solution (I think !)','2004-01-17 02:58:28',0,'I suspect that theoretically n can be infinite, but your thoughts do suggest that it is just possible that there is a limit and it is relatively low. Either way, your solution as posted is flawed.\r\n\r\nYour first error is the assumption that \"The first two have to be placed at least 1/2 apart.\" If the first is placed just before .5 and the second just after, they satisfy the conditions of the game and are far less than 1/2 apart. (Since, in this case, both would be the middle third of the line, you could not progress to n=3, but then you would need only choose a point immediately after .666... -- which is only slightly more than 1/6, and still far less than 1/2 -- and there will still be somewhere to place the third point.)\r\n\r\nYour second error concerns the algorithm for placing the points. It fails at n = 6 regardless of your formula. Since, starting with point 4, each point is placed between the last point placed and 1, there is never a point placed between 0 and .333... Once the length of a segment drops to .1666... or lower there are segments in that range without points.\r\n\r\nNote: For reasons SilverKnight explains in the previous response, the points in your algorithm should be irrational numbers arbirarily close to the numbers listed. (As long as n remains finite, a chosen point can be rational, p/q [reduced], provided it is not true that p ≤ q ≤ n, but for infinite n that eliminates all rationals\r\n\r\nEdit: added following paragraph\r\n\r\nWhile I was composing this, Penny and SilverKnight both posted new responses. My reference to SK\'s \"last\" reponse refers to his last previous response. (His second)\n\nEdited on January 17, 2004, 3:04 am',11104,0);
INSERT INTO comment VALUES (11108,1589,4507,'Penny','re(2): Solution (I think !)','2004-01-17 03:32:15',1,'I think not, Penny......\n\nEdited on January 18, 2004, 5:27 am',11107,0);
INSERT INTO comment VALUES (11119,1589,2682,'exoticorn','re(2): Solution','2004-01-18 06:36:27',0,'Ok, here is the program I used. It is written in Ruby (www.ruby-lang.org).\r\nIt doesn\'t print out the solution as points but rather as ranges in which to place the points.\r\n\r\nTo answer you second questions: Either the algorithm I used is flawed or there simply isn\'t any solution with more than 17 points. I\'m personally in favour of the latter hypothesis, but feel free to prove me wrong ;)\r\n\r\n\r\nrequire \'rational\'\r\n\r\nclass Rational\r\n def inspect\r\n \"%d/%d\" % [@numerator, @denominator]\r\n end\r\nend\r\n\r\ndef rec(ranges, solution)\r\n level = ranges.size\r\n \r\n if level == 1\r\n p ranges + solution\r\n throw :found\r\n end\r\n \r\n step = Rational(1, level)\r\n right = 0\r\n ranges.map! do |range|\r\n left = right\r\n right += step\r\n return if left >= range.end || right <= range.begin\r\n ([left, range.begin].max)..([right, range.end].min)\r\n end\r\n \r\n next_ranges = []\r\n until ranges.empty?\r\n cur_range = ranges.shift\r\n rec(next_ranges + ranges, [cur_range] + solution)\r\n next_ranges << cur_range\r\n end\r\nend\r\n\r\nfor level in 2..18\r\n printf \\\"Level: %d\\n\\\", level\r\n catch :found do\r\n rec([Rational(0, 1)..Rational(1, 1)] * level, [])\r\n end\r\nend\r\nBut, you give no proof of those constraints or even reasons to accept them as assumptions.',11108,0);
INSERT INTO comment VALUES (11110,1589,4507,'Penny','re(4): Solution (I think !)','2004-01-17 10:36:59',1,'I don\'t know if............. \n\nEdited on January 18, 2004, 5:28 am',11109,0);
INSERT INTO comment VALUES (11118,1380,5178,'Dan Porter','Why do you need Z?','2004-01-18 06:10:14',0,'Think of a top down view. Point A is directly above point C so they appear to be one point. Also, line CP is is diectly above AP. So far in this veiw you have one straight line. Now draw a second line of equal length to show angle APB. Draw a third line of equal lenght just a few degrees off of PB to show angle CPD. Now complete both isosceles triangles by drawing AB and CD. The solution is as I stated before. ABDC is not a quadralateral rather AD is the line of intersection between plane ACD and ABD. Vertex D has 4 serfaces and point P is shared by the triangles. Think of it this way. You can make AP any length as long as BP is the same. Also, you can make AB any length without regard to CD. By changing AP and AB you can always place point A diectly above point C and still have 2 isosceles triagles sharing point P no mater where in space P may lay. Do you self a favor, draw segment AD!\r\n \r\nBy the way. If I wanted to find the angle to straighten the table leg show as BD I wouldn\'t even focus on vertex D but vertex B so when I got an angle to correct by it would be based on the table top and not the angle of another lag to the floor. Angles to the floor change as you straighten legs! This means you need to fold the quad on the BC line of intersecting planes. But this is another problem. ',NULL,0);
INSERT INTO comment VALUES (11111,1505,1754,'Rachel Mantis','re: Found the Answer','2004-01-17 11:47:07',0,'Ah, now I see it. The nth letter of the alphabet is represented by the number n(n+1).',9861,0);
INSERT INTO comment VALUES (11112,676,1754,'Rachel Mantis','Solution','2004-01-17 11:58:56',0,'Heron\'s formula states that the area of any triangle is √p(p-a)(p-b)(p-c), where p is the semiperimeter, and a, b, and c are the sides. Let b = x, a = x - d, and c = x + d; then the area is √(3x/2)(x/2 + d)(x/2)(x/2 - d). Simplifying, this is x/2 * √3x^2/4 - d^2.\r\n\r\nThe area of a triangle with side length s is s^2 * (√3)/4. s = x in this case, so:\r\n\r\nx/2 * √(3x^2/4 - d^2) = x^2 * (√3)/4 * 3/5\r\n√(3x^2/4 - d^2) = 3x/10 * √3\r\n3x^2/4 - d^2 = 27x^2/100\r\n12/25 * x^2 = d^2\r\nd = 2x/5 * √2\r\n\r\nThe ratio is then x - 2x/5 * √2 : x : x + 2x/5 * √2. Cancelling out the x\'s:\r\n\r\n(5 - 2√2)/5 : 1 : (5 + 2√2)/5\r\n\r\n(Honestly, did you guys think it would come out with rationals? The area of an equilateral triangle always involves √3 in some way.)',NULL,0);
INSERT INTO comment VALUES (11113,676,3558,'Tristan','re: Solution','2004-01-17 12:26:21',0,'You said, \"...the area is √(3x/2)(x/2 + d)(x/2)(x/2 - d). Simplifying, this is x/2 * √3x^2/4 - d^2.\"\r\n\r\nCheck your math. It actually simplifies to x/2 * √(3x²/4 - 3d².',11112,0);
INSERT INTO comment VALUES (11114,1589,153,'TomM','Six point counter-example','2004-01-17 13:03:34',0,'Point A = .1\r\nPoint B = .55\r\n\r\n0 <.1<.5\r\n.5<.55<1\r\n\r\nPoint C = .9\r\n\r\n0<.1<.333...\r\n.333...<.55<.666...\r\n.666...<.9<1\r\n\r\nPoint D = .3\r\n0<.1<.25\r\n.25<.3<.5\r\n.5<.55<.75\r\n.75<.9<1\r\n\r\nPoint E = .7\r\n\r\n0<.1<.2\r\n.2<.3<.4\r\n.4<.55<.6\r\n.6<.7<.8\r\n.8<.9<1\r\n\r\nPoint F = .4\r\n\r\n0<.1<.1666...\r\n.1666<.3<.333...\r\n.333...<.4<.5\r\n.5<.55<.666...\r\n.666...<.7<.8333...\r\n.8333...<.9<1\r\n\r\nI found this by \"working backward\": I started with six points correctly placed and eliminated one leaving the other five correctly placed for the previous step, etc.\r\n\r\nActually I was working on an indirect proof of Penny\'s theory and expected to be unable to find a proper point C to complete a counter-example.',11110,0);
INSERT INTO comment VALUES (11115,1388,3558,'Tristan','One solution','2004-01-17 16:38:40',3,'K=king; Q=queen; n=knight\r\n\r\n-------Q\r\n-n------\r\n--------\r\n---nn---\r\n---nn---\r\n--------\r\n------K-\r\nQ-------\r\n\r\nIn this solution, I assumed that occupied spaces already count as under attack.',NULL,0);
INSERT INTO comment VALUES (11116,1589,2682,'exoticorn','Solution','2004-01-17 17:08:52',3,'I can place 17 points, for example like this:\r\n0.95, 0.27, 0.54, 0.14, 0.71, 0.42, 0.85, 0.07, 0.62, 0.353, 0.77, 0.21, 0.48, 0.9, 0.01, 0.65, 0.3\r\n\r\nI cannot place 18 points.\r\n\r\nOk, I have to admit that I had to write a computer program to succesfully place that many points. ;)',NULL,0);
INSERT INTO comment VALUES (11117,1589,3172,'SilverKnight','re: Solution','2004-01-17 22:29:00',4,'Exoticorn, I\'ve verified your answers. And they work for 17 points! Well done. I wonder if anyone can get 18 or more....\r\n____________________________________\r\n\r\nFirst, why don\'t you post the program you used?\r\n\r\nSecond, (to play Devil\'s Advocate) why was your program unable to continue and get an eighteenth (or higher) point?\n\nEdited on January 18, 2004, 3:44 am',11116,0);
INSERT INTO comment VALUES (11121,1589,153,'TomM','My algorithm','2004-01-18 12:47:21',0,'I have not worked with programming languages very extensively, or very recently, so I can\'t write programs, but the algorithm I used to find the six point solution is below:\r\n\r\n
_/ _/ _/ _/
_/ _/ _/
_/_/_/ _/_/_/ _/_/
_/ _/ _/
_/ _/ _/ _/
_/_/_/ _/ _/
\r\nStep 1: \r\n Divide the like into n segments\r\n Label the segments\r\n α = (0 -- 1/n)\r\n β = (1/n -- 2/n)\r\n . . . \r\n ν = ([n-1]/n -- 1)\r\n\r\nStep 2:\r\n \"Eliminate\" one segment \r\n Label any point in that segment N\r\n\r\nStep 3: \r\n Refine ranges for the remaining segments:\r\n 0<α<1/n \r\n 0<α<1/(n-1) \r\n -----\r\n 0<α<1/n\r\n\r\n 1/n<β<2/n \r\n 1/(n-1)<β<2/(n-1) \r\n -----\r\n 1/(n-1)<β<2/n\r\n\r\n . . . \r\n\r\n (n-1)/n<ν<1 \r\n (n-2)/(n-1)<ν<1 \r\n ----- \r\n (n-1)/n<ν<1\r\n\r\n Repeat steps 2 and 3 for n\'=(n-1), retaining and\r\n further refining ranges\r\n\r\n If sucessful, you have a solution for N points. \r\n If not sucessful (if in Step 3 the two inequalities\r\n used to refine a range do not overlap) return to\r\n step 2 and \\\"eliminate\\\" a different range. \r\n If all ranges have been unsuccessful, return \r\n to Step 2 of the previous level and \\\"eliminate\\\"\r\n a different range.Edited to restore original formatting\n\nEdited on January 19, 2004, 12:30 am',11119,0);
INSERT INTO comment VALUES (11127,1587,5015,'joel','that\'s correct charlie','2004-01-19 02:22:06',0,'through creation of imaginary lines you can form a square in the middle so r= √2-1',NULL,0);
INSERT INTO comment VALUES (11128,1445,4098,'lovejoy','','2004-01-19 03:02:17',0,'help me out please someone,the solution to \"I coax the lazy\" etc,is given as being one set of scrabble letters, but reading the comments no one gave that as an answer, What am I missing here? ',NULL,0);
INSERT INTO comment VALUES (11129,1445,3172,'SilverKnight','re: No Subject','2004-01-19 03:42:19',0,'Lovejoy wrote:\r\n\"What am I missing here?\"\r\n\r\nYou\'re not missing anything.... No one figured out the solution that Gamer had in mind. A scholar, or perhaps Levik, decided that the solution should be posted and did so.',11128,0);
INSERT INTO comment VALUES (11122,1589,153,'TomM','re: My algorithm (correction)','2004-01-18 13:20:58',0,'For some reason, after I corrected the formatting, I lost some lines from Step 2 (refining the ranges) -- they show up fine in the text box but print in the dialog box as blank lines. They should read:\r\n\r\n0<α<1/n \r\n0<α<1/(n-1)\r\n -----\r\n 0<α<1/n\r\n\r\n\r\n 1/n<β<2/n \r\n1/(n-1)<β<2/(n-1)\r\n -----\r\n 1/(n-1)<β<2/n\r\n\r\n . . . \r\n\r\n (n-1)/n<ν<1 \r\n(n-2)/(n-1)<ν<1\r\n ----- \r\n (n-1)/n<ν<1',11121,0);
INSERT INTO comment VALUES (11123,1284,5234,'mobb','chessboard','2004-01-18 13:34:27',0,'I THINK IT IS NOT THAT COMPLEX- 60 POSSIBILITIES DIVIDED BY 249984 TOTAL = .OOO240015\r\n',NULL,0);
INSERT INTO comment VALUES (11124,1284,5234,'mobb','CHESSBOARD','2004-01-18 13:40:09',0,'MY APOLOGIES - i JUST REREAD THE PROBLEM. I WAS LOKKING AT IT AS 3 CONNECTING DIAGONALS\r\n',NULL,0);
INSERT INTO comment VALUES (11125,1574,4507,'Penny','An alternative method','2004-01-18 22:37:38',3,'This method will sort the coins with a minuimum of 5 balances, and a maximum of 12. \r\n\r\nDivide the 12 coins into 3 groups of 4 coins each. (Let c indicate a 24g coin, and C a 25g coin). \r\n\r\n(1) Do 2-3 preliminary balances to determine the group weight relationships.\r\n\r\n(2) If all 3 groups are of equal weight, then the coin distribution can only be (CCcc CCcc CCcc), and 3-9 additional balances will be required. For each of the 3 equal groups: divide it into two 2-coin subgroups, and balance them. If the 2 subgroups are equal, exchange 2 coins and balance them again. If they are still equal, one more coin exchange can produce inequality.\r\n \r\n(3) If one group is lighter, and the other 2 are equally heavier, then the coin distribution must be (cccc CCCc CCCc), and 4 additional balances will be required. For each of the 2 equally heavier groups, divide it into two 2-coin subgroups, and balance them. Then balance the 2 coins of the lighter subgroup.\r\n \r\n(4) If 1 group is heavier, and the other 2 are equally lighter, then the coin distribution must be (CCCC Cccc Cccc), and 4 additional balances are required. For each of the 2 equally lighter groups, divide it into two 2-coin subgroups, and balance them. Then balance the 2 coins of the heavier subgroup.\r\n\r\n(5) If all 3 groups are of different weight, between 2 and 8 additional balances are required. First, divide the heaviest group into two 2-coin subgroups, and balance them. If they are equal, then the coin distribution must be (cccc CCcc CCCC). If not, then the distribution is (Cccc CCcc CCCc). (a) If the distribution is (cccc CCcc CCCC), divide the middle group into two 2-coin subgroups, and balance them. If they are equal, exchange 2 coins and re-balance them. If they are still equal, one more coin exchange will produce inequality. (b) If the distribution is (Cccc CCcc CCCc), first divide the lightest group into two 2-coin subgroups, and balance them. Then balance the 2 coins of the heavier subgroup. Next, divide the middle group into two 2-coin subgroups, and balance them. If the result is equality, exchange 2 coins and re-balance them. If they are still equal, one more coin exchange will produce inequality. Finally, divide the heavier group into two 2-coin subgroups, and balance them. Then balance the 2 coins of the lighter subgroup.\r\n \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\n\nEdited on January 18, 2004, 11:18 pm',NULL,0);
INSERT INTO comment VALUES (11126,1574,4507,'Penny','re: An alternative method','2004-01-18 23:22:54',0,'My last revision of \"An alternative method\" gives a method with a minimum of 5 balances, and a maximum of 12. \r\n ',11125,0);
INSERT INTO comment VALUES (11130,1286,3172,'SilverKnight','solution (spoiler)','2004-01-19 08:42:32',3,'The order of the horses is:\r\nFOURTH\r\nSECOND\r\nFIFTH\r\nFIRST\r\nTHIRD\r\n\r\nI solved it by filling out the grid below... You can see below which sentence gave me the clue to say that a given horse could or could not come in any given position. Where you see (6), I had to go back to the third statement after having read the 5th statement.\r\n\r\nFor instance, the first statement was \"\'FIRST\' did not come in first\", so I placed N(1) in the appropriate position.\r\n
\r\nn=1 and n=6 are the only integers for which the value of m is an integer.\r\nSince the ceremony lasted more than one day, the ceremony lasted 6 days and 36 medals were given out.\n\nEdited on January 29, 2004, 2:47 pm',NULL,0);
INSERT INTO comment VALUES (11412,1472,5392,'Pablo','My Solution (corrected)','2004-01-29 15:25:48',3,'(I don\'t know why the previous message was crash)\r\n\r\n\r\nI defined the square in the range \r\n- 0.5 < x < 0.5 and \r\n- 0.5 < y < 0.5\r\n\r\nI can divide the square in four sub squares, \r\none in each cuadrant.\r\n\r\nI will find the probability that the end point\r\nlies on the original square given that the start\r\npoint lies on the first quadrant\r\n\r\nfinally i must multiply this probability by four\r\nsince there are four quadrants.\r\n\r\nOn the first quadrant two types of points are\r\nidentified:\r\n\r\n- The one that lies under the curve \r\n 0.5-sqrt(0.5*0.5-(x-0.5)(x-0.5))\r\n- The one that lies over the same curve.\r\n\r\nthe diference between these two types of point is:\r\n\r\n\r\nType 1: If we draw a circle with center in a\r\npoint of this type, the circle intercept the\r\noriginal square 4 times.\r\n\r\nType 2: The circle intercept the original Square\r\nonly 2 times\r\n\r\nThe importance of knowing how many times the\r\nsquare is intercepted is that one can know\r\nexactly from what angle to what angle a end\r\npoint is outside of the original Square.\r\n\r\nIn Type 1 there are two angle zones where the\r\nend point is outside in Type 2 there is only one\r\nzone\r\n\r\nTo find the probability (already multiplied by four): \r\n\r\nType 1: \r\n\r\nThe integral from x=0 to x=0.5 of \r\nthe integral from y=0 to 0.5-sqrt(0.5*0.5-(x-0.5)*(x-0.5)) of \r\n\r\n( \r\n2*pi \r\n- 2*arcsin( sqrt(0.5*0.5-(0.5-x)(0.5-x))/0.5) \r\n- 2*arcsin( sqrt(0.5*0.5-(0.5-y)(0.5-y))/0.5) \r\n) /2/pi * dx * dy /0.25 \r\n\r\nType 2: \r\n\r\nThe integral of x=0 to x=0.5 of \r\nthe integral of y=0.5-sqrt(0.5*0.5-(x-0.5)(x-0.5)) of \r\n\r\n( \r\n2*pi \r\n-pi/2 \r\n- arcsin( sqrt(0.5*0.5-(0.5-y)(0.5-y))/0.5) \r\n- arcsin( sqrt(0.5*0.5-(0.5-x)(0.5-x))/0.5)) \r\n) /2/pi * dx * dy /0.25 \r\n\r\n\r\nThese two integrals has three parts each that\r\ngive the result \r\n\r\n(4-pi)/4 \r\n\r\n(pi*pi-12)/16/pi \r\n\r\n(pi*pi-12)/16/pi \r\n\r\n3Pi/16 \r\n\r\n(-pi*pi-4)/32/pi \r\n\r\n(-pi*pi-4)/32/pi \r\n\r\nAdding these 6 parts gives the result of: \r\n\r\n1-7/4/pi or aproximately 0.4429576992 \r\n\r\n\r\n\r\nPablo Meraz \r\n',NULL,0);
INSERT INTO comment VALUES (11413,1601,1575,'DJ','answer (somewhat spoiler)','2004-01-29 15:40:43',3,'The guy in the mirror is holding up the hand on the same side of the mirror as I am, on my right. If I was to stand in his position and do the same thing, I would be raising my left hand, but to do so, I first have to turn around.\r\n\r\nOn the other hand (npi), to say that I am looking up when the other guy is looking up is also true. Up and down are defined in the same way no matter which way you turn around.\r\n\r\nWe think the mirror reverses right and left because those directions are relative to our bodies, and change as we move around. Up and down are also relative, I suppose, but relative to the earth (in general), and is not dependent on whether you are looking at the mirror or inside it.\r\n\r\nHere is another interesting discussion of the same topic ..',NULL,0);
INSERT INTO comment VALUES (11414,1601,1301,'Charlie','solution','2004-01-29 16:00:52',3,'Physically and mathematically the only distinguished direction with regard to the plane of the mirror is the direction perpendicular to the mirror, toward or away from it, either in front or in back. And in fact this is the only direction in which the mirror reverses.\r\n\r\nWhen it is said that the mirror reverses left and right that is a semantic distinction based on the perceived characteristics of the fictitious person \"in\" the mirror, that is, your reflection. In fact, the reflection of your own right hand is still on your right. If you are facing north into the mirror, your right hand is to the east and the reflection of that hand is also to the east. The only thing is, that you look at that reflection in the mirror and say that that reflected right hand is a left hand, that is, the left hand of that fictitious person in the mirror. Why do we say this?\r\n\r\nA good way of defining left and right (which actually can\'t be done from scratch) for purposes of this description, is that side which is clockwise relative to the front of the body, as seen from above.\r\n\r\nAs mentioned in the first paragraph, up and down are not changed, so \"above\" is still \"above\". But front and back have been reversed. So now, clockwise from your front is not the same direction as clockwise from the reflection\'s front. That is why, semantically, we call that reflection of your right hand, that is still to your own right, a left hand, as it appears to be attached to a \"person\" who is facing the opposite direction.',NULL,0);
INSERT INTO comment VALUES (11415,1298,5285,'Ady TZIDON','my solution','2004-01-29 16:13:53',3,'on the last day n medals were given , said number being 6/7 of the number left day before after awarding n-1 medals( call it db)\r\nn=6/7 *db \r\ndb=7/6*n so n is a multiple of 6: 6, 12, 18...\r\nlets try the smallest one ( 6 awarded last day) and work our way backwards: \r\n\r\nthere were 6 days:\r\n\r\nat the beginning of day 6 ..... 6 medals =6+0\r\nat the beginning of day 6 .....12 medals=5+7\r\nat the beginning of day 6 .....18 medals=4+14\r\nat the beginning of day 6 .....24 medals=3+21\r\nat the beginning of day 6 .....30 medals=2+28\r\nat the beginning of day 6 .....36 medals=1+35\r\n \r\nso: the answer is 36 medals awarded \r\n during 6 days 6 each day\r\n',NULL,0);
INSERT INTO comment VALUES (11416,1391,3807,'DrBob','','2004-01-29 16:48:00',0,'18-(15/3) = 13\r\n36-(10+13) = 13\r\n39/(27-24) = 13',NULL,0);
INSERT INTO comment VALUES (11417,1467,153,'TomM','re(2): Barbarians at the gates !!','2004-01-29 17:09:27',0,'>>But at least I spared all the villagers. :-) \r\n\r\nThe operation was a success, but the patient died. :) \r\n\r\nYour solution which \"spared\" the villagers requires that the village is already dead (or abandoned).',11391,0);
INSERT INTO comment VALUES (11418,1601,3992,'Jane Doe','This is science right ?','2004-01-29 18:06:27',0,'I don\'t understand what needs to be solved here...isn\'t it scientific fact that a mirror will reflect only the light that falls upon it? \r\n\r\nIf I were to raise my right hand in front of a real person instead of a mirror, then the person would still see what the mirror would have seen, i.e., the image raising it\'s left hand. Similar principles aren\'t they? \r\n\r\nOr do they not teach these things in schools anymore? ',NULL,0);
INSERT INTO comment VALUES (11419,1467,2899,'Brian Wainscott','re: What about this?','2004-01-29 18:23:48',0,'I think your answer is still too high: you can have 16 lines through the center and 8 through the edges. A hexagon with villagers at the points and centers of the sides would give 12 lines through the center and 6 along the edges, which is more than enough and only requires 13 villagers. But this still seems too high as it allows for up to 36 barbarians.\r\n\r\nYou\'ve pointed out something that I think bears repeating:\r\n\r\nGamer carefully reworded this puzzle after earlier confusion. He specifically states that each bullet went over 3 villager\'s heads, and killed a person. There is no requirement that that person be a villager. I somehow like the idea that all the barbarians die, and the villagers are all spared.\r\n\r\nI also fully agree with Charlie\'s point that a person can only be killed once, so no person is shot twice.\r\n',11410,0);
INSERT INTO comment VALUES (11420,731,2184,'mark hartman','solution','2004-01-29 18:34:50',0,'This problem is easily solved with mod 7 arithmetic (ie Base 7 arithmetic - usually learned in number theory). \r\nWe are looking for solutions for n such that 2^n = 6 mod 7.\r\n2^1 = 2 mod 7\r\n2^2 = 4 mod 7\r\n2^3 = 1 mod 7\r\n2^4 = 2*(2^3) mod 7 = 2 mod 7\r\n2^5 = 2*(2^4) mod 7 = 4 mod 7\r\n2^6 = 2*(2^5) mod 7 = 1 mod 7\r\netc.\r\nThere is no solution for n.',NULL,0);
INSERT INTO comment VALUES (11421,1601,4982,'Dan Blume','Alice didn\'t worry about it','2004-01-29 18:38:23',3,'The directions \"up, down, east, west, north, south are fixed with relationship to the local surface of the earth. So if you raised the eastern hand, then so would the reflection.\r\n\r\nLeft and right are relative to the person/image. Similar to clockwise, counterclockwise. Since the image is rotated 180 degrees along the vertical plane, the relative directions of left/right also rotate.',NULL,0);
INSERT INTO comment VALUES (11422,731,2184,'mark hartman','re: la meme Janette mais autrement coifee!','2004-01-29 18:42:49',0,'An unusual approach, but I don\'t think its valid. For the first term, k*2^3 is even regardless of k; so if k is odd, both the first and second term are even, resulting in an even value for the right side. So it is possible to have an even value for the right side (of your second equation). What you need to show is the right side cannot be a multiple of 2, a harder task.',10980,0);
INSERT INTO comment VALUES (11423,1467,3172,'SilverKnight','re(2): What about this?','2004-01-29 19:26:50',0,'Well, call me old fashioned, but I kinda like it when the problem is clearly stated, such that it\'s not easily open to disparate interpretations.\r\n\r\nHeck, when the discussion here started questioning whether or not it is okay for barbarians to be the \'person\' shot... Gamer should pipe up... and offer a comment.\r\n\r\nOtherwise, the \"difficulty\" of the problem lies not within the problem, but with poor/ambiguous language. And that is rarely fun (unless we\'re talking about problems that use that as the main point... such as Buying Chestnuts).\r\n\r\nAnd of course, if that is the case, the problem should be in \"tricks\".',11419,0);
INSERT INTO comment VALUES (11424,1583,5345,'Rawlyn','I\'m on it','2004-01-29 20:56:53',0,'Thanks for pointing this one out to me Brian. I\'ll be writing a GA to look for good candidates the next time I get to a computer, in a couple of days. What a goodie - just the sort of thing I\'m looking for!',NULL,0);
INSERT INTO comment VALUES (11425,1459,5402,'peggy mashburn','re: Is this Solution','2004-01-29 23:52:05',0,'hi.. I got the same answer w/ the 1st person being B.. ',11407,0);
INSERT INTO comment VALUES (11426,1554,5404,'Tyler','','2004-01-30 00:11:38',2,'Wait, isn\'t the easiest way to find who is the liar or not to ask the question:\r\n\r\n*am I you?*\r\n\r\nif no - it is the knight\r\nif yes - it is the liar',NULL,0);
INSERT INTO comment VALUES (11427,1298,5306,'Purna','','2004-01-30 01:34:11',3,' m=36 medals in total were awarded during (n=6) days with 6 medals each day. \r\n\r\n',NULL,0);
INSERT INTO comment VALUES (11428,1601,2716,'Federico Kereki','Answer','2004-01-30 07:14:38',3,'The mirror doesn\'t \"reverse left and right\"; your brain does. The mirror reverses the front-back directions. ',NULL,0);
INSERT INTO comment VALUES (11429,1410,4830,'Jils','Equations','2004-01-30 08:45:09',0,'If the time was H:M:S\r\nI managed to get:\r\nH + M/60 + S/3600 = M/5 + S/300 = S/5\r\nand from there proved that 2=2....\r\n',NULL,0);
INSERT INTO comment VALUES (11430,1410,4830,'Jils','Integers','2004-01-30 09:27:50',3,'If M and H have to be integer, you can look at all the solutions of M=59*S/60 for all integer M and see if any of the values for M and S would give an integer H. I cannot find one, so I would have to say no, there is no other time.',NULL,0);
INSERT INTO comment VALUES (11431,1583,1920,'Brian Smith','re: I\'m on it - Good luck','2004-01-30 09:38:33',0,'Good luck. Let us know when you get a solution.',11424,0);
INSERT INTO comment VALUES (11432,1410,1301,'Charlie','solution','2004-01-30 09:39:00',3,'The hour and the minute hand are together once every 12/11 hour. The number of hours past noon is the first column on the below table; then the time in h:mm:ss.sss format and the position in degrees clockwise from the 12-o\'clock position of the hour-, minute- and second-hands:\r\n PLACE
',NULL,0);
INSERT INTO comment VALUES (11131,1286,4507,'Penny','The easiest puzzle in floobelian history !!!','2004-01-19 09:15:33',3,'FOURTH 1st; SECOND 2nd; FIFTH 3rd; FIRST 4rth; THIRD 5rth.\r\n\r\n(I nearly fell over when I read SilverKnight\'s solution. Talk about killing a mosquito with a sledgehammer !!!!!!)\n\nEdited on January 19, 2004, 9:22 am',NULL,0);
INSERT INTO comment VALUES (11132,1286,3386,'Victor Zapana','solution (same as sks) but diff approach','2004-01-19 09:35:59',0,'FOURTH SECOND FIFTH FIRST THIRD\r\nI used the following approach:\r\nLet\'s say: \r\nFir= First\r\nS= Second\r\nT= Third\r\nFo= Fourth\r\nFif= Fifth\r\nThe outcome of the race will be:\r\n____ ____ ____ ____ ____
1 2 3 4 5
NAME _____ _____ _____ _____ _____
| | | | | |
FIRST | N(1)| N(6)| N(5)| Y(6)| N(3)|
|_____|_____|_____|_____|_____|
| | | | | |
SECOND | N(2)| Y(6)| N(5)| N(6)| N(2)|
|_____|_____|_____|_____|_____|
| | | | | |
THIRD | N(3)| N(5)| N(5)| N(5)| Y(5)|
|_____|_____|_____|_____|_____|
| | | | | |
FOURTH | Y(5)| N(4)| N(5)| N(5)| N(5)|
|_____|_____|_____|_____|_____|
| | | | | |
FIFTH | N(5)| N(5)| Y(5)| N(5)| N(5)|
|_____|_____|_____|_____|_____|\r\n
\r\nThe second number is (P+P^2+P^3+...) + 2, obviously even, so it cannot be a prime number.',NULL,0);
INSERT INTO comment VALUES (11140,1459,1626,'Gamer','re: Miraculous Melons ?????','2004-01-19 14:14:16',0,'I didn\'t call it by the name of the problem I found it from, rather something in the context so that I would get original responses rather than something copied and pasted *cough*',11042,0);
INSERT INTO comment VALUES (11141,1599,1301,'Charlie','','2004-01-19 14:21:12',3,'The first of the two numbers, in order to be prime, must actually be written in an even base. In an odd base, the value would be the sum of an even number of odd numbers, resulting in an even number, which can\'t be prime if it\'s larger than 2, which this would be. So by the first number, the base must be even. (for example 11 is prime in base 10, 12, 16 or 18).\r\n\r\nBut if the base is even, then the second number is even, which again, can\'t be prime, as it is also larger than 2, the only even prime.',NULL,0);
INSERT INTO comment VALUES (11142,1445,1626,'Gamer','','2004-01-19 14:36:21',0,'I think everyone thought Penny\'s solution was logical enough that everyone would have thought this was solved, so I posted the actual solution. :)',NULL,0);
INSERT INTO comment VALUES (11144,1599,4374,'Richard','ET?','2004-01-20 00:45:06',4,'Are you perhaps an extraterrestrial? You are very perceptive, that\'s for sure. Good solution!',11141,0);
INSERT INTO comment VALUES (11145,1589,5256,'Paul','Solution (Infinite Points)','2004-01-20 01:06:18',0,'Start with a small number e (for epsilon). Your first point is 1/2+e. The sequence goes as follows (all numbers are +e):\r\n1/2, 1/4,3/4, 1/8,3/8,5/8,7/8, 1/16,3/16,5/16,7/16,9/16,11/16,13/16,15/16, etc.\r\n\r\nJustification: Well I haven\'t taken the effort to completely justify, but if you try some it seems like the next point in this \"dyadic\" sequence always fills in the gap you need. Assuming this does continue to work (for e small enough), I figure there should be some argument with inequalities to justify.',NULL,0);
INSERT INTO comment VALUES (11146,1286,4098,'lovejoy','seems easy?','2004-01-20 01:20:39',0,'fourth\r\nsecond\r\nfifth\r\nfirst\r\nthird\r\nI think',NULL,0);
INSERT INTO comment VALUES (11147,1589,2682,'exoticorn','re: Solution (Infinite Points)','2004-01-20 02:52:12',0,'A nice thought, but it already fails for 5 points:\r\n\r\nThe sorted first 5 points are: 1/8, 1/4, 3/8, 1/2, 3/4\r\nNow this means that 1/2+e has to be greater than 3/5, and therefore e has to be greater than 0.1.\r\n\r\nBut if you now look at the first 3 points: 1/4, 1/2, 3/4, you\'ll notice that 1/4+0.1 is greater than 1/3, so there is no choice of e that will make this work.',11145,0);
INSERT INTO comment VALUES (11148,1589,153,'TomM','Possible correction to infinite point solution','2004-01-20 06:17:55',0,'A valiant effort, and on first look satisfying, but as exoticorn points out, it fails at 5 points. I suspect it fails similarly at every level k where k=(2^n)+1 points. \r\n\r\nI have not yet tested it out yet, but I\'d like to suggest that point A be just ε. Point B would be Paul\'s Point A (ε+(1/2)). Point C would be Paul\'s Point B (ε+(1/4), etc. This would relieve the \"strain\" on the first segment at levels k=(2^n)+1 points. It may just move that strain to a different point, (It does -- at level 3 with points ε, ε+.25 and ε+.5, ε must lie between .16 and .33, a very high value for a \"vanishingly small\" number) and the points may need to be added in each level range 2^(n-1)<k≤2^n in an order other than simply with numerators 1,3,5... to relieve that strain.\r\n\r\nAnother possibility might be to start with A=ε, B= 1-ε, and then start adding Paul\'s sequence with C=ε+.5, D=ε+.25, etc.',11145,0);
INSERT INTO comment VALUES (11149,1599,2716,'Federico Kereki','Solution','2004-01-20 08:06:02',3,'If the first number is more than two digits long, independently of the number base, you could write
\r\n111111....11 = 11 x 10101...1
\r\nso the number would be composite.
\r\nIf the first number is two digits long, the number base could be either 1 (not possible, because then a \"2\" wouldn\'t be used in the second number) or a prime, greater than 2, minus 1, which works out to an even number.\r\nresult eqtn. assoc \r\n-12 2 2 36 / (10 - 13)\r\n-12 3 2 24 / (27 - 29)\r\n-39 1 2 3 * (5 - 18)\r\n-39 2 1 (10 - 13) - 36\r\n-8.333333333333333D-02 2 1 (10 - 13) / 36\r\n-8.333333333333333D-02 3 1 (27 - 29) / 24\r\n-87 1 2 3 - (18 * 5)\r\n-87 3 1 (24 - 27) * 29\r\n 12 2 2 36 / (13 - 10)\r\n 12 3 2 24 / (29 - 27)\r\n 26 1 2 18 + (5 + 3)\r\n 26 3 1 (24 - 27) + 29\r\n 33 1 2 18 + (5 * 3)\r\n 33 2 1 (10 - 13) + 36\r\n 39 1 2 3 * (18 - 5)\r\n 39 2 1 (13 - 10) + 36\r\n 59 1 2 5 + (18 * 3)\r\n 59 2 1 (10 + 13) + 36\r\n 8.333333333333333D-02 2 1 (13 - 10) / 36\r\n 8.333333333333333D-02 3 1 (29 - 27) / 24\r\n 87 1 1 (18 * 5) - 3\r\n 87 3 1 (27 - 24) * 29\r\n
\r\n--------\r\nThe eqtn. column identifies the set of numbers used, and the assoc column lists which operator was done first. I\'ve put parentheses around those, even when not needed, for clarity.',11212,0);
INSERT INTO comment VALUES (11214,1391,3372,'Sam','re: Attempt at a computer solution -- results','2004-01-22 11:40:17',0,'There was also the possibility of exponentiation. Maybe that would allow you to get all three solutions?',11213,0);
INSERT INTO comment VALUES (11215,1583,4670,'e.g.','Hopeless...','2004-01-22 11:52:27',1,'I think this problem is hopeless without a computer, and I\'m quite interested in seeing how it is proved that the solution is optimum.
\r\nI don\'t like problems which are basically impossible to do by hand and so this gets a \"1\" rating -- sorry!',NULL,0);
INSERT INTO comment VALUES (11216,1289,4830,'Jils','One direction at a time','2004-01-22 12:05:49',2,'Its quite easy to see this one is you consider one direction at a time. Take a general rectangle of a x b squares and consider first the \"a\" direction. \r\n\r\nThere is first of all the largest possible side (a) \r\n\r\nThen there are 2 possible ways of placing the length (a-1), 3 ways of placing (a-2) etc all the way down to the single square where there are \"a\" ways. Adding up there is the sum:\r\n1+2+3+4+5+6+......+a\r\nThe sum of an arithmetic series is the average of the first and last term multiplied by the number of terms i.e. (1+a)*a/2\r\n\r\nSimilarly in the b direction there are (1+b)*b/2 possibilities. So overall in both directions there are (1+a)*a*(1+b)*b/4.\r\n\r\nThe values here give 11,550.\r\n\r\nInterestingly this can be taken to three dimensions - (1+a)*a*(1+b)*b/6 etc\r\n ',NULL,0);
INSERT INTO comment VALUES (11217,1289,4830,'Jils','re: One direction at a time','2004-01-22 12:08:15',0,'Sorry (1+a)*a*(1+b)*b*(1+c)*c/6',11216,0);
INSERT INTO comment VALUES (11218,1391,5285,'Ady TZIDON','an error in your DATA','2004-01-22 12:12:32',2,'You erroneously entered 3,5,18 in your DATA line \r\nin place of 3, 15, 18 -\r\ntherefore the executed program tried to solve another\r\npuzzle...\r\n\r\nGive it another trial + add EXPONENT as an option\r\n\r\nAdy',NULL,0);
INSERT INTO comment VALUES (11219,1583,4507,'Penny','re: Hopeless...','2004-01-22 12:34:57',0,'I have a very visual, basic impression that, in about a week or so, I\'ll be solving problems like this in no time.\r\n\r\n:-)',11215,0);
INSERT INTO comment VALUES (11220,1583,3172,'SilverKnight','re(2): Hopeless...','2004-01-22 12:38:25',0,'Huh!?!? Are we to understand, Penny, that you are learning to code?',11219,0);
INSERT INTO comment VALUES (11221,1289,4374,'Richard','re(2): One direction at a time','2004-01-22 13:18:40',0,'(1+a)*a*(1+b)*b*(1+c)*c/8? 2*2*2=8, not 6.\r\n',11217,0);
INSERT INTO comment VALUES (11222,1391,1301,'Charlie','re: an error in your DATA','2004-01-22 13:19:05',0,'I\'ve changed that 5 to a 15 and the results still do not have a triple:\r\n\r\n-12 2 2 36 / (10 - 13)\r\n-12 3 2 24 / (27 - 29)\r\n-13 1 1 (15 / 3) - 18\r\n-13 2 1 (10 - 36) + 13\r\n-39 1 2 15 - (18 * 3)\r\n-39 2 1 (10 - 13) - 36\r\n-8.333333333333333D-02 2 1 (10 - 13) / 36\r\n-8.333333333333333D-02 3 1 (27 - 29) / 24\r\n 12 2 2 36 / (13 - 10)\r\n 12 3 2 24 / (29 - 27)\r\n 13 1 2 18 - (15 / 3)\r\n 13 2 1 (36 - 10) - 13\r\n 39 1 1 (18 * 3) - 15\r\n 39 2 1 (13 - 10) + 36\r\n 8.333333333333333D-02 2 1 (13 - 10) / 36\r\n 8.333333333333333D-02 3 1 (29 - 27) / 24\r\n
\r\n----\r\nExponentiation is considered as in\r\nCASE 5 \r\n IF LOG(opnd(eq, 1)) * opnd(eq, 2) < 300 * LOG(10) THEN \r\n rslt1a = opnd(eq, 1) ^ opnd(eq, 2) \r\n ELSE \r\n rslt1a = 1: err1 = 1 \r\n END IF \r\n\r\nIt is the case that when the result is huge, above about 10^300, we ignore the answer,\r\nbut unmatched lines in the original output do show up as in:\r\n14348925 1 1 (3 ^ 15) + 18\r\nIt\'s just that none of these match anything.',11218,0);
INSERT INTO comment VALUES (11223,1391,1575,'DJ','re(2): an error in your DATA','2004-01-22 13:29:35',2,'The second error in the data was my fault -- I looked back at my solution, and the 29 is supposed to be 39... sorry about that =\\',11222,0);
INSERT INTO comment VALUES (11224,1391,3172,'SilverKnight','solution :-)','2004-01-22 13:42:05',3,'AHA!\r\n\r\nWith correct figures:\r\n\r\n(1) 13 = 18 - (15/3)\r\n(2) 13 = 36 - 10 - 13\r\n(3) 13 = 39 / (27-24)',NULL,0);
INSERT INTO comment VALUES (11225,1391,5285,'Ady TZIDON','DJ U BAD BOY','2004-01-22 13:50:58',0,'IT IS INDEED AN EASY PUZZLE-\r\nWHEN GIVEN THE RIGHT NUMBERS...\r\nWHOM SHOULD I CHARGE FOR MY VALUABLE TIME SPENT IN VAIN TRYING TO GET A \"13\" OUT OA WRONG 3-TUPLE???',NULL,0);
INSERT INTO comment VALUES (11226,1590,5285,'Ady TZIDON','SOLUTION','2004-01-22 13:56:21',0,'50=25+25=49+1\r\n65=64+1=49+16\r\n85=81+4=49+36\r\n\r\nady',NULL,0);
INSERT INTO comment VALUES (11227,1391,3172,'SilverKnight','re: DJ U BAD BOY','2004-01-22 14:00:29',0,'Send all request for remittance to:\r\n____________________________________________________________\r\n\r\nLevik c/o Flooble Enterprises\r\n2.71828 Transcendental Dr.\r\nNew York, NY 31415\r\n____________________________________________________________\r\n\r\nYou must include a self addressed stamped envelope.\r\nYou must specify the problem, and amount of time expended.\r\nNo requests larger than twice e ^ π (U.S. Dollars) will be honored.\r\nAll requests must be submitted in triplicate.\r\nPlease allow 6-8 weeks for delivery.\r\n\r\nThank you,\r\n\r\nFlooble Remittance Services\r\nremittance@flooble.com\r\n1-877-flooble',11225,0);
INSERT INTO comment VALUES (11228,1391,1301,'Charlie','re: solution :-) -- There\'s also... (variations)','2004-01-22 14:37:37',0,'(2) 13 = 36 - (10 + 13)\r\n\r\nand \r\n\r\n(1) -13 = 15/3 - 18\r\n(2) -13 = 10 - 36 + 13\r\n(3) -13 = 39/ (24 - 27)',11224,0);
INSERT INTO comment VALUES (11229,1591,4507,'Penny','There must be some bugs in this solution !!!','2004-01-22 14:45:02',3,'[note.... NOT TRYING TO CHEAT....this is now edited after Richard, SilverKnight and Charlie pointed out that the original answer was wrong...] \r\n\r\n[IT IS NOT CHEATING TO UPDATE SOLUTIONS AS LONG AS YOU STATE UP FRONT THAT YOU DID SO]\r\n\r\n[Updated now for the THIRD -- and LAST - time, after Charlie had to point out to me that when you subtract a negative number. you are really adding a positive number...SHEESH !!]\r\n\r\nAnswer: 6.6666666667 inches per bug, 20 inches combined for the three bugs.\r\n\r\nExplanation:\r\n\r\nWhen I saw that this puzzle involved spirals, and that the concept of a spiral was a real challenge even for the ancient Greek Archimedes, who remains to this day the most gifted of mathematicians (he was doing the equivalent of both differential and integral calculus when Newton\'s and Leibnitz\'s ancestors were hunting the wild boar in the forests of Europe), I decided I would need a little help solving it, so I quickly attended Harvard. (physics.harvard.edu)\r\n \r\nIf N bugs begin at the vertices of a regular N-polygon of length L, then at any point in time, they will be at the vertices of a regular N-polygon. This is the only formation that respects the symmetry of the N bugs. This polygon will diminish and rotate until it shrinks to a point in the center of the original polygon.\r\n\r\nThe relative speed of two adjacent bugs is constant. That is because the relative angle of the two bug\'s motion is always the same. If V is the absolute speed of the bugs, then the rate at which the separation between two adjacent bugs diminishes is:\r\n\r\nVr = V*(1-cos[2*pi/N radians])\r\n\r\nThen if N bugs start at a distance L apart, and if they always move at relative speed Vr, then they will meet in time T = L/(V*(1-cos[2*pi/N radians])) \r\n\r\nV is constant. \r\n\r\nThen each bug will have gone:\r\n\r\nV*T = L/(1-cos[2*pi/N radians])\r\n\r\nFor L=10, N=3 \r\n\r\n10/(1-cos[2*pi/N radians]) \r\n= 10/(1-cos[120 degrees])\r\n= 10/1.5\r\n= 6.6666666667\r\n \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\n\nEdited on January 23, 2004, 11:05 pm',NULL,0);
INSERT INTO comment VALUES (11230,1591,1301,'Charlie','solution','2004-01-22 14:54:39',3,'In the 4-bugs problem, each bug was headed directly for his neighbor and his neighbor\'s motion had no effect, so that the total distance traveled was exactly the initial distance to his neighbor.\r\n\r\nIn this problem, the decrease in distance results not only from each bug\'s individual motion, but is assisted by the pursued neighbor\'s motion, which has a component toward the pursuer. Thus the pursuer (as each is, in turn) does not have to travel as far as the full distance to the pursuee.\r\n\r\nIf the speed of motion is taken as 1, a vector diagram will have a 30-60-90 triangle, with the hypotenuse being 1 and the leg representing the component of motion toward the pursuer being 1/2. (The component perpendicular to the pursuer\'s motion being (√3)/2, but that\'s beside the point.)\r\n\r\nAs a result, the pursuer is contributing a speed of 1, while the pursuee is contributing a speed of 1/2 in closing their gap. So each pursuer need go only 2/3 the full original distance to his neighbor (while the neighbor in effect reduces the distance by 1/3--a 2:1 ratio), or six and two thirds inches.',NULL,0);
INSERT INTO comment VALUES (11231,1591,1301,'Charlie','re: solution','2004-01-22 14:59:13',3,'Oh yes, since each bug goes 6+2/3 inches, as a group they have gone 20 inches.',11230,0);
INSERT INTO comment VALUES (11232,1591,4507,'Penny','re(2): solution','2004-01-22 15:03:05',0,'Well, Charlie, our answers only differ by 224,535%. My three bugs are gonna be a lot more exhausted than yours....\r\n\r\n:-)\r\n',11231,0);
INSERT INTO comment VALUES (11244,1591,1301,'Charlie','re(2): There must be some bugs in this solution !!!','2004-01-22 17:46:55',0,'Yes, Penny\'s calculator was in degree mode but she entered the angle in radians.',11239,0);
INSERT INTO comment VALUES (11233,1345,5286,'franny','The flaw in this puzzle','2004-01-22 15:30:36',0,'Lesa posted a solution that works; however, for this to work, the red shirt that Betty buys has to be her 2nd shirt. I think this is an assumption that very few people would make. Most people would assume that it is Betty\'s first shirt because she is buying it at the same time as Carol is buying the $40 shirt--the Blue one--which is Carol\'s first shirt. That is the major problem with this puzzle--the time line is presented in a very screwed up manner. If Betty buys the red shirt as her first one, nothing works out correctly as far as money goes, and believe me, I tried every possible combination!',NULL,0);
INSERT INTO comment VALUES (11234,1574,2899,'Brian Wainscott','re: will this work','2004-01-22 15:40:30',0,'No. There are a lot of possibilities that you are not considering. Remember, you have no idea which of the 12 coins is which. It is very possible that all 6 of your initial pairs will balance. Then what will you do? You then have 6 pairs, which you know are equal to each other, but you don\'t know which pairs are light and which are heavy. You have used 6 weighings, and essentially returned to the initial problem but with 6 unknown items (pairs of coins) instead of 12.\r\n\r\nBut don\'t give up -- it is a very interesting problem to think about....',11201,0);
INSERT INTO comment VALUES (11235,655,4718,'Jack Squat','no brackets','2004-01-22 15:48:04',0,'I don\'t recall reading anything about the use of brackets. \r\n\r\nTake a 3. Now divide it by 7. Now add 3 to that. Now multiply that by 7. You have 24.',NULL,0);
INSERT INTO comment VALUES (11236,660,4718,'Jack Squat','more slices','2004-01-22 15:58:50',0,'Better yet, roll the pizza into a ball, just one cut gives several pieces.',NULL,0);
INSERT INTO comment VALUES (11237,1289,5097,'Cindy','My answer','2004-01-22 16:27:32',0,'I got 44099\r\n\r\nI made a table 20 x 20. (which I can\'t cut and paste here since it\'s too big.) And calculated all rectangle/square sizes. Those 1 square tall, could fit on each line 20 times. Those 2 squares tall 19 times, those 3 squares 18 times, etc. Each total (expept the perfect squares, would be multiplied by 2, to account for the vertical as well.... Does that make sense?',NULL,0);
INSERT INTO comment VALUES (11238,1459,5097,'Cindy','re(2): Solution','2004-01-22 16:37:41',0,'poopie....',11211,0);
INSERT INTO comment VALUES (11239,1591,4374,'Richard','re: There must be some bugs in this solution !!!','2004-01-22 16:45:58',0,'L/(1-cos[2*pi/N]) with L=10 and N=3 is \r\n10/(1-cos(120 degrees))=10/(1-(-1/2))=\r\n=10/(3/2)=20/3=Charlie\'s answer.\r\nThis time I don\'t find your comment humorous.\r\n\r\n',11229,0);
INSERT INTO comment VALUES (11240,1591,5287,'ackv','solution','2004-01-22 16:51:02',0,'The path of each bug will trace a circle whose diameter will be 10\". Since the bugs all met at the center. It is 1/4th of the circumference of the circle. So, (22/7)*2.5\".',NULL,0);
INSERT INTO comment VALUES (11241,1289,4374,'Richard','re: My answer','2004-01-22 16:59:17',0,'20 x 20 should give 44100 by the formula n(n+1)m(m+1)/4 (see previous comments) with n=m=20, so you missed one. The problem statement is for 20 x 10, however, so the answer to the problem as stated is 11550.',11237,0);
INSERT INTO comment VALUES (11242,1591,4507,'Penny','re(2): There must be some bugs in this solution !!!','2004-01-22 17:21:58',0,'Well, at least the formula was right......\r\n \r\n\n\nEdited on January 22, 2004, 5:42 pm',11239,0);
INSERT INTO comment VALUES (11245,1026,5288,'David Frazer','re: 182','2004-01-22 18:12:37',0,'How did you arrive at this solution?',11086,0);
INSERT INTO comment VALUES (11243,1391,5285,'Ady TZIDON','re(2): DJ U BAD BOY','2004-01-22 17:34:06',0,'I WAIVE ALL MY CLAIMS TO COMPENSATION. My loss was offset by the fun provided by your methamagical address.\r\nplease call me at (314)-1-592-6535 or PHI-1618\r\n\r\nADY\r\n',11227,0);
INSERT INTO comment VALUES (11246,1591,3172,'SilverKnight','re(3): There must be some bugs in this solution !!!','2004-01-22 18:43:34',0,'That can happen when you get your formulas off a website and you don\'t verify your answer, or figure out the meaning behind the formula.\r\n\r\nBTW, Penny, you updated your answer (below) with \'20\' but that\'s not quite right either....',11244,0);
INSERT INTO comment VALUES (11247,1591,4507,'Penny','re(4): There must be some bugs in this solution !!!','2004-01-22 19:23:52',0,'SK: \"BTW, Penny, you updated your answer (below) with \'20\' but that\'s not quite right either....\"\r\n \r\nBut I did make it clear that it was updated, that it was wrong originally... Isn\'t 20 inches per bug (60 total) the right answer? 20 (total) was Charlie\'s answer, and you don\'t seem to be picking on him. I guess you prefer to fight with girls. Anyway, that calculator of mine was a free Internet download, and it\'s been worth every cent!! \r\n\r\n\r\n\r\n\n\nEdited on January 22, 2004, 7:32 pm',11246,0);
INSERT INTO comment VALUES (11248,1591,4507,'Penny','re(2): solution','2004-01-22 20:23:06',0,'\"...each bug goes 6+2/3 inches...\"\r\n\r\nStop that, Charlie, you\'re making him jealous !!!!!',11231,0);
INSERT INTO comment VALUES (11249,1591,3172,'SilverKnight','re(5): There must be some bugs in this solution !!!','2004-01-23 00:37:21',0,'umm... no... Charlie\'s answer is 20/3 inches each (or 20 inches total for ALL 3).',11247,0);
INSERT INTO comment VALUES (11250,1591,1301,'Charlie','re: There must be some bugs in this solution !!!','2004-01-23 00:40:34',0,'Re:\r\n\"10/(1-cos[2*pi/N radians]) \r\n= 10/(1-cos[120 degrees]) \r\n= 20\"\r\n\r\nSince cos(120 degrees) = -.5, it follows that\r\n1-cos(120 degrees) = 1.5, and\r\n10/1.5 = 6.666666666666... \r\n\r\n',11229,0);
INSERT INTO comment VALUES (11251,1599,5285,'Ady TZIDON','SOLUTION','2004-01-23 03:28:43',3,'the answer: THERE IS A MISTAKE SOMEWHERE...\r\nthe explanation:\r\n\r\nThe second number may be written as 11111...2=\r\nq*(1111...0)+2= which implies:\r\n q (the base of the counting system)>2\r\n q is odd - OTHERWISE the second number is even THEREFORE NOT A PRIME\r\n\r\nthe first number 1+q+q^2+q^3+...q^(2k-1)=\r\n (1+q)*(1+q^2+q^4+...q^(2k-2))\r\n is even for an odd q\r\n\r\nif the first number is odd than the second is even\r\n\r\nconclusion: the two number differ in parity therefore cannot be both primes.\r\nady\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (11252,1289,4830,'Jils','re(3): One direction at a time','2004-01-23 03:34:28',0,'Yep, that is so!!! I think I need a holiday!',11221,0);
INSERT INTO comment VALUES (11253,1591,2716,'Federico Kereki','re: solution','2004-01-23 08:59:40',1,'Nope, the path is spiral-like, and not a circle.',11240,0);
INSERT INTO comment VALUES (11254,1293,3172,'SilverKnight','solution','2004-01-23 09:47:03',3,'zero\r\n________________________\r\n\r\nOnly the one\'s digit is relevant here, so 1 is congruent to 11 is congruent to 91, etc... and the zeroes (10, 20, 30, etc...) all end in zero... so we can ignore them.\r\n\r\nSo, for each of the nine \'congruence sets\' such as 1, 11, 21, 31, ... 91 through 9, 19, 29, etc... each member in the set, raised to 99th power, end in the same digit.\r\n\r\nAnd all nine of the \'congruence sets\' have 10 elements.... since we\'re adding them all up 10x(ANY digit) ends in zero.\r\n\r\nSo, the total summation must end in zero.\r\n',NULL,0);
INSERT INTO comment VALUES (11255,1293,5285,'Ady TZIDON','SOLUTION','2004-01-23 09:57:59',0,'It must be zero, since whatever result is achieved from the summation of the first ten members (actually it is 5 but that is irrelevant) is then repeated nine more times so we have summation of this digit 10 times .\r\n\r\nRemark(NOT NEEDED TO SOLVE THE PUZZLE): the last digit of Nth power of any number is equal to the last digit of Kth power of said number iff(=if and only if) M mod 4= N mod 4 i.e. consider the 3th power instead of the 99th.\r\n\r\nady\n\nEdited on January 23, 2004, 10:29 am',NULL,0);
INSERT INTO comment VALUES (11256,1293,5285,'Ady TZIDON','re: solution','2004-01-23 10:03:35',1,'I did not see your solution- mine is truly isomorphic with yours- but I saw it only after submission...\r\nBIG MINDS THINK ALIKE\r\nady',11254,0);
INSERT INTO comment VALUES (11257,1293,1301,'Charlie','re: solution','2004-01-23 10:07:55',0,'Wow SK, I had gone through all of the below before reading your solution and realizing that the number that I would be multiplying that final 8 by was 10:\r\n\r\nA number ending in a digit 0 will have powers that all end in 0.\r\n\r\nA number ending in 1 will have powers all ending in 1.\r\n\r\nA number ending in 2 will have powers with ending digits that cycle 2, 4, 8, 6 in a cycle of 4. As 99 is congruent to 3 mod 4, 2^99 ends in 8, the third in the cycle.\r\n\r\nA number ending in 4 will have powers with ending digits that cycle 4, 6 in a cycle of 2. As 99 is congruent to 1 mod 2, 4^99 ends in 4, the first in the cycle.\r\n\r\nA number ending in 5 will have powers all ending in 5.\r\n\r\nA number ending in 6 will have powers all ending in 6.\r\n\r\nA number ending in 7 will have powers with ending digits that cycle 7, 9, 3, 1 in a cycle of 4. As 99 is congruent to 3 mod 4, 7^99 ends in 3, the third in the cycle.\r\n\r\nA number ending in 8 will have powers with ending digits that cycle 8, 4, 2, 6 in a cycle of 4. As 99 is congruent to 3 mod 4, 8^99 ends in 2, the third in the cycle.\r\n\r\nA number ending in 9 will have powers with ending digits that cycle 9, 1 in a cycle of 2. As 99 is congruent to 1 mod 2, 9^99 ends in 9, the first in the cycle.\r\n\r\nAdding these up mod 10, a complete decade sums to 8.\r\n\r\nMultiply that by 10, and the last digit is of course zero as SK has said.\r\n\r\nAt least my method would work even if it had started at say 11^99.\r\n\r\nSimpler still is the straightforward way of using the extended precision capability of UBASIC:\r\n\r\n10 for i=1 to 99\r\n20 t=t+i^99\r\n30 next\r\n40 print t\r\nrun\r\n 5812206997600753463391342462747345840904209101124814483884686650470731323698643\r\n56708140949517237598499723088539628510405242259308985010276468113327453424717072\r\n493455029858959571265494893360597217500\r\nOK\r\n
\r\n----\r\nwhere the last of the 198 digits is indeed zero.\r\n\r\n\r\n',11254,0);
INSERT INTO comment VALUES (11258,1293,5285,'Ady TZIDON','re(2): solution','2004-01-23 10:21:36',0,'THE RESULT IS STILL ZERO AND ALL I WROTE IS CORRECT EXCEPT THE CYCLE BEING FOUR AND NOT FIVE i.e. 99=3 mod 4.\r\n being a newcomer to the site I do not know how to edit my solution and so I post this comment\r\n\r\nady',11257,0);
INSERT INTO comment VALUES (11259,1293,1301,'Charlie','re(2): solution --- Gosh!!!..','2004-01-23 10:22:38',0,'... I left out 3:\r\n\r\nA number ending in 3 will have powers with ending digits that cycle 3, 9, 7, 1 in a cycle of 4. As 99 is congruent to 3 mod 4, 3^99 ends in 7, the third in the cycle. \r\n\r\nThat makes one decade add up to 5 mod 10.\r\n\r\n',11257,0);
INSERT INTO comment VALUES (11260,1293,3172,'SilverKnight','re(2): solution','2004-01-23 10:36:32',0,':-)\r\n\r\nWell, in the interests of being honest... so did I (though I didn\'t do any computer program), and then after realizing that they all \'cancel\' I deleted that section.',11257,0);
INSERT INTO comment VALUES (11261,1293,5285,'Ady TZIDON','re(3): solution --- Gosh!!!..','2004-01-23 10:38:04',1,'right you are CHARLIE\r\nActually it is only the 5 that counts within a decade since 5+t and 5-t complement each other e.g. 2^3=8 8^3=2 8+2=0 (all taken mod 10) so go 1&9 3&7 4&6.... only 5 and 0 left.\r\nady',11259,0);
INSERT INTO comment VALUES (11262,1293,1301,'Charlie','re(3): solution','2004-01-23 10:38:36',0,'The way to edit one\'s comments is to select that comment, and below the comment\'s text will be a place where it says \"This is your comment\". Near that is a link that says \"Edit comment\". But this feature is generally looked upon as to be used only to correct typos, so a follow-up note is good as a general practice anyway (as I did in correcting my leaving out of the digit 3 in my analysis).\r\n\r\nRegarding your correction to\r\n\"Remark(NOT NEEDED TO SOLVE THE PUZZLEW): the last digit of Nth power of any number is equal to the last digit of Kth power of said number iff(=if and only if) M mod 5= N mod 5 i.e. consider the 4th power instead of the 99th.\"\r\n\r\nFirst I assume you mean K rather than M as M has not been introduced. And your correction indicates mod 4 rather than mod 5. So it would read\r\n\r\nthe last digit of Nth power of any number is equal to the last digit of Kth power of said number iff(=if and only if) K mod 4 = N mod 4 i.e. consider the 3rd power instead of the 99th.\r\n\r\nActually the word should be \"if\" rather than \"iff\", as K = N mod 4 (which is another way of saying K mod 4 = N mod 4) is sufficient for the last digits to be the same, but not always necessary. For example, 4^3 ends in 4 as does 4^5 even though 3 and 5 have different congruences mod 4. The \"iff\" holds in both directions only for numbers ending in 2, 3, 7 and 8; the other digits have cycles of length 1 or 2.\r\n',11258,0);
INSERT INTO comment VALUES (11263,1293,5285,'Ady TZIDON','re(4): solution','2004-01-23 10:41:49',0,'thanks\r\ni did it\r\nady',11262,0);
INSERT INTO comment VALUES (11264,1466,5285,'Ady TZIDON','SOLUTION','2004-01-23 12:04:06',0,'top+bottom=pi*(a^2+b^2)\r\nside surface=h*(b/a)*pi*(a+b)\r\nadd up =pi*(a^2+b^2+h*(b/a)*(a+b))\r\n\r\njust by looking at it\r\nady\n\nEdited on January 23, 2004, 12:09 pm',NULL,0);
INSERT INTO comment VALUES (11265,1466,1301,'Charlie','solution','2004-01-23 12:14:20',0,'The slant height, s, of the truncated cone is s = ã((b-a)^2+h^2).\r\n\r\nThe slant height that the full, untruncated cone (let\'s call it r, as it will later serve as a radius) would have then is given by\r\n\r\nr/s = b/(b-a)\r\nor\r\nr = b*s/(b-a)\r\n\r\nConsider the conical surface of the truncated cone as made of paper, and cut along a line perpendicular to the top and bottom. Then lay this developpable surface flat. The arc formed by the top and the arc formed by the bottom will be concentric, as each will be perpendicular to the (now duplicated) cut line at either end of the curved strip. The base arc will be the outer arc, with a radius of curvature equal to r, the slant height of the fully restored cone.\r\n\r\nThe circumference of the bottom of the cone before it was laid out was 2*pi*b.\r\n\r\nThe fraction of a circle that the two arcs span about their common center is then 2*pi*b/(2*pi*r) = b/r.\r\n\r\nIf complete, the outer circle would have area pi*r^2, but that must be multiplied by b/r, resulting in pi*b*r. Likewise the inner sector of a circle to be subtracted out is pi*a*(r-s). After the subtraction we have \r\n\r\npi*(b*r-a*(r-s))\r\n\r\nThis can be exemplified in a program:\r\n\r\npi = 4 * ATN(1)\r\nDO\r\n INPUT \"a,b,h\"; a, b, h\r\n s = SQR((b - a) ^ 2 + h * h)\r\n r = b * s / (b - a)\r\n PRINT \"Area is\"; pi * (b * r - a * (r - s))\r\nLOOP\r\n\r\nwith some sample output:\r\na,b,h? 1,2,3\r\nArea is 29.80377\r\na,b,h? 5,6,7\r\nArea is 244.3586\r\na,b,h? 7,10,3\r\nArea is 226.587\r\n
\r\n------\r\nThere are alternative formulations for the area of the smaller sector, which are equivalent.\r\n\r\nThis is the area of the side only. For the whole frustum, add in the area of the top and bottom, pi*(a^2 + b^2).\n\nEdited on January 23, 2004, 12:17 pm',NULL,0);
INSERT INTO comment VALUES (11266,1466,4374,'Richard','Solution','2004-01-23 13:12:00',3,'If we develop the surface of a full cone with radius R and height H we get a \"piece of pie\" with circular edge of length 2*pi*R cut from the \"pie\" of radius S=sqrt(R^2+H^2). This piece has area (R/S)*pi*S^2 = pi*R*S. By similar triangles, the given truncated cone is truncated from a cone of radius b and height h*(b/(b-a)) = h + h*(a/(b-a)) = h + h\'. The surface area of the truncated cone can thus be found by subtraction of the surface area of a full cone of height h\' and radius a from that of a full cone of height h+h\' and radius b. Thus the surface area of the truncated cone is pi*(b*t-a*s) where t=sqrt(b^2+(h+h\')^2) and s=sqrt(a^2+h\'^2).',NULL,0);
INSERT INTO comment VALUES (11267,1569,1301,'Charlie','re: I think this pseudocode will do it','2004-01-23 14:07:48',0,'The only differences I can see between Penny\'s solution and the official one are that:\r\n\r\n1. The official one does not store an array of all the possible orders of letter positions to be changed, but rather generates each new one as the processing goes along.\r\n\r\n2. The official solution tries each of the other 25 letters at each position, then does a binary search on the word list, rather than the sequential search for a word larger than PRIORWORD. I\'m not sure the \"larger\" part would allow a transition from, say \"ford\" to \"food\", unless there\'s something I missed seeing about an initialization of PRIORWORD. Oh, yes, I see it at S0005. The only disadvantage is the slowness of a sequential search.\r\n\r\nOther than that it\'s basically the same--just differences between a long string vs. an array of strings and things like that.\n\nEdited on January 23, 2004, 2:10 pm',11094,0);
INSERT INTO comment VALUES (11268,58,4718,'Jack Squat','Differnt first weighing','2004-01-23 15:11:06',3,'1st weigh: split flour into 10-lb bags.\r\nResult: 2 10-pounders (probably in multiple bags)\r\n\r\n2nd weigh: 9-lb weight on one side against 5-lb weight plus enough flour from one bag to have scale balance.\r\nResult: 1 10-pounder, 1 4-pounder, 1 6-pounder\r\n\r\n3rd weigh: repeat 2nd step, pouring from the 6-lb bag to match the two weights.\r\nResult: 1 10-pounder, 2 4-pounders, 1 2-pounder\r\n\r\n4th & 5th weighs: Repeat 2nd and 3rd steps pouring from the 10-lb bag to match the weights.\r\nResult: 4 4-pounders, 2 2-pounders\r\n\r\n6th - 9th weighs: For the next 4 weighs, split a 4-lb bag into 2 2-lb bags.\r\nResult: 10 2-pounders, and probably a crapload of loose flour in the air.',NULL,0);
INSERT INTO comment VALUES (11269,1380,4197,'luminita','to SK','2004-01-23 17:08:49',0,'yes, that\'s what I had in mind - I was wrong because of an optical illusion: I supposed the figure is in 3D.\r\nOf course I had a problem in interpreting angles in space, but I considered the projections. And so on ...',11103,0);
INSERT INTO comment VALUES (11270,706,5297,'NK','Another Approach','2004-01-23 18:19:54',0,'I arrived at an answer of 6 with the following approach:\r\n\r\nLet x = 20! = 2432902008176640000\r\n\r\nThus, (20!)! = x! = (x)(x-1)(x-2)…(21)(x)\r\n\r\nIf we define y = (x-1)(x-2)…(21), then\r\n\r\n(20!)! = y*x^2\r\n\r\nx^2 has a last non-zero digit of 6 (note the last non-zero digit of 4 in x above). \r\n\r\ny, having a very large number of powers of 10, will end in many more zeros than x^2. \r\n\r\nMultiplying x^2 by y will, therefore, not affect the last non-zero digit of x^2. Thus, (20!)! has a last non-zero digit of 6.',NULL,0);
INSERT INTO comment VALUES (11271,1466,5285,'Ady TZIDON','general equation:','2004-01-24 02:33:31',3,'\r\n\r\n \r\n\r\n\r\n\r\n\r\n\r\ngeneral equation:\r\n--------------------------------------------------------------------------------\r\n\r\n \r\n \r\nFrustrum (= truncated cone): \r\n \r\n Volume = 1/3 (pi)* h *( a^ 2 + b^ 2 + a*b )\r\n\r\nSurface Area = Lateral Area + Area of Base 1 + Area of Base 2\r\n\r\n\r\nLA = (pi)* hs * ( a+b ) \r\nhs = SQROOT [ (a-b) ^2 + h^ 2 ]\r\nAB 1 = (pi)*a^2 \r\nAB 2 = (pi)*b^2 \r\nthat replaces my previous entry\r\n\r\nady\r\n\r\n\r\n\r\n\r\n--------------------------------------------------------------------------------\r\n \r\n \r\n',NULL,0);
INSERT INTO comment VALUES (11272,1293,5306,'Purna','','2004-01-24 05:04:34',0,'',NULL,0);
INSERT INTO comment VALUES (11273,1293,5306,'Purna','','2004-01-24 05:04:45',0,'',NULL,0);
INSERT INTO comment VALUES (11274,1293,5306,'Purna','last digit','2004-01-24 05:08:27',3,'(1)^99+(2)^99+....+(98)^99+(99)^99\r\n=1+(((2)^100)/2)+(((3)^100)/3)+....+(((98)^100)/98)+(((99)^100)/99)\r\n=1+last digit(2/2)+last digit(3/3)+last digit(4/4)+....+last digit(99/99)\r\n=1+1+1.....99 times(last digit)\r\n=9.\r\nso the last digit of the given series is 9.',NULL,0);
INSERT INTO comment VALUES (11275,670,5306,'Purna','Digit number','2004-01-24 06:17:38',3,'For a given number to be divisible by 13, the sum of all the digits of the given number must be divisible by 13.\r\nSo when we add the 50 digits we get \r\n(49+26th digit) which has to be divisible by 13.So the smallest value should be 3 which satisfies the given condition.\r\nSo the 26th digit has to be 3.\r\n',NULL,0);
INSERT INTO comment VALUES (11276,1284,5306,'Purna','Chessboard','2004-01-24 06:32:37',3,'The total number of occurences is \r\n 64C3\r\nand the desirable outcomes is\r\n 16C3\r\n\r\nSo the required probability is\r\n\r\n 16\r\n C \r\n 3\r\n ---------------\r\n 64\r\n C\r\n 3 \r\n =0.037878.....',NULL,0);
INSERT INTO comment VALUES (11277,1286,5306,'Purna','Horse Race','2004-01-24 07:11:51',3,'Order of finish\r\n\r\nPosition\r\n 1.Fourth horse\r\n 2.Second horse\r\n 3.Fifth horse\r\n 4.First horse\r\n 5.Third horse',NULL,0);
INSERT INTO comment VALUES (11278,1284,1301,'Charlie','re: Chessboard','2004-01-24 10:11:43',0,'I think what you are solving here is the probability that all three will lie on one of the two main diagonals without regard to whether they are on the same one or not.',11276,0);
INSERT INTO comment VALUES (11279,1394,4507,'Penny','Official solution (spoiler)','2004-01-24 10:24:18',2,'http://rec-puzzles.org/new/sol.pl/analysis/boy.girl.dog\r\n\r\nI would not have copied this one verbatim from the Internet. I would have changed the participants from \"boy, girl, dog\" to \"hockey player, geisha girl and aardvark, moving at 8mph, 3 mph and 20mph\" \r\n\r\n:-)\n\nEdited on January 24, 2004, 10:28 am',NULL,0);
INSERT INTO comment VALUES (11280,230,5299,'Nick','','2004-01-24 11:53:11',0,'',NULL,0);
INSERT INTO comment VALUES (11281,1277,5299,'Nick','','2004-01-24 11:58:37',0,'',NULL,0);
INSERT INTO comment VALUES (11282,1345,5299,'Nick','','2004-01-24 12:04:53',0,'',NULL,0);
INSERT INTO comment VALUES (11283,1394,4374,'Richard','re: Official solution (spoiler)','2004-01-24 12:25:45',0,'Your link gives an interesting argument that, however, assumes that at some point the dog is between the boy and the girl. Reading the problem carefully, it seems quite possible that the dog will take off at ten miles an hour and keep going straight ahead for the hour and never be between the boy and the girl. The problem is not what I would call well-posed, in any event.',11279,0);
INSERT INTO comment VALUES (11284,1466,4374,'Richard','re: general equation:','2004-01-24 12:36:19',0,'Nobody cares about the area of the base which is a simple circle of radius b. It is the area of the rest that counts. If the cone were not truncated and had height H, this area would be pi*b*H. Because it is truncated, we need to subtract pi*a*h\' where h\' is the height of the cone that was cut off in the trucation. Aside from justifying the pi*b*H formula, the problem is to find h\' (hence H also) in terms of h, and this can be readily done using similar triangles. Your formulas are way different from what is correct.\r\n\r\n(Added in later edit: Sorry. I was a bit confused. Your formulas are correct according to \"Handbook of Mathematical Formulas and Integrals, 2nd ed.\" by Alan Jeffrey. The LA formula differs considerably in form from the one involving the given variables a,b, and h that comes out directly using the difference method, but they do give exactly the same result.)\r\n\r\n\n\nEdited on January 26, 2004, 5:25 pm',11271,0);
INSERT INTO comment VALUES (11285,1394,1301,'Charlie','thoughts','2004-01-24 14:34:48',1,'This is the same as the Bee problem in reverse (here and here). In the bee problem, the two travelers bounding the area in which the bee shuttles back and forth approach from being apart. Here the two travelers bounding the area in which the dog is free to shuttle start together and move apart.\r\n\r\nThe problem is that the bee problem can start from either of the two travelers or anywhere in between and still it happens that there are infinitely many reversals at the end. Here the infinitely many reversals come at the beginning, so there is no defined direction in which the dog is facing at the beginning, and infinitely many reversals, so that\'s neither odd nor even.\r\n\r\nSince the bee problem could have begun with the shuttler anywhere in between the outliers, this can end up with the dog anywhere between the boy and the girl.',NULL,0);
INSERT INTO comment VALUES (11286,670,4374,'Richard','re: Digit number','2004-01-24 17:51:29',0,'You write \"For a given number to be divisible by 13, the sum of all the digits of the given number must be divisible by 13.\" This is false, as 13 itself testifies. The sum of the digits is divisible by 9 if and only if the number is divisible by 9, but with 13 in place of 9, this doesn\'t work. The digits must be weighted by numbers congruent to the power of 10 of their place, modulo the divisor in question. With the divisor 9, things work out so nicely because 10^n is always congruent to 1 modulo 9. Modulo 13, the powers of 10 are not all congruent to 1, however.\r\n \r\n',11275,0);
INSERT INTO comment VALUES (11287,1554,5312,'les1021','re: The answer','2004-01-24 19:40:45',0,'ok thats just gay cuz dat didnt even make any sense cuz duh they r goin 2 reply but your trying to figure out who is a liar and who is a knight retard mother fucker!!!!!!!!',10818,0);
INSERT INTO comment VALUES (11288,1394,4507,'Penny','Question','2004-01-24 20:02:59',4,'It is not clear to me how all three can start walking simultaneously from the same starting point (the puzzle says they are initially standing together) in the same direction, and the dog still be trotting back and forth between the boy and the girl. The dog is faster than the boy, so by the time the boy has gotten any distance ahead of the girl, the dog will be ahead of him. So when does the dog initially embark (no pun intended), and when does he start trotting back and forth? Is there some subtle calculus here that escapes me? \n\nEdited on January 24, 2004, 8:05 pm',NULL,0);
INSERT INTO comment VALUES (11289,1394,4374,'Richard','re: Question','2004-01-24 20:43:45',0,'There can be no initial time for the dog to reverse its course, so the dog does not reverse its course. Hence the dog is 10 miles ahead of the starting point one hour after the start. The problem would make more sense if it were given that the dog first reverses its course at some definite time T and then goes back and forth after that.',11288,0);
INSERT INTO comment VALUES (11290,1394,153,'TomM','re: Question: \"Abandon All Common Sense...\"','2004-01-24 20:51:54',0,'This is an exercise in the pure mathematics of a situation. The problem says to ignore certain real-world complications. Unfortunately ignoring those complications means either abandoning all common sense or divorcing the mathematics of the puzzle from the situation used to set it up. \r\n\r\nIn the first few moments, the situation makes no sense in the real world where the dog can\'t turn instantaneously nor move back and forth in infinitesimal increments in infinitesimal time units. It is hard to picture in the forward direction at all. \r\n\r\nThe problem is much better conceptualized as a variant on the bee problem played backward. The infinite number of instantaneous switchbacks in infinitesimal increments still don\'t make any real-world sense, but at least they are easier to imagine.',11288,0);
INSERT INTO comment VALUES (11291,1459,5315,'Raymond Chow','Possible Solution','2004-01-24 21:41:19',0,'coming in 1st is wearing the:\r\ngreen shirt, green suspenders, and blue tie\r\ncoming in 2nd is wearing the:\r\nblue shirt, red suspenders, white tie\r\ncoming in 3rd is wearing the:\r\nred shirt, white suspenders, red tie\r\nand finally the guy being question and 4th is:\r\nblue shirt, blue suspenders, and green tie',NULL,0);
INSERT INTO comment VALUES (11292,1394,4507,'Penny','Sit !! Stay !!','2004-01-24 22:47:48',0,'If you change the puzzle to state that the boy and the girl start walking simultaneously, and the dog waits obediently for five minutes before taking off after them, then the puzzle makes more sense.\r\n\r\nBoy\'s speed = 4mph = 0.07 miles/minute\r\nGirl\'s speed = 3mph = 0.05 miles/second\r\nDog\'s speed = 10 mph = 0.17 miles/minute\r\n\r\nAfter 5 minutes, the boy has gone 0.35 miles, the girl 0.25, and then the dog em\"barks\".\r\n\r\nAfter another 2.08 minutes, the boy has gone to 0.35 + 0.07*2.08 = 0.50. The girl has gone to 0.05*2.08 + 0.25 = 0.35. The dog has reached the girl at 0.17*2.08 = 0.35\r\n\r\nIn the next 1.5 minutes, the boy goes to 0.50 + 0.07*1.5 = 0.61. The dog reaches the boy by going to 0.35 + 1.5*0.17 = 0.61. The girl gets to 0.35 + 1.5*0.05 = 0.43\r\n\r\nNow the dog reverses course for the first time. He is 0.61 - 0.43 = 0.18 away from the girl, and trots to her at relative speed 0.17 + 0.05 = 0.22 miles/minute. It takes the dog 0.82 minutes to get to the girl. So now the boy is at 0.61 + 0.82*0.07 = 0.67. The girl and the dog are at 0.43 + 0.82*0.05 = 0.47. \r\n\r\nOnce again the dogged hound reverses course. In the next 2 minutes the dog goes to 0.47 + 0.17*2.00 = 0.81, where he meets the boy. The girl goes to 0.47 + 0.05*2.00 = 0.57.\r\n\r\nNow the dog turns and heads for the girl. They are now 0.81 - 0.57 = 0.24 mile apart, which the dog covers at relative speed 0.17 + 0.05 = 0.22 miles/minute. This takes the dog 0.92 minute. Now the dog and the girl are at \r\n0.57 + 0.92*0.05 = 0.62. The boy is at 0.81 + 0.92*0.07 = 0.87.\r\n\r\netc............\r\n\r\nIf I could write a program at this point, I would have the answer. (I will have Visual Basic on my desktop in a week or two. That should be interesting.) \r\n\r\n\n\nEdited on January 24, 2004, 10:54 pm',NULL,0);
INSERT INTO comment VALUES (11293,1509,5320,'Jen T','Hmmm.. so twhat day then....','2004-01-24 23:52:45',0,'March 14 1996',NULL,0);
INSERT INTO comment VALUES (11294,1394,5285,'Ady TZIDON','re: Sit !! Stay !!','2004-01-25 07:15:47',0,'I wholly agree with Penny. \r\nThe \"simultaneous\" start invites variety of interpretations and without any refinements leaves the final location of Rex undefined.\r\n\r\nAsy',11292,0);
INSERT INTO comment VALUES (11295,1294,4507,'Penny','Solution','2004-01-25 12:18:54',3,'Zero',NULL,0);
INSERT INTO comment VALUES (11296,1294,1626,'Gamer','re: Solution','2004-01-25 12:28:03',0,'When you \"move\" the zero, there won\'t be a left end to place it at.',11295,0);
INSERT INTO comment VALUES (11297,1294,4507,'Penny','re(2): Solution','2004-01-25 13:22:47',0,'Gamer: \"When you \'move\' the zero, there won\'t be a left end to place it at.\"\r\n\r\nSure there will. Zero can be written with more than one position.\r\n\r\nZero before the move: 0000000\r\nZero after the move: 0000000 \r\n',11296,0);
INSERT INTO comment VALUES (11298,1294,4507,'Penny','Question','2004-01-25 13:25:14',4,'Ravi, did you mean \"the smallest nonnegative number\"?',NULL,0);
INSERT INTO comment VALUES (11299,1294,3386,'Victor Zapana','','2004-01-25 13:31:39',0,'he probably does coz the smallest nonnegative number that would work is... really really really small',NULL,0);
INSERT INTO comment VALUES (11300,1294,3386,'Victor Zapana','ramblings','2004-01-25 13:45:27',0,'It cant be a 1-digit number\r\n\r\n2 digit number:\r\nideally, it would be: (for number xy)\r\n1.5 (10x + y) = 10y + x\r\n15x + 1.5y = 10y + x\r\n14x = 8.5y\r\nBecuase 14x and 8.5y are both WHOLE NUMBERS, y must be even 2,4,6,8 (im not agreeing with Penny on the 000 idea). In addition x and y must both be whole numbers between 0 and 9.\r\n8.5 x 2= 17 REJECT not divisible by 14\r\n8.5 x 4= 34 REJECT not divisible by 14\r\n8.5 x 6= 51 REJECT not divisible by 14\r\n8.5 x 8= 68 REJECT not divisible by 14\r\nIt cannot be a 2-digit number\r\n\r\n3-digit number:\r\nideally, it would be: (for number xyz)\r\n1.5 (100x + 10y + z) = 100z + 10x + y\r\n150x + 15y + 1.5z = 100z + 10x + y\r\n140x + 14y = 98.5z \r\n14(10x + y) = 98.5z \r\nBecause 14, 10x+y, and 98.5z are all WHOLE NUMBERS, z must be even, so its either 2,4,6,8. (not including 0 coz i disagree with penny with the 000 idea) \r\n98.5 x 2= 197 REJECT not divisible by 14\r\n98.5 x 4= 394 REJECT not divisible by 14\r\n98.5 x 6= 591 REJECT not divisible by 14\r\n98.5 x 8= 788 REJECT not divisible by 14\r\nSo, it is not a 3-digit number.\r\n\r\nto be continued\n\nEdited on January 25, 2004, 1:45 pm',NULL,0);
INSERT INTO comment VALUES (11301,1294,3386,'Victor Zapana','ramblings 2','2004-01-25 13:51:28',0,'4-digit number:\r\nideally, it would be: (for number abcd)\r\n1.5 (1000a + 100b + 10c + d) = 1000d + 100a + 10b + c\r\n1500a + 150b + 15c + 1.5d = 1000d + 100a + 10b + c\r\n1400a + 140b + 14c = 998.5d\r\n14 (100a + 10b + c)= 998.5d\r\nbecause 14(100a + 10b + 10c) and 998.5d are both WHOLE NUMBERS, d must be even, so it is 2,4,6,8 (not including 0 look at previous post) also, a, b, c are between 0 and 9.\r\n998.5 x 2= 1997 REJECT not divisible by 14\r\n998.5 x 4= 3994 REJECT not divisible by 14\r\n998.5 x 6= 5991 REJECT not divisible by 14\r\n998.5 x 8= 7988 REJECT not divisible by 14\r\nAhhh, it\'s not a 4-digit number either.. -cries-\r\n\r\nto be continued\r\n\r\nPenny\'s idea seems more and more plausible lol.\r\n\n\nEdited on January 25, 2004, 1:52 pm',NULL,0);
INSERT INTO comment VALUES (11302,1294,3386,'Victor Zapana','ramblings 3','2004-01-25 13:56:22',0,'5-digit number:\r\nideally, it would be: (for number abcde)\r\n1.5 (10000a + 1000b + 100c + 10d+ e) = 10000e + 1000a + 100b + 10c + d\r\n15000a + 1500b + 150c + 15d + 1.5e = 10000e + 1000a + 100b + 10c + d\r\n14000a + 1400b + 140c + 14d = 9998.5e\r\n14 (1000a + 100b + 10C + d) = 9998.5e\r\nLike before, e must be even 2,4,6, or 8.\r\n9998.5 x 2= 19997 REJECT not divisible by 14\r\n9998.5 x 4= 39994 REJECT not divisible by 14\r\n9998.5 x 6= 59991 REJECT not divisible by 14\r\n9998.5 x 8= 79988 REJECT not divisible by 14\r\nGAH, it is not a 5 digit number\r\n\r\nto be continued\n\nEdited on January 25, 2004, 2:11 pm',NULL,0);
INSERT INTO comment VALUES (11303,1294,3386,'Victor Zapana','ramblings 4','2004-01-25 14:03:02',0,'6-digit number:\r\nideally, it would be: (for number abcdef)\r\n1.5 (100000a + 10000b + 1000c + 100d + 10e + f) = 100000f + 10000a + 1000b + 100c + 10d + e\r\n150000a + 15000b + 1500c + 150d + 15e + 1.5f = 100000f + 10000a + 1000b + 100c + 10d + e\r\n140000a + 14000b + 1400c + 140d + 14e = 99998.5f\r\n14 (10000a + 1000b + 100c + 10d + e) = 99998.5f\r\nLike before, f must be 2, 4, 6, or 8.\r\n99998.5 x 2= 199997 REJECT not divisible by 14\r\n99998.5 x 4= 399994 ACCEPTED divisible by 14.\r\nSo, f is 4.\r\n399994 / 14= 28571.\r\n\r\nto be continued ',11302,0);
INSERT INTO comment VALUES (11304,1294,3386,'Victor Zapana','Conclusion of the Ramblings','2004-01-25 14:05:01',3,'(this shud be read last, after u read all the other \"ramblings...,\" or at least ramblings 4.)\r\nits a 6-digit number: abcde4\r\n\r\n10000a + 1000b + 100c + 10d + e = 28571\r\na = 2\r\nb = 8\r\nc = 5\r\nd = 7\r\ne = 1\r\nSo, the number is 285714.\r\n\r\nAlso, just from my thoughts, I think it can\'t be 0, coz it says \"precisely 50%,\" and 0 can be 1.983% of 0, 2.124% of 0, 3% of 0, etc. and not only be 50%\r\n\r\nEdited on January 25, 2004, 2:09 pm\n\nEdited on January 25, 2004, 2:12 pm',11303,0);
INSERT INTO comment VALUES (11305,1294,5285,'Ady TZIDON','a non-zero solution','2004-01-25 15:16:14',3,' ans: 285714\r\n\r\ncan get it by solving :\r\n\r\n10*m+c= 2/3*( c*10^k+m)\r\nwhich transforms into: \r\n28m=2c*10^k-3c\r\nwhich leads to :\r\n\r\n28*m=c*199....97 \r\n\r\nhence c=4 m=28571\r\nand the combined number 428571\r\n\r\nOR c=8 m=57142\r\nand the combined number 571428\r\n\r\n\r\n\r\n\r\nAnother method is by looking at the multiples of the periodic decimal representation of 1/7:\r\n1 142857\r\n2 285714\r\n3 428571\r\n4 571428\r\n5 714285\r\n6 857142 \r\n\r\nHERE YOU CLEARLY SEE BOTH ANSWERS\r\n i.e. 2/7=>3/7 and 4/7=>6/7\r\n\r\nsince the problem requested the smallest number\r\nthe answer is 285714 .\r\nady',NULL,0);
INSERT INTO comment VALUES (11306,1294,1626,'Gamer','re(3): Solution','2004-01-25 16:01:28',0,'Leading zeroes aren\'t allowed unless specified by the problem. So adding extra zeroes aren\'t allowed.',11297,0);
INSERT INTO comment VALUES (11307,1229,5329,'keith','solution','2004-01-25 17:01:03',0,'If I did the math right, then here is the solution:\r\n\r\na) grandpa=16384\r\n grandma=18837\r\n\r\nb) grandpa gives more\r\n grandpa=67108864\r\n grandma=44378442',NULL,0);
INSERT INTO comment VALUES (11308,1459,5330,'Jon','My answer...','2004-01-25 17:59:36',0,'I have the speaker (\"B\") as the last to enter.\r\nPerson 1: Blue shirt, Red tie, Green suspenders\r\nPerson 2: White shirt, Blue tie, Red suspenders\r\nPerson 3: Green shirt, White tie, White suspenders\r\nPerson 4: Red shirt, Green tie, Blue suspenders',NULL,0);
INSERT INTO comment VALUES (11309,1459,5334,'Venkatesh','My Solution','2004-01-25 22:27:36',0,'Hi guys ,\r\ni am Venkatesh an engg student in India.This is my first hit at this site . nyways this is my solution.\r\nsu - Suspenders , sh - shirt , t tie\r\nA B C D\r\nG su - W t - R sh - R t \r\nB sh - G sh - R su - W sh \r\nG t - W su - B t - B su \r\nthe 4 of \'em enter in the order A,B,C,D\r\nB: Well, I know that the only person that came in between the person with the red shirt and the person with the green suspenders (in no particular order) was wearing a white tie.\r\n\r\nso .. the order thus far is {sh=shirts,su=suspenders,t=tie}\r\neither R sh - W t - G su --- 1\r\n or G su - W t - R sh --- 2\r\n Well, I know that the person wearing the green shirt came in just before the person wearing the red suspenders, and he came in just before the person wearing the red tie.\r\n\r\nthis tells us tht \r\nG sh- R su - R t ---3\r\nAlso the person narrating this must have come early to have witnessed all this . he wears either a red shirt or a blue shirt so the green shirt ought to be the 2nd guy in .\r\ncomparing this with the prev statements \r\n3 does not match with 1 because the 3rd guy in order will be wearing both red and green suspenders so .. order 1 is wrong .. combining order 2 and 3 and the fact tht the first guy either wears a blue or a red shirt... red shirt is ruled out coz the 3rd guy wears the red shirt acc to order 2\r\nso the order is\r\nG su - W t - R sh - R t \r\nB sh - G sh - R su - \r\n\r\nWe took a picture of all four of us. It showed three of us standing: the person with the blue shirt on the left, the person with the blue tie in the middle, and the person with the white suspenders on the right. The other person was sitting down in the middle because he arrived last of all four of us\r\ncomparing this to the above order \r\nthe 2nd person wears white suspenders\r\nthe 3rd person wears blue tie\r\nalso \r\nthe first guy wears a green tie \r\nthe order becomes\r\n\r\nG su - W t - R sh - R t \r\nB sh - G sh - R su - \r\nG t - W su - B t -\r\n\r\nputting the remaining together \r\nthe final order becomes\r\nG su - W t - R sh - R t \r\nB sh - G sh - R su - W sh \r\nG t - W su - B t - B su \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (11310,1459,4507,'Penny','re: My answer...','2004-01-26 01:29:44',0,'The puzzle states: \"the only person that came in between the person with the red shirt and the person with the green suspenders (in no particular order) was wearing a white tie.\"\r\n\r\nJon has two people like that coming in.\r\n',11308,0);
INSERT INTO comment VALUES (11311,1459,4507,'Penny','re: Possible Solution','2004-01-26 01:35:16',0,'The puzzle refers to \"THE person with the blue shirt\".\r\n\r\nRaymond Chow has two people in blue shirts. That\'s the only problem with his solution.\n\nEdited on January 26, 2004, 1:56 am',11291,0);
INSERT INTO comment VALUES (11312,1459,5267,'cogitater','re: My Solution','2004-01-26 03:12:17',0,'Venkatesh, If I am interpreting your solution correctly, you have the last person in wearing a blue tie and white suspenders. From the description of the photograph we know that the blue tie and white suspenders were worn by two different people.',11309,0);
INSERT INTO comment VALUES (11313,1459,5267,'cogitater','re: Possible Solution','2004-01-26 03:35:49',0,'Penny, I\'m having a problem understanding your critique of R. Chow\'s solution. You state that his having 2 people wearing blue shirts is his only mistake, yet none of his answer agrees with yours. Sup with that? As I recall, your solution was correct, but his is almost totally different. ',11291,0);
INSERT INTO comment VALUES (11314,1394,3275,'retiarius','Barking mad solution','2004-01-26 05:53:46',0,'The very confused dog ends 3 + x from the starting point.\r\nHe has travelled for time t1 towards the boy and for time t2 towards the girl.\r\nTherefore, 10 t1 - 10 t2 = 3 + x\r\nConsidering relatives speeds t1/t2 = 13/6\r\nt1 = 1- t2\r\nTherefore, 6 - 6 t2 = 13 t2\r\nt2 = 6/19, t1 = 13/19\r\n70/19 = 3 + x\r\nx = .68\r\nThe dog is .68 miles from the girl.\r\nWhat direction is he facing?\r\nLet me think about that!\r\n',NULL,0);
INSERT INTO comment VALUES (11315,1466,4830,'Jils','re(2): general equation:','2004-01-26 06:51:04',0,'Actually I did it by integration and came up with the same formula as Ady. I can\'t see how its wrong....',11284,0);
INSERT INTO comment VALUES (11316,707,5337,'andreas','ages of 3 persons','2004-01-26 07:20:15',0,'hi bryan,\r\n\r\ni got nearly same solution like it is posted but i got the following ages:\r\nblake 24 instead of 84\r\ncalvin 84 instead of 36\r\nedgar 36 instead of 24\r\n\r\nall other details like name, jobs a.s.o. same like you. could you check whether my solution is also possible. i could not find a hint which would speak against it.\r\n\r\nthanks from germany\r\nandreas\r\n',NULL,0);
INSERT INTO comment VALUES (11317,1394,4830,'Jils','Any which way','2004-01-26 08:55:19',0,'Working backwards, if the boy was catching up the girl and the dog started somewhere between them, it wouldn\'t matter who he ran to first as they\'d all end up together (at the start).\r\n',NULL,0);
INSERT INTO comment VALUES (11318,840,4865,'Heartberry','FAVORITE!','2004-01-26 09:17:24',1,'This is my favorite riddle that got me hooked on riddles a few years ago!',NULL,0);
INSERT INTO comment VALUES (11319,1399,1920,'Brian Smith','The word is...','2004-01-26 09:28:00',3,'The word is cable.\r\nC A B L E\r\n3,1,2,12,5',NULL,0);
INSERT INTO comment VALUES (11320,1399,1301,'Charlie','But it could also be...','2004-01-26 09:36:17',0,'C L A Y\r\n3,12,1,25\r\n\r\nI\'m sure that\'s the ambiguity.\r\n(unless CLAY is not considered a common word).',11319,0);
INSERT INTO comment VALUES (11321,1294,4906,'stan','re: Conclusion of the Ramblings','2004-01-26 09:54:15',1,'The problem doesn\'t actually specify that the answer must be integral does it? Why wouldn\'t 2.85714 work? (Or .285714 if the preceeding \"0\" isn\'t required?) For that matter (and I\'m just working from Victor\'s previous reasoning) there may a number 1.********** that would work and be smaller, but have more \"digits\" than 6.\r\n\r\n',11304,0);
INSERT INTO comment VALUES (11322,707,1567,'Bryan','re: ages of 3 persons','2004-01-26 10:37:26',0,'andreas, I assume from your comment that you found Calvin to be the banker. Clue (3) implies the banker is one of the two youngest men. Therefore, Calvin must be 24 or 36. Start with this hint and see if it helps :P',11316,0);
INSERT INTO comment VALUES (11323,1459,4507,'Penny','re(2): Possible Solution','2004-01-26 11:16:36',0,'cogitater writes: \"Penny, I\'m having a problem understanding your critique of R. Chow\'s solution. You state that his having 2 people wearing blue shirts is his only mistake, yet none of his answer agrees with yours. Sup with that? As I recall, your solution was correct, but his is almost totally different.\"\r\n\r\nEven though our answers are almost totally different, Raymond Chow\'s answer would be as good as mine, except that the puzzle refers to \"THE person with the blue shirt\", implying that there was only one person in a blue shirt, and Raymond\'s answer has two people in blue shirts.\r\n\r\nMy answer (using the shirt/tie/suspenders notation and the \"less than\" time of arrival notation) was\r\n\r\nBGG < GWW < RBR < WRB\r\n\r\nRaymond\'s is:\r\n\r\nGBG < BWR < RRW < BGB\r\n\r\nBoth of these solutions match every one of the puzzle statements:\r\n\r\n\"the only person that came in between the person with the red shirt and the person with the green suspenders (in no particular order) was wearing a white tie...the person wearing the green shirt came in just before the person wearing the red suspenders, and he came in just before the person wearing the red tie...a picture...showed...the person with the blue shirt on the left, the person with the blue tie in the middle, and the person with the white suspenders on the right. The other person was sitting... [B was wearing a] green tie [and] a red or blue shirt...\"\r\n\r\nRaymond\'s solution and my solution fit all those statements. The only reason I prefer my solution to his, is that I only have one person in a blue shirt, and the puzzle implies that there was only one such person. \r\n\r\n\r\n\r\n\r\n \r\n\r\n\r\n\r\n\r\n\n\nEdited on January 26, 2004, 11:24 am',11313,0);
INSERT INTO comment VALUES (11324,1399,5285,'Ady TZIDON','one more... Internet bound','2004-01-26 11:16:46',0,'cable, ... clay \r\n\r\n& to rhyme: Ebay(!!) : 31=5 MOD 26= E; 2,1,21=BAY\r\n\r\nJUST CABLE E-BAY TO GET SOME CLAY\r\n\r\nady\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (11325,1294,5285,'Ady TZIDON','re(2): Conclusion of the Ramblings','2004-01-26 11:28:19',1,'Stan\r\n Not quite. In both cases placing the last digit at the left end will not create a 50% increase:\r\n 2.85714=>42.8571\r\n.285714=>4.28571\r\n\r\nBy the same token 1.@^^$#...^Z=>Z1.@^^$#...^\r\n\r\nady',11321,0);
INSERT INTO comment VALUES (11326,1399,4507,'Penny','re: one more... Internet bound','2004-01-26 11:28:21',0,'LOL',11324,0);
INSERT INTO comment VALUES (11327,1399,5285,'Ady TZIDON','re(2): one more... Internet bound +LOL','2004-01-26 11:33:40',0,'P,\r\nWHR S YR SNS F HMR ??\r\n',11326,0);
INSERT INTO comment VALUES (11328,1294,2716,'Federico Kereki','Standard solution','2004-01-26 11:41:02',3,'There\'s an standard solution using continued fractions. Assume we are looking for a number abc...z.\r\n 100 point 5\r\n 200 data 1,2,3,4,5,6,5,4,3,2,1\r\n 300 dim W(11)\r\n 400 for I=1 to 11\r\n 500 read W(I)\r\n 600 TotWays=TotWays+W(I)\r\n 700 next\r\n 800\r\n 900\r\n1000 for Turn=1 to 2000\r\n1100 T=0\r\n1200 Sg=-1:Ways=0\r\n1300 for W1=0 to 1\r\n1400 Ways=Ways+W(1)*W1\r\n1500 for W2=0 to 1\r\n1600 Ways=Ways+W(2)*W2\r\n1700 for W3=0 to 1\r\n1800 Ways=Ways+W(3)*W3\r\n1900 for W4=0 to 1\r\n2000 Ways=Ways+W(4)*W4\r\n2100 for W5=0 to 1\r\n2200 Ways=Ways+W(5)*W5\r\n2300 for W6=0 to 1\r\n2400 Ways=Ways+W(6)*W6\r\n2500 for W7=0 to 1\r\n2600 Ways=Ways+W(7)*W7\r\n2700 for W8=0 to 1\r\n2800 Ways=Ways+W(8)*W8\r\n2900 for W9=0 to 1\r\n3000 Ways=Ways+W(9)*W9\r\n3100 for W10=0 to 1\r\n3200 Ways=Ways+W(10)*W10\r\n3300 for W11=0 to 1\r\n3400 Ways=Ways+W(11)*W11\r\n3500 T=T+Sg*(1-((TotWays-Ways)/TotWays)^Turn)\r\n3600 Ways=Ways-W(11)*W11\r\n3700 Sg=-Sg\r\n3800 next W11\r\n3900 Ways=Ways-W(10)*W10\r\n4000 Sg=-Sg\r\n4100 next W10\r\n4200 Ways=Ways-W(9)*W9\r\n4300 Sg=-Sg\r\n4400 next W9\r\n4500 Ways=Ways-W(8)*W8\r\n4600 Sg=-Sg\r\n4700 next W8\r\n4800 Ways=Ways-W(7)*W7\r\n4900 Sg=-Sg\r\n5000 next W7\r\n5100 Ways=Ways-W(6)*W6\r\n5200 Sg=-Sg\r\n5300 next W6\r\n5400 Ways=Ways-W(5)*W5\r\n5500 Sg=-Sg\r\n5600 next W5\r\n5700 Ways=Ways-W(4)*W4\r\n5800 Sg=-Sg\r\n5900 next W4\r\n6000 Ways=Ways-W(3)*W3\r\n6100 Sg=-Sg\r\n6200 next W3\r\n6300 Ways=Ways-W(2)*W2\r\n6400 Sg=-Sg\r\n6500 next W2\r\n6600 Ways=Ways-W(1)*W1\r\n6700 Sg=-Sg\r\n6800 next W1\r\n6910 P=T-PrevT\r\n6950 ExpVal=ExpVal+Turn*P\r\n7000 print Turn,P,T\r\n7100 PrevT=T:Ppp=PrevP:PrevP=P\r\n7200 next Turn\r\n7300 print ExpVal\r\n
\r\n------\r\nBy flipping sg from positive 1 to negative 1 and back each time a throw total comes in or out of the ORed set, the proper sign is applied when that ORed probability is added in (or, consequently, subtracted out).\r\n\r\nThe program calculates each probability (which is in fact a cumulative probability) and finds the individual probability that that throw would be the one to complete the set by subtracting the cumulative probability from the previous cumulative probability. Each individual probability multiplied by the number of throws is added into the expected value.\r\n\r\nBy the time 2000 throws have been made the total probability is close enough to 1 for 24 significant digits, and the expected value comes out to 61.2173847639571980537370.\r\n\r\nAn artifact of doing it this way is that we can also get the mode and the median:\r\n\r\n34 0.017375360700789131212236 0.220565986006324770340293\r\n35 0.017473676386676434347342 0.238039662393001204687635\r\n36 0.017510455835875378339185 0.255550118228876583026821\r\n37 0.017492202669494406266952 0.273042320898370989293774\r\n38 0.017425077816538910306595 0.29046739871490989960037\r\n39 0.01731485097448574303068 0.30778224968939564263105\r\n40 0.01716687506726530698634 0.324949124756660949617391\r\n41 0.016986077815400902055923 0.341935202572061851673315\r\n42 0.016776965733031975914904 0.35871216830509382758822\r\n43 0.016543636875769735968425 0.375255805180863563556645\r\n44 0.016289799495065753579066 0.391545604675929317135712\r\n45 0.016018794429128916085576 0.407564399105058233221288\r\n46 0.015733619599724859039908 0.423298018704783092261197\r\n47 0.015436955410310670563372 0.438734974115093762824569\r\n48 0.015131190173936084062307 0.453866164289029846886877\r\n49 0.014818444956775478994304 0.468684609245805325881182\r\n50 0.014500597420046446390173 0.483185206665851772271355\r\n51 0.014179304391944190500357 0.497364511057795962771713\r\n52 0.013856023012360844243681 0.511220534070156807015394\r\n53 0.013532030374900937773496 0.524752564445057744788891\r\n
\r\n-----\r\nThe mode is 36, having the highest individual probability (about 1.751%) of being the throw that completes the set. The median is just above 51 throws.\r\n\r\nA similar program, run for the original problem of one die being tossed, and getting all 6 possible results, gives, in part:\r\n\r\n9 0.075017146776406035665287 0.189043209876543209876529\r\n10 0.082768918609967992684039 0.271812128486511202560568\r\n11 0.084394290123456790123451 0.356206418609967992684019\r\n12 0.081609262011211028129202 0.437815680621179020813222\r\n13 0.076042513421057088181005 0.513858194042236108994228\r\n14 0.068987154809400290907168 0.582845348851636399901396\r\n15 0.061367389743463996944156 0.644212738595100396845553\r\n16 0.053791659090958983844544 0.698004397686059380690098\r\n
\r\n---- \r\nThis shows that the mode for the number of tosses needed is 11 and the median is just below 13 and the run verifies that the mean is 14.7.\r\n\n\nEdited on January 26, 2004, 5:29 pm',11332,0);
INSERT INTO comment VALUES (11336,1459,5267,'cogitater','re(3): Possible Solution','2004-01-26 18:25:44',0,'I see another problem with Raymond\'s solution. He has B arriving last. From B\'s use of the word \"know\" and A\'s use of the word \"notice\" in describing B\'s knowledge of the order of arrival, we know that B personally observed these arrivals. From this we know B would have to have come in first or second. We can eliminate second because be could not had a green tie. Be could not have made the observations he describes if he came in last',11323,0);
INSERT INTO comment VALUES (11337,1466,4374,'Richard','Geometric Interpretation of Simpler Formula?','2004-01-26 19:06:43',4,'To show\r\n\r\npi*b*sqrt(b^2+((h*b/(b-a))^2)-pi*a*sqrt(a^2+((h*a/(b-a))^2) \r\n\r\n= pi*(a+b)*sqrt((b-a)^2+h^2)\r\n\r\nwrite\r\n\r\nb^2 + (h^2*b^2)/(b-a)^2 = b^2*((b-a)^2+h^2)/(b-a)^2 and\r\n\r\na^2 + (h^2*a^2)/(b-a)^2 = a^2*((b-a)^2+h^2)/(b-a)^2. Hence \r\n\r\npi*b*sqrt(b^2+((h*b/(b-a))^2)-pi*a*sqrt(a^2+((h*a/(b-a))^2)\r\n\r\n= (pi* (b^2-a^2)/(b-a))*sqrt((b-a)^2+h^2)\r\n\r\n= pi*(a+b)*sqrt((b-a)^2+h^2).\r\n\r\nThus the area of the curved part of the truncated cone can be expressed in the simpler form\r\n\r\npi*(a+b)*sqrt((b-a)^2+h^2) given by Ady TZIDON as well as in the form\r\n\r\npi*b*sqrt(b^2+((h*b/(b-a))^2)-pi*a*sqrt(a^2+((h*a/(b-a))^2)\r\n\r\ngeometrically obtained by removing a small full cone from a larger one. Is there a simple geometric interpretation for the simpler formula?',11334,0);
INSERT INTO comment VALUES (11338,1592,4507,'Penny','re: The other answers','2004-01-26 20:42:33',0,'Don\'t ever go to Las Vegas, Charlie. The casino owners might send \"Bruno\" and \"Vito\" to pay you a visit.',11335,0);
INSERT INTO comment VALUES (11339,1592,3372,'Sam','re: solution','2004-01-26 21:19:23',0,'(Please excuse the following if the math is inexcusable...)\r\n\r\nThe probability of NOT having seen a specific number after 14.7 times, if I\'ve understood this correctly, should be\r\n\r\n(5/6 ^ 14.7)\r\n\r\nThus the probability of not having seen ANY one number after 14.7 throws should be\r\n\r\n(5/6 ^ 14.7) * 6 = 41.13%\r\n\r\nSo what makes this the expected result? It\'s not the point where the p of seeing all six number rises above 50%, for instance. Indeed, it hardly seems related at all to the probability of seeing all six.\r\n\r\nI understand Federico\'s answer, I\'m just wondering how, if at all, this could be worked out just by the probabilities of seeing (or not seeing) all six.',11338,0);
INSERT INTO comment VALUES (11340,1459,5347,'Troy','Timely Manner','2004-01-26 21:33:16',0,'Figured it out, took maybe 10 minutes. Good one though',NULL,0);
INSERT INTO comment VALUES (11341,1592,1301,'Charlie','re: The other answers','2004-01-26 22:44:38',0,'Here\'s a result from a simulation verifying, in addition to the mean, also the mode and median previously posted:\r\n\r\nmean= 14.69898\r\n 6 1490 1490\r\n 7 3874 5364\r\n 8 5929 11293\r\n 9 7494 18787\r\n10 8174 26961\r\n11 8632 35593\r\n12 8296 43889\r\n13 7533 51422\r\n14 6834 58256\r\n15 6187 64443\r\n16 5386 69829\r\n17 4643 74472\r\n18 3947 78419\r\n19 3420 81839\r\n20 2996 84835\r\n\r\nwhere the program is\r\nDEFDBL A-Z\r\n\r\nRANDOMIZE TIMER\r\nDIM numT(50)\r\ntotTook = 0: totTrials = 0\r\nFOR trial = 1 TO 100000\r\n totTrials = totTrials + 1\r\n REDIM had(6)\r\n numHad = 0: thisTook = 0\r\n DO\r\n r = INT(RND(1) * 6 + 1)\r\n IF had(r) = 0 THEN\r\n had(r) = 1\r\n numHad = numHad + 1\r\n END IF\r\n totTook = totTook + 1\r\n thisTook = thisTook + 1\r\n LOOP UNTIL numHad = 6\r\n IF thisTook <= 50 THEN\r\n numT(thisTook) = numT(thisTook) + 1\r\n ELSE\r\n numT(0) = numT(0) + 1\r\n END IF\r\nNEXT trial\r\nPRINT \\\"mean=\\\"; totTook / totTrials\r\nFOR i = 6 TO 20\r\n cumP = cumP + numT(i)\r\n PRINT USING \\\"## ##### #####\\\"; i; numT(i); cumP\r\nNEXT\r\n\r\nmean= 61.05001\r\n33 1702 20384\r\n34 1680 22064\r\n35 1803 23867\r\n36 1791 25658\r\n37 1759 27417\r\n38 1667 29084\r\n39 1783 30867\r\n40 1810 32677\r\n41 1716 34393\r\n42 1623 36016\r\n43 1609 37625\r\n44 1644 39269\r\n45 1590 40859\r\n46 1578 42437\r\n47 1582 44019\r\n48 1502 45521\r\n49 1497 47018\r\n50 1462 48480\r\n51 1396 49876\r\n52 1400 51276\r\n53 1313 52589\r\n54 1343 53932\r\n55 1280 55212\r\n56 1309 56521\r\n57 1237 57758\r\n58 1204 58962\r\n59 1152 60114\r\n60 1144 61258\r\n\r\nfrom\r\n\r\nDEFDBL A-Z\r\n\r\nRANDOMIZE TIMER\r\nDIM numT(100)\r\ntotTook = 0: totTrials = 0\r\nFOR trial = 1 TO 100000\r\n totTrials = totTrials + 1\r\n REDIM had(12)\r\n numHad = 0: thisTook = 0\r\n DO\r\n r = INT(RND(1) * 6 + 1)\r\n r2 = INT(RND(1) * 6 + 1)\r\n r = r + r2\r\n IF had(r) = 0 THEN\r\n had(r) = 1\r\n numHad = numHad + 1\r\n END IF\r\n totTook = totTook + 1\r\n thisTook = thisTook + 1\r\n LOOP UNTIL numHad = 11\r\n IF thisTook <= 100 THEN\r\n numT(thisTook) = numT(thisTook) + 1\r\n ELSE\r\n numT(0) = numT(0) + 1\r\n END IF\r\nNEXT trial\r\nPRINT \\\"mean=\\\"; totTook / totTrials\r\nFOR i = 11 TO 60\r\n cumP = cumP + numT(i)\r\n IF i > 32 THEN\r\n PRINT USING \"## ##### #####\"; i; numT(i); cumP\r\n END IF\r\nNEXT\r\n
\r\n--------\r\n--------',11335,0);
INSERT INTO comment VALUES (11342,697,5306,'Purna','House no','2004-01-26 23:01:17',3,'\r\ncase1: Mr Y lives in house numbered 83 with Mr X at 73. \r\n \r\ncase2: Mr Y lives in house numbered 23 with Mr X at 13.\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (11343,1592,1301,'Charlie','re(2): solution','2004-01-26 23:04:56',0,'Two corrections on the difficulties presented:\r\n\r\nRegarding:\r\n\"The probability of NOT having seen a specific number after 14.7 times, if I\'ve understood this correctly, should be \r\n\r\n(5/6 ^ 14.7) \r\n\r\nThus the probability of not having seen ANY one number after 14.7 throws should be \r\n\r\n(5/6 ^ 14.7) * 6 = 41.13% \"\r\n\r\nAside from the fact that you can\'t actually have 14.7 throws (a minor point here), you can\'t add up (which is what multipliction by 6 is here) all six probabilities to come up with the total probability that any one of them would happen. Just think: after one throw, the probability that you haven\'t gotten a particular side to show is 5/6. The probability is not (5/6 ^ 1) * 6 of not having seen ANY one number after 1 throw. The events are not mutually exclusive, so you can\'t just add the probabilities. I can\'t give you an actual value for 14.7 throws, as such a number of throws does not exist. However, from the table I posted as The other answers, the probability of having completed all 6 at 14 throws is 0.582845348851636399901396, and at 15 throws is 0.644212738595100396845553. The probability that one or more did not yet come up is the complement of each of these, or 41.7% and 35.6% respectively. Interpolating to 14.7 would give 39.23%.\r\n\r\nWhich brings us to the second item:\r\n\"So what makes this the expected result? It\'s not the point where the p of seeing all six number rises above 50%, for instance. Indeed, it hardly seems related at all to the probability of seeing all six. \"\r\n\r\nThe expected value is the average, or mean, value. What you are describing is the median value, which in this instance in the above referenced comment I note is just below 13. Suppose there were four boxes with money inside: $1, $2, $3 and $100. You pick one at random. Your median winnings would be 2.50, but the mean (the expected value) is 26.50, even though you only have 1 chance in 4 of picking a larger amount.\r\n\r\n',11339,0);
INSERT INTO comment VALUES (11344,1286,5353,'sophea','re: The easiest puzzle in floobelian history !!!','2004-01-27 00:17:45',0,'How did you get that?? i got THIRD in 1st place, FIRST in 2nd, FOURTH in 3rd, SECOND in 4th and FIFTH in 5th',11131,0);
INSERT INTO comment VALUES (11345,1509,5352,'Phil','Solution','2004-01-27 00:24:02',3,'
\r\n(1999^1999) mod 9 =
\r\n(1999 mod 9)^1999 mod 9 =
\r\n1^1999 mod 9 = 1\r\n',11351,0);
INSERT INTO comment VALUES (11354,1293,4670,'e.g.','re: last digit','2004-01-27 09:16:50',1,'How come you get from last_digit((2^100)/2 to last_digit(2/2)?? The last digit of 2^100 is 6, so the result should be 3, not 1; the whole reasoning is wrong.',11274,0);
INSERT INTO comment VALUES (11355,1297,5285,'Ady TZIDON','re(3): super easy //e.g +GAMER','2004-01-27 09:41:02',0,'as THE BARD said:\r\n....to the selfsame tune and words...\r\n\r\nady',11353,0);
INSERT INTO comment VALUES (11356,1390,1413,'dave domingo','re(2): 2/3 of an answer','2004-01-27 09:55:08',0,'Hi Brian. I think Tom is accounting for the cats being grossly outnumbered in the beginning. In fact, if the cats were only slightly bigger and tougher than the rats, you could argue that you need a 1-to-1 ratio for the cats to kill any rats at all, regardless of the time alotted (unless it\'s like a kung fu movie where they come at you one at a time).',11162,0);
INSERT INTO comment VALUES (11357,1297,4374,'Richard','re(2): super easy','2004-01-27 12:03:26',0,'http://mathforum.org/library/drmath/sets/select/dm_mod.html',11351,0);
INSERT INTO comment VALUES (11358,1297,3172,'SilverKnight','re(3): super easy','2004-01-27 12:19:08',0,'Uh, yes... thanks for the link... my point was that Ady didn\'t justify the argument... just made a jump to a conclusion. (I wasn\'t arguing the conclusion ;-).\r\n\r\nWhen one submits a solution.... BEST, he should explain the reasoning behind it... or at least provide a link to justify the conclusion.\r\n\r\n- SK',11357,0);
INSERT INTO comment VALUES (11359,1618,3386,'Victor Zapana','','2004-01-27 13:15:47',0,'tho im sure this probably isnt the answer, but is it 3^4/5^4? or... mebe its 1- (2^4/5^4) cant remember',NULL,0);
INSERT INTO comment VALUES (11360,1618,1301,'Charlie','solution','2004-01-27 13:41:23',3,'The probability that, during a given round, no one wins is 1 - 3/5 = 2/5. This is the product of the probabilities that the first player doesn\'t win, the 2nd player also doesn\'t win, and likewise the 3rd and 4th. As all of these are the same, x^4=2/5 where x is the probability that on one turn one player does not win.\r\n\r\nThe fourth root of 2/5 is .7952707287670506, so the probability of a win on a given turn is 1 - .7952707287670506 = .2047292712329494. So this is the probability of the first player\'s immediate win.\r\n\r\nThe probability that the 2nd player will win on his first turn is .7952707287670506 * .2047292712329494, representing the probability the first player does not win multiplied by the probability that the 2nd player then does win.\r\n\r\nThe 3rd player likewise has to wait for players 1 and 2 to lose before being given the opportunity to win, and therefore has probability .7952707287670506^2 * .2047292712329494 of winning in the first round.\r\n\r\nThe 4th player then has probability of winning of .7952707287670506^3 * .2047292712329494 of winning on the first round.\r\n\r\nThese come out to .2047292712329494, .1628151967333748, .1294821601605017 and .1029733718731742 for the 1st, 2nd, 3rd and 4th players, respectively. As a check, they do add to .6, the probability that one of the players will win within the round.\r\n\r\nSome player will eventually win, and the probability will be in proportion to the individual probabilities within one round. As they add up to .6, we must divide each of the above individual-round probabilities by .6 to get the overall probability that that person will ultimately win, giving probabilities of .3412154520549157, .2713586612222914, .2158036002675029, .1716222864552903 respectively, or about 34%, 27%, 22% and 17% for the first, second, third and fourth players respectively.',NULL,0);
INSERT INTO comment VALUES (11361,1618,1920,'Brian Smith','solution','2004-01-27 13:56:34',0,'Let \'a\' be the probability the first person wins a round, \'b\' for the second, \'c\' for the third, and \'d\' for the fourth.\r\n\r\nSince all four players have the same probability of winning in any round,\r\na = (1-a)b = (1-a)(1-b)c = (1-a)(1-b)(1-c)d\r\n\r\nThis yields b = a/(1-a), c = a/(1-2a), d = a/(1-3a)\r\n\r\nThe proability of no one winning the round is (1-a)*(1-b)*(1-c)*(1-d) = (1 - 3/5)\r\n\r\n(1 - a)*(1 - a/(1-a) )*(1 - a/(1-2a) )*(1 - a/(1-3a) ) = 2/5\r\n\r\n(1 - a)*( (1-2a)/(1-a) )*( (1-3a)/(1-2a) )*( (1-4a)/(1-3a) ) = 2/5\r\n\r\n1 - 4a = 2/5\r\n\r\na = 3/20\r\nb = (3/20)/(1-3/20) = 3/17\r\nc = (3/20)/(1-6/20) = 3/14\r\nd = (3/20)/(1-9/20) = 3/11',NULL,0);
INSERT INTO comment VALUES (11362,1394,5097,'Cindy','tee hee','2004-01-27 14:03:51',0,'Well if the boy and girl start walking, with the boy taking wider and faster steps than the girl, until as time goes by, the distance between boy and girl get further. Which means poor little Rover, for the first minutes is spining in a circle going from girl to boy to girl to boy. He gets so dizzy, he vomits and passes out. ',NULL,0);
INSERT INTO comment VALUES (11363,1618,3172,'SilverKnight','solution','2004-01-27 14:04:28',3,'Dang... Brian beat me to it... but my solution agrees with his... a nifty problem:\r\n_______________________________________________\r\n\r\nThe four probabilities are:\r\n3/20\r\n3/17\r\n3/14\r\n3/11\r\nrespectively.\r\n_______________________________________________\r\n\r\nProof:\r\n\r\nLet the respective probabilities for winning on each person\'s turn be represented by w, x, y, and z respectively.\r\n\r\n\"The chance of winning in any given round is 3/5\" means that the change of NOBODY winning in a round is 2/5. This is equivalent to:\r\n[1]: (1-w)(1-x)(1-y)(1-z) = 2/5\r\n\r\nNow, because they all have equal odds of winning a game, we must take position into account.... because the first person has the advantage of position. Therefore, the first person must be least likely to win on his given turn. This gives the following equality:\r\nw = (1-w)x = (1-w)(1-x)y = (1-x)(1-x)(1-y)z\r\n\r\nwhich leads to the following equations...\r\n\r\n[2]: x = w/(1-w)\r\n[3]: y = w/(1-2w)\r\n[4]: z = w/(1-3w)\r\n\r\nNow we have 4 equations and 4 unknowns.\r\n\r\nPlug equations 2, 3, and 4 into equation 1, and we see that\r\nw = 3/20\r\n\r\nPlugging this value into equations 2, 3 and 4, we get\r\nx = 3/17\r\ny = 3/14\r\nz = 3/11\r\n',NULL,0);
INSERT INTO comment VALUES (11364,1618,1301,'Charlie','re: solution -- on second thought','2004-01-27 14:14:29',3,'I may have been reading the puzzle wrong. If the idea is that each player have the same ultimate chance of winning, then within each round, each player must have a different chance of getting an immediate win.\r\n\r\nWe want each player to have an equal chance of winning within a round, and the total chance is .6, so each one is to have a 15% chance of winning in each round, including the first round.\r\n\r\nThus the first player must be given a 15% chance of an immediate win. Then, as the second player is to have an overall probability of a first round win of 15%, his turn probability must be .15/(1-.15) = 3/17. The third player must then be given .15/(1-.3) chance of winning or 3/14. The 4th player is then given probability of .15/(1-.45) = 3/11.\r\n\r\nThus if the randomizing procedure for use by player 1 gives him 3/20 probability of a win (when he shoots, draws or whatever procedure is used to randomize), that for player 2 gives him a 3/17 probability of a win, that for player 3 a 3/14 win probability and for player 4 a 3/11 chance of a win, then in each round each will have an overall 15% probability of a win given that he has to await a failure by his predecessors. Then each has an even chance of winning the game as a whole.',11360,0);
INSERT INTO comment VALUES (11365,1618,3172,'SilverKnight','re: Charlie\'s solution','2004-01-27 14:17:11',0,'Charlie,\r\n\r\nYou wrote:\r\n\"Some player will eventually win, and the probability will be in proportion to the individual probabilities within one round.\"\r\n\r\nBut the problem states, as a given:\r\n\"They all have even odds of winning a game.\"\r\n\r\nThese are in contradiction.',11360,0);
INSERT INTO comment VALUES (11366,1618,3172,'SilverKnight','re(2): Charlie\'s solution','2004-01-27 14:18:27',0,'ahhh.... I see you posted right before I did.',11365,0);
INSERT INTO comment VALUES (11367,1618,1301,'Charlie','re(2): Charlie\'s solution','2004-01-27 14:19:19',0,'I had initially misread that as being each turn\'s chance was the same. By the time I corrected myself, two other, correct, postings had been made.',11365,0);
INSERT INTO comment VALUES (11368,1394,4374,'Richard','re: Sit !! Stay !!','2004-01-27 14:36:27',0,'It would be nice to assume the dog stays for time d, get a solution in terms of d, and take the limit as d approaches zero. Don\'t look at me to do this, but maybe somebody (Charlie?) will do it.',11292,0);
INSERT INTO comment VALUES (11369,1446,1413,'dave domingo','guessing before reading','2004-01-27 17:52:00',0,'310 chestnuts.\r\n\r\n\"A sixth\" means a sixth of a chestnut. \"Five too many\" means 5/6 too many. \r\n\r\nYou can get 31/6 chestnuts for a buck; you can get 31 for $6; you can get 310 for $60.\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (11370,1618,4507,'Penny','Question','2004-01-27 18:45:07',4,'Whoops....I just re-read the puzzle. Let me change my question to:\r\n\r\nWhat is the largest lake in South America ?\n\nEdited on January 27, 2004, 6:50 pm',NULL,0);
INSERT INTO comment VALUES (11371,1459,5368,'Jim','Solution','2004-01-27 23:33:36',0,'First, Blue Shirt, Green Suspenders, Blue Tie\r\nSecond, Green Shirt, White Suspenders, White Tie\r\nThird (\"B\" in the dialogue), Red Shirt, Red Suspenders, Green Tie\r\nLast, White Shirt, Blue Suspenders, Red Tie',NULL,0);
INSERT INTO comment VALUES (11372,1459,4507,'Penny','re: Solution','2004-01-27 23:49:25',0,'The puzzle states that \"We took a picture of all four of us. It showed three of us standing: the person with the blue shirt on the left, the person with the blue tie in the middle...\"\r\n\r\nYour solution has one person wearing the blue shirt and the blue tie.',11371,0);
INSERT INTO comment VALUES (11373,1408,3275,'retiarius','Solution','2004-01-28 08:41:32',0,'Series are n^2 to base 3 and 4 respectively.\r\nNext in series are 9^2:\r\nto base 3 = 10000\r\nto base 4 = 1101',NULL,0);
INSERT INTO comment VALUES (11374,990,5338,'chuck','solution','2004-01-28 08:56:38',3,'the pitcher came into the game, didnt start it, and the game went into extra innings',NULL,0);
INSERT INTO comment VALUES (11375,1408,4507,'Penny','Solution','2004-01-28 10:05:29',3,'(1) (1,11,100,121,221,1100,1211,2101...) \r\nis the series of perfect squares (1,4,9,16,25,36,49,64...) in the base 3 number system. The next three terms are 10000 [81 (base 3)],\r\n10201 [100 (base 3)], 11111 [121 (base 3)] \r\n \r\n(2) (1,10,21,100,121,210,301,1000) \r\nis the same series in the base 4 number system.\r\nThe next three terms are 1101 [81 (base 4)], \r\n1210 [100 (base 4)], 1321 [121 (base 4)]\r\n\r\n\r\n\r\n\n\nEdited on January 28, 2004, 10:34 am',NULL,0);
INSERT INTO comment VALUES (11376,1408,5285,'Ady TZIDON','SOLUTION','2004-01-28 11:02:03',0,'10000 for 1st 1101 for the 2nd series\r\nBoth are squares of consecutive integers 1 to 8; first in ternary second in 4-base system\r\n\r\nady',NULL,0);
INSERT INTO comment VALUES (11377,1459,5377,'stewards','solution','2004-01-28 11:42:43',0,'1st was the person with a blue shirt, red suspenders, and a green tie\r\n\r\n2nd was the person with a red shirt, blue suspenders, and a blue tie\r\n\r\n3rd was the person with a green shirt, white suspenders, and a white tie\r\n\r\n4th was the person with a white shirt, green suspenders, and a red tie\r\n',NULL,0);
INSERT INTO comment VALUES (11378,1399,5377,'stewards','these are the only possible combinations, provided that you cant go past 26','2004-01-28 12:03:09',0,'3 1 2 1 2 5\r\n\r\n\r\n3 12 1 2 5 C L A B E\r\n3 12 12 5 C L L E\r\n3 12 1 25 C L A Y\r\n3 1 21 2 5 C A U B E\r\n3 1 21 25 C A U Y\r\n3 1 2 12 5 C A B L E\r\n3 1 2 1 25 C A B A Y\r\n3 1 2 1 2 5 C A B A B E\r\n\r\nclay and cable are the only two are common words\r\n\r\ncase if you do 3,1, 21-2, 5 but i dont think that is permitted. im sure several other combinations would arise from this.\r\n',NULL,0);
INSERT INTO comment VALUES (11379,1399,5377,'stewards','','2004-01-28 12:04:34',0,'cell if you group as 3,12,12,5 and think of it as a loop of ...3,1,2,1,2,5,3,1,2...for the numbers, and go backwards, 3,5,12,12',NULL,0);
INSERT INTO comment VALUES (11380,1459,4507,'Penny','re: solution','2004-01-28 13:05:46',0,'Sorry, stewards, the puzzle states that \"the person wearing the green shirt came in just before the person wearing the red suspenders, and he came in just before the person wearing the red tie\".\r\n',11377,0);
INSERT INTO comment VALUES (11381,329,4865,'Heartberry','Guess','2004-01-28 13:42:06',3,'June :)',NULL,0);
INSERT INTO comment VALUES (11382,1459,5377,'stewards','re(2): solution','2004-01-28 14:44:13',0,'okay, i see that NOW obvious mistake. i put him first because of something i wasnt quite clear on. If the person with the green tie knows the order everyone came, do we need to suspect he was there to see the order of people, or can we assume he has the ability to talk to the other people once they are there and assertain the information that way?\r\n',11380,0);
INSERT INTO comment VALUES (11383,1467,4670,'e.g.','Upper bound','2004-01-28 14:45:22',1,'If we had two circles with 32 people in each, properly aligned, the shooting could occur, so 64 is an upper bound for the answer, and of course, 32 is a lower bound..A.....\r\n......B\r\n..CDE..\r\n..FGH..\r\n..IJK..\r\nL......\r\n.....M.
This is 13 villagers. Every line of three villagers has two bullets passing over it, one from each direction (for instance CDE and EDC). Since there are 16 lines of three villagers in this arrangement, the 32 barbarians can indeed kill one barbarian each. The 16 lines of three are:
FGH
IJK
CFI
DGJ
EHK
CGK
EGI
ADH
ACJ
BEF
BHJ
LFD
LIH
MJF
MKD',NULL,0);
INSERT INTO comment VALUES (11390,1467,4507,'Penny','Barbarians at the gates !!','2004-01-28 15:57:56',3,'[Technical note: When the following solution was posted, the puzzle read \"...every bullet went over 3 PEOPLE\'S heads before it killed another person...\" The puzzle has since been updated to disallow this solution.]\r\n\r\nThis solution has zero villagers, thanks to barbarian stupidity and the concept of \"friendly fire\". The barbarians practiced the old Greek formation of the phalanx (literally, \"a log of wood\") and formed themselves around the village in four columns of eight men. (The barbarians are around the village in the sense that there are barbarians to the east, north, south and west of the village). There is not a word in the puzzle that forbids this interpretation.\r\n\r\nBarbarians B1 thru B8 lined up in a single column pointing at the village from the west. B1 fired east over B2,B3,B4 and killed B5. B2 fired east over B3,B4,B5 and killed B6. B3 fired east over B4,B5,B6 and killed B7. B4 fired east over B5,B6,B7 and killed B8. B5 thru B8 were confused. B5 fired fired west over B4,B3,B2 and killed B1. B6 fired west over B5,B4, B3 and killed B2. B7 fired west over B6,B5,B4 and killed B3. B8 fired west over B7,B6,B5 and killed B4.\r\n\r\nBarbarians B9 thru B16 lined up in a single column pointing at the village from the south. B9 fired north over B10,B11,B12 and killed B13. B10 fired north over B11,B12,B13 and killed B14. B11 fired north over B12,B13,B14 and killed B15. B12 north fired over B13,B14,B15 and killed B16. B13 thru B16 were confused. B13 fired south over B12,B11,B10 and killed B9. B14 fired south over B13,B12,B11 and killed B10. B15 fired south over B14,B13,B12 and killed B11. B16 fired south over B15,B14,B13 and killed B12.\r\n\r\nBarbarians B17 thru B24 lined up in a single column pointing at the village from the east. B17 fired west over B18,B19,B20 and killed B21. B18 fired west over B19,B20,B21 and killed B22. B19 fired west over B20,B21,B22 and killed B23. B20 west fired over B21,B22,B23 and killed B24. B21 thru B24 were confused. B21 fired east over B20,B19,B18 and killed B17. B22 fired east over B21,B20,B19 and killed B18. B23 fired east over B22,B21,B20 and killed B19. B24 fired east over B23,B22 and B21 and killed B20.\r\n\r\nBarbarians B25 thru B32 lined up in a single column pointing at the village from the north. B25 fired south over B26,B27,B28 and killed B29. B26 fired south over B27,B28,B29 and killed B30. B27 fired south over B28,B29,B30 and killed B31. B28 fired south over B29,B30,B31 and killed B32. B29 thru B32 were confused. B29 fired north over B28,B27,B26 and killed B25. B30 fired north over B29,B28,B27 and killed B26. B31 fired north over B30,B29,B28 and killed B27. B32 fired north over B31,B30,B29 and killed B28.\r\n\r\n\r\n\r\n\r\n\r\n\n\nEdited on January 28, 2004, 5:57 pm',NULL,0);
INSERT INTO comment VALUES (11391,1467,4507,'Penny','re: Barbarians at the gates !!','2004-01-28 16:42:15',0,'This is clearly not the solution Gamer was looking for. He wants a complex math solution involving a circle with 32 intersecting lines crossing it. He should have specified that each bullet goes over three VILLAGER\'S heads, and also that each of the barbarians fires INTO the village. Little loopholes... But at least I spared all the villagers.\r\n \r\n:-) ',11390,0);
INSERT INTO comment VALUES (11392,1467,3172,'SilverKnight','Solution','2004-01-28 16:48:43',3,'With the assumption that barbarians are NOT killing other barbarians... and that everyone must be shot only once... (meaning, as e.g. mentioned earlier, that it must be AT LEAST 32)...\r\n\r\nThe answer is 32. I\'m trying to put together a text picture that will exemplify this... but it\'s not easy. I\'ll post when I have it ready.',NULL,0);
INSERT INTO comment VALUES (11393,1467,3172,'SilverKnight','Full Solution (re: Solution)','2004-01-28 17:12:11',3,'The following diagram shows how to place 16 villagers in such a way that 16 barbarians can line up on the outside and shoot them all (satisfying the constraints of the problem).\r\n\r\nThere are 8 lines of consequence:\r\nABFI\r\nCDIK\r\nNMHF\r\nPOKH\r\nBGHL\r\nDEFG\r\nMLKJ\r\nEIJO\r\n\r\nYou\'ll notice that *EACH* of the 16 letters is at the end of *ONE* (and only one) of these lines.\r\n\r\nIf we draw a circle around this \"grid\", each line will intersect this circle in two points (for a total of 16 intersections). We merely put a barbarian at these intersections, and each barbarian will shoot into the circle, along the line. Each of the 16 barbarians will kill a different villager.\r\n. . . . . . . . . . . . . . . . . .
This shows how 16 barbarians kill 16 peasants.\r\n\r\nIt is now a simple matter to rotate the whole diagram (by say, 5 degrees) and overlay it on top of itself, to double the number of barbarians shooting and villagers killed.',11392,0);
INSERT INTO comment VALUES (11394,1467,1626,'Gamer','re(2): Barbarians at the gates !!','2004-01-28 17:46:54',0,'I changed the problem so it reflects the problem I set it up as. :)',11391,0);
INSERT INTO comment VALUES (11395,1467,3172,'SilverKnight','re(3): Barbarians at the gates !!','2004-01-28 17:54:06',0,'Dangit Gamer... are you saying that the same person can be shot multiple times?\r\n\r\nIf so... that\'s what I said in the second comment. And Charlie said that you meant that each person can be shot only once.\r\n\r\nAnd in all this time, you didn\'t bother to clarify the situation. You still haven\'t.\r\n__________________\r\n\r\nTo clarify,\r\nCan a barbarian shoot another barbarian (as Bryan suggested)?\r\n\r\nCan the same villager be shot multiple times? (as I suggested)?\r\n\r\nAnd must all the villagers be dead at the end of the simultaneous shooting, or can some still be alive?\n\nEdited on January 28, 2004, 7:28 pm',11394,0);
INSERT INTO comment VALUES (11396,1205,5382,'dan thewlis','2 timers???','2004-01-28 19:17:14',0,'why not just set one going on double speed and then when that reaches exactly five minutes, set another one at double speed for an hour which should stop after 30 minutes. The first timer should beep after its half an hour, if the other one that was put on is stopped as soon as the first one beeps, that will be on exactly 25 minutes, will it not????? So i think the answer is 2 timers',NULL,0);
INSERT INTO comment VALUES (11397,1467,3172,'SilverKnight','upper bound','2004-01-28 19:34:41',1,'This time...\r\n\r\nAssuming that ONLY villagers (not barbarians) can be killed.\r\nAssuming that we can shoot the same villagers more than once.\r\nAssuming that not all villagers must be killed.\r\n\r\nThe following diagram shows how to place 24 villagers in such a way that 36 (4 more than required) barbarians can line up on the outside and shoot them all (satisfying the constraints of the problem).\r\n\r\nThere are 18 lines of consequence:\r\n\r\nAFSX\r\nBDTV\r\nCEUW\r\nKLMN\r\nGHIJ\r\nOPQR\r\nKOVX\r\nGPTW\r\nHLSU\r\nDFMQ\r\nBEIR\r\nACJN\r\nABGK\r\nCDHO\r\nEFLP\r\nIMST\r\nJQUV\r\nNRWX\r\n\r\nIf we draw a circle around this \"grid\", each line will intersect this circle in two points (for a total of 36 intersections). We merely put a barbarian at any of these intersections, and each barbarian will shoot into the circle, along the line.\r\n
. . . . . . . . . . . A . . . . . .
. . . . . . . . . . . . . . . . . .
. . . . . . . . . . B . . . . . . .
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. . . . . . . . . . . . . . . . . .
. C . . . . . . . . . . . . . . . .
. . . D . . . E F . G . . . . . . .
. . . . . . . . . . H . . . . . . .
. . . . . . . I . . . . . . . . . .
. . . . . . . J . K L . . . M . . .
. . . . . . . . . . . . . . . . N .
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. . . . . . . O . . . . . . . . . .
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. . . . . . P . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .
\r\nThere are 36 positions on which to place 32-36 barbarians.\r\nThis creates a new upper bound of 24 villagers required to fulfill the requirements.',NULL,0);
INSERT INTO comment VALUES (11398,1408,5384,'Larry','Sequence','2004-01-28 20:09:48',0,'The sequences represent i^2 for i=1,2,3,...,8\r\nfirst in base 3 then in base 4',NULL,0);
INSERT INTO comment VALUES (11399,1461,5384,'Larry','Solution','2004-01-28 20:18:12',0,'The sequence of triangle numbers is (i)(i+1)/2\r\nMultiplying this by 8 then adding 1 equals: \r\n4i(i+1) +1 = 4i^2 + 4i +1 = (2i+1)^2\r\n',NULL,0);
INSERT INTO comment VALUES (11400,1467,1301,'Charlie','huh?','2004-01-28 22:10:44',4,'I know that a person can be shot a multitude of times. But killed more than once? I don\'t think so. If a shot killed somebody who had already been shot, then the first shot did not kill the victim.',NULL,0);
INSERT INTO comment VALUES (11401,1205,1301,'Charlie','re: 2 timers???','2004-01-28 22:12:53',0,'\"(they do not have dials on telling you how long they\'ve been going - they just beep when the time is up)\" so you can\'t tell when it reaches exactly 5 minutes.',11396,0);
INSERT INTO comment VALUES (11402,1467,3172,'SilverKnight','re: huh?','2004-01-28 22:58:24',0,'lol !\r\n\r\nGamer, please clarify the problem... see the questions in this previous comment.',11400,0);
INSERT INTO comment VALUES (11403,1467,3172,'SilverKnight','re: upper bound, same assumptions','2004-01-29 00:31:00',0,'A sort of better upper bound... same number of villagers, but can handle up to 40 barbarians.\r\n\r\nAnd clearly, we can remove any one of these villagers, and still be able to deal with at least 32 barbarians... so this provides an upper bound of 23.\r\n\r\nSame assumptions:\r\nAssuming that ONLY villagers (not barbarians) can be killed.\r\nAssuming that we can shoot the same villagers more than once.\r\nAssuming that not all villagers must be killed.\r\n\r\nHere, we\'ve got still got 24 villagers in such a way that up to 40 barbarians can line up on the outside and shoot (satisfying the constraints of the problem).\r\n\r\nThere are 20 lines of consequence:\r\n\r\nEFGH\r\nIJKL\r\nMNOP\r\nQRST\r\nCJNU\r\nDKOV\r\nAFRW\r\nBGSX\r\nBDHL\r\nAGKP\r\nCFOT \r\nEJSV\r\nINRX\r\nMQUW\r\nIECA\r\nMJFB\r\nQNGD\r\nURKH\r\nWSOL\r\nXVTP\r\n\r\n
. . . . . . . A . . . . . . .
. . . . . . B . C . . . . . .
. . . . . . . . . . . . . . .
. . . . . . D . E . . . . . .
. . . . . . . F . . . . . . .
. . G . H . . . . . I . J . .
. K . . . L . . . M . . . N .
. . O . P . . . . . Q . R . .
. . . . . . . S . . . . . . .
. . . . . . T . U . . . . . .
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. . . . . . V . W . . . . . .
. . . . . . . X . . . . . . .
. . . . . . . . . . . . . . .. . . . . . . . . . . . . .
\n\nEdited on January 29, 2004, 12:55 am',11397,0);
INSERT INTO comment VALUES (11404,1459,5267,'cogitater','re(3): solution','2004-01-29 03:17:25',0,'Stewards, your question regarding whether B\'s knowledge of the order of arrival came from personal observation or hearsay is an excellent one and critical to the solution of the problem. You are on the right track. When I first considered that question I was concerned that the author may have been imprecise or ambiguous in his language and left us without sufficient clues to solve the problem. However that is not the case. If you look closely at the language used by A and B, paying particular attention to words connoting the certainty of his knowledge, the source of his knowledge, and the perspective from which he derived it, you can answer your own question. No reason for sadness, yours is a bright inquiring mind benefiting from healthy exercise. Neither is ignorance your problem, if that were the case you would not be interested in a site like this. The point is to have fun, make a few new neuron connections in the brain, and hopefully improve our deductive reasoning. Good luck and enjoy.',11382,0);
INSERT INTO comment VALUES (11405,1297,5306,'Purna','SOD','2004-01-29 03:39:07',3,'\r\nWe have a rule that the digit sum of a given number is equal to product of the digit sums of the individual factors of the given number.\r\n\r\nThe digit sum of 19999 is equal to 1.\r\nSo sum of the digits of given number is 1.',NULL,0);
INSERT INTO comment VALUES (11406,1297,5306,'Purna','SOD','2004-01-29 03:39:57',3,'\r\nWe have a rule that the digit sum of a given number is equal to product of the digit sums of the individual factors of the given number.\r\n\r\nThe digit sum of 19999 is equal to 1.\r\nSo sum of the digits of given number is 1.',NULL,0);
INSERT INTO comment VALUES (11407,1459,5391,'York','Is this Solution','2004-01-29 08:39:52',0,'1st Blue Shirt, Green Tie, Green Suspenders\r\n2nd Green Shirt, White Tie, White Suspenders\r\n3rd Red Shirt, Blue Tie, Red Suspenders\r\n4th White Shirt, Red Tie, Blue Suspenders\r\nIs this Correct',NULL,0);
INSERT INTO comment VALUES (11408,1298,3172,'SilverKnight','solution','2004-01-29 12:19:34',3,'m = 36 medals over 6 days\r\n\r\nOn the 1st day, 1 + (1/7)*35 = 6 medals awarded (30 remain)\r\nOn the 2nd day, 2 + (1/7)*28 = 6 medals awarded (24 remain)\r\nOn the 3rd day, 3 + (1/7)*21 = 6 medals awarded (18 remain)\r\nOn the 4th day, 4 + (1/7)*14 = 6 medals awarded (12 remain)\r\nOn the 5th day, 5 + (1/7)*7 = 6 medals awarded (6 remain)\r\nOn the 6th day, the 6 remaining medals were awarded.\r\n_________________________________________\r\n\r\nI simply set this up on an excel spreadsheet, and realized that because m-1 must be divisible by seven, the original number must be 8, or 15, or 22, etc...\r\n\r\nI simply tried the first few numbers and stumbled upon the solution....\r\n
. . . . . . . . . . . . . .
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. . . . . A . B . . . . . .
. . . . C . . . D . . . . .
. . . E . F . G . H . . . .
. . I . J . . . K . L . . .
. . . . . . . . . . . . . .
. . M . N . . . O . P . . .
. . . Q . R . S . T . . . .
. . . . U . . . V . . . . .
. . . . . W . X . . . . . .
. . . . . . . . . . . . . .
. . . . . . . . . . . . . .
. . . . . . . . . . . . . .Day given rem. given2 also remain
\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (11409,1472,5392,'Pablo','My Solution','2004-01-29 12:30:44',0,'I defined the square in the range - 0.5 < x < 0.5 and -0.5
0 36
1 1 35 5 30
2 2 28 4 24
3 3 21 3 18
4 4 14 2 12
5 5 7 1 6
6 6 0 0 0\r\n 1.091 1:05:27.27 32.72727273 32.72727273 163.63636364\r\n 2.182 2:10:54.55 65.45454545 65.45454545 327.27272727\r\n 3.273 3:16:21.82 98.18181818 98.18181818 130.90909091\r\n 4.364 4:21:49.09 130.90909091 130.90909091 294.54545455\r\n 5.455 5:27:16.36 163.63636364 163.63636364 98.18181818\r\n 6.545 6:32:43.64 196.36363636 196.36363636 261.81818182\r\n 7.636 7:38:10.91 229.09090909 229.09090909 65.45454545\r\n 8.727 8:43:38.18 261.81818182 261.81818182 229.09090909\r\n 9.818 9:49: 5.45 294.54545455 294.54545455 32.72727273\r\n10.909 10:54:32.73 327.27272727 327.27272727 196.36363636\r\n12.000 12: 0: 0.00 0.00000000 0.00000000 0.00000000\r\n
\r\n----\r\nIn none of these instances does the angle of the second hand match the angle of the other two hands except at 12. Of course you could say that midnight is different from noon, but both are 12 o\'clock.',NULL,0);
INSERT INTO comment VALUES (11433,1459,5406,'Anu','Try this','2004-01-30 09:49:32',0,'Person Shirt Tie Suspender\r\n1 Red Gr Wh\r\n2 Bl Wh Red \r\n3 Wh Blue Gr\r\n4 Gr Red Blue\r\n \r\n',NULL,0);
INSERT INTO comment VALUES (11434,1467,5391,'York','2nd try','2004-01-30 10:00:03',3,'ok, 12 villagers. 10 in the shape of a pentagon.(5 on the points, 5 in the middle of each side) One in the middle and one off center and higher than center. If the pentagon is point up than that piont is A, lableing clockwise through J. Now the center is K and the off center point is L. Now the sides form ABC, CDE, EFG, GHI, IJA forming 5 lines. Lines aslo form AKF, BKG, CKH, and so on forming 10 lines. the point L lines up to form ALG and CLI forming 2 lines. Total we have 17 lines with 2 barbarians on each end. this totals for 34 barbarians. \r\nWhat do you think?\r\n ',NULL,0);
INSERT INTO comment VALUES (11435,1467,5391,'York','re(2): What about this?','2004-01-30 10:01:51',0,'Brian, \r\nThanks for the input. Please take a look at my \"2nd try\". Let me know what you think.\r\nYork',11419,0);
INSERT INTO comment VALUES (11436,500,5407,'Ashley','Love this one','2004-01-30 11:09:46',0,'Suicide, I believe. :)',NULL,0);
INSERT INTO comment VALUES (11437,525,5407,'Ashley','Almost confusing','2004-01-30 11:11:38',0,'One - himself.',NULL,0);
INSERT INTO comment VALUES (11438,540,5407,'Ashley','You took my riddle!','2004-01-30 11:15:33',0,'Well, it\'s not really mine, but I did want to post it. Of course, I\'ve heard it a bit differently -\r\n\r\nThirty white horses\r\nUpon a red hill\r\nFirst they chomp\r\nThen they stomp\r\nThen they stand still.\r\n\r\nOh, the answer is teeth.',NULL,0);
INSERT INTO comment VALUES (11439,861,5407,'Ashley','It\'s a Hobbit riddle?','2004-01-30 11:19:21',0,'My sister told me this one. My guess is a fish.\r\n\r\n<\\\"><<<<<<<<>< -FISH!',NULL,0);
INSERT INTO comment VALUES (11440,543,5407,'Ashley','Breakfast','2004-01-30 11:25:58',0,'An egg. It was a board opener in my sixth grade science class. Of course, I was told container, not box. A box sounds kinda inaccurate.',NULL,0);
INSERT INTO comment VALUES (11441,1618,5285,'Ady TZIDON','my solution','2004-01-30 11:54:53',3,'let pa pb pc pd denote probability of winning within the 1st round by players A B C D respectively. Let x denote probability of winning the game per se regardless of player\'s place in the round.\r\n\r\nCLEARLY:\r\npa=x\r\npb=x*( 1-x)\r\npc=x*( 1-x)*(1-pb)\r\npd=x*( 1-x)*(1-pb)*(1-pc)\r\nand pa+pb+pc+pd=3/5\r\n\r\nsubstituting and solving we get\r\nx=pa=19.5%\r\npb=15.7%\r\npc=13.2%\r\npd=11.5%\r\n\r\n\r\nto get the values of probabilities for the whole game (multiple rounds) we multiply those values\r\nby 5/3 ( infinite geometric series) to get:\r\n\r\n PA = 32.6 % \r\n PB= 26.18 % \r\n PC= 22.0 %\r\n PD= 19.17 %\r\nady\n\nEdited on January 30, 2004, 11:57 am',NULL,0);
INSERT INTO comment VALUES (11442,1410,4374,'Richard','I Say No','2004-01-30 12:35:46',0,'Using the natural scale of angular measure of \"clock face hours\" the equations for all hands to point at the same place are\r\nt=12t-12k=720t-12m where m and k are integers and t is \"time.\" Hence 11t=12k and 719t=12m so 719k=11m and k=11j, m=719j since 719 and 11 are coprime. Thus t=12j where j is any integer. The time must be a multiple of 12.\n\nEdited on February 1, 2004, 8:34 pm',NULL,0);
INSERT INTO comment VALUES (11443,1459,5408,'lucas','solution','2004-01-30 12:38:52',0,'1st: Green tie, Blue shirt, Green suspenders\r\n2nd: White tie, Green shirt, White suspenders\r\n3rd: Blue tie, Red shirt, Red suspenders\r\n4th: Red tie, White shirt, Blue suspenders',NULL,0);
INSERT INTO comment VALUES (11444,1410,3172,'SilverKnight','re: solution','2004-01-30 13:45:41',3,'Well... Charlie... (and DJ),\r\n\r\nWe might assume that the hour, minute, and second hands are ALWAYS in a \'60th of a circle\' position. (That is, they don\'t swing smoothly, they \'jerk\' 6 degrees when appropriate.) This is the behavior in many digital watches.\r\n\r\nIn other words... the hour hand stays pointing to the 12 until 12:12, at which time it points 6 degrees off of noon. At 12:24, it points to 12 degrees off of noon. At 12:36 it points to 18 degrees. At 12:48, it points to 24 degrees, and at 1:00 it points to 30 degrees (pointing to the one).\r\n\r\nIn this case, at 1:05, it would still be be pointing to 30 degrees.\r\n\r\nThe minute hand would \'jerk\' forward every minute. So, at 1:05 it would reach the 30 degree mark.\r\n\r\nThe second hand would \'jerk\' forward every second. So, at 1:05:05, the second hand would also reach the 30 degree mark.\r\n\r\nAnd similarly, this would happen at the other conjunctions.\r\n\r\nSo, each of the 11 times (in a 12-hour period), the second hand would catch up to them. And in all 11 cases, we would have a \'conjunction\' of the hands.\r\n\r\n- SK',11432,0);
INSERT INTO comment VALUES (11445,1618,3172,'SilverKnight','re: my solution','2004-01-30 14:08:05',0,'Ady, you wrote:\r\n\"CLEARLY:\r\npa=x\r\npb=x*( 1-x)\r\npc=x*( 1-x)*(1-pb)\r\npd=x*( 1-x)*(1-pb)*(1-pc)\r\nand pa+pb+pc+pd=3/5\"\r\n\r\nthis is not the case (well the last line anyway...)\r\n\r\nIt should read:\r\n(1-pa)(1-pb)(1-pc)(1-pd) = (1 - 3/5)\r\n\r\n',11441,0);
INSERT INTO comment VALUES (11446,1468,1920,'Brian Smith','Answer','2004-01-30 14:08:41',0,'(16!)/(4!*4!*4!*4!) = 63063000',NULL,0);
INSERT INTO comment VALUES (11447,1583,3172,'SilverKnight','re(2): I\'m on it - Good luck','2004-01-30 14:11:34',0,'And CLEARLY, we need a computer program to intelligently \'brute force\' the solution... \r\n\r\n(The \"simplest-minded\" brute force of trying every digit in every position has 10^81 possibilities... which is too many to deal with, but this solution space can be very well pruned.)\r\n\r\nI, uh, have to go to another meeting.... Charlie...? :-)',11431,0);
INSERT INTO comment VALUES (11448,1468,1301,'Charlie','Solution','2004-01-30 14:37:03',3,'Label the strings A, B, C and D.\r\n\r\nWhen a given string is shot at, there\'s no choice as to which ball on the string to hit, so the number of ways is just the ways of rearranging four A\'s, four B\'s, four C\'s and four D\'s, which is:\r\n\r\n16!/(4!*4!*4!*4!) = 63,063,000 ',NULL,0);
INSERT INTO comment VALUES (11449,1293,3735,'Nick Hobson','Last two digits','2004-01-30 15:22:31',3,'By the remainder theorem (also known as the factor theorem), non-zero (a - b) divides (a^n - b^n). For odd n, we therefore have (a - (-b)) divides (a^n - (-b)^n), or (a + b) divides (a^n + b^n).\r\n\r\nFor odd n, we can also explicitly factorize a^n + b^n, as follows. Writing n = 2m+1, we have:\r\na^(2m+1) + b^(2m+1) = (a + b)(a^2m - a^(2m-1)b + a^(2m-2)b^2 - ... - ab^(2m-1) + b^2m).\r\n\r\nRewriting the series as (1^99 + 99^99) + (2^99 + 98^99) + ... + (49^99 + 51^99) + (50^99), 100 divides each of the first 49 bracketed terms by the factor theorem. Since 100 divides 50^2, it also divides 50^99.\r\n\r\nTherefore 100 divides the whole series, and the last two digits are 00.\r\n\r\nEdited on January 31, 2004, 7:53 am\n\nEdited on January 31, 2004, 8:06 am',NULL,0);
INSERT INTO comment VALUES (11450,1583,5345,'Rawlyn','Best solution I\'ve found yet','2004-01-30 19:23:54',1,'Well, after four hours coding, and about ten runs so far I\'ve found a solution with a sequence of length 97. \'Ere \'tis.\r\n\r\nSequence: 606 - 702 (97)\r\n\r\n2 1 6 1 0 2 6 6 1\r\n1 3 6 4 2 5 0 8 3\r\n9 5 6 6 1 7 6 9 5\r\n6 2 5 6 4 6 6 6 2\r\n9 7 4 6 3 8 6 8 0\r\n1 9 6 4 8 3 6 7 0\r\n6 1 6 5 6 6 9 6 7\r\n3 2 6 7 3 6 2 0 7\r\n7 6 4 0 9 6 1 8 6\r\n\r\nGeneration: 10942\r\n\r\nIf anyone can pick out any errors I\'d be glad of the help - my eyes are tired! :P\r\n\r\nOh, Brian, would a number such as 001 count? I\'ve only been checking the range of numbers 100-999 - if I\'m wrong it\'s easily changed :)',NULL,0);
INSERT INTO comment VALUES (11451,1583,5345,'Rawlyn','re: Best solution I\'ve found yet','2004-01-30 19:25:30',0,'Oops - just noticed \"no leading zeros\". Should have read that. Just ignore me....',11450,0);
INSERT INTO comment VALUES (11452,1583,5345,'Rawlyn','Very slightly better...','2004-01-30 19:51:05',0,'Sequence: 200 - 297 (98)\r\n\r\n1 6 4 2 5 0 2 2 1\r\n9 8 5 1 1 9 6 0 3\r\n2 8 2 2 3 4 2 3 7\r\n6 7 2 8 2 2 2 0 2\r\n1 1 2 7 8 0 5 2 0\r\n6 2 5 5 6 4 9 3 8\r\n9 2 4 2 2 2 2 2 2\r\n2 7 9 4 2 1 3 6 2\r\n2 0 2 7 7 8 9 5 6\r\n\r\nGeneration: 1261',NULL,0);
INSERT INTO comment VALUES (11453,1583,5345,'Rawlyn','Yet another','2004-01-30 21:03:22',1,'Sequence: 501 - 599 (99)\r\n\r\n5 9 8 5 9 3 5 0 2\r\n0 7 1 5 3 6 5 6 9\r\n9 4 5 5 0 7 5 2 8 \r\n5 5 0 4 1 8 5 3 0\r\n9 6 5 1 3 2 5 5 1\r\n4 7 1 0 5 8 5 9 9\r\n8 5 5 5 6 4 5 4 5\r\n5 4 8 9 6 2 3 7 4\r\n2 8 5 7 2 5 5 5 7\r\n\r\nGeneration: 4401\r\n\r\nYawn it\'s getting late but I have to sit here clicking \"GO\" over and over... :P\r\n',NULL,0);
INSERT INTO comment VALUES (11454,1583,3172,'SilverKnight','re: Very slightly better...','2004-01-30 21:21:00',0,'Does the problem mean the WHOLE number must be in a straight line? Or can you take a turn midway through the number?\r\n\r\nBrian, do you want to comment?',11452,0);
INSERT INTO comment VALUES (11455,1583,5345,'Rawlyn','Again...','2004-01-30 21:47:13',0,'Sequence: 800 - 899 (100)\r\n\r\n6 7 8 5 9 8 4 6 6\r\n9 8 7 1 7 4 8 6 1\r\n1 9 0 8 8 3 8 2 8\r\n8 8 8 6 9 8 8 0 8\r\n3 0 5 5 0 3 2 1 4\r\n0 8 5 7 1 6 7 9 1\r\n8 6 8 8 8 8 8 8 8\r\n3 7 2 5 3 8 2 4 1\r\n0 0 4 8 3 2 8 5 2\r\n\r\nGeneration: 8153\r\n\r\nSilverKnight - it would certainly be an interesting problem if you\'re allowed to turn corners.',NULL,0);
INSERT INTO comment VALUES (11456,1293,4374,'Richard','re: Last two digits','2004-01-30 22:09:15',0,'\"By the remainder theorem (also known as the factor theorem), non-zero (a + b) divides (a^n + b^n).\"\r\n\r\nBut if I take a=3, b=1, and n=2, a^n+b^n=10, while a+b=4 and 4 does not divide 10. It is true that a-b divides a^n-b^n.',11449,0);
INSERT INTO comment VALUES (11457,1468,4374,'Richard','Masterful Obfuscation','2004-01-31 01:09:24',0,'The obfuscation employed in the problem statement is masterful, but with enough thought one finally cuts through it to see that what we are doing is sucessively choosing in any order any of the strings that haven\'t yet been completely wiped out. This is the same as making up all possible strings of 16 characters chosen from an alphabet of 4 characters each of which is to be used exactly 4 times. This is a special case of the problem of strings made out of a multiset, and the count of all possible such strings is a multinomial coefficient. The answer in the particular case of the present problem is as given in the previous two comments.',NULL,0);
INSERT INTO comment VALUES (11458,1468,5285,'Ady TZIDON','re: Masterful Obfuscation','2004-01-31 03:39:21',0,'I agree.\r\nIt is the 1st time a problem gets a \"5\" rating from me.\r\n\r\nady',11457,0);
INSERT INTO comment VALUES (11459,1468,4507,'Penny','Solution','2004-01-31 05:02:27',3,'This answer is the same as Charlie\'s, but not half as elegant as his.\r\n\r\nIf the balls are hanging in this formation:\r\n\r\nb01....b02....b03....b04\r\nb05....b06....b07....b08\r\nb09....b10....b11....b12\r\nb13....b14....b15....b16 \r\n\r\nThen the order of balls shot must include these sequences:\r\n\r\n {b13, b09, b05, b01}\r\n [b14, b10, b06, b02}\r\n {b15, b11, b07, b03}\r\n {b16, b12, b08, b04}\r\n\r\nIf N is all the ways to merge these four sequences that preserve the internal sequence orders, the N*[(4!)^4)] = all the ways to order 16 balls = 16!\r\n \r\nN = (16!)/[(4!)^4] \r\n = (20,922,789,888,000)/(331,776)\r\n\r\nN=63,063,000 = the number of ways to shoot the glass balls\r\n',NULL,0);
INSERT INTO comment VALUES (11460,1293,3735,'Nick Hobson','re(2): Last two digits','2004-01-31 07:57:31',1,'\"But if I take a=3, b=1, and n=2, a^n+b^n=10, while a+b=4 and 4 does not divide 10. It is true that a-b divides a^n-b^n.\"\r\n\r\nThanks Richard, you\'re right, I was a little hasty there! I meant to say that (a + b) divides (a^n + b^n), for *odd* n. This does follow from the remainder theorem, and I\'ve edited my post accordingly.\n\nEdited on January 31, 2004, 7:59 am',11456,0);
INSERT INTO comment VALUES (11461,1300,5285,'Ady TZIDON','my solution','2004-01-31 10:03:03',0,'answer :53\r\n m*(m-3)/2=1325\r\n >> m=53\r\n\r\nady',NULL,0);
INSERT INTO comment VALUES (11462,1618,5285,'Ady TZIDON','re(2): my solution','2004-01-31 10:21:39',0,'sk\r\nI still believe I am right (please specify why not): pa pb etc are EXCLUSIVE probabilities and therefore may be just added up.-\r\ne.g. pc is a probability of player C winning in\r\nthe 1st round taking into account that A and B did not win.\r\nYou may also verify my figures by simulating the game and running it for ,say, 10000 times. \r\n\r\nady',11445,0);
INSERT INTO comment VALUES (11463,1294,5419,'Dale','re(2): Standard solution','2004-01-31 10:28:53',0,'10 CLS\r\n20 PRINT \"FIMD THE SMALLEST NUMBER SUCH THAT IF ITS RIGHT MOST\"\r\n30 PRINT \"DIGIT IS PLACED AT ITS LEFT END, THE NEW NUMBER SO\"\r\n40 PRINT \"FORMED IS PRECISELY FIFTY PERCENT LARGER THAN THE\"\r\n50 PRINT \"ORIGINAL NUMBER.\"\r\n60 A = 0: B = 0: C = : D = 1: E = 0: F = 0 \r\n120 F = F + 2 \r\n121 IF F > 9 THEN F = 0: E=E+1 \r\n122 IF E > 9 THEN E = 0: D=D+1123 IF D > 9 THEN D = 0: C=C+1\r\n124 IF C > 9 THEN C = 0: B=B+1\r\n125 IF B > 9 THEN B = 0: A=A+1\r\n126 IF A > 9 THEN 250\r\n130 N1 = A * 100000 + B * 10000 + C * 1000 + D * 100 + E * 10 + F\r\n140 N2 = F * 100000 + A * 10000 + B * 1000 + C * 100 + D * 10 + E\r\n146 REM WAIT &H20, 1\r\n201 REM PRINT USING \"# # # # # # # # # # # #\"; A; B; C; D; E; F; F; A; B; C; D; E\r\n202 REM PRINT USING \"###,###,###,### ###,###,###,###\"; N1; N2\r\n222 IF N2 = (N1*.5)+N1 THEN 230 ELSE 120\r\n230 PRINT USING \"#,###,### #,###,###\"; N1; (N2 * .5) + N2\r\n240 REM PRINT CHR$(12)\r\n250 END\r\n',11347,0);
INSERT INTO comment VALUES (11464,1294,5419,'Dale','re(2): Standard solution','2004-01-31 10:35:11',0,'10 CLS\r\n20 LPRINT \"FIMD THE SMALLEST NUMBER SUCH THAT IF ITS RIGHT MOST\"\r\n30 LPRINT \"DIGIT IS PLACED AT ITS LEFT END, THE NEW NUMBER SO\"\r\n40 LPRINT \"FORMED IS PRECISELY FIFTY PERCENT LARGER THAN THE\"\r\n50 LPRINT \"ORIGINAL NUMBER.\"\r\n60 A = 0: B = 0: C = 0: D = 0: E = 0: F = 0\r\n70 A = A + 1\r\n80 B = B + 1\r\n90 C = C + 1\r\n100 D = D + 1\r\n110 E = E + 1\r\n120 F = F + 2\r\n130 N1 = A * 100000 + B * 10000 + C * 1000 + D * 100 + E * 10 + F\r\n140 N2 = F * 100000 + A * 10000 + B * 1000 + C * 100 + D * 10 + E\r\n150 IF F > 9 THEN F = 0: GOTO 110\r\n160 IF E > 9 THEN E = 0: GOTO 100\r\n170 IF D > 9 THEN D = 0: GOTO 90\r\n180 IF C > 9 THEN C = 0: GOTO 80\r\n190 IF B > 9 THEN B = 0: GOTO 70\r\n200 IF A > 9 THEN 250\r\n210 REM LPRINT USING \"###,###,###,### ###,###,###,###\"; N1; N2\r\n220 IF N2 = (N1 * .5) + N1 THEN 230 ELSE 120\r\n230 LPRINT USING \"#,###,### #,###,###\"; N1; N2\r\n231 LPRINT USING \"#,###,### * .5 = #,###,### + #,###,### #,###,###\"; N1; N1 * .5 + N1; N1; N2\r\n240 LPRINT CHR$(12)\r\n250 END\r\n\r\n',11347,0);
INSERT INTO comment VALUES (11465,1618,5285,'Ady TZIDON','another remark to SK \'S solution','2004-01-31 10:37:38',0,'both of us interpret differently the statement \"They all have even odds of winning a game. \"\r\nIt is my understanding that the rules of the game imply a certain well-defined probability figure\r\nx (=pa) for a single history-independent (=memory-less) event.\r\nA valid example of such a game ( e.g. for x=2 0%)//rem: I CORRECTED THE ERRONEOUS NUMBERS WRITTEN PREVIOUSLY// is drawing one marble out of bag with 1 red and 4, black marbles and counting a draw of a red as a \"win\", IF BLACK THE MARBLE IS RETURNED INTO THE BAG AND THE GAME CONTINUES. \r\n\r\nAlso the numbers qualifying as an answer to the \"game of luck\" should add up to 100%-\r\nwhich they do in my case and do not in yours.\r\n\r\nWill appreciate your (or other members) comments\r\n\r\nady\n\nEdited on January 31, 2004, 6:18 pm',NULL,0);
INSERT INTO comment VALUES (11466,1300,4507,'Penny','Solution','2004-01-31 10:43:08',3,'Answer: it has 53 vertices.\r\n\r\nExplanation:\r\n\r\nIf a polygon has N vertices, then every vertex has (N-3) vertices that are nonadjacent, with a diagonal between them. Since every diagonal connects 2 vertices, division by 2 will avoid counting diagonals twice.\r\n\r\nIf N(N-3)/2 = 1325,\r\n\r\nthen N=53\r\n\n\nEdited on February 1, 2004, 10:08 am',NULL,0);
INSERT INTO comment VALUES (11467,1294,5285,'Ady TZIDON','re(3): Standard solution DALE - I WONDER','2004-01-31 10:45:52',0,'DALE - I WONDER:\r\na/ where are your answers (= output??)\r\nb/ how did you know to assume a 6-digit answer??\r\n\r\nady',11464,0);
INSERT INTO comment VALUES (11468,1294,5419,'Dale','re(3): Standard solution','2004-01-31 11:00:38',0,'This is the results of running the basic program:\r\n285,714 428,571\r\n285,714 * .5 = 428,571 + 285,714\r\nWhen the program would not produce an results, I would add another register. - Dale',11464,0);
INSERT INTO comment VALUES (11469,1618,1301,'Charlie','re: another remark to SK \'S solution','2004-01-31 11:50:33',0,'It was initially my misinterpretation also that a \"game\" was one player\'s turn during one round. But that is not the case, as the puzzle states that \"When someone wins, the game ends.\" Before someone wins the same game is still on. The idea is to adjust the probabilities for each player so that each has the same chance of winning the total game.\r\n\r\nBut even with the idea that there is a constant x, which is the probability of winning on a given turn, assuming you get to your turn, the set of equations you originally give is wrong:\r\n\r\nThe probability that c would win on a given turn, taking into consideration the previous probabilities is given by you as pc = x*(1-x)*(1-pb)\r\n\r\nHowever, pb is the probability that B would win already reduced by the chance that A did not win. The actual probability that C would be given a chance is (1-x)*(1-x), and so the probability pc is x*(1-x)*(1-x), rather than x*(1-x)*(1-pb), as we are assuming an equal chance of any given turn producing a winner.\r\n\r\nLook at my original solution to see how this (actually incorrect) assumption should work out. For the actual way Tristan intended, see SK\'s solution and my correction to my own post.',11465,0);
INSERT INTO comment VALUES (11470,1618,1301,'Charlie','re(2): another remark to SK \'S solution','2004-01-31 11:53:51',0,'By the way, a way to do this would be to have 3 red balls and 17 white balls in a box. When a player draws a red ball he wins and the game ends. When A, B or C draws a white ball, two more white balls are removed from the box before the next player\'s turn. Of course if D draws a white ball, all the balls go back in the box for A\'s next turn, as a new round begins.',11469,0);
INSERT INTO comment VALUES (11471,1300,3992,'Jane Doe','Common sense','2004-01-31 12:01:22',2,'A diagonal is a line that connects two vertices. A square has 2 diagonals, an octagon has 4 diagonals....and so on and so forth. Therefore, a polygon with 1325 diagonals should have 1325*2 vertices = 2650.',NULL,0);
INSERT INTO comment VALUES (11472,69,5285,'Ady TZIDON','a philosophical remark -better late than never','2004-01-31 12:16:03',1,'the existing relation between the three speeds: \r\n1/60+1/90=2/72\r\nmakes the solution independent of the uphill and downhill distribution and therefore we can assume a flat roat of length d and an average speed of 72:\r\n2*d=9*72 ==> d=9*36= 324\r\n\r\nady\r\n ',NULL,0);
INSERT INTO comment VALUES (11473,1300,5285,'Ady TZIDON','re: Common sense it is not','2004-01-31 12:41:00',1,'jANE\r\n Two samples do not a rule make\r\n Please read Penny\'s comment and draw an octagon with 5\r\ndiagonals out of every vertix... HOW MANY ALTOGETHER?\r\n\r\nady\n\nEdited on January 31, 2004, 12:44 pm',11471,0);
INSERT INTO comment VALUES (11474,1618,5285,'Ady TZIDON','re(3): another remark to SK \'S solution','2004-01-31 13:02:39',1,'I believe that further correspondance is really counter-productive, since both of us define different games.\r\nYour remark about inserting x instead of pb and pc is a valuable one and I am going to correct my answers accordingly -later.\r\nIt would be beneficial for everybody if the author (Tristian) will specify the nature of the game e.g. in terms of marbles in a bag. As you know in my model one draws a marble( the same distribution for everybody)- if won the game ends,- if not the marble is returned.\r\n\r\nI do not know how to pass my remarks to the author of the puzzle- may be you do.\r\n\r\nady\r\n,',11470,0);
INSERT INTO comment VALUES (11475,1300,1626,'Gamer','re(2): Common sense it is not','2004-01-31 13:21:55',0,'That would work, except every vertice has more than one diagonal coming off of it (as long as there are more than 4 sides), so the previously given solutions are better.',11473,0);
INSERT INTO comment VALUES (11476,1293,5285,'Ady TZIDON','re(2): last digit','2004-01-31 13:23:30',1,'you mean 8 not 3....\r\n\r\n2 to any positive integer power ends with an even digit\r\n\r\nady',11354,0);
INSERT INTO comment VALUES (11477,1300,5285,'Ady TZIDON','re(3): Common sense it is not ATT: GAMER','2004-01-31 13:34:54',0,'Dear GAMER\r\n PLEASE RE-READ MY COMMENT ... SLOWLY-\r\nTHERE IS ABSOLUTELY NOTHING WRONG WITH IT.\r\nYour amendment does not clarify a thing.\r\n\r\nady\r\n\r\n\n\nEdited on January 31, 2004, 1:38 pm',11475,0);
INSERT INTO comment VALUES (11478,511,5345,'Rawlyn','Tao','2004-01-31 13:36:01',0,'I hate questions which involve \"God\". Why? \"God\" means many different things to many different and is (as far as I can tell) undefineable. This pretty much makes the whole question completely meaningless.\r\n\r\nIn my world, \"God\" and the rock are one and the same, part of an ever wandering void. Although I cannot pick myself up, I can pick up my pet cat, and we, like God and the rock are also part of the same whole. So the answer - yes and no, but it doesn\'t really matter anyways...\r\n\r\nPeace,\r\nRawlyn.',NULL,0);
INSERT INTO comment VALUES (11479,348,5345,'Rawlyn','re: an alternate solution','2004-01-31 13:47:51',0,'Is a painting of a man still called \"a man\" or has it now become \"a painting of a man\"?',4864,0);
INSERT INTO comment VALUES (11480,1300,1301,'Charlie','re: Common sense','2004-01-31 13:50:59',0,'An octagon has 20 diagonals: Each of the 8 vertices can connect to any of 5 of the other vertices (just not to itself nor to either immediate neighbor). So far we\'ve counted 40; but we\'ve counted each one twice--once in each direction, so there are 20. A diagonal of a polygon should not be confused with the diameter of a circle. The latter must go through the center, but the former need not.',11471,0);
INSERT INTO comment VALUES (11481,1618,1301,'Charlie','re(4): another remark to SK \'S solution','2004-01-31 14:09:22',0,'\"I believe that further correspondance is really counter-productive, since both of us define different games.\"\r\n\r\nAs noted, my initial post assumed the same game you are talking about. I later modified it to treat the whole event as the single game.\r\n\r\n\"Your remark about inserting x instead of pb and pc is a valuable one and I am going to correct my answers accordingly -later. \"\r\n\r\nHopefully, when you do the math, you will see that what you call x is 1 minus the fourth root of 2/5.\r\n\r\n\"It would be beneficial for everybody if the author (Tristian) will specify the nature of the game e.g. in terms of marbles in a bag. As you know in my model one draws a marble( the same distribution for everybody)- if won the game ends,- if not the marble is returned. \"\r\n\r\nTwo problems here: (1) Tristan\'s idea was that the puzzle was to find the nature of the game given the specifications. (2) In this case marbles in a bag wouldn\'t work for the idea of the game as you see it, and as I originally saw it: the odds are irrational. As it turns out, in the other interpretation, the odds are rational, and can be expressed as I stated in a previous post, in terms of marbles in a bag.\r\n\r\nPerhaps Tristan was infelicitous in specifying \"Every time a player takes a turn, they have a certain chance of winning,\" making it sound as if each turn by each player had the same probability of a win. What apparently was meant was that \"Every time a given player takes a turn, he or she has a certain chance of winning.\"\r\n\r\n\"I do not know how to pass my remarks to the author of the puzzle- may be you do. \"\r\n\r\nI\'m sure Tristan will be logging on to see these comments.\r\n\r\n\r\n\r\n\r\n',11474,0);
INSERT INTO comment VALUES (11482,1300,1626,'Gamer','re(2): Common sense','2004-01-31 14:46:41',0,'Note that I was not talking about your solution Ady, but Jane Doe\'s solution instead.',11480,0);
INSERT INTO comment VALUES (11483,1294,5419,'Dale','gold','2004-01-31 15:10:09',4,'Five pirates looted a ship and stole a box of gold coins. They decided to divide the coins the next day. That night one of the pirates for some unknown reason threw the first coin into the ocean then divided the box of gold into 5 stacks. The pirate took one of the stacks of coins and put them in his pocket. The remaining 4 stacks were returned to the box. During the night the rest of the pirates did the same thing. The next morning all the pirates threw the first coin into the ocean then divided the box of coins into 5 stacks Each pirate took one of the stacks to add to the other stack they had acquired. What is the least amount of gold coins had to be in the box ?',NULL,0);
INSERT INTO comment VALUES (11484,1294,3172,'SilverKnight','re: gold','2004-01-31 16:11:13',0,'Dale,\r\n\r\nFirst and foremost: please do not post problems as comments to other problems. You should submit the problems to the site, and let them await their turn. What\'s more, you might choose to become more familiar with this site and the problems in the archives, because...\r\n\r\nSecond, this problem was posted 10 months ago under the name Monkeys and Coconuts.\r\n\r\n- SK\r\n',11483,0);
INSERT INTO comment VALUES (11485,1618,5285,'Ady TZIDON','re(5): another remark to SK \'S solution','2004-01-31 17:51:41',1,'Charlie,\r\nThanks for your remarks.\r\nHowever you did not comment about the sum of the probabilities not being equal to 1 (100%).\r\nI still maintain that ambiguity prevails.\r\nI put the problem on hold untill further clarifications\r\nand if none come up I will solve the problem upon \r\nwell-defined assumptions.\r\nAnd again- your comments are appreciated.\r\nady',11481,0);
INSERT INTO comment VALUES (11486,1618,3172,'SilverKnight','re(6): another remark to SK \'S solution','2004-01-31 18:54:46',0,'I must have missed something Ady...\r\n\r\nWho said there\'s a 100% chance of anything occuring? (except that EVENTUALLY, after perhaps many rounds, someone must win)\r\n\r\nWhat Tristan wrote is clear.',11485,0);
INSERT INTO comment VALUES (11487,1467,5429,'Jesse','Assumptions...facts','2004-01-31 20:24:17',0,'The answer is 7.\r\n\r\nFacts:\r\nThere is a town.\r\nThere are 32 barbarians.\r\nFire exactly at the same time.\r\nBullet must go over 3 villagers heads before \"contact\", dead or alive.\r\nNo one was at the same place at the same time (IE: Standing on someones head)\r\n\r\nImmediate Assumptions (possibly not reality):\r\n\r\nTown is round.\r\nBarbarians line up single file side ways.\r\nArrows hit different individuals.\r\n\r\nMy thoughts:\r\n\r\nThe definition of around is as follows; \"On all sides of; encircling; encompassing; so as to make the circuit of; about.\" dictionary.com\r\nSo the assumption that the town is round can possibly be inaccurate. For instance if the town were square or rectangular then 4 barbarians, Could be \"around\" the city covering all 4 sides. So if the barbarians lined up single file, 8 to a file, on all four sides then they would be around the town. Here is a illuastration.\r\n\r\nB\'s represent barbarians and T\'s townspeople.\r\n\r\n B\r\n B\r\n B\r\n B\r\n B\r\n B\r\n B\r\n ...........\r\n . T .\r\nBBBBBBBB. TTTT .BBBBBBBB\r\n . T .\r\n . T .\r\n ...........\r\n B\r\n B\r\n B\r\n B\r\n B\r\n B\r\n B\r\n B\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (11488,1467,5429,'Jesse','illustration wrong... Explained below.','2004-01-31 20:34:34',0,'32 barbarians split into 4 groups of 8. 8 on each side of a square shaped town. They all line up single file. The towns people huddle fearfully in the middle of the town in the shape of a T. 4 across and 3 down:\r\n \r\nATTC\r\nT\r\nT\r\nB\r\n\r\nThe barbarians situated on the north side would fire and hit \"B\". The barbarian on the east would hit \"A\". South \"A\". West \"C\". Thus only 7 towns people.\r\n',NULL,0);
INSERT INTO comment VALUES (11489,1284,5388,'Eliza','','2004-02-01 02:38:55',0,'',NULL,0);
INSERT INTO comment VALUES (11490,1284,5388,'Eliza','solution','2004-02-01 02:41:36',0,'I wonder why my last attempt at posting didn\'t work...\r\nAnyway, thank goodness I saved my solution before posting! :D\r\n\r\n\r\nI\'m not sure if I got this right, but here\'s what I did:\r\n\r\nThe first square gets chosen at random--it doesn\'t matter whether it\'s black or white.\r\nThe probability for the next two squares being chosen on the same diagonal depends on the first square chosen. I separated the two colors and only dealt with one color, because the results for each color would be the same, and the problem doesn’t require that we specify a color.\r\n\r\nSo, if the first square was A1, the probability for the second square to be on the A1-H8 diagonal is 7/63, and for the third square, 6/62. Multiply the two, and you get 42/3906.\r\n\r\nThe same goes for all the other squares on the A1-H8. However, some squares are part of only one diagonal (A1, H8, A7, B8, etc.), while others are part of two diagonals. Therefore, I dealt with each of 32 same-color squares individually, and got:\r\n\r\nA1: 42/3906 (A1-H8 diagonal)\r\nH8: 42/3906 (A1-H8 diagonal)\r\nB2: 42/3906 (A1-H8 diagonal); and 2/3906 (A3-C1 diagonal)\r\nG7: 42/3906 (A1-H8 diagonal); and 2/3906 (F8-H6 diagonal)\r\nC3: 42/3906 (A1-H8 diagonal); and 12/3906 (A5-E1 diagonal)\r\nF6: 42/3906 (A1-H8 diagonal); and 12/3906 (D8-H4 diagonal)\r\nD4: 42/3906 (A1-H8 diagonal); and 30/3906 (A7-G1 diagonal)\r\nE5: 42/3906 (A1-H8 diagonal); and 30/3906 (B8-H2 diagonal)\r\nA3: 20/3906 (A3-F8 diagonal); and 2/3906 (A3-C1 diagonal)\r\nC1: 20/3906 (C1-H6 diagonal); and 2/3906 (A3-C1 diagonal)\r\nF8: 20/3906 (A3-F8 diagonal); and 2/3906 (F8-H6 diagonal)\r\nH6: 20/3906 (C1-H6 diagonal); and 2/3906 (F8-H6 diagonal)\r\nB4: 20/3906 (A3-F8 diagonal); and 12/3906 (A5-E1 diagonal)\r\nD2: 20/3906 (C1-H6 diagonal); and 12/3906 (A5-E1 diagonal)\r\nE7: 20/3906 (A3-F8 diagonal); and 12/3906 (D8-H4 diagonal)\r\nG5: 20/3906 (C1-H6 diagonal); and 12/3906 (D8-H4 diagonal)\r\nC5: 20/3906 (A3-F8 diagonal); and 30/3906 (A7-G1 diagonal)\r\nD6: 20/3906 (A3-F8 diagonal); and 30/3906 (B8-H2 diagonal)\r\nE3: 20/3906 (C1-H6 diagonal); and 30/3906 (A7-G1 diagonal)\r\nF4: 20/3906 (C1-H6 diagonal); and 30/3906 (B8-H2 diagonal)\r\nA5: 12/3906 (A5-E1 diagonal); and 6/3906 (A5-D8 diagonal)\r\nD8: 12/3906 (D8-H4 diagonal); and 6/3906 (A5-D8 diagonal)\r\nE1: 12/3906 (A5-E1 diagonal); and 6/3906 (E1-H4 diagonal)\r\nH4: 12/3906 (D8-H4 diagonal); and 6/3906 (E1-H4 diagonal)\r\nB6: 30/3906 (A7-G1 diagonal); and 6/3906 (A5-D8 diagonal)\r\nC7: 30/3906 (B8-H2 diagonal); and 6/3906 (A5-D8 diagonal)\r\nF2: 30/3906 (A7-G1 diagonal); and 6/3906 (E1-H4 diagonal\r\nG3: 30/3906 (B8-H2 diagonal); and 6/3906 (E1-H4 diagonal)\r\nA7: 30/3906 (A7-G1 diagonal); and 6/3906\r\nB8: 30/3906 (B8-H2 diagonal)\r\nG1: 30/3906 (A7-G1 diagonal)\r\nH2: 30/3906 (B8-H2 diagonal)\r\n\r\n\r\nThis makes a total of 58 values. To get an average, I added up all the numerators, and they gave me a total of 1176.\r\n1176 is not divisible by 58, so instead I multiplied the denominator by 58: 3906 * 58 = 226548.\r\n\r\nThe resulting fraction is: 1176/226548 or:\r\n14/2697',NULL,0);
INSERT INTO comment VALUES (11491,1459,4507,'Penny','re: Try this','2004-02-01 09:01:30',0,'Sorry, the puzzle states that the person wearing the green shirt came in just before the person wearing the red suspenders.',11433,0);
INSERT INTO comment VALUES (11492,1618,1301,'Charlie','re(6): another remark to SK \'S solution','2004-02-01 12:06:36',0,'re:\r\n\"However you did not comment about the sum of the probabilities not being equal to 1 (100%). \"\r\n\r\nActually I think the question had been whether\r\npa+pb+pc+pd=3/5\r\nand this is true per your interpretation of the game, but, even then, not given the way they were calculated in\r\npa=x \r\npb=x*( 1-x) \r\npc=x*( 1-x)*(1-pb) \r\npd=x*( 1-x)*(1-pb)*(1-pc) \r\ndue to the use of pb and pc in the formulae for pc and pd instead of x.\r\n\r\nAnd again, this is in your current and my original interpretation of the puzzle, which is not the intent of the poser, who wanted the situation to be considered:\r\n\"When someone wins, the game ends. They all have even odds of winning a game.\" That is, the whole set of possibly multiple rounds is one game, and the author wants each player to have the same chance of winning that game.\r\n\r\nThe only problem I see is in the singular construal of the word \"they\" in \"Every time a player takes a turn, they have a certain chance of winning.\" \"They have\" actually means \"he or she has\". We can see this from the wording of the puzzle as a whole--specifically the two sentences I quoted before.\r\n\r\n',11485,0);
INSERT INTO comment VALUES (11493,1395,3372,'Sam','','2004-02-01 12:20:21',0,'Hmmm... well let me just flip through my little Hofstadter booklet...\r\n\r\nNo no, I\'ll try to work one out on my own.\r\n\r\nThere will be a dozen places on the net where these sentances can be found. Can we all attempt to work them out without using other people\'s? Anyone can do a search...\r\n:)',NULL,0);
INSERT INTO comment VALUES (11494,1395,5285,'Ady TZIDON','see: METAMAGICAL THEMAS','2004-02-01 12:42:49',3,'By all means see: METAMAGICAL THEMAS by D.Hofstadter p.27.\r\n\r\nI am too lazy to copy but there are several pearls there. Especially I like the one starting with:\r\n\" Only a fool would take trouble to verify that this sentence was composed of ten a\'s, three b\'s.......\"\r\n\r\nAnd remember:\r\n\"yields falsehood when appended \r\nto its quotation \" yields falsehood when appended to its quotation. (SAME SOURCE)\r\n\r\nady\r\n',NULL,0);
INSERT INTO comment VALUES (11495,1395,5033,'Captain Paradox','Two sentencess','2004-02-01 13:48:02',3,' This sentence contains thirty-eight letters.\r\n
Heh, I first heard this riddle when I was six. It was in my Greek mythology coloring book.',10623,0);
INSERT INTO comment VALUES (11521,1583,1920,'Brian Smith','To Rawlyn','2004-02-02 13:35:09',0,'I would like to take a look at the algorithm you are using to generate these results. You can email me at brianscsmith AT yahoo DOT com',NULL,0);
INSERT INTO comment VALUES (11522,1619,3172,'SilverKnight','Full Solution','2004-02-02 13:48:34',3,'729 unit cubes\r\n____________________________________________\r\n\r\nIf we make a large cube which is 9 unit cubes on a side then it is comprised of 9x9x9 = 729 unit cubes.\r\n\r\nThe interior is a 7x7x7 cube, therefore, the surface is made up of 729 - 7x7x7 = 729 - 343 = 386 unit cubes, and each face is 9x9=81 unit cubes, so the interior square of each face is 7x7=49 unit cubes.\r\n\r\nBut we have to come up with 217 cubes, which is 169 cubes fewer than the 386 surface cubes.\r\n\r\nNow, if we don\'t paint THREE sides of the large cube, that all share the same corner, then we will avoid painting the interiors of the sides (3 x 49 = 147 unit cubes), 3 common sides (3 x 7 = 21 unit cubes) and 1 common corner (1 unit cube). Therefore, we have avoided painting (147 + 21 + 1 =) 169 unit cubes leaving 217 painted, which is what we were looking for!\r\n__________________\r\n\r\nAlternatively (and equivalently), if we paint THREE sides of the large cube, that all share the same corner, then we paint 3x81 cubes, less the 3 2-side intersections -(3x8), less the 1 3-side intersection (counted twice) -2, = 243 - 24 - 2 = 217 painted, which is what we were looking for.\r\n__________________\r\n\r\nSo far, we\'ve proved that this is *a* solution....\r\n__________________\r\n\r\nTo prove this is the *only* solution:\r\n\r\nA 7-cube has 7x7x7 - 5x5x5 = 343 - 125 = 218 surface cubes, which is one too many, and we can\'t reduce the painted cubes by 1, so all solutions must be larger than a 7-cube.\r\n\r\nIf we go up to a 15x15 cube, one side is 225 cubes, so, we know all solutions, are smaller than a 15-cube.\r\n\r\nAlso, we can rule out 14x14 (because we can\'t get to 217 with sides of 196 cubes).\r\nWe can rule out 13x13 (because we can\'t get to 217 with sides of 169).\r\nWe can rule out 12x12 (because we can\'t get to 217 with sides of 144).\r\n\r\nNow we know the solution set lies (inclusively) between a 8-cube and an 11-cube.\r\n\r\nWith an 8 cube, the faces are 64 a piece... if we paint three faces with only two shared edges (must share at least two), we paint 64x3 - (8x2) = 192-16 = 176, too few. If we paint four faces with four shared edges (must share at least 4), then we get 64x4 - 4x8 = 256 - 32 = 216, too few, and if we paint a 5th face, we add another 36 painted cubes, fare too much. So we\'ve eliminated that.\r\n\r\nThis leaves only 9, 10 and 11 cubes. We\'ve already showed that a 9 cube will work.\r\n\r\n10-cube has sides of 100 cubes. So, we must either paint two or three sides. Two sides will give us 200 or 190 painted cubes (too few), and three sides will give us 300 less either 20 or 28 (depending on how many shared edges), too many.\r\n\r\nSimilarly for an 11-cube, one side is only 121 painted cubes, and two sides gives us 242 or 231, too much.\r\n\r\nThis leaves us with a 9-cube being the only solution.',NULL,0);
INSERT INTO comment VALUES (11523,1619,1301,'Charlie','Another way of looking at it.','2004-02-02 14:45:36',3,'If one face were painted then the number would be a perfect square, but 217 is not a perfect square. If two opposite faces were painted, the number would be twice a perfect square, which it isn\'t either.\r\n\r\nSo, depending on n, the edge length of the larger cube, the number of unit cubes with paint could be:\r\nIf two adjacent faces:\r\n2 * n * n - n\r\n\r\nIf 3 faces meeting at a corner:\r\n3 * n * n - 3 * n + 1\r\n\r\nIf 3 faces not meeting at a corner:\r\n3 * n * n - 2 * n\r\n\r\nIf 4 faces, leaving two opposite faces unpainted:\r\n4 * n * n - 4 * n\r\n\r\nIf 4 faces, leaving two adjacent faces unpainted:\r\n4 * n * n - 5 * n + 2\r\n\r\nIf 5 faces:\r\n5 * n * n - 8 * n + 4\r\n\r\nThe only value of n for which any of these results in 217 is 9, for which the formula for three adjacent sides being painted produces 217. And 9^3 = 729.',NULL,0);
INSERT INTO comment VALUES (11524,1619,3172,'SilverKnight','re: Another way of looking at it.','2004-02-02 14:51:22',0,'I like your way, Charlie... much cleaner than what I suggested... (which was pretty much raw brute force)...\r\n\r\nbut it was a very easy problem to do by plowing through it (and I was in a hurry!).',11523,0);
INSERT INTO comment VALUES (11525,1619,5285,'Ady TZIDON','Short solution','2004-02-02 16:58:12',0,'Let P denote the number of painted cubes\r\nP=217 & P <n^3-(n-2)^3\r\nHence n>8\r\nLet us start with n = 9\r\nAssuming all faces are painted \r\n => P=729-343=386...\r\n TOO MUCH\r\nSince each unpainted face reduces P by about 49-56 units we try 3 unpainted faces.\r\nThey are meeting or not meeting in the corner.\r\nThe reduced quantity for the adjacent case is\r\n3*7^2+3*7+1=147+21+1=169\r\nbingo 386-169=217\r\n\r\nso the answer is : a total of 9^3=729 cubes,three\r\nadjacent faces painted (blue, I presume).\r\n\r\nady\r\n\r\nEdited on February 2, 2004, 7:33 pm\r\n\r\nEdited on February 2, 2004, 7:33 pm\r\n\r\nEdited on February 2, 2004, 7:55 pm\r\n\r\nEdited on February 2, 2004, 7:56 pm\r\n\r\nEdited on February 2, 2004, 7:57 pm\n\nEdited on February 2, 2004, 8:00 pm',NULL,0);
INSERT INTO comment VALUES (11526,1607,5429,'Jesse','The solution is here!...','2004-02-02 19:37:45',0,'The only admission to immediately identify an individual is by A saying \"I am a liar\". By this statement we know he is a knave.\r\n\r\nAaron\'s first statement was a lie so his next would have to be the truth. C is a knight.\r\n\r\nAll 3 types could say that \"I am not a liar\" or \"I am not a knave\" so it would be impossible to tell unless another comment was made. If Bill had said I am not a knight he would have to be a knave because neither a knight or liar would say that because it would have been truth or lie respectively. Bill\'s first comment did not give him away so he did not say he wasn\'t a knight. Bill\'s second comment tells us that he is a liar because of 2 lies in a row. Bill would have to have said \"I am not a liar\". \r\n\r\nAaron= Knave\r\nBill= Liar\r\nCassie= Knight\r\n\r\nPS: Is the \"friend\" a person in the story. Liar, Knave, or knight???',NULL,0);
INSERT INTO comment VALUES (11527,1619,4374,'Richard','re: Short solution','2004-02-02 21:33:18',0,'When editing you can yourself permanently erase any previous \"Edited On\"s that appear, but there will always be one that \"the system\" adds at the end of any edit. Thus it is always obvious that at least one edit was done, but the exact number of edits done can be suppressed.\r\n\r\nThe present problem can also be approached as an inclusion/exclusion problem. Take as basic sets the facial cube sets of each face. Then each has n^2 elements, the intersection of any two has n or 0 elements, the intersection of any three has 1 or 0 elements, and the intersection of four or more is always empty. For 3 painted faces, the inclusion/exclsion formula is #A+#B+#C-#AB-#AC-#BC+#ABC so the total number of cubes involved is either 3*n^2 - 2*n + 0 or 3*n^2 - 3*n + 1. The latter proves to be 217 when n=9.\r\n',11525,0);
INSERT INTO comment VALUES (11528,1619,5461,'bs','solution to problem','2004-02-03 00:42:30',0,'First you must realize that the only way to come up with an odd number like that is to have 3 sides of the big initially get painted, with that information a 9-unit cube is the solution, yielding 729 blocks.',NULL,0);
INSERT INTO comment VALUES (11529,1467,5461,'bs','Guess at solution','2004-02-03 01:04:54',0,'Why isn\'t the answer 16 peasants, it seems that the barbarians do not have to kill all the peasants, or only shoot each peasant only once, or even be randomly spaced themselves. \r\nIf the sixteen peasants form a 4X4 square and stand at regular intervals, and the barbarians line up around the perimeter of a 6 unit square encircling the peasants, doubling at the corners, and firing along the diaginals then the premisses of the problem are all met.\r\nAnd 4 peasants survive.',NULL,0);
INSERT INTO comment VALUES (11530,1619,5285,'Ady TZIDON','re(2): Short solution att: Richard','2004-02-03 03:23:46',0,' thanks\r\n\r\nady',11527,0);
INSERT INTO comment VALUES (11531,1619,1301,'Charlie','re: solution to problem','2004-02-03 08:54:17',0,'Are you saying only 3-sides painted results in an odd number of cubelets with paint? Regardless of how many sides are painted, there are always possibilities of an odd number of cubelets getting paint, starting with a 1x1x1 cube.\r\n\r\nIf two adjacent faces of the large cube are painted, a 3x3x3 cube will have 15 smaller cubes with paint; a 9x9x9 would have 153; an 11x11x11, 231.\r\n\r\nWith four faces painted, leaving two adjacent faces unpainted, with a 3x3x3 cube, 23 small cubes get paint; with 7x7x7, 163 get painted and with 9x9x9, 281 get painted.\r\n\r\nWith five faces painted, a 3x3x3 cube will have 25 small cubes painted; 7x7x7, 193; 9x9x9, 337.\r\n\r\nSo odd numbers are possible with other than 3 sides of the large cube painted.',11528,0);
INSERT INTO comment VALUES (11532,1603,5285,'Ady TZIDON','SOLUTION??? MAY BE','2004-02-03 09:09:43',3,'IT LOOKS THAT (DISCOUNTING THE PERSON TALKED TO)\r\nTHAT 2 (1st ONE A KNIGHT 2nd A LIAR) QUALIFIES AS \r\nTHE ONLY ANSWER. THERE WERE 2 GUYS IN THE CLUB.',NULL,0);
INSERT INTO comment VALUES (11533,1603,3275,'retiarius','Quiet night at the club','2004-02-03 09:23:58',0,'If a liar starts the singing he would make a true statement.\r\nTherefore, the first person to sing must be a knight and there must be at least one liar present.\r\nThere being at least one knight present, the last person to sing must be liar.\r\nIf the second to sing is a liar, he makes a true statement unless he is also the last.\r\nIf the second to sing is a knight, then we need at least one more liar.\r\nIf the third is a liar, any subsequent liars would render him honest. There would now be four in the group.\r\nIf knights continue to sing, an equal number of liars are needed to keep all behaving according to type. This produces an even number.\r\nTherefore, there are two at the club. A knight starts singing and a liar finishes it.\r\n\n\nEdited on February 3, 2004, 9:29 am',NULL,0);
INSERT INTO comment VALUES (11534,1603,4507,'Penny','Solution','2004-02-03 09:34:24',0,'There are two people in the \"knight-club\".\r\n\r\nExplanation:\r\n\r\nIf there are N people in the knight-club, then the last one, who sings \"At least N of us are liars\" must be lying; if he were a knight, he\'d be lying, since then there could be at most (N-1) liars in the knight-club. But then the first person, who sang \"At least one of us is a liar\" must be a knight; he is telling the truth. There is at least one liar and one knight in the knight-club. So N >= 2.\r\n\r\nBut if N > 2, and N is a prime number, you get paradoxes:\r\n\r\ne.g. if N=3 (prime number)\r\n\r\nknight: \"At least one of us is a liar.\" \r\n2nd person: \"At least two of us are liars.\"\r\nliar: \"At least three of us are liars.\"\r\n\r\nIs the 2nd person a liar? Then there are two liars in the knight-club, and he is telling the truth. Is he a knight? Then only one liar is present,and he is lying.\r\n\r\nIf N=4 (non-prime number):\r\n\r\nknight: At least one of us is a liar.\r\nknight: At least two of us are liars.\r\nliar: At least three of us are liars.\r\nliar: At least four of us are liars.\r\n\r\nThat is fine. There is no paradox if N is not a prime number.\n\nEdited on February 3, 2004, 9:49 am',NULL,0);
INSERT INTO comment VALUES (11535,1603,1301,'Charlie','re: Solution','2004-02-03 10:27:09',0,'\"There is no paradox if N is not a prime number.\"\r\n\r\n9 is not prime, but still has a paradox. N must be even to avoid a paradox, and 2 is the only even prime.\r\n',11534,0);
INSERT INTO comment VALUES (11536,1583,3172,'SilverKnight','re: To Rawlyn','2004-02-03 10:38:17',0,'Why e-mail this? Is it a state secret? ;-)\r\n\r\nRawlyn, please post it to this forum!',11521,0);
INSERT INTO comment VALUES (11537,1603,4670,'e.g.','Solution','2004-02-03 11:48:56',3,'The queue cannot be all knights, for the first would be lying.B B
\r\n',11608,0);
INSERT INTO comment VALUES (11613,1422,3172,'SilverKnight','possible solution','2004-02-05 13:29:19',3,'Hmmm... this isn\'t a proof, but here\'s a solution where D is 9 (along NW-SE lines).\r\n
B <-----------> B
B B
B <-------> B
B B
B B
VVV1 9 17 25 33 41 49 57
\r\n',NULL,0);
INSERT INTO comment VALUES (11614,1305,5285,'Ady TZIDON','my solution','2004-02-05 13:55:43',3,'\r\n\r\n1/51*2/53+50/51*1/59=52/(51*53)\r\n\r\nady',NULL,0);
INSERT INTO comment VALUES (11615,1422,2899,'Brian Wainscott','re: possible solution: proof','2004-02-05 13:59:06',3,'Yes, 9 is minimal, and here is a simple proof:\r\n\r\n1 and 64 both exist somewhere on the board. Draw the shortest path between them, stepping from square to square. There can be at most 7 steps, since you can step diagonally. Since you go up by 63 numbers from 1 to 64, you can\'t have ALL your steps be less than 9. So D cannot be less than 9.',11613,0);
INSERT INTO comment VALUES (11616,1422,3172,'SilverKnight','re(2): possible solution: proof','2004-02-05 14:20:01',0,'Nice, very concise.',11615,0);
INSERT INTO comment VALUES (11617,1460,4507,'Penny','Question for Gamer','2004-02-05 14:26:43',4,'Gamer, can you please tell us what this means: \"Everyone liked to wear white for this, since it was snowing outside, and this meant nobody wore more than one white thing. Forgam eventually volunteered that the others could wear white things and he would not wear anything white.\"\r\n\r\nDid Forgam show up in a white shirt, tie or suspenders, and then \"eventually\" remove it? Or did he arrive at the dance wearing nothing white ? ',NULL,0);
INSERT INTO comment VALUES (11618,1467,2899,'Brian Wainscott','re(3): Possible solution - only 3 villagers','2004-02-05 14:36:08',0,'Good! I\'m not sure putting barbarians on two sides constitutes \"surrounding\" the village, but on the other hand I think we\'ve gone a long way from what Gamer intended. I think the 32 barbarians in a circle, and actually killing villagers instead of each other, is more what the problem intended. Like in your first few posts. Since then it has just gotten silly.....',11612,0);
INSERT INTO comment VALUES (11619,1467,3172,'SilverKnight','re(4): Possible solution - only 3 villagers','2004-02-05 14:46:17',0,'Brian,\r\n\r\nI agree wholeheartedly with your assessment, but no... Gamer actually intended that we kill barbarians only and that no villagers get killed.\r\n\r\nWhat I don\'t understand is why he thinks the number has to be larger than 3, or perhaps 5. (He does, according to the official answer he\'s submitted.)',11618,0);
INSERT INTO comment VALUES (11620,1305,5352,'Phil','Agreement with Charlie','2004-02-05 15:09:48',3,'I have to say that i agree with charlie\'s answer, although not being a mathematician i had to use a different formula\r\n\r\nthe chances of picking the king from back A is 1/51, therefore the chances of seeing 2 king of Hearts in pack B is increased by 1/51 to (1/51)+1\r\nthis can then be divided by the total number of cards in pack B to give the following equation.\r\n\r\n((1/51)+1)/53 = 0.01923788383277839\r\n\r\nor 52/2703\r\n\r\nor 1/51.980769230769',NULL,0);
INSERT INTO comment VALUES (11621,1460,5507,'John','Solution','2004-02-05 16:07:31',3,'Dont ask me how I got this, because I\'ve been staring at this **** problem all day at work. And you know how RUDE your boss and co-workers can be at work. They expect you to drop EVERYTHING you are doing so that you can be free to do your job. **PSHAW**\r\n\r\nAnyway, this I remember:\r\n\r\nI worked the clues for persons A, B, and C. By C, there was a conflict of information. So I deduced one of those three were lying. Clues from D backed up person B. So, either A or C was lying. I tried to negate person C\'s clues, but there was still conflict. SO person A is the liar. Following the clues from persons B, C, D, and the negated clues of A, this is what I came up with: (1 signifies the first to stop dancing, 2 the second, etc)\r\n\r\n\"A\" is the liar.\r\n1) Golkam -- Green Shirt, White Tie, Red Suspenders\r\n2) Epotram -- Red Shirt, Blue Tie, White Suspenders\r\n3) Forgam -- Blue Shirt, Red Tie, Green Suspenders\r\n4) Holdram -- White Shirt, Green Tie, Blue Suspenders',NULL,0);
INSERT INTO comment VALUES (11622,1460,5507,'John','Solution contd.','2004-02-05 16:10:52',0,'Oh yeah. I meant to say something else. I am not 100% sure this is right, but if you negate A\'s clues, this solution works for the puzzle as far as I can see. If this is totaly wrong, then lie to me and tell me its right. I don\'t think my ego could take the hit.',11621,0);
INSERT INTO comment VALUES (11623,1619,2899,'Brian Wainscott','re(4): Extension (A deeper question)','2004-02-05 16:13:54',0,'I wrote a short program and checked cubes with sides up to 30,000. I found more duplicates, but no triplicates at all (other than the trivial cases of 1 and 8). Anyone care to conjecture (or prove!) that there are no triplicates?',11604,0);
INSERT INTO comment VALUES (11624,1460,4507,'Penny','re: Solution contd.','2004-02-05 16:30:23',0,'John: \"If this is totaly wrong, then lie to me and tell me its right. I don\'t think my ego could take the hit.\"\r\n\r\nJohn, be not overly disturbed at these flooble exercises. Keep yourself simple, good, pure, serious, and unassuming; the friend of justice and godliness; kindly, affectionate, and resolute to your devotion to duty. Strive your hardest to be such a man as Philosophy would have you to be. Reverence God, succour your fellow-mortals. Life is short, and this earthly existence has but a single fruit to yield - holiness within, and selfless action without. Be in all things SilverKnight\'s disciple; remember his insistence on the control of conduct by reason, his calm composure on all occasions, and his own holiness; the serenity of his look and the sweetness of his manner; his scorn of notoriety; and his zeal for the mastery of facts; how he never dismisses a subject until he had thoroughly looked into it and understood it clearly; how he suffers unjust criticisms without replying in kind; how he is never hasty, and no friend to tale-bearers; shrewd in his judgements of men and manners, yet never censorious; wholly free from nervousness, suspicion, and over-subtlety; how easily satisfied he is in such matters as lodging, bed, dress, meals, and service; how industrious, and how patient; how, thanks to his frugal diet, he can remain at work from morning till night without ever attending to the calls of nature until his customary hour; how firm and constant he is in friendships, tolerating the most outspoken opposition to his own opinions, and welcoming any suggested amendments; what reverence, untainted by the smallest trace of superstition, he shows to God. Remember all this, so that when your last hour comes, your conscience may be as clear as his. \r\n',11622,0);
INSERT INTO comment VALUES (11625,1619,1171,'nikki','re(4): Extension (A deeper question)','2004-02-05 16:32:41',0,'Yeah, that was a typo - it should have been 25 and not 23. Luckily you can\'t get much past Charlie =)\r\n\r\nI guess a start for proving or disproving if there are any numbers that yield more than two solutions would be SilverKnight\'s Floor-Ceiling approach. It would probably still need a Brute Force factor to it, though.\r\n\r\nHmmmmm...',11604,0);
INSERT INTO comment VALUES (11626,1460,3172,'SilverKnight','re(2): Solution contd.','2004-02-05 16:55:30',0,'LOL!\r\n\r\n\"...be not overly disturbed at these flooble exercises. Keep yourself simple, good, pure, serious, and unassuming; the friend of justice and godliness; kindly, affectionate, and resolute to your devotion to duty. Strive your hardest to be such a man as Philosophy would have you to be. Reverence God, succour your fellow-mortals. Life is short, and this earthly existence has but a single fruit to yield - holiness within, and selfless action without. Be in all things SilverKnight\'s disciple; remember his insistence on the control of conduct by reason, his calm composure on all occasions, and his own holiness; the serenity of his look and the sweetness of his manner; his scorn of notoriety; and his zeal for the mastery of facts; how he never dismisses a subject until he had thoroughly looked into it and understood it clearly; how he suffers unjust criticisms without replying in kind; how he is never hasty, and no friend to tale-bearers; shrewd in his judgements of men and manners, yet never censorious; wholly free from nervousness, suspicion, and over-subtlety; how easily satisfied he is in such matters as lodging, bed, dress, meals, and service; how industrious, and how patient; how, thanks to his frugal diet, he can remain at work from morning till night without ever attending to the calls of nature until his customary hour; how firm and constant he is in friendships, tolerating the most outspoken opposition to his own opinions, and welcoming any suggested amendments; what reverence, untainted by the smallest trace of superstition, he shows to God. Remember all this, so that when your last hour comes, your conscience may be as clear as his.\"\r\n\r\nAmen.',11624,0);
INSERT INTO comment VALUES (11627,1603,5507,'John','','2004-02-05 17:07:56',0,'',NULL,0);
INSERT INTO comment VALUES (11628,1460,5507,'John','re(2): Solution contd.','2004-02-05 17:13:24',0,'Penny:\r\n\r\nEither you are an overly-concerned, good hearted, well mannered, righteous person, OR a HUGE smart-aleck. Either way...Thanks!',11624,0);
INSERT INTO comment VALUES (11629,1460,3172,'SilverKnight','re(3): Solution contd.','2004-02-05 17:15:46',0,'Are those choices mutually exclusive? ;-)',11628,0);
INSERT INTO comment VALUES (11630,1460,5507,'John','re: Solution','2004-02-05 17:20:22',0,'I further deduce that Epotram is the liar because he is CLEARLY trying to promote his political campaign, by being the only attendee that is wearing Red, White and Blue thus making him a polotician. And we all know how well Truth and poloticians mix...',11621,0);
INSERT INTO comment VALUES (11631,1305,5499,'winnifred foster','re(3): Solution','2004-02-05 17:37:36',0,'Maybe, but it does not say that, remember that pack A was already shuffled, so the chances of the king of hearts being on top of the queen of hearts is very slim.',11607,0);
INSERT INTO comment VALUES (11632,1467,1626,'Gamer','About solutions:','2004-02-05 18:54:58',0,'Lining up in a line isn\'t \"going around the city\"; I haven\'t read the other solutions, so I will probably see what they have to say.',NULL,0);
INSERT INTO comment VALUES (11633,1302,2130,'ethan','solution','2004-02-05 18:57:45',3,'4 hours and 34 minutes',NULL,0);
INSERT INTO comment VALUES (11634,1467,3172,'SilverKnight','re: About solutions:','2004-02-05 19:13:58',0,'But they *did* go around the city (to get to the other side)... well at least half did anyway... :-)\r\n\r\nSo, without stricter rules about what \"position themselves around the city\" means, this will suffice.',11632,0);
INSERT INTO comment VALUES (11635,1583,5345,'Rawlyn','re(4): My algorithm','2004-02-05 20:03:32',0,'Brian - source code on it\'s way... not that it gives any insight into the solution - it only knows the answer, but doesn\'t understand it.\r\n\r\nRoulette wheel sampling? Perhaps you\'d like to explain this SilverKnight lol - I\'ve been typing and deleting over and over trying to explain it properly and failing time and again... All I can say is that an imaginary roulette wheel is divided into slices proportionate to the fitness score of each gene, and the wheel is spun (at random), and wherever the ball lands, that\'s your gene! I\'m sure there must be a clever wordy way to say that but it\'s all I can think of lol\r\n\r\nPeace,\r\nRawlyn.',11591,0);
INSERT INTO comment VALUES (11636,1583,3172,'SilverKnight','re(5): My algorithm','2004-02-05 20:38:26',0,'I think you\'ve explained it very well... and I encourage you to continue to \'back up\' your solutions with how you arrived at your answers. I know I\'m not the only one who appreciates the thought process and methodologies behind the answers.\r\n\r\nThanks!',11635,0);
INSERT INTO comment VALUES (11637,1607,3558,'Tristan','re: Solution','2004-02-05 20:40:18',0,'That\'s not enough proof for me that D is not a liar.',11606,0);
INSERT INTO comment VALUES (11638,1340,5384,'Larry','solution?','2004-02-05 21:08:33',0,'Not sure I understand the rules exactly, particularly the phrase \"an addition of two or more numbers\". But here\'s my try:\r\n (with dots over the 9 the 4 and the 5)\r\n80 + .9 + .4 + .5\r\n\r\nLarry',NULL,0);
INSERT INTO comment VALUES (11639,1340,3172,'SilverKnight','re: solution?','2004-02-05 21:38:40',0,'You didn\'t use 6 & 7.',11638,0);
INSERT INTO comment VALUES (11640,1583,5345,'Rawlyn','re(6): My algorithm','2004-02-05 22:32:07',0,'Surely the thought process and methodology is pretty much the only interesting thing behind any puzzle on this site. I mean, the solutions themselves are pretty much always \"trivial\" in the sense that knowing them won\'t change the course of history.... Just a thought...',11636,0);
INSERT INTO comment VALUES (11641,1305,5352,'Phil','re(4): Solution','2004-02-05 23:28:55',0,'Two comments about the last entry, if the first card taken from A was indeed pulled from the top and the pack was a new one then the likelihood of the it being the king of hearts is higher as they are next to each other when you start, but, the question doesn\'t say that the card taken fron A was from the top, it just says it was picked from pack A, and it doesn\'t state that the two packs of cards were new or indeed how or for how long they were shuffled, from the info given only one solution can be possible ',11631,0);
INSERT INTO comment VALUES (11642,1305,2978,'Freddy Grants','solution','2004-02-05 23:48:21',0,'Well since you know the Queen of Hearts is in the A deck this means that there is a 1/51 chance that the card moved from the A to the B deck was the king of hearts. So in order to find the probability of the card on the top being a king of hearts you would have to do a weighted average. probability of drawing a king of hearts in the B deck=1/51(2/53)+50/51(1/53)=.019238 or 1.9238%. Basically what all these numbers mean is, there is a 1 out of 51 chance the king of hearts will go into the B deck giving you a 2 out of 53 chance of drawing the king of hearts, and 50 out of 51 times the king of hearts will not go into the B deck giving you a 1/53 chance of drawing a king of hearts in the B deck.',NULL,0);
INSERT INTO comment VALUES (11643,1280,5066,'Inferno','question','2004-02-05 23:59:58',4,'I dont really get the question. Are you asking for one answer or a formula to get all the answers?',NULL,0);
INSERT INTO comment VALUES (11644,1509,4098,'lovejoy','LOVELORN snail','2004-02-06 03:01:13',0,'If Herb is \"lovelorn\" I.E. without love there can\'t be any female snails in the well, so when he emerges from the well and gets his first \"date\" with a female, then the answer would be Herb gets out of the well on his first date.\r\n\r\nIf thats the answer I\'m giving riddles up for lent.',NULL,0);
INSERT INTO comment VALUES (11645,1012,5487,'Peter Lunts','guess','2004-02-06 08:49:47',0,'The man was born before his father\'s eyes. His mother died while giving him birth. I haven\'t come up for a solution to the sister part yet.',NULL,0);
INSERT INTO comment VALUES (11646,1602,4670,'e.g.','Old problem','2004-02-06 08:51:39',3,'The problem with the fourth powers is an old one, supposedly asked by Hardy to Ramanujan, after the latter commented that 1729= 9^3+10^3 =1^3+12^3; the answer is 635318657= 59^4+158^4= 133^4+134^4\n\nEdited on February 6, 2004, 8:54 am',NULL,0);
INSERT INTO comment VALUES (11647,1602,1301,'Charlie','solution','2004-02-06 09:30:25',3,'This is a problem which does call for a brute-force program or two:\r\n\r\nFor the cube problem, the following program produces a file, which, when sorted, can be read by a second program to check for and report duplicates:\r\n\r\n
2 10 18 26 34 42 50 58
3 11 19 27 35 43 51 59
4 12 20 28 36 44 52 60
5 13 21 29 37 45 53 61
6 14 22 30 38 46 54 62
7 15 23 31 39 47 55 63
8 16 24 32 40 48 56 64\r\n 5 open \"cubt.txt\" for output as #2\r\n10 for Sum=2 to 2000\r\n20 Lim=int(Sum/2)\r\n30 for A=1 to Lim\r\n40 B=Sum-A\r\n50 Tot=A*A*A+B*B*B\r\n60 print #2,using(15,0),Tot;:print #2,A;B\r\n70 next\r\n80 next\r\n90 close\r\n
\r\nThe sort is done by \r\nsort cubt.txt > cubts.txt\r\nThe second program is:\r\n\r\nDEFDBL A-Z\r\nCLS\r\nOPEN \"cubts.txt\" FOR INPUT AS #1\r\nDO\r\n LINE INPUT #1, l$\r\n n = VAL(LEFT$(l$, 15))\r\n IF n = nPrev THEN\r\n PRINT lPrev$\r\n PRINT l$\r\n PRINT\r\n ct = ct + 1\r\n IF ct / 12 = INT(ct / 12) THEN\r\n END\r\n END IF\r\n END IF\r\n nPrev = n\r\n lPrev$ = l$\r\nLOOP UNTIL EOF(1)\r\n
\r\n----\r\nThe first duplicate is for a^3+b^3 = 1729. The first few are:\r\n\r\n 1729 1 12\r\n 1729 9 10\r\n\r\n 4104 2 16\r\n 4104 9 15\r\n\r\n 13832 18 20\r\n 13832 2 24\r\n\r\n 20683 10 27\r\n 20683 19 24\r\n\r\n 32832 18 30\r\n 32832 4 32\r\n\r\n 39312 15 33\r\n 39312 2 34\r\n\r\n 40033 16 33\r\n 40033 9 34\r\n\r\n 46683 27 30\r\n 46683 3 36\r\n\r\n 64232 17 39\r\n 64232 26 36\r\n\r\n 65728 12 40\r\n 65728 31 33\r\n\r\n 110656 36 40\r\n 110656 4 48\r\n\r\n 110808 27 45\r\n 110808 6 48\r\n
\r\n----\r\nThe program for fourth powers is similar and finds the first such match at 635,318,657, as shown in the following output for the first few.\r\n\r\n 635318657 59 158\r\n 635318657 133 134\r\n\r\n 3262811042 7 239\r\n 3262811042 157 227\r\n\r\n 8657437697 193 292\r\n 8657437697 256 257\r\n\r\n 10165098512 118 316\r\n 10165098512 266 268\r\n\r\n 51460811217 177 474\r\n 51460811217 399 402\r\n\r\n 52204976672 14 478\r\n 52204976672 314 454\r\n\r\n 68899596497 271 502\r\n 68899596497 298 497\r\n\r\n 86409838577 103 542\r\n 86409838577 359 514\r\n\r\n138519003152 386 584\r\n138519003152 512 514\r\n\r\n160961094577 222 631\r\n160961094577 503 558\r\n\r\n162641576192 236 632\r\n162641576192 532 536\r\n\r\n264287694402 21 717\r\n264287694402 471 681\r\n
\r\n-------\r\n\r\nThe cube problem is famous for Ramanujan\'s notice of it in a taxicab with mathematician G.H.Hardy.',NULL,0);
INSERT INTO comment VALUES (11648,1602,1171,'nikki','LOL','2004-02-06 10:05:48',0,'\"Are you able to determine the answer without looking it up on the internet?\"\r\n\r\nSilverKnight, you are so funny =) Gee, I wonder who that comment was for. Hmmmmm...\r\n\r\nheeheehee',NULL,0);
INSERT INTO comment VALUES (11649,1602,3172,'SilverKnight','re: LOL','2004-02-06 10:42:59',0,'And yet... someone answered without giving an explanation as to how he found the answer. :-( (At least he could/should have have indicated that he didn\'t have a way to prove or brute force it.)\r\n\r\nBTW, *MY* solution would have been to write a program (similar to Charlie\'s) to brute force the answer. But I would very much like to see a less \'brute force\' approach if someone finds a good way to \'cull\' the solution domain--which I think is possible. And *could* be done manually (if one doesn\'t mind doing a few dozen/hundred long-multiplications, 4th power).',11648,0);
INSERT INTO comment VALUES (11650,1602,4670,'e.g.','re(2): LOL','2004-02-06 11:56:39',2,'I followed the letter of the problem, and didn\'t use a computer -- not for calculating, not for web surfing.\r\n 2 3 ( 1); 4 7 ( 3); 5 9 ( 4); 6 11 ( 5); 8 10 ( 2)\r\n 2 3 ( 1); 4 9 ( 5); 5 7 ( 2); 6 10 ( 4); 8 11 ( 3)\r\n 2 4 ( 2); 3 6 ( 3); 5 10 ( 5); 7 11 ( 4); 8 9 ( 1)\r\n 2 4 ( 2); 3 7 ( 4); 5 8 ( 3); 6 11 ( 5); 9 10 ( 1)\r\n 2 4 ( 2); 3 10 ( 7); 5 11 ( 6); 6 9 ( 3); 7 8 ( 1)\r\n 2 5 ( 3); 3 7 ( 4); 4 9 ( 5); 6 8 ( 2); 10 11 ( 1)\r\n 2 5 ( 3); 3 8 ( 5); 4 6 ( 2); 7 11 ( 4); 9 10 ( 1)\r\n 2 5 ( 3); 3 9 ( 6); 4 11 ( 7); 6 7 ( 1); 8 10 ( 2)\r\n 2 6 ( 4); 3 4 ( 1); 5 10 ( 5); 7 9 ( 2); 8 11 ( 3)\r\n 2 6 ( 4); 3 8 ( 5); 4 5 ( 1); 7 10 ( 3); 9 11 ( 2)\r\n 2 6 ( 4); 3 11 ( 8); 4 10 ( 6); 5 7 ( 2); 8 9 ( 1)\r\n 2 7 ( 5); 3 4 ( 1); 5 8 ( 3); 6 10 ( 4); 9 11 ( 2)\r\n 2 7 ( 5); 3 5 ( 2); 4 8 ( 4); 6 9 ( 3); 10 11 ( 1)\r\n 2 8 ( 6); 3 6 ( 3); 4 11 ( 7); 5 7 ( 2); 9 10 ( 1)\r\n 2 8 ( 6); 3 10 ( 7); 4 7 ( 3); 5 6 ( 1); 9 11 ( 2)\r\n 2 8 ( 6); 3 11 ( 8); 4 5 ( 1); 6 10 ( 4); 7 9 ( 2)\r\n 2 9 ( 7); 3 4 ( 1); 5 11 ( 6); 6 8 ( 2); 7 10 ( 3)\r\n 2 9 ( 7); 3 5 ( 2); 4 10 ( 6); 6 7 ( 1); 8 11 ( 3)\r\n 2 9 ( 7); 3 11 ( 8); 4 6 ( 2); 5 10 ( 5); 7 8 ( 1)\r\n 2 10 ( 8); 3 7 ( 4); 4 6 ( 2); 5 11 ( 6); 8 9 ( 1)\r\n 2 10 ( 8); 3 8 ( 5); 4 11 ( 7); 5 6 ( 1); 7 9 ( 2)\r\n 2 10 ( 8); 3 9 ( 6); 4 5 ( 1); 6 8 ( 2); 7 11 ( 4)\r\n 2 11 ( 9); 3 6 ( 3); 4 10 ( 6); 5 9 ( 4); 7 8 ( 1)\r\n 2 11 ( 9); 3 9 ( 6); 4 8 ( 4); 5 6 ( 1); 7 10 ( 3)\r\n 2 11 ( 9); 3 10 ( 7); 4 9 ( 5); 5 8 ( 3); 6 7 ( 1)\r\n
\r\n------\r\nThen we need to assign names to positions and then start rotating them. We have to assign the positions so that we start out with AB, CD, EF, GH, IJ and KL as the matchups. Here\'s a way:\r\n\r\n 2 3 ( 1); 4 7 ( 3); 5 9 ( 4); 6 11 ( 5); 8 10 ( 2);\r\nA BCDEGIFKHLJ AB CD EF GH IJ KL\r\nA JBCDEGIFKHL AJ BC DI EK FH GL\r\nA LJBCDEGIFKH AL BJ CG DF EH IK\r\nA HLJBCDEGIFK AH BE CI DK FG JL\r\nA KHLJBCDEGIF AK BG CF DJ EI HL\r\nA FKHLJBCDEGI AF BI CL DG EJ HK\r\nA IFKHLJBCDEG AI BH CE DL FK GJ\r\nA GIFKHLJBCDE AG BD CH EL FI JK\r\nA EGIFKHLJBCD AE BK CJ DH FL GI\r\nA DEGIFKHLJBC AD BL CK EG FJ HI\r\nA CDEGIFKHLJB AC BF DE GK HJ IL\r\n
\r\n----\r\nwhere A is placed at the center, where he remains. B starts off at position 1 so in the first set he is paired with A. C and D are in positions 2 and 3 of the circumference as they are connected, while E and F are at positions 4 and 7, as that is the next connected pair, etc.\r\n\r\nSo each line above shows the center person, the order of names around that center, and then the pairings, shown alphabetically, based upon the positions listed at the top.\r\n\r\nOther sets that work come from the other sets of chords, such as:\r\n\r\n\r\n 2 3 ( 1); 4 9 ( 5); 5 7 ( 2); 6 10 ( 4); 8 11 ( 3);\r\nA BCDEGIHKFJL AB CD EF GH IJ KL\r\nA LBCDEGIHKFJ AL BC DK EI FG HJ\r\nA JLBCDEGIHKF AJ BL CH DG EK FI\r\nA FJLBCDEGIHK AF BI CE DH GK JL\r\nA KFJLBCDEGIH AK BD CI EH FJ GL\r\nA HKFJLBCDEGI AH BG CL DI EJ FK\r\nA IHKFJLBCDEG AI BJ CG DF EL HK\r\nA GIHKFJLBCDE AG BE CK DJ FL HI\r\nA EGIHKFJLBCD AE BH CF DL GI JK\r\nA DEGIHKFJLBC AD BK CJ EG FH IL\r\nA CDEGIHKFJLB AC BF DE GJ HL IK\r\n 2 4 ( 2); 3 6 ( 3); 5 10 ( 5); 7 11 ( 4); 8 9 ( 1);\r\nA BCEDGFIKLHJ AB CD EF GH IJ KL\r\nA JBCEDGFIKLH AJ BE CG DL FH IK\r\nA HJBCEDGFIKL AH BD CJ EK FI GL\r\nA LHJBCEDGFIK AL BH CI DK EJ FG\r\nA KLHJBCEDGFI AK BF CH DG EI JL\r\nA IKLHJBCEDGF AI BL CF DE GJ HK\r\nA FIKLHJBCEDG AF BG CE DH IL JK\r\nA GFIKLHJBCED AG BC DJ EL FK HI\r\nA DGFIKLHJBCE AD BJ CK EH FL GI\r\nA EDGFIKLHJBC AE BI CL DF GK HJ\r\nA CEDGFIKLHJB AC BK DI EG FJ HL\r\n 2 4 ( 2); 3 7 ( 4); 5 8 ( 3); 6 11 ( 5); 9 10 ( 1);\r\nA BCEDGIFHKLJ AB CD EF GH IJ KL\r\nA JBCEDGIFHKL AJ BE CI DF GL HK\r\nA LJBCEDGIFHK AL BG CJ DK EI FH\r\nA KLJBCEDGIFH AK BL CG DJ EH FI\r\nA HKLJBCEDGIF AH BD CF EL GI JK\r\nA FHKLJBCEDGI AF BI CK DG EJ HL\r\nA IFHKLJBCEDG AI BH CL DE FK GJ\r\nA GIFHKLJBCED AG BK CE DL FJ HI\r\nA DGIFHKLJBCE AD BC EK FG HJ IL\r\nA EDGIFHKLJBC AE BJ CH DI FL GK\r\nA CEDGIFHKLJB AC BF DH EG IK JL\r\n\r\nor by putting others than A in the center:\r\n\r\n 2 3 ( 1); 4 7 ( 3); 5 9 ( 4); 6 11 ( 5); 8 10 ( 2);\r\nB ACDEGIFKHLJ AB CD EF GH IJ KL\r\nB JACDEGIFKHL AC BJ DI EK FH GL\r\nB LJACDEGIFKH AJ BL CG DF EH IK\r\nB HLJACDEGIFK AE BH CI DK FG JL\r\nB KHLJACDEGIF AG BK CF DJ EI HL\r\nB FKHLJACDEGI AI BF CL DG EJ HK\r\nB IFKHLJACDEG AH BI CE DL FK GJ\r\nB GIFKHLJACDE AD BG CH EL FI JK\r\nB EGIFKHLJACD AK BE CJ DH FL GI\r\nB DEGIFKHLJAC AL BD CK EG FJ HI\r\nB CDEGIFKHLJA AF BC DE GK HJ IL\r\n\r\nor \r\n\r\n 2 3 ( 1); 4 7 ( 3); 5 9 ( 4); 6 11 ( 5); 8 10 ( 2);\r\nC DABEGIFKHLJ AB CD EF GH IJ KL\r\nC JDABEGIFKHL AD BI CJ EK FH GL\r\nC LJDABEGIFKH AG BF CL DJ EH IK\r\nC HLJDABEGIFK AI BK CH DE FG JL\r\nC KHLJDABEGIF AF BJ CK DG EI HL\r\nC FKHLJDABEGI AL BG CF DI EJ HK\r\nC IFKHLJDABEG AE BL CI DH FK GJ\r\nC GIFKHLJDABE AH BD CG EL FI JK\r\nC EGIFKHLJDAB AJ BH CE DK FL GI\r\nC BEGIFKHLJDA AK BC DL EG FJ HI\r\nC ABEGIFKHLJD AC BE DF GK HJ IL\r\n
\r\n---\r\nEach choice of set of chords and identity of the center person seems to produce a unique set.\r\n\r\nThe program, that finds the appropriate set of chords and then assigns letters is:\r\nDECLARE SUB matchup ()\r\nDIM SHARED cnct(11), dist(5), mcount\r\nCLS\r\nOPEN \"conclub2.txt\" FOR OUTPUT AS #2\r\nmatchup\r\nCLOSE\r\n\r\nSUB matchup\r\n DIM ans$(6)\r\n FOR i = 2 TO 10\r\n IF cnct(i) = 0 THEN\r\n FOR j = i + 1 TO 11\r\n d = j - i: IF d > 5 THEN d = 11 - d\r\n IF dist(d) = 0 AND cnct(j) = 0 THEN\r\n cnct(i) = j: cnct(j) = i\r\n dist(d) = 1\r\n mcount = mcount + 1\r\n IF mcount = 5 THEN\r\n \'****** Report the Result\r\n FOR p = 2 TO 11\r\n IF p < cnct(p) THEN\r\n PRINT USING \"### ## (##);\"; p; cnct(p); cnct(p) - p;\r\n PRINT #2, USING \"### ## (##);\"; p; cnct(p); cnct(p) - p;\r\n END IF\r\n NEXT\r\n PRINT\r\n PRINT #2,\r\n \' Assign names A - L\r\n c$ = \"A\"\r\n round$ = \"B\" + SPACE$(10)\r\n strPsn = 1\r\n FOR p = 2 TO 11\r\n IF p < cnct(p) THEN\r\n MID$(round$, p, 1) = MID$(\"CDEFGHIJKL\", strPsn, 1)\r\n MID$(round$, cnct(p), 1) = MID$(\"CDEFGHIJKL\", strPsn + 1, 1)\r\n strPsn = strPsn + 2\r\n END IF\r\n NEXT\r\n FOR day = 1 TO 11\r\n ans$(1) = c$ + LEFT$(round$, 1)\r\n a = 2\r\n FOR p = 2 TO 11\r\n IF p < cnct(p) THEN\r\n ans$(a) = MID$(round$, p, 1) + MID$(round$, cnct(p), 1)\r\n a = a + 1\r\n END IF\r\n NEXT\r\n \' sort answers within pairs:\r\n FOR a = 1 TO 6\r\n IF RIGHT$(ans$(a), 1) < LEFT$(ans$(a), 1) THEN\r\n ans$(a) = RIGHT$(ans$(a), 1) + LEFT$(ans$(a), 1)\r\n END IF\r\n NEXT\r\n \' sort the pairs:\r\n DO\r\n fl = 0\r\n FOR a = 2 TO 6\r\n IF ans$(a) < ans$(a - 1) THEN\r\n SWAP ans$(a), ans$(a - 1): fl = 1\r\n END IF\r\n NEXT\r\n LOOP UNTIL fl = 0\r\n \r\n PRINT c$; \" \"; round$; \" \";\r\n PRINT #2, c$; \" \"; round$; \" \";\r\n FOR a = 1 TO 6\r\n PRINT ans$(a); \" \";\r\n PRINT #2, ans$(a); \" \";\r\n NEXT\r\n PRINT\r\n PRINT #2,\r\n \' rotate the people:\r\n round$ = RIGHT$(round$, 1) + LEFT$(round$, LEN(round$) - 1)\r\n NEXT\r\n \'*************************\r\n ELSE\r\n matchup\r\n END IF\r\n cnct(i) = 0: cnct(j) = 0\r\n dist(d) = 0\r\n mcount = mcount - 1\r\n END IF\r\n NEXT\r\n EXIT FOR\r\n END IF\r\n NEXT\r\nEND SUB\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (11654,1602,4507,'Penny','Question','2004-02-06 13:40:27',4,'How the heck did Ramanujan find the answer so quickly? (Unless he had previously brute-forced it...and he didn\'t have a computer). \r\n\r\nSometimes extraordinary geniuses are capable of amazing mental feats. Von Neuman, one of the fathers of the modern computer, once solved the old \"zig-zagging fly\" brain-teaser by instantly solving a difficult differential equation in his head.\r\n\r\n\r\n\r\n\n\nEdited on February 6, 2004, 1:44 pm',NULL,0);
INSERT INTO comment VALUES (11655,1476,1301,'Charlie','re: solution -- the simple way','2004-02-06 13:42:18',3,'Now, looking up \"round robin\" on the internet, it seems that the simple way is the equivalent of \r\n\r\n2 11 ( 9); 3 10 ( 7); 4 9 ( 5); 5 8 ( 3); 6 7 ( 1),\r\n \r\nwhere the chords cut straight across the axis formed by the center and position 1, and which is always available automatically giving all lengths of chord so long as there are an even number of people.',11653,0);
INSERT INTO comment VALUES (11656,1305,5352,'Phil','Agreement with nobody','2004-02-06 13:45:34',1,'We\'ve all been duped, or should i say we\'ve all duped ourselves, the chances of picking the king from back A is not 1/51, you select the 1st card from pack A before you know that the Queen of hearts was the top card, therefore the chances of seeing 2 king of Hearts in pack B is increased by 1/52 to (1/52)+1 \r\nthis can then be divided by the total number of cards in pack B to give the following equation. \r\n\r\n((1/52)+1)/53 = 0.01923076923076923\r\n\r\nor 1/52.00000000000000208\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (11657,1602,3172,'SilverKnight','re: Question','2004-02-06 13:50:01',0,'I\'ve thought the same thing.... I\'m guessing he might have been able to do the cubic in his head (although with some time for thought).\r\n\r\nPossibly, he previously remembered many cubes in his mind (as we typically remember 169, 196, 225, 256, ...) and was able to consider a bunch. The solution has cubes no higher than 12^3, and so could be \'brute forced\' relatively easily. And this, I think, is how the story goes. I believe it ends with Ramanujan asking about the 4th power, but he didn\'t have the answer handy....\r\n\r\nI may be misremembering the story.\r\n\r\nEither way, I seriously doubt a person, even he, could have done the quartic challenge in his head.',11654,0);
INSERT INTO comment VALUES (11658,1422,4906,'stan','Followup Questions','2004-02-06 14:10:06',4,'Could a smaller D be achieved if the diagonals didn\'t count? How?',NULL,0);
INSERT INTO comment VALUES (11659,1305,1301,'Charlie','re: Agreement with nobody','2004-02-06 14:20:34',0,'Comments on several things:\r\n\"the chances of seeing 2 king of Hearts in pack B is increased by 1/52 to (1/52)+1\"\r\n\r\nThe probability of this was given as 1/51, and you are actually changing it to 1/52. In doing so, you are agreeing with stan\'s original post. The figure (1/52)+1 can\'t be a probability as it exceeds 1. It is a numerator as it represents the sum of a couple of conditional probabilities -- there is always at least one king of hearts, and a certain probability of a second.\r\n\r\n\"or 1/52.00000000000000208\"\r\n\r\nThe difference from 1/52 is illusory, due to rounding errors in the calculation. ((1/52)+1)/53 = (53/52)/53 = 1/52 exactly, as stan had said, so you really agree with stan.\r\n\r\n\"the chances of picking the king from back A is not 1/51, you select the 1st card from pack A before you know that the Queen of hearts was the top card,\"\r\n\r\nHaving seen the queen of hearts, we know now that the chosen card was not the queen of hearts. If the probability were 1/52 of the card having been the king of hearts, that would be the probability for each of the 51 possibilites, and the total would be only 51/52 of any card having been chosen. But we know for a fact at probability 1 (not 51/52) that some card was chosen.\r\n\r\nWe need to use Baye\'s formula for the probability that the king of hearts was chosen, given that the queen of hearts was not chosen:\r\n\r\np(k|~q) = p(k&~q)/p(~q) = p(k)/p(~q), since k and q are mutually exclusive.\r\n\r\nThen,\r\np(k|~q) = p(k)/p(~q) = (1/52)/(51/52) = 1/51\r\n\r\nHere, the | within p(k|~q) is read as \"given\".',11656,0);
INSERT INTO comment VALUES (11660,1305,5352,'Phil','re(2): Agreement with nobody','2004-02-06 14:42:25',1,'Mmmmmm.....\r\nNow that really has confused me, but you are right. so now i don\'t know if i agree with charlie or stan, i\'ll flip a coin......\r\n......It\'s Charlie again.\r\nI do appologise for not being a mathematician, it just all seams to sit right one minute and then someone comes and explains it in a way i still don\'t understand.',11659,0);
INSERT INTO comment VALUES (11661,1583,3172,'SilverKnight','re(7): My algorithm','2004-02-06 14:56:47',0,'You\'re correct... so I shouldn\'t have to urge *anybody* to explain \"the thought process and methodology\" when they post a solution, right?',11640,0);
INSERT INTO comment VALUES (11662,1602,1626,'Gamer','A way to do it.','2004-02-06 15:06:51',0,'The cube thing could be done more easily than it seems. If you ever saw the cube root of 12, 1728, you could think \"Wow; if you add the one at the beginning to the end, it\'s also a perfect cube\", then you would be set up for knowing the answer.',NULL,0);
INSERT INTO comment VALUES (11663,1583,5345,'Rawlyn','re(8): My algorithm','2004-02-06 15:07:19',0,'Well I\'d continue urging lol\r\n\r\nThe thought process and methodology is the thing of interest here - I personally couldn\'t care less what the answer to most problems is, but the fact that someone got the solution in the first place, that\'s the interesting thing. In the case of perplexus, I\'d give this formula:\r\n\r\nMEANS > END\r\n\r\nPeace,\r\nRawlyn.',11661,0);
INSERT INTO comment VALUES (11664,1602,4374,'Richard','Hardy\'s Story','2004-02-06 16:17:23',0,'Hardy, after telling the \"1729\" part of the story (1729 was the cab number Hardy had ridden to visit Ramanujan) then adds \"I asked him, naturally, whether he could tell me the solution of the corresponding problem for fourth powers; and he replied, after a moment\'s thought, that he knew no obvious example, and supposed that the first such number must be very large.\" I have copied this from Hardy\'s \"Ramanujan\" where Hardy is quoting from his own memoir of Ramanujan that he contributed to Ramanujan\'s \"Collected Papers.\"\n\nEdited on February 6, 2004, 10:31 pm',NULL,0);
INSERT INTO comment VALUES (11665,359,5345,'Rawlyn','Gems?','2004-02-06 19:50:55',0,'Oooh an upmarket version lol For the rest of us, I think traditionally it was played in the dirt with pebbles... but lets not argue - just \"gems\" made me laugh so much...\r\n\r\nPeace,\r\nRawlyn.',NULL,0);
INSERT INTO comment VALUES (11666,1305,5525,'G','A KING INDEED','2004-02-06 20:16:53',0,'removing of one card from deck A would result in a 1/52 chance of being a king of hearts. however i card from deck A we know is a queen of hearts. so then chances of first card from deck A being a king of hearts are 1/51. shuffled with deck B there is a 1/51/53 chance of the exact same card being picked. but also deck B already has 1 king of hearts so then to answer your question the chances are \r\n1/51/53*2=2/2703 or\r\n\r\nso 51*53=2703 plus the existing king\r\n2/2703\r\n\r\nplease let me know if this is wrong or right?\r\nmy brain is hurting......',NULL,0);
INSERT INTO comment VALUES (11667,1602,5285,'Ady TZIDON','re: A way to do it.===> NO WAY','2004-02-07 04:05:04',0,'....\" cube thing could be done more easily than it seems. If you ever saw the cube root of 12, 1728, you could think \"Wow; if you add the one at the beginning to the ...\r\n\r\n\r\nTHERE TOO MANY ERRORS\r\n IN THIS STATEMENT TO UNDERSTAND WHAT YOU HAD IN MIND...\r\n\r\na Please explain\r\nb In the future- eschew obfuscation\r\n\r\nady',11662,0);
INSERT INTO comment VALUES (11668,1460,1626,'Gamer','Solution','2004-02-07 09:11:05',1,'\n\nEdited on February 7, 2004, 9:11 am',NULL,0);
INSERT INTO comment VALUES (11670,1307,153,'TomM','I overslept and my dog ate my homework','2004-02-07 11:00:33',3,'The boy left home at 7:05. He thought it was 4:55. he arrived at school at 7:25, 20 minutes after 7:05 and 150 minutes after 4:55\r\n\r\nThe time that the boy left was h1:m1 that is h1 hours and m1 minutes after midnight.\r\n\r\nThe time he thought it was was h2:m2\r\n\r\nThe time he arrived at school was h3:m3\r\n\r\nh2 = 1-h1 (mod 12) => h1 + h2 =11 [For example, If the hour hand was between 3 and 4, the boy thought it was between 8 and 9 and h1 = 3, h2 = 8]\r\n\r\nm2 = -m1 (mod 60) => m1 + m2 =60\r\n\r\n------\r\n\r\n60h1 + m1 + 20 = 60h3 + m3\r\n\r\n60h2 m2 + 150 = 60h3 + m3 = 60h1 + m1 + 20\r\n\r\n60(h1-h2) + (m1-m2) = 130\r\n60(2h1-11) + (2m1-60) = 130\r\n120h1 - 660 + 2\r\n120h1 + 2m1 - 720 = 130\r\n120h1 + 2m1 = 850 \r\n\r\n0<2m1≤120 and h1 is an integer, so 120h1 must be a multiple of 120\r\n\r\n850 = 840 + 10 is the only way to satisfy these conditions, so m1 = 5 and 120h1 = 840 => h1 = 7\r\n\r\n\n\nEdited on February 7, 2004, 11:03 am',NULL,0);
INSERT INTO comment VALUES (11669,1460,1626,'Gamer','Solution','2004-02-07 09:11:05',1,'I hope that\'s the solution too; it\'s what I got. Good job in working it out.\r\n\r\nMy solutions is longer than most because I wanted to make sure I didn\'t foul anything up when I made this :)',NULL,0);
INSERT INTO comment VALUES (11671,1307,5285,'Ady TZIDON','my solution','2004-02-07 11:04:53',3,'ANSWER: 13:25\r\n\r\nSolution: denote the time( observed by the boy) y minutes after 12:00\r\n\r\nthe actual time then is -y \r\n\r\nso\r\n\r\ny+150=-y+20\r\n2y=-130\r\ny=-65 minutes afternoon i.e. 10:55 so real time 1s 13:05 the boy arrived to school 20 minutes later\r\ni.e. about 13:25 \r\n\r\nady\n\nEdited on February 7, 2004, 11:58 am',NULL,0);
INSERT INTO comment VALUES (11672,1307,5285,'Ady TZIDON','there are 2 valid answers (or even 4)','2004-02-07 12:26:14',0,'both 7:25 (either AM or PM) \r\nand 1:25 (either AM or PM) qualify as MATHEMATICAL valid ANSWERS for T.O.A.\r\n\r\n\r\nClearly the minutes must be :05\r\nand the hours H0+HA=11 mod 12 i.e. 11,23,35..\r\n & HA-HO=3 \r\nHA- hour of arrival HO- hour of observation\r\n\r\nsolving we get 4 answers within the 24 hour interval: 1, 7, 13, 19\r\n\r\nhowever the boy leaves in the morning and this constraint voids all the answers\r\n save 7:05 for leaving home = 7:25 for arriving to school. \r\n\r\nady',NULL,0);
INSERT INTO comment VALUES (11673,1601,5338,'chuck','i think....','2004-02-07 12:30:06',0,'imagine that the reflected image was a person standing in fromt of you, he\'d be rotated 180 degrees--- so the mirror doesnt switch the imagine side to side it merely switches it back to front so if you raise you rigth hand it switches the image back to front and you see it as it being on the oposite side of your body',NULL,0);
INSERT INTO comment VALUES (11674,1388,5338,'chuck','impossible....','2004-02-07 12:38:46',0,'when a piece is occuping a square, that square isnt under attack or in possible ange for attack so thats impossible\r\n',NULL,0);
INSERT INTO comment VALUES (11675,835,5338,'chuck','duh','2004-02-07 13:00:19',0,'there cant be more than eight ',NULL,0);
INSERT INTO comment VALUES (11676,334,5530,'Sandu-Dragu Vlad','Solution','2004-02-07 13:33:30',0,'Verses/rhyme\r\nLight(The moon only reflexes light)\r\nShadow\r\nHorizont, or maybe Rainbow',NULL,0);
INSERT INTO comment VALUES (11677,1531,5530,'Sandu-Dragu Vlad','Solution(eeeeeeeaaaasy) in coordinates','2004-02-07 14:17:35',0,'First son:\r\n(15,30)(15,45)(45,45)(45,15)(30,15)(30,30)\r\n\r\nSecond son:\r\n(0,30)(0,60)(30,60)(30,45)(15,45)(15,30)\r\n\r\nThird son:\r\n(30,60)(60,60)(60,30)(45,30)(45,45)(30,45)\r\n\r\nFourth son:\r\n(30,0)(30,15)(45,15)(45,30)(60,30)(60,0)',NULL,0);
INSERT INTO comment VALUES (11678,1307,153,'TomM','re: there are 2 valid answers (or even 4)','2004-02-07 18:49:37',0,'The fact that, originally, both of us derived equations that only led to one of the two solutions suggests that we were making assumtions about modular arithmetic that are not quite quite correct. I\'m still not sure why they were not, or how they differed so as to lead to the different solutions.',11672,0);
INSERT INTO comment VALUES (11679,1284,5539,'mike','correct solution','2004-02-07 19:40:21',0,'I believe I have framed the problem correctly (The real challenge w/prob. theory) and have concluded the solution is\r\n\r\nPROBABILITY = .0015681\r\n\r\n(or)\r\n\r\nroughly 637 TO 1',NULL,0);
INSERT INTO comment VALUES (11680,1284,5539,'mike','grammar','2004-02-07 22:05:42',0,'By the way, although it has zero to do w/mathematics , people \"lie\" - things \"lay\"',NULL,0);
INSERT INTO comment VALUES (11681,1284,1301,'Charlie','re: grammar','2004-02-07 22:20:18',0,'From Random House Unabridged dictionary. Several of the meanings relate to object. Meaning 6 is probably most pertinent here.\r\n\r\nlie², v., lay, lain, ly·ing, n.\r\n –v.i.\r\n1. to be in a horizontal, recumbent, or prostrate position, as on a bed or the ground; recline.\r\n2. (of objects) to rest in a horizontal or flat position: The book lies on the table.\r\n3. to be or remain in a position or state of inactivity, subjection, restraint, concealment, etc.: to lie in ambush.\r\n4. to rest, press, or weigh (usually fol. by on or upon): These things lie upon my mind.\r\n5. to depend (usually fol. by on or upon).\r\n6. to be placed or situated: land lying along the coast.\r\n7. to be stretched out or extended: the broad plain that lies before us.\r\n8. to be in or have a specified direction; extend: The trail from here lies to the west.\r\n9. to be found or located in a particular area or place: The fault lies here.',11680,0);
INSERT INTO comment VALUES (11682,1307,5285,'Ady TZIDON','re(2): there are 2 valid answers (or even 4) ==>TomM','2004-02-08 01:01:27',0,'TomM\r\n ...both of us derived equations that only led to one of the two solutions ....\r\n\r\nThat is true for my 1st posting - the second takes into account all the possibilities. As to the wording of the problem- \"morning\" it was and \"morning\" it stays.\r\n\r\nHave fun\r\nady\r\n',11678,0);
INSERT INTO comment VALUES (11683,1284,5285,'Ady TZIDON','re(2): grammar JUST A REMARK','2004-02-08 01:12:58',0,'JUST A REMARK - NOTHING PERSONAL\r\n\r\n...Figures can\'t lie but liars can figure...\r\n\r\nady',11681,0);
INSERT INTO comment VALUES (11684,1581,5544,'Russ','Solution','2004-02-08 04:36:41',3,'Alan\'s probability of survival is 1/3\r\nCharlie\'s probability of survival is 2/3\r\n\r\nStealing from Penny\'s post:\r\n(1) Bob to be spared, and warden says \"Charlie\" - 1/3\r\n(2) Charlie is to be spared, and the warden says \"Bob\" - 1/3\r\n(3) Alan is to be spared, the warden flips a coin, Charlie \"wins\", and the warden says \"Charlie\" - (1/2)(1/3) = 1/6\r\n(4) Alan is to be spared, Bob \"wins\" the coin flip, and the warden says \"Bob\" -(1/2)(1/3) = 1/6\r\n\r\nNow, the Warden says \"Bob\" so we can eliminate cases 1 and 3. The only possible cases are 2 (Charlie is to be spared 1/3 chance) and 4 (Alan is to be spared 1/6 chance). Because some possibilities were eliminated, our posibilities don\'t add up to 1 anymore, only 1/2. So we need to scale them up to 1 to restore our sense of probability. :) So...\r\n\r\nChance Charlie to be spared is 1/3 * 2 = 2/3\r\nChance Alan to be spared is 1/6 * 2 = 1/3\r\n\r\n~\r\n\r\nLooking at it a different way, we can ask \"What information did Alan gain from the Warden\'s response?\" The answer is none. Alan knew that the Warden was going to say \"Bob\" or \"Charlie\" regardless of whether Alan was to be pardoned, so how did he benefit from the response \"Bob?\" Alan\'s chance remained at 1/3 after he heard \"Bob.\" However, Bob\'s chance dropped to 0 when the Warden said he wasn\'t going to be pardoned. Bob\'s 1/3 chance before the response went to Charlie after the response.',10982,0);
INSERT INTO comment VALUES (11685,334,5285,'Ady TZIDON','my letter','2004-02-08 05:09:55',0,'my letter: the letter S\r\n\r\nady',NULL,0);
INSERT INTO comment VALUES (11686,1307,5546,'se ross','','2004-02-08 08:37:40',0,'He reaches school at 7:25am,\r\nwhich means he left home at 7:05am,\r\nwhich was a mirror image of 4:55am,\r\n2.5 hours later.\r\nNotice the problem states \"in the morning\"',NULL,0);
INSERT INTO comment VALUES (11687,1509,5547,'Gayln Adams','solution','2004-02-08 11:08:51',0,'he got out MAR. 12',NULL,0);
INSERT INTO comment VALUES (11688,1420,1301,'Charlie','Computer Used','2004-02-08 11:09:34',3,'A computer search shows that \"beefily\" and \"billowy\" are the two longest words with letters in alphabetical order. If one doesn\'t like double letters (for strict monotonically increasing letter value), one letter shorter are \"almost\", \"begins\", \"biopsy\", \"chimps\", \"chinos\", \"chintz\" and \"ghostly\".\r\n\r\nFor reverse alphabetical order the longest is \"trollied\". One letter less avoids a double letter in \"sponged\" and \"wronged\".\r\n\r\nThe last \"word\" that the computer finds \"in alphabetical order\" is just \"x\". As there might be considered problems with that, the next-last is \"tux\", and after that (actually, before, in the alphabet), is \"sty\".\r\n\r\nFor reverse alphabetical order of its letters, the first word found is \"a\", whose letters are both in reverse alphabetic order as well as alphabetic order. The same quibble can be made about the second word found, \"aa\" (a type of lava). Then comes \"ba\", not too common a word. Then comes \"ebb\". The only problem for the purist here is the double letter. Then come \"ed\" (as in \"sex ed\" or \"driver\'s ed\") and \"fa\" (a note on the diatonic scale--or a long, long way to run in the Sound of Music). But a word that all can agree is common enough is \"fed\".\r\n\r\nThe program is:\r\n\r\nwdLim = 25\r\nREDIM save$(wdLim)\r\nOPEN \"words.txt\" FOR INPUT AS #1\r\nDO\r\n LINE INPUT #1, l$\r\n IF LCASE$(l$) = l$ THEN\r\n good = 1\r\n FOR i = 2 TO LEN(l$)\r\n IF MID$(l$, i, 1) < MID$(l$, i - 1, 1) THEN good = 0: EXIT FOR\r\n NEXT\r\n IF good THEN\r\n IF LEN(l$) > 5 THEN\r\n PRINT l$\r\n END IF\r\n IF LEN(l$) > LEN(save$(wdLim)) THEN\r\n FOR i = 1 TO wdLim\r\n IF LEN(l$) > LEN(save$(i)) THEN\r\n FOR j = i TO wdLim\r\n SWAP save$(j), l$\r\n NEXT\r\n EXIT FOR\r\n END IF\r\n NEXT\r\n END IF\r\n END IF\r\n END IF\r\nLOOP UNTIL EOF(1)\r\n\'FOR i = 1 TO 25\r\n\' PRINT save$(i)\r\n\'NEXT\r\nCLOSE\r\n\r\n\r\nwdLim = 25\r\nREDIM save$(wdLim)\r\nOPEN \"words.txt\" FOR INPUT AS #1\r\nDO\r\n LINE INPUT #1, l$\r\n IF LCASE$(l$) = l$ THEN\r\n good = 1\r\n FOR i = 2 TO LEN(l$)\r\n IF MID$(l$, i, 1) > MID$(l$, i - 1, 1) THEN good = 0: EXIT FOR\r\n NEXT\r\n IF good THEN\r\n IF LEN(l$) > 6 THEN PRINT l$\r\n IF LEN(l$) > LEN(save$(wdLim)) THEN\r\n FOR i = 1 TO wdLim\r\n IF LEN(l$) > LEN(save$(i)) THEN\r\n FOR j = i TO wdLim\r\n SWAP save$(j), l$\r\n NEXT\r\n EXIT FOR\r\n END IF\r\n NEXT\r\n END IF\r\n END IF\r\n END IF\r\nLOOP UNTIL EOF(1)\r\n\'FOR i = 1 TO 25\r\n\' PRINT save$(i)\r\n\'NEXT\r\nCLOSE\r\n\r\nwdLim = 25\r\nREDIM save$(wdLim)\r\nOPEN \"words.txt\" FOR INPUT AS #1\r\nDO\r\n LINE INPUT #1, l$\r\n IF LCASE$(l$) = l$ THEN\r\n good = 1\r\n FOR i = 2 TO LEN(l$)\r\n IF MID$(l$, i, 1) < MID$(l$, i - 1, 1) THEN good = 0: EXIT FOR\r\n NEXT\r\n IF good THEN\r\n FOR j = 1 TO wdLim\r\n SWAP save$(j), l$\r\n NEXT\r\n END IF\r\n END IF\r\nLOOP UNTIL EOF(1)\r\nFOR i = 1 TO wdLim\r\n PRINT save$(i)\r\nNEXT\r\nCLOSE\r\n\r\n\r\nwdLim = 25\r\nREDIM save$(wdLim)\r\nOPEN \\\"words.txt\\\" FOR INPUT AS #1\r\nwCt = 0\r\nDO\r\n LINE INPUT #1, l$\r\n IF LCASE$(l$) = l$ THEN\r\n good = 1\r\n FOR i = 2 TO LEN(l$)\r\n IF MID$(l$, i, 1) > MID$(l$, i - 1, 1) THEN good = 0: EXIT FOR\r\n NEXT\r\n IF good THEN\r\n wCt = wCt + 1\r\n IF wCt <= wdLim THEN\r\n save$(wCt) = l$\r\n END IF\r\n END IF\r\n END IF\r\nLOOP UNTIL EOF(1)\r\nFOR i = 1 TO wdLim\r\n PRINT save$(i)\r\nNEXT\r\nCLOSE\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (11689,1420,1301,'Charlie','re: Computer Used--BTW, the full output','2004-02-08 11:17:15',3,'\r\nabbess\r\nabhors\r\naccent\r\naccept\r\naccess\r\naccost\r\nadders\r\nadeems\r\nafflux\r\nalmost\r\nbeefily\r\nbegins\r\nbegirt\r\nbeknot\r\nbellow\r\nbijoux\r\nbillow\r\nbillowy\r\nbiopsy\r\nbloops\r\nblotty\r\ncellos\r\nchills\r\nchilly\r\nchimps\r\nchinos\r\nchintz\r\nchippy\r\nchirrs\r\nchitty\r\nchivvy\r\nchoosy\r\nchoppy\r\nclotty\r\ndehort\r\ndekkos\r\nefflux\r\neffort\r\nfillos\r\nfloors\r\nfloosy\r\nfloppy\r\nflossy\r\nghosty\r\ngloppy\r\nglossy\r\nhillos\r\nknotty\r\n\r\nsniffed\r\nspiffed\r\nsponged\r\nspoofed\r\nspooked\r\nspooled\r\nspooned\r\ntrigged\r\ntrolled\r\ntrollied\r\nvroomed\r\nwoolled\r\nwronged\r\n\r\nx\r\ntux\r\nsty\r\npsst\r\npry\r\noy\r\noxy\r\nox\r\now\r\nos\r\nort\r\nors\r\nor\r\nopt\r\nops\r\nop\r\noot\r\noops\r\nnu\r\nnow\r\nnot\r\nnosy\r\nnos\r\nnor\r\n\r\na\r\naa\r\nba\r\nbaa\r\nebb\r\ned\r\nfa\r\nfed\r\nfee\r\nfeed\r\nged\r\ngee\r\ngeed\r\nha\r\nhe\r\nheed\r\nid\r\nif\r\niff\r\njee\r\njeed\r\njib\r\njibb\r\njiff\r\njig\r\n
\r\n---------\r\nExcept for the first group, there was a limit of 25 on the number to be found.\r\n\n\nEdited on February 8, 2004, 11:22 am',11688,0);
INSERT INTO comment VALUES (11690,1420,5285,'Ady TZIDON','no computer at all','2004-02-08 11:59:39',0,'1 almost , bellow\r\n2 ???\r\n3 x\r\n4 jig\r\n\r\n\r\n\r\n....in COMPUTERESQUE it sounds better...\r\n\r\nady\r\n',NULL,0);
INSERT INTO comment VALUES (11691,1420,5285,'Ady TZIDON','another word ( no computer)','2004-02-08 12:04:37',0,'\r\nStyx -a river in Hades - qualifies if capital letters are allowed \r\n\r\nNo computer - just general knowledge \r\n\r\nady\r\nBTW : I LIKED THIS PUZZLE.',NULL,0);
INSERT INTO comment VALUES (11692,1284,5539,'mike','sorry charlie','2004-02-08 12:48:14',0,'I was wrong. I stand corrected.\r\n... probability of simple adages planted in your brain by teachers being accurate : apparently minimal....',NULL,0);
INSERT INTO comment VALUES (11693,1420,5345,'Rawlyn','re: Computer Used','2004-02-08 14:36:23',0,'Very interesting... I\'d be interested to see the \"words.txt\" file that you were using here. Does it contain every single word in the English language?\r\n\r\nEven if it doesn\'t could I by any chance request a copy? - no end of word puzzle solving fun could be had with it!\r\n\r\nPeace,\r\nRawlyn.\r\n\r\np.s. if you\'re willing to let me see, could you send to rawlyn(at)hotmail(dot)com - thanks :)',11688,0);
INSERT INTO comment VALUES (11694,1420,5345,'Rawlyn','stupid answers','2004-02-08 14:39:19',0,'Would \"aaaaaaaaah\" count for an answer to question 1? And what about the classic sleepy word for in comics \"zzzzzzzzzz\"?\r\n\r\n:D tee hee\r\n\r\nPeace,\r\nRawlyn.',NULL,0);
INSERT INTO comment VALUES (11695,1420,4507,'Penny','The English langauge is just too funny for words !!','2004-02-08 14:41:32',1,'As my friend Carol aptly notes:\r\n\r\n\"There is no egg in eggplant or ham in hamburger; neither apple nor pine in pineapple. English muffins were not invented in England or french fries in France. Sweetmeats are candies, while sweetbreads, which aren\'t sweet, are meat. \r\nWe take English for granted. But if we explore its paradoxes, we find that quicksand can work slowly, boxing rings are square, and a guinea pig is neither from Guinea nor is it a pig. And why is it that writers write, but fingers don\'t fing, grocers don\'t groce, and hammers don\'t ham?\r\nIf the plural of tooth is teeth, why isn\'t the plural of booth beeth? One goose, 2 geese. So, one moose, 2 meese? One index, two indices? Is cheese the plural of choose? If teachers taught, why didn\'t preachers praught? If a vegetarian eats vegetables, what does a humanitarian eat?\r\nIn what language do people:\r\nRecite at a play, and play at a recital?\r\nShip by truck and send cargo by ship?\r\nHave noses that run and feet that smell?\r\nPark on driveways and drive on parkways?\r\nHow can a slim chance and a fat chance be the same, while a wise man and a wise guy are opposites? When a house burns up, it burns down.\r\nYou fill in a form by filling it out and an alarm clock goes off by going on. When the stars are out, they are visible, but when the lights are out, they are invisible. And why, when I wind up my watch, I start it, but when I wind up this essay, I end it?\"\r\n',NULL,0);
INSERT INTO comment VALUES (11696,1420,5345,'Rawlyn','re: The English langauge is just too funny for words !!','2004-02-08 14:56:24',0,'And what makes the English language so much like an Engl anyways... :P',11695,0);
INSERT INTO comment VALUES (11697,1420,5345,'Rawlyn','re: another word ( no computer) other rivers','2004-02-08 15:01:11',0,'Don\'t know if you were interested Ady, but there are six rivers of Hell in total, Acheron, Avernus, Cocytus, Lethe, Phlegethon and your own Styx. It\'s amongst some of the most useless information in my head, so I\'m just glad to have the opportunity to use it lol\r\n\r\nPeace,\r\nRawlyn.',11691,0);
INSERT INTO comment VALUES (11698,1420,1301,'Charlie','re(2): Computer Used','2004-02-08 16:00:32',0,'Wordlists are available at http://www.puzzlers.org/wordlists/dictinfo.php\r\n\r\nI think I downloaded my most recently used one (and renamed it) from the Enable set.',11693,0);
INSERT INTO comment VALUES (11699,1420,5345,'Rawlyn','re(3): Computer Used','2004-02-08 16:10:10',0,'Ooh nice - thanks :)',11698,0);
INSERT INTO comment VALUES (11700,1302,5548,'Seth','Potential Solution','2004-02-08 16:10:23',0,'I worked through the problem and got the same answers as Dave as well as many others. After re-reading the problem I agree with tim that the semantics are a bit tricky, and we need to drop the final iteration of the cannibal being eaten. \r\n\r\nThe first cannibal was eaten in 120/5 minutes, or 24 minutes. The second cannibal weighing 1.2C...or 1.2 times the original mass of the cannibals, was eaten in 120*1.2/4, or 36 minutes. The 4 remaining cannibals had 1.2C/4 (.3) added to their current weight of 1.2C and now weighed 1.5. \r\nThis goes on until two, not one cannibal is left. The reason again being an issue of semantics, as the question is looking for one remaining consumer. \r\nWhen all the figures are added up I got an even 4 hours. \r\n24 mins for the first at 1.0C\r\n36 mins for the second at 1.2C\r\n60 mins for the third at 1.5 C\r\nand 120 mins for the last at 2.0C. \r\n\r\nThis leaves 2 cannibals that both way 3x their starting body weight, and if one was to eat the other it\'d take 3.0C*120/1 minutes - 6 hours in other words. So in the end, if the one was to eat all 5 others it would as others have said, take ten hours, but since he\'s only eating 4 others, it will take him only 4 hours.\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (11701,1051,5345,'Rawlyn','Hmm','2004-02-08 16:38:10',3,'My solution is:\r\n\r\nMagic green round-assed two-legged cow from space.\r\n\r\nThe problem with riddles of this nature is that they never seem to specify that it must be something in the real world. No doubt there are an infinity unreal object which fit this description...\r\n\r\nPeace,\r\nRawlyn.',NULL,0);
INSERT INTO comment VALUES (11702,1420,4507,'Penny','re(2): another word ( no computer) other rivers','2004-02-08 16:50:45',0,'Rawlyn: \"Don\'t know if you were interested Ady, but there are six rivers of Hell in total\".\r\n\r\nWhen Joan Rivers dies, there\'ll be seven.\r\n\r\n:o)',11697,0);
INSERT INTO comment VALUES (11703,1420,5285,'Ady TZIDON','re: The English langauge is just too funny for words==>Penny !!','2004-02-08 17:31:11',1,'Penny\r\n I do not know who Carol is- anyway the source of all the\r\npuns and idiosyncrasies you\'ve quoted is no other than Richard Lederer , a writer of about 20 books on this subject, the funniest being \"The anguished English\".\r\nMake your day , look it up.\r\nady',11695,0);
INSERT INTO comment VALUES (11704,1420,4507,'Penny','re: no computer at all','2004-02-08 18:23:12',0,'That was a neat trick, Ady, getting your post on the flooble website without using a computer !!!!',11690,0);
INSERT INTO comment VALUES (11705,1420,5345,'Rawlyn','re(3): another word ( no computer) other rivers','2004-02-08 18:55:47',0,'Penny - I salute you! Thanks for making me burst out laughing :P lol oh that was a beauty....',11702,0);
INSERT INTO comment VALUES (11706,1420,1626,'Gamer','re: The English langauge is just too funny for words !!','2004-02-08 20:00:34',0,'I think you have hit on some of the major points of interest. I think the idea of plurals is interesting. How come deer and sheep are both plural and singular? If mice is the plural of mouse, is spice the plural of spouse? Even having sounds is interesting. I think I found a site once that showed there were 10 or some different sounds for u.\r\n\r\nPlus, the old \"ghoti\" problem is interesting (which is already on the site by the way)',11695,0);
INSERT INTO comment VALUES (11707,1420,5345,'Rawlyn','re(2): The English langauge is just too funny for words !!','2004-02-08 20:23:31',0,'There are loads of sounds for \"ough\"... I won\'t list them - could be a future puzzle in it?',11706,0);
INSERT INTO comment VALUES (11708,1312,5554,'molly','SOLUTION','2004-02-08 22:41:22',0,'ALICIA GOT AL FIVE CORRECT.\r\n\r\n1. EGGS\r\n2. EVAPORATION\r\n3. ALLIGATOR\r\n4. KANGAROO\r\n5. TEETH',NULL,0);
INSERT INTO comment VALUES (11709,288,4507,'Penny','By Jove, my quick study of lexicography won a prize.','2004-02-09 00:11:39',3,'Pangrams are sentences containing all the letters of the alphabet. Here is a list of hilarious pangrams. \r\n\r\nBy Jove, my quick study of lexicography won a prize. \r\n\r\n\"Quit beer,\" vows dizzy, puking, Michael J. Fox. \r\n\r\nA large fawn jumped quickly over white zinc boxes. \r\n\r\nA mad boxer shot a quick, gloved jab to the jaw of his dizzy opponent. \r\n\r\nA popular belief is that fornication would be a quick fix for some overzealously judicious governments. \r\n\r\nA quart jar of oil mixed with zinc oxide makes a very bright paint. \r\n\r\nA quick brown fox jumps over the lazy dog. \r\n\r\nA quick movement of the enemy will jeopardize six gunboats. \r\n\r\nA very bad quack might jinx zippy fowls. \r\n\r\nAbout sixty codfish eggs will make a quarter pound of very fizzy jelly. \r\n\r\nAlfredo just must bring very exciting news to the plaza quickly. \r\n\r\nAll questions asked by five watch experts amazed the judge. \r\n\r\nAmazingly few discotheques provide jukeboxes. \r\n\r\nAn inspired calligrapher can create pages of beauty using stick ink, quill, brush, pick-axe, buzz saw, or even strawberry jam. \r\n\r\nAnxious Paul waved back his pa from the zinc quarry just sighted. \r\n\r\nAs we explored the gulf of Zanzibar, we quickly moved closer to the jutting rocks. \r\n\r\nAstronaut Quincy B. Zack defies gravity with six jet fuel pumps. \r\n\r\nBack in June we delivered oxygen equipment of the same size. \r\n\r\nBack in my quaint garden, jaunty zinnias vie with flaunting phlox. \r\n\r\nBan foul, toxic smogs which quickly jeopardize lives. \r\n\r\nBarkeep, a flaming tequila swizzle and a vodka and Ajax, hold the cherry. \r\n\r\nBaroque...hell, just mix a dozen wacky pi fonts & you\'ve got it. \r\n\r\nBawds jog, flick quartz, vex nymph. \r\n\r\nBig July earthquakes confound zany experimental vow. \r\n\r\nBlowzy frights vex, and jump quick. \r\n\r\nBlowzy night-frumps vex\'d Jack Q. Blowzy red vixens fight for a quick jump. \r\n\r\nBrawny gods just flocked up to quiz and vex him. \r\n\r\nBreezily jingling $3,416,857,209, wise advertiser ambles to the bank, his exchequer amplified. \r\n\r\nBrick quiz whangs jumpy veldt fox. \r\n\r\nCozy lummox gives smart squid who asks for job pen. \r\n\r\nCozy sphinx waves quart jug of bad milk. \r\n\r\nCrazy Fredericka bought many very exquisite opal jewels. \r\n\r\nCwm kvutza qoph jynx fled brigs. \r\n\r\nCwm, fjord-bank glyphs vext quiz. \r\n\r\nDangerously frozen, he quickly judged his extremities to be waterproof. \r\n\r\nDoxy with charming buzz quaffs vodka julep. \r\n\r\nDr. Jekyll vows to finish zapping quixotic bum. \r\n\r\nDub waltz, nymph, for quick jigs vex. \r\n\r\nDumpy kibitzer jingles as exchequer overflows. \r\n\r\nEbenezer unexpectedly bagged two tranquil aardvarks with his jiffy vacuum cleaner. \r\n\r\nEmily Q. Jung-Schwartzkopf XV, B.D. \r\n\r\nExquisite farm wench gives body jolt to prize stinker. \r\n\r\nExquisite wizard flock behaving jumpy. \r\n\r\nFabled reader with jaded, roving eye seized by quickened impulse to expand budget. \r\n\r\nFew quips galvanized the mock jury box. \r\n\r\nFive big quacking zephyrs jolt my wax bed. \r\n\r\nFive jumbo oxen graze quietly with packs of dogs. \r\n\r\nFive or six big jet planes zoomed quickly by the tower. \r\n\r\nFive wine experts jokingly quizzed chablis sample. \r\n\r\nFjord-buck zags whelm qvint pyx. \r\n\r\nFor only $49, jolly housewives made \"inexpensive\" meals using quick-frozen vegetables. \r\n\r\nForsaking monastic tradition, twelve jovial friars gave up their vocation for a questionable existence on the flying trapeze. \r\n\r\nFoxy Gen. Schwarzkopf jumbled Iraqi TV. \r\n\r\nFoxy nymphs grab quick-lived waltz. \r\n\r\nFred specialized in the job of making very quaint wax toys. \r\n\r\nFreight to me sixty dozen quart jars and twelve black pans. \r\n\r\nFrowzy things plumb vex\'d Jack Q. Frozen buyer just quickly keyed shocking weaver\'s $34,825,679 complexion. \r\n\r\nFrumpy veld wags quiz jack-in-the-box. \r\n\r\nGlum Q. Schwarzkopf jinxed by TV. \r\n\r\nGrumpy wizards make toxic brew for the evil queen and jack. \r\n\r\nGuzzling of jaunty exile wrecks havoc at damp banquet. \r\n\r\nGyps balk nth fjord cwm quiz, vex. \r\n\r\nG. W. Bush quickly fixed prize jam on TV. \r\n\r\nHark, toxic jungle water vipers quietly drop on zebras for meals! \r\n\r\nHow jolly vexing a fumble to drop zucchini in the quicksand! \r\n\r\nHow quickly daft jumping zebras vex. \r\n\r\nHow razorback jumping frogs can level six piqued gymnasts. \r\n\r\nHow razorback jumping frogs level six piqued gymnasts! \r\n\r\nHow razorback-jumping frogs can level six piqued gymnasts! \r\n\r\nHow vexing a fumble to drop a jolly zucchini in the quicksand. \r\n\r\nI have quickly spotted the four women dozing in the jury box. \r\n\r\nI was temporarily forced to zig-zag and quiver furiously around big junky xylophones. \r\n\r\nIf Jack quiz bald nymphs grow vext. \r\n\r\nJ Q Schwartz flung D V Pike my box. \r\n\r\nJ. Q. Vandz struck my big fox whelp. \r\n\r\nJ. Hoefler cabled: \"puzzling over waxy kumquats.\" \r\n\r\nJack amazed a few girls by dropping the antique onyx vase! \r\n\r\nJack believed we quiz sphinx from Egypt. \r\n\r\nJack Farmer realized that the big yellow quilts were expensive. \r\n\r\nJack-in-the-box quiz fed grumpy wolves. \r\n\r\nJackdaws love my big sphinx of quartz. \r\n\r\nJaded zombies acted quaintly but kept driving their oxen forward. \r\n\r\nJail zesty vixen who grabbed pay from quack. \r\n\r\nJay visited back home and gazed upon a brown fox and quail. \r\n\r\nJeb quickly drove a few extra miles on the glazed pavement. \r\n\r\nJelly-like above the high wire, six quaking pachyderms kept the climax of the extravaganza in a dazzling state of flux. \r\n\r\nJim just quit and packed extra heavy bags for Liz Owen. \r\n\r\nJimmy and Zack, the police explained, were last seen diving into a field of buttered quahogs. \r\n\r\nJink cwm, zag veldt, fob qursh pyx. \r\n\r\nJolly few pangrams vanquished by exotic kudzu. \r\n\r\nJolly housewives made inexpensive meals using quick-frozen vegetables. \r\n\r\nJudge Powell quickly gave six embezzlers stiff sentences. \r\n\r\nJudges vomit; few quiz pharynx block. \r\n\r\nJumbling vext frowzy hacks PDQ. \r\n\r\nJump by vow of quick, lazy strength in Oxford. \r\n\r\nJumpy wizard quit having black foxes. \r\n\r\nJumpy zebra vows to quit thinking coldly of sex. \r\n\r\nJunky qoph-flags vext crwd zimb. \r\n\r\nJust be very quick when fixing zip code mail. \r\n\r\nJust keep examining every low bid quoted for zinc etchings. \r\n\r\nJust work for improved basic techniques to maximize your typing skills. \r\n\r\nKing Alexander was just partly overcome after quizzing Diogenes in his tub. \r\n\r\nLazy jackal from raiding xebec prowls the quiet cove. \r\n\r\nLazy movers quit hard packing of jewelry boxes. \r\n\r\nMany big jackdaws quickly zipped over the fox pen. \r\n\r\nMany-wived Jack laughs at probes of sex quiz. \r\n\r\nMartin J. Hixeypovzer quickly began his first word. \r\n\r\nMay Jo equal the fine record by solving six puzzles a week? \r\n\r\nMeg Schwarzkopf quit Jynx Blvd. \r\n\r\nMeghan deftly picks valuable jewels: onyx, quartz. \r\n\r\nMilk-vat fez bugs qoph-crwd jynx. \r\n\r\nMix Zapf with Veljovic and get quirky beziers. \r\n\r\nMonique, the buxom coed, likes to fight for Pez with the junior varsity team. \r\n\r\nMr. Jock, TV quiz Ph.D., bags few lynx. \r\n\r\nMurky haze enveloped a city as jarring quakes broke forty-six windows. \r\n\r\nMy grandfather picks up quartz and valuable onyx jewels. \r\n\r\nMy help squeezed back in again after six and joined the weavers. \r\n\r\nNancy Bizal exchanged vows with Robert J. Kumpf at Quincy Temple. \r\n\r\nNew job: fix Mr. Gluck\'s hazy TV, PDQ! \r\n\r\nNo kidding, Lorenzo called off his trip to visit Mexico City just because they told him the conquistadores were extinct. \r\n\r\nNow is the time for all quick brown dogs to jump over the lazy lynx. \r\n\r\nNth balks gyp, vex cwm fjord quiz. \r\n\r\nNth black fjords vex Qum gyp wiz. \r\n\r\nNth quark biz gyps cwm fjeld vox. \r\n\r\nNth zigs block Qum dwarf jive pyx. \r\n\r\nOn the boardwalk grave playful lizards quickly jump and exercise. \r\n\r\nOozy quivering jellyfish expectorated by mad hawk. \r\n\r\nPack my box with five dozen liquor jugs. \r\n\r\nPangrams have subjects like \"dewy fox quiz.\" \r\n\r\nPerhaps President Clinton\'s amazing sax skills will be judged quite favorably. \r\n\r\nPhlegms fyrd wuz qvint jackbox. \r\n\r\nPicking just six quinces, new farm hand proves strong but lazy. \r\n\r\nPickled, Gorbachev jumps tawny fax quiz. \r\n\r\nPlaying jazz vibe chords quickly excites my wife. \r\n\r\nPrized waxy jonquils choke big farm vats. \r\n\r\nProdigal lesbians from Venezuela know just exactly how to eat quiche. \r\n\r\nPuzzled women bequeath jerks very exotic gifts. \r\n\r\nPyx crwth fjeld, quok, vang, zimbs. \r\n\r\nPyx vang quiz: komb crwth fjelds. \r\n\r\nQuartz glyph job vex\'d cwm finks. \r\n\r\nQuestions of a zealous nature have become by degrees petty waxen jokes. \r\n\r\nQuick fawns jumped over a lazy dog. \r\n\r\nQuick jigs for waltz vex bad nymph. \r\n\r\nQuick wafting zephyrs vex bold Jim. \r\n\r\nQuick waxy bugs jump the frozen veldt. \r\n\r\nQuick zephyrs blow, vexing daft Jim. \r\n\r\nQuixotic knights\' wives are found on jumpy old zebras. \r\n\r\nQuixotic Republicans vet first key zero-growth jeremiad. \r\n\r\nQuiz explained for TV show by Mick Jagger. \r\n\r\nQursh gowf veldt jynx zimb pack. \r\n\r\nRaving zibet chewed calyx of pipsqueak major. \r\n\r\nSex prof gives back no quiz with mild joy. \r\n\r\nSix big devils from Japan quickly forgot how to waltz. \r\n\r\nSix big juicy steaks sizzled in a pan as five workmen left the quarry. \r\n\r\nSix boys guzzled cheap raw plum vodka quite joyfully. \r\n\r\nSix crazy kings vowed to abolish my quite pitiful jousts. \r\n\r\nSix javelins thrown by the quick savages whizzed forty paces beyond the mark. \r\n\r\nSix of the women quietly gave back prizes to the judge. \r\n\r\nSix plump boys guzzled cheap raw vodka quite joyfully. \r\n\r\nSixty zippers were quickly picked from the woven jute bag. \r\n\r\nSixty-five wildly panting fruitflies gazed hungrily at the juicy bouncing kumquats. \r\n\r\nSphinx of black quartz: judge my vow. \r\n\r\nSqudgy fez, blank jimp crwth vox. \r\n\r\nSuez sailor vomits jauntily abaft while waxing parquet decks. \r\n\r\nSympathizing would fix Quaker objectives. \r\n\r\nThe exodus of jazzy pigeons is craved by squeamish walkers. \r\n\r\nThe explorer was frozen in his big kayak just after making queer discoveries. \r\n\r\nThe five boxing wizards jump quickly. \r\n\r\nThe job of waxing linoleum frequently peeves chintzy kids. \r\n\r\nThe job requires extra pluck and zeal from every young wage earner. \r\n\r\nThe jukebox music puzzled a gentle visitor from a quaint valley town. \r\n\r\nThe July sun caused a fragment of black pine wax to ooze on the velvet quilt. \r\n\r\nThe public was amazed to view the quickness and dexterity of the juggler. \r\n\r\nThe quick brown fox jumps over a lazy dog. \r\n\r\nThe risque gown marked a very brazen exposure of juicy flesh. \r\n\r\nThe sex life of the woodchuck is a provocative question for most vertebrate zoology majors. \r\n\r\nThe vixen jumped quickly on her foes barking with zeal. \r\n\r\nTheir kind aunt was subject to frequent dizzy spells, thus causing much anxiety and worry. \r\n\r\nThumb frowzly, vexing jacks, PDQ. \r\n\r\nTravelling beneath the azure sky in our jolly ox-cart, we often hit bumps quite hard. \r\n\r\nTurgid saxophones blew over Mick\'s jazzy quiff. \r\n\r\nTwo hardy boxing kangaroos jet from Sydney to Zanzibar on quicksilver pinions. \r\n\r\nUphill jogging will tax pounding heart muscle very quickly; better to be lazy! \r\n\r\nVeldt jynx grimps waqf zho buck. \r\n\r\nVerbatim reports were quickly given by Jim Fox to his amazed audience. \r\n\r\nVexed funky camp juggler quit show biz. \r\n\r\nVext cwm fly zing jabs Kurd qoph. \r\n\r\nVictors flank gyp who mixed job quiz. \r\n\r\nVictors flank gypsy who mixed up on job quiz. \r\n\r\nViewing quizzical abstracts mixed up hefty jocks. \r\n\r\nWaltz, dumb nymph, for quick jigs vex. \r\n\r\nWaltz, nymph, for quick jigs vex bud. \r\n\r\nWaqf vozhd trecks, jumbling pyx. \r\n\r\nWas there a quorum of able whizzkids gravely exciting the jaded fish at ATypI? \r\n\r\nWatch all five questions asked by experts amaze the judge. \r\n\r\nWavy Jake\'s fat zebra had Mexican pig liquor. \r\n\r\nWe could jeopardize six of the gunboats by two quick moves. \r\n\r\nWe crazed folk quit having sex, be jumpy. \r\n\r\nWe dislike to exchange job lots of sizes varying from a quarter up. \r\n\r\nWe have just quoted on nine dozen boxes of gray lamp wicks. \r\n\r\nWe promptly judged antique ivory buckles for the next prize. \r\n\r\nWe quickly seized the black axle and just saved it from going past him. \r\n\r\nWest quickly gave Bert handsome prizes for six juicy plums. \r\n\r\nWham, volcano erupts fiery liquid death onto ex-jazzbo Kenny G. \r\n\r\nWhen waxing parquet decks, Suez sailors vomit jauntily abaft. \r\n\r\nWhen we go back to Juarez, Mexico, do we fly over picturesque Arizona? \r\n\r\nWheneer the black fox jumped the squirrel gazed suspiciously. \r\n\r\nWhile making deep excavations we found some quaint bronze jewelry. \r\n\r\nWhy jab, vex quartz-damping flocks? \r\n\r\nWill Major Douglas be expected to take this true-false quiz very soon? \r\n\r\nWilliam Jex quickly caught five dozen Republicans. \r\n\r\nWilliam said that everything about his jacket was in quite good condition except for the zipper. \r\n\r\nWolves exit quickly as fanged zoo chimp jabbers. \r\n\r\nWorn DJ: vex Gk HQ, clamp fubsy zit. \r\n\r\nWould you please examine both sizes of jade figures very quickly. \r\n\r\nWoven silk pyjamas exchanged for blue quartz. \r\n\r\nXV quick nymphs beg fjord-waltz. \r\n\r\nXylophone wizard begets quick jive form. \r\n\r\nYou go tell that vapid existentialist quack Freddy Nietzsche that he can just bite me, twice. \r\n\r\nYou will quite often be amazed by Jock\'s very weighty, size six sporran! \r\n\r\nZany Jacques French\'s pub mixed watery vodka gimlets. \r\n\r\nZelda quickly wove eight nubby flax jumpers.\r\n',NULL,0);
INSERT INTO comment VALUES (11710,1602,4507,'Penny','re: Hardy\'s Story','2004-02-09 01:27:22',0,'That\'s strange. I\'ve read all the Hardy Boys/Nancy Drew novels, and I don\'t remember this anecdote.....',11664,0);
INSERT INTO comment VALUES (11711,288,5285,'Ady TZIDON','re: By Jove, etc ====> Pewnnywon a prize.','2004-02-09 02:04:11',0,'Penny,\r\n\r\npangrams are plenty...\r\nshort ones are few...\r\nout of \"my\" 20\r\n2 are for you: \r\n\r\n\r\n\r\n\r\nBlowzy night-frumps vex\'d Jack Q. (26 letters) \r\nGlum Schwartzkopf vex\'d by NJ IQ. (26 letters) \r\n\r\nbtw ,\r\nit\'s \"jumps\" & \"a lazy dog\" and not \"jumped\" & \"the lazy dogs\"\r\n\r\nady\r\n--------------------------------------------------------------------------------\r\n\n\nEdited on February 9, 2004, 2:07 am',11709,0);
INSERT INTO comment VALUES (11712,1605,5352,'Phil','More balls than most','2004-02-09 07:03:53',3,'firstly draw an imaginary cube using the centres of each of the spheres as the points on the box.\r\nthen use Pythagarus (i think) theory across one face to find the length of the diagonal. use this length as the base in a second triangle and use the measure of one edge as the second, calculate the third using said theory. subtract the length of to radii from this and the diameter of the sphere in the middle is given, half this to show radius\r\n\r\n1. (R1+R2)^2+(R3+R4)^2=X^2 \r\n X=Diagonal length across centre of spheres on same face\r\n2 (R5+R6)^2+X^2=Z^2\r\n Z=length across centre of spheres directly opposite\r\n3. (Z - (R1+R2))/2 = Radius of small sphere\r\n\r\nplacing in the figures\r\n\r\n1. (1+1)^2+(1+1)^2=X^2\r\n1a. Sqroot of X=2.8284271247\r\n2. (1+1)^2+X^2 =Z^2\r\n2a. Sqroot of Z=3.4641016151\r\n3. (3.4641016151-(1+1))/2=0.732050807568 units of length for the radius of the centre sphere.\r\n\r\nI have a feeling that there is an easier way to calculate this, but without an education i\'m unable, i should have tried harder in school.\r\n\r\nPhil\n\nEdited on February 9, 2004, 7:11 am',NULL,0);
INSERT INTO comment VALUES (11713,1605,3275,'retiarius','solution','2004-02-09 07:26:20',0,'Each large sphere touches the face of the cube at a distance of √2 from its closest corner.\r\nThus the centre of each sphere is √3 from its nearest corner.\r\nEach diagonal is √(4^2 + 4^2 + 4^2) = √48\r\nTherefore, the radius of the small sphere = (√48 - 2√3 - 2)/2 = √3 - 1\r\n\r\n\r\nEdited on February 9, 2004, 7:27 am\n\nEdited on February 9, 2004, 7:28 am',NULL,0);
INSERT INTO comment VALUES (11714,1407,5487,'Peter Lunts','question','2004-02-09 08:17:35',0,'you must define a row: is it only horizontal and vertical, or can it be diagonal also?\r\n',NULL,0);
INSERT INTO comment VALUES (11715,1459,5559,'kenthank','solution','2004-02-09 08:20:07',0,'1st: white shirt, green tie, white suspender\r\n2nd: green shirt, blue tie, green suspender\r\n3rd: blue shirt, white tie, red suspender\r\n4th: red shirt, red tie, blue suspender',NULL,0);
INSERT INTO comment VALUES (11716,633,5487,'Peter Lunts','guess','2004-02-09 08:48:27',0,'water and ice are special. when water freezes instead of contracting it expands. that is why if you leave a glass of water out in the cold it will burst. so therefore when water becomes ice it has a lesser density. so that is why it floats on the more dense substance -- water.',NULL,0);
INSERT INTO comment VALUES (11717,1605,5391,'York','Different Sulution','2004-02-09 10:01:16',3,'the center sphere would have a radius of:\r\n(suare root of 2)-1\r\nor\r\n.414213562\r\n\r\nI came about this by looking at the problem in 2-d. The radii of the circles form a 2 unit square with arcs extending 1 unit into the square from all four corners. the distance between the arcs diagonally will form the diameter of the center circle. useing a^2 + b^2 = C^2, I found the length of the diagonal to be √8. this minus the radii of the two arcs, 1 each, havled is the radius of the center circle. \r\nI think?\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (11718,1605,1301,'Charlie','re: Different Sulution','2004-02-09 11:19:57',0,'The problem with this is that the plane on which this occurs, one unit behind the front plane of the cube, does not contain the center of the small red sphere. That sphere is farther back, allowing its radius to be larger than if it had to fit in the middle of the plane containing the centers of four of the spheres.',11717,0);
INSERT INTO comment VALUES (11719,360,5407,'Ashley','Funny story','2004-02-09 12:12:34',0,'I\'m glad you are taking the time to read this. All right, I recall a funny story about this riddle...
My brother once asked this exact riddle to a friend of his. After stating the answer and still confusing the boy, my brother broke it down for him -
\"What is greater than God?\" he asked.
\"Nothing,\" the boy replied.
\"What is more evil than the Devil?\"
\"Nothing.\"
\"What do the poor have?\"
\"Nothing\"
\"What do the rich need?\"
\"Nothing\"
\"What is it that if you eat, you\'ll die?\"
\"Poison.\"
Apparently, that little genius just didn\'t get the concept.',NULL,0);
INSERT INTO comment VALUES (11720,1498,1301,'Charlie','solution','2004-02-09 12:28:05',3,'This problem presents a Markov chain of probabilities that the user will have x unseen problems at any given stage of the two-week period. At each time there is a certain probability there are no problems left unseen, a certain probability that 1 is still unseen, etc. Call these probabilities u(0), u(1), etc. They change as time progresses.\r\n\r\nAfter that first Sunday\'s problem posting, there are 20 problems on the site, all of them unseen by this user. So the probability that 20 are unseen--i.e., u(20), at this stage, is 1 and all the other probabilities are zero.\r\n\r\nEach time the user looks at a random problem, the probability that the number of unseen problems goes down by 1 is just the number of unseen problems divided by the total number of problems on the site. So, if n is the number of problems on the site at a given stage, the new value for each u(i) is equal to the old value of u(i) times (1-u(i))/n plus the old value of u(i+1) times u(i+1)/n, as each old probability has conditional probabilities of u(i)/n of going one lower, or (1-u(i))/n of remaining at the same value.\r\n\r\nOf course every time a puzzle is posted, it is unseen by the user, so each probability is advanced one position in the array, that is each new u(i+1) is equal to the old u(i). \r\n\r\nWhen two problems are posted, it\'s perfectly OK to transition the new u(i+2) = the old u(i) for all i. However, you can\'t do that when transitioning for the user\'s seeing new problems, as the transition probabilities change, and each transition has to be done individually, five times per evening.\r\n\r\nThe program shown below computes this Markov chain for the 15 days asked for, and shows the reciprocal of the probability u(0) (i.e., the probability that zero remain unseen), at the end of days 8 and 15.\r\n\r\nThe results are:\r\n\r\n 15 16 17 18 20\r\n 1 .581 .363 .053 .002\r\n\r\n 12 13 14 15 16 17 22\r\n 2 .084 .298 .365 .197 .050 .006\r\n\r\n 9 10 11 12 13 14 15 16 17 24\r\n 3 .003 .029 .122 .257 .298 .197 .076 .017 .002\r\n\r\n 8 9 10 11 12 13 14 15 16 17 26\r\n 4 .004 .027 .094 .199 .266 .228 .126 .045 .010 .001\r\n\r\n 7 8 9 10 11 12 13 14 15 16 17 28\r\n 5 .003 .015 .054 .133 .218 .244 .188 .099 .036 .009 .001\r\n\r\n 6 7 8 9 10 11 12 13 14 15 16 17 30\r\n 6 .001 .005 .023 .070 .146 .217 .228 .171 .092 .035 .009 .002\r\n\r\n 5 6 7 8 9 10 11 12 13 14 15 16 31\r\n 7 .001 .006 .024 .068 .140 .207 .222 .175 .100 .042 .013 .003\r\n\r\n 4 5 6 7 8 9 10 11 12 13 14 15 16 32\r\n 8 .001 .004 .018 .055 .119 .189 .220 .189 .121 .057 .020 .005 .001\r\n 563860447.1492637\r\n\r\n 5 6 7 8 9 10 11 12 13 14 15 16 34\r\n 9 .003 .013 .041 .097 .167 .212 .202 .144 .077 .031 .009 .002\r\n\r\n 5 6 7 8 9 10 11 12 13 14 15 16 17 36\r\n10 .002 .008 .029 .075 .141 .198 .209 .167 .102 .047 .017 .004 .001\r\n\r\n 5 6 7 8 9 10 11 12 13 14 15 16 17 38\r\n11 .001 .005 .020 .055 .113 .176 .207 .187 .129 .068 .028 .009 .002\r\n\r\n 5 6 7 8 9 10 11 12 13 14 15 16 17 18 40\r\n12 .001 .003 .012 .038 .087 .149 .196 .198 .155 .094 .044 .016 .005 .001\r\n\r\n 6 7 8 9 10 11 12 13 14 15 16 17 18 42\r\n13 .002 .008 .025 .063 .120 .176 .200 .177 .122 .066 .028 .009 .002\r\n\r\n 5 6 7 8 9 10 11 12 13 14 15 16 17 18 43\r\n14 .001 .004 .014 .041 .088 .147 .190 .193 .153 .096 .047 .019 .006 .001\r\n\r\n 5 6 7 8 9 10 11 12 13 14 15 16 17 18 44\r\n15 .001 .006 .022 .056 .110 .166 .195 .181 .132 .077 .035 .013 .004 .001\r\n 1291015550.712306\r\n
\r\n-------\r\nThe numbers in the left column are the day numbers. The numbers on the right are the total number of problems on the site at the end of that day. The top row of numbers in the middle for each day show the values of x for which u(x)>.0005 for that day, and just below that is the corresponding u(x).\r\n\r\nWe see that the probability the user would have seen all the problems (non left unseen) on day 8 would be 1/563,860,447. At the end of day 15 it would be 1/1,291,015,551.\r\n\r\nNote that on the first day, the most likely unseen amount is 15, but the drop from day to day slows down quite soon.\r\n\r\nThe program is:\r\n\r\nCLS\r\nDEFDBL A-Z\r\nmaxSub = 100\r\nDIM unseen(maxSub), newRow(maxSub)\r\n\'unseen contains the prob that that many (its subscript) are still unseen\r\n\r\ntotProbs = 19\r\nunseen(19) = 1\r\n\r\nFOR day = 1 TO 15\r\n IF day MOD 7 = 1 OR day MOD 7 = 0 THEN\r\n totProbs = totProbs + 1\r\n shift = 1\r\n ELSE\r\n totProbs = totProbs + 2\r\n shift = 2\r\n END IF\r\n FOR i = maxSub TO 0 STEP -1\r\n IF i >= shift THEN\r\n unseen(i) = unseen(i - shift)\r\n ELSE\r\n unseen(i) = 0\r\n END IF\r\n NEXT\r\n FOR rProb = 1 TO 5\r\n REDIM newRow(maxSub)\r\n FOR i = 0 TO totProbs\r\n pNew = i / totProbs\r\n IF i > 0 THEN newRow(i - 1) = newRow(i - 1) + pNew * unseen(i)\r\n newRow(i) = newRow(i) + (1 - pNew) * unseen(i)\r\n NEXT\r\n FOR i = 0 TO totProbs\r\n unseen(i) = newRow(i)\r\n NEXT\r\n NEXT\r\n \r\n FOR i = 0 TO totProbs\r\n IF unseen(i) >= .0005 THEN\r\n PRINT USING \" ##\"; i;\r\n END IF\r\n NEXT\r\n PRINT TAB(75); totProbs\r\n PRINT USING \"##\"; day;\r\n FOR i = 0 TO totProbs\r\n IF unseen(i) >= .0005 THEN\r\n PRINT USING \" .###\"; unseen(i);\r\n END IF\r\n NEXT\r\n PRINT\r\n IF day MOD 7 = 1 AND day > 1 THEN\r\n PRINT 1 / unseen(0)\r\n END IF\r\n PRINT\r\nNEXT\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (11721,1602,4374,'Richard','re(2): Hardy\'s Story','2004-02-09 12:58:27',0,'\"Oh, for the love of Pete,\" said Tom Swift gaily.\n\nEdited on February 11, 2004, 2:51 pm',11710,0);
INSERT INTO comment VALUES (11722,1231,5407,'Ashley','re(2): WRONG, Gamer !!!!!!!!','2004-02-09 13:08:17',0,'Touché.',7999,0);
INSERT INTO comment VALUES (11723,1231,5407,'Ashley','re: WRONG, Gamer !!!!!!!!','2004-02-09 13:08:25',0,'Just for the record, \"Why anyone would go out in this weather is beyond me....\" is NOT a question. If it did end in a question mark, then you would be questioning yourself. It is, quite clearly, a statement. On the other hand, \"Why would anyone go out in this weather?\" is a definite question.
Just listen to yourself ranting about a simple riddle. The horse doesn\'t have to be famous to make a riddle about it. Besides, if you think about it, the horse who had great fame could just be a random statement, while the horse in the painting (not being famous), was named \'What do you think.\' Nah, that\'s silly, but STILL!!',7979,0);
INSERT INTO comment VALUES (11724,29,5350,'Poliahu','Yeah!','2004-02-09 15:30:46',0,'I got it right!!! :)',NULL,0);
INSERT INTO comment VALUES (11725,1362,5350,'Poliahu','Im Lost','2004-02-09 15:32:16',0,'Do you Mean overall only once or once per solution?',NULL,0);
INSERT INTO comment VALUES (11726,990,5350,'Poliahu','ANSWER??','2004-02-09 15:34:46',0,'Tied 0-0 in the 9th--- new pitcher-- lets in one home run or sumthing like that.',NULL,0);
INSERT INTO comment VALUES (11727,405,5350,'Poliahu','Answer!! (And i came up with it myself! Aren\'t You proud??)','2004-02-09 15:38:54',0,'From (4,4) to (1,1) to (1,4) to (4,1) to (1,1) ',NULL,0);
INSERT INTO comment VALUES (11728,965,5350,'Poliahu','I think...','2004-02-09 15:57:19',0,'Ajax 1st& Knight (Cuz he wouldn\'t be able to say \"As i said before\")\r\nCicero: 2nd, Knave (Random Guess! 0:-) )\r\nBalthazar: 3rd, Liar (Random Guess! 0:-) )',NULL,0);
INSERT INTO comment VALUES (11729,1466,5563,'Mike','Solution','2004-02-09 16:21:20',3,'(pi b²√(b²+h²)+(pi b²)+(pi a²)',NULL,0);
INSERT INTO comment VALUES (11730,1498,5345,'Rawlyn','Great puzzle!','2004-02-09 17:35:40',0,'I like the idea of a puzzle on the site being about the puzzles on the site :) It\'s not my sort of puzzle I\'m afraid but I still think it\'s a beauty!\r\n\r\nPeace,\r\nRawlyn.',NULL,0);
INSERT INTO comment VALUES (11731,1498,4507,'Penny','Question for Gamer','2004-02-09 18:03:15',4,'Gamer, are the following assumptions correct? If they are, I will have to wait to solve this one until my programming skills with Visual Basic are properly developed. I\'m still going through the course materials.\r\n\r\nAssumptions: 2 new problems come in, each at any random time of the day or night, each weekday, and 1 new problem comes in at any random time of the day or night, each weekend (Saturday or Sunday). The Random button is truly random. The possibilities for the number of puzzles on the website when she clicks on Random button five times each evening then are:\r\n\r\nSunday evening:\r\n\r\n20-20-20-20-20 \r\n20-20-20-20-21\r\n20-20-20-20-22\r\n20-20-20-21-21\r\n20-20-20-21-22\r\n20-20-20-22-22\r\n20-20-21-21-21\r\n20-20-21-21-22\r\n20-20-21-22-22\r\n20-21-21-21-21\r\n20-21-21-21-22\r\n20-21-21-22-22\r\n20-21-22-22-22\r\n20-22-22-22-22\r\n\r\nMonday evening:\r\n \r\n22-22-22-22-22 \r\n22-22-22-22-23\r\n22-22-22-22-24\r\n22-22-22-23-23\r\n22-22-22-23-24\r\n22-22-22-24-24\r\n22-22-23-23-23\r\n22-22-23-23-24\r\n22-22-23-24-24\r\n22-23-23-23-23\r\n22-23-23-23-24\r\n22-23-23-24-24\r\n22-23-24-24-24\r\n22-24-24-24-24\r\n23-23-23-23-23\r\n23-23-23-23-24\r\n23-23-23-24-24\r\n23-23-24-24-24\r\n23-24-24-24-24\r\n24-24-24-24-24\r\n\r\nTuesday evening: \r\n\r\n24-24-24-24-24 \r\n24-24-24-24-25\r\n24-24-24-24-26\r\n24-24-24-25-25\r\n24-24-24-25-26\r\n24-24-24-26-26\r\n24-24-25-25-25\r\n24-24-25-25-26\r\n24-24-25-26-26\r\n24-25-25-25-25\r\n24-25-25-25-26\r\n24-25-25-26-26\r\n24-25-26-26-26\r\n24-26-26-26-26\r\n25-25-25-25-25\r\n25-25-25-25-26\r\n25-25-25-26-26\r\n25-25-26-26-26\r\n25-26-26-26-26\r\n26-26-26-26-26\r\n\r\nEtc...............................',NULL,0);
INSERT INTO comment VALUES (11732,1498,1626,'Gamer','About Flooble','2004-02-09 18:06:11',0,'The reason \"Sunday Evening\" was in there was to show you that any problems were already posted. If you look at any problem, you will see it is usually posted (or is supposed to be posted) in the afternoon, and another one in the morning if applicable.',NULL,0);
INSERT INTO comment VALUES (11733,1498,4507,'Penny','re: About Flooble','2004-02-09 19:01:02',0,'Gamer: \"...any problems were already posted [when she starts selecting her 5 random problems on any given night]\".\r\n\r\nThanks. I guess the flooble veterans like Charlie would have known that. Then the problem is not as difficult as it would have been with my assumptions, but it probably still requires a software program to be written to solve it. If there are 20 problems the first Sunday night, and she clicks 5 times, there are a lot of possibilities, ranging from getting the same problem 5 times, to getting 5 distinct problems. On the following Monday night, when she clicks 5 times, not only do I have to worry about duplicates among these 5, but also about problems being duplicates of those of the previous day. On Tuesday I have 2 previous days to contend with. The complications mount up, and a program is probably required to sort them out. \r\n\r\nbtw...why is the protaganist of your puzzle a female? Did you have anyone in particular in mind ? \r\n\r\n:-)',11732,0);
INSERT INTO comment VALUES (11734,1605,5352,'Phil','Stumbling merrily away','2004-02-09 19:12:09',3,'I think i\'ve stumbled on another more simple method of calculating the radius of the smaller circle firstly work out the length of the line that connects two diagonal corners, then divide this by 4 (centres of the circles intersect this line into quarters), then subtract 1 (initial radius unit)\r\n\r\n (4^2)*3 = 48\r\n Sqroot 48 = 6.9282032302755\r\n 6.9282032302755/4 = 1.7320508075688772\r\n1.7320508075688772 - 1 = 0.7320508075688772\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (11735,1407,3558,'Tristan','re: question','2004-02-09 20:13:39',0,'A row in this problem can be in any direction, or the task would be impossible. Of course, it all has to be on one plane - you can\'t plant trees above each other.',11714,0);
INSERT INTO comment VALUES (11736,1270,5265,'Nikki','THE SOLUTION!!!','2004-02-10 02:54:55',0,'Allison...Thrust...Birdseed...6\r\nBrewer...Robin...Suet...10\r\nChandler...Blackbirt...Toast...2\r\nDennis...Sparrow...Bread...4\r\nEmery...Cardinal...Cake...10',NULL,0);
INSERT INTO comment VALUES (11737,672,5487,'Peter Lunts','guess','2004-02-10 08:45:12',0,'i expect the sword to slice through the shield, but she shield will not be destroyed',NULL,0);
INSERT INTO comment VALUES (11738,1437,4507,'Penny','Solution, unless I am overlooking something again :-(','2004-02-10 10:20:37',3,'None of Mrs. Putnam\'s students would be so geeky as to write down a null set.\r\n\r\nDiasallowing null sets, there are 13,680 UNORDERED triples (A, B, C) of sets like these. If the triples are ordered, there are 13,680*(3!) = 82,080 possibilities.\r\n\r\nExplanation: \r\n\r\n{1 number}U{1 number}U{8 numbers}: 10*9 = 90 unordered possibilities \r\n{1 number}U{2 numbers}U{7 numbers}: \r\n10*(9*8/2!) = 360 \r\n{1 number}U{3 numbers}U{6 numbers}: \r\n10*(9*8*7/3!) = 840\r\n{1 number}U{4 numbers}U{5 numbers}: \r\n10*(9*8*7*6/4!) = 1260\r\n{2 numbers}U{3 numbers}U{5 numbers}: \r\n(10*9/2!)*(8*7*6/3!) = 2520\r\n{2 numbers}U{4 numbers}U{4 numbers}: \r\n(10*9/2!)*(8*7*6*5/4!) = 3150\r\n{2 numbers}U{2 numbers}U{6 numbers}: \r\n(10*9/2!)*(8*7/2!) = 1260\r\n{3 numbers}U{3 numbers}U{4 numbers}: \r\n(10*9*8/3!)*(7*6*5/3!) = 4200 \r\n\r\n90+360+840+1260+2520+3150+1260+4200=13,680 \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\n\nEdited on February 10, 2004, 10:45 am',NULL,0);
INSERT INTO comment VALUES (11739,670,5297,'NK','Another Approach','2004-02-10 10:32:01',0,'I get an answer of 8 using the following approach:\r\n\r\nA 50-digit integer, N, with all digits equal to 1, can be obtained as follows:\r\n\r\nN = (10^50)/9 - 1/9\r\n\r\nThis can be converted to a 50-digit integer, M, with all 1s except for the digit x in the 26th position, by addition:\r\n\r\nM = N + x*10^25\r\n\r\nwhere x is chosen to make M divisible by 13.\r\n\r\nIf we divide (10^50)/9 by 13 we get a repeating pattern of the six numbers 854700, beginning in the 48th digit to the left of the decimal. This means that the decimal part of the resulting number is 0.854700854700...\r\n\r\nIf we divide 1/9 by 13 we get this same repeating pattern as follows: 0.008547008547...\r\n\r\nTaking the difference (i.e., calculating N/13), we get for the decimal part: 0.8461538462, with the last decimal rounded. \r\n\r\nWe want an x such that (x*10^25)/13 will have a decimal part that, when added to N/13, gives all zeros to the right of the decimal (i.e., makes M an integer). The integer 8 meets this condition, because 8/13 gives a repeating pattern of the six numbers 615384. Calculating (8*10^25)/13 leads to the the following decimal portion: 0.1538461538 to 10 decimal places. The leading 6 in the series ends up to the left of the decimal. Now we add the decimal portions of N/13 and (8*10^25)/13:\r\n\r\n0.8461538462 + 0.1538461538 = 1.0000000000\r\n\r\nThus, M is divisible by 13 if the number 8 occupies the 26th digit.',NULL,0);
INSERT INTO comment VALUES (11740,1437,5285,'Ady TZIDON','my solution','2004-02-10 10:33:08',3,'Answer: =58968\r\n\r\nWhy:\r\nEach of the numbers 1,2,3,....10 belongs to one of the sets- we assume no empty set due to the teachers demand. \r\nLet ABBBCACCCB denote situation where 1 and 6 are in A , 2 3 4 AND 10 in B etc\r\nClearly it isomorphic to a base- THREE 10 digit presentation where all 3 digits have to be present\r\n\r\nall possibilities: 3^10\r\ntwo digits only 3* (2^10-2)\r\none digit only 3 \r\n\r\nAnswer: 3^10-3* 2^10 - 6-3 =59049- 3*1022 - 3=58968\r\n\r\n\r\nady\r\n\r\n\n\nEdited on February 10, 2004, 10:44 am',NULL,0);
INSERT INTO comment VALUES (11741,1437,1301,'Charlie','solution','2004-02-10 10:45:08',3,'For ordered triples:\r\nEach of the elements belongs to one of the three sets; there are 3^10=59,049 ways of doing this.\r\n\r\nFor unordered triples:\r\nMost of the triples appear 3!=6 times as ordered triples. One, ({1, 2, 3, 4, 5, 6, 7, 8, 9, 10},{},{} ), appears only three times, so before dividing by 6 we have to add 3 in order to treat this one case as if it appeared 6 times.\r\n\r\n(59049+3)/6 = 9842 unordered triplets.\n\nEdited on February 10, 2004, 10:46 am',NULL,0);
INSERT INTO comment VALUES (11742,1437,5285,'Ady TZIDON','Penny u r overlooking something again :-(','2004-02-10 10:47:56',2,'Penny \r\nI believe one has to count ORDERED \"triples\".\r\nPlease see my solution -your comments will be appreciated\r\n\r\nady',11738,0);
INSERT INTO comment VALUES (11743,1437,1301,'Charlie','re: my solution','2004-02-10 10:52:08',0,'Are you saying ({1,2,3,4},{5,6,7,8,9,10},{}), for example, shouldn\'t be counted as one of the triplets?',11740,0);
INSERT INTO comment VALUES (11744,1437,4507,'Penny','re: solution','2004-02-10 10:52:13',0,'The intersection of the three sets has to be null. ',11741,0);
INSERT INTO comment VALUES (11745,1437,5285,'Ady TZIDON','re: solution','2004-02-10 10:55:19',1,'Charlie\r\na. For ordered triples: you have to carefully discount the empty sets: each student was asked to write numbers and not display wiseguyness ,\r\nb.For unordered triples: you have to be careful not to count things twice- choices with one empty set were ignored by you.\r\n\r\nPlease comment upon my solution\r\nady',11741,0);
INSERT INTO comment VALUES (11746,1437,3172,'SilverKnight','re: solution','2004-02-10 10:56:23',0,'Charlie (and others working on this),\r\n\r\nAm I misreading the problem when I suggest that the triples might be something like:\r\n{1, 2, 3, 4, 5, 6}\r\n{4, 5, 6, 7, 8}\r\n{8, 9, 10}\r\n\r\n... where 4, 5, 6, and 8 are all in more than one set?\r\n\r\nThe conditions of the problem (the union and intersection) still hold, but your statement \"Each of the elements belongs to [only] one of the three sets\" and your math, has the implication of the added word \'only\'.\r\n\r\nI think you need to account for this.\r\n\r\n- SK',11741,0);
INSERT INTO comment VALUES (11747,1437,1920,'Brian Smith','Solution','2004-02-10 10:58:38',0,'Since there are three sets, a number can be in two of them and still not be in the intersection of all three. Then, for any one interger, there are six different ways it can be found among A, B, and C: only in A, only in B, only in C, in A and B, in A and C, in B and C.\r\n\r\nIn total there are 6^10 = 60466176 possible triplets (A, B, and C).\r\n\r\nThis number includes empty sets. There are 3^10 triplets with A empty, likewise for B and C. The set with A, B empty was counted twice, likewise with A, C and B, C.\r\n\r\nThe total number of triplets with empty sets is 3*3^10-3 = 177144\r\n\r\nThe total number of triplets with no empty sets is 60466176 - 177144 = 60289032.',NULL,0);
INSERT INTO comment VALUES (11748,1437,5285,'Ady TZIDON','re(2): my solution','2004-02-10 10:58:51',0,'Yes, sir I DO\r\nHowever you are free to make other assumptions as long as you specify what is counted and what is not.\r\nIt does not look logical to dissallow two empty sets while ignoring one empty set...\r\n\r\n\r\n\r\nady',11743,0);
INSERT INTO comment VALUES (11749,1437,5285,'Ady TZIDON','re(2): solution','2004-02-10 11:00:42',0,'It is accounted for: empty intersection\r\n\r\nady',11746,0);
INSERT INTO comment VALUES (11750,1437,1301,'Charlie','re(2): solution','2004-02-10 11:00:46',0,'You are right, SK. Just because the intersection of the three is empty does not mean the intersection of any pair is empty.',11746,0);
INSERT INTO comment VALUES (11751,1437,1301,'Charlie','re(3): my solution','2004-02-10 11:07:22',0,'I did allow one empty set: they count among the 3^10, and in tracking unordered triples, I added 3, rather than subtracting 3, before the division by 6. Those are precisely the double null-set triples that are counting.\r\n\r\nBut this is moot, as SK has pointed out, and as Brian Smith has incorporated in his solution: a given number (given element) may appear in two of the sets.',11748,0);
INSERT INTO comment VALUES (11752,1437,5285,'Ady TZIDON','re: Solution - I\'ll drink to that','2004-02-10 11:10:41',0,'B.S.\r\n\r\nI have jusr re-read the question.\r\nYour solution is right - mine is not.\r\nI assumed exclusivity which was not requested.\r\n\r\nI saluTe the author and upgrade my vote.\r\n\r\nady',11747,0);
INSERT INTO comment VALUES (11753,1437,5285,'Ady TZIDON','re(4): my solution','2004-02-10 11:12:54',0,'Charlie\r\n\r\nyes .....this is moot\r\n\r\n\r\nady',11751,0);
INSERT INTO comment VALUES (11754,1437,3172,'SilverKnight','re(3): solution','2004-02-10 11:13:33',0,'No Ady... your use of the empty intersection does not account for it.\r\n\r\nBrian incorporated it, though.',11749,0);
INSERT INTO comment VALUES (11755,670,5297,'NK','Correction to Another Approach','2004-02-10 11:21:08',0,'In my solution (see Another Approach), I lost sight of the fact that x gets added to the 1 that\'s already there, so the correct answer is 9, not 8.',NULL,0);
INSERT INTO comment VALUES (11756,1437,3172,'SilverKnight','re: Solution - not yet?','2004-02-10 11:26:26',0,'Brian,\r\n\r\nI don\'t understand the second half of your \'solution\'.\r\nYou wrote:\r\n\"There are 3^10 triplets with A empty, likewise for B and C. The set with A, B empty was counted twice, likewise with A, C and B, C.\r\n\r\nThe total number of triplets with empty sets is 3*3^10-3 = 177144\"\r\n\r\nI don\'t believe you properly accounted for the requirement that the intersection of all three MUST be the null set.\r\n\r\n- SK',11747,0);
INSERT INTO comment VALUES (11757,1437,4507,'Penny','Game, set and match !!!!','2004-02-10 11:31:50',0,'You are right again, SilverKnight. (I am beginning to feel like one of the hapless students of Professor Kingsfield in \"The Paper Chase\")\r\n\r\n(A int B) int C = {}\r\n\r\nIf C has just 1 number (there are 10 such sets), then any two sets A and B, neither of which have that number, will work. Each of the other nine numbers can be in A, in B, or both \r\n10*(3^9)\r\n\r\nIf C has 2 numbers (10*90 sets), \r\n90*(3^8)\r\n \r\nIf C has 3 numbers (10*9*8=720)\r\n720*(3^7)\r\n\r\nIf C has 4 numbers, (10*9*8*7=5040)\r\n5040*(3^6) \r\n\r\nIf C has 5 numbers (10*9*8*7*6 = 30240)\r\n30240*(3^5) \r\n\r\nIf C has 6 numbers (10*9*8*7*6*5 = 151200)\r\n151200*(3^4)\r\n\r\nIf C has 7 numbers (10*9*8*7*6*5*4 = 604800)\r\n604800*(3^3)\r\n\r\nIf C has 8 numbers (10*9*8*7*6*5*4*3=1814400)\r\n1814400*(3^2)\r\n\r\n\r\n\r\n\n\nEdited on February 10, 2004, 11:41 am',NULL,0);
INSERT INTO comment VALUES (11758,1437,3172,'SilverKnight','re: Game, set and match !!!!','2004-02-10 11:39:29',0,'Penny,\r\n\r\nYou wrote:\r\n\"If C has just 1 number (there are 10 such sets), then any two sets A and B, neither of which have that number, will work.\r\n10*(3^9) = 196830 \"\r\n\r\nThough that is true, any two sets, where not both have that number will also work.\r\n\r\nSo, if C = {1}\r\nThen as long as at least one of set A and B don\'t have it (and they include all the remaining 9 numbers), it will ALSO produce a valid solution.\r\n\r\n(e.g., A = {1, 2, 3, 4, 5, 6, 7} and B = {2, 8, 9, 10} )\r\n',11757,0);
INSERT INTO comment VALUES (11759,1437,4507,'Penny','re(2): Game, set and match !!!!','2004-02-10 12:08:54',0,'Maybe I should just ride into the subset..... \r\n\r\n(A int B) int C = {} \r\n\r\nIf C has just 1 number (there are 10 such sets), then any two sets A and B, where A is any subset of the remaining 9 numbers, and B is any subset of all 10 numbers, should do the trick. A set of 9 elements has 2^9 subsets. A set of 10 elements has 2^10 subsets.\r\n(10)*(2^9)*(2^10)=5242880\r\n\r\nIf C has just 2 numbers (there are 10*9 such sets), then any two sets A and B, where A is any subset of the remaining 8 numbers, and B is any subset of all 10 numbers, will work. A set of 8 elements has 2^8 subsets. \r\n(10*9)*(2^8)*(2^10)=23592960\r\n\r\nIf C has just 3 numbers (there are 10*9*8 such sets), then any two sets A and B, where A is any subset of the remaining 7 numbers, and B is any subset of all 10 numbers, will work. \r\n(10*9*8)*(2^7)*(2^10)=94371840\r\n\r\nBut the numbers begin to overwhelm my primitive calculator.........\n\nEdited on February 10, 2004, 12:10 pm',11758,0);
INSERT INTO comment VALUES (11760,1437,3172,'SilverKnight','re(3): Game, set and match !!!!','2004-02-10 12:14:34',0,'\"If C has just 1 number (there are 10 such sets), then any two sets A and B, where A is any subset of the remaining 9 numbers, and B is any subset of all 10 numbers, should do the trick. A set of 9 elements has 2^9 subsets. A set of 10 elements has 2^10 subsets.\r\n(10)*(2^9)*(2^10)=5242880\"\r\n\r\nand for completeness...\r\n\r\nwhere B is any subset of the remaining 9 numbers and A is any subset of all 10 numbers, should also do the trick.... (I just switched A and B in what Penny said--quoted above.)',11759,0);
INSERT INTO comment VALUES (11761,1437,5285,'Ady TZIDON','re: Solution FINAL WORD','2004-02-10 13:01:06',1,'BS\'s solutiom is correct except for small amendment which I am going to suggest: \r\n\r\nHe wrote: \r\n ...\"This number includes empty sets. There are 3^10 triplets with A empty, likewise for B and C. The set with A, B empty was counted twice, likewise with A, C and B, C. \r\n\r\nThe total number of triplets with empty sets is 3*3^10-3 = 177144 \r\n\r\nThe total number of triplets with no empty sets is 60466176 - 177144 = 60289032...\"\r\n\r\n\r\nMy remark : add 3 for the number of \"choices\" deducted twice- when counting \"triplets with no empty sets\"\r\n\r\nthe AAAAA.. choice is deducted when counting A*B & A*C\r\netc \r\nso the correct answer is 60289032+3= 60289035\r\n\r\n60289035\r\n\r\n A little, but important correction...\r\n\r\nady\r\n\r\n',11747,0);
INSERT INTO comment VALUES (11762,1437,4507,'Penny','Is this right ?','2004-02-10 13:02:43',4,'No it isnt. I am not restricting it to subsets whose union includes all 10 numbers. I am also failing to eliminate duplicates.\r\n\r\nAnswer: 12,006,914,172 unordered triples, and (12,006,914,172)*(3!) =72,041,485,032 ordered triples. (This is essentially the same as my original answer, 13,680, if you allow for rounding errors on my calculator)\r\n\r\nExplanation: \r\n\r\n(A int B) int C = {} \r\n\r\nIf C has just 1 number (there are 10 such sets), then any two sets A and B, where A is any subset of the remaining 9 numbers, and B is any subset of all 10 numbers, should do the trick. A set of 9 elements has (2^9)-1 nonnull subsets. A set of 10 elements has (2^10)-1 nonnull subsets.\r\n\r\nIf C has 2 number (there are 10*9 such sets), then any two sets A and B, where A is any subset of the remaining 8 numbers, and B is any subset of all 10 numbers, should do the trick. A set of 8 elements has (2^8)-1 nonnull subsets. \r\n\r\netc....\r\n\r\n(10)*(2^9-1)*(2^10-1) + (10*9)*(2^8-1)*(2^10-1) \r\n+ (10*9*8)*(2^7-1)*(2^10-1) + (10*9*8*7)*(2^6-1)*(2*10-1) \r\n+ (10*9*8*7*6)*(2^5-1)*(2^10-1) \r\n+ (10*9*8*7*6*5)*(2^4-1)*(2^10-1) \r\n+ (10*9*8*7*6*5*4)*(2^3-1)*(2^10-1)\r\n+ (10*9*8*7*6*5*4*3)*(2^2-1)*(2^10-1)\r\n\r\n= 1023*[(10)*(2^9-1) + (10*9)*(2^8-1) + (10*9*8)*(2^7-1) \r\n+ (10*9*8*7)*(2^6-1) + (10*9*8*7*6)*(2^5-1) \r\n+ (10*9*8*7*6*5)*(2^4-1) + (10*9*8*7*6*5*4)*(2^3-1)\r\n+ (10*9*8*7*6*5*4*3)*(2^2-1)]\r\n \r\n= 1023*[(10)*(511) + (10*9)*(255) + (10*9*8)*(127) \r\n+ (10*9*8*7)*(63) + (10*9*8*7*6)*(31) \r\n+ (10*9*8*7*6*5)*(15) + (10*9*8*7*6*5*4)*(7)\r\n+ (10*9*8*7*6*5*4*3)*(3)]\r\n\r\n= 1023*[(10)*(511) + (90)*(255) + (720)*(127) \r\n+ (5040)*(63) + (30240)*(31) \r\n+ (151200)*(15) + (604800)*(7)\r\n+ (1814400)*(3)]\r\n\r\n= 1023*[(5110) + (22950) + (9144) \r\n+ (317520) + (937440) \r\n+ (768000) + (4233600)\r\n+ (5443200)]\r\n\r\n= 1023*11736964 = 12,006,914,172\r\n\r\n\r\n\n\nEdited on February 10, 2004, 1:57 pm',NULL,0);
INSERT INTO comment VALUES (11763,1437,1301,'Charlie','re(2): Solution - not yet?','2004-02-10 13:24:41',0,'In the choices for where a given number could go, there were six choices; none of them was A and B and C. Any given number went into at most two subsets. I think Brian had it right.',11756,0);
INSERT INTO comment VALUES (11764,1437,1301,'Charlie','re(2): Solution FINAL WORD','2004-02-10 13:30:02',0,'But the three were already added in, by Brian, to the final total by their being subtracted out from the amount to be subtracted from the overall total.',11761,0);
INSERT INTO comment VALUES (11765,1437,5285,'Ady TZIDON','re(3): Solution FINAL WORD(by Charlie','2004-02-10 14:50:41',0,'no ,they were not...\r\ntry it with 4 numbers only 1 2 3 4 with the same restrictions and you will see that his formula FAILS...\r\n\r\nady',11764,0);
INSERT INTO comment VALUES (11766,670,5285,'Ady TZIDON',' so easy','2004-02-10 15:08:55',3,'\r\n1001=7*11*13\r\nso A=111111 = 111*1001 is divisible by 13 \r\n\r\nour number can be written AAAA1XAAAA\r\nX= the 26th digit \r\n\r\nSINCE AAAA is divisible by 13\r\nwe are left with simple problem 1X -FOR WHAT VALUE IF X IS 1X DIVISIBLE BY 13??\r\n\r\nThe answer of cours is 3 ( three) \r\n\r\nady ',NULL,0);
INSERT INTO comment VALUES (11767,1437,1920,'Brian Smith','re(4): Solution FINAL WORD','2004-02-10 15:13:44',0,'My formula is f(n) = 6^n - (3*3^n - 3) if no empty sets are allowed.\r\nf(1) = 0 is correct since at least one of A, B and C must be empty for the intersection to be empty.\r\n\r\nf(2) = 36 - (3*9 - 3) = 12. The triples (A,B,C) are:\r\n({1},{1},{2})\r\n({1},{2},{1})\r\n({2},{1},{1})\r\n({1},{2},{2})\r\n({2},{1},{2})\r\n({2},{2},{1})\r\n({1,2},{1},{2})\r\n({1,2},{2},{1})\r\n({1},{1,2},{2})\r\n({2},{1,2},{1})\r\n({1},{2},{1,2})\r\n({2},{1},{1,2})\r\n\r\nf(3) = 138 and f(4) = 1056 are longer to list.\r\nf(3) = 216 - (3*27 - 3) = 138\r\nf(4) = 1296 - (3*81 - 3) = 1056',11765,0);
INSERT INTO comment VALUES (11768,1437,1301,'Charlie','re(4): Solution FINAL WORD(by Charlie','2004-02-10 15:53:24',0,'Here are the 1056 predicted by Brian Smith\'s formula. What\'s missing? (forgive the lack of braces and parentheses, but you can gather the sets).\r\n123 4 4 \r\n12 3 4 \r\n124 3 4 \r\n12 34 4 \r\n12 4 3 \r\n124 4 3 \r\n12 4 34 \r\n123 3 4 \r\n1234 3 4 \r\n123 34 4 \r\n123 4 3 \r\n1234 4 3 \r\n123 4 34 \r\n124 3 3 \r\n12 34 3 \r\n12 3 34 \r\n124 34 3 \r\n124 3 34 \r\n12 34 34 \r\n13 2 4 \r\n134 2 4 \r\n13 24 4 \r\n1 23 4 \r\n14 23 4 \r\n1 234 4 \r\n14 2 3 \r\n1 24 3 \r\n1 2 34 \r\n14 24 3 \r\n14 2 34 \r\n1 24 34 \r\n13 23 4 \r\n134 23 4 \r\n13 234 4 \r\n134 2 3 \r\n13 24 3 \r\n13 2 34 \r\n134 24 3 \r\n134 2 34 \r\n13 24 34 \r\n14 23 3 \r\n1 234 3 \r\n1 23 34 \r\n14 234 3 \r\n14 23 34 \r\n1 234 34 \r\n13 4 2 \r\n134 4 2 \r\n13 4 24 \r\n14 3 2 \r\n1 34 2 \r\n1 3 24 \r\n14 34 2 \r\n14 3 24 \r\n1 34 24 \r\n1 4 23 \r\n14 4 23 \r\n1 4 234 \r\n134 3 2 \r\n13 34 2 \r\n13 3 24 \r\n134 34 2 \r\n134 3 24 \r\n13 34 24 \r\n13 4 23 \r\n134 4 23 \r\n13 4 234 \r\n14 3 23 \r\n1 34 23 \r\n1 3 234 \r\n14 34 23 \r\n14 3 234 \r\n1 34 234 \r\n123 2 4 \r\n1234 2 4 \r\n123 24 4 \r\n12 23 4 \r\n124 23 4 \r\n12 234 4 \r\n124 2 3 \r\n12 24 3 \r\n12 2 34 \r\n124 24 3 \r\n124 2 34 \r\n12 24 34 \r\n123 23 4 \r\n1234 23 4 \r\n123 234 4 \r\n1234 2 3 \r\n123 24 3 \r\n123 2 34 \r\n1234 24 3 \r\n1234 2 34 \r\n123 24 34 \r\n124 23 3 \r\n12 234 3 \r\n12 23 34 \r\n124 234 3 \r\n124 23 34 \r\n12 234 34 \r\n123 4 2 \r\n1234 4 2 \r\n123 4 24 \r\n124 3 2 \r\n12 34 2 \r\n12 3 24 \r\n124 34 2 \r\n124 3 24 \r\n12 34 24 \r\n12 4 23 \r\n124 4 23 \r\n12 4 234 \r\n1234 3 2 \r\n123 34 2 \r\n123 3 24 \r\n1234 34 2 \r\n1234 3 24 \r\n123 34 24 \r\n123 4 23 \r\n1234 4 23 \r\n123 4 234 \r\n124 3 23 \r\n12 34 23 \r\n12 3 234 \r\n124 34 23 \r\n124 3 234 \r\n12 34 234 \r\n134 2 2 \r\n13 24 2 \r\n13 2 24 \r\n134 24 2 \r\n134 2 24 \r\n13 24 24 \r\n14 23 2 \r\n1 234 2 \r\n1 23 24 \r\n14 234 2 \r\n14 23 24 \r\n1 234 24 \r\n14 2 23 \r\n1 24 23 \r\n1 2 234 \r\n14 24 23 \r\n14 2 234 \r\n1 24 234 \r\n134 23 2 \r\n13 234 2 \r\n13 23 24 \r\n134 234 2 \r\n134 23 24 \r\n13 234 24 \r\n134 2 23 \r\n13 24 23 \r\n13 2 234 \r\n134 24 23 \r\n134 2 234 \r\n13 24 234 \r\n14 23 23 \r\n1 234 23 \r\n1 23 234 \r\n14 234 23 \r\n14 23 234 \r\n1 234 234 \r\n23 1 4 \r\n234 1 4 \r\n23 14 4 \r\n2 13 4 \r\n24 13 4 \r\n2 134 4 \r\n24 1 3 \r\n2 14 3 \r\n2 1 34 \r\n24 14 3 \r\n24 1 34 \r\n2 14 34 \r\n23 13 4 \r\n234 13 4 \r\n23 134 4 \r\n234 1 3 \r\n23 14 3 \r\n23 1 34 \r\n234 14 3 \r\n234 1 34 \r\n23 14 34 \r\n24 13 3 \r\n2 134 3 \r\n2 13 34 \r\n24 134 3 \r\n24 13 34 \r\n2 134 34 \r\n3 12 4 \r\n34 12 4 \r\n3 124 4 \r\n4 123 4 \r\n4 12 3 \r\n4 124 3 \r\n4 12 34 \r\n3 123 4 \r\n34 123 4 \r\n3 1234 4 \r\n34 12 3 \r\n3 124 3 \r\n3 12 34 \r\n34 124 3 \r\n34 12 34 \r\n3 124 34 \r\n4 123 3 \r\n4 1234 3 \r\n4 123 34 \r\n34 1 2 \r\n3 14 2 \r\n3 1 24 \r\n34 14 2 \r\n34 1 24 \r\n3 14 24 \r\n4 13 2 \r\n4 134 2 \r\n4 13 24 \r\n4 1 23 \r\n4 14 23 \r\n4 1 234 \r\n34 13 2 \r\n3 134 2 \r\n3 13 24 \r\n34 134 2 \r\n34 13 24 \r\n3 134 24 \r\n34 1 23 \r\n3 14 23 \r\n3 1 234 \r\n34 14 23 \r\n34 1 234 \r\n3 14 234 \r\n4 13 23 \r\n4 134 23 \r\n4 13 234 \r\n23 12 4 \r\n234 12 4 \r\n23 124 4 \r\n2 123 4 \r\n24 123 4 \r\n2 1234 4 \r\n24 12 3 \r\n2 124 3 \r\n2 12 34 \r\n24 124 3 \r\n24 12 34 \r\n2 124 34 \r\n23 123 4 \r\n234 123 4 \r\n23 1234 4 \r\n234 12 3 \r\n23 124 3 \r\n23 12 34 \r\n234 124 3 \r\n234 12 34 \r\n23 124 34 \r\n24 123 3 \r\n2 1234 3 \r\n2 123 34 \r\n24 1234 3 \r\n24 123 34 \r\n2 1234 34 \r\n234 1 2 \r\n23 14 2 \r\n23 1 24 \r\n234 14 2 \r\n234 1 24 \r\n23 14 24 \r\n24 13 2 \r\n2 134 2 \r\n2 13 24 \r\n24 134 2 \r\n24 13 24 \r\n2 134 24 \r\n24 1 23 \r\n2 14 23 \r\n2 1 234 \r\n24 14 23 \r\n24 1 234 \r\n2 14 234 \r\n234 13 2 \r\n23 134 2 \r\n23 13 24 \r\n234 134 2 \r\n234 13 24 \r\n23 134 24 \r\n234 1 23 \r\n23 14 23 \r\n23 1 234 \r\n234 14 23 \r\n234 1 234 \r\n23 14 234 \r\n24 13 23 \r\n2 134 23 \r\n2 13 234 \r\n24 134 23 \r\n24 13 234 \r\n2 134 234 \r\n34 12 2 \r\n3 124 2 \r\n3 12 24 \r\n34 124 2 \r\n34 12 24 \r\n3 124 24 \r\n4 123 2 \r\n4 1234 2 \r\n4 123 24 \r\n4 12 23 \r\n4 124 23 \r\n4 12 234 \r\n34 123 2 \r\n3 1234 2 \r\n3 123 24 \r\n34 1234 2 \r\n34 123 24 \r\n3 1234 24 \r\n34 12 23 \r\n3 124 23 \r\n3 12 234 \r\n34 124 23 \r\n34 12 234 \r\n3 124 234 \r\n4 123 23 \r\n4 1234 23 \r\n4 123 234 \r\n23 4 1 \r\n234 4 1 \r\n23 4 14 \r\n24 3 1 \r\n2 34 1 \r\n2 3 14 \r\n24 34 1 \r\n24 3 14 \r\n2 34 14 \r\n2 4 13 \r\n24 4 13 \r\n2 4 134 \r\n234 3 1 \r\n23 34 1 \r\n23 3 14 \r\n234 34 1 \r\n234 3 14 \r\n23 34 14 \r\n23 4 13 \r\n234 4 13 \r\n23 4 134 \r\n24 3 13 \r\n2 34 13 \r\n2 3 134 \r\n24 34 13 \r\n24 3 134 \r\n2 34 134 \r\n34 2 1 \r\n3 24 1 \r\n3 2 14 \r\n34 24 1 \r\n34 2 14 \r\n3 24 14 \r\n4 23 1 \r\n4 234 1 \r\n4 23 14 \r\n4 2 13 \r\n4 24 13 \r\n4 2 134 \r\n34 23 1 \r\n3 234 1 \r\n3 23 14 \r\n34 234 1 \r\n34 23 14 \r\n3 234 14 \r\n34 2 13 \r\n3 24 13 \r\n3 2 134 \r\n34 24 13 \r\n34 2 134 \r\n3 24 134 \r\n4 23 13 \r\n4 234 13 \r\n4 23 134 \r\n3 4 12 \r\n34 4 12 \r\n3 4 124 \r\n4 3 12 \r\n4 34 12 \r\n4 3 124 \r\n4 4 123 \r\n34 3 12 \r\n3 34 12 \r\n3 3 124 \r\n34 34 12 \r\n34 3 124 \r\n3 34 124 \r\n3 4 123 \r\n34 4 123 \r\n3 4 1234 \r\n4 3 123 \r\n4 34 123 \r\n4 3 1234 \r\n234 2 1 \r\n23 24 1 \r\n23 2 14 \r\n234 24 1 \r\n234 2 14 \r\n23 24 14 \r\n24 23 1 \r\n2 234 1 \r\n2 23 14 \r\n24 234 1 \r\n24 23 14 \r\n2 234 14 \r\n24 2 13 \r\n2 24 13 \r\n2 2 134 \r\n24 24 13 \r\n24 2 134 \r\n2 24 134 \r\n234 23 1 \r\n23 234 1 \r\n23 23 14 \r\n234 234 1 \r\n234 23 14 \r\n23 234 14 \r\n234 2 13 \r\n23 24 13 \r\n23 2 134 \r\n234 24 13 \r\n234 2 134 \r\n23 24 134 \r\n24 23 13 \r\n2 234 13 \r\n2 23 134 \r\n24 234 13 \r\n24 23 134 \r\n2 234 134 \r\n23 4 12 \r\n234 4 12 \r\n23 4 124 \r\n24 3 12 \r\n2 34 12 \r\n2 3 124 \r\n24 34 12 \r\n24 3 124 \r\n2 34 124 \r\n2 4 123 \r\n24 4 123 \r\n2 4 1234 \r\n234 3 12 \r\n23 34 12 \r\n23 3 124 \r\n234 34 12 \r\n234 3 124 \r\n23 34 124 \r\n23 4 123 \r\n234 4 123 \r\n23 4 1234 \r\n24 3 123 \r\n2 34 123 \r\n2 3 1234 \r\n24 34 123 \r\n24 3 1234 \r\n2 34 1234 \r\n34 2 12 \r\n3 24 12 \r\n3 2 124 \r\n34 24 12 \r\n34 2 124 \r\n3 24 124 \r\n4 23 12 \r\n4 234 12 \r\n4 23 124 \r\n4 2 123 \r\n4 24 123 \r\n4 2 1234 \r\n34 23 12 \r\n3 234 12 \r\n3 23 124 \r\n34 234 12 \r\n34 23 124 \r\n3 234 124 \r\n34 2 123 \r\n3 24 123 \r\n3 2 1234 \r\n34 24 123 \r\n34 2 1234 \r\n3 24 1234 \r\n4 23 123 \r\n4 234 123 \r\n4 23 1234 \r\n123 1 4 \r\n1234 1 4 \r\n123 14 4 \r\n12 13 4 \r\n124 13 4 \r\n12 134 4 \r\n124 1 3 \r\n12 14 3 \r\n12 1 34 \r\n124 14 3 \r\n124 1 34 \r\n12 14 34 \r\n123 13 4 \r\n1234 13 4 \r\n123 134 4 \r\n1234 1 3 \r\n123 14 3 \r\n123 1 34 \r\n1234 14 3 \r\n1234 1 34 \r\n123 14 34 \r\n124 13 3 \r\n12 134 3 \r\n12 13 34 \r\n124 134 3 \r\n124 13 34 \r\n12 134 34 \r\n13 12 4 \r\n134 12 4 \r\n13 124 4 \r\n1 123 4 \r\n14 123 4 \r\n1 1234 4 \r\n14 12 3 \r\n1 124 3 \r\n1 12 34 \r\n14 124 3 \r\n14 12 34 \r\n1 124 34 \r\n13 123 4 \r\n134 123 4 \r\n13 1234 4 \r\n134 12 3 \r\n13 124 3 \r\n13 12 34 \r\n134 124 3 \r\n134 12 34 \r\n13 124 34 \r\n14 123 3 \r\n1 1234 3 \r\n1 123 34 \r\n14 1234 3 \r\n14 123 34 \r\n1 1234 34 \r\n134 1 2 \r\n13 14 2 \r\n13 1 24 \r\n134 14 2 \r\n134 1 24 \r\n13 14 24 \r\n14 13 2 \r\n1 134 2 \r\n1 13 24 \r\n14 134 2 \r\n14 13 24 \r\n1 134 24 \r\n14 1 23 \r\n1 14 23 \r\n1 1 234 \r\n14 14 23 \r\n14 1 234 \r\n1 14 234 \r\n134 13 2 \r\n13 134 2 \r\n13 13 24 \r\n134 134 2 \r\n134 13 24 \r\n13 134 24 \r\n134 1 23 \r\n13 14 23 \r\n13 1 234 \r\n134 14 23 \r\n134 1 234 \r\n13 14 234 \r\n14 13 23 \r\n1 134 23 \r\n1 13 234 \r\n14 134 23 \r\n14 13 234 \r\n1 134 234 \r\n123 12 4 \r\n1234 12 4 \r\n123 124 4 \r\n12 123 4 \r\n124 123 4 \r\n12 1234 4 \r\n124 12 3 \r\n12 124 3 \r\n12 12 34 \r\n124 124 3 \r\n124 12 34 \r\n12 124 34 \r\n123 123 4 \r\n1234 123 4 \r\n123 1234 4 \r\n1234 12 3 \r\n123 124 3 \r\n123 12 34 \r\n1234 124 3 \r\n1234 12 34 \r\n123 124 34 \r\n124 123 3 \r\n12 1234 3 \r\n12 123 34 \r\n124 1234 3 \r\n124 123 34 \r\n12 1234 34 \r\n1234 1 2 \r\n123 14 2 \r\n123 1 24 \r\n1234 14 2 \r\n1234 1 24 \r\n123 14 24 \r\n124 13 2 \r\n12 134 2 \r\n12 13 24 \r\n124 134 2 \r\n124 13 24 \r\n12 134 24 \r\n124 1 23 \r\n12 14 23 \r\n12 1 234 \r\n124 14 23 \r\n124 1 234 \r\n12 14 234 \r\n1234 13 2 \r\n123 134 2 \r\n123 13 24 \r\n1234 134 2 \r\n1234 13 24 \r\n123 134 24 \r\n1234 1 23 \r\n123 14 23 \r\n123 1 234 \r\n1234 14 23 \r\n1234 1 234 \r\n123 14 234 \r\n124 13 23 \r\n12 134 23 \r\n12 13 234 \r\n124 134 23 \r\n124 13 234 \r\n12 134 234 \r\n134 12 2 \r\n13 124 2 \r\n13 12 24 \r\n134 124 2 \r\n134 12 24 \r\n13 124 24 \r\n14 123 2 \r\n1 1234 2 \r\n1 123 24 \r\n14 1234 2 \r\n14 123 24 \r\n1 1234 24 \r\n14 12 23 \r\n1 124 23 \r\n1 12 234 \r\n14 124 23 \r\n14 12 234 \r\n1 124 234 \r\n134 123 2 \r\n13 1234 2 \r\n13 123 24 \r\n134 1234 2 \r\n134 123 24 \r\n13 1234 24 \r\n134 12 23 \r\n13 124 23 \r\n13 12 234 \r\n134 124 23 \r\n134 12 234 \r\n13 124 234 \r\n14 123 23 \r\n1 1234 23 \r\n1 123 234 \r\n14 1234 23 \r\n14 123 234 \r\n1 1234 234 \r\n123 4 1 \r\n1234 4 1 \r\n123 4 14 \r\n124 3 1 \r\n12 34 1 \r\n12 3 14 \r\n124 34 1 \r\n124 3 14 \r\n12 34 14 \r\n12 4 13 \r\n124 4 13 \r\n12 4 134 \r\n1234 3 1 \r\n123 34 1 \r\n123 3 14 \r\n1234 34 1 \r\n1234 3 14 \r\n123 34 14 \r\n123 4 13 \r\n1234 4 13 \r\n123 4 134 \r\n124 3 13 \r\n12 34 13 \r\n12 3 134 \r\n124 34 13 \r\n124 3 134 \r\n12 34 134 \r\n134 2 1 \r\n13 24 1 \r\n13 2 14 \r\n134 24 1 \r\n134 2 14 \r\n13 24 14 \r\n14 23 1 \r\n1 234 1 \r\n1 23 14 \r\n14 234 1 \r\n14 23 14 \r\n1 234 14 \r\n14 2 13 \r\n1 24 13 \r\n1 2 134 \r\n14 24 13 \r\n14 2 134 \r\n1 24 134 \r\n134 23 1 \r\n13 234 1 \r\n13 23 14 \r\n134 234 1 \r\n134 23 14 \r\n13 234 14 \r\n134 2 13 \r\n13 24 13 \r\n13 2 134 \r\n134 24 13 \r\n134 2 134 \r\n13 24 134 \r\n14 23 13 \r\n1 234 13 \r\n1 23 134 \r\n14 234 13 \r\n14 23 134 \r\n1 234 134 \r\n13 4 12 \r\n134 4 12 \r\n13 4 124 \r\n14 3 12 \r\n1 34 12 \r\n1 3 124 \r\n14 34 12 \r\n14 3 124 \r\n1 34 124 \r\n1 4 123 \r\n14 4 123 \r\n1 4 1234 \r\n134 3 12 \r\n13 34 12 \r\n13 3 124 \r\n134 34 12 \r\n134 3 124 \r\n13 34 124 \r\n13 4 123 \r\n134 4 123 \r\n13 4 1234 \r\n14 3 123 \r\n1 34 123 \r\n1 3 1234 \r\n14 34 123 \r\n14 3 1234 \r\n1 34 1234 \r\n1234 2 1 \r\n123 24 1 \r\n123 2 14 \r\n1234 24 1 \r\n1234 2 14 \r\n123 24 14 \r\n124 23 1 \r\n12 234 1 \r\n12 23 14 \r\n124 234 1 \r\n124 23 14 \r\n12 234 14 \r\n124 2 13 \r\n12 24 13 \r\n12 2 134 \r\n124 24 13 \r\n124 2 134 \r\n12 24 134 \r\n1234 23 1 \r\n123 234 1 \r\n123 23 14 \r\n1234 234 1 \r\n1234 23 14 \r\n123 234 14 \r\n1234 2 13 \r\n123 24 13 \r\n123 2 134 \r\n1234 24 13 \r\n1234 2 134 \r\n123 24 134 \r\n124 23 13 \r\n12 234 13 \r\n12 23 134 \r\n124 234 13 \r\n124 23 134 \r\n12 234 134 \r\n123 4 12 \r\n1234 4 12 \r\n123 4 124 \r\n124 3 12 \r\n12 34 12 \r\n12 3 124 \r\n124 34 12 \r\n124 3 124 \r\n12 34 124 \r\n12 4 123 \r\n124 4 123 \r\n12 4 1234 \r\n1234 3 12 \r\n123 34 12 \r\n123 3 124 \r\n1234 34 12 \r\n1234 3 124 \r\n123 34 124 \r\n123 4 123 \r\n1234 4 123 \r\n123 4 1234 \r\n124 3 123 \r\n12 34 123 \r\n12 3 1234 \r\n124 34 123 \r\n124 3 1234 \r\n12 34 1234 \r\n134 2 12 \r\n13 24 12 \r\n13 2 124 \r\n134 24 12 \r\n134 2 124 \r\n13 24 124 \r\n14 23 12 \r\n1 234 12 \r\n1 23 124 \r\n14 234 12 \r\n14 23 124 \r\n1 234 124 \r\n14 2 123 \r\n1 24 123 \r\n1 2 1234 \r\n14 24 123 \r\n14 2 1234 \r\n1 24 1234 \r\n134 23 12 \r\n13 234 12 \r\n13 23 124 \r\n134 234 12 \r\n134 23 124 \r\n13 234 124 \r\n134 2 123 \r\n13 24 123 \r\n13 2 1234 \r\n134 24 123 \r\n134 2 1234 \r\n13 24 1234 \r\n14 23 123 \r\n1 234 123 \r\n1 23 1234 \r\n14 234 123 \r\n14 23 1234 \r\n1 234 1234 \r\n234 1 1 \r\n23 14 1 \r\n23 1 14 \r\n234 14 1 \r\n234 1 14 \r\n23 14 14 \r\n24 13 1 \r\n2 134 1 \r\n2 13 14 \r\n24 134 1 \r\n24 13 14 \r\n2 134 14 \r\n24 1 13 \r\n2 14 13 \r\n2 1 134 \r\n24 14 13 \r\n24 1 134 \r\n2 14 134 \r\n234 13 1 \r\n23 134 1 \r\n23 13 14 \r\n234 134 1 \r\n234 13 14 \r\n23 134 14 \r\n234 1 13 \r\n23 14 13 \r\n23 1 134 \r\n234 14 13 \r\n234 1 134 \r\n23 14 134 \r\n24 13 13 \r\n2 134 13 \r\n2 13 134 \r\n24 134 13 \r\n24 13 134 \r\n2 134 134 \r\n34 12 1 \r\n3 124 1 \r\n3 12 14 \r\n34 124 1 \r\n34 12 14 \r\n3 124 14 \r\n4 123 1 \r\n4 1234 1 \r\n4 123 14 \r\n4 12 13 \r\n4 124 13 \r\n4 12 134 \r\n34 123 1 \r\n3 1234 1 \r\n3 123 14 \r\n34 1234 1 \r\n34 123 14 \r\n3 1234 14 \r\n34 12 13 \r\n3 124 13 \r\n3 12 134 \r\n34 124 13 \r\n34 12 134 \r\n3 124 134 \r\n4 123 13 \r\n4 1234 13 \r\n4 123 134 \r\n34 1 12 \r\n3 14 12 \r\n3 1 124 \r\n34 14 12 \r\n34 1 124 \r\n3 14 124 \r\n4 13 12 \r\n4 134 12 \r\n4 13 124 \r\n4 1 123 \r\n4 14 123 \r\n4 1 1234 \r\n34 13 12 \r\n3 134 12 \r\n3 13 124 \r\n34 134 12 \r\n34 13 124 \r\n3 134 124 \r\n34 1 123 \r\n3 14 123 \r\n3 1 1234 \r\n34 14 123 \r\n34 1 1234 \r\n3 14 1234 \r\n4 13 123 \r\n4 134 123 \r\n4 13 1234 \r\n234 12 1 \r\n23 124 1 \r\n23 12 14 \r\n234 124 1 \r\n234 12 14 \r\n23 124 14 \r\n24 123 1 \r\n2 1234 1 \r\n2 123 14 \r\n24 1234 1 \r\n24 123 14 \r\n2 1234 14 \r\n24 12 13 \r\n2 124 13 \r\n2 12 134 \r\n24 124 13 \r\n24 12 134 \r\n2 124 134 \r\n234 123 1 \r\n23 1234 1 \r\n23 123 14 \r\n234 1234 1 \r\n234 123 14 \r\n23 1234 14 \r\n234 12 13 \r\n23 124 13 \r\n23 12 134 \r\n234 124 13 \r\n234 12 134 \r\n23 124 134 \r\n24 123 13 \r\n2 1234 13 \r\n2 123 134 \r\n24 1234 13 \r\n24 123 134 \r\n2 1234 134 \r\n234 1 12 \r\n23 14 12 \r\n23 1 124 \r\n234 14 12 \r\n234 1 124 \r\n23 14 124 \r\n24 13 12 \r\n2 134 12 \r\n2 13 124 \r\n24 134 12 \r\n24 13 124 \r\n2 134 124 \r\n24 1 123 \r\n2 14 123 \r\n2 1 1234 \r\n24 14 123 \r\n24 1 1234 \r\n2 14 1234 \r\n234 13 12 \r\n23 134 12 \r\n23 13 124 \r\n234 134 12 \r\n234 13 124 \r\n23 134 124 \r\n234 1 123 \r\n23 14 123 \r\n23 1 1234 \r\n234 14 123 \r\n234 1 1234 \r\n23 14 1234 \r\n24 13 123 \r\n2 134 123 \r\n2 13 1234 \r\n24 134 123 \r\n24 13 1234 \r\n2 134 1234 \r\n34 12 12 \r\n3 124 12 \r\n3 12 124 \r\n34 124 12 \r\n34 12 124 \r\n3 124 124 \r\n4 123 12 \r\n4 1234 12 \r\n4 123 124 \r\n4 12 123 \r\n4 124 123 \r\n4 12 1234 \r\n34 123 12 \r\n3 1234 12 \r\n3 123 124 \r\n34 1234 12 \r\n34 123 124 \r\n3 1234 124 \r\n34 12 123 \r\n3 124 123 \r\n3 12 1234 \r\n34 124 123 \r\n34 12 1234 \r\n3 124 1234 \r\n4 123 123 \r\n4 1234 123 \r\n4 123 1234 \r\n',11765,0);
INSERT INTO comment VALUES (11769,1437,1301,'Charlie','re(5): Solution FINAL WORD(by Charlie','2004-02-10 15:58:42',0,'By the way the program that produced the list is\r\n\r\nOPEN \"setmeup.txt\" FOR OUTPUT AS #2\r\nDATA 1,2,3,12,13,23\r\nFOR i = 1 TO 6\r\n READ choice$(i)\r\nNEXT\r\nDIM set$(3)\r\n\r\nFOR c1 = 1 TO 6\r\n FOR c2 = 1 TO 6\r\n FOR c3 = 1 TO 6\r\n FOR c4 = 1 TO 6\r\n ERASE set$\r\n c$ = choice$(c1)\r\n FOR i = 1 TO LEN(c$)\r\n set$(VAL(MID$(c$, i, 1))) = set$(VAL(MID$(c$, i, 1))) + \"1\"\r\n NEXT\r\n c$ = choice$(c2)\r\n FOR i = 1 TO LEN(c$)\r\n set$(VAL(MID$(c$, i, 1))) = set$(VAL(MID$(c$, i, 1))) + \"2\"\r\n NEXT\r\n c$ = choice$(c3)\r\n FOR i = 1 TO LEN(c$)\r\n set$(VAL(MID$(c$, i, 1))) = set$(VAL(MID$(c$, i, 1))) + \"3\"\r\n NEXT\r\n c$ = choice$(c4)\r\n FOR i = 1 TO LEN(c$)\r\n set$(VAL(MID$(c$, i, 1))) = set$(VAL(MID$(c$, i, 1))) + \"4\"\r\n NEXT\r\n good = 1\r\n FOR i = 1 TO 3\r\n IF set$(i) = \"\" THEN good = 0\r\n NEXT\r\n IF good THEN\r\n gdCt = gdCt + 1\r\n PRINT #2, set$(1); \" \"; set$(2); \" \"; set$(3); \" \"\r\n END IF\r\n NEXT\r\n NEXT\r\n NEXT\r\nNEXT\r\nCLOSE\r\nPRINT gdCt\r\n\r\n
\r\n---------\r\n---------',11768,0);
INSERT INTO comment VALUES (11770,1437,5285,'Ady TZIDON','re(5): Solution FINAL WORD revisited','2004-02-10 16:38:55',1,'Both the formula and the solution are ok\r\nI DID NOT NOTICE THAT YOU DEDUCTED THE 3 REDUNDANT CHOICES\r\n\r\nerrare humanum est\r\nady',11767,0);
INSERT INTO comment VALUES (11771,1437,4507,'Penny','re: Is this right ?','2004-02-10 16:47:23',0,'Penny: \"If C has 2 numbers (there are 10*9 such sets), then any two sets A and B, where A is any subset of the remaining 8 numbers, and B is any subset of all 10 numbers, should do the trick.\"\r\n\r\nPenny doesn\'t make sense. These combinations include \r\nC={1,2}, B={1,2,3,4}, A={3,4}.\r\nA U B U C = {1,2,3,4}\r\n\r\nIt is also wrong to assume that if there are three subsets A,B,C such that A U B U C = {1,2,3,4,5,6,7,8,9,10} and \r\nA int B int C = {}, then at least two of them must have null intersection.\r\n\r\nWhat about:\r\nA = {1,3}, B={1,2}, C={2,3,4,5,6,7,8,9,10} \r\n\r\nAt this rate I\'ll have the cure for cancer any day now.... \n\nEdited on February 10, 2004, 4:49 pm',11762,0);
INSERT INTO comment VALUES (11772,670,5297,'NK','Re so easy','2004-02-10 18:13:08',0,'(Responding to Ady TZIDON)\r\n\r\nThat\'s a nifty approach, but don\'t we count digits beginning at the decimal? If so, you still might get a variant of your method to work.',NULL,0);
INSERT INTO comment VALUES (11773,1605,5579,'superfuous_nut','i\'ll give it a swing','2004-02-10 18:54:03',0,'the cube is 4x4x4. the farthest corners are then √(4²+4²+4²) or √48.\r\n\r\nthe spheres are 2 units in diameter each. they take up a total of 4 units of the √48 distance. which leaves (√48 - 4) of gap. half of this space is between them and half is at the corner.\r\n\r\nmy solution is (√48-4)/2 for a diameter or (√48-4)/4 for a radius.\r\n\r\nr=0.73205...\r\n',NULL,0);
INSERT INTO comment VALUES (11774,670,5297,'NK','re: Re so easy','2004-02-10 19:03:12',0,'In fact, counting from the decimal makes your number\r\n\r\nAAAAx1AAAA\r\n\r\nx=9 gives 91, which is divisible by 13. Thus, we both get the same answer (9), but your approach is MUCH easier.',11772,0);
INSERT INTO comment VALUES (11775,1509,5352,'Phil','Alternative Solution','2004-02-10 19:06:46',3,'Most wells would be described as being \"deep\", not \"tall\", from this it is impossible to calculate the internal height of the well since we don\'t know the depth below the surface of the ground.\r\n\r\nas a result, herb must be already out of the well, so the final answer must be 14th February 1996, he was at the bottom on the outside.',NULL,0);
INSERT INTO comment VALUES (11776,1399,5062,'Steve','','2004-02-10 21:02:41',0,'i think cable and clay are the only words and we are reading too much into this\r\n',NULL,0);
INSERT INTO comment VALUES (11777,1622,3351,'Eric','one idea','2004-02-10 21:38:44',1,'One word that came to mind was \"sunshine\". It could be considered synonymous with both \"sun\" and \"shine\", although \"shine\" usually means something else. This doesn\'t work as well for me as the word \"sunlight\". \r\nFor example:\r\n\r\nI am going outside in the sun.\r\nI am going outside in the light.\r\nI am going outside in the sunlight.\r\n\r\nThese seem like synonymous sentences. I look forward to seeing some other answers to this.\r\n\r\nEdited on February 10, 2004, 9:44 pm\n\nEdited on February 10, 2004, 9:44 pm',NULL,0);
INSERT INTO comment VALUES (11778,1498,5580,'paul','Wow','2004-02-10 21:54:57',0,'that is a very confusing problem',NULL,0);
INSERT INTO comment VALUES (11779,1622,5580,'paul','simple','2004-02-10 21:59:17',0,'buttocks = butt',NULL,0);
INSERT INTO comment VALUES (11780,1399,5580,'paul','simple','2004-02-10 22:04:38',0,'the answer is \r\n\r\nCA BABES\r\nor\r\nCalifornia girls',NULL,0);
INSERT INTO comment VALUES (11781,1399,5580,'paul','other answer was messed up','2004-02-10 22:06:06',0,'the answer is Cable',NULL,0);
INSERT INTO comment VALUES (11782,1379,5580,'paul','# 3','2004-02-10 22:11:20',0,'Piqua, Ohio',NULL,0);
INSERT INTO comment VALUES (11783,1622,3372,'Sam','re: simple','2004-02-11 00:28:48',0,'>> buttocks = butt\r\n\r\nI\'ve never had the urge to kick someone in the \"ocks\" however...',11779,0);
INSERT INTO comment VALUES (11784,1622,4507,'Penny','Two more','2004-02-11 06:02:21',3,'overdone \r\npotbelly ',NULL,0);
INSERT INTO comment VALUES (11785,1622,4507,'Penny','More possibilities','2004-02-11 07:05:05',3,'upstanding\r\nuttermost\r\naye-aye\r\nbye-bye\r\ndownfallen\r\nwhippersnapper\r\novermuch\r\noverplus\r\nclose-by\r\ngoody-goody\r\nall-inclusive\r\nall-encompassing\r\noverthrown\r\nfuddy-duddy\r\nmuckrake\r\nhurly-burly\r\nsingsong\r\ntopsy-turvy\r\nbygone',NULL,0);
INSERT INTO comment VALUES (11786,670,5285,'Ady TZIDON','re(2): Re so easy SECOND OPINION att :NK','2004-02-11 07:24:20',2,' NK,\r\nTake a number, say 652 . When you say its first digit is 6 second is 5 etc you count from left to right.\r\nThat\'s the way I did it. ( i did it my way..)\r\nOf course you are free to define it the other way \r\nand then X1=91 ===> X=9 .\r\n\r\nSo you and I solved two problems for the price of one.\r\n\r\nenjoy, enjoy\r\n\r\nady',11774,0);
INSERT INTO comment VALUES (11787,1622,4507,'Penny','Three more','2004-02-11 07:36:16',3,'manservant\r\ncodfish\r\nladylove',NULL,0);
INSERT INTO comment VALUES (11788,1622,3172,'SilverKnight','re(2): simple','2004-02-11 07:58:40',0,'I have...',11783,0);
INSERT INTO comment VALUES (11789,1622,4507,'Penny','Also there is....','2004-02-11 08:12:32',3,'Quagmire',NULL,0);
INSERT INTO comment VALUES (11790,1605,5391,'York','re(2): Different Sulution','2004-02-11 08:46:33',0,'Thanks Charlie. In my attenpt to simplify the problem, I lost track of the alignment of the center circle. Again thanks for the correction. \r\nYork ',11718,0);
INSERT INTO comment VALUES (11791,1321,3275,'retiarius','aplles and oranges','2004-02-11 09:11:59',0,'Each has n apples when the new trading begins.\r\nThey make 2n * 2/5 instead of n/2 + n/3 shillings\r\nThus 5n/6 - 4n/5 = 7\r\nn = 210\r\nThey make 168 shillings\r\nSmith makes 84 instead of 70 shillings, gaining 14 shillings\r\nJones makes 84 instead of 105 shillings, losing 21 shillings\r\n',NULL,0);
INSERT INTO comment VALUES (11792,1321,4507,'Penny','Solution (no applet used)','2004-02-11 09:17:32',3,'OK, I\'ll bite. This may not be the core solution. \r\n\r\nAfter reading retiarius\'s solution, I realize that I interpreted \"there appears to be a shortage of seven shillings\" differently than he did. My original answer appears as a footnote.\r\n\r\nLets say each woman put N apples in the pile. \r\n\r\n(4/5)N = (1/2)N + (1/3)N - 7\r\n\r\nN = 210\r\n\r\nMrs Jones should have gotten 105 shillings, but actually got 84 shillings. She lost 21 shillings.\r\n\r\nFootnote: My original solution read:\r\n\r\nMrs. Jones meant to sell these apples for \r\n(2/5)*(2N) = (4/5)N shillings, but the amount was found to be (4/5)N - 7 shillings.\r\n\r\nEach woman got [(4/5)N - 7]/2 =(2/5)N - 7/2 shillings\r\n\r\nMrs. Jones whould have gotten N/2 shillings if she hadn\'t given them to Mrs. Smith.\r\n\r\nMrs. Jones lost N/2 - [(2/5)N - 7/2]\r\n= (1/10)N + 7/2 shillings\r\n\r\n\r\n\n\nEdited on February 11, 2004, 9:31 am',NULL,0);
INSERT INTO comment VALUES (11793,1622,3372,'Sam','Huh?? (re: Two more)','2004-02-11 12:08:10',0,'Um, am I confused as to what is supposed to be done? Aren\'t the two parts supposed to be synonymous?\r\n\r\nAs far as I understand,\r\n\r\nover != done\r\npot != belly\r\nup != standing\r\ndown != fallen\r\nover != much\r\nman != servent\r\n\r\nand so on...\r\n\r\nQuagmire, however, seems perfect.\r\n(Quag = mire = quagmire = a low lying bog)\n\nEdited on February 11, 2004, 12:08 pm',11784,0);
INSERT INTO comment VALUES (11794,1622,3172,'SilverKnight','re: Huh?? (re: Two more)','2004-02-11 12:31:10',0,'Oh woe is me! What is the world coming to, when I find myself defending Penny\'s responses! :-)\r\n\r\nAnyway, Sam, I think, in context, all of these are synonyms:\r\n
\r\n',11793,0);
INSERT INTO comment VALUES (11795,1622,122,'Happy','another','2004-02-11 14:08:10',0,'taxicab',NULL,0);
INSERT INTO comment VALUES (11796,1622,5586,'MarcAllen','Castle of Greyskull','2004-02-11 14:14:34',0,'He-Man',NULL,0);
INSERT INTO comment VALUES (11797,1622,5586,'MarcAllen','re: Castle of Greyskull','2004-02-11 14:16:26',0,'oh, and bathtub',11796,0);
INSERT INTO comment VALUES (11798,1622,4507,'Penny','re: Castle of Greyskull','2004-02-11 14:18:57',0,'Thanks for the lowdown !!!!!',11796,0);
INSERT INTO comment VALUES (11799,1622,153,'TomM','re(2): Huh?? (re: Two more)','2004-02-11 14:20:53',0,'>>Anyway, Sam, I think, in context, all of these are synonyms: \r\n\r\n\r\nThe problem, though, is that it takes a context to make the connection. One or both of the parts has another different, more common meaning, or their usual connotation is slightly different. When you hear the word \"pot\" for example, unless you already know that you are referring to a belly, or the context makes it clear. \r\n\r\nAnd even so, you had trouble equating up=standing=upstanding and down=fallen=downfallen.\r\n\r\nThe thing is not that they are wrong, but that another word is so obviously right that these are shown to be inferior substitutes.',11794,0);
INSERT INTO comment VALUES (11800,1626,4507,'Penny','For those who are not familiar with dominoes...','2004-02-11 14:22:18',2,'http://boardgamecentral.com/games/dominoes.html',NULL,0);
INSERT INTO comment VALUES (11801,1415,5587,'Chuck Horn','A Boy, a Girl, a Dog, and a Bicycle','2004-02-11 14:25:17',0,'I hope that the answer is 5 hours. Otherwise what is the purpose of taking a walk. If this were a race where it didn\'t matter if everyone separated, we could plot out the shortest time. Before I do that, I want to eliminate the obvious.',NULL,0);
INSERT INTO comment VALUES (11802,238,4257,'Jack McBarn','Solution','2004-02-11 14:28:06',3,'5 up [5=5,3=0]\r\nPour 5>3 [5=2,3=3]\r\nEmpty 3 [5=2,3=0] \r\nPour 5>3 [5=0,3=2]\r\nFill 5 [5=5,3=2] \r\nPour 5>3 - stop when 3 full[5=4,3=3] ',NULL,0);
INSERT INTO comment VALUES (11803,1626,4507,'Penny','Here is a picture of double-sixes dominoes','2004-02-11 14:35:09',2,'http://www.unclesgames.com/product_info.php?ref=3&products_id=507&affiliate_banner_id=1',11800,0);
INSERT INTO comment VALUES (11804,1622,3172,'SilverKnight','re(3): Huh?? (re: Two more)','2004-02-11 14:37:16',0,'The original posting had more than those you mentioned, and was associated with other postings as well.... And while each particular pairing has varying degrees of success, the original criticism applied to the whole group of them.\r\n\r\nYou, also didn\'t mention man=servent or over=done, which are more reasonable. The others are still worthy of note, and with such a problem, your notion of \"obviously right\" is hard to swallow.\r\n\r\nIf one wants an \"obviously right\" answer, one should TD those problems that allow for multiple answers and/or \"degrees of correctness\".',11799,0);
INSERT INTO comment VALUES (11805,1626,5285,'Ady TZIDON','Not sure- just intuition','2004-02-11 14:54:11',2,'\r\n\r\nIt looks like 1/6- is the answer.\r\n\r\nOnly if the pieces are similar say 1-5 and 2-5.,the chain is possible.\r\nSince for any given 1-domino only one matching 2- domino exists - out of 6, my result follows.\r\n6 and not 7 since 2-1 should not be counted twice.\r\n\r\nady',NULL,0);
INSERT INTO comment VALUES (11806,1626,5285,'Ady TZIDON','SOLUTION now','2004-02-11 15:20:05',0,'answer : 17/48\r\n\r\nSOLUTION: build a table 7*7 showing all possible pairs of 1-dom and 2-dom\r\nout of 49 possible pairs one is precluded : intersection of 1-2 and 2-1.\r\n\r\nnow insert * in any square of a table which enables the \" happy ending\" and count the ***.\r\n\r\nI GOT 17 OUT OF 48 POSSIBLE (7 -DIAGONAL AND 11 \r\n1-2 THE WHOLE ROW AND 2-1 THE WHOLE COLUMN - ONE COMMON)\r\n\r\nBEATIFUL PUZZLE\r\n\r\nady ',NULL,0);
INSERT INTO comment VALUES (11807,1622,5285,'Ady TZIDON','re(4): Huh?? (re: Two more) servAnt','2004-02-11 16:10:21',0,'it is servAnt not servEnt\r\n\r\nady',11804,0);
INSERT INTO comment VALUES (11808,1626,3172,'SilverKnight','solution :-)','2004-02-11 16:23:22',0,'17/48 - I agree with Ady...\r\n___________________________\r\n\r\nThere are 7 number (0, 1, 2, 3, 4, 5, and 6), and each of them is displayed 8 times (for a total of 56). Since there are 2 on each domino, we should find 56/2 = 28 dominoes. Verified.\r\n\r\nNow, to have a chain, clearly every number must match up with a match. Therefore, we must have an even number of them along the chain. Therefore, the two \"ends\" of the chain MUST match.\r\n\r\nEquivalently, If the ends of the chain don\'t match, then we can\'t make a chain using all the dominoes.\r\n\r\n(Corollary: if the ends of the chain *do* match, then we CAN make a chain using all the dominoes... left to prove as an exercise to the reader.)\r\n\r\nSo, if, for example, the two dominoes are (1,3) and (2,4), then we will be unable to make a chain. (This is because they share no number, so we can\'t have the ends equal.)\r\n____________________________________________\r\n\r\nNot including the the 1,2 domino, there are:\r\n6 x 6 = 36 different possibilities ( (0,1) & (0,2), (0,1) & (3,2), etc. )\r\n\r\nIncluding the 1,2 domino, there are:\r\n2 x 6 = 12 different possibilities ( (1,2) & (x,1), (1,2) (x,2))\r\n\r\nTotal: 48 equally likely possibilities\r\n\r\nOf them, only the following have a *match* at the ends:\r\n\r\nwith (1,2) - 12 combinations\r\n(1,2) (0,1)\r\n(1,2) (1,1)\r\n(1,2) (3,1)\r\n(1,2) (4,1)\r\n(1,2) (5,1)\r\n(1,2) (6,1)\r\n(2,1) (0,2)\r\n(2,1) (2,2)\r\n(2,1) (3,2)\r\n(2,1) (4,2)\r\n(2,1) (5,2)\r\n(2,1) (6,2)\r\n\r\nwithout (1,2) - 5 combinations\r\n(0,1) (2,0)\r\n(3,1) (2,3)\r\n(4,1) (2,4)\r\n(5,1) (2,5)\r\n(6,1) (2,6)\r\n\r\nTotal of 17 successful combinations over 48 equally likely possibilities.',NULL,0);
INSERT INTO comment VALUES (11809,1622,3172,'SilverKnight','re(5): Huh?? (re: Two more)','2004-02-11 16:29:14',0,'Yes, it is.\r\n\r\nI kept the misspelling from the earlier comment. (Please see the referenced postings.)\r\n\r\nAlso, we CAPITALIZE the first letter of a sentence, and end them with periods (.).\r\n\r\n;-)\r\n\r\n- SK',11807,0);
INSERT INTO comment VALUES (11810,1626,1301,'Charlie','re: solution :-)','2004-02-11 17:52:55',0,'Are you sure you\'ve considered all the ways leading to the choice of what you see?',11808,0);
INSERT INTO comment VALUES (11811,1626,3172,'SilverKnight','re(2): solution :-)','2004-02-11 17:54:56',0,'not anymore!!!! :-)\r\n\r\nAt least not when you ask me like that.... (well gotta run for now... I\'ll look again later.) In the mean time... someone take advantage of this lapse and PROVE ME WRONG!',11810,0);
INSERT INTO comment VALUES (11812,1415,4374,'Richard','re: A Boy, a Girl, a Dog, and a Bicycle','2004-02-11 21:11:39',0,'See comments 5,7, and 8.',11801,0);
INSERT INTO comment VALUES (11813,1622,5285,'Ady TZIDON','re(6): Huh?? (re: Two more)======> SK','2004-02-11 21:26:22',3,'\r\nSK,\r\n\r\nTouche!!\r\n\r\n\r\ntou·ché = Pronunciation Key (t-sh)\r\ninterj. \r\nUsed to acknowledge a hit in fencing or a successful criticism or an effective point in argument.\r\n\r\n\r\nAdy. \r\nN.B. I still like the modest \" ady \". ',11809,0);
INSERT INTO comment VALUES (11814,1626,3558,'Tristan','solution?','2004-02-11 23:53:25',3,'I\'m not very confident in this, but isn\'t the 1,1 dominoe twice as likely to be the one chosen? Likewise for the 2,2 dominoe?\r\n\r\nIf this is the case, I just double a column and a row in the table Ady suggested and get 63 possibilities. 19 of the possibilities match. \r\n\r\nSo the probability is 19/63\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (11815,1270,5596,'Katrina','solution','2004-02-12 00:14:55',3,'Allison, 6, thrush, birdseed\r\nBrewer, 10, robin, suet\r\nChandler, 2, blackbird, toast\r\nDennis, 4, sparrow, bread\r\nEmery, 8, cardinal, cake\r\n',NULL,0);
INSERT INTO comment VALUES (11816,1626,3172,'SilverKnight','re(3): solution :-)','2004-02-12 05:31:23',4,'BTW, Charlie....\r\n\r\nRegarding your problem\'s statement:\r\n\"You look at only one of the two numbers on each domino, choosing at random which end to look at. You see that the number you look at on the first domino is 1. The number you see on the second domino is 2...\"\r\n\r\nI read this to be equivalent to:\r\n\"One domino has at least one \'1\' on it, and the other domino has at least one \'2\' on it.\"\r\n\r\nIt seems (to me) that Ady interpreted it in the same manner. Are we understanding the problem correctly?\r\n\r\n-SK',11811,0);
INSERT INTO comment VALUES (11817,1622,1183,'fwaff','re(4): Huh?? (re: Two more)','2004-02-12 06:07:53',3,'I think TomM\'s point is that while most of Penny\'s solutions fit A=B (eg over=done), they don\'t generally fit A=B=AB (eg over and done do not mean the same as overdone). Penny\'s one \'obviously right\' answer is quagmire where both halves of the word are common abbreviations (and therefore synonyms) with the whole word. Of the other suggestions posted the only \'obviously right\' ones (IMHO) are taxicab and bathtub.\r\n\r\nFWIW I agree 100% with SK on the principle of \'obviously right\' regarding problems of this type. Anyway from pedants\' corner, the correct answer to the problem is \"yes\".',11804,0);
INSERT INTO comment VALUES (11818,1626,1301,'Charlie','re(4): solution :-)','2004-02-12 08:39:37',0,'Your paraphrase is not as specific in the method of choosing two dominos and the ends to look at. Ask which is a more likely domino to choose: for example, the 1-5 or the 1-1. Also determine at random an end to look at.',11816,0);
INSERT INTO comment VALUES (11819,1622,1920,'Brian Smith','Out of all the responses so far ......','2004-02-12 09:07:34',0,'Out of all the responses so far, I think the best ones are taxicab and quagmire. Those are probably the two words the puzzle is asking for.\n\nEdited on February 12, 2004, 10:41 am',NULL,0);
INSERT INTO comment VALUES (11820,1500,4670,'e.g.','Acorns','2004-02-12 10:00:17',3,'A=8, B=2, C=6.
From A\'s statement, C=AB-A-B =(A-1)(B-1)-1
Equating, (B-1)B(B+1)=(A-1)(B-1)-1, so (B-1)[(A-1)-B(B+1)]=1. As both factors must be integers, it follows that B-1=1 (so B=2) and A-1=7 (so A=8).\r\n\r\nEdited on February 12, 2004, 10:03 am\n\nEdited on February 12, 2004, 10:04 am',NULL,0);
INSERT INTO comment VALUES (11821,1500,1301,'Charlie','re: Acorns ... because','2004-02-12 10:05:43',3,'(B-1)B(B+1) = AB-A-B\r\n(B-1)B(B+1) = (A-1)(B-1)-1\r\n\r\n(B-1)(B(B+1)-(A-1)) = -1\r\n\r\nSo B must be 2 (it can\'t be zero), and then A solves to 8, making C=6.',11820,0);
INSERT INTO comment VALUES (11822,1500,4670,'e.g.','re(2): Acorns ... because','2004-02-12 10:35:14',1,'I do not want to start a flames war, but your reply doesn\'t add anything to my post...',11821,0);
INSERT INTO comment VALUES (11823,1500,3172,'SilverKnight','re(3): Acorns ... because','2004-02-12 11:18:11',0,'You tell \'im e.g. !!!\r\n\r\nCharlie\'s always starting stuff and offending people around here!',11822,0);
INSERT INTO comment VALUES (11824,1626,3172,'SilverKnight','re(5): solution :-)','2004-02-12 12:15:05',0,'Different (correct?) solution, agreeing with Tristan:\r\n19/63\r\n_______________________________________\r\n\r\nOkay... here\'s my qualified response:\r\n\r\nIt\'s not clear to me that our previous interpretation is \'wrong\'. But if I understand what Charlie is getting at, then the previous answers are not what he is looking for, and here\'s his line of reasoning. (I hope Charlie will continue to comment, so we\'re not left in limbo, wondering...)\r\n_______________________________________\r\n\r\nLet us \'name\' each domino by using its 2 sides, lower number first (doubles are ok too)... Then the 28 dominoes are:\r\n\r\n(0,0) (0,1) (0,2) (0,3) (0,4) (0,5) (0,6)\r\n(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)\r\n(2,2) (2,3) (2,4) (2,5) (2,6)\r\n(3,3) (3,4) (3,5) (3,6)\r\n(4,4) (4,5) (4,6)\r\n(5,5) (5,6)\r\n(6,6)\r\n\r\nWe can then draw a grid 28x28 showing the intersections of the first domino with the second domino.... (the diagonal line down the center is thrown away, because we can\'t pull the same domino twice).\r\n\r\nOkay, now, for simplicity (longer, but easier, IMHO, to understand) let us make four of these grids:\r\n
\r\n\r\nGrid 1\r\nThe possible dominos to be seen:\r\n\r\n(2,2)(1,1) (2,3)(1,1) (2,4)(1,1) (2,5)(1,1) (2,6)(1,1)\r\n(2,2)(1,2) (2,3)(1,2) (2,4)(1,2) (2,5)(1,2) (2,6)(1,2)\r\n(2,2)(1,3) (2,3)(1,3) (2,4)(1,3) (2,5)(1,3) (2,6)(1,3)\r\n(2,2)(1,4) (2,3)(1,4) (2,4)(1,4) (2,5)(1,4) (2,6)(1,4)\r\n(2,2)(1,5) (2,3)(1,5) (2,4)(1,5) (2,5)(1,5) (2,6)(1,5)\r\n(2,2)(1,6) (2,3)(1,6) (2,4)(1,6) (2,5)(1,6) (2,6)(1,6)\r\n\r\n(1,1)(2,2) (1,2)(2,2) (1,3)(2,2) (1,4)(2,2) (1,5)(2,2) (1,6)(2,2)\r\n(1,1)(2,3) (1,2)(2,3) (1,3)(2,3) (1,4)(2,3) (1,5)(2,3) (1,6)(2,3)\r\n(1,1)(2,4) (1,2)(2,4) (1,3)(2,4) (1,4)(2,4) (1,5)(2,4) (1,6)(2,4)\r\n(1,1)(2,5) (1,2)(2,5) (1,3)(2,5) (1,4)(2,5) (1,5)(2,5) (1,6)(2,5)\r\n(1,1)(2,6) (1,2)(2,6) (1,3)(2,6) (1,4)(2,6) (1,5)(2,6) (1,6)(2,6)\r\n\r\nOf these 60, 18 (in bold) will work.\r\n\r\n\r\n Grid 2\r\nThe possible dominos to be seen:\r\n\r\n(1,1)(0,2) (1,2)(0,2) (1,3)(0,2) (1,4)(0,2) (1,5)(0,2) (1,6)(0,2)\r\n(1,1)(1,2) (1,3)(0,2) (1,4)(0,2) (1,5)(0,2) (1,6)(0,2)\r\n(1,1)(2,2) (1,2)(2,2) (1,3)(2,2) (1,4)(2,2) (1,5)(2,2) (1,6)(2,2)\r\n(2,2)(0,1) (2,3)(0,1) (2,4)(0,1) (2,5)(0,1) (2,6)(0,1)\r\n(2,2)(1,1) (2,3)(1,1) (2,4)(1,1) (2,5)(1,1) (2,6)(1,1)\r\n\r\nOf these 27, 7 (in bold) will work.\r\n\r\n\r\nGrid 3\r\n\r\n(0,1)(2,2) (0,1)(2,3) (0,1)(2,4) (0,1)(2,5) (0,1)(2,6)\r\n(0,2)(1,1) (0,2)(1,2) (0,2)(1,3) (0,2)(1,4) (0,2)(1,5) (0,2)(1,6)\r\n(1,1)(2,2) (1,1)(2,3) (1,1)(2,4) (1,1)(2,5) (1,1)(2,6)\r\n(1,2)(1,1) (1,2)(1,3) (1,2)(1,4) (1,2)(1,5) (1,2)(1,6)\r\n(2,2)(1,1) (2,2)(1,2) (2,2)(1,3) (2,2)(1,4) (2,2)(1,5) (2,2)(1,6)\r\n\r\nOf these 27, 7 (in bold) will work.\r\n\r\n\r\nGrid 4\r\n\r\n(0,1)(0,2) (0,1)(1,2) (0,1)(2,2)\r\n(0,2)(0,1) (0,2)(1,1)\r\n(1,1)(0,2) (1,1)(1,2) (1,1)(2,2)\r\n(1,2)(0,1) (1,2)(1,1)\r\n(2,2)(0,1) (2,2)(1,1)\r\n\r\nOf these 12, 6 will work.\r\n\r\n\r\nNow.... we total the possibilities up: 60 + 27 + 27 + 12 = 126\r\nwe total the working combinations: 18 + 7 + 7 + 6 = 38\r\n\r\n38/126 = 19/63\n\nEdited on February 12, 2004, 12:18 pm',11818,0);
INSERT INTO comment VALUES (11825,1500,4507,'Penny','OAK, I think I got it :-)','2004-02-12 12:33:30',3,'Let A,B, and C be the three total nuts on the day of these sciuridae quercus queries. A>=2. B>=1. \r\nC = (B-1)*(B)*(B+1) = A*B-(A+B)\r\n\r\n(B-1)*(B)*(B+1)=A*B-(A+B)\r\n\r\n(B^2-B)*(B+1)=A*B-(A+B)\r\n\r\nB^3-B^2+B^2-B=A*B-A-B\r\n\r\nB^3=A*B-A\r\n\r\nB^3=A(B-1)\r\n\r\nA=8, B=2, C=6 is one solution. Are there others? \r\n',NULL,0);
INSERT INTO comment VALUES (11826,1270,5601,'eric','answer','2004-02-12 12:46:25',0,'allison,6,birdseed,thrush \r\nbrewer,10,suet,robin\r\nchandler,2,toast,blackbird\r\ndennis,4,bread,sparrow\r\nemery,8,crumbs,cardinal',NULL,0);
INSERT INTO comment VALUES (11827,1270,5601,'eric','put crumbs instead of cake crumbs','2004-02-12 12:50:25',0,'allison,6,birdseed,thrush\r\nbrewer,10,suet,robin\r\nchandler,2,toast,blackbird\r\ndennis,4,bread,sparrow\r\nemery,8,cake, cardinal',NULL,0);
INSERT INTO comment VALUES (11828,1438,4507,'Penny','Shocking !!! :-)','2004-02-12 12:52:08',2,'You don\'t need to have the technical knowledge required to solve problems like this. You hire people like that. \r\n\r\nIf this puzzle doesn\'t just scream \"LOOK UP THE ANSWER ON THE INTERNET !!!!!\"\r\n\r\nhttp://vlsicad.ucsd.edu/courses/ece20b/wi04/lecture/scratch/ece20b-slides4-6up.pdf (Requires Adobe Acrobat)\n\nEdited on February 12, 2004, 12:54 pm',NULL,0);
INSERT INTO comment VALUES (11829,1270,5601,'eric','read other 2 posts, theyre all right','2004-02-12 12:54:37',0,'mrs. allison,6,thrush,birdseed\r\nmrs. brewer,10,robin, suet\r\nmrs. chandler,2 blackbird,toast\r\nmrs. dennis, 4, sparrow, bread\r\nmrs. emery, 8, cardinal, cake crumbs',NULL,0);
INSERT INTO comment VALUES (11830,1500,5285,'Ady TZIDON','my solution','2004-02-12 13:02:29',3,'a=b^3/(b-1)\r\na=(b^3-1+1)/(b-1)= integer+1/(b-1)\r\nso 1/(b-1) has to be an integer\r\nhence b=2 a=8 c=6 is the only solution\r\n\r\nady',NULL,0);
INSERT INTO comment VALUES (11831,1438,3172,'SilverKnight','re: Shocking !!! :-)','2004-02-12 13:25:42',0,'I, admittedly, only scanned the pdf document you referenced, but I don\'t see the answer to this problem in there.... (Although the information in the document may help one get to the answer.)\r\n\r\nPenny, please mention where in this document the answer is.',11828,0);
INSERT INTO comment VALUES (11832,1438,4507,'Penny','re(2): Shocking !!! :-)','2004-02-12 13:53:09',0,'Right you are, SilverKnight. The answer is not in that document. I should not have stated that it was. It does contains information suitable to the nature of my post, which was \"Hints and/or Tips\". I should have made that clear.',11831,0);
INSERT INTO comment VALUES (11833,1500,2899,'Brian Wainscott','Solution','2004-02-12 14:06:16',3,'Let the number each has today be given by a, b, c respectively.\r\n\r\nB\'s statement about C tells us c=(b-1)*b*(b+1)=b^3-b\r\nA\'s statement tells us c=a*b-a-b\r\n\r\nSetting these equal we have b^3=a(b-1). Subtract 1 from each side and\r\ndivide by b-1. (If b=1 then c=0 AND c=-1 which is impossible).\r\nThis gives us b^2+b+1=a-1/(b-1). Since the left side is an integer, the\r\nright side must also be, so b=2. Solving for a and c we get:\r\n\r\na=8\r\nb=2\r\nc=6\r\n\r\n(After writing this up, I saw that Ady had posted essentially the same thing. But since I\'d gone to all that effort...perhaps the detail will enlighten someone?)\n\nEdited on February 12, 2004, 4:29 pm',NULL,0);
INSERT INTO comment VALUES (11834,1626,1301,'Charlie','re(6): solution :-)','2004-02-12 14:06:40',0,'Thank you for making the grids. I was going to but then got daunted, but that\'s about what I would have done. I would not leave you folks in limbo; at the very least I\'ll make the solution public before the problem disappears from the bottom of the home page (and of course journeymen will see it sooner).\r\n\r\nI tried to make the explanation of the randomization as explicit as possible by randomizing both the domino chosen and its orientation (vis-a-vis its visibility). That made it more explicit than the problem of Simple Coins, where one (I at least) had to assume that the narrator chose at random which coin to report about. Here we explicitly say that the end of the domino to look at is determined at random.\r\n\r\nI notice the scare quotes around \'wrong\' in regard to the previously proposed solution. A simulation program would come out with a certain percentage found. I can\'t think of a simulation program that agrees with the randomization in the puzzle that would produce the original proposed answer, except by forcing it in choosing the \"other\" side of each domino (but, anyway, that\'s not agreeing with the randomization specified). Though I didn\'t ask for simulation programs in the puzzle, they certainly are welcome in probability problems, to verify analytic solutions.',11824,0);
INSERT INTO comment VALUES (11835,1438,2716,'Federico Kereki','Classic solution','2004-02-12 14:36:18',3,'http://www.acm.org/jquest/cacm/p87-wos.pdf',NULL,0);
INSERT INTO comment VALUES (11836,1438,4507,'Penny','re: Classic solution','2004-02-12 14:50:56',1,'\"Triple Negative\" gets the \"Most Esoteric Puzzle\" prize. ',11835,0);
INSERT INTO comment VALUES (11837,1478,5601,'eric','solution','2004-02-12 16:14:56',0,'james best, 2nd, chocolatecake\r\nben jones, 1st, fruitcake\r\nvickey andrews, 4th, cheesecake\r\nnigel stevens, 3rd, spongecake',NULL,0);
INSERT INTO comment VALUES (11838,1622,2899,'Brian Wainscott','re: Out of all the responses so far ......','2004-02-12 16:42:53',0,'Perhaps geographic/linguistic region plays a part here, but I\'ve never heard of a \"quag.\" I don\'t doubt everyone, I\'ve just never heard this particular term. Then again I wouldn\'t have immediately recognized \"oleo\" either. Taxicab is a slam dunk as far as I can see...',11819,0);
INSERT INTO comment VALUES (11839,1438,1575,'DJ','Wow','2004-02-12 17:44:40',0,'The thought and effort going in to solving this problem is staggering ...',NULL,0);
INSERT INTO comment VALUES (11840,1438,4507,'Penny','re: Wow :-)','2004-02-12 17:48:46',0,'OK, DJ, I\'ll try to come up with an answer to this one. No doubt I\'ll have my usual spectacular success.',11839,0);
INSERT INTO comment VALUES (11841,1438,3172,'SilverKnight','re: Classic solution','2004-02-12 18:25:06',4,'FK (or anyone),\r\n\r\nPlease help me understand this diagram....\r\n\r\nI was looking at the figure 4 in the \"classic solution\". If one looks at the second major column of gates (from top to bottom reads: Or, Or, And, Or, And, Or, And), there is an input that is shared among three of the \'Or\'s and one \'And\'. I do not see where it is coming from.\r\n\r\nIs there an error in this diagram? Or (as is more likely) am I misunderstanding it?\r\n\r\n- SK',11835,0);
INSERT INTO comment VALUES (11842,1438,4507,'Penny','Circuits acrobatics !! (Solution)','2004-02-12 18:30:53',3,'I can just hear it now...\"You copy/paste stuff off the Internet, but you don\'t understand it\". (You have a point. I don\'t understand it fully. Doubtless the smarter flooblers will improve upon it...). \r\n\r\n(http://rec-puzzles.org/new/sol.pl/logic/inverter)\r\n\r\nSolution found at above website:\r\n\r\n\"Can a digital logic circuit with two inverters invert N independent inputs? The circuit may contain any number of AND or OR gates.\r\n\r\nSolution:\r\n\r\nIt can be shown that N inverters can invert 2^N-1 independent inputs, given an unlimited supply of AND and OR gates. The classic version of this puzzle is to invert 3 independent inputs using AND gates, OR gates, and only 2 inverters.\r\n\r\nThis is solved by:\r\n\r\nn1 = not(i1 and i2 or i1 and i3 or i2 and i3);\r\nn2 = not((i1 or i2 or i3) and n1 or i1 and i2 and i3);\r\no1 = (i2 or i3 or n2) and n1 or i2 and i3 and n2;\r\no2 = (i1 or i3 or n2) and n1 or i1 and i3 and n2;\r\no3 = (i1 or i2 or n2) and n1 or i1 and i2 and n2;\r\n\r\ni1, i2, and i3 are the inputs, n1 and n2 are the inverted signals, and o1, o2, and o3 are the outputs. \"and\" has higher precedence than \"or\".\r\n\r\nSo, start with N inverters. Replace 3 of them with 2.\r\nKeep doing that until you\'re down to 2 inverters.\r\n\r\nI was skeptical at first, because such a design requires so much feedback that I was sure the system would oscillate when switching between two particular states. But after writing a program to test every possible state \r\nchange (32^2), it appears that this system settles after a maximum of 3 feedback logic iterations. I did not include gate delays in the simulation, however, which could increase the number of iterations before the system\r\nsettles.\r\n\r\nIn any case, it appears that the world needs only 2 inverters! :-) \"\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\n\nEdited on February 13, 2004, 5:45 am',NULL,0);
INSERT INTO comment VALUES (11843,1500,4374,'Richard','re: Solution, being technical','2004-02-12 19:32:58',0,'Just being technical: a=b=c=0 also solves the equations even though nobody has seen fit to rule it out -- it is clearly ruled out, however, by A\'s statement and also by B\'s statement.',11833,0);
INSERT INTO comment VALUES (11844,1622,4507,'Penny','re(2): Out of all the responses so far ......','2004-02-12 20:58:37',0,'Right out of the Merriam-Webster online dictionary:\r\n\r\nMain Entry: quag\r\nPronunciation: \'kwag, \'kwäg\r\nFunction: noun\r\nEtymology: origin unknown\r\nDate: 1589\r\n: MARSH, BOG \r\n',11838,0);
INSERT INTO comment VALUES (11845,1438,3172,'SilverKnight','re: Circuits acrobatics !! (Solution)','2004-02-13 01:53:40',0,'Why not post the program you wrote to test every possible state change?',11842,0);
INSERT INTO comment VALUES (11846,1438,4507,'Penny','re(2): Circuits acrobatics !! (Solution)','2004-02-13 05:36:32',0,'That program was written by the author of the website solution that I copy/pasted. I just went back and edited that post to make that clearer.\r\n\r\nSorry. \n\nEdited on February 13, 2004, 5:46 am',11845,0);
INSERT INTO comment VALUES (11847,1390,5610,'Alan Berris','re: the real solution','2004-02-13 08:00:21',0,'I believe Penny is absolutely correct.\r\nSorry Dan but domestic cats rarely kill for food, it\'s usually for fun.',NULL,0);
INSERT INTO comment VALUES (11848,1623,4068,'Bruno','1, 2, or 3 ?','2004-02-13 10:48:22',0,'I\'d say #3, because he was the only one essential to save her life.\r\n\r\nThey could have found where she lives without the help of the mirror, and they could have traveled by car, plane, train, etc.',NULL,0);
INSERT INTO comment VALUES (11849,1623,5391,'York','I think?','2004-02-13 10:54:24',3,'The wizard. He was the \"man who saved his daughter\". He should get to marry her.',NULL,0);
INSERT INTO comment VALUES (11850,1438,1301,'Charlie','re: Circuits acrobatics !! (Solution)-- does not scale up.','2004-02-13 11:21:31',0,'After composing what I show below, I noticed on the original post copied from the internet, that the description says:\r\n\"N inverters can invert 2^N-1 independent inputs\"\r\n\r\nSubstitute N=2, and that says that 2 inverters can invert 3 independent inputs. In the below, I was trying to invert 4 independent inputs. According to the quoted source, this is not part of the possibility, though the current puzzle asks us to let 2 inverters work for an arbitrarily large number of bit streams.\r\n\r\n\r\nThe following program works fine as given for three inputs and three outputs:\r\nCLS\r\nFOR i1 = 0 TO -1 STEP -1\r\n FOR i2 = 0 TO -1 STEP -1\r\n FOR i3 = 0 TO -1 STEP -1\r\n n1 = NOT (i1 AND i2 OR i1 AND i3 OR i2 AND i3)\r\n n2 = NOT ((i1 OR i2 OR i3) AND n1 OR i1 AND i2 AND i3)\r\n o1 = (i2 OR i3 OR n2) AND n1 OR i2 AND i3 AND n2\r\n o2 = (i1 OR i3 OR n2) AND n1 OR i1 AND i3 AND n2\r\n o3 = (i1 OR i2 OR n2) AND n1 OR i1 AND i2 AND n2\r\n PRINT i1, i2, i3\r\n PRINT o1, o2, o3\r\n PRINT\r\n NEXT\r\n NEXT\r\nNEXT\r\n\r\nThe programming language uses -1 for true (on) and 0 for false (off). The results come out fine:\r\n\r\n 0 0 0\r\n-1 -1 -1\r\n\r\n 0 0 -1\r\n-1 -1 0\r\n\r\n 0 -1 0\r\n-1 0 -1\r\n\r\n 0 -1 -1\r\n-1 0 0\r\n\r\n-1 0 0\r\n 0 -1 -1\r\n\r\n-1 0 -1\r\n 0 -1 0\r\n\r\n-1 -1 0\r\n 0 0 -1\r\n\r\n-1 -1 -1\r\n 0 0 0\r\n
\r\nwhere the input line is above the output line.\r\n\r\nIn my first attempt to scale this up to four inputs and outputs, I assumed that all possible pairwise ANDed inputs were to be ORed together for negation in n1, and in n2 there\'d be an ORing of all the inputs as well as an ANDing:\r\n\r\nCLS\r\nFOR i1 = 0 TO -1 STEP -1\r\n FOR i2 = 0 TO -1 STEP -1\r\n FOR i3 = 0 TO -1 STEP -1\r\n FOR i4 = 0 TO -1 STEP -1\r\n n1 = NOT (i1 AND i2 OR i1 AND i3 OR i2 AND i3 OR i1 AND i4 OR i2 AND i4 OR i3 AND i4)\r\n n2 = NOT ((i1 OR i2 OR i3 OR i4) AND n1 OR i1 AND i2 AND i3 AND i4)\r\n o1 = (i2 OR i3 OR i4 OR n2) AND n1 OR i2 AND i3 AND i4 AND n2\r\n o2 = (i1 OR i3 OR i4 OR n2) AND n1 OR i1 AND i3 AND i4 AND n2\r\n o3 = (i1 OR i2 OR i4 OR n2) AND n1 OR i1 AND i2 AND i4 AND n2\r\n o4 = (i1 OR i2 OR i3 OR n2) AND n1 OR i1 AND i2 AND i3 AND n2\r\n PRINT i1, i2, i3, i4\r\n PRINT o1, o2, o3, o4\r\n PRINT\r\n NEXT\r\n NEXT\r\n NEXT\r\nNEXT\r\n\r\nThis did not work out:\r\n\r\n 0 0 0 0\r\n-1 -1 -1 -1\r\n\r\n 0 0 0 -1\r\n-1 -1 -1 0\r\n\r\n 0 0 -1 0\r\n-1 -1 0 -1\r\n\r\n 0 0 -1 -1\r\n 0 0 0 0 BAD\r\n\r\n 0 -1 0 0\r\n-1 0 -1 -1\r\n\r\n 0 -1 0 -1\r\n 0 0 0 0 BAD\r\n\r\n 0 -1 -1 0\r\n 0 0 0 0 BAD\r\n\r\n 0 -1 -1 -1\r\n-1 0 0 0 BAD\r\n\r\n-1 0 0 0\r\n 0 -1 -1 -1\r\n\r\n-1 0 0 -1\r\n 0 0 0 0 BAD\r\n\r\n-1 0 -1 0\r\n 0 0 0 0 BAD\r\n\r\n-1 0 -1 -1\r\n 0 -1 0 0\r\n\r\n-1 -1 0 0\r\n 0 0 0 0 BAD\r\n\r\n-1 -1 0 -1\r\n 0 0 -1 0\r\n\r\n-1 -1 -1 0\r\n 0 0 0 -1\r\n\r\n-1 -1 -1 -1\r\n 0 0 0 0\r\n\r\n
\r\n---------\r\n\r\nThen I tried putting all the triplets this time in making up n1, rather than pairs, figuring that this might have to scale up with the number of inputs, but this didn\'t work either:\r\n\r\nCLS\r\nFOR i1 = 0 TO -1 STEP -1\r\n FOR i2 = 0 TO -1 STEP -1\r\n FOR i3 = 0 TO -1 STEP -1\r\n FOR i4 = 0 TO -1 STEP -1\r\n n1 = NOT (i1 AND i2 AND i3 OR i1 AND i2 AND i4 OR i1 AND i3 AND i4 OR i2 AND i3 AND i4)\r\n n2 = NOT ((i1 OR i2 OR i3 OR i4) AND n1 OR i1 AND i2 AND i3 AND i4)\r\n o1 = (i2 OR i3 OR i4 OR n2) AND n1 OR i2 AND i3 AND i4 AND n2\r\n o2 = (i1 OR i3 OR i4 OR n2) AND n1 OR i1 AND i3 AND i4 AND n2\r\n o3 = (i1 OR i2 OR i4 OR n2) AND n1 OR i1 AND i2 AND i4 AND n2\r\n o4 = (i1 OR i2 OR i3 OR n2) AND n1 OR i1 AND i2 AND i3 AND n2\r\n PRINT i1, i2, i3, i4\r\n PRINT o1, o2, o3, o4\r\n PRINT\r\n NEXT\r\n NEXT\r\n NEXT\r\nNEXT\r\n\r\n\r\n 0 0 0 0\r\n-1 -1 -1 -1\r\n\r\n 0 0 0 -1\r\n-1 -1 -1 0\r\n\r\n 0 0 -1 0\r\n-1 -1 0 -1\r\n\r\n 0 0 -1 -1\r\n-1 -1 -1 -1\r\n\r\n 0 -1 0 0\r\n-1 0 -1 -1\r\n\r\n 0 -1 0 -1\r\n-1 -1 -1 -1\r\n\r\n 0 -1 -1 0\r\n-1 -1 -1 -1\r\n\r\n 0 -1 -1 -1\r\n-1 0 0 0\r\n\r\n-1 0 0 0\r\n 0 -1 -1 -1\r\n\r\n-1 0 0 -1\r\n-1 -1 -1 -1\r\n\r\n-1 0 -1 0\r\n-1 -1 -1 -1\r\n\r\n-1 0 -1 -1\r\n 0 -1 0 0\r\n\r\n-1 -1 0 0\r\n-1 -1 -1 -1\r\n\r\n-1 -1 0 -1\r\n 0 0 -1 0\r\n\r\n-1 -1 -1 0\r\n 0 0 0 -1\r\n\r\n-1 -1 -1 -1\r\n 0 0 0 0\r\n\r\n
\r\n-------\r\nSo we still lack a general way of doing this for more than three inputs/outputs.\r\n\n\nEdited on February 13, 2004, 11:26 am',11842,0);
INSERT INTO comment VALUES (11852,1623,4507,'Penny','Solution','2004-02-13 11:32:31',3,'The king had her marry the guy with the horse.\r\n\r\nExplanation:\r\n\r\nThe king thought: \"She might get sick again. The guy with the apple will not be much help; she ate his apple -- it\'s gone. The guy with the mirror? He won\'t be much help either. They\'ll be living together, so he\'ll know where she is; he won\'t need to look in that mirror except to shave in the morning. But that horse will come in handy to get her quickly to the best clinic anywhere in the world.\"\r\n\r\n(btw, York, that wizard is dead).',NULL,0);
INSERT INTO comment VALUES (11853,1623,5391,'York','re: Solution','2004-02-13 12:20:26',0,'Aren\'t you assumeing that the wizard is dead? The problem never says this. The problem reads \"A wizard left each of his three sons a gift before he died.\" This is of course in past tence but so is the rest of the story. So, the wizard gives his sons their gifts, the action of the story takes place, the king gives his daughter to the wizard, and he dies on their wedding night. This is my reasoning. What do you think?',11852,0);
INSERT INTO comment VALUES (11851,1623,2716,'Federico Kereki','Original answer','2004-02-13 11:25:01',3,'In the original tale (from the Arabian Nights) the king had the princes compete to see who could fire an arrow farthest away; let\'s assume this isn\'t the expected answer...\r\n307.95 180.14 127.81 99.14 81.00 68.49 59.33 52.33 46.81\r\n 307 181 127 100 81 70 57 55 45\r\n
\r\n\r\nwhere the top line shows the theoretic number based on 1023 trials, and the bottom line shows the number actually found, for the leading digits 1 through 9.\r\n\r\nFor the first 196 powers of 37, the distribution is:\r\n\r\n59.00 34.51 24.49 18.99 15.52 13.12 11.37 10.03 8.97\r\n 62 31 27 18 17 15 8 8 10\r\n
\r\n------------\r\nI\'ll leave to others to do Chi-square tests to see the goodness of fit, but it looks good to me.\r\n\r\nAs specifically applied to powers of given numbers, the distribution law (which also applies to not just the leftmost single digit, but the leftmost n digits) depends on the property of the logarithm of the base number being not only irrational, but normal. (A description of that is at http://mathworld.wolfram.com/NormalNumber.html).\r\n\r\nThe logarithm of a power of a number is the logarithm of that number multiplied by the power. Here are the common logarithms of the first few powers of 2:\r\n\r\n 1 0.301029995663981195213738894724492\r\n 2 0.602059991327962390427477789448986\r\n 3 0.903089986991943585641216684173479\r\n 4 1.204119982655924780854955578897972\r\n 5 1.505149978319905976068694473622465\r\n 6 1.806179973983887171282433368346958\r\n 7 2.107209969647868366496172263071451\r\n 8 2.408239965311849561709911157795945\r\n 9 2.709269960975830756923650052520438\r\n 10 3.010299956639811952137388947244931\r\n 11 3.311329952303793147351127841969424\r\n 12 3.612359947967774342564866736693917\r\n 13 3.91338994363175553777860563141841\r\n 14 4.214419939295736732992344526142904\r\n 15 4.515449934959717928206083420867397\r\n 16 4.81647993062369912341982231559189\r\n 17 5.117509926287680318633561210316383\r\n 18 5.418539921951661513847300105040876\r\n 19 5.719569917615642709061038999765369\r\n 20 6.020599913279623904274777894489862\r\n 21 6.321629908943605099488516789214356\r\n 22 6.622659904607586294702255683938849\r\n 23 6.923689900271567489915994578663342\r\n 24 7.224719895935548685129733473387835\r\n 25 7.525749891599529880343472368112328\r\n 26 7.826779887263511075557211262836821\r\n 27 8.127809882927492270770950157561315\r\n 28 8.428839878591473465984689052285808\r\n 29 8.729869874255454661198427947010301\r\n 30 9.030899869919435856412166841734794\r\n
\r\n----\r\nWell actually, these are only approximations to numbers that go on forever.\r\n\r\nSeeking, say, a 9 as the leading digit of the power is equivalent to asking that the mantissa (that\'s the part to the right of the decimal in the logarithm), be greater than or equal to .95424250943932487459005580651023....\r\n\r\nIf the common logarithm of 2 is normal, rather than contrived so that when you multiply by various integers you get an uneven distribution of numbers after the decimal, you will be getting the equivalent of Benford\'s Law. In fact, the multiplication process may make even such contriving impossible, and make it not even necessary for the log(2) to be normal. I\'ll leave that for someone else to show, if it\'s true.\r\n\r\nBut this applies to sets of leading digits as well as single digits. For a power of 24 to begin 937, the mantissa of its log should be between log(9.37) and log(9.38) (again, common logarithms), which is, between .971739590887778263027576732122158 and .972202838379064460075086782543197. Doing the arithmetic, about 1 out of 2159 powers of 24 (or any number other than a power of 10) should begin 937.\r\n\r\nThus this UBASIC program finds powers of 24 that start with 937 if they are below 24^80000:\r\n\r\n 5 point 7\r\n 10 A=log(9.38)/log(10)\r\n 20 B=log(9.37)/log(10)\r\n 40 I=1:Lps=log(24)/log(10):Lp2=Lps\r\n 50 for I=2 to 80000\r\n 60 Lp2=Lp2+Lps\r\n 70 Mant=Lp2-int(Lp2)\r\n 80 if Mant<A and Mant>B then print I,Lp2,using(1,15),10^Mant:HCtr=HCtr+1\r\n 90 next\r\n100 print HCtr\r\n
\r\n--------\r\nIt finds the following:\r\n\r\n8198 11314.971759551746176031333127739615413 9.370430669854714\r\n9997 13797.971783390925411293637140523656415 9.370945043204185\r\n11796 16280.971807230104646555941153307697416 9.371459444789278\r\n13595 18763.971831069283881818245166091738418 9.371973874611544\r\n15394 21246.971854908463117080549178875779419 9.372488332672533\r\n17193 23729.97187874764235234285319165982042 9.373002818973794\r\n18992 26212.971902586821587605157204443861422 9.373517333516877\r\n20791 28695.971926426000822867461217227902423 9.374031876303334\r\n22590 31178.971950265180058129765230011943425 9.374546447334714\r\n24389 33661.971974104359293392069242795984426 9.375061046612568\r\n26188 36144.971997943538528654373255580025427 9.375575674138447\r\n27987 38627.972021782717763916677268364066429 9.376090329913900\r\n29786 41110.97204562189699917898128114810743 9.376605013940479\r\n31585 43593.972069461076234441285293932148431 9.377119726219735\r\n33384 46076.972093300255469703589306716189433 9.377634466753218\r\n35183 48559.972117139434704965893319500230434 9.378149235542480\r\n36982 51042.972140978613940228197332284271436 9.378664032589071\r\n38781 53525.972164817793175490501345068312437 9.379178857894542\r\n40580 56008.972188656972410752805357852353438 9.379693711460445\r\n49383 68158.971749444240230660566460986268355 9.370212590681410\r\n51182 70641.971773283419465922870473770309357 9.370726952059808\r\n52981 73124.971797122598701185174486554350358 9.371241341673171\r\n54780 75607.971820961777936447478499338391359 9.371755759523049\r\n56579 78090.971844800957171709782512122432361 9.372270205610992\r\n58378 80573.971868640136406972086524906473362 9.372784679938551\r\n60177 83056.971892479315642234390537690514364 9.373299182507275\r\n61976 85539.971916318494877496694550474555365 9.373813713318715\r\n63775 88022.971940157674112758998563258596366 9.374328272374421\r\n65574 90505.971963996853348021302576042637368 9.374842859675943\r\n67373 92988.971987836032583283606588826678369 9.375357475224833\r\n69172 95471.972011675211818545910601610719371 9.375872119022639\r\n70971 97954.972035514391053808214614394760372 9.376386791070915\r\n72770 100437.972059353570289070518627178801373 9.376901491371209\r\n74569 102920.972083192749524332822639962842375 9.377416219925073\r\n76368 105403.972107031928759595126652746883376 9.377930976734058\r\n78167 107886.972130871107994857430665530924378 9.378445761799714\r\n79966 110369.972154710287230119734678314965379 9.378960575123594\r\n37\r\n
\r\n------\r\nIt shows i, common log(24^i) (to a limited accuracy), and the antilog of the mantissa of that logarithm. At the end it shows that 37 numbers satisfying the criterion have been found in the 80000 powers of 24. That\'s about 1 in 2162, close to the 1 in 2159 expected on average.\r\n\r\nThe purpose of the antilog of the mantissa of the logarithm is to show the first several digits of the power. Don\'t trust the last one as is could be rounded up based on the subsequent digit (nor trust the next-to-last if the last is a zero, etc.). \r\n\r\nAn interesting note is the recurrence of powers at an interval of 1799, due to the first five digits of 24^1799 being \"10000\". The error does build up, and there is one \"correction\" power of 8803 (between 40580 and 49383) which power of 24 begins \"998989\". It was such a \"gap\" at the beginning of the run that made me extend the search first to 8,000 and then to 80,000 powers of 24. This could be considered a lack of normality in the log of 24--I\'m not sure--but as seen here, it doesn\'t affect the overall distribution in the long run.\r\n\r\nBut in any event, this gives us a clue to the proof that all sets of beginning digits will eventually be reached. In order for that not to happen, the mantissas would have to constantly cycle in a limited set, repeating every so often. But in order for that to happen, some power of the number in question must also be a power of 10. That is, say in the example of the preceding paragraph, if the match of mantissas every 1799 powers of 24 had been exact, that would have meant that 24^1799 was a power of 10. But that\'s impossible, as 24 is not a power of ten and is an integer and therefore not a power of a root of 10. Thus, for any integer other than powers of 10, the mantissas of the logarithms of its powers must increase (or decrease) up to a certain point, and then cycle through the unit length at a different offset each time, and thus eventually approaching any point within the unit line to any desired degree of accuracy.\n\nEdited on February 15, 2004, 11:05 am',NULL,0);
INSERT INTO comment VALUES (11897,17,1,'levik','dope','2004-02-15 10:54:16',0,'dope\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (11898,1623,4507,'Penny','re: sandra','2004-02-15 11:57:42',0,'The puzzle states: \"Then the third son took his apple to the princess, who ate it and recovered full health instantly.\" \r\n\r\nSo she ate the entire apple.\r\n\r\nAs for the seeds, she might suddenly came down with an acute illness before those seeds had a chance to grow into apple trees. \r\n',11883,0);
INSERT INTO comment VALUES (11900,1453,4507,'Penny','re: Solution','2004-02-15 13:01:34',4,'What\'s the connection to the title of the puzzle? \n\nEdited on February 15, 2004, 1:01 pm',11892,0);
INSERT INTO comment VALUES (11901,68,5636,'carolyn','solution','2004-02-15 13:37:19',0,'incredibly easy. took me 2 seconds to figure out. but i think in words, not in numbers. \r\nthey\'re alphabetical',NULL,0);
INSERT INTO comment VALUES (11902,1453,1301,'Charlie','re(2): Solution','2004-02-15 15:18:08',0,'The title \"West Side\" is a reference to the fact that the West usually appears to the left on a map, and the questions and solution refer to the leftmost digit or digits in various powers of numbers.',11900,0);
INSERT INTO comment VALUES (11903,1623,5628,'sandra','penny\'s response','2004-02-15 18:30:27',0,'But these were \'magic\' seeds...from the same line that Jack\'s seeds came from and we all know how fast his grew.',11898,0);
INSERT INTO comment VALUES (11904,1469,3558,'Tristan','re: GOT IT !!!!!!!!!','2004-02-15 19:15:22',0,'So then it seems there are multiple solutions, because the number in the blank could be anything that is 14 mod 26. I also wonder what would have made us think the answer is 84.',11891,0);
INSERT INTO comment VALUES (11905,1623,5635,'hywnchika','Lucky Man','2004-02-15 19:17:19',0,'The guy who spread the rumor married the princess!',NULL,0);
INSERT INTO comment VALUES (11906,1445,5635,'hywnchika','DISNEY???','2004-02-15 19:18:12',0,'It could be snow white',NULL,0);
INSERT INTO comment VALUES (11907,1547,5635,'hywnchika','No Subject','2004-02-15 19:18:48',0,'S-mile-S',NULL,0);
INSERT INTO comment VALUES (11908,1509,5635,'hywnchika','No Subject','2004-02-15 19:19:57',0,'Because it was leap year, the snail got out on March 12',NULL,0);
INSERT INTO comment VALUES (11909,1623,3558,'Tristan','life-saving','2004-02-15 19:24:29',0,'Would the daughter marry the one who immediately saved her life, or the one who set up a chain reaction that eventually led to her life being saved? The latter certainly wasn\'t any of those brothers, and the king, \"intended to let one of them marry the princess.\" So therefore, the son who had an apple marries the princess.\r\n\r\nThat was sure a greedy princess to eat up the whole apple which instead could have been used to grow panaceas for all diseases in the world. It was also greedy for that son to give it to her.',NULL,0);
INSERT INTO comment VALUES (11910,1469,1626,'Gamer','Interesting Idea:','2004-02-15 19:50:45',0,'That\'s too much work in my opinion for a 3/5 problem, and it\'s not the solution I had intended, but you have it on the right track. 3=R is there twice because it appears in the original message twice.',NULL,0);
INSERT INTO comment VALUES (11911,1509,5641,'jessica','?','2004-02-15 20:18:02',0,'march 13..if i calculated right?',NULL,0);
INSERT INTO comment VALUES (11912,543,5641,'Bonzai','No Subject','2004-02-15 20:21:24',0,'eggs',NULL,0);
INSERT INTO comment VALUES (11913,859,5641,'Bonzai','No Subject','2004-02-15 20:24:35',0,'time..that ones easy',NULL,0);
INSERT INTO comment VALUES (11914,467,5641,'Bonzai','0_0','2004-02-15 20:28:23',0,'A man. as a baby he crawls. Ashe ages he stands upright and walks and as he gets older he is assited by a cane (third leg)',NULL,0);
INSERT INTO comment VALUES (11915,360,5641,'Bonzai','0_0','2004-02-15 20:29:02',0,'Nothing',NULL,0);
INSERT INTO comment VALUES (11916,315,5641,'Bonzai','0_0','2004-02-15 20:32:22',0,'he\'s looking at a picture of himself?',NULL,0);
INSERT INTO comment VALUES (11917,1623,4507,'Penny','re: Lucky Man','2004-02-15 21:22:59',0,'hywnchika wrote: \"The guy who spread the rumor married the princess!\"\r\n\r\nWhat ? The princess married Matt Drudge ?!?! ',11905,0);
INSERT INTO comment VALUES (11918,1300,5528,'shawn','My Solution','2004-02-15 22:19:54',3,'The formula for number of diagonals in a polygon is\r\nn(n-3)/2 where n is the number of sides.\r\nSince here, we are given the number of diagonals,\r\nn(n-3)/2=1325\r\nn*n - 3n = 2650\r\nn*n - 3n - 2650 = 0,\r\nwe get n as 53. Hence the number of sides is 53, and since the number of sides = number of vertices, the number of vertices is 53.\r\nThanks\r\n',NULL,0);
INSERT INTO comment VALUES (11919,1469,4507,'Penny','re: Interesting Idea:','2004-02-16 06:32:58',4,'Gamer: \"...it\'s not the solution I had intended...\"\r\n\r\nWell, I had a feeling that \"DRIERS\" is not a message that the CIA would want to encrypt. But it is still interesting that DRIERS was the only legitimate word that came up. What are the odds that out of 26 random 6 letter combinations of the form 123_24, there would be one and only one valid word ? \n\nEdited on February 16, 2004, 6:39 am',11910,0);
INSERT INTO comment VALUES (11920,1453,4670,'e.g.','Initial numbers','2004-02-16 08:07:16',3,'If A^B starts with N, then there exists K so that Nx10^K<=A^B<(N+1)x10^K. Taking decimal logarithms, K+log(N)<=Bxlog(A)\r\ns# zone zone 4 zone 3 zone 2 zone 1 total on brush\r\n 1 2 0.25000000 0.37500000 0.00000000 0.37500000 0.00000000\r\n 2 4 0.00000000 0.62500000 0.00000000 0.37500000 0.00000000\r\n 3 3 0.31250000 0.00000000 0.31250000 0.37500000 0.00000000\r\n 4 2 0.31250000 0.15625000 0.00000000 0.53125000 0.00000000\r\n 5 1 0.31250000 0.15625000 0.26562500 0.00000000 0.26562500\r\n 6 4 0.00000000 0.46875000 0.26562500 0.00000000 0.26562500\r\n 7 3 0.23437500 0.00000000 0.50000000 0.00000000 0.26562500\r\n 8 2 0.23437500 0.25000000 0.00000000 0.25000000 0.26562500\r\n 9 1 0.23437500 0.25000000 0.12500000 0.00000000 0.39062500\r\n10 4 0.00000000 0.48437500 0.12500000 0.00000000 0.39062500\r\n11 3 0.24218750 0.00000000 0.36718750 0.00000000 0.39062500\r\n12 2 0.24218750 0.18359375 0.00000000 0.18359375 0.39062500\r\n13 1 0.24218750 0.18359375 0.09179688 0.00000000 0.48242188\r\n14 4 0.00000000 0.42578125 0.09179688 0.00000000 0.48242188\r\n15 3 0.21289063 0.00000000 0.30468750 0.00000000 0.48242188\r\n16 2 0.21289063 0.15234375 0.00000000 0.15234375 0.48242188\r\n17 1 0.21289063 0.15234375 0.07617188 0.00000000 0.55859375\r\n18 4 0.00000000 0.36523438 0.07617188 0.00000000 0.55859375\r\n19 3 0.18261719 0.00000000 0.25878906 0.00000000 0.55859375\r\n20 2 0.18261719 0.12939453 0.00000000 0.12939453 0.55859375\r\n21 1 0.18261719 0.12939453 0.06469727 0.00000000 0.62329102\r\n22 4 0.00000000 0.31201172 0.06469727 0.00000000 0.62329102\r\n23 3 0.15600586 0.00000000 0.22070313 0.00000000 0.62329102\r\n24 2 0.15600586 0.11035156 0.00000000 0.11035156 0.62329102\r\n25 1 0.15600586 0.11035156 0.05517578 0.00000000 0.67846680\r\n26 4 0.00000000 0.26635742 0.05517578 0.00000000 0.67846680\r\n27 3 0.13317871 0.00000000 0.18835449 0.00000000 0.67846680\r\n28 2 0.13317871 0.09417725 0.00000000 0.09417725 0.67846680\r\n29 1 0.13317871 0.09417725 0.04708862 0.00000000 0.72555542\r\n30 4 0.00000000 0.22735596 0.04708862 0.00000000 0.72555542\r\n31 3 0.11367798 0.00000000 0.16076660 0.00000000 0.72555542\r\n32 2 0.11367798 0.08038330 0.00000000 0.08038330 0.72555542\r\n33 1 0.11367798 0.08038330 0.04019165 0.00000000 0.76574707\r\n34 4 0.00000000 0.19406128 0.04019165 0.00000000 0.76574707\r\n35 3 0.09703064 0.00000000 0.13722229 0.00000000 0.76574707\r\n36 2 0.09703064 0.06861115 0.00000000 0.06861115 0.76574707\r\n37 1 0.09703064 0.06861115 0.03430557 0.00000000 0.80005264\r\n38 4 0.00000000 0.16564178 0.03430557 0.00000000 0.80005264\r\n39 3 0.08282089 0.00000000 0.11712646 0.00000000 0.80005264\r\n40 2 0.08282089 0.05856323 0.00000000 0.05856323 0.80005264\r\n41 1 0.08282089 0.05856323 0.02928162 0.00000000 0.82933426\r\n42 4 0.00000000 0.14138412 0.02928162 0.00000000 0.82933426\r\n43 3 0.07069206 0.00000000 0.09997368 0.00000000 0.82933426\r\n44 2 0.07069206 0.04998684 0.00000000 0.04998684 0.82933426\r\n45 1 0.07069206 0.04998684 0.02499342 0.00000000 0.85432768\r\n46 4 0.00000000 0.12067890 0.02499342 0.00000000 0.85432768\r\n47 3 0.06033945 0.00000000 0.08533287 0.00000000 0.85432768\r\n48 2 0.06033945 0.04266644 0.00000000 0.04266644 0.85432768\r\n49 1 0.06033945 0.04266644 0.02133322 0.00000000 0.87566090\r\n50 4 0.00000000 0.10300589 0.02133322 0.00000000 0.87566090\r\n51 3 0.05150294 0.00000000 0.07283616 0.00000000 0.87566090\r\n52 2 0.05150294 0.03641808 0.00000000 0.03641808 0.87566090\r\n53 1 0.05150294 0.03641808 0.01820904 0.00000000 0.89386994\r\n54 4 0.00000000 0.08792102 0.01820904 0.00000000 0.89386994\r\n55 3 0.04396051 0.00000000 0.06216955 0.00000000 0.89386994\r\n56 2 0.04396051 0.03108478 0.00000000 0.03108478 0.89386994\r\n57 1 0.04396051 0.03108478 0.01554239 0.00000000 0.90941232\r\n58 4 0.00000000 0.07504529 0.01554239 0.00000000 0.90941232\r\n59 3 0.03752264 0.00000000 0.05306503 0.00000000 0.90941232\r\n60 2 0.03752264 0.02653252 0.00000000 0.02653252 0.90941232\r\n61 1 0.03752264 0.02653252 0.01326626 0.00000000 0.92267858\r\n62 4 0.00000000 0.06405516 0.01326626 0.00000000 0.92267858\r\n63 3 0.03202758 0.00000000 0.04529384 0.00000000 0.92267858\r\n64 2 0.03202758 0.02264692 0.00000000 0.02264692 0.92267858\r\n65 1 0.03202758 0.02264692 0.01132346 0.00000000 0.93400204\r\n66 4 0.00000000 0.05467450 0.01132346 0.00000000 0.93400204\r\n67 3 0.02733725 0.00000000 0.03866071 0.00000000 0.93400204\r\n68 2 0.02733725 0.01933035 0.00000000 0.01933035 0.93400204\r\n69 1 0.02733725 0.01933035 0.00966518 0.00000000 0.94366722\r\n70 4 0.00000000 0.04666760 0.00966518 0.00000000 0.94366722\r\n71 3 0.02333380 0.00000000 0.03299898 0.00000000 0.94366722\r\n72 2 0.02333380 0.01649949 0.00000000 0.01649949 0.94366722\r\n73 1 0.02333380 0.01649949 0.00824974 0.00000000 0.95191696\r\n74 4 0.00000000 0.03983329 0.00824974 0.00000000 0.95191696\r\n75 3 0.01991665 0.00000000 0.02816639 0.00000000 0.95191696\r\n76 2 0.01991665 0.01408320 0.00000000 0.01408320 0.95191696\r\n77 1 0.01991665 0.01408320 0.00704160 0.00000000 0.95895856\r\n78 4 0.00000000 0.03399984 0.00704160 0.00000000 0.95895856\r\n79 3 0.01699992 0.00000000 0.02404152 0.00000000 0.95895856\r\n80 2 0.01699992 0.01202076 0.00000000 0.01202076 0.95895856\r\n81 1 0.01699992 0.01202076 0.00601038 0.00000000 0.96496894\r\n82 4 0.00000000 0.02902068 0.00601038 0.00000000 0.96496894\r\n83 3 0.01451034 0.00000000 0.02052072 0.00000000 0.96496894\r\n84 2 0.01451034 0.01026036 0.00000000 0.01026036 0.96496894\r\n85 1 0.01451034 0.01026036 0.00513018 0.00000000 0.97009912\r\n 86 4 0.00000000 0.02477070 0.00513018 0.00000000 0.97009912\r\n 87 3 0.01238535 0.00000000 0.01751553 0.00000000 0.97009912\r\n 88 2 0.01238535 0.00875776 0.00000000 0.00875776 0.97009912\r\n 89 1 0.01238535 0.00875776 0.00437888 0.00000000 0.97447800\r\n 90 4 0.00000000 0.02114311 0.00437888 0.00000000 0.97447800\r\n 91 3 0.01057156 0.00000000 0.01495044 0.00000000 0.97447800\r\n 92 2 0.01057156 0.00747522 0.00000000 0.00747522 0.97447800\r\n 93 1 0.01057156 0.00747522 0.00373761 0.00000000 0.97821561\r\n 94 4 0.00000000 0.01804678 0.00373761 0.00000000 0.97821561\r\n 95 3 0.00902339 0.00000000 0.01276100 0.00000000 0.97821561\r\n 96 2 0.00902339 0.00638050 0.00000000 0.00638050 0.97821561\r\n 97 1 0.00902339 0.00638050 0.00319025 0.00000000 0.98140586\r\n 98 4 0.00000000 0.01540389 0.00319025 0.00000000 0.98140586\r\n 99 3 0.00770194 0.00000000 0.01089219 0.00000000 0.98140586\r\n100 2 0.00770194 0.00544610 0.00000000 0.00544610 0.98140586\r\n101 1 0.00770194 0.00544610 0.00272305 0.00000000 0.98412891\r\n102 4 0.00000000 0.01314804 0.00272305 0.00000000 0.98412891\r\n103 3 0.00657402 0.00000000 0.00929707 0.00000000 0.98412891\r\n104 2 0.00657402 0.00464853 0.00000000 0.00464853 0.98412891\r\n105 1 0.00657402 0.00464853 0.00232427 0.00000000 0.98645318\r\n106 4 0.00000000 0.01122255 0.00232427 0.00000000 0.98645318\r\n107 3 0.00561128 0.00000000 0.00793554 0.00000000 0.98645318\r\n108 2 0.00561128 0.00396777 0.00000000 0.00396777 0.98645318\r\n109 1 0.00561128 0.00396777 0.00198389 0.00000000 0.98843706\r\n110 4 0.00000000 0.00957905 0.00198389 0.00000000 0.98843706\r\n111 3 0.00478952 0.00000000 0.00677341 0.00000000 0.98843706\r\n112 2 0.00478952 0.00338671 0.00000000 0.00338671 0.98843706\r\n113 1 0.00478952 0.00338671 0.00169335 0.00000000 0.99013042\r\n
\r\n----\r\nThis is fewer squeezes than starting at zone 4 initially, which takes 116 squeezes.',NULL,0);
INSERT INTO comment VALUES (11952,315,4507,'Penny','Solution','2004-02-17 08:51:34',3,'Just assign symbols.\r\n\r\n\"A is the man in the picture.\r\nB is the father of A.\r\nC is my father.\r\nC is the father of B.\r\nSince I have no siblings, I am B.\r\nA is my son.\"\r\n\r\nThe man is looking at a picture of his son.',NULL,0);
INSERT INTO comment VALUES (11953,1624,5660,'Wengel','Solution','2004-02-17 10:54:36',0,'hand 1, 11 - 3min\r\nhand 2, 10 - 6min\r\nhand 3, 6 - 4min\r\nand it took exactly one hour',NULL,0);
INSERT INTO comment VALUES (11954,1624,1301,'Charlie','solution','2004-02-17 11:46:54',3,'The 3-minute, 4-minute and 6-minute hands advance the following number of number positions each minute:\r\n\r\n0 0 0\r\n4 3 2\r\n8 6 4\r\n0 9 6\r\n4 0 8\r\n8 3 10\r\n0 6 0\r\n4 9 2\r\n8 0 4\r\n0 3 6\r\n4 6 8\r\n8 9 10\r\n0 0 0\r\n
\r\n--------\r\nThen, showing all the possible initial positions of the three hands (6 permutations), we get the following. The amount of advance table above is repeated on the left, and then the six permutations of the hands appear in six major columns to the right. Within each column the subcolumns are 3-minute, 4-minute and 6-minute hands:\r\n\r\n\r\n0 0 0: 1 2 3; 1 3 2; 2 1 3; 2 3 1; 3 1 2; 3 2 1\r\n4 3 2: 5 5 5; 5 6 4; 6 4 5; 6 6 3; 7 4 4; 7 5 3\r\n8 6 4: 9 8 7; 9 9 6; 10 7 7; 10 9 5; 11 7 6; 11 8 5\r\n0 9 6: 1 11 9; 1 12 8; 2 10 9; 2 12 7; 3 10 8; 3 11 7\r\n4 0 8: 5 2 11; 5 3 10; 6 1 11; 6 3 9; 7 1 10; 7 2 9\r\n8 3 10: 9 5 1; 9 6 12; 10 4 1; 10 6 11; 11 4 12; 11 5 11\r\n0 6 0: 1 8 3; 1 9 2; 2 7 3; 2 9 1; 3 7 2; 3 8 1\r\n4 9 2: 5 11 5; 5 12 4; 6 10 5; 6 12 3; 7 10 4; 7 11 3\r\n8 0 4: 9 2 7; 9 3 6; 10 1 7; 10 3 5; 11 1 6; 11 2 5\r\n0 3 6: 1 5 9; 1 6 8; 2 4 9; 2 6 7; 3 4 8; 3 5 7\r\n4 6 8: 5 8 11; 5 9 10; 6 7 11; 6 9 9; 7 7 10; 7 8 9\r\n8 9 10: 9 11 1; 9 12 12; 10 10 1; 10 12 11; 11 10 12; 11 11 11\r\n0 0 0: 1 2 3; 1 3 2; 2 1 3; 2 3 1; 3 1 2; 3 2 1\r\n
\r\n-----------\r\nThe only column that also includes a 6, a 10 and an 11 in the same group is the column headed 2 3 1, meaning the 3-minute hand was on the 2, the 4-minute hand was on the 3 and the 6-minute hand was on the 1. After 5 minutes the 3-minute hand was on the 10, the 4-minute hand was on the 6 and the 6-minute hand was on the 11.\n\nEdited on February 17, 2004, 11:48 am',NULL,0);
INSERT INTO comment VALUES (11955,1624,5661,'Gabe','Solution','2004-02-17 13:03:22',3,'The 3-min hand moves +1/15 sec= +4/min\r\nThe 4-min hand moves +1/20 sec= +3/min\r\nThe 6-min hand moves +1/30 sec= +2/min\r\nTherefore, all hands align with a number simultaneously at 1-min intervals. \r\nIf the 3-min hand starts at 2, then it will be on 10 after 5 minutes\r\nIf the 4-min hand starts at 3, then it will be on 6 after 5 minutes\r\nIf the 6-min hand starts at 1, then it will be on 11 after 5 minutes\r\nTherefore, the solution is that the 3-min hand started on 2 and was then seen again on 10, the 4-min hand started on 3 and was then seen again on 6, and the 6-min hand started on 1 and was then seen again on 11 ',NULL,0);
INSERT INTO comment VALUES (11956,1507,5481,'John','solution','2004-02-17 13:07:12',3,'-------------7\r\n------------3 2\r\n-----------5 9 4\r\n----------6 1 0 8\r\n',NULL,0);
INSERT INTO comment VALUES (11957,1507,5481,'John','oops wrong,i forgot the bottom row!!! :(','2004-02-17 13:10:39',0,'wrong',11956,0);
INSERT INTO comment VALUES (11958,1623,5617,'jen','wait i think i know it now...','2004-02-17 18:19:25',0,'maybe she marries the one with the apple cuz he\'s the only one that cant get the gift his father keft him back\r\n\r\n...i still think its the wizard though',NULL,0);
INSERT INTO comment VALUES (11959,1628,3558,'Tristan','re(2): thoughts what is d2?','2004-02-17 18:19:40',0,'\"d2\" is a way of designating a difficulty level of 2. If you look to the right of the problem title, you will see a colored bar showing the difficulty level out of 5. It\'s not always very accurate, but we try.',11947,0);
INSERT INTO comment VALUES (11960,1581,5658,'Wendy','No Subject','2004-02-17 18:26:52',0,'Presuming the warden didn\'t lie to Alan, and he followed his instructions.....then only 2 posibilities can occur.\r\n1. \"If Charlie is to be pardoned, tell me Bob.\",\r\ntherefore Charlie lives.\r\n2. \"If I\'m to be pardoned, flip a coin and tell me Charlie or Bob.\",\r\ntherefore Alan lives.\r\nSo what it all boils down to...there is 2 men left with a chance of a pardon...therefore\r\nEACH ASSUMED CORRECTLY..1/2 CHANCE.',NULL,0);
INSERT INTO comment VALUES (11961,1514,5658,'Wendy','Solution???','2004-02-17 18:34:53',0,'O.K., I\'m going to think like a 5 yr old here. What is a triangle? ...A 3 sided figure.\r\nHow many sides (sticks) to make a triangle? ... 3\r\nChances of making a triangle with 3 sticks?...100%',NULL,0);
INSERT INTO comment VALUES (11962,1474,5658,'Wendy','Solution???','2004-02-17 18:43:44',0,'It\'s too early in the morning to think....so.\r\nTo guarantee 3 of a kind, you must draw 39 cards.\r\nNo matter how many more decks you add to the pile, you will still need 39 cards to guarantee another 3 of a kind. Therefore I am going to say ..the chances stay the same.',NULL,0);
INSERT INTO comment VALUES (11963,1623,5666,'Frank Riddle','A plausible answer','2004-02-17 18:53:25',0,'The king should borrow the mirror from the eldest son. Having done so, he should ask to see the future husband of his daughter. This is the person she should marry.',NULL,0);
INSERT INTO comment VALUES (11964,1509,5666,'Frank Riddle','A matter of math','2004-02-17 19:05:28',3,'March 12th. The snail makes a net total of 1 foot progress each day. At the end of the 27th day (which would be March 11th), the snail has slid back down so as to be 3 feet from the top of the well. The next day, he climbs up those three feet and is out of the well. He sleeps peacefully outside the well, and thus does not slide back down.',NULL,0);
INSERT INTO comment VALUES (11965,1469,1626,'Gamer','re(6): Interesting Idea:','2004-02-17 19:50:42',0,'Here\'s another hint: The letters to numbers isn\'t A=1, B=2; in fact, less than 10 letters (by my thoughts) can be translated this way.',11950,0);
INSERT INTO comment VALUES (11966,1454,3172,'SilverKnight','full solution','2004-02-17 21:28:47',3,'a = 0.205728733062
\r\nWhere:\r\na = the number of white bulls\r\nb = the number of black bulls\r\nc = the number of spotted bulls\r\nd = the number of brown bulls\r\ne = the number of white cows\r\nf = the number of black cows\r\ng = the number of spotted cows\r\nh = the number of brown cows\r\n\r\nand the numbers are the fraction of the herd that they make up (adding to 1)\r\n_______________________________________________\r\n\r\nThis problem is actually much easier than one might think at first glance.\r\n\r\nIt\'s a straight forward solution of 8 linear equations.\r\n\r\n(It is interesting to note that DJ didn\'t ask how many of each type there is in the herd; he asked what the composition is. This is because there isn\'t enough information to determine the size of the herd. Although, a related question might be... what is the minimum size of the herd?)\r\n\r\nIf is first key to realize that the second paragraph (about the bulls) refers to only the bulls... whereas, the third paragraph (about the cows) refers to the cattle referring to the bulls and cows.\r\n\r\nIf we assign the eight letters as described above. Then we need 8 equations to solve them all. The seven that DJ gives us are:\r\n\r\nabout the bulls\r\nA = (1/2 + 1/3)B + D\r\nB = (1/4 + 1/5)C + D\r\nC = (1/6 + 1/7)A + D\r\n\r\nabout the cows\r\nE = (1/3 + 1/4)(B + F)\r\nF = (1/4 + 1/5)(C + G)\r\nG = (1/5 + 1/6)(D + H)\r\nH = (1/6 + 1/7)(A + E)\r\n\r\nimplied by question: must add up to one\r\nA + B + C + D + E + F + G + H = 1\r\n\r\nAt this point, you have 8 equations and 8 unknowns... have at it!\r\n\r\n(Okay.. you may find it a bit tedious... so I suggest you do what I did...)\r\n\r\nNow solve by using matrices:\r\n\r\n
b = 0.148058144818
c = 0.146024886899
d = 0.082346945713
e = 0.143014314093
f = 0.097109250770
g = 0.069773448145
h = 0.107944276500 6 -5 0 -6 0 0 0 0 0
\r\nThis is an equivalent matrix for the system of equations above, and if you solve it, you\'ll find the answers above. I used, everyone\'s favorite tool... EXCEL!',NULL,0);
INSERT INTO comment VALUES (11967,1623,5673,'amber','Welll....the solution might be','2004-02-18 02:38:00',0,'The solution might be to allow the son with the apple to marry his daughter because in the eyes of the king and princess he is the only one who had given somthing. The king and princess never saw the son with the mirror or the son with the horse do anything. Also the son with the apple could have used the mirror and horse without either brother realizing anything (assuming he brings them both back unharmed).',NULL,0);
INSERT INTO comment VALUES (11968,1624,5285,'Ady TZIDON','my solution -no calculators','2004-02-18 03:49:37',3,'The hands advance: 4 numbers/min....denote hand A\r\n 3 numbers/min .... B\r\n 2 numbers/min ..... C\r\n Only hand A can reach 10 by even number per minute in 2, 5, 8 , 11 etc increments of four,\r\nderived from 2+4*k=10 mod 12\r\nNow looking for the hour eleven it is either\r\n1+2*k=11 or 3+3*k=11 (all mod 12) \r\n 3+3*k=11 is impossible since only one side is divisible by three so 3+3*k=6 mod 12 is the third equation,the second being 1+2*k=11 mod 12.\r\nSo far we have identified the hands : \r\n A on 2 k=2,5,8,11,...\r\nB on 3 k=1,5,9 ,13,\r\nC on 1 k=5,11,17\r\n\r\nans; new position within 5 minutes:\r\n2+5*4= 22==>10\r\n3+5*3= 18==>6\r\n1+5*2= 11\r\nq.e.d.\r\n\r\nady',NULL,0);
INSERT INTO comment VALUES (11969,1454,5285,'Ady TZIDON','Why bother?','2004-02-18 03:56:18',4,'??Where is the challenge to solve linear equations?...\r\n\r\nady',NULL,0);
INSERT INTO comment VALUES (11970,1454,4507,'Penny','re: Why bother?','2004-02-18 04:36:50',0,'http://www.andrews.edu/~calkins/profess/cattle.htm',11969,0);
INSERT INTO comment VALUES (11971,1509,4098,'lovejoy','re: A matter of math','2004-02-18 05:19:59',0,'Problem with this answer Frank is that I tried it a couple of weeks ago and apparently it\'s not what Silverknight is looking for.',11964,0);
INSERT INTO comment VALUES (11972,702,4507,'Penny','Another answer','2004-02-18 06:13:11',3,'A closed-door meeting.\r\n\r\nWhen the meeting is open, it is closed to the public. When the meeting is closed, its proceedings are open to public scrutiny. ',NULL,0);
INSERT INTO comment VALUES (11973,1469,4830,'Jils','Idea','2004-02-18 08:50:44',1,'Mmm, letters, numbers and an equals sign - might be to do with a keyboard (computer variety)...',NULL,0);
INSERT INTO comment VALUES (11974,1509,5352,'Phil','re: Alternative Solution','2004-02-18 09:26:52',3,'I previously said \"the final answer must be 14th February 1996, he was at the bottom on the outside.\" however i neglected to include the calculations from the top of the well to the ground.\r\n\r\nthe effect of gravity is -6ft/24hrs,\r\nplus he climb under his own steam at a rate of (net)3ft/16hrs - (no movement for 8 hrs)\r\nso the time taken for him to get from the top to the bottom is:-\r\n\r\n30ft/(-6ft+-3ft) = -3.3333 days\r\n\r\nhe actually got out of the well on 10th February 1996.\r\n\r\n',11775,0);
INSERT INTO comment VALUES (11975,363,4507,'Penny','Solution','2004-02-18 09:32:35',3,'HOE. \r\n\r\nThe first guy must have had a letter in {HRPDV}. That effectively stubs TOE. The remaining possibilities are HOE,OAR,PAD,VAT. \r\n\r\nIf the real word was OAR, the first logician had an R. If the 2nd had an O, he would have been undecided between HOE and OAR; if an E, stuck between HOE and TOE. So that leaves OAR dead in the water.\r\n\r\nThe remaining possibilities are HOE, PAD and VAT.\r\n\r\nIf the real word was PAD, then the first 2 logicians had a P and a D, in either order, and the 3rd had an A. The 3rd would not be able to decide between PAD and VAT. He would have reasoned that if it was PAD, the first guy had a P and the second a D, or vice versa, so both the 1st and 2nd guys would have known that the word is PAD. If it was VAT, the first guy had a V and knew that the word is VAT, and the 2nd, holding a T, would have known that the word is VAT. So that scratches PAD.\r\n \r\nThe remaining possibilities are HOE and VAT.\r\n\r\nFor the same reason that PAD was scratched, VAT fails the acid test.\r\n\r\nThat leaves HOE. The first guy must have had an H. The 2nd and 3rd guys would have reasoned as in the preceeding paragraphs and eliminated every word except HOE. So only HOE would not have been heaved by them. \r\n',NULL,0);
INSERT INTO comment VALUES (11976,17,1,'levik','re(2): dope','2004-02-18 09:50:20',0,'Yes, it was, though I swear I thought I had
0 20 -9 -20 0 0 0 0 0
-13 0 42 -42 0 0 0 0 0
0 -7 0 0 12 -7 0 0 0
0 0 -9 0 0 20 -9 0 0
0 0 0 -11 0 0 30 -11 0
-13 0 0 0 -13 0 0 42 0
1 1 1 1 1 1 1 1 1
\r\n deleted it....
\r\n\r\n\r\n',11932,1);
INSERT INTO comment VALUES (11977,1503,1301,'Charlie','no proof, but...','2004-02-18 10:48:01',2,'
blh = 1
amt = n
round = 0
DO
round = round + 1
IF amt < blh THEN EXIT DO
amt = amt - blh
amt = amt * 2
blh = blh * 2
LOOP
PRINT n, round
NEXT
5 6
6 7
7 8
8 9
9 10
10 11
11 12
12 13
13 14
14 15
15 16
16 17
17 18
18 19
19 20
20 21
21 22
22 23
23 24
24 25
25 26
26 27
27 28
28 29
29 30
30 31
31 32
32 33
33 34
34 35
35 36
36 37
37 38
38 39
39 40
40 41
R(1)=2(R(0)-1)=2R(0)-2
R(2)=2(R(1)-2)= 2R(1)-4
R(3)=2(R(2)-4)= 2R(2)-8
...
R(n)=2(R(n-1)-2^(n-1))= 2R(n-1)-2^n
R(n)=2(2R(n-2)-2^(n-1))-2^n= 4R(n-2)-2x2^n
R(n)=4(2R(n-3)-2^(n-2))-2.2^n= 8R(n-3)-3.2^n
...
R(n)= 2^m.R(n-m) - m.2^n
200001
Consider the number 99999 (five digits) adding 21 does produce a multiple of 10, namely 100020 -- a six digit number. Reversing produces 20001, a five-digit number. Fortunately, performing the operations a second time does reduce the digits to four.
For any number of digits there are numbers that do not reduce performing the sequence once. As long as the number of digits is greater than two, however, they all do reduce on the second pass.
Two digit numbers are a tougher breed, however. In the higher numbers the \"glitch\" only occurs when all the digits before the last two are 9\'s. The ten\'s digit, however, can be as low as 4 in some cases. And this affects two-digit numbers drastically.
This is where I bogged down. Other than individually evaluating each of the 98 numbers 2-99, I can\'t think of how to prove they will all reduce.\n\nEdited on February 22, 2004, 11:55 pm',12123,0);
INSERT INTO comment VALUES (12126,1464,4507,'Penny','No Subject','2004-02-23 02:11:20',0,'
Set two: y=t;x=k;z=kt
12 = 2*2*3, then f = 2*3 = 6
gcd(6,1) = 1 \'+\'
gcd(6,2) = 2 \'=\'
gcd(6,3) = 3 \'=\'
gcd(6,4) = 2 \'=\'
gcd(6,5) = 1 \'+\'
gcd(6,6) = 6 \'=\'
6: +===+=
10 = 2*5, then f = 2*5 = 10
gcd(10,1) = 1 \'+\'
gcd(10,2) = 2 \'=\'
gcd(10,3) = 1 \'+\'
gcd(10,4) = 2 \'=\'
gcd(10,5) = 5 \'=\'
gcd(10,6) = 2 \'=\'
gcd(10,7) = 1 \'+\'
gcd(10,8) = 2 \'=\'
gcd(10,9) = 1 \'+\'
gcd(10,10) = 10 \'=\'
10: +=+===+=+=
13: ++++++++++++=
14: +=+=+===+=+=+=
15: ++=+==++==+=++=
16: +=
17: ++++++++++++++++=
18: +===+=
19: ++++++++++++++++++=
20: +=+===+=+=
x² + 6x + y² + 6y + 18 = 144.
x = (3/2)*(sqrt(17) - 1 - sqrt(14 - 2*sqrt(17))).
\r\n',NULL,1);
INSERT INTO comment VALUES (12143,1256,5757,'ParryHotter','Not an answer','2004-02-23 14:51:44',0,'
By \"the pencil is pointed uphill\", in order to have a problem we must assume this means the large end is uphill of the small end, rather than the other way around, otherwise the pencil is already in its stable position.
Whose views on quotation are fine,
Boston names Boston
and Boston names Boston
But 9 doesn\'t designate 9.\"
Set one: y=k;x=t;z=kt
Set two: y=t;x=k;z=kt
my k is your x0 in one instance and your y0 in the other.
x=x0, y=y0+b*t, z=z0+c*t; where c=b*x0
x=x0+a*t, y=y0, z=z0+c*t; where c=a*y0
the implication is that y0 and z0 are independently assignable, but this is not the case while still fitting the original surface. On the surface, z0 must equal x0 times y0. Together with your caveat that c=b*x0, your first set becomes
\r\n
\r\nGood point!
\r\n\r\n\r\n',12154,1);
INSERT INTO comment VALUES (12178,1640,5777,'Thalamus','re: Solution','2004-02-24 13:01:53',0,'Wow! I hope there\'s an easier way to produce this sequence.\r\n\r\n',12138,1);
INSERT INTO comment VALUES (12179,1626,5777,'Thalamus','cool problem!','2004-02-24 13:06:29',0,'\r\n\r\n\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12180,1642,4507,'Penny','But on the other hand....','2004-02-24 14:18:03',0,'
\r\n
\r\n5 x 6 x 7 x 8 = 1680 which IS divisible by 4... (notice that 8 = 2³ and 6 has only one 2 as a factor)\r\n\r\n',12183,1);
INSERT INTO comment VALUES (12186,99,5345,'Rawlyn','Hmm Grahams Number?','2004-02-24 16:39:43',2,'
\r\n
\r\nShape the lump of lead into a wing (airfoil) and accelerate it through a medium (e.g., air).
\r\n',12220,1);
INSERT INTO comment VALUES (12222,1655,5788,'Tempe Everson','Solution/Idea/Question','2004-02-25 22:06:49',0,'Since lead is less dense than liquid mercury, put the lump of lead in mercury-- or was it assumed that the lead would be floating in water?\r\nDensity of lead = 11.3 g/cm3\r\nDensity of mercury = 13.6 g/ml\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (12223,1655,5788,'Tempe Everson','Solution/Idea/Question','2004-02-25 22:07:19',0,'Since lead is less dense than liquid mercury, put the lump of lead in mercury-- or was it assumed that the lead would be floating in water?\r\nDensity of lead = 11.3 g/cm3\r\nDensity of mercury = 13.6 g/ml\r\n\r\n\r\n',NULL,0);
INSERT INTO comment VALUES (12224,1602,5666,'Frank Riddle','re(4): A way to do it.===> NO WAY, not quite','2004-02-25 23:42:14',0,'
\r\n',NULL,1);
INSERT INTO comment VALUES (12231,171,5757,'ParryHotter','piece o\' pie','2004-02-26 10:52:59',0,'
\r\n
\r\nThere are only 8 positions with two lies because there now must be one truth.
\r\n(9*8)/2=36 combos
\r\n
\r\nWith three lies we are down to 6 positions of freedom.
\r\n(7*6+6*5+5*4+4*3+3*2+2*1)/2=56 combos
\r\n
\r\nNow we are up to and four lies and down to 4 positions.
\r\n(1*5*4+2*4*3+3*3*3+4*2*1)/2=35 combos
\r\n
\r\nThere are 6 combos with five lies.
\r\n
\r\nTotal number of combinations is 1+10+36+56+35+6=144
\r\n
\r\nThat\'s \"one gross\" solution!
\r\n
\r\nSorry about the solution being in the title but I thought most people wouldn\'t get it until they solved it them selves. I guess I\'m saying it\'s more of a hint than a solution. Besides I couldn\'t resist. ;8^)
\r\n\n\nEdited on February 27, 2004, 5:41 pm',NULL,0);
INSERT INTO comment VALUES (12281,1565,5285,'Ady TZIDON','classic distance','2004-02-27 18:38:23',3,'ans : 5 (units)\r\nsol: f=dist^2=25-24cosA\r\nIf distance increases most rapidly so does its square.\r\ntherefore we can differentiate f ( dist^2):\r\nf\'=24sinA\r\nf\'\'=-24cosA=0\r\ncosA=0=====> A=90,270 DEGREES\r\n\r\nPythagoras he say: dist=5\r\n\r\nady',NULL,0);
INSERT INTO comment VALUES (12282,1565,3172,'SilverKnight','re: classic distance','2004-02-27 19:09:34',0,'huh? ... jeez Ady... what do you have against defining WHAT the variable is (in English) before using it? And then showing why you are setting up an equation that way...\r\n\r\nWhat you are trying to do isn\'t at all clear to me.\r\n\r\nI offer you this, this, and this as examples of clear comments.\n\nEdited on February 27, 2004, 7:17 pm',12281,0);
INSERT INTO comment VALUES (12283,1565,885,'np_rt','Analytic Solution (with no errors I hope)','2004-02-28 00:45:57',0,'
25*cos(5.5t)-24(cos(5.5t))^2=12*(sin(5.5t))^2
=12*(1-(cos(5.5t))^2) \r\n
12(cos(5.5t))^2-25*cos(5.5t)+12=0
\"The works of this learned Italian mathematician were so much above the level of mathematical knowledge even of the scientists of that time, that their influence on the mathematical literature becomes noticeable only in two centuries after his death at the end of the 15th century, when many of his theorems and problems were entered by Leonardo da Vinci\'s friend, and professor of many Italian universities, Luca Pacioli, in his works. In the beginning of the 16th century, a group of talented Italian mathematicians, Ferro, Cardano, Tartaglia, and Ferrari, used Fibonacci\'s work to arrive at the solution of cubical and biquadrate equations and so gave birth to modern algebra\".
\r\nTo keep the arch the smallest lets make the small diameter 0 forcing the large diameter to be 1.\r\n
\r\nThis means the 0 end of the pencil never moves and is the center of the arch.\r\n
\r\nThe length of the arch is 144 pi and one revolution travels 1 pi.\r\n
\r\nThe solution is 144 pi / 1 pi = 144 / 1 = 144.\r\n
\r\nP.S. Just read the other posts. I can see how the non-tangent measure of length could be more correct, However, I don\'t think thats what they were looking for.\r\n
\r\nEdited on February 28, 2004, 10:40 pm\n\nEdited on February 28, 2004, 10:54 pm',NULL,0);
INSERT INTO comment VALUES (12303,1526,5687,'Ariel','Solution1','2004-02-28 23:21:15',0,'First black and white are symetrical so i will use white to move first. The correct sequence is as follows (with annotation): \r\nMOVE \r\n1.a2-b3 \r\n\r\na4-b3 is the only other legal move and leaves only b3-a4 as a legal move so it is a dead end \r\n\r\n2.e4-b1 \r\n\r\nthe only other legal move, a3-a2, puts us in the same position as before so it can be disregarded as will all such moves. \r\n\r\n3.e2-d3 \r\nagain the only legal move \r\n4. b3-d1 \r\nditto \r\n5. b1-a2 \r\nwhite has no legal moves so black must choose between b1-a2 d3-e4 and d3-c4 either of the latter move\'s limits the movement of that bishop and the third move places a black bishop in the \"a\" file wihout limiting the moves of the other bishop. \r\n\r\n6.d3-c4 \r\nwhite still without moves. \r\nd3-e4 if futile because the a4 bishop would not be able to get off the long diagnol a4-d1 until the b1 e4 diagnol is free. so we free it now by d3-c4 \r\n\r\n7. a4-c2 \r\nwe need to clear the a4-d1 diagnol for the black bishop on c4 so one of the white bishops must go to e4. we may as well move the a4 bishop as the d1 bishop is in position to take e2 when it is free. \r\n\r\n8. c2-e4 \r\nonly legal move \r\n\r\n\r\nat this point black still can not move so white must move but his only legal move without backtracking is d1-a4 and then back to d1 which means we have reached a deadlock and there is no solution. ',NULL,0);
INSERT INTO comment VALUES (12304,1648,5843,'eleusive','easier solution','2004-02-28 23:37:55',0,'You can do a simple indirect proof here. Negate the implication, and try to prove that the assumption is no longer true. Hence, assume that (A is not B or A is not 45 degrees, or B is not 45 degrees) or C is not 90 degrees. Then you turn this into an indirect proof by cases. Standard proof procedure.',NULL,0);
INSERT INTO comment VALUES (12305,51,5687,'Ariel','POST SOLUTION TIDBIT','2004-02-28 23:47:55',0,'the 17/18 of remaining cow should have been split equally (17/54 of a cow for each) so the third son got gyped as he recieved only 6/54 of a cow whereas the second son recieved 18/54 and the first son recieved 27/54 of a cow totalling 51/54 or 17/18 \r\n\r\nconclusions.\r\n1youngest always gets the worst of everything ...horses and education\r\n2 never trust a stranger who offers to do you a favor.',NULL,0);
INSERT INTO comment VALUES (12306,47,5687,'Ariel','old problem new phrasing','2004-02-28 23:56:12',0,'this problem is the same as the old 3 prisoners are set up each wearing a hat either white or black picked from a bag of 3 black and 2 white hats.\r\nthe first two prisoners can not guess the color of their hats but the third can based on the answers of the firt two. (since neither of the first two sages can tell that they too have a mark they continue to laugh while the third realizes this and knows that only if he too had a mark would the others be laughing. but since this is based on the assumption that the other two would stop if they knew they too were marked all three should stop laughing or the assumption is false or the third sage is wiser than the other two.',NULL,0);
INSERT INTO comment VALUES (12307,421,5845,'LicKa','re:','2004-02-29 01:42:14',0,'well if u open up a manhole, u notice that there are holders for the cover so u could also do that with any other shape.\r\n',2685,0);
INSERT INTO comment VALUES (12308,1648,3750,'mohan','re(2): solution','2004-02-29 03:08:26',0,'w.r.t your comment, in a triangle, all sines are positive.',12255,0);
INSERT INTO comment VALUES (12309,1526,5833,'ThoughtProvoker','re: Solution1','2004-02-29 04:52:32',0,'Ariel wrote:
\r\n\"...which means we have reached a deadlock and there is no solution.\"
\r\n
\r\nBut didn\'t Eric, in the first comment to this problem, show that there *is* a solution to this problem?
\r\n
\r\nTP
\r\n\r\n\r\n',12303,1);
INSERT INTO comment VALUES (12310,1652,5833,'ThoughtProvoker','No Subject','2004-02-29 04:55:38',4,'This is funny!
\r\n
\r\nFederico, where did you hear this one?
\r\n',NULL,1);
INSERT INTO comment VALUES (12311,1583,5833,'ThoughtProvoker','re: Again...','2004-02-29 05:00:08',0,'so... is this it? or can it get better? What\'s the solution?\r\n\r\n',11455,1);
INSERT INTO comment VALUES (12312,1526,1301,'Charlie','re: Solution1','2004-02-29 10:14:44',0,'The problem allows successive moves by the same color. Black and white need not alternate.',12303,1);
INSERT INTO comment VALUES (12313,1623,5178,'Axorion','as a father','2004-02-29 10:36:42',0,'Being the father of a 21 year old daughter I would pick the one with the horse. The one with the apple thinks he can buy her and may trade her out for something he wants more at a later date. The one with the mirror is a playboy, still looking around. The one with the horse is the only one who has the means to get her the heck out of my house. While she is gone I will move without a forewarding address. After all he\'s got a horse, he\'ll be running around on her! ;8^)\r\n\n\nEdited on February 29, 2004, 10:51 am',NULL,0);
INSERT INTO comment VALUES (12314,1564,5285,'Ady TZIDON','JUST CONT\'EM','2004-02-29 10:37:35',3,'JUST COuNT\'EM ..... u missing in the title..\r\n\r\nANS: 2301 DIVISORS\r\n\r\nSOL: 10^40 HAS 41*41=1681 DIVISORS (2^40*5^4)\r\n.. 20^30 HAS 21*31=1891 DIVISORS\r\n\r\nTHE GCD OF THE GIVEN NUMBERS HAS 41*31=1271 DIV.\r\n\r\nANS: 1681 + 1891 - 1271= 2301 DIVISORS\r\n\r\nady\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\n\nEdited on February 29, 2004, 10:52 am',NULL,0);
INSERT INTO comment VALUES (12315,1644,3735,'Nick Hobson','Not a cube','2004-02-29 11:00:33',0,'Euler showed that the only solution of y2 - x3 = ±1 is (x,y) = (2,3), a special case of Catalan\'s Conjecture, which has recently been proved.
Using Euler\'s result, n(n+1)(n+2)(n+3) = (n2+3n+1)2 - 1 cannot be a perfect cube. However, there must be a more elementary solution!
Incidentally, Erdos and Selfridge proved that the product of any number of consecutive positive integers is never a perfect power.
20^30 = 2^60 * 5^30
\r\n\r\nNow that I\'ve covered the silly stuff, it seems to me you have 3 tires going 1 mile for a total of 3 miles on 5 tires. That means each tire gets .6 miles. If you go .4 miles then change the 2 rear tires, go .2 miles, put one of the old rear on the front, go .2 miles, put the other old rear on the front and go .2 miles you will have put .6 miles on each tire.
\r\n\r\n(in tenths)
\r\n44400
\r\n64422
\r\n66444
\r\n66666
\r\n\r\nCan anyone do it in less than 3 changes?
\r\n\n\nEdited on February 29, 2004, 11:52 am',NULL,0);
INSERT INTO comment VALUES (12318,1564,3558,'Tristan','solution','2004-02-29 12:18:43',3,'
\r\n\r\nwhile n>9
\r\n until n/10=int(n/10)
\r\n n=n+7
\r\n loop
\r\n n=~n
\r\nloop
\r\nrem n is now less than 10 and greater than 0
\r\nwhile n>1
\r\n select n
\r\n case=2, n=~(n+7+7+7+7) rem n=3
\r\n case=3, n=~(n+7) rem n=1
\r\n case=4, n=~(n+7+7+7+7+7+7+7+7) rem n=6
\r\n case=5, n=~(n+7+7+7+7+7+7+7) rem n=4
\r\n case=6, n=~(n+7+7) rem n=2
\r\n case=7, n=~(~(n+7)+7+7+7+7+7+7+7) rem n=9
\r\n case=8, n=~(n+7+7+7+7+7+7) rem n=5
\r\n case=9, n=~(n+7+7+7) rem n=3
\r\nloop
\r\nrem n is now equal to 1
\r\n',NULL,0);
INSERT INTO comment VALUES (12320,1328,1626,'Gamer','re: No Subject','2004-02-29 14:55:32',0,'Unfortunately, that answer is not as good as any other. The idea here is to come up with the best answer, not just a correct one, so putting all these into a polynomial finder isn\'t a good solution for any of these if there is a better answer.',11979,0);
INSERT INTO comment VALUES (12321,1565,5821,'joe','re: why calculus','2004-02-29 16:52:18',0,'90 degree relationship holds true only if the hour and minute hands are of the same length.',12301,0);
INSERT INTO comment VALUES (12322,1328,5285,'Ady TZIDON','re(2): No Subject ===> better, best etc att : Gamer','2004-02-29 17:59:04',1,'Gamer\r\nI beg to differ about the objectivity of the word \"better\" or \"best\". May be we could agree upon \"shorter\" or \" more esthetic ? \" ...May be not.\r\nTo continue series 1,4.... what is \"better\"?\r\n\r\na 1,4,7,10,...............arithmetic series \r\nb 1,4,16,64...............geometric\r\nc 1,4,9,16,25,............squares\r\nd 1,4,11,44,111,444.......ones on odd places,fours on even\r\ne 1,4,9,61,52,............squares inverted\r\nf 1,4,11,22,37............a(n)= 2n^2-3n+2 \r\ng 1,4,9,22,49............a(n)= n^3-5n^2+11n-6\r\nh 1,4,5,9,14,............fibo with 1,4 initialization etc\r\netc\r\nIn the above series only 2 samples were given. However I wanted to illustrate the folllowing fact: ONE CANNOT DEFINE A SERIES UNAMBIGUOUSLY BY PROVIDING SOME OF ITS MEMBERS.\r\nPlease look up SLOANE on the web and try to get definition for any series of yours( SLOANE asks for some 30 numbers!!-)\r\n\r\nI hope you agree with me.\n\nEdited on February 29, 2004, 6:00 pm',12320,0);
INSERT INTO comment VALUES (12323,1565,5178,'Axorion','re(2): why calculus','2004-02-29 18:14:12',0,'As I stated if both hands are the same length the length of the unknown segment is 0. If my methods are incorrect how was I able to come up with SQRT(7) = 2.64575? This is the same answer other posts using calculus came up with.
\r\nPosted by Dan Porter now posting as Axorion.\r\n\r\nEdited on February 29, 2004, 6:16 pm\n\nEdited on February 29, 2004, 6:20 pm',12321,0);
INSERT INTO comment VALUES (12324,24,5799,'red_sox_fan_032003','disappointed','2004-02-29 18:19:48',0,'Expected a more challenging problem this was disappointing',NULL,1);
INSERT INTO comment VALUES (12325,1628,5178,'Axorion','re: A solution with just one pair of quotation marks','2004-02-29 20:19:43',0,'Ah... Sarcasm! But is it the writers or yours Penny? Don\'t worry, ether way you\'re \"fine\". ;8^)\n\nEdited on February 29, 2004, 8:22 pm',11942,0);
INSERT INTO comment VALUES (12326,1637,5858,'Slobodan','No Subject','2004-03-01 07:55:36',0,'I think that the problem can be solved with the help of Integer programing. The object is to get 100 animals, right? The way I see it, there are two constraints: \r\n\r\n1. 8*P + 1*Ch + 80*Cw = 800\r\n(where P stands for the quantity of pigs bought, Ch marks the quantity of chicken bought, and Cw marks the number of cows bought)\r\nThe meaning of it: all of the money must be spent\r\n\r\n2. P + Ch + Cw = 100 \r\nThe meaning: The number of animals bought must be 100,\r\n\r\n3. P <= 99\r\n\r\nand the function to which the constraints apply, which I think should be:\r\n\r\nmaxZ = P + Ch + Cw\r\n(or minZ, it\'s all the same in this case).\r\n\r\nIf the problem were to be done \"on foot\" (i.e. manually), then whoever is solving it would have to go through 59 iterations (i.e. steps). I\'ve used a little software which does the needed math (and that only after the user sets the problem in the form of constraints and object function), and the solution (a unique solution, I think) is:\r\n\r\nPigs = 21, Chickens = 72, Cows = 8',NULL,0);
INSERT INTO comment VALUES (12327,1530,3275,'retiarius','Solution','2004-03-01 10:32:08',0,'Method:\r\n\r\n1.........................93\r\n 3\r\n-------------------------\r\n3..........................9\r\n\r\nAnswer:\r\n1034482758620689655172413793\n\nEdited on March 1, 2004, 10:33 am',NULL,0);
INSERT INTO comment VALUES (12328,1530,1301,'Charlie','another method--computer-assisted','2004-03-01 10:44:05',3,'
<U> 1
</U>3)3
</U>3)310
<U>3</U>
10
<U>9
</U> 1
divisor = 3
temp = 3
quot$ = \"\"
DO
q = temp \\ divisor
r = temp MOD divisor
quot$ = quot$ + LTRIM$(STR$(q))
IF q = 3 AND r = 0 THEN EXIT DO
temp = r * 10 + q
LOOP
and finds 1034482758620689655172413793
(with commas, that\'s 1,034,482,758,620,689,655,172,413,793).
---
3)310
3
---
10
9
--
11...3\r\n<U>× 3</U>\r\n31...\r\n
So, the last digit of the product must be 9 (3×3): 1...93\r\n<U>× 3</U>\r\n<U> 9</U>\r\n31...9\r\n
The next to last digit must be 7 (3×9 is 27): 1...793\r\n<U>× 3</U>\r\n 9\r\n<U> 27 </U>\r\n31...79\r\n
The third-to-last digit is 3 (the 2 carried over from 27, plus the last digit of 7×3=21): 1...3793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n<U> 21 </U>\r\n31...379\r\n
Continuing thus: 1...13793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n 21\r\n<U> 9 </U>\r\n31...1379\r\n\r\n1...413793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n 21\r\n 9\r\n<U> 3 </U>\r\n31...41379\r\n\r\n1...413793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n 21\r\n 9\r\n 3 </U>\r\n31...41379\r\n\r\n1...413793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n 21\r\n 9\r\n 3 </U>\r\n31...41379\r\n\r\n1...2413793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n 21\r\n 9\r\n 3\r\n<U> 12 </U>\r\n31...241379\r\n\r\n1...72413793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n 21\r\n 9\r\n 3\r\n 12\r\n<U> 6 </U>\r\n31...7241379\r\n\r\n1...172413793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n 21\r\n 9\r\n 3\r\n 12\r\n 6\r\n<U> 21 </U>\r\n31...17241379\r\n\r\n1...5172413793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n 21\r\n 9\r\n 3\r\n 12\r\n 6\r\n 21\r\n<U> 3 </U>\r\n31...517241379\r\n\r\n1...55172413793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n 21\r\n 9\r\n 3\r\n 12\r\n 6\r\n 21\r\n 3\r\n<U> 15 </U>\r\n31...5517241379\r\n\r\n1...655172413793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n 21\r\n 9\r\n 3\r\n 12\r\n 6\r\n 21\r\n 3\r\n 15\r\n<U> 15 </U>\r\n31...65517241379\r\n\r\n1...9655172413793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n 21\r\n 9\r\n 3\r\n 12\r\n 6\r\n 21\r\n 3\r\n 15\r\n 15\r\n<U> 18 </U>\r\n31...965517241379\r\n\r\n1...89655172413793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n 21\r\n 9\r\n 3\r\n 12\r\n 6\r\n 21\r\n 3\r\n 15\r\n 15\r\n 18\r\n<U> 27 </U>\r\n31...8965517241379\r\n\r\n1...689655172413793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n 21\r\n 9\r\n 3\r\n 12\r\n 6\r\n 21\r\n 3\r\n 15\r\n 15\r\n 18\r\n 27\r\n<U> 24 </U>\r\n31...68965517241379\r\n\r\n1...0689655172413793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n 21\r\n 9\r\n 3\r\n 12\r\n 6\r\n 21\r\n 3\r\n 15\r\n 15\r\n 18\r\n 27\r\n 24\r\n<U> 18 </U>\r\n31...068965517241379\r\n\r\n1...20689655172413793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n 21\r\n 9\r\n 3\r\n 12\r\n 6\r\n 21\r\n 3\r\n 15\r\n 15\r\n 18\r\n 27\r\n 24\r\n 18\r\n<U> 0 </U>\r\n31...2068965517241379\r\n\r\n1...620689655172413793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n 21\r\n 9\r\n 3\r\n 12\r\n 6\r\n 21\r\n 3\r\n 15\r\n 15\r\n 18\r\n 27\r\n 24\r\n 18\r\n 0\r\n<U> 6 </U>\r\n31...62068965517241379\r\n\r\n1...8620689655172413793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n 21\r\n 9\r\n 3\r\n 12\r\n 6\r\n 21\r\n 3\r\n 15\r\n 15\r\n 18\r\n 27\r\n 24\r\n 18\r\n 0\r\n 6\r\n<U> 18 </U>\r\n31...862068965517241379\r\n\r\n1...58620689655172413793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n 21\r\n 9\r\n 3\r\n 12\r\n 6\r\n 21\r\n 3\r\n 15\r\n 15\r\n 18\r\n 27\r\n 24\r\n 18\r\n 0\r\n 6\r\n 18\r\n<U> 24 </U>\r\n31...5862068965517241379\r\n\r\n1...758620689655172413793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n 21\r\n 9\r\n 3\r\n 12\r\n 6\r\n 21\r\n 3\r\n 15\r\n 15\r\n 18\r\n 27\r\n 24\r\n 18\r\n 0\r\n 6\r\n 18\r\n 24\r\n<U> 15 </U>\r\n31...75862068965517241379\r\n\r\n1...2758620689655172413793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n 21\r\n 9\r\n 3\r\n 12\r\n 6\r\n 21\r\n 3\r\n 15\r\n 15\r\n 18\r\n 27\r\n 24\r\n 18\r\n 0\r\n 6\r\n 18\r\n 24\r\n 15\r\n<U> 21 </U>\r\n31...275862068965517241379\r\n\r\n1...82758620689655172413793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n 21\r\n 9\r\n 3\r\n 12\r\n 6\r\n 21\r\n 3\r\n 15\r\n 15\r\n 18\r\n 27\r\n 24\r\n 18\r\n 0\r\n 6\r\n 18\r\n 24\r\n 15\r\n 21\r\n<U> 6 </U>\r\n31...8275862068965517241379\r\n\r\n1...482758620689655172413793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n 21\r\n 9\r\n 3\r\n 12\r\n 6\r\n 21\r\n 3\r\n 15\r\n 15\r\n 18\r\n 27\r\n 24\r\n 18\r\n 0\r\n 6\r\n 18\r\n 24\r\n 15\r\n 21\r\n 6\r\n<U> 24 </U>\r\n31...48275862068965517241379\r\n\r\n1...4482758620689655172413793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n 21\r\n 9\r\n 3\r\n 12\r\n 6\r\n 21\r\n 3\r\n 15\r\n 15\r\n 18\r\n 27\r\n 24\r\n 18\r\n 0\r\n 6\r\n 18\r\n 24\r\n 15\r\n 21\r\n 6\r\n 24\r\n<U> 12 </U>\r\n31...448275862068965517241379\r\n\r\n1...34482758620689655172413793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n 21\r\n 9\r\n 3\r\n 12\r\n 6\r\n 21\r\n 3\r\n 15\r\n 15\r\n 18\r\n 27\r\n 24\r\n 18\r\n 0\r\n 6\r\n 18\r\n 24\r\n 15\r\n 21\r\n 6\r\n 24\r\n 12\r\n<U> 12 </U>\r\n31...3448275862068965517241379\r\n\r\n1...034482758620689655172413793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n 21\r\n 9\r\n 3\r\n 12\r\n 6\r\n 21\r\n 3\r\n 15\r\n 15\r\n 18\r\n 27\r\n 24\r\n 18\r\n 0\r\n 6\r\n 18\r\n 24\r\n 15\r\n 21\r\n 6\r\n 24\r\n 12\r\n 12\r\n<U> 9 </U>\r\n31...03448275862068965517241379\r\n\r\n1...1034482758620689655172413793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n 21\r\n 9\r\n 3\r\n 12\r\n 6\r\n 21\r\n 3\r\n 15\r\n 15\r\n 18\r\n 27\r\n 24\r\n 18\r\n 0\r\n 6\r\n 18\r\n 24\r\n 15\r\n 21\r\n 6\r\n 24\r\n 12\r\n 12\r\n 9\r\n<U> 0 </U>\r\n31...103448275862068965517241379\r\n
Finally, we have a digit 1 without a carry (the other ones were actually 11). This 1 can be used as the first digit, giving the final answer: 1034482758620689655172413793\r\n<U>× 3</U>\r\n 9\r\n 27\r\n 21\r\n 9\r\n 3\r\n 12\r\n 6\r\n 21\r\n 3\r\n 15\r\n 15\r\n 18\r\n 27\r\n 24\r\n 18\r\n 0\r\n 6\r\n 18\r\n 24\r\n 15\r\n 21\r\n 6\r\n 24\r\n 12\r\n 12\r\n 9\r\n 0\r\n<U>3 </U>\r\n3103448275862068965517241379\r\n
Of course, that is just the smallest answer. If we didn\'t make that 1 be the first digit, and kept going, the whole process would just repeat itself. The next smallest number, then, would be 10344827586206896551724137931034482758620689655172413793, and so on.',NULL,1);
INSERT INTO comment VALUES (12334,1530,2716,'Federico Kereki','Standard solution','2004-03-01 12:00:48',3,'There\'s a standard way of solving this kind of \"move-to-the-beginning\" problems. Assume the solution is a number abc...3 and let X be the continued fraction 0.abc...3abc...3abc...3...
105263157894736842
18
Move the 3 , mult. by 2 .
157894736842105263
18
Move the 3 , mult. by 3 .
1034482758620689655172413793
28
Move the 4 , mult. by 2 .
210526315789473684
18
Move the 4 , mult. by 3 .
1379310344827586206896551724
28
Move the 4 , mult. by 4 .
102564
6
Move the 5 , mult. by 2 .
263157894736842105
18
Move the 5 , mult. by 3 .
1724137931034482758620689655
28
Move the 5 , mult. by 4 .
128205
6
Move the 5 , mult. by 5 .
102040816326530612244897959183673469387755
42
Move the 6 , mult. by 2 .
315789473684210526
18
Move the 6 , mult. by 3 .
2068965517241379310344827586
28
Move the 6 , mult. by 4 .
153846
6
Move the 6 , mult. by 5 .
122448979591836734693877551020408163265306
42
Move the 6 , mult. by 6 .
1016949152542372881355932203389830508474576271186440677966
58
Move the 7 , mult. by 2 .
368421052631578947
18
Move the 7 , mult. by 3 .
2413793103448275862068965517
28
Move the 7 , mult. by 4 .
179487
6
Move the 7 , mult. by 5 .
142857
6
Move the 7 , mult. by 6 .
1186440677966101694915254237288135593220338983050847457627
58
Move the 7 , mult. by 7 .
1014492753623188405797
22
Move the 8 , mult. by 2 .
421052631578947368
18
Move the 8 , mult. by 3 .
2758620689655172413793103448
28
Move the 8 , mult. by 4 .
205128
6
Move the 8 , mult. by 5 .
163265306122448979591836734693877551020408
42
Move the 8 , mult. by 6 .
1355932203389830508474576271186440677966101694915254237288
58
Move the 8 , mult. by 7 .
1159420289855072463768
22
Move the 8 , mult. by 8 .
1012658227848
13
Move the 9 , mult. by 2 .
473684210526315789
18
Move the 9 , mult. by 3 .
3103448275862068965517241379
28
Move the 9 , mult. by 4 .
230769
6
Move the 9 , mult. by 5 .
183673469387755102040816326530612244897959
42
Move the 9 , mult. by 6 .
1525423728813559322033898305084745762711864406779661016949
58
Move the 9 , mult. by 7 .
1304347826086956521739
22
Move the 9 , mult. by 8 .
1139240506329
13
Move the 9 , mult. by 9 .
10112359550561797752808988764044943820224719
44
FOR movthe = 2 TO 9
FOR multby = 2 TO movthe
ct = 0
PRINT #2, \"Move the\"; movthe; \", mult. by\"; multby; \".\"
divisor = multby
temp = movthe
quot$ = \"\"
DO
q = temp \\ divisor
r = temp MOD divisor
quot$ = quot$ + LTRIM$(STR$(q))
ct = ct + 1
IF q = movthe AND r = 0 THEN EXIT DO
temp = r * 10 + q
LOOP
PRINT #2, ct
NEXT
NEXT
\r\n
\r\nThese problems are tremendously easy when Charlie or someone else posts the solution already.
\r\n
\r\n
\r\n\r\n\r\n',12358,1);
INSERT INTO comment VALUES (12360,1661,4374,'Richard','re: solution','2004-03-02 13:10:47',0,'
\r\n\"Through S draw a parallel to BC; let T be its intersection with BC...\"
\r\n
\r\nBut there is no intersection with BC if it is parallel. And the\r\nsame goes for your parallel through Z. Do you mean \"drop a\r\nperpendicular\"?
\r\n
\r\n-SK
\r\n\r\n\r\n',12364,1);
INSERT INTO comment VALUES (12366,1632,1575,'DJ','re(2): Possible solution','2004-03-02 14:25:18',0,'
11 10
13 2
17 4
19 2
23 4
29 6
31 2
37 6
41 4
43 2
47 4
53 6
59 6
61 2
67 6
71 4
73 2
79 6
83 4
89 6
97 8
101 4
103 2
107 4
109 2
113 4
121 8
127 6
131 4
137 6
139 2
143 4
149 6
151 2
157 6
163 6
167 4
169 2
173 4
179 6
181 2
187 6
191 4
193 2
197 4
199 2
209 10
211 2
high = 11
span = 11
DIM hist(span, 5)
FOR n = 1 TO max + span
FOR i = 1 TO span - 1
FOR j = 1 TO 5
hist(i, j) = hist(i + 1, j)
NEXT
NEXT i
IF n MOD 2 = 0 THEN hist(span, 1) = 1: ELSE hist(span, 1) = 0
IF n MOD 3 = 0 THEN hist(span, 2) = 1: ELSE hist(span, 2) = 0
IF n MOD 5 = 0 THEN hist(span, 3) = 1: ELSE hist(span, 3) = 0
IF n MOD 7 = 0 THEN hist(span, 4) = 1: ELSE hist(span, 4) = 0
IF n MOD 11 = 0 THEN hist(span, 5) = 1: ELSE hist(span, 5) = 0
good = 1
IF n < span THEN
FOR i = 14 - n TO span - 1
FOR j = 1 TO 5
IF hist(i, j) = 1 AND hist(span, j) = 1 THEN good = 0
NEXT
NEXT
ELSE
FOR i = 1 TO span - 1
FOR j = 1 TO 5
IF hist(i, j) = 1 AND hist(span, j) = 1 THEN good = 0
NEXT
NEXT
END IF
IF good THEN
PRINT n, n - prevN
IF n > 1 AND n - prevN > maxdiff THEN maxdiff = n - prevN: maxAt = n
prevN = n:
END IF
NEXT n
PRINT maxdiff, maxAt /\\
',12384,1);
INSERT INTO comment VALUES (12387,1668,1575,'DJ','Poor Solution','2004-03-03 16:31:15',0,'
/__\\
/| |\\
/ | | \\
/| |\\
/ | | \\ Locks\r\n 1 2 3 4 5 6 7 8 9 10
\r\n',12394,0);
INSERT INTO comment VALUES (12396,1668,4507,'Penny','re: Solution','2004-03-03 18:35:54',0,'
1 | X X X X X X
2 | X X X X X X
3 | X X X X X X
4 | X X X X X X
5 | X X X X X X
call the Keys 1, 2, 3, 4, 5. \r\n
Brenda holds lock B and Key 2 + a copy of Key 4
Charlie holds lock C and Keys 3 + a copy of Key 5
David holds lock D and Keys 4 + a copy of Key 1
Eileen holds lock E and keys 5 + a copy of Key 2 \r\n
\r\n
\r\nIt should go without saying that a solution is not a full solution if\r\nit does not only demonstrate the answer, but also the means to the\r\nanswer.
\r\n\r\n\r\n',12399,1);
INSERT INTO comment VALUES (12403,1668,4507,'Penny','re: Cost effective solution','2004-03-03 19:54:15',4,'
Brenda holds lock B and Key 2 + a copy of Key 4
Charlie holds lock C and Keys 3 + a copy of Key 5
David holds lock D and Keys 4 + a copy of Key 1
Eileen holds lock E and keys 5 + a copy of Key 2\"
81 (89 in base 9)
98 (89 in base 9)
Thus the cost is $1 per 5 1/6 chestnuts, or $(6/31) each.
So $60 gets you 310 chestnuts, which should be enough even for the village smithy.
\r\n
\r\nAs 3 of 5 need access,
\r\nthen the minimum LOCK limit is 3;
\r\nhaving single keys only can be ruled out.
\r\n
\r\nBy combinations [5!/(2!*3!)= 10] the suggestion is 10 keys.
\r\n
\r\nThe following table will suggest otherwise:
\r\n
\r\nTable: Person
\r\n----------------------------------------------
\r\nKey A B C D E
\r\n1 x x x x
\r\n2 x \r\n x x \r\n
\r\n3 \r\nx x \r\nx
\r\n----------------------------------------------
\r\n
\r\nIn the table Key 1 seems to be over-committed.
\r\nConsider the removal of Key E1.
\r\n
\r\nThis leaves 9 keys that are needed, as per the table, but remove
\r\nany one of the Key1\'s from the top Key 1 row.
\r\n
\r\nMy proof is: (having removed A1, C1, D1 OR E1),
\r\ncover 2 alpha columns and test for a 3 key satisfaction.
\r\n
\r\nSolution: 9 keys, 4 people get 2 but one soul gets 1 such the table
\r\ndistribution is obeyed. \r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12415,215,5285,'Ady TZIDON','induction does it','2004-03-04 03:30:15',3,'induction is the shortest proof:\r\nfor n=1 8*1+1 ok\r\n\r\ngiven the formula holds for n\r\n\r\nfor n+2 (next odd) 8*( n+2)+1= (8*n+1)+16\r\n\r\nqed\r\nady',NULL,0);
INSERT INTO comment VALUES (12416,1530,5892,'empraptor','complete set of answers, mathy reasoning','2004-03-04 03:33:39',0,'AB 1
\r\n
AC 2
AD 3
AE 4
BC 5
BD 6
BE 7
CD 8
CE 9
DE 10A: 5 6 7 8 9 10
\r\n
B: 2 3 4 8 9 10
C: 1 3 4 6 7 10
D: 1 2 4 5 7 9
E: 1 2 3 5 6 8
\r\n
\r\nIt\'s just that I wrote last time that n=0 produces a solution that\r\nsatisfies the equation made to model the problem. That it\r\nsatifies the equation but is not a valid solution because that would\r\nmake X=0 and X wouldn\'t end with 3. But now I look and realize\r\nX=0 DOESN\'T satisfy the equation at all. So we\'re all the merrier\r\nbecause we don\'t have to justify eliminating n=0 case with words. \r\nThe equation takes care of it.
\r\n
\r\n
\r\n\r\n\r\n',12418,1);
INSERT INTO comment VALUES (12444,1672,1301,'Charlie','My analysis','2004-03-04 15:02:25',3,'The problem is not one of physics, but of biology (human physiology in particular). The retina contains light sensitive cells. Some, called rods, are sensitive to low light levels and are not differentiated by color sensitivity, and so allow you to see in black and white in low illumination. Other receptor cells, called cones, come in three varieties, \"red sensitive\", \"green sensitive\" and \"blue sensitive\". These categorizations are oversimplifications, as each has a response curve of different degrees of sensitivity to various wavelengths of light, and in fact overlap considerably.\r\n\r\nSo let\'s not oversimplify to that great a degree, but simplify enough so we can use some concrete numbers. \r\n\r\nLet\'s say the responsiveness of the three types of cell to some distinct wavelengths of light are as follows:\r\n\r\n\r\nLight \"red-sens cell\" \"green-sens cell\" \"blue-sens cell\"\r\n7000-red 6 4 0\r\n yellow 5 5 1\r\n green 4 6 2\r\n cyan 2 7 4\r\n4500-blue 1 6 5\r\n
\r\n--------\r\nso that if monochromatic (single wavelength) yellow light hits the retina, the R, G and B cells will respond in a ratio of 5:5:1. But if a mix of monochromatic red and monochromatic green falls on the retina the response ratio will be 6+4:4+6:2 = 10:10:2 = 5:5:1, which is the same as for the monochromatic yellow light.\r\n\r\nA similar scheme would work for cyan from blue and green. It\'s likely that other well-spaced sets of three wavelength could serve as primary colors, but it\'s also likely that the choice of r,g and b is somewhat optimal given the spectral response characteristics of the three types of cone, and is able to reproduce more wavelengths of monochromatic light than other combinations. (Nothing guarantees being able to reproduce exactly the 3-level cell response ratios of all wavelengths of monochromatic light.)\r\n\r\nIn practice, most light is not monochromatic, nor even consisting of line spectra (a select group of distinct wavelengths), but rather exhibits a continuous spectrum. If the visible range of wavelengths is present in approximately equal proportions, all the cones will be stimulated equally and we\'ll see white or gray depending on the illumination level. It\'s a philosophical question as to whether everyone sees this the same way; but whatever way we see it, that is what we\'ve been taught is called \"white\". It is actually more complicated than this as the brain interprets differences in the response ratio from one part of the retina to another. So, for example if all the cones are stimulated equally at level 3 in one patch on the retina and at level 6 in another patch, it\'s likely the former will be perceived as gray and the latter as white. Then at another time when again all the cones in one patch are equally responding at level 6, and in another patch at level 12, the level-6 area this time will be perceived as gray as the level-12 area now \"looks\" white. In this manner, objects maintain a color constancy even when viewed in bright light or dim light.\r\n\r\nSome characteristics of light can play tricks on the color sensing of the eye-brain combination. Most fluorescent lights have notable line spectra rather than continuous spectra. The spectral lines (mix of distinct frequencies) are sufficiently spread so the light looks white, but objects viewed under them may have irregular reflecting spectral properties, and the wavelength of good reflection might not always correspond to the distinct wavelengths in the light, and so the object could look a different color under fluorescent from the way it looks under a continuous spectrum such as sunlight.\r\n\r\nAlso, for example, the moon looks really bright even though it\'s dark rock, since is in bright sunlight even though it is night time (usually) and you are looking against a dark background. The brain is again comparing relative levels and understanding the moon to be bright.\r\n\r\nCertainly if more than 3 primaries were used, it would not hurt the approximation process to the color matching. In fact, if the entire reflectance or radiation spectrum of a given patch could be duplicated exactly, the eye would have no way of discerning it from the original.\r\n\r\nI understand that birds may have four different color sensors, and so would need at least four primary colors, but more wouldn\'t hurt either.\r\n\r\n\r\n\r\nEdited on March 4, 2004, 3:06 pm\n\nEdited on March 4, 2004, 3:06 pm',NULL,0);
INSERT INTO comment VALUES (12445,1672,3992,'Jane Doe','I may be completely off the mark...','2004-03-04 15:53:57',2,'
\r\n
\r\nAs 3 of 5 need access,
\r\nthen the minimum LOCK limit is 3;
\r\nhaving single keys only can be ruled out.
\r\n
\r\nBy combinations [5!/(2!*3!)= 10] the suggestion is 10 keys.
\r\n
\r\nThe following table will suggest otherwise:
\r\n
\r\nTable: Person
\r\n----------------------------------------------
\r\nKey A B C D E
\r\n1 x x x x
\r\n2 x \r\n x x \r\n
\r\n3 \r\nx x \r\nx
\r\n----------------------------------------------
\r\n
\r\nIn the table Key 1 seems to be over-committed.
\r\nConsider the removal of Key E1.
\r\n
\r\nThis leaves 9 keys that are needed, as per the table, but remove
\r\nany one of the Key1\'s from the top Key 1 row.
\r\n
\r\nMy proof is: (having removed A1, C1, D1 OR E1),
\r\ncover 2 alpha columns and test.
\r\n
\r\nSolution: 9 keys, 4 people get 2 but one soul get 1 such the table
\r\ndistribution is obeyed.\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12447,1668,3172,'SilverKnight','re: 2 for all but 1','2004-03-04 17:15:58',0,'Brian,
\r\n
\r\nHow is distribution obeyed?
\r\n
\r\nMany pairs, together, have all three keys. So if I remove (as you\r\nsuggest) E1, then Person A and B (or B&C, or C&D, or B&D,\r\netc.) together have all three keys and can open the chest.
\r\n
\r\nBut the problem says only when at least three are present.
\r\n
\r\n
\r\n\r\n\r\n',12446,1);
INSERT INTO comment VALUES (12448,483,3735,'Nick Hobson','Comment on official solution','2004-03-04 17:46:09',1,'I like the following lines in the \"official\" solution to this puzzle:\r\n\r\n\"1024x - 15625y = 11529 for (a) and \r\n1024x - 15625y = 8404 for (b). \r\n\r\nFrom these equations, we obtain: x (minimum) = 15621 for (a) and x (minimum) = 3121 for (b).\"\r\n\r\nWaving a magic wand and pulling the solution to such equations out of a hat, without providing the method, is tantamount to simply guessing the answer!',NULL,0);
INSERT INTO comment VALUES (12449,1672,1567,'Bryan','re: My analysis','2004-03-04 18:40:31',0,'Darn it, Charlie, I was gonna say that. (Sure I was;)',12444,1);
INSERT INTO comment VALUES (12450,1668,4507,'Penny','re(2): Revised solution to revised puzzle','2004-03-04 21:16:52',0,'
\r\nI was suggesting that 4 locks are therefore the minimum and with 10\r\nkeys distributed in pairs to each person such that each has a unique\r\npair.
eg
\r\n \r\n Person
Lock \r\nA B C \r\n D E
1 \r\n x \r\n x
\r\n 2 x \r\n x \r\n x
\r\n 3 \r\n x x \r\nx
4 \r\n x \r\n \r\n x
I note however that B, C and E could not open the chest.
\r\nBack to the drawing board!
\r\n statement
\r\nSince the only one with two False statements (let alone two false statements that correspond to the guilty parties), is:\r\nD is the killer and B is the accomplice. ',NULL,0);
INSERT INTO comment VALUES (12465,1532,4323,'Benjamin J. Ladd','Quick question:','2004-03-05 15:19:12',4,'When you are taking away the 1/8 area of each square face, do you mean\r\nfrom the original cube regardless of what has been taken away, or do\r\nyou mean 1/8 of the area of the remaining face? I hope this\r\nquestion makes sense.
Killer Accomplice A B C D
A B T T T T
A C T T T T
A D T T T F
B A T T T T
B C F T T T
B D T F F F
C A T T T T
C B F T T T
C D T T T F
D A T T T F
D B T F T F
D C T T T F
\r\n
\r\nThanks,
\r\nJordan
\r\n\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12466,1666,4507,'Penny','Solution','2004-03-05 16:05:02',3,'
25 cos(x) - 24 cos^2(x) - 12 sin^2(x)
25 cos(x) - 12 cos^2(x) - [12 sin^2(x) + 12 cos^2(x)]
25 cos(x) - 12 cos^2(x) - 12 or
solving the quadratic gives 2 values for cos(x): 3/4 and 4/3 but only 3/4 can be valid since the cosine can\'t be greater than 1.
the angle is arccos(.75) = .7227 radians = 41.41 degrees
distance is 2.646 = sqrt(7)
d\' = 3
and there is a right angle between the hour hand and a line connecting the tips of the 2 hands
1132
2212
4213
^^^^
3412
234
1
3
set d\" to zero.
or t is about 2:23
and d(t)=4.551
\r\n
\r\n(Therefore, it *is* just as true to say that the sun rotates around the\r\nearth as it is to say that the world revolves around ME! ;-)\r\n\r\n',12478,1);
INSERT INTO comment VALUES (12488,1503,5927,'jk','solution','2004-03-07 04:07:31',3,'
\r\n\r\n
a(i,j)=a(i,j)
b(i,j)=a(9-i,j)
c(i,j)=a(i,9-j)
d(i,j)=a(9-i,9-j)
e(i,j)=a(j,i)
f(i,j)=a(9-j,i)
g(i,j)=a(j,9-i)
h(i,j)=a(9-j,9-i)
Note: There are 10 mutually exclusive sets of squares such that for each square in a given set, all of its mirrors are in the set, but no non-mirrors:
0 1 2 3 3 2 1 0
1 4 5 6 6 5 4 1
2 5 7 8 8 7 5 2
3 6 8 9 9 8 6 3
3 6 8 9 9 8 6 3
2 5 7 8 8 7 5 2
1 4 5 6 6 5 4 1
0 1 2 3 3 2 1 0
If the symmetry is physical, then in one of these mirroring schemes, x(i,j), it is true that a jump connects a(i1,j1) to a(i2,j2) iff a jump connects x(i1,j1) to x(i2,j2).
If the symmetry is temporal, then the sequence of jumps can be shifted to start at a square (Due to the re-entrant condition, any valid sequence can be shifted to start on any given square.) such that:
Given n = the number of the jump which lands on a(i,j),
and m = the number of the jump which lands on x(i,j),
Either n - m = ±32 or n + m = 0(mod 64).
The first temporal symmetry condition (n - m =±32) always results in a physical symmetry, and does not need to be considered separately.
The second temporal symmetry condition [n + m = 0 (mod 64)] may also always result in a physical symmetry, but I have not tested it enough to be sure.
Notice that in the second temporal symmetry condition x(i,j)=a(i,j) for the squares at n=0 and n=32.
Conjecture: Except for the corner case [where, for example a(1,1) must connect with both a(2,3) and a(3,2)], the two squares any given square connects with cannot be in the same mirror set. For example, a(5,5) cannot connect to both a(6,7) and a(7,6) because they are both in mirror set 5.
(Edited to correct a minor typo)\n\nEdited on March 7, 2004, 9:45 pm',NULL,0);
INSERT INTO comment VALUES (12506,1575,3558,'Tristan','I\'m hungry','2004-03-07 19:18:59',0,'I\'m onto something; it\'s hard to see, but it has to do with turkey...',NULL,1);
INSERT INTO comment VALUES (12507,1575,4507,'Penny','Question for DJ','2004-03-07 19:28:06',4,'
',NULL,1);
INSERT INTO comment VALUES (12513,1575,5384,'Larry','No Subject','2004-03-07 20:25:51',0,'I\'m on to something, it\'s hard to see, but it has to do with WMD.<o:p></o:p>
Since the title is \" XX \", maybe it was censored by Levik ??? (This problem is on its way to become the all-time top rated problem !!!)
2. A PERFECT statement -no errors.
3. A full list of non-personal parameters affecting politician\'s decision
have fun!!
ady
\r\n
\r\nAnyway, DJ - if you have more like this up your sleve, please\r\ncross-browser check them. Mozilla was choking on this one (and still\r\nhas a hickup or two)
\r\n
\r\nAlso, make sure to fix your solution.
\r\n\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12525,1575,3172,'SilverKnight','I fixed my earlier (incorrect) answer...','2004-03-08 08:12:50',0,'see the previous comment.\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12526,1575,1686,'DuCk','Solution...','2004-03-08 08:39:27',0,'I\'m onto something; it\'s hard to see, but it has to do with Destiny...',NULL,1);
INSERT INTO comment VALUES (12527,1575,1686,'DuCk','side note','2004-03-08 08:42:19',0,'this was one of the funnest problems I\'ve ever seen on the site. Thanks DJ???',NULL,1);
INSERT INTO comment VALUES (12528,1670,4830,'Jils','My Guess','2004-03-08 08:47:21',0,'
\r\n
\r\n.. That\'s why you didn\'t get the correct answer ...
\r\n\r\n\r\n',11585,1);
INSERT INTO comment VALUES (12538,1575,1575,'DJ','re: hrmph','2004-03-08 13:35:48',0,'The problem underwent several version changes to make sure everything\r\nwould work in all [common] browsers. I tested in IE 6, Mozilla and\r\nFirefox, and Netscape, and it\'s working fine.
\r\n
\r\nActually, I\'m running Mozilla on Fedora (UNIX) right now, and it\'s working .. are you sure you did it right? =P
\r\n\r\n\r\n',12524,1);
INSERT INTO comment VALUES (12539,1533,4670,'e.g.','Almost there','2004-03-08 13:56:17',0,'I found two solutions, but in eleven moves, so it\'s back to searching...
\r\n
\r\nA right, D left, A down, B left, D right, D up, C right, A up, D down, B left, B down.
\r\n
\r\nA right, A down, C right, B left, A up, B right, C up, D left, A down, D right, D up.
\r\n
\r\n',NULL,1);
INSERT INTO comment VALUES (12540,1666,4670,'e.g.','Solution','2004-03-08 14:00:00',3,'If A was guilty, the only way he could be telling a lie would be if B\r\nalso was guilty, and C wasn\'t innocent -- and that would imply three\r\nguilty parties. A similar reasoning shows that if C cannot be guilty\r\neither, so B and D are the guilty ones.
\r\n
\r\nAs C told the truth, if B was the killer, D would be innocent; but as\r\nwe know that D was guilty, then B wasn\'t the killer -- he was the\r\naccomplice, and D thus was the killer.
\r\n\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12541,1533,5852,'Coda','re: Almost there','2004-03-08 14:00:04',0,'Yes, I got that too. I can\'t figure out how it is possible in 10 moves!',12539,1);
INSERT INTO comment VALUES (12542,1533,3172,'SilverKnight','solution (spoiler()','2004-03-08 14:05:11',3,'INITIAL POSITION:
',NULL,0);
INSERT INTO comment VALUES (12543,1533,575,'not_so_einstein','Solution','2004-03-08 14:18:41',3,'1: Move B from E1 to E4 (stops to D)\r\n2: Move A from A1 to E1 (stops to the edge)\r\n3: Move A from E1 to E3 (stops to B in E4)\r\n4: Move A to the darkened square\r\n\r\nnote: This can be done to all of the rooks.\r\nNote: I did´t peak the other answers (yet :P)',NULL,0);
INSERT INTO comment VALUES (12544,1533,3172,'SilverKnight','re: Solution','2004-03-08 14:23:57',0,'Then, on move 4... A will continue THROUGH the darkened square and end\r\nup at A3. (Remember, the problem says that the rooks continue\r\nuntil they hit another rook or the edge of the board.)\r\n\r\n',12543,1);
INSERT INTO comment VALUES (12545,1533,2716,'Federico Kereki','Ten moves','2004-03-08 15:17:50',3,'A moves right.\r\nD moves left.\r\nC moves up, then right.\r\nA moves down, then left, then up.\r\nB moves down, then left, then up.\r\nDone!\r\n',NULL,0);
INSERT INTO comment VALUES (12546,1575,4507,'Penny','Do you suppose that......','2004-03-08 15:53:04',0,'
A...B
.....
.....
.....
C...D
1:
A...B
C....
.....
.....
....D
2:
A....
C....
.....
....B
....D
3:
....A
C....
.....
....B
....D
4:
.....
C....
....A
....B
....D
5:
.....
C....
....A
B....
....D
6:
.....
C....
....A
B....
D....
7:
.....
C....
B...A
.....
D....
8:
.....
C....
...BA
.....
D....
9:
.....
C....
D..BA
.....
.....
10
.....
C....
..DBA
.....
.....
\r\n
\r\nThat being said, Jane, your solution is a correct one. \r\nUnfortunately, I\'m guessing that you found this on the internet or in a\r\nbook, or some other source, as you did not show how you found it.
\r\n
\r\nFor others\' benefit, there ARE other solutions to this problem.
\r\n\r\n\r\n',12573,1);
INSERT INTO comment VALUES (12575,1575,4507,'Penny','re(2): solution','2004-03-09 15:40:58',0,'You can\'t be serious !!',12572,1);
INSERT INTO comment VALUES (12576,1666,4507,'Penny','re(2): solution','2004-03-09 16:39:43',0,'
The container is a good conductor of heat, the freezer needs some defrosting such that there is an irregular surface with relatively few points of contact with the container. Thus hot water warms the container, melts the frost which allows the metal container to make excellent contact with the source of coldness.
\r\n
\r\nSeems to me that the mistake is that calling S and (S --> G) both \"Statement S\" results in an equivocation.
\r\n
\r\nSo, step 8 is a no-go. The label \"Statement S\" can\'t refer to both S and (S --> G).
\r\n
\r\nUsing material implication, you could build (S --> G) out of S (by\r\nadding ~G, then perfoming implication). But just because this operation\r\nis permissible doesn\'t seem to license the claim that S \'contains\' the\r\nconditional (S --> G), and thus that the statements are one and the\r\nsame (allowing this reductio to \'work\'.)
\r\n\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12589,1666,5970,'Matthew Pianalto','re: full solution','2004-03-09 21:18:16',0,'So far as I can tell, Silver Knight is correct, except that on row 2 of\r\nhis table, the t-value under A\'s statement should be F. (b/c C is\r\nguilty as accomplice in that scenario.)
\r\n
\r\nSo D killed, and B helped. Is this wrong?
\r\n\r\n\r\n',12464,1);
INSERT INTO comment VALUES (12590,1680,3351,'Eric','re(2): lower square - failure','2004-03-09 21:23:50',1,'
\r\n
\r\nSince the first part of the statement is false (A isn\'t\r\ninnocent), the second part can be anything, and the truth value\r\nis true.
\r\n
\r\nThis is similar to my saying, \"If the sky is always orange, then I can fly.\" (A true statement.)
\r\n\r\n\r\n',12589,1);
INSERT INTO comment VALUES (12595,1666,5970,'Matthew Pianalto','re(3): full solution','2004-03-10 03:49:37',0,'I\'m sorry. You\'re quite right. I had the antecedent labeled as T, which\r\nwas wrong. I hope you\'ll forgive my coming off so \'sloppily corrective\'\r\non my first go-round.
\r\n\r\n\r\n',12594,1);
INSERT INTO comment VALUES (12596,1533,5970,'Matthew Pianalto','Got it (in 10)','2004-03-10 04:37:37',0,'Thought I had it in less than this, but must have been deluded.
\r\n1. D to E2
\r\n2. A to A4
\r\n3. A to E4
\r\n4. D to A2
\r\n5. B to E3
\r\n6. C to A3
\r\n7. B to B3
\r\n8. D to E2
\r\n9. A to E3
\r\n10. A to C3
\r\n
\r\n\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12597,1680,4507,'Penny','If all goes well today.....','2004-03-10 07:31:49',0,'
\r\n
\r\nDoing the whole round trip (40 miles) at 30 mph would also require 80 minutes.
\r\n
\r\nSo, in order to manage the 30 mph average, you\'d have to do the return\r\ntrip in 0 minutes flat, which would require infinite speed.
\r\n\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12600,1698,4507,'Penny','Solution','2004-03-10 08:49:39',3,'
\r\n
\r\nThis is generally referred to as a \"red herring\", and it holds a\r\ntime-honored tradition in problem telling (of course, to lead\r\nwould-be-solvers down a dead end).
\r\n\r\n\r\n',12602,1);
INSERT INTO comment VALUES (12604,1680,1920,'Brian Smith','Solution using 1','2004-03-10 11:33:31',0,' [1 1 1] [0 2 1] [1 0 2]
\r\n
a*[1 1 1] + b*[2 1 0] + c*[2 1 0]
[1 1 1] [1 0 2] [0 2 1] [31 13 19]
',NULL,1);
INSERT INTO comment VALUES (12605,1680,4830,'Jils','Sequences','2004-03-10 11:53:25',1,'
[73 37 1]
[ 7 61 43]
DIM noDays(12, 600)
trials = 200000
FOR trial = 1 TO trials
REDIM bday(365)
maxRep = 0
FOR people = 1 TO 600
bd = INT(RND(1) * 365 + 1)
bday(bd) = bday(bd) + 1
IF bday(bd) > maxRep THEN
maxRep = bday(bd)
IF maxRep < 13 THEN
noDays(maxRep, people) = noDays(maxRep, people) + 1
END IF
END IF
NEXT
NEXT
FOR rep = 2 TO 12
ct = 0
FOR i = 1 TO 600
ct = ct + noDays(rep, i)
IF ct >= trials / 2 THEN PRINT rep, i, ct / trials: EXIT FOR
NEXT
NEXT
3 88 .51103
4 186 .50154
5 313 .504695
6 460 .50365
10 for Needed=2 to 13
15 People=20
20 repeat
25 People=People+1
30 Prob=fnProbSucc(People,Needed)
40 until Prob>=0.5
50 print Needed,People,Prob
90 next
900 end
999 \'
1000 fn1dApRinN(N,R)
1010 local P
1020 P=combi(N,R)*(1/365)^R*(364/365)^(N-R)
1030 return(P)
1099 \'
1100 fnAtLeastRinN(N,R)
1110 local P
1111 local I
1120 P=1
1130 for I=0 to R-1
1140 P=P-fn1dApRinN(N,I)
1150 next
1160 return(P)
1199 \'
1200 fnProbSucc(People,HowMany)
1210 local PAtLeast
1211 local P
1220 PAtLeast=fnAtLeastRinN(People,HowMany)
1250 P=365*PAtLeast-combi(365,2)*PAtLeast^2+combi(365,3)*PAtLeast^3-combi(365
,4)*PAtLeast^4+combi(365,5)*PAtLeast^5
1270 return(P)
3 88 0.500024238908916008751425954604806345304855138599
4 188 0.50121973720291497376553934602377971816400640167
5 315 0.503716145942477034440763359178102928683134514473
6 462 0.503692442151314437034595863350466252672421876767
7 624 0.50023923568884182819567190051858113365279781384
8 800 0.500195974660549653670527200105639158839275552604
9 987 0.500416377508527652709622327057735734378561391984
10 1183 0.500100393247427978545737350820694555937017652788
11 1388 0.501858680817548576454867836197064871061046632628
12 1599 0.501682818386226699143745804914276827734503416906
13 1816 0.501342696818721244403330383903198902341179454911
3 87 .50081
4 187 .50653
5 312 .500095
6 460 .503405
7 622 .5020250000000001
8 798 .50124
9 985 .50041
10 1182 .50198
11 1386 .501405
12 1596 .501255
\r\n
\r\nHad you any luck with your code?
\r\n\r\n\r\n',12601,1);
INSERT INTO comment VALUES (12622,1680,1920,'Brian Smith','More Solutions','2004-03-11 17:14:14',0,'[ 47 113 17]
\r\n
[ 29 59 89]
[101 5 71][ 43 139 37]
\r\n
[ 67 73 79]
[109 7 103][ 59 113 41]
\r\n
[ 53 71 89]
[101 29 83]
Smallest twin prime magic squares[107 281 59] | [109 283 61]
',NULL,1);
INSERT INTO comment VALUES (12623,1683,3172,'SilverKnight','re: Simulations and approximation','2004-03-11 17:36:21',0,'Well, not to interrupt the heavy flow of comments, but let me confirm\r\nthat Charlie\'s answers are very close to correct (and some of them\r\nare), but there is still room for a \"more exact\" solution.
[101 149 197] | [103 151 199]
[239 17 191] | [241 19 193]
\r\n
\r\nStill, my hat\'s off to Charlie\'s well thought out description of the problem solution.
\r\n\r\n\r\n',12620,1);
INSERT INTO comment VALUES (12624,1680,5777,'Thalamus','re: More Solutions','2004-03-11 17:49:33',0,'Cool! Where\'d you find these?\r\n\r\n',12622,1);
INSERT INTO comment VALUES (12625,1535,2184,'mark hartman','solution','2004-03-11 18:51:05',0,'Solution generated by p,b,c
\r\n
[P -6B-12C P P-12B -6C]
[P-12B P -6B -6C P -12C]
[P -6C P-12B-12C P- 6B ]
20 Limit=1000
30 P=Start
40 while P<Limit
50 Bcmax=P\\12
60 for Bcsum=3 to Bcmax
70 for B=2 to (Bcsum-1)
80 C=Bcsum-B
85 if C>=B then 190
90 if not fnIsPrime(P-6*B) then 190
100 if not fnIsPrime(P-12*B) then 190
110 if not fnIsPrime(P-6*C) then 190
120 if not fnIsPrime(P-12*C) then 190
130 if not fnIsPrime(P-6*B-6*C) then 190
140 if not fnIsPrime(P-12*B-6*C) then 190
150 if not fnIsPrime(P-6*B-12*C) then 190
160 if not fnIsPrime(P-12*B-12*C) then 190
170 if B=(2*C) then 190
180 print P,B,C,
182 Solutions=Solutions+1
184 if (P-12*B-12*C)>1 then 189
186 print \"*\";
188 One=One+1
189 print \" \"
190 next B
200 next Bcsum
210 P=nxtprm(P)
220 wend
225 print Solutions,One
230 end
320 fnIsPrime(Number)
330 Returnvalue=0
340 if nxtprm(Number-1)-Number=0 then Returnvalue=1
345 if Number=1 then Returnvalue=1
350 return(Returnvalue)
\r\n
\r\nWith 20 stubs, he could smoke 4 cigars, and would be left with 4\r\nstubs. He could then go to a friend, borrow a stub, make a fifth cigar,\r\nsmoke it, and return the stub to the friend.
\r\n
\r\nSo, the answers are 6 (with no trickery) and 5 (with a little trickery)!
\r\n',NULL,1);
INSERT INTO comment VALUES (12636,1692,1301,'Charlie','some findings by brute force','2004-03-12 14:01:47',1,'
0 0 0 0
1 1 1 1
1 0 0 1
1 1 1 1
1 1 0 0
1 1 0 0
0 0 0 1
1 0 0 0
0 0 0 1
0 1 0 0
1 0 1 1
0 1 0 0
1 0 1 0
0 0 0 1
1 0 0 0
0 0 1 0
0 0 1 0
1 1 0 1
1 1 0 0
0 1 1 0
0 0 0 0
1 0 0 1
0 1 0 1
0 1 0 1
0 1 1 1
0 0 1 1
0 0 1 1
1 0 0 0
0 0 0 0
0 1 1 0
0 1 1 0
0 1 0 0
1 0 1 1
0 0 1 1
0 1 1 1
1 1 1 0
1 1 0 1
1 1 0 1
0 0 1 0
0 1 0 1
1 1 1 0
0 1 1 1
1 0 1 1
1 0 1 0
1 0 1 0
1 1 1 0
1 0 0 1
1 1 1 1
0 0 0 0
The 5x5, solved by brute force computer program finds only one basic solution and three rotations:
1 1 0 1 1
1 1 1 0 0
0 1 1 1 0
1 0 1 1 0
DEFINT A-Z
CLEAR , , 4000
DIM SHARED flip(6, 6)
DIM SHARED lit(6, 6)
vary 1, 1
STATIC sCt
FOR cyc = 1 TO 3
IF r = 4 AND c = 4 THEN
GOSUB checkIt
ELSE
IF c = 4 THEN r1 = r + 1: c1 = 1: ELSE c1 = c + 1: r1 = r
vary r1, c1
END IF
flip(r, c) = 1 + flip(r, c) MOD 6
lit(r, c) = 2 + lit(r, c) MOD 3
lit(r - 1, c) = 1 + lit(r - 1, c) MOD 3
lit(r, c - 1) = 1 + lit(r, c - 1) MOD 3
lit(r + 1, c) = 1 + lit(r + 1, c) MOD 3
lit(r, c + 1) = 1 + lit(r, c + 1) MOD 3
NEXT cyc
EXIT SUB
bad = 0
FOR row = 1 TO 4
FOR col = 1 TO 4
IF lit(row, col) <> 2 THEN bad = 1: EXIT FOR
NEXT
IF bad THEN EXIT FOR
NEXT
IF bad = 0 THEN
FOR i = 1 TO 4
FOR j = 1 TO 4
PRINT flip(i, j);
NEXT
PRINT
NEXT
sCt = sCt + 1: PRINT sCt
IF sCt MOD 7 = 0 THEN DO: LOOP UNTIL INKEY$ > \"\"
END IF
RETURN
\r\n\r\n10^x,numbers,digits,total of,total of
\r\nplace,per place,per place,digits,numbers
\r\n1,9,9,9,9
\r\n2,90,180,189,99
\r\n3,900,2700,2889,999
\r\n4,9000,36000,38889,9999
\r\n5,222,1110,39999,10221
\r\n\r\nSince 10221 uses 39999 digits the first digit of the next number 10222 is the solution.
\r\n\r\nThe answer is 1.
\n\nEdited on March 13, 2004, 6:19 pm',NULL,0);
INSERT INTO comment VALUES (12650,1681,3735,'Nick Hobson','Non-calculus solution','2004-03-13 18:36:53',3,'
$60 - Emily: blue and red ($20)
$60 - Alice: green ($50) and yellow ($10)
$50 - Betty: orange ($30) and red ($20)
$50 - Carol: blue and yellow ($10) \r\n$30 = 10 + 20\r\n$40 = 10 + 30\r\n$50 = 10 + 40\r\n$50 = 20 + 30\r\n$60 = 10 + 50\r\n$60 = 20 + 40\r\n$70 = 20 + 50\r\n$70 = 30 + 40\r\n$80 = 30 + 50\r\n$90 = 40 + 50
Since Diane spent the most, and the other two pairs of girls spent the same amounts [1], possible triples of the amounts spent are, at first glance: 50, 60, 70 (10,40;20,30;10,50;20,40;20,50)\r\n50, 60, 70 (10,40;20,30;10,50;20,40;30,40)\r\n50, 60, 80 (10,40;20,30;10,50;20,40;30,50)\r\n50, 60, 90 (10,40;20,30;10,50;20,40;40,50)\r\n50, 70, 80 (10,40;20,30;20,50;30,40;30,50)\r\n50, 70, 90 (10,40;20,30;20,50;30,40;40,50)\r\n60, 70, 80 (10,50;20,40;20,50;30,40;30,50)\r\n60, 70, 90 (10,50;20,40;20,50;30,40;40,50)
However, we are also told that two of each color shirt were bought, eliminating most of the above combinations (the underlined priced appear three times, and the italicized values appear only once in the invalid combinations). The only valid result (in bold), then, is that Diane spent $80, while the other pairs of girls spent $50 and $60 on their clothes, respectively: 80 = 30 + 50 (Diane)\r\n60 = 20 + 40\r\n60 = 10 + 50\r\n50 = 20 + 30\r\n50 = 10 + 40
\r\n80 = 30 + 50 (Diane)\r\n60 = 20 + 40 (Emily/Carol)\r\n60 = 10 + 50 (Alice/Betty)\r\n50 = 20 + 30 (Alice/Betty)\r\n50 = 10 + 40 (Emily/Carol)
Carol didn\'t buy a twenty-dollar shirt with Alice [4]; it must have cost ten dollars [4], and by elimination, we know what price shirts everyone bought: 80 = 30 + 50 (Diane)\r\n60 = 20 + 40 (Emily)\r\n60 = 10 + 50 (Alice)\r\n50 = 20 + 30 (Betty)\r\n50 = 10 + 40 (Carol)
Now, to match prices to colors: \r\n$10: yellow\r\n 20\r\n 30\r\n 40: blue\r\n 50
Alice and Betty did not buy any shirts in common [above], so Alice\'s fifty-dollar shirt was not yellow [$10], blue [$40], orange [4], or red [5]; it was green. $10: yellow\r\n 20\r\n 30\r\n 40: blue\r\n 50: green
By elimination, Betty\'s twenty- and thirty-dollar shirts were red and orange, in some order. Emily bought a twenty-dollar shirt, but it was not orange [4]; it must have been red. That leaves the orange shirt at $30: $10: yellow\r\n 20: red\r\n 30: orange\r\n 40: blue\r\n 50: green
So, to recap: $80 - Diane: green ($50) and orange ($30)\r\n$60 - Emily: blue and red ($20)\r\n$60 - Alice: green ($50) and yellow ($10)\r\n$50 - Betty: orange ($30) and red ($20)\r\n$50 - Carol: blue and yellow ($10)
',NULL,1);
INSERT INTO comment VALUES (12652,1681,4323,'Benjamin J. Ladd','It seems to me...','2004-03-13 23:48:24',4,'
1 75557863725914323419136
2 151115727451828646838272
3 226673591177742970257408
4 302231454903657293676544
5 377789318629571617095680
6 453347182355485940514816
7 528905046081400263933952
8 604462909807314587353088
9 680020773533228910772224
10 755578637259143234191360
87 6573534144154546137464832
88 6649092007880460460883968
89 6724649871606374784303104
90 6800207735332289107722240
91 6875765599058203431141376
92 6951323462784117754560512
93 7026881326510032077979648
94 7102439190235946401398784
95 7177997053961860724817920
96 7253554917687775048237056
97 7329112781413689371656192
98 7404670645139603695075328
99 7480228508865518018494464
100 7555786372591432341913600
101 7631344236317346665332736
102 7706902100043260988751872
103 7782459963769175312171008
9116 688785485725434972288843776
93116 7035646038702238139496267776
943116 71259830205729413045761867776
9243116 698390099130818297424590667776
90243116 6818577060929878494374606667776
900243116 68020446678920480463874766667776
9400243116 710262288349192229526530766667776
90400243116 6830449250148252426476546766667776
910400243116 68787897505397997630168066766667776
9010400243116 680806593685304017325169666766667776
92010400243116 6952109282936192861113457666766667776
912010400243116 68909557538185938064804977666766667776
866 65433109986641804080971776
6866 518780292342127744595787776
86866 6563409390415273618126667776
586866 44342341253372435327694667776
7586866 573247387334772699261646667776
77586866 5862297848148775338601166667776
677586866 51197016083697369390082766667776
9677586866 731217789616926280162306766667776
69677586866 5264689613171785685310466766667776
769677586866 58155194221311812078705666766667776
7769677586866 587060240302712076012657666766667776
77769677586866 5876110701116714715352177666766667776
616 46543644055163223226187776
90616 6846751379387452330948427776
930616 70315356909155484003022667776
930616 70315356909155484003022667776
94930616 7172754547145101885401806667776
904930616 68374624165135703854901966667776
704930616 53263051419952839171074766667776
7704930616 582168097501353103105026766667776
97704930616 7382375832833642210827266766667776
9497704930616 717626294856428282350705666766667776
91497704930616 6913371120381402802719857666766667776
911497704930616 68870819375631148006411377666766667776
6×10k = 0 (mod 2k+1)
7×10k = 2k (mod 2k+1)
15 Pow=10:Num=6
20 repeat
25 Fl=0
28 if rnd>0.5 then Bg=9:Nd=0:Stp=-1:else Bg=0:Nd=9:Stp=1
30 for I=Bg to Nd step Stp
40 Trial=Num+I*Pow
50 if Fl=0 and (((Trial*D)@(10*Pow))\\Pow=6 or ((Trial*D)@(10*Pow))\\Pow=7) then
60 :Num=Trial:Pow=Pow*10:Fl=1
70 next
80 *Foundit
85 print:print Trial,Trial*D
90 until Num>10^100
100 N=(Trial*D)@10^76
110 print N,N@D
[x][x][x][x]
[x][x][x][x]
[x][x][x][x]
moves that can be made are like thus (square clicked is bold) \r\n
[x][.][x][x]
[x][x][x][x]
[x][x][x][x]
\r\n
[x][.][.][.]
[x][x][x][.]
[x][x][x][x]
\r\n
[x][.][.][.]
[x][x][.][.]
[x][.][.][.]
\r\n
[.][.][.][.]
[.][.][.][.]
[.][.][.][.]
For the geometric equation of the side area, consider a cylindar instead of a truncated cone (is this called a frustum?). Anyway, consider a cylindar of radius (a+b)/2. The side area of that would be h*2*Pi*[(a+b)/2] = h*Pi*(a+b)
fleys flick flics flied flier flies fling flint flips flirt flite flits float flock flocs floes flogs flong flood floor flops flora floss flota flour flout flown flows flubs flued flues fluff fluid
fluke fluky flume flump flung flunk fluor flush flute fluty fluyt flyby flyer flyte }
{ cablet cachet callet camlet caplet carnet carpet casket cermet chalet claret closet collet coquet cornet corset corvet cosset cruset cullet curvet cutlet cygnet }
{ maar mabe mace mach mack macs made mads maes mage magi mags maid mail maim main mair make mako male mall malm malt mama mana mane mano mans many maps marc mare mark marl mars mart mash mask mass mast mate math mats matt maud maul maun maut mawn maws maxi maya mayo mays maze mazy mead meal mean meat meed meek meet meld mell
mels melt memo mems mend meno menu meou meow mere merk merl mesa mesh mess meta mete meth mewl mews mhos mibs mica mice mick midi mids mien miff migg migs mike mild mile milk mill milo mils milt mime mina mind mine mini mink mint minx mire miri mirk mirs miry mise miso miss mist mite mitt mity mixt moan moas moat mobs mock mode modi mods mogs moil mojo moke
mola mold mole moll mols molt moly mome momi moms monk mono mons mony mood mool moon moor moos moot mope mops mopy mora more morn mors mort mosk moss most mote moth mots mott moue move mown mows moxa mozo much muck muds muff mugg mugs mule mull mumm mump mums mumu muns muon mura mure murk murr muse mush musk muss must mute muts
mutt myna myth}
(1,0) (1,1)
(2,0) (2,1) (2,2)
(3,0) (3,1) (3,2) (3,3)
(4,0) (4,1) (4,2) (4,3) (4,4)
(5,0) (5,1) (5,2),(5,3) (5,4) (5,5)
...
(n,0) (n,1) (n,2) (n,3) (n,4) (n,5) ... (n,n)
...
\r\nThe fourth typed 5, which is a prime
\r\nThe fifth typed 23, and 2x3 = 6
\r\nThe sixth typed 7, another prime
\r\nThe seventh typed 222, and 2x2x2=8...
\r\n
\r\nso I\'d say Agent Argent had to type 33, since 3x3=9.
\r\n\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12682,1264,6033,'jet','maybe...','2004-03-16 09:26:00',0,'0 1 2 1 0
',NULL,1);
INSERT INTO comment VALUES (12684,1675,6039,'K','solution','2004-03-16 10:44:26',0,'
1 1 2 1 1
2 2 0 2 2
1 1 2 1 1
0 1 2 1 0var letters = \"abcdefghijklmnopqrstuvwxyz\";
var vals = new Array();
for (var i = 1; i <= 26; i++) {
var n = i*(i+1);
vals[n] = letters.charAt(i-1);
}function parseCode(val) {
if (val == \"/\")
return \" \";
else if (isInteger(val))
return vals[code[i]];
else
return \" \" + val + \" \";
}function isInteger(val){
var string=\"1234567890\";
for(var i = 0; i < val.length; i++)
if(string.indexOf(val.charAt(i)) == -1)
return false;
return true;
}var code = \"6 342 30 2 132 / 420 72 30 / 12 240 20 30 / 420 240 / \";
code += \"342 30 506 30 2 156 / 2 / 42 2 182 240 462 380 / 272 72 3\";
code += \"42 2 380 30 / 2 210 20 / 90 420 380 / 2 462 420 72 240 34\";
code += \"2 : 420 240 / 6 30 / 240 342 / 210 240 420 / 420 240 / 6 \";
code += \"30 ; 420 72 2 420 / 90 380 / 420 72 30 / 306 462 30 380 4\";
code += \"20 90 240 210 . ~ 552 90 156 156 90 2 182 / 380 72 2 132 \";
code += \"30 380 272 30 2 342 30\".split(\" \");var result = \"\";
for (var i = 0; i < code.length; i++) {
result += parseCode(code[i]);
}document.write(result);
\r\nbreak the code to reveal a famous phrase and its author :
',NULL,1);
INSERT INTO comment VALUES (12693,1685,2899,'Brian Wainscott','Solution','2004-03-16 15:02:30',3,'Someone (Charlie I think?) went through this in one of\r\nthe previous problems.\r\n\r\nThe key is the instantaneous closing velocity between the\r\nbugs. Consider the bug A at the bottom left. At the instant\r\nthey start, he heads to the right at a speed of 1 inch per second.\r\nThe bug B he is headed toward moves with a velocity of\r\n(1/2, sqrt(3)/2). This means that A is approaching B at\r\na speed of 1/2 at that instant.\r\n\r\nAs the motion progresses, the relative positions change\r\nbut the angles never do. A will continue to approach B\r\nat a rate of 1/2. This means they will meet in 20 seconds.\r\nSo each bug will have traveled 20 inches.',NULL,0);
INSERT INTO comment VALUES (12694,1685,1171,'nikki','Solution','2004-03-16 16:55:35',3,'
to be or not to be ; that is the question . ~ william shakespeare
\r\n
\r\nWhile you have the right idea... you have a bug in your program:
\r\n
\r\nyour fast pointer jumps TWO nodes each cycle. It is possible that\r\nyou are only one away from the end of the list... and you will\r\ndereference the NULL pointer (if fast->next is NULL), and your code\r\nwill throw an exception.
\r\n\r\n\r\n',12700,1);
INSERT INTO comment VALUES (12703,1458,1301,'Charlie','re: Am I being thick','2004-03-17 08:21:39',0,'That\'s touching it with a gas--the extra air in the breath.',12697,1);
INSERT INTO comment VALUES (12704,1737,5285,'Ady TZIDON',' speedy SOLUTION','2004-03-17 08:33:57',3,'it took me 5 sec to arrive at 37\r\n\r\nif I find a smaller number I\'ll post a new solution\r\n\r\nady \r\nREM: ORIGINALLY I PUY 53 AND THEN (stupid!!) \"corrected \" to 37\r\n5 sec is good enough - the rest is tragedy..\r\n\r\n.... not to be carried away\r\n\r\nady\r\n\r\n\r\n\r\nEdited on March 17, 2004, 8:36 am\n\nEdited on March 17, 2004, 3:40 pm',NULL,0);
INSERT INTO comment VALUES (12705,1737,5285,'Ady TZIDON','Best and final','2004-03-17 08:38:42',3,'17\r\n\r\nTHE WORDING WAS TRICKY \r\nTHE ANS IS FINAL\r\nedited: NO IT IS NOT-- 17 DIVIDES 17 \r\n\r\n\r\nSEE MY ORIGINAL ANSWER ==1st POSTING\r\nady\r\n\r\n\n\nEdited on March 17, 2004, 2:41 pm',NULL,0);
INSERT INTO comment VALUES (12706,1737,5777,'Thalamus','re: Best and final','2004-03-17 08:41:55',0,'very interesting... but last time I checked... 17 is divisible by 17.
\r\n
\r\n\"THE ANS IS FINAL\"... Ady... you crack me up.
\r\n\r\n\r\n',12705,1);
INSERT INTO comment VALUES (12707,1737,4670,'e.g.','re: Best and final','2004-03-17 08:42:39',0,'17 is divisible by a number below 20...\r\n\r\n',12705,1);
INSERT INTO comment VALUES (12708,1737,5352,'Juggler','re: Best and final','2004-03-17 08:44:27',0,'
DIM pr(8)
FOR i = 1 TO 8
READ pr(i)
NEXT
i = 20
DO
i = i + 1
good = 1
FOR j = 1 TO 8
q = i \\ pr(j)
IF q * pr(j) = i THEN good = 0: EXIT FOR
NEXT
IF good THEN
n$ = LTRIM$(STR$(i))
l = LEN(n$)
s = 0
FOR j = 1 TO l
s = s + VAL(MID$(n$, j, 1))
NEXT
avg = s / l
IF avg = INT(avg) THEN
IF avg MOD 2 = 0 AND avg > 2 AND avg < 9 THEN
PRINT i
ct = ct + 1
IF ct = 40 THEN END
END IF
END IF
END IF
LOOP
71
79
97
1069
1087
1249
1357
1429
1447
1483
1537
1591
1609
1627
1663
1681
1753
1861
1933
1951
2059
2077
2239
2257
2293
2347
2383
2419
2437
2473
2491
2581
2617
2671
2707
2833
2851
2923
3049
\r\n
\r\nFrom the looks of previous problems (and their associated comment\r\nlists), it seems that this happens a lot.... Why did this\r\nparticular instance pique your interest?\r\n\r\n',12719,1);
INSERT INTO comment VALUES (12721,1737,5285,'Ady TZIDON','mea culpa','2004-03-17 14:30:58',1,'you are right\r\nI GOOFED\r\nedition 2: you are not right\r\nwe GOOFED (3+7)/2=odd\r\n\r\nplease refer to my 1st post\r\n\r\nSPEED IS BEAUTIFUL (SAID THE PUSHER)\r\n\r\n\r\n\r\n\r\nady\r\n\r\n\n\nEdited on March 17, 2004, 3:09 pm',12709,0);
INSERT INTO comment VALUES (12722,1675,775,'Cory Taylor','re: a practical solution','2004-03-17 14:35:56',0,'
\r\n
\r\nHe said 37 is the right answer. Please read Charlie\'s solution.
\r\n\r\n\r\n',12721,1);
INSERT INTO comment VALUES (12724,1737,5285,'Ady TZIDON','re: Pay Attention/ speedy is better','2004-03-17 14:39:26',0,'Please read my 1st post : IT WAS 53 AND THEN EDITED TO 37\r\nHeaven knows why I tried to improve my original solution\r\nI have to edit the amendment\r\nady\r\n\r\n\r\nady\n\nEdited on March 17, 2004, 3:37 pm',12719,0);
INSERT INTO comment VALUES (12725,1706,4670,'e.g.','Half a solution','2004-03-17 14:54:52',3,'Applying Pythagoras, AP squared plus CP squared must equal BP squared plus DP squared, so DP = √6.\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12726,511,6056,'darren','on god','2004-03-17 16:48:20',0,'Who is to say this god is omni-potent, us? the god itself? What if a new more powerful god spontaneously appears?',NULL,0);
INSERT INTO comment VALUES (12727,1623,6056,'darren','King decides','2004-03-17 17:08:31',0,'The man who saved the Princess was the King!\r\n\r\nHence he could marry her himself, there are precedents!',NULL,0);
INSERT INTO comment VALUES (12728,1737,6044,'Wally','re: Solution','2004-03-17 17:16:14',0,'Is the average of the digits not 5? Or am I missing something?',12709,0);
INSERT INTO comment VALUES (12729,1737,1575,'DJ','re(2): Solution','2004-03-17 20:38:08',0,'Since the only even numbers between 3 and 9 are 4, 6, and 8 -- no, the average of the digits isn\'t five.',12728,1);
INSERT INTO comment VALUES (12730,1706,6028,'Barrett Hasseldine','re: Half a solution','2004-03-17 20:53:19',0,'I\'ll agree with that. I did it another way, again using Pythag\'s Thm 4 times to get that length(DP) = SQRT(6).\r\nAs for the angle...yeah',12725,0);
INSERT INTO comment VALUES (12731,1706,1301,'Charlie','the other half','2004-03-17 22:03:40',0,'
cos(BPC) = (9+4-S^2)/12
cos(APC) = (1+9-2*S^2)/6
BP^2=x^2+y^2 = 4
CP^2=x^2+z^2 = 9
DP^2=w^2+z^2
s^2=13-12cosB
s^2=15-6sqrt(6)cosC
s^2=7-2sqrt(6)cosD
Also, A+B+C+D = 2pi
\r\n
\r\n1. a to D1
\r\n2. d to B1
\r\n3. c to A1
\r\n4. c to A3
\r\n5. b to E5
\r\n6. b to C5
\r\n7. b to C2
\r\n8. a to D5
\r\n9. a to C5
\r\n10. a to C3... voila!
\r\n\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12739,511,4739,'ben','Reading to deep','2004-03-18 08:44:12',2,'I think it\'s obvious that the God in this question is the steriotypical omnipotent being that we learn about in primary school. To philophosise about the whos? and whats?..etc is a bit pointless. And if the question is pointless why post an answer at all!',NULL,0);
INSERT INTO comment VALUES (12740,1706,1920,'Brian Smith','Two possibilities','2004-03-18 09:22:22',0,'
Let P be at (x,y).
(AP)^2 = 1 = x^2 + y^2
(BP)^2 = 4 = (x-d)^2 + y^2
(CP)^2 = 9 = (x-d)^2 + (y-d)^2
(DP)^2 = x^2 + (y-d)^2
((x-d)^2 + y^2) - (x^2 + y^2) = 4 - 1
d^2 - 2dx = 3
x = (d^2 - 3)/(2d)
y = (d^2 - 5)/(2d)
P is outside the square in this case.
(sqrt(5 - 2*sqrt(2)))^2 = 1^2 + 2^2 - 2*1*2*cos(angle APB)
P is inside the square in this case.
(sqrt(5 + 2*sqrt(2)))^2 = 1^2 + 2^2 - 2*1*2*cos(angle APB)If we call the first A a, then
aGYa produces
YGM
a E
ASRthen aASa produces
YGM
A E
SaRthen AYGA produces
GAM
Y E
SaRthen aREa produces
GAM
Y a
SREthen aMAa produces
GaA
Y M
SREand aGYa produces
YGA
a M
SREThat\'s 6 x 4 = 24 moves.
But there were two places where a was moved twice in a row.
So once those two pairs are shortcutted, this is a 20-move solution.
',NULL,1);
INSERT INTO comment VALUES (12757,1536,1575,'DJ','one way','2004-03-18 17:19:33',3,'G A M
Y E
A S RG M
Y A E
A S R G M
Y A E
A S RY G M
A E
A S RY G M
A A E
S RY G M
A A E
S RY G M
A E
S A RY G M
A E
S A R G M
Y A E
S A RG M
Y A E
S A RG A M
Y E
S A RG A M
\r\n
Y A E
S RG A M
Y A E
S RG A M
Y A E
S R G A M
Y A
S R EG A
Y A M
S R EG A
Y A M
S R E G A
Y A M
S R EY G A
A M
S R EY G A
\r\n
A M
S R E
\r\n
\r\nPerhaps the taxi driver took a wrong turn, so was going in \"the wrong\r\ndirection\" but not committing a traffic violation. The question\r\nremains, of course, how the policemen would know this.
\r\n\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12764,1536,5285,'Ady TZIDON','re(2): it is MORE......... att: Federico','2004-03-19 08:11:10',1,'ok\r\nby now I saw it done\r\nthanks\r\nady',12762,0);
INSERT INTO comment VALUES (12765,1718,2839,'FatBoy','No Subject','2004-03-19 08:54:38',0,'If they were police in my city, the answer would probably be that they did not feel like interrupting their conversation.',NULL,1);
INSERT INTO comment VALUES (12766,1694,2839,'FatBoy','re: Well now...','2004-03-19 08:56:11',0,'Thanx Sam, I\'m gald someone noticed/commented on my little joke',12695,1);
INSERT INTO comment VALUES (12767,1735,4670,'e.g.','Possibility','2004-03-19 09:06:01',3,'All I could find is that if you take the first and last three letters,\r\nyou get words: HARD, SING, HACK, DAFT, BILE, DENT, FEET and IONS... I\r\ndon\'t know if that\'s the solution, but it\'s something in common, at\r\nleast! ;-)\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12768,1536,1301,'Charlie','my final answer','2004-03-19 11:00:59',3,'Here are the 6 sequences that accomplish this in 18 moves,
which is in fact the minimum.
All leave the G at the top middle position.
All start fromgAm
y e
asrwhere the all letters except the first A have been converted to lower case:
ygAygasregaAyagmag 18
yga
A m
sre
ygAygasgaAyagremag 18
yga
A m
sre
yasreyagAaymaygAyg 18
yga
A m
sre
yasyagAayremaygAyg 18
yga
A m
sre
AgyasreAaygaAmagyA 18
yga
A m
sre
AgyasAaygaAremagyA 18
yga
A m
sreThese were found by the recursive program:
DECLARE SUB showBoard ()
DECLARE SUB move ()
DEFINT A-Z
DATA g,A,m,y,\" \",e,a,s,r
DIM SHARED board$(3, 3)
FOR i = 1 TO 3
FOR j = 1 TO 3
READ board$(i, j)
NEXT
NEXT
DIM SHARED seqX(16), seqY(16)
DATA 1,2, 1,3, 2,3, 3,3, 3,2, 3,1, 2,1, 1,1
DATA 1,2, 1,3, 2,3, 3,3, 3,2, 3,1, 2,1, 1,1
FOR i = 1 TO 16
READ seqY(i)
READ seqX(i)
NEXTDIM SHARED gX, gY, blX, blY, hist$
gY = 1: gX = 1
blY = 2: blX = 2
hist$ = \" \"CLS
showBoardmove
SUB move
STATIC solCt
IF LEN(hist$) > 19 THEN EXIT SUB
lMove$ = RIGHT$(hist$, 1)
IF blX = 2 AND blY = 2 THEN
mY = 2: mX = 1: GOSUB moveIt
mX = 3: GOSUB moveIt
mY = 1: mX = 2: GOSUB moveIt
mY = 3: GOSUB moveIt
ELSEIF blY = 2 AND blX = 1 THEN
mY = 1: mX = 1: GOSUB moveIt
mY = 3: GOSUB moveIt
mY = 2: mX = 2: GOSUB moveIt
ELSEIF blY = 2 AND blX = 3 THEN
mY = 1: mX = 3: GOSUB moveIt
mY = 3: GOSUB moveIt
mY = 2: mX = 2: GOSUB moveIt
ELSEIF blY = 1 AND blX = 2 THEN
mX = 1: mY = 1: GOSUB moveIt
mX = 3: GOSUB moveIt
mX = 2: mY = 2: GOSUB moveIt
ELSEIF blY = 3 AND blX = 2 THEN
mX = 1: mY = 3: GOSUB moveIt
mX = 3: GOSUB moveIt
mX = 2: mY = 2: GOSUB moveIt
ELSEIF blY = 1 AND blX = 1 THEN
mX = 1: mY = 2: GOSUB moveIt
SWAP mX, mY: GOSUB moveIt
ELSEIF blY = 1 AND blX = 3 THEN
mX = 2: mY = 1: GOSUB moveIt
mX = 3: mY = 2: GOSUB moveIt
ELSEIF blY = 3 AND blX = 1 THEN
mX = 2: mY = 3: GOSUB moveIt
mX = 1: mY = 2: GOSUB moveIt
ELSEIF blY = 3 AND blX = 3 THEN
mX = 3: mY = 2: GOSUB moveIt
SWAP mX, mY: GOSUB moveIt
END IF
EXIT SUBmoveIt:
IF board$(mY, mX) <> RIGHT$(hist$, 1) THEN
hist$ = hist$ + board$(mY, mX)
sblY = blY: sblX = blX: sgY = gY: sgX = gX
board$(blY, blX) = board$(mY, mX)
board$(mY, mX) = \" \"
IF board$(blY, blX) = \"g\" THEN
gY = blY: gX = blX
END IF
blY = mY: blX = mX move
IF LEN(hist$) > 8 THEN GOSUB checkIt
board$(sblY, sblX) = \" \"
board$(blY, blX) = RIGHT$(hist$, 1)
hist$ = LEFT$(hist$, LEN(hist$) - 1)
gY = sgY: gX = sgX: blY = sblY: blX = sblX
END IF
RETURNcheckIt:
good = 0
FOR i = 1 TO 7 STEP 2
IF gY = seqY(i) AND gX = seqX(i) THEN
good = 1: EXIT FOR
END IF
NEXT
IF good THEN
FOR j = 1 TO 7
IF LCASE$(board$(seqY(i + j), seqX(i + j))) <> MID$(\"amersay\", j, 1) THEN
good = 0: EXIT FOR
END IF
NEXT
END IF
IF good THEN
PRINT hist$, LEN(hist$) - 1
showBoard
solCt = solCt + 1
IF solCt / 10 = INT(solCt / 10) THEN : DO: LOOP UNTIL INKEY$ > \"\"
END IF
RETURN
END SUBSUB showBoard
FOR i = 1 TO 3
FOR j = 1 TO 3
PRINT board$(i, j);
NEXT
PRINT
NEXT
END SUB
',NULL,1);
INSERT INTO comment VALUES (12769,1536,1301,'Charlie','re: my final answer','2004-03-19 11:11:53',0,'gAm
\r\n
y e
asr
yasreyagAmyagsreagmAsrem 24
sAy
r g
ema
emAgyesaesmramrAgysrAgyA 24
sAy
r g
ema
AgyAemgyAesaesmramrgyAsr 24
sAy
r g
ema
sremAsyaremyagsAyagremag 24
sAy
r g
ema ygAmersygAmersygAmersA 22
\r\n
ers
m A
agy
AmersAygmersAygmersAyg 22
ers
m A
agy ygAmersygAmgAayAgmag 20
ame
g r
yAs
yasyAgaAysAygmersAyg 20
ame
g r
yAs
AgyasAaygaAsygamersA 20
ame
g r
yAs
AmersaygmAaygaAmagyA 20
ame
g r
yAs
DECLARE FUNCTION lcm! (a!, b!)
DECLARE FUNCTION gcd! (a!, b!)
DIM SHARED hist(21), tot
hist(1) = n: tot = n
try 1
NEXT
dnd = a
dvr = b
DO
r = dnd MOD dvr
dnd = dvr
dvr = r
LOOP UNTIL r = 0
gcd = dnd
END FUNCTION
lcm = a * b / gcd(a, b)
END FUNCTION
STATIC lmax
IF tot = 21 THEN
l = hist(1)
FOR i = 1 TO n
l = lcm(l, hist(i))
NEXT
IF l > lmax THEN
t = 1
lmax = l
PRINT
FOR i = 1 TO n
PRINT hist(i);
NEXT
PRINT : PRINT l
END IF
ELSE
IF 21 - tot >= hist(n) THEN
FOR addIn = hist(n) TO 21 - tot
tot = tot + addIn
hist(n + 1) = addIn
try n + 1
tot = tot - addIn
NEXT
END IF
END IF
END SUB
6
10
12
14
20
30
42
60
210
420 6 2 4 4
\r\n
7 3 4 12
8 3 5 15
9 4 5 20
10 2 3 5 30
11 5 6 30
12 3 4 5 60
13 6 7 42
14 3 4 7 84
15 3 5 7 105
16 4 5 7 140
17 2 3 5 7 210
18 5 6 7 210
19 3 4 5 7 420
20 5 7 8 280
21 2 3 4 5 7 420
22 3 3 4 5 7 420
23 3 5 7 8 840
24 7 8 9 504
25 4 5 7 9 1260
26 3 5 7 11 1155
27 4 5 7 11 1540
28 2 3 5 7 11 2310
29 5 7 8 9 2520
30 3 4 5 7 11 4620
31 5 7 8 11 3080
32 3 4 5 7 13 5460
33 3 3 4 5 7 11 4620
34 3 5 7 8 11 9240
35 7 8 9 11 5544
36 4 5 7 9 11 13860
37 3 3 5 7 8 11 9240
38 4 5 7 9 13 16380
39 3 5 7 11 13 15015
40 5 7 8 9 11 27720
41 2 3 5 7 11 13 30030
42 5 7 8 9 13 32760
43 3 4 5 7 11 13 60060
44 5 7 8 11 13 40040
45 2 3 4 5 7 11 13 60060
46 3 3 4 5 7 11 13 60060
47 3 5 7 8 11 13 120120
48 7 8 9 11 13 72072
49 4 5 7 9 11 13 180180
50 3 3 5 7 8 11 13 120120DECLARE SUB try (n!)
DECLARE FUNCTION lcm! (a!, b!)
DECLARE FUNCTION gcd! (a!, b!)
CLEAR , , 4000DIM SHARED hist(200), histMax(200), tot
DIM SHARED goalTot, lmax, nForMax
FOR goalTot = 6 TO 50
lmax = 0
FOR n = 2 TO goalTot - 2
hist(1) = n: tot = n
try 1
NEXT
t = 0
FOR i = 1 TO nForMax
t = t + histMax(i)
NEXT
PRINT t; TAB(7);
FOR i = 1 TO nForMax
PRINT histMax(i);
NEXT
PRINT TAB(30); lmax
NEXT goalTotFUNCTION gcd (a, b)
dnd = a
dvr = b
DO
r = dnd MOD dvr
dnd = dvr
dvr = r
LOOP UNTIL r = 0
gcd = dnd
END FUNCTIONFUNCTION lcm (a, b)
lcm = a * b / gcd(a, b)
END FUNCTIONSUB try (n)
',12778,1);
INSERT INTO comment VALUES (12780,1770,1301,'Charlie','re(5): My solution','2004-03-19 23:01:58',0,'The obvious bug in my previous post is that it does not allow for the maximum just to be concentrated in one loop (one number). The best you can do with 6 stations is to connect them all in a cycle of 6, not to have a cycle of 2 and a cycle of 4, devolving to just a period of 4.',12779,1);
INSERT INTO comment VALUES (12781,1735,4507,'Penny','Letters in common','2004-03-20 09:17:02',3,'
IF tot = goalTot THEN
l = hist(1)
FOR i = 1 TO n
l = lcm(l, hist(i))
NEXT
IF l > lmax THEN
t = 1
lmax = l
FOR i = 1 TO n
histMax(i) = hist(i)
NEXT
nForMax = n
END IF
ELSE
IF goalTot - tot >= hist(n) THEN
FOR addIn = hist(n) TO goalTot - tot
tot = tot + addIn
hist(n + 1) = addIn
try n + 1
tot = tot - addIn
NEXT
END IF
END IF
END SUBHere\'s a chart for dimensions 1 through 7:
\r\n
V E F S
2 1 0 0 0 0 0 0 line segment
4 4 1 0 0 0 0 0 square
8 12 6 1 0 0 0 0 cube
16 32 24 8 1 0 0 0 hypercube
32 80 80 40 10 1 0 0
64 192 240 160 60 12 1 0
128 448 672 560 280 84 14 1
Could he be a knave? Let\'s assume so and see what happens.
2 is false, so A must have said what he wasn\'t.
3 is true so he knows what A is, therefore A\'s answer must have been \"I\'m not a knight\". So A is a knave telling truth.
4 is false so B says he\'s either knave or knight or a liar.
5 is true so A is lying and C is either knave or liar.
6 is false so friend doesn\'t yet know what C is.
7 is true so B says C is knave.
8 is false -irrelevant
9 is true. Since we don\'t yet know what C is, the only way this is possible is if we already know what B is, which means B\'s statement about himself was that he is a liar, which we know is false, so he is a knave and his next statement (about C) is true so C is a knave.
But which solution is correct? Either there is no way to tell, in which case the riddle is unsolvable or else the clue lies in the title and the last statment contradicting each other, giving us the hint that everyone is in fact a knave.
The solution she gives there is
\"Then each bug will have gone:
V*T = L/(1-cos[2*pi/N radians]) \"
For L=10, N=6
10/(1-cos[2*pi/6 radians])
= 10/(1-cos[60 degrees])
= 10/0.5
=20',NULL,1);
INSERT INTO comment VALUES (12804,1623,6116,'Galendir','Solution','2004-03-21 14:36:07',3,'The brother who gave her the apple, because the other two could still use their gifts, but the third brother lost the use of his for the sake of the princess.',NULL,1);
INSERT INTO comment VALUES (12805,1770,6116,'Galendir','My Solution','2004-03-21 15:31:25',3,'
B H S N T T S P A Z
C A M U H I R L C Z
C T A M A S A H L Y
D I L B T E A I R U
D S L E A T I E D W
D T E R L E E B R W
E H S S L L R A O X
The next part is still mixed up, so rearrange the last column into reverse alphabetical order, to get:
B H S N T T S P A Z
C T A M A S A H L Y
E H S S L L R A O X
D T E R L E E B R W
D S L E A T I E D W
A W E T O T N T E V
D I L B T E A I R U
Reading down from the middle column gives:
Two - x
Three - x
Four - x
Five - x
Six - x
Seven - x
Eight - x
Nine - x
Ten - x
Eleven - x
Twelve - x
\r\n1. it is positive
\r\n2. It is not divisible by any number lower than 20:
\r\n 53/2=26.5
\r\n 53/3=17.67
\r\n 53/4=13.25
\r\n 53/5=10.6
\r\n 53/6=8.833
\r\n 53/7=7.571
\r\n 53/8=6.625
\r\n 53/9=5.89
\r\n 53/10=5.30
\r\n 53/11=4.818
\r\n 53/12=4.42
\r\n 53/13=4.08
\r\n 53/14=3.786
\r\n 53/15=3.533
\r\n 53/16=3.3125
\r\n 53/17=3.12
\r\n 53/18=2.944
\r\n 53/19=2.789
\r\n3. the average of its digits is 4 ((5+3)/2=4)
\r\n\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12810,1539,4507,'Penny','re: Fully explained solution','2004-03-21 17:56:10',0,'
\r\n\r\n
\r\n\r\nAn equation for n bottles would be: (2n)+(3(n-1))+(3(n-2))+(3(n-3))+(3(n-4))...(3(n-(n-1)))+(3(n-(n-0)))
\r\n\r\nbecause one only counts the first number of bottles twice and then each ensuing number of bottles three times:
\r\ne.g. \"99 bottles of beer on the wall, 99 bottles of beer. Take one down, pass it around, 98 bottles of beer on the wall. 98 bottles of beer on the wall, 98 bottles of beer...\"
\r\n\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12813,649,6114,'logischer Verstand','a possible answer','2004-03-21 23:37:55',3,'For this problem, I will refer to the first bag (the bag containing 3\r\nblack marbles and 1 white marble) as bag A and the second bag (the bag\r\ncontaining 3 white marbles and 1 black marble) as bag B.
\r\n
\r\nFirst, let\'s take into account the probability one picked bag A\r\n(1/2). The probability that, on the first draw, one drew out a\r\nblack marble is 3/4. The probability that one drew out a black\r\nmarble on the second\r\ndraw would again be 3/4. Thus, the probability that one draws a\r\nblack marble on both tries is (3/4)*(3/4)=9/16. Do not forget the\r\nprobability they picked bag A, so (9/16)*(1/2)=9/32 of a chance that\r\none randomly drew two black marbles out of randomly picked bag A.
\r\n
\r\nSecond, we must take into account the probability of this also\r\nhappening with one randomly picking bag B (which has 1/2\r\nprobability). The probability of one drawing a black marble out\r\non both tries in bag B would be: (1/4)*(1/4)*(1/2)=1/32.
\r\n
\r\nThus, the probability of this event happening would be (9/32)+(1/32)=10/32 or 5/16.
\r\n
\r\n\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12814,1675,6116,'Galendir','Proposed solution','2004-03-21 23:46:32',3,'
Displace the remaining tea in the measuring cup with enough ice cubes to bring the liquid level back up to the 4 cup mark. (Be sure to count them.) The total volume of the ice will be equal to 2 cups of water.
Add that many again ice cubes to the pitcher.
A = 3.75
3.75/9B = B/15
56.25 = 9B²
B² = 6.25
B = 2.5
a/b = 4a/9b or <p>
a/b = 4b/9a <p>
9a^2 = 4b^2 <p>
3a = 2b
Width 15, Height 10 (little rectangles 2.5 x 5/3)
What are? Water
Sorry.
Also can form a tsunami
10^(-7) moles per liter hydronium ions
\r\n\r\nLet y stand for how long the sheet is, then:
\r\n\r\n(y/9)=(15/4)
\r\n\r\n(9*15)/4=y=33.75
\r\n\r\nThe sheet is 33.75\" x 15\"\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12941,1549,1301,'Charlie','re: thoughts','2004-03-24 08:38:04',0,'... and if that\'s the answer, it\'s more like adding 4/5 of \"seven\" to 1/3 of \"twelve\" and not dividing anything.',12940,1);
INSERT INTO comment VALUES (12942,1549,1920,'Brian Smith','Solution','2004-03-24 08:48:28',0,'
One fifth of seven is \"v\"
lv=55 and v=5 in Roman numerals.
lv/v = 55/5 = 11
\r\n
\r\nIt\'s not. If it was the midpoint it would be in the middle of the circle. That\'s like, so first grade...
\r\n\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12955,357,6159,'Shanna','Answer here','2004-03-24 17:10:18',3,'
\r\n
\r\nwas up late last night too tired to think much
\r\nsooo whats your solution?
\r\n
\r\n
\r\n1 + 7 = 8
\r\n8 / 2 = 4 average is even and between 3 & 9
\r\n17 is not divisible by any number below 20
\r\n ( unless you count itself ??? 17/17 = 1)
\r\nin that case it would have to be
\r\n37
\r\n
\r\n\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12863,1706,6114,'logischer Verstand','an answer','2004-03-22 18:56:25',3,'Instead of using pure mathematics to solve this problem, I used\r\nexperimentation instead (but there were still some preliminary\r\nmathematics).
\r\n
\r\nBecause AP=1 and CP=3, the longest possible diameter AC of square ABCD\r\nis 4 (1+3). Thus, the longest side length is: 2(a^2)=(4^2)
\r\n2(a^2)=16
\r\n(a^2)=8
\r\na=sqrt(8) or about 2.82.
\r\n
\r\nUsing experimentation, one can find the necessary side length so that\r\narcs with radii of 1 (with an origin at point A), 2 (with an origin at\r\npoint B), and 3 (with an origin at point C) meet at a single point P\r\ninside square ABCD is equal to 2.79. Through simple measurement,\r\nDP=2.45 or sqrt(6) and angle APB=137.4 degrees (an estimate).
\r\n
\r\n
\r\n\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12865,1721,4507,'Penny','yo','2004-03-22 19:37:08',0,'Some have been banned from this forum for engaging in personal attacks. A word to the wise.',NULL,1);
INSERT INTO comment VALUES (12866,1539,4507,'Penny','yo, oh, yo yo, yo yo, calling yo yo.......','2004-03-22 19:44:15',0,'
24578
24557
24558
25578
45578
24557 = 6
24558 = 7
25578 = 1
45578 = 3
... because it\'s cold there, get it? I know, it\'s not funny, but I\'m easily amused. Maybe because I\'m from the midwest too.
and that\'s my story
\r\n4 circles of 7 6 5 3
\r\nhavn\'t put the math to this but feels good if
\r\ni understand it right ? what say?
\r\n\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12920,1770,6158,'Jen','Novice','2004-03-23 19:19:09',3,'Maybe I am looking at this too naively. But, I think it is 20. I guess if I have to prove why. There are 21 circles. You blow the whistle once, the monkey goes to #2, blow it a second time it goes to #3. Showing a pattern of n - 1 = (number). 21-1=20. You would not count the first one as number 2, because then you would \"spill over\" and the dance would end. The dance would end at 21 whistles. So any more than 20 would be too many. The maximum times he could blow would be 20.',NULL,0);
INSERT INTO comment VALUES (12921,1801,3558,'Tristan','re: you tell me what subject be','2004-03-23 19:56:43',0,'
\r\n
\r\n
\r\nAND THE ANSWER IS>>>THE STARS
\r\n\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12923,686,6159,'Shanna','Simple as pie (And for me they arent usually that simple)','2004-03-23 20:09:15',0,'It was on a TV screen\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12924,428,6159,'Shanna','Kind of an answer...but...','2004-03-23 20:19:34',0,'
\r\n
\r\nI never was good at that British stuff...so I dunno if I\'m right or not...
\r\n
\r\n
\r\nLike hahahahahahahahaha
\r\nha
\r\nha
\r\n\r\n\r\n',4534,1);
INSERT INTO comment VALUES (12926,383,6159,'Shanna','DUDE THIS IS EASY','2004-03-23 20:28:33',0,'THIS IS IN THE BOOK OF PSALMS IN THE BIBLE
\r\n
\r\nSO EASY MAN
\r\n
\r\n
\r\nA STATUE
\r\n
\r\n
\r\nI swear i haven\'t looked @ the answer!!!
\r\n\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12927,344,6159,'Shanna','I swear','2004-03-23 20:39:57',0,'Have you been reading the back of the easy mac packs?
\r\n
\r\n
\r\nHe put a hole in the barrel
\r\n\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12928,334,6159,'Shanna','LOL','2004-03-23 20:49:33',0,'The answer to this riddle\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12929,1546,1301,'Charlie','re(2): with a computer (or a table of squares)','2004-03-23 20:58:57',0,'
Not true. The 5 tuple belonging to the original number is
either
8 5 4 7 2 or
8 5 4 5 2 or
8 5 5 7 2
All that out of \"digits sum\" consideration.
The prob. of the hundreds digit being even need to be evaluated for each of the cases along with the 5-tuples prob. as well. >>
\r\n
\r\nSo the answer is a chicken
\r\n\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12936,1718,6159,'Shanna','The easiest in the world (Heard it before)','2004-03-24 06:10:31',0,'The taxi driver wasn\'t...drumroll...driving the taxi!!!!
\r\n
\r\n
\r\nLOL
\r\n\r\n\r\n',NULL,1);
INSERT INTO comment VALUES (12937,211,6148,'rich harran','Ok, not it\'s not','2004-03-24 06:27:28',0,'ignored the even stretch of the band doh!',12875,0);
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post text,
authorId int(10) unsigned default NULL,
authorName varchar(40) default NULL,
posted datetime default NULL,
PRIMARY KEY (postId)
) TYPE=MyISAM;
--
-- Dumping data for table 'forumpost'
--
INSERT INTO forumpost VALUES (1,1,3,'Forums!','Hey, everyone, we have forums!\r\n\r\nJust wanted you to know.\r\n\r\nI probably need to figure some of the stuff out before everything works, but, hey, it\'s a start :)',1,'levik','2002-11-30 12:18:55');
INSERT INTO forumpost VALUES (2,1,3,'Re: Forums!','This is a test reply',1,'levik','2002-11-30 12:19:12');
INSERT INTO forumpost VALUES (3,1,3,'Re: Forums!','This is levik testing anonymous posting',NULL,'Bob','2002-11-30 12:53:22');
INSERT INTO forumpost VALUES (4,1,3,'Does this work?','It does',227,'Dulanjana','2002-11-30 16:09:46');
INSERT INTO forumpost VALUES (5,1,3,'Nice','Damn! I need to learn how to create forums :(((( ',746,'Raveen','2002-11-30 19:08:01');
INSERT INTO forumpost VALUES (6,2,4,'This is for?','\'Higher Ranking\' members to post.... ?',746,'Raveen','2002-11-30 19:10:24');
INSERT INTO forumpost VALUES (7,1,3,'Suggestions','Should there be a special forum like General, for \'Suggestions\' ? ',746,'Raveen','2002-11-30 19:16:48');
INSERT INTO forumpost VALUES (8,3,3,'Suggestions','The table on the right always blocks part of the table on the left. I mean, look, \'Logout\' is half covered. And on some pages, the problems are covered. Am I the only one who sees this problem? My resolution is 1024 x 768.',746,'Raveen','2002-11-30 19:25:54');
INSERT INTO forumpost VALUES (9,3,3,'Re: Suggestions','What browser are you using?',1,'levik','2002-11-30 21:16:09');
INSERT INTO forumpost VALUES (10,3,3,'Re: Suggestions','IE 6',746,'Raveen','2002-11-30 22:13:32');
INSERT INTO forumpost VALUES (11,3,3,'ok now','It seems to be OK now!',746,'Raveen','2002-11-30 22:18:25');
INSERT INTO forumpost VALUES (12,4,5,'Broken Link =D','The \'Your Information\' link is broken, its linked to http://www.flooble.com/\"user.php/\"\r
\n\"\"\r
\n\r
\n',746,'Raveen','2002-11-30 22:21:00');
INSERT INTO forumpost VALUES (13,4,5,'Re: Broken Link =D','Ought to be fixed. Thank you.',1,'levik','2002-12-01 05:47:58');
INSERT INTO forumpost VALUES (14,3,3,'Re: Suggestions','It\'s not really fixed, I just made it less apparent. \r
\n\r
\nThere seems to be an IE bug that makes it fail to figure in padding specified in the stylesheet for the purpose of calculating the width of a cell.\r
\n\r
\nThis causes it to think that the cell is \"wider\" than it actually is, and all the right-aligned elements are rendered too close to thecells edge, resulting in some parts not fitting into the cell.\r
\n\r
\nAll I did is reduce CSS-specified padding from 4 pixels to 2, so the effect is diminished, but not gone completely.\r
\n\r
\nIE\'s great, isn\'t it? This site works perfect with Mozilla browsers.',1,'levik','2002-12-01 05:54:57');
INSERT INTO forumpost VALUES (15,1,3,'Re: Forums!','Does leapfrogging work?',1,'levik','2002-12-01 07:23:09');
INSERT INTO forumpost VALUES (16,2,4,'Re: This is for?','Yea i guess so. And What do you discuss here?',227,'Dulanjana','2002-12-01 20:31:38');
INSERT INTO forumpost VALUES (17,2,4,'We discuss...','We shall discuss what we will discuss. HEY! is that a paradox by any chance? :S',746,'Raveen','2002-12-02 00:03:51');
INSERT INTO forumpost VALUES (18,3,3,'Table Bug','Yea, spotted a button half covered by the table, but wasn\'t a hinderence to navigation, so didn\'t \'bitch\' about it! \r
\nHehe yea, IE rulz!',746,'Raveen','2002-12-02 00:09:13');
INSERT INTO forumpost VALUES (19,2,4,'Re: This is for?','I don\'t think so.',1,'levik','2002-12-02 04:43:38');
INSERT INTO forumpost VALUES (20,5,5,'Latest Comments Numbering..','Good addition! Now it doesn\'t seem like the site is inactive everytime I return to the site and have to go looking for new posts! A certain Thumbs Up :D',746,'Raveen','2002-12-02 04:54:50');
INSERT INTO forumpost VALUES (21,5,5,'Re: Latest Comments Numbering..','I\'m actually considering adding a \"New for You\" page, that would show each visitor new problems, comments (and now, possibly, forum posts) that have been added since he last visited.\r
\n\r
\nBut I\'m still not sure how all of that can be done in a way that wouldn\'t kill the system by doing too many queries.',1,'levik','2002-12-02 08:02:09');
INSERT INTO forumpost VALUES (22,3,3,'Re: Suggestions','Let\'s not start a flame war here....',1,'levik','2002-12-02 08:02:57');
INSERT INTO forumpost VALUES (23,2,4,'Re: This is for?','Okay, how about we all refuse to discuss what we\'re discussing then? Is that better. ;-)\r
\nOkay, this doesn\'t seem the board for this kind of chatter - I\'ll stop now.',250,'Nick Reed','2002-12-02 08:04:11');
INSERT INTO forumpost VALUES (24,3,3,'Re: Suggestions','hmmm.. yeah sure, whatever that means! :p',746,'Raveen','2002-12-02 22:46:43');
INSERT INTO forumpost VALUES (25,5,5,'how about....','Latest posts numbering for the forum too ?',746,'Raveen','2002-12-02 23:28:18');
INSERT INTO forumpost VALUES (26,6,4,'So...','So Hows life?:s:s (What else have we got to discuss?!:)',227,'Dulanjana','2002-12-04 13:57:06');
INSERT INTO forumpost VALUES (27,6,4,'how about....','Is the world really round?',746,'Raveen','2002-12-04 21:46:14');
INSERT INTO forumpost VALUES (28,7,3,'mystery Water Problem','ok i have heard of this problem before but now i can not figure it our. ok here it is \r
\n\r
\na man drives into town with two full 20 gallon tanks filled with water. two men come to buy water and each want two gallons of water but the problem is that one man has a 5 Gal. can and the other a 3 Gal. can. how with out measuring in anyway or wasting any water can you get 2 gallons in each of the cans.',879,'Anthony','2002-12-06 15:02:37');
INSERT INTO forumpost VALUES (29,7,3,'Answers...','You will find answers to this here -> http://www.flooble.com/perplexus/show.php?pid=238\r
\n\r
\n(Is HTML allowed here?)\r
\nBOLD',746,'Raveen','2002-12-07 01:46:16');
INSERT INTO forumpost VALUES (30,7,3,'Link...','Water Question... <a href=\\\"http://www.flooble.com/perplexus/show.php?pid=238\\\" Click here for Answers to your question \n Click Here ',746,'Raveen','2002-12-07 01:50:29');
INSERT INTO forumpost VALUES (32,8,6,'Meanings...','Rational = ?\r
\n(will be posting more as I come across)',746,'Raveen','2002-12-07 01:52:13');
INSERT INTO forumpost VALUES (33,8,6,'Re: Meanings...','A \"Rational\" number as I recall is a number that can be expressed as a fraction of two integers.\r
\n\r
\n1/2 is rational, as is 124356/986865.\r
\n\r
\nPi (3.14....) is not.',1,'levik','2002-12-07 18:29:04');
INSERT INTO forumpost VALUES (34,7,3,'Re: mystery Water Problem','This is a quite different problem. \r
\n
\nYou can\'t waste any water (in fact in the original by Sam LLyod, I believe it is actually milk.) \r
\n
\nAlso, I believe the two Large tanks the peddler has are filled to the brim (these two are his first customers of the day). \r
\n
\nI don\'t remember the sequence, but it takes a lot of juggling, and (if I recall correctly) in the end, each of the two tanks is down by the two gallons that one of the men bought. ',153,'TomM','2002-12-08 13:43:04');
INSERT INTO forumpost VALUES (35,8,6,'Re: Meanings...','The name is not because 1/2 is any more sensible than √2, but rather that 1/2 is the \"ratio\" between 1 and 2, or 2 and 4, 3 and 6, etc.',153,'TomM','2002-12-08 13:48:18');
INSERT INTO forumpost VALUES (36,7,3,'Re: mystery Water Problem','Yes, my mistake.',746,'Raveen','2002-12-09 00:00:44');
INSERT INTO forumpost VALUES (37,8,6,'Re: Meanings...','Hey, I actually never knew that :)\r
\n\r
\nLearn something new every day.',1,'levik','2002-12-09 05:52:28');
INSERT INTO forumpost VALUES (38,9,3,'Ratings.','People seem to be forgetting to rate problems again. Ratings are kind of important, because I they allow groupings of problems by quality. With ratings we can see \"top problems\" as well as recent top, which are the highest rated for the month.\r
\n\r
\nAdditionally, I am looking to add an advanced search page (as the number of problems is growing it will make more sense), and filtering by score (Slashdot-style) would be useful.\r
\n\r
\nFinally, and this is not something I\'m sure about, I\'m thinking of having high-rating problems count for more when calculating user promotions. But this may prove too difficult to do.\r
\n\r
\nSO.... If you\'re logged in and looking at a problem you haven\'t rated yet, it will give you a small reminder by \"animating\" the rating prompt of the page. Hopefully nothing too distracting.',1,'levik','2002-12-09 05:57:56');
INSERT INTO forumpost VALUES (39,5,5,'Re: Latest Comments Numbering..','Done (if with a little bit of a delay)',1,'levik','2002-12-09 06:04:19');
INSERT INTO forumpost VALUES (40,9,3,'Re: Ratings.','No, not at all distractiong! Actually I didn\'t notice it untill I read Nicks message on the chatterbox and looked for it! ',746,'Raveen','2002-12-09 20:55:07');
INSERT INTO forumpost VALUES (41,9,3,'Re: Ratings.','ok, I just realized how helpful it is :D Thumbs Up! :p',746,'Raveen','2002-12-09 21:00:54');
INSERT INTO forumpost VALUES (42,8,6,'More meaning to it','Any number that can be expressed in (p/q) form where p and q are integers and q is non-zero is a rational number.\r
\n\r
\ne.g = 1/2, 0.33333...., 0.5\r
\n\r
\nAll numbers that aren\'t rational are irrational!\r
\n\r
\ne.g - pi , e , sqrt2, \r
\n\r
\nNote: Pi is not equal to 22/7 as some think. It is approximately equal to 22/7. It is irrational so it cannot be expressed in ratinal form.',227,'Dulanjana','2002-12-10 01:32:31');
INSERT INTO forumpost VALUES (43,10,6,'Another meaning...','What is a transcendal number? I have heard that Pi^2 is transcendal. Any ideas?',227,'Dulanjana','2002-12-10 01:33:47');
INSERT INTO forumpost VALUES (44,9,3,'Re: Ratings.','I noticed that for ages you can see what ratings people give, on average, and how many problems they\'ve submitted, by viewing their user stats. It might also be interesting to see the average rating of their problems too - this might be an interesting way to see if a person generally submits poor problems, or whatnot... Just a thought.',250,'Nick Reed','2002-12-10 02:13:45');
INSERT INTO forumpost VALUES (45,9,3,'Re: Ratings.','Not so sure about this. Is it really a good idea to publicly give negative feedback to people genuinely trying to contribute content?',103,'friedlinguini','2002-12-10 04:49:31');
INSERT INTO forumpost VALUES (46,10,6,'Re: Another meaning...','It\'s a number that isn\'t a root of any polynomial with rational coefficients, if I remember correctly. The square root of 2 isn\'t transcendental because it\'s a root of x^2 = 2. Not sure if complex numbers, quaternions, etc. can be transcendental...',103,'friedlinguini','2002-12-10 04:54:34');
INSERT INTO forumpost VALUES (47,9,3,'Re: Ratings.','Ah, true I suppose. I\'ll hush now then. ;-)',250,'Nick Reed','2002-12-10 08:11:34');
INSERT INTO forumpost VALUES (48,9,3,'Re: Ratings.','Hmmm, you both have good points. On one hand it\'s rather interesting to see people\'s average problem scores. On the other, fl is right about embarrasing people who are doing their best.\r
\n\r
\nI will have to think about it some more.',1,'levik','2002-12-10 09:36:31');
INSERT INTO forumpost VALUES (49,10,6,'Re: Another meaning...','Umm....Whats polynomial? (co-efficient is the 2 in 2x or the 3.5 in 3.5x right?)',227,'Dulanjana','2002-12-10 13:55:29');
INSERT INTO forumpost VALUES (50,10,6,'Re: Another meaning...','A polynomial is the sum of a number of \"terms\" where each \"term\" is of the form\r
\n[coeficient * (base1 ^ exponent1) * (base2 ^ exponent2) etc. the coefficient and the exponents are constants, the bases are variables.)\r
\n\r
\nIt\'s easier to give examples of polynomials than to define them:\r
\n\r
\nSome binomials (polynomials of two terms) include 2x + y, 5x² - 2x, 15y - 7, 4x²y - 3xy², and ax + b\r
\n\r
\nSome trinomials (polynomials of three terms) include x² - 2x +1, 5x + 6y + 3, and ax + by + cz\r
\n\r
\nA trancendental number is a number that either cannot be expressed as a polynomial(or its root), or only as a polynomial(or its root) which has an infinite number of terms.\r
\n\r
\nOf the three most famous non-trivial irrational numbers, pi and e are transcendental, while phi (the golden mean) is not, since it equals 1/2 + √5/2\r
\n\r
\nThe sequence of types of numbers goes \r
\n\r
\nIntegers\r
\n\r
\nRational Numbers (integers plus fractions)\r
\n\r
\nReal numbers (rational and irrational numbers, including transcendentals)\r
\n\r
\nComplex numbers (reals, imaginaries, and vector sums of a real and an imaginary part) \r
\n[Imaginary numbers are the product of a real absolute value and ±i, the square root of -1]',153,'TomM','2002-12-10 15:42:18');
INSERT INTO forumpost VALUES (51,9,3,'Re: Ratings.','A slight variation on Nick Reed\'s suggestion: Rather than posting the average rating of submitted problems, post a total of the ratings of all puzzles (the average rating times the number of submitted puzzles if my explanation wasn\'t too clear). Put up a link to \"Top Puzzlers\" or something like, listing either all contributors or the top N contributors. That way, even a Rating 1 puzzle will boost the submitter\'s score (hey, it was good enough to get accepted, right?). Ranking submitters on the same page also adds a competitive element that ought to create an incentive for people to submit problems.',103,'friedlinguini','2002-12-11 03:47:27');
INSERT INTO forumpost VALUES (52,11,5,'Forum thread suggestion','Currently, reading and responding to a thread is a two-step process. You click on the thread, then if you want to respond to it, you click on a link which takes you to a text box. Problem is, you sometimes want to refer back to a previous post, which is no longer visible. Why not add a text box to the bottom of the thread view? It saves an extra step of indirection and also solves the problem of not being able to refer back to previous comments.',103,'friedlinguini','2002-12-11 10:04:23');
INSERT INTO forumpost VALUES (53,12,4,'The queued limitation','Yep, its a good idea. Thought it was a headache to see 19 on queue. and to say two days per problem * 19 problems = 38 days till the last problem comes up!',227,'Dulanjana','2002-12-11 18:47:45');
INSERT INTO forumpost VALUES (54,12,4,'Re: The queued limitation','Actually, it\'s been a pretty stable one problem per day for about the past month or so. Except when we had the Quick Brown Fox problem, and I pushed another one that afternoon.',1,'levik','2002-12-12 01:41:05');
INSERT INTO forumpost VALUES (55,11,5,'Re: Forum thread suggestion','Yep, good suggesion. \r
\n',227,'Dulanjana','2002-12-12 03:53:39');
INSERT INTO forumpost VALUES (56,11,5,'Re: Forum thread suggestion','Allright, already! Stop badgering me! :)\r
\n\r
\nIt is a good idea, and I will add the feature first chance I get.',1,'levik','2002-12-12 05:03:36');
INSERT INTO forumpost VALUES (57,11,5,'Re: Forum thread suggestion','Ya gotta learn to stop asking for suggestions. :-)>',103,'friedlinguini','2002-12-12 05:18:39');
INSERT INTO forumpost VALUES (58,11,5,'Re: Forum thread suggestion','There, you happy? Now it will be much more of a hassle to add paging. \r
\n(you know, the thingie that breaks threads up into pages once they reach gargantuan proportions?)\r
\n\r
\nAnyway, enjoy, and keep the suggestions coming... Doh!',1,'levik','2002-12-12 11:42:28');
INSERT INTO forumpost VALUES (59,7,3,'Re: mystery Water Problem','Markings: \r
\n 1st 20 gallon tank 2nd 20 gallon tank\r
\n 3 gallon can 5 gallon can\r
\n\r
\n1) fill both cans, each from different tank:\r
\n 17 15\r
\n 3 5\r
\n2) empty the 3 gallon can into the second tank:\r
\n 17 18\r
\n 0 5\r
\n3) fill the 3 gallon can from the first tank:\r
\n 14 18\r
\n 3 5\r
\n4) empty the 5 gallon can into the first tank:\r
\n 19 18\r
\n 3 0\r
\n5) empty the 3 gallon can into the 5 gallon can:\r
\n 19 18\r
\n 0 3\r
\n6) fill the 3 gallon can from the second tank:\r
\n 19 15\r
\n 3 3\r
\n7) fill the 5 gallon can to the top from the 3 gallon can (2 gallons):\r
\n 19 15\r
\n 1 5\r
\n8) empty 1 gallon from the 3 gallon can into the second tank:\r
\n 19 16\r
\n 0 5\r
\n9) fill the 3 gallon can from the 5 gallon can:\r
\n 19 16\r
\n 3 2\r
\n10) fill the first tank to the top from the 3 gallon can:\r
\n 20 16\r
\n 2 2\r
\n\r
\nI don\'t know if what I got is the shortest solution to this problem...',283,'lucky','2002-12-13 04:13:09');
INSERT INTO forumpost VALUES (60,13,5,'Problems in forums','I think I am going to ask you guys to try and refrain from posting new problems in forums as a rule of thumb. The reason being that a problem posted in the forum will not be properly added to the database, and thus will not be counted for all the site\'s purposes. For example, it will not be \"credited\" tot he poster, and will not count towards a user level quota. It will not come up as an \"oldie\", or as a \"random\" problem. It will never be the problem of the day, which is perplexus\' way of letting users sydicate our contents. And it won\'t come up in search results (which is probably more of a defficiency on the part of the site\'s code, but that\'s just how it is for now)\r
\n\r
\nSo I would appreciate it if you would submit any new problems through the site\'s submission process. While it may sometimes take a while for the problem to be voted through the queue, once it is, it will be the top problem on the site for at least a day, making sure that it gets a lot of exposure and discussion.\r
\n\r
\nSorry if this seems rather harsh.\r
\n\r
\n- administration. :)',1,'levik','2002-12-13 05:47:32');
INSERT INTO forumpost VALUES (61,14,6,'Any difference','What is the difference between a theorem, axiom, corollary, and lemma?',227,'Dulanjana','2002-12-17 15:41:24');
INSERT INTO forumpost VALUES (62,14,6,'Re: Any difference','In general:\r
\nTheorem - something that is proven\r
\nAxiom - something that is simply assumed to be true (same as postulate)\r
\nCorollary - something which is trivially proven from a theorem\r
\nLemma - something that gets proven in the course of proving a theorem',103,'friedlinguini','2002-12-18 02:16:53');
INSERT INTO forumpost VALUES (63,14,6,'Re: Any difference','Just to expand:\r
\n\r
\nAn axiom (or postulate) is the basic building block on which proofs are built. It is usually, but not always intuitively obvious. Of the five axioms of Euclidean geometry, the first four are intuitively obvious; the fifth is not. Dropping or changing it leads to the creation of non-Euclidean geometries.\r
\n
\nA theorem is a statement which has been proven. A lemma and a corollary are theorems that are special case scenarios of other theorems.\r
\n
\nIf before you can prove Theorem A, you need to prove special case B as a separate theorem, then Theorem B is a lemma of Theorem A.\r
\n
\nIf special case B is a commonly seen variant on Theorem A, (often with an additional conclusion not included in the general case), then (since most of the work was done in proving Theorem A) Theorem B is a corollary of Theorem B. ',153,'TomM','2002-12-18 03:38:38');
INSERT INTO forumpost VALUES (64,14,6,'Re: Any difference','Just for the uninitiated (not that I know anyone in particular :D), what ARE the five postulates of Euclidean geometry?',1,'levik','2002-12-18 05:18:08');
INSERT INTO forumpost VALUES (65,14,6,'Re: Any difference','http://mathworld.wolfram.com/EuclidsPostulates.html\r
\n\r
\n1. A straight line segment can be drawn joining any two points. \r
\n2. Any straight line segment can be extended indefinitely in a straight line. \r
\n3. Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center. \r
\n4. All right angles are congruent. \r
\n5. If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough. This postulate is equivalent to what is known as the parallel postulate.',103,'friedlinguini','2002-12-18 05:42:40');
INSERT INTO forumpost VALUES (66,14,6,'Re: Any difference','I guess you can call those 5 postulates the rules of the game of geometry!\r
\n\r
\nNow I will take the pythogorean theorem\r
\n\r
\na^2 + b^2 = c^2\r
\na^2 = c^2 - b^2\r
\na^2 = (c + b)(c - b)\r
\n\r
\n\"The product of the sum and difference of the hypotenuse and side of a right angled triangle equals the square of the third side\" (Just made this up)\r
\n\r
\nWill this be a corrolary?',227,'Dulanjana','2002-12-18 16:55:08');
INSERT INTO forumpost VALUES (67,14,6,'Re: Any difference','By the way is it OK to \"assume\" in mathmatics? Shouldnt everthing be proven right?',227,'Dulanjana','2002-12-18 16:57:28');
INSERT INTO forumpost VALUES (68,15,6,'sinh, cosh, tanh whats this?','What exactly is the meaning of sinh, cosh, tanh? Heard that they are \"hyperbolic functions\" What is the meaning? \r
\n(I think there is also cosech, sech, coth too)',227,'Dulanjana','2002-12-19 00:17:54');
INSERT INTO forumpost VALUES (69,15,6,'Re: sinh, cosh, tanh whats this?','They are functions that have some properties similar to sin, cos, tan, etc. For example, \r
\ne^(ix) = cos x + i sin x => e^x = cosh x + sin x (where i = sqrt(-1))\r
\nsin x = x - x^3/3! +x^5/5! - x^7/7!... => sinh x = x + x^3/3! + x^5/5! + x^7/7!...\r
\ncos x = 1 - x^2/2! + x^4/4! -x^6/6!... => cosh x = 1 +x^2/2! + x^4/4! + x^6/6!...\r
\n\r
\nThey get used a lot in differential equations, which answers questions like \"What path does an object take if its speed is proportional to its distance from some point?\"',103,'friedlinguini','2002-12-19 02:54:51');
INSERT INTO forumpost VALUES (70,14,6,'Re: Any difference','Your statement would be a corollary of the Pythagorean Theorem.\r
\n\r
\nAssumptions are generally OK as long as they\'re mentioned as such. Eventually, though, you have to make some assumptions (which generally wind up being your axioms). In other cases, you can assume A as long as your only goal is to prove that B is true if A is true.',103,'friedlinguini','2002-12-19 02:59:42');
INSERT INTO forumpost VALUES (71,16,5,'Arrow icons','You may have noticed the arrow icons that I just added for moving to next/previous post when looking at problems. Are these better/worse/the same than the >> and << arrows that were used before?\r
\n\r
\nAny suggestions? (I\'m still pretty set in having posts appear in reverse chronological order)',1,'levik','2002-12-23 08:43:46');
INSERT INTO forumpost VALUES (72,16,5,'Re: Arrow icons','The only gripe I have is that they\'re a little faint on that background. Otherwise, I think the notion of up versus down is an improvement over forward vs. backward.',103,'friedlinguini','2002-12-23 09:22:55');
INSERT INTO forumpost VALUES (73,16,5,'Re: Arrow icons','I changed them around a bit. \r
\n\r
\nAny Better?',1,'levik','2002-12-23 18:43:53');
INSERT INTO forumpost VALUES (74,17,6,'HTML codes for use on the site','Many of you know this, but many do not, so here goes...\r
\n\r
\nWhen posting problems and comments on the site, you have the ability to use some HTML codes to format your text. Not all the codes are allowed, but there should be enough for basic formatting:\r
\n\r
\n<br> : line BReak, will go to the next line\r
\n\r
\n<p> : Paragraph, will skip a line before the next bit of text\r
\n(The two tags above are not needed when posting comments, line breaks are converted automatically)\r
\n\r
\n<b> ... </b> : Bold text - the text between these tags will be bold.\r
\n\r
\n<i> ... </i> : Italic text - the text between these two tags will be italicised.\r
\n\r
\n<a href=\"http://some.url.com/page.html\">Link Text</a> : A Link, will show as text between the tags, pointing to the specified URL.\r
\n\r
\nIf i remember more that are supported on the site, I will post them. Also, if you think some are missing, let me know, and we\'ll see about adding them. No images, forms or tables though.',1,'levik','2002-12-24 07:40:18');
INSERT INTO forumpost VALUES (75,17,6,'Re: HTML codes for use on the site','I\'m guessing MathML is out of the question...',103,'friedlinguini','2002-12-24 09:50:47');
INSERT INTO forumpost VALUES (76,16,5,'Re: Arrow icons','They look good to me.',103,'friedlinguini','2002-12-24 10:17:32');
INSERT INTO forumpost VALUES (77,17,6,'Re: HTML codes for use on the site','Honestly, I don\'t really know much about MathML other than the fact that it exists. Doesn\'t it only work well with Mozilla-based browsers?\r
\n\r
\nIf you can give me a good reference link, and it turns out to be more widely supported than I think it is, we can possibly think about hacking it in.\r
\n\r
\n(I\'m toying with an idea of \"attachments\" to comments/problems)',1,'levik','2002-12-26 05:19:36');
INSERT INTO forumpost VALUES (78,17,6,'Re: HTML codes for use on the site','http://www.w3c.org/Math\r
\n\r
\nProbably just a pipe dream right now. It apparently freezes Phoenix for Windows for some reason. Support for Mozilla under Windows is OK decent, but not perfect. IE works pretty well with right plugin (i.e., MathPlayer), but will simply strip MathML tags without warning or an offer to download the plugin if you don\'t have it. Don\'t know about Netscape or Opera, and I don\'t know about other platforms.\r
\n\r
\nStill, one can always dream. :-)>\r
\n\r
\nWhat do you mean by attachments? As in uploading images? That would be nice and would significantly reduce the need for MathML...',103,'friedlinguini','2002-12-26 07:04:01');
INSERT INTO forumpost VALUES (79,17,6,'Re: HTML codes for use on the site','My thought was a yahoo-style \"add atachment\" button, with a drop down of supported typed - for example \"image\", \"mathML\", etc.\r
\n\r
\nClick it and you get a popup with the appropriate interface (depending on what you picked) - Text area for MathML, file upload for the image.\r
\n\r
\nThe problem is that there\'s no good way to display images inline - there\'s never a guarantee that they won\'t break the layout unless I do some heavy duty analysing. this is why I was always reluctant to add support.',1,'levik','2002-12-26 07:38:29');
INSERT INTO forumpost VALUES (80,17,6,'Re: HTML codes for use on the site','MathML isn\'t really anything more than additional tags that could appear in an HTML document. It seems to me that there wouldn\'t be much reason to handle it as a separate attachment.\r
\n\r
\nLarge images in a problem would probably be handled at the approval stage. Comments (and forum postings?) would be trickier. Perhaps Resize and/or Delete links available to users of a certain level (where Resize would just add WIDTH and HEIGHT attributes to the IMG tag)? Another approach might be to take the images out-of-line. That is, make a link available for breaking out the image in a popup.\r
\n\r
\nIn principle, being able to upload images would be a cool feature. It broke my heart to vote against that Prove the Pythagorean Theorem problem...',103,'friedlinguini','2002-12-26 08:18:49');
INSERT INTO forumpost VALUES (81,18,5,'Problem Rating','Well this is just a suggesion. Since alot of problems are not getting rated why not introduce a system like this\r
\n After a person has signed up why not introduce a system where the percentage of problems he rates after he has signed up is a qualification for him to become an apprentice, student, journeyman etc.\r
\n\r
\ne.g - to become an apprentice you need to rate 60% of all problems on live after you have signed up\r
\n\r
\nSince there will be a problem (When a person rates 1 problem off 2 its 50%, doesnt look too fair then) How bout introducing demotions onto flooble? that means the person would have to consistently rate problems. as soon as his percentage drops under a certain amount he becomes an apprentice or student etc, This way the person can rate again and get a higher user level. What do yyou think? ',227,'Dulanjana','2002-12-26 16:00:04');
INSERT INTO forumpost VALUES (82,18,5,'Re: Problem Rating','Not sure about that one... The reason that ratings don\'t figure more into ranking than they do is because I didn\'t want people to be rating problems artificially, just to get an advancement. The reason that going from Novice to Student requires for you to have rated a problem is simply to show that you figured out that the site has this functionality, and you know how to use it.\r
\n\r
\nIf rating were beneficial to rank, people may end up ranking problems \"just because\", and that would cause the scores to become inaccurate.\r
\n\r
\nAlso, I think you misunderstand the purpose of ranks on the site. It is not supposed to be a competition of any kind, nor a reward. Quite simply, it is designed as a way for people who have shown that they can responsibly participate in the site to be able to do more. It is a way to have the site running in my absence. Once someone has reached a particular rank, they are entrusted witha certain amount of \"power\" over the site, and at the higher rank, this power spreads from their own problems to those of others.\r
\n\r
\nIn other words, you are not currently ranked a Journeyman as a reward for all the problems you have submitted, but because I know you will make good decisions about wether a problem belongs on the site or not. And that fact will not change if you decide to go away for a couple of months and stop participating.\r
\n\r
\nThus the idea of demotions would run counter to purpose of having ranks in the first place.',1,'levik','2002-12-27 01:56:28');
INSERT INTO forumpost VALUES (83,17,6,'Re: HTML codes for use on the site','If we could open images in a pop-up (similar to the preview pop-up for comments) would that solve the problem? \r
\nLinks are already supported, and I\'m not surethat there are any other attachments other than animations (and if they were animated *.gif\'s, they would be included in the image support) that really needs be supported.',153,'TomM','2002-12-27 02:00:08');
INSERT INTO forumpost VALUES (84,17,6,'Re: HTML codes for use on the site','BTW Netscape 6.x and 7.0 use the Mozzilla browser, so in theory, only 4.x and earlier would not support MathML',153,'TomM','2002-12-27 02:03:58');
INSERT INTO forumpost VALUES (85,17,6,'Re: HTML codes for use on the site','That\'s allright (about Netscape 4). This site\'s use of DIV layers and CSS makes it almost unbrowsable with that browser anyway. It represents less than 1% of the web audience today, so I don\'t think we should worry too much over it.\r
\n\r
\nI have considered popup images for a while, but this would be a less than optimal solution.',1,'levik','2002-12-27 02:09:02');
INSERT INTO forumpost VALUES (86,17,6,'Re: HTML codes for use on the site','Re: TomM\'s comment on MathML - You\'d think so, but Phoenix is based on Mozilla as well, but freezes when it tries to load a page containing MathML. That\'s why I was reluctant to assume it would work.',103,'friedlinguini','2002-12-27 03:57:07');
INSERT INTO forumpost VALUES (87,17,6,'Re: HTML codes for use on the site','That\'s why I said \"in theory\" I haven\'t tested it out for myself.',153,'TomM','2002-12-27 09:48:38');
INSERT INTO forumpost VALUES (88,17,6,'Re: HTML codes for use on the site','OK, I looked at the site that FL linked to (above). According to the site, Netscape 6.x works if you have the plug-in, and 7.0 works natively. \r
\nI looked at the test pages using 7.0, and all of the test examples worked (more or less -- the overhead bar of the radical was a bit too thick). \r
\n\r
\nThere was a pop-up dialogue box suggesting adding a couple of special fonts. I\'ll have to find out where I can find them.',153,'TomM','2002-12-27 09:58:27');
INSERT INTO forumpost VALUES (89,19,4,'\"Inappropriate\" problems','I want to address the notion that was brought up in the Queue comments about a problem being inappropriate for perplexus. (I believe this was one of those grid type logic problems.)\r
\n\r
\nWhile it\'s true that I have previously stated that I don\'t like this sort of problems myself, I did not mean for that to be a guide to the upper ranking users for the voting on problems.\r
\n\r
\nThe reason I implemented the voting process is so that people could see the problems they like appear on perplexus. Now it\'s true, that I think arithmetics problems should not be posted on this site, the design of the ranking system is such that no person who wants to see arithmetics problems will end up in the position to vote them up. (Thus the requirement for more than 5 accepted problems to become a Journeyman.)\r
\n\r
\nFrom this follows, that it is my belief that if someone has achieved the Journeyman rank, they are in general qualified to make their own judgement about which problems are appropriate for the site, and which aren\'t.\r
\n\r
\nTherefore, my personal distaste towards a type of problem should nor hinder anyone who likes it from giving it the thumbs up, especially if you think it will generate meaningfull and entertaining discussion.\r
\n\r
\nSorry for the ramble.',1,'levik','2002-12-30 05:19:40');
INSERT INTO forumpost VALUES (90,20,3,'LOGIC problems?','I am saddened to see the site having less interesting logic problems of late. I realize that be becoming more popular, we are exposing ourselves to a larger percentage of Riddle submissions, as riddles are a more mass-market form of brain teasing, but I\'m sure everyone would agree that this site could definitely use some problems that one needs to do a fair bit of reasoning over.\r
\n\r
\nMy hunt for such puzzles has generally come up empty, and regretfully, I do not have as much time to devote to this site lately as I would have liked.\r
\n\r
\nConsider this a cry for help, to all our visitors, to find, or at least point me in the direction of, some really good challenging problems. Any help in this reguard would be greatly appreciated!',1,'levik','2003-01-07 06:30:49');
INSERT INTO forumpost VALUES (91,20,3,'Re: LOGIC problems?','Yes, my apologies - I was intending to create some new puzzles of this sort, as I quite enjoy them too. I\'ll try to remember to have a good think along these lines...',250,'Nick Reed','2003-01-07 07:11:02');
INSERT INTO forumpost VALUES (92,20,3,'Re: LOGIC problems?','Heh, no apologies neccessary from anyone. You least of all, considering you actually came up with a puzzle or two especially for the website.\r
\n\r
\nI guess I was just exressing some built up dismay over all these riddles. When I built the site, one thing I didn\'t envision was a riddle archive :)',1,'levik','2003-01-07 11:09:21');
INSERT INTO forumpost VALUES (93,21,3,'Puzzles','Four Men Crossing a Bridge:\r
\n\r
\nThere are four men who would all like to cross a rickety old bridge. (Perhaps it is more accurate to say that they\'d like to get to the other side.) The old bridge will only support 2 men at a time, and it is night time, so every crossing must use the one flashlight that they all share. The four men each have different walking speeds; the fastest each of them can cross is 1 minute, 2 minutes, 5, minutes, and 10 minutes. If they pair up, since they must share the flashlight, they can only cross in the time that it would take the slower of the two. Given that the shortest time to get them all across is 17 minutes total, how should they all cross? ',1145,'tom','2003-01-12 07:17:12');
INSERT INTO forumpost VALUES (94,7,3,'Re: mystery Water Problem','Well done!',1145,'tom','2003-01-12 07:37:30');
INSERT INTO forumpost VALUES (95,21,3,'Re: Puzzles','Two points:\r
\n\r
\nFirst, this problem is already on the site at http://www.flooble.com/perplexus/show.php?pid=10\r
\n\r
\nSecond the proper way to submit a problem is through the \"Submit a problem link\" just under the Log In/Log Out button. Your problem will not show up immediately, as only one new problem a day is released and there is currently a backlog of 24 problems, but unless it is rejected (usually because it duplicates an earlier problem, as this one does -- and you will be notified if that\'s the case), it will turn up in a couple of weeks. \r
\n',153,'TomM','2003-01-12 09:45:14');
INSERT INTO forumpost VALUES (96,21,3,'Re: Puzzles','TomM\'s absolutely right. I ask people not to post problems in the forums, since here they won\'t be read by as many people, and won\'t have the chance to be featured as the \"Latest\" problem. (Which would be a great shame if it was a good puzzle.)\r
\n\r
\nIn addition, I think you will agree that the design of perplexus\' main is pretty well suited for posting and discussing problems: the user\'s comments are not shown all at once, and neither is the solution - this gives our visitors a chance to think about it on their own, but also get help if they can\'t solve the problem. Plus comments allow you to indicate the level of \"spoilage\".\r
\n\r
\nPerhaps I should make this thread \"sticky\"... But that would require implementing stickyness :)',1,'levik','2003-01-13 08:33:37');
INSERT INTO forumpost VALUES (97,9,3,'Re: Ratings.','i find that unless I really enjoy a puzzle, I won\'t rate it because I\'m not able to guarantee subjectiveness. e.g. if I\'ve seen a puzzle before, its hard to rate properly, or if it isn\'t my style (along with levik - i think - i don\'t really appreciate a riddle, even if it is a good one), so I stay out of the game. The base reason has been highlighted by you guys above - I don\'t really want to \"hurt\" someones feelings with an undeserved bad rating, but at the same time don\'t want to water down the rating scheme by giving marks too generously. I guess I would make a poor teacher...',775,'Cory Taylor','2003-01-14 06:03:37');
INSERT INTO forumpost VALUES (98,22,5,'problem acceptance comments','I like the way the problems are currently submitted. It provides great opportunity for other great puzzlers to take a look at (and possibly correct or add to) your problems before being broadcast to the world. My suggestion though, is that while in acceptance phase, someone who has seen the puzzle before, or has other such advantages, is certainly able to post, I think that the same comments in the live area are inappropriate. To illistrate my point requires a bit of blame throwing, for which I apologize. I submitted a puzzle about the word \"facetiously\", and got a great addition to the problem from a ranking member, which I added to the solution (and credited). Then the same poster repeats the comment in the live section, when its clear that this was a puzzle they\'d seen before. My opinion here is that that was unfortunate because it a)prevents others from actually doing the puzzle and b)makes me look like an idiot for not knowing the complete answer to my own puzzle.\r
\nTo restate, I certainly did not mean this as fingerpointing, but just needed to illustrate my point. I have a huge respect for people in this world who can view \"quirky\" personality traits (like loving puzzles) proudly, and this extends to all of the common posters here.',775,'Cory Taylor','2003-01-14 06:19:01');
INSERT INTO forumpost VALUES (99,9,3,'Re: Ratings.','A problem\'s obscurity can also be a point in its favor. The fewer people that have heard of a problem, the more interesting it is likely to be. I think the best approach is just to vote in a way consistent with how much you enjoy the puzzle. Your vote won\'t be the only one, so you needn\'t worry about being the one who hurt a poster\'s feelings..',103,'friedlinguini','2003-01-14 06:30:09');
INSERT INTO forumpost VALUES (100,22,5,'Re: problem acceptance comments','As the unnamed fingerpointee, let me first say no offense is taken, and no apology is needed.\r
\n
\nAs to the merits of my posting part of the answer in the comments section, I might not have made the comment if I had known that you had credited me by name in the solution. I have no way of seeing the solution you wrote up. I marked my comment as a solution (there isn\'t really an icon for a partial solution) and also titled my comment appropriately, so I don\'t think that I have ruined the discussion for anybody who didn\'t want to know the answer.\r
\n
\nIt might have been inappropriate for me to post a comment based on some discussion that occurred during the acceptance phase with other people. However, both the comment during acceptance and the comment in the general problem discussion were solely my own contributions, and were made in different contexts (one was in response to the original \'and possibly unique\' part of the problem, and the other was just a part of the solution). I don\'t think offering insight into a problem in one forum should preclude me from offering it in another, especially when they are geared toward different audiences.\r
\n
\nAnybody who saw my comment during the acceptance stage already knows what I had to say. To anyone who sees it now, it\'s just an ordinary comment. If my name is in the solution to the problem, perhaps the easiest solution is just to take it out.',103,'friedlinguini','2003-01-14 06:51:59');
INSERT INTO forumpost VALUES (101,23,3,'Two a day?','Alan writes:\r
\n
\nlevik i was just wondering instead of publishing one problem per day y not make it 2? Every day under latest there could be two problems and this would speed things up for the problems in the queue. (if there is only 1 problem that has 3 thumbs up then only 1 could be posted under latest.) \r
\n
\nSo the reason it\'s currently one problem as the latest, is so that that latest problem receives the most attention from visitors, and hopefully the most comments.\r
\n
\nWhile it\'s possible to have more than one \"latest\" problem (like \"Latest\", and \"Previous\" - next to latest) and push them live two a day, I personally think that would be overloading the front page with too much content. \r
\n
\nTo me personally, problems spending a long time in the queue is not a problem, but I can totally see how it\'s frustrating to someone who submits a problem they want to see up on the site. (I\'m even guessing that\'s what triggered Alan\'t post)\r
\n
\nBut if anyone else has thoughts on the subject, I\'d love to hear them.',1,'levik','2003-01-26 06:35:50');
INSERT INTO forumpost VALUES (102,23,3,'Re: Two a day?','I think this a tricky subject. Personally, I quite like the one/day regularity, but the days with multiple puzzles per day were also quite fun. However, with the current queue it does mean that someone could post a puzzle and not see it appear for almost a month and a half. I think a new user could easily get bored waiting to see their puzzle-contributions turn up with it this way, thus reducing the amount of people who stay around on the site for any period of time. And I\'ve noticed the amount in the queue is gradually increasing, so the input is obviously more than 1 per day (on average), so the 1 per day output back onto the site seems a little unbalanced.\r
\n\r
\nAs for the thought about requiring \"Latest\" and \"Previous\", I don\'t that\'s needed. Even if they were being posted 50 a day, the term \"Latest\" for the last one is still valid. And with the last dozen still being visible on the front page, a user can always see what\'s recent (similarly with the \"New Comments\" link, being able to track recent threads).\r
\n\r
\nMaybe a balance could be worked out. A few ideas I have are:\r
\n\r
\n1) The site has 1 problem per day on weekdays, 2 per day at weekends\r
\nor\r
\n2) The site has 2 problems per day on weekdays, 1 per day at weekends\r
\n(depending on any feedback you have on when site traffic is high)\r
\n\r
\nI\'ve a few other ideas, but nothing that could be easily automated or generalised. It\'s all a bit vague, really.\r
\n\r
\nAny help? I doubt it...',250,'Nick Reed','2003-01-26 11:21:58');
INSERT INTO forumpost VALUES (103,23,3,'Re: Two a day?','Well, if anything, weekends are definitely our slower time. A lot of people come from google, searching for \"logic puzzles\" and \"brainteasers\". I\'m assuming these are people surfing at work, since it drastically falls off during the weekend.\r
\n\r
\nI guess I don\'t really mind if two problems end up being pushed during the weekdays (monday through thursday - friday is also kinda slow), especially if these problems are not particularly difficult, such as riddles and stuff - problems where not much discussion is possible.\r
\n\r
\nThe only issue will be knowing when two problems have already been pushed. It\'s pretty easy to see if the latest problem is from today or yesterday, but it may be less obvious if the next to latest one is. So if any of the scholars out there want to push a second problem sometime in the afternoon, I would ask that you check that only one has been pushed so far.\r
\n\r
\nIn other words - use your judgement. ',1,'levik','2003-01-27 04:13:41');
INSERT INTO forumpost VALUES (104,24,3,'Top-rated Problems','I was looking in the top-rated problems recently and noticed something about how they\'re arranged (aside from the obious fact they\'re in order of rating) All the problems that got 5 were in the top but it seems like after that there is no special order (unless it is chronological and I missed it) But anyways the #1 problem is changing chameleons. It has recieved 2 votes and has 5. After that the #2 problem is yum, arsenic and it has recieved 10 votes and also has a 5.
\n\r
\nInstead it is a rank he bestows on those journeymen whom he feels have demonstrated that he can trust their judgment concerning the site. It began with being able to submit a puzzles live, instead of adding them to the queue (back when he was the only one who could \"push\" queued submissions), so that the site would remain active even when he could not access a computer to web-master it for a few days. When he added the \"vote on queued submissions feature, he gave the scholars the ability to \"push\" the good problems for the same reason.\r
\n\r
\nAltogether, it is rather like some sites where the webmaster appoints moderators for the different discussion fora. ',153,'TomM','2003-01-28 20:54:44');
INSERT INTO forumpost VALUES (112,25,5,'Re: Scholar Level','Thanks TomM. This is exactly correct. The only thing I want to add is that NOT being promoted to Scholar level is not in any way an indication that you\'re not good enough.\r
\n\r
\nAs TomM has said, the idea behind Scholars is the ability of the site to operate in my absense. I beleive that if there was another user with my level of access to the site, confusion would result, since communication would have to exist between two admins to ensure we\'re in tune. Likewise, I believe too many scholars can result in some confusion as well. For example, the more people have the power to push the problems live, the higher the odds of problems being pushed out of turn.\r
\n\r
\nAs it stands I am comfortable witht he number of active Scholars on the site. I AM considering adding more \"power\" to the scholars, and if at that point it looks like more are needed, I will go through a round of \"recruitment\". (The last such round was when I was leaving for a 10 day vacation.)\r
\n\r
\nP.S. The ability to submit a problem live directly occured before user voting and queue. At the time, this was the only way a problem could appear on the site without my involvement. Because we have the queue voting now, there is no real need for it, and noone ever uses it. The only reason I don\'t disable it is because I can trus all who can access this feature not to use it needlessly.',1,'levik','2003-01-29 01:44:53');
INSERT INTO forumpost VALUES (113,23,3,'Re: Two a day?','As I said, I have no objections over two problems pushed per day, especially in categories like Riddles or Tricks. The scholars should feel free to do it.\r
\nI myself will probably stick to one a day for the most part, but this is more an issue of free time than anything. Most days I only have time to be here in the morning and at night, and I believe that if a second problem were to be pushed, it should be done around lunchtime or in the afternoon.',1,'levik','2003-01-29 04:37:28');
INSERT INTO forumpost VALUES (114,26,5,'Small request','How about a Search box in the problem queue for hunting down dupes?',103,'friedlinguini','2003-01-29 06:26:47');
INSERT INTO forumpost VALUES (115,23,3,'Re: Two a day?','For the issue of posting two problems a day 1 thing to keep in mind is if the question is already solved. Look at the comments and see if some1 figured it out if so a new problem should be posted (but no more than two a day.)',1072,'Alan','2003-01-29 07:20:44');
INSERT INTO forumpost VALUES (116,26,5,'Re: Small request','Yes thats a good idea but then again two questions could have the same gist but totally different wording. I\'m not to sure if it will eliminate the problem.',1072,'Alan','2003-01-29 07:21:57');
INSERT INTO forumpost VALUES (117,26,5,'Re: Small request','It wouldn\'t eliminate the problem. However, there have been plenty of occasions where I\'ve been sure that I\'ve seen a problem before, but want to come up with something definite before saying so.',103,'friedlinguini','2003-01-29 09:31:22');
INSERT INTO forumpost VALUES (118,26,5,'Re: Small request','I know the feeling. That\'s why I usually right-click on the \"xx New\" link and open it in a new window, keeping the home page available to access the search feature. And yes, some problems are worded similarly to other, completely different ones, and I have had to read the two side-by-side to be sure it was not a dupe. ',153,'TomM','2003-01-29 17:08:44');
INSERT INTO forumpost VALUES (119,26,5,'Re: Small request','I added the box to the queue page (and yes, it opens a new window for searches :)\r
\n\r
\nKeep the requests coming (and keep \'em as easy as this one :)',1,'levik','2003-01-29 18:14:37');
INSERT INTO forumpost VALUES (120,27,5,'Solution too early?','Levik: \"Hey Ravi, how come you never submit solutions to your puzzles? (it would make my life easier down the line if you did)\"\r
\n\r
\nRavi Raja: \"ya Levik I would have surely done that, but the first time I did it (the puzzle whose subject was: Guessme One), the solution was then posted on the site too early........ so I thought that after majority of the members of the site commented on my problem, only after that i\'ll submit the solution.........\"\r
\n\r
\n(The above comments were exchanged in the queue)\r
\n\r
\nSo to address this, I want to mention why and when I post solutions to the problems/puzzles on this site. In my experience, 90% of the visitors do not comment on puzzles that are not the latest puzzle. The notable exception is when a first-time visitor comes to the site and is so interested that they go through all the categories and all the problems. But this is rare.\r
\n\r
\nTherefore, it is my experience that once a puzzles has been knocked off of the latest spot, and once none of the \"new comments\" belong to the puzzle, it will only get sporadic discussion on it, mostly driven by new users.\r
\n\r
\nWhile a lot of the problems are solved by this time, and posting the solution doesn\'t give anything away, there are a few instances (as with \"Guessme One\") where the puzzle was unsloved. However, as I have stated, I believe that this puzzle would not have gotten too much further comments. This is why I generally post solutions to puzzles after two to four days of the initial posting.\r
\n\r
\nAlso, once a puzzle has a posted solution, it becomes \"eligible\" for flooble Puzzle Of the Day - a syndication service where other sites get to display one of our puzzles remotely. This can actually make people comment on it more.\r
\n\r
\nSo, Ravi, I hope I have explained my solution policy sufficiently for you to reconsider your current \"no soluiton\" practice. If you (or anyone else) disagree, I\'d love to hear reasons.',1,'levik','2003-01-30 01:49:31');
INSERT INTO forumpost VALUES (121,27,5,'Re: Solution too early?','This discussion is related to the case of not submitting a solution because you do not have it. In this case you should make it clear that you do not know. Im saying this because it has happened to me while creating puzzles (eg logical limbo) that i could not solve.',251,'Cheradenine','2003-01-30 06:54:35');
INSERT INTO forumpost VALUES (122,27,5,'Re: Solution too early?','For a while I was actually considering a checkbox to mark that you do not know a solution. This would then become visible on the Queue interface. (Also, possibly the site would insist that you either check the box or put in something for the solution.) Any thoughts on this? \r
\n\r
\nIf I do it, this may take some time to accomplish, so don\'t expect it to be like today.',1,'levik','2003-01-30 09:38:28');
INSERT INTO forumpost VALUES (123,27,5,'Re: Solution too early?','Sounds good. Still in terms of prioritising your work, this should be at the lower end since it is not a frequent situation. Most puzzles are taken from somewhere else and thus already have a solution.',251,'Cheradenine','2003-01-30 22:37:20');
INSERT INTO forumpost VALUES (124,28,3,'Brainteasers: The Aftermath','Found this link on BBSpot. I hope people get a kick out of it:\r
\n\r
\nBrainteasers: The Aftermath',103,'friedlinguini','2003-01-31 04:37:42');
INSERT INTO forumpost VALUES (125,23,3,'Re: Two a day?','There\'s a big string of riddles in the queue right now. I don\'t have a problem with riddles per se, but given the lack of comments on them right now I\'d say that people are starting to burn out on them, myself included. I think these would be prime candidates for going twice per day.',103,'friedlinguini','2003-02-03 05:00:42');
INSERT INTO forumpost VALUES (126,23,3,'Re: Two a day?','Yes. I definetely agree with this. And i,m pretty sure ravi has another 10-20 or so of those coming up.',1072,'Alan','2003-02-03 09:56:18');
INSERT INTO forumpost VALUES (127,23,3,'Re: Two a day?','As I have already said, I am all for it. Friedlinguini, you should feel free to push these problems two a day. It\'s just that I believe the best time for pushing a second problem is in the afternoon, and being at work then I generally am not able to do this.',1,'levik','2003-02-03 15:42:11');
INSERT INTO forumpost VALUES (128,23,3,'Re: Two a day?','On a peripherally related subject, there seems to be a bit of a stalemate in the top two problems. Is anybody else going to vote on them?',103,'friedlinguini','2003-02-04 02:04:10');
INSERT INTO forumpost VALUES (129,19,4,'Re:','I agree strongly and with the recent barrage of ravi\'s proble i\'ve noticed some things. The first being that a lot of ravi\'s problems having the same concept. We only need one problem with one concept do a certain amount of problems. So in other words some problems have to be deleted. Also don\'t just submit a problem to get a higher rank. If you\'re a journeyman and want to be scholar don\'t just submit 25 puzzles that are all about the same thing. Another thing is that a lot of problems in the queue need to be deleted. Don\'t think its mean to vote thumbs down on some problems. If a problem doesn\'t belong or has the same concept of solving or answering then it doesn\'t belong.',1072,'Alan','2003-02-06 13:06:10');
INSERT INTO forumpost VALUES (130,19,4,'Re:','Alan, I sort of agree woth you. You are a journeyman, and as such can voice your opinion in the queue on individual problems which you don\'t believe should be on the site. (I myself like math/logic-related stuff much more interesting than riddles and word tricks.) I find that if you express it early and strong, people may come to see your point and vote in line with you.\r
\n\r
\nWith over seventy problems in the queue, other users will probably not be as hesitant to Thumbs Down a problem as they were when submissions were few and far between.',1,'levik','2003-02-06 18:32:40');
INSERT INTO forumpost VALUES (131,29,3,'300 Problems!!!!','I don\'t know if anyone noticed, but we reached 300 problems live on the site today! This is a huge milestone in my mind, considering the site has been up less than a year.\r
\n\r
\nI would like to extend my thanks to everyone who has contributed to the site, whether by submitting one of the 300 problems now live, or the 70+ now in the queue, or posting one of almost 2,500 comments - all these things make the website an attractive place for people who like to exercise their brain.\r
\n\r
\nOn another note, this site was mentioned in this month\'s South Nevada MENSA newsletter, (which you can read at http://www.southernnevada.us.mensa.org/mindbets/current.php3 - click \"From the Editor\"). It was actually a problem submitted by Happy that they chose to print. I\'m a bit miffed that they don\'t really mention the name of the site, and I never asked to have my name on there, but I think it\'s cool for the site to get some exposure like this.',1,'levik','2003-02-09 18:18:19');
INSERT INTO forumpost VALUES (132,29,3,'Re: 300 Problems!!!!','Congrats on both counts, levik! It does seem odd that they\'d use your name rather than the site\'s name, but at least they got the URL right. :-)>',103,'friedlinguini','2003-02-10 02:57:31');
INSERT INTO forumpost VALUES (133,30,5,'Browsers and Chatterboxes?','Some weirdness I\'ve noticed, but only pinned down recently. If I\'m running Phoenix, I see different Chatterbox contents than if I\'m running IE. It seems that Phoenix displays older messages (the latest message I see on the front page Chatterbox is from February 13th). Is it possible that the Chatterbox contents come from something that isn\'t marked as dynamic content, and might thus be cached by a browser?',103,'friedlinguini','2003-02-20 18:07:59');
INSERT INTO forumpost VALUES (134,30,5,'Re: Browsers and Chatterboxes?','My guess is that your computer has been turned on continuosly since at least Feb 13. You see, that\'s I moved the chatterbox server, and re-pointed its DNS. So you\'re probably one of the very few people who still connect to the old server (which is still active for the time being). \r
\n\r
\nWindows is pretty notorious for caching DNS data until it\'s restarted, as far as I know.',1,'levik','2003-02-21 01:45:21');
INSERT INTO forumpost VALUES (135,30,5,'Re: Browsers and Chatterboxes?','That could be it - I rarely power-cycle my puter. On the other hand, I was using different browsers on the same hardware simultaneously to nail down the behavior. Maybe Phoenix maintains a local DNS cache? *shrug*',103,'friedlinguini','2003-02-21 02:16:24');
INSERT INTO forumpost VALUES (136,30,5,'Re: Browsers and Chatterboxes?','It\'s probably more likely that explorer does. Depending on your version of Windows, explorer may run as the same instance that powers your desktop. In that case, you never really quit out of it, even though you may close all the explorer windows.',1,'levik','2003-02-21 05:11:55');
INSERT INTO forumpost VALUES (137,30,5,'Re: Browsers and Chatterboxes?','Actually, I rarely close out Phoenix. There\'s always one tab or another that I\'ve left open (Mmmmmmm.... tabbed browsing.... *drool*). Besides, Phoenix is the one showing the old messages.',103,'friedlinguini','2003-02-21 05:21:47');
INSERT INTO forumpost VALUES (138,31,4,'Riddles','Ok I have a comment to make about riddles and problems that are coming in.
Firstly i think that all riddles that contain a things such as names are not appropriate as their can technically be an infinite amount of names. I think problems of this style are not neccesary.
Problems that contain \"random combination logic\" as i like to call it. An example is a problem that goes like \"My first is in \"trace\" but not in \"tear\" and so on. The logic is to randomly combine letters \"even as it may be in a systematic order\" to try to find the word.
Lastly i\'ve noticed questions (I think from new users that try to suck up although they may have good intentions)that have questions about flooble itself. Once again these questions really require not much logic but as i like to call it, problems like these require \"site scrounging\". I really think questions like these (and the other two specified above) should not be neccesary.
\nI don\'t think answers need to be set in stone to be appropriate. Having multiple possible answers is not such a bad thing as long as they require some thought. This encourages more discussions about the problems.
\nI don\'t think \"bad\" problems are really such an obstacle in the queue. If a problem is bad, it will get voted out of the queue and won\'t delay the posting of subsequent problems.
\nJust my 2.3 cents.',103,'friedlinguini','2003-02-21 12:29:11');
INSERT INTO forumpost VALUES (141,31,4,'Re: Riddles','My view is that the only thing this situation really requires is for Journeymen to take be a little more active in voting. Generally we all agree on wether a problem should be in or out, it just takes a while to get over the vote threshold. \r
\n\r
\nPersonally, I have the ability through admin tools to do whatever I want, and the votes be damned, but I prefer to only use that in rare cases. (Like I just manually deleted the second incarnation of the Chicken and Hen and River problem because it reached -3 and then Erin +1\'ed it back to the non-deletable -2.)\r
\n\r
\nIn most cases however, I believe the voting system works well, if slow at times. It\'s unavoidable that as the number of problems on the site grows, so will the number of submitted dupes, which means that in general for each problem accepted we might have one to two being turned down. This means that at two problems pushed live every day, we can be going though as much as 8 in the queue. (That makes the 6.6 month figure a little overblown)\r
\n\r
\nOne thing that can be done to speed things up is for everyone who knows enough about the site, to do a search before submitting a problem, to see if it\'s there already. Dupes like the chiken/river problem, the missing dollar problem etc, could be avoided with a simple search. It doesn\'t really slow down the rate at which new problems make it through the queue, but it does give the voters more to do. ',1,'levik','2003-02-21 15:12:00');
INSERT INTO forumpost VALUES (142,31,4,'Re: Riddles','yes i agree with that but levik since your admin (and u vote in only the queue) why not just delete the missing dollar and other dupes you\'re 100% sure shouldn\'t belong? Why wait until the missing dollar reaches -3? We all know it should be deleted anyway. Unless this creates some sort of major hassle for you (which i hope it doesn\'t). Like you said journeymen don\'t log on that much so getting that problem out of the way asap would help then right?',1072,'Alan','2003-02-21 15:32:27');
INSERT INTO forumpost VALUES (143,31,4,'Re: Riddles','One thing I\'d like to add is that I think people should submit solutions to their problems right away if they have \'em. I keep finding myself having to bug Ravi Raja to post the solutions, and now I need one for Alan\'s peanut problem as well.',1,'levik','2003-02-22 19:42:18');
INSERT INTO forumpost VALUES (144,33,4,'Flooding','I was thinking about it today, and I realized that having somebody monopolize the queue like Ravi has done is not good for the site in the long term. There\'s currently almost 250 problems in the queue, and only 30 or so are submitted by users other than Ravi Raja.\r
\n\r
\nNow the effect of having such a large queue is that many people do not want to bother submitting a problem when they would have otherwise (if the queue was shorter). Worse than that, people who DO post a problem, will have to wait quite a while for it to be voted on, and will get an impression that it is simply being ignored. This may give people an idea that we\'re running an exclusive club type of a site here, and possibly turn away valuable new members.\r
\n\r
\nTherefore, I\'m going to have to ask Ravi to not post any more problems until the queue gets down to a more managable size. Ravi, don\'t get me wrong, I am absolutely grateful to you for all the great puzzles you have given us, and no doubt will continue to give, but I just think it will be better for the site in the long term if the problems queue is at a more managable size.\r
\n\r
\nLest anyone think I\'m discriminating against Ravi, I am thinking of adding some sort of a safeguard that will not allow one to submit problems under certain conditions (like If the queue exceeds 30, AND you have over 10 problems in the queue AND your problems make up over 33% of the problems in the queue). What do you guys think about that?',1,'levik','2003-02-22 19:57:51');
INSERT INTO forumpost VALUES (145,33,4,'Re: Flooding','I\'d hate to see the site lose problems. What about mucking around with the ordering rather than imposing restrictions on whether or not someone can submit a problem? For example, if person A has more than 2 problems in a row in the queue, and person B then submits a new problem, person B\'s problem automatically gets bumped up to where person A\'s 3rd problem currently lies in the queue. Re-sort every time a new problem gets added and every time a problem gets pushed live, but don\'t change the previous order unless it breaks the preconditions (so that you don\'t always have person A\'s problems in the top two spots in the queue). I imagine it would be a nightmare to implement if you\'re only using database queries, but I don\'t know if you have additional resources available to you.',103,'friedlinguini','2003-02-23 02:28:09');
INSERT INTO forumpost VALUES (146,33,4,'Re: Flooding','hey its alright Levik.......I have stopped submitting any more problems.......until the number of problems in the queue get down to 30.....but please do not delete my problems or please do not do what friedlinguini has mentioned that someone else\'s puzzle will be put in between because I have taken a LOT OF TROUBLE doing this, that is posting problems in the site and for the site.........so PLEASE PLEASE DO NOT DELETE my problems......I have really stopped submitting more problems on the site as you have said......and whay should i get you wrong........i can understand what you are trying to say and can understand the problem which the other members of the site have to face ......waiting for their problems to be approved........that\'s all I would like to say but please do consider my problem too........and do not delete the ones submitted by me.........its a REQUEST.........:) THANK YOU.........',979,'Ravi Raja','2003-02-23 05:21:31');
INSERT INTO forumpost VALUES (147,20,3,'Re: LOGIC problems?','hey Levik......I have submitted a lot of Logic problems on the site.......recently as you can see from the list........I hope you will like them.........',979,'Ravi Raja','2003-02-23 06:01:50');
INSERT INTO forumpost VALUES (148,33,4,'Re: Flooding','Don\'t worry, there will be no deleting of anyones problems without having them be put to a vote first. I didn\'t ask you to hold off submitting new ones because I don\'t like you or the problems you submit, but simply so that others could get a chance to participate.',1,'levik','2003-02-23 06:26:21');
INSERT INTO forumpost VALUES (149,31,4,'Re: Riddles','o i didn\'t make one for the peanut problem. cuz the question merely came to me sorry about that levik. i\'nm pertty sure one person would have the solution though',1072,'Alan','2003-02-23 07:21:39');
INSERT INTO forumpost VALUES (150,33,4,'Re: Flooding','Personally if there were to be a limit set, i think that any one person should have a maximum of 6 pending problems. why? first of all some new users are rank crazy and thjey\'ll want to submit 6 problems to get to journeymen rank. This limit will still allow them to be happy. Of course i really don\'t think there should be a set limit due to the fact that the only cause of the size of the queue is ravi.',1072,'Alan','2003-02-23 07:27:02');
INSERT INTO forumpost VALUES (151,20,3,'Re: LOGIC problems?','I think we should open ourselves up to a new line of logic problems which i call \"real world problems\" (ust a term i made up). This includes questions like \"why are manholes round\" and \"why does ice float in water\"Asking about why things are the way they are(as long as an answer isn\'t based on questionable modern theory e.g why do things travelling at the speed of light not age?) would be a great addition to the site.',1072,'Alan','2003-02-23 07:33:02');
INSERT INTO forumpost VALUES (152,20,3,'Re: LOGIC problems?','BTW questions like \"how things work\" i don\'t htink would fit under this new style of problem. it should have a short simple comprehendable answer and it should be something like an everyday thing we never wonder about.',1072,'Alan','2003-02-23 07:39:00');
INSERT INTO forumpost VALUES (153,33,4,'Re: Flooding','well Alan....first of all I am not rank crazy.......yes I do ask Levik about my user\'s level........but that is all in his hands and I cannot do anything with it.......whenever he pushes me to a higher level.....i\'ll be there......or else i\'ll remain the same.......so please do not say that I am submitting problems to make my rank better......but instead yes I would like to contribute as many good problems to the site as possible and that is what I am doing.......and by the way.....Alan .......you must be knowing that I am a Journeyman and not a Novice or a Student...........anyways I have stopped submitting so many problems at the same time.......but at least I would like to ask Levik if I can still keep submitting 2 or 3 problems a week or so ????????........if not then I can stop doing it until the length of the queue reduces to about 50........and after all it is not my fault that I am going on submitting problems......well others can also do that.....and they do......but the only difference is that they submit a fewer number of problems compared to what I do.........that was all I had to say about all this flooding of problems on this site..........\r
\n',979,'Ravi Raja','2003-02-23 20:52:02');
INSERT INTO forumpost VALUES (154,31,4,'Re: Riddles','yes Levik........the problems that you will find in the latter part of the list have their answers provided with them........only the ones in the first half might not be having them but I\'ll surely post them........but one thing you will have to check Levik and that is the solution does not appear too early in the site.........as what happened with my first problem.......just after three or four comments by the other users, i have seen that the solution has been put up and now everyone can see it.........so please do see that this does not happen...........thank you',979,'Ravi Raja','2003-02-23 20:59:30');
INSERT INTO forumpost VALUES (155,31,4,'Re: Riddles','Ravi, I generally put up a solution two or three days after the problem has been up (if it\'s available).\r
\n\r
\nBy that time, I find that for the most part people will no longer comment on it. (Of course if there is still an active discussion around it, that\'s a different matter.)\r
\n',1,'levik','2003-02-24 03:58:40');
INSERT INTO forumpost VALUES (156,33,4,'Re: Flooding','Ravi, I\'m sure that Alan was not referring to you when he said rank crazy. (Or typed. Whatever.) Think of it from a new users point of view. Remember how cool you thought this site was when you first came across it - you wanted to get involved immediately, didn\'t you. Well, the site is setup so that to do so requires you to submit x number of problems etc, and so you do. I\'d bet it would have been a little frustrating (especially as a new site user) to have to wait 3 months before your first problem came up and you could do whatever it is the next \"level\" could do. I admit that I was quite disappointed at my last puzzle submission to see 192 problems in the queue, knowing that even at 3 per day that it would be summer before its looked at.\r
\n\r
\nI fully agree with f.l. about the re-sorting. I don\'t want to discourage anyone from putting in problems, and I think that this would accomplish it from all perspectives (new submitters and chronic submitters alike).',775,'Cory Taylor','2003-02-24 04:06:05');
INSERT INTO forumpost VALUES (157,33,4,'Re: Flooding','yes Cory.....i am not accusing Alan for that but I was just trying to remove all sorts of misunderstandings regarding this.......i agree that when I was new to the site i was rank crazy too......but not now........and yes who is not interested in submitting problems........and i am also sorry to hear that you will have to wait so long for your problem to be approved by the journeymen and other users with higher levels.......so now even I have decided that I will be submitting 2 or 3 problems a week and not more than that........if that is fine with everyone then its alright otherwise please do let me know about it........well i am not misunderstanding anyone and neither i would like anybody else to misunderstand me........we are all a playing the same role of making this site a great success........with thousands of problems and so on........so PLEASE DO LET ME KNOW WHENEVER I AM GOING WRONG ANYWHERE........all of you have the right to correct me and point out my mistakes.........just like you all have discussed about this flooding of problems and i decided to reduce the number of submissions from my part( for the time being)..........similarly if there is anything else where someone else is facing a problem because of me........please do let me know........i\'ll try my level best to correct myself..........thank you',979,'Ravi Raja','2003-02-24 05:20:22');
INSERT INTO forumpost VALUES (158,34,4,'Queue ranking','After some thought on friedlinguini\'s proposal of \"Inserting\" problems from underrepresented users into the queue, I have decided this to be a very good alternative. By doing so, the \"wait penalty\" is shifted from low-volume submitters to be shared with high-volume submitters, who caused the congestion in the first place (inasmuch as fanatically contributing to a site CAN be a problem :)\r
\n\r
\nSo I was going to sit down and figure out a good algorithm for weighing down (and up) of the queue problems, but then realized that I had better take this discussion to the masses, given that this site is all about solving weid problems.\r
\n\r
\nTo start, let me tell you how things work now. All problems are stored in a table, each one assigned a sequential ID, and its submission date is also stored. Currently, the queue is sorted by date first, and ID second. (So if two problems are submitted on the same day, the one with the lower ID will show up first.) (So yes, fl, all I have to rely on here are Database queries.)\r
\n\r
\nI was thinking of adding another column to the problems table: the Queue Weight (let\'s abbreviate it as QW). My thought is that this will factor in to the sort order: Things would be sorted by QW first, then date then ID,\r
\nSo that all the problems with QW of 1 would come before those with QW of 2, reguardless of the date.\r
\n\r
\nMy idea is to have a script run nightly to calculate the QW of every problem in the queue: each user will get QW=1 for the first 5 problems in the queue, QW=2 for the rest (higher values become irrelevant as only the top 10 problems are visible for voting).\r
\n\r
\nThis makes the system \"fluid\". In the current situation, Ravi\'s problems would almost always hold top 5 of the 10 available spots, at least at the start of the day. However the problem with this is that if a problem of Ravi\'s is pushed, this number will go down to 4, revealing a new problem in 10th slot. But when the QWs are re-calculated at night, another one of Ravi\'s problems will get upgraded from 2 to 1, thus pushing that last problem down and out again.\r
\n\r
\nPerhaps making QW more fine-grained is the answer: 1 for problems 1-3, 2 for 4-6, etc..? Any comments/ideas?',1,'levik','2003-02-24 06:14:55');
INSERT INTO forumpost VALUES (159,34,4,'Re: Queue ranking','Here\'s an alternate approach that might work - for each problem author, store the date of their most recently pushed problem. If the author has never submitted a problem, use some arbitrarily early date. Sort by this date, then QW (I\'d actually have a single-problem granularity), then submission date, and finally ID. This way, you get a sort of a round robin going on among problem submitters. What\'s nice about this method is that first-time submitters always get top priority, and the ordering remains pretty stable, so there shouldn\'t be many surprises during the re-sort. One possible downside (and by \"possible\" I mean that it\'s not necessarily a bad thing) is that infrequent submitters will get priority over regulars. It might be possible to tweak it so that a new submission gets placed just after one pass through the round-robin, but I don\'t know an elegant way to do this offhand.',103,'friedlinguini','2003-02-24 09:51:19');
INSERT INTO forumpost VALUES (160,34,4,'Re: Queue ranking','Another possible problem with the approach I suggested is that if I have multiple problems in the queue, and one of them gets rejected, all my other submissions move up in rank so that my next submission takes the place of the rejected one. This might not be a horrible consequence, but it bears consideration.',103,'friedlinguini','2003-02-24 09:58:33');
INSERT INTO forumpost VALUES (161,33,4,'Re: Flooding','I strongly agree with cory and ravi i was not referring to you when i said rank crazy. Ravi u said 2 or 3 problems a week? what happened to none. Now seriously although i really really don\'t like to single out people u truly are the reason that every person will have to wait for a problem to come in especially since i think more than 80% of the queue are your questions. Yes i do know you are contributing to the site, but u have had a LOT of dupes. E.g the missing dollar etc. Personally if u r trying to make the site a success and are willing enough to take the time to make all those problems, then maybe you could run through the sites problems and/or run a simple search for every problem you\'ve made at which point u mark that problem with a comment and u can ask levik to run through all the problems in the queue (aside from the ten most recent) and simply be able to quickly delete all those problems that are marked with one of your comments, (since noone else has voted on them)',1072,'Alan','2003-02-24 10:27:57');
INSERT INTO forumpost VALUES (162,34,4,'Re: Queue ranking','I have a pretty good idea. What u do is have each user have their own personal set of problems, ordered by date submission, at which point some program would choose one problem submitted by every user. So now every user has one problem in the queue. At which point the computer runs through again and every user\'s second problem (every user that has one) will then be posted and so on. At which point the individual protions of questions (The set of questions in which 1 was taken from every user) will then be ordered by date and so on. this way new users to the site will have no advantage as their problem would merely be posted to the back of the first set of question. Also after u submit a problem instead of saying the number of problems in the queue you could tell them their \"question position\" there was another good point about this system i thought up but i can\'t remember it. d\'oh!',1072,'Alan','2003-02-24 10:36:55');
INSERT INTO forumpost VALUES (163,31,4,'Re: Riddles','yes i agree. seeing as how leviks been with the site ever since it started he should (and does) have a general idea of comment patterns etc. so if he says a solution should be posted to a problem generally 2 or 3 days after i think hes right and know\'s what he\'s doing. SO Ravi you generally should add solutions to your problems (No offence most of them aren\'t that hard as i usually comment i figured it out in 10 secs(No lies))',1072,'Alan','2003-02-24 10:40:43');
INSERT INTO forumpost VALUES (164,34,4,'Re: Queue ranking','If I\'m not mistaken, this is effectively the same as levik\'s original suggestion, with QW spanning a single problem per user. It still has the same problem with a single submitter potentially monopolizing the top spot in the queue. I do like the idea of letting users see what position within the queue their problem occupies, though that\'s probably a topic for a different thread.',103,'friedlinguini','2003-02-24 12:11:47');
INSERT INTO forumpost VALUES (165,34,4,'Re: Queue ranking','o i guess i really didn\'t understand leviks way. except 1 question=qw of1 and 2 questions=qw2',1072,'Alan','2003-02-24 13:29:31');
INSERT INTO forumpost VALUES (166,33,4,'Re: Flooding','Alan, you have to realize that even if 50% of the problems Ravi has submitted were dupes, this would not be slowing down problems moving though the queue at all (in fact it would make the problems at the back move faster!) \r
\n\r
\nThis is because we would still be maintaining a 2 on weekday 1 on weekend rate, and having dupes in the queue does not affect that.',1,'levik','2003-02-24 15:08:10');
INSERT INTO forumpost VALUES (167,34,4,'Re: Queue ranking','friedlinguini - I think with your scheme, we are actually penalizing people like Ravi who submit a lot. I don\'t really want to do that. All I want is to give everyone a chance to be voted on. If there are 10 problems in the queue that are visible, even if the first spot is monopolized by one user, there\'s nothing to say that you can\'t push problem #3 instead. Having the granularity of QW be > 1 rewards anyone for multiple submission by guaranteeing them a proportional number of \"visible\" slots. \r
\n\r
\nCurrently we tend to push the problem sitting highest in the queue, but really, there\'s no reason to do this always.',1,'levik','2003-02-24 15:14:47');
INSERT INTO forumpost VALUES (168,33,4,'Re: Flooding','True but as stated before it scares away other new users, who do not yet know or understand that unless it is explained. Also i hope by the way i worded my previous post that it didn\'t seem like i said 80% are dupes.',1072,'Alan','2003-02-24 15:28:37');
INSERT INTO forumpost VALUES (169,31,4,'Re: Riddles','I trust you Alan..........and also Levik and that is what I exactly was trying to say...........that if there is no active discussion regarding that problem, then the solution can always be submitted...........but I was just saying so that people on the site can appreciate my problems........well not exactly appreciate but yes........at least let me know whether the problems that I have been submitting are good enough or not............being easy or difficult is a different case.............i want to know about the quality of the problems bein posted by me..........!!!!!!!......................that is all I would like to say................thank you',979,'Ravi Raja','2003-02-24 18:20:55');
INSERT INTO forumpost VALUES (170,33,4,'Re: Flooding','yes Alan.....now I realize that I have becoma a headache for everyone who wants to post problems on the site............but I have already discussed with Levik about this that later (and now also) i hardly get time to go through all the problems on the site and so it is not possible for me to say whether the problem that I have submitted is a dupe of any other problem or not.............but Yes, Levik being the Director of the site and knowing more than anyone else has the right to delete the problems submitted by me that are the dupes of problems already submitted................i will never say no for that...........and why do you want to reduce my submission to none .......instead of 2 or 3 problems \"A WEEK\" ???????...................i just did not understand that............i do not think that this amount of submission will again be creating such a problem like that I have created at present (making other users wait for long until all my problems have been approved and submitted)..................please do comment on this ....................thank you',979,'Ravi Raja','2003-02-24 18:32:16');
INSERT INTO forumpost VALUES (171,34,4,'Re: Queue ranking','I don\'t really regard it as a penalty. The time any user has to wait before seeing a problem come up is limited only by the number of users with pending problems. The time that passes before a user\'s next problem comes up is completely independent of the number of problems the user has submitted or the number that have been pushed live. While it might take quite some time before Ravi\'s 100th problem sees the light of day, his next one will appear in fairly short order. In fact, the only thing that could keep Ravi\'s 100th problem from eventually appearing would be an arbitrarily large number of people submitting problems. Any time you rank one author\'s problems over another, somebody is going to get \"penalized\".\r
\n\r
\nI think pushing the highest problem is really the only way to guarantee some measure of fairness.',103,'friedlinguini','2003-02-25 02:37:41');
INSERT INTO forumpost VALUES (172,33,4,'Re: Flooding','2 or 3 a week will be a problem. Even i\'m not going to submit problems. We want the queue to be reduced, not enlargened and every little bit enlarges it. and 2 or 3 a week still enlarges the queue by 30 problems once its finally empty.',1072,'Alan','2003-02-25 03:32:42');
INSERT INTO forumpost VALUES (173,33,4,'Re: Flooding','Alan, you\'re being too harsh, I think. 2 or 3 a week will be fine in my eyes - especially if we implement some of the measures we are talking about in the other thread.',1,'levik','2003-02-25 04:25:38');
INSERT INTO forumpost VALUES (174,33,4,'Re: Flooding','Thanks Levik........I still have a good collection of problems of different categories.........and I\'ll keep submitting them as I have mentioned(2 or 3 a week).......and this time surely with solutions........',979,'Ravi Raja','2003-02-25 06:59:16');
INSERT INTO forumpost VALUES (175,34,4,'Re: Queue ranking','I thought a little about how to implement your idea, fl, and I think that for now at least I will stick to my way, and see how well it\'ll work. Adding two extra fields to the problems table for the purpose of queue sorting seems excessive. Hopefully, sometime on weekend I will have the time to make these changes.',1,'levik','2003-02-25 11:01:29');
INSERT INTO forumpost VALUES (176,34,4,'Re: Queue ranking','Technically, I think you ought to be able to implement it with only QW as an additional field. I\'m not really a database guy, but it might even be possible to implement without that. Anyway, it seems to me that if you did decide to use my approach, the easiest way would be to first implement your approach, and then use mine as an extension. If your approach winds up being good enough, I don\'t see much reason to go to any extra work.',103,'friedlinguini','2003-02-25 12:23:23');
INSERT INTO forumpost VALUES (177,34,4,'Re: Queue ranking','Well, the QW stuff got implemented :) I would appreciate any feedback on it, and if you guys notice any weirdness, let me know.',1,'levik','2003-02-26 06:50:18');
INSERT INTO forumpost VALUES (178,34,4,'My Hard Work pays me nothing.........','Levik.....\"PLEASE DO NOT\" apply that QW rule that you have already applied..........there are reasons for which I am REQUESTING you for doing so........the reason is that........I have mentioned before also that I have worked day and night on most of the problems.......typing the problems and their solutions.......and all such things..........if now anybody else\'s problem gets submitted first which later you will find that is similar to a problem which I have submitted (which actually at that moment will be in the approval\'s list, that is in the queue).......in that case you all will say that it is a dupe and there is a similar problem already submitted in the site and thus that particular problem will be voted a Thumbs Down and finally will be removed from the queue..........which I would never like to happen..........it will be like a nightmare for me..........I just want to ask you one question.... I have been working so hard to submit these problems and is this what I am going to get in return ???????? I am really feeling so bad that I am just not able to explain it to you..........just for the benefit of others.........I had also stopped submitting problems which you can clearly find out from the date of submission of my last problem.......well any ways......I am now feeling extremely helpless and I have nothing more to say about this.........thank you :( :( :( :(',979,'Ravi Raja','2003-02-26 19:41:05');
INSERT INTO forumpost VALUES (179,34,4,'Re: Queue ranking','Hmmm... Ravi does bging up an interesting point. I have not consideres this little loophole inthe QW scheme. Any ideas on mitigating it? I have to admit, I feel really clever for having come up with this system, and would be loath to see it fall into disuse mere days after being implemented.',1,'levik','2003-02-27 01:43:44');
INSERT INTO forumpost VALUES (180,34,4,'Re: Queue ranking','Any time there\'s a problem duplicate in the queue, somebody is going to have his or her work trashed with no fault on the part of either submitter. There\'s no way around that with only a fraction of the queue visible to submitters. All things being equal, the fair thing to do is for the first submitter\'s problem be accepted and all others dumped. However, I don\'t think that it\'s a very big difference in what\'s fair. I realize that Ravi has put in a tremendous amount of work submitting problems, but that doesn\'t mean that an individual submission of his is worth more than somebody else\'s individual submission.\r
\n\r
\nIf we assume that dupes should be eliminated based on the order in which the problems were received, levik will either have to revert back to the original ordering scheme or to decouple the \'judging\' order from the order in which problems are pushed live. In order to make this work, problem judgers will have to be able to see every problem that has been deemed acceptable but not pushed onto the site proper in order to check for dupes. I think this leads to the \'exposure\' problem that limited the visible queue to 10 problems. IMO, that\'s not the route to take.\r
\n\r
\nWhat it comes down to is that somebody has to get hurt. I see no good way around that. The only question is who. It sucks to have to make a decision like that, but I would vote for using a scheme that spreads the pushed problems around among more submitters. For this site to run sustainably in anything like its curent form, new submitters must always be encouraged, and I think that the full weight of a huge problem queue is a very discouraging thing. ',103,'friedlinguini','2003-02-27 02:34:17');
INSERT INTO forumpost VALUES (181,34,4,'Re: Queue ranking','Wow... Well said :)\r
\n\r
\nSorry, Ravi, after thinking about it, I have also come to decide that the downside of the QW system is much MUCH less than the upside. Look at it this way, right now, your problems mostly still get the priority, so even in the unlikely situation that the queue contains problems that are duplicates of yours, there\'s still a good chance that your problems will show up first (because for the forseeable future, you will hold the top three spots of the queue).\r
\n\r
\nAnd the probability of dupes in the queue is not too great to begin with. Most dupes we see nowadays are copies of problems that were posted on the site within the first six months of its operation. It\'s those very well known puzzles that new users submit. Because more recent problems are forced to be more original, there is much less of a chance that they will be duplicated. \r
\n\r
\nSo overall, even if some of your problems get voted as dupes due to this effect, it should not be more than like 5 out of the 200 you have in the queue, which is a 2.5% margin.',1,'levik','2003-02-27 05:29:19');
INSERT INTO forumpost VALUES (182,34,4,'Re: Queue ranking','I agre. Most of the duplicates that Ravi has had rejected previously are duplicates of problems that have been on the site for months, or more.\r
\n\r
\nOut of the 200+ problems in the queue, it is not likely that there will be more than 5 (if any) that are rejected because of the weighting scheme moving up someone else\'s version before Ravi\'s ',153,'TomM','2003-02-27 05:50:06');
INSERT INTO forumpost VALUES (183,34,4,'Re: Queue ranking','On top of that why does it matter whether ravi\'s problem or someone else\'s problem gets posted to the site? Since both users are merely submitting problems to make the site better then what difference does it make whos problem is posted if both the problems are the same? The only difference is the submitter of the puzzle, but if both submitters are journeymen than the difference is negligible because there is no set amount of problems you must submit to become a scholar. So if you\'re a journeymen and someone else\'s problem goes up first then don\'t worry about it to much.',1072,'Alan','2003-02-27 14:20:09');
INSERT INTO forumpost VALUES (184,35,5,'Problem flagging','Hey levik how about a way to \"flag problems u submitted?\" What does it mean to flag a problem? Well lets say u submit a problem, like when i submitted nothing in everything, and a few days later you realize its a bad problem and want it deleted. Y not just give the option of flagging your problem so it gets deleted? Also if you\'ve submitted problems, but then all of the sudden on the site see the same problem, u would then need to flag ur problem to get rid of it?
\nBTW: levik you still haven\'t responded to \"sorry to bug you again levik\" in this forum?
\nSorry about all the questions but i have one more. do u mind when ppl type with slang like in this sentence and bad grammar?',1072,'Alan','2003-02-27 14:24:39');
INSERT INTO forumpost VALUES (185,35,5,'Re: Problem flagging','Alan, I don\'t think something such as what you propose is neccessary. After all, if you realize the problem to be a dupe or something, you can always leave a note on it asking it be deleted, and that note will be visible when the problem gets to voting. What would probably be a good idea is allowing users who have reached some rank (probably apprentice) to delete problems that have not yet been approved. I may end up implementing that.\r
\n\r
\nSorry for not respondin to your previous post. The idea is good, and I figured I\'d just do it, but so far the time has not presented itself.\r
\n\r
\nAs far as slang/grammar, I can\'t say I mind horribly, but realize that whenever you post problems that way, I will have to go and fix it, since I want the stuff on this site to be up to some level of professional looking-ness stuff thingy. Well, you get what I mean. So yeah, it would be better if people would take the time to submit stuff properly written, but I\'m not about to start turning down problems because of bad spelling/grammar. \r
\n\r
\nOverall, unless you\'re typing on a cell phone keypad, I\'ve never understood the urge of people to save two keystrokes by turning nice looking \"you are\" into a horribly immature \"u r\". But that\'s my personal taste, and I\'m not about to force it on anyone.',1,'levik','2003-02-27 18:49:34');
INSERT INTO forumpost VALUES (186,34,4,'Re: Queue ranking','hey fried......i never say that my individual submission is worth more than somebody else\'s individual submission.......secondly, for Alan.......I am not doing this to be turned to a Scholar from a Journeyman but only because I have been working hard typing those problems and solutions all day and night......as you have yourself seen that in very less time the number of pending problems went up to around 300..........so I am not worried about my user level but then you also have to think about my hard work.......what about that......I keep on typing problems and solutions and finally what I get is that my problem is rejected...being considered as a dupe of a problem alrerady submitted by some other user (whose actual date of submission was a few days after that of mine, but just because of this QW rule......is first seen on the site).......do you think I will like that...well I believe if there was any other user in my place , then that person would have also done the same thing........and would have been complaining about the same problem that I am facing.........so please never say that again that I am doing this to become a Scholar......and lastly....if suppose any problem is there which is in the queue......which I have already submitted or may be a similar one.....with the same concept.......but some other user\'s problem appears in the list before for the approval, then can I post a comment saying that such a problem has been submitted by me before........but has not been approved yet......????????...that is, it is still in the queue somewhere........in that case what are you people going to do..........are you going to consider my problem or the one the other user has submitted ............that is all I wanted to discuss regarding this......and I hope Levik.......you will not disappoint me....whatever decision you take...........thank you........\r
\n\r
\n',979,'Ravi Raja','2003-02-27 19:28:42');
INSERT INTO forumpost VALUES (187,34,4,'Re: Queue ranking','It was never my intent to put words into your mouth. I know you never said that your problems were worth more than somebody else\'s. I only said that in order to make my main point - if there\'s a dupe, SOMEBODY\'s problem has to get deleted.\r
\n\r
\nYou ask us to put ourselves in your shoes; now put yourself in the shoes of some newbie submitter. You\'ve just gotten to this site. You like it. You want to contribute. You have a good problem in mind, and searching around the site you don\'t see it listed anywhere, so you make your submission. Weeks go by, and you never hear anything about your problem and you don\'t see it get posted. Instead, you just keep seeing problems from this Ravi guy. One day, Ravi posts YOUR problem. The words have been changed around, but it\'s still your problem. How come he gets credit for it? More weeks go by. Eventually, you get told that your problem has been rejected because it is a duplicate of the one Ravi posted, even though you never saw Ravi\'s problem until much later. You get disgusted and you leave the site forever.\r
\n\r
\nRavi, while you\'ve never said that you feel that your problems are more important than anybody else\'s, you\'re asking that the volume of your work be taken into account when considering individual problems, which really isn\'t fair to the people who only post a few problems, including first-time submitters. You have to give other people a chance to be heard. If you\'re disappointed that one of your 200+ problems gets rejected because it\'s a duplicate, how do you think someone who submits for the first time would feel if their only submission got thrown out months later?',103,'friedlinguini','2003-02-28 02:15:24');
INSERT INTO forumpost VALUES (188,35,5,'Re: Problem flagging','for problems i will always type them professionally as if it were a professional problem. Also for the ability to delete unapproved problems, should this power be entrusted to apprentices? if this were to be implemented i\'d say only scholars be granted this, seeing as how they have the \"live problem power\" but if u feel differently from this perhaps a forum thread may be neccesary.',1072,'Alan','2003-02-28 10:18:56');
INSERT INTO forumpost VALUES (189,34,4,'Re: Queue ranking','Also ravi in response to what you said \"I am not doing this to be turned to a Scholar from a Journeyman \" i never said you were. I said if rank is not an issue then why does it matter what problem gets posted? and you said you did a lot of work typing all those problems. Well why should the effort you put in all your other problems be taken into consideration when its only one problem being compared to one another. The comparison is between the effort of 2 problems, not all of then each user submitted, thus meaning the problems will probably have an amount of effort almost equivalent to eachother. Of course, in my opinion \"effort\" should never be the deciding factor. Think of it this way, two people are applying for a doctor job. One tries really hard and gets 85% on his final test. The other didn\'t try at all and gets 90%. Who are you gonna hire? Well i\'m gonna hire the person who\'s more likely to save someone\'s life.
2. he wrote the test fine so he\'d do an operation as if it were a test',1072,'Alan','2003-02-28 10:37:39');
INSERT INTO forumpost VALUES (190,35,5,'Re: Problem flagging','well, this ability would only apply to people\'s own problems obviously. as such, I think an apprentice will know enough about the site to be able to do this.',1,'levik','2003-02-28 11:49:27');
INSERT INTO forumpost VALUES (191,34,4,'Re: Queue ranking','okay i agree with both of you Fried and Alan......thanks a lot.....but still I see one thing which is bothering me a lot.......when the total number of pending problems was 285(say), then the number of problems pending (which were submitted by me) was 250, (the figures have randomly been chosen, just to explain a point), so I had noticed that this difference was 35 or 36 for a few days and also all the 10 problems in the queue were those submitted by me.........but now I see that this difference has increased to 40 or more and not even a single problem (only two of them which were there before also) is there in the queue..............so what happened to my problems ?..... after the QW rule has been implemented, I see that only the three problems that were on top of the list of pending problems (that too which had received three thumbs ups and were ready to be shown up on the site) were there and all the other problems were from other users........its alright that four or five of my problems get rejected just because similar ones have been submitted by new users.........i won\'t mind and I can understand everything as you have explained Fried............but why not my problems are being pushed up in the queue.......and why everytime I see a new name ???????.....anyways, just like you have mentioned that a person gets disgusted and leaves the site forever.........similarly i felt the same thing when I saw that the QW rule was implemented and all my problems from the queue were removed and new problems(submitted by other users) were pushed up..........obviously I am not saying that its your or anybody else\'s fault.........even i understand the problem and thus I have even stopped submitting problems for the past few days......i do not know whether you know this or not, but I am sure Levik knows this........so when I understand other\'s problems why don\'t people understand me ?........i am not doing it for my rank/level........i am not saying that my problems are more important.........neither i accused fried or Alan for saying that (because that was not said for me....i know).........but now how long have I to wait for my problems to be approved and show up on the site ?????.........well i am accepting all your decisions and i agree with your arguments as well.........so i hope this also has some solution............thank you.......',979,'Ravi Raja','2003-02-28 20:43:29');
INSERT INTO forumpost VALUES (192,34,4,'Re: Queue ranking','You\'ve got the top three spots in the queue and you\'ve had a problem pushed every day for the last four days, both before and after QW was instated. You want more?',103,'friedlinguini','2003-03-01 03:42:24');
INSERT INTO forumpost VALUES (193,34,4,'Re: Queue ranking','that\'s what I said fried that the top three problems are mine only because they had been voted thumbs up at least thrice and was supposed to be shown up on the site...........but the remaining 7 problems belonged to someone else........anyways fried thans to you, Alan and Levik for clearing all my doubts and now it hardly matters to me............all i am doing nowdays is just waiting when i get to see my problems on the site.........that\'s it.....thank you and all once again............',979,'Ravi Raja','2003-03-01 04:39:57');
INSERT INTO forumpost VALUES (194,36,4,'New QW thread','I started a new thread because the first one was getting a bit long, and I don\'t want to implement forum thread paging yet :)\r
\n\r
\nOK, It seems to me that Ravi, you\'re still a little unclear about how the QW rule functions. (And how it applies to your situation curently) So here goes again (I really want you, and everyone to understand that this system is very fair to all users).\r
\n\r
\nProblems in the queue used to be sorted by order of submission. Thus if someone (Ravi) submitted 20 problems in one sitting, they would all show up in one long stretch. However, now, problems are sorted by QW first, and then problems with the same QW will be sorted by order of submission. This means that if two problems have QW = 1, the earlier problem will show up first, but problems with QW = 2 will show up after all the QW=1 problems.\r
\n\r
\nQW is recalculated every night on the following principle. For every user, their first three problems are given QW of 1. Problems 4 - 6 get QW of 2, etc.\r
\n\r
\nAs a result, no person will have more than three problems shown in the queue unless every other person with pending problems also has theirs shown. This means, Ravi that your top three spots are not a result of discrimination, but directly come from this rule. The reason they all have thumbs up already, is because they were probably voted on BEFORE the QW rules were instituted. Once these problems get pushed, new problems you have submitted will start showing up in these slots. \r
\n\r
\nAlso, because the you have submitted the vast majority of the problems in the queue, most of the time the three problems that are yours will be shown as the TOP three in the queue, almost guaranteeing that one of the two problems pushed daily will be yours.\r
\n\r
\nNot a bad deal, overall, and it allows new users to have their problems pushed through quicker, while still guaranteeing your problems exposure.\r
\nThe only thing you\'re losing is that one of your problems will be pushed on most days instead of two.\r
\n\r
\n',1,'levik','2003-03-01 08:36:28');
INSERT INTO forumpost VALUES (195,36,4,'Re: New QW thread','Thanks a lot Levik. Now I understand the rule perfectly but still have one question and that is this - you said that: For every user, their first three problems are given QW of 1. Problems 4 - 6 get QW of 2, etc. In that case suppose that i have 6 problems posted on one particular day, then what is going to happen ? Three of them will be given a QW = 1 as is understood from the rule and what about the remaining three ? will that be given a QW = 2 and they will be in the queue after the first three have been shown up on the site ? is that so ? If I have any more doubts, I will surely ask you and confirm their solutions. Thank You.\r
\n\r
\n',979,'Ravi Raja','2003-03-01 22:10:45');
INSERT INTO forumpost VALUES (196,36,4,'Re: New QW thread','i\'m not to sure about what you\'re asking but i think i have the general idea of it. You see ravi qw is re-calculated every night. So lets take your 3 problems that have qw=1 and lets say one of the gets posted. well later that night. the qw of all problems will be recalculated so one of your problems that has qw=2 will then have qw=1 and if you have problems with qw=3 one of them will have qw=2. Also if you submit 6 problems all at once i believe they all have qw=5(as a default) but then once qw is calculated they will all be assigned their rightful qw\'s accordint to time submitted.',1072,'Alan','2003-03-02 08:10:16');
INSERT INTO forumpost VALUES (197,37,5,'Names','On the site i\'ve noticed another user that goes by the nick alan. ( at least i\'m pretty sure of this seeing as how i don\'t remember posting \"hello\" on chatterbox) So i think it should be set up so that two users can\'t have the same nick. Although i know a lot of people would like the name alan(because a lot of people\'s names are alan) they could just pick a totally different nick that has nothing to do witht heir name. like q-bert or trigger etc.',1072,'Alan','2003-03-02 08:13:29');
INSERT INTO forumpost VALUES (198,36,4,'Re: New QW thread','That\'s correct. QW does not change when problems are \"posted\". It only happens once a day (at night actually). That is why if you have 3 problems with QW of 1, and they show up in the queue, and one of them gets posted, you will only see 2 problems in the queue - since you now only have 2 pending problems with QW 1. Also, the QW is calculated on ALL the pending problems you have, no matter if you posted them all at once, or one a day.',1,'levik','2003-03-02 12:17:03');
INSERT INTO forumpost VALUES (199,36,4,'Re: New QW thread','Thanks Alan, Thanks Levik.',979,'Ravi Raja','2003-03-03 03:46:15');
INSERT INTO forumpost VALUES (200,37,5,'Re: Names','This is an interesting issue. The site currently enforces unique login functionality, but allows you to pick any name you wish. Unfortunately, I was thinking of people who would either pick \"names\" to be their logins (and therefore the name would be unique) or a full name (first and last) which would ensure that duplicates are highly unlikely. I\'m not sure what to do in a situation where people want to go by their first names only... \r
\n\r
\nIf anyone has thoughts on this, please chime in',1,'levik','2003-03-03 04:33:47');
INSERT INTO forumpost VALUES (201,37,5,'Re: Names','How about using logins rather than names as the default way of referring to a user?',103,'friedlinguini','2003-03-03 06:06:40');
INSERT INTO forumpost VALUES (202,37,5,'Re: Names','Well I think it will be berrter if we use our full names instead of our login names just like what most of the users (including myself) is doing. In that case chances are less, in fact very less that two people will be using the same name and in case you still find two people with the same first as well as last names, in that case the first preference will be given to that user who has registered before and as a result of which the second one will have to change his details (in fact just a change in the name I mean).If this is done then the user\'s logins will also remain hidden and all the users will be sharing different names. So, here the first preference must be given to that Alan who has registered before and not to the one who has registered later (the one who wrote Hello in the chatterbox). And such cases are very rare may be 1 in 10 or still less, i mean say 1 in 25, that is 4 in 100 or so. I do not know what others have to say about this (that logins must remain hidden and the one who registerd first must be given the choice or the first preference and accordingly the new user has to act). This was just a suggestion from my part and the rest depends on what the majority says. Thank You.',979,'Ravi Raja','2003-03-03 06:42:24');
INSERT INTO forumpost VALUES (203,37,5,'Re: Names','I am sorry, in the first line the first line the seventh word is actually \"BETTER\". I noticed the mistake after I posted the comment. Sorry again.',979,'Ravi Raja','2003-03-03 06:45:49');
INSERT INTO forumpost VALUES (204,37,5,'Re: Names','I like the freedom the extra \"layer\" of having a name gives. You can always set it to the login name (as I have, and other people on the site, such as fl), or your full name (Ravi, Cory, etc). \r
\n\r
\nBecause most of the places where people\'s names are shown, they are linked to their user info pages, the potential for \"pretending\" to be someone else is small.\r
\n\r
\nThe more I think about it, the more I\'m leaning towards this not being a serious issue with the setup, but more a social issue of having people pick responsible \"names\". Perhaps I will make it so that your name cannot be the same as someone else\'s login. But I\'m not even sure that\'s neccessary.',1,'levik','2003-03-03 06:52:29');
INSERT INTO forumpost VALUES (205,38,7,'New forum','This is a forum made specifically with new users or casual visitors in mind.\r
\n\r
\nPeople who are new to the site can come here and ask questions about any of its features, and introduce themselves while they\'re at it. Let\'s make them feel welcome!',1,'levik','2003-03-03 14:57:02');
INSERT INTO forumpost VALUES (206,39,5,'Notifications?','I want to throw this idea out for general discussion (maybe someone has thought of this in the past, and thought it through better than me).\r
\n\r
\nI am thinking of email notifications to people when a problem of theirs gets pushed live to the site. A simple email going out telling the person about it, with the link to the front page and to the problem itself. I think this would serve us well in the current situation where problems take a long time to come up to the site after submission (a number of people may simply give up and not come back).\r
\n\r
\nWe currently send out a notice when a problem is voted down, but nothing for problems that get through. What do you think?',1,'levik','2003-03-03 16:48:11');
INSERT INTO forumpost VALUES (207,39,5,'Re: Notifications?','Yes Levik it\'s good and I too have received a few e-mails saying that most of my problems have been rejected either because the concept of that problem was similar to a problem already submitted or it was a dupe. But I would like to tell you one more thing Levik and that is when I received that mail, only the subject of the two problems (mine, which was rejected and the other one which is there on the site) is mentioned in the mail. It would be better if the two problems are also written under the respective subjects so that one can compare the two problems and then understand why his/her problem has been rejected. Like you know I have submitted a lot many problems and so I just don\'t remenber what the exact problem was under a particular heading and so when I received the mail of rejection I just could not compare the two problems. So, if you think its possible, please do as I have suggested. That is one problem that I was facing. If I have any more problems or suggestions, i\'ll surely be posting them. Please do let me know what do you think about this suggestion of mine. Thank you.',979,'Ravi Raja','2003-03-03 17:07:48');
INSERT INTO forumpost VALUES (208,39,5,'Earlier, not \"better\"','Ravi- Your problems were not rejected because the other version was \"better.\" It was just because the other problem was submitted earlier, and was already on the site.\r
\n\r
\nThere are many times when the rejected version is much better than the earlier version, but instead of dropping the earlier one with all its attached comments we reject the later one.\r
\n\r
\nIf you have the titles of the problem of which yours is a duplicate, you can always use the site search box to find it',153,'TomM','2003-03-03 23:34:55');
INSERT INTO forumpost VALUES (209,39,5,'Re: Notifications?','Levik It sounds entirely reasonable. You might also consider a brief notification when it enters the \"top ten\" list and the voters can see it.',153,'TomM','2003-03-03 23:37:16');
INSERT INTO forumpost VALUES (210,39,5,'Re: Notifications?','It\'s a good idea in principle, but I\'d like to see it as an option. While it is a useful feature, nobody likes getting mail they didn\'t ask for.',103,'friedlinguini','2003-03-04 01:08:01');
INSERT INTO forumpost VALUES (211,39,5,'Re: Notifications?','It is possible this e-mail for posted problems could get a little frustrating. maybe it should be an option you can turn on/off within your user info page. you could also the turn off e-mails for deleted problems.',1072,'Alan','2003-03-04 10:10:51');
INSERT INTO forumpost VALUES (212,39,5,'Re: Notifications?','I think the rejection email is pretty important - unless you are a high level user with access to the queue, you will most likely not know that your problem got deleted and why.',1,'levik','2003-03-04 18:09:30');
INSERT INTO forumpost VALUES (213,39,5,'Re: Notifications?','i agree that the subject of the problem(that is on the site) is provided along with that of mine (which has been rejected) in the mail but I am just suggesting that it would be much better if the problems too are there along with their corresponding subjects. So that a user can see and realize that yes the problem that has been submitted by him/her is a dupe of a problem that has been submitted or may be the one on the site is a better version compared to the one he/she had submitted and therefore has been rejected. That was what I was trying to say Fried and nothing else. This is just a suggestion from my part that\'s it and the rest is all in the hands of the director. Thank you.',979,'Ravi Raja','2003-03-04 18:22:52');
INSERT INTO forumpost VALUES (214,23,3,'Re: Two a day?','Presumably you can choose which problem to post rather than just having to post the oldest eligible one (this is sounding scarily like the flooble question again!). Anyway, how about posting a riddle and a \'non-riddle\' each day. That way the queue comes down quicker (or at least grows more slowly) and there\'s always a latest \'real\' problem for those not too keen on riddles.',1183,'fwaff','2003-03-05 06:04:06');
INSERT INTO forumpost VALUES (215,39,5,'Re: Notifications?','In addition to this, I would find it useful to be able to check the queue status of my problems. To illustrate, with the current queue sitting around 200 problems, and without the desire to keep a tally sheet by my computer of how many new problems have been posted, all I can do is calculate an initial \"expected\" date (# of prob/~2.5), and then wait it out. I submitted a problem about 2-3 weeks ago, but now have no idea where it sits (other than ~knowing~ it\'s probably at least another month away yet). This ability may make the notification of live problems uneccesary, while simultaneously eliminating any emails people would get that they potentially wouldn\'t want, as per some comments above. Definitely you must keep the rejection email though.',775,'Cory Taylor','2003-03-05 07:23:36');
INSERT INTO forumpost VALUES (216,37,5,'Re: Names','Tickled that my name was mentioned..\r
\nhehe',775,'Cory Taylor','2003-03-05 07:26:27');
INSERT INTO forumpost VALUES (217,34,4,'Re: Queue ranking','Wow, people getting very touchy, and I\'m certain I won\'t make it any better. I think that the ranking thing is great for another reason. I find that a persons problem submissions are heavily based on their personal preferences, situations etc, making them hold a similar \"flavor\" (look at my submissions - heavily based on math and patterns). While RR\'s problems are great for the site (don\'t take this poorly Ravi - I\'m just one person here), I don\'t find them interesting (for the most part). A ranking system allows a little greater divergence of puzzle topics, which stretches our brains a bit more, which is of course why we\'re here in the first place.',775,'Cory Taylor','2003-03-05 07:45:31');
INSERT INTO forumpost VALUES (218,17,6,'Re: HTML codes for use on the site','Ummm levik in one of my problems i\'m makling a solution to a problem with a txt based table/graph but the site won\'t allow more than 1 space. Is there any way to make a larger space between two numbers/letters?',1072,'Alan','2003-03-05 08:24:10');
INSERT INTO forumpost VALUES (219,38,7,'Re: New forum','Just a quick note to say - Great site!\r
\n\r
\nI\'m a math teacher and I send any students who are interested enough here to find odd puzzles that many of the more traditional sites just don\'t have.',1435,'Nigel Nisbet','2003-03-05 08:30:30');
INSERT INTO forumpost VALUES (220,38,7,'Re: New forum','Well, that\'s very kind of you to send us all that traffic. As a teacher, you\'re probably also in a pretty good position to offer up a problem or two of your own (no pressure though :)\r
\n
\nWhen I was just starting the site, I thought about making a special kind of \"teacher\" account, that would allow people to compose quizzes out of problems that existed on the site by adding them to a \"basket\", and then getting the ones they picked all on one page fit for printing.\r
\n
\nBut then I realized that these kinds of problems are better as extra credit. Who\'d want to give a test/quiz made up entirely of extra credit problems? :)',1,'levik','2003-03-05 10:44:55');
INSERT INTO forumpost VALUES (221,17,6,'Re: HTML codes for use on the site','There\'s the \"pre\" tag, but that\'s being escaped because it screws up too much if you forget to close it, as far as I recall.\r
\n\r
\nJust put \"<pre> ... </pre> around your table, and then when It gets to posting time, I will make this work by going into admin.',1,'levik','2003-03-05 10:47:51');
INSERT INTO forumpost VALUES (222,39,5,'Re: Notifications?','Hmmm... The problem is that there is no good (read: easy) way to determine this. We\'re already showing you the QW of all your problems (which isn\'t much, since it\'s easily calculated), but the actual ranking change continually. But it\'s a good idea that I should think about some more. Perhaps there is a way we could \"approximate\" this once every night.',1,'levik','2003-03-05 10:51:16');
INSERT INTO forumpost VALUES (223,23,3,'Re: Two a day?','I\'ve been sort of trying to do this over the last week. (Usually it translates into a \"Ravi\" and a \"non Ravi\" problem, but the last couple of days his were more math-oriented)',1,'levik','2003-03-05 10:56:45');
INSERT INTO forumpost VALUES (224,34,4,'Re: Queue ranking','I understand Cory but the thing is that I am not sticking to just one topic, but I am submitting a vaiety of problems with varying difficulties so that if one problem submitted by me is too difficult for one user then another problem of mine might be easier and that can encourage that user to try another one. I just don\'t submit problems of one kind and of difficulty level 4 or 5 or anything such. Anyway, I am not bothered anymore about the ranking but I will be surely happy if people came and say( I mean post a comment saying) that they like the different types of problems submitted by me. That\'s it. If you have anything else to say Cory, you can go ahead with your doubts and point out if I am going wrong anywhere.Thank You.',979,'Ravi Raja','2003-03-06 00:44:52');
INSERT INTO forumpost VALUES (225,34,4,'Re: Queue ranking','It\'s not a matter of going wrong. Regardless of how much variety you try to put into your problems, there is, as Cory puts it, a \'flavor\' to different submitters\' problems. Nobody is going to submit a problem they don\'t like or don\'t understand, so it\'s only natural that different submitters will submit different kinds of problems. For example, I couldn\'t see you submitting a hard physics or calculus problem. Conversely, I couldn\'t see someone like Cheradenine submitting a riddle. Making sure that a variety of posters get heard increases the richness of the site as well as giving everybody a chance to participate.',103,'friedlinguini','2003-03-06 04:08:49');
INSERT INTO forumpost VALUES (226,38,7,'Re: New forum','H\'lo all. I guess I\'m not new, but I can\'t resist the temptation of an (almost) empty forum...\r
\n\r
\nLevik, I want to say that I truly enjoy your site, I think you do a great job.',775,'Cory Taylor','2003-03-06 05:04:12');
INSERT INTO forumpost VALUES (227,40,6,'perfect squares','I want to confirm something that I think to be true. Does zero count as a perfect square, or does the definition exclude this trivial case?',775,'Cory Taylor','2003-03-06 05:08:36');
INSERT INTO forumpost VALUES (228,5,5,'Re: Latest Comments Numbering..','On the homepage it\'s currently showing \'Forums(12)\' which I take to mean that there are 12 new postings in the forums. However, once I go into the forums section the individual forums show: General Discussion (2); Commons (3); Reference (2); and New Users (2). Which is a total of only 9.\r
\n\r
\nIs this because there are some forums to which I don\'t have access - presumably there is some restriction based on level?\r
\n\r
\nClearly this \'glitch\' is incredibly minor, but you did say to point out anything that wasn\'t right.',1183,'fwaff','2003-03-06 05:09:56');
INSERT INTO forumpost VALUES (229,40,6,'Re: perfect squares','My understanding is that a perfect square is essentially the square of an integer. Since zero is an integer, then presumably it\'s square is perfect.',1183,'fwaff','2003-03-06 05:28:37');
INSERT INTO forumpost VALUES (230,5,5,'Re: Latest Comments Numbering..','fwaff - you are absolutely correct in your assumption. There is a forum for upper level users, who have access to the pending problems queue. I guess I should figure out a way to not have the posts you can\'t read figure in to the new posts number.',1,'levik','2003-03-06 05:55:44');
INSERT INTO forumpost VALUES (231,41,5,'Ratings (appoximately)','Just implemented a small feature where it will show you the score for a problem on the index pages (sill need to add this to search results)\r
\n\r
\nThese are only updated once daily (as opposed to when you actually go to the problem, it will show you the true rating).',1,'levik','2003-03-06 05:59:59');
INSERT INTO forumpost VALUES (232,5,5,'Re: Latest Comments Numbering..','Thanks for the quick answer.\r
\n\r
\nLike I said it\'s really minor, so it\'s not worth fretting about - if a quick and simple solution leaps out at you then go for it, otherwise leave it as it is. Looking through the forum postings it appears that most come from high-level regulars anyway, so there\'s probably only a small number of people who\'d ever notice. Besides, I\'m sure you\'ve got enough to do keeping up with Ravi\'s seemingly inexhaustible supply of problems!\r
\n\r
\nKeep up the good work :-)',1183,'fwaff','2003-03-06 06:16:40');
INSERT INTO forumpost VALUES (233,42,3,'Problems from Webring partners?','Is it legitimate to restate a problem from one of the sites on the same webring as Flooble, such as Braingle?',1301,'Charlie','2003-03-06 10:53:03');
INSERT INTO forumpost VALUES (234,42,3,'Re: Problems from Webring partners?','I would not object to this, if proper credit is provided in the problem\'s text.\r
\nHowever, their policies may differ. If they come up with their puzzles on their own, they may take some issue with copying. However, since most puzzles like this are pretty much free-floating in the web, you never know.',1,'levik','2003-03-06 14:14:48');
INSERT INTO forumpost VALUES (235,2,4,'Re: This is for?','Heres a better way to put it Nick. We all discuss to refuse to discuss what we are discussing??? Sounds boring PJ...... I quit. Just wanted to post something, as I am here for the first time.',834,'Gautam','2003-03-06 17:51:39');
INSERT INTO forumpost VALUES (236,36,4,'Re: New QW thread','Its nice to see people using out brains to solve the situation on hands on this site. I have one query too. Is this QW (I would like to refer it \'Quick Wit\') system, going to be implemented through out or only temporarily till the congestion is resolved?',834,'Gautam','2003-03-06 18:04:04');
INSERT INTO forumpost VALUES (237,43,4,'Stalemates','Anybody got any bright ideas about what to do if a problem in the top 10 slots of the queue hovers with a score between -2 and 2 votes? While it\'s not a critical problem as long as there\'s at least one problem where there\'s a clear consensus, it seems to me that it\'s the nature of undecided problems to slowly accumulate in the top 10 list, giving problem pushers fewer choices. Is it a big enough problem to worry about? After N days without getting enough votes to push live or to dump should a problem just be pushed down in the queue? Does levik just assume final do-or-die authority (not that he doesn\'t have it already, but at least this would formalize it)?',103,'friedlinguini','2003-03-07 02:10:48');
INSERT INTO forumpost VALUES (238,34,4,'Re: Queue ranking','You will surely come across such problems submitted by me Fried. \"Rome was not built in a day\". you know that. So all you have to do is just wait for a few more days and you will find those problems too on the site.',979,'Ravi Raja','2003-03-07 03:44:18');
INSERT INTO forumpost VALUES (239,36,4,'Re: New QW thread','Well Gautam I think it will be implemented throughout. Who knows when a similar situation might arise someday even after the congestion is resolved.',979,'Ravi Raja','2003-03-07 03:47:53');
INSERT INTO forumpost VALUES (240,36,4,'Re: New QW thread','Besides, the system doesn\'t realy do anything to resolve the congestion (the number of problems in the queue is actually still climbing). The system is meant to provide for more diversity in problems posted, and ensure that people who submit one or two problems are not horribly penalized by having to wait for three months because someone else submitted 100 problems before. (Note that it will do nothing to help in a situation where we have 100 people submitting 1 problem each - but in that case, little *CAN* be done.)',1,'levik','2003-03-07 09:07:07');
INSERT INTO forumpost VALUES (241,34,4,'Re: Queue ranking','Please use the new queue ranking thread levik has made. Like he said before he doesn\'t want to program multi-paged queue threads. Oh yeah don\'t posty \"i\'ll do that alan\" in this thread. Just go to the new thread and post any response you would normally have to this.',1072,'Alan','2003-03-07 10:47:30');
INSERT INTO forumpost VALUES (242,36,4,'Re: New QW thread','How about making problems 1-2 qw=1 problems 3-4 qw=2 etc. I think this way ravi will still gte one problem posted per day (thus having no impact on her question stream) but now a lot of new users, could quickly get their problems through(and advanced users two who came up with recent great ideas for problems)',1072,'Alan','2003-03-07 10:50:41');
INSERT INTO forumpost VALUES (243,17,6,'Re: HTML codes for use on the site','When I need more than one space at one point on a line, I alternate normal spaces (using the space bar key) with non-breaking spaces (character code nbsp).\r
\n\r
\nJust type a space, then type an ampersand (&) to indicate the start of a character code, followed by the code nbsp and a semi-colon (;) to indicate the end of the character code. Then type another space and code another non-breaking space, etc. \r
\n\r
\nYou may want to use the preview feature to make sure you don\'t have too many or too few spaces in the posted version.',153,'TomM','2003-03-07 13:23:49');
INSERT INTO forumpost VALUES (244,17,6,'Re: HTML codes for use on the site','heh - I use that trick as well from time to time. :)\r
\n\r
\nI have been considering opening up some more pesky HTML tags to some higher ranking people, but since rank on this site is not (and shouldn\'t be) indicative of one\'s profficiency with html, I\'m not sure this is such a good idea.',1,'levik','2003-03-07 18:15:20');
INSERT INTO forumpost VALUES (245,33,4,'Is This Fair ?','Hey Levik, I have submitted a similar problem (with the subject Hats Off !!!! as you can check in the list of the problems that I have submitted along with its date of submission) as what has been submitted by Anoop with the subject Hats Off (presently in the queue) and if this one(the one submitted by Anoop) comes up on the site then mine will be rejected. Is that fair ? I had discussed this with you in the forums and I had been told that the date of submission will be considered in such a case. Now what happened ? I think that my problem was submitted before Anoop submitted the similar version. As I had discussed before, I do not want my problem to get rejected and I hope it does not. Also you said that when the number of problems that was pending from my part was 200 then the remaining 40 problems were from the other users and so the number of dupes can be at most 5. now just see it yourself. Everyone is going on submitting problems and if they are similar to the ones that I have submitted and come up first on the site then not 5 but 55 of my problems can get rejected. Along with this I had in between pointed out that the difference between the number of problems submitted by me and those by the other users was 37 or 38, but now you can see it yourself that this difference is gradually increasing. Out of 10 problems that I have submitted there comes 1 (now there in the queue) and is of a similar concept so that will be accepted and mine will be rejected. So if this continues then this 1 out of 10 can be converted to 2 out of 10 and just imagine in that case how many of my problems(that has been actually submitted long time back) gets rejected because they are similar to the ones submitted by other users long after I have submitted mine. I hope you will take a FAIR decicion for this and will not disappoint me. That was all I wanted to say. Thank You.\r
\n',979,'Ravi Raja','2003-03-07 20:17:54');
INSERT INTO forumpost VALUES (246,33,4,'Re: Flooding','Ravi, please search the site for a problem called \"Colored hats\". Your problem is an exact duplicate of that much older problem. (This is exactly what I told you - your chances of having a dupe in the queue are much smaller than having a dupe already on the site)\r
\n\r
\nAs far as Anoop\'s problem, it seems different in principle. (Or maybe he just made a mistake submitting it)',1,'levik','2003-03-08 04:23:10');
INSERT INTO forumpost VALUES (247,33,4,'Re: Flooding','and ravi as i have said before if there are two problems that are exactly the same then what does it matter who\'s problem goes on the site? The only time i can see someone complaining is if there problem has a much better wording of both the problem and the solution, but in most of your problems \"which as said before has a certain flavour, just like all other users\" there is not much complexity required in the wording of both problem and solution. So if both these problems are the why does it matter which one appears on the site? Both users are trying to makre the site better right? so what difference does it make what problem gets posted. Is it because it says problems posted in your user details. Does it really matter in any way? Ravi please answer this one question, what is the importance of having YOUR problem posted to the site as opposed to someone ELSE\'S problem posted to the site',1072,'Alan','2003-03-08 06:00:17');
INSERT INTO forumpost VALUES (248,33,4,'Re: Flooding','Of course not Alan. My detils shows Problems posted by me dos not make me say that but I think I have discussed this before with you also then why are you trying to show that I am bothered about my details and user level. It is all because it takes a lot of effort yping such lengthy problems and their solutions. Now I hope it is clear to you why I am arguing on this topic. \r
\nNext I would like to ask Levik that I agree that this problem (Hats off!!!!) which has been submitted by me but is not in the queue is a dupe of a problem \"Coloured Hats\" which is already there on the site. Now suppose that such a problem was not there on the site and a similar situation arises, then which problem will be considered first, the one submitted by Anoop(which appears in the wueue before my problem does) or the one submitted by me ?',979,'Ravi Raja','2003-03-08 21:31:58');
INSERT INTO forumpost VALUES (249,33,4,'Re: Flooding','I never mind Alan, if anybody ELSE\'s problem gets submitted on the site. Though I am arguing about the two problems (the ones submitted by Anoop and the other by me), I have given a Thumbs Up to Anoop\'s problem in the queue and also along with it I have posted a comment regarding this problem. So, this makes it clear that I don\'t mind if Anoop\'s problem is posted and mine is rejected. So please do not say that again.',979,'Ravi Raja','2003-03-08 21:42:03');
INSERT INTO forumpost VALUES (250,44,3,'Search Results','Levik, here is one problem that I am facing and have been facing since when and I do not know whether anybody else has also suffered or not but now I think its time to discuss on this topic and find a solution for it. I have been facing problems with the searching of problems on this site. I type the name of the problem in the box where we are supposed to type the name of the problem and the result (the required problem) is in front of us (on the screen). But I have noticed that it is case sensitive and many other things like that. For example: I typed the subject \"Coloured Hats\" in the search box and the page showed me \"No results found\" ( a similar message in fact, not been writtn in exact words but means the same thing). Next I typed \"Colored Hats\" and the problem (on the site) was there in front of me. Similarly I tried for the same thing (\"Colored Hats.\"), [this time the spelling was correct but I intentionally put a fullstop \".\" after the word \"Hats\"] and again the screen showed the same message (no results were found). This was just an example. I have been facing this problem while searching for many other problems. So, I believe something has to be done to solve this problem (may be the search engine of this site should not be so much case/letter sensitive that even the addition of a fullstop will not show you the problem you are looking for). Instead it should show all the results (problems on the site) that contain the same (actually similar/identical) words/phrases that the user types in the search box. In that case I agree that the search results MIGHT give you a long list of problems, but I believe that this list will contain at most 20 - 25 problems and no more. SO at least the user will not have to try going for different combinations of letters and punctuation marks in order to get the problem he/she is looking for. With that list of 20 - 25 problems, he/she will be easily able to find out the problem he/she had searched for. I do not know whether this problem had been discussed before or not (as I had told you before that I might hardly get time to surf through the entire site) so I thought I would better discuss the problem I ( and may be other users too) have been facing with you so that you can do something about it and this indeed will help the users a lot. I hope you understand my problem and take the necessary steps as soon as possible. Thank You.',979,'Ravi Raja','2003-03-09 03:34:57');
INSERT INTO forumpost VALUES (251,44,3,'Re: Search Results','Ravi-\r
\n\r
\nMost search engines are not designed to recognize that \"British\" and \"American\" spellings are the same word (coloured/colored), and \"extraneous\" punctuation often confuses them. \r
\n\r
\nIt is because they are not designed to parse sentences, but merely compare strings. \r
\n\r
\nUsually they are only case-sensitive in one direction: searching for \"hats\" will bring up both \"hats\" and \"Hats,\" but searching for \"Hats\" only brings up \"Hats.\"\r
\n\r
\nThe best way to search is to just type the most important two or three words in the phrase in all lower-case. If a word is spelled differently in American usage from British usage, leave it out of the search terms, if you can. If you need it, make two searches spelling the word each way',153,'TomM','2003-03-09 04:17:52');
INSERT INTO forumpost VALUES (252,44,3,'Re: Search Results','Thanks TomM. ',979,'Ravi Raja','2003-03-09 05:05:21');
INSERT INTO forumpost VALUES (253,45,4,'How a Puzzle is Voted On.','When a puzzle is in the voting stage, do the voters see the solution? I\'m asking this in regard to my US,MS,HS,TS(&DS) puzzle, where Ravi left a note concerning the significance of the parenthesized item. The solution indicates the reason, and I\'d hate to think that this particular puzzle would be approved without the voters\' seeing the solution, as it might not be considered an appropriate sequence problem, given its solution, which might be considered of local (NYC area) interest only.',1301,'Charlie','2003-03-09 07:44:17');
INSERT INTO forumpost VALUES (254,45,4,'Re: How a Puzzle is Voted On.','Since the same people who vote on a puzzle will be the ones trying to solve it, we do not see the answer, and most of us would not look even if we could.\r
\n\r
\nOccassionally if it seems too esoteric, or if we suspect that an important piece of information is missing, we will ask levik, the site\'s webmaster, to \"peek\" at the answer and report back, but that is a rare occassion.\r
\n\r
\nDon\'t worry about a problem being too regional, unless it is incomprehensible to people not familiar with the area -- and even that can be fixed by adding a short explanation. We have had problems presented in terms of America dollars, English pounds, and Indian Rupees. As long as we know the relationship between the coin and paper denmination (1 dollar = 100 cents, etc.) the currency does not really matter. (Of course if the regionalism is in the answer, you need to be more careful.) ',153,'TomM','2003-03-09 09:33:39');
INSERT INTO forumpost VALUES (255,33,4,'Re: Flooding','Please Ravi i am NOT saying your concerned about ur rank. And u say u take a lot of effort typing up ur problems correct? yes it may be lengthy and time consuming but fact of the matter is whats done is done. You can\'t undo ur work in these problems, so i\'m merely asking what difference does it make which problem gets posted on the site. On top of that its not about a person\'s effort in ALL their problem\'s its about the effort in both problems that are the same, and since there the same problem, the give or take of a few seconds of work(on the single problem) shouldn\'t be all that important. And as (fl i beleive it was but i could be wrong) has pointed out before either way someone\'s work will have to be deleted. so even though u put a lot of effort into that one problem, so has some1 else.',1072,'Alan','2003-03-09 14:44:32');
INSERT INTO forumpost VALUES (256,33,4,'Re: Flooding','Its ok Alan, I understand. Then all I can do is vote a Thumbs Up to that problem. That\'s it. Anyway it doesn\'t matter whatever it be. Let the things be as they are. And I am sorry Alan if I have said anything wrong for you, PLEASE DON\'T MIND, I hope you understand. Thanks.',979,'Ravi Raja','2003-03-09 18:29:34');
INSERT INTO forumpost VALUES (257,46,4,'Hat down in apology','Dear members,\r
\n\r
\nI apologise for all the confusion and mayhem i seemed to have caused with my completely worthless wording of the \"hats off\" problem.\r
\n\r
\nThe unforgivable mistakes in it are - \r
\n1. All 3 hats cannot be of the same colour; the hangman and the convicts are aware of this.\r
\n2. Each person is supposed to guess the colour of his hat, not that of ALL.\r
\n\r
\nI have posted the solution.\r
\n\r
\nI am sorry for all the chaos. I think I wrote it down a little too hastily.\r
\nI also realise it\'s rather similar to the coloured hats problem. I just didn\'t know there was such a similar problem in the archives.\r
\n\r
\nTotally my oversight.... I apologise again.',1299,'Anoop','2003-03-10 06:00:35');
INSERT INTO forumpost VALUES (258,46,4,'Re: Hat down in apology','Not to worry. I fixed the wording for you, and even threw in a thumbs up for good measure. This will probably be the longest debated queue problem for a while.\r
\n\r
\nSee, Ravi? This problem turned out to be different from yours after all.',1,'levik','2003-03-10 06:37:04');
INSERT INTO forumpost VALUES (259,46,4,'Re: Hat down in apology','Its ok Anoop it happens so, but my case seems to be worse than yours. Well you found out your mistake when the problem is still in the wueue but just see the blunder that I have made in my problem (Cattle Selling) which is now on the site. I am sorry friends/members, this time its my time to apologise. I actually made a mistake while solving the problem and that\'s the reason why the figures in my problem don\'t satisfy the conditions.\r
\n\r
\nWell I think in the problem (\"Cattle Selling\"), the statement that says: \"My friend received from the dealer in total Rupees 301\", should be actually: \"My friend received from the dealer in total Rupees 285\". Now I believe the problem is correct and you must be getting a solution (integral and not fractional) for the number of animals of each type in the farm. \r
\n\r
\nI am really SORRY for such a mistake. I will be posting this in the comment list too and I would REQUEST Levik that if possible, please do change the figures in my problem if that is possible for you to do, or else before reading my apology note in the comment list, everyone will try to solve the problem as given in the front page (with the wrong data). \r
\n\r
\nI don\'t have anything else to say after committing such a bad mistake/blunder, but it was all a mistake and I again apologise for it. ',979,'Ravi Raja','2003-03-10 06:39:38');
INSERT INTO forumpost VALUES (260,38,7,'Re: New forum','I am new to this site and I would just like to say how much I enjoy all the amazing riddles and puzzles that can be found here. ',1637,'chris','2003-03-10 12:18:34');
INSERT INTO forumpost VALUES (261,38,7,'Re: New forum','Thank you Chris, and welcome.\r
\n\r
\nIf you don\'t mind my asking, how did you find this site?',1,'levik','2003-03-10 13:14:49');
INSERT INTO forumpost VALUES (262,38,7,'Re: New forum','Hey Levik, there is only one answer whcih every new user would give to this question you have put forward and that is: \"EXCELLENT\", and may be more but I think they will fall short of adjectives describing how good this site is and how well you take care of everything here. I know that I was not supposed to answer to this question of yours but I think that is the response you are going to get from any new user of this site. :):):):)',979,'Ravi Raja','2003-03-10 23:13:06');
INSERT INTO forumpost VALUES (263,38,7,'Re: New forum','*grin* I\'m not quite sure that\'s what levik meant...',103,'friedlinguini','2003-03-11 01:44:46');
INSERT INTO forumpost VALUES (264,38,7,'Re: New forum','Yes, perhaps I should rephrase that to be:\r
\n\r
\n\"How did you first find out about this site?\" :)',1,'levik','2003-03-11 01:53:02');
INSERT INTO forumpost VALUES (265,47,5,'Your info. in your words','A news field was added to the user info screen. It\'s a free form text area\r
\nto write anything you want about yourself. Just don\'t go overboard.\r
\n\r
\n(Some html codes will work in there, so EXPERIMENT - but not too much :)\r
\n\r
\nIf anyone is worried that their name may leave any ambiguities as to their gender, they should feel free to indicate the correct one in this area.',1,'levik','2003-03-11 05:52:11');
INSERT INTO forumpost VALUES (266,38,7,'Re: New forum','I rarely (apart from time spent on this site) think about just how ambigous the English language can be. I never would have interpreted Leviks question the way Ravi did, and even after being confused as to why that comment appeared here (rather than somewhere else), I wouldn\'t have caught that the \"intterpretation\" of the question was the problem without f.l.\'s comment. I wonder if this could become the basis for a riddle...\r
\n\r
\nIn answer to your \"intended\" question Levik, I did a i.e. search for \"puzzle\" + \"-crossword\", and your site was the first of the matches that had decent (read \"worthy of visiting\") content.',775,'Cory Taylor','2003-03-11 06:57:30');
INSERT INTO forumpost VALUES (267,38,7,'Re: New forum','Found you by searching on internet for logic puzzles. How do you try a hand at solving some of the puzzles...like the one on front page about convicts and hats?\r
\n ',1663,'kc','2003-03-11 08:57:35');
INSERT INTO forumpost VALUES (268,38,7,'Re: New forum','Just click the puzzle\'s title to go to its page, then if you\'re logged in, you will see a link to post a comment under the puzzle\'s text. Post your solution there (but don\'t give it away in the subject)\r
\n\r
\nAnd welcome to the site :)',1,'levik','2003-03-11 09:19:07');
INSERT INTO forumpost VALUES (269,38,7,'Re: New forum','I am new to this site and have already posted an answer to the blindfolded 3 hats puzzle. However, I have read the answers by others and they all seem to have found the same answer I did. So why did the site say No Answers have been submitted?\r
\n',1667,'Erlys','2003-03-11 16:26:09');
INSERT INTO forumpost VALUES (270,38,7,'Re: New forum','The site did not say no answers submitted but yet \"no solution yet\" this simply means the solution has not been posted to the site.',1072,'Alan','2003-03-11 16:36:24');
INSERT INTO forumpost VALUES (271,38,7,'Re: New forum','I thought I had the solution. Does \"No Solution\" mean I am wrong?',1667,'Erlys','2003-03-11 17:13:33');
INSERT INTO forumpost VALUES (272,38,7,'Re: New forum','No, it just means that the \"official\" version is not public yet.\r
\n\r
\nFor most problems, users submit a solution as well, but that remains hidden for the first few days the problem is public.\r
\n\r
\nWelcome to the site.',1,'levik','2003-03-12 01:39:16');
INSERT INTO forumpost VALUES (273,45,4,'Re: How a Puzzle is Voted On.','I\'m sorry to say that in this case, the regional slant was just too strong.\r
\n\r
\nIn addition, I just don\'t believe that there is much thinking to be involved in solving the problem. You will either just guess it, or you won\'t. (I didn\'t, and I happen to live in NYC)\r
\n\r
\nBy the way, as far as solutions go, they are not visible, but there is a number showing the length of the solution text in characters. This is so that if the problem seems \"unsolvable\", people can tell if the author submitted a solution or not. I believe that the presence and length of a solution can affect the problem\'s odds of being approved in such a situation.',1,'levik','2003-03-13 06:57:10');
INSERT INTO forumpost VALUES (274,48,5,'Unsolved problem order','I was looking at the list of unsolved problems and noticed that they are in no particular arranged order(at least none i noticed). I think that it probably would be good if they were orderd by the following crudentials.
1.Difficulty 5 has highest value in list
2.Comments the more the better
3. Score',1072,'Alan','2003-03-13 12:20:40');
INSERT INTO forumpost VALUES (275,48,5,'Re: Unsolved problem order','I agree that an ordering is sensible, but believe it is better for those with the least comments to be at the top to encourage discussion on them. Also the unsolved problems with the most comments already appear on the \'Most Commented On\' list and often re-appear on the \'New Comments\' list, so why should they receive further promotion?\r
\n\r
\nNow that a couple of problems appear every day I often miss some of them when they are the \'Latest Problem\' and the only way I see them is by looking at the \'New Comments\' and \'Unsolved Problems\' - this is also true of problems posted at the weekend as I\'m generally a \'lunchtime at work\' floobler. I think that one use of the unsolved list is to give recent problems a good airing and thus a fair chance of being discussed and solved, so why not enhance this benefit by putting them at the top of the list? \r
\n\r
\nAs an additional suggestion, how about not posting the formal solution to a problem until there is at least one Solution comment? Rather than posting solutions by default after a few days.\r
\n\r
\nAs an example, I think that Charlie\'s chess problem missed out (or rather we missed out on it) because it only spent a short time as \'Latest\' during which no comments were posted, so nobody saw it on the \'New Comments\' list. As a result the solution was posted before anybody actually solved it.',1183,'fwaff','2003-03-13 22:14:27');
INSERT INTO forumpost VALUES (276,48,5,'Re: Unsolved problem order','Is what fwaff refers to actually the result of the recent problem list being too easy to miss? It does appear below the random problem on the home page, so you can actually catch up by scrolling below the random problem from the past. Maybe a couple of these could be moved above the random problem so they\'d be more easily seen. And being only a couple, they wouldn\'t prevent the random problem from being seen.',1301,'Charlie','2003-03-14 03:30:53');
INSERT INTO forumpost VALUES (277,48,5,'Re: Unsolved problem order','Thanks Charlie, I never noticed that list before - on the homepage screen I see the Recent one, usually see at least the top of the Oldie (depending on the length of the Recent problem) and have never thought to scroll down further to see what\'s beyond. Doh!\r
\n\r
\nI\'m off to hang my head in shame now!',1183,'fwaff','2003-03-14 04:14:03');
INSERT INTO forumpost VALUES (278,48,5,'Re: Unsolved problem order','I am currently thinking of adding a \"digest\" page, where you will be able to see the problems for the last X days. \r
\n\r
\nThe problems would be shown in the same way as the \"Latest\" and \"Oldie\" are on the front page: just the body + the comment count. You would have to go to the actual problem\'s page to read the comments though.\r
\n\r
\nThe X would be \"changable\", probably from a pull down - from one day to seven, ten and fifteen, I\'m thinking, and default to the number of days since your last visit, or 2 whichever is greater.\r
\n\r
\nComments?',1,'levik','2003-03-14 10:10:37');
INSERT INTO forumpost VALUES (279,48,5,'Re: Unsolved problem order','The pull-down, changeable last X days seems like a lot of work. Try it with a standard 3 or 4 days first: we\'d be talking about 6 to 8 puzzles on that digest page; more could become troublesome',153,'TomM','2003-03-14 15:16:35');
INSERT INTO forumpost VALUES (280,45,4,'Re: How a Puzzle is Voted On.','Now I\'m curious: What was the sequence?\r
\n\r
\nAfter the note about New York regionalism, I started thinking about the intersections where Broadway crosses the numbered avenues and thought that I recognized the second, third, and half of the fourth: Madison Square, Herald Square, and Times Square. ',153,'TomM','2003-03-14 15:27:58');
INSERT INTO forumpost VALUES (281,45,4,'Re: How a Puzzle is Voted On.','That was it. There\'s also Union Square and Columbus Circle. (I don\'t remember what the other half of Times Square was)',1,'levik','2003-03-14 20:09:07');
INSERT INTO forumpost VALUES (282,45,4,'Re: How a Puzzle is Voted On.','Where Broadway crosses 7th Avenue, on the one side is Times Square and on the other the lesser known Duffy Square, where the TKTS booth is. That\'s why the parenthetical (&DS) as they share 7th Ave.',1301,'Charlie','2003-03-15 07:07:49');
INSERT INTO forumpost VALUES (283,45,4,'Re: How a Puzzle is Voted On.','Well, when it right comes down to it, the northern \"half\" of Herald Square (at 6th Ave*) is Greeley Square.\r
\n\r
\nBTW, isn\'t it odd that all of these hour-glass shaped plazas are called \"squares,\" except the last one?\r
\n\r
\n* I know that it\'s been \"Avenue of the Americas\" since the 1964 World\'s Fair, but if you call it that, you only show that you are not a New Yawker',153,'TomM','2003-03-15 21:56:42');
INSERT INTO forumpost VALUES (284,45,4,'Re: How a Puzzle is Voted On.','Yes, \"Ave of the Americas\" never cought on the way \"Park Ave. South\" did for 4th Ave. (the basis for the numerical position of Union Sq.). Sixth Ave. was renamed \"Ave. of the Americas\" in 1945, so of course that does include \"since the 1964 World\'s Fair\". Within Verizon, though, the HQ bldg is known as 1095 A/A with the slash pronounced as \"of\" when spoken, rather than as 1095 Sixth Ave.',1301,'Charlie','2003-03-16 07:09:05');
INSERT INTO forumpost VALUES (285,45,4,'Re: How a Puzzle is Voted On.','Huh. I could have sworn that I remember that the press made a big deal out of the re-naming, at the time of the Fair. I know I can\'t be remembering 1945, because I wasn\'t around yet, then.\r
\n\r
\nBut a quick session with Google shows me that most sites that mention the name change agree with you that it was 1945. ',153,'TomM','2003-03-16 21:26:37');
INSERT INTO forumpost VALUES (286,49,4,'Solved Unsolved Puzzle','Trading Cards was submitted by levik in the hopes that “Perhaps one day, someone will come along and solve it :)” (comment 4). As Steve Hutton mentions in comment 35, “So, if this problem has been answered by two different methods doesn\'t it count as solved?” My comments 23-25 solved part B by the inclusion/exclusion method of “Probability of All of a Set”, and Steve Hutton’s comment 8 set up the outline for a completely different method of solution of part B (a Markov chain) which I implemented in comment 29. In fact a third very elegant method of solution for part B (direct expected length via recursion) was posted by Rick in comment 31, which had merely to be adjusted to fit the packets-of-5 nature of the problem. Part A was solved via inclusion/exclusion in comment 26 (with a couple of typos corrected in 27 and 28), and via Markov chain, proposed in comment 9, and corrected and implemented in comments 33 and 34. I know that an individual comment is not large enough to hold the full solution, but levik, as the original proposer, could put an official solution together, perhaps based only on the Markov chain model, which seems simpler. All the solutions agree on the final answers to the two parts.',1301,'Charlie','2003-03-17 04:05:01');
INSERT INTO forumpost VALUES (287,49,4,'Re: Solved Unsolved Puzzle','Charlie, there is nothing sinister about the fact that the problem remains \"unsolved\". I simply was not aware that these solutions have been posted.\r
\n(Lately, I don\'t have time to always read the new comments).\r
\n\r
\nI will fix this with a \"solution\" referencing user comments.',1,'levik','2003-03-17 07:19:17');
INSERT INTO forumpost VALUES (288,49,4,'Re: Solved Unsolved Puzzle','I didn\'t think there was anything sinister. I just wanted to bring it to your attention. I see you didn\'t need the individual references, as your solution just refers to the comments, but just in case you wanted to paste together a separate solution I provided them.',1301,'Charlie','2003-03-17 08:00:23');
INSERT INTO forumpost VALUES (289,50,5,'Chatterbox','I\'ve noticed recently an increasing amount of chatter in the Chatterbox that consists of \'newbies\' (for want of a better word and I don\'t mean this in any derogatory way) saying \"hello\" and then getting grumpy when there\'s no immediate response. This is usually followed by one of the \'regulars\' giving the same explanation about it not being live and how there aren\'t generally many people on the site at any one time.\r
\n\r
\nHow about putting a box on the homepage (or maybe even on each page) showing who is actually logged in to the site. For an example of what I mean have a look on Braingle.com, it\'s about half way up each page on the right hand side.\r
\n\r
\nThe upside to this is also the same as the possible downside in that it would allow non-problem-specific chat between \'genuine flooblers\', but also runs the risk of turning an \'excellent puzzle/problem site with a chat facility\' into another \'chat-room with some interesting puzzles\'.\r
\n\r
\nJust a thought, feel free to knock it back if you think it\'s a duffer.',1183,'fwaff','2003-03-18 21:50:37');
INSERT INTO forumpost VALUES (290,50,5,'Re: Chatterbox','I have actually been thinking along the same lines... Unfortunately, there\'s currently no easy way to tell who is logged in to the system, and who is not (since there is no notification when someone leaves the page).\r
\n\r
\nI will think on it though (I know such scripts exist - maybe I can steal one :) and try and come up with a solution.',1,'levik','2003-03-19 02:03:17');
INSERT INTO forumpost VALUES (291,51,3,'Submitter\'s view of pending puzzles.','When I submitted my first few puzzles I didn\'t realize that one had to click on Edit Problem in order to see the voters\' responses--I only realized that later. Perhaps the word \"response(s)\" itself could be made into a link to the same page to make it more apparent for new submitters.',1301,'Charlie','2003-03-19 09:55:37');
INSERT INTO forumpost VALUES (292,52,5,'truncated comments','Previously when I tried to post too long a comment, it would merely give a blank preview. But today I see that a post which is just a few lines too long was actually truncated in the posting area. Can there be a fix for this?',1301,'Charlie','2003-03-19 16:27:46');
INSERT INTO forumpost VALUES (293,52,5,'Re: truncated comments','Hmmm... I wonder if this is actually a problem with the javascript used to do preview - somehow I think if you submitted the comment, it would go through.\r
\n\r
\nPerhaps if I have the time this weekend I will look into it.',1,'levik','2003-03-19 16:54:17');
INSERT INTO forumpost VALUES (294,53,5,'Submitter\'s view of pending puzzles.','I had submitted this in General Discussion, but I think that was the wrong place:\r
\n\r
\nWhen I submitted my first few puzzles I didn\'t realize that one had to click on Edit Problem in order to see the voters\' responses--I only realized that later. Perhaps the word \"response(s)\" itself could be made into a link to the same page to make it more apparent for new submitters. \r
\n',1301,'Charlie','2003-03-20 04:02:12');
INSERT INTO forumpost VALUES (295,53,5,'Re: Submitter\'s view of pending puzzles.','Good idea.\r
\n\r
\nLet me do this...',1,'levik','2003-03-20 04:34:28');
INSERT INTO forumpost VALUES (296,50,5,'Re: Chatterbox','OK, I don\'t know if anyone noticed this, but I implemented it yesterday. On most pages it will now say how many people are browsing the site. Clicking the little \"who?\" button should open a box with a list.\r
\n\r
\nThis uses some javascript trickery, so I would appreciate if someone lets me know when they have problems.',1,'levik','2003-03-20 04:41:23');
INSERT INTO forumpost VALUES (297,50,5,'Re: Chatterbox','You\'re a genius :-)\r
\n\r
\nIt\'s working fine and I think it\'s a neat addition.',1183,'fwaff','2003-03-21 02:17:57');
INSERT INTO forumpost VALUES (298,52,5,'Re: truncated comments','Hmmm... Looking back at what was, I think, the comment that had prompted this, I see that the lines that I thought were deleted found their way to near the top. Of course I could have accidentally cut and pasted, but I don\'t think that was what happened--that\'s two steps, not just one. The specific comment was #23 under Best Strategy, where the equation is shown before the description of how it was derived. I had thought it disappeared completely, and so put it into the follow-up comment, #24.',1301,'Charlie','2003-03-21 08:44:54');
INSERT INTO forumpost VALUES (299,54,5,'Suggestion for more problem ratings','Make the \"Rate This Problem\" widget available from the front page for the latest problem, and maybe people who wouldn\'t otherwise comment on it might give it a rating.',103,'friedlinguini','2003-03-21 09:16:33');
INSERT INTO forumpost VALUES (300,17,6,'Re: HTML codes for use on the site','Do these html codes work on the queue comment submition part of the site. I tried making a link but it didn\'t work.',1072,'Alan','2003-03-22 05:13:04');
INSERT INTO forumpost VALUES (301,17,6,'Re: HTML codes for use on the site','No - those are strictly for short suggestion. I wanted to discourage excess discussion there, so people would save it for when the problem is live.',1,'levik','2003-03-22 05:34:53');
INSERT INTO forumpost VALUES (302,17,6,'Re: HTML codes for use on the site','well ireally just wanted to show a link to show what a problem was a dupe of',1072,'Alan','2003-03-22 05:42:58');
INSERT INTO forumpost VALUES (303,38,7,'Re: New forum','I found this site by searching for puzzles and riddles on yahoo(I think). Sorry it took me so long to answer.',1637,'chris','2003-03-22 17:56:07');
INSERT INTO forumpost VALUES (304,17,6,'Re: HTML codes for use on the site','Hmmm... well, traditionally I would just put the problems name in the comment. the search box is right there, and will open in a new window, so anybody who wants to see the problem will still be able to do so fairly easily.',1,'levik','2003-03-23 04:28:25');
INSERT INTO forumpost VALUES (305,55,3,'Anything and everything',' Is this really a forum for discussing anything and everything?',1660,'Tim Axoy','2003-03-23 07:10:24');
INSERT INTO forumpost VALUES (306,56,7,'Tim Axoy',' Hi,I am Tim Axoy!\r
\nI have a brother names Tim and sisters named Gladys,Katherine,and Eileen.\r
\nI like math and logic.\r
\n',1660,'Tim Axoy','2003-03-23 07:15:34');
INSERT INTO forumpost VALUES (308,57,3,'No,no,no',' This says,\"This is a forum for discussing anything and everything.\"\r
\nActually,because problems are not allowed,you cannot discuss anything and everything.\r
\nWhy is that?',1660,'Tim Axoy','2003-03-23 09:15:57');
INSERT INTO forumpost VALUES (309,21,3,'F\'s and more F\'s',' Here is a puzzle.\r
\nRead the following sentence.\r
\nFive fruits of five colors,one of which is the apple of my eye,are fun.\r
\nHow many F\'s are in the sentence?\r
\n Here is the answer.\r
\nFive Fruits oF Five colors,one oF which is the apple oF my eye,are Fun.\r
\n1 2 3 4 5 6 7\r
\n7 F\'s.\r
\n',1660,'Tim Axoy','2003-03-23 09:26:33');
INSERT INTO forumpost VALUES (310,37,5,'Alan and Alan',' I cannot believe two people go by Alan on this site.',1660,'Tim Axoy','2003-03-23 09:31:04');
INSERT INTO forumpost VALUES (311,3,3,'Re: Suggestions','I\'ve got a suggestion. I thinf it would be nice if you could see how your pending problems were being voted on.',1637,'chris','2003-03-23 13:08:45');
INSERT INTO forumpost VALUES (312,21,3,'Re: Puzzles','Tim i don\'t see why ur posting this in a forum? if its a puzzle u made up you should submit or if you have a solution then post a comment to that question. Not in a forum',1072,'Alan','2003-03-23 14:38:21');
INSERT INTO forumpost VALUES (313,57,3,'Re: No,no,no','Tim i would just like to say a few things. 1. Don\'t try to contradict the system. It says anything and evertything but there obiously are boundaries. For instance you wouldn\'t talk about where u can download roms would u? Just like in real life. The U.S.A and Canada are both free countries but can u just go out and kill a man? of course not
2.please do not create multiple threads. try to sum up all your thoughts in one thread unless they are two seperate ideas. Thank you',1072,'Alan','2003-03-23 14:41:40');
INSERT INTO forumpost VALUES (314,3,3,'Re: Suggestions','On the home page click on \"# problems pending\". A list of your problems will appear. If any notes or responses have taken place in the voting, the comment \"# response(s)\" will appear. If it doesn\'t it means it hasn\'t reached the voting stage, or it\'s too soon for anyone to have responded or voted yet. But if it does appear, click on it to see a page that has the responses, including any votes.\r
\n',1301,'Charlie','2003-03-23 14:43:54');
INSERT INTO forumpost VALUES (315,58,4,'Forum puzzle trap','I\'ve noticed there are quite a few puzzles being posted in forums and its obious this problem will come up from tiome to time, so why not put up a forum \"trap\" where there is a submit a puzzle forum which easily redirects the confused user to the submit your problem page',1072,'Alan','2003-03-23 14:45:16');
INSERT INTO forumpost VALUES (316,3,3,'Re: Suggestions','thanks',1637,'chris','2003-03-23 18:16:38');
INSERT INTO forumpost VALUES (317,59,5,'What is','What is queue weight? I was looking at my pending problems and saw this. What does it mean?',1637,'chris','2003-03-23 19:22:28');
INSERT INTO forumpost VALUES (318,55,3,'Re: Anything and everything','Yes, this forum is for \"DISCUSSING\" \"Anything and Everything\", \"But NOT for SUBMITTING PROBLEMS AND POSTING SOLUTIONS OF PROBLEMS\". \r
\n\r
\nThe site provides you facilities for doing that also. There is a \"Submit A Problem\" option just above the \"Search Box\" to submit your problems and an option \"Post A Comment\" under the text of every problem for posting your solutions or methods related to the corresponding problem(s).\r
\n\r
\n',979,'Ravi Raja','2003-03-23 19:56:07');
INSERT INTO forumpost VALUES (319,58,4,'Re: Forum puzzle trap','I do not think it is necessary Alan. The user, if without browsing the site properly goes on submitting anything anywhere then its his/her fault. If he can see this \"Forums\" link, then why not the \"Submit A Problem\" link which is just above the \"Search Box\" or just under the \"Your Information\" and \"Log Out\" options. If not that also, there\'s a chatterbox available (which of course is not a live one, but now there is a facility to see who\'s online and who\'s not) where he can leave his/her questions/queries regarding a particular topic (like where and how to post a problem and their solutions, etc.). There are many such things so I don\'t think its necessary to put up a forum \"trap\" as you call it. \r
\nIf anyone thinks I am wrong and it is required then please do point it out. Thank You.\r
\n',979,'Ravi Raja','2003-03-23 20:21:31');
INSERT INTO forumpost VALUES (320,59,5,'Re: What is','In order to move certain problems (especially those submitted by new members) through the waiting line (queue) faster, Levik has given the two oldest problems by each submitter a \"heavier\" \"queue weight.\"\r
\n\r
\nThe full details are explained in the Queue Ranking and QW threads in the \"Library\" forum',153,'TomM','2003-03-23 20:44:17');
INSERT INTO forumpost VALUES (321,56,7,'Re: Tim Axoy','*waves*',103,'friedlinguini','2003-03-24 01:15:06');
INSERT INTO forumpost VALUES (322,57,3,'Re: No,no,no','Tim. Actually, there\'s nothing I can do to stop you from positng puzzles in the forum.\r
\n\r
\nHowever, i fyou look at this post, I explain there why posting a puzzle there is not such a hot idea.\r
\n\r
\n(To sum it up, your puzzle doen\'t get as much exposure as it would otherwise, and there\'s no way for people to post comments that are not immediately visible by others, etc)\r
\n\r
\nThe reason why I ask that you do not post puzzles to the forums is not because I\'m mean, but because I think it would be a waste of a puzzle.',1,'levik','2003-03-24 01:46:34');
INSERT INTO forumpost VALUES (323,59,5,'Re: What is','Actually, since users Novices and Students don\'t have access to that forum, I should probably explain it here.\r
\n\r
\nAbout a month ago, we reailzed that the queue has grown to an unmanagable size (we had over 200 pending problems then). At that point prolems were voted on and approved on a first come first serve basis. (It was, in other words, a true queue.) We realized that this is pretty bad for new users: somebody submitting a problem would have to wait for over six months before they saw it posted. They would lose interest and never come back to the site.\r
\n\r
\nThe problem was, most of the pending puzzles were submitted by the same person, so in effect, the new users were being penalized because of his generocity. So we added a new feature called the queue weight (QW). This allows more users to have their problems voted on and pushed, because now the problems are sorted by QW in ascending order. (That is ALL problems with QW of 1 come before any problem with QW of 2.) QW of each problem is recalculated every night in the following manner:\r
\n\r
\nFor each person with submitted problems, their first three get a QW of 1, next three - 2, etc.(It\'s possible we will consider decreasing this number to two problems or even one, if we see a lot of same people occupying the queue.)',1,'levik','2003-03-24 01:56:36');
INSERT INTO forumpost VALUES (324,58,4,'Re: Forum puzzle trap','Alan, I don\'t think that there\'s \"QUITE A FEW\" puzzles being posted in the forums. In fact, I think there\'s just two, one of them was posted the week forums went live, and after I asked people to not post puzzles, nobody has done so until Tim Axoy the other day.\r
\n\r
\nSo I don\'t think it\'s a big problem now. (maybe in the future.) For now Tim canc ertainly re-submit his problem properly. And if he asks, I can even delete that forum post of his, though I beleive the damage is already done.',1,'levik','2003-03-24 02:00:48');
INSERT INTO forumpost VALUES (325,21,3,'I can do it','I can do anything and everything here.',1660,'Tim Axoy','2003-03-24 02:13:43');
INSERT INTO forumpost VALUES (326,60,5,'Levik','I think I know who owns this site:levik.\r
\n',1660,'Tim Axoy','2003-03-24 02:16:34');
INSERT INTO forumpost VALUES (327,56,7,'Re: Tim Axoy','* waves * from me too........hello Tim how old are you ? ',979,'Ravi Raja','2003-03-24 04:12:52');
INSERT INTO forumpost VALUES (328,59,5,'Re: What is','I see. So this way more people get to see their problems on the site faster.',1637,'chris','2003-03-24 05:57:44');
INSERT INTO forumpost VALUES (329,61,4,'Insta-posting Scholars','So I was thinking about removing the scholars\' privilege of pushing a problem they submit live to the server.\r
\n\r
\nWhen this was first conceived, there was no \"queue\": nobody could vote on anything, and the volume of submissions was so low that there was never a wait.\r
\n\r
\nThe only time this was used was when I went on vacation a couple of times (once again - there was no voting, so this was the only way to have new problems on the site)\r
\n\r
\nWith the voting in place, I believe this to no lonber be needed.',1,'levik','2003-03-24 06:13:53');
INSERT INTO forumpost VALUES (330,37,5,'Gautam and Gautam Joshi','Alan,I saw two dudes named Gautam and Gautam Joshi,just like Alan and Alan.',1660,'Tim Axoy','2003-03-24 07:26:36');
INSERT INTO forumpost VALUES (331,50,5,'I am a newbie','I am a newbie.\r
\nI just signed up 1+1/2 weeks ago.',1660,'Tim Axoy','2003-03-24 07:28:49');
INSERT INTO forumpost VALUES (332,57,3,'Everything in the universe','It is really not everything in the universe,but it says so.',1660,'Tim Axoy','2003-03-24 07:30:43');
INSERT INTO forumpost VALUES (333,62,6,'Primes','Why are there infinity primes,as in Primary Problem?\r
\n',1660,'Tim Axoy','2003-03-24 07:32:23');
INSERT INTO forumpost VALUES (334,21,3,'Re: Puzzles','What you can\'t do is get other people to read and/or discuss your puzzles after you submit them to the wrong place.',103,'friedlinguini','2003-03-24 09:04:42');
INSERT INTO forumpost VALUES (335,62,6,'Re: Primes','Did you read the solution?',103,'friedlinguini','2003-03-24 09:12:13');
INSERT INTO forumpost VALUES (336,61,4,'Re: Insta-posting Scholars','I don\'t think anybody has been doing it anyway, so there doesn\'t seem to be much reason to keep it around.',103,'friedlinguini','2003-03-24 09:13:26');
INSERT INTO forumpost VALUES (337,61,4,'Re: Insta-posting Scholars','Well why not keep it as a backup plan? lets say no problem in the queue has 3 tu your on vacation or something. Well a scholar cannot view the rest of the problems in the queue, so he may need to puch a problem live that he simply makes up or has pending but seeing as how he is a scholar he should therefore know what is appropriate or not. Of course if somebody abuses this privelege then he will either have this ability taken away or demoted back to journey men',1072,'Alan','2003-03-24 10:11:40');
INSERT INTO forumpost VALUES (338,61,4,'Re: Insta-posting Scholars','Which goes back to my question some time ago about stalemates in the queue....',103,'friedlinguini','2003-03-24 10:30:27');
INSERT INTO forumpost VALUES (339,21,3,'My puzzle','Why can I not put a puzzle in this forum?',1660,'Tim Axoy','2003-03-24 13:06:32');
INSERT INTO forumpost VALUES (340,62,6,'The largest prime p','Suppose there is a largest prime,p.\r
\nMultiplying all the numbers up to p,we get a super large number we will denote as P.\r
\nP+1 cannot be composite because it has no prime factors in common with P.\r
\nP+1 cannot be prime because p is the largest prime and there are no primes bigger than it.\r
\nThat is a contradiction,so there are infinity primes.\r
\n',1660,'Tim Axoy','2003-03-24 13:11:17');
INSERT INTO forumpost VALUES (341,63,3,'a/s/l anyone?','I was just wondering what everyone\'s a/s/l was so I would not call a he a she or a she a he by accident. I would also just like to know where eveyone is at and how old they are. I am 16/m/LA ',1637,'chris','2003-03-24 18:25:23');
INSERT INTO forumpost VALUES (342,63,3,'Re: a/s/l anyone?','A couple of weeks or so ago there was a lot of a/s/l exchanging going on in the chatterbox. Partly because chatterbox is not permanent, and for other reasons, levik added a box in our profiles to \"introduce\" ourselves. To view someone\'s profile, just click on their name. to view or update your own profile, click on the \"Your Information\" link just above the \"Submit a Problem\" link.\r
\n\r
\nBTW, just for the record: 50/m/NJ',153,'TomM','2003-03-24 22:14:55');
INSERT INTO forumpost VALUES (343,21,3,'Re: Puzzles','I didn\'t say you couldn\'t. It\'s just that you won\'t get much of an audience for it. The Submit a Puzzle link on the front page is a much better place.',103,'friedlinguini','2003-03-25 02:57:26');
INSERT INTO forumpost VALUES (344,20,3,'Asr,Bohob,and Criil','I like liars and knights problems.\r
\nThey are logic problems.\r
\nAsr,Bohob,and Criil\r
\nThree inhabitants of this land,Asr,Bohob,and Criil,are having a conversation together.\r
\nAsr:We are all liars.\r
\nBohob:One and no more than one of us is a knight.\r
\nWhat are each?\r
\nAnswer to Asr,Bohob,and Criil\r
\nAsr cannot be a knight because if he was,then they would be all liars,including Asr,but Asr is a knight by supposition.\r
\nTherefore,Asr is a liar,so there really is at least one knight among the three.\r
\nWe will call it the good knight.\r
\nIf Bohob is a liar,then Criil has to be the good knight,so there is one and no more than one knight among them,so Bohob is a liar telling the truth.\r
\nTherefore,Bohob is a knight,so there is only one knight,which must be Bohob,among them,so Criil is a liar,and Bohob is the good knight.\r
\nAsr is a liar,Bohob is a knight,and Criil is a liar.\r
\n\r
\n',1660,'Tim Axoy','2003-03-25 02:57:57');
INSERT INTO forumpost VALUES (345,64,7,'Twin chat','Tim:Tim,what do you like?\r
\nTim:Logic and math.\r
\nTim:Do you like puzzles?\r
\nTim:Yes.',1660,'Tim Axoy','2003-03-25 02:59:16');
INSERT INTO forumpost VALUES (346,20,3,'Re: LOGIC problems?','Relativity is questionable modern theory? Its application might be, but that\'s true of any sort of science. Heck, plenty of the riddles that get submitted are on an awfully shaky application of principles.',103,'friedlinguini','2003-03-25 03:02:55');
INSERT INTO forumpost VALUES (347,38,7,'Re: New forum','Hiya, I was bored one day so I typed brainteasers into yahoo. Love this site, but i\'m supposed to be working!',1732,'Helen','2003-03-25 03:28:22');
INSERT INTO forumpost VALUES (348,38,7,'Re: New forum','Hi, Helen.\r
\n\r
\nJudging by the traffic patterns of this site (most people come during business hours), a lot of us are supposed to be working ;)\r
\n\r
\nAnd I\'m sure a lot are - a little 5 minute brain-break has never hurt anyone.',1,'levik','2003-03-25 05:02:58');
INSERT INTO forumpost VALUES (349,20,3,'Re: LOGIC problems?','Tim, why are you still posting problems in the forums? \r
\n\r
\nIt\'s not interesting at all when you post a problem and the answer is immediately visible. It\'s really a waste of a good problem.\r
\n\r
\nI think this site is made great because it encourages people to solve these puzzles. This is done best by submitting them through the normal process - by clicking the submission link.\r
\n\r
\nI will really appreciate it if you do not post problems in the forums anymore.',1,'levik','2003-03-25 07:34:07');
INSERT INTO forumpost VALUES (350,20,3,'Re: LOGIC problems?','levik it will be better if you delete all such posts and comments of Tim from the forums. I mean the problems which he has been submitting here. Otherwise everyone will see the problem as well as the solution and when its on the site there will be at most 5 comments to that problem or may be none. And if still Tim does not understand what he is asked to do then let things happen as they are. he will be the one to suffer and may be then he will realize his mistake. ',979,'Ravi Raja','2003-03-25 07:53:33');
INSERT INTO forumpost VALUES (351,63,3,'Re: a/s/l anyone?','I´m 16/m/Finland',575,'not_so_einstein','2003-03-25 09:48:14');
INSERT INTO forumpost VALUES (352,63,3,'a/s/l mystery','What is a/s/l?\r
\n',1660,'Tim Axoy','2003-03-25 11:32:18');
INSERT INTO forumpost VALUES (353,61,4,'Re: Insta-posting Scholars','I think with the active size of the queue at 10 problems, a fully stalemated queue is highly unlikely.\r
\n\r
\nA problem that remains in the queue for a long enough period will eventually be thumbed down and deleted to free up slots (there\'s currently enough active vote-enabled users to overrule a vocal minority of 1-2.)',1,'levik','2003-03-25 13:10:14');
INSERT INTO forumpost VALUES (354,63,3,'Re: a/s/l anyone?','a/s/l stands for age/sex/location .Like how old are you, are you a dude or a girl, and where you are from.',1637,'chris','2003-03-25 14:20:40');
INSERT INTO forumpost VALUES (355,38,7,'Re: New forum','Hey levik!\r
\nCongratulations!\r
\nIt\'s a great site!!\r
\nThis week I\'m on hollidays, so I\'ve been visiting the page quite a lot! I\'m sort of new here, and I wish to be promoted soon... By the way, can I write comments on problems that are already solved?? And approximately how long does it take for a problem to be posed, after I submit it?\r
\nI found the page with google, I think...',1767,'Fernando','2003-03-25 16:38:48');
INSERT INTO forumpost VALUES (356,38,7,'Re: New forum','Fernando - welcome to the site (congratulations on being promoted - you\'re now a student)\r
\n\r
\nYou can post comments to any problem you wish, they\'re never \"closed\".\r
\n\r
\nAs far as the time it takes to see a submited a problem go live, unfortunately I would say it\'s around a month right now possibly even more. So bear with us.',1,'levik','2003-03-26 01:43:29');
INSERT INTO forumpost VALUES (357,65,5,'!','In the other forums,! denotes a new thread.\r
\nIn this forum,it does not.\r
\nLevik,I think you need to put ! by the new threads in Commons.',1660,'Tim Axoy','2003-03-26 01:56:58');
INSERT INTO forumpost VALUES (358,66,3,'Hey,dudes','Hey,dudes.\r
\nI want to chat with someone on this forum.\r
\n',1660,'Tim Axoy','2003-03-26 02:00:12');
INSERT INTO forumpost VALUES (359,66,3,'Re: Hey,dudes','You can chat with everyone but the problem is that everyone may not be online at the same time when you are. So you can post what you want to say and then the person concerned will reply. But it will be better if you use the CHATTERBOX instead of using the forum for chatting.',979,'Ravi Raja','2003-03-26 03:33:41');
INSERT INTO forumpost VALUES (360,63,3,'Re: a/s/l anyone?','29/y/Arizona',103,'friedlinguini','2003-03-26 03:36:24');
INSERT INTO forumpost VALUES (361,65,5,'Re: !','I like the heading: \"! !\"',103,'friedlinguini','2003-03-26 03:37:18');
INSERT INTO forumpost VALUES (362,65,5,'Re: !','The exclamation (!) denotes all threads with posts within the last 24 hours. It works in all forums.',1,'levik','2003-03-26 04:14:12');
INSERT INTO forumpost VALUES (363,63,3,'Re: a/s/l anyone?','14/m/canada',1072,'Alan','2003-03-26 10:40:13');
INSERT INTO forumpost VALUES (364,67,4,'QW change?','hey was the qw equation changed to be problems 1-2 qw=1 3-4 qw=2? It seems this way because ravi has only 1 prob in the queue and noone has 3 questions',1072,'Alan','2003-03-26 10:47:05');
INSERT INTO forumpost VALUES (365,67,4,'Re: QW change?','No it was not changed. Ravi has 1 right now because one was pushed this morning and one got deleted.\r
\n\r
\nAs far as nobody having 3, it\'s possible - they are sorted by date as well.',1,'levik','2003-03-26 11:15:56');
INSERT INTO forumpost VALUES (366,68,4,'New colour?','When i fist visited flooble i loved it alot and tried to look at every puzzle, but obne thing seemed to have make it boring, that would be the white-blue and grey-blue background colours of floobe. Now of course i\'ve gotten usede to it bit if flooble were to be given a new type of background what colour do ut hink could look better? i\'d say a toned lime/grass green on the current background. definetely not anything neon.
don\'t take this the wrong way i\'m not saying the backgrounds needs a change but why not experiment around?',1072,'Alan','2003-03-26 13:19:00');
INSERT INTO forumpost VALUES (367,56,7,'HI.','Hi everybody.',1709,'silvis','2003-03-26 13:53:41');
INSERT INTO forumpost VALUES (368,38,7,'Re: New forum','It\'s a great site Levik.\r
\nCongrats!!!\r
\nI have a question though...\r
\nAre there always 10 problems on the queue line, or sets of 10 that go down???',1709,'silvis','2003-03-26 13:57:01');
INSERT INTO forumpost VALUES (369,63,3,'Re: a/s/l anyone?','58/m/NJ',1301,'Charlie','2003-03-26 14:11:15');
INSERT INTO forumpost VALUES (370,68,4,'Re: New colour?','I\'d prefer a cheery yellow to a sickly green.\r
\n\r
\n',1301,'Charlie','2003-03-26 14:14:20');
INSERT INTO forumpost VALUES (371,38,7,'Re: New forum','I have another question, levik...\r
\nI sent 2 problems already, but I didn\'t send the solution... When should I actually write down the solution?? After some have posted some somments, or when the problem goes live, or now???',1767,'Fernando','2003-03-26 14:23:24');
INSERT INTO forumpost VALUES (372,38,7,'Re: New forum','You can pretty much do it whenever you although to keep the site running smoothly it is usually best that you add on the solution when it makes it to the queue(or when it recieves it\'s first comment. The only reason for this is if people are in doubt of solution to that problem they can see that one has been made(not actually see it) and get your problem posted faster',1072,'Alan','2003-03-26 14:34:16');
INSERT INTO forumpost VALUES (373,63,3,'Re: a/s/l anyone?','hey fried, what does 29/y/Arizona mean ? I understand 29/m/Arizona and 29/f/Arizona but not 29/y/Arizona. ',979,'Ravi Raja','2003-03-26 20:12:01');
INSERT INTO forumpost VALUES (374,56,7,'Re: Tim Axoy','hie silvis',979,'Ravi Raja','2003-03-26 20:37:39');
INSERT INTO forumpost VALUES (375,68,4,'Re: New colour?','Wouldn\'t it be better if there\'s an option in every user\'s page with different colors for the background. So that if Alan prefers his page\'s background color to be like what he said \"a toned lime/grass green \", he would select that color and simply change the color of his page\'s background and at the same time Charlie can change the color of his page\'s background to \" a cherry yellow to a sticky green\" color as he prefers it to be.\r
\n\r
\nOf course there can be \"MANY \" such combinations of colors and it is not possible to have all of them but why not keep options for the simple ones like \"Red, Pink, Blue, Green, Yellow, Orange, White, Purple, Brown, Black,......etc\". I hope you understand what I am trying to say. \r
\n\r
\nThe concept is just like changing the backgroung colour( appearance) of your personal INBOX in Yahoo or Sify and all such. (Only those will know who have ever tried this).\r
\n\r
\nIf you like my suggestion then please reply and post a comment saying what you feel about this idea of mine. \r
\n\r
\n\r
\nThank You.',979,'Ravi Raja','2003-03-26 20:53:08');
INSERT INTO forumpost VALUES (376,38,7,'Re: New forum','Thanks Alan!',1767,'Fernando','2003-03-27 01:05:34');
INSERT INTO forumpost VALUES (377,63,3,'Re: a/s/l anyone?','It means I have a sick sense of humor.',103,'friedlinguini','2003-03-27 02:42:34');
INSERT INTO forumpost VALUES (378,69,5,'New postings','The number of new forum postings (i.e., in the last 24 hours) isn\'t a very helpful statistic unless a user notices the number going up. The problem is that posts silently fall out of the window and push the number down. If I stop by the site and see that there are 18 new forum posts, and then visit again two hours later and see that there are still 18 new forum posts, I don\'t know if there\'s anything I haven\'t read. An ideal statistic would be something like \"Unread posts.\" If that\'s not feasible, then a timestamp for the most recent post might be.\r
\n\r
\nThis also applies to problem comments, though I don\'t read all of those...',103,'friedlinguini','2003-03-27 04:05:18');
INSERT INTO forumpost VALUES (379,63,3,'Re: a/s/l anyone?','I am guessing that the Y means yes. Right?',1637,'chris','2003-03-27 07:19:32');
INSERT INTO forumpost VALUES (380,69,5,'Re: New postings','Actually, I was thinking of having a \"digest\" mode for new forum posts (the same as for problems). You would click it to see the latest posts over a period of X days.\r
\n\r
\nIs anyone finding the problems difest page useful by the way?',1,'levik','2003-03-27 07:42:41');
INSERT INTO forumpost VALUES (381,63,3,'Re: a/s/l anyone?','I think it\'s pretty safe to assume that \"y\" in the center of an \"a/s/l\" tuple is equivalent to an \"m\".',1,'levik','2003-03-27 07:43:58');
INSERT INTO forumpost VALUES (382,68,4,'Re: New colour?','Hmmm... I mean I\'m all for choice and everything... but this doesn\'t seem like a worthwhile endeavor to me. The thing is, most colors can probably be changed rather easily by adjusting the stylesheet, but the images (what few there are) on this site are made with the default \"blue\" background in mind.\r
\n\r
\nAlso, this blue/grey color scheme is flooble, and I\'m not sure I want to change it - it\'s kind of a branding thing by now. \r
\n\r
\nHonestly I would rather focus on adding new features and or making the default design more pleasant than allowing everyone to pick their colors.',1,'levik','2003-03-27 07:48:24');
INSERT INTO forumpost VALUES (383,70,5,'Small update','There have been some questions recently about how long problems take to get pushed through. While this is not an exact process by any means, I made a small update to the site that allows people to track their problems\' progress...\r
\n\r
\nWhen you go to \"My Problems\", end click edit on any of the problems you have, if that problem is not yet live, you will see it\'s approximate queue position. These get recalculated nightly, so they\'re not realtime. Also, if your problem is in position 20, this does not mean that it will be the 20th problem to get posted from this point: Due to the QW rules, it is possible for problems to \"cut in line\".\r
\n\r
\nHowever, once you see a problem reach position 10 or less, this problem is probably visible to the voting members of the site, and should start receiving votes and feedback soon.',1,'levik','2003-03-27 08:36:30');
INSERT INTO forumpost VALUES (384,56,7,'Re: Tim Axoy','Now the Important question is, Do you enjoy Cornbread?',NULL,'Aspiring Novice','2003-03-27 16:12:24');
INSERT INTO forumpost VALUES (385,56,7,'Re: Tim Axoy','that was me O.o',NULL,'Lucifer','2003-03-27 16:12:40');
INSERT INTO forumpost VALUES (386,63,3,'Re: a/s/l anyone?','Yeah, I don\'t believe any F would put Y. Unles...',1637,'chris','2003-03-27 17:54:40');
INSERT INTO forumpost VALUES (387,63,3,'Re: a/s/l anyone?','See, there\'s the rub. I\'d rather not have my gender affect how I\'m treated in a conversation by way of people\'s prejudices. Besides, what gender someone claims to be online is rarely more than a suggestion.',103,'friedlinguini','2003-03-28 01:51:21');
INSERT INTO forumpost VALUES (388,71,3,'Hey!','Hi,guys!',1660,'Tim Axoy','2003-03-28 06:18:20');
INSERT INTO forumpost VALUES (389,56,7,'Re: Tim Axoy','No I enjoy \"Pi\" (Pie), because \"Pi are squared\". lol. :) :)',979,'Ravi Raja','2003-03-28 06:32:16');
INSERT INTO forumpost VALUES (390,14,6,'Re: Any difference','It\'s OK to assume things which you know HAVE BEEN PROVEN before, like in a book, in a class, or something you\'ve proved yourself...',1767,'Fernando','2003-03-28 08:35:51');
INSERT INTO forumpost VALUES (391,17,6,'Re: HTML codes for use on the site','I have seen that some problems have their own images (for example: \"9 dots\" in shapes by Gautam)... I recently submitted a problem that requires an image... I tried to use the <img src> command, but didn\'t work... so then I worte something like: \"Note: image needed located at .......\"\r
\nCan anybody help me out, please?',1767,'Fernando','2003-03-28 08:55:59');
INSERT INTO forumpost VALUES (392,72,5,'User levels...','I was wondering if it was possible to make a page that shows who are the Scholars/Journeymen, and pehaps also Apprentices...',1767,'Fernando','2003-03-28 09:45:17');
INSERT INTO forumpost VALUES (393,63,3,'Re: a/s/l anyone?','Hey everyone!\r
\n18/m/Venezuela (South America)',1767,'Fernando','2003-03-28 11:48:21');
INSERT INTO forumpost VALUES (394,66,3,'OK','OK.',1660,'Tim Axoy','2003-03-28 13:04:44');
INSERT INTO forumpost VALUES (395,17,6,'Re: HTML codes for use on the site','If you need to include an image, the best way is to submit the problem with a note at the end to remind levik to include the image. \r
\nThen e-mail him a copy of the image and a note telling him which problem the image belongs to. \r
\n\r
\nIn the case you described where you have already put the image up separately on the web, your email could just confirm that.\r
\n\r
\nIn either case, when the problem comes up for voting, include a new note reminding levik about the need to include the image.',153,'TomM','2003-03-28 13:07:42');
INSERT INTO forumpost VALUES (396,17,6,'Re: HTML codes for use on the site','Thanks a lot, Tom!',1767,'Fernando','2003-03-28 19:19:07');
INSERT INTO forumpost VALUES (397,72,5,'Re: User levels...','Exactly Fernando. Even I was thinking about that. You click on Apprentice or Journeymen or Scholar and the list of the corresponding users is there in front of you. Is that what you are trying to say ? If not make a different page then just similar such links will do (just like \"Your Information\", \"Forums\", \"Most Commented On\", etc.).',979,'Ravi Raja','2003-03-28 19:31:32');
INSERT INTO forumpost VALUES (398,72,5,'Re: User levels...','yes, Ravi, that\'s what I meant!!!',1767,'Fernando','2003-03-29 04:46:29');
INSERT INTO forumpost VALUES (399,17,6,'Re: HTML codes for use on the site','I generally process all images that go into problems to give them that \"flooble border\". Also, I like them hosted on the site itself - that\'s just more reliable.',1,'levik','2003-03-29 05:28:16');
INSERT INTO forumpost VALUES (400,73,7,'hello!','hi everyone... im new here.. just getting used to it.. =) haha.. ',1819,'karla','2003-03-30 01:51:36');
INSERT INTO forumpost VALUES (401,73,7,'Re: hello!','Welcome to the site, Karla. I hope you enjoy your stay :)',1,'levik','2003-03-30 03:20:29');
INSERT INTO forumpost VALUES (402,55,3,'Discussing problems','It is for DISCUSSING PROBLEMS probably.',1822,'Tim Axoy','2003-03-30 07:02:47');
INSERT INTO forumpost VALUES (403,21,3,'A is a liar and B is a knight','Ravi,why do you say my puzzle is impossible?\r
\nThe answer is that A is a liar and B is a knight.',1822,'Tim Axoy','2003-03-30 07:58:54');
INSERT INTO forumpost VALUES (404,65,5,'Test','OK,Lev,here is a test.',1822,'Tim Axoy','2003-03-30 11:34:04');
INSERT INTO forumpost VALUES (405,69,5,'Journeyman','I wish I am a Journeyman.',1822,'Tim Axoy','2003-03-30 11:35:25');
INSERT INTO forumpost VALUES (406,73,7,'New','Hi,Karla!',1822,'Tim Axoy','2003-03-30 11:36:49');
INSERT INTO forumpost VALUES (407,74,4,'New for you page','I remember reading a post where levik talked about a new for you page and i think it would be quite helpful,(since i\'m a common user of flooble) i was just gone for a 2 day vacation and i get a feeling i missed out on some of the posts in the forum, of course for some this new for u page could be a bother so i think it should be togglable (yes i know this word doesn\'t exist, but on a site of this caliber i think the average person would figure out the combination of a root word and a suffix)',1072,'Alan','2003-03-30 15:33:08');
INSERT INTO forumpost VALUES (408,73,7,'I like math and logic','I like math and logic.\r
\nWhat do you like?',1822,'Tim Axoy','2003-03-31 02:30:20');
INSERT INTO forumpost VALUES (409,21,3,'Guessme 1-9','Ravi Raja,I saw your problems Guessme 1-9.\r
\nCan you make a tenth one?',1822,'Tim Axoy','2003-03-31 02:42:15');
INSERT INTO forumpost VALUES (410,21,3,'I saw it','I saw that,too,Tim.',1822,'8466849','2003-03-31 02:55:30');
INSERT INTO forumpost VALUES (411,21,3,'Re: Puzzles','If A is a liar then when he says that both himself and B is a liar then he is speaking the truth (unless you consider the two together), or else if seen individually, we see that A though being a Liar, is speaking the truth. \r
\n\r
\nAnd yes I\'ll surely make the tenth one. :)',979,'Ravi Raja','2003-03-31 02:57:23');
INSERT INTO forumpost VALUES (412,75,6,'Director','Lev,I saw you were the only one ranked Director.\r
\nCan I be one,too,Lev?',1822,'Gladys','2003-03-31 03:06:42');
INSERT INTO forumpost VALUES (413,75,6,'Re: Director','Although i\'m not levik i\'m pretty sure i can answer this question. No, well at least probably not. Administartor is the highsest rank on the site and when you have the rank of administrator you must learn all the tools (which levik would have to teach to you, which is time consuming) On top of that you would need to know a lot about scripting and code.',1072,'Alan','2003-03-31 10:06:16');
INSERT INTO forumpost VALUES (414,21,3,'Re: Puzzles','Tim you had asked me the question where A says, \"At least one of A and B is a Liar\".\r
\n\r
\nThis is possible for three cases:\r
\n(1) A: Knight, B: Knight\r
\n(2) A: Liar, B: Liar\r
\n(3) A: Knight, B: Liar\r
\n\r
\nIsn\'t this correct Tim ?',979,'Ravi Raja','2003-03-31 23:06:46');
INSERT INTO forumpost VALUES (415,73,7,'Re: hello!','Even I like Math and Logic :)',979,'Ravi Raja','2003-03-31 23:22:35');
INSERT INTO forumpost VALUES (416,21,3,'A is a knight and B is a liar','Actually,(3) is the one and only way it can be possible.\r
\nIt is only possible if A is a knight and B is a liar.\r
\nIf A is a liar,then there would be at least one liar,and A,being a liar,would not have told the truth.\r
\nTherefore,A is a knight,so there really is at least one liar,but A is not a liar,so the liar is B.',1822,'Tim Axoy','2003-04-01 02:39:01');
INSERT INTO forumpost VALUES (417,73,7,'Re: hello!','I wouldn\'t mind seeing the site have some more paradoxes. if you think of one submit it.',1072,'Alan','2003-04-01 04:05:08');
INSERT INTO forumpost VALUES (418,74,4,'Re: New for you page','I was thinking of doing something along these lines for a while now. The problem though is that marking off each item you\'ve \"seen\" (i.e. forum post, problem, comment, solution) is prohibitively complex right now (as of today - about 5,000 such \"items\" times almost 2,000 users, and growing).\r
\n\r
\nThe only other thing it could be keyed off of is the last visit date. But there\'s no guarantee that you\'ve read everything on your last visit, so there will still be some slippage. \r
\n\r
\nI guess a good \"hack\" to this would be to allow you to pick the number of days to go back, and just default it to when you last visited.',1,'levik','2003-04-01 04:20:41');
INSERT INTO forumpost VALUES (419,76,4,'Tim Axoy','Perhaps I\'m overreacting, but I think this guy is really annoying. (In all his incarnations - he has at least 3 accounts I think, and has changed names repeatedly on at least one of them, just to post silly off topic things everywhere.)\r
\n\r
\nI know he\'s only 9, but I think his junk comments are making the site less usable, like spam does to email.\r
\n\r
\nWhat (if anything) do you think should be done? I guess if others don\'t find him to be as annoying as I do, I will just sit back and shut up.',1,'levik','2003-04-01 04:25:48');
INSERT INTO forumpost VALUES (420,76,4,'Re: Tim Axoy','I find him annoying. Perhaps the other hijinks can be glossed over but he deliberately gives answers in the subject line. (well, I\'ve seen at least one, anyway)',1301,'Charlie','2003-04-01 05:08:49');
INSERT INTO forumpost VALUES (421,76,4,'Re: Tim Axoy','well Levik, you\'re the Director, i.e. site GOD! You can do whatever you want about him.\r
\n\r
\nOn a related note, there are always people that a given person won\'t mesh with, but that doesn\'t mean that other will feel the same way. I\'d like to say that I have no opionion in this case (I actually only pay attention to the posters name if it is one of a very select few - yourself, TomM, F.L. and maybe 2 or 3 more, as I\'ve kinda gotten a fell for your (net) personalities) otherwise I consider it simply a random comment, so maybe others haven\'t noticed. Also, the rest of us wouldn\'t have the resources to know that these 3 accounts are all his, or that he has been name changing. If, for example, his three accounts are all moderately annoying, his net effect on the site is completely annoying. I\'ve no way of linking them, and this just expands the reasons why I tend to overlook the posters ID.\r
\n\r
\nThis doesn\'t mean that you shouldn\'t take action (whatever that may be), but I guess my point is that you need to consider that. (Which is of course the entire point of your post, so effectually I\'m just taking up text space. Now that I\'ve determined that, I\'m just taking up even MORE!. It\'s a vicious cycle...)\r
\n\r
\nIn the end, I don\'t think that you should be asking us about this kind of thing, despite the fact that you want to get our opinions etc., in order to keep this site as much as possible what we want it. Imagine that he has another account that you\'re not aware of, and happens to have access to this board - don\'t you think this would be a little upsetting to him, hearing that we\'re all ganging up on him or whatever the outcome is. Or that he does stay around long enough to get to this post, only to find that early on there was such opposition (again - or whatever. I don\'t know how the others are reacting/feeling/etc.) It boils down to being one of the unpleasant duties of the domain master to make these decisions.\r
\n\r
\nOver and Out',775,'Cory Taylor','2003-04-01 05:10:27');
INSERT INTO forumpost VALUES (422,21,3,'Re: Puzzles','hey 8466849, whats your number?\r
\nhehe\r
\n',775,'Cory Taylor','2003-04-01 05:14:26');
INSERT INTO forumpost VALUES (423,49,4,'Re: Solved Unsolved Puzzle','Another \"unsolved\" puzzle you might want to look at again is Minimum Value, where it seems friedlinguini\'s first post, Evil!, has been verified, by vohonam, and by the Excel solver function.',1301,'Charlie','2003-04-01 05:14:54');
INSERT INTO forumpost VALUES (424,77,4,'Congratulations to me','Yah - I made it to journeyman, so now you are all doomed to see my ramblings on even more areas of the site!!',775,'Cory Taylor','2003-04-01 05:16:42');
INSERT INTO forumpost VALUES (425,77,4,'Re: Congratulations to me','Congratulations indeed. Unfortunately with this long queue, it takes longer than it should for some people to reach this level.\r
\n\r
\nI actually wanted to manually promote you last week, but saw that you only had one problem to go and that it was coming up, so I figured it would be better if you got there on your own steam :)\r
\n\r
\nNow go VOTE! :)',1,'levik','2003-04-01 05:25:17');
INSERT INTO forumpost VALUES (426,49,4,'Re: Solved Unsolved Puzzle','Hey, thanks for bringing that to my attention. I put the solution in.\r
\n\r
\nLet me know if you find anymore :) (there\'s nothing I hate more than having the number of unsolved problems be higher than it needs to be)',1,'levik','2003-04-01 05:29:13');
INSERT INTO forumpost VALUES (427,76,4,'Re: Tim Axoy','Cory - You are right. Ultimately, the decision will have to be mine. I\'m just trying to gague the level of impact Tim is having on the site. For example, if because of comments like his you find yourself \"ignoring\" everyone but 5-10 users on this site, I believe this to be tremendously damaging.\r
\n\r
\nI want this site to be a place where every comment is worth reading, and every question is worth answering. While that is a utopian goal, there are some steps that could be taken to get ourselves closer to it.\r
\n\r
\nI have been considering requiring a unique email verification to sign up for an account on the site. Just to make things a little more difficult for people who don\'t really want to be here. On the other hand, I kind of dislike it when sites do that to me... But I\'m beginning to see their point.',1,'levik','2003-04-01 05:35:21');
INSERT INTO forumpost VALUES (428,76,4,'Re: Tim Axoy','There are laws about collecting personally identifiable information from kids. you might want to bear those in mind. Moreover, unique e-mails are a dime a dozen as long as Hotmail is around.\r
\n\r
\nAs far as what to do about Tim Axoy, I just tend to disregard what he says. Other people may be more bothered. Whenever you build an online community, there are always going to be some bad apples.\r
\n\r
\nOne possibility might be to give users an Ignore list (editable, and masks comments rather than completely hiding them so that people can look at individual comments from Ignored users on a case-by-case basis).\r
\n\r
\nA more drastic (though often necessary) solution is to make sure you have the ability to modify or delete posts.',103,'friedlinguini','2003-04-01 09:09:44');
INSERT INTO forumpost VALUES (429,76,4,'Re: Tim Axoy','Just to clarify how i run through the site, I don\'t ignore posts from people who haven\'t met some readability status, I simply don\'t associate the posters name with what I\'m reading. This allows me to see all the comments, while placing possibly heavier emphasis on those which I deem likely to be {correct, valid, meaningful or whatever}, while if I do see a comment that tweaks my brain by another user, they get filed (within my expanding brain) into another category of posters who may arrive on my \"A\" list soon. As usual, I\'m having trouble concretely explaining how my brain works here, but hopefully you get the gist of it - I\'m not missing any comments, but a user like Tim Axoy doesn\'t stick out in my head, as his comments are quite happily lumped in with 50% of the other users.',775,'Cory Taylor','2003-04-01 09:43:21');
INSERT INTO forumpost VALUES (430,49,4,'Re: Solved Unsolved Puzzle','I recall once upon a time you mentioning that you were planning on adding some sort of attahment device for solutions. If you have this set up, let me know and I\'ll finish off the 0-150 in 2003 puzzle that I simply didn\'t want to rewrite or retype lots of messy functions. I currently have about 3/4 of them stored in an excel file around here somewhere...',775,'Cory Taylor','2003-04-01 09:53:22');
INSERT INTO forumpost VALUES (431,49,4,'Re: Solved Unsolved Puzzle','If you ever finish this, do email it to me... While no such device currently exists, I will be happy to upload the file to the server and simply link to it manually.',1,'levik','2003-04-01 11:02:40');
INSERT INTO forumpost VALUES (432,76,4,'Re: Tim Axoy','Well yes i do find tim axoy quite annoying but when i found out he was 9 it was quite a shock. I think the e-mail verification is a great idea, because i would sign up for an account and have msn open (which gives you automatic e-mail notice) then boom. Well levik as said before you are \"god\"(well ok site god) but what i would suggest is that e-mail tim axoy and tell himthat you are deleting two fo his accounts and that any pending problems from his old accoutn will be moved to his new account and give him his \"1-warning\" to stop doing things like posting random weird comments in the forum and in the chatterbox.Now of course i don\'t know if he has e-mail if not, then perhaps a comment in the forum? well anyways Tim Axoy said himself he likes math and logic and anyone who enjoys math and logic (as opposed to riddles, word problems. no offence to people who like these types of problems) he might be pretty smart so with a good warning he might shape up. Of course levik if this is a lot of work then you have the final say
\nI\'m Manoj Nair, an engineer, doing M.Tech. in IIT. I came to know abt this site through GOOGLE....I would like to be a part of the site...and I love puzzles....',1854,'Manoj Nair','2003-04-03 03:08:23');
INSERT INTO forumpost VALUES (439,78,7,'Re: Hello all','*waves* Pull up a rock and give levik a poke in the head. Welcome to the site. What are M.Tech. and IIT?',103,'friedlinguini','2003-04-03 03:20:58');
INSERT INTO forumpost VALUES (440,78,7,'Re: Hello all','fried \'IIT\' is the abbreviation for \'Indian Institute Of Technology\'.\r
\nWelcome to the site Manoj. You are doing M.Tech. and I am doing B.Sc. (Mathematics) and planning to do M.Sc. (from IIT Kgp.), depending on whether I get through the admission test or not. :) ',979,'Ravi Raja','2003-04-03 03:31:34');
INSERT INTO forumpost VALUES (441,78,7,'Re: Hello all','Welcome, welcome. Always nice to see a fresh \"face\" - I hope you enjoy your stay.\r
\n\r
\nBe sure to holler if you have questions.',1,'levik','2003-04-03 05:30:08');
INSERT INTO forumpost VALUES (442,79,5,'Time Zone','Why are the times of posting listed as 6 hours earlier than Eastern? That\'s a time zone out in the Pacific somewhere. I could understand 5 hours later than EST, as GMT, but this goes the other way, and too far to be in the U.S.',1301,'Charlie','2003-04-03 09:56:46');
INSERT INTO forumpost VALUES (443,77,4,'Re: Congratulations to me','Alan, how can you forget \'Charlie\' ? ',979,'Ravi Raja','2003-04-04 00:05:11');
INSERT INTO forumpost VALUES (444,79,5,'Re: Time Zone','I have SOOOOO been wondering this. I thought maybe the site was set in Hawaii, but then I found out that Mr Director is from the East Coast, so I just gave up trying to explainify it.',775,'Cory Taylor','2003-04-04 04:18:49');
INSERT INTO forumpost VALUES (445,80,7,'Hello, First time here','I am a student (a 44 year old) and I am taking a critical thinking class now. I was looking at different sites on the web and came across this one. I look forward to solving (or try solving) the problems in this site. Hello and I look forward to exchanging ideas or questions with any who wish to chat.',1866,'kenny','2003-04-04 05:44:44');
INSERT INTO forumpost VALUES (446,80,7,'Re: Hello, First time here','Welcome to the site, kenny. Send your classmates over, too. :-)>',103,'friedlinguini','2003-04-04 06:41:14');
INSERT INTO forumpost VALUES (447,77,4,'Re: Congratulations to me','o thought charlie was a scholar? well if not then he should be on that list to.',1072,'Alan','2003-04-04 09:50:20');
INSERT INTO forumpost VALUES (448,81,4,'New category','Well, here i am with yet another idea for flooble and igaurantee you its better than the \"forum puzzle trap\". Anyways I was thinking of a new category, I\'m not to sure what it would be called but it would be along the lines of \"subliminal messages\" or \"encryption\". There are actually quite a bit of problems on the site that can be refitted into this category. Of what i briefly checked in general and riddles i\'ve noticed that the following problems would be able to fit into this new category. The flooble code, word rebus, talking gibberish, greetings and possibly girlfriends name. There\'s also a problem in the queue that is pure encryption and it wouldn\'t really fit in any of the site\'s category\'s. On top of that since flooble is growing and we are \"running out\" of the classic problems everyone\'s heard then i think this category would prevent future problems of having problems either \"unorganized\" or \"having to create and find all the problems that fit into this category. If this were to be created then simply everytime someone comes across a puzzle like this on the site they could simply post it in the forums(but there wouldn\'t be that many) sorry about the run-on sentences. thought\'s anyone?',1072,'Alan','2003-04-04 10:13:36');
INSERT INTO forumpost VALUES (449,79,5,'Re: Time Zone','Actually there is a simple and meaningless explanation.\r
\n\r
\nThe server clock is wrong. It\'s been wrong for the last two years, and remains wrong now.\r
\n\r
\nThe reason that I don\'t simply change it, is because a lot of things are scheduled with the assumption that it\'s wrong, and thus may happen at wrong times if the clock were to be set straight. While I could just fix everything all at once (and should probably), I am currently just way too lazy :)',1,'levik','2003-04-04 10:53:20');
INSERT INTO forumpost VALUES (450,81,4,'Re: New category','I\'d love to hear people\'s thoughts on this. Personally I think that the problems you are mentioning are OK where they are right now, but I am not against a new category if it really is warranted.',1,'levik','2003-04-04 10:55:18');
INSERT INTO forumpost VALUES (451,77,4,'Re: Congratulations to me','....and what about Fried ?',979,'Ravi Raja','2003-04-04 22:53:21');
INSERT INTO forumpost VALUES (452,81,4,'Re: New category','You can give the name \"Miscellaneous Problems\" (which do not fall under any of the mentioned categories) to the new category or may be some other better name that others can suggest where such problems can be posted which do not fall under any of the categories mentioned.',979,'Ravi Raja','2003-04-04 22:59:29');
INSERT INTO forumpost VALUES (453,81,4,'Re: New category','Better name: what do you think about the name: \" MIXED BAG \" ?',979,'Ravi Raja','2003-04-04 23:00:39');
INSERT INTO forumpost VALUES (454,81,4,'Re: New category','Also problems like \"Two men and the mountains\" posted by Jennifer and \"Death Came\" posted by Anoop, etc. are supposed to be put under a different category (which is usually given the name \"Lateral Thinking Puzzles\") and not under the category \"Riddles\". But now its too late and the problems have been submitted under those categories and possibly levik can create the new category and shift such problems there.\r
\n\r
\nI do not know what others have to say regarding this but I just suggested what I felt was correct and now anybody who have to say anything else (I mean if anybody has any better suggestions), then please do post it. \r
\n\r
\n(I have suggested a name for the new category in which problems like word rebus, talking gibberish, greetings, girlfriend\'s name, etc. and similar problems like what Alan has suggested can be posted). \r
\n\r
\nThat was all from my part. Thank You.',979,'Ravi Raja','2003-04-04 23:10:19');
INSERT INTO forumpost VALUES (455,81,4,'Re: New category','Ravi if u looked at all the problems i talked about you\'d notice they all have the same type of style to them. Encryption. This is what i meant by a new category i didn\'t pick those problems out of thin air. in word rebus m/l=a was actually a way of encoding a certain word(but don\'t want to give away solution to people who want to try it) In talking gibberish the whole series of numbers said had a different meaning because it was encoded. This is not a new ctaegory because the other problems don\'t fit but because they would fit in an \"encryption\" category better. So a name like \"mixed bag\" would give a new user (who might like encryption) no idea whats in that category. Also lateral thinking puzzles is also a good idea because of the fact that universities usually teach lateral thinking, so then all we\'d have to get is a university student whos been exposed to this or simply someone who knows this and ou problem database is expanded.(and i\'m pretty sure lateral thiniking problems is searched in google a lot) ',1072,'Alan','2003-04-05 05:14:11');
INSERT INTO forumpost VALUES (456,81,4,'Re: New category','Fl is a scholar so is jim lyon (please tell me i spelt his name correctly) i believe the 4 people mentioned are pretty much the people who should have the next promotion ( once again i\'m NOT asking for it) i doubt theres any other \"common\" user we forgot.',1072,'Alan','2003-04-05 05:17:03');
INSERT INTO forumpost VALUES (457,82,5,'Am I going crazy?','When i came to the site today everything seems to be in larger font or bold? is it a problem with my web browser or was it changed? if so i think the old style looked better. with a nice small font it gave the site a professional ambience. with this the site seems weird and bulky. ',1072,'Alan','2003-04-05 05:19:36');
INSERT INTO forumpost VALUES (458,83,5,'blank comments','A problem I mentioned a while ago in the chatterbox, which more of an annoyance than a bug, and probably only affects people as dumb as me anyway, is that I have the bad habit of typing the subject and hitting \'enter\' instead of \'tab,\' thus posting a blank comment. The simplest suggestion, which would prevent that specific case but not prevent blank comments altogether, would be to disable the form submission until the comment box had been selected. Once the box is selected, hitting \'enter\' merely types a new line, and the post button has to be clicked on or \'tabbed\' to in order to submit.\r
\nSomething like <textarea onFocus=\\\"post.disabled=false\\\"> and then <input type=submit name=post value=Post disabled=true> in the tag for the button would work. The other option would be to modify the PHP to not display a comment if it is blank. That would be more thorough, but perhaps less favorable as sometimes people intentionally leave just a word or two in the subject with no following comment. The focus/disable option would allow people to still do that (if you want them to be able to), but make sure that when they do, it is on purpose.\r
\n\r
\nAnyway, just a thought. Again, I don\'t know how much access anyone has to the nitty-gritty of the webpages and the source files, but modifying show.php when op=post to include those few parameters in the tags would be extremely simple if they can be accessed.\r
\n\r
\n=)',1575,'DJ','2003-04-05 06:25:58');
INSERT INTO forumpost VALUES (459,82,5,'Re: Am I going crazy?','I haven\'t noticed a difference. It\'s odd, though, because even if your browser\'s display font size was changed, the text on this page would still look the same.',1575,'DJ','2003-04-05 06:27:49');
INSERT INTO forumpost VALUES (460,80,7,'Re: Hello, First time here','Welcome, Kenny. I hope you enjoy your stay. Let us know if you have any questions.',1,'levik','2003-04-05 06:35:23');
INSERT INTO forumpost VALUES (461,82,5,'Re: Am I going crazy?','Alan, what browser are you seeing this problem with?',1,'levik','2003-04-05 06:39:14');
INSERT INTO forumpost VALUES (462,83,5,'Re: blank comments','DJ, the other day I added some javascript to the form\'s \"onlcick\" that doesn\'t allow you to press the button unless there is something in the text area.\r
\n\r
\nAre you still having a problem with blank comments? if so, what browser are you on\r
\n?',1,'levik','2003-04-05 06:42:07');
INSERT INTO forumpost VALUES (463,81,4,'Re: New category','I disagree that the essence of The Flooble Code had to do with encryption. It was a probability problem. If it had asked to actually find flooble in some text, that would be an encryption problem. ',1301,'Charlie','2003-04-05 06:50:51');
INSERT INTO forumpost VALUES (464,82,5,'Re: Am I going crazy?','i am using internet explorer 5 (i know its version 5) but i think its possible that it is 5.2 (again not to sure, only sure about it being vers.5)',1072,'Alan','2003-04-05 14:15:38');
INSERT INTO forumpost VALUES (465,77,4,'Re: Congratulations to me','friedlinguini is a scholar.',1072,'Alan','2003-04-05 14:16:24');
INSERT INTO forumpost VALUES (466,81,4,'Re: New category','oooo jeez ok the comment two before this one was actually meant for another thread ( the congrats to me thread)',1072,'Alan','2003-04-05 14:17:57');
INSERT INTO forumpost VALUES (467,82,5,'Re: Am I going crazy?','Anyone else using IE 5 have this problem? I only have 6, and it seems to look OK in 6. Are you sure you didn\'t change anything about your system fonts that may have caused this?',1,'levik','2003-04-05 20:31:54');
INSERT INTO forumpost VALUES (468,82,5,'Re: Am I going crazy?','Same here Alan. Me too using IE 5, but it seems better to me with this larger font size. I don\'t think there is any harm in it. In fact this seems to be much better (for me at least). ',979,'Ravi Raja','2003-04-06 04:04:24');
INSERT INTO forumpost VALUES (469,77,4,'Re: Congratulations to me','Oops then I am sorry. That was my mistake. :(',979,'Ravi Raja','2003-04-06 04:20:27');
INSERT INTO forumpost VALUES (470,37,5,'Re: Names','I would agree that having people with the same name is rare, but it might be like that birthday problem. With 365 different \"possible\" names, you would only need 20-30 people to have odds of having two people with the same name.\r
\n',1626,'Gamer','2003-04-06 05:09:16');
INSERT INTO forumpost VALUES (471,82,5,'Re: Am I going crazy?','Oh! I see the bigger font size, but it might just be the wierdo computer instead... I was wondering about this as well.',1626,'Gamer','2003-04-06 05:10:32');
INSERT INTO forumpost VALUES (472,21,3,'Re: Puzzles','And another reason (as I learned with one of my problems) is the \"common\" 100 or so puzzles are already on the site. Submitting the problem helps filter out some of the repeat problems.\r
\n\r
\nI like your guessme and other puzzles, so do create others!',1626,'Gamer','2003-04-06 05:14:12');
INSERT INTO forumpost VALUES (473,40,6,'Re: perfect squares','I agree with fwaff, I always remember this because the first differences between them are the odd numbers: 1 3 5 7, and without zero, you wouldn\'t have the 1.',1626,'Gamer','2003-04-06 05:16:06');
INSERT INTO forumpost VALUES (474,84,6,'Check on divide by zero?','Does 0/0 = 7? (or any other number)\r
\n\r
\nI always said yes, since (0/0)*0 =7*0, which equals 0= 7*0 equals 0=0 which is a tautology. Is this right?',1626,'Gamer','2003-04-06 05:20:00');
INSERT INTO forumpost VALUES (475,82,5,'Re: Am I going crazy?','i\'m positive i didn\'t touch the font settings and since this seems to be a debate i\'ll vote no to bigger font sizes. I believe the site should have a sleek professional look where as big bulky letters are kind of childish. Its sort of handing in a term paper thats font size 16 courier.',1072,'Alan','2003-04-06 06:32:55');
INSERT INTO forumpost VALUES (476,84,6,'Re: Check on divide by zero?','ummm not to sure on this. ok i admit i\'m only in gr.9 but i found something wrong with your point. lets say i wanted to say 4/2=10 so then to prove i just have to go (4/2)*0=10*0 so 0=0 but then again this is totally wrong. i think its possible you\'re misdoing a formula or i should keep my mouth shut til gr.12',1072,'Alan','2003-04-06 06:37:23');
INSERT INTO forumpost VALUES (477,84,6,'Re: Check on divide by zero?','0/0 is undefined. Later, as you get into calculus, you\'ll see functions where the numerator and denominator each approach zero, and the function approaches a given value at such a point, but the point itself is undefined.\r
\n',1301,'Charlie','2003-04-06 07:17:23');
INSERT INTO forumpost VALUES (478,85,4,'Deletion of 3-Thumbs-Down Puzzles','Aren\'t submitted puzzles with 3 thumbs down supposed to be deleted automatically? The Numbers Game has had 3 (now 4) thumbs down for a couple of days now. Is it actually a manual task to delete such puzzles, like the posting of puzzles?',1301,'Charlie','2003-04-06 07:29:01');
INSERT INTO forumpost VALUES (479,85,4,'Re: Deletion of 3-Thumbs-Down Puzzles','The deletion of a -3 point puzzle needs to be \"pushed,\" just like the posting of a +3 point puzzle. I never do it myself because \"pushing\" the rejection triggers an e-mail to the submitter in which we are required to explain why, and somehow I come off sounding \"mean-spirited\" in print often enough without volunteering to kick someone while they\'re down. ',153,'TomM','2003-04-06 11:15:38');
INSERT INTO forumpost VALUES (480,82,5,'Re: Am I going crazy?','There, I think I figured it out. Better?',1,'levik','2003-04-07 01:52:16');
INSERT INTO forumpost VALUES (481,84,6,'Re: Check on divide by zero?','Hehe... This reminds me of good old Dulanjana - hasn\'t been around for a while now, but I remember there was a time when we used to get questions dealing with division by zero almost daily :)',1,'levik','2003-04-07 01:54:57');
INSERT INTO forumpost VALUES (482,84,6,'Re: Check on divide by zero?','Actually, he was just on a couple of days ago.',103,'friedlinguini','2003-04-07 03:32:47');
INSERT INTO forumpost VALUES (483,21,3,'Re: Puzzles','Actually Gamer those problems (Riddles) had been all given the same subject Guess What/Who and that is why Levik changed the first few to Guessme One, Two, Three and so later when I posted more riddles, I myself gave the subject\'s names as Guessme Four, Five, Six, ....and so on. But now you will find the riddles submitted by me (though less in number compared to the ones posted before) have a different subject, that is, other than Guessme Ten, Eleven,....and so on.\r
\n\r
\nAnd yes Gamer I have posted a few more riddles but with a different subject. But if you people like that kind of a subject (I mean Guessme 1, Guessme 2, Guessme 3, Guessme 4,....,etc.), then I\'ll change the subjects of the other riddles that I have submitted. \r
\n\r
\nPlease do reply to this one stating whether I should change the subject or not. \r
\nThank You.',979,'Ravi Raja','2003-04-07 04:35:42');
INSERT INTO forumpost VALUES (484,82,5,'Re: Am I going crazy?','Yes Levik, now its better. I mean the same as before (I think), if not smaller. :)',979,'Ravi Raja','2003-04-07 04:46:21');
INSERT INTO forumpost VALUES (485,21,3,'Re: Puzzles','I think subjects like Yes, Sir are, in my opinion, good as they are. :)\r
\n\r
\nI have only been around for a month or so (my first problem is on the site), so I haven\'t seen some of the old items on the site.',1626,'Gamer','2003-04-07 09:51:03');
INSERT INTO forumpost VALUES (486,82,5,'Re: Am I going crazy?','I think I like it smaller... Big letters were harder for me to read.',1626,'Gamer','2003-04-07 09:52:02');
INSERT INTO forumpost VALUES (487,84,6,'Re: Check on divide by zero?','Ok... :) (In response to Alan) The idea I was using to multiply by zero was to undo division, multiply. Divide by zero = multiply by zero.',1626,'Gamer','2003-04-07 09:54:29');
INSERT INTO forumpost VALUES (488,82,5,'Re: Am I going crazy?','actually yes it seems to be better.',1072,'Alan','2003-04-07 10:18:58');
INSERT INTO forumpost VALUES (489,82,5,'Re: Am I going crazy?','I use Netscape Navigator v 7.01 and, though I haven\'t had this problem on this site, I do get it occassionally on another site.\r
\n\r
\nEvery so often, for a day or two the normal fontface is replaced by a different, larger one. Then, suddenly, everything\'s back to normal for a week or two until the next incident.\r
\n\r
\nIt\'s confusing and annoying, but ultimately, I decided, it\'s no big deal.',153,'TomM','2003-04-07 15:40:17');
INSERT INTO forumpost VALUES (490,84,6,'Re: Check on divide by zero?','Well, if high profile physicists can use that approach, why not everybody? In truth, you canget rid of a divide by zero with a multiplication of zero, but you must have a pretty in depth knowledge of math and number theory (which I don\'t so I\'m not going to attempt explaining it to you). The problems you will encounter here is that, as shown in all sorts of calculus type questions, 0/0 leads to an ambiguous result, and so you must know where the zeros come from and how exactly they will interact. The process of using a multiplication by zero to eliminate infinities is called renormalization, and is a key aspect to most macro physics models like unified therories and string theories. However, unless you\'ve the extensive mathematical background of a theoretical physicist, I\'d stay away.',775,'Cory Taylor','2003-04-08 04:28:36');
INSERT INTO forumpost VALUES (491,83,5,'Re: blank comments','The problem is not that I try to click the button before I type the comment in. The \'onclick\' you implemented will prevent people from intentionally leaving blank comments. However, you don\'t have to click the button to submit the form, wherein lies my problem. It is an altogether trivial problem, but I have inadvertently posted blank comments many times by pushing enter out of habit after the subject. The disabling mechanism I proposed above would prevent that from happening, and would not interfere in any way with using the form. Thanks.\r
\n\r
\n=)',1575,'DJ','2003-04-08 06:59:42');
INSERT INTO forumpost VALUES (492,86,7,'Problems','How do I know if a problem I have submitted has been approved or not? That is after it has been voted on.',1637,'chris','2003-04-08 08:11:46');
INSERT INTO forumpost VALUES (493,38,7,'Re: New forum','Nice site. There is a nice mix of problems and puzzles here.',1920,'Brian Smith','2003-04-08 09:44:36');
INSERT INTO forumpost VALUES (494,63,3,'Re: a/s/l anyone?','Hey FLOOBLEers! I just signed up. Im 13/m/uk',1919,'Lewis','2003-04-08 09:59:42');
INSERT INTO forumpost VALUES (495,63,3,'Re: a/s/l anyone?','Welcome to the site Lewis. :)',979,'Ravi Raja','2003-04-09 00:13:37');
INSERT INTO forumpost VALUES (496,86,7,'Re: Problems','CRIS: Under the \"Logout\" button you can see an option \" n problems Pending \" (those \'n\' problems which you have submitted) and among those \'n\' problems, if any voting or any comment has been posted for any of them, then you will see a statement just next o your problem (in the same line) saying: \'y\' comments and you can check those comments. In those comments either you will find Thumbs Up or Thumbs Down or any other comment regarding the problem (say if any changes are to be made, or if you have made any sort of mistake in the statement of the problems or any other suggestions). If there are three TU s , then your problem can come up on the site any time (depending on when the Scholars or the Director pushes it up), if there are three TD s, then your problem is soon going to be out of the queue, and if neither of them then you will have to wait until your problem gets (+3) points.',979,'Ravi Raja','2003-04-09 00:36:52');
INSERT INTO forumpost VALUES (497,86,7,'Re: Problems','Oops I am sorry. it should have been CHRIS and not CRIS. Sorry for that CHRIS.',979,'Ravi Raja','2003-04-09 00:37:48');
INSERT INTO forumpost VALUES (498,83,5,'Re: blank comments','DJ, I understood the problem... It\'s just that i was under the impression that when you submit the form by pressing \"enter\", the onClick of the submit button gets called.\r
\n\r
\nI guess I will just move the empty text checking to the onSubmit handler. I just find the disabling mechanism to be a little non-obvious to the user - they may see that the post button is disabled, and not realize why. This may prevent them from posting (they will think they\'re not alowed or something)\r
\n\r
\nAlso, if in explorer submission by \"Enter\" is not done through the submit button, having the button disabled will probably not disable the form.',1,'levik','2003-04-09 01:56:41');
INSERT INTO forumpost VALUES (499,63,3,'Re: a/s/l anyone?','I am with fried... I always say \"Old enough, no thanks, here\"',1626,'Gamer','2003-04-09 14:43:08');
INSERT INTO forumpost VALUES (500,86,7,'Chris and cris...I made a mistake!!','Ravi and Cris or Ravi and Chris?',1846,'Tim Axoy Disn1','2003-04-09 14:43:39');
INSERT INTO forumpost VALUES (501,84,6,'Infinity=0/0','0/0 is infinity,of course.\r
\nI think so.',1846,'Tim Axoy Disn1','2003-04-09 14:45:33');
INSERT INTO forumpost VALUES (502,20,3,'Re: LOGIC problems?','Or maybe you can let journeymen have that privelege. I know some admins are tired of looking around the site, and just let other smart people delete such a submission when they see it. I don\'t know how you are, so I don\'t know :)',1626,'Gamer','2003-04-09 14:47:57');
INSERT INTO forumpost VALUES (503,20,3,'Re: LOGIC problems?','I am actually liking math problems more than logic problems, but I try to think of logic problems when I can :)',1626,'Gamer','2003-04-09 14:49:59');
INSERT INTO forumpost VALUES (504,23,3,'Re: Two a day?','I know that it took about a month for my number sequence problem to go... I saw the queue was around 300 today! (When I submitted a problem)',1626,'Gamer','2003-04-09 14:52:29');
INSERT INTO forumpost VALUES (505,86,7,'Re: Problems','That\'s ok. I understand what you said ravi, but I had 5 problems in the queue And now I have only 3. Two are missing. Does that mean they have been voted thumbs down?',NULL,'chris','2003-04-09 16:59:27');
INSERT INTO forumpost VALUES (506,83,5,'Re: blank comments','Yeah, I see [now] what you mean about the disabled button being confusing. Disabling the submit it will, indeed, prevent the form from being submitted at all, but it is probably not the best solution. It was just the simplest thing I could think of that would solve the problem without changing the functionality of the forms. But, it is probably also the only way that will change the physical appearance of the page. So, do what you have to (or don\'t, as it appears I am the only person with this problem), and always second-guess anything I say. Good job (seriously). Thanks.\r
\n=)',1575,'DJ','2003-04-10 01:30:36');
INSERT INTO forumpost VALUES (507,83,5,'Re: blank comments','I actually did the onSubmit thing yesterday - let me know if you still experience the problem. (Seems to work for me in IE 6 and Mozilla, but I\'m not sure if you\'re using a different browser version)',1,'levik','2003-04-10 01:49:19');
INSERT INTO forumpost VALUES (508,84,6,'Re: Check on divide by zero?','0/0 = undefined.',103,'friedlinguini','2003-04-10 02:48:10');
INSERT INTO forumpost VALUES (509,86,7,'Re: Problems','If they have been voted Thumbs Down and have been removed from the queue, then it obviously must have been a DUPE of some problem which is already there in the site and you will be notified of the removal of your problem from the queue through e-mail. I mean you will receive a mail saying that your problem has been removed because it was a DUPE of a problem whose subject will also be mentioned in your mail. So you check your inbox and then you will get the answer to your question chris.',979,'Ravi Raja','2003-04-10 04:05:15');
INSERT INTO forumpost VALUES (510,87,6,'Levik!','How do I get back to my old account?\r
\nReply quickly!',NULL,'Tim Axoy','2003-04-10 09:20:32');
INSERT INTO forumpost VALUES (511,88,4,'problem difficulties','There seems to have been a lot of problems recently which the voters and the submittters seem to be at odds regarding the difficulty level of the problems (I don\'t know if this is a more long standing problem as I\'ve only had viewing privelidges of the queue for a short time).\r
\n\r
\nI know from my expereince that it is very hard to evaluate the difficulty level of your own problems, particularly if they are original (i.e. not borrowed). One of my problems that I saw as very easy turned out to be not so much, and one of my problems that I though would be very cahllenging turned out to be solved by a reader before I knew it had made it on the site...\r
\n\r
\nMy question is this - Is there maybe a better system for labelling the difficulty of our problems? Of course the immediate solution I have is that the voters can not only vote tu or td, but also for their idea of the appropriate difficulty level. When the problem is posted it gets whatever the average happens to be. Of course this is far from a perfect solution, as it completely removes the power of the author from the equation, and because (especially for non-original problems) there is a much higher liklihood that the problem or some variant has been seen and solved by a large number of the voters, which will tend to lower problems difficulty levels(its hard to remember how much you struggled with a problem that you solved 5 years ago...)\r
\n\r
\njust my 3 cents worth (no self esteem issues here)',775,'Cory Taylor','2003-04-10 10:37:45');
INSERT INTO forumpost VALUES (512,89,5,'Delete,delete,delete','Levik,can I delete any problems?\r
\n\r
\n',1660,'Tim Axoy','2003-04-10 11:41:37');
INSERT INTO forumpost VALUES (513,75,6,'Gladys\'s kiss on the cheek','Look at title.',1660,'Tim Axoy','2003-04-10 11:43:02');
INSERT INTO forumpost VALUES (514,57,3,'It is no problem! No,it is!','I want to post problems!\r
\nOK?',1660,'Tim Axoy','2003-04-10 11:44:49');
INSERT INTO forumpost VALUES (515,86,7,'Thumbs down or thumbs up?','I like all of my puzzles to be voted thumbs up.\r
\nWill I get warned if one puzzle gets voted like that?\r
\nI hope so.',1660,'Tim Axoy','2003-04-10 11:46:41');
INSERT INTO forumpost VALUES (516,76,4,'Re: Tim Axoy','I tend to be very easy-going and tolerant, but even I must admit that this site is not as pleasant a place to visit when Tim has been \"polluting\" the chatterbox, and forums and ignoring suggestions that he not give away his answers in the titles of his comments.\r
\n\r
\nYou may have to make a decision whether you want to keep all your old members and attract more like them, or avoid hurting Tim\'s feelings. It\'s a hard choice, but that\'s why you are the director.',153,'TomM','2003-04-10 13:04:06');
INSERT INTO forumpost VALUES (517,57,3,'Re: No,no,no','No, it\'s not... You can actually post whatever, but people can change their opinion about you.',1626,'Gamer','2003-04-10 14:18:14');
INSERT INTO forumpost VALUES (518,89,5,'Re: Delete,delete,delete','Nope... And I don\'t think you would want to (except maybe the ones on the forum and chatterbox which shouldn\'t be there)',1626,'Gamer','2003-04-10 14:19:53');
INSERT INTO forumpost VALUES (519,87,6,'Re: Levik!','You certainly are demanding for asking a favor of someone else. Just log out and log back in... ',1626,'Gamer','2003-04-10 14:21:16');
INSERT INTO forumpost VALUES (520,75,6,'Re: Director','You probably aren\'t the object as well... ',1626,'Gamer','2003-04-10 14:23:08');
INSERT INTO forumpost VALUES (521,76,4,'Re: Tim Axoy','Just look at the sequence of comments on Strawberries. Tim\'s subject \"C tells the truth and lies\" gives away part of the solution, and his subject \"No one likes strawberries because...\" gives away the final answer. When DJ points out that these things shouldn\'t be given away in the subject, he shouts DO NOT CRITICIZE ME!',1301,'Charlie','2003-04-10 17:09:40');
INSERT INTO forumpost VALUES (522,89,5,'Re: Delete,delete,delete','Which problems do you want to delete, Tim? The ones in the queue?',1,'levik','2003-04-10 18:11:00');
INSERT INTO forumpost VALUES (523,87,6,'Re: Levik!','Tim, You seem to have found a way to get back into your old account. Please stick to it, and don\'t make any new ones. \r
\n\r
\nIf you have questions, email me.',1,'levik','2003-04-10 18:16:08');
INSERT INTO forumpost VALUES (524,86,7,'Re: Problems','No Tim only if your problem gets three or more Thumbs Down and is deleted from the queue, only then you will be informed otherwise not.',979,'Ravi Raja','2003-04-10 23:10:20');
INSERT INTO forumpost VALUES (525,89,5,'Only some!','I only want to delete some of them. \r
\nProbably Unknown answers and A conversation.',1660,'Tim Axoy','2003-04-11 02:02:12');
INSERT INTO forumpost VALUES (526,57,3,'OK,guys. Solve it.','Here is a problem.\r
\nJohn,Jack,and Jill are the characters.\r
\nJohn:Jack and Jill are of the same type.\r
\nIs there an even or an odd number of knights among them?\r
\n ',1660,'Tim Axoy','2003-04-11 02:08:45');
INSERT INTO forumpost VALUES (527,13,5,'I agree.','I really do not.\r
\nHa!',1660,'Tim Axoy','2003-04-11 02:15:49');
INSERT INTO forumpost VALUES (528,13,5,'Re: Problems in forums','Levik: \r
\n\r
\nFirstly, your comment isn\'t harsh it\'s restating what are (to most) the well understood rules of your site - it\'s no different to asking guests not to smoke in your house, or more to the point telling them bluntly to put that damn cigarette out when you have beforehand politely asked them not to smoke. \r
\n\r
\nSecondly, the fact that the search function doesn\'t look in the forums for problems is because they shouldn\'t be there. It is not a deficiency of the siteis code, it is a deficiency in the ability of some guests to have the courtesy of following the sites rules.\r
\n\r
\nFinally, please keep up the good work. This is an outstanding site that brings much pondering and amusement to many honoured guests.\r
\n\r
\nKeep smiling,\r
\n\r
\nFwaff',1183,'fwaff','2003-04-11 04:09:25');
INSERT INTO forumpost VALUES (529,86,7,'Re: Problems','Why is Chris\' name a different colour on his post above beginning \"That\'s ok...\" All the other names are the smae blueish (how blue are they? Check out the blue vote on floobles main site), but this one is decidedly black. What gives?',775,'Cory Taylor','2003-04-11 04:22:50');
INSERT INTO forumpost VALUES (530,57,3,'Re: No,no,no','Tim - enough. How many times do you need to be asked to not post your problems here. Believe me, I understand that you may be frustrated by the long wait when sending your problems through the queue, but the rest of us wait patiently and so should you.\r
\n\r
\nTo others, I respectfully request that you ignore all puzzle posts in the forums as a passive way of discouraging this unwanted behavior.',775,'Cory Taylor','2003-04-11 04:30:02');
INSERT INTO forumpost VALUES (531,90,5,'Long Comments','Is there a limitation on the size of comments posted toward problems? I know that I have had to break apart a comment and continue it on another comment if it exceeded about 25 lines, and I\'ve seen others do that also. Yet today I see a very long comment (Software Solution) posted against the puzzle Grid Pathways. Is it a function of the browser? I\'m using IE 6.0. There\'s no difficulty posting long solutions in the submitted puzzle area--the limitation applies only to comments under posted puzzles.',1301,'Charlie','2003-04-11 04:35:58');
INSERT INTO forumpost VALUES (532,86,7,'Re: Problems','Also as I move my cursor over the blue names the name becomes underlined to show that it is a link, however on the black chris there is no underlining and no link.',1183,'fwaff','2003-04-11 04:37:07');
INSERT INTO forumpost VALUES (533,89,5,'Re: Delete,delete,delete','Leave notes under those problems that you want to delete them, and when they get to voting people will give them thumbs down',1,'levik','2003-04-11 05:31:51');
INSERT INTO forumpost VALUES (534,90,5,'Re: Long Comments','I\'m honestly not sure why this would be. There\'s nothing in the software that makes it behave that way. One hting I can think of is thta perhaps this limit is only effective for preview (i.e. previews of longer comments don\'t work, but posting would be OK). Can somebody email me with a copy of a comment that they were unable to post to the site? I will then look into it.',1,'levik','2003-04-11 05:34:34');
INSERT INTO forumpost VALUES (535,86,7,'Re: Problems','It\'s simple. Some forums (the ones that say \"everyone\" can post) really do let everyone post. Even people who aren\'t logged in. Those people get to type in their names - they can type in anything they want. But the name is not a link. Names with links are logged in users (these can be verified by clicking on the link).\r
\nChris probably just posted that comment without logging in.',1,'levik','2003-04-11 05:37:16');
INSERT INTO forumpost VALUES (536,76,4,'Re: Tim Axoy','I think I will give Tim a day or two to pull his act together (everyone here can encourage him). If he doesn\'t, I will probably have to ban him. (But please do not warn him about that - I don\'t want him to know)',1,'levik','2003-04-11 05:39:38');
INSERT INTO forumpost VALUES (537,90,5,'Re: Long Comments','I have experienced the same problem with a few lengthy problems (for example, I have been unable to post my full solution for the yet-unsolved \'Locked Safe\' problem). I\'m actually on a computer at school right now, but if it will be helpful, I\'ll try to post here the entire comment (it\'s saved in a text file on my home computer). There have been a few other comments that didn\'t work, I\'m assuming because of length, but I cannot remember any others offhand.\r
\n=)',1575,'DJ','2003-04-11 05:40:06');
INSERT INTO forumpost VALUES (538,86,7,'Re: Problems','Ahhhh it all makes sense now.\r
\nThanks for the simple explanation.\r
\n:-)',1183,'fwaff','2003-04-11 06:18:43');
INSERT INTO forumpost VALUES (539,57,3,'?','There has to be some way to enforce a rule that has been made by levik. I don\'t agree either, but when someone makes a rule about thir site, it is common curtousey to follow it . I can\'t spell. oh well',1947,'Jon','2003-04-11 07:31:20');
INSERT INTO forumpost VALUES (540,90,5,'Re: Long Comments','The next time it happens, I\'ll have to check. Perhaps it had been a confluence of two things: inability of the preview to handle it, and taking so long to compose the long post that my login timed out. Or perhaps composing it offline in Word and copying and pasting introduced bad codes, etc. Next time I see a need for a long comment, I\'ll compose in Notepad so as not to get wrong codes, and make sure I\'m logged on, and ignore an inability to preview. I\'ll see what happens then.',1301,'Charlie','2003-04-11 08:29:08');
INSERT INTO forumpost VALUES (541,91,4,'\"Borrowed\" puzzles','What\'s the policy on submitting/posting problems from other sources on the Flooble site? I know a lot of the problems here are classics or are derived from similar problems, and I see no problem with that, but I have also seen at least one problem that seems to have been cut and pasted (nearly in its entirety) from a copyrighted source elsewhere on the web. Any legal or moral concerns there?',1567,'Bryan','2003-04-11 08:58:05');
INSERT INTO forumpost VALUES (542,90,5,'Re: Long Comments','I am having the same problem, Charlie, having done everything you just suggested. I always write only in notepad, I\'m already logged in, and I skipped the preview - to no avail. One such comment (and I have modified it several times but it is still too long, if that is the problem) follows (after *** to the end of this message):\r
\n\r
\n***\r
\nI had \'proved\' an 8-digit solution before, but my oversight was that the reverse of x is not necessarily x. So, I will redo the problem, with the invented notation of X being the reverse of x (if x=123, X=321). As before, I will attempt to prove that a number relates to itself, which by property E means that it must be a solution and open the lock. The shortest solution still presumably has the form of xx2 or x2x2, where x is a series of 1s, 5s, and 9s that enumerates the steps needed to find that very arrangement.\r
\nFirst, for xx2, lets work backwards:\r
\nxx2 - 2XX - XX - xx - x\r
\nor\r
\nxx2 - 2XX - XX - X - x.\r
\nA consecutive reversal (5) and repetition (9) are interchangeable. This yields the following proof:\r
\n2x2 ~ x\r
\n92x2 ~ xx\r
\n592x2 ~ XX\r
\n1592x2 ~ 2XX\r
\n51592x2 ~ xx2\r
\n:. x must equal 51592, and this shows that 51592515922 relates to itself and therefore is a combination that opens the safe. Also (using the 5-9 commutability), 51952519522 opens the safe by similar proof.\r
\n\r
\nNow, work backwards again to find x2x2:\r
\nx2x2 - 2X2X - 2X - X - x\r
\nor\r
\nx2x2 - x2 - 2X - X - x.\r
\nThus we have the proofs:\r
\n2x2 ~ x\r
\n52x2 ~ X\r
\n152x2 ~ 2X\r
\n9152x2 ~ 2X2X\r
\n59152x2 ~ x2x2\r
\n:. x = 5915, and 5915259152 relates to itself and must open the safe. Also:\r
\n2x2 ~ x\r
\n52x2 ~ X\r
\n152x2 ~ 2X\r
\n5152x2 ~ x2\r
\n95152x2 ~ x2x2\r
\n:. x=9515, and 9515295152 also relates to itself and must open the safe.\r
\nSuch solutions were come upon previously by other people. The next step is what eluded me for some time; that finding a solution one way may make it possible to find others another way.\r
\nAn inspection of the latter two valid combinations reveals that both are repeats of some number. A simple proof, from the definitions, shows that:\r
\n2y2 ~ y\r
\n92y2 ~ yy\r
\nSo, for any repeated number yy, 92y2 is related to it. And, if yy opens the safe (see where I\'m going now?), then 92y2 must also open the safe, to conform to property E. Therefore, the solutions 9515295152 and 5915259152 each yield another solution, and we have that:\r
\n2951522 ~ 95152\r
\n92951522 ~ 9515295152\r
\nand\r
\n2591522 ~ 59152\r
\n92591522 ~ 5915259152.\r
\nTherefore, we have found two 8-digit solutions, 92591522 and 92951522.\r
\n\r
\n!!',1575,'DJ','2003-04-11 09:46:42');
INSERT INTO forumpost VALUES (543,90,5,'Re: Long Comments','So, that\'s pretty lengthy, and I can think of no reason why that should prevent it from being submitted; nor can I think of any other explanation. Thoughts?',1575,'DJ','2003-04-11 09:47:33');
INSERT INTO forumpost VALUES (544,57,3,'Re: No,no,no','Yes, I would ask the same thing as Cory does.. Even if he says \"Is it too hard for you?\", \"Please respond!!!!!!!!!!\", such retorts, just ignore them.\r
\n\r
\nJust look at Ravi! He has so many problems waiting...',1626,'Gamer','2003-04-11 09:54:56');
INSERT INTO forumpost VALUES (545,91,4,'Re:','Well for the legal issue i know that if you\'re in canada absolutely anything written by any author is protected by the Canadian Copyright act and is copyrighted until 50 years after the authors death. So then why are we allowed to post problems from other sites? I\'m not to sure the answer to this (so correct me if I\'m wrong) but when articles or text is placed on the internet by the original author or with his permission it has been released into the \"public Domain\" When things are released into the public Domain it becomes legal for them to be taken, modified etc, unless otherwise stated on the document. So as for taking problems from sites like braingle etc, i think that it is okay as long as we give credit to them at the bottom of the page. If it says that the rights to publish that document was only for one site we cannot post it because this is against the law.',1072,'Alan','2003-04-11 10:35:51');
INSERT INTO forumpost VALUES (546,90,5,'Re: Long Comments','Whatever the cause, the long comment problem has been with us a long time. Most of us have learned to adapt and break up our long responses into two or more comments. Not an ideal solution, but not terribly onerous either.',153,'TomM','2003-04-11 12:00:38');
INSERT INTO forumpost VALUES (547,92,4,'Preferences?','I\'m relatively new to the site and am still picking up the unwritten rules of the place. (Which reminds me: written guidelines would be useful to would-be puzzle makers. If they already exist and I missed \'em, please point me in the right direction.) Some of the other forums have been illuminating, but I would still like to ask the higher-ranking members of perplexus for their preferences in puzzles submitted to this site. I\'m not only asking what types of puzzles you like, but what, ideally, the puzzles should accomplish. \r
\n\r
\nAre you looking for problems with clear-cut solutions, or ones that foment discussion? Do you want to more level 5\'s, or 3\'s? Something you can solve in 2 minutes, or 20, or keeps you puzzling for days? Are there any problems you\'d like to see that no one seems to be submitting? Anything that would cause you to puke if you saw another one?\r
\n\r
\nI guess what I\'m asking for is a vision statement. Requests/advice greatly appreciated.\r
\n',1567,'Bryan','2003-04-11 12:47:19');
INSERT INTO forumpost VALUES (548,92,4,'Re: Preferences?','I know, Bryan, You\'ll probably be very excited to see a reply to your posting, but it, unfortunately, is simply an opinion I would like to enforce. What ARE we looking for here?',775,'Cory Taylor','2003-04-11 22:03:37');
INSERT INTO forumpost VALUES (549,91,4,'Re:','I think from a legal standpoint, it\'s somewhat of a grey area - so many sites on the internet cut and paste each other\'s content that it becomes a moot point. Personally of course I would prefer this not to occur on most occasions. Re-wording a problem is allright in my eyes, and credit should be given with a link, but I would rather not see cut and pastes unless it\'s a VERY successful wording of a VERY good puzzle.\r
\n\r
\nTo get back to the legal side, if anyone ever requested that we take down a puzzle because it\'s someone\'s intellectual property, and was able to back that claim up, I would take it down. By posting problems that are cut and pasted from another site, the probability that this will eventually happen increases.',1,'levik','2003-04-11 23:32:57');
INSERT INTO forumpost VALUES (551,92,4,'Re: Preferences?','Are you looking for problems with clear-cut solutions, or ones that foment discussion? Do you want to more level 5\'s, or 3\'s? Something you can solve in 2 minutes, or 20, or keeps you puzzling for days?\r
\n\r
\nYes.\r
\n\r
\nSeriously though, as you have hopefully seen from your stay here, we like to keep things mixed up here. There\'s nothing more satisfying than finding a definitive solution that clicks. On the other hand, a prolonged and heated discussion will make you want to come back and argue your point. Hard puzzles offer more challenge, but easy ones boost your self confidence.',1,'levik','2003-04-11 23:39:44');
INSERT INTO forumpost VALUES (552,86,7,'Re: Problems','And what if a user who is a member of the site but posts a message typing his/her name in the box corresponding to \"Name\" without logging in ? I\'ll give it a try by posting a message out here with the usual name but without logging in. Let\'s see what happens. ',NULL,'Ravi Raja','2003-04-12 04:51:20');
INSERT INTO forumpost VALUES (553,86,7,'Re: Problems','Okay I can see it now. I got it. :):):):)',NULL,'Aspiring Novice','2003-04-12 04:52:54');
INSERT INTO forumpost VALUES (554,93,3,'Homer\'s and Horace\'s personalities','There are two interesting twins,Homer and Horace,that have two personalities,State 1 and State 2.\r
\nHomer tells the truth in State 1 and lies in State 2 while Horace lies in State 1 and tells the truth in State 2.\r
\nOnce,one of them claimed to be in State 1.\r
\nWho was he?',1660,'Tim Axoy','2003-04-12 12:03:15');
INSERT INTO forumpost VALUES (555,93,3,'Re: Homer\'s and Horace\'s personalities','Tim-\r
\n\r
\nPlease. Please! PLEASE!!!\r
\n\r
\nDo not post problems in the forums or in the chatterbox. \r
\n\r
\nI know it can be a long wait when you submit them properly, but when they do get on the site in the proper place and format, then they are available indefinitely for future members to find and enjoy.',153,'TomM','2003-04-12 13:02:38');
INSERT INTO forumpost VALUES (556,93,3,'Re: Homer\'s and Horace\'s personalities','And nobody (if they agree with us) will solve your problems unless they are in the actual process of getting apporved. So please don\'t post them here or chatterbox... It\'s just not a good idea.',1626,'Gamer','2003-04-12 13:56:38');
INSERT INTO forumpost VALUES (557,83,5,'Re: blank comments','Yeah, I just did it again, haha..and a little popup told me that I am a moron.\r
\n\r
\nIt\'s great. Thanks.\r
\n\r
\n=)',1575,'DJ','2003-04-12 17:59:43');
INSERT INTO forumpost VALUES (558,93,3,'Solve it quick!','nm',1660,'Tim Axoy','2003-04-13 02:56:15');
INSERT INTO forumpost VALUES (559,1,3,'Long time','No one has been on here for a long time.',1660,'Tim Axoy','2003-04-13 02:58:19');
INSERT INTO forumpost VALUES (560,21,3,'Personality puzzle:State 1 and State 2','Do you see Homer\'s and Horace\'s personalities?',1660,'Tim Axoy','2003-04-13 04:58:13');
INSERT INTO forumpost VALUES (561,94,3,'Tim Axoy','Ok, everyone... I know that Tim Axoy has been breaking a lot of unwritten rules on this site, posting stuff in a distracting manner, etc. I\'m sure nobody was all too comfortable being in the position of asking him to folow rules that should have been clear all along (and asking repeatedly).\r
\n\r
\nThis morning I talked to Tim in the Chatterbox (the conversation should be in history for a couple of days), and he would not be very responsive. I had to threaten him with the possible deletion of his account before getting a wholly unsatisfying commitment that \"I will behave\".\r
\n\r
\nI hope he will. If he does not, I believe that the site is currently big enough and active enough, that the loss of one user should not damage us - especially when this person is creating as much mischief as Tim. I realize that he is only 9 years old, and may simply not know better, but I don\'t want the time I spend running this website to be taken up by babysitting one boy who wants his problems to be solved NOW.\r
\n\r
\nTim, let this be a warning to you - I *WILL* delete your account if you do not stop annoying my visitors and making the site a chore to read by polluting it with garbage.',1,'levik','2003-04-13 05:21:58');
INSERT INTO forumpost VALUES (562,94,3,'OK','OK,Levik,I promise I will behave.\r
\n',1660,'Tim Axoy','2003-04-13 07:47:37');
INSERT INTO forumpost VALUES (563,93,3,'Re: Homer\'s and Horace\'s personalities','what does nm mean ?!',1919,'Lewis','2003-04-13 09:39:18');
INSERT INTO forumpost VALUES (564,63,3,'ENGLAND','Am i the only one here from the UK',1919,'Lewis','2003-04-13 09:56:02');
INSERT INTO forumpost VALUES (565,95,7,'Hey guys! New here.','Hey everyone! I\'m iris, 17, new to this forum, but I\'ve been visiting the flooble perplexus for awhile. I hope the forum\'s fun!',1975,'iris','2003-04-13 13:12:23');
INSERT INTO forumpost VALUES (566,63,3,'I am a he,not a she.','I am a he,not a she.',1660,'Tim Axoy','2003-04-13 13:30:46');
INSERT INTO forumpost VALUES (567,49,4,'Re: Solved Unsolved Puzzle','I don\'t know if Ravi has used any other means to contact you, levik, but I haven\'t seen any posts in the Forums, regarding his comments 74 and 84 to his Around the World solution, directed toward you, where he says he sent a changed solution. Posting these notes to you there are probably not the best way to contact you. But it would be good to put that into the solved category.',1301,'Charlie','2003-04-13 16:37:23');
INSERT INTO forumpost VALUES (568,63,3,'Re: a/s/l anyone?','hey everyone? just joined yesterday. I don\'t have a problem with posting my gender (or race). the only discrimination i see today are United Negro College Fund, Black Entertainment Television, etc... don\'t get me wrong, one of my best friends (before he moved) was a Negro, and i am very close with several orientals. i have no problems with them being here in america, but i do have problems having to pay them money because they don\'t look like me. 18/m/CA',1971,'Steven','2003-04-13 20:18:15');
INSERT INTO forumpost VALUES (569,96,5,'Guest users,who are you???','Who are the Guest users???',1660,'Tim Axoy','2003-04-14 02:47:51');
INSERT INTO forumpost VALUES (570,93,3,'Re: Homer\'s and Horace\'s personalities','Generally it means \"never mind\".',103,'friedlinguini','2003-04-14 03:52:14');
INSERT INTO forumpost VALUES (571,49,4,'Re: Solved Unsolved Puzzle','Yes. I was waiting for Ravi to re-evaluate his solution, but then kinda forgot about it and never checked back. Thanks for pointing it out to me.',1,'levik','2003-04-14 03:59:44');
INSERT INTO forumpost VALUES (572,95,7,'Re: Hey guys! New here.','*waves*',103,'friedlinguini','2003-04-14 04:47:01');
INSERT INTO forumpost VALUES (573,90,5,'DOH! (long comments)','DOH!!!!\r
\n\r
\nJust realized the cause of the long comments issues! The form submitting comments was set to be a method \"GET\" form (those who know a little bit about how web scripts work will now let out a groan and think: \"Levik is an idiot\").\r
\n\r
\nFor everyone else\'s sake, I will say that \"Get\" forms are posted in the URL bar of your browser - this means that the long comment you just typed in is being crammed in to that tiny field JUST big enough to fit \"http://www.flooble.com/perplexus/\". Naturally, most browsers cut this field off at SOME length, resulting in the problems people have been having.\r
\n\r
\nI just changed it to using the POST method, so hopefully this will resole everything.',1,'levik','2003-04-14 05:39:01');
INSERT INTO forumpost VALUES (574,63,3,'Re: a/s/l anyone?','Hey, I am 18/m/Minnesota. sure don\'t ya know',1947,'Jon','2003-04-14 07:54:36');
INSERT INTO forumpost VALUES (575,96,5,'Re: Guest users,who are you???','They are people who aren\'t logged in but are still looking at the site. You don\'t have to be logged in to view problems, but to make a post of any sort you do have to log in. In order to submit a problem you have to log in too.',1947,'Jon','2003-04-14 07:57:51');
INSERT INTO forumpost VALUES (576,63,3,'Re: a/s/l anyone?','Hey Jon, seeing you\'re from Minnisota - Go Wild!!, beat them Avalanche (so my Oilers don\'t have to play them in the next round!!!) (eh!)\r
\nPS 28/m/Edmonton Alberta\r
\n\r
\n',775,'Cory Taylor','2003-04-14 09:21:25');
INSERT INTO forumpost VALUES (577,63,3,'Re: a/s/l anyone?','Yes... I agree with steven... I don\'t understand \"Reverse discrimination\"... (On the college issue) I think we should give points on a \"culture test\" not on a race observation. ',1626,'Gamer','2003-04-14 09:54:34');
INSERT INTO forumpost VALUES (578,96,5,'Re: Guest users,who are you???','Before you got a name to log in, you would be a guest user.',1626,'Gamer','2003-04-14 09:55:13');
INSERT INTO forumpost VALUES (579,95,7,'Re: Hey guys! New here.','Hi! :)',1626,'Gamer','2003-04-14 09:56:25');
INSERT INTO forumpost VALUES (580,95,7,'Re: Hey guys! New here.','Welcome to the site. Holler if anything is unclear.',1,'levik','2003-04-14 10:18:07');
INSERT INTO forumpost VALUES (581,96,5,'No wonder','No wonder they were not posting.\r
\nNo one not logged in can post.',1660,'Tim Axoy','2003-04-14 10:36:24');
INSERT INTO forumpost VALUES (582,63,3,'Re: a/s/l anyone?','Wandering O/T here, but I think that giving some underprivileged races a boost is not nearly as bad as some of the other stuff that can get people into a college. The assumptions being made are that (1) college admissions must be \'fair\' to all ethnicities, and that (2) some ethnicities have institutionalized disadvantages compared to others. Affirmative action is an attempt to rebalance the scales. The difference is that affirmative action is spelled out as an explicit policy. By itself, a policy giving certain races extra benefits is a Bad Thing. However, the situation is complicated by the fact that affirmative action corrects a problem caused by a myriad of unwritten and even unconscious policies which give some races a disadvantage.\r
\n\r
\nAs far as UNCF and BET go, they\'re both private endeavors. You are under no obligation to give your money to UNCF at all if you don\'t want to, and BET exists because of a white culture bias on mainstream TV. If the bias did not exist, cable companies wouldn\'t bother carrying BET.',103,'friedlinguini','2003-04-14 11:37:14');
INSERT INTO forumpost VALUES (583,63,3,'a/s/l=9/boy/Grobe','OK?',1660,'Tim Axoy','2003-04-14 11:50:56');
INSERT INTO forumpost VALUES (584,63,3,'Re: a/s/l anyone?','Only 9 ? So Sweet. :)',979,'Ravi Raja','2003-04-14 21:02:41');
INSERT INTO forumpost VALUES (585,63,3,'Fooled!','9/boy/Virginia',1660,'Tim Axoy','2003-04-15 02:28:51');
INSERT INTO forumpost VALUES (586,90,5,'Re: Long Comments','Works great! The squeaking shoe gets the new sole.\r
\n\r
\nI think that the following is something new: posting the comment after time out results in a blank comment being posted to the puzzle, rather than merely forgetting about the post altogether. But that\'s better than not being able to post long comments.',1301,'Charlie','2003-04-15 05:55:33');
INSERT INTO forumpost VALUES (587,63,3,'Re: a/s/l anyone?','Fool Again - Westlife or Tim Axoy - lol :)',979,'Ravi Raja','2003-04-15 06:13:13');
INSERT INTO forumpost VALUES (588,63,3,'Re: a/s/l anyone?','33/not on a first date/San Diego',1567,'Bryan','2003-04-15 10:09:15');
INSERT INTO forumpost VALUES (589,76,4,'Re: Tim Axoy','A little detective work (well, this is a puzzle site after all) regarding the chatterbox contents this morning. Levik, the was an innappropriate message from lil tim that seemed to have been relied to by his mother, which you then responded to. I was a little curious about this because the other login that was used (by her), where she mentioned that she didn\'t realize that there was a chatterbox on the site, struck me as odd, beacuase I remembered making a joke about that login name being all numbers (anyways...), so I looked back and sure enough it is the same login. 8466489 or something like that. I find it suspicious that a user could navigate the site to find the forums to post in, but never see the chatterbox - the forums are somewhat hidden but the chatterbox is right there in your face. Out of curiosity then, I checked the 846\'s login info, and guess whose email pops up? Timaxoy at something or other...\r
\n\r
\nI\'m not saying anything here, except that these circumstances are a little wierd, and it seems like some way for a little Tim to cover up a mistake he knows he made. Of course I\'m not a psychology major. The folowing path gets you to the forum page with 846\'s comment of about 15 days ago.\r
\n\r
\nforums->general->puzzles (~21)\r
\n\r
\nA little further investigation shows that it is quite possible that this account was created to simply agree with Tim on some comment he made about a puzzle as it says simply \"I saw that too Tim\", closely after a comment from Tim Axoy.\r
\n\r
\nMore possibly circumstantial evidence is that 846 has 3 problems poending in the queue. Isn\'t this a convenient number based on the queue weighting system we have here? I\'d even bet that they\'re of the same category that Tim seems to prefer.\r
\n\r
\nOK - the end of my little rant here. I apologize for extending this little dilemmna. (man I really need to learn how to spell)',775,'Cory Taylor','2003-04-16 04:55:22');
INSERT INTO forumpost VALUES (590,97,5,'Pi','The symbol for pi looks a lot like a lower-case n, as evidenced by the discussion in the problem queue for \"Who Ordered the Pi?\". Perhaps italicizing and/or switching to a different font when someone clicks the pi button would make it more obvious?',103,'friedlinguini','2003-04-16 06:02:10');
INSERT INTO forumpost VALUES (591,97,5,'Re: Pi','Ditto.',1567,'Bryan','2003-04-16 06:48:06');
INSERT INTO forumpost VALUES (592,98,5,'\"Back to problem\"','When editing a solution for a proposed problem, the \"Back to problem\" button seems to link to the home page rather than the edit problem page.',1567,'Bryan','2003-04-16 06:52:57');
INSERT INTO forumpost VALUES (593,98,5,'Re:','Yes Bryan that is what actually happens. When you click on that button, the next page that appears in front of you is the \"Home Page\" and not to the corresponding problem whose solution box is in front of you. I hope something is done about it. Even I face a lot of problems with that. ',979,'Ravi Raja','2003-04-16 07:26:32');
INSERT INTO forumpost VALUES (594,97,5,'Re: Pi','I think switching to a different font will do. So that the two vertical lines and the bar on top of them is clear and anyone will then understand that it is not \'n\' but \'pi\'π',979,'Ravi Raja','2003-04-16 07:33:17');
INSERT INTO forumpost VALUES (595,97,5,'Re: Pi','π',979,'Ravi Raja','2003-04-16 07:36:08');
INSERT INTO forumpost VALUES (596,97,5,'Re: Pi','n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π n π ',979,'Ravi Raja','2003-04-16 07:38:57');
INSERT INTO forumpost VALUES (597,97,5,'Re: Pi','In the above post of mine I have posted \'n\' and \'pi\' alternately.',979,'Ravi Raja','2003-04-16 07:40:49');
INSERT INTO forumpost VALUES (598,76,4,'Re: Tim Axoy','Way to go Cory :)\r
\n\r
\nA little further detective work would have uncovered that both messages were posted off the same account (account ID 1660). It\'s easy enough to do: chatterbox and forums will post with your current Name. You can change it in user preferences screen, post and change it back. \r
\n\r
\nI was aware Tim was doing this back when it was first posted, but didn\'t think it a big deal. You can see this stuff by clicking the link next to the post. (in case of the chatterbox posts, it\'s still in history)',1,'levik','2003-04-16 07:46:43');
INSERT INTO forumpost VALUES (599,98,5,'Re:','There is (as always) a very simple excuse for this. The \"back to problem\" link takes you to view the problem on the site. However, if you try to view the problem on the site, and that problem is not approved yet, you are redirected to the home page.\r
\n\r
\nThis is because the first occurence of the edit solution page was when viewing a live problem which you submitted (it should still offer a link to edit solution if the solution is not yet live). The idea was that you would click that link, edit your solution, and then return back to the problem VIEW page (not the EDIT page which was added later)\r
\n\r
\nOf course all these explanations do not address the fact that the current behavior is wrong and should be fixed. Perhaps there should be 2 separate links ?',1,'levik','2003-04-16 09:23:02');
INSERT INTO forumpost VALUES (600,98,5,'Re:','If it isn\'t too hard to program, I would suggest the link default to the edit page for the problem, and if that page no longer exists because the problem is live, then link to the home page. Doable?',1567,'Bryan','2003-04-16 10:55:23');
INSERT INTO forumpost VALUES (601,99,7,'Hi!','I\'m new. Where can I find the most difficult riddles?',1994,'Tiffy','2003-04-16 16:17:11');
INSERT INTO forumpost VALUES (602,99,7,'Re: Hi!','Welcome to our humble virtual abode!\r
\nAll of the puzzles on the site are classified as to type, so my first suggestion is to go the the \"riddles\" page. From the main page, the category links all show near the top of the page, with riddles showing at the bottom rightof that list. As for the problem difficulty, each puzzle is rated by the puzzle submitter as to its difficulty level. This is shown as a small graphic to the right of the puzzle name with 1 to 5 small colored bars, with 1 bar meaning easy and 5 bars the most difficult.\r
\nEnjoy your stay here!',775,'Cory Taylor','2003-04-17 04:01:51');
INSERT INTO forumpost VALUES (603,7,3,'Without wasting any?','Anthony,really can he not waste any of it?\r
\nI give up.',1660,'Tim Axoy','2003-04-17 11:22:49');
INSERT INTO forumpost VALUES (604,21,3,'8466849,what is your number?','Funny question,Cory!',1660,'Tim Axoy','2003-04-17 11:24:07');
INSERT INTO forumpost VALUES (605,76,4,'Re: Tim Axoy','Hi ya all! I am now \"higher ranking member\" and was confused. I was thinking\" I don\'t remember this forum being here?\" Then I remembered I became an Apprentice and understood. Spooky!\r
\n\r
\nOk, I have had to deal with people like him all the time. I actually thought it wasn\'t legal to have kids under 13 chatting online, but I don\'t know anything. Most people around his age (all the way up to 13/14 from what I have seen) are like that... They want attention, and want to show their smarts. I wouldn\'t be suprised if some problems he doesn\'t even solve. He just looks at the answer in the posts below then says the answer again and again.',1626,'Gamer','2003-04-17 11:48:49');
INSERT INTO forumpost VALUES (606,77,4,'Re: Congratulations to me','Congrats to you, Cory. I thought I\'d jump on this thread (the subject is apropos) to say that I made Journeyman today! \r
\n\r
\nA question for you others: if a problem in the queue has two TU and a note saying it should get a third TU when something administrative is done (like changing its topic), should I vote right away, assuming Levik or a scholar will read the note and make the change before posting? Or should I wait to see the change before voting? Or should I send a message to Levik et al asking if they saw the note? ',1567,'Bryan','2003-04-18 05:02:11');
INSERT INTO forumpost VALUES (607,77,4,'Re: Congratulations to me','Way to go Bryan! I remember (way back all of 3 weeks ago) when I first got to vote on the problem submissions, it was pretty exciting.\r
\n\r
\nFrom my vast experience, I\'d say that if there is a note requesting a change ~that you agree with~, don\'t vote it up untill the change is made, as there are cases when only Levik can do it - he\'ll see it eventually. Once a problem get to a score of three, it can be pushed by anyone at the rank of scholar, even before the change is made. Of course, theres no stopping others from giving the thumbs up if they don\'t think the change is required.\r
\n\r
\nDon\'t worry that a problem will sit there for a long time waiting for this change to happen. After a couple of days of being on the list as a stagnant problem, it\'ll get the votes it needs to get posted. Usually this only happens when the puzzle submitter has stopped coming to the site, as most people are quite willing to tweak their problems a bit to get them posted.\r
\n\r
\n',775,'Cory Taylor','2003-04-18 06:41:59');
INSERT INTO forumpost VALUES (608,77,4,'Re: Congratulations to me','I got to apprentice yesterday! Which means this is my second post on the Library! I have some problems waiting as well... Good job you all...\r
\n\r
\nI have seen (in the time I have been on here) all mentioned earlier as being smart/active and I would give my half-vote in that favor.',1626,'Gamer','2003-04-18 06:48:21');
INSERT INTO forumpost VALUES (609,77,4,'Re: Congratulations to me','Congo Bryan (journeyman) and Gamer (Apprentice) :) Keep Moving :)',979,'Ravi Raja','2003-04-18 08:15:02');
INSERT INTO forumpost VALUES (610,49,4,'Re: Solved Unsolved Puzzle','Okay Levik, now I think next in the queue are the twp problems \"The Flooble Question\" by Alan and \" A Locked Safe\" by Levik, [whose solution has been provided by DJ in the Forums (Commons) under the topic \"Long Comments\"]. Here is where you will find the solution of the problem \"A Locked Safe\": http://www.flooble.com/perplexus/forum.php?fid=5&tid=90\r
\n\r
\nThese are not the only ones but there are other problems too like: \"Zero to 150 in 2003\" by Raveen and \"Niners\" by Levik, \"Bascule\'s Book\" by Cheradenine and \"Grid Pathways\" by Nick Reed which have all been submitted sometime in the year 2002 but still doesn\'t provide a solution. Something has to be done for all these problems. How will one know what the correct solution of those problems is? \r
\n\r
\nThat was all. Awaiting other user\'s comments regarding this. Thank You.\r
\n\r
\n',979,'Ravi Raja','2003-04-18 08:47:33');
INSERT INTO forumpost VALUES (611,49,4,'Re: Solved Unsolved Puzzle','Regarding Bascule\'s book, I think the consensus is that there is no set solution as it would depend on the probability distribution for lengths of books, and there is no such reference that we can turn to. The discussion does bring up the topic of Benford\'s law, and that is about the closest thing to a solution that we could get.\r
\n\r
\nAs for The Flooble Question, that was vexed by changing ideas as to the order in which approved problems got posted. I had simulated what turned out to be a flawed version via a computer program and posted the result split over I think 6 parts due to the problem posting long comments at the time. Subsequently, under two different versions of the posting sequence, I merely reported the findings in terms of the step at which everything got posted, as I did not look forward to splitting a couple of hundred lines into pieces that fit comments. That\'s not really a solution, but rather a \"take my word for it\" answer. If someone clarifies the rules as to the exact sequence in which 3-or-higher-thumbs-up problems get posted, I could put up the simulation results (in a format similar to that multi-parter to which I referred). I think there was only one rule system that resulted in all 40 puzzles originally in the queue of getting posted. It was a while back, so my memory is not fresh on the subject.',1301,'Charlie','2003-04-18 09:17:47');
INSERT INTO forumpost VALUES (612,100,4,'Discovered leviks login password','Hey, levik I know your password. and if you think I\'m bluffing, I\'ll send you an e-mail to tell you the word. I won\'t go public on it if you promote me to scholar',1567,'Bryan','2003-04-18 13:37:37');
INSERT INTO forumpost VALUES (613,100,4,'Re: Discovered leviks login password','Bryan, this is a fairly silly thing to say. You just made Journeyman, and already you want to be a scholar. By blackmailing me no less.\r
\n\r
\nI would appreciate it if you would email me how you discovered my password (if you did indeed discover it) so I can fix a potential vulnerability in the site.\r
\n\r
\nHowever, you have to be pretty naive to think I would cave in to your demands and make you a scholar.',1,'levik','2003-04-18 14:57:12');
INSERT INTO forumpost VALUES (614,49,4,'Re: Solved Unsolved Puzzle','Thanks Charlie for that. But that was just for the two problems Bascule\'s Book and The Flooble Queation. What about the remaining problems that I have mentioned ? Can Levik or anybody else help by providing the correct (Full) solution(s) for the remaining problem(s) that were posted in 2002 ?',979,'Ravi Raja','2003-04-18 23:08:58');
INSERT INTO forumpost VALUES (615,100,4,'Re: Discovered leviks login password','I downloaded a special program that locates where passwords are are saved. It\'s a complicated process, but I also have the passwords from every one else on the site. I haven\'t logged in under them yet, so don\'t worry. I think you might be interested to know that I have the password to TimAxoy\'s account. Interested?',1567,'Bryan','2003-04-19 03:16:47');
INSERT INTO forumpost VALUES (616,100,4,'Re: Discovered leviks login password','Bryan, somehow, I think you\'re full of it. Like I said, if you can email me the details or proof, I would welcome it so that I can close up this hole. The name of the program you claim to have would be a start.\r
\n\r
\nAs for your offer about Tim\'s password, I think you fail to realise that as the author of the site, and the owner of the server it sits on, I can easily look that up in the database if need be. (I can also change it, and any other piece of information about this site directly in the database, which I sometimes end up having to do as a last resort. A hypothetical example was if someone was silly enough to hijack my account on this site and I wanted to make sure that they never show up on here again.)',1,'levik','2003-04-19 04:05:51');
INSERT INTO forumpost VALUES (617,49,4,'Re: Solved Unsolved Puzzle','Thank you charlie for pointing these out. I am not at home right now, and will not be able to take the time to make the solutions myself, but hopefully will remember to when I get back. (Please, please, please bug me again if it\'s not done in the next couple of days - it\'s panning out to be a busy weekend)',1,'levik','2003-04-19 04:16:56');
INSERT INTO forumpost VALUES (618,100,4,'Re: Discovered leviks login password','One question. Will you be willing to promote me to scolar if I send you details. I need to know Y/N?',1567,'Bryan','2003-04-19 04:22:17');
INSERT INTO forumpost VALUES (619,100,4,'Re: Discovered leviks login password','Bryan quit being a twit. Until today, my respect for you has done nothing but grow, as you\'ve got some great problems, and good insight on others problems. \r
\n\r
\nHowever, after checking out the site today, I think that either you\'ve got a friend logging in under your password trying to cause you a little havoc, or you\'re completely socially inept.\r
\n\r
\n1. You don\'t put in a solution to a problem (pillar) that says levik can kiss your ass. What grade is taht? 5?\r
\n\r
\n2. You don\'t blackmail people. This is just wrong dude. You get what you deserve in this world, not what you scare others into. And especially in a case like this, I don\'t think that you\'re going to convince anyone anyways. Take your little power trip and go home.\r
\n\r
\n3. You don\'t insult people who are trying (and doing very well) to make the site a great place to visit. I\'m referring to your comment to Ravi about one of the problem submissions. I don\'t think that RR is vain, and I\'m sure that you shouldn\'t have posted it.\r
\n\r
\nNow, quit all this baby behavior, and let\'s see if you can\'t start (re)gaining some respect around here.',775,'Cory Taylor','2003-04-19 06:05:07');
INSERT INTO forumpost VALUES (620,100,4,'Re: Discovered leviks login password','Theories:\r
\n1. Bryan has used Tim Axoy\'s password and posted a calculus solution to the Odd Pillar, instead of posting it as his solution.\r
\n2. Tim Axoy has hacked into Bryan\'s account and acts like Tim Axoy, including hijacking the solution as his own, while substituting a comment for the solution.',1301,'Charlie','2003-04-19 06:37:38');
INSERT INTO forumpost VALUES (621,100,4,'Re: Discovered leviks login password','Besides all which - why do you care if you\'re a scholar or not? Seems a funny thing to make an issue out of...',775,'Cory Taylor','2003-04-19 07:40:05');
INSERT INTO forumpost VALUES (622,89,5,'OK,I did it.','Maybe you should look at my problems now to see which ones I want to delete.',1660,'Tim Axoy','2003-04-19 08:19:20');
INSERT INTO forumpost VALUES (623,100,4,'Re: Discovered leviks login password','It isn\'t me who\'s been posting comments like that. I\'m happy to know that Cory has respect for me, and I don\'t want to lose that respect because of something I haven\'t done. Maybe someone\'s hacking into my account or something, but I swear it\'s not me being so rude. You should believe me because there\'s no reason why I would try to sabatage a website I\'ve contributed so much to. Hopefully you\'ll give me the benifit of the doubt. ',1567,'Bryan','2003-04-19 09:56:27');
INSERT INTO forumpost VALUES (624,101,4,'any one affected','Some users may have noticed that I\'ve been posting rude or innapropriate comments, etc. I wanted to inform everyone that it\'s not my fault that they wer posted, but I also do not know who really is to blame. Ravi and levik, I want to personally apologize to you for what happened and hope ever has been causing this trouble will stop. ;)',1567,'Bryan','2003-04-19 10:07:11');
INSERT INTO forumpost VALUES (625,100,4,'Re: Discovered leviks login password','Ought to be easy enough to check if levik keeps a log of IPs people log in from.',103,'friedlinguini','2003-04-19 10:32:55');
INSERT INTO forumpost VALUES (626,100,4,'Re: Discovered leviks login password','And even if you did discover someone\'s (or mine for that matter) password. I would know it wasn\'t the actual person if he/she started acting mean and bad for no reason at all. I personally thought you were the same type as Cory (or other \"elders\"... too many to list), but obviously you aren\'t.\r
\n\r
\nAnd an accomplice to a crime is committing it as well. I think hacking other\'s people\'s passwords is a crime. Downloading an immoral program is being an accomplice. Do the logic to figure out what I mean.\r
\n\r
\nMy favorite quote is \"If you cheat for something, you don\'t deserve it.\" Just think of figuring out how this applies to you as a \"bonus puzzle\" that you don\'t even need to hack to get.\r
\n\r
\nI don\'t understand why you would say something like that... Maybe somebody stole YOUR password and is posing as you :)',1626,'Gamer','2003-04-19 11:27:18');
INSERT INTO forumpost VALUES (627,100,4,'Re: Discovered leviks login password','This seriously makes no sense.
Ok bryan after doing some thinking based on the events i really can\'t say i think you\'re either 1.bryan 2.a hacker who took bryan\'s account 3.tim axoy who took bryans account but anyways some VERY important point for people to think about.
Note: Everytime I say bryan I am referring to whichever of the three scenarios I listed is true.
\r
\n1. Bryan has levik\'s account password. Why not go into levik\'s account and promote yourself to scholar. Are you computer illiterate? well then how\'d you download the password program and use it?\r
\n2. If you are computer illeterate and did the rest with slight knowledge why not just steal someone else\'s account who is a scholar?\r
\n3. Real bryan we need you to be honest, did you use a simple password that a nine year old would be able to get after entering password after password? if so then say so. (I can near gaurantee no other apprentice\'s will hack you) also If someone posts a response to this that isn\'t you e-mail me because I log on VERY frequently so i will tell this forum the truth about the fake post.\r
\n4. Could anyone check if their is a relation between grobe and virginia(or san diego) read the asl post in general discussion to understand this. If i think of anything else i\'ll point it out.',1072,'Alan','2003-04-19 14:43:40');
INSERT INTO forumpost VALUES (628,100,4,'Re: Discovered leviks login password','To the real Bryan. Is comment 7 under Peculiar Pillar your submitted solution?\r
\n',1301,'Charlie','2003-04-19 17:42:25');
INSERT INTO forumpost VALUES (629,100,4,'Re: Discovered leviks login password','If so, we could look at scenario 2 in my post above.\r
\n',1301,'Charlie','2003-04-19 17:43:19');
INSERT INTO forumpost VALUES (630,101,4,'Re: any one affected','It\'s alright Bryan. No apologies. If you accept that you have committed a mistake by using such words then the best thing is that you realized your mistake and that you will not be doing that again. ',979,'Ravi Raja','2003-04-19 22:59:24');
INSERT INTO forumpost VALUES (631,102,5,'How often do they...','How often to problems get posted nowadays?',1660,'Tim Axoy','2003-04-20 03:08:16');
INSERT INTO forumpost VALUES (632,103,4,'Queue Disappeared','Does the disappearance of the queue have anything to do with the hacking (potential or otherwise) and the Bryan posts, etc.?',1301,'Charlie','2003-04-20 04:42:41');
INSERT INTO forumpost VALUES (633,103,4,'Re: Queue Disappeared','I see the Chatterbox is gone also.',1301,'Charlie','2003-04-20 04:44:26');
INSERT INTO forumpost VALUES (634,50,5,'Re: Chatterbox','Most of the time I log on I usually do not find the chatterbox. I mean that place is empty, with just the heading on top: Chatterbox, but I am not able to view it. Is it a problem with my computer or others too are facing this problem ?',979,'Ravi Raja','2003-04-20 04:49:52');
INSERT INTO forumpost VALUES (635,50,5,'Re: Chatterbox','Usually I see the following message there: \"This flooble chatterbox is temporarily unavailable. It will be back up shortly\". Is that what everyone sees or is it me only ?',979,'Ravi Raja','2003-04-20 05:00:16');
INSERT INTO forumpost VALUES (636,103,4,'Re: Queue Disappeared','Which queue are you talking about Charlie? I have already posted a comment regarding the chatterbox problem in the Forums (Commons), I think. Also the color of the entire page is changing. ',979,'Ravi Raja','2003-04-20 05:10:53');
INSERT INTO forumpost VALUES (637,100,4,'Re: Discovered leviks login password','How do we know who is \"real Bryan\"? I am not sure what a fake Bryan would say, but this goes back to the \"I am telling the truth\", which is sensible to say if you were lying or telling the truth.\r
\n\r
\nAlan\'s first two points are interesting. I wonder about those problems as well.\r
\n',1626,'Gamer','2003-04-20 05:16:15');
INSERT INTO forumpost VALUES (638,100,4,'Re: Discovered leviks login password','In \"A Game of Craps\", [Bryan] (so we know it\'s the login-name) posted a sensible solution to this about 3 hours and 20 minutes late from when he posted this post-sequence. So we know [Bryan] is at least been on from the time he created this post-sequence, or the person who stole his account is smart too.\r
\n\r
\nDoes real-Bryan have any reason not to visit the forums and see this post-sequence, or inability to read these posts?',1626,'Gamer','2003-04-20 05:23:51');
INSERT INTO forumpost VALUES (639,100,4,'Re: Discovered leviks login password','I too have something in my mind. There are a fe points which are bothering me. Sometimes I think (using some reasonings) that it \"IS\" Bryan who is doing all this and sometimes it makes me conclude that it is \"Not\" Bryan. I\'ll soon be posting those comments and thoughts of mine. Can\'t post them right away. I hope everyone understands the reason why. (Because we do not know exactly who it is who has been doing all this). ',979,'Ravi Raja','2003-04-20 05:27:33');
INSERT INTO forumpost VALUES (640,100,4,'Re: Discovered leviks login password','Even if he does and posts a comment Gamer, then how can you differentiate the real one (Bryan) from the Hacker ?',979,'Ravi Raja','2003-04-20 05:29:49');
INSERT INTO forumpost VALUES (641,50,5,'Re: Chatterbox','There was a problem with the chatterbox server yesterday afternoon. It has been fixed, and now everything should be back to normal.',1,'levik','2003-04-20 06:14:44');
INSERT INTO forumpost VALUES (642,102,5,'Re: How often do they...','Often.\r
\n\r
\nOnce a day on weekends, twice on weekdays.',1,'levik','2003-04-20 06:15:25');
INSERT INTO forumpost VALUES (643,103,4,'Re: Queue Disappeared','I can still see the queue fine, and the colors are OK. (Let me know if this is not the case for you guys)\r
\n\r
\nThe chatterbox issue is unrealted to Bryan - it was an outage on the chatterbox server affecting the service globally, and has now been restored. ',1,'levik','2003-04-20 06:17:09');
INSERT INTO forumpost VALUES (644,100,4,'Re: Discovered leviks login password','You don\'t. I will be dealing with this in email by sending messages to Bryan\'s \"known good\" address. We will determine if it\'s been him or someone else doing this stuff, and then I will let you guys know.',1,'levik','2003-04-20 06:19:20');
INSERT INTO forumpost VALUES (645,50,5,'Re: Chatterbox','Yes now its alright Levik. Thank You.',979,'Ravi Raja','2003-04-20 06:29:52');
INSERT INTO forumpost VALUES (646,103,4,'Re: Queue Disappeared','Yes now its alright Levik. I only had problems with the chatterbox to which you have replied and the color of the page, which is also back to normal now. Even I found the queue fine. I do not know what Charlie saw. May be now its fine with him too.',979,'Ravi Raja','2003-04-20 06:34:21');
INSERT INTO forumpost VALUES (647,100,4,'Re: Discovered leviks login password','Yes and i think right i should say any possible \"solutions to the problem SHOULD NOT and i repeat SHOULD NOT be posted in this forum. Using simple logic you should understand bryan (when i say bryan I am referring to which of the three scenarios is true in my previous post) will log on and see this solution and this might allow him to find a way around. Any good ideas should be e-mailed to levik but as levik has a possible solution there probably is no need. Before reading your last post Levik I e-mailed bryan to and i get a strange feeling we both had a similar idea to solving the problem.
\n\r
\nI don\'t understand what a \"solution\" is... Is that knowing who is who/ or protecting your password from being hacked?',1626,'Gamer','2003-04-20 09:28:12');
INSERT INTO forumpost VALUES (649,104,5,'can anyone delete his/her own comments?','Can anyone delete his/her own comments when they are accidently posted more than one time or due to someother reason.\r
\nWell, I think there should be an option... What u guys say?',2005,'Aamir Rashid','2003-04-20 13:31:02');
INSERT INTO forumpost VALUES (650,100,4,'Re: Discovered leviks login password','lol I think its rather funny how i used the word solution in my last post. By solutio I meant solution to the problem. In other words a method to figure out what REALLY is going on.',1072,'Alan','2003-04-20 13:32:09');
INSERT INTO forumpost VALUES (651,105,4,'Uh, this is the REAL Bryan','Guys and gals - No, the last two wacko forum threads under my name were not me. As one of you surmised, I had thoughtlessly used a lame password (the same as my login name, I am ashamed to admit), which has since been changed. I suspect it took a certain juvenile relatively little time to guess it, and I don\'t think for a second he has a password-getting program. Anyone reading this who has an obvious password, save yourself the headache and change it now.\r
\n\r
\nBefore this post, my last post was the comment on the Craps puzzle. Anything between then and now is bogus. I would find the whole episode amusing but for the fact that some people were insulted and Levik has had to waste his time dealing with it. He and I are e-mailing to sort it out.\r
\n\r
\nI\'ll take a look at the solution to the pillar problem and get it fixed. If anyone knows of anything else that needs my attention on this site, drop me a line. Until then, keep puzzling. lol',1567,'Bryan','2003-04-20 19:01:20');
INSERT INTO forumpost VALUES (652,105,4,'This is too easy','After grumbling about what a pain it was going to be to recreate the solution statement for the Peculiar Pillar (it\'s pretty lengthy), I saw that Tim Axoy had thoughtfully included it as comment #7. Now, not only do I not have to rewrite the darn thing, but I know without question who hacked me! Thanks, Tim! (Oh, without my password, he probably can\'t read that.)\r
\n\r
\nRegardless of what action, if any, Levik plans to take against Tim, I think the solution should simply refer to his comment, left in his name. It makes a good story that way. lol',1567,'Bryan','2003-04-20 19:23:28');
INSERT INTO forumpost VALUES (653,104,5,'Re: can anyone delete his/her own comments?','I think that it does not matter much. That rarely happens with any user and an extra comment is not going to harm anyone or change the original solution or anything such. So it is alright with me if you don\'t have that option of deleting that extra comment.',979,'Ravi Raja','2003-04-20 21:40:50');
INSERT INTO forumpost VALUES (654,50,5,'Re: Chatterbox','But what happened to the \"Previous Messages\" page? I am not able to view even a single comment when I click on the \"Previous Messages\" link. Only a new page/window opens and I can see a few things and I see this: \"Warning: mysql_fetch_array(): supplied argument is not a valid MySQL result resource in /home/projects/flooble.com/chatterdocs/hist.php on line 11\", written on top of the page. What has happened to that page? \r
\n ',979,'Ravi Raja','2003-04-20 21:44:49');
INSERT INTO forumpost VALUES (655,104,5,'Re: can anyone delete his/her own comments?','yes, u r right Ravi.It doesn\'t matter at large but isn\'t it more appropriate to reedit and make corrections in your comments if it has been posted rather than posting another comment telling that this thing went wrong in my first one. This will also save time of the person reading comments, the site looks neat and also counting of comments will be more accurate. I appreciate that there is a preview button but if this is not a tough job to introduce a new button, my idea is not that bad. ',2005,'Aamir Rashid','2003-04-21 00:06:42');
INSERT INTO forumpost VALUES (656,105,4,'Re: Uh, this is the REAL Bryan','OK, let me just say that I\'m also looking into this whole incident, and I don\'t believe Tim is the culprit.\r
\n\r
\nMore news a little later.',1,'levik','2003-04-21 02:05:28');
INSERT INTO forumpost VALUES (657,100,4,'Re: Discovered leviks login password','Was it the real Bryan who voted thumbs up on the Twins Riddle?\r
\n\r
\n',1301,'Charlie','2003-04-21 04:22:01');
INSERT INTO forumpost VALUES (658,50,5,'Re: Chatterbox','Thanks for bringing this to my attention, Ravi. In general, if chatterbox \"misbehaves\", it\'s probably an issue with the chatterbox service (which is a separate part of flooble that runs on a separate server)\r
\n\r
\nIn cases like these, it may be better to drop me a quick email, because it probably means it\'s screwed up for the other 60,000 chatterbox subscribers as well, and should be fixed.',1,'levik','2003-04-21 04:23:51');
INSERT INTO forumpost VALUES (659,103,4,'Re: Queue Disappeared','Saturday night and Sunday morning I had clicked on \"### new\", and had gotten a mostly blank background-colored screen with just the heading on it and it happened a couple of times. Today it seems ok.',1301,'Charlie','2003-04-21 04:25:23');
INSERT INTO forumpost VALUES (660,106,4,'So what happened?','If you\'ve already read Bryan\'s earlier post, you will know that he was not the one who has been using his account to post stupid things on this board, as well as in comments/solutions/etc.\r
\n\r
\nA lot of you may have suspected Tim of doing that in his name, but Tim is innocent here. (and a victim to the same exact predicament).\r
\n\r
\nBy looking at the logs of people\'s logins, I was able to determine that the culprit was a user on the site called \"luvya2003\". This person does not have a valid email address on file, so I could not get in touch with them even if I wanted.\r
\n\r
\nIt so happens that there are a couple of luvya\'s problems in the visible queue right now. Vote on them how you will, but realize that this person will probably not be coming back to the site any time soon (not if I can help it anyway).\r
\n\r
\nI have been aware of this person since late last afternoon, but did not want to say anything until I was sure that Bryan had his password changed, and until I had a mechanism in place to ensure that luvya doesn\'t come to bother us any more.\r
\n\r
\nP.S. Please, please, do not have your passwords be the same as your login names. If you can read this forum, chances are that somebody would be able to cause a little havoc by \"hacking\" into your account.',1,'levik','2003-04-21 04:36:11');
INSERT INTO forumpost VALUES (661,107,5,'Passwords','Some people on this site, (you know who you are), have their passwords set to be the same thing as their login name.\r
\n\r
\nAs some of you may know such a case lead to a hijacked account on this site in the past few days.\r
\n\r
\nI ask you to please make sure your password is not something obvious. It doesn\'t have to be a marvel of secure encryption, but at least make sure it\'s not anything that is printed on your user info page in plain text.\r
\n\r
\nI know that some people create their accounts quickly just to get through it and be able to post, and maybe you\'re not even sure you want to stick around for long at that point, so you just type in the same thing in the password field as the login field. But, please, if you are still here, and you are reading this post, and you are advancing in ranks on this site, make sure your password in not an obvious one.\r
\n\r
\nThe damage that a hijacker would cause is mostly to your comments, problems and reputation.',1,'levik','2003-04-21 04:40:47');
INSERT INTO forumpost VALUES (662,105,4,'Re: Uh, this is the REAL Bryan','Sorry for the assumption about Tim. I guess it WAS too easy.',1567,'Bryan','2003-04-21 05:05:58');
INSERT INTO forumpost VALUES (663,100,4,'Re: Discovered leviks login password','No, my thumbs down was cleared, and the TU wasn\'t mine. I have since gone through the queue to correct comments under my name that I myself didn\'t write.\r
\n\r
\nI posted no comments of any type between 2003-04-18 17:59:32 and 2003-04-20 19:01:20. Anything with my name on it in that time frame (and conceivably some items outside that time frame as well, but I haven\'t seen any yet) was the poser.',1567,'Bryan','2003-04-21 05:10:49');
INSERT INTO forumpost VALUES (664,106,4,'Re: So what happened?','I knew it from before itself that very soon the culprit\'s name will be announced. This, being a site for solving puzzles and problems, is a site where all the visitors/users/members are \"INTELLECTUALS\", and who ever has been playing a fool around was in trouble and I knew that he/she would soon be caught. Everyone makes mistakes and this person (the Hacker) also left something behind something (obviously not intentionally), as a clue for to determine who he/she is. \r
\nSo now I hope everything is alright and the site is safe now from all those problems that we (the users, particularly Bryan and Tim) have been facing till now.',979,'Ravi Raja','2003-04-21 06:41:00');
INSERT INTO forumpost VALUES (665,102,5,'April 19','April 19 had no problems at all!\r
\nIt should have had some!',1660,'Tim Axoy','2003-04-21 09:36:12');
INSERT INTO forumpost VALUES (666,106,4,'Re: So what happened?','This luvya2003 dude has been on the site on that name. I saw it when I did the \"Who\'s here\" type thing. I agree with you two... I always read that.\r
\n\r
\nI didn\'t see what the hacker left behind that\'s not in this post-chain. Can you e-mail me (at the address in my lookup) about it?\r
\n\r
\nI hope Tim and Bryan are safe from any more hacking.',1626,'Gamer','2003-04-21 10:19:08');
INSERT INTO forumpost VALUES (667,104,5,'Re: can anyone delete his/her own comments?','AAmir I couldn\'t agree with you anymore. While although its not that significant this doesn\'t change that fact that 1. it still has some significane, no matter how little this significance may be
\n',1660,'Tim Axoy','2003-04-21 12:41:03');
INSERT INTO forumpost VALUES (670,75,6,'Hi,Gladys! Wanna go out on a date?','Look at title.',1660,'Tim Axoy','2003-04-21 12:49:21');
INSERT INTO forumpost VALUES (671,105,4,'Re: Uh, this is the REAL Bryan','Sorry i just read and found out it was the user luvya2003 or something like that. ',1072,'Alan','2003-04-21 12:51:48');
INSERT INTO forumpost VALUES (672,108,7,'Gladys','Hi,my name is Gladys!',1660,'Gladys','2003-04-21 12:52:24');
INSERT INTO forumpost VALUES (673,95,7,'Waves...the ocean...Oceania...Australia','Giggle.',1660,'Tim Axoy','2003-04-21 12:54:40');
INSERT INTO forumpost VALUES (674,38,7,'Problems and puzzles','Yes,Brian Smith.',1660,'Tim Axoy','2003-04-21 12:57:22');
INSERT INTO forumpost VALUES (675,75,6,'Re: Director','I don\'t think you as a 9 year old would be old enough to be a boyfriend :)',1626,'Gamer','2003-04-21 13:58:29');
INSERT INTO forumpost VALUES (676,109,6,'Plurals as restrictions?','I always thought if plurals were used, the answer couldn\'t be one.\r
\n\r
\nFor example: I have 10 apples. I want to put some apples in one barrel and some apples in another barrel so that the product of apples in barrels is the least possible.\r
\n\r
\nThe answer can\'t be 0 (of course) or 1x9=9, because I said \"some apples\" and 1 apple isn\'t apples.\r
\n\r
\nI wasn\'t going to ask about this, but many problems are including such a solution, and wondered if the problem creators didn\'t want such a restriction on the problem.',1626,'Gamer','2003-04-21 14:07:31');
INSERT INTO forumpost VALUES (677,109,6,'Re: Plurals as restrictions?','From my logic course about a decade ago, the word \"some\" implies at least one, which of course includes one. Strict English however has another opinion. I believe that the answer to your question is dependant on the situation, but that generally speaking, for logic problems, \"some\" doesn\'t exclude the possibility of a or an.',775,'Cory Taylor','2003-04-21 16:37:32');
INSERT INTO forumpost VALUES (678,82,5,'Re: Am I going crazy?','When i came on yesterday most of the writing on the site was in italics. Was it just my computer going weird or did anyone see this?',1919,'Lewis','2003-04-21 22:35:05');
INSERT INTO forumpost VALUES (679,108,7,'Re: Gladys','Tim... Didn\'t we agree that there would not be any more name jumping and posting sily messages?',1,'levik','2003-04-22 01:48:33');
INSERT INTO forumpost VALUES (680,103,4,'Re: Queue Disappeared','It was probably the slow chatterbox. If you are on IE, the page is not \"drawn\" until all data is loaded, including chatterbox. As that was having some issues, i tmay have taken some time to get loaded, so for a while the page would have looked hung.',1,'levik','2003-04-22 01:51:53');
INSERT INTO forumpost VALUES (681,108,7,'OK,Lev.','OK,Lev.\r
\nSorry.',1660,'Tim Axoy','2003-04-22 02:19:31');
INSERT INTO forumpost VALUES (682,82,5,'Re: Am I going crazy?','Yes, intermittently I see many comments, etc. in italics. I don\'t know if it has to do with one of the problems including italics near the end and possibly not closing the italics, or what.',1301,'Charlie','2003-04-22 04:56:14');
INSERT INTO forumpost VALUES (683,109,6,'Some 1\'s?','Would you like some 1\'s?',1660,'Tim Axoy','2003-04-22 10:07:19');
INSERT INTO forumpost VALUES (684,97,5,'Re: Pi','ummm no it isn\'t tim. Pi (from what i understand) is a relation between the diameter of a circle and its circumference. pi is an irrational number and it never has an end. by is approximetely = 7/22 i believe',1072,'Alan','2003-04-22 10:14:50');
INSERT INTO forumpost VALUES (685,97,5,'Re: Pi','How about 22/7? \r
\n\r
\nOr better yet, 355/113.',1301,'Charlie','2003-04-22 10:42:26');
INSERT INTO forumpost VALUES (686,97,5,'Re: Pi','Or how about 31416/10000? (Which equals 3927/1250)\r
\n\r
\nIt cant be expressed at all that way.',1626,'Gamer','2003-04-22 11:07:14');
INSERT INTO forumpost VALUES (687,109,6,'Re: Plurals as restrictions?','No, I don\'t mean some indicates plural... I mean APPLES instead of apple... If a plural noun was used, would the solution have to be plural.',1626,'Gamer','2003-04-22 11:11:46');
INSERT INTO forumpost VALUES (688,97,5,'Re: Pi','aha - how about 3pi/3!!!',775,'Cory Taylor','2003-04-22 12:51:47');
INSERT INTO forumpost VALUES (689,109,6,'Re: Plurals as restrictions?','OK, I missed the subtlety here. In logical deduction, saying that some A are B or other such comments mean at least 1 A are B. I think to leave that behind and travel into the world of strict English, (and I most certainly vcould be wrong here - I don\'t have a dictionary to check this and its something my parents taught me when I was a kid) doesn\'t a \"couple\" mean 2, a \"few\" mean 3 and \"some\" mean 4 or more?\r
\n\r
\nAll aside, without a more precisely worded question, I would have to agree with you that when you put apples (without the word some) into a barrel then you\'ve put at least 2 there. Maybe we have a Language guru hangin around who is infinitely more qualified than I to answer this (could you tell by my poor grammar??).',775,'Cory Taylor','2003-04-22 13:01:38');
INSERT INTO forumpost VALUES (690,109,6,'Re: Plurals as restrictions?','In the absence of a language guru I suggest that you use sheep. That way your problem becomes:\r
\n\r
\nI have 10 sheep. I want to put some sheep in one barrel and some sheep in another barrel so that the product of sheep in barrels is the least possible. \r
\n\r
\nAn alternative wording to eliminate \'some\':\r
\n\r
\nI have 10 sheep and 2 barrels. I want to put sheep in each of the barrels such that the product of sheep in barrels is the least possible. \r
\n\r
\nHmmm... you may also want to use fields instead of barrels!\r
\n',1183,'fwaff','2003-04-22 22:28:55');
INSERT INTO forumpost VALUES (691,97,5,'Re: Pi','Alan, I think Pi is equal to the ratio of the circumference of a circle to its diameter and is therefore equal to 22/7 and not 7/22.',979,'Ravi Raja','2003-04-22 23:29:39');
INSERT INTO forumpost VALUES (692,100,4,'Re: Discovered leviks login password','Hey now everything is clear and the Hacker is gone, but there are still a few questions and comments that are bothering me. I mean I am not getting the answer to some questions, I am not able to understand what some (particular) comments posted actually meant,....,etc. I know that most of you would not like to discuss on this topic anymore but I just want to know if you people are interested. \r
\nOkay I\'ll do that only if LEVIK says YES. So, Levik, what do you say ? Should I post away those comments (doubts), regarding the discovery of passwords and all tose stuff, or just forget them?',979,'Ravi Raja','2003-04-22 23:55:45');
INSERT INTO forumpost VALUES (693,110,5,'Goner?','What happened to my problem,A liars and knights paradox,Levik?\r
\nDid you delete it?',1660,'Tim Axoy','2003-04-23 02:49:14');
INSERT INTO forumpost VALUES (694,110,5,'Hurryup','Levik?',1660,'Tim Axoy','2003-04-23 05:20:54');
INSERT INTO forumpost VALUES (695,100,4,'Re: Discovered leviks login password','Post them in a separate thread if you wish.',1,'levik','2003-04-23 05:40:12');
INSERT INTO forumpost VALUES (696,109,6,'Re: Plurals as restrictions?','Personally, I think it depends on the context.\r
\n\r
\nFor me, saying \"some people got on the bus\" means that more than one person got on the bus.\r
\n\r
\nOn the other hand, if i hear \"some of the people on the bus got off\", i would not exclude the possibility of only 1 person getting off.',1,'levik','2003-04-23 05:43:40');
INSERT INTO forumpost VALUES (697,109,6,'Some cars','Some cars rattle.\r
\nMy car is some car.\r
\nNo wonder my car rattles!',1660,'Tim Axoy','2003-04-23 05:45:05');
INSERT INTO forumpost VALUES (698,110,5,'Re: Goner?','I didn\'t delete it, but it\'s possible somebody else did, if it got three thumbs down. Personally, I didn\'t vote on it, since I wasn\'t sure about it.',1,'levik','2003-04-23 05:46:58');
INSERT INTO forumpost VALUES (699,110,5,'Re: Goner?','Tim, you were asked to change the wordings of the problem I believe. So if possible, do change it and post it again. I don\'t think it was a dupe of any other problem. So you have the option of changing the wordings , I mean framing the question properly and then again submitting it. Then I\'m sure it will get 3 TUs instead of 3 TDs.',979,'Ravi Raja','2003-04-23 08:28:23');
INSERT INTO forumpost VALUES (700,111,3,'Computer/Programming puzzles','I myself am a programmer by trade, though I focus more on web-related stuff than hard-core optimization/design/algorithms. I know that a number of other users on this site have at least some knoweledge of computer programming as well.\r
\n\r
\nI was thinking recently of having a computer programming category on this site (potentially this could turn into a whole sub-tree if we get a lot of such puzzles). Such problems could involve such things as clever tricks, semi-obscure algorithms, or perhaps even original or real-life problems.\r
\n\r
\nI\'m just wondering what others would think about this before I add a new category, or look for puzzles.',1,'levik','2003-04-23 08:34:35');
INSERT INTO forumpost VALUES (701,110,5,'Re: Goner?','Actually, I edited the problem to look better and added line breaks - it was worded as good as it coul have to begin with.\r
\n\r
\nMy problem with that.. er... problem... was that it was essentially a statement calling itself false.',1,'levik','2003-04-23 08:36:29');
INSERT INTO forumpost VALUES (702,109,6,'Re: Plurals as restrictions?','Well is there any point in discussing these anymore, that too here in the forums ? I mean the users are going to post their problems as they do. Then we can post our doubts (whatever we are discussing here), but related to that particular problem\'s wordings/grammar, before voting for their problems. I mean by leaving a Note as we generally do while voting them. Since there are many such words and sentences that come up with such ambiguity and everything cannot be cleared just by going on discussing such things in the forums. So it would be better we should comment only on those particular lines of the problems in the Queue which are not clear to us, so that the problem is framed properly before being pushed up on the site. \r
\nThat was just my point of view regarding these discussions. If I am wrong then you all can surely continue with your discussions here in the forums.\r
\nThank You.',979,'Ravi Raja','2003-04-23 08:44:02');
INSERT INTO forumpost VALUES (703,112,4,'Politically Correct Police','The purpose of this thread is to point out the approaching promotion of a certain floobler (about whom there was a lengthy discussion concluded recently)to the point where this board becomes viewable by him. Should this series of comments stick around and thus be viewed by him when he gets here? Just a thought.\r
\n\r
\nOf course, I\'m purposely hiding the identity in question, but anybody whose been here more than a week will kwon who I mean.',775,'Cory Taylor','2003-04-23 08:47:57');
INSERT INTO forumpost VALUES (704,111,3,'Re: Computer/Programming puzzles','That\'s a good idea Levik. Tow or three of my problems too have been solved using Programming and I am sure there are many problems which can be solved in that manner. So what are you waiting for Levik. You can go ahead with your work. \r
\nI believe others agree with me. Let\'s see. ;)',979,'Ravi Raja','2003-04-23 08:52:03');
INSERT INTO forumpost VALUES (705,112,4,'Re: Politically Correct Police','Thinking in one way I would like to say that let him view the comments that have been posted. May be then he would realize that whatever he was doing was wrong even after being warned by other users. We had not been discussing about him without any reasons. After all he was going against the rules of the site (not always) but at the same time we had considered another factor too because of which he was declared innocent and is still here on the site. But now I think he has changed and is not like before and I believe after reading all those comments he will completely stop doing all those stuff. \r
\n(Well the name of the person has not been mentioned by Cory but I think I have not made a mistake in judging who that person is whom Cory is referring to in the comment above). ',979,'Ravi Raja','2003-04-23 09:05:22');
INSERT INTO forumpost VALUES (706,113,5,'Who\'s Online','Does anyone think that there should be a similar \" Who\'s Online \" link above the \" Queue Chatterbox \" too ? ',979,'Ravi Raja','2003-04-23 09:16:27');
INSERT INTO forumpost VALUES (707,111,3,'Re: Computer/Programming puzzles','I don\'t know what you\'d put in here that wouldn\'t go into other slots? I would worry that problems you\'d need programs for might exclude anyone who wasn\'t a programmer...',1626,'Gamer','2003-04-23 11:08:41');
INSERT INTO forumpost VALUES (708,112,4,'Re: Politically Correct Police','I also think (If I know who you are talking about) might calm down and be good... I don\'t know... I don\'t think we haven\'t been doing anything terrible.\r
\n\r
\nRemember that the problem has to appear on the site for it to count towards rank. So this long queue will impair anyone from getting a rank quicklyu.',1626,'Gamer','2003-04-23 11:13:02');
INSERT INTO forumpost VALUES (709,112,4,'Re: Politically Correct Police','I agree with Ravi on this. ',1,'levik','2003-04-23 11:13:03');
INSERT INTO forumpost VALUES (710,111,3,'Re: Computer/Programming puzzles','No, you guys misunderstood me. I wasn\'t talking about problems that you would need to write a program to solve. What I meant was problems about programming.\r
\n\r
\nFor example: what\'s a good way to sort an array of 10 numbers? N numbers? Does the answer change depending on N?\r
\n\r
\nI believe such puzzles can be of a lot of interest to people who are into math and know even a little about programming and algorithms. And I would also have to think of a good way to not have these problems intimidate others. \r
\n\r
\nFor example, perhaps an option (on by default) that would prevent these problems showing up on the front page (you would have to click on the category to see them). I once considered doing this for Calculus problems, but there were never enough of them on the site to bother.',1,'levik','2003-04-23 11:25:34');
INSERT INTO forumpost VALUES (711,111,3,'Re: Computer/Programming puzzles','I\'m a little skeptical. Problems like this would be very domain dependent. The answer to your sorting question would look very different depending on whether you\'re using assembly, C++, SQL, Prolog, or something else. I\'d say take a page from the Extreme Programming camp and wait until you have some problems before you worry about the category.',103,'friedlinguini','2003-04-23 12:27:23');
INSERT INTO forumpost VALUES (712,112,4,'Re: Politically Correct Police','The rule of thumb is that you shouldn\'t post something that you wouldn\'t want to get back to someone. For all we know, the person in question knows a journeyman from the site and has been following this forum anyway.',103,'friedlinguini','2003-04-23 12:33:04');
INSERT INTO forumpost VALUES (713,111,3,'Re: Computer/Programming puzzles','Hmmm... Perhaps sorting is a bad example. Here\'s another one, which I think is really interesting: (I read this on the forums of the TechInterview.Org website.)\r
\n\r
\nSuppose you have some function that is able to generate a random number between 1 and 5. Using this, how would you generate a truly random number between 1 and 7? \r
\n\r
\nI would have liked to submit it to the queue if we had a computer section, but am willing to sacrifice it to illustrate my point. :)',1,'levik','2003-04-23 12:56:34');
INSERT INTO forumpost VALUES (714,111,3,'Re: Computer/Programming puzzles','I think that more categories are fine - each user is going to chose on their own which categories etc. they bother with, but I don\'t think that programming problems would \"scare\" away very many people here, though there might be a number who aren\'t interested in them. For example, I rarely give more than a few seconds to a riddle, but I log in about 50,000 times a day anyways.\r
\nIf you\'re adverse to creating a group for this, remember that a problem can often fit into more than one category. As a point in fact, I\'ve come up with a preliminary thought about your 1-7 problem that could place it in probabilities\" (assuming that my idea works).\r
\nI guess that the bottom line is that we shouldn\'t be losing problems for a lack of a category to house them. (Lateral thinking puzzles anyone?)',775,'Cory Taylor','2003-04-23 13:54:25');
INSERT INTO forumpost VALUES (715,110,5,'My problem was so good,it should not hav','e gotten three thumbs down.',1660,'Tim Axoy','2003-04-23 14:00:50');
INSERT INTO forumpost VALUES (716,114,5,'From Liars and knights to Logic','I am not an apprentice yet,but I want my problem,Homer and Horace 1,which is in the Liars and knights category,to be in the Logic category.\r
\nLevik,can you,by any chance,change it?',1660,'Tim Axoy','2003-04-23 14:07:52');
INSERT INTO forumpost VALUES (717,111,3,'Re: Computer/Programming puzzles','I am certainly in favor of a computer programming category. I\'ve certainly used computer programs to help solve other puzzles, and puzzles specifically geared for programming would definitely be interesting.',1301,'Charlie','2003-04-23 18:28:27');
INSERT INTO forumpost VALUES (718,115,7,'Hi..','Hi guys. I am new here. My friend told me about this site and I found it very interesting....',1983,'Ahmed','2003-04-24 01:05:38');
INSERT INTO forumpost VALUES (719,111,3,'Re: Computer/Programming puzzles','Oh... It sounds like a fun idea... I agree with what Cory said.',1626,'Gamer','2003-04-24 01:52:13');
INSERT INTO forumpost VALUES (720,112,4,'Re: Politically Correct Police','I agree with fried here. :)',1626,'Gamer','2003-04-24 01:53:28');
INSERT INTO forumpost VALUES (721,110,5,'Re: Goner?','Actually, it was essentially a dupe of one already on the queue (True or False--Part 1), which was already in a form good for posting and had been put onto the queue before Liars and Knights Paradox, and that one got the TUs. It was a coincidence that they reached voting almost simultaneously (liars and knights having advanced due to queue weighting).',1301,'Charlie','2003-04-24 03:18:03');
INSERT INTO forumpost VALUES (722,113,5,'Re: Who\'s Online','Actually, I find the Chatterbox thing, especially with the \"Who\'s online\" a bit annoying. Every once in a while I see \"I know you\'re on line, why aren\'t you answering?\" and I don\'t know how long ago it was posted, as I\'ve been too busy doing other things on the site to look at the Chatterbox. But so long as there is such a button, there\'s no reason why it shouldn\'t be available everywhere.',1301,'Charlie','2003-04-24 03:22:12');
INSERT INTO forumpost VALUES (723,111,3,'Re: Computer/Programming puzzles','Im interested in a computer/programming category too. But caution needs to be excersized so that the problems do not become like computer programming assignments.',1920,'Brian Smith','2003-04-24 06:23:21');
INSERT INTO forumpost VALUES (724,114,5,'I need an answer!','My problem is going to go in the queue soon.\r
\nPlease change the category.',1660,'Tim Axoy','2003-04-24 08:11:36');
INSERT INTO forumpost VALUES (725,114,5,'Come on!!!','!!!!',1660,'Tim Axoy','2003-04-24 10:02:50');
INSERT INTO forumpost VALUES (726,114,5,'Come on!!!','!!!!',1660,'Tim Axoy','2003-04-24 10:03:09');
INSERT INTO forumpost VALUES (727,115,7,'Is your...?','Is your friend registered?',1660,'Tim Axoy','2003-04-24 10:32:19');
INSERT INTO forumpost VALUES (728,114,5,'Re: From Liars and knights to Logic','Tim ask once and u will be heard. Levik will change the category but he isn\'t going to do it right away because he might not be on or have read this yet.',1072,'Alan','2003-04-24 12:42:25');
INSERT INTO forumpost VALUES (729,114,5,'Novice and Student \'Rights\' Adjustment','Wouldn\'t it be easier just to give all members the right to change the category of their pending problems? Novices and students, who haven\'t had as much experience with this sight, are more likely to make mistakes in what subject they consider their pending problems than apprentices, journeymen, scholars, and the director. Also, lesser-status members will not have worry about TDs simply because of the category and will not have to depend on levik to take care of these little problems. ',1645,'luvya2003','2003-04-24 13:09:58');
INSERT INTO forumpost VALUES (730,111,3,'Re: Computer/Programming puzzles','Dang!\r
\n\r
\nI was actually looking for a sneaky way to offload the task of programming new features onto my visitors :)',1,'levik','2003-04-24 18:48:43');
INSERT INTO forumpost VALUES (731,114,5,'Re: From Liars and knights to Logic','Luvya, I don\'t think that the problems are voted TD just because the category is different. We just ask the users to change the category before pushing the problem up on the site and if the user is a Novice or a student or so who cannot change the category of the problems he/she has submitted, then Levik takes care of that and does the remaining work. \r
\n',979,'Ravi Raja','2003-04-24 23:44:03');
INSERT INTO forumpost VALUES (732,113,5,'Re: Who\'s Online','Charlie one day even I posted such a comment referring to you because I wanted you to go through an answer submitted by me. You say that you are usually too busy doing other things on the site and so you hardly get time to see the comments on the chatterbox. Isn\'t that so. But that does not mean others too are not interested in the comments posted in the chatterbox. Many of the users have doubts and questions regarding posting their thoughts/solution and also \"Submitting\" a new problem on the site and they ask for help by posting their questions in the chatterbox. And most of the time (not always) I have been answering to their questions. At the same time I go through the comments posted in the forums (Commons, Reference, Library,....and others) and if needed I post my suggestions there too. So I feel the need of it and not you and thus it does not mean that others too do not need it. Anyway Charlie, thanks for your suggestion and I would like to hear from others too what they think about this.',979,'Ravi Raja','2003-04-24 23:54:34');
INSERT INTO forumpost VALUES (733,116,4,'Blank Puzzles in the Queue','Levik, can something be done about preventing puzzles with no title and no puzzle body from appearing in the voting queue? One such is pid=751, by luvya2003, and there was another one, 748, that has apparently been removed manually from the queue viewing. Also, if there is a puzzle, but no title (I don\'t know if this has occurred), perhaps it should have \"No Title\" shown for its title, so that it can be clicked on.',1301,'Charlie','2003-04-25 03:14:48');
INSERT INTO forumpost VALUES (734,113,5,'Re: Who\'s Online','Perhaps levik could work on an Instant Message type screen, which would pop up regardless of what screen you\'re on, when someone else on line wanted to get your attention. Many times I am on the puzzle queue voting area for a while, and log out from there, never even seeing the main chatterbox, and when I log on later I see someone was looking for me. (Yes usually you Ravi). The Chatterbox, as an add-on to this site doesn\'t really serve as a chat room, nor is it an IM. It is more like a more easily accessed forum.',1301,'Charlie','2003-04-25 03:20:40');
INSERT INTO forumpost VALUES (735,113,5,'Re: Who\'s Online','Or am I missing something here? I see there\'s a Pop It Up button on the chatterbox that I\'ve just tried. Does it signal something when someone posts a chatterbox entry? I see it is not permanently on-top, but maybe its reference on the Windows task bar turns orange? I haven\'t tried it popped up for long, but maybe that\'s an answer.',1301,'Charlie','2003-04-25 03:27:01');
INSERT INTO forumpost VALUES (736,113,5,'Re: Who\'s Online','Exactly Charlie that was what I was trying to say. As you have mentioned in your comment that you are usually you are on the puzzle queue voting area you are not able to view those comments that have been posted for you in the main chatterbox. And if suppose I am there too then I would not know even whether you\'re online or not. But if that Who\'s Online button was there too then I understand that you being a Journeyman, there is every possibility that you\'re there in that voting area and so I\'ll post a message for you there. \r
\nSecondly, I to never would say that the chatterbox here serves as a chatroom but I wanted it so that if any user on the site has any problem/question regarding anything on the site then he/she could instantly post that comment in the chatterbox referring to the person who\'s online. ',979,'Ravi Raja','2003-04-25 04:11:28');
INSERT INTO forumpost VALUES (737,116,4,'Re: Blank Puzzles in the Queue','I don\'t think so Charlie. But I believe that Levik should delete all such problems (without the Subject as well as Text) from the list even before it reaches the queue. Only those problems should reach the queue which has something written in it. I mean a proper puzzle and not a BLANK Text.',979,'Ravi Raja','2003-04-25 04:31:16');
INSERT INTO forumpost VALUES (738,113,5,'Re: Who\'s Online','The who\'s online feature shows ALL the users. Even if Charlie is currently looking at the queue, he would show up in the \"Who\'s on\" window of the main page. (There\'s not a way right now to tell where the person is)\r
\n\r
\nI never invisioned chatterbox to be a way for people to effectively talk to one another - it was more like a place where you could at least type something in, back when there were no forums.\r
\n\r
\n(The popup window is not really intended as IM either - you have to manually reload it whenever you want to check for new messages and it doesn\'t in any way draw attention to itself. It was merely designed as a way people could keep chattering without being stuck on the same page)',1,'levik','2003-04-25 07:07:11');
INSERT INTO forumpost VALUES (739,116,4,'Re: Blank Puzzles in the Queue','Levik, isn\'t there a program that goes through the queue and reassings queue weights based on the person\'s name and a count of how many appear for that name? Can\'t that program also look at the title, and at least assign a queue weight that will keep the problem from showing up for voting? Say that\'s queue weight 4; then it would probably also be an easier task for you to look at all the QW 4 puzzles for investigation.',1301,'Charlie','2003-04-25 07:40:47');
INSERT INTO forumpost VALUES (740,116,4,'Re: Blank Puzzles in the Queue','Assigning a queue weight on how many of the problems are submitted by a particular person is alright but I don\'t find any good reason why the queue weights should be assigned to the problems based on the person\'s name. ',979,'Ravi Raja','2003-04-25 08:02:05');
INSERT INTO forumpost VALUES (741,116,4,'Re: Blank Puzzles in the Queue','Oops sorry it should go like this: Assigning a queue weight to a problem on the basis of how many of the problems are submitted by a particular person is alright but I don\'t find any good reason why the queue weights should be assigned to the problems based on the person\'s name. \r
\n',979,'Ravi Raja','2003-04-25 08:04:42');
INSERT INTO forumpost VALUES (742,116,4,'Re: Blank Puzzles in the Queue','What I mean is, that one can only determine if the person has 3, etc. already with QW 1, only if the program examines the name. How else would it determine which was the 4th puzzle in the queue by the same person without looking at the name associated with the puzzle?\r
\n',1301,'Charlie','2003-04-25 08:16:35');
INSERT INTO forumpost VALUES (743,116,4,'Re: Blank Puzzles in the Queue','In other words, I was pointing out that in order to do the weighting on the number of problems already in the queue for that person, the program that runs must examine the name. And if it examines the name, why can\'t it examine the title, and assign a QW of, say, 4 for blank titles, to keep them from showing up in the voting area.',1301,'Charlie','2003-04-25 08:19:47');
INSERT INTO forumpost VALUES (744,114,5,'Re: From Liars and knights to Logic','Hey luvya have you read the library forum? Recently that is? I think there\'s a few more problems levik needs to take care of.......',1072,'Alan','2003-04-25 10:17:29');
INSERT INTO forumpost VALUES (745,117,4,'Problem condensing','Although i Know this isn\'t a big issue, I have seen it a few times and in the future, users aspiring to be journeymen, will submit problems that all follow the same principles. For example lets take the 39 coins problem(I am fine with the fact it had been posted) Lets say the author had also mad a n coins problem with 5 weighings, and then submitted another n+whatever coins problem with 6 weighings. Well all these problems could really be fit together in one problem.
\n\r
\nThe only problem with this strategy is how would a journeyman-voter know if the puzzle is a duplicate (or it is too hard/easy) if it doesn\'t have a solution?\r
\n\r
\nMy idea is just to put in a note (when I click on my problems, edit problem) but I don\'t know if that is good.',1626,'Gamer','2003-04-25 15:25:34');
INSERT INTO forumpost VALUES (748,118,4,'Re: Solution posted?','gamer. A pending problem\'s solution is not viewable by members of the site except for levik (but he\'s admin) You can submit a solution and noone will see it. (Until it\'s posted, at which point i believe scholars have the power to but rarely will)',1072,'Alan','2003-04-25 15:50:40');
INSERT INTO forumpost VALUES (749,109,6,'Re: Plurals as restrictions?','Ravi, please see my note on Professor and Students. It has three thumbs up, so could be posted soon, but has this ambiguity as to whether \"years\" implies more than one year.',1301,'Charlie','2003-04-25 16:12:52');
INSERT INTO forumpost VALUES (750,118,4,'Re: Solution posted?','The solution, even if it is submitted at the same time as the puzzle, is not visible in the voting queue, nor when it finally gets posted, at least for a few days. The only one who has the ability to \"peek\" is levik, and he will only do so if there is a serious question about the problem.',153,'TomM','2003-04-25 18:02:39');
INSERT INTO forumpost VALUES (751,109,6,'Re: Plurals as restrictions?','Yes Charlie, obviously \'yearS\' does imply more than 1 \"YEAR\". ',979,'Ravi Raja','2003-04-26 04:08:34');
INSERT INTO forumpost VALUES (752,118,4,'Re: Solution posted?','Oh! I didn\'t know that :) Sorry about the trouble...',1626,'Gamer','2003-04-26 04:43:49');
INSERT INTO forumpost VALUES (753,114,5,'Re: From Liars and knights to Logic','That\'s a fun idea.',1626,'Gamer','2003-04-26 04:51:39');
INSERT INTO forumpost VALUES (754,109,6,'Re: Plurals as restrictions?','Yet no one would phrase a question \"how many years or year have you been ...\". One is a valid answer to how many years one has been doing something, or how many years old someone is, etc.',1301,'Charlie','2003-04-26 09:44:11');
INSERT INTO forumpost VALUES (755,109,6,'Re: Plurals as restrictions?','How many year isn\'t correct period, since if you know 1 year you wouldn\'t need to ask the question. Maybe that\'s why we don\'t say it that way... but you did bring up a good point Charlie :) ',1626,'Gamer','2003-04-26 13:39:06');
INSERT INTO forumpost VALUES (756,114,5,'Do not worry.','I now think it should not be changed to logic.',1660,'Tim Axoy','2003-04-26 18:06:31');
INSERT INTO forumpost VALUES (757,118,4,'Re: Solution posted?','No trouble. If you don\'t ask questions, how are you going to learn?',153,'TomM','2003-04-26 19:04:36');
INSERT INTO forumpost VALUES (758,119,5,'A figure within the problem','Hi, Guys.\r
\n\r
\nI want to post a problem including a figure(a shape for axample ) but I don\'t know how to do that. how can I ??',1983,'Ahmed','2003-04-26 22:16:27');
INSERT INTO forumpost VALUES (759,119,5,'Re: A figure within the problem','Ahmed you submit the problem and if you have the figure with you then mail it to Levik letting him know the figure is related to which problem of yours. Then he\'ll take care of the rest.',979,'Ravi Raja','2003-04-27 04:08:10');
INSERT INTO forumpost VALUES (760,109,6,'Re: Plurals as restrictions?','I just don\'t understand what I am supposed to do. I mean what changes I am supposed to make in the problem (Professor and Students) which is there in the queue. Bryan is asking for one change and Charlie for something else. Levik Please help me out with this problem (changes in the problem). You can go through its solution and then push the problem up on the site.',979,'Ravi Raja','2003-04-27 04:17:02');
INSERT INTO forumpost VALUES (761,109,6,'Re: Plurals as restrictions?','I just don\'t understand what I am supposed to do. I mean what changes I am supposed to make in the problem (Professor and Students) which is there in the queue. Bryan is asking for one change and Charlie for something else. Levik Please help me out with this problem (changes in the problem). You can go through its solution and then push the problem up on the site.',979,'Ravi Raja','2003-04-27 04:17:28');
INSERT INTO forumpost VALUES (762,114,5,'Levik explains it.','ON one of its votes/notes,Levik liked it how it was,so I now think he is correct.',1660,'Tim Axoy','2003-04-27 04:41:49');
INSERT INTO forumpost VALUES (763,109,6,'Re: Plurals as restrictions?','Here\'s is by far the simplest thing to do. year/years. When we speak we can say \"year or years\" if we\'re explaining a problem but when it is written it is done like this.',1072,'Alan','2003-04-27 06:12:15');
INSERT INTO forumpost VALUES (764,117,4,'Re: Problem condensing','I really would never want to post in reply to my own comment but this is no longer or more recent thread with no exclamation mark and i want people to read this. (I don\'t think anyone has because there are no posts on it.
\n\r
\nIf a rule is put in place, we also can\'t expect previous submissions to follow this new rule or set of rules. \r
\n\r
\nAs for 2-colors vs 3-colors, one has already been posted, and the more challenging one is awaiting post. Some scholar or director must have seen fit not to ask for a condensation.\r
\n\r
\nLooking ahead in the queue, via the pid=### technique, it doesn\'t look as if the submitter of these two puzzles has any 4-colors, etc. in mind.',1301,'Charlie','2003-04-27 07:33:50');
INSERT INTO forumpost VALUES (766,114,5,'Oh,no! It should be changed to Logic bec','ause Liars and knights deals with people that either always tell the truth or always lie,but Logic can have a choice of \"Liars and knights\" problems or \"Half and half\" problems.',1660,'Tim Axoy','2003-04-27 09:36:26');
INSERT INTO forumpost VALUES (767,109,6,'Re: Plurals as restrictions?','It\'s alright Alan. I\'ve changed the problem myself and now there\'s nothing wrong with it. It\'s all done. ',979,'Ravi Raja','2003-04-28 01:17:24');
INSERT INTO forumpost VALUES (768,36,4,'Re: New QW thread','I\'d like to point out that this system isn\'t quite working as we (well I) expected. I\'ll give you a personal example.\r
\n\r
\nI have one problem in the queue. When it was submitted, there were about 375 problems in the queue, so without the queue weight system it would\'ve taken (at 2 problems per day) roughly six months to see it through to posting, which was quite daunting. The queue system having been recently introduced, I didn\'t really know what to expect for the actual length of time to post though.\r
\n\r
\nThree weeks ago, for the first time, I noticed the appoximate queue position marker on my pending problem, it said my problem was approximately 51. This was three weeks ago, and I have seen probably 50 puzzles go through the queue, either being posted or rejected, and checking the queue position of my problem this morning found it at position 38. At this rate it\'ll be another 7 weeks before my problem get to the voting board.\r
\n\r
\nAll in all, the posting of my problem has not been greatly speeded (although certainly somewhat speeded). I\'m certain that others are seeing this, though my situation seems somewhat unique, as I tend to have only a single problem in the queue at a time - therefore I pay more attention to its location etc.\r
\n\r
\nI\'m not saying that something has to/should be done about this - I just wanted to point it out b/c I don\'t think the weighting system is accomplishing what it was impemented for.\r
\n\r
\nFinally, I\'ll give you my reasonings on the why of this problem, which certainly is no more than a guess. While the weighting system quickly pushes your problem through the first 100 or so problems that are all from multiple submitters, as problems from these authors get posted or deleted, then their lower ranked problems with an earlier submission date then jump past the problem submitted by the new user, which then becomes stagnant in the queue. Of course this is what happens - but this queue system was brought in when most problems were from one person, and it worked just fine, as only one set of problems was jumping past yours. Now, however, the situation seems that nobody submits a single problem (its rare in my brief experience with the problem submissions to see a problem by a particular author without another 2 or more by the same author shortly thereafter), which causes many sets of problems to be jumping past yours.\r
\n\r
\nI don\'t really have a(nother) solution to suggest, but I thought I\'d see what you folks think.',775,'Cory Taylor','2003-04-28 04:29:00');
INSERT INTO forumpost VALUES (769,36,4,'Re: New QW thread','Personally, I blame the recalculation of QW every night. While the current system prevents a single submitter from monopolizing the queue, it does not prevent a group of them from doing so. As of this posting, there are five different submitters represented, and they are the same five that we have been seeing for several days. At risk of sounding too pompous, I\'d again suggest the round-robin variant of QW that I suggested in the original thread as a solution.',103,'friedlinguini','2003-04-28 06:11:28');
INSERT INTO forumpost VALUES (770,117,4,'Re: Problem condensing','D\'oh! I didn\'t realize I\'d opened a can of worms with that pid thing. I\'d suggest that people not use that technique for peeking ahead, as it defeats the purpose of the 10-problem limit in the queue.',103,'friedlinguini','2003-04-28 06:13:45');
INSERT INTO forumpost VALUES (771,36,4,'Re: New QW thread','well i think an even simpler way to do it would be this. Then again this might be same as friendlinguini\'s. Get one problem from every author (1st problem=qw of 1)(2nd problem qw=2). Now they are all sent to the queue. (so far pretty much the same. BUT remove the date auto-sort feature. This way every new problem by a user falls at the back of the qw=1 column every single user\'s problems will be spread out much more evenly. ANd a newly submitted problem will go throught INCREDIBLY fast. ( If a user with no problems were to submit something in the queue it would be viewed in a matter of days. I think this is by FAR the best solution. What does everyone else think. If you are all for this please say so.',1072,'Alan','2003-04-28 09:00:35');
INSERT INTO forumpost VALUES (772,117,4,'Re: Problem condensing','The \"tradition\'s\" that take place in these problem series is actually due to the fact that different author\'s had different concepts of how to reform the problem. If you search pearls you\'ll notice it was submitted levik, levik, happy, alan. On top of that the two submitted by levik were different in solving concept. Also with the colours that was an example. I never intended to imply that jonathan waltz was just doing that to climb up in rank.',1072,'Alan','2003-04-28 09:04:46');
INSERT INTO forumpost VALUES (773,111,3,'Re: Computer/Programming puzzles','So, is the Algorithms category that Tim is asking about in the main Chatterbox the new puzzle category for Computer/Programming puzzles? Since it\'s there, I assume it\'s open for submissions. Are solutions to be provided in a sort of pseudo-code and perhaps exemplified by a reasonable programming language? ',1301,'Charlie','2003-04-28 09:16:26');
INSERT INTO forumpost VALUES (774,36,4,'Re: New QW thread','From my personal point of view this would be the best strategy, because as I mentioned I typically have just one problem in the queue. What it boils down to unfortunately (for me), is what\'s most fair for all users in general, and this would really hurt a lot of the submitters.\r
\n\r
\nI think a middle ground might be appropriate. The reality is that with nightly sorting of the queue, more than 2 queue weights are really redundant, but if we lowered the number of puzzles for each user with queue weight 1 to just one, then it might sort this out.\r
\n\r
\nA further suggestion in the case where something like this doesn\'t work, it might help to have some sort of time add function apply to all puzzles currently in the queue by a particular user when another of that users puzzles jump in queue weighting. What I propose is to add a day (or 6 hours; 2 days, whatever) to the submissions time of a persons problems each time a puzzle of theirs is posted. This is probably unclear, so I\'ll give a small example\r
\n\r
\nwith 10 problems (by a unique user) in the queue each submitted on day 1, and a \"push back\" value of 1 day,\r
\noriginally there are 3 problems with qw=1 which will show up in the voting queue almost simultaneously, and 7 sitting near the bottom of the list (but with a submission date that would allow them to jump when a puzzle leaves the queue). The first problem gets posted, allowing the 4th puzzle to jump to qw=1. At this time the problems submitted 5-10 have a day added to their submission date, making them seem like more recent submissions than they are, which COULD allow other problems to avoid being jumped. Then it looks like problems 1-4 are submitted on day 1, but 5-10 are submitted on day 2. This would continue, and assuming that the submitter gets a single puzzle submitted each day, would end up with the system thinking that 1-4 were on day 1, 5 was on day 2, 6 was on day 3, 7 was on day 4 etc.\r
\n\r
\nPicking a time jump variable might be a bit of an excercise (first entry to the algorithms category perhaps?), or we could just adopt a value and see how it affected things. I would suggest that one day is appropriate.\r
\n\r
\nOf course yes, I\'m being very presumptuous here in that I\'m talking (writing-typing) that this is a sold idea, but that\'s just the easier way to speak (dang - type) of it. And also, I\'m not doing any of the (programming) work, so it\'s always easy to come up with extravagent solutions... ',775,'Cory Taylor','2003-04-28 10:24:51');
INSERT INTO forumpost VALUES (775,111,3,'Re: Computer/Programming puzzles','I wondered about giving a solution too. I wanted to show a solution like I did with my other submissions, but I thought would that put too much emphasis on one way to do it? ',1626,'Gamer','2003-04-28 12:35:38');
INSERT INTO forumpost VALUES (776,117,4,'Re: Problem condensing','I also have sequels to problems, because either a problem on the site reminds me of something (as in 4 digit number II), has me discover a possible \"answer\" that wasn\'t it (as in b1f2g3j1v2!), or makes me want to create a puzzle of my own (as in Three more logicians)',1626,'Gamer','2003-04-28 12:42:23');
INSERT INTO forumpost VALUES (777,111,3,'Re: Computer/Programming puzzles','When should we expect the first computer/programming type puzzles to appear?',1920,'Brian Smith','2003-04-29 09:25:34');
INSERT INTO forumpost VALUES (778,120,3,'Posting Pictures','How can you post a picture with a problem? I have seen it ine but can\'t do it myself.',1947,'Jon','2003-04-29 09:46:59');
INSERT INTO forumpost VALUES (779,120,3,'Re: Posting Pictures','*done',1947,'Jon','2003-04-29 09:47:23');
INSERT INTO forumpost VALUES (780,36,4,'Re: New QW thread','building on this idea of trying to have a way so that a users on problems don\'t jump i say that the following could happen.
Change the queue calculation function to only calculate problems in which qw in not=1.
let the queue calculation function happen every night (with its new code)
\n\r
\n(FL, I\'ll have to go back and re-read your original proposal now. From what I remember now, it was a strategy that strongly favored first-time posters. However, if you look at the history of this site, a lot of times, first time problems are either none too good one-offs by users who don\'t visit the site more than 2-3 times, or they can be dupes by submitted by users who don\'t know better yet - but in many cases can later become \"productive\" members of the site.)\r
\n\r
\nThe easiest (and probably the least effective) solution would of course be reducing the QW granularity from 3 to 2 or 1. Cory\'s pushback idea will probably work but for some reason I\'m hesitant to play with the submission date even more (I\'m actually not very happy that it changes when the problem goes live, and have taken steps to one day fix that)\r
\n\r
\nAlan, I\'m not quite sure I understand what you\'re proposing.',1,'levik','2003-04-30 02:11:24');
INSERT INTO forumpost VALUES (785,121,5,'Re: Deleting my own pending problems','Don\'t you mean TD-ing :)?\r
\n\r
\nAnyway, put a bunch of stars in the beginning of the problem names (****) and I will go through the queue ina day or so to delete them.',1,'levik','2003-04-30 02:22:43');
INSERT INTO forumpost VALUES (786,111,3,'Re: Computer/Programming puzzles','I have submitted a couple that are in the queue now, and everyone who wants to should feel free. Perhaps I may even push one out of order so that the category at least has one problem in it.\r
\n\r
\nAs far as solutions go, as with many existing problems on the site, some things can be done in different ways, but there is sometimes a best known way to do them. Excersise judgement (as always). When asked how to swap two integers without a third variable, you may find it more useful to explain the process than to provide the code (which will not be immediately obvious).\r
\n\r
\nPerhaps it may be time to come back to the attachment idea after all. ',1,'levik','2003-04-30 02:28:17');
INSERT INTO forumpost VALUES (787,36,4,'Re: New QW thread','Basically the effect was like the current QW, but with a granularity of one problem and with a \'memory\' such that problems would not get reshuffled when sorted (or at least it would look that way in a large queue). In a nutshell, you do a primary sort on QW and a secondary sort on the last time a submitter\'s problem was pushed. The system could be made to favor first-time posters by playing with the latter timestamp (which would obviously be otherwise undefined). If you don\'t want to favor first-timers, just set that date to the date of their first submission.\r
\n\r
\nYou could also get some interesting behavior by using a QW granularity other than one. In cases like that, for example, Ravi (to continue picking on him :-)>) might have three problems in the queue with QW of 1. If one of his problems got picked, the other two would go to the end of all the QW 1 problems when the re-sort occurs. That behavior might come in handy with some stalemated problems, though you\'d get a lot of problems popping in and out of the top 10.',103,'friedlinguini','2003-04-30 04:04:51');
INSERT INTO forumpost VALUES (788,111,3,'Re: Computer/Programming puzzles','Levik, you can submit a problem without even bringing it in the queue. So why don\'t you post two Model Problems of these type in the corresponding category so that others get a clear idea of it. A maximum of two (ONLY FROM YOU) will do and then the rest will follow the proper rules and will then be submitted. That is, from the list to the queue and then from the queue to the site. What do you and others have to say for this? Please comment. Just an idea from my part. Thank You.',979,'Ravi Raja','2003-04-30 04:53:51');
INSERT INTO forumpost VALUES (789,121,5,'Re: Deleting my own pending problems','Do not go for deleting the problems luvya. Why don\'t you submit some other puzzle in their place. I mean why not riddles? At least they will not be given TDs (Thumbs Down), or any other problem belonging to some other categories, say Algorithms, the NEW one. But yes if others permit you to do so. Or else....you know what. You have no other option but delete all those problems that you have submitted (only the Lateral Thinking ones).',979,'Ravi Raja','2003-04-30 05:12:41');
INSERT INTO forumpost VALUES (790,111,3,'Re: Computer/Programming puzzles','I agree with ravi. It will be a while before any make it through the queue system. I don\'t think any one has a problem with posting up one or two of these types of problems to get them going. I would like to see this kind so I can try them out. Anyone else?',1947,'Jon','2003-04-30 07:28:49');
INSERT INTO forumpost VALUES (791,36,4,'Re: New QW thread','I\'m not convinced that popping in and out is a good thing. It\'s one of the more unfortunate (in my eyes) side effects of the current scheme. \r
\n\r
\nNot only is it confusing to the submitter (people wonder where their problems went, or why they are not getting pushed after a long time with 3TUs), but also it can throw the voters who may forget the reason for voting one way or another. ',1,'levik','2003-04-30 07:46:22');
INSERT INTO forumpost VALUES (792,111,3,'Re: Computer/Programming puzzles','I don\'t think that would be fair. Here\'s what we\'ll do:\r
\n\r
\nThere\'s already a submission from Gamer that is for that category, and it\'s pretty good. \r
\n\r
\nI will wait a couple of days, and then pick one that I think is the best illustration of the type of puzzle that should be in the category, and push it out of turn (It will be one of the two problems pushed on that day - the other will go through regular voting)\r
\n\r
\nSo submit away!',1,'levik','2003-04-30 07:52:15');
INSERT INTO forumpost VALUES (793,36,4,'Re: New QW thread','Well levik what friedlinguini has proposed is basially my idea except for one thing. DON\'T re-sort the problems that have qw=1. So that way whenever a problem just starts to have qw=1 it will be the last problem in the qw=1 \"line/order\". Lets say there are 30 problems in the queue. ok. Now lets call these problems 1,2,3,4....,30. problems 1-10 have qw=1 and were all submitted on April 2 then problem 11-30 have qw=2. ok now problem 1 got posted causing problem 11 to enter the queue with qw=1 But instead of being at position 1 it would be at position 10. If you understand this then readin my earlier comment may make you understand.',1072,'Alan','2003-04-30 10:44:37');
INSERT INTO forumpost VALUES (794,121,5,'Re: Deleting my own pending problems','ummmm Ravi that would not be quite fair. As we have said before doing that is pretty much \"reserving a spot in the queue. Please luvya this is taboo so don\'t do it. On top of that please don\'t give any other new users the idea of doing it.',1072,'Alan','2003-04-30 10:47:57');
INSERT INTO forumpost VALUES (795,121,5,'Re: Deleting my own pending problems','I was thinking the same thing along the lines of Alan, but I think when you edit the problem it posts the new date on the problem... That is what happened when I (unknowing that this would happen) added solutions to many of my problems.\r
\n\r
\nI think a delete problem would be useful. Sometimes I submit a problem only to see I overlooked it in the problem archives. ',1626,'Gamer','2003-04-30 15:07:08');
INSERT INTO forumpost VALUES (796,121,5,'Re: Deleting my own pending problems','Actually Alan, I did not give luvya the permission to do so as is clear from one of the lines in my post which says: \"But yes if others permit you to do so.\" Or else who am I to ask him to do things on a site whose director is someone else, that is, if the site belongs to someone else. So please do not take it otherwise. I did not want luvya to break the rules of this site. ',979,'Ravi Raja','2003-05-01 04:04:41');
INSERT INTO forumpost VALUES (797,121,5,'Re: Deleting my own pending problems','But that puts the burden on us. By default, a submitter should not be able to change a problem to a completely different one. The suggestion shouldn\'t even come up.',103,'friedlinguini','2003-05-01 06:06:40');
INSERT INTO forumpost VALUES (798,121,5,'Re: Deleting my own pending problems','I\'ve wanted to delete a few problems that were duplicates of other problems that appeared after I had first submitted it. And I have, not knowing the \'taboo,\' changed a couple of those problems to new ones (with the same topic). I figured that would be easier than having to wait for it to get into the voting queue only to be thumbed down anyway. Also, I didn\'t know the datestamp on the problem changed when you update it? I have been pretty often modifying the title, or tweaking the wording of the problem or the solution, on problems that are waiting. Does that push them to the back of the queue again?',1575,'DJ','2003-05-01 06:29:29');
INSERT INTO forumpost VALUES (799,36,4,'Re: New QW thread','The problem is you need some kind of re-sort because the QW for each problem will change as problems get pushed.',103,'friedlinguini','2003-05-01 07:16:00');
INSERT INTO forumpost VALUES (800,121,5,'Re: Deleting my own pending problems','Gamer: the behavior you describe (in requerd to the date changing after you edit a problem) is not intentional, and is probably a bug. A person should not be penalized for fixing errors in the problem\r
\n\r
\nIf you could email me to tell me exactly what you edited and at what stage in the problem\'s life cycle (was it pending, approved, or solved?) I will look into the behavior.',1,'levik','2003-05-01 08:53:58');
INSERT INTO forumpost VALUES (801,121,5,'Re: Deleting my own pending problems','I believe that a delete problem button would be helpful, but what is wrong with lateral think puzzles?\r
\n',1947,'Jon','2003-05-01 09:52:41');
INSERT INTO forumpost VALUES (802,121,5,'Re: Deleting my own pending problems','Well i can pretty much put it this way. A lateral thinking problem has no wrong answer. At flooble we want people tio try to figure out the answer. there is nothing to figure out if there is no wrong answer. Hey if lateral think was a university course (I\'m talking about using only types of problems like \"how\'d he die\" or \"what happened\") then every student might as well just get 100%',1072,'Alan','2003-05-01 10:23:55');
INSERT INTO forumpost VALUES (803,121,5,'Re: Deleting my own pending problems','Yeah, deleting problems would be a good feature. . I keep finding more and more problems that I have submitted that are duplicates of other ones, either problems that were still in queue but ahead of mine when I put them up, or ones in the wee back corners of the site that I am just now coming across. Plus, I don\'t see really what there is to abuse about letting people delete their own queue problems. If the problem is a duplicate, it will prevent more unnecessary waiting for them to be voted TD, and will also prevent \"reserving\" a spot in the queue when someone changes a submitted problem to a new one.\r
\nThe only thing about such a feature, the \"one-click\" design of the rest of the page should probably be modified to have some kind of \"Do you really want to delete?\" confirmation page or popup. Submitting a partial comment or something is one matter, but accidentally deleting a problem that has been sitting in queue for a month and a half is quite another. But I really think that such would be a useful feature with not many potential abuses that I can recognize.\r
\n\r
\n\r
\n//On a side note, \"queue\" is a really fun word to type.\r
\n//queuequeuequeuequeuequeuequeue. . ..',1575,'DJ','2003-05-01 14:38:33');
INSERT INTO forumpost VALUES (804,122,5,'Accomodating algorithms','With the addition of the \'algorithms\' category, which will involve, to my understanding, computer programming functions and the like, there are a few changes that might be prudent.\r
\n\r
\nFirst, in one of the problems I was submitting, I ended a line with a brace { followed by a break tag
, which somehow caused the entire next line to disappear until another
, which was ignored as well. I\'m not sure why that happened like it did, but I cannot get the problem to display the way I want it to.\r
\n\r
\nMy suggestion would be to enable the <pre> tag, for preformatted text, which could be used for any computer code that will be displayed. Text will show up in a fixed-with font, and eliminate the need to manually type in
tags or to line things up. I think such a change would be simple and effective for a practical display of typed code.\r
\n\r
\nMy other suggestion, which would be a little more work, but a little more flexible perhaps, would be to just invent a tag like <code> for people to use. With PHP it would be relatively easy to change that tag to display however you wanted it to, such as changing the font, replacing end of line with
tags automatically, perhaps, and even replacing leading spaces with tabs or indented lines. Maybe even indent the whole section of code, in the same way the <blockquote> HTML tag works. I dunno. There are a lot of possiblities.\r
\n\r
\nMaybe this question could be one of the first problems to put into the category. =P',1575,'DJ','2003-05-01 15:00:03');
INSERT INTO forumpost VALUES (805,122,5,'Re: Accomodating algorithms','Oops, every time I type out >br< or in the previous post it didn\'t show up. Silly me. Maybe the forum needs a preview button for morons like me.',1575,'DJ','2003-05-01 15:02:02');
INSERT INTO forumpost VALUES (806,122,5,'Re: Accomodating algorithms','That, and I don\'t know which is \"greater than\" and which is \"less than.\" I meant, of course, the <br> tag.',1575,'DJ','2003-05-01 15:03:35');
INSERT INTO forumpost VALUES (807,123,4,'queue change vote','ok after reading the forum about deleting your own problems i made this response.
\nI found your site while i was searching for logic problems.\r
\nIt\'s really great.',2117,'Grumph NOBIAK','2003-05-02 03:05:29');
INSERT INTO forumpost VALUES (810,125,4,'Bait and switch','In the current queue, Tim Axoy pulled the trick of replacing one problem with another. What\'s different about this time is that the old problem already had some votes on it. I really think this is a problem that needs to be fixed.\r
\n\r
\nHere\'s a silly idea that might be worth considering: once a problem has been submitted, it can only be changed by a high-ranking member OTHER than the one that submitted it. This also gives reason to enforce the so far unwritten rule that one person can only have one account. For accountability purposes, edits would have to be logged - at least, say, until a day or two after a problem gets pushed to avoid hogging resources. I think edits would get made faster this way and it would avoid problem switching.\r
\n\r
\nThoughts?',103,'friedlinguini','2003-05-02 03:46:15');
INSERT INTO forumpost VALUES (811,123,4,'Re: queue change vote','vote yes, but simplified. More than two different queue weights are redundant with the current sorting scheme, so just give two problems qw=1, and the rest qw=2.',775,'Cory Taylor','2003-05-02 04:00:16');
INSERT INTO forumpost VALUES (812,125,4,'Re: Bait and switch','hes a sneaky little 9 year old isn\'t he.\r
\nYes, we must find a solution to this problem, or else it will become commonplace very quickly (how many people have used the problem.pid to advance view in the queue since this possibility was announced?).\r
\n\r
\nWhile it is unrealistic to totally eliminate multiple accounts per user, this goal should at least receive some serious thought',775,'Cory Taylor','2003-05-02 04:03:36');
INSERT INTO forumpost VALUES (813,125,4,'Re: Bait and switch','Well I have posted a comment regarding this in the Notes/Votes corresponding to that problem. According to me Tim has just changed the subject of his problem. previously he had submitted that problem with the subject: \"A hard knights and liars puzzle\" and now he has changed the subject to \"unknown Answers\". Just go through the comments posted by Bryan and me there.',979,'Ravi Raja','2003-05-02 04:51:24');
INSERT INTO forumpost VALUES (814,124,7,'Re: A little french in the Flooble.com w','Welcome to the site, Grumph. (Do you mind if we call you Grumph?)',1,'levik','2003-05-02 05:02:25');
INSERT INTO forumpost VALUES (815,124,7,'Re: A little french in the Flooble.com world','No problem ;-Þ',2117,'Grumph NOBIAK','2003-05-02 05:33:53');
INSERT INTO forumpost VALUES (816,125,4,'Re: Bait and switch','Note my first comment under the problem where I ask about the meaning of a sentence. Do you see anything that that comment could possibly refer to in the problem as it now stands? As I remember, the original problem was a colored-marks-on-foreheads type of puzzle.',103,'friedlinguini','2003-05-02 06:00:18');
INSERT INTO forumpost VALUES (817,125,4,'Re: Bait and switch','I don\'t remember posting a thumbs up on any colored-marks-on-foreheads problem. I do remember it for the puzzle as it stands now, so any switch of the sort must have been before I gave thumbs up.',1301,'Charlie','2003-05-02 09:28:13');
INSERT INTO forumpost VALUES (818,123,4,'Re: queue change vote','Hey, don\'t forget, the highest possible queue weight for puzzles with blank titles (or at least for puzzles with blank puzzle bodies).',1301,'Charlie','2003-05-02 09:31:33');
INSERT INTO forumpost VALUES (819,123,4,'Re: queue change vote','I agree with Cory',1626,'Gamer','2003-05-02 11:18:09');
INSERT INTO forumpost VALUES (820,123,4,'Re: queue change vote','ok well fine this what we are voting on now. Problems 1-2 will have qw=1, and problems with blank titles have qw=highest possible value. Cory, gamer is tiull assume you are voting yes? Charlie are you a yes as well?',1072,'Alan','2003-05-02 15:58:50');
INSERT INTO forumpost VALUES (821,123,4,'Re: queue change vote','That suits me. I actually have no preference of 2 or 3 with QW 1, but as it seems there are a sufficient number of people excluded by 3, then change to 2. I just like to see the puzzles keep coming in, regardless of whose they are. I originally interpreted your request for yes votes to those strongly in favor (\"only if you want to justify it or try to sway other people\'s opinions.\"), but I guess that applied just to the paragraph break thing.',1301,'Charlie','2003-05-02 17:21:20');
INSERT INTO forumpost VALUES (822,108,7,'Re: Gladys','hi Gladys! i\'m new too',2131,'joe','2003-05-03 22:18:26');
INSERT INTO forumpost VALUES (823,126,7,'HK engineer','I\'m joe. I\'m new here. I live in hong Kong. I found the site using Copernic Search Engine while searching \"Logic Puzzles\" I did one and tried to submit my answer, so decided to register as I couldn\'t submit my answer.',2131,'joe','2003-05-03 22:19:49');
INSERT INTO forumpost VALUES (824,73,7,'Re: hello!','Ravi..I\'ve solved your problem. Do I post a solution somewhere?\r
\nHi Karla !',2131,'joe','2003-05-03 22:30:35');
INSERT INTO forumpost VALUES (825,95,7,'Re: Hey guys! New here.','Levic, I\'m wondering how to input my solution to a problem or do you not do that?',2131,'joe','2003-05-03 22:31:23');
INSERT INTO forumpost VALUES (826,95,7,'Posting Solutions','You can\'t actually post the proper solution (unless its your puzzle) but you can post what you think as a comment by clicking \'post a comment\'.',1919,'Lewis','2003-05-03 23:18:26');
INSERT INTO forumpost VALUES (827,73,7,'Re: hello!','Yes as I have mentioned in the chatterbox replying to your question. You can post the solution the way it is done but NOT in the SUBJECT BOX. ',979,'Ravi Raja','2003-05-04 04:14:57');
INSERT INTO forumpost VALUES (828,126,7,'Re: HK engineer','Hi joe. I found the site using a search engine too, but i searched for \'brainteasers\'.',1919,'Lewis','2003-05-04 06:41:32');
INSERT INTO forumpost VALUES (829,73,7,'Re: hello!','I like math and logic, but I am not good at solving those logic problems :)',1626,'Gamer','2003-05-04 09:10:29');
INSERT INTO forumpost VALUES (830,127,4,'auto-log out un-post','sometimes when i post a comment or problem it will not be submitted. After i TRY submitting the page will refresh to whatever you were at and you would not be logged in. I believe this is because everytime it has happened i had another flooble page opened where i was not looged in.',1072,'Alan','2003-05-04 13:44:48');
INSERT INTO forumpost VALUES (831,128,3,'The existence of god','Note: Please if you are going to take place in this discussion then please read all comments already posted. Or else you may end up repeating something or making a point that has already been contradicted. Firstly, I would like to say to hank who wrote this line \"2.) Alan, sounds like you\'re saying God is dead (spoken like a true catholic)\" I sure hope this wasn\'t sarcastic. If you want to talk about faith, then don\'t criticize other\'s beliefs. Because that\'s what faith is about. Your personal \"beliefs\" The same goes for you dj. You called my belief \"piddly\" Although i know in debates some can get angry, it is NO-ONE\'S position to say another person\'s belief is stupid (since god can neither be proved nor disproved) due to the fact it is faith. it is what YOU believe in. I believe that there is only one way to truly perceive things but then again that is what I BELIEVE. (This actually results in a sort of belief paradox) in other words, this forum is to be used for DEBATE only. I do NOT want to see other people\'s beliefs insulted, I know this may be somewhat hard to control because even I may do it. But please this is a debate, refrain from mocking other\'s beliefs. It is ok to say something like. \"what would make you think that\" (If it was implied to be respectfully asked) but it is not ok to say \"Your stupid to believe that\".
\n\r
\nI think depriving someone of religion is like deleting all the fun and/or hope from their life. Alan, please don\'t stir up the bee-hive... It will just come back to sting you. Or maybe you are being hacked... otherwise you wouldn\'t make such a belligerant statement. I hope the latter is the case...',1626,'Gamer','2003-05-04 16:32:36');
INSERT INTO forumpost VALUES (833,127,4,'Re: auto-log out un-post','Maybe it\'s a punisment from God! :P (Just kidding)',1626,'Gamer','2003-05-04 16:34:28');
INSERT INTO forumpost VALUES (834,128,3,'Re: The existence of god','Please don\'t take offense to this: It\'s not true as it\'s in the Old Testament. (Genesis, at the end of Chapter 3)\r
\n\r
\n\"Then the lord levik said \"See, the man has become like one of us, knowing religion and atheism; and now, he might reach out his hand and take also from the take also from the tree of problems and solve, and participate forever. Therefore the lord levik sent him forth from the garden of this discussion, to till the problems from which he was taken. \"',1626,'Gamer','2003-05-04 16:46:53');
INSERT INTO forumpost VALUES (835,127,4,'Re: auto-log out un-post','Seriously, I think maybe there is something so that one place the web thinks you are logged in and one place that you aren\'t. I personally haven\'t ever had this happen to me, but I think your theory is a good one.',1626,'Gamer','2003-05-04 17:01:59');
INSERT INTO forumpost VALUES (836,128,3,'Re: The existence of god','If you think that God doesn\'t have any power, then it\'s easy to say that stories like Noah\'s disprove the stories of the Bible. However, if you want to pursue the question of how Noah took animals from all over the world on the ark, this question assumes that the world before the flood was like the world is today with animals specialized for certain areas. Today the world is 70% water and the oceans separate the continents. Also, some animals only live in a few selected locations. The Bible teaches that before the flood the water was gathered into one place (Genesis 1:9). There was probably one ocean and much more landmass. Also, if the climate was more temperate animals could live in all types of places which means Noah did not have to go gather animals from all over the world. In fact, the Bible says that the animals came to Noah (Genesis 6:20).\r
\n\r
\nMuch, maybe even most of the old testament defies natural explanation, from Noah and the ark to Moses and the plagues and the parting of the Red Sea. That is not to mention, of course, the story of creation itself. The God I believe in, however, is omnipotent and can do such things, and the debate over the possibilities of such miraculous events is really a non-issue.\r
\n\r
\nAnd yes, Alan, I think that belief in a god who is dead and has no power to do anything is quite piddly.\r
\n\r
\nI won\'t continue to repeat myself about why God\'s existence cannot be proven, scientifically. I myself have witnessed miracles, healings, and really nothing compared to what has happened. I\'m not talking about the old testament or in Jesus\' day, but go to Central and South America where bars and police stations are decaying from disuse, because of what God is doing there, and someone being raised from the dead is a commonplace sight. God most certainly does have an impact on our world, and your \'theory\' does not fit very well at all. Even if you don\'t believe in documented natural and medical miracles, the biggest impact God has is simply in peoples\' lives, daily. If you care to dismiss such miracles without any explanation except that you don\'t believe that God can do anything in the world, well, I\'m not sure I can help you there.\r
\n\r
\nNow, to evolution. Obviously, it cannot be proven, certainly as evolution or speciation has never been observed, nor have we even seen the emergence of a favorable trait that did not already exist as part of the gene pool for a species (think of Darwin\'s sparrows, Mendel\'s beans, or those moths in Alaska). Evolution has not been proven to any degree. There have been times when people thought it was, and then the evidence has been discredited, and people still believe what is now regarded as invalid. Textbooks still print it, as with Menkel\'s malproportioned drawings that are supposed to show the similiarities between embryos of humans and different species. He was forced in his own lifetime to publicly admit that his drawings were contrived and intentionally misdrawn to support embryologists, yet current textbooks still print his drawings as evidence of common ancestral evolution, in lieu of actual representations of the various embryos.\r
\n\r
\nPopular misconceptions such as this have led people to belive that evolution has been proven and there is proof to back it up, when really none exists. Other very popular misbeliefs regard the supposed evolution of humans from apes and \'homonid\' skeletons that have been found. All but three of the twelve specimens claimed to be links between man and apes have been shown to be either entirely apes, or entirely ancient human beings. The \'three\' were Nebraska Man, an entire species formed from a single tooth (only to be found later that it was a pig\'s tooth), Orce Man, based on the skullcap of a donkey, and Piltdown Man, a complete hoax that fooled the scientific community for years, which was an ape\'s jawbone placed with a human skull. Of the others, most were entire models formed only from partial teeth and jawbone fragments, and were actually nothing more than apes. Other more complete fossils, were also apes, such as the [in]famous Lucy and the four supposed members of the Australopithecus genus, were three feet tall and were examined with the conclusion that the skull had no human features at all. Homo erectus was thought to be less than human simply because early speculations were made that his brain appeared markedly smaller than that of a modern man. Now, it is admitted that \"there are men of marked intelligence walking about today whose brains are as small or smaller\" than that of Homo erectus. Cro-magnon Man were \"indistiguishable in body and brain\" from modern humans, and the skeleton used to create Neanderthal Man is identical to that of a modern elderly man with arthritis.\r
\n\r
\nAlso, since such a vast fossil record exists for dinosaurs and other ancient beings, as well as fossils of animals that are still alive today, how do you explain that there has never been found any species that is a link between two other species? Not only have no actual \'homonids\' been found, no transitional species of any supposed evolutionary step. An animal that is often cited as a link between dinosaurs and reptiles and birds is achaeopteryx, an ancient bird that had rows of tiny teeth. It was once believed to have solid bones, unlike the hollow bones of modern birds, and to have much more simple feathers. A complete skeleton found in 1977 showed that its bones were indeed hollow and it\'s feathers were barbed and identical in structure and composition to those of modern birds of flight.\r
\n\r
\nDarwin himself admitted that the biggest obstacle to \'proving\' evolution lay in the lack of fossil evidence. He stated in The Origin of Species that \"the geological record is extremely important and this fact will explain why we do not find intermediate varieties, connecting together all the extinct and existing forms of life by the finest graduated steps. He who rejects these views on the nature of the geological record, whill rightly reject my whole theory.\" He had complete faith that future evidence would eventually prove his theory. That has not happened; to the contrary, the geological record is more complete than ever (obviously, it\'s not becoming less complete) and the lines between different species are becoming more and more distinct.\r
\n\r
\nI never said that C-14 dating showed that humans and dinosaurs had lived together; rather, I said that the C14 dating methods used to say that dinosaurs lived so many millions of years ago (and before humans or other mammals) are erroneous and obsolete, although scientists commonly use selected examples to back up a particular point and disregard anything else.\r
\n\r
\nWhenever the worldview of evolution is questioned, this topic always comes up. Let me first explain how carbon dating works and then show you the assumptions it is based on. Radiation from the sun strikes the atmosphere of the earth all day long. This energy converts about 21 pounds of nitrogen into radioactive carbon 14. This radioactive carbon 14 slowly decays back into normal, stable nitrogen. Extensive laboratory testing has shown that about half of the C-14 molecules will decay in 5730 years. This is called the half-life. After another 5730 years half of the remaining C-14 will decay leaving only ¼ of the original C-14. It goes from ½ to ¼ to 1/8, etc. In theory it would never totally disappear, but after about 5 half lives the difference is not measurable with any degree of accuracy. This is why most people say carbon dating is only good for objects less than 40,000 years old. Nothing on earth carbon dates in the millions of years, because the scope of carbon dating only extends a few thousand years. Willard Libby invented the carbon dating technique in the early 1950\'s. The amount of carbon 14 in the atmosphere today (about .0000765%), is assumed there would be the same amount found in living plants or animals since the plants breathe CO2 and animals eat plants. Carbon 14 is the radioactive version of carbon.\r
\n\r
\nSince sunlight causes the formation of C-14 in the atmosphere, and normal radioactive decay takes it out, there must be a point where the formation rate and the decay rate equalizes. This is called the point of equilibrium. Let me illustrate: If you were trying to fill a barrel with water but there were holes drilled up the side of the barrel, as you filled the barrel it would begin leaking out the holes. At some point you would be putting it in and it would be leaking out at the same rate. You will not be able to fill the barrel past this point of equilibrium. In the same way the C-14 is being formed and decaying simultaneously. A freshly created earth would require about 30,000 years for the amount of C-14 in the atmosphere to reach this point of equilibrium because it would leak out as it is being filled. Tests indicate that the earth has still not reached equilibrium. There is more C-14 in the atmosphere now than there was 40 years ago. This would prove the earth is not yet 30,000 years old! This also means that plants and animals that lived in the past had less C-14 in them than do plants and animals today. Just this one fact totally upsets data obtained by C-14 dating. Also, the lower level of C-14 in the past would mean that a test performed today would seem to show that the specimen is much older than it really is.\r
\n\r
\nThe carbon in the atmosphere normally combines with oxygen to make carbon dioxide (CO2). Plants breathe CO2 and make it part of their tissue. Animals eat the plants and make it part of their tissues. A very small percentage of the carbon plants take in is radioactive C-14. When a plant or animal dies it stops taking in air and food so it should not be able to get any new C-14. The C-14 in the plant or animal will begin to decay back to normal nitrogen. The older an object is, the less carbon-14 it contains. One gram of carbon from living plant material causes a Geiger counter to click 16 times per minute as the C-14 decays. A sample that causes 8 clicks per minute would be 5,730 years old (the sample has gone through one half life), and so on.\r
\n\r
\nAlthough this technique looks good at first, carbon-14 dating primarily rests on two simple assumptions. They are, obviously, assuming the amount of carbon-14 in the atmosphere has always been constant, and its rate of decay has always been constant. Neither of these assumptions is provable or reasonable. An illustration may help: Imagine you found a candle burning in a room, and you wanted to determine how long it was burning before you found it. You could measure the present height of the candle (say, seven inches) and the rate of burn (say, an inch per hour). In order to find the length of time since the candle was lit we would be forced to make some assumptions. We would, obviously, have to assume that the candle has always burned at the same rate, and assumes an initial height of the candle. The answer changes based on the assumptions. Similarly, scientists do not know that the carbon-14 decay rate has been constant. They do not know that the amount of carbon-14 in the atmosphere is constant. Present testing shows the amount of C-14 in the atmosphere has been increasing since it was first measured in the 1950\'s. This may be tied in to the declining strength of the magnetic field. \r
\n\r
\nHow about these examples:\r
\nShells from living snails were carbon dated as being 27,000 years old. (Science vol. 224, 1984, pp. 58-61)\r
\nLiving mollusk shells were dated up to 2300 years old. (Science vol. 141, 1963, pp.634-637)\r
\nA freshly killed seal was carbon dated as having died 1300 years ago! (Antarctic Journal vol. 6, Sept-Oct. 1971, p.211)\r
\n\"One part of the Vollosovitch mammoth carbon dated at 29,500 years and another part at 44,000.\"\r
\n\"One part of Dima\" [a baby frozen mammoth] was 40,000, another part was 26,000 and the \"wood immediately around the carcass\" was 9-10,000. \r
\n(Troy L. Pewe, Quaternary Stratigraphic Nomenclature in Unglaciated Central Alaska, Geological Survey Professional Paper 862 (US Gov. printing office, 1975) p. 30.)\r
\n\"The lower leg of the Fairbanks Creek mammoth had a radiocarbon age of 15,380 RCY, while its skin and flesh were 21,300 RCY.\r
\n(In the Beginning, Walt Brown, p. 124)\r
\n\r
\nAlso interesting to note is radioactive dating of rocks. Of course, rocks do not take in CO2, nor do they die and stop taking it in. The use of potassium-argon (K-Ar) dating is used instead. The new lava dome of Mt. St. Helens was formed when it erupted in 1986. In 1997, five specimens were taken from this dome at five different locations and subjected to conventional Potassium-Argon dating. The results indicated ages of less than one half to almost three million years old, all from eleven year old rock. We know when this dome formed. When we date rock of known age we test the claims and we see obvious failures. But, when we date rock of unknown age, we are assured that the results are accurate.\r
\n\r
\nWhat I did say was that dinosaurs and humans co-existed. There have been trails of dinosaur and human tracks on top of each other that fossilized. People have tried to speculate that the human tracks were made millions of years later. Now, suppose you saw several footprints in a sidewalk and someone said, \"This print was made ten years after the one beside it.\" Would you buy that? No way! We understand that tracks in mud do not last long. To be preserved, they must be solidified rapidly, within days. Once the material hardens, the tracks are preserved and footprints will no longer leave an impression. Furthermore, exposed tracks weather rapidly. Therefore, we know the next layer was deposited immediately and rapidly. More than one such series of tracks have been found in different parts of Texas and Mexico. Also, ceramic sculptures, wall paintings, and tapestries from ancient peoples in Mexico and from Native American tribes show perfect representations of dinosaurs as we know today that they would have looked like. Most markedly, perhaps, are the models of Iguanadon, whose skeleton baffled scientists for nearly fifty years as to how to put it together correctly. Of course, ceramic figurines (ca. 800 BC-200 AD) from Acambro Mexico, have iguanadon and other dinosaurs perfectly represented. Finally, there are many instances of both human and dinosaur fossils that appear out of place in the geological record, either with respect to the supposed dates of the rocks they are found in or to other fossils in the same series of strata; such cases are usually overlooked.\r
\n\r
\nAs to your garble, Alan, about the new testament, that is more of a theological debate than a logical one as you have tried to make it. God the Father, Jesus, and the Holy Spirit are still three distinct persons or entities, but one God. I don\'t understand it, nor do I expect to be able to, ever, so of course I will not try to explain it. Jesus cried out, \"why have You forsaken me?\" because God had. Jesus, though having lived a perfect life, was bearing the weight of all sin for all mankind. That means that the wrath and anger God would have directed at us was directed at Jesus instead. The rest of your banter is confusing Jesus and God the Father with the entire Godhood; Jesus\' death as a man did not mean God was dead (maybe Hank\'s assumptions were accurate after all).\r
\n\r
\n.. Gamer, I have no idea what you\'re saying or what you\'re trying to say, if anything at all, so I am not going to respond to it other than this sentence.\r
\n\r
\nI look forward to further debate, but these are still nothing more than empty words. I cannot prove that God exists, and even if I could, it wouldn\'t mean anything unless you let it. Again I implore, ask God to make Himself real to you. I promise, that\'s all the proof you\'ll ever need.',1575,'DJ','2003-05-05 02:27:09');
INSERT INTO forumpost VALUES (837,127,4,'Re: auto-log out un-post','That\'s really weird - if you are logged in, you should be logged in no matter how many pages you open. Which browser are you on?',1,'levik','2003-05-05 06:11:42');
INSERT INTO forumpost VALUES (838,123,4,'Re: queue change vote','OK, starting tonight, the QW granularity will be set to 2. (That is only the first two problems of each user will get QW=1).\r
\n\r
\nLet\'s see if this increases our diversity.',1,'levik','2003-05-05 06:12:32');
INSERT INTO forumpost VALUES (839,126,7,'Re: HK engineer','Welcome Joe. I hope you enjoy your stay here. ',1,'levik','2003-05-05 06:22:28');
INSERT INTO forumpost VALUES (840,128,3,'Re: The existence of god','I personally find the whole argument very entertaining, you can actually tell a lot about a person based on their views and how they\'re defended. To put myself on the block here, I am a devout agnostic (hey - is that a paradox?). I have a lot of friends who are very religeous, and a lot of friends who are very atheist, and both groups know all the arguments of the \"other\" side, yet remain fast in their belief.\r
\n\r
\nThis topic really boils down to who can modify the pertinent information the best - I\'ve often seen long lists of comments supporting fervishly (is that a word, or is it feverishly) defending a position that they are not qualified to do. For example, I fully believe in evolution, but I\'m certainly not qualified to defend it. I don\'t read the journals or do the research, so it\'s just a belief. I also believe that if there IS a god, he\'s not going to care that I don\'t believe in him (it\'s like a human killing an ant that had the audacity to not scatter from his footstep - why would such an immensely powerful being care about my particular beliefs about him (or of course her!) - all of course granting that I lead a morally sound life (i.e. I don\'t break any of the \"rules\"), which I certainly do, at least for western religeons sake - I don\'t know about other religeons, because, frankly, I don\'t care (remember - I\'m agnostic right).\r
\n\r
\nAnyways, my point is this. This argument really will never be resolved, and I think a lot of people put way too much personal stake in being right on this one. It should be enough for the religeous among us to know that they\'re going to heaven or whatever, and it should be enough for the non-religeous to take the most of the one life here they get. All we accomplish is a bunch of people on one side offending a bunch of people on the other side and vice-versa, while the few in the middle become more exasperated by it.',775,'Cory Taylor','2003-05-05 07:02:04');
INSERT INTO forumpost VALUES (841,128,3,'Does God exist?','A:Does god exist?
\r
\nB:I think so.
\r
\nA:If God exists,then does the devil exist?
\r
\nB:If that is true,then God exists.\r
\nDoes God exist?',1660,'Tim Axoy','2003-05-05 07:33:41');
INSERT INTO forumpost VALUES (842,128,3,'Re: The existence of god','Basically what I meant to say in the first post was like what Cory said in his post, only apparently more confusingly.\r
\n\r
\nThe second paragraph was more of a joke... It\'s \"modified\" from a bible verse... saying what I thought in the first post.\r
\n\r
\nI personally am kind of an anti-convertist when it comes to religion. I know I wouldn\'t want anyone trying to convert me to another religion, and so I don\'t do it to others.\r
\n\r
\nPlease excuse me for not reading DJ\'s post, as I am not here to debate (Is that ok?)',1626,'Gamer','2003-05-05 10:01:37');
INSERT INTO forumpost VALUES (843,128,3,'Re: The existence of god','First of all (since this was a little unclear) this debate originated in the problem can or cannot.
\n
1. Simpler organisms came before more complex ones (This also means invertabraes came before vertabraes, therefore fossils would only start showing up when animals evolved into inveratabraes)
2.All animals come from parent animals. If you know gr.9 science you should know this. And don\'t try arguing where did the very first unicellular organism come from, because the theory behind that is that a chemical reaction took place creating it.
If time>30 then log-out active user else do nothing.
how was that?',1072,'Alan','2003-05-05 12:57:21');
INSERT INTO forumpost VALUES (846,123,4,'Re: queue change vote','thank you levik. I greatly appreciate such a change',1072,'Alan','2003-05-05 13:13:20');
INSERT INTO forumpost VALUES (847,128,3,'Re: The existence of god','Too much for you too... You didn\'t read MY post that you can\'t have a debate without hurting someone and name calling.\r
\n\r
\nI am not calling you malicious, but you aren\'t benevolent to your opponents either. Getting mad at others in discussion isn\'t going to solve anything. (It seems like you are using \"implied insults\" in your discussion)',1626,'Gamer','2003-05-05 13:19:33');
INSERT INTO forumpost VALUES (848,127,4,'Re: auto-log out un-post','I have had to log in when I first visitited the site... (in a while) I have never had to do that before...',1626,'Gamer','2003-05-05 14:51:53');
INSERT INTO forumpost VALUES (849,128,3,'Re: The existence of god','I honestly never meant to imply insults in my comment. and yes that truly is a perfect point. a debate canot go on without some anger, but without name-calling. If you ignore \"implied insults\" whose existence is dependent on the intentions of the user who typed the comments then there can be nothing. The only implied insult which i made (and i do apologize for being a hypocrite) would be in the second paragraph of my second post. I was angry at the fact that in his first post in this discussion he still called my belief piddly. Despite the fact i made it very clear in my first post that i didn\'t want this type of thing to go on.',1072,'Alan','2003-05-05 15:50:13');
INSERT INTO forumpost VALUES (850,128,3,'Re: The existence of god','I don\'t think you meant to be mean... I don\'t think you are being too insulting, just sounds way too mean (like the gr.9 science thing... \"Well tell what has MORE proof\", \"as you have said yourself\",) so on... Maybe that is neccesary, in which I will just walk away...\r
\n\r
\nNote to Alan: Don\'t go balistic on me (please), but how would you explain going from sentience to non-sentience, or from non-creation (of the universe and things like that) to creation. I was wondering about that, and you seem smart :)',1626,'Gamer','2003-05-05 16:20:53');
INSERT INTO forumpost VALUES (851,128,3,'Re: The existence of god','Don\'t worry famer, i\'ll be more than happy to explain. Well for going to non-sentient to non-sentient involves the growth of our brain. Technically there is never a point in time when we are non sentient or not alive. As we both know in reproduction a single sperm cell wil join with a single egg cell, both of which are living. when they join they are still living. Technically we are sentient as long as we are living, even oif as one cell. But its only when our brains develop we start to think and remember. As for the creation of the universe, no-one is for sure but i have my own theory which I will explain. At first in the universe there was nothing. Now this \"nothing\" cannot be looked at as a thing, so it has no size no dimension etc. Now all this nothing was \"trying\" to find something. All this nothing acted on eachother as a vacuum and this turned the nothing into energy. But the nothing is infinetely small, hence causing the big bang to be an infinetely small point of energy, because the \"nothing\" was infinetely small and this nothing is also infinite. (Infinite to the point where matter is as dense as possibl in an infiniteley small spot.',1072,'Alan','2003-05-06 03:51:23');
INSERT INTO forumpost VALUES (852,125,4,'Re: Bait and switch','Sorry I have neglected to post my views on this (thanks for prodding me, FL)\r
\n\r
\nI want to make clear that my views here only apply to when somebody completely changes a problem after getting some (positive) votes on it. This is of course unacceptable, but probably impossible to prevent in a good way. (I do not think that prohibiting someone from editing their own problem is a good way - if a particular user becomes this much of a problem, I would rather kick him/her off than inconvinience all the others to such an extent.)\r
\n\r
\nI have been toying with the idea of letting high-ranking users be able to edit others\' problems in some cases (for example if the author is a novice and cannot do this themselves, or they have not come to the site for some amount of time). However, this seems to me to be pushing too much responsibility onto scholars. (Wouldn\'t want people to think I\'ve gotten so lazy that I\'m trying to get them to run my site for me :)\r
\n\r
\nOn a marginally related note of \"reserving\" spots in the queue, I honestly do not see anything wrong with somebody completely changing a problem that has yet to be voted on (for example if a problem you submitted last week turned up on the site posted by someone else). Since the person probably made an honest mistake, there is no reason to make them wait all that time again.\r
\n\r
\nI know some people disagree with me on this, but that\'s just my view.',1,'levik','2003-05-06 05:38:44');
INSERT INTO forumpost VALUES (853,127,4,'Re: auto-log out un-post','The login is done by session - if you do not check the \"remember me\" box it will probably time out (and you will be logged out) after 30 minutes of inactivity.\r
\n\r
\nCheck the box when logging in and you should not see as many problems.',1,'levik','2003-05-06 05:44:57');
INSERT INTO forumpost VALUES (854,125,4,'Re: Bait and switch','I myself have replaced or exchanged some of my pending problems, and I appreciate the flexibility to do so. However, I have never done so after a puzle received responses/votes from others. If we lose the ability to edit our own problems, we won\'t be able to respond to the feedback of voters. On the other hand, if nothing is done, it is only a matter of time before bait and switch succeeds in getting a puzzle posted that no one voted for (perhaps someone did this already?). Perhaps a puzzle should be removed from the queue the instant it gets 3 TU so the author can\'t tamper with it?',1567,'Bryan','2003-05-06 07:19:04');
INSERT INTO forumpost VALUES (855,128,3,'Re: The existence of god','I posted this before, in the problem, but here goes again. This question by Ravi is a very good thought provocer. Anyone who beleives in a God sees this as simply sure, God can do anything. If he wanted to make a stone he coulnd\'t lift then he would. He would also then be able to make himself lift it. For people who choose not to beleive in a God as I have put it, that makes it a paradox, which is correct. Who are we to try and understand what we can\'t possibly understand. Not saying that we shouldn\'t try, but this is really very interesting when both sides agree and disagree at the exact same time with the exact same point. ',1947,'Jon','2003-05-06 08:46:37');
INSERT INTO forumpost VALUES (856,125,4,'Re: Bait and switch','The idea is to submit a problem called \"Space reserver\", which isn\'t a problem at all, just there until I think of a problem. This would \"save\" a spot in the queue for when I think of a puzzle.\r
\n\r
\nI agree with Bryan :)',1626,'Gamer','2003-05-06 12:12:06');
INSERT INTO forumpost VALUES (857,128,3,'Re: The existence of god','One important key to the success of the human race is to try to figure everything out, and as one principle everything in the universe obeys the laws of existence(as i call it). Now the laws of existence, are the boundaries of what thibngs can and cannot do. Humans do not have a perfect grasp on the laws of existence but yet we are at a start. physics, relativity, electricity. We MUST keep on trying to understand everything. I\'m sorry but sitting back and saying \"God just did it\" isn\'t good enough for me. Look at the amish for example. Would you like to be an amish person? Would you like to be bound by your beliefs. My beliefs are set up in such a way that the ability to uncover the laws of existence are not bound by my beliefs.
\n\r
\nTo me it sounds like the core difference in Alan and DJ\'s viewpoints is that DJ has \'faith\' whereas Alan has \'beliefs\'. \r
\n\r
\nSince DJ is quoting the book of Genesis I assume that he is some form of Christian (Catholic, Protestant, Methodist,....) and as such has faith that the Christian bible contains the true explanation of creation. Therefore, if the bible says that \"God did it\", then DJ\'s faith means that he believes that God did it.\r
\n\r
\nAlan on the other hand has taken information from numerous sources and constructed his own belief system which is subject to change as knowledge of the laws of existence change. Although he is a Catholic he does not believe in the holy trinity - therefore does not have faith that the bible contains only truth. Instead he\'s taken what he believes to be the most rational explanations currently existing to form his belief system, such that should a more rational explanation appear (eg firm proof that the Egyptians were really a race from another planet from which humans are descended) then his beliefs will change accordingly.\r
\n\r
\nRegarding the comments on utopia, I see this as more a state of mind than a physical world. I agree with Gamer\'s inference that the Amish are close to their version of utopia. They are surrounded by people who share their beliefs and goals, they work to the common good rather than working for themselves, and although they are aware of the \'progress\' made by the world outside they only accept new ideas if they firmly believe that they will make their lives simpler and the community stronger.\r
\n\r
\nAs a final thought, why is it that when there is any debate on the existence of god it is always the Christian god that is debated? Nobody ever seems to argue about the existence of Shiva, Brahma, Vishnu, Jupiter, Zeus, Odin.... ',1183,'fwaff','2003-05-06 23:49:02');
INSERT INTO forumpost VALUES (862,128,3,'Re: The existence of god','So-called \'rational\' thought will only take you so far. Quantum mechanics places limits on what we can measure in a lab. Goedel\'s Theorem places limits on what we can mathematically prove. The Halting Problem places limits on what computers as we know them can compute. The laws of science are still constructed on faith: faith in what you\'ve read, faith in your own senses, faith that the laws still held true while nobody was watching, and faith that they will continue to work in the future.\r
\n\r
\nScience has no good definition of sentience, even though it\'s something everybody (well, I\'m making an assumption about people whose minds I can\'t read) experiences. Science has not provided any kind of halfway-decent explanation for humor. I don\'t think any Judeo-Christian religion has really addressed whether God has a sense of humor, even though it could profoundly reflect on how people relate to him.\r
\n\r
\nThere are internal contradictions within the Bible. To me, that is sufficient evidence that it should not be taken as a perfect text - an approximation at best and an anthology of fiction at worst. This, however, does not disprove the existence of God, only a particular view of Him.\r
\n\r
\nI think it is arrogant for any being as puny as ourselves to claim to understand the infinite. There\'s a lot that we don\'t know. There\'s a lot that we can never know if we continue to cling to tried-and-true assumptions. That means there are a lot of places for God, if he exists, to hide: in the spontaneous creation and destruction of particle-antiparticle pairs, in good jokes told at a party, or in your own (for lack of a better word) soul. Who are we to say he\'s not there?',103,'friedlinguini','2003-05-07 04:08:06');
INSERT INTO forumpost VALUES (863,128,3,'Re: The existence of god','I mostly agree with FL, though regarding the Bible I lean toward the \"anthology of fiction[mostly]\" end of the scale. Perhaps finding God in one\'s soul could be translated as finding Brahman in Atman, just to get out of our western views on the subject, and preconceived notions of what God is like.',1301,'Charlie','2003-05-07 08:25:54');
INSERT INTO forumpost VALUES (864,128,3,'Re: The existence of god','Yes fl you\'ve made a very good point. Is this debate wrapped up now? Anyways about sentience. (Since it seems to come up a lot) i think i\'ll give a bit of input on that. I consider sentience to be the fuctioning of a cell nucleus. Why? Well as we all know thoughts are created by patterns of neurons fired off inside of cells. What controls these explosions. commands from the nucleus of the cell. There really is no difference between the working of one nucleus as opposed to another. The only reason people think we\'re in a state of non-sentience is because our body\'s develop the memory portion later in our life. According to the cell theory, all cells come from pre-existing cells. So technically we are never in a state of non-sentience (until after we die if we have not reproduced) The only thing that can be debated about is the first cell, which was believed to have been created by chemical reactions.
\n\r
\nI found you via Google. I think I have solved one of the puzzles that does not yet show a solution. Do I propose my solution in the form of a remark, or is there a special \"enter solution\" function?\r
\n\r
\nLooks like a fun site.\r
\n\r
\nHS',2171,'Hank Schutz','2003-05-07 12:17:45');
INSERT INTO forumpost VALUES (866,129,7,'Re: Greetings and ??','Welcome to the site!\r
\n\r
\nJust post your solution as a comment. Please don\'t reveal the solution in the comment header.',103,'friedlinguini','2003-05-07 12:41:20');
INSERT INTO forumpost VALUES (867,130,7,'Newbie','Hey there!\r
\n\r
\nI\'m new here, I found this site by going to google and typing in logic puzzles. I haven\'t checked out any puzzles yet, but this site looks pretty cool! \r
\nI\'m a CSR at a call center, have a serious boyfriend who I love very much. :)\r
\nI love challenging puzzles. I also love to read and watch movies.',2180,'Cara','2003-05-08 08:14:06');
INSERT INTO forumpost VALUES (868,130,7,'Re: Newbie','Hi :) I am only an apprentice, but I still like it here :) It\'s cool :)',1626,'Gamer','2003-05-08 12:03:07');
INSERT INTO forumpost VALUES (869,130,7,'Re: Newbie','Well, that\'s good. :) I\'m glad it hasn\'t gotten boring. I read through a lot of stuff already, and I like some of the questions. I find I really like the riddles. I\'m trying to think up something to submit now. :)',2180,'Cara','2003-05-09 03:52:42');
INSERT INTO forumpost VALUES (870,125,4,'Re: Bait and switch','Yeah, what I did (once only) was submit a technical problem and solution, then discovered I had an over-simplified answer, and not enough time to figure out what the correct answer was. Rather than change my problem statement to \"Sorry, guys, give this 3 TD, I screwed up\" I replaced it with the next puzzle I came up with. Now that I think about it, however, I might just put that statement there next time and put my new puzzle at the end of the queue. Hmmm...',1567,'Bryan','2003-05-09 10:28:21');
INSERT INTO forumpost VALUES (871,125,4,'Re: Bait and switch','Yes... I notice what Bryan means... I was just saying that was a major problem for anyone who hadn\'t seen.\r
\n',1626,'Gamer','2003-05-09 11:21:12');
INSERT INTO forumpost VALUES (872,131,7,'Silly Jilly','I am a new one!',2196,'Silly Jilly','2003-05-10 11:40:39');
INSERT INTO forumpost VALUES (873,128,3,'Re: The existence of god','I think anyone visiting here and intrigued by this should read the posts to the \'Can or Cannot\' paradox as well. ',2174,'Vinodhan Selvarajalu','2003-05-11 03:22:01');
INSERT INTO forumpost VALUES (874,128,3,'Re: The existence of god','well its rather quite funny, as this debate started by those very comments',1072,'Alan','2003-05-11 10:29:11');
INSERT INTO forumpost VALUES (875,131,7,'Re: Silly Jilly','Wellcome to the site, Silly. (Can we call you Silly?) :)',1,'levik','2003-05-11 11:15:00');
INSERT INTO forumpost VALUES (876,100,4,'I have not hacked into Bryan\'s account!','Charlie,mind your post!',1660,'Tim Axoy','2003-05-11 13:11:48');
INSERT INTO forumpost VALUES (877,100,4,'Re: Discovered leviks login password','Nope, but somebody possibly hacked into both of your posts.',1626,'Gamer','2003-05-11 14:47:23');
INSERT INTO forumpost VALUES (878,100,4,'New forum or not','Is this a new forum?\r
\nI just saw it recently.',1660,'Tim Axoy','2003-05-12 02:18:25');
INSERT INTO forumpost VALUES (879,100,4,'Bryan!','Bryan,I saw The Odd Pillar was your problem.\r
\nYou wanted to submit a solution,but you did not want others to see you submitted it to your own problem.\r
\nTherefore,you went under my name.\r
\nRavi Raja thought it was me,and said,\"Oh My God!\"',1660,'Tim Axoy','2003-05-12 02:22:17');
INSERT INTO forumpost VALUES (880,131,7,'Yes.','You can call me silly.\r
\nMotto:I am so silly.',2196,'Silly Jilly','2003-05-12 02:32:50');
INSERT INTO forumpost VALUES (881,100,4,'Re: Discovered leviks login password','Tim, this forum is not new, but becomes available only when you reach Apprentice level, which is why you only noticed it recently.\r
\n\r
\nThat was not Bryan who did the posting of that solution, but a hacker, who apparently hacked not only Bryan\'s account but yours as well, so he could delete Bryan\'s solution from the official answer, and post it under your name.\r
\n',1301,'Charlie','2003-05-12 04:09:31');
INSERT INTO forumpost VALUES (882,100,4,'Other forums?','Are there any other forums here,Levik,that I am not seeing?',1660,'Tim Axoy','2003-05-13 03:06:10');
INSERT INTO forumpost VALUES (883,100,4,'Re: Discovered leviks login password','Yes. there\'s the \"You have to be 13 to read this\" forum, and the \"Everyone whose name doesn\'t start with a T\" forum, and of course the \"Super Secret\" forum.\r
\n\r
\nCrap. I probably should not have said anything about the \"Super Secret\" forum.\r
\n\r
\nSeriously though, this is it. No more hidden forums :)',1,'levik','2003-05-13 11:32:01');
INSERT INTO forumpost VALUES (884,106,4,'Luvya2003 must love 2003!','Yes!',1660,'Tim Axoy','2003-05-13 13:24:02');
INSERT INTO forumpost VALUES (885,49,4,'Solved lock puzzle','I solved lock puzzle.\r
\n',1660,'Tim Axoy','2003-05-13 13:28:45');
INSERT INTO forumpost VALUES (886,132,4,'When do I get to see the hidden forums?','Look at title.',1660,'Tim Axoy','2003-05-13 13:29:48');
INSERT INTO forumpost VALUES (887,132,4,'Re: When do I get to see the hidden foru','Would anyone care to field that one?',1,'levik','2003-05-14 05:23:36');
INSERT INTO forumpost VALUES (888,133,6,'Programming for 1000 digit numbers?','Does anybody know where I can find a programming environment capable of 1000 digit numbers?',NULL,'Brian Smith','2003-05-14 06:01:55');
INSERT INTO forumpost VALUES (889,132,4,'Please answer.','Please tell me when.',1660,'Tim Axoy','2003-05-14 06:09:10');
INSERT INTO forumpost VALUES (890,132,4,'Re: When do I get to see the hidden forums?','Never Tim, because there are no other Forums other than the ones which you can see. \r
\n(1) General Discussions\r
\n(2) Commons\r
\n(3) Reference\r
\n(4) New Users \r
\n(5) Library\r
\n\r
\nThat\'s it.',979,'Ravi Raja','2003-05-14 06:09:42');
INSERT INTO forumpost VALUES (891,133,6,'Re: Programming for 1000 digit numbers?','UBASIC. \r
\n Try http://archives.math.utk.edu/software/msdos/number.theory/ubasic/.html\r
\n(looks odd, but that was copied from the browser)\r
\n\r
\nOther sites have it and also show up in a Google search for UBASIC.',1301,'Charlie','2003-05-14 06:12:03');
INSERT INTO forumpost VALUES (892,132,4,'Tricked!','I thought there was the 13 and older and People whose names do not start with T and The secret one.',1660,'Tim Axoy','2003-05-14 07:32:32');
INSERT INTO forumpost VALUES (893,134,4,'I have a question','What was the first problem ever submitted on this site?\r
\nLevik might know the answer.',1660,'Tim Axoy','2003-05-14 07:34:39');
INSERT INTO forumpost VALUES (894,133,6,'Re: Programming for 1000 digit numbers?','It\'s a popular tool, so I\'m sure there is freely-available code for whatever language you like.',103,'friedlinguini','2003-05-14 08:45:41');
INSERT INTO forumpost VALUES (895,133,6,'Re: Programming for 1000 digit numbers?','To clarify about UBASIC in particular: It\'s a language and environment in itself, that handles over 2000-digit numbers as part of its regular structure. It isn\'t an add-in for a language.',1301,'Charlie','2003-05-14 09:42:04');
INSERT INTO forumpost VALUES (896,132,4,'Re: When do I get to see the hidden forums?','Shhh! Don\'t tell Ravi!',103,'friedlinguini','2003-05-14 10:23:38');
INSERT INTO forumpost VALUES (897,132,4,'Tricked?','Are those REAL forums or not?',1660,'Tim Axoy','2003-05-14 12:54:25');
INSERT INTO forumpost VALUES (898,132,4,'Re: When do I get to see the hidden forums?','no (at leats i don\'t think so) and fl\'s post was just a joke(quite a funny one i might add)',1072,'Alan','2003-05-14 16:06:02');
INSERT INTO forumpost VALUES (899,134,4,'Re: I have a question','I believe the first day flooble opened multiple questions were posted by levik (on 2002-03-28) As for the VERY first one idono. Levik?',1072,'Alan','2003-05-14 16:09:50');
INSERT INTO forumpost VALUES (900,88,4,'Re: problem difficulties','I would appreciate it if we could all weigh in on this subject, as it seems to me that roughly half the difficulty levels I see assigned are too high (IMHO). In an effort not to be the self-appointed difficulty gestapo, I restrain myself from commenting on the difficulty level proposed for each problem I see, but much of the time I am just biting my tongue.\r
\n\r
\nI really like Cory\'s suggestion. In addition, I recommend a definition of difficulty levels be available somewhere on the site, using examples to show what makes something a difficulty level 1, 2, 3, 4, or 5.\r
\n\r
\nIs this topic important to others, or is it just my pet peeve (and Cory\'s)?',1567,'Bryan','2003-05-15 04:52:17');
INSERT INTO forumpost VALUES (901,88,4,'Re: problem difficulties','I like the voting idea as well. I think it has a strong parallel with the problem ratings except that I think that it should be possible for the original poster to rate the difficulty, and for queue moderators (for lack of a better term) to do so as well.',103,'friedlinguini','2003-05-15 06:26:26');
INSERT INTO forumpost VALUES (902,77,4,'I am almost Journeyman!','1 more problem till me being Journeyman!',1660,'Tim Axoy','2003-05-15 10:12:14');
INSERT INTO forumpost VALUES (903,88,4,'Re: problem difficulties','Yes, it\'s probably a good idea for the moderators to be able to vote on difficulty level. Also a good idea to have sample problems of the various difficulty levels in the different categories, as a model for difficulty levels.',1301,'Charlie','2003-05-15 10:52:10');
INSERT INTO forumpost VALUES (904,88,4,'Re: problem difficulties','Yes but don\'t forget a person could fall into a problems trap and assume the easiest solution (e.g ameoba colony i think or some other one were u start off with 2 amoebas and every minute they split into 2 more) anyways a voting system sounds good, But the submitter\'s opinion of the difficulty should be worth so much more. (lets say the equivalent of 3 results) so that if the 3 other users (the ones giving thumbs up) all choose something else (which they agree on) with one other person, the difficulty will be changed',1072,'Alan','2003-05-15 11:37:23');
INSERT INTO forumpost VALUES (905,88,4,'Re: problem difficulties','My proposal:\r
\n\r
\nDifficulty voting can only be done while the problem is in the queue. \r
\n\r
\nJourneymen+ who can TU/TD a problem can also vote on a difficulty.\r
\n\r
\nYou can ONLY vote on a difficulty after you TU\'d a problem. Clearing/reversing the TU removes your vote.\r
\n\r
\nEach person\'s difficulty vote (if any) will be shown next to their TU comment.\r
\n\r
\nOriginal submitter\'s opinion counts for more. Currently I think this should be 66% of the vote if 1-2 votes, 50% if 3-4 votes and 33% if 5+ votes. Or we could just do what Alan said and make submitter count as 3 people.\r
\n\r
\nWhile the problem is in the queue, it will show the submitter\'s original difficulty at the top, plus current calculated \"voted\" difficulty at the bottom. \r
\n\r
\nWhen the problem is pushed, it\'s actual difficulty is updated to the calculated one.\r
\n\r
\nOr do you think we should retain the originally submitted difficulty as well?\r
\n\r
\nFinally, I do not think giving \"reference\" problems for difficulty is a good idea. It is way too subjective a matter, and really should be approached on a case by case basis. One thing I want to stress is that if the problem is solved in 10 seconds with integral calculus, it is not a difficulty 1 problem (actually, it should probably not be on this site to begin with).',1,'levik','2003-05-15 11:54:01');
INSERT INTO forumpost VALUES (906,135,4,'Are we self running?','I am going to be going on vacation early in july, and will not be administering the site in that period of time (about a week).\r
\n\r
\nSince this disastrous turn of events happened last year, I have tried to make this site be able to operate at least for brief periods of time without my intervention.\r
\n\r
\nRight now, the only thing I can think of that would be an issue in my absense, is the posting of solutions - usually I \"enable\" them manually 3-4 days after the problem goes live, but this is done through an admin interface that noone else has access to. \r
\n\r
\nHigher ranked users can \"push\" the solutions to their own problems, but I would love to resove this issue to generalize it for everyone\'s problems. (Also maybe I will get to address allowing high-levelers to edit other\'s problems, as well as anything else you guys think is needed.) \r
\n\r
\nI am bringing it up this far in advance so that hopefully we can come up with a solution and I can implement and see the inevitable flaws in it (and maybe even fix them!) by the time I have to leave.\r
\n\r
\nIn any case, here\'s your chance to chime in on how you think the site should be run democratically :)',1,'levik','2003-05-15 12:02:08');
INSERT INTO forumpost VALUES (907,88,4,'Re: problem difficulties','I have a minor quibble with forbidding difficulty changes once the problem goes live, but only a minor one. Other than that, it sounds good to me.',103,'friedlinguini','2003-05-15 12:56:25');
INSERT INTO forumpost VALUES (908,135,4,'Re: Are we self running?','Why not just push solutions automatically after, say, 96 hours?',103,'friedlinguini','2003-05-15 13:13:59');
INSERT INTO forumpost VALUES (909,135,4,'Re: Are we self running?','Yes, I like fried\'s idea... \r
\n\r
\nWould a manual override feature for the solutions be good for the lower classes? For example if someone posted a hard (but solvable) puzzle that nobody got in 3-4 days...?',1626,'Gamer','2003-05-15 15:01:57');
INSERT INTO forumpost VALUES (910,77,4,'Re: Congratulations to me','Me too Tim! *Sigh* It moves so slowly...',1626,'Gamer','2003-05-15 15:02:32');
INSERT INTO forumpost VALUES (911,88,4,'Re: problem difficulties','I think we need a level to base things on... I am always confused \"Is this a level 1 problem... level 2?) I never know what level mine is... and would really appreciate journeymen able to tell me :)',1626,'Gamer','2003-05-15 15:05:36');
INSERT INTO forumpost VALUES (912,136,4,'Duplicate solutions','I think there should be something around to tell users to read the posts before giving a solution of their own, particularly with the \"light bulb\", because I see many of the same exact solution (particularly with problems that have one set answer) in a problem. I understand that sometimes people may submit a solution at the same time, but this is in the far minority.',1626,'Gamer','2003-05-15 15:08:58');
INSERT INTO forumpost VALUES (913,137,7,'Hi all','Hello friends,\r
\nplease welcome me to the Group.\r
\n\r
\nAbout me, I am a software engineer. And i love to solve puzzles which improves my aptitude. I just started making this as a habit.\r
\n\r
\nI came to know about this site through Google search.\r
\n\r
\ncheers,\r
\nSwaroop',2237,'swaroop','2003-05-15 20:03:56');
INSERT INTO forumpost VALUES (914,136,4,'Re: Duplicate solutions','I believe that this should not be done. People want the satisfaction of posting a solution before seeing one anywhere else. \r
\n\r
\nThis also makes people post wrong solution which can yield interesting discussion. If I solved a problem, I would definitely be tempted to go and post my solution first, and look at others\' later.\r
\n\r
\nBesides, realizing that you have already read this solution should not take more than a few seconds.',1,'levik','2003-05-15 20:54:06');
INSERT INTO forumpost VALUES (915,135,4,'Re: Are we self running?','fried: solutions are not always correct, not always properly formatted, and actually not even always there. Automatically pushing them would be asking for trouble unless there were quite a few other rules involved.\r
\n\r
\nGamer: not sure what you are talking about.',1,'levik','2003-05-15 20:55:44');
INSERT INTO forumpost VALUES (916,135,4,'Re: Are we self running?','The easiest answer is simply to not push any solutions until you get back. Not exactly desirable, but I don\'t think anybody will panic too much.\r
\n\r
\nQuestionable solutions may not be such a bad thing. It\'ll only be for a week, and we could debate solutions in the comment area anyway.\r
\n\r
\nIf you want solutions to be checked, there\'s going to have to be moderation of some kind. You could check a bunch of problem solutions yourself, mark the ones you deem acceptable, and then only show those in the queue while you\'re gone. That way, you could post solutions automatically. I imagine that would be the simplest moderation solution from a coding standpoint.\r
\n\r
\nIf you want us checking solutions, you\'ll have to decide whether you want it to be before the problems are pushed, after, or both. That implies at least one new page. How comfortable are you with the idea of some people being able to look at solutions before they\'re official?',103,'friedlinguini','2003-05-16 04:08:06');
INSERT INTO forumpost VALUES (917,88,4,'Re: problem difficulties','Finally my wait is over...\r
\n\r
\nSince this now seems to be a topic of discussion, I will continue on. I like the idea that the submitter gets a more heavily weighted vote than the rest of us, however, under Leviks proposal which would seem a fair way to do this, I would change one thing. First, realize that only in very rare cuircumstances do problems get more than 4 TU\'s, which means that the user\'s chosen difficulty level is realistically going to dominate most situations, and this could very easily be exploited (consider if someone, for whatever reason, really wanted to have a puzzle posted at level three - if they submit it as level 5 and 4 TU-ers vote for level one, this makes the problem a three). I would suggest either a smaller weighting (such as worth 1.5 votes) to the submitters pick, or opening the difficulty to all who don\'t vote TD, which could increase the number of votes on a problem dramatically. I\'d personally prefer the first solution, as the second could again be easily used unfairly (I envision a world where people are one-ing other problems when they disagree with a consensus that the problem should go live...)\r
\n\r
\nOn the matter of reference problems, I agree completely with Levik. While in principle I agree that this might make things more clear, the subjective nature is in fact the very root of this problem. If a person has difficulty picking a difficulty level fairly, they will likely also have difficulty matching it to a very discreet problem set example (which of course could be quite arbitrarily ranked to begin with).\r
\n\r
\n',775,'Cory Taylor','2003-05-16 04:22:42');
INSERT INTO forumpost VALUES (918,137,7,'Re: Hi all','Welcome to the site Swaroop. \r
\n\r
\nDo I hear an accent? :)',1,'levik','2003-05-16 04:23:46');
INSERT INTO forumpost VALUES (919,135,4,'Re: Are we self running?','Levik you can vote a TU on those problems (after going through their solutions)which are yet to come up in the queue, that is, which are still in the pending problems list and are expected in the queue within three or four days (during the time of your leave) and also you can approve those problems too which are there in the queue just before you are planning to leave, so that the Scholars can push those problems up on the site and when required, and their solutions too and this can easily continue for about a week or two.\r
\n\r
\nSo all that I want to say is that before leaving, you can go through those problems in the queue and also in the list of pending problems (which are expected in the queue in the very next few days, that is with QW 1, 2 or 3, or so), whose solutions are provided by the submitter(s) of the corresponding problems and vote them a TU (the FIRST vote will be from you) so that the Scholars and the Journeymen can understand that the problem for which you have voted has a proper solution and in your absence the solution too can be made public and I believe that if this method is applied, then neither problems will remain hung up in the queue nor there will be any confusion regarding the posting of solutions, I mean making solutions public.\r
\n\r
\n(Once again, I am sorry if I have not been able to explain properly what I want to say, and if it is really so, then PLEASE do let me know so that I can again frame the entire thing in a proper manner and re-write it).\r
\n\r
\nThank You.',979,'Ravi Raja','2003-05-16 05:17:24');
INSERT INTO forumpost VALUES (920,135,4,'Re: Are we self running?','This solution could work as long as there aren\'t ten or more problems without acceptable solutions to come up in the next few days.',103,'friedlinguini','2003-05-16 05:59:04');
INSERT INTO forumpost VALUES (921,88,4,'Re: problem difficulties','I would think that if voting on the difficulty of a problem were included with voting thumbs up, more people would be inclined to vote on a problem that already had say 4 thumbs up. As it is now, there\'s not much incentive to add one more vote, but in the changed circumstances there would be.\r
\n\r
\nPerhaps levik, as well as the originator, could also have 3 votes.\r
\n\r
\nPerhaps also, even the dissenters, who vote thumbs down, should have a vote on the difficulty level.',1301,'Charlie','2003-05-16 06:02:47');
INSERT INTO forumpost VALUES (922,135,4,'Re: Are we self running?','I think we should just have one person given the ability to post solutions. I nominate Friedlinguini for this position of authority. Also, do we have enough scholars? I know charlie and friedlinguini are both around enough to maintain the site but is 2 enough, things can happen and they happen quite easily',1072,'Alan','2003-05-16 10:09:15');
INSERT INTO forumpost VALUES (923,88,4,'did I do that','Everyone seems to be talking about problem referncing. Did i say that. I never said to compare to a problem but my point about ameoba colony was that when i saw it i would\'ve said \"57 minutes is the answer, duh\" and given it a 1 difficulty vote, despite the fact the answer is actually half an hour. Also seeing as how levik is leaving for vacation should this be something that is only implemented afgter he gets back?',1072,'Alan','2003-05-16 10:15:22');
INSERT INTO forumpost VALUES (924,100,4,'Alan,mind your post,too!','In your post(the tenth post from the top),you said I took Bryan\'s account.\r
\nI did not!',1660,'Tim Axoy','2003-05-16 10:44:22');
INSERT INTO forumpost VALUES (925,135,4,'Re: Are we self running?','While putting me in charge of something like that might make a decent stop-gap measure, what I gathered from the thread topic was that the goal was to come up with a system that didn\'t rely on any one person - I certainly don\'t want that responsibility every time levik leaves town, and we shouldn\'t have to elect someone every time he does either.',103,'friedlinguini','2003-05-16 13:14:50');
INSERT INTO forumpost VALUES (926,135,4,'Re: Are we self running?','Well Fried, in that case the users should be asked to submit the solutions to those problems too during that time so that they can be approved. Levik should either post such a comment in the forums for them or a mail to all with the same text must be sent to only those users whose problems are there in the queue without solutions. I don\'t think there\'ll be many of them. And after all a mail with the same text is to be sent to them asking them to submit the solutions to their problems so that they can be approved. I think that the users will co-operate with us. \r
\nIf in case the solution is not provided, then I think that the scholars can themselves look after those problems. Just see the solution of my problem \"Fathers and Sons\". This is not the only one but there are many other problems whose solutions were not provided by me but was posted by someone else, may be Levik only, (I don\'t know for sure by whom) and the reason was that those problems had unique answers and everyone was sure of the answer. So, we can push only those problems up on the site (from the queue) whose answers we know for sure, even if they are not provided by the submitter. The rest is all that I have explained in my previous post/comment. \r
\nIf I am going wrong anywhere, please do point out my mistake. This was a suggestion/idea for this topic from my part. Let\'s see what others have to say for this.\r
\nThank You.',979,'Ravi Raja','2003-05-16 19:15:46');
INSERT INTO forumpost VALUES (927,137,7,'Re: Hi all','Hey swaroop. Welcome to the site :o)',1919,'Lewis','2003-05-16 21:47:30');
INSERT INTO forumpost VALUES (928,138,7,'just came across.......','hi....\r
\nwell, I came across this site through a friend of mine. He asked me a few qurs and here i am...',2246,'abhi','2003-05-16 23:36:39');
INSERT INTO forumpost VALUES (929,138,7,'Re: just came across.......','Do you know the username of the friend that got u here? just wonderin who it is. Hope u enjoy it here',1072,'Alan','2003-05-17 07:04:08');
INSERT INTO forumpost VALUES (930,100,4,'Re: Discovered leviks login password','i\'m sorry tim. I was merely trying to slve a situation. I apologize for falsely accusing you',1072,'Alan','2003-05-17 07:06:10');
INSERT INTO forumpost VALUES (931,17,6,'Re: HTML codes for use on the site','p\r
\n
\nbr
\r
\nb\r
\ni',1660,'Tim Axoy','2003-05-17 07:14:28');
INSERT INTO forumpost VALUES (932,135,4,'Re: Are we self running?','Friedlinguini makes a very good point about not having the site run on one person, but in fact it needs to be run by a group of people. The more people + The more abilities those people have = the more efficiently the site will run. So I think that one more rank should be added like scholar+ (Or whatever name it should be given.) and that fried should be promoted to this rank) Also ravi could be promoted to scholar. That would give us 2 scholars that log on frequently, one scholar+ and a couple of journeymen,(me, dj, gamer, and anyone else i missed) Technically this is still running on the concept of having one person running the site (FL) but (fl) i think you log on enough to solve most of these issues right? also charlie could become a scholar+ as well. Having 3 responsible, scholar abilitied users (Fl, ravi and charlie) along with a bunch of apprentices (as mentioned before) the site should run very smoothly. Also at the submit a problem screen instead of puuting \"solution (optional)\" it should be something along the lines of \"Solution (optional, but without your problem may get deleted)\" if these changes are made then the site should be totally elf-running',1072,'Alan','2003-05-17 07:19:44');
INSERT INTO forumpost VALUES (933,135,4,'Re: Are we self running?','I don\'t think I will ever get my final problem to the queue! :D\r
\n\r
\nI agree... I think something like Solution(reccomended), because otherwise people might not submit puzzles that they don\'t know the answer to, but would be interesting.',1626,'Gamer','2003-05-17 10:51:19');
INSERT INTO forumpost VALUES (934,135,4,'Re: Are we self running?','Alan - I do not think we need another group of users. Any new \"abilities\" can be added to one of the existing groups (in this case mostly Jorneyman and Scholar)\r
\n\r
\nFor the solution issues, I was actually thinking of a queue-like page of unsolved problems. Once the problem is on the site say 3 days and has no posted solution, it would appear the the solution queue, and it\'s submitted solution would become visible to Journeymen and Scholars who wish to look at it.\r
\n\r
\nAt this point I am not sure if we need voting for something like that - right now I am only thinking of letting Journeymen post notes on the solution - and a scholar can \"publish\" the solution once the problem has had it visible for at least a day.',1,'levik','2003-05-17 13:48:37');
INSERT INTO forumpost VALUES (935,124,7,'How I found this site','I found this site searching for logic problems,too.\r
\n',1660,'Tim Axoy','2003-05-17 14:36:24');
INSERT INTO forumpost VALUES (936,135,4,'Re: Are we self running?','That sounds like a good idea levik. I\'ve wondered about quality control on submitted solutions. A gather that you at least sometimes (always?) look at the submitted solution before posting it. Vetting by Journeymen and Scholars is a good idea. Though in the case of the recent Pentagon problem, it was only a clue the originator provided that allowed a solution (at least on my part), so a reading of the solution would have spoiled some fun. But of course knowing the schedule the originator could time his clue accordingly. In this instance I think the clue came after 2 days any way, so a third day revelation of the solution would not have cut off solving.',1301,'Charlie','2003-05-18 05:11:16');
INSERT INTO forumpost VALUES (937,139,7,'caio','Hello everyone. My name is Jackie. I am a nineteen year old college junior majoring in Art and in Economics (odd combo, huh?) Well... I found this site on google as I was looking for logic problems. I look forward to challenging my mind on this site :)\r
\n-arrivederci ',2256,'Jackie','2003-05-18 06:40:41');
INSERT INTO forumpost VALUES (938,139,7,'Re: caio','good luck and welcome aboard!',775,'Cory Taylor','2003-05-18 07:30:27');
INSERT INTO forumpost VALUES (939,17,6,'DoubleRe: HTML codes for use on the site','pp\r
\n
\nbrbr
\r
\nbb\r
\nii',1660,'Tim Axoy','2003-05-18 07:47:41');
INSERT INTO forumpost VALUES (940,130,7,'Re: Newbie','wow... scary... first day here and i already see a familiar name... whell.. dun knoe you personally... but hey my name\'s cara too... lol... haf a nice day!',2259,'calla tah-n','2003-05-18 20:55:54');
INSERT INTO forumpost VALUES (941,140,4,'MAIN CHARACTER','Who do you think is the main character in my problems?',1660,'Tim Axoy','2003-05-19 02:09:33');
INSERT INTO forumpost VALUES (942,141,4,'LEV EPSHTEYN','Levik,is your name Lev Epshteyn?',1660,'Tim Axoy','2003-05-19 02:10:14');
INSERT INTO forumpost VALUES (943,140,4,'Re: MAIN CHARACTER','Timothy McVeigh?',103,'friedlinguini','2003-05-19 03:47:18');
INSERT INTO forumpost VALUES (944,140,4,'Why?','Why do you think Timothy McVeigh?',1660,'Tim Axoy','2003-05-19 05:02:16');
INSERT INTO forumpost VALUES (945,142,7,'Go fish!','Hi!',NULL,'Go fish!','2003-05-19 05:21:05');
INSERT INTO forumpost VALUES (946,143,3,'Best puzzle for the masses','I want to promote this site offline by printing one of the problems found here on a business-sized card to be distributed somehow in the real world.\r
\n\r
\nI\'d like to ask people\'s opinion on which problem this should be. \r
\n\r
\nThere are a few requirements: it has to be fairly easy to solve (definitely without using any heavy duty math), but still give one a sense of satisfaction having solved it. It has to be relatively short, to match the attention span of whoever picks up the card, also to fit on the card in the first place in a font that\'s big enough to be readable. It should be interesting enough that a person who\'s not neccessarily a puzzles fan, would still be interested in giving it a couple of minutes\' thought - and may even tell a friend or two. Well, you get the point.\r
\n\r
\nLooking at the problems currently listed as top rated, you will notice that most of them do not fit these criteria very well, so I wanted to ask the visitors here what their opinion was on the matter.\r
\n\r
\nPlease \"nominate\" any problem you wish here (provide a link to make it easier to find), and we\'ll see if maybe we can come up with something to draw in the crowds.',1,'levik','2003-05-19 05:45:17');
INSERT INTO forumpost VALUES (947,143,3,'Re: Best puzzle for the masses','Drew and Mohammad.',1660,'Tim Axoy','2003-05-19 05:52:39');
INSERT INTO forumpost VALUES (948,143,3,'Re: Best puzzle for the masses','I\'d propose an additional requirement that the puzzle not be too well known.\r
\n\r
\nIt\'s not a very highly rated one, but I\'d say \"The party\" is a pretty good representation.',103,'friedlinguini','2003-05-19 07:02:55');
INSERT INTO forumpost VALUES (949,143,3,'Re: Best puzzle for the masses','Well my suggestion would be to put up a few \"PARADOXES\" and \"FAMOUS RIDDLES\" as \"Paradoxes\" are interesting topics which can make people get into thinking leaving all the other things aside and \"Famous Riddles\" because most of them are heard by people somewhere or the other place (for example: in some books or some other sites or may be anywhere else). These might seem interesting to them and they would always like to go through the other problems too. \r
\n',979,'Ravi Raja','2003-05-19 07:38:30');
INSERT INTO forumpost VALUES (950,143,3,'Re: Best puzzle for the masses','Selected problems (at most 3) from the \'Knights and Liars\' category might also help.',979,'Ravi Raja','2003-05-19 07:42:40');
INSERT INTO forumpost VALUES (951,143,3,'Re: Best puzzle for the masses','Here are a few of them as what I would suggest: (You might think that most of them are problems submitted by me only, but I have suggested them because they are small, particularly in paradoxes, and the current members of the site have liked them too). Any of them can be selected.\r
\n\r
\n(1) \'Girlfriend\'s name\' submitted by terry (Riddles)\r
\n(2) \'Errors\' submitted by Levik (Riddles)\r
\n(3) \'Brothers and Sisters\' submitted by cges (Riddles)\r
\n(4) \'Requires All Knowledge\' submitted by Erin (Riddles)\r
\n(5) \'Liar or Not\' submitted by Raveen (Paradoxes) \r
\n(6) \'The (in)famous Barber\' submitted by Levik (Paradoxes)\r
\n(7) \'Paradox or a Riddle\' submitted by Ravi Raja (Famous Riddles)\r
\n(8) \'Yes Sir\' submitted by Ravi Raja (Riddles)\r
\n(9) \'Journey To St. Ives\' submitted by Ravi Raja (Famous Riddles)\r
\n(10)\'Can or Cannot\' submitted by Ravi Raja (Paradoxes)\r
\n(11)\'True or False - Part1\' submitted by Ravi Raja (Paradoxes)\r
\n',979,'Ravi Raja','2003-05-19 07:47:24');
INSERT INTO forumpost VALUES (952,143,3,'Re: Best puzzle for the masses','Drew and Mohammad come back.',1660,'Tim Axoy','2003-05-19 07:55:04');
INSERT INTO forumpost VALUES (953,142,7,'Re: Go fish!','Welcome to this site,Go fish!',1660,'Tim Axoy','2003-05-19 08:12:56');
INSERT INTO forumpost VALUES (954,142,7,'Re: Go fish!','hello!!!',2263,'mars','2003-05-19 10:34:01');
INSERT INTO forumpost VALUES (955,141,4,'Re: LEV EPSHTEYN','Yes it is. It says so on my website.\r
\n\r
\nI prefer to use \"levik\" on the web, since it\'s my nickname, and is quite a bit easier to spell.\r
\n\r
\nPlease don\'t ask questions you already know answers to.',1,'levik','2003-05-19 13:10:42');
INSERT INTO forumpost VALUES (956,144,4,'Solutions queue','Anyone notice the new solutions queue page? (It\'s a link at the top of the existing queue page, which Journeymen+ have access to.)\r
\n\r
\nLet me know what you think about it. This was a simpler change than the difficulty voting (since it\'s making a new page, not retrofitting an existing one), so I made this first.\r
\n\r
\nSpeaking of difficulty voting, Did we ever come up with a good way to counterbalance original submitter\'s opinion against that of the voters?',1,'levik','2003-05-19 13:13:17');
INSERT INTO forumpost VALUES (957,143,3,'Re: Best puzzle for the masses','I think \r
\nBrothers and Sisters\r
\nRequires All Knowledge\r
\nFour digit number\r
\nYes Sir\r
\nMagic Trick\r
\nHow many letters\r
\n\r
\n are very good... As a general rule, I just say what OTHER\'S puzzles are good, and not my own. Mine that are good will be mentioned by others. This way I don\'t seem like I am favoring my own puzzles.',1626,'Gamer','2003-05-19 15:07:55');
INSERT INTO forumpost VALUES (958,143,3,'Re: Best puzzle for the masses','Probably for your criteria, the \'Brothers and Sisters\' one is the best for your criteria. :) I think Yes sir! would be good, but many might not get that.',1626,'Gamer','2003-05-19 15:10:10');
INSERT INTO forumpost VALUES (959,144,4,'Re: Solutions queue','Latest suggestion I think was to allow the submitter\'s vote and levik\'s vote each to have a weight of 3, and journeymen and scholars a weight of 1. I don\'t know if anyone agreed that thumbs-down voters would or would not get to vote on difficulty, with myself favoring such.',1301,'Charlie','2003-05-19 16:21:08');
INSERT INTO forumpost VALUES (960,144,4,'Re: Solutions queue','And no, I hadn\'t noticed the link to the solutions queue. It was in a heading that I just ignore. Also, it appears in white lettering, and I\'ve come to expect links to be in blue. (or is it very pale blue?--it looks white to me). But now that I know it\'s there, it looks like it works fine.',1301,'Charlie','2003-05-19 16:35:06');
INSERT INTO forumpost VALUES (961,144,4,'Re: Solutions queue','Are the comments to be visible to the individual submitters (who may not be journeymen)? I would assume so. Also, the requirement that at least one comment must be made before posting it seems to be able to be satisfied by merely one comment by the same person posting it. If the purpose is discussion, this would seem to defeat it, as a scholar can post a comment, that presumably no one will see, and then shortly thereafter (within a minute) post the solution. Maybe it should require at least one comment by someone other than the scholar doing the posting.',1301,'Charlie','2003-05-19 16:44:05');
INSERT INTO forumpost VALUES (962,144,4,'Re: Solutions queue','Charlie: the notes left on the comment are not yet visible to the submitters - so far they are for discussion among high-rankers only. I plan to make them visible on the \"edit solution\" page, but considering noone ever goes there, I will have to first implement some sort of notification system.\r
\n\r
\nAs far as publishing a solution with the only comment being yours, I mostly wanted the one comment restriction so that people do not post solutions automatically - so that at least some consideration is given. I think that I can generally trust the scholars to not publish solutions that are not up to par.\r
\n\r
\nToday I thought of letting people \"nominate\" solutions among the problem\'s comments - since we often end up doing this anyway, it may be a good idea.',1,'levik','2003-05-19 19:05:04');
INSERT INTO forumpost VALUES (963,143,3,'Re: Best puzzle for the masses','Hmmm... I was kinda hoping to avoid riddles. I know a lot of people like them, but I personally prefer logical problems more, and would love to attract that type of people to the site.\r
\n\r
\nI like to think of it as the logic puzzles site that has riddles, rather than a riddles site with some logic puzzles.\r
\n\r
\nMaybe it\'s just me. \r
\n\r
\nUltimately though, I do not think that riddles can give one as much satisfaction when solving as a good logical chestnut, and therefore it\'s not as good a candidate to draw people in.',1,'levik','2003-05-19 19:09:05');
INSERT INTO forumpost VALUES (964,143,3,'Re: Best puzzle for the masses','Here are a few problem which I would suggest from the other categories:\r
\n\r
\nA Pack of Prudent Pirates submitted by Levik (Logic)\r
\nMutually Friendly submitted by Levik (Logic)\r
\nTies submitted by Half-Mad (Logic)\r
\nThe Four Mathematicians submitted by Ravi Raja (Logic)\r
\nMr. and Mrs. Brown submitted by Levik (Logic)\r
\nThe Three sages submitted by Levik (Logic)\r
\nLight bulb submitted by Half-Mad\r
\nThe Three Logicians submitted by Ravi Raja (Logic)\r
\nAn arrangement of 15 submitted by Levik (Numbers)\r
\nSelf-Descriptor submitted by Levik (Numbers)\r
\nSelf-Descriptor part2 submitted by Happy (Numbers)\r
\nThe Ten Statements submitted by Ravi Raja (Logic)\r
\nTwo numbers submitted by Happy (Numbers)\r
\nFathers and Sons submitted by Ravi Raja (Logic)\r
\nUnknown Answers submitted by Tim Axoy (Knights and Liars)\r
\nFour-Digit Number submitted by Ravi Raja (Just Math)\r
\n\r
\n\r
\n\r
\n\r
\n',979,'Ravi Raja','2003-05-20 01:15:39');
INSERT INTO forumpost VALUES (965,143,3,'Re: Best puzzle for the masses','Levik, in your first comment you had mentioned something like this: \"........it should be interesting enough that a person who\'s not neccessarily a puzzles fan, would still be interested in giving it a couple of minutes\' thought........\" and so I suggested for Riddles (Famous). \r
\nAnyway, if not riddles, then Paradoxes is not a bad suggestion. If you want to avoid riddles, you can but not Paradoxes. They are indeed interesting. Readers usually just can\'t themselves out of the loop and start looking for their solutions. This might make them think more on those problems and search for more. There are more good problems too besides the ones listed above but either they are too long or a bit more tough compared to the ones listed above and may not be able to draw the attention of people who are not puzzle solvers (or puzzle fans as you had mentioned). That was all I wanted to say on this topic. Thank You. \r
\n',979,'Ravi Raja','2003-05-20 04:14:50');
INSERT INTO forumpost VALUES (966,143,3,'Re: Best puzzle for the masses','Personally, I\'m not a big fan of paradoxes. I haven\'t seen one yet where the self-contradiction wasn\'t easy to spot, and there\'s not much to do once you\'ve spotted it. They\'re not very satisfying because you don\'t get any closure from an actual solution - all you\'re left with is some logically inconsistent statements.',103,'friedlinguini','2003-05-20 07:10:36');
INSERT INTO forumpost VALUES (967,143,3,'Re: Best puzzle for the masses','I agree with friedlinguini on paradoxes...\r
\n\r
\nI would think A Pack of Prudent Pirates or The three Logicians would fit well for your idea, or possibly the puzzle I had where you add a 4 digit number to it\'s reverse, and it\'s the original number with a 0 at the end (which I am in the process of getting ok)\r
\n\r
\n',1626,'Gamer','2003-05-20 10:03:43');
INSERT INTO forumpost VALUES (968,143,3,'Re: Best puzzle for the masses','Well seeing as how your making business cards i\'m assuming this would be a rather small project (The making of the card that is) so that the same card could be made but with two different puzzles. I think 1 should have a riddle and 1 should be logic oriented (Including math). This way we would appeal to both groups of puzzle people. Riddle lovers and math lovers. Anyways 2 problems i highly recommend. 1. String around the cylinder. 2. 2 colors',1072,'Alan','2003-05-20 11:06:39');
INSERT INTO forumpost VALUES (969,145,4,'Journeyman Timothy','Now I am(ALMOST)a Journeyman.\r
\n',1660,'Tim Axoy','2003-05-20 13:02:32');
INSERT INTO forumpost VALUES (970,143,3,'Re: Best puzzle for the masses','Ravi,thank you for putting it my problem.',1660,'Tim Axoy','2003-05-20 13:06:44');
INSERT INTO forumpost VALUES (971,50,5,'Re: Chatterbox','60000?',1660,'Tim Axoy','2003-05-20 13:09:08');
INSERT INTO forumpost VALUES (972,145,4,'Re: Journeyman Timothy','Does anyone wanna congrat me?',1660,'Tim Axoy','2003-05-20 14:39:00');
INSERT INTO forumpost VALUES (973,88,4,'Re: problem difficulties','I would say the author of a puzzle is, in most instances, too close to the problem to be the best judge of its difficulty level. Example: I thought my puzzle \"a2o3t6t7\" was a difficutly 2 or 3, while voters commented it should be 4 or 5. Other puzzles that take me a lot of effort to create I want to assign level 5, but they may be a 3 or 4 to solve. For this reason, I would not weigh the author\'s initial difficulty setting any more strongly than the \"difficulty votes\" of the voters who give TU/TD.\r
\n\r
\nOther than that, I support Levik\'s proposal, and think it should be implemented when he can get to it (I ask Levik for too much as it is -- let him have his vacation:)',1567,'Bryan','2003-05-20 19:13:37');
INSERT INTO forumpost VALUES (974,140,4,'Re: friedlinguini\'s guess','Bless you. I appreciate a y with a sense of humor.',1567,'Bryan','2003-05-20 19:17:20');
INSERT INTO forumpost VALUES (975,145,4,'Re: Journeyman Timothy','Now I am a Journeyman.',1660,'Tim Axoy','2003-05-21 02:41:10');
INSERT INTO forumpost VALUES (976,88,4,'Re: problem difficulties','100% agreement with Bryan.',775,'Cory Taylor','2003-05-21 04:12:27');
INSERT INTO forumpost VALUES (977,140,4,'Re: MAIN CHARACTER','and see, he(she?) didn\'t want gender affecting this in our little cyber-world...',775,'Cory Taylor','2003-05-21 04:14:30');
INSERT INTO forumpost VALUES (978,143,3,'Re: Best puzzle for the masses','my 3 cents worth.\r
\nBasing on the need for shortness (to fit on a card) appropriate difficulty(not so hard to scare people away if no answer is included(which it shouldnt be) and not too easy that people will dismiss it), I\'d like to second the choices of \"2 colors\" and \"the party\". Certainly though, there are lots of good choices.',775,'Cory Taylor','2003-05-21 04:23:23');
INSERT INTO forumpost VALUES (979,146,6,'sequences','A question I have that I need answered for one of my pending problems. \r
\n\r
\nIs there a difference (mathematically) between a sequence of numbers and a patterned set of numbers? For example, if the answer is no (no difference), then one could extend this meaning a create a \"series\" of letters, for arguments sake lets say hbtyhbtyhbhbhbty where this \"sequence\" is formed from the first letter of the words in the song \"happy birthday\". I was under the impression that a sequence relied upon some mathematical or computational \"rule\" to progress from one term to the next, while a patterned set of numbers were simply a group of numbers in which the order they are presented contains some significance.\r
\n',775,'Cory Taylor','2003-05-21 04:29:13');
INSERT INTO forumpost VALUES (980,145,4,'Re: Journeyman Timothy','Congratulations Tim !! :) ',979,'Ravi Raja','2003-05-21 04:39:45');
INSERT INTO forumpost VALUES (981,88,4,'Re: problem difficulties','Bryan, the reason that I think the submitter should have more input in the difficulty than everyone else, is that they are potentially the only person who knows the correct solution. As Alan said, you may think the problem is easy, but miss a vital step precluding it from being solved in the \"easy\" way you envision. (It can also work the other way).\r
\n\r
\n',1,'levik','2003-05-21 07:01:31');
INSERT INTO forumpost VALUES (982,146,6,'Re: sequences','A sequence is an ordered, um, sequence of numbers. The numbers don\'t have to be unique, and there doesn\'t have to be a specific rule as long as the sequence is well-defined.\r
\n\r
\nA set is not ordered and all elements are assumed to be unique.\r
\n\r
\nFor the sake of completeness, a series is defined as the summation of all numbers in a sequence.',103,'friedlinguini','2003-05-21 07:20:29');
INSERT INTO forumpost VALUES (983,146,6,'Re: sequences','ok then, 5,8,2,3,5,8,2,3,5,8,5,8,5,8,2,3 would be a sequence because it is the number of letters in the word to the happy birthday song, correct?\r
\nCan you expand this to using letters as in my first post?',775,'Cory Taylor','2003-05-21 08:36:56');
INSERT INTO forumpost VALUES (984,88,4,'Re: problem difficulties','Yeah, Levik, that thought occurred to me as well. But what I\'m thinking is that the author\'s initial difficulty level serves as a starting point, as well as a guide to voters. If the voters feel a different difficulty level is warranted, and the author disagrees, he or she can leave a comment to this effect. I know if I saw a comment from the author defending the original difficulty level, I would respect and support their view, especially if the author is someone with a track record at perplexus.\r
\n\r
\nBased on recent puzzle submissions, it seems that whenever voters have suggested a different difficulty level, the author has agreed. Therefore, it seems to me tht giving the author\'s \"difficulty vote\" the same weight as that of the TU/TD voters will yield an accurate difficulty level more often than if the author\'s preference is more heavily weighted.',1567,'Bryan','2003-05-21 08:49:49');
INSERT INTO forumpost VALUES (985,134,4,'Re: I have a question','The VERY FIRST problem that was posted/submitted on the site was: \r
\nBurning ropes (Posted on 2002-03-28) by Levik\r
\n',979,'Ravi Raja','2003-05-21 08:50:59');
INSERT INTO forumpost VALUES (986,143,3,'Re: Best puzzle for the masses','100% agreement with Cory.',1567,'Bryan','2003-05-21 09:00:03');
INSERT INTO forumpost VALUES (987,17,6,'HTML codes not mentioned yet','I occasionally use list items. Minus the extra spaces that follow, they are:\r
\n\r
\n< ul >\r
\n< li > dog\r
\n< li > cat\r
\n< /ul >\r
\n\r
\n\r
\r
\n
\n
\n
\n\r
\n< ol >\r
\n< li > dog\r
\n< li > cat\r
\n< /ol >\r
\n\r
\n\r
',1567,'Bryan','2003-05-21 09:21:14');
INSERT INTO forumpost VALUES (988,17,6,'Re: HTML codes for use on the site','Oh... That looks\r
\n
\n
\n
\n\r
\n
\n
\n\nYou will see a solution I did not post that says TimAxoy.',1660,'Tim Axoy','2003-05-21 13:12:57');
INSERT INTO forumpost VALUES (992,142,7,'Re: Go fish!','I have seen some people with black names like Go fish!\'s and some with blue.\r
\nWhat does it mean?',1660,'Tim Axoy','2003-05-21 13:41:48');
INSERT INTO forumpost VALUES (993,134,4,'Re: I have a question','I know the first one signed up on here was Levik.\r
\nWho was the second?\r
\nWhat number was I?',1660,'Tim Axoy','2003-05-21 13:48:11');
INSERT INTO forumpost VALUES (994,143,3,'Re: Best puzzle for the masses','What I really love about \"The Party\" is that the solution is VERY satisfying, much like unraveling a good mystery.\r
\n\r
\nHowever, I fear that 90% of the people would not come up with it. Maybe I\'m wrong though.\r
\n\r
\n(Please don\'t mind my being picky - it\'s just that if I will end up plopping down 100-200 dollars for business card printing, I would like for the content to be as good as it can).',1,'levik','2003-05-22 02:15:37');
INSERT INTO forumpost VALUES (995,143,3,'Re: Best puzzle for the masses','Also - what do people think about \"Burning Ropes\"? I know I\'m biased (I liked this puzzle so much that it was one of the reasons to start this site), but I really think it could be a good match.',1,'levik','2003-05-22 02:18:06');
INSERT INTO forumpost VALUES (996,143,3,'Re: Best puzzle for the masses','All you can do is ask. I solved the party, but couldn\'t get burning ropes (going on memory that burning ropes was trying to time 45 minutes with 2 ropes), so either I\'m the abnormality (likely unfortunately) or burning ropes is harder than you realize (its a simple enough concept, but definitely not something I\'d have thought of).\r
\n\r
\nOn a side note, how does a guy survive in NYC when a mere set of business cards cost that much? You can probably get yourself a self-making card program for much less than that. My company has one, as I\'m sure many others do. On top of that, outsourcing business cards here costs about $15-$25 (CDN) per 1000 cards, so I have to admit that I\'m awfully shocked.',775,'Cory Taylor','2003-05-22 04:09:14');
INSERT INTO forumpost VALUES (997,143,3,'Re: Best puzzle for the masses','Levik, have you considered printing a different puzzle on each side of the cards? Costs more, but you increase the potential of putting out a puzzle that the reader can solve, and two-sided business cards are themselves a rarity, sure to add to the interest level.',1567,'Bryan','2003-05-22 04:53:34');
INSERT INTO forumpost VALUES (998,142,7,'Re: Go fish!','Even when you are not logged in you can post a comment in this forum and there\'s a space/box provided to write your name. If you type Tim Axoy there, then after the comment is posted, your name will appear in Black and if you are logged in then it will appear in Blue. \r
\nI hope you got it.',979,'Ravi Raja','2003-05-22 05:10:11');
INSERT INTO forumpost VALUES (999,82,5,'Re: Am I going crazy?','yep u r....sry!',2282,'Kelsey','2003-05-22 09:49:42');
INSERT INTO forumpost VALUES (1000,143,3,'Re: Best puzzle for the masses','Yes burning ropes is one of the most genius puzzles i\'ve ever heard in my life. I\'m all for burning ropes.',1072,'Alan','2003-05-22 10:20:53');
INSERT INTO forumpost VALUES (1001,143,3,'Re: Best puzzle for the masses','Ok i\'m a little confused about the party. I read the solution, and agreed with the double number partner concept (I\'m trying not to give away the answer so bear with me) But how do we know that bille and alice had that much handshakings a piece? how do we know its not one of the other sets of numbers?',1072,'Alan','2003-05-22 10:32:41');
INSERT INTO forumpost VALUES (1002,134,4,'Re: I have a question','tim to see what number you are find a way to clikc on your own link and then see the number to the left of the address bar.',1072,'Alan','2003-05-22 10:33:34');
INSERT INTO forumpost VALUES (1003,142,7,'Re: Go fish!','So Go fish!,you\'re not really logged in!',1660,'Tim Axoy','2003-05-22 11:06:16');
INSERT INTO forumpost VALUES (1004,145,4,'Re: Journeyman Timothy','Promote me to scholar.',1660,'Tim Axoy','2003-05-22 11:12:38');
INSERT INTO forumpost VALUES (1005,134,4,'Re: I have a question','Who was the second one to sign up here?',1660,'Tim Axoy','2003-05-22 11:14:19');
INSERT INTO forumpost VALUES (1006,131,7,'Re: Silly Jilly','Click on my name and see my info!',2196,'Silly Jilly','2003-05-22 11:18:01');
INSERT INTO forumpost VALUES (1007,143,3,'Re: Best puzzle for the masses','Alan, I responded in a comment attached to the problem, so as not to give away the solution in here.',103,'friedlinguini','2003-05-22 15:54:42');
INSERT INTO forumpost VALUES (1008,147,5,'Submitting Problems','Before a problem is first submitted, the \'preview\' shows the problem and the solution on the same page for review before submitting the problem to the queue. Thereafter, you can only edit/view one of them at a time. I think, and I\'m not sure how you would implement it, really, that it would be much easier to tweak problems and keep them consistent if you could see both at the same time. Just a minor thing, but it\'s rather an annoyance to have to click back and forth to make sure the solution correctly addresses the problem posted.',1575,'DJ','2003-05-22 17:55:29');
INSERT INTO forumpost VALUES (1009,142,7,'Re: Go fish!','No Tim. Go Fish is not really logged in and so am I. You see !!',NULL,'Ravi Raja','2003-05-23 04:28:16');
INSERT INTO forumpost VALUES (1010,145,4,'Re: Journeyman Timothy','When pigs fly',1,'levik','2003-05-23 04:30:01');
INSERT INTO forumpost VALUES (1011,147,5,'Re: Submitting Problems','How about if you could see the problem text when editing the solution? Would that help?',1,'levik','2003-05-23 04:35:18');
INSERT INTO forumpost VALUES (1012,147,5,'Re: Submitting Problems','Yeah, that would suffice as well, and I\'m sure be a lot easier to implement. Good idea. =)',1575,'DJ','2003-05-23 06:07:58');
INSERT INTO forumpost VALUES (1013,142,7,'Re: Go fish!','Ravi Raja,how can you both be logged in and not logged in?',1660,'Tim Axoy','2003-05-23 09:23:14');
INSERT INTO forumpost VALUES (1014,145,4,'Re: Journeyman Timothy','What is,\"When pigs fly?\"\r
\nDoes that mean you\'re gonna promote me to scholar when pigs fly??',1660,'Tim Axoy','2003-05-23 09:25:24');
INSERT INTO forumpost VALUES (1015,131,7,'Re: Silly Jilly','Change it!\r
\nIt says your password,and people can easily get in your account!',1660,'Tim Axoy','2003-05-23 09:27:35');
INSERT INTO forumpost VALUES (1016,142,7,'Re: Go fish!','Not logged in?
\r
\nOh,yeah?\r
\n
\nOh,am I logged in?
\r
\nNo?
\r
\nEh?\r
\n
\nWell,I might be logged in.
\r
\nI might not.
\r
\nLa,la,la.
\r
\nLa,la.\r
\n
\nKerchoo!
\r
\nNo,I am not logged in!
\r
\nOh,no!
\r
\nWow!\r
\n
\nI am not!
\r
\n
\nA funny thing to say!
\r
\nMy gosh!\r
\n
\nReally am I logged in?
\r
\nEh,eh?
\r
\nAnswer is what?
\r
\nLike what?
\r
\nLike what answer?
\r
\nYo?\r
\n
\nTime to leave.
\r
\nI like this site.
\r
\nMe,oh,my.\r
\n
\nA bunch of hugs and kisses.
\r
\nXXXXXXXXXX
\r
\nOOOOOOOOOO
\r
\nYour friend,Go fish!',NULL,'Go fish!','2003-05-23 09:34:45');
INSERT INTO forumpost VALUES (1017,143,3,'Re: Best puzzle for the masses','I thought burning ropes is good for a concise puzzle, but I think the party is good too. Or maybe a number puzzle like niners or something like that.',1626,'Gamer','2003-05-23 10:13:47');
INSERT INTO forumpost VALUES (1018,142,7,'Re: Go fish!','The first letters spell this.\r
\n
\nNO ONE WILL KNOW I AM REALLY TIM AXOY.\r
\n
\nGo fish!,are you really Tim Axoy?',2196,'Silly Jilly','2003-05-23 13:07:02');
INSERT INTO forumpost VALUES (1019,148,3,'A locked safe','I solved the locked safe problem.\r
\nWhy does it still have no solution?',2196,'Silly Jilly','2003-05-23 13:20:02');
INSERT INTO forumpost VALUES (1020,149,7,'No Subject','Hi everybody. Im from Tucson AZ...I found this site while looking for brain teasers. Duh I guess....but I\'m looking for a problem in specific. Haven\'t been able to find it though. It\'s about 2 guys meeting and one has to guess the other\'s children\'s age. For information he tells his that there sum minus a number is a certain number...there is where I forget how the problme goes...then he says the product is the same as the number of the us that just passed by. At the end he tells him the oldest one has blue eyes. I\'m not sure if you have heard of anything like that. By the way...this is a great site, I\'ll get all my friends over..THNX',2290,'Fred','2003-05-23 17:50:46');
INSERT INTO forumpost VALUES (1021,149,7,'edit','fifth line 3rd to last word should be bus not us...sorry\r
\n',2290,'Fred','2003-05-23 17:52:24');
INSERT INTO forumpost VALUES (1022,150,4,'Discovered Silly Jilly\'s login password','Have you seen someone named Silly Jilly?\r
\nShe is new to this site.\r
\nShe put her password in her account!',1660,'Tim Axoy','2003-05-24 02:58:32');
INSERT INTO forumpost VALUES (1023,151,3,'Discovered Silly Jilly\'s login password','Have you seen someone named Silly Jilly?\r
\nShe is new to this site.\r
\nShe put her password in her info!',1660,'Tim Axoy','2003-05-24 03:00:10');
INSERT INTO forumpost VALUES (1024,150,4,'EDIT!','I mean info,not account.',1660,'Tim Axoy','2003-05-24 03:00:47');
INSERT INTO forumpost VALUES (1025,150,4,'Re: Discovered Silly Jilly\'s login password','Hey,guys!\r
\nWe\'ll sneak into her account.\r
\nHer password is SillyJilly.\r
\nHer login is SillyJilly,too.',1660,'Tim Axoy','2003-05-24 04:26:00');
INSERT INTO forumpost VALUES (1026,142,7,'Re: Go fish!','Tim, when you are not logged in, your name when typed in the bar appears in Black and when logged in appears in Blue. I never said that a person can be both logged in and not logged in. ',979,'Ravi Raja','2003-05-24 04:41:50');
INSERT INTO forumpost VALUES (1027,150,4,'Re: Discovered Silly Jilly\'s login password','Tim now will you STOP behaving like that. You promised Levik that you\'ll be behaving properly. Didn\'t you? Then why do you do all those things. No one is going to sneak into Silly\'s account so there\'s no use of giving away her login and password like this in the forums.\r
\nPlease don\'t do that.\r
\n',979,'Ravi Raja','2003-05-24 04:45:54');
INSERT INTO forumpost VALUES (1028,149,7,'Re: No Subject','Welcome to the site Fred. These are the two problems I believe you are looking for Fred. \r
\n\r
\nThe three daughters in LOGIC by maverick http://www.flooble.com/perplexus/show.php?pid=237\r
\n\r
\nProfessor and Students in LOGIC\r
\nhttp://www.flooble.com/perplexus/show.php?pid=506\r
\n\r
\n',979,'Ravi Raja','2003-05-24 04:57:00');
INSERT INTO forumpost VALUES (1029,149,7,'Re: No Subject','The three daughters in LOGIC by maverick \r
\n
\r
\nhttp://www.flooble.com/perplexus/show.php?pid=237 \r
\n
\nProfessor and Students in LOGIC \r
\n
\r
\nhttp://www.flooble.com/perplexus/show.php?pid=506 \r
\n\r
\n\r
\n',979,'Ravi Raja','2003-05-24 04:57:57');
INSERT INTO forumpost VALUES (1030,151,3,'Re: Discovered Silly Jilly\'s login password','I think an e-mail to the person involved would be more appropriate than broadcasting such information here.',1301,'Charlie','2003-05-24 06:05:31');
INSERT INTO forumpost VALUES (1031,143,3,'Re: Best puzzle for the masses','I\'d vote for Fly on a Cube.',1301,'Charlie','2003-05-24 06:08:25');
INSERT INTO forumpost VALUES (1032,150,4,'Re: Discovered Silly Jilly\'s login password','Tim, If you know this for a fact, then the honorable thing to do is to e-mail Silly Jilly, warning her of her exposure. You also put this in the general forum where anyone can see it. That\'s not good.',1301,'Charlie','2003-05-24 06:11:03');
INSERT INTO forumpost VALUES (1033,145,4,'Re: Journeyman Timothy','I\'m sure levik means on their own power, not in airplanes.',1301,'Charlie','2003-05-24 06:13:09');
INSERT INTO forumpost VALUES (1034,142,7,'Re: Go fish!','No,Silly,I am not Go fish!.',1660,'Tim Axoy','2003-05-24 12:12:35');
INSERT INTO forumpost VALUES (1035,17,6,'Re: HTML codes for use on the site','\r
',1660,'Tim Axoy','2003-05-24 13:41:03');
INSERT INTO forumpost VALUES (1036,143,3,'Re: Best puzzle for the masses','my few cents:\r
\n
\n
\n
\n
\n
\nI agree that paradoxes might get people to come looking for a solution, but what will they think when they get here just to see that the solution is \"it\'s a paradox, there is no answer\"? also, i say nay to famous riddles, because i think more people will come here if they see something original. also, i definitely agree with probably a more math-y based problem than a riddle, since that is what comprises most of the problems here, and in my opinion the more interesting ones with more discussion and debate.\r
\n\r
\nas for specific problems, i think \"the party\" is a good one, as are \"an arrangement of 15,\" \"ten statements\" (which would might be better shortened to five or six), and \"burning ropes\" or \"string around the cylinder\" if they are not too long. \"Large number\" is interesting, but only moreso after you have seen or figured out that it is zero. Problems like \"niners\" or \"2 colors\" where you have to prove something are good, but I don\'t think as appropriate for a business card kind of thing. A concrete numerical solution might be preferable, as opposed to a proof or a process, depending on the problem (not all the problems i have mentioned fit that criterium either).',1575,'DJ','2003-05-24 16:54:21');
INSERT INTO forumpost VALUES (1037,152,7,'I am new.','I am new.\r
\nHello,everyone!',2296,'Bob Jock','2003-05-25 03:39:43');
INSERT INTO forumpost VALUES (1038,152,7,'Re: I am new.','Welcome to the site Bob.',979,'Ravi Raja','2003-05-25 04:10:23');
INSERT INTO forumpost VALUES (1039,152,7,'Re: I am new.','Hi,Daddy!',1660,'Tim Axoy','2003-05-25 05:18:33');
INSERT INTO forumpost VALUES (1040,17,6,'Re: HTML codes for use on the site','\r
\n
\n
\n
\n
\n
\n
\n',1660,'Tim Axoy','2003-05-25 06:29:29');
INSERT INTO forumpost VALUES (1041,143,3,'Re: Best puzzle for the masses','The reason I like \"Burning ropes\" is that it\'s viral - there\'s no way that you can be explained the soluiton and not understand it. \"The Party\" has a few steps one must take before solving it, and I personally found that some of my friends had trouble following as I explained the solution. \r
\n\r
\nThat said, \"Fly on cube\" is pretty good too (especially so since it has an image) - but the concept involved is basic geometry and may not be as appealing to some people.\r
\n\r
\nAs far as printing costs, the price I mentioned is based on twosided full-color cards on glossy stock (I want them to be in flooble blue and with the perplexus logo one side).\r
\n\r
\nI\'m sure I could get plain old black on white cards significantly cheaper.',1,'levik','2003-05-25 06:33:39');
INSERT INTO forumpost VALUES (1042,143,3,'Re: Best puzzle for the masses','Yes i totally agree about burning ropes, and when i hear dthe answer i said to myself \"That is so genius\" also string around the cylinder also requires a good amount of logic',1072,'Alan','2003-05-25 08:20:38');
INSERT INTO forumpost VALUES (1043,145,4,'Re: Journeyman Timothy','I think the expression originates on the fat connotation that pigs got, such that they could never fly... :)',1626,'Gamer','2003-05-26 17:11:20');
INSERT INTO forumpost VALUES (1044,88,4,'Re: problem difficulties','Yes... Often times an easy problem can have a more complex solution, or the other way around too... I understand what you mean levik, but I think Bryan\'s idea is good too. If voters take into consideration that the problem may be harder if the difficulty is harder, it might work. But I am not a journeyman yet, so I wouldn\'t know.',1626,'Gamer','2003-05-26 17:15:58');
INSERT INTO forumpost VALUES (1045,140,4,'Re: MAIN CHARACTER','It\'s Timola the super Riddle solver! It has paradoxes to fight!',1626,'Gamer','2003-05-26 17:17:21');
INSERT INTO forumpost VALUES (1046,143,3,'Re: Best puzzle for the masses','I think Burning Ropes is a good puzzle :) I thought it was a cool idea when I saw it, as I would never have thought of that!',1626,'Gamer','2003-05-26 17:21:37');
INSERT INTO forumpost VALUES (1047,78,7,'Re: Hello all','Hi all,\r
\nI\'m Surajee, from Hyderabad in India; When I first chanced on this site, I was amused to see vast info on logic puzzles which I like the most. Looking forward to contribute to the interests of the site.\r
\n',2312,'Surajee','2003-05-26 23:01:45');
INSERT INTO forumpost VALUES (1048,78,7,'Re: Hello all','Welcome to the site Surajee and do go ahead with your contributions.\r
\nBut at the same time I have to tell you one thing that you need to be patient because your contributions might not show up early on the site. Well you will soon come to know why when you will learn about the Rules of the site (Problem Submission and Deletion). But do not hesitate to submit problems from your part.\r
\nThank You.',979,'Ravi Raja','2003-05-27 07:13:45');
INSERT INTO forumpost VALUES (1049,17,6,'Re: HTML codes for use on the site','I think that tables would be extremely useful, or at least the <pre> tags. Since the page is in PHP (I love this language), it should be relatively easy to detect any time there is a <pre or <table without a corresponding <pre> or <table> and append the closing tags to the offending comment or problem (note that you detect a <table and not a <table> since there may be parameters that follow). It seems that a table is called for quite often on the site without any really good way to generate it.',1575,'DJ','2003-05-27 16:09:56');
INSERT INTO forumpost VALUES (1050,17,6,'Re: HTML codes for use on the site','rather, append the closingtags </table>: or </pre>',1575,'DJ','2003-05-27 16:11:12');
INSERT INTO forumpost VALUES (1051,63,3,'Levik?','Levik\'s a/s/l is what?',1660,'Tim Axoy','2003-05-28 03:09:09');
INSERT INTO forumpost VALUES (1052,140,4,'Re: MAIN CHARACTER','Tim Axoy.',1660,'Tim Axoy','2003-05-28 03:11:47');
INSERT INTO forumpost VALUES (1053,17,6,'Re: HTML codes for use on the site','Did Timothy play with the ball?
\r
\nDid Timothy play with the ball?
\r
\nDid Timothy play with the ball?
',1660,'Tim Axoy','2003-05-28 04:27:37');
INSERT INTO forumpost VALUES (1054,140,4,'Re: MAIN CHARACTER','Rosencrantz & Gildenstern',1575,'DJ','2003-05-28 08:46:51');
INSERT INTO forumpost VALUES (1055,17,6,'Re: HTML codes for use on the site','I will look into PRE, but I am definitely not allowing TABLE and related tags - there\'s too much potential for abuse, and it\'s hardly ever needed... In fact I remember only one or two cases.',1,'levik','2003-05-28 09:20:16');
INSERT INTO forumpost VALUES (1056,148,3,'Re: A locked safe','It has been solved in the comments for some time. I am also wondering when an official solution will be posted.',1920,'Brian Smith','2003-05-28 14:29:52');
INSERT INTO forumpost VALUES (1059,154,3,'Re: Google Puzzle Championship','Before submitting puzzles, make sure that you are allowed to do so! Copyrights can be a pain (though if it went to court you could always make a fuss about the Google cache :-)> )',103,'friedlinguini','2003-05-29 05:13:58');
INSERT INTO forumpost VALUES (1060,17,6,'Re: HTML codes for use on the site','PRE is a must if you want programming-type puzzles. The space-nbsp trick gets old pretty quickly.',103,'friedlinguini','2003-05-29 05:16:29');
INSERT INTO forumpost VALUES (1061,154,3,'Re: Google Puzzle Championship','This looks cool... I have much going on too... but I am good at number places and the shark problems :)',1626,'Gamer','2003-05-29 14:53:22');
INSERT INTO forumpost VALUES (1058,154,3,'Google Puzzle Championship','Today is the last day to register yourself for the Google Puzzle Championship - which anyone can participate in for a chance to qualify for the world puzzle championship team.\r
\n\r
\nI unfortunately lack the time to take part, but I think a lot of people on the site would enjoy such an activity. Besides, I dare say you guys have had a lot of practice!\r
\n\r
\nAnyone who participates is welcome to tell us how it went, and to submit the puzzles they were given (with proper attribution!)',1,'levik','2003-05-29 04:29:07');
INSERT INTO forumpost VALUES (1062,154,3,'Re: Google Puzzle Championship','How did you learn about it?',1660,'Tim Axoy','2003-05-29 15:39:19');
INSERT INTO forumpost VALUES (1063,88,4,'Re: problem difficulties','One thing I have noticed on the site is that the extremes, especially upper extremes, have been largely avoided. Looking at the 15 most recent problems on the main page, nine have difficulty 3, five have difficulty 2, and one with difficulty 1. Some, for instance \"10001, 100010001...\" and possibly a few of the others, could have been given a higher difficulty rating.\r
\nIt seems to me that, especially since most of the people voting on the problems can solve a complex calculus problem as if it were counting to ten, that they are reluctant to rate a problem as 4 if they can solve it or think they can solve it in a few minutes. And a difficulty of 5 is sacred or something. Just an observation, but I think that a lot of methods and thought processes that come naturally for most seasoned puzzlegoers and math whizzes are not so simple for anyone else coming to the site. In general, though, it seems that the voters tend to diminish the difficulty of the problems since they are all so proficient at solving them.\r
\nOften, too, one\'s own puzzle will seem too easy, since they (hopefully) know the solution, and a puzzle will always seem easier to a voter who has solved it or seen a similar problem before. Also, as Bryan noted, a problem that took a lot of time to create, or that seems very \'clever,\' the author will want to give it a higher difficulty rating.\r
\nUltimately, though, the author/submitter will usually have the best idea what the solution entails and how difficult it should be for anyone. I think giving voters an easy way to rate the difficulty alongside the TU/TD would be useful, but I don\'t like the idea of the voters\' ratings having the ability to override the author\'s submission (of course, as I am not yet a Journeyman and my problems are usually debated, that could be expected). What I would suggest is, the difficulty rating would be entirely separate from the TU/TD selection, but each person would have the option of waiting to TU a problem until they find the difficulty agreeable as well. Or, change the TU/TD to a mandatory three-option TU/TD/NW where a voter can say that they like the problem, but it \'needs work,\' besides just giving a thumbs up or down. I\'m not sure how that would work into the overall voting scheme; perhaps 3 NW votes could \'freeze\' the problem in queue, overriding both the TU and TD votes, until the problem is changed. That way, the author still has control of the problem, but voters who don\'t like what they see can request a few changes without having to thumb it down, or without a few easier-going voters pushing the problem ahead regardless. Just a thought, as I really don\'t know firsthand how the voting/comment system works.',1575,'DJ','2003-05-29 16:57:34');
INSERT INTO forumpost VALUES (1064,17,6,'Re: HTML codes for use on the site','<pre> is a definite must, I think, especially with the inception of the algorithms category. I don\'t see how tables could be abused, especially if you make sure to close the tags, and only allow certain parameters like width and height. Granted, almost anything you can do with a table you can do with a <pre> tag by spacing it out (which is a heck of a lot easier than rows upon rows of and fifty previews to line things up like it is now), but most everything it seems would be easier with tables, especially once you have more than two or three columns. And again, I like to think myself pretty proficient with HTML and PHP both, and I fail to see what type of \'abuse\' could arise from allowing the <table> tag.',1575,'DJ','2003-05-29 17:28:08');
INSERT INTO forumpost VALUES (1065,17,6,'Re: HTML codes for use on the site','Also, an obscure point, I have wanted to use the strikeout tag (<s>) a few times in forming lists and whatnot where certain elements need be removed or \'crossed out,\' and might make a simple but potentially useful addition to the bag of flooble HTML tricks.',1575,'DJ','2003-05-29 17:32:02');
INSERT INTO forumpost VALUES (1066,143,3,'Re: Best puzzle for the masses','I just read burning ropes and I totally agree that it\'s the best - its not an easy question, but anybody could understand the solution. If your just using one, I think that it should be this one.',1919,'Lewis','2003-05-30 06:58:45');
INSERT INTO forumpost VALUES (1067,17,6,'Re: HTML codes for use on the site','That\'s a <s>stupid<s> good idea!',1626,'Gamer','2003-05-30 10:28:01');
INSERT INTO forumpost VALUES (1068,17,6,'Re: HTML codes for use on the site','Hmmm... <s>bad<s> good',1626,'Gamer','2003-05-30 10:28:25');
INSERT INTO forumpost VALUES (1069,17,6,'Re: HTML codes for use on the site','ok I give up... How does it work???',1626,'Gamer','2003-05-30 10:28:47');
INSERT INTO forumpost VALUES (1070,88,4,'Re: problem difficulties','But, as shown through my boring puzzle \"Average of Reciprocals\", a puzzle you think is just right could be easy to people who are better at math or logic than you are. For example, they may think of a shorter or easier solution, which would make the problem eaiser that the solver thought it would be.\r
\n\r
\n',1626,'Gamer','2003-05-30 10:31:42');
INSERT INTO forumpost VALUES (1071,17,6,'Re: HTML codes for use on the site','First, I believe that it has been disabled on this site, which is why DJ asked about re-enabling it.\r
\n\r
\nAnd second, the closing tag needs a backslash (/) at the beginning.\r
\n\r
\nJust to test my belief that it is disabled: <S>test<S>',153,'TomM','2003-05-30 11:00:21');
INSERT INTO forumpost VALUES (1072,17,6,'Re: HTML codes for use on the site','Yup, disabled.',153,'TomM','2003-05-30 11:00:45');
INSERT INTO forumpost VALUES (1073,17,6,'Re: HTML codes for use on the site','Hmmph-- I know I included the backslash! That must be how it disabled it. Sorry for assuming you\'d missed it, Gamer.',153,'TomM','2003-05-30 11:02:38');
INSERT INTO forumpost VALUES (1074,17,6,'Re: HTML codes for use on the site','Just to throw in a bit of pedantry, that\'s a forward slash.',103,'friedlinguini','2003-05-30 11:35:28');
INSERT INTO forumpost VALUES (1075,88,4,'Re: problem difficulties','For the record, I didn\'t have a problem with the difficulty of \"Average of Reciprocals.\" I figured that you\'d basically wind up with two camps of people: those who knew enough algebra that they wouldn\'t think twice about how to solve it and those who hadn\'t yet learned about the quadratic equation and would be unlikely ever to get it. There might be a small group of people in the middle who were pretty good with algebra but hadn\'t quite gotten as far as the QE, but were just bright enough to derive it for themselves. The problem would have appeal for that latter group, but I think they\'d be a very small minority of the visitors to the site.',103,'friedlinguini','2003-05-30 11:39:55');
INSERT INTO forumpost VALUES (1076,17,6,'Re: HTML codes for use on the site','I had to do it twice to make sure I included it! I was like \"Didn\'t I include a backslash?!?!\", but now I know I\'m not going crazy!',1626,'Gamer','2003-05-30 16:07:04');
INSERT INTO forumpost VALUES (1077,88,4,'Re: problem difficulties','Ok... Thanks to all who contributed in helping me understand!',1626,'Gamer','2003-05-30 16:15:50');
INSERT INTO forumpost VALUES (1078,155,4,'Solutions allowed?','Would having an option to allow a solution to be read along with the problem be a good idea? Although I understand anyone who votes on the problem might not want to see the solution, but I have had a problem or two in which I think this could be helpful. Or is it too rare an event for the trouble?',1626,'Gamer','2003-05-30 16:19:53');
INSERT INTO forumpost VALUES (1079,156,7,'Yo!','Hey everyone! I\'m 15, play chess, basketball, karate. This site is awesome, I found it on google, and hope you guys think up some more decent puzzles.',2341,'Pickels','2003-05-30 18:03:08');
INSERT INTO forumpost VALUES (1080,17,6,'Re: HTML codes for use on the site','<s> strikeout <s> ',979,'Ravi Raja','2003-05-30 18:18:05');
INSERT INTO forumpost VALUES (1081,17,6,'Re: HTML codes for use on the site','<s> strikeout <s> \r
\n',979,'Ravi Raja','2003-05-30 18:19:30');
INSERT INTO forumpost VALUES (1082,17,6,'Re: HTML codes for use on the site','Where\'s the forward slash going? The entire expression remains as it is but the slash disappears !! It does not work the way we want it to. ',979,'Ravi Raja','2003-05-30 18:20:33');
INSERT INTO forumpost VALUES (1083,156,7,'Re: Yo!','Welcome to the site Pickels. :) ',979,'Ravi Raja','2003-05-30 18:24:27');
INSERT INTO forumpost VALUES (1084,157,3,'Static Queque','I have submitted around 12 problems under various categories. Whenever I check the Pending problems status, the queque no. for each problem appears to be same from the date of submission. I do not know whether I am seeing the updated status or the old status everytime. Has anyone else faced a similar situation?',2148,'Jayaram S','2003-05-30 19:13:54');
INSERT INTO forumpost VALUES (1085,17,6,'Re: HTML codes for use on the site','Strikeout should be fixed.\r
\r
\nPre - \r
\n formatted text \r
\nshould be
\nEnabled for Apprentices and above.',1,'levik','2003-05-30 19:19:54');
INSERT INTO forumpost VALUES (1086,17,6,'Re: HTML codes for use on the site','However, because line breaks in comments and forums are automatically turned into BR\'s, all PRE\'d text there will be double-spaced. (Problems and solutions will not have this issue)',1,'levik','2003-05-30 19:21:36');
INSERT INTO forumpost VALUES (1087,157,3,'Re: Static Queque','One of my problems seems to have been 22nd in the queue for a few days now. I\'m not sure whether the rest of mine are having the same problem though.',1919,'Lewis','2003-05-30 21:13:09');
INSERT INTO forumpost VALUES (1088,157,3,'Re: Static Queque','It does take some time Jayaram. The problems in the queue are voted, then pushed up in the site or out of the queue and then the new problem from the pending list enters the queue. Since there are so many pending problems so may be because of that you are facing that problem. But do not worry, your problem will soon be there in the queue as the queue is always moving (though slowly). ',979,'Ravi Raja','2003-05-30 21:17:58');
INSERT INTO forumpost VALUES (1089,155,4,'Re: Solutions allowed?','Well i guess this COULB be made but maybe instead of displaying the solution there is a link on the problem in the queue. Yes as you said this would be a rare event but nevertheless if it has a chance of happening and you believe it will happen thenthe option should be at you control (Correct me if i\'m wrong but i think the solution queue only displays posted problems?)',1072,'Alan','2003-05-31 03:43:12');
INSERT INTO forumpost VALUES (1090,157,3,'Re: Static Queque','It does take a while ;) My second problem had been voted on, and I submitted it about 50 days ago! I don\'t know why the queue number would be the same though.',1626,'Gamer','2003-05-31 06:14:55');
INSERT INTO forumpost VALUES (1091,17,6,'Re: HTML codes for use on the site','strikeout',1626,'Gamer','2003-05-31 06:15:51');
INSERT INTO forumpost VALUES (1092,17,6,'Re: HTML codes for use on the site','Ok it\'s not fixed fixed!',1626,'Gamer','2003-05-31 06:16:17');
INSERT INTO forumpost VALUES (1093,158,5,'Order of things','I have been puzzling about the order of two things: The order of comments from journeymen (and above) on problems, and the order that the \"Problems submitted\" are listed. I can\'t see any way that they are organized... Is there an order I don\'t see?',1626,'Gamer','2003-05-31 06:20:10');
INSERT INTO forumpost VALUES (1094,17,6,'Re: HTML codes for use on the site','No!',1660,'Tim Axoy','2003-05-31 06:42:28');
INSERT INTO forumpost VALUES (1095,157,3,'Re: Static Queque','My problems don\'t seem to be moving, either, but I am not sure if that is an actual bug or simply a result of an overloaded queue. I have also noticed that a few of my problems that had a queue position higher than 90 or 100 seemed to suddenly jump to around 10 when voters began to comment on them. Again, this could be a result of \'queue weight,\' as I am not sure still exactly how that works.\r
\n\r
\nOne other thing, though, that I have noticed is that nothing seems to be in order chronologically any more, at least in the queue. It seems that every second or third problem I submit to the queue \'sticks\' to the top of the list, above current problems and any earlir submissions. For example, the dates on my submitted problems (in the order they are showing up on my page) are:\r
\n\r
\r
\nDate Weight Position\r
\n5/28 16 313\r
\n5/13 11 282\r
\n5/28 16 314\r
\n5/26 Current Problem (that\'s the date it was posted, not submitted)\r
\n5/28 \" \"\r
\n4/1 1 6 (Currently in voting queue)\r
\n4/2 1 8 (Currently in voting queue)\r
\n4/2 2 99\r
\n4/2 2 100\r
\n4/10 3 136\r
\n4/10 3 137\r
\n. . .\r
\n
\nThe rest of the problems appear to be in order. Aside from the odd problems at the beginning, it does seem that the queue position is not updating, at least, not until a problem reaches the voting queue.\r
\n',1575,'DJ','2003-05-31 06:50:35');
INSERT INTO forumpost VALUES (1096,155,4,'Re: Solutions allowed?','I\'m sorry everyone, but I\'m REALLY against showing the solution to anyone prior to having the problem go live.\r
\n\r
\nThink about it. A lot of active users (and commenters) on this site have been around for a while, and are now Journeymen. A number of others will be soon. If they got to see the solution before the problem is live, we would lose a big part of the discussion.',1,'levik','2003-05-31 06:55:29');
INSERT INTO forumpost VALUES (1097,157,3,'Re: Static Queque','Whoa, my comment died...I know that I closed the <pre> tag, but perhaps it was too wide? For some reason, the text stopped wrapping, not sure why that would have happened. Anyway, let me continue:\r
\n\r
\nAside from the odd problems at the beginning, it does seem that the queue position is not updating, at least, not until a problem reaches the voting queue. I\'ve noticed that problems don\'t seem to move, but had previously attributed it to the slow queue itself. However, under closer scrutiny, I doubt that of the problems I submitted April 2, 91 problems were submitted after the first one before I got to the latter two, for example. Any ideas?',1575,'DJ','2003-05-31 06:56:13');
INSERT INTO forumpost VALUES (1098,158,5,'Re: Order of things','This is what happens when you build parts of a system that you don\'t use.\r
\n\r
\nNaturally this should have been done by date - let\'s see if it\'s any better now.',1,'levik','2003-05-31 06:58:36');
INSERT INTO forumpost VALUES (1099,17,6,'Re: HTML codes for use on the site','\r
\r
\nThe pre appears\r
\n to be\r
\n working\r
\n but\r
\n although:\r
\n
\nWhat happens if I leave a really long line of comment after closing the </pre> tage? I did this before, in another forum, and it seemed to kill the text wraparound.\r
\nLet\'s see what happens...',1575,'DJ','2003-05-31 07:00:57');
INSERT INTO forumpost VALUES (1100,158,5,'Re: Order of things','It\'s still not working for me...see the comment I left under the \"Static Queue\" thread in the General forum. And yes, voter comments are out of order for me too.',1575,'DJ','2003-05-31 07:04:24');
INSERT INTO forumpost VALUES (1101,17,6,'Re: HTML codes for use on the site','The next line of text will not wraparound. Hm..',1575,'DJ','2003-05-31 07:04:33');
INSERT INTO forumpost VALUES (1102,157,3,'Re: Static Queque','The discrepancy you are seeing is due to the Queue Weight mechanism. Essentially it means that everybody\'s first two problems come before anyone\'s third and fourth problem.\r
\n\r
\nThat\'s the queue weight: your first two problems in the queue have a weight of 1, next two are weighed 2, etc. A queue is ordered in a way that all QW 1 problems come before QW2 ones. However, once a problem with QW1 us either pushed live or deleted, that night a QW2 problem is promoted to QW1 to take its place.\r
\n\r
\nI am betting you will see one of your QW2 problems jump ahead as soon as either one of the QW1 problems is moved out of the Queue one way or another.',1,'levik','2003-05-31 07:05:47');
INSERT INTO forumpost VALUES (1103,155,4,'Re: Solutions allowed?','I agree with levik. I\'m not a Journeyman yet, but I will be soon, and I really don\'t even want the temptation of that option when looking at new problems. Isn\'t it enough that voters see all the problems days or weeks before they go live? It seems that there only a few minutes as it is before Charlie or someone posts a solution to a newly live problem. If knowing something about the solution is necessary while a problem is in the voting queue, just ask the author (as with my \"honor your mother\" problem).\r
\n\r
\nAs an aside, how do the solutions for live problems decide to be posted? Is it a timed event, or just whenever levik decides that the discussion is done?',1575,'DJ','2003-05-31 07:18:10');
INSERT INTO forumpost VALUES (1104,157,3,'Re: Static Queque','HOORAY!\r
\nMy frozen problem just moved ONE SPACE FORWARD!!!',1919,'Lewis','2003-05-31 08:17:59');
INSERT INTO forumpost VALUES (1105,155,4,'Re: Solutions allowed?','Generally it\'s not very precise :) I will look at the front page, and see how far down the unsolved problems extend... If it goes too far for my liking, I will post a few solutions.\r
\n\r
\nHowever, recently, I added a way for journeymen to see and comment on submitted solutions after the problem has been live for 2 days. After 4 days, scholars can make these solutions live.',1,'levik','2003-05-31 09:00:46');
INSERT INTO forumpost VALUES (1106,155,4,'Re: Solutions allowed?','Ok... I see your point. I think the recent addition would be useful instead. :)',1626,'Gamer','2003-05-31 10:46:17');
INSERT INTO forumpost VALUES (1107,157,3,'Re: Static Queque','*Celebrates* Yay!',1626,'Gamer','2003-05-31 10:47:01');
INSERT INTO forumpost VALUES (1108,88,4,'Re: problem difficulties','Also, rather than a limited set of specific examples, perhaps somewhere on the site, like on the problem submission page, could be a rubric for giving a problem a difficulty rating. A lot of discrepancy could be avoided that way, and any disputes would have something fall back on, like a reason you think the problem should or should not be given a specific difficulty.\r
\n\r
\nOf course, I still also like the three-option idea I mentioned above, but no one has commented on that. What do you think?',1575,'DJ','2003-05-31 15:35:32');
INSERT INTO forumpost VALUES (1109,154,3,'Re: Google Puzzle Championship','Those were 23 of the best and hardest problems I have ever seen.\r
\nIt was fun, but when I went to submit my solution I kept getting \"Server busy; try again\" errors for an hour after the test ended. I\'m sure it didn\'t matter, as I only had solved enough for 170 out of 400 possible points, but I was still disappointed that I never had anything to show for it, but it was fun and I am still working on some of the problems. Most of them are digrams or grids and not really fitting for the usual kinds of problems on this site. Just wondering, did anyone else try it?',1575,'DJ','2003-05-31 16:28:13');
INSERT INTO forumpost VALUES (1110,154,3,'Re: Google Puzzle Championship','PS: Thanks, levik, for bringing it to my attention! It was a lot of fun. Also, I have a copy of the PDF file (and the password, since it is encrypted) for anyone who wants to look at the problems.',1575,'DJ','2003-05-31 16:35:14');
INSERT INTO forumpost VALUES (1111,63,3,'Re: a/s/l anyone?','Levik,what is your a/s/l?',1660,'Tim Axoy','2003-06-01 02:24:14');
INSERT INTO forumpost VALUES (1112,159,3,'Knights and liars problems','Here is a way to solve Knights and liars problems using propositional logic.\r
\n
\n1:Suppose a knight or a liar says,\"The proposition P is true.\"\r
\nWe notice that if they are a knight,then P is true and if P is true,then they are a knight,so they are a knight if and only if P is true.\r
\nIn symbols,K<->P is true,where K is the proposition that they are a knight.\r
\n
\n2:We use ~ to mean not,& to mean and,v to mean or,-> to mean if-then,and <-> to mean if-and-only-if.\r
\n
\n3:In a puzzle with more than one person,we let Kk be the proposition that the kth person is a knight.\r
\n
\n4:We let ~K be the proposition that a person is a liar and ~Kk be the proposition that the kth person is a liar.\r
\n
\n5:Example:A says,\"B and I are both liars.\"\r
\nLet A be the first person and B be the second person,so K1=A is a knight,K2=B is a knight,~K1=A is a liar,and ~K2=B is a liar.\r
\nA asserted (~K1)&(~K2),so by 1,K1<->((~K1)&(~K2)) is true.\r
\nObviously K1 is false since if it was true,then K1 and K2 would both be false,which is a contradiction.\r
\nSince K1 is false and equivalent to (~K1)&(~K2),(~K1)&(~K2) is also false,but ~K1 is true,so ~K2 is false.\r
\nTherefore,K1 is false and K2 is true,so A is a liar and B is a knight. ',1660,'Tim Axoy','2003-06-01 03:19:50');
INSERT INTO forumpost VALUES (1113,63,3,'Re: a/s/l anyone?','You don\'t need to ask twice!',1626,'Gamer','2003-06-01 07:26:27');
INSERT INTO forumpost VALUES (1114,17,6,'Re: HTML codes for use on the site','I love you.',1660,'Tim Axoy','2003-06-01 08:56:03');
INSERT INTO forumpost VALUES (1115,17,6,'Re: HTML codes for use on the site','I love you.
',1660,'Tim Axoy','2003-06-01 08:58:29');
INSERT INTO forumpost VALUES (1116,160,7,'hello','Just signed up for this site and wanted to say hi.I have not had a chance to look around yet so if you have any favorites you think I would enjoy let me know.But please I am kind of a beginer so keep me in the medium ones!',2355,'annastashya','2003-06-01 16:58:39');
INSERT INTO forumpost VALUES (1117,161,7,'Maybe I\'ll get smarter?','HI, I found the flooble website from a Xanga.com members Chatterbox. I now have a chatter box on my website (MissAmerazia on Xanga). My boyfriend independently found the flooble site and got really excite about the calculus problems. Something I can\'t really relate to. :) Anyway, I\'m a college student in Cali and I thought this website might help stretch my brain in areas that I usually try to avoid (math, science etc.) sayonara~ \r
\n\r
\n',2356,'Stefanie','2003-06-01 21:33:49');
INSERT INTO forumpost VALUES (1118,162,7,'Maybe I\'ll get smarter?','HI, I found the flooble website from a Xanga.com members Chatterbox. I now have a chatter box on my website (MissAmerazia on Xanga). My boyfriend independently found the flooble site and got really excite about the calculus problems. Something I can\'t really relate to. :) Anyway, I\'m a college student in Cali and I thought this website might help stretch my brain in areas that I usually try to avoid (math, science etc.) sayonara~ \r
\n\r
\n',2356,'Stefanie','2003-06-01 21:35:02');
INSERT INTO forumpost VALUES (1119,159,3,'Another example','This example is called,\"Why no one can claim to be a liar.\"\r
\nObviously,there is no proposition K such that K<->(~K) is true.\r
\n
\nSuppose A says,\"I am a liar.\"\r
\nA asserted ~K,and by our knights and liars trick,K<->(~K) is true.\r
\nHowever,that is impossible.',1660,'Tim Axoy','2003-06-02 02:46:56');
INSERT INTO forumpost VALUES (1120,154,3,'Re: Google Puzzle Championship','DJ: I would like to go through those problems. Please send me those problems and please check your inbox too. I have sent you a mail regarding these problems.',979,'Ravi Raja','2003-06-02 05:11:07');
INSERT INTO forumpost VALUES (1121,154,3,'Re: Google Puzzle Championship','DJ: I would like to go through those problems. Please send me those problems and please check your inbox too. I have sent you a mail regarding these problems.\r
\nThank You',979,'Ravi Raja','2003-06-02 05:11:17');
INSERT INTO forumpost VALUES (1122,162,7,'Re: Maybe I\'ll get smarter?','Welcome to the site, Stefanie. We get a lot of people here from Xanga\'s wide use of chatterbox, but few of them ever stay long enough to make an account :)\r
\n\r
\nWelcome aboard. (Bring friends :)',1,'levik','2003-06-02 09:34:27');
INSERT INTO forumpost VALUES (1123,160,7,'Re: hello','Welcome to the site. I would suggest you browse to the earlier problems (they would be on the higher numbered pages in their respective categories) They tend to require more creativity than hard-core math, so may be easier for you.',1,'levik','2003-06-02 09:36:00');
INSERT INTO forumpost VALUES (1124,160,7,'Re: hello','There are a lot of easier, but fun, puzzles in the \'Liars and Knights\' category in \'Logic\'.',1919,'Lewis','2003-06-02 10:23:05');
INSERT INTO forumpost VALUES (1125,17,6,'Re: HTML codes for use on the site','Other codes that might be found useful are subscripts (<sub>) and superscripts (<sup>). Subscripts would make many algebra problem solutions less confusion by, say, replacing x1, x2, x3 with actual subscripted variables. Superscripts are useful, of course, for exponents (other than x¹, x², and x³ which are always available).',1575,'DJ','2003-06-02 10:28:57');
INSERT INTO forumpost VALUES (1126,154,3,'Re: Google Puzzle Championship','Yes dj i wouldn\'t mind seeing these problems either. If it isn\'t to much trouble could you send them to me as well?\r
\n',1072,'Alan','2003-06-02 10:33:09');
INSERT INTO forumpost VALUES (1127,163,5,'New bugs?','I have noticed a few problems with the <pre> tag, presumably due to the way PHP handles arrays. First, the closing tag does not always work, leaving all remaining text within the tag, and if it happens to be a paragraph (or more than one line long), it will overflow the width of the containing box. Also, for some of my problems for the algorithms category, the programming codes are not properly handled, changing some quotes (\") into escaped quotes (\\\") each time I modify the problem. So, something that starts out as printf(\"-\") will after a few modifications become printf(\\\\\\\\\"-\\\\\\\\\"), and so on. It does this whether I type in the quotes directly or if I use the HTML " code. Obviously, I can\'t offer a remedy without knowing how the page works, but perhaps the stripslashes() function in PHP3+ would serve as a solution.\r
\n\r
\nJust a test:\r
\n\r
\n\r
\r
\nstring hi=\"Hello\";\r
\nprintf(\"Hello\\n\");\r
\nprintf(hi);\r
\n
\nAnd now I\'ll type a big long line to see if it will still wraparound. Note, I made sure to close the </pre> tag..\r
\n',1575,'DJ','2003-06-02 12:06:12');
INSERT INTO forumpost VALUES (1128,163,5,'Re: New bugs?','The quotes don\'t seem to be a problem right now, but you can see the wraparound bug. Perhaps the quotes are only a problem in problems and solutions, which are set up somewhat differently than the comments and forum posts.',1575,'DJ','2003-06-02 12:12:03');
INSERT INTO forumpost VALUES (1129,17,6,'Re: HTML codes for use on the site','Also, it might be nice to unlock the \'type\' parameter for ordered and unordered lists (<ol> and <ul>), so that we can make lists using numbers, letters, numerals, discs, circles, squares, etc, besides the default numbers for <ol> and circles for <ul>.',1575,'DJ','2003-06-02 12:30:09');
INSERT INTO forumpost VALUES (1130,163,5,'Re: New bugs?','And actually, looking at the page source, the tags are showing up correctly. I can think of no reason it would mess up like that, unless one of the scripts linked by source is doing something..\r
\n\r
\nI guess nothing is ever as simple as it seems.',1575,'DJ','2003-06-02 13:20:14');
INSERT INTO forumpost VALUES (1131,154,3,'jumping on bandwagon','I would also like to see the puzzles. I didn\'t enter because in typical google/yahoo/hotmail style, non-US residents were not eligible...',775,'Cory Taylor','2003-06-02 13:23:28');
INSERT INTO forumpost VALUES (1132,154,3,'Re: Google Puzzle Championship','Thank you dj for sending me the puzzles. I appreciate it a lot. cory, i\'ll send you the puzzles.',1072,'Alan','2003-06-02 13:52:08');
INSERT INTO forumpost VALUES (1133,154,3,'Re: Google Puzzle Championship','Cory, you should have recieved the file by now. Regarding your statement about ineligibility, well, it was the US Puzzle Championship. I believe, though, that residents of other countries were allowed to enter, and the same test was used to determine the members of both the US and Canadian puzzle teams.\r
\n\r
\nIn fact, the rules page stipulates:\r
\n\"The top two US contestants will be selected for the US Team to compete at the World Puzzle Championship in the Netherlands in October, 2003.\r
\nThe top 25 US contestants will receive a prize, donated by team sponsor Binary Arts.\r
\nThe top three Canadian contestants will be invited to join the Canadian Team to complete at the World Puzzle Championship. Alternates will be selected if necessary, based on test results and availability to compete.\r
\nScores for participants from other countries will be tallied and may be forwarded to the corresponding WPC team organizer for consideration. If there is no organized team, you may be contacted regarding potential individual WPC participation.\"',1575,'DJ','2003-06-02 16:04:22');
INSERT INTO forumpost VALUES (1134,17,6,'Re: HTML codes for use on the site','Actually, since one of the reasons levik resticted so many html codes is to assure that the \"look\" or \"style\" of the page matches the \"look\" or \"style\" of the rest of the site, restricting the type of bullets in lists to the standard ones makes sense. (Although I can see that using different ordered list bullets might be desirable in constructing an outline.)',153,'TomM','2003-06-02 16:30:53');
INSERT INTO forumpost VALUES (1135,154,3,'Me too, DJ','I suppose I should read the forum more frequently. DJ, could you send me the pdf and password? Thanks.',1567,'Bryan','2003-06-02 17:19:20');
INSERT INTO forumpost VALUES (1136,154,3,'Re: Google Puzzle Championship','I didn\'t enter as I was in the same boat with levik, but I would like to see them too! Mail it to the address on my profile.',1626,'Gamer','2003-06-03 02:19:38');
INSERT INTO forumpost VALUES (1137,17,6,'Re: HTML codes for use on the site','The suggestions I am making here are generally as I notice something I would like to do or something that would potentially make the site easier to read and give the problems and solutions a good look that is easily achieved rather than manual spacing or messy algebraic equations, as the case may be. Whenever I am posting a problem, solution, or comment and notice something that I would normally do in HTML to format the text, but cannot, I suggest it be reinstated if I feel it would be useful.\r
\n\r
\nSpecifically, regarding the list types, the convention for problems with multiple parts or more than one question to answer is for each item to be assigned a lowercase letter, as in: \r
\n\"a. What is the answer?\r
\n b. Prove that this is the only solution.\r
\n c. What if you changed x to 3?\"\r
\netc... This is simply and neatly achieved by using <ol type=\"a\">, whereas the <ol> tag defaults to Arabic (1, 2, 3, ...) ordered listing.\r
\nAlso, for problems with more than one major part, it is perhaps desirable to list them with capitalized Roman numerals (I, II, III, IV, ...).\r
\nThe other thing, especially regarding a consistent style of the site, is that an unordered list default to \"disc\" bullets, but when nested within another list, it changes to \"circle\" bullets. This happened in one of my problems, where I had a numbered list of items, one of which had several bulleted points, and I was going to change the bullets to the solid discs to match the rest of the site.\r
\n\r
\n\r
\r
\n
\n
\n\r
\n
\n
\n
\n
\n
\n\r
',1575,'DJ','2003-06-03 02:41:56');
INSERT INTO forumpost VALUES (1138,154,3,'jumping on bandwagon','Same was the reason for me. As I am from India, after registering, you are supposed to receive a mail from them confirming your registration but nothing of that sort happened. I did not receive any mails and therefore no password and so no puzzles. :( :(',979,'Ravi Raja','2003-06-03 04:36:07');
INSERT INTO forumpost VALUES (1139,17,6,'Re: HTML codes for use on the site','DJ: I understand that these may be more convenient, but unfortunately I cannot currently allow the use of types, because of the difficulty of checking for well-formed tags. Already the HTML-filtering code is more complex than I would like it. Perhaps one day I will find a good pluggable solution to this (maybe something like the Bulletin Board codes used on some forums) - but until then we\'ll have to make do with default lists. \r
\n
\n
\n
\n
\n\r
\nThe technical aspect of it is pretty much the only motivator here - I do not really object to people using \"empty\" bullets at all (so your example above is actually fine)',1,'levik','2003-06-03 05:53:26');
INSERT INTO forumpost VALUES (1140,164,4,'Scholars','What are the names of the scholars?',1660,'Tim Axoy','2003-06-03 05:59:36');
INSERT INTO forumpost VALUES (1141,17,6,'Re: HTML codes for use on the site','I assumed that the reasoning behind disallowing types or other parametrized tage was due to the complex programming required, especially trying to allow only certain parameters for use within the tag. I feel as if people think I am imposing demands on levik or on the site, but in running several websites for other people I know all too well what it\'s like to try to keep up with the technical and stylistic demands of other people for a site. Please take my suggestions as just that, mere suggestions.',1575,'DJ','2003-06-03 12:21:27');
INSERT INTO forumpost VALUES (1142,17,6,'Re: HTML codes for use on the site','I\'d be surprised if there isn\'t decent preexisting code for stripping \"bad\" HTML from the contents of a web form. By the way, any chance of getting the extra line breaks out of the <pre>-formatted text?',103,'friedlinguini','2003-06-03 13:23:56');
INSERT INTO forumpost VALUES (1143,17,6,'Re: HTML codes for use on the site','Comment 1 on Quaker Queens of Chess uses pre, and looks single-spaced. Had it been fixed already?\r
\n\r
\n',1301,'Charlie','2003-06-03 16:18:20');
INSERT INTO forumpost VALUES (1144,17,6,'Re: HTML codes for use on the site','Or is it a smaller typeface, which partially masks the double spacing? It looks like that might be the case from DJ\'s 5-31 test above, though it\'s hard to tell on the Quaker Queen comment as only *\'s and .\'s are present.',1301,'Charlie','2003-06-03 16:23:10');
INSERT INTO forumpost VALUES (1145,17,6,'Re: HTML codes for use on the site','I didn\'t notice that there ever was a problem with the double-spaced text. If there was, levik fixed it shortly after enabling the tag.',1575,'DJ','2003-06-03 16:24:35');
INSERT INTO forumpost VALUES (1146,165,4,'User search/list?','So people have been asking for a user search/list feature - and I have been thinking about it too prior to now, but without a good soluiton.\r
\n\r
\nSimply listing everyone is really impractical (even though there is an unlisted page to see everyone: it\'s here...\r
\n\r
\nA simple search box seems like it would not be sufficient, at least not without a good way to find close matches, which may be difficult. And I don\'t really want to make a page listing all the upper ranking users because that would expose them to people bugging them about various stuff such as \"when will my problem show up\"',1,'levik','2003-06-03 17:32:46');
INSERT INTO forumpost VALUES (1147,154,3,'Re: Google Puzzle Championship','You did not need to recieve an email or anything else in order to do the puzzles. When you went to the page levik linked above, and signed up, you were taken to another page with a link on it. That page said to go to the link and save the bookmark, as you would not recieve the link to that page again. The file with the test problems, as well as its password, a practice test, the rules, everything was on the second page after you signed up. You needed no password to access anything except to open the test file itself, and I\'m not sure that I even did get anything by email from them. If I did, it was trivial, because everything for the test was right online.',1575,'DJ','2003-06-04 02:33:09');
INSERT INTO forumpost VALUES (1148,17,6,'Re: HTML codes for use on the site','Kk',1660,'Tim Axoy','2003-06-04 02:57:16');
INSERT INTO forumpost VALUES (1149,17,6,'Re: HTML codes for use on the site','\r
',1301,'Charlie','2003-06-04 03:48:40');
INSERT INTO forumpost VALUES (1150,17,6,'Re: HTML codes for use on the site','I\'ve found that a paragraph entered even before the pre tag is extending out (getting cut off) beyond the right margin. See my posted comment on \"Move the 2 - Double the Number\". The first paragraph was before any pre tag. It seems the only reason that any of the remainder of the paragraph is showing is that I had copied and pasted from Notepad while Notepad was in word wrap mode, and it took the line breaks where Notepad had them. (...which is a strange feature in itself, as notepad shouldn\'t send automatic line breaks into the clipboard, but apparently it does.)',1301,'Charlie','2003-06-04 04:09:46');
INSERT INTO forumpost VALUES (1151,17,6,'Re: HTML codes for use on the site','Ugh. Seems like a browser-specific issue, then. In Mozilla Firebird, the chessboard solution looks double-spaced. In IE, it looks fine. More fun for the lev-man. :-)>',103,'friedlinguini','2003-06-04 04:44:12');
INSERT INTO forumpost VALUES (1152,166,4,'DJ or .?','Did DJ or . make Going up?',1660,'Tim Axoy','2003-06-04 05:33:59');
INSERT INTO forumpost VALUES (1153,165,4,'Re: User search/list?','Another thing I just thought of. If the masses are looking for a list of the scholars so that they know what to exeplify so as to become one also, that defeats the wonderfulness of just being able to come here and be yourself. Maybe this is a little unclear, but my point revolves around the fact that there have been many comments I\'ve seen where somebody is asking how to get promoted from where they are to the next level, and I see this level listing as a way for people to facilitate their promotion - which I feel is not necessarily a good thing. Just hang around for a while and you\'ll get there works much better from my point of view - it avoids the situation where somebody new here sees that they need x of this requirement and y of that requirement so they just do that to get the \"level\", while sidesteping any relevant addition to the site as a whole.\r
\nunderlined within pre\r
\n
\nOK, so now I realize that I\'m rambling, and to boot and somewhat (only somewhat) off topic, so I\'ll end it with this. Originally I hought this would be a great idea, but for those of us that hang around a lot, we don\'t really need the attachment of a label to help us decide who we should be listening to, emulating, following or what have you.',775,'Cory Taylor','2003-06-04 07:46:10');
INSERT INTO forumpost VALUES (1154,163,5,'Re: New bugs?','Another thing I saw is people (like the uid=3 and such) where the user hasn\'t logged in in over 12000 days, which is about 37 or 38 years I think. Unless this site is up for 38 years, that is obviously a problem.',1626,'Gamer','2003-06-04 09:43:17');
INSERT INTO forumpost VALUES (1155,17,6,'Re: HTML codes for use on the site','Well, based just on the HTML, something that is typed as:\r
\n\r
\nsome text\r
\n<pre>\r
\nline of something\r
\nsomething else\r
\n</pre>\r
\nthe end.\r
\n\r
\nis automatically changed (in comments and forums) to:\r
\n\r
\nsome text\r
\n<br>\r
\n<pre>\r
\n<br>\r
\nline of something\r
\n<br>\r
\nsomething else\r
\n<br>\r
\n</pre>\r
\n<br>\r
\nthe end.\r
\n\r
\nwhen it is submitted. This will appear double-spaced in IE and double- or triple-spaced in other browsers. Levik must have added a fix to somehow disable the line breaks or the <br> within the </pre> tag, without changing the page source, I would assume with Javascript or some other client-side browser-controlled language. With an older browser or a third-party browser that did not have full JS support, those fixes will probably not appear correctly.',1575,'DJ','2003-06-04 10:02:36');
INSERT INTO forumpost VALUES (1156,165,4,'Re: User search/list?','That comprehensive list, by name alphabetically, is of course very large and not very useful as it is. If there were some way to sort out active members, perhaps by the datestamp of their last post, comment, login, or something like that, and perhaps active \'veteran\' members based on the date they signed up. Those might be more useful, I think.\r
\n\r
\nAs it is now, I totally agree with Cory. Just being around the site and reading peoples\' comments, problems, whatever, you can get a good idea of who is around, who knows what they\'re talking about most of the time, even who just puts up mindless drivel. It\'s certainly a web community environment, though perhaps in not being centered around problems rather than people or discussion tends to change the feel a bit.\r
\n\r
\nI never thought or cared about other people\'s ranks until levik mentioned that there are only 2 or 3 needed. Actually, as far as \"figuring out\" who the site\'s named scholar\'s are, it really didn\'t take me very long. There are a few that I haven\'t seen around the site in a while, if at all since I have been here, but even from just looking at some of the older problems it was not too hard to figure out who the scholars are. There were a few users who I thought might have been up there too, like fwaff, Cory Taylor, Gamer, and a few others. Just from being around, you get familiar with the site and the other people here.',1575,'DJ','2003-06-04 11:09:42');
INSERT INTO forumpost VALUES (1157,163,5,'Re: New bugs?','Those users have not been recorded as having ever logged on, so that time is just from the start of system time, which on most systems is (I think) 1970. On this site, it doesn\'t appear that anything before May 5 of last year was properly logged, and anyone with a uid < 65 (except, of course, for number 1, levik) is not showing up as having ever logged on, even if they have left comments or posted problems.',1575,'DJ','2003-06-04 11:22:48');
INSERT INTO forumpost VALUES (1158,17,6,'Re: HTML codes for use on the site','Either that or IE is rendering the text incorrectly (I\'m more upset at Microsoft than usual right now, so that seems to be the most likely answer).',103,'friedlinguini','2003-06-04 11:24:44');
INSERT INTO forumpost VALUES (1159,17,6,'Re: HTML codes for use on the site','I don\'t think so, because the second snippet of code in my previous post will always show up as double-spaced in IE without some sort of JS post scripting. Try it for yourself; copy the text into notepad and save it with a .htm extension, then open it with IE. You\'ll see the double spaces, actually quadruple between the first two lines of text (\"some text\" and \"line of something\"). It seems that levik intentionally (and quite painstakingly, I\'m sure) fixed the bug.\r
\n\r
\nIn any case, IE is rendering the text correctly, and the Mozilla browser is showing it incorrectly.',1575,'DJ','2003-06-04 12:56:10');
INSERT INTO forumpost VALUES (1160,140,4,'Rosencrantz & Gildenstern','Who are Rosencrantz & Gildenstern?\r
\nGildenstern was a character in Bryan\'s puzzle about the best room at the inn.\r
\n',1660,'Tim Axoy','2003-06-04 13:26:52');
INSERT INTO forumpost VALUES (1161,166,4,'Re: DJ or .?','DJ,you changed your name to . sometime today!',1660,'Tim Axoy','2003-06-04 13:27:54');
INSERT INTO forumpost VALUES (1162,140,4,'Re: Tim\'s Q','Tim, if you want to learn who Rosencrantz & Gildenstern are, read Shakespeare\'s Hamlet.',1567,'Bryan','2003-06-04 14:01:21');
INSERT INTO forumpost VALUES (1163,165,4,'Re: User search/list?','Although I agree all the way with you Cory, I don\'t think it would be easy to get to apprentice (or any higher rank) without submitting problems or being interested. It took me about one month to two months to get my problems up there... so you would need to be patient in flooble. If you weren\'t interested in flooble, you would have likely \"forgotten\" about flooble by that time.\r
\n\r
\nI agree with DJ\'s last point. It\'s not too hard to figure out who the smart ones are and who aren\'t... I think this was one of the major agreements against the \"Bryan\'s Identity crisis\" posts... He is a good flooble person, and would likely not do that.',1626,'Gamer','2003-06-04 16:58:19');
INSERT INTO forumpost VALUES (1164,108,7,'Re: Gladys','Tim!',1660,'Tim Axoy','2003-06-05 03:08:38');
INSERT INTO forumpost VALUES (1165,17,6,'Re: HTML codes for use on the site','\r
',1301,'Charlie','2003-06-05 03:44:07');
INSERT INTO forumpost VALUES (1166,17,6,'Re: HTML codes for use on the site','AS OPPOSED TO NON-PRE\'D TEXT:pppppppppppppp\r
\nI\'M TYPING IN UPPER CASE plus some descenders:ppppppppppp\r
\nTO GET A BETTER FEEL FOR THE SIZE OF THE FONT:ppppppppppp\r
\nWHEN THIS IS WITHIN PRE TAGS pppppppppppppppppppppppppppp\r
\n
\nCONTINUED HERE ON THIS LINE pppppppppppppp\r
\nAND TO MAKE A THIRD pppppppppppppppppp\r
\n',1301,'Charlie','2003-06-05 03:46:31');
INSERT INTO forumpost VALUES (1167,159,3,'Re: Knights and liars problems','Does anyone like this?',1660,'Tim Axoy','2003-06-06 06:14:15');
INSERT INTO forumpost VALUES (1168,110,5,'Re: Goner?','A:B is a liar.
\r
\nB:A is a knight.',1660,'Tim Axoy','2003-06-06 06:15:55');
INSERT INTO forumpost VALUES (1169,75,6,'Re: Director','Gladys.',1660,'Tim Axoy','2003-06-06 06:16:44');
INSERT INTO forumpost VALUES (1170,166,4,'Re: DJ or .?','DJ!',1660,'Tim Axoy','2003-06-06 06:17:26');
INSERT INTO forumpost VALUES (1171,159,3,'Re: Knights and liars problems','Hmmmm.... I was a little confused at first but now I understand. Very nice Tim :)',1919,'Lewis','2003-06-06 12:21:06');
INSERT INTO forumpost VALUES (1172,75,6,'Re: Director','Especially since you are both the boyfriend (Tim) and the girlfriend (Gladys).',1919,'Lewis','2003-06-06 12:24:32');
INSERT INTO forumpost VALUES (1173,167,7,'What\'s new? Me!','I\'m as moist as a snackcake down there-Jerri Blank',2385,'Bradley A. Esparza','2003-06-07 02:01:57');
INSERT INTO forumpost VALUES (1174,63,3,'Re: a/s/l anyone?','40/m/Seattle',2385,'Bradley A. Esparza','2003-06-07 02:12:53');
INSERT INTO forumpost VALUES (1175,167,7,'Re: What\'s new? Me!','I forgot to mention that I found the site from a link to fun stuff from the American Dialect Society email list.',2385,'Bradley A. Esparza','2003-06-07 02:24:18');
INSERT INTO forumpost VALUES (1176,167,7,'Re: What\'s new? Me!','Welcome to Flooble,Bradley A. Esparza.',1660,'Tim Axoy','2003-06-07 02:46:38');
INSERT INTO forumpost VALUES (1177,159,3,'Re: Knights and liars problems','Anyone else?',1660,'Tim Axoy','2003-06-07 09:33:55');
INSERT INTO forumpost VALUES (1178,75,6,'Re: Director','How did you find that out?',1660,'Tim Axoy','2003-06-08 02:27:27');
INSERT INTO forumpost VALUES (1179,75,6,'Re: Director','hehehe',1919,'Lewis','2003-06-08 02:28:48');
INSERT INTO forumpost VALUES (1180,168,6,'Cool.','Cool.',NULL,'URGENTOOT','2003-06-08 02:42:13');
INSERT INTO forumpost VALUES (1181,169,3,'500!','Hey, everyone! We\'re up to 500 problems today! (For those counting, the site\'s up about 15 months)\r
\n\r
\nThanks go out to everyone who\'s contributed, wether by posting comments or submitting problems. The site would not be what it is without you!',1,'levik','2003-06-08 09:07:53');
INSERT INTO forumpost VALUES (1182,169,3,'Re: 500!','Levik, is that 500 problems posted, or just 500 problems in front of my latest submission in the queue? Just kidding -- this is a great site; I\'m not surprised at all by it\'s success, or yours. Please keep up the good work :)',1567,'Bryan','2003-06-08 09:18:50');
INSERT INTO forumpost VALUES (1183,165,4,'Re: Gamer\'s plug','Thanks for the good word.',1567,'Bryan','2003-06-08 09:25:23');
INSERT INTO forumpost VALUES (1184,169,3,'Re: 500!','Yay... I agree with Bryan. It\'s like: Your problem is as place 10430953 in the queue.',1626,'Gamer','2003-06-08 13:35:35');
INSERT INTO forumpost VALUES (1185,170,4,'Cool symbols','i must say the symbols for each problem is rather neat, but in riddles you have a picture of the riddler? Is the riddler not copyrighted? Also in the general problem description it says \"or chich we are too lazy to classify will go here. \" I think chich should be which',1072,'Alan','2003-06-08 16:24:04');
INSERT INTO forumpost VALUES (1186,169,3,'Re: 500!','February 9 marked the 300th problem, and as of that date we had 70 problems in the queue. Today is June 9, only 120 days later, and we have 470 problems in the queue. At this rate, less than 2 weeks from now, there will be as many problems in the queue as there are which have been posted!',775,'Cory Taylor','2003-06-09 06:13:46');
INSERT INTO forumpost VALUES (1187,171,3,'Partial goodbye','Well folks, it\'s been a great ride, but unfortunately the road construction season here in Northern Alberta is once again upon us, and as a worker in this field my free time will shortly be dramatically reduced. In fact, my employer has decided to send me away for the entire season to a job north of where anybody should realistically live (Fox Creek, Alberta if anybody cares) for the entire season (which ends mid-October). I\'ll still be popping in of course on rain days and holidays etc., but certainly not on the scale I have been since I showed up here. I\'ll miss you guys and girls!',775,'Cory Taylor','2003-06-09 06:20:37');
INSERT INTO forumpost VALUES (1188,171,3,'Re: Partial goodbye','Take care, Cory. Don\'t let the caribou bite.',103,'friedlinguini','2003-06-09 07:14:32');
INSERT INTO forumpost VALUES (1189,171,3,'Re: Partial goodbye','Do come back Cory - we\'ll hopefully still be here in October. \r
\n\r
\n(Hey, who knows some of your problems might even make it to the site by then - though we can\'t promise anything :)',1,'levik','2003-06-09 07:41:27');
INSERT INTO forumpost VALUES (1190,170,4,'Re: Cool symbols','The riddler is copyrighted, but perhaps our use here is fair? Well, if the copyright holder cares to object to the usage of that image on the site I will promptly take it down. It wasn\'t really what I would call an optimal choice, but if anyone wants to propose a better icon for \"Riddles\", I\'m all ears - I couldn\'t think of anything myself.',1,'levik','2003-06-09 07:45:41');
INSERT INTO forumpost VALUES (1191,170,4,'Re: Cool symbols','In this case, it\'s actually a trademark issue, not a copyright one. Not sure if there\'s such thing as fair use for trademarks, other than acknowledging their owners.',103,'friedlinguini','2003-06-09 08:23:44');
INSERT INTO forumpost VALUES (1192,172,5,'Crypto','In light of this problem, I\'m thinking of making a cryprography category on the site.\r
\n\r
\nIdeas for an icon, as well as links to existing problems that should go there are now being solicited. (or perhaps the category should be named something else? should it be top-level, or in an existing cat.?)',1,'levik','2003-06-09 08:48:41');
INSERT INTO forumpost VALUES (1193,172,5,'Re: Crypto','I think cryprography should be a sub-category branching off of general. I don\'t think there\'ll be enough problems in this category to bother making a whole new one. Another problem that could fit into this category is a2o3t6t7 by brian. As for an icon, perhaps the 1001100010101 series that you get on computers, like in The Matrix.',1919,'Lewis','2003-06-09 09:01:22');
INSERT INTO forumpost VALUES (1194,171,3,'Re: Partial goodbye',':) We will miss you! Hope you do as well fixing/constructing the roads as you do in solving puzzles! :D',1626,'Gamer','2003-06-09 09:18:02');
INSERT INTO forumpost VALUES (1195,172,5,'Re: Crypto','I agree with Lewis, however I do have some ciphers saved up... :)\r
\n\r
\nI haven\'t submitted any others yet, as I didn\'t know if ciphers were good puzzles.',1626,'Gamer','2003-06-09 09:25:50');
INSERT INTO forumpost VALUES (1196,170,4,'Re: Cool symbols','I think a person with a ? over their head might be a good alternative if you didn\'t want that icon.\r
\n\r
\nI personally have looked at all of the previous problems (I think) and so I don\'t really click on those links. I just see the puzzles from the main page.',1626,'Gamer','2003-06-09 09:30:06');
INSERT INTO forumpost VALUES (1197,172,5,'Re: Crypto','I certainly like them. Its always a good type of puzzle to get you thinking.',1919,'Lewis','2003-06-09 09:36:08');
INSERT INTO forumpost VALUES (1198,164,4,'Re: Scholars','What are the names of the scholars?',1660,'Tim Axoy','2003-06-09 10:20:58');
INSERT INTO forumpost VALUES (1199,171,3,'Re: Partial goodbye','Bye,Cory!',2374,'J','2003-06-09 10:30:59');
INSERT INTO forumpost VALUES (1200,167,7,'Re: What\'s new? Me!','Hi,Bradley!',2374,'J','2003-06-09 10:31:34');
INSERT INTO forumpost VALUES (1201,168,6,'URGENTOOT!','URGENTOOT,you are not logged in!',2374,'J','2003-06-09 10:32:15');
INSERT INTO forumpost VALUES (1202,164,4,'Re: Scholars','Why do you always post things twice?',775,'Cory Taylor','2003-06-09 11:33:44');
INSERT INTO forumpost VALUES (1203,164,4,'Re: Scholars','Why do you always post things twice?',775,'Cory Taylor','2003-06-09 11:33:47');
INSERT INTO forumpost VALUES (1204,164,4,'Re: Scholars','Answer my question first.',1660,'Tim Axoy','2003-06-09 13:24:10');
INSERT INTO forumpost VALUES (1205,159,3,'J','Interesting.',2374,'J','2003-06-09 13:29:57');
INSERT INTO forumpost VALUES (1206,172,5,'Re: Crypto','Sounds like a good idea. I have a few interesting cryptograhpy puzzles.\r
\n\r
\nFor an icon, I would suggest something like the word \'puzzle\' in red letters on top of the string \'qvaamf\' in black letters.',1920,'Brian Smith','2003-06-09 17:14:31');
INSERT INTO forumpost VALUES (1207,173,6,'To Tim Axoy','Tim, I have deactivated your account. I think you know why. Email me if you want it back.',1,'levik','2003-06-09 17:37:14');
INSERT INTO forumpost VALUES (1208,172,5,'Re: Crypto','I will work on the icon and add the cateogry when it\'s ready then...\r
\n\r
\nOne note is that, I don\'t think we should have the hard-core crypto stuff on this site (such as algorithms requiring months of computer time to break, or ciphers the key to which is not in the problem body - for example having an encryption based on some famous series) Let\'s have codes that are fun and not too difficult. Self contained would be best.',1,'levik','2003-06-09 17:46:39');
INSERT INTO forumpost VALUES (1209,172,5,'Re: Crypto','Cool - that was quick. I like the icon. :o)\r
\n\r
\nI also agree about not having them too hard - I don\'t know how to do the computer related puzzles, like algorithms, and I assume that a few other people don\'t either.',1919,'Lewis','2003-06-09 21:27:59');
INSERT INTO forumpost VALUES (1210,173,6,'Re: To Tim Axoy','I want it back.\r
\nP. S. Why did you?',NULL,'Tim Axoy','2003-06-10 01:59:09');
INSERT INTO forumpost VALUES (1211,173,6,'Re: To Tim Axoy','Tim - I\'m not Levik, but it probably involves opening other accounts etc that he has already warned you not to do.',1919,'Lewis','2003-06-10 06:15:50');
INSERT INTO forumpost VALUES (1212,173,6,'Re: To Tim Axoy','And trying to \"trade votes\", like vote for problems and expect people to vote for your problems. Although I am reluctant to see my problem get thumbs downed, if I know why it has been decided against, it\'s good not to pollute the queue with it.\r
\n\r
\nAnd I agree with Lewis, didn\'t he post a warning post?',1626,'Gamer','2003-06-10 06:50:23');
INSERT INTO forumpost VALUES (1213,164,4,'Re: Scholars','Cory\'s question isn\'t a question, it\'s a warning... Posting improperly (like screaming IN ALL CAPS and posting numerous things twice) isn\'t good for your reputation.',1626,'Gamer','2003-06-10 06:51:46');
INSERT INTO forumpost VALUES (1214,172,5,'Re: Crypto','Yes... All ciphers I would submit wouldn\'t require the use of a computer to decrypt. I too was surprised to see Cryptography appear that early, and I love the icon... Good job! :)',1626,'Gamer','2003-06-10 06:53:48');
INSERT INTO forumpost VALUES (1215,173,6,'Re: To Tim Axoy','I closed it because you created an account as \"J\" - after I repeatedly told you NOT to open other accounts. I have better things to do with my time than look through posts on this site trying to figure out if every new user is you again.\r
\n\r
\nThis is the fourth account of yours I have had to close, and I have given you two warnings prior to this time.\r
\n\r
\nIf you want your account back, you will have to email me (not post a message here) - and then we will discuss it.',1,'levik','2003-06-10 09:25:49');
INSERT INTO forumpost VALUES (1216,170,4,'Re: Cool symbols','I was actually thinking that on the front page, for each new puzzle, there would be an icon of that puzzle\'s category featured there as well - you would be able to click it to go the the category. Not sure about it yet though.',1,'levik','2003-06-10 09:28:11');
INSERT INTO forumpost VALUES (1217,170,4,'Re: Cool symbols','i was thinking the same thing - i didn\'t notice the puzzle icons until you mentioned them. i rarely browse puzzles by category, looking usually at the newest problems, newly commented, and unsolved problems. visitors to the site might be more apt to look by category, but perhaps putting the icons (or a quarter-sized counterpart) to display with each problem would be a nice touch as well.',1575,'DJ','2003-06-10 16:31:08');
INSERT INTO forumpost VALUES (1218,164,4,'Don\'t do it','Not to mention continually posting the solutions in the title',1575,'DJ','2003-06-10 16:32:49');
INSERT INTO forumpost VALUES (1219,17,6,'Effect of PRE tag','On my latest posting, the comment on Mind Boggling, the only paragraphs that refuse to word wrap are the first ones after the </pre> tag that closes the pre text. Subsequent paragraphs word wrap properly until the next <pre> </pre> set.',1301,'Charlie','2003-06-11 03:10:53');
INSERT INTO forumpost VALUES (1220,172,5,'Re: Crypto','There is an endless supply of letter-for-letter Cryptograms that can be found all over game magazines, newpapers, and the like, as well as myriad crostics and anagram puzzles. Such puzzles, though, would seem not to have much explanation or discussion in solving them..',1575,'DJ','2003-06-11 03:35:30');
INSERT INTO forumpost VALUES (1221,174,5,'Putting Pictures in Pending Problems','Levik - I have seen some problems with pictures on them. How do you do it?',1919,'Lewis','2003-06-11 05:36:58');
INSERT INTO forumpost VALUES (1222,17,6,'Re: HTML codes for use on the site','Man this thread is way too long... I\'ll have to get around to posting a new one to summarize all the changes from this one.',1,'levik','2003-06-11 08:00:13');
INSERT INTO forumpost VALUES (1223,174,5,'Re: Putting Pictures in Pending Problems','Oh, and how do you put links to other comments/problems etc in?',1919,'Lewis','2003-06-11 09:20:52');
INSERT INTO forumpost VALUES (1224,175,5,'a suggestion for comments','I am a relatively new user on this site. One thing that I think could be a lot better is if no comments were made visible until AFTER the solution is posted, or make a requirement that no comments cannot contain the solution. I suggest this because I will spend a long time solving a problem, but even though there is no solution posted, there are a bunch of comments that say the same exact thing in different terms. I think it would be better if comments were made visible only after the solution is posted. then more people can feel that they sincerely solved the problem, kind of like a test in school; it doesn\'t matter who gets done first or last, as long as you get it right. It wouldn\'t be fair if one student who solves the problem first shouts out the answer in front of the whole class, would it? \r
\n\r
\nAlso, this could benefit the ranking process. For example, once a novice gets x amount of problems correct, she can become a student, etc. Just an idea...\r
\n\r
\nJesart ',2256,'Jackie','2003-06-11 15:51:20');
INSERT INTO forumpost VALUES (1226,175,5,'Re: a suggestion for comments','Some puzzles are so difficult they call for a collaboration. Some are paradoxical and benefit from discussion. In any case, the rule is to label full solutions with an indication that that\'s what they are, so those who don\'t wish to see them can avoid doing so. That\'s what makes it different from calling out the answer. That\'s also the reason for making sure that everyone avoids putting the actual answer in the title of his or her comment, and leave the answer in the body of the text, with the appropriate warning label in the title, usually together with the appropriate light bulb that indicates a full solution.',1301,'Charlie','2003-06-11 16:58:59');
INSERT INTO forumpost VALUES (1227,174,5,'Re: Putting Pictures in Pending Problems','You can put links by using the code \r
\n\r
\n<a href=\"http://your.link.here/\">Link Text</a>\r
\n\r
\nImages are a bit trickier. If you have an image, post a problem without it , and email it to me directly. I will then add it.',1,'levik','2003-06-12 02:00:51');
INSERT INTO forumpost VALUES (1228,169,3,'Re: 500!','Now it\'s June 12, and there are exactly 500 problems in the queue (at this time), this site really has lots of problems! :)',1626,'Gamer','2003-06-12 09:03:13');
INSERT INTO forumpost VALUES (1229,175,5,'Re: a suggestion for comments','If I figure out the answer to a problem after 5 people have figured it out too, I don\'t post a comment saying I have figured it out, or even how to figure it out if it\'s the same as the other 5 people have said. I am just content knowing I solved it without looking at the comments.\r
\n\r
\nIt\'s not like shouting out the answer, it\'s like turning in the answer first... I wouldn\'t feel bad turning in the correct answer last. People who put the answer in the subject are like shouting out the answer.',1626,'Gamer','2003-06-12 09:07:32');
INSERT INTO forumpost VALUES (1230,176,5,'Problem flooding revisited','Well, it\'s time to face it - we have way too many incoming problems for the way in which we are posting them. (For those who don\'t know - it\'s 2 every weekday and one every weekend day.) The number of problems in the queue is still growing significantly faster than they are bing pushed live.\r
\n\r
\nIn the short term, I propose that we raise the bar for the problems to get on the site. While we can only accept 12 problems a week, there\'s no limit to how many we can reject. (Mind you, I am not suggesting people should TD problems that deserve a TU, but perhaps sometimes when you are not sure wether a problem deserves a third TD, and it\'s a tossup between that and abstaining, maybe a journeyman should deal the final blow more readily.)\r
\n\r
\nObviously, I would rather accomodate all the problems we get - but for that we need to radically change the way that problems get posted. Because (as far as I know) people only come to this site a couple of times a day, pushing more than two problems daily would probably reduce the exposure of each problem.\r
\n\r
\nOn the other hand, we have to ask if EVERY problem that goes live on the site deserves to front page spot? And if not, then where would it go so that people can still see it? Does anyone visit the digest page? It doesn\'t really seem like it.\r
\n\r
\nAh... I don\'t really know what to do about this - but I would gladly take suggestions.',1,'levik','2003-06-12 11:38:42');
INSERT INTO forumpost VALUES (1231,176,5,'Re: Problem flooding revisited','It comes down to a question of bandwidth. People are submitting problems at a faster rate than you are willing to expose them on the front page. You have several options: increase the rate at which problems appear on the front page, allow fewer problem submissions, be more stringent in dumping problems, or allow problems to go live without necessarily appearing on the front page. Of those options, I would favor the last one, since I think it\'s best to get as many problems on the site as possible, but still allow the best problems to shine.\r
\n\r
\nkuro5hin.org has a queue somewhat similar to this one with four voting options: Front Page (+1), Section Page Only (+1), Abstain (0), and Dump It (-1). You could adapt this strategy so that a TU could count either toward the front page or toward a particular puzzle category. 3 TU\'s in the front page option qualifies the problem to go on the front page, while 3 TU\'s in either option qualifies the problem for an appearance in a particular section.\r
\n\r
\nThere are two drawbacks that I can think of to this approach. One is that a good problem might get 2 front page TU\'s and 1 category TU, but then quickly get pushed to the category page when it might otherwise eventually qualify for the front page. Another issue is that a problem might quickly qualify for a category page and not get seen by many reviewers, which opens up the possibility that duplicates might slip by. Both of these would be fixed by requiring that problems spend a minimum of, say, 48-72 hours in the queue before they can be pushed (no minimum for getting dumped).\r
\n\r
\nTo get non-front page problems more exposure, I\'d augment the Categories section to display something like \"Riddles (2 new)\", rather than just \"Riddles\" if two riddles had been pushed in the last 24 hours.\r
\n\r
\nWhat do you guys think?',103,'friedlinguini','2003-06-12 13:27:39');
INSERT INTO forumpost VALUES (1232,176,5,'Re: Problem flooding revisited','I usually visit the other problems (the recent ones still on the front page) if I haven\'t seen them before. It not being school season makes it easier for me to visit the site at different times of the day.\r
\n\r
\nI don\'t know advanced coding, but how hard would it be to put 2 or so problems on the front page where \"latest problem\" is now? (in full context, just like in the \"Latest Problem\" section) I think that might make the queue go quicker, in addition to the \"good problem\" queue for 3TU problems. Plus, you can always see a problem in \"Oldies\" if you miss it the first time. That has happened to me a few times :)\r
\n\r
\nDo other Journeymen think that the queue voting process would be the \"limiting factor\" if the problems were sped up (the queue problems flow more rapidly)\r
\n\r
\nI don\'t think we need an abstain. (\"note\" does the same thing, only it doesn\'t need to be cleared when we want to vote again.)\r
\n\r
\nI don\'t agree with thumbing down problems like Erin\'s plane problem quickly before we have a chance to decide them, just so we get a questionable problem out of the way.\r
\n',1626,'Gamer','2003-06-12 14:30:19');
INSERT INTO forumpost VALUES (1233,173,6,'Re: To Tim Axoy','I left an e-mail to you about how you discovered that I was J.',NULL,'Tim Axoy','2003-06-13 02:39:24');
INSERT INTO forumpost VALUES (1234,176,5,'Re: Problem flooding revisited','I still have mixed feelings about how to clear the queue more efficiently.\r
\nOn one hand, it seems voters are too reluctant to vote TD on a problem unless it is a duplicate, or an extremely poor problem. As a result, seven of the ten problems in the voting queue are waiting for changes to be made or for more people to vote one way or another to move it, and the pages on the front page are becoming mediocre and uninteresting for discussion.\r
\nOn the other hand, to new users who have submitted a few simple problems and waited a month or two just for the voters to see them, it seems rather harsh to TD them.\r
\nOne way to move out a few \'lesser\' problems without having them necessarily spotlighted on the front page, with the existing implementation, is to submit two problems one right after another. Then, the first problem is still made live, and found at the bottom of the front page as well as the digest page (which, by the way, I do look at), but it may not recieve as much attention as some problems that have been deemed \'better.\' If we made this a regular practice, three or four problems a day could be made live, with one \'good\' problem to be the feature problem for each day. That might be preferable, too, since (I\'m assuming) many people get on only once a day at around the same time, so if two problems go live at different times of the day, they may be missed. I was also thinking something along the lines of what Gamer suggested, to make more recent problems besides the single latest more prominent on the front page, either by putting more than one problem in full text, or perhaps just displaying the two or three next-most recent problems above the \'Oldie\' problem. I think either of those would make people more likely to look at more than just the current problem. Just some thoughts to throw around..\r
\n\r
\nI offered an idea like the \'abstain\' vote (with a different name) a few weeks ago in another thread, but no one commented on the idea then. Now that I can see the voting queue, though, it seems like that would only further impede the process. Also, I really think the minimum queue time is not a good idea, for two main reasons: first, we are trying to make things move more quickly. As it is, it usually takes a day or two for all the voters to see it and vote and quibble and whatnot, if not longer. Second, I don\'t like overexposure to the problems in the voting queue before they are made live for everyone to comment on and solve. It seems now that for even the lengthiest problems you cannot get to a newly posted problem without Charlie or someone having already posted a complex solution within a few minutes or hours of the problem being made live. While of course anyone is still free to comment and solve the problem on their own, going to a newly-posted problem and finding three comments that say \"Solution\" I think discourages people from commenting or even attempting the problem. If you look at many of the earlier problems, there is a lot of discussion and attempts at the problem before anything was ever concluded. Any site can list a bunch of problems with a solution; to make these problems \'live\' and open for people to solve, I think it\'s important that people have a chance to look at a \'fresh\' problem or one with only a few thoughts in the comments, or they will be discouraged from saying anything at all. I know that for me, it\'s disappointing to see a potentially interesting problem like the recent \"Quaker Queens\" problem, only to find that Charlie has not only posted a solution, but every possible solution, along with a 120-line program to find them. I found a couple arrangements with pen and paper and a little logic...but after that, why bother? .. That\'s pretty much an unrelated issue, except that moving problems through the queue to be live more quickly will hopefully inspire a little more discussion. A lot of it, too, is simply discretion on the part of those with access to the voting queue. It shouldn\'t be a race or competition to solve the problems first, but a collaboration and discussion at finding a solution.\r
\n\r
\nBack to topic:\r
\nPersonally, I think the voting queue should be more of a voting queue. As it is, it seems more like an editing team or something; throw away duplicates and tell authors how to modify the problems so that they will read better on the site. I think, if you don\'t like a problem, vote it down. There are a lot of better problems in queue, just waiting to make it into the voting, while we fiddle around with a slew of \"okay,\" uninteresting problems. This might also be less of a problem if we make more problems live more quickly.\r
\n\r
\nThose are my thoughts.',1575,'DJ','2003-06-13 03:45:58');
INSERT INTO forumpost VALUES (1235,176,5,'Re: Problem flooding revisited','The minimum queue time certainly should not be used in isolation. It was intended to supplement a system that would otherwise allow problems to move through the queue very quickly--just not to the front page. A little quick math shows that 72 hours is probably too long. 24 might be appropriate.\r
\n\r
\nAs a matter of personal honor, I don\'t put any work and not too much thought into any problem in the queue (obviously it\'s not possible to avoid thinking about the problem at all). I also avoid commenting on posted problems for a while so that other people have a chance to get a good look at them. While I don\'t think there would be any way to enforce it, it might be worthwhile to have a sort of code of ethics for problem reviewers. That\'s a bit off-topic for this thread, but it might be worth starting another thread.',103,'friedlinguini','2003-06-13 04:59:22');
INSERT INTO forumpost VALUES (1236,173,6,'Re: To Tim Axoy','I thought you were J for two reasons.\r
\n\r
\n1. On the \'about\' it said \'I like puzzles\', and his login was \'Weirdo\'.\r
\n\r
\n2. All of his comments were just \'I know - A= liar, B= knight\' sort of things, and had no explanations.',1919,'Lewis','2003-06-13 05:31:09');
INSERT INTO forumpost VALUES (1237,173,6,'Re: To Tim Axoy','Levik:\r
\n\r
\nAs a suggestion for a potential improvement I know that this should more normally be posted in the Commons forum, but given the subject I think here\'s appropriate.\r
\n\r
\nWhy don\'t you change the sign up process so that a potential new Floobler only supplies their name/alias and email address. After checking that there isn\'t already an account for that particular email address the \'system\' would then email a password to them which could then be changed when the Floobler logged in. I\'ve seen this process used on other sites where registration is required and assume the \'system\' to be some clever bit of code rather than a person. \r
\n\r
\nIn this way you can at least limit people to one Flooble-id per email account. I\'m not naive enough to think that a person can only have one email address, but from my very limited experience it is more hassle to set up an email account than it is to sign up for Flooble - even if this isn\'t strictly true then having to create a new email address AND a new Flooble-id is more time consuming than just creating a new Flooble-id.\r
\n\r
\nTo be honest I think it\'s a shame that you may need to spend time making such an \'improvement\', but it may be less time consuming than baby-sitting.\r
\n\r
\nKeep smiling :-)',1183,'fwaff','2003-06-13 06:03:47');
INSERT INTO forumpost VALUES (1238,176,5,'Re: Problem flooding revisited','One of the things I often tell people who submit brute force solutions is \"How could you use logic/number sense/smarts to figure this problem out, rather than trial and error (which is what the computer does)\". I actually even put this in \"Squares Probability\", as that is the whole point of the problem.\r
\n\r
\nSaying how you figured the problem out is almost more important than the solution (if not more), because knowing the solution feeds the man for a day, where knowing how to solve the solution feeds him until he gets tired of fish. :)\r
\n\r
\nAnd I agree with the voting queue, the only problem there is being deadlocked with problems like Erin\'s airplane problem. ',1626,'Gamer','2003-06-13 06:05:42');
INSERT INTO forumpost VALUES (1239,176,5,'Re: Problem flooding revisited','I know, I know - I\'m supposed to be gone already - but its raining and they don\'t make roads in the rain...\r
\n\r
\nI think this really boils down to the issue that sure, there are 500 problems in the queue, but i\'d be willing to bet that 75% of them are from 20 submitters. My thoughts on this have been spoken, so I won\'t rehash them (yet), but maybe if we\'re considering \"raising the bar\", I\'d suggest that it is the problems submitted by the constant submitters that need a closer eye. As DJ mentioned, it\'s not really a great way to enlarge the subscirbers group to make somebody new wait 3 months or more for their first problem get booted. Established flooblers, on the other hand (especially journeymen+ with acces to the queue) are likely much more tolerant of seeing their problems TD\'d.\r
\n\r
\nF.l., I appreciate that there are others out there who aren\'t remarking on problems they\'ve had a chance to see in the queue - it really doesn\'t seem fair. I support this 99%, the last 1% being that for some problems, if a voter didn\'t post something immediately, maybe no one ever would. Hard to guage from a purely hypothetical standpoint.\r
\n\r
\n(it\'s later) So now I can re-support my queue solution. As a test of the new system with two problems receiving top queue weight, I have submitted a problem and been keeping close track of it. I have no problem with the other journey men etc taking a look at it before it reaches the queue - it may be interesting to see what happens to the average persons first submission (this problem was submitted when I had no others in the queue as well. Also note that the situation has worsened considerably since the problems creation), but that\'ll be up to the boss man - Levik knows the problem name/pid so he can announce the pid if he thinks it might be relevant.\r
\n\r
\nI really think that some solution needs to be created to deal with 10 people collectively owning the queue. As my problem illustrates (or just take my word for it), the queue jumping negates 60-70% of the purpose of the weighting system. A side effect of creating this kind of sanctioning for mass-submitters, is that they will dramatically lessen their personal submissions (effectively only submitting their best ones - saving us the task of TDing them as well as not hogging the queue for others).\r
\n\r
\nAs an optional method of reducing the queue, while probably a lot of work, the main page could be tiled to show two new problems side by side. On my browser anyways, there\'s plenty of room to show this (course then we might lose some of our pop-up space... which is bad, right?), which could mean that we post 4 problems a day during the week and 2 each sat/sun. If this is adopted, a slight increase in the length of the old problems listed would be justified, but I don\'t see a problem with that as there is a scroll bar to see further down the page.\r
\n\r
\nHope there\'s not too many typos...',775,'Cory Taylor','2003-06-13 07:31:39');
INSERT INTO forumpost VALUES (1240,176,5,'Re: Problem flooding revisited','For the problem of 10 people collectively owning the queue, I don\'t know how difficult the following would be to implement, but my suggestion is that no problems be promoted to queue weight 1 until there are no other QW 1 problems left in the submission queue. The problem with this is that it might take a long time to get back to particular individuals, even if their submissions were made quite a bit earlier. Even more complicated would be combination weighting schemes involving recency of submission along with the present queue weight criteria.\r
\n\r
\n',1301,'Charlie','2003-06-13 08:36:41');
INSERT INTO forumpost VALUES (1241,176,5,'Re: Problem flooding revisited','The output of this would be equivalent to the QW alternative I\'ve been hyping.',103,'friedlinguini','2003-06-13 10:42:33');
INSERT INTO forumpost VALUES (1242,173,6,'Re: To Tim Axoy','This idea has been batted around before. I still think it\'s a good one. However, when I signed up, I did so with a fake e-mail address because I don\'t like having mine posted on the web, obfuscated for bots or not. If levik does go down this road, I\'d ask for the option to keep e-mail addresses private.',103,'friedlinguini','2003-06-13 10:50:14');
INSERT INTO forumpost VALUES (1243,170,4,'Re: Cool symbols','Well I was gone for about a week because my internet got disconnected so my family had to swith to cable. But i\'m back now and for the riddles symbol what if we have a picture of an owl? aren\'t owl\'s supposed to symbolize wisdom?',1072,'Alan','2003-06-13 11:23:36');
INSERT INTO forumpost VALUES (1244,173,6,'Re: To Tim Axoy','Yes... I did the same thing as fried did, so the first problem I submitted, I don\'t know why it got rejected...\r
\n\r
\nI have two e-mail addresses, one for questionable online services (the ones that promise everything for nothing), which I await spam to enter... I usually send stuff there that could still be retrievable, but is not checked usually, and another that is checked much more, and isn\'t posted unless I think the site is good :)\r
\n\r
\nI would agree with that \"improvement\" would help out, but I have met a few people (particularly my age and younger) that don\'t have an e-mail address yet. And usually creating a new e-mail is like trying to switch your long-distance service. It might be cheaper, but is a bigger pain so nobody wants to do it.',1626,'Gamer','2003-06-13 11:45:35');
INSERT INTO forumpost VALUES (1245,177,7,'S\'up?','hey evrybody,\r
\ni jus joined 2day, ne1 wanna be my friend???\r
\nn i have no idea how i found this site!!lol!!!\r
\ner, introduce my self... um...\r
\nim 13 n in the 10th grade, my names maryam, i live in the uk, uh.. i like to uh read, write, play some sports, chill out w/frendz, think of some more ways to exploit(big word lol!!!) my parents into buyin me stuff... ne1 wanna talk 2 me??',2438,'Maryam','2003-06-13 11:48:48');
INSERT INTO forumpost VALUES (1246,172,5,'Re: Crypto','I\'m glad crypto is being added as a subcategory. I have another code in the queue, no harder than a2o3t6t7, but completely different in execution. You should see it around December :P',1567,'Bryan','2003-06-13 12:49:40');
INSERT INTO forumpost VALUES (1247,172,5,'Re: Crypto','I added a hard crypto, which I hope isn\'t too hard to the queue about a week ago, when I heard cryptos were ok. :)',1626,'Gamer','2003-06-13 16:35:16');
INSERT INTO forumpost VALUES (1248,172,5,'Re: Crypto','I am planning on submitting another one once I can get it checked.\r
\n\r
\nBy the way, a2o3t6t7 was 5 out of 5 (when submitted at least), so it couldn\'t be harder! :D',1626,'Gamer','2003-06-13 16:36:47');
INSERT INTO forumpost VALUES (1249,172,5,'Re: Crypto','I submitted 2 cryptos - one if 4 out of 5 and the other is 2 out of 5.',1919,'Lewis','2003-06-13 21:32:25');
INSERT INTO forumpost VALUES (1250,173,6,'Re: To Tim Axoy','The reason this was never asked for before, was exactly what you guys have been saying - I never wanted to make disclosing a real email a requirement for signing up here. \r
\n\r
\nI will have to think long about this one - probably you will still be able to pick your password, but will have to click some sort of a validation link that gets emailed to you before it will work.',1,'levik','2003-06-14 11:32:44');
INSERT INTO forumpost VALUES (1251,177,7,'Re: S\'up?','Well, Maryam. Welcome to the site. I think you will find it easier to make friend here if you take the time to spell out words. Show others you respect them enough to hit a few extra keys, and it\'s amazing how fast people will warm up to you.',1,'levik','2003-06-14 11:35:09');
INSERT INTO forumpost VALUES (1252,176,5,'Re: Problem flooding revisited','These are all pretty interesting proposals that I will have to think on.\r
\n\r
\nOne additional thing occured to me today thogh that I\'d like your input on: \r
\n\r
\nIt seems that a lot of the \"lesser\" problems we get are submitted by people who are trying to get ahead on the site. To that end, I think some of our volume may be alleviated by enabling a couple of policy changes:\r
\n\r
\n1) Require a person to be a Studend before being able to submit a problem. This makes sense especially since Novices don\'t really have the ability to do anything with problems they have submitted - plus I believe that letting people submit on the first day is not the greatest of ideas. Let them hang around on the site and get a feel for it - it can take as little as 24 hours to become a Student here anyway (mind you I don\'t believe the way of becoming one should be advertised lest people start posting just for the sake of getting the rank)\r
\n\r
\n2) Somehow enable people to get promoted without having submitted so many problems. Perhaps a nomination scheme: a journeyman would be able to nominate a Student to become an apprentice - given that the Student has met certain requirements (for example - a week of membership + X number of comments/ratings) After a Student has 3-5 nominations, a Scholar will be able to promote them. The process of becoming a Journeyman would still require problems on the site, but perhaps with a nomination, it could be set to lower than the current 6 - you could become a Journeyman with 3 problems + 5 nominations for instance.\r
\n\r
\nWhat do you think?',1,'levik','2003-06-14 11:42:41');
INSERT INTO forumpost VALUES (1253,176,5,'Re: Problem flooding revisited','I think that\'s a good idea too, and you\'re right, it does seem that people are submitting problems just for the sake of promotion.\r
\nWhile it\'s easy to see who are contributing members and deserve promotion, that is largely subjective, and a fixed set of criteria would be difficult to come by. There are a good number of deserving members who have not submitted any or many problems, but have shown a particular contribution to the site through comments and whatnot.\r
\n\r
\nPerhaps in place of a fixed set of requirements, a \'point system\' could be implemented, for example any comment could be worth two point, a full solution to a problem worth three points, a vote on a problems rating worth one point, a submitted/approved problem worth five, etc. Then someone with 20 points could be a student, 50 for an apprentice, 100 for a journeyman, perhaps coupled with how long they have been a member or how frequently they contribute. The values for contribution and advancement would be different, of course, but you get the gist. That would be a little more abstract, and cut down on people simply submitting poor or uninteresting problems for the sake of advancement, but still have a good way of telling who is contributing to the site. That\'s not to say that someone couldn\'t, then, come and leave 50 comments all at once. Also, perhaps hiding the actual point system would prevent people from mass-commenting, or extra consideration on the frequency of comments would help prevent that. Or, a person can only earn 10 points for comments left within a 24-hour period, something like that. In any case, not advertising the way to advance as anything more than a point system based on the user\'s contribution is almost certainly the best way to prevent people from trying to do just enough to advance, but the ambiguity may discourage some people or make them question the obhectivity of the system.\r
\n\r
\nAll in all, though, I think a more general measure of contribution rather than basing rank on specific criteria would be useful, and help to prevent people from \'jumping hoops\' just to get to the next level.',1575,'DJ','2003-06-14 14:14:20');
INSERT INTO forumpost VALUES (1254,177,7,'Re: S\'up?','Hi, maryam! You didn\'t list math or logic puzzles with your hobbies, so I hope you enjoy them..that\'s what this site it about! It\'s a good way to exercise your brain and have some fun. =)',1575,'DJ','2003-06-14 14:36:21');
INSERT INTO forumpost VALUES (1255,176,5,'Re: Problem flooding revisited','DJ - your proposed system seems to me to be a step in the wrong direction - you are proposing we say that a comment is worth X ratings, and a problem - X comments. I think that just as you said, there\'s not a unified system that would work well, especially one based on points or any kind of rigid criteria.\r
\n\r
\nFor example, The Mighty Puck has come pretty close to becoming a journeyman by submitting nothing but riddles pasted in from The Hobbit. \r
\n\r
\nThe system of nominations I am proposing would probably do away with a need for a rigid and complicated structure of promotions, by replacing it with a human element.',1,'levik','2003-06-14 14:46:58');
INSERT INTO forumpost VALUES (1256,172,5,'Re: Crypto','Didn\'t I suggest thios as a category a long time ago? well in the case that their are some problems that aren\'t in this category that should be you could look at the post which i started about a new category (which is this)',1072,'Alan','2003-06-14 17:01:14');
INSERT INTO forumpost VALUES (1257,172,5,'Re: Crypto','nevermind the link is here any problems that are mentioned there should be gien thought for being posted in this new category.',1072,'Alan','2003-06-14 17:05:28');
INSERT INTO forumpost VALUES (1258,176,5,'Re: Problem flooding revisited','I agree with that... I just became a journeyman (about a week ago), but I saw that Tim Axoy was one about 1 or 2 weeks before... submitting easier problems like \"This statement is false\" or \"I am not a knight, what am I?\" as problems...\r
\n\r
\nI agree with the \"student\" before posting problems idea, it sounds like a good idea.\r
\n\r
\nI would like your idea of loosening problems with nominations. I had 4 problems for the longest time, and was waiting for my other problems to get through from the queue.\r
\n\r
\nMy proposition is needing a sum of 15 (or some other number) of problem difficulty levels before you can be a journeyman. If \"difficulties\" isn\'t thought to be a good answer for how \"good/complex\" a problem is, maybe journeymen could rate the problem. Then they could rate a more complex problem (like Mind Boggling or another problem) better than a problem like \"This statement is false\".',1626,'Gamer','2003-06-15 11:56:20');
INSERT INTO forumpost VALUES (1259,176,5,'Re: Problem flooding revisited','I just wanted to end the idea that you have to submit problems to advance, and hence a lot of newcomers are submitting poorer problems merely to gain the next level. My point it, it is possible to be a contributing member without submitting problems, and in truth the members that I consider to contribute the most are not the ones that submit the most problems, but the ones that leave comments to more problems and more frequently. That\'s why with the point system, I suggested extra weight or consideration on the frequency of comments, as well as their number.\r
\n\r
\nPersonally, I think that while we don\'t want people doing just a poor minimum to earn a rank, the process should be more objective than subjective. People will want to know (I think, at least) that their contribution (comments, ratings, submissions) to the site are the basis for advancement, not the personal approval of some gentry. However, I can see that no matter how you change the criteria for advancement, users like Tim Axoy will be able to jump through the proverbial hoops to automatic advancement unless there is a human element involved.\r
\n\r
\nAlso, I recognize some potential problems and abuses with the method I suggested, so I have a few more suggestions to make that incorporates the ideas that everyone has pur together here (I recant whatever previous statements I made, and while I\'m still sketchy about the idea of nomination/approval for advancement, it seems to be the most favorable way to go, and I\'ll stick with it).\r
\n\r
\nFirst, to address the flooded queue that started this thread, I still think that the option to delete one\'s own problems would greatly diminish the queue, especially those by new users who submit a few problems just for the sake of advancement or for whatever reason, and then decide that they are not up to par with the site, or later realize that is a duplicate problem. Speaking from experience, the first few problems I submitted were not very good (although a few made it through the voting queue anyway), and three or four were duplicates of previously submitted problems (one of which was made live while mine was still waiting). Allowing people to delete their own problems (with, of course, due confirmations and warnings against accidental button clicks) I believe would both reduce the queue size and raise the quality of problems submitted, or at least those reaching the voting queue.\r
\n\r
\nMy next suggestion is a rearrangement of the user levels themselves. I agree that it would be prudent to only allow problems to be submitted to Students who have been around the site for at least a little while, and then to only allow apprentice users to modify submitted problems is fine. I did not see the reasoning behind disallowing the category change at first, but I assume it is to prevent people from submitting blank problems to save a spot in the queue, or later changing a problem to a better one (as I noted in a related thread, I did that, unwittingly violating the site\'s unwritten lawbook, because I noticed a duplicate problem and did not have the ability to delete it). If that is the case, I would suggest that Apprentice users would be allowed to change everything about a problem except for its title. It would be hard to change a problem to a completely different one, or to pre-save a spot in the queue, when you could not change the title to a problem once it has been submitted. Also, when a problem reaches the voting queue, a change in category is suggested by the voters much more often than a change in the problem\'s title (except for things like \'Leg Byes,\' but that\'s a different story...), so that change would mean requiring less manual intervention from levik. I think we should eliminate the requirement on problem submission/approval for Apprentices altogether, replacing it with a standard based on how long a person has been a member and by how often they contribute to the site. Advancement this far, I think, can be done automatically, without the need for voters or higher-ranked members to intervene. Alternately, the human intervention in this step could be minimal, such as merely requiring two members ranked Journeyman or higher to click a button that says \'Approve\' for qualifying members. Really, though, I don\'t think anything of that sort is necessary.\r
\n\r
\nMy last suggestion is mostly redundant of what others have said. To become a Journeyman, a user would have to be a member for at least a month or two. I would say an \'active\' member, however that would be established, as I maintain that the singlemost determinant or most telling measure of a person\'s contribution to the site is the frequency and quality of their comments. In any case, I think requiring someone to be around for a length of time, as someone suggested earlier, would be good to make sure that not only is someone contributing to the site, but they are interested enough to stick around.\r
\nThen, they would have to be nominated by a Journeyman or Scholar (or Director, although I\'m sure \'worthy\' users will be noticed before levik feels the need to step in). This step would probably eliminate the need for any measurement of how often a person contributes, since I imagine that they will need to be quite active for someone to notice and nominate them. After nomination, there should be some sort of deliberation, perhaps in a separate voting queue, with a minimum time, say a week, for people to discuss and evaluate a person\'s contribution to the site, and what they would offer to the voting queue. The ultimate decision should be somewhat different; rather than a sum total of TU or TD votes, I can think of two ways to go. First, voters would have to reach some sort of unanimity (like a jury), or perhaps allow for only a single dissenting vote (no more than one \'nay\' for every six \'yeas\' or something). The other way to go would be, after the week of discussion, levik would have the final word. As to the method of deliberating..I think it would also be useful to allow nominees to speak on their own behalf, and to say what they think they would contribute to the voting process.\r
\n\r
\nIn sum, as everything I have just said is very long-winded (I wrote it, what would you expect..) and confusing, here is my suggestion for the new ranking system (much of which is copied from the current \'levels\' page).\r
\n\r
\nNovice\r
\nThis is the basic level, assigned at signup. Most users are currently in this category. Novices can rate problems and post comments and solutions, as well as read and post to selected discussion forums.\r
\n\r
\nStudent\r
\nA Novice is promoted to Student if they have rated at least one problem and posted at least three comments [as is currently the case]. Students can submit new problems to the queue and modify the text, difficulty, and category (but not the title) of problems before they are approved and made live on the site. Students may also delete their own pending problems before they are approved, as well as add and edit the solution to their own submitted problems before the solution is posted to the live site.\r
\n\r
\nApprentice\r
\nA Student becomes an apprentice if they have been a Student for at least two weeks, and have posted at least 11 problems with timestamps on at least four different days during that time. [Tthat is the easiest way I can think of to put some sort of weight on how often a person visits the site as well as how much they have to comment. Two days a week is certainly not excessive. Further, I don\'t know why eleven comments, but it\'s the current standard, different than the overused standard multiple of five, and I like it.]\r
\n\r
\nJourneyman\r
\nJourneymen are the stewards of the site. They have the ability [as now] to decide when to make the solutions to their own problems public, as well as access to problems submitted by others, which they can vote for giving them \"Thumbs Up\" (+1) or \"Thumbs Down\" (-1). An apprentice can become a Journeyman only if they are nominated by another user who already has the rank of Journeyman or higher, based on their contribution to the site through comments, problem ratings, forum discussion, and problem submissions. After being nominated, a special voting forum for Journeymen, Scholars, the Director, and the nominee to deliberate, after which time frame the voters must reach consensus, allowing for only one dissenting vote. If there is more than one vote agaisnt their promotion, a nominee is rejected (which would rarely happen, and only if there are very serious objections to a person\'s nomination), after which the user would again have to wait two weeks before being nominated again. At the expense of seeming elitist or clique-ish, we will reiterate that the responsibility of selecting problems to post on the site is an important one, indeed the foundation of the site itself. As such, there is no accurate rubric or criteria that can ratea user\'s contribution to the site, besides the other users themselves.\r
\n\r
\nScholar\r
\nScholars are able to edit their problems that are \"live\" on the site (in addition to pending problems). They can also change the status of their problems from \"pending\" to \"live\" and back. Upon submitting a problem to the website, they are given the option of making this problem live immediately. Scholars can now also make \"live\" problems of others that have reached a score of 3 through voting. Like Journeymen, one cannot reach the rank of Scholar automatically. The Director of the site will manually promote Journeymen as needed based on their overall contribution and judgement. There is no need for more than a few active Scholars to help run the site, so this promotion does not happen often.\r
\n\r
\nDirector\r
\nThe Director is the administrator of the site, given access to backend administration tools. Currently, the only Director on the website is Levik, and it will probably stay this way for a while.',1575,'DJ','2003-06-15 14:57:57');
INSERT INTO forumpost VALUES (1260,176,5,'Re: Problem flooding revisited','One of the best things about submitting problems is the time it takes to do so. The queue is so long that anyone who comes upon the site must wait at least a month for their problems to be posted. If they forget about the site before a month (as many will do), then that ends the problem.\r
\n\r
\nAnd one of the other things Journeymen can do is Thumbs Down a bad problem. If we see bad problems (like too easy ones, or near duplicates), shouldn\'t we say that in the problem?\r
\n\r
\nMy feel about the levels is it is good to give the tools to the student to change the things about their problem, but just not the title.\r
\n\r
\nAbout the submit problem idea, would it be good to have a maximum of 2 problems submitted per day? That way the user would have to be here for more days to get a promotion. It might also lessen the queue.\r
\n\r
\nAnd also for the \"bare bones problem\", just add up the difficulties (or goodness amount) of each problem, so you measure it overall problem goodness instead of how many problems they submit.',1626,'Gamer','2003-06-16 02:03:58');
INSERT INTO forumpost VALUES (1261,176,5,'Re: Problem flooding revisited','In regard to the Queue Weight reworking, it would seem appropriate that no more than two Riddles get queue weight 1. Right now, Riddles seem to be building up in the queue, as they arrive there in the top 10, but with so many recently, they tend not to get pushed, and just build up in the queue.',1301,'Charlie','2003-06-16 04:11:41');
INSERT INTO forumpost VALUES (1262,176,5,'Re: Problem flooding revisited','Gamer, in your suggestion to have a maximum of 2 problems submitted per day, I\'m sure you mean per person. Just want to make that explicit.\r
\n ',1301,'Charlie','2003-06-16 04:13:40');
INSERT INTO forumpost VALUES (1263,176,5,'Re: Problem flooding revisited','Coming back to the original question, I believe that the only long term answer is to raise the bar on what\'s posted. This gives two major benefits: firstly, the overall quality of the problems (and therefore the site) improves - to use Gamer\'s expression the average \"goodness\" of the problems increases; and secondly the queue diminishes through not only the initial deletions, but also through fewer submissions as people decide not to bother submitting poor problems. \r
\n\r
\nIf you try the alternative route of simply increasing the rate at which problems are published then you are actively promoting quantity over quality which when combined with the current promotions system encourages some people to submit poor problems. Ultimately this choice will cause the queue to grow rather than reduce. \r
\n\r
\nI\'m a firm believer that what was once excess will become the norm. In Flooble\'s case this can either mean that today\'s poor problems (eg I am not a knight) become typical of the site; or that today\'s absorbing problems (eg Mind Boggling) become merely average. I guess I know which direction you\'d prefer things to go and as uncomfortable as it may feel at the end of the day it\'s up to the Journeymen to become more ruthless to prevent the downward spiral.',1183,'fwaff','2003-06-16 05:04:45');
INSERT INTO forumpost VALUES (1264,176,5,'Re: Problem flooding revisited','I think that\'s a good idea... I think harder problems should appear on the site. I think making problems harder (like proving something instead of just coming up with a solution, or expanding the problem to similar sets, or so on) is also a good lesson to put in the problem.\r
\n\r
\nAlthough the \"goodness rating\" might be harder to put in, I think it would be useful. Rather than just a \"difficulty\" setting, you can say how good the problem is. That way a good problem (like Burning ropes, Mind Boggling, or Letter Cubes) can be seen as a good problem, and may be able to count more towards any promotions than a simple problem would.\r
\n\r
\nI did mean to say 2 problems per person, and amaybe only 2 or 3 of the same type of problem per week per person. This way, the problems will get staggered out each week. Or, you could have it so that the first riddle is queue weight 1, then the second is queue weight 2, the third is queue weight 3, and so on.',1626,'Gamer','2003-06-16 06:20:11');
INSERT INTO forumpost VALUES (1265,176,5,'Re: Problem flooding revisited','There already is a \"goodness rating\". It\'s just that people rarely seem to use it, despite levik\'s flashy JavaScript stuff.',103,'friedlinguini','2003-06-16 06:25:20');
INSERT INTO forumpost VALUES (1266,178,5,'Submission bar raised to Student level','As the first step to lightening the load in the queue (See discussion here), I have made a decision today to require a user to be of a Student rank in order to submit problems.\r
\n\r
\nThis should not present any difficulty for anyone who is truly interested in the site, and will hopefully weed out some \"fluff\" submissions.',1,'levik','2003-06-16 07:31:29');
INSERT INTO forumpost VALUES (1267,178,5,'Re: Submission bar raised to Student level','Does this means that problems submitted by novices that are currently in the queue are going to get deleted?',1919,'Lewis','2003-06-16 07:45:59');
INSERT INTO forumpost VALUES (1268,178,5,'Re: Submission bar raised to Student lev','I hope not. Novices put work into those problems, and there\'s no reason their efforts should just be dumped.',103,'friedlinguini','2003-06-16 07:57:28');
INSERT INTO forumpost VALUES (1269,178,5,'Re: Submission bar raised to Student lev','Sirry if I wasn\'t clear - no problems are being deleted from the queue due to this change. Let me know though if anything seems weird or wrong.',1,'levik','2003-06-16 08:45:56');
INSERT INTO forumpost VALUES (1270,178,5,'Re: Submission bar raised to Student level','I think it sounds good, just have them get a \"Submit a problem\" link as well, and when they click it, inform them that the need to be a student. Otherwise we will have many \"How do I submit a problem\" questions by new people to the site.\r
\n',1626,'Gamer','2003-06-16 13:06:08');
INSERT INTO forumpost VALUES (1271,178,5,'Re: Submission bar raised to Student lev','Hmmm... I haven\'t actually thought about that... That\'s a good idea. I have currenly removed the link for them, but I guess I will add it in the next couple of days.',1,'levik','2003-06-16 16:37:43');
INSERT INTO forumpost VALUES (1272,176,5,'Re: Problem flooding revisited','To take fried\'s point before coming back to the topic, I agree that the existing \'goodness rating\' is rarely used (and I\'m as guilty as anyone), but that only comes into play once a problem is already live on the site. If you (collectively as the guardians/director of the site) wish the existing goodness rating to be more actively used then why not include it in the voting process? That way any problem made live will always have at least 3 votes and from there you should find that more people vote, if only to disagree with the journeyman judging panel. As with my point above on becoming more ruthless in separating the wheat from the chaff - where you lead, we shall follow!\r
\n\r
\nWhich leads nicely back to the original question...... following a suggestion made earlier about the \'abstain\' option, if you include goodness rating in the voting process then a voter could give a problem a rating and not a TU/TD to register that they have seen the problem and are not sure whether or not it is good enough. You could have the same rule as now regarding 3TU to be posted and 3TD to be deleted. Additionally you may have a \'limbo\' list of problems with say 6 or more votes that have not yet reached either 3TU or 3TD and then it\'s up to Levik to have the casting vote, or the journeyman have a week to decide on its fate before it\'s deleted, or some other rule.\r
\n\r
\nAlternatively you could get rid of the TU/TD and have a simpler system based on the goodness rating - eg minimum of 5 votes and an average score >3.5 That way the abstainers can sit on the fence by giving it a 3',1183,'fwaff','2003-06-16 23:05:48');
INSERT INTO forumpost VALUES (1273,173,6,'angsta','I am not angsta.\r
\nOne of you thought I was on the chatterbox.',NULL,'Tim Axoy','2003-06-17 02:31:25');
INSERT INTO forumpost VALUES (1274,173,6,'Re: To Tim Axoy','Tim - I\'m still waiting for you to reply to my email. Your account will not be returned until we talk it out. (And I would [b]REALLY[/b] not recomment you make any new ones.)',1,'levik','2003-06-17 05:03:31');
INSERT INTO forumpost VALUES (1275,176,5,'Re: Problem flooding revisited','Sorry if I have missed something obvious, but I don\'t know of where the \"goodness rating\" is... (If it would be difficulty, I think I addressed that above. /|\\)\r
\n\r
\nThe reason I wanted the goodness rating put in is to make the promotions based on problem quality, not problem quantity. This would make an boring problem (like I am not a knight) to be worth less than a better problem (like Letter cubes or Four digit number) would be, such that you could have 6 or 7 boring problems and still not be a journeyman, but you could submit 4 or 5 great problems and be a journeyman. (If we wanted to base it on problem submission.)',1626,'Gamer','2003-06-17 05:49:39');
INSERT INTO forumpost VALUES (1276,176,5,'Re: Problem flooding revisited','Not to annoy anybody but, exactly what is the problem with having such a large queue? I assume its not a matter of storage considering the suggestion of accelerating problem posting as a solution (ie this would just move the data).\r
\n\r
\nIf the problem is really quality, lets not cofuse ourselves, that is not the same issue as queue size. Imagine the queue where full of excellent problems, would it still be an issue that it is ~500 long?',251,'Cheradenine','2003-06-17 23:03:55');
INSERT INTO forumpost VALUES (1277,176,5,'Re: Problem flooding revisited','The problem is that it\'s frustrating to submit a problem, only to have to wait months for anybody to even look at it. Often, people will simply stop visiting the site by the time their problem becomes visible to reviewers. This makes it impossible to get last-minute fixes into problems (or sometimes to just get a solution).',103,'friedlinguini','2003-06-18 03:42:55');
INSERT INTO forumpost VALUES (1278,176,5,'Re: Problem flooding revisited','Also, its even more frustrating to submit a problem, wait months and then having it TD\'d.',1919,'Lewis','2003-06-18 04:16:05');
INSERT INTO forumpost VALUES (1279,176,5,'Re: Problem flooding revisited','If the problem is essentially the delay between submitting and posting i propose to review problems from the beginning of the queue, not the end. \r
\n\r
\nThis method fights flooding in the following way\r
\n\r
\n1) invalid problems are deleted quickly, and will not pollute the queue. this applies both to low quality, and also duplicates. additionally, the problem with duplicate order inversion is eliminated (a concern voiced by ravi i think)\r
\n\r
\n2) users receive instant feedback about their problems. this ensures that they\r
\nadapt in a timely fashion to the site\'s standards, and will not submit crap which quickly bounces back to them. the opposite also holds, users will know if their puzzle was in fact accepted and will be encouraged by it promptly. (even if it wont actually be posted promptly, altho they could be informed of ETA)\r
\n\r
\n3) related to 2), problem acceptance can be better used as a metric for user contribution, because acceptance does not merely imply pressing a submit button, but an actual review. the concern that users spam problems to gain promotion (stupid as this is) is therefore addressed.\r
\n\r
\n4) if to better control queue velocity (QW) for problems, review at the beginning of the queue can be used to control how fast a problem surfaces depending on how good it is. (this is related to the idea of rating problems outright in the review, appart from TU/TD which someone already suggested here) this mechanism also results in more feedback to the poster.\r
\n\r
\n5) last minute fixes and problem editing is generally possible because the user will normally be around shortly after posting (this problem was suggested by fl above)\r
\n\r
\n6) if the queue is still large, problem reviewers may have forgotten the problem since their review and may have more fun with it when it actually comes out!\r
\n\r
\nThe other end of the queue is only used to mechanically push the problems live, and perhaps control uniform category distribution. Anyway, just a thought.',251,'Cheradenine','2003-06-18 04:19:24');
INSERT INTO forumpost VALUES (1280,176,5,'Re: Problem flooding revisited','Both good points (referring to the last two comments), and I think the problem is a combination of the two. If they are not related, then queue size and problem quality both are issues to look at.\r
\n\r
\nIf problem quality were the only problem, and nobody was submitting problems, then proposed solutions such as making advancement based on the quality of problems submitted might be better considerations. As it stands, however, the problem queue is overwhelmingly large, filled with (I\'m sure) a good number of very good problems, but largely with mediocre, uninteresting problems submitting by people looking for advancement.\r
\n\r
\nNow, do you think if everyone were capable of finding/writing excellent puzzles, they would not be submitted first? I believe that even if you require that users submit a certain number of \"good\" problems, none or few would be detered from submitting the same types of problems that we have been seeing. Perhaps the problem would be worse still, if people realize that each problem they submit might not count toward their rank. So now, instead of submitting just the three problems needed to advance, they put in four or five just in case a few of them are not good enough.\r
\n\r
\nAlso, especially for new users, what is a good problem in a high school math class or a riddle in a magazine or something, will almost certainly not be seen as such an interesting problem to veteran members of this site. I\'m pretty sure that few people submit \"poor\" puzzles and problems on purpose (how alliterative!).\r
\n\r
\nAs such, I continue to strongly suggest that the requirement on submitting problems for advancement be removed, at least for the \'lower\' ranks. When one is interested enough in the site, and finds/composes a truly good problem, I don\'t think we will have any trouble getting people to submit them.\r
\n\r
\nThe troubles with both the size of the problem queue and the quality of its contents, I believe, lies in the requirement of submitted problems for advancement.',1575,'DJ','2003-06-18 04:25:12');
INSERT INTO forumpost VALUES (1281,179,5,'Aw fiddle, another riddle.','Some people have mentioned elsewhere about not having too many riddles posted in favour for more logic and math problems. \r
\n\r
\nBecause riddles don\'t usually take so long to work out, I think riddles should be posted in groups (of about three). Thus giving users more to think about and helping to reduce the queue length (another problem being raised).\r
\n\r
\nI don\'t dislike riddles, its just that sometimes I come on, hoping for a good old puzzle to tax the brain, and I find a riddle, which I solve in about a minute. Although they are fun, there\'s not much depth.\r
\n\r
\nThen again, it might just be me. What does everyone else think?',1919,'Lewis','2003-06-18 04:28:13');
INSERT INTO forumpost VALUES (1282,179,5,'Re: Aw fiddle, another riddle.','I tend to agree - the problem is that we get a lot of riddles submitted, since they\'re easier to come by than the kinds of puzzles you and I like.\r
\n\r
\nIf we don\'t push them, they end up crowding the queue. Right now, however, we seem to be nearing the end of the latest riddle-block, with some more difficult puzzles coming up.',1,'levik','2003-06-18 05:05:22');
INSERT INTO forumpost VALUES (1283,176,5,'Re: Problem flooding revisited','Actually, my previous comment referred the two problms before the two preceding it, but this thread is moving faster than I am.\r
\n\r
\nAs to Cheradenine\'s (btw, hello, I haven\'t seen you around here in a few months) suggestion, I can certainly see the reasoning behind the theory, but in practice I\'m not convinced it will work as intended.\r
\n\r
\nFirst, The main reason for this is the amount of deliberation that each problem recieves in the voting queue now, not to mention the fact that to actually move the voting to the beginning instead of the end, there are still 500 problems that we need to go through before that is accomplished.\r
\nIf the voting queue were still limited to ten problems at a time, then we would have the same bottleneck effect as we are seeing now, where a hefty chunk of problems sit there for quite a few days as the voters and the author debate the problem and any changes that need to be made. During that time, more problems would be submitting, and would only trickle slowly into the newly-moved voting queue, likely only to suffer the same sort of debate.\r
\n\r
\nSecond, if the size of the new queue were not limited, I can picture only chaos, with piles of pending problems, some requiring debate or editing, some simply requiring more votes one way or another. With the ten problems in queue now, I have trouble keeping track of what ones have been decided on, what ones have new comments or changes, etc. That could possibly be alleviated with \"new comment\" or \"new change\" indicators, like the red \"!\" next to updated threads in the forum, but I imagine that it would soon be found overwhelming.\r
\n\r
\nThird, once problems have made it through the voting queue, they sit for just as long waiting to make it onto the site. That is, unless we push more problems live daily, and I\'m sure most would agree that such is not a favorable solution. Also, there are a few problems with having an extensive queue of approved problems waiting to be made live. First, there is too much exposure to the problems for the voters, a problem even with the short-term queue as it is now. That would even be a problem if the problems were hidden once they were approved, I imagine.\r
\nAlso, if that were the case (approved problems were hidden), there would likely be some issues with duplicate problems for which it would be necessary to look at some already approved problems (\"This sounds familiar, is it the same problem as that old one?\").\r
\nWhether or not reviewers recall the problems, I think it is still best to make them live as soon as possible after the voting.\r
\n\r
\nLastly, due to the wait now between problem approval and problem posting, it would be necessary to make sure that a solution is provided with the problem before it is approved, especially with newer users who aren\'t guaranteed to be around when the problem goes live. Levik can always manually enter something like \"fl came up with a good solution here\" as has been needed in the past with an absent author of a problem, but that, of course, is not favorable either.\r
\n\r
\nThere have been a number of suggestions regarding how to better move problems through the voting queue. I certainly agree that something could be done. However, I think we first need to deal with problems that are being submitted.',1575,'DJ','2003-06-18 05:19:19');
INSERT INTO forumpost VALUES (1284,176,5,'Re: Problem flooding revisited','If people knew that bad problems would be thumbs-downed (and so they would prevent other good problems from getting to the queue that could help their \"rank\"), they would likely be less likely to submit bad problems. If queue voters didn\'t allow bad problems in (which is what is happening now), new people not seeing any benefit to submitting bad problems would stop submitting them.\r
\n\r
\nPlus, \"good problems\" (higher goodness rating) were never referred to as an item needed for ranks (by me at least), they only would count more than less good problems. Because any queue weight would only allow 2 problems to be in the queue at a time, but not affect quality, new people/rank-worried people would note that 2 good problems in the queue would help with ranks quicker than 2 half as good problems in the queue with 2 other half as good problems waiting to make it in the queue.\r
\n',1626,'Gamer','2003-06-18 05:50:58');
INSERT INTO forumpost VALUES (1285,176,5,'Re: Problem flooding revisited','Hi DJ\r
\n\r
\nThe strategy i propose requires reviewing rate to match submission rate. Funnily, this requirement is made possible through the application of the strategy itself, because it should reduce submission rate and increase rejection rate. (For example, the cost of discard/deletion for further editing/fixing is almost zero, by virtue of the strategy itself). If it were the case that rates were in fact disparate, responsibility can be finally deferred onto director (as was in the beginning anyway) to ensure prompt resolution of inputs if journeymen etc could not cope.\r
\n\r
\nYour third point assumes that the queue would be just as long when reviewed up front, when it could be reduced for just that reason. If in fact it were still long, at least there would be no trash, a problem which most suggestions here have been aimed at anyway.\r
\n\r
\nAs to the availability of solutions, the situation would at worst be exactly as it is now, but normally better because the time of review coincides roughly with submission.\r
\n',251,'Cheradenine','2003-06-18 06:02:47');
INSERT INTO forumpost VALUES (1286,176,5,'Re: Problem flooding revisited','Your comments have led me to another idea (which may or may not have been what was originally intended, but it was at least not how I took it at first). Suppose eash user had a backlog of problems that were rejected from the site. Then, if voters did not like a problem exactly as it was submitted, for formatting or revision or something else, they could note that and immediately TD it, removing it from the voting queue. The user would then be able to revise the problem (on their own time) and resubmit the problem, which using the system that Cheradenine suggested will immediately reenter the voting queue.\r
\nProblems that are submitted and ready to be posted will pass through the voting queue without trouble, thus encouraging people to take care of editing and formatting first.\r
\n\r
\nOf course, some problems will still need to be discussed by the voters and the author for clarification and whatnot, but perhaps if thumbed-down problems were returned to the author rather than deleted, we would be able to move the queue faster. I think that will help some, although seeing some problems the second or third time around might be a little tedious.\r
\n\r
\nAs an aside, perhaps there could be a second option to vote problems down on the basis of being duplicates, in which case they would be deleted.',1575,'DJ','2003-06-18 06:25:52');
INSERT INTO forumpost VALUES (1287,176,5,'Re: Problem flooding revisited','It seems the good ideas are starting to gel. I really like DJ’s proposal for a user’s TD backlog, with those problems going back to the front of the voting queue when the user edits and resubmits the problem. That way, the voting queue gets weeded quickly, and editing is done on the user’s own time. In addition, I propose that puzzles that don’t get voted in within a certain period of time, say four days in the voting queue, get kicked out automatically to this backlog list. If Journeymen can’t decide they like a problem in that much time, it probably isn’t a great problem in the first place, and if the lack of voting was just due to a holiday weekend or something, the user can resubmit the puzzle, no harm done. This brings up a good point, however: a resubmitted problem from the backlog list should have the original comments attached, so Journeymen can tell if the areas for improvement were addressed. In any case, this proposal allows puzzles to be quickly approved or kicked out, so more puzzles will pass through the voting queue in a week. When Journeymen are active, I can imagine 8 of the 10 puzzles in the voting queue being new each day.\r
\n\r
\nAs for the issue of puzzle quality, I feel the TU/TD should be replaced with puzzle ranking, as proposed by fwaff et al. A puzzle receiving five or more numerical votes averaging at least 3.5 is in, 5+ votes averaging <3.5 is out, and less than 5 votes by the 96th hour in the voting queue causes it to get kicked back to the backlog, where its voting history is erased -- after resubmission, the puzzle should start with a clean slate and be judged based on its merits after being edited.\r
\n',1567,'Bryan','2003-06-18 10:37:12');
INSERT INTO forumpost VALUES (1288,180,5,'The riddle problem','Ok this relates to the problem of the queue having to many problems in it but still is a somewhat different topic. Now as we all know the queue is growing extrememly fast and i think that there is one category of problem that is causing it to grow. Riddles. I say that it might be a good idea that a user should only be allowed to submit riddles if they have had lets say 6 other problems posted to the site. Almost every new user that comes to the site just says \"hey i\'ll submit riddles to improve my rank\". Well now, by making this restriction i think the site will now get less riddles (which a lot of people will be happy about) and less problems in the queue (another good thing)',1072,'Alan','2003-06-18 10:42:56');
INSERT INTO forumpost VALUES (1289,180,5,'Re: The riddle problem','I would agree with that, but I don\'t particulary like riddles as much as other puzzles, so I don\'t know if I am being biased or anything like that.',1626,'Gamer','2003-06-18 13:32:56');
INSERT INTO forumpost VALUES (1290,180,5,'Re: The riddle problem','How about this: every user can submit only one riddle. Ever. I wouldn\'t be too broken up about it...',1575,'DJ','2003-06-18 16:59:56');
INSERT INTO forumpost VALUES (1291,180,5,'Re: The riddle problem','Hear, hear!',1567,'Bryan','2003-06-18 17:10:34');
INSERT INTO forumpost VALUES (1292,180,5,'Re: The riddle problem','Not sure I like that idea. Suppose one user has a talent for writing good riddles. Do we indiscriminately kill off all but one of his submissions? I think the best course of action is to just be very picky about the riddles we accept.',103,'friedlinguini','2003-06-19 05:52:18');
INSERT INTO forumpost VALUES (1293,180,5,'Re: The riddle problem','And what if I submit a riddle, and then see a riddle I like much more? I think we should be picky, but of course saying this is one thing, and enacting it is another.',1626,'Gamer','2003-06-19 06:02:17');
INSERT INTO forumpost VALUES (1294,176,5,'Re: Problem flooding revisited','I think Bryan\'s idea (in the last paragraph) would be useful. \r
\n\r
\nAlso, when I look at the queue right now, the problems come in slowly. Only two problems come into the queue each day, or sometimes 3 or 4 due to TD problems. This means that the number of days it takes from submission to voting is around the number of problems in the queue divided by 3 ... Even if we TD 9 problems per week, a queue with 480 problems (which we are over currently) would make a problem from submission to queue in 60 days!\r
\n\r
\nWhen I looked at the queue, some problems are getting TD, even though they are good problems, but they lack good wording. Having a place where they can be put aside would be helpful for the submitter. There are two problems though: When should the problem come back in? Should it go to the back of the queue? Also, we would need to be able to send some problems not to the backlog, like duplicates and problems that are not appropriate for the site (like lateral thinking problems, and just math homework problems).\r
\n',1626,'Gamer','2003-06-19 06:11:19');
INSERT INTO forumpost VALUES (1295,180,5,'Re: The riddle problem','In my original post i was saying that riddles are simply locked until they reach a certain rank. That way all the site \"newbs\" who just want to go up a rank by submitting tons of riddles (where the answer is either nothing, life or outer space) simply won\'t be able to submit this.',1072,'Alan','2003-06-19 08:55:08');
INSERT INTO forumpost VALUES (1296,176,5,'Re: Problem flooding revisited','I really do like bryans idea as well but instead of getting rid of tu/td and having the time thing, we shoukld just put in and \"edit vote\" so it will be thumbs up or thumbs down or edit or note. after 3 edits and a time period expires, then the problem will be kicked back, an automatically generated e-mail will be sent and if the author does not edit it by the time it gets in the queue again, it is deleted.',1072,'Alan','2003-06-19 09:01:34');
INSERT INTO forumpost VALUES (1297,173,6,'Re: To Tim Axoy - Just a question','What\'s happened to all of Tim\'s pending problems?',1919,'Lewis','2003-06-19 09:54:35');
INSERT INTO forumpost VALUES (1298,173,6,'Re: To Tim Axoy','They are still there, being voted on as if he was here.',1626,'Gamer','2003-06-19 12:17:19');
INSERT INTO forumpost VALUES (1299,181,5,'After submitting a problem...','I noticed this when I submitted a problem:\r
\n\r
\nBecause we want to give every problem equal exposure, we will generally only \"publish\" one problem per day. This means that even if your problem gets the (+3) score, it may not appear on the site immediately. Please be patiend. \r
\n\r
\nFirst of all, 2 problems are published on weekdays. Also, you mistyped patient.\r
\n',1626,'Gamer','2003-06-19 16:03:15');
INSERT INTO forumpost VALUES (1300,180,5,'Re: The riddle problem','My suggestion was a joke, if you didn\'t catch that...\r
\n\r
\nStill, I think there should be some limitations on riddle submission, because in truth this is not a riddle site, but a math puzzle site. I have not yet seen a riddle that was difficult enough to spend more than a few seconds on that still bore a credible solution, and certainly none as satisfying to solve as a good logic problem.',1575,'DJ','2003-06-19 17:02:58');
INSERT INTO forumpost VALUES (1301,180,5,'Re: The riddle problem','I believe this site is for any puzzle that requires some logic to solve, be it a math problem or not (and in fact, the math problem cannot be a simple plug-and-chug, homework type problem if it wants 3TU). I agree with DJ, however, that most of the riddles seen so far have been pretty obvious and unsatisfying. If puzzles were approved by grades instead of a simple TU/TD, I doubt many would pass.',1567,'Bryan','2003-06-19 19:27:45');
INSERT INTO forumpost VALUES (1302,180,5,'Re: The riddle problem','The two riddles I liked yet was the \"The poor have, the rich want, and if you eat it you\'ll die\", but I could have handled only one of those \"NOTHING\" riddles instead of two (or three or four if any are in the queue)\r
\n\r
\nI also liked Yes, sir! lots as well, because I hadn\'t seen that one before.\r
\n\r
\nI think logic and math puzzles like Four Digit Number and Letter Cubes would be good for the site, and not that many more riddles.',1626,'Gamer','2003-06-20 01:43:56');
INSERT INTO forumpost VALUES (1303,180,5,'Re: The riddle problem','Ah, if only you could see my pending problems! Oh well, there\'s always 2004.',1567,'Bryan','2003-06-20 05:07:25');
INSERT INTO forumpost VALUES (2933,376,7,'Hi ! every1','Hello friends,\r
\n\r
\nMy name is Raza and I am from India . I am an undergraduate student of computer science . I chose Computer Science as it offers ample scope for personal creativity and insight and was thus an obvious choice for someone like me who adores problem solving to the core.\r
\nI came across flooble perplexus while searching the web for some mathematical workout, and I have every reason to believe that I\'ve come to the right place :-)\r
\n\r
\n',5257,'Raza','2004-01-20 08:07:41');
INSERT INTO forumpost VALUES (1305,180,5,'Re: The riddle problem','Yeah, I know how you feel, Bryan - if only you could see my pending problems (including Letter Cubes 2, haha...)',1575,'DJ','2003-06-20 05:35:07');
INSERT INTO forumpost VALUES (1306,183,7,'nope.','Greetings gentlefolk!\r
\n\r
\nSome time ago, I found this site not quite by accident. I do attend school, but must work as a warehouseman to make a living. There is an alarmingly low level of thought and common sense at my place of employment; as of late I have been posing games of trivia and 20 questions to a few of my co-workers to try to make things a bit more interesting. Trivia turned out to be not so entertaining; either you know the answer or you don\'t. 20 questions is a much happier game. You don\'t know the answer immediatly, and must ask and link together questions to form a hypothesis and solve the problem (a process I am sure you are aware of. To the point...).\r
\n \r
\nBut I\'m the only one providing problems!\r
\n\r
\nThis is not happy for two reasons. First I enjoy solving puzzles almost as much as I enjoy rambling on in on-line forums (in case you haven\'t noticed). No one has questions for me to solve. Second, I\'m running out!\r
\n\r
\nSo I turned to the web and found flooble.com. Again I have purpose!\r
\n\r
\nI am in awe! I go to school and study math , philosophy, and computer systems. I thought I was clever, perhaps even smart, but wow! So much brain power in one place! Consider me humbled.\r
\n\r
\nAnyhoo, I have enjoyed what I have seen so far, and will try not to look at the answers without first trying to solve the puzzle.\r
\n\r
\nflooble.com makes my brain hurt! \r
\n\r
\n ',2436,'Chris','2003-06-20 05:58:28');
INSERT INTO forumpost VALUES (1307,184,5,'Problem Comments','One minor change I might suggest is in the voting queue, disable only the voting dropdown menu instead of the entire comment line for one\'s own problems. What I mean is, when my problems are in the queue, and I want to make a comment, there is a message stating \"You submitted this problem, and cannot vote for it.\" I then have to go to my list of submitted problems and find the one in question (as they are still not quite sorted properly) in order to comment from there. The sorting problem has been mentioned before, but I see no reason why we shouldn\'t be able to comment on our own problems without voting (perhaps even leave the menu, but with \'Note\' as the only option).',1575,'DJ','2003-06-20 06:21:09');
INSERT INTO forumpost VALUES (1308,183,7,'Re: nope.','That\'s what it\'s here for. :)\r
\nWelcome to the site Chris. I hope you\'ll be posting some of your own puzzles onto this site, although beware that the queue is about two months long.',1919,'Lewis','2003-06-20 06:48:25');
INSERT INTO forumpost VALUES (1309,185,4,'The queue needs help now!','We have generated quite a few good ideas in the \"Problem flooding revisited\" thread, and I urge Levik to take action soon or ask us for more input so he can do so. It is little wonder the queue is so long -- the ten problems being voted on now are mostly stagnant and wallowing in indecision by voters and the need for rewrites by submitters. Also, half of them don\'t even spark my interest. I think we are about to TD all riddles just because they are riddles (I know I\'m considering it), which is not very fair, but I\'m not sure what else to do.',1567,'Bryan','2003-06-20 07:02:23');
INSERT INTO forumpost VALUES (1310,185,4,'Re: The queue needs help now!','I have TDed less amusing riddles... I think we are all riddled out for a while. Any riddles that \"are a little good\" are going to be scrapped because we need other problems in my opinion.\r
\n\r
\nI wouldn\'t TD just because it\'s a riddle, but if it\'s not a great one I don\'t know what else to do.',1626,'Gamer','2003-06-20 11:23:37');
INSERT INTO forumpost VALUES (1311,183,7,'Re: nope.','Lewis is right, and I too am interested in all the smart people here.',1626,'Gamer','2003-06-20 11:25:14');
INSERT INTO forumpost VALUES (1312,184,5,'Re: Problem Comments','Oh, I wanted to say this too but forgot :) I agree with DJ, when I have been voting and saw my problem there, I would click on it and read the problem\'s comments, but would have to move to the Your problems page to post comments.',1626,'Gamer','2003-06-20 11:27:23');
INSERT INTO forumpost VALUES (1313,180,5,'Re: The riddle problem','I always want to say \"I solve this like I did in my problem [problem that hasn\'t reached the queue yet]\" :)',1626,'Gamer','2003-06-20 11:29:52');
INSERT INTO forumpost VALUES (1314,185,4,'Re: The queue needs help now!','As we can all see riddles are a problem. SO now lets be harsh with riddles then and along with the riddle restriction the queue shoul dincrease a lot less.
\n\r
\nLogs can be of any \"base\", through there are two bases that are most prominent. When written as log, if there is no base mentioned (usually a number in brackets or subscript after the word log), then it is assumed to mean a base 10 log. If written as ln, it (always) means the base e log (e is an irrational number which is very important in Calculus. It\'s value is approximately 2.72). Now there are three parts to a log equation, and if you know two of them, with a little mathematical manipulation you can calculate the third.\r
\n\r
\na typical log equation is as shown log(10)100=2\r
\n\r
\nThe first part, the 10, is the \"base\". As Ive mentioned, if there is no mention of the base, and the equation is written \"log\" and not \"ln\", then you assume that the base is 10.\r
\nThe second part is the number to which you are applying the log function, and the third is the \"answer\" to the log question. With a litttle experience, you will learn to see easily how these numbers are related, but to start out, the way that this log function is defined is as follows; the \"base\" of the log is the base of an exponential equation. The answer to the question is the exponent of the base, and the number which you were originaly logging is the answer to this modified expression. Following the example above, when you create an exponential expression with 10 as the base and 2 as the exponent, the result is 100. (10^2=100)\r
\nRemember that any number can be the base, it simply means that a little bit more complicated math results, for example\r
\nlog(4)64=3, because 4^3=64.\r
\n\r
\nWith a little exposure to this system, you\'ll see that a number whose log (base 10) is one more than anothers, the first number is 10 times (because that is the base) greater than the first. For example if log x=34.115 and log y=35.115, then we know that y=10x.\r
\n\r
\nLogs, while a difficult concept, are quite useful, especially in more advanced math. Here in Canada, we cover logs as curriculum around grade 10, so I would expect, Lewis, that this topic is not terribly far off in your scholastic endeavors.\r
\n',775,'Cory Taylor','2003-06-21 13:46:39');
INSERT INTO forumpost VALUES (1318,186,6,'Re: Log?','Logarithmic scales are what I see them used for (like pH and such)... Think of a logarithmic scale like a normal scale, except multiplying instead of adding.\r
\n\r
\nI can\'t tell you too much, am undereducated (at least relative to others) in math, but the way I always remembered it was \"logs are exponents\".',1626,'Gamer','2003-06-21 17:17:58');
INSERT INTO forumpost VALUES (1319,187,7,'The Gong Problem','Hey everyone, i am new, and last semester my teacher gave us a problem that seemed simple enough, but no one could find the answer. Ironically enough, she was fired by third quarter because of funding cuts, and we never found the answer. I am dying to know the answer and the problem goes as follows: \"It takes seven seconds for a clock to strike seven gongs, how long will it take it to strike ten gongs (hint: the answer is not ten seconds.\" If anyone knows the answer, it would be greately appricated, along with a detailed explanation of how such a conclusion was reached. Thanks a bunch.\r
\n-Dom',2513,'Dom','2003-06-22 17:19:12');
INSERT INTO forumpost VALUES (1320,187,7,'Re: The Gong Problem','Actually, we aren\'t actually allowed to post problems here... but if I could say what the answer was, I would say that time isn\'t measured after the last gong... So 7/(7-1) is the time in seconds for it to strike 7 gongs. (The time measured is between each gong, and there are 6 \"betweens\" for the gongs)... So now all you need to find is 10 * (7/6), which is 11 2/3.',1626,'Gamer','2003-06-22 18:17:08');
INSERT INTO forumpost VALUES (1321,180,5,'Re: The riddle problem','I understand the problem with riddles. Too many of them in the queue...\r
\nThis is unfortunate. I love to write riddles and solve them, although problems I have looked at in the Logic section are delightfully challenging. I would, however, like the opportunity to post some riddles I have edited. Let me know what you think. Thanx!',2436,'Chris','2003-06-23 00:55:19');
INSERT INTO forumpost VALUES (1322,186,6,'Re: Log?','Be concerned with logarithmic functions but not terrified; if you plan on pursueing a study in math, logarithmic functions will come around to get you. Consider a log as the inverse of an exponent, study their properties, ask questions when you are confused, and you should be ok. And don\'t forget repetition, repetition, repetition. If you wish, you may try entering the term \"math\" in a search engine on your computer and see the results. I have found a few helpful sites... ',2436,'Chris','2003-06-23 01:07:16');
INSERT INTO forumpost VALUES (1323,180,5,'Re: The riddle problem','Make sure they aren\'t duplicates (we have had sooo many of them), and aren\'t the \"My first is in sail but not in boat\", or that the answer is a letter (Without me love couldn\'t exist).\r
\n\r
\nI think the fact is riddles are easier to find (or create), than other puzzles, so we get more of them.',1626,'Gamer','2003-06-23 05:29:38');
INSERT INTO forumpost VALUES (1324,187,7,'Re: The Gong Problem','There\'s actually already a problem on this site very similar to that one.',1919,'Lewis','2003-06-23 07:50:17');
INSERT INTO forumpost VALUES (1325,173,6,'Re: To Tim Axoy','I want my account back.',NULL,'Tim Axoy','2003-06-23 12:35:28');
INSERT INTO forumpost VALUES (1326,173,6,'Re: To Tim Axoy','Tim don\'t you understand what levik is saying? This is not to be discussed here. But in facty over e-mail',1072,'Alan','2003-06-23 13:11:26');
INSERT INTO forumpost VALUES (1327,186,6,'Logs and logarithmic scales','Since I seem to be older than most here, I\'m not sure that any of you knew of them, much less remember them, but when I think of logs and logarithmic scales, i fondly remeber slide rules.\r
\n\r
\nSlide rules were two piece \"rulers\" whose main scales (labelled for some arcane reason the \"C\" and \"D\" scales) were used to multiply large numbers. Other scales performed other operations. (This was before calculators became handheld and \"scientific\" calculators became affordable.)\r
\n\r
\nYou can see the way two ruler scales can be used to perform a binary operation by using two ordinary rulers to perform addition. Say you want to add 5 + 2. Slide the first ruler so that the \"zero point\" is aligned with the \"5\" on the second ruler. Then find the \"2\" on the first ruler. The marking (\"7\") on the second ruler next to that \"2\" is the result you are seeking. (2 inches beyond 5 inches is 7 inches.)\r
\n\r
\nA slide rule\'s \"C\" and \"D\" scales were marked, not in linear distance, but in the \"common log\" (base 10 log) of that distance. It worked because (10^a)(10^b) = 10^(a+b), which also means that log(A) + log(B) = log(AB), so you were adding the logs the same way you added inches in my last paragraph.\r
\n\r
\nHere are some sites about logarithms:\r
\n\r
\nhttp://www.sosmath.com/algebra/logs/log1/log1.html\r
\nhttp://www.sosmath.com/algebra/logs/log4/log44/log44.html\r
\nhttp://www.physics.uoguelph.ca/tutorials/LOG/\r
\n\r
\nAnd some about slide rules:\r
\n\r
\nhttp://www.sphere.bc.ca/test/sruniverse.html\r
\nhttp://www.hpmuseum.org/srinst.htm\r
\nhttp://www.eminent.demon.co.uk/sliderul.htm\r
\nhttp://www.dotpoint.com/xnumber/hp.htm\r
\n\r
\n\r
\n',153,'TomM','2003-06-23 15:16:28');
INSERT INTO forumpost VALUES (1328,188,7,'Hello!','Hi there everyone, I\'m new here. I accidentally found this site when I was looking for brainteasers for use at my school activities. By the way, I was from my college\'s maths society, so naturally, we need these questions for use there.\r
\n\r
\nThese site is pretty cool isn\'t it? So well organized and managed, as well as problems of all sorts. It\'s fun! Anyway, nice to know such a good site and all of you here. See ya around!',2536,'Peter','2003-06-23 22:49:35');
INSERT INTO forumpost VALUES (1329,189,5,'Just a Suggestion...','I\'m new here, so I don\'t know the system very yet, I mean how you all find these questions and stuff, but I got a little suggestion here:\r
\n\r
\nHave you read the book \"the art of problem solving \" by Paul Zeitz? well I read it many times and its pretty good for anyone who is interested in knowing maths. So why dont you try it? Some of the solutions there is so simple that you couldnt think of it when you see so hard a question!\r
\n\r
\nWell maybe you have read it, but as i said, this is just my recommendation...',2536,'Peter','2003-06-23 22:56:07');
INSERT INTO forumpost VALUES (1330,180,5,'Re: The riddle problem','But this is a puzzle site isn\'t it? So if we have riddles, we should have those which are able to make us think, and not those which are so \"twisted\" and full of nonsense, where the answers are not logical at all. Putting aside these, the rest should be easliy accepted.\r
\n\r
\nThe more the merrier, I guess..',2536,'Peter','2003-06-23 22:59:38');
INSERT INTO forumpost VALUES (1331,50,5,'Re: Chatterbox','levik, you are really clever...to mannage and maintain this stuff here...high praise for you...i\'m really impressed!\r
\n\r
\nI\'m a newbie here, just signed up now...\r
\n\r
\nMaybe you would think why I am online at this time? Well its afternoon for me over here... :)',2536,'Peter','2003-06-23 23:06:59');
INSERT INTO forumpost VALUES (1332,190,3,'Triangles?','OK, so I saw a problem on site dealing with an equilateral triangle nestled within a circle, such that the three corners of the triangle were in contact with the perimeter, yada, yada, yada. I solved it and wanted to post the results, but, alas! the problem went and hid. Anyone know where I can find it? I\'d love to compare results...',2436,'Chris','2003-06-24 01:54:28');
INSERT INTO forumpost VALUES (1333,190,3,'Re: Triangles?','Found it in the search. Never mind...',2436,'Chris','2003-06-24 01:59:45');
INSERT INTO forumpost VALUES (1334,191,6,'Spacing in Problems','In the most recent problem (Leapfrog), DJ spaced out everything evenly with extra spaces and such... I have been unsuccessful when doing that, extra spaces between things just get deleted. Plus, things don\'t line up right for me.\r
\n\r
\nThree Spaces Between Words\r
\nOne Space Between Words\r
\n\r
\nBoth of these would only have 1 space\r
\n\r
\nWWWWW|\r
\n\r
\n-----|\r
\n\r
\nIIIII|\r
\n\r
\nThese would all have different | stopping places.',1626,'Gamer','2003-06-24 04:52:15');
INSERT INTO forumpost VALUES (1335,191,6,'Re: Spacing in Problems','It looks fine when typing it.\r
\n\r
\nQQQQQ|\r
\nWWWWW|\r
\n#####|\r
\n~~~~~|\r
\n[[[[[|\r
\n*****|\r
\n+++++|\r
\n\r
\nBut when you post it it looks all wierdo',1626,'Gamer','2003-06-24 04:53:59');
INSERT INTO forumpost VALUES (1336,191,6,'Re: Spacing in Problems','That\'s because the text entry fields use a monospaced font. Also, HTML treats all strings of whitespace as a single space for plain text. Try using the <tt> or <pre> tags.',103,'friedlinguini','2003-06-24 05:03:58');
INSERT INTO forumpost VALUES (1337,192,5,'Where\'s my problem?','Not for the first time, I have a puzzle which made it to the voting queue, received several comments, then disappeared before reaching +3 or -3. If history repeats itself, it should show up again in half a week to conclude voting. Is this a bug in the queue algorhythm? This puzzle had QW 1, and with it gone there is now another puzzle from Ravi, which I would hazard to guess has a lower QW priority <grin>.',1567,'Bryan','2003-06-24 05:04:48');
INSERT INTO forumpost VALUES (1338,192,5,'Re: Where\'s my problem?','What happens is the QW for each problem gets recalculated every night. That\'s why Ravi always has two problems at the top of the queue every morning regardless of how often we push or dump his problems. ',103,'friedlinguini','2003-06-24 05:28:54');
INSERT INTO forumpost VALUES (1339,180,5,'Re: The riddle problem','Yes peter the only thing is that we are trying to make the number of the problems in the queue go down, and we are also faced with the problem of nmot seeing many good logic problems and math etc. A large portion of the queue is riddles, so by implementing this solution we can eliminate these two problems.',1072,'Alan','2003-06-24 06:07:17');
INSERT INTO forumpost VALUES (1340,186,6,'Re: Log?','Heh - I remember those from when I was a kid. My parents had a whole bunch from their college days. \r
\n\r
\nThey weren\'t really using them anymore, so I was allowed to play with them - I always thought the sliding center was a lot of fun.\r
\n\r
\nNeedless to say, I never did figure out how to use the darn things.',1,'levik','2003-06-24 07:40:18');
INSERT INTO forumpost VALUES (1341,188,7,'Re: Hello!','Hey Peter - welcome to Flooble. I hope you stay here long enough to actually see this message, unlike some people. ;)',1919,'Lewis','2003-06-24 07:56:06');
INSERT INTO forumpost VALUES (1342,186,6,'Re: Log?','Thanks for all your help guys, I appreciate it.\r
\n\r
\nI\'m currently reviewing the websites TomM mentioned, so (hopefully) next time I come on I\'ll be able to solve problems like \'A Couple of Logs\'. :)',1919,'Lewis','2003-06-24 08:19:18');
INSERT INTO forumpost VALUES (1343,192,5,'Re: Where\'s my problem?','You aren\'t alone (as I said before), my problem Reusable Question met the same fate.',1626,'Gamer','2003-06-24 09:41:42');
INSERT INTO forumpost VALUES (1344,50,5,'Re: Chatterbox','And where is \'over here\'?',1919,'Lewis','2003-06-24 12:02:15');
INSERT INTO forumpost VALUES (1345,191,6,'Re: Spacing in Problems','Put things inside <pre> tags like this:\r
\n<pre>\r
<lt;/pre>\r
\nword word\r
\n word (space) word\r
\netc..\r
\n
\n\r
\nAlso, to put extra spaces inside normal text, hitting the space bar more than once in a row, or at the beginning of a line, will be deleted. You can type in between words(word word shows up as word ) for the extra spaces.\r
\n\r
\n(Now let\'s hope everything shows up the way I want it to..)',1575,'DJ','2003-06-24 12:32:50');
INSERT INTO forumpost VALUES (1346,191,6,'Re: Spacing in Problems','| | | |\r
\r
\n | |\r
\n| | | |
\n\r
\n| | | |\r
\n | |\r
\n| | | |\r
\n\r
\n| | | |\r
\n | |\r
\n| | | |\r
\n\r
\n\r
\n\r
\n',1626,'Gamer','2003-06-24 13:20:17');
INSERT INTO forumpost VALUES (1347,191,6,'Re: Spacing in Problems','All of them looked like the top one when formatted, with 1 enter between each.',1626,'Gamer','2003-06-24 13:21:52');
INSERT INTO forumpost VALUES (1348,191,6,'Re: Spacing in Problems','I\'m assuming those were <pre>, <tt>, and nothing, in that order...\r
\n<pre> (pre-formatted text) will preserve your spacing and alignment in a fixed width font\r
\n<tt> (typewriter text) will display a fixed width font, but you will still lose extra spaces',1575,'DJ','2003-06-24 19:56:31');
INSERT INTO forumpost VALUES (1349,193,7,'newbie','Hi everyone,this is a coool site.I have been a visitor here for sometime(a month or so) and have been solving the puzzles.The site is terrific from the design(mounted balls for the logo..) to the features(puzzles ,poetry,the member ranking scheme...) to the way it is so interactive.\r
\n So I decided to become a member.The puzzles are really fun and there are so many.I look forward to the action(of solving them).\r
\nP.S: I found the site through google search for puzzles and this is the only site I come back to of the lot posted there.\r
\nc ya,\r
\nrajesh',2545,'rajesh','2003-06-24 21:20:34');
INSERT INTO forumpost VALUES (1350,169,3,'Re: 500!','More than two weeks later, still hovering around 500, and slowly increasing...',1575,'DJ','2003-06-25 01:22:49');
INSERT INTO forumpost VALUES (1351,169,3,'Re: 500!','Ah, but only because Ravi dropped like 25 overnight.\r
\n\r
\nHis problems don\'t really slow us down, since he\'s got the top two spots reguardless.',1,'levik','2003-06-25 01:58:53');
INSERT INTO forumpost VALUES (1352,191,6,'Re: Spacing in Problems','TT works better in comments and forums, because the site\'s code turns all returns into BR tags (this causes PRE text to look double-spaced in these areas) - while TT does not handle multiple spaces, you can easily compensate for using non-whitespace characters for padding:\r
\n ___123\r
\n _33451\r
\n ____33',1,'levik','2003-06-25 02:02:44');
INSERT INTO forumpost VALUES (1353,169,3,'Re: 500!','Strictly from my interest in solving problems, I am curious why he has the top two spots regardless. friedlinguini said the same thing before and I never asked.',1567,'Bryan','2003-06-25 05:34:31');
INSERT INTO forumpost VALUES (1354,169,3,'Re: 500!','From what I understand, I don\'t think it\'s anything manual. The whole idea is Ravi would have lots of problems in clumps in the queue if it wasn\'t for queue weight. But, since there is queue weight, only his first 2 problems would appear. But when one of his gets off the queue, another one gets back on because he submitted it before any of the recent problems were submitted. For example:\r
\n\r
\nSuppose the queue only had 6 problems in it. (with only 2 from each person) and RRRARBARACBBC... was the order the problems were in (R is Ravi\'s problem, ABC are someone else\'s)\r
\n\r
\nWhen Ravi drops 3 of them off, they sit in line together. So far the queue would look like this: RRABAC, because you would skip over any of Rs after the first two and any A after the first two.\r
\n\r
\nThen the first R gets approved for the site, so the line looks like this: RRARBARACBBC..., and the queue looks like this: RRABAC. There are still two Rs because out of the 6 next in line, at least 2 are Rs. Then after the next R is taken off the site (RARBARACBBC...), the queue looks like RARBAC. Potentially, if Ravi goes on some long vacation (as seen by the next part of the queue) he could lose his spots in the queue. After the next 3 problems are put on the site (BARACBBC), the queue would look like BARACB, and there would on be 1 R.\r
\n',1626,'Gamer','2003-06-25 06:09:03');
INSERT INTO forumpost VALUES (1355,169,3,'Re: 500!','This is why I think owner the top spot in the queue should be rotated.',103,'friedlinguini','2003-06-25 06:22:41');
INSERT INTO forumpost VALUES (1356,169,3,'Re: 500!','Why is the \"top spot\" better than any other spot? Just because it usually gets voted on first? (Note: Ravi doesn\'t have any problems in the queue as of now... maybe they all got deleted)',1626,'Gamer','2003-06-25 08:29:10');
INSERT INTO forumpost VALUES (1357,169,3,'Re: 500!','I mean the problems in the queue got deleted... so vote on the problems now because by tommorrow 2 of them won\'t be there for voting (as Ravi\'s will have taken their place)',1626,'Gamer','2003-06-25 08:30:31');
INSERT INTO forumpost VALUES (1358,193,7,'Re: newbie','Hi, rajesh. I had the same experience; of the myriad sites with math or logic problems, this was the only one whose problems were very good or very difficult. If you like to be made to think, then this is definitely the place to be. Have fun!\r
\n\r
\n=)',1575,'DJ','2003-06-25 12:04:09');
INSERT INTO forumpost VALUES (1359,194,4,'the most commented on... or is it?','Well i was just looking at the most commented on and i noticed around the world was number 1. Then when looking to see how so many comments could have been posted I looked at all of them and noticed that almost more than half were posted by Ravi. Every comment was addressing one persons opinion while her comments could have been condensed into one statement responding to everybody. Now I have nothing against Ravi and whats done is done. But I think it should be said now that people should not be doing this. Also I think we should add some more categories for top_____. Also Despite the fact I\'ve been around this site for a while I\'m a little confused. What does the rating of a problem mean? I always thought you were just rating the problem on account of how much you liked it but recently I was led to believe it may refer to difficulty. Which is correct?',1072,'Alan','2003-06-25 15:30:13');
INSERT INTO forumpost VALUES (1360,194,4,'Re: the most commented on... or is it?','Not that what I say amounts to anything, but I have mentioned to Ravi (see comments for Hearts and Spades) that it\'s unnecessary and rather annoying to go through a string of meaningless comments such as \"still you made a mistake\" to everything everyone else has written. At the time, it didn\'t seem like many people agreed with me, so I don\'t know if it ever will be said. As a few people said, it\'s an annoyance, but it\'s also hard to say that anyone is actually doing anything wrong.\r
\n\r
\nAs to your other question, I think that problem rating is indeed simply a measure of how much someone liked the problem -- at least, I\'ve never heard otherwise. If I am guessing correctly, you thought it may have referred to difficulty in recent discussion of ranking criteria and problem submission, where a few people suggested that problem difficulty should have a bearing on how problems were accepted, and it was countered that a hard problem isn\'t necessarily a \"good\" one, so it should go by problem rating. Also, quite a few times people have used \"rating\" to refer to the difficulty level of the problem, which I know has caused some confusion to other people. But yes, as far as I know, rating a problem is just a measure of how good you think it is, not how hard it is (although more difficult problems are often better than simple or trivial ones).\r
\n\r
\nI think it would be nice to see more \"top\" lists, but I don\'t know what they could include besides number of comments and peoples\' votes. Difficulty, perhaps? One suggestion I might have is, for within each category, the ability to list problems by rating or difficulty, instead of just reverse chronological order. Like, you could look at \"top rated\" or \"most difficult\" or even \"easiest\" problems of each category, not just on the entire site.',1575,'DJ','2003-06-25 20:16:50');
INSERT INTO forumpost VALUES (1361,194,4,'Re: the most commented on... or is it?','Perhaps a more accurate way of measuring this is the number of different people that have commented on a problem.',103,'friedlinguini','2003-06-26 05:18:30');
INSERT INTO forumpost VALUES (1362,194,4,'Re: the most commented on... or is it?','This might work, but then you would get the ones that everyone knows, and there are 10 or 20 of the exact same solution submitted by 10 or 20 different people.\r
\n\r
\n(To go back ot the other comments) And some comments aren\'t even related to the problem... I think I remember seeing many comments in Can or Cannot relating to \"Does God exist\" rather than the actual problem itself... And I would imagine that \"Around the world\" would fall under the same criteria as well...',1626,'Gamer','2003-06-26 07:11:57');
INSERT INTO forumpost VALUES (1363,176,5,'Re: Problem flooding revisited','I think we really need this edit vote. So many problems are comming with little errors (like spelling errors and such) and readibility errors, such that you would be hindered in solving them, by people that aren\'t able to make such changes. The problem is good itself, but problems\' written quality is going downhill...\r
\n\r
\nI like the 1-5 system for voting, but there might be another choice \"Edit please!\".',1626,'Gamer','2003-06-26 07:17:14');
INSERT INTO forumpost VALUES (1364,194,4,'Re: the most commented on... or is it?','Even still, if 20 different people post the same solution, how can you say all of those comments don\'t count? It\'s not ideal, maybe, but I think only fair. Also, it seems that the comments to \'Around the World\' do indeed pertain to the problem, just (as Alan said) more than half of them are by Ravi responding - usually needlessly - to everyone\'s ideas or comments. My suggestion, then, would be to count all comments (including multiple comments by one user, as that usually indicates a discussion worthy of \'most commented on\') except for those left by the author/submitter of the problem.',1575,'DJ','2003-06-26 09:01:23');
INSERT INTO forumpost VALUES (1365,193,7,'Re: newbie','I was lucky enough to choose this site first out of all of the sites that came from the search.\r
\n\r
\nI guess I thought \'Flooble? What does that mean?\' and clicked on it! :o)',1919,'Lewis','2003-06-26 09:32:03');
INSERT INTO forumpost VALUES (1366,194,4,'Re: the most commented on... or is it?','I would say \"Different good comments\", but that might take too long/too much work.\r
\n\r
\nWould most comments = easiest, thinking that a hard question will get less discussion (from multiple solutions and such) than an easier one with many solutions?\r
\n\r
\nI don\'t really care too much about most commented on, as I don\'t really use it too much... Mostly just the digest.',1626,'Gamer','2003-06-26 09:50:41');
INSERT INTO forumpost VALUES (1367,176,5,'Re: Problem flooding revisited','When I right out my problems, I always seem to make loads of mistakes. But when I check it I don\'t find any. After about a fortnight if I check it again for some reason I can suddenly see all the mistakes. Perhaps if the problems were arranged in queue order in \'my problems\' it would be easier to edit problems before they reach voting.\r
\n\r
\nPS I know this isn\'t related to the topic of this thread, but it is linked to the comment above.',1919,'Lewis','2003-06-26 09:54:46');
INSERT INTO forumpost VALUES (1368,195,5,'Queue Idea','When I noted the queue, I saw there were new problems in the queue, and all the old problems that were there got bumped down. Theoretically, if 2 or 3 people \"control\" 2 spots each in the queue, that narrows it down to 5 for everyone else, especially if their problems bump others\' down....\r
\n\r
\nMy idea for this would be to not allow problems to get bumped down. Any queue-weight calculations resulting in problems moved to the queue should get spots 11, 12, 13, so on so that they don\'t bump the existing problems out of the way.',1626,'Gamer','2003-06-28 04:28:11');
INSERT INTO forumpost VALUES (1369,195,5,'Re: Queue Idea','The secondary sort on most recently pushed problem would fix this, though if applied every time a problem disappeared from the queue, it would have some weird effects on QW groupings of more than one.\r
\n\r
\nAnother possibility would be to calculate QW on a problem only when it gets submitted, with a secondary step that any time all QW 1 problems are pushed or dumped, the QW of every problem gets decremented.',103,'friedlinguini','2003-06-28 16:07:51');
INSERT INTO forumpost VALUES (1370,195,5,'Re: Queue Idea','Currently levik only uses two queue weights, so under that suggestion, if a person submitted 10 problems, after the first 2 (queue weight 1) no more of his problems would show up until everyone else\'s first two showed up. If someone else submitted 10 problems, but spaced them at 2 per month, he could prevent the first person\'s problems from ever showing up. Also, once all the QW=1 problems were finished, all the QW=2 problems would become QW=1 and we would have the same problem as before QWs were instituted.\r
\n\r
\nTo properly implement your suggestion, levik would need to create a hierarchy of QWs: the first two get QW=1, the next two get QW=2, etc. And still the first problem mentioned above will not be prevented. I\'m not sure he wants to go to all that trouble for a dubious gain.',153,'TomM','2003-06-28 17:19:19');
INSERT INTO forumpost VALUES (1371,195,5,'Re: Queue Idea','It is still possible to stall the queue under my suggestion, but I think it\'s a bit less likely than you\'re making it out to be. It would require a number of people submitting problems at a trickle\'s pace such that they always had no less than one and no more than two pending submissions at any given time. It would also have to be done by enough submitters to fill the visible portion of the queue. To fix that issue, store some extra fields with each user record containing the QW of their last submission and the number of problems they have submitted at that QW. Heck it would even make calculating a new problem\'s QW simpler. Just remember to decrement user QW (to a minimum of zero) if all the problem QWs get decremented as well.\r
\n\r
\nI\'m not certain what problem you see with decrementing the QW. Since every QW gets decremented at once, the relative ordering of problems does not change. In fact the only reason I threw it in there was to keep the numbers from getting large.\r
\n\r
\nRe: your second paragraph: Isn\'t that what he does already? Or am I missing something?',103,'friedlinguini','2003-06-29 03:18:15');
INSERT INTO forumpost VALUES (1372,195,5,'Re: Queue Idea','>> It is still possible to stall the queue under my suggestion, but I think it\'s a bit less likely than you\'re making it out to be. It would require a number of people submitting problems at a trickle\'s pace such that they always had no less than one and no more than two pending submissions at any given time. It would also have to be done by enough submitters to fill the visible portion of the queue. \r
\n\r
\nI was not suggesting that the entire queue would often be stalled, but that someone who submitted more than two puzzles at a time might be disadvantaged to the point where his third puzzle might never rise to the top ten. Your solution might work if levik changed the QW system as I mentioned would be necessary in my last post (and which you apparently assume is how it is already).\r
\n\r
\n>>Re: your second paragraph: Isn\'t that what he does already? Or am I missing something? \r
\n\r
\nAs I said in the first sentence, currently levik only works with two queue weights: the oldest two problems by each submitter are QW = 1 and all the rest are QW = 2. Since that has the effect of limiting each submitter to two puzzles in the top ten at any time, it is all that needed to be done to achieve that goal. To add a complete hierarchy of QWs, whether recalc\'ed every night as is done now, or even following your suggestion, would involve much more coding, and the gain would seem to be so minimal.\r
\n\r
\n',153,'TomM','2003-06-29 06:21:20');
INSERT INTO forumpost VALUES (1373,195,5,'Re: Queue Idea','Actually, that isn\'t true as far as I have seen... Every 2 problems get a queue weight. The first 2 get QW=1, the second 2 get QW=2, the third 2 get QW=3, and so on...\r
\n\r
\nI am not as concerned with controlling the queue as others, just worried that someone with only riddles (like Ravi or TMP) when we are tired of riddles, would always take up two spots, which would bring the queue size down (and slow down problem visibility)... I am concerend with having problems bumped, such that a problem could be in the queue one day and gone the next.\r
\n\r
\nMy solution would just involve any new QW=1 problems to the end of the queue so that problems aren\'t getting bumped out.',1626,'Gamer','2003-06-29 09:54:56');
INSERT INTO forumpost VALUES (1374,196,5,'How do I','How do I access the digest page. Like how do I find it from flooble. I still don\'t know where to click.',1072,'Alan','2003-07-01 07:51:34');
INSERT INTO forumpost VALUES (1375,196,5,'Re: How do I','Right below the Forums link is Newest Problems, which is the digest page (/digest.htm)',1626,'Gamer','2003-07-01 10:05:05');
INSERT INTO forumpost VALUES (1376,197,7,'No Subject','hi im new :p ',2599,'amy','2003-07-02 08:34:16');
INSERT INTO forumpost VALUES (1377,197,7,'Re: No Subject','Welcome to the site.',103,'friedlinguini','2003-07-02 08:43:39');
INSERT INTO forumpost VALUES (1378,198,7,'hey all','Hey, I\'m new too. My family has been trading Nigerian Scam email responses for months now, and my dad sent the Flooble thing to me, which I thought was wonderful, so I started poking around the Flooble site. Great stuff here! Definitely something I\'ll be spending some time on this summer whenever I\'m not working or sleeping (maybe an hour or two per week...). Anyway, just wanted to say hi to everyone and share how I found this place.\r
\nPeace\r
\n~K~',2604,'Koren','2003-07-02 14:48:08');
INSERT INTO forumpost VALUES (1379,187,7,'Re: The Gong Problem','My take on this problem would be that these seven gongs that the clock strikes are when it strikes 7:00, so you would have to wait an hour until it started striking 8:00 before the next three gongs would be struck. Thus, it would take from 7:00:00 to 8:00:03, or 60 minutes and 3 seconds, which would be 3603 seconds.\r
\nPeace\r
\n~K~',2604,'Koren','2003-07-02 14:56:07');
INSERT INTO forumpost VALUES (1380,197,7,'Re: No Subject','Hello :b',1626,'Gamer','2003-07-03 05:58:07');
INSERT INTO forumpost VALUES (1381,197,7,'Re: No Subject','Hello :b',1626,'Gamer','2003-07-03 05:58:08');
INSERT INTO forumpost VALUES (1382,199,5,'Vacation','Well - I\'m going to be away starting tomorrow afternoon, and trough next Sunday. (Jul 4 - 13).\r
\n\r
\nHopefully nothing horrible should happen in the interrim - journeymen and scholars have enough priviliges to keep 90% of the site\'s features running smoothly.\r
\n\r
\nIf something does go wrong rendering the site unusable, do come back around the 14th :)\r
\n\r
\nSee you all when I get back.',1,'levik','2003-07-03 09:06:21');
INSERT INTO forumpost VALUES (1383,199,5,'Re: Vacation','Have a good one.',103,'friedlinguini','2003-07-03 10:38:06');
INSERT INTO forumpost VALUES (1384,198,7,'Re: hey all','Hi!',NULL,'xmas1000','2003-07-03 10:39:33');
INSERT INTO forumpost VALUES (1385,199,5,'Re: Vacation','Ok :)',1626,'Gamer','2003-07-03 12:28:36');
INSERT INTO forumpost VALUES (1386,200,4,'Its working','I am very glad to notice the queue starting to diminish and at quite a rapid rate. But i thik there should be one more issue that should be cleared up. Problems that need fixing up. My first suggestion is that if the user is gone for more than two weeks (possibly one) or if their problem is in the queue for 4 or more days awaiting fix-ips iot should automatically be td\'ed (Unless its really good and everyone agrees on levik fixing it up.)\r
\nAs for the two week rule you can be exempted from this if you post in the forums that you are on vacation. Just as long as it isn\'t a SUPER long one. (3 weeks tops) I am only saying this because I know the queue will move even quicker now. (Who knows maybe levik could come home from vacation to flooble and see the queue at 400)',1072,'Alan','2003-07-03 14:24:57');
INSERT INTO forumpost VALUES (1387,200,4,'Re: Its working','Or another idea I had... Let a user manually put your problems out of the queue if you are going to be on vacation. This way, any problems with a queue weight of 1 would instead have a queue weight of 2. (or higher if seen neccesary) This would keep the problem out of the queue until the user was ready.\r
\n\r
\nI still am a fan of the \"Edit\" vote... which if you get 3 edit votes it disallows it to enter the site until editted (and maybe makes the problem \"td\"ed if it\'s not changed within 3 days or so) Many problems are getting thumbs up even though they need editting (at least in my opinion), or the difficulty changed.',1626,'Gamer','2003-07-03 14:39:11');
INSERT INTO forumpost VALUES (1388,201,4,'Quick Switch','Out of the problems I submit, if I have one that will reach the queue soon, but it\'s not very good, and one that will reach the queue much later, but is much better, is it abiding by rules to switch these? (Like copy and paste, and such)\r
\n\r
\n',1626,'Gamer','2003-07-03 14:49:24');
INSERT INTO forumpost VALUES (1389,201,4,'Re: Quick Switch','Yes i\'d say so. This would technically violate the rules but if you know that both problems are siteworthy the it would be ok.',1072,'Alan','2003-07-05 09:44:07');
INSERT INTO forumpost VALUES (1390,202,7,'Another first posting :)','Hey everyone,\r
\nThis is my first posting, and it\'s not gonna be too different from everyone else\'s, but oh well. I\'m an 18-year old sophomore at Duke University, thinking about double-majoring in economics and English with a minor in math, and a puzzle nut. (Particularly word games...anyone here play Boggle?)\r
\n\r
\nAnyway, I just found this site 5 minutes ago. Looks really interesting! I look forward to puzzling with y\'all.\r
\n\r
\nAndrew',2627,'Andrew','2003-07-05 17:30:21');
INSERT INTO forumpost VALUES (1391,202,7,'Re: Another first posting :)','Hey Andrew - welcome to Flooble.\r
\n\r
\nIf you like boggle try this puzzle.',1919,'Lewis','2003-07-06 00:53:59');
INSERT INTO forumpost VALUES (1392,202,7,'Re: Another first posting :)','Whoops that didn\'t work.\r
\n\r
\nAnyway the puzzle I tried to link is called \'Mind Boggling\'',1919,'Lewis','2003-07-06 00:55:22');
INSERT INTO forumpost VALUES (1393,202,7,'Re: Another first posting :)','Mind Boggling',1301,'Charlie','2003-07-06 06:14:02');
INSERT INTO forumpost VALUES (1394,202,7,'Re: Another first posting :)','Mind Boggling Link',NULL,'Aspiring Novice','2003-07-06 07:30:32');
INSERT INTO forumpost VALUES (1395,202,7,'Re: Another first posting :)','That was me trying again, but I forgot to log in :)',1919,'Lewis','2003-07-06 07:31:20');
INSERT INTO forumpost VALUES (1396,202,7,'Re: Another first posting :)','Mid Boggling Link',1919,'Lewis','2003-07-06 07:34:26');
INSERT INTO forumpost VALUES (1397,202,7,'Re: Another first posting :)','YESSSS',1919,'Lewis','2003-07-06 07:34:44');
INSERT INTO forumpost VALUES (1398,203,4,'Can\'t understand','I believe I should post the solution to make the least of these digits but I\'m only educated in math to the grade nine level, so i don\'t know who has the smallest number. If someone could do this for me it would be appreciated greatly.',1072,'Alan','2003-07-06 08:09:06');
INSERT INTO forumpost VALUES (1399,201,4,'Re: Quick Switch','Actually, this is discussed in another thread (I forget which), and the general consensus was that this should not be done because it sets a bad precedent and can even lead to swapping puzzles AFTER the first one gets 3TU! Similarly, we should not \"submit\" a blank puzzle just to reserve a space in the queue, then replace it later when we come up with a good puzzle. If your first puzzle isn\'t very good and you can\'t fix it before it gets to the top of the queue, it will get deleted (you can even replace it with a note saying \"delete me\"), and your better problem will post when it posts :P',1567,'Bryan','2003-07-07 11:51:27');
INSERT INTO forumpost VALUES (1400,204,7,'No Subject','Hi. I\'m new at this.',2639,'Billie Freeman','2003-07-07 15:40:37');
INSERT INTO forumpost VALUES (1402,206,3,'Favourite Puzzle','This forum hadn\'t been used for a while, so I thought I would start a new thread.\r
\n\r
\nWhat\'s everybody\'s favourite puzzle on this site? Mine would probably be \'Yum, Arsenic\'.',1919,'Lewis','2003-07-08 09:44:20');
INSERT INTO forumpost VALUES (1403,207,7,'Hey everyone','I am all new to this site, so be nice and make me feel very welcome! :)',2653,'Lucy','2003-07-08 10:25:39');
INSERT INTO forumpost VALUES (1404,207,7,'Re: Hey everyone','Hello Lucy! Welcome to Flooble. I hope you enjoy your time here :0)',1919,'Lewis','2003-07-08 10:36:48');
INSERT INTO forumpost VALUES (1405,206,3,'Re: Favourite Puzzle','3 colors. What can I say I love everything about it.',1072,'Alan','2003-07-08 12:50:20');
INSERT INTO forumpost VALUES (1406,206,3,'Re: Favourite Puzzle','I prefer 2 colors to 3 colors, but both are good.',1919,'Lewis','2003-07-09 05:12:21');
INSERT INTO forumpost VALUES (1407,17,6,'Re: HTML codes for use on the site','<pre>pre<pre>',NULL,'URGENTOOT','2003-07-09 06:15:14');
INSERT INTO forumpost VALUES (1408,206,3,'Re: Favourite Puzzle','Yeah, “3 colors” is a good one - it took me hours to figure out, and I enjoyed every minute of it. And for a pure math problem, my favorite is “Let it Snow”, which is amazing for all the variables you need to add yourself, which later cancel out, leaving a solution dependent only on the information given! \r
\n\r
\nBut my overall favorite has to be “Five Tenants”, since it’s the first and only true logic problem (using a grid for elimination) I ever wrote, and it turned out really well. I guess I’m grading it on a different scale, as an author rather than a solver ;)',1567,'Bryan','2003-07-10 05:54:29');
INSERT INTO forumpost VALUES (1409,205,7,'Re: Hi. I\'m new at this.','me too',2672,'Stephanie','2003-07-10 14:10:30');
INSERT INTO forumpost VALUES (1410,205,7,'Re: Hi. I\'m new at this.','how did u find out about this web site',2672,'Stephanie','2003-07-10 14:11:20');
INSERT INTO forumpost VALUES (1411,205,7,'Re: Hi. I\'m new at this.','fine dont answer me',2672,'Stephanie','2003-07-10 14:12:34');
INSERT INTO forumpost VALUES (1413,73,7,'Re: hello!','tim, i like science and history',2672,'Stephanie','2003-07-10 14:15:32');
INSERT INTO forumpost VALUES (1414,205,7,'Re: Hi. I\'m new at this.','You have to wait more than 1 minute 14 seconds for a response Stephanie....',1919,'Lewis','2003-07-10 21:13:42');
INSERT INTO forumpost VALUES (1415,207,7,'Re: Hey everyone','hey Lucy!have fun!if u like puzzles u will find a lot of good puzzles here.other than that too there r a lot of good things happening here.so hang around.',2545,'rajesh','2003-07-10 22:04:26');
INSERT INTO forumpost VALUES (1416,201,4,'Re: Quick Switch','But if you post a few blank puzzles the queue weight will just be higher so you don\'t really gain much of an advantage.\r
\n\r
\nBTW, I only just discovered that this forum existed. Is that why when I was a student on the home page it said there was some new entries in the forum, but when I looked there wasn\'t?',1919,'Lewis','2003-07-11 01:15:52');
INSERT INTO forumpost VALUES (1417,208,4,'Secret Forum!','I just became an apprenrice when \'Do It Again\' got posted and I was wondering why this forum was kept a secret? I didn\'t know it existed, and it doesn\'t mention it in the user levels bit.\r
\n\r
\nAnyway I was wondering once you become a journeyman, do you get to see all of the problems in the queue, or only the top 10 or something? And is there any forums for just journeymen?',1919,'Lewis','2003-07-11 01:38:07');
INSERT INTO forumpost VALUES (1418,200,4,'Re: Its working','I think the edit vote is a good idea. If you get an edit vote from a journeymen the problem should be set aside untill that journeymen (or maybe a scholar or Levik) has accepted that the problem has been correctly edited, and the problem will re-enter the queue at the same QW as it was before.',1919,'Lewis','2003-07-11 03:07:52');
INSERT INTO forumpost VALUES (1419,208,4,'Re: Secret Forum!','Only the top 10 are shown in the displayed panel; and there are no additional forums beyond this one.\r
\n\r
\nDue to the changes in QW that occur out of synchrony with postings and deletions, some puzzles are in the top ten and out again to be temporarily replaced by others, so at any given time a journeyman could have seen somewhat more than 10 of the pending puzzles.',1301,'Charlie','2003-07-11 09:29:39');
INSERT INTO forumpost VALUES (1420,208,4,'Re: Secret Forum!','Oh, also, though there is no additional forum, there is a separate Chatterbox on the voting queue panel to discuss voting issues.\r
\n',1301,'Charlie','2003-07-11 09:31:24');
INSERT INTO forumpost VALUES (1421,209,4,'My Problems','I know this issue has been raised before, but I think it needs mentioning again.\r
\n\r
\nWhen you click on \'My Problems\' link, the order of the problems is seemingly random. I think they should be ordered by position in queue, to make it easier to do last minute corrections before they get to voting.\r
\n\r
\nI have 46 problems pending, and I have trouble finding the ones near the front of the queue. Think of poor DJ and Ravi who have even more!',1919,'Lewis','2003-07-11 12:13:09');
INSERT INTO forumpost VALUES (1422,210,4,'My Vacation','Well guys starting tommorow I\'ll be gone on a 2 week vacation. Which reminds me. levik can u have a digest for forums to. So that way when I get back I\'ll be able to see what I\'ve been missing?',1072,'Alan','2003-07-11 16:16:31');
INSERT INTO forumpost VALUES (1423,209,4,'Re: My Problems','yeah, it\'s quite cumbersome trying to look for problems, check the queue position, edit solutions, etc, when nothing is in much of an order. right now, though, levik is gone, and i\'m sure the glitch is unintentional and he\'ll fix it as soon as he figures out what the problem is.',1575,'DJ','2003-07-11 18:38:02');
INSERT INTO forumpost VALUES (1424,208,4,'Re: Secret Forum!','oh, and don\'t forget the elusive \'unapproved solutions\' queue, with no apparent purpose other than to allow scholars to post solutions while the director is gone and leave undeliverable comments to the problems\' authors, haha...',1575,'DJ','2003-07-11 18:40:29');
INSERT INTO forumpost VALUES (1425,200,4,'Re: Its working','usually if a problem needs editing, everyone agrees that it does, but some people would rather push through the rough version than wait around in queue for the author to return (which sometimes may never happen) or for levik to manually fix something. . . for which reason, i still advocate that deleted problems (except duplicates, perhaps) could be stored somewhere in a user\'s pending problem listing for editing and resubmission, on their own time. i think then voters will be a little less reluctant with a td vote on a messy problem, and potentially good problem that may need an overhaul will not be lost forever.\r
\n\r
\nfor right now, there are quite a few problems that need editing, from users that are no longer around, bouncing in limbo because a few overhopeful people are convinced that somehow the problems will make themselves site ready and have left a stubborn tu on a submission that can\'t go through (pardon the cynicism; i intend humor, not offense..). There are at least three or four problems that have sat in queue all week and longer with nothing happening at all. i think (and i know at least some people agree) that a problem that has sat in limbo for so long is probably not all that siteworthy, and certainly not in its current state. I just think people need to be a little more gratuitous with the thumbs down..',1575,'DJ','2003-07-11 18:54:39');
INSERT INTO forumpost VALUES (1426,210,4,'Re: My Vacation','On the main page for each forum, where it lists the threads in that forum, it also gives the date and time (?)* of the last pot in each thread.\r
\n\r
\nJust open any thread that had a posting after your vacation started. Since the threads are re-ordered according to to the timestamp, it\'s easy enough to find them all at the top of the list.\r
\n\r
\n* I still am not sure what timezone levik\'s computer is set for. ',153,'TomM','2003-07-12 00:24:34');
INSERT INTO forumpost VALUES (1427,210,4,'Re: My Vacation','Ooops! that should read \"... the last post in each thread.\"',153,'TomM','2003-07-12 00:26:41');
INSERT INTO forumpost VALUES (1428,200,4,'Re: Its working','I don\'t think a good problem should be pushed out just because the Director is away on vacation and thus unable to fix the wording. We\'ve had enough problems going through that the schedule of postings has kept up, even fortuitously getting 7-11 on 7-11. If the problems clear out soon when levik gets back, then there\'s the brighter side of not having overexposure of the ones that follow (of course at the expense of much overexposure of these).\r
\n\r
\nThe above applies to the non-riddle part of the voting queue, as for riddles:\r
\n\r
\nAs for myself I hate to vote one way or another on Riddles, as I don\'t understand them or what makes one good and another bad or how to judge, not even knowing the answer. I\'d also hate to have to send a reply to the author that we just don\'t like riddles any more, as there is the category for them.',1301,'Charlie','2003-07-12 06:59:38');
INSERT INTO forumpost VALUES (1429,201,4,'Re: Quick Switch','Yes, you just discover it when you become an Apprentice (See at the main page, where you click on Library) it says \"Can be read by Apprentice Users\"\r
\n\r
\nBoth my problems are pretty long away from the queue.. is it OK then? (Assuming they are both valid problems, and not blank ones)\r
\n\r
\nThe idea of submitting blank problems is then \"everyone\" would have 2 spots in the queue if they had two problems. But \"everyone\" can\'t have have 2 spots in the queue, so 5 people would have 2 spots in the queue, and the others wouldn\'t have any.',1626,'Gamer','2003-07-12 08:07:38');
INSERT INTO forumpost VALUES (1430,209,4,'Re: My Problems','Yes I agree with you Lewis! I always feel like complaining but then remember them :D',1626,'Gamer','2003-07-12 08:08:28');
INSERT INTO forumpost VALUES (1431,200,4,'Re: Its working','I think problems with an edit vote should be put aside until they get changes made... I don\'t like to delete them or otherwise get rid of them.\r
\n\r
\nI usually will only judge a riddle if I know the answer... I personally still like riddles, but we had way too many of them at one time...\r
\n\r
\nI think Journeymen shouldn\'t give a problem a third TU if they think it still needs editting though too.',1626,'Gamer','2003-07-12 08:13:51');
INSERT INTO forumpost VALUES (1432,206,3,'Re: Favourite Puzzle','Yeah, Bryan, it\'s hard not to be partial to your own problems..\r
\n\r
\nI like problems that are simple in concept, but perhaps long or complex to solve, such as Multiple Choice Quiz or A Locked Safe (although levik still has not posted a solution to that one). Measure that Angle was another good problem.',1575,'DJ','2003-07-12 09:15:46');
INSERT INTO forumpost VALUES (1433,206,3,'Re: Favourite Puzzle','I tend to work the other way - I always think that my problems are absolutely horrible and are always going to get TD\'d (although that is sometimes the case).',1919,'Lewis','2003-07-12 10:48:08');
INSERT INTO forumpost VALUES (1434,209,4,'Re: My Problems','Yes but you have a rather pathetic 31 problems pending. HA :o)\r
\n\r
\nActually, it\'s quality over quantity isn\'t it....',1919,'Lewis','2003-07-12 10:50:36');
INSERT INTO forumpost VALUES (1435,209,4,'Re: My Problems','why is 31 pending problems pathetic? and yes, would you rather have 50 crappy problems or 2 really good ones? i know i have a lot pending, but believe or not i try to be pretty discriminate about the caliber of problems i submit.',1575,'DJ','2003-07-12 14:14:00');
INSERT INTO forumpost VALUES (1436,209,4,'Re: My Problems','DJ - it was a joke - thats why there\'s a smiley face at the end - OK?',1919,'Lewis','2003-07-12 23:37:24');
INSERT INTO forumpost VALUES (1437,209,4,'Re: My Problems','Sorry if you thought I was being serious',1919,'Lewis','2003-07-12 23:52:14');
INSERT INTO forumpost VALUES (1438,209,4,'Re: My Problems','no..sorry if i sounded serious, because i really don\'t care.',1575,'DJ','2003-07-13 04:57:41');
INSERT INTO forumpost VALUES (1439,211,5,'Back From vacation','OK - I flew in back from Costa Rica this afternoon (and highly recommend visiting there if you haven\'t).\r
\n\r
\nSince I doubt I will be able to sift through everything that happened on the site in the last week, is there anything requireing my immediate attention?',1,'levik','2003-07-13 13:50:32');
INSERT INTO forumpost VALUES (1440,211,5,'Re: Back From vacation','No emergencies, but a couple of problems in the voting queue need your editing. Some voters have given up on Age of Ages, in the absence of your ability to modify, and Two Geometric Series also needs your editing, given the author\'s absence. In the solution queue Letter Sequence needs a change, and Happy might not be reading the solution queue comments.',1301,'Charlie','2003-07-13 16:38:48');
INSERT INTO forumpost VALUES (1441,211,5,'Re: Back From vacation','Welcome back!\r
\n\r
\nNot much is different than when you left (including, I think, some of the problems in queue). There are a few problems from absent or negligent authors that could use manual editing, but mostly it seems that there is disagreement over what constitutes a siteworthy problem (\"How close can a problem be before it\'s considered a dupe?\" \"Need a solution be submitted for a problem to be posted?\"). These discords have deadlocked a few problems in the voting queue, as I\'m sure you will notice.\r
\n\r
\nIt looks as if things are just starting to clear up, though; it\'s just a matter of waiting for everyone to come around and catch up on the goings-down (haha).\r
\n\r
\nAlso, if it\'s not a great bother, could you manually fix the link in my solution to \'Random Primes\'?\r
\n\r
\nThanks, and it\'s good to know that you\'re back around.',1575,'DJ','2003-07-13 21:11:39');
INSERT INTO forumpost VALUES (1442,63,3,'Re: a/s/l anyone?','24/possessor of a Y chromsome/Manchester, UK.\r
\n\r
\nWith modern times\' availability of the sex change operation, I think my response is more apt. (But, there\'s also the argument about the difference being the presence of one or two X chromosomes, not the presence of a Y...)\r
\n\r
\nI\'m rambling. Sorry.',2710,'Richie','2003-07-14 02:28:44');
INSERT INTO forumpost VALUES (1443,73,7,'Re: hello!','Erm... maybe I\'m reading something into this, but I\'ve noticed the ladies get a bit more of a warm welcome to their first posts than the guys...\r
\n\r
\n..and also, maybe the little grey folk *do* control my thoughts.... lol\r
\n\r
\nR.',2710,'Richie','2003-07-14 02:32:47');
INSERT INTO forumpost VALUES (1444,211,5,'Re: Back From vacation','Actually, after pushing this morning\'s problem, there\'s nothing pushable in the queue for the afternoon until a problem gets fixed up. Two Geometric Series has 3 TU but has a grammar problem that you could fix up. ',1301,'Charlie','2003-07-14 03:23:08');
INSERT INTO forumpost VALUES (1445,211,5,'Re: Back From vacation','My problem \'Numbered Letters\' has three TU\'s.',1919,'Lewis','2003-07-14 05:18:11');
INSERT INTO forumpost VALUES (1446,211,5,'Re: Back From vacation','Got the two \"problem\" problems sorted out... I think... \r
\n\r
\nSorry, DJ, but I cannot easily fix comment contents (there\'s no admin tool for that) I\'ll try to fix it in the database directly when I get the chance.',1,'levik','2003-07-14 06:26:01');
INSERT INTO forumpost VALUES (1447,211,5,'Re: Back From vacation','This morning, before levik (I assume it was levik as he fixed it up) pushed \'Two Geometric Series\', \'Numbered Letters\' had been temporarily pushed out of the visible top-10 voting queue by last nights QW shuffling. It is now back with its 3 TU.',1301,'Charlie','2003-07-14 06:29:08');
INSERT INTO forumpost VALUES (1448,211,5,'Re: Back From vacation','Levik, I\'m still seeing a 5 on the difficulty of Age of Ages, where you said you changed it.',1301,'Charlie','2003-07-14 06:35:06');
INSERT INTO forumpost VALUES (1449,211,5,'Re: Back From vacation','BTW, welcome back Levik!',1919,'Lewis','2003-07-14 07:56:50');
INSERT INTO forumpost VALUES (1450,211,5,'Re: Back From vacation','I am rather tired of Age of Ages being there... but if others want it I will change my vote.',1626,'Gamer','2003-07-14 08:17:00');
INSERT INTO forumpost VALUES (1451,200,4,'Re: Its working','The queue depletion will work as long as people stop dumping problems; it seems the number of problems in the queue goes downward, then upward.',1626,'Gamer','2003-07-14 15:59:05');
INSERT INTO forumpost VALUES (1452,200,4,'Re: Its working','The only way to make the queue size go down is to TD more problems. No matter how effiecient everything else is, there are still only two problems a day being posted. The number of problems being submitted, while it can lapse into a lull once in a while, is really increasing or at least pretty constant.\r
\nWe don\'t need to worry about running out of problems, and I have said many times in the past, there are tons of great problems waiting, why fuss over poorly worded, trivial, mediocre problems? The caliber of problems people submit is going to match the problems going live on the site, good or bad.',1575,'DJ','2003-07-14 18:33:28');
INSERT INTO forumpost VALUES (1453,17,6,'Re: HTML codes','I noticed that the <pre> tags are disabled in comments again, is that on purpose? The <tt> tag is almost as useless as normal text in making lists, tables, displaying programs, except that you know that your rows of chars are going to make the text line up properly. Still rather cumbersome..\r
\n\r
\nJust checking:\r
\n\r
\nHello\r
\n I\r
\n am\r
\n DJ\r
\n\r
\n\r
',1575,'DJ','2003-07-15 05:46:54');
INSERT INTO forumpost VALUES (1454,212,7,'Hey!','Hey everyone I\'m just trying to meet people because I\'m new so anybody talk to me.',2728,'Amanda','2003-07-15 15:19:38');
INSERT INTO forumpost VALUES (1455,200,4,'Re: Its working','But that is like saying \"kill everyone who isn\'t smart, as they will hurt the society\"... I know Sensible Sequence was a good problem, but it was poorly worded. If you mean poorly worded problems that don\'t have anyone here to fix them, that\'s ok, but you shouldn\'t TD something just because it\'s worded badly if it\'s a good problem.',1626,'Gamer','2003-07-15 15:48:57');
INSERT INTO forumpost VALUES (1456,200,4,'Re: Its working','How is \"only post good problems\" like saying \"kill everyone who isn\'t smart\"?\r
\nHi\r
\n I\r
\n am\r
\n DJ\r
\n
\nPoorly worded problems are more of an annoyance than a problem, when we have to wait for the author to edit it while it sits in queue. The \'edit\' vote or a user backlog of deleted problem would be invaluable, but will take time to implement, so that\'s fine for now.\r
\nAs far as that goes, Gamer, you suggested previously that journeymen shouldn\'t give a third TU on a problem that needs editing, yet you have done that a few times even on problems that are in queue now. If it needs editing, fine, but at least get it done before the problem goes live.\r
\n\r
\nMore than that, my main peeve is the \"trivial, mediocre\" problems. We hem and haw over them in voting, until finally the deadlock leans far enough one way or another to post or delete the problem. If it gets posted, that\'s a spot a potentially more interesting or thought-provoking problem could have been put up on that day, and really just bottlenecking the queue of waiting problems. There is an abundance of puzzle or riddle sites on the internet where you can find two-second no-brainers. In my eyes, this site is the best balance of a user-geared comment/forum and challenging problems I can wrap my head around all day. I\'d like to see it stay that way (forgive the melodrama); and I think the purpose of the voting queue is not just to week out dupes or illegible submissions -- one person can do that-- but also to maintain the quality of problems going up.\r
\n\r
\nSo, as long as I have a vote in the queue, I\'m going to use it as such (for the most part; I don\'t think I am altogether unreasonable). Of course, any of us voting at all is a privelege, not a right, and levik is quite a macromanager to have entrusted the problem selection to the site\'s users. That, too, sets this site apart from \"one-man\" sites or other seemingly indiscriminate puzzle sites. That said, I should like to know what levik\'s opinion is; what types of problems should or shouldn\'t go through, what is expected of the voters, etc. There seems to be a lot of dissent, and I really hope to resolve that instead of fuel it.',1575,'DJ','2003-07-15 18:03:27');
INSERT INTO forumpost VALUES (1457,200,4,'Re: Its working','No, I was meaning TDing a good problem that needed some wording work, when the person was around to fix it.\r
\n\r
\nI don\'t think I have done that to any problems except any with minor mistakes... Unless a problem is in tricks or another like catergory, small things like question marks and commas shouldn\'t disallow a problem from reaching the site. \r
\n\r
\nI would agree with your second paragraph... I think that\'s what I meant.\r
\n\r
\nWe need to come to an agreement on what to do about problems like Number machine 3, and duplicates like that too, so that we don\'t hold up voting.',1626,'Gamer','2003-07-16 08:37:39');
INSERT INTO forumpost VALUES (1458,213,5,'Slow server?','Just wondering if the server has been particularly slow for anyone else in the last couple of days. I\'m trying to find the root of the problem, but would also like to ensure it\'s not just my ISP/computer that makes the site seems slow as molasses in January.\r
\n\r
\nAnyone else see the same problem?',1,'levik','2003-07-17 19:05:28');
INSERT INTO forumpost VALUES (1459,213,5,'Re: Slow server?','Mine\'s been going slowly when the pop-ups er.. pop-up. Also when I try to go on the main page its slow, but thats understandable.',1919,'Lewis','2003-07-17 20:57:06');
INSERT INTO forumpost VALUES (1460,213,5,'Re: Slow server?','I noticed a major slow down a day and a half ago. It still seems slow now but slightly faster than yesterday.',1567,'Bryan','2003-07-18 05:01:13');
INSERT INTO forumpost VALUES (1461,213,5,'Re: Slow server?','Yeah, I\'ve noticed the same thing for the past few days. Right at this moment, it seems to be a little faster, but pages are taking longer to load than normal.',1575,'DJ','2003-07-18 05:42:01');
INSERT INTO forumpost VALUES (1462,214,4,'Stealing Puzzles','I just wanted to know something. To what extent can problems on this site be taken from other places? I found a website called \'Brain Food\' and looked at a set of logic problems, and the first three were \'Box, Locks and Keys\', \'Coin in a bottle\' and \'Life or Death.\r
\n\r
\nIm not accusing the submitters of these puzzles of copying, its just that these problems have probably been seen by other people and passed on and are not original. Some other problems like \'Name Game\' and \'PQR(S)\' are also on other websites.\r
\n\r
\nI was just wondering what everybody\'s views on this was. I personally think that the problems should be to some extent original.',1919,'Lewis','2003-07-18 11:04:12');
INSERT INTO forumpost VALUES (1463,213,5,'Re: Slow server?','It seemed slow, but not enough to be a problem or anything',1626,'Gamer','2003-07-18 13:42:33');
INSERT INTO forumpost VALUES (1464,214,4,'Re: Stealing Puzzles','I think you should say \"Non original\" or \"from www.takenfromhere.com\" or something like that... Many of my problems are original.',1626,'Gamer','2003-07-18 13:45:07');
INSERT INTO forumpost VALUES (1465,214,4,'Re: Stealing Puzzles','I\'ve included both original puzzles, and \"classic\" puzzles, but very rarely \"borrowed\" ones. I have always credited the original author when known.',153,'TomM','2003-07-18 19:44:18');
INSERT INTO forumpost VALUES (1466,214,4,'Re: Stealing Puzzles','Well I don\'t think this is the only site containing so many puzzles. When you search for puzzles or any such thing (related to puzzles), the search engine will give as a result not only the name of this site but the names of other sites too where many such puzzles can be found and those are the \"Actual/Original Forms\" in which they are found not only on different sites but also in various puzzle books. \r
\nSo I don\'t think that the submitters should be blamed for this. Just like I had submitted a few puzzles that I had found in a puzzle \"Book\" but I never knew that they (the same puzzles with the exact wordings) are there on \'any other site\' too.',979,'Ravi Raja','2003-07-18 20:14:20');
INSERT INTO forumpost VALUES (1467,214,4,'Re: Stealing Puzzles','I think you should designate which problems are original, and which problems are not. ',1626,'Gamer','2003-07-19 04:47:14');
INSERT INTO forumpost VALUES (1468,214,4,'Re: Stealing Puzzles','Most of my problems are totally original, and any that aren\'t are very loosely based on something else that I have heard from a friend etc. I think if somebody sees a good problem they think the users of this site would like then they could use it but credit it to the site/book that they got it from, and also try to change it as much as possible without totally affecting the idea of the puzzle.',1919,'Lewis','2003-07-19 09:43:30');
INSERT INTO forumpost VALUES (1469,214,4,'Re: Stealing Puzzles','Perhaps there could be a \'classic puzzles\' category?',1919,'Lewis','2003-07-19 09:44:07');
INSERT INTO forumpost VALUES (1470,214,4,'Re: Stealing Puzzles','I think this would be more complicated too... For example, Sled Shiver Sally was completely my creation, but the idea is old for rhyming like that.\r
\n\r
\nAlso, I have a few puzzles that I don\'t know where they came from... What should I say for that? \"Nonoriginal!\" (One such problem is my recent \"Disaster Description\")\r
\n\r
\nIf the puzzle is copied directly, I think it would be good to say where you got it from (if you know).',1626,'Gamer','2003-07-19 09:55:22');
INSERT INTO forumpost VALUES (1471,215,4,'Duplicate problems','Many duplicates are voted down because they are already on the site. It also seems like duplicates of idea (age problems, liars and knight problems...) are allowed on the site.\r
\n\r
\nWhat happens when a problem is submitted that only changes one thing (for example, four light bulbs instead of three, or a different result from a number generating machine)? Do we let the problem through even though it is almost the same, or say it\'s a duplicate?\r
\n\r
\nI don\'t know how much work this would be, but I think adding any new wanted results to the original problem. (For example, putting all Number Machine wanted results on the same problem.)',1626,'Gamer','2003-07-19 10:00:58');
INSERT INTO forumpost VALUES (1472,215,4,'Re: Duplicate problems','At this point that\'s at the discretion of the voter. Problems like \"four light switches..\" and the \"number machine\" problems, in my opinion, are too close and don\'t really add anything we haven\'t seen before. Others, such as the tricky pearls series, or my word meld and letter cubes series, while having a common idea, change enough that each problem is indeed its own problem. Sometimes, there are multiple parts to the same problem, when the processes are too similar.\r
\n\r
\nI think I know what you mean in the last paragraph (you didn\'t form a coherent sentence), but I\'m not sure dredging up old, \"closed\" problems is a good idea. Do we spotlight it on the front page again, with all its old comments, and simply add a step to the question? That would be rather troublesome and confusing, I think. What exactly did you have in mind?',1575,'DJ','2003-07-19 13:29:53');
INSERT INTO forumpost VALUES (1473,215,4,'Re: Duplicate problems','The problem with each voting our own way is we get deadlocked. Because we need a 3-person majority, problems get stuck in the queue that are contraversial. That might not be a bad thing, but it does tend to slow down the queue.',1626,'Gamer','2003-07-19 16:37:43');
INSERT INTO forumpost VALUES (1474,215,4,'Re: Duplicate problems','How can one know how, say, Four Light Switches changes the solution to the light bulb problem, without discussing the solution to Four Light Switches. On first look, it doesn\'t seem that the solution to the earlier problem will solve the newer one.',1301,'Charlie','2003-07-20 03:51:38');
INSERT INTO forumpost VALUES (1475,215,4,'Re: Duplicate problems','You can\'t -- which is why I started discussing the solution to the problem. It turned out, as I suspected, that the \'new\' problem is pretty much a dupe, and the extra light bulb is allowed in this problem by a consideration that is iffy at best.',1575,'DJ','2003-07-21 04:09:09');
INSERT INTO forumpost VALUES (1476,215,4,'Re: Duplicate problems','Is four light switches like the problem where there\'s three switches outside a room and you can only look in once?',1919,'Lewis','2003-07-21 04:28:21');
INSERT INTO forumpost VALUES (1477,215,4,'Re: Duplicate problems','Yes... I forgot you can\'t see the queue. :)',1626,'Gamer','2003-07-21 16:26:47');
INSERT INTO forumpost VALUES (1478,215,4,'Re: Duplicate problems','Im only an apprentice...:(',1919,'Lewis','2003-07-21 20:49:00');
INSERT INTO forumpost VALUES (1479,216,3,'Order of Posting','I am confused about what order problems are being released. I thought if a problem was first into the queue, it would be first out, but I know more recent problems have been pushed instead. What is the order things are posted?',1626,'Gamer','2003-07-23 02:45:10');
INSERT INTO forumpost VALUES (1480,216,3,'Re: Order of Posting','My personal method is \"highest score that also includes a solution\". Otherwise, Ravi always gets the first (and sometimes only) problem every day, as long as people approve at least one of his problems.',103,'friedlinguini','2003-07-23 04:37:33');
INSERT INTO forumpost VALUES (1481,217,3,'NEED HELP!','I just signed up and see that we\'re not supposed to post problems...but this isn\'t a problem. It\'s more of a riddle and from the looks of things here, I think most of you would be able to solve it in 2 seconds. Can someone please help me? I need to have it done by Monday...or I\'m going to lose a HUGE bet!',2832,'Tara','2003-07-23 15:59:13');
INSERT INTO forumpost VALUES (1482,217,3,'Re: NEED HELP!','What\'s the question?',2839,'Andrwe Mitchell','2003-07-24 02:52:11');
INSERT INTO forumpost VALUES (1483,217,3,'Re: NEED HELP!','Yeah, whats the question?',2840,'Becky','2003-07-24 02:59:13');
INSERT INTO forumpost VALUES (1484,217,3,'Re: NEED HELP!','If you were the one that e-mailed me, send it in e-mail :)',1626,'Gamer','2003-07-24 03:24:40');
INSERT INTO forumpost VALUES (1485,216,3,'Re: Order of Posting','I don\'t think my problem will ever get posted! There are always ones better than it.',1626,'Gamer','2003-07-24 03:25:21');
INSERT INTO forumpost VALUES (1486,216,3,'Re: Order of Posting','I think it should be the one nearest the front of the queue that has 3 TU\'s that gets posted. (I just want one more of my problems posted so i can become a journeyman! Not asking you to post mine first. Really ;)',1919,'Lewis','2003-07-24 04:04:12');
INSERT INTO forumpost VALUES (1487,173,6,'Re: To Tim Axoy','So levik, is Tim getting his account back? If he wants it I think he now knows not to do it again (hey, do it again, thats my problem!).',1919,'Lewis','2003-07-24 04:12:42');
INSERT INTO forumpost VALUES (1488,216,3,'Re: Order of Posting','Fortunately, Gamer, I rarely get to the queue before somebody else posts the first problem of the morning. :-)>',103,'friedlinguini','2003-07-24 04:47:37');
INSERT INTO forumpost VALUES (1489,200,4,'Re: Its working (not really)','Does anyone else realize... the only way to expedite the queue is to TD more problems! The rate of posting problems will not increase, and the rate of submitted problems will not decrease (in the long run), and we will be forever stuck with 500+ problems waiting in a three-month queue unless we start to be more choosy about the problems that go on the site. A \'problem\' (I use the term loosely) like Escape is not a problem at all; it is a set of meaningless sentences (\"My hat is red or blue. It is not blue. What color is my hat?\"). Passers-by to the site were leaving comments entitled \"Duuhh,\" and if that\'s the kind of problem that was on the front page when I first came here, it wouldn\'t have held my attention (or my interest) any longer than the few seconds it took to do the elimiination in my head.\r
\n\r
\nThere is no shortage of problems, good ones, waiting to be posted, escpecially with Ravi\'s 100+ (I have many, too, but I daresay I\'m a little more discriminate about the caliber of problem I submit) that we can afford to drop a painfully simple problem, and the queue won\'t go anywhere until that\'s what we start doing.',1575,'DJ','2003-07-24 06:20:10');
INSERT INTO forumpost VALUES (1490,200,4,'Re: Its working','I agree with DJ. Although I didn\'t find Escape that bad, I\'m younger than most regular visitors to the site (im 13) so I wouldn\'t find it so easy. I do think it would be better if the only problems let on the site were problems good enough to get a rating of 3 or higher, even if it means TDing a lot of my pending problems.',1919,'Lewis','2003-07-24 07:54:51');
INSERT INTO forumpost VALUES (1491,216,3,'Re: Order of Posting','That would be me :)\r
\n\r
\nI generally DO post the first one that\'s in the queue and eligible (making it Ravi\'s if he has one)\r
\n\r
\nUnfortunately due to an increased workload lately, a few minutes in the morning is all I can afford to spend on the site, and that is literally with the alarm clock still ringing in my ears.\r
\n\r
\nHopefully this situation will improve soon, but for the time being a do apologize for my absenteism.',1,'levik','2003-07-24 12:03:29');
INSERT INTO forumpost VALUES (1492,218,4,'queue weight (wait) info','As a lot of people, myself included, have been wondering exactly what the delay is between the submission of a problem and its posting date, I conducted a little experiment. I submitted a problem when there were 400 other problems in the queu and recorded the problem queue position each time I logged in, to watch its progress, and more importantly to see how long the delay time is. As my problem has reached the queue, I am posting the results here, so all can get a feel for what the situation is, taking into account the most recent queue weighting system (2 problems with qw=1).\r
\n\r
\nPuzzle Submitted (Sequence and Pattern Exam) May 12 when there were 400 (other) problems in the current queue. The most recently posted problem was \"Next in line\". The following data shows the dates I checked in and the corresponding queue position (e.g. May 13-19,72 means that from may 13 to may 19 the problem showed an approximate queue position of 72). My apologies for the lack of more recent data, but I have been stationed out of town for a month and a half and have only been able to check in on my days off or by quickly checking in from our dialup field connection.\r
\n\r
\n(May 13-19,72:May 20-21,71:May 22-23,70:May 24-25,69:May 26,68:May 27,67:May 28,66:May 29-30-31,65:June 1-2,64:June 3,63:June 4,59:June 5-12,57:June 13,56:June 16,54:June 20,51:June 21,49:June 24,45:June 27-30,42:July 4,32:July 9,26:July 17,16:July 21,14:July 24 - received its first noting)\r
\n\r
\nThis shows that, with 400 problems in the queue, it takes about 74 days to travel through the queue. Extrapolating to 500 problems gives a current delay time of 93 days. I\'ve said my peace.\r
\n\r
\n',775,'Cory Taylor','2003-07-24 17:43:07');
INSERT INTO forumpost VALUES (1493,214,4,'Re: Stealing Puzzles','I have found yet more \'borrowed puzzles. If you look on http://puzzles.about.com/gi/dynamic/offsite.htm?site=http%3A%2F%2Fwww.crpuzzles.com%2Flogic%2Findex.html you\'ll see the puzzle \'Jeoprady\' and \'Letter Cubes 2\' near the top and further down \'Letter Cubes 1\', with pretty much the exact wording thats on Flooble\'s version.\r
\n\r
\nI don\'t know if I\'m looking into this too much, but it seems that a lot of the \'borrowed\' puzzles are from less well known sites that we\'re not as likely to see...',1919,'Lewis','2003-07-24 23:22:49');
INSERT INTO forumpost VALUES (1494,214,4,'Re: Stealing Puzzles','I don\'t mind people taking the best puzzles from other sites, as long as they designate that it\'s from wherever it\'s from.',1919,'Lewis','2003-07-24 23:38:30');
INSERT INTO forumpost VALUES (1495,214,4,'Re: Stealing Puzzles','Most of my puzzles like that are hand made :) So I don\'t mind taking puzzles like that as long as you say where it\'s from. I haven\'t directly copied a puzzle from another place yet, and besides Sled Shiver Sally (which was based on a nonoriginal idea), Sensible Sequence is the only other problem I used an idea that wasn\'t mine.\r
\n\r
\nI don\'t know if people didn\'t think borrowing puzzles was a problem. I think it is always good to say where you got a puzzle from, not only to be naming your \r
\nsource, but many times when levik has named a source, I go there and find other \r
\ngood puzzles :)',1626,'Gamer','2003-07-25 05:05:04');
INSERT INTO forumpost VALUES (1496,200,4,'Re: Its working','I personally was for dropping Escape, as I found it too easy. But many of the problems in the queue don\'t fit into that group in my opinion...\r
\n\r
\nI think why the queue has gotten so large is because people see a puzzle on another site and paste it in here... That way we have many of the puzzles on the other sites as well as original ones.\r
\n\r
\nWould your new TD method TD on easier math problems like The Great Rating as well? I think that would be only fair, but how would you decide what puzzle had math too easy or too hard?',1626,'Gamer','2003-07-25 05:11:12');
INSERT INTO forumpost VALUES (1497,200,4,'Re: Its working','Just to clarify, Lewis said problems should be good enough to get a rating of 3 or higher, not ones with a difficulty of 3. Someone suggested something similar, like instituting a 1-5 rating system in the voting queue. Maybe that should be considered again..',1575,'DJ','2003-07-25 06:07:57');
INSERT INTO forumpost VALUES (1498,214,4,'Re: Stealing Puzzles','I think Sled Shiver Sally was original because an idea as general as rhymeing (is that spelt right?) isn\'t really copied if you use it.',1919,'Lewis','2003-07-25 06:22:06');
INSERT INTO forumpost VALUES (1499,200,4,'Re: Its working','I think The Great Rating was fine. As people said, if they saw escape on the front they may not have interest in coming back. Likewise, if they came on and found a 5 difficulty calculus problem they might get scared away. All I\'m saying is, it\'s okay to have some easy problems now and then.',1919,'Lewis','2003-07-25 07:34:38');
INSERT INTO forumpost VALUES (1500,219,7,'Hello','I just thought I\'d check this out...Don\'t know what else to say, though',2855,'Kesia Ihle','2003-07-25 08:57:54');
INSERT INTO forumpost VALUES (1501,173,6,'Re: To Tim Axoy','Does Tim know how to work e-mail? I think so, but just making sure :)\r
\n\r
\n',1626,'Gamer','2003-07-25 14:55:03');
INSERT INTO forumpost VALUES (1502,200,4,'Re: Its working','I never said, or meant, that we should have only hard problems and no easy ones. We just need interesting problems. That applies to ridiculously easy submissions and impossibly hard problems both. A good problem, in my opinion, has a clear purpose in what it\'s asking for, but will require a little thought and mind-bending to come up with a solution or a process. It might be good to establish some sort of rubric for what is site-worthy and what is not.',1575,'DJ','2003-07-25 17:16:29');
INSERT INTO forumpost VALUES (1503,214,4,'Re: Stealing Puzzles','Lewis, I don\'t think the links are necessary -- we believe you. Actually, though, the sites you posted are not whence I got the problems that I submitted, and very often I see the same puzzles on many different puzzle sites, usually without an author. That\'s the main reason they\'re not cited; I doubt that those sites wrote the problems either (at least one of them is copying, if not both).\r
\n\r
\nI cite the author of a problem when it\'s clear that it actually is the original creator of the puzzle, usually if it came from a \'personal\' webpage someone made rather than a \'public\' site akin to this one. As TomM said, credit the original author when known, a case I have found to be rare. I would guess that 80-90% of the problems on this site came from somewhere else (the user submitting the problem didn\'t author it), and I don\'t really see a problem with it.',1575,'DJ','2003-07-25 17:26:07');
INSERT INTO forumpost VALUES (1504,219,7,'Re: Hello','Hi, welcome to the site. I hope you like math and logic puzzles, and being challenged, because (usually) that\'s what you\'ll find here. Have fun!\r
\n=)',1575,'DJ','2003-07-25 17:27:37');
INSERT INTO forumpost VALUES (1505,173,6,'Re: To Tim Axoy','I have emailed back and forth with Tim and his father, and let them know that Tim can have his account back if he writes me a substantil (as in more than one or two lines) email explaining why he keptmaking accounts when asked not to, and promising not to do it again.\r
\n\r
\nThis happened the week after Tim\'s suspention, and I am yet to see anything back.\r
\n\r
\nBut the offer still stands.',1,'levik','2003-07-26 02:48:53');
INSERT INTO forumpost VALUES (1506,216,3,'Re: Order of Posting','By the \'first one\' in queu, I assume you mean by the time/date stamp; but that\'s not always (in fact, rarely) the first problem to make it into the queue. It seems that while the queue wieight allows problems from other and newer users to make it into the queue sooner, that method is counterproductive, since Ravi had hundreds of problems already in February, which are just now being shown, but the rest of the queue is in May. I think the order of posting should be consistent with the order that problems make it into the queue, or else the purpose of the queue weight is diminished, and we still have to see Ravi\'s problems every single day.',1575,'DJ','2003-07-26 05:44:33');
INSERT INTO forumpost VALUES (1507,216,3,'Re: Order of Posting','I think I remember seeing a note on a forum saying that levik prefers Riddles and similar problems to appear in the first puzzle of the day. Also easier puzzles are held or expedited to weekend slots. I don\'t know if there are any other preferences as far as timing. Sometimes when I push something I\'ll choose something that I don\'t have a clue about, so I\'m not tempted to post an answer right away. But I avoid voting on or pushing riddles. But since levik is up early in the morning Monday - Thursday, there\'s ample opportunity for those. But it does affect the order of postings.',1301,'Charlie','2003-07-26 10:29:30');
INSERT INTO forumpost VALUES (1508,214,4,'Re: Stealing Puzzles','I have to wonder: what is the point of copying a puzzle from somewhere else and posting it here? Maybe people can convince themselves they are doing it just to share puzzles they really like, but I say: post a thread in the Forum directing us to that particular website/book/etc. instead, and leave it at that. \r
\n\r
\nTo me, anyone submitting unoriginal puzzles (or, in any case, doing so without attributing the source or acknowledging it as a classic) is either committing plagiarism or trying to make rank at this site. If as much effort went into creating interesting new puzzles as in trotting out old ones, Flooble would be much more exciting and valuable.',1567,'Bryan','2003-07-27 18:28:13');
INSERT INTO forumpost VALUES (1509,200,4,'What DJ said','\"It might be good to establish some sort of rubric for what is site-worthy and what is not. \"\r
\n\r
\nHear, hear! Sounds like a topic for a new thread :P',1567,'Bryan','2003-07-27 18:32:08');
INSERT INTO forumpost VALUES (1510,214,4,'Re: Stealing Puzzles','I totally agree with you Bryan. I have nothing else to say.',1919,'Lewis','2003-07-27 23:22:21');
INSERT INTO forumpost VALUES (1511,128,3,'Re: The existence of god','Personally... I feel that in all my years of seeking truth, as we all know to some degree,a higher power with beyond imagination intelligence created creation; (us). We refer to this as being \"God.\" We are living proof because here we are.So this conclusion can be questioned to ponder that if such an intelligent infinite power exists (which it does), than, dont you think this highest ranked \"Supreme Being\" that created this planet and everything in it, dont you think \"Supreme Being\" could preserve a little book (Holy Bible)as the stories in it to benefit mankind?...And to have thee power to say exactly what He wants.Remember this is the same God that created the entire universes, the eternal cosmos. And still from that point on till now creation is still filling up that eternity of black emptiness. My point is trust in the bible, it is so simple... yet beyond profound.The depths of the truth......simply unimaginable! and then I thought...could it all be true?Jehovah?\r
\n ',2898,'gina','2003-07-28 13:27:46');
INSERT INTO forumpost VALUES (1512,214,4,'Re: Stealing Puzzles','What, then, is the point of this site? I don\'t think it\'s a contest to see who can author the best problems. I can say quite honestly (no convincing necessary) that I submit puzzles because I think they will make this site better and other people will enjoy them. If people wanted links to other pages with puzzle site, they\'d type \"puzzles\" into a search engine. And frankly, most of those pages are not that good, and this is one of if not the best collection of puzzles on a webpage. That is why I submit the \'better\' problems I have found from other sites, as well as original problems, and why I am so particular about the quality of problems that get posted. If someone wants a bunch of mundane ten-second problems to kill time, they\'ll go to braingle and look at all the answers.\r
\n\r
\nAlso, I\'m not going to give credit to another site that has just cut-and-pasted a problem from somewhere else, and the original author is unknown. I\'d rather \'trot out\' some interesting second-hand problems than see boring new ones (Escape). Besides my original problems, I have some problems from personal pages and publications that are credited to their authors; others (like those mentioned above), that appear verbatim on several different pages, are not cited to any particular site. I\'m obviously not trying to make rank, and if it\'s plagiarism, to whom should I give credit? I\'ve seen copied problem from ambiguous sources submitted by many different people (including levik) with no citation, and obviously there are more that I haven\'t noticed. You are making a big deal out of nothing.\r
\n\r
\nIf we spent as much time controlling the quality of the problems as arguing about where they came from, then I propose that flooble would be much more interesting and valuable.',1575,'DJ','2003-07-28 15:53:42');
INSERT INTO forumpost VALUES (1513,80,7,'Re: Hello, First time here','I think i am to young for this page because there is nothing to do!',2900,'jess','2003-07-28 19:17:13');
INSERT INTO forumpost VALUES (1514,214,4,'Re: Stealing Puzzles','Hmm... now I agree with DJ...',1919,'Lewis','2003-07-28 21:11:20');
INSERT INTO forumpost VALUES (1515,220,4,'Petition Director','As some of you may have noticed, I have not been around much lately, to my great displeasure. I am truly greatful to the people who help keep this site running on day to day basis - Scholars and Journeymen.\r
\n\r
\nIt is unfortunate that sometimes you guys are more aware of what is going on with the site than I myself am. To take a little advantage of this fact, and to help me utilise what little time I get to spend on the site better, I have added a \"Petition\" feature.\r
\n\r
\nIt allows you to send me messages about particular features of the site, or problem areas or whatever. I know that some of you already do this, in chatterbox or forums, or even problem comments - but I do not always have the chance to look in all those places anymore, so here\'s a place where I am sure to notice your request - be it a feature request, or an urgent bug report. Or perhaps even a question.\r
\n\r
\nIf you have something that you think warrants my personal attention, please use this new feature - it should appear under the \"Your Problems\" link in the top-right corner.\r
\n\r
\nIt\'s not restricted to higher ranks, but I don\'t want to advertise it to others just yet, which is why I am posting it in this forum.\r
\n\r
\nLet me know what you think.',1,'levik','2003-07-29 10:03:40');
INSERT INTO forumpost VALUES (1516,220,4,'Re: Petition Director','I think perhaps restricting it to higher ranks could be quite a good idea, otherwise people like \'qw\' will end up posting lots of rubbish in it, but the problem with this is people who have been on the site a while and are trustworthy but aren\'t apprentices or above, like fwaff, won\'t be able to use it.',1919,'Lewis','2003-07-29 10:08:43');
INSERT INTO forumpost VALUES (1517,221,7,'Hi.','Hi, I like math stuff, and DJ made me join..it looks pretty cool. :)',2912,'Talon5000','2003-07-29 13:10:08');
INSERT INTO forumpost VALUES (1518,220,4,'Re: Petition Director','I think this is a good idea, and makes it a lot easier to bring things to your attention that will be easier for you to find. I\'ll try not to annoy you too much with it... =P',1575,'DJ','2003-07-29 16:19:36');
INSERT INTO forumpost VALUES (1519,208,4,'Re: Secret Forum!','Ha! they\'re now (Sort of) deliverable....\r
\n\r
\nHm. Well, at least if the person bothers to check.',1,'levik','2003-07-30 01:55:41');
INSERT INTO forumpost VALUES (1521,173,6,'Re: To Tim Axoy','Yes Gamer, Tim does know how to send e-mails. Just check the 6th comment from the beginning (or Tim\'s second comment from the beginning). And anyway, a boy who says that he likes math and logic, you can never expect that he doesn\'t know how to send e-mails.',979,'Ravi Raja','2003-07-30 05:18:13');
INSERT INTO forumpost VALUES (1522,221,7,'Re: Hi.','Welcome to the site Talon \r
\nYour submitted problems might take time to move up on the site but I hope that does not make you stop posting problems. Everyone would like your active participation on this site :)',979,'Ravi Raja','2003-07-30 05:22:00');
INSERT INTO forumpost VALUES (1523,222,7,'Re: hi everyone','Welcome to the site Darpan\r
\n[Note: Please do not mind but this is the same comment I am posting which I posted for Talon, but I think it is necessary that a new user knows everything beforehand]\r
\nYour submitted problems might take time to move up on the site but I hope that does not make you stop posting problems. Everyone would like your active participation on this site :)\r
\nBy the way, do you stay in India Darpan ? Where are you from and what do you do ?\r
\n',979,'Ravi Raja','2003-07-30 05:27:03');
INSERT INTO forumpost VALUES (1524,222,7,'Re: hi everyone','I hope you don\'t mind my asking questions, Darpan.',979,'Ravi Raja','2003-07-30 05:28:26');
INSERT INTO forumpost VALUES (1525,221,7,'Re: Hi.','Hey, Jerry.. glad you could make it! =P Have fun...',1575,'DJ','2003-07-30 09:22:03');
INSERT INTO forumpost VALUES (1526,220,4,'Re: Petition Director','Wow, that did get a fast response--the forward and backward in the posted problems. Thanks, levik.',1301,'Charlie','2003-07-31 06:18:42');
INSERT INTO forumpost VALUES (1527,223,4,'Pushing order','I\'d like to establish some guidelines for when and how problems get pushed by me and the scholars on the site.\r
\n\r
\nWe are all (hopefully) aware that it\'s one problem on weekdays, and two on weekends. However, everyone uses a different tactic, and I would like to propose a \"uniform\" strategy.\r
\n\r
\nThe \"morning problem\" stays in the top spot less than the \"afternoon\" problem, so less interesting problems (riddles, etc) that are easily solvable and not very discussion prone should go up in the morning.\r
\n\r
\nBecause only one problem goes up per day on the weekends, it should be a moderately interesting one.\r
\n\r
\nI believe that we should try and avoid a situation where two consecutive problems are from the same person or in the same category - the site looks more diverse if there are no \"streaks\" of similar problems, or problems from one user.\r
\n\r
\nI believe the problem to be pushed should be the highest one in the queue that qualifies under the above. Exceptions can be made for good problems that have hung around the bottom of the queue for a long time.\r
\n\r
\nThis is the rules I generally follow. If anyone has any additional suggestions, or arguments agains any of my points, please let me know, I\'m very flexible, as long as we all follow the same strategy.',1,'levik','2003-07-31 06:26:04');
INSERT INTO forumpost VALUES (1528,223,4,'Re: Pushing order','It sounds good. One thing to consider though is, if a given person other than Ravi also has a string of puzzles close in submittal time, it could lead to an alternation of a Ravi problem with that person\'s problem for a while, unless the diversity criterion is expanded to consider more than just one person. Probably consideration should be made for the length of time a puzzle has been visible in the queue. (But that might be hard to track if going only by memory.)',1301,'Charlie','2003-07-31 06:33:45');
INSERT INTO forumpost VALUES (1529,223,4,'Re: Pushing order','Another thought is that, if queue voters were able to mark or vote on a problem being a \"morning problem\" or \"weekend problem\" as opposed to a regular problem, the posting could be made automatic at specific times of day. We recently had a day on which all the scholars and the director must have been busy in the afternoon and we had only the morning problem that day. I know that starting next week I may very well be quite busy and away from my normal computer during the day if I\'m called out to do an emergency assignment for a while.',1301,'Charlie','2003-07-31 06:40:13');
INSERT INTO forumpost VALUES (1530,223,4,'Re: Pushing order','I don\'t get why somebody always seems to have the top two spots in the queue. before I became a journeyman you guys mentioned that Ravi always had it, which was true until the two most recent problems got posted. Now I seem to have the No1 and No2 spots.',1919,'Lewis','2003-07-31 08:50:27');
INSERT INTO forumpost VALUES (1531,223,4,'Re: Pushing order','Levik: Just to clarify, I am pretty sure that you meant one problem on the weekends and two each weekday.\r
\n\r
\nLewis: The reason for that is the way the queue weight system works. Each person\'s oldest two problems are given a queue weight of 1, the next couple a weight of 2, and so on. When one of the QW1 problems is posted or deleted, half the problems (the oldest of each pair) is moved up in rank, so that the oldest two of the remaining problems now have a weight of 1. Only QW1 problems are shown in the voting queue, and only the oldest problems available.\r
\nSo, suppose a bunch of problems were submitted in the following order, where each letter is a different person:\r
\nA B C R R R R R R R R R R R D E R R R R R R F E G H I R R R R R J K L M E\r
\nAt first, the voting queue will look like: A B C R R D E F E G\r
\nThen, as the top problems get posted or deleted, it will look like:\r
\nB C R R D E F E G H\r
\nC R R D E F E G H I\r
\nR R D E F E G H I J\r
\nR R D E F E G H I J\r
\nR R D E F E G H I J\r
\nR R D E F E G H I J\r
\nR R D E F E G H I J\r
\nR R D E F E G H I J\r
\nR R D E F E G H I J\r
\nR R D E F E G H I J\r
\nR R D E F E G H I J\r
\nR R D E F E G H I J\r
\nR R D E F E G H I J\r
\nR D E R F E G H I J\r
\nD E R R F E G H I J\r
\nE R R F E G H I J K\r
\nR R F E G H I J K E\r
\nR R F E G H I J K E\r
\nSo, you see, the reason one person\'s puzzles are always at the top, seemingly, is because they \'bulk-submit\' problems, such as every single riddle from a website or every problem from a puzzle book, all at once. When it is one person who is constantly submitting problems en masse (no names), it will seem as if that person\'s problems are always at the front of the queue, while everyone else\'s problems slowly trickle through (problems are not only posted or deleted from the top of the queue, as in my example).',1575,'DJ','2003-07-31 10:32:11');
INSERT INTO forumpost VALUES (1532,223,4,'Re: Pushing order','I noticed the most frequent letter just happened to be \'r\' :)',1919,'Lewis','2003-07-31 10:54:11');
INSERT INTO forumpost VALUES (1533,223,4,'Re: Pushing order','.. pure coincidence ..',1575,'DJ','2003-07-31 12:09:41');
INSERT INTO forumpost VALUES (1534,223,4,'Re: Pushing order','Also, one thing you might want to add, is the diversity not only from problem to problem, but from day to day.\r
\nMany people are online only once a day, or for the same time frame every day, and if someone is only on in the mornings, say, they won\'t want to see Ravi\'s riddles every single morning, even if the aren\'t necessarily consecutive problems.\r
\n\r
\nSo, if it\'s plausible, perhaps if a problem in a given category from a certain user is posted on Monday, we don\'t push another problem from the same category or user until Wednesday, if other problems are available.\r
\n\r
\nAnother proposal might be, while problems will be moved into the voting queue in chronological order, they could be shown in the order that they entered the visible queue. That way, we could push problems in more of a \"FIFO\" manner, rather than have the oldest problems, which often come in \'clumps,\' always moved first.\r
\n\r
\nThe reason I\'m putting this here instead of the \'petition director\' is that I want to know what everyone else thinks..',1575,'DJ','2003-07-31 12:22:46');
INSERT INTO forumpost VALUES (1535,223,4,'Re: Pushing order','It\'s not a bad idea. I would have implemented it a while ago were it not for the simple reason that it isn\'t very easy to do. Not without adding new columns to the tables and other such annoying rubbish. \r
\n\r
\nThe problem is, right now, there is no distinction on the backend between the visible and invisible parts of the queue. All the problems are sorted together, and then the first ten are shown. There isn\'t even a concept of when something has entered the queue.',1,'levik','2003-07-31 14:51:43');
INSERT INTO forumpost VALUES (1536,220,4,'Re: Petition Director','That was a good idea, Charlie, I like it.\r
\nThis is working very well so far, and it would seem to make things quite a bit easier for levik to handle. Thanks, lev, for the fast responses.',1575,'DJ','2003-07-31 15:24:17');
INSERT INTO forumpost VALUES (1537,214,4,'Re: Stealing Puzzles','I think the problem I had was I was surprised when I heard others had copied problems from other sites when I had just been thinking \"What a cool problem you created!\"\r
\n\r
\nBefore I came to flooble, I had a very small group of puzzle sites, not knowing about braingle or any of the such sites. As I said in my last post, if I see a source, I will go there to find other puzzles. I remember in the queue when I asked for where all these riddles were copied from, I went there and enjoyed many other puzzles... The links levik has used came from GOOD puzzle sites, rather that sites that appear high on search engines and can be found easily.\r
\n\r
\nIf a source can\'t be given (which I have said before can be the case), just say it\'s a \"classic puzzle\" or something like that... Many good puzzles (like burning ropes and such) may have no known origin.\r
\n\r
\nI\'m not saying it\'s any worse to find a good puzzle than to author one, just I don\'t know the difference.',1626,'Gamer','2003-08-01 10:34:19');
INSERT INTO forumpost VALUES (1538,220,4,'Re: Petition Director','Should only major things be petitioned or small things like the mistakes on the \"Submitted problem\" screen and the past problem of confusing order of problems?',1626,'Gamer','2003-08-01 11:18:55');
INSERT INTO forumpost VALUES (1539,220,4,'Re: Petition Director','I think it\'s pretty much anything you see that needs fixing and requires levik\'s attention, typos in a solution or on a page, glitches or whatnot. Whereas before requests like that, in a chatterbox, problem comment, forum thread, etc, would have been difficult for levik to find and deal with, the petition director means he only has to look in one place and can handle everything at once.\r
\nI\'m sure the backend is set up so that the changes to be made are fairly easy, once he is aware of the problem.\r
\n\r
\nSo, forgive me for putting words in levik\'s mouth, but I think you could bring anything to his attention, however small, and he can deal with it much more easily now than before.',1575,'DJ','2003-08-01 11:24:49');
INSERT INTO forumpost VALUES (1540,220,4,'Re: Petition Director','Well said DJ. This really helps me make more use of the little time I can devote to this site. It cuts down on the time it takes me to become aware of problems, and increases the time I can devote to getting them fixed.',1,'levik','2003-08-01 13:32:29');
INSERT INTO forumpost VALUES (1541,220,4,'Re: Petition Director','I also want to add that I truly appreciate these submissions, and that they contribute as much to the quality of this site as do great puzzles.\r
\n',1,'levik','2003-08-01 13:36:56');
INSERT INTO forumpost VALUES (1542,220,4,'Re: Petition Director','Even little things like the submitted d on patiend? I just want to make sure I am not taking up your time with spelling/grammar when I shouldn\'t be.',1626,'Gamer','2003-08-01 16:03:42');
INSERT INTO forumpost VALUES (1543,220,4,'Re: Petition Director','Whether you\'re running a business or a website, presentation is everything. If you noticed the error, someone else probably will too, potentially lowering their opinion, if only subconsciously, of the site and the person running it. I\'m sure the few seconds it takes levik to fix something even small like that are well worth it.',1575,'DJ','2003-08-01 16:14:24');
INSERT INTO forumpost VALUES (1544,224,7,'new here','\r
\n Hi everyone, I found this site while looking for logic puzzles from a google search. Actually it was the first site I tried, but I liked it so much I thought I\'d stay awhile. The puzzles here have a good range of difficulty, and the harder ones, though sometimes too hard for me, are still fun to try.\r
\nHope to get to know you all as time goes by.\r
\nSalem',2921,'Salem D','2003-08-01 17:21:10');
INSERT INTO forumpost VALUES (1545,224,7,'Re: new here','Hey Salem, welcome to Flooble. It seems everyone found this site on a google search. I hope you stay around long enough for you to get to know the people on the site (unklike some people). :o)',1919,'Lewis','2003-08-01 22:32:29');
INSERT INTO forumpost VALUES (1546,214,4,'Re: Stealing Puzzles','I get annoyed when people copy riddles from other sites. We already have too many riddles for our liking, and don\'t want riddles that a few of us probably have already seen on Braingle or something. Problems like \'Letter Cubes\' are an example of a good puzzle that users of this site would enjoy, but if they do get copied, the source should be credited if possible or at least stated that it wasn\'t original.',1919,'Lewis','2003-08-01 22:37:21');
INSERT INTO forumpost VALUES (1547,173,6,'Re: To Tim Axoy','I know why Tim kept making accounts. All of his different alias all have only posted comments on his puzzles. Also all of them have an average vote of 5, so he made them to comment on and vote 5 for his own puzzles (as Ravi said in the comments for Drew and Mohammad Come Back)',1919,'Lewis','2003-08-02 05:05:37');
INSERT INTO forumpost VALUES (1548,214,4,'Re: Stealing Puzzles','Levik made the comment in the General Discussion forum (in \"Problems from Webring partners?\") that puzzles from other sites are ok and should appear with attribution given.',1301,'Charlie','2003-08-02 05:35:44');
INSERT INTO forumpost VALUES (1549,214,4,'Re: Stealing Puzzles','I had asked that in preparation for submitting Amoeba Colony.',1301,'Charlie','2003-08-02 05:37:38');
INSERT INTO forumpost VALUES (2932,372,7,'Re: Hello','i like puzzles- both solving and inventing\r
\nin the nearest future will send you all some of my toughest..\r
\nregards\r
\nady',NULL,'ady','2004-01-20 03:49:21');
INSERT INTO forumpost VALUES (1551,225,7,'Re: dorkdork & gina.. same person','erm... who\'s gina??',1919,'Lewis','2003-08-02 07:44:07');
INSERT INTO forumpost VALUES (1552,226,4,'No solution still OK?','I have submitted a few problems where the solution is unknown by me... Are they still fine? I know some problems are better when a solution is known, and are not as good without a solution.',1626,'Gamer','2003-08-02 10:16:44');
INSERT INTO forumpost VALUES (1553,226,4,'Re: No solution still OK?','For me it\'s a judgement call, though I tend to favor problems with solutions over ones without.',103,'friedlinguini','2003-08-02 10:47:48');
INSERT INTO forumpost VALUES (1554,227,7,'Howdy! I\'m new here y\'all','Hey yall....im new here just postin to say howdy....im from Texas just incase ya couldn\'t tell.... hey yall email me sometime...even if it is just to say hi! my email is softball_chicka_123@hotmail.com\r
\n\r
\ntalk to yall later\r
\nrikki ',2968,'Rikki','2003-08-02 18:33:36');
INSERT INTO forumpost VALUES (1555,226,4,'Re: No solution still OK?','I think it depends on the problem. If its a question with a single answer, but is so hard that you can\'t solve it, I think no. If the problem is about a \'best way\' or, as in \'Scale Game\' in the queue, the most amount of coins, pearls etc. that you could need, then I think that\'s OK without a solution.',1919,'Lewis','2003-08-02 22:12:19');
INSERT INTO forumpost VALUES (1556,226,4,'Re: No solution still OK?','Well, yes, it depends on the problem. But for problems about finding a \'best way\' to do something, I think there should be a solution, and there definitely should be a \'way\' to do it at all. I think the only types of problems that would be okay without a solution are paradoxes, where the point of the problem is a discussion, algorithms, where it\'s clear that it\'s possible to solve, but you\'re trying to find the best way to do it, or games, such as \'zero to 100 in 1996,\' where everyone is supposed to generate the best list or something.\r
\nThat\'s not even saying all problems in those categories need not have solutions; problems like \'the guilty demon\' (paradoxes) and \'tic tac toe\' (games) are specific problems with a set solution that should be included with the problem.\r
\n\r
\nAll logic problems, L&K and W&S problems, Probability, Shapes, Word Problems and Cryptography, Numbers and Sequences, Riddles, and Just Math and Calculus problems should definitely have a solution.\r
\nIt is a different case, as Gamer mentioned, where perhaps it is a really difficult calculus problem and you don\'t know the exact answer, but in general a problem should include a solution, and should definitely have a solution.\r
\n\r
\nTo specifically address Scale Game, I think that while it\'s a very \'nice\' problem, and well-worded, it\'s a terrible example of a W&S problem. To be so specific (there are exactly 10 coins, 2 heavy and 2 light, you have three weighings, find one fake coin...), when the problem can\'t be solved, is unacceptable. However, I do like the problem, and the new logic that goes with having both heavy and light coins, so I think someone should perhaps \'fix up\' this problem and come up with a solvable variation. Cory, when submitting it, seemed to think that there was an answer (\"the solution to this is far beyond my abilities\"), but I think we\'ve agreed that there isn\'t. So, get rid of it in favor of something that will be more satisfying when it\'s actually solved..',1575,'DJ','2003-08-03 06:51:46');
INSERT INTO forumpost VALUES (1557,228,4,'Posting unapproved problems?','Two of DJ\'s recent problems, \"Keeps on Ticking...\" and \"Ducks in a Row\", have been posted, and I saw neither of them in the voting queue first (which I check every weekday and usually once on the weekend). Did they get voted on and I just missed them?',1567,'Bryan','2003-08-04 06:48:50');
INSERT INTO forumpost VALUES (1558,228,4,'Re: Posting unapproved problems?','Yes, I TU\'ed both of them, and I saw them on different days too. Must have just been bad timing on your part.',1919,'Lewis','2003-08-04 07:14:38');
INSERT INTO forumpost VALUES (1559,128,3,'Re: The existance of god','The paradox that started this whole discussion is an interesting one that tells a lot about paradoxes but noting about the existance of God.\r
\n\r
\nThe answer is surprisingly simple can God create as stone that he (she, it) can not lift? Of course, He (she,it) would do so by chosing to give up that portion of their omnipotence. He (she, it) would no longer be omnipotent but that does not mean he (she it) would no longer be god. Omnipottence is a characteristic of God not the definition of God.\r
\n\r
\nIt is not really a paradox unless you say can God (or other omnipotent entity) create as stone that he can not lift while remaining omnipotent? This boils down to Can an entity cease to be omnipotent and remain omnipotent? which is inherantly a contradiction which is the nature of paradox.',2839,'Andrew Mitchell','2003-08-04 08:06:14');
INSERT INTO forumpost VALUES (1560,228,4,'Re: Posting unapproved problems?','I don\'t know why they would have been posted so quickly... There must have been older problems there worth posting too!',1626,'Gamer','2003-08-04 12:30:58');
INSERT INTO forumpost VALUES (1561,228,4,'Re: Posting unapproved problems?','Occassionally, a problem can spend several days fluctuating in the 9th - 12th place range in the queue. It will appear and be commented/voted on in the morning, and drop back at night, or vice-versa. If you only check at the wrong time, you can miss it before it is pushed. Some of the older puzzles are still waiting for their third TU, or need re-writes.',153,'TomM','2003-08-04 13:48:57');
INSERT INTO forumpost VALUES (1562,228,4,'Re: Posting unapproved problems?','Both problems went through the voting and were TUed ... the first one, Keeps on Ticking, was pulled from the bottom of the queue, I assume, because although it was at the bottom of the voting queue, the other problems were still in limbo in voting or were simply trivial \'weekday morning\' problems. I didn\'t push that one; I don\'t usually push my own problem, especially from the bottom of the queue, unless it is the only TUed problem or the only approved suitable one.\r
\nThe other problem, Ducks in a Row, had already been through voting, but in editing it I did something that pushed it way back and messed up the date stamp. That\'s why, even before the problem was pushed, it was showing up in the unapproved solutions queue, saying the problem was 12296 days old or something. I asked levik to put it back into the queue, but since it was already voted on, it was a weekday afternoon, and there weren\'t really any more involved problems in queue right now, levik just made it the newest problem on the front page.\r
\n\r
\nLevik only made me a scholar less than a week ago, and I don\'t know how all the new \'toys\' work just yet. Both problems were legitimately voted on, although I messed up the one somehow (I\'m still not sure what happened). Sorry if anyone thought I was just trying to prematurely push my own problems...',1575,'DJ','2003-08-04 14:34:46');
INSERT INTO forumpost VALUES (1563,229,7,'Hi','Hi there, stumbled to this site from a google search. Found some of the questions very challenging. I\'m from Malaysia(south east asia). Anyone here from this region?',2992,'Chan Wah','2003-08-04 15:19:40');
INSERT INTO forumpost VALUES (1564,228,4,'Re: Posting unapproved problems?','I haven\'t seen either of them, but I didn\'t visit the queue for one or two days and was only making a guess... :)',1626,'Gamer','2003-08-04 15:33:56');
INSERT INTO forumpost VALUES (1565,228,4,'Re: Posting unapproved problems?','Hopefully levik\'s new response score by each problem in the queue will make this more noticable',1626,'Gamer','2003-08-04 18:43:03');
INSERT INTO forumpost VALUES (1566,228,4,'Re: Posting unapproved problems?','I didn\'t know you were a scholar DJ. Well done!',1919,'Lewis','2003-08-04 22:37:09');
INSERT INTO forumpost VALUES (1567,206,3,'Re: Favourite Puzzle','Now I understand 3 colors, and I agree that it\'s brilliant.\r
\n\r
\nI also saw a new puzzle that I really like. \'A Queen\'s Decree\' is a brilliant logic puzzle submitted by Levik.',1919,'Lewis','2003-08-04 23:46:57');
INSERT INTO forumpost VALUES (1568,206,3,'Re: Favourite Puzzle','I like the grid logic puzzles that we were talking about. I like A Queen\'s Decree and the other logic puzzles like that.\r
\n\r
\nMy favorite short puzzle is the \"I don\'t know it... I knew you didn\'t\" one. :)',1626,'Gamer','2003-08-05 04:43:51');
INSERT INTO forumpost VALUES (1569,230,5,'Possible weirdness in the days to come','Ok guys... There is a pretty good chance that we\'re going to be moving servers in the next couple of days.\r
\n\r
\nThose of you familiar with website management will know that this usually involves some periods of weirness when you inconsistently hit both the old and the new servers. This results in problems and comments which get posted only to disappear, and fun things of that nature.\r
\n\r
\nPlease disregard such minor inconveniences for the time being. Once the move is done, things should be back to normal.',1,'levik','2003-08-05 16:02:50');
INSERT INTO forumpost VALUES (1570,231,7,'Another Newbie here!','Hello to everyone. Looks like a truly GREAT site! I found this site today and I fell in love with it immediately\r
\n\r
\nI was a Math Major in College and a High School Math Teacher for 12 years. However, I am ashamed to say that I have been stumped by most of the puzzles I have seen here so far. I think I have been able to solve one of the half dozen or so I have looked at. LOL.\r
\n\r
\nAnyway, I\'ll keep trying and I\'ll have some fun and meet some great puzzlers. I\'ll be happy to help when and where I can and I trust y\'all will do the same. Feel free to say hi!',3005,'Mathcop','2003-08-05 16:06:12');
INSERT INTO forumpost VALUES (1571,231,7,'Re: Another Newbie here!','By the way, I found your site when I was on another site that had a chatterbox. Someone asked where they could get one and another suggested to come to flooble.com. I just dropped by to check it out and have been like a kid in a candy shop ever since!',3005,'Mathcop','2003-08-05 16:08:52');
INSERT INTO forumpost VALUES (1572,231,7,'Re: Another Newbie here!','You can look at some of the other puzzles too... they are pretty cool! :) (Check Favorite puzzles for some reccomendations.)',1626,'Gamer','2003-08-05 16:59:26');
INSERT INTO forumpost VALUES (1573,228,4,'Re: Posting unapproved problems?','DJ -- I trust ya. I just thought there might be a glitch or something on the site (no offense, Levik). On on!',1567,'Bryan','2003-08-06 11:00:42');
INSERT INTO forumpost VALUES (1574,230,5,'Re: Possible weirdness in the days to come','Thanks for the heads up. I just tried posting to another thread and, instead of my message being added, I wound up logged out and on the home page! I had to log in, go back to the Forum, and retype my comment. I thought I was going crazy until I saw your note here ;)',1567,'Bryan','2003-08-06 11:06:37');
INSERT INTO forumpost VALUES (1575,230,5,'Re: Possible weirdness in the days to come','Thats what happened to me when I tried to post a comment :o)',1919,'Lewis','2003-08-06 11:37:05');
INSERT INTO forumpost VALUES (1576,232,7,'Newbie here...','Hey all, I\'m a newbie here to the site, just introducing myself, like asked to... Found the site from a search engine (Lycos) and so here I am :-) Like to know anything else or more, drop me a line, love to meet some new friends... Thanxz... :-)',3020,'Mikal','2003-08-06 16:22:44');
INSERT INTO forumpost VALUES (1577,206,3,'Re: Favourite Puzzle','I wonder how many people looked for \"I don\'t know it..I knew you didn\'t\" in the search box... :p',1919,'Lewis','2003-08-06 16:40:50');
INSERT INTO forumpost VALUES (1578,232,7,'Re: Newbie here...','Hey Mikal, welcome to Flooble.:0)\r
\n\r
\nI hope you stick around long enough to enjoy the great puzzles here. Maybe someday you\'ll post your own great puzzles!',1919,'Lewis','2003-08-06 16:46:17');
INSERT INTO forumpost VALUES (1579,220,4,'Re: Petition Director','I hope nobody asks Levik to fix the spelling mistakes in the problem \'Errors\' ;)\r
\n\r
\nI just wanted to say that the Petition Director is working very well, mainly because of the fast responses you give, Levik. You fixed my problem within 15 minutes of me submitting it!',1919,'Lewis','2003-08-06 16:50:49');
INSERT INTO forumpost VALUES (1580,206,3,'Re: Favourite Puzzle','Heh, I\'m still not sure what puzzle that is referring to..',1575,'DJ','2003-08-06 17:15:38');
INSERT INTO forumpost VALUES (1581,220,4,'Re: Petition Director','Guys, I\'m glad you like the feature. While I cannot guarantee a 15 minute turnaround time (in fact I can almost surely tell you it will generally take longer), I will relaly try to address all the issues you bring up (even if all it involves is telling you that the way it is now is for a reason).\r
\n\r
\nAnd no, there is no uch thing as a problem being too small. DJ is absolutely right about that.',1,'levik','2003-08-07 07:36:03');
INSERT INTO forumpost VALUES (1582,230,5,'Re: Possible weirdness in the days to come','hey is this server weirdness the reason tis thread is in two forum categories? Or was that done on purpose?',1072,'Alan','2003-08-07 11:04:26');
INSERT INTO forumpost VALUES (1583,233,4,'Combining puzzles','A number of puzzle reviewers have suggested that the several \"Words in Common\" puzzles be combined, and I wanted more input on this. It won\'t hurt my feelings or anything to have them combined, but I think that, from the POV of a puzzle solver, it is more enjoyable to have one puzzle, figure out the solution (perhaps quickly, or perhaps after much trying), and have the satisfaction of completing it, and on another day have the same experience with another puzzle. If I combine them all, like the recent \"Sequence and Pattern Exam\", then like that problem, I expect the easy ones to be completed and the hard ones to be ignored when a solution doesn\'t present itself in a relatively short period of time.\r
\n\r
\nI don\'t think that puzzles need to generate discussion to be worthy of standing on their own, uncombined. Neither do I think that puzzles should be combined just for the sake of shortening the queue, as the needs of the many (puzzle solvers) outweigh the needs of the few (puzzle submitters).\r
\n\r
\nHow do others feel?',1567,'Bryan','2003-08-07 11:11:58');
INSERT INTO forumpost VALUES (1584,233,4,'Re: Combining puzzles','I think the needs of the puzzle solvers also include new puzzles. If all of the puzzles were grouped together, that need would be helped more than if the puzzles were seperated.\r
\n\r
\nIf people do ignore the hard ones when they are solving them together, I don\'t expect they would do any differently when the puzzle was alone.\r
\n\r
\nWhen I completed a sequence from \"Sequence and Pattern Exam\", I felt happy that I completed it too. I don\'t know if others are the same way, but I wouldn\'t feel less satisfaction from puzzles grouped together than puzzles put apart.',1626,'Gamer','2003-08-07 12:58:37');
INSERT INTO forumpost VALUES (1585,233,4,'Re: Combining puzzles','Hmm... \'Sequence and Pattern Exam\' was a good puzzle, but I don\'t think other puzzles should do the same. With \'Words in Common\' I think perhaps they should be condensed into groups of maybe two or three, but no more.',1919,'Lewis','2003-08-07 13:30:27');
INSERT INTO forumpost VALUES (1586,234,4,'Help with Algorithms','OK, I posted this in the libray rather than the regular forums as most of the people it is aimed at are Journeyman.\r
\n\r
\nI REALLY don\'t have any clue how to do Alogorithms, I wondered if you guys could help? I\'m not expecting you to tell me everyting, but perhaps give some links to other helpful sites or something. Some of the problems seem very interesting and I would like to be able to solve them. Thank you.',1919,'Lewis','2003-08-07 17:28:44');
INSERT INTO forumpost VALUES (1587,234,4,'Re: Help with Algorithms','See, I\'m so bad at algorithms I can\'t even spell it right ;)',1919,'Lewis','2003-08-07 17:29:37');
INSERT INTO forumpost VALUES (1588,206,3,'Re: Favourite Puzzle','It\'s called \"Two Numbers\"',1626,'Gamer','2003-08-07 18:33:22');
INSERT INTO forumpost VALUES (1589,234,4,'Re: Help with Algorithms','What an algorithm is for me is a set of steps telling you how to do something. For example, to find the number of squares of any size on a square chess board type board with n spaces on each side, you add up the squares from n squared down to 1 squared. (For a 4x4 board it would be 16 + 9 + 4 + 1 or 30.) Using a formula (and proving it) would be much harder to do. \r
\n\r
\nI think the algorithm problems here ask for a set of steps to carry out a task (for example, create a random number between 5 and 10)',1626,'Gamer','2003-08-07 18:37:01');
INSERT INTO forumpost VALUES (1590,234,4,'Re: Help with Algorithms','Some of them, like the random number generators, are aimed more at computer programming, but they can be approached from any direction; an algorithm is just a fixed method to approaching a problem. Some of my algorithms in queue are geared more toward the general case, although they could be implemented or simulated with a computer program.',1575,'DJ','2003-08-07 21:29:02');
INSERT INTO forumpost VALUES (1591,230,5,'Re: Possible weirdness in the days to come','I didn\'t notice anything really wrong duting the changeover, and everything seems to be going smoothly (and quickly) now..\r
\nI do have one slightly related question. I had a flooble notepad (for the problem \'Zero to 150 in 2003\') that seems to be no longer available. It\'s been a while since I\'ve tried to look at it, so I was wondering if that was a side effect of the switched servers or some other reason, such as deletion of an inactive page or something.',1575,'DJ','2003-08-08 09:10:45');
INSERT INTO forumpost VALUES (1592,200,4,'Re: Its working','The queue is starting to go down now. Journeymen might notice that many of the problems that came are either duplicates or way too easy and this helps shorten the queue.\r
\n\r
\nVisitor\'s problems seem to be voted on quicker than it would seem looking at the queue, due to queue weight and queue composition because visitors make up less than half the queue. It would seem newcomers only have to get through the other half; this means that if they are submitting \"classic puzzles\" (ones which are already on the site), their submissions will get TDed, and the queue will go down faster.',1626,'Gamer','2003-08-08 14:52:17');
INSERT INTO forumpost VALUES (1593,235,6,'Word lists','Charlie and some others (was it DJ?) have written short programs that access a word list from somewhere in order to solve word problems. Where can I find these word lists? Also, I am assuming the program is written in C. Forgive my ignorance, but can you buy C propramming software for the PC at your corner computer store?',1567,'Bryan','2003-08-08 16:10:47');
INSERT INTO forumpost VALUES (1594,235,6,'Re: Word lists','If you check out the Cygwin project, you can get a whole Unix-ish environment for Windows, including a C compiler, for free. There are also plenty of free graphical programming environments available for download from various places. There are also commercial alternatives. You can order the Standard Edition of Microsoft Visual C++.NET from Amazon.com for around $100. It all depends on how much time and/or money you\'re willing to spend. Personally, I like the Cygwin angle.',103,'friedlinguini','2003-08-08 17:36:44');
INSERT INTO forumpost VALUES (1595,235,6,'Re: Word lists','If you look at the comments or submitted solution to \'Thirteen Words,\' you will find the lists (and how to get them) that both Charlie and I have been using. Also, I have been programming in javascript, just because it\'s easy for anyone to use, test, or modify the code in notepad, then open the file with a web browser to see the results. Other times I have used C++, for which I use MS Visual Studio. Charlie uses QBASIC or QuickBASIC or something like that (I don\'t know the differences); I\'m not sure where to find those.',1575,'DJ','2003-08-08 18:02:03');
INSERT INTO forumpost VALUES (1596,230,5,'Re: Possible weirdness in the days to come','One possible wierdness is the queue shrinking 10 or 15 problems in one day! (I added 2 or 3 today, so that\'s surprising to me.)',1626,'Gamer','2003-08-08 19:33:33');
INSERT INTO forumpost VALUES (1597,235,6,'Re: Word lists','For a QuickBasic compiler you can go to Quick Basic Cafe, and click on Compilers on the left, under Downloads. Then click on QBasic 4.5 in the Name column (next to \"Simply the Best\" in the description column). Don\'t choose the German version unless that\'s what you want (I mention this because that\'s the only one whose description says 4.5, in addition to its link).\r
\n\r
\nQuickBasic was sold as a compiler a while back. QBASIC was a strictly interpreted language, whose interpreter was given away with some later versions of DOS; it ran about 5 times more slowly than QuickBasic, but had mostly the same syntax.\r
\n\r
\nBoth, being DOS programs, run in a Command Prompt window.',1301,'Charlie','2003-08-08 21:41:47');
INSERT INTO forumpost VALUES (1598,230,5,'Re: Possible weirdness in the days to co','The pads got moved over in the transition - if you had a working pad before, you should have still had it after the move. The only thing is that they (as chatterboxes) are deleted if not used for around a month, so yours may have been deleted in those moves.',1,'levik','2003-08-09 12:19:29');
INSERT INTO forumpost VALUES (1599,235,6,'Re: Word lists','[gets on soapbox]\r
\nAlso, should anyone be interested in Java, some of the best tools for that are available free of charge from the Eclipse project (You will need to have a Java VM installed, which you can get from Sun\'s Java site\r
\n[leaves soapbox]',1,'levik','2003-08-09 12:22:10');
INSERT INTO forumpost VALUES (1600,206,3,'Re: Favorite Puzzle','Oh, right.. I remembered it but I couldn\'t find it, since that\'s not how it was worded. =P',1575,'DJ','2003-08-11 05:07:15');
INSERT INTO forumpost VALUES (1601,236,7,'The newest newbie','Hey all. I\'m Dan the Canadian! I just got into brainteasers after buying a book of them for something to do on a long trip, and I am currently addicted to them. This site is incredible and is really helping me build my skill as a \"solutionist\" as you might say. I found this site after scouring the internet for a quick fix of brainteasers when I was done my book. I looked it up on google and here I am. Someone plz drop a line, I\'d love to hear from you. --Dan',3075,'Daniel','2003-08-11 05:47:08');
INSERT INTO forumpost VALUES (1602,237,3,'A silly whim','Feeling a tad boring, old, yawny,\r
\nI said, a new denoter really excites.\r
\nWell, maybe I\'ll try changing hopless exceedinly literal log-ins.\r
\n',2839,'FatBoy','2003-08-11 08:28:18');
INSERT INTO forumpost VALUES (1603,236,7,'Re: The newest newbie','Hey daniel. Welcome to the site. If you\'re looking for some good puzzles check out 3 colors and all the pearls problems. But those are just my favourites. There are many more great puzzles on this site so look around.',1072,'Alan','2003-08-11 13:10:39');
INSERT INTO forumpost VALUES (1604,237,3,'Re: A silly whim','Nice tameechew, Andrew. Maybe you should submit some puzzles to the queue!',1567,'Bryan','2003-08-11 14:35:00');
INSERT INTO forumpost VALUES (1605,237,3,'Re: A silly whim','I will, one day. As of right now I really don\'t think I can come up with anything that would be worth anyone\'s time (witness my fairly lame little introduction).\r
\nI like to do the puzzles but am completely baffled at how to create them.',2839,'FatBoy','2003-08-11 15:18:06');
INSERT INTO forumpost VALUES (1606,237,3,'Re: A silly whim','Don\'t worry FatBoy/Andrew, I felt the same when I started. The time when you think of puzzles is usually when you\'re not really trying to.',1919,'Lewis','2003-08-11 15:53:54');
INSERT INTO forumpost VALUES (1607,237,3,'Re: A silly whim','Yes... I will think of something, then say... hey, that would make a good puzzle :) On some of the ideas I have had, it\'s harder to make the puzzle than to solve it! :)',1626,'Gamer','2003-08-11 17:23:32');
INSERT INTO forumpost VALUES (1608,237,3,'Re: A silly whim','I don\'t think there are that many people that don\'t use a name here... I use a screen name here because that\'s what I have always done, but I don\'t suppose you would need to.',1626,'Gamer','2003-08-11 17:25:48');
INSERT INTO forumpost VALUES (1609,236,7,'Re: The newest newbie','Also check out Yes Sir! and Burning Ropes! :) Those are good... (Check the Favorite puzzles post for more)',1626,'Gamer','2003-08-11 17:26:45');
INSERT INTO forumpost VALUES (1610,237,3,'Re: A silly whim','I usually try to come up with either a: paradoxes or b: Other problems that are based on proofs from other problems. Using a proof can help you take an old problem, create a Sequel and make it more complex just using the concept behind the earlier proof. (As long as the proof is explained of course) thats what i did with my pearls problems.',1072,'Alan','2003-08-11 19:32:45');
INSERT INTO forumpost VALUES (1611,238,4,'New Scholar ability','I have just added an ability for scholars to edit solutions in the solution queue.\r
\n\r
\nRight now all the solutions in the solution queue can be edited by scholars, with no exceptions, though I am hoping that active users\' solutions will not need to be touched.\r
\n\r
\nIf anyone has suggestions as to how this would be better implemented, (i.e. allowing editing only in some instances) - speak up.\r
\n\r
\nAs always, any other comments are also welcome.',1,'levik','2003-08-13 11:29:08');
INSERT INTO forumpost VALUES (1612,238,4,'Re: New Scholar ability','I think it\'s a good idea, and many of the \'bug levik\' petitions are correcting or changing some solution waiting to be posted. You could make some sort of restriction that we would only edit solutions by inactive users, but all too often the ones that need changing are active users even who just don\'t look at the comments, where something needs to be added or changed (or where they have switched problems entirely and forgotten to switch the solutions). So, it\'s probably best left open and up to the discretion of the scholars. Of course, changes should be suggested in comments first and given a couple of days, for active users.',1575,'DJ','2003-08-13 18:46:29');
INSERT INTO forumpost VALUES (1613,239,3,'good site','here is a great site http://www.flooble.com/perplexus/forum.php?fid=3',1637,'chris','2003-08-13 19:15:11');
INSERT INTO forumpost VALUES (1614,238,4,'Re: New Scholar ability','I was going to suggest that you make it possible to edit problems with no submitted solution, but I see you\'ve taken care of that already as well. I just wanted to ask, before doing anything to them, if you want us to resolve older problems that have been solved in comments for some time, such as \'Maximum Value\' and your problem, \'A Locked Safe.\' I will add solutions to these, but not post them, as I do not know if they have intentionally been left unsolved, or just for lack of time.',1575,'DJ','2003-08-13 19:41:11');
INSERT INTO forumpost VALUES (1615,238,4,'Re: New Scholar ability','They have been left unsolved because I was never aware that they were solved in the comments (I did not and do not know the solutions to them myself)\r
\n\r
\nFeel free to edit the solution to your liking, as I unfortunately completely lack the time to do so.',1,'levik','2003-08-13 22:36:08');
INSERT INTO forumpost VALUES (1616,238,4,'Re: New Scholar ability','One thing I forgot to mention is that ALL HTML codes are available when editing solutions this way, so while you have more flexibility as far as what can be done, do try to close any critical tags.',1,'levik','2003-08-13 22:37:02');
INSERT INTO forumpost VALUES (1617,239,3,'Re: good site','thanks... we\'ll make a note of it :)',1,'levik','2003-08-14 13:33:59');
INSERT INTO forumpost VALUES (1618,239,3,'Re: good site','Wow chris, funnily enough I had been on that webiste JUST before going on to this page! Shock horror!',1919,'Lewis','2003-08-14 17:36:37');
INSERT INTO forumpost VALUES (1619,237,3,'Re: A silly whim','hey, Lewis, Gamer and Alan\r
\nthanks for the encoragment.\r
\nI\'ve submitted two. THey\'re not great (they\'re more riddles than puzzles) but what the heck?',2839,'FatBoy','2003-08-14 19:10:20');
INSERT INTO forumpost VALUES (1620,240,4,'Posting solutions prematurely','I feel that solutions to puzzles should not be posted until after someone has posted a solution of his own first (e.g., Tricky Code was not solved, and after several days the solution provided was posted). What do others think?',1567,'Bryan','2003-08-15 14:49:41');
INSERT INTO forumpost VALUES (1621,240,4,'Re: Posting solutions prematurely','I agree; even if the problem has stopped getting new comments for a few days, it will be in the \'unsolved problems\' listing, and people may still be trying to solve the problem (I\'m still trying to figure out the tricky code). Until a definite solution shows up, or at least one that everyone agrees on, I agree that the solution should remain unposted.',1575,'DJ','2003-08-15 18:15:53');
INSERT INTO forumpost VALUES (1622,240,4,'Re: Posting solutions prematurely','Perhaps levik could unpost the solution to that one..',1575,'DJ','2003-08-15 18:24:42');
INSERT INTO forumpost VALUES (1623,240,4,'Re: Posting solutions prematurely','I think Tricky Code was posted too soon... We could have been at that for a while :)\r
\n\r
\nI also don\'t like the fact that you can post a solution in your pending problems... I think there should be a \"Are you sure you want to post the solution\", or even take out of posting the solution out of the author\'s hands.',1626,'Gamer','2003-08-15 21:34:00');
INSERT INTO forumpost VALUES (1624,240,4,'Re: Posting solutions prematurely','Sometimes I feel a solution is neccesary to eliminate doubts. For example, on the \"Where\'s the Exit?\" problem, I had to be told why I was wrong before I understood why. I think others were the same way as well. This would also help problems which persist to be good even though they look easy (like On the Line); If anyone was willing to read the solution, they could explain how the problem is fine actually, or not fine. :)',1626,'Gamer','2003-08-16 00:21:49');
INSERT INTO forumpost VALUES (1625,241,3,'Blackout','So who was affected and how? \r
\n\r
\nThe server seems to have held - it\'s in New Jersey, but I believe the facility has backup generators running. Would anyone who had access to the net comment on the site\'s availability?\r
\n\r
\nMyself, I was stuck in Manhattan for the night, spent it with a few people over at a friend\'s house, and then slowly made my way home (to Brooklyn) this afternoon. The power at my house didn\'t come on until like 7 - 8 PM, one of the last parts of New York City to do so.\r
\n\r
\nNow it\'s your turn',1,'levik','2003-08-16 01:49:18');
INSERT INTO forumpost VALUES (1626,241,3,'Re: Blackout','I was slghtly too far away to get affected (England) but when i came on it was working but slowly. 28 hours... the longest I\'ve ever had is about 2 or 3 hours!',1919,'Lewis','2003-08-16 03:53:47');
INSERT INTO forumpost VALUES (1627,240,4,'Re: Posting solutions prematurely','Yes, as far as that goes, I still advocate that submitted problems should include a solution, except in exceptional circumstances. Bryan is referring, I think, to posting a live solution to a problem once it is on the site. While there is a mandatory four-day wait, if the problem is still in discussion or unsolved at that point, we should wait to put up a solution until it is solved in the comments.',1575,'DJ','2003-08-16 07:17:34');
INSERT INTO forumpost VALUES (1628,240,4,'Re: Posting solutions prematurely','I remember that someone said, regarding a problem submitted without a solution, that that was the reason for the \'unsolved problems\' page. This is a good time to make that distinction; I think the purpose of that page is for problems that we haven\'t solved yet in comments%2
\n\n\r
\nSome aspects made for a somewhat interesting puzzle. A 12-hour electronic clock that reset to 12:00 at the resumption of power is 9 hours 28 minutes behind. So power resumed at 9:28. A mechanical electric clock is 3 hours 20 minutes behind. So the power was out a total of that much time. But it didn\'t start just at 6:08; it started earlier, but came back and went out again--as evidenced by the TiVo, which is set to record channel 2 between 4 and 4:30 and channel 4 between 4:58 and 7:30 PM. That recording was broken into segments during which the power was on, and showed the power off from 4:08 to 4:14, 4:16 to 4:20, 4:23-4:27; 5:00 - 5:08; 5:14-5:19 and 5:47 onward. So it must have been intermittently on in between thereafter so that only 3 h 20 m would have been lost by the time power came back for good at 9:28.\r
\n\r
\nSo much for making a puzzle out of the blackout. I guess I like to make a puzzle out of anything.\r
\n\r
\nStrangely enough, a scroll at the end of Who Wants to be a Millionaire just before 4:30 on channel 2 indicated Westchester, Long Island and NJ without power but didn\'t mention NYC for some reason. That was quickly followed by a Dan Rather report that mentioned blackouts affecting city hall, the west side of Manhattan and a couple of other spots in Manhattan.\r
\n\r
\nBy the way the Flooble clock seems to be set to the correct time now. I just noticed, with all this mention of the time. So can one go by posting times to see when people were making posts to Flooble?',1301,'Charlie','2003-08-16 15:14:56');
INSERT INTO forumpost VALUES (1630,240,4,'Re: Posting solutions prematurely','I don\'t think it makes sense withholding a solution that the poser has given just because it has not been solved in the comments. I\'m fairly sure that levik wants to have as few as possible in the unsolved category, and that the only reason he went to post solutions (as solutions) from the comments is to make up for the lack thereof from the poser.\r
\n\r
\nIn the particular instance of Tricky Code: the solution actually hasn\'t been posted on the site--only the solution queue, which is automatic. But now that it has been seen, who is going to solve it in the site comments? Once you leave out the journeymen, scholars and director, it\'s not likely to get solved, especially as it disappears from the home page.\r
\n\r
\nI doubt that there would be a way for levik to have the system hold off the posting of the solution onto the solution queue, except in general for all puzzles, even if the solution has been found in the queue, except perhaps by relying on the Full Solution icon, but that\'s an iffy thing. A putative solution may not really be one, and a real solution might not be marked by a solution icon.',1301,'Charlie','2003-08-16 15:30:53');
INSERT INTO forumpost VALUES (1631,241,3,'Re: Blackout','Well its a bit confusing doing that. As you can probably guess I didn\'t post my last comment at 3 am, so I\'ve just got to work out the time difference. At the moment I\'m at 8:56 (just writing that so I can work out the difference :)',1919,'Lewis','2003-08-16 15:44:14');
INSERT INTO forumpost VALUES (1632,241,3,'Re: Blackout','That\'s because with the recent server move, the site is now on New York time (US Eastern time to be precise). You being in England would account for such a time difference.',1,'levik','2003-08-16 17:39:01');
INSERT INTO forumpost VALUES (1633,240,4,'Re: Posting solutions prematurely','No, we are talking about actually posting a problem to the live site. Tricky Code was still unsolved, but the solution was posted after only a few days. I\'m assuming Bryan asked levik to take it back off for now. There needn\'t be anything programmed in to keep them out of the unapproved list, just discretion on the scholars\' parts to wait until a problem is solved.\r
\n\r
\nEven if a problem goes a long time without being answered, like \'Maximum Value\' or \'A Locked Safe,\' if it is in the unsolved problems listing, it will eventually be tackled, if a solution is possible. I would think such a problem would be the purpose of the unsolved problems queue, not for problems that the author/submitter did not care to put an answer to.',1575,'DJ','2003-08-16 20:20:56');
INSERT INTO forumpost VALUES (1634,241,3,'Re: Blackout','Here in upstate New York we lost power for a little while, but the town I live in has a municipal power company and a plant right on the St. Lawrence, so we were out only for an hour or so. The surrounding areas, getting their power from Niagara Mohawk, were not so lucky, for the most part, losting power for most of the day and evening.\r
\n\r
\nActually, the town I work in did not lose power at all; the reason the power shut off in such a wide area is due to an automatic electronic tripping system that prevents a surge from damaging systems over a wide range on the grid. This town\'s power company, though, is so old that all of those tripping devices are manual; someone has to actually go down to the power company and flip off the switches. Of course, that didn\'t happen in the few seconds that the rest of the northeast lost power, so in that town and the surrounding area nothing happened at all. I was surprised to go into work and find everything working normally (usually a power outage in a food-processing plant means a lot of lost product), and it was interesting to hear the reason for it.\r
\n\r
\nAs far as this site goes, my cable (and thus my Internet) was down for a day and a half, so I wasn\'t able to get on and check. Actually, I was on here typing a comment or something when my screen went black.',1575,'DJ','2003-08-16 20:32:29');
INSERT INTO forumpost VALUES (1635,241,3,'Re: Blackout','I live in toronto and was at a swimming pool when it happened. Hung out with some friends and while riding my bike on the way home I get a flat. Well there goes what I was going to do during this Powerout. Wasn\'t so bad thought. Had power the next day.',1072,'Alan','2003-08-16 23:57:57');
INSERT INTO forumpost VALUES (1636,242,4,'-3 Deletion','When are problems voted -3 deleted? It seems to vary from time to time...',1626,'Gamer','2003-08-17 19:47:28');
INSERT INTO forumpost VALUES (1639,242,4,'Re: -3 Deletion','-3 problems, like +3 problems are deleted by scholars. This allows a -3 problem to be \"redeemable\" - perhaps someone finds some new info on it, or it turns out to not be a dupe as people thought...\r
\n\r
\nSo pretty much whenever one of the scholars or myself get around to it, they will be looked over and deleted as appropriate.',1,'levik','2003-08-17 22:49:13');
INSERT INTO forumpost VALUES (1640,242,4,'Re: -3 Deletion','Oh, Ok... I never understood that, and it makes sense now...',1626,'Gamer','2003-08-18 10:52:21');
INSERT INTO forumpost VALUES (1641,243,5,'I can\'t submit anything','It will not let me submit my riddles and stuff! Why is this? I cant find the \"submit\" button thing. HELP',2121,'Chaz','2003-08-18 12:34:01');
INSERT INTO forumpost VALUES (1642,243,5,'Re: I can\'t submit anything','If you are on the home page, the \"submit\" link is above the \"Who\" (is online) button. If you\'ve gotten past that point, after typing in your puzzle, you must Preview it first, then you\'ll be given a submit button.',1301,'Charlie','2003-08-18 15:06:05');
INSERT INTO forumpost VALUES (1643,244,7,'How are yez?','Hello, I\'m new here too. Found this site through Google. Wanted something to entertain myself when I get bored in work, like right now!',3155,'Harriet','2003-08-19 04:27:29');
INSERT INTO forumpost VALUES (1644,223,4,'Re: Pushing order','Now that we\'re pushing from the top of the queue, what is happening is that puzzles that come into the visible queue spend a lot of time visible but not getting anywhere fast. This happens even as intervening bad puzzles get bumped out, as there\'s still a good supply of lower numbered pid\'s.\r
\n\r
\nTo prevent the overexposure that the limit of 10 was designed to prevent, perhaps we should go back to 3 puzzles per submitter getting a QW of 1. As it turns out, even invisible (because of QW 2) puzzles are becoming visible and getting posted before puzzles that have been seen for a while. Why not show them all along instead of prematurely showing puzzles that will still take a while to get to the top?',1301,'Charlie','2003-08-19 11:37:59');
INSERT INTO forumpost VALUES (1645,223,4,'Re: Pushing order','I know this isn\'t the first time that I have seen problems get 3 TU and sit in the queue for a while... I think anything to help aleviate this condition would be good...\r
\n\r
\nCharlie has a good idea... Although it would take longer for a submitted problem to get to the queue, it would likely take the same amount of the time to get to the queue. If reforming the queue isn\'t possible (because it takes too much work), this is a good idea :)',1626,'Gamer','2003-08-19 14:19:38');
INSERT INTO forumpost VALUES (1646,223,4,'Re: Pushing order','If the oldest problems in the queue were pushed instead of the problems at the top of the queue, it would alleviate this problem; however I think changing the pushing order would be unnneccesary, especially if other methods were adopted.',1626,'Gamer','2003-08-19 14:26:16');
INSERT INTO forumpost VALUES (1647,128,3,'Re: The existence of god','I feel that because we are imperfect, we are not worthy of such information in the exsistence of God (Jehovah).It would be extremely awsome to know intricate detail of the exsistence of the \"Most High\", but... as human beings we must first learn to believe that what the Bible says, is true, and go on from there. Step by step an individual will come to unlock his own personal experiences in his knowledge and relationship with God (Jehovah) and expand in his closeness with God (Jehovah) as well. Do not believe in your own understanding or that of other men, for who are we to think we might know anything of true values or Truth itself? We are fools to even consider such, remember, things of the world are not of God (Jehovah\'s) Light, and most people don\'t even realize that the Earth itself is governed by Satan and his crew. ',2898,'dorkdork','2003-08-19 19:48:10');
INSERT INTO forumpost VALUES (1648,128,3,'Re: The existence of god','If God is omnipotent and all-good, why let Earth be governed by Satan and his crew. If God can preserve his holy literature, it could be the Vedas, the Quran, the Gospel according to Peanuts, ....',1301,'Charlie','2003-08-20 08:36:45');
INSERT INTO forumpost VALUES (1649,128,3,'Re: The existence of god','What makes you think that the earth is governed by satan and his crew?\r
\nSeems to me, we have made most of our own messes.\r
\nJust because God is Omnipotent doesn\'t mean he has to clean up after us.',2839,'FatBoy','2003-08-20 08:41:38');
INSERT INTO forumpost VALUES (1650,128,3,'Re: The existence of god','I really think this post is an eye sore for the flooble crew... We usually are open to all sorts of different problems, but here we are arguing about religion... Religion and science are like oil and water. If they mixed, one of them couldn\'t happen-- Religion is based on things you can\'t observe and science is based on things you can observe.\r
\n\r
\nIn any event, I feel debating about religion is like debating a paradox... People will think they are right, likely because they see something a different way.',1626,'Gamer','2003-08-20 16:03:46');
INSERT INTO forumpost VALUES (1651,128,3,'Re: The existence of god','Hey, Gamer,\r
\nc\'mon, an eye sore? Isn\'t that a bit strong?\r
\nSome of the posts here are not the best thought out things I\'ve ever read but I think most people are entering into the debate in the right spirit.\r
\nReligion is mankind\'s oldest puzzle and isn\'t this site all about puzzles?\r
\nI think Alan showed admirable maturity moving the dabate here from where it started. Here it out of the way and anyoe who is not interested is free to ignore it.\r
\nWhy would someon who did not want to debate religion even visit a thread called \"the existance of GOd\"?\r
\nIF tis size is causing problems for those who maintain the site, I could see how something should be done about it. If not, what\'s the harm in allowing falks a place to air there views?',2839,'FatBoy','2003-08-21 10:25:49');
INSERT INTO forumpost VALUES (1652,128,3,'Re: The existence of god','No, actually Religion isn\'t a puzzle, and can\'t be. In my opinion, puzzles would need some sort of \"logical\" work or at least an answer... (like riddles have different components you need to fulfill), so puzzles are more logic based. And I think that you can believe in religion because there is a 1/infinity chance of it not existing, but once you are sure it exists it becomes science and not religion. And when you have an answer, you are sure it works (if you test it thoroughly enough; not the \"I think this is the answer!\")\r
\n\r
\nMaybe this stems from my disbelief in debates that don\'t accomplish anything... If someone read something in here, it may alter somebody\'s beliefs or make them mad; not at whoever said it, but the idea itself. Even if the idea was said only in a debate, if it\'s true it will still carry the same weight.\r
\n\r
\nI am unsure if this debate would fall under that catergory, but it\'s something to think about. If someone shouts something at you, they might not mean it, but it still will hurt just the same.',1626,'Gamer','2003-08-21 21:54:25');
INSERT INTO forumpost VALUES (1653,231,7,'Re: Another Newbie here!','hey im new here i have this summer math assignment to do and they are puzzles...if you wanna help here is one. \r
\nDidty gold coins are presented to you, but onee of the fifty is a fake. you are given a balacne scale (2 trays that will balance if both contain the same weight) and are told that the fake gold coin weighs more that each of the identical real ones. can you determine the least number of times you must weigh coins to guarantee discovery of the fake coin??',3208,'dea','2003-08-23 13:49:59');
INSERT INTO forumpost VALUES (1654,231,7,'Re: Another Newbie here!','thats fifty gold coins sorry i said didty',3208,'dea','2003-08-23 13:50:51');
INSERT INTO forumpost VALUES (1655,231,7,'heres another puzzlle','a group of students went to dinner together and decided to split the bill evenly but,, before the check arrives, 2 of the studnets left the restaurant. the total bill for all was $63. the mathematcis student discovers that if each of the students remaining pays $2 extra,, the bill will be paid in full. how many students originally sat down to dinner???',3208,'dea','2003-08-23 13:52:56');
INSERT INTO forumpost VALUES (1656,231,7,'and another puzzle','a 40 pound stine used for weighing feed on as anitque faemers balance scale broke apart into 4 pieces. (a balance scale consists of 2 trays that will balance if each possesses the same weight.) those 4 pieces can now be used togehter or seperately to weigh any amount in whole pound increments from 1 pound to 40 pounds. what are the weights of those four stone pieces>>?????',3208,'dea','2003-08-23 13:55:25');
INSERT INTO forumpost VALUES (1657,231,7,'last puzzle','a box contains 3 black and 2 white hats. 3 men standing i a line are facing forward and can see only the person or persons in front of them. each of the 3 men had one of the hats placed on is head but does not see which color. each man can, however see any hats in front of him or another man and each know what was in the box. when the man in rear is asked what color hishat is he replies \" i dont know \" when the man in the middle is asked he answers \" i dont know\" when the man in front is asked he responds \" mine is black and that is no guess!\"\" he was right. how did he know??',3208,'dea','2003-08-23 13:59:35');
INSERT INTO forumpost VALUES (1658,245,7,'math puzzles i need help please!!','hey im new here i have this summer math assignment to do and they are puzzles...if you wanna help here is one. \r
\nFifty gold coins are presented to you, but onee of the fifty is a fake. you are given a balacne scale (2 trays that will balance if both contain the same weight) and are told that the fake gold coin weighs more that each of the identical real ones. can you determine the least number of times you must weigh coins to guarantee discovery of the fake coin?? \r
\n \r
\n\r
\n \r
\n\r
\na group of students went to dinner together and decided to split the bill evenly but,, before the check arrives, 2 of the studnets left the restaurant. the total bill for all was $63. the mathematcis student discovers that if each of the students remaining pays $2 extra,, the bill will be paid in full. how many students originally sat down to dinner??? \r
\n \r
\na 40 pound stine used for weighing feed on as anitque faemers balance scale broke apart into 4 pieces. (a balance scale consists of 2 trays that will balance if each possesses the same weight.) those 4 pieces can now be used togehter or seperately to weigh any amount in whole pound increments from 1 pound to 40 pounds. what are the weights of those four stone pieces>>????? \r
\n \r
\na box contains 3 black and 2 white hats. 3 men standing i a line are facing forward and can see only the person or persons in front of them. each of the 3 men had one of the hats placed on is head but does not see which color. each man can, however see any hats in front of him or another man and each know what was in the box. when the man in rear is asked what color hishat is he replies \" i dont know \" when the man in the middle is asked he answers \" i dont know\" when the man in front is asked he responds \" mine is black and that is no guess!\"\" he was right. how did he know?? \r
\n \r
\n',3208,'dea','2003-08-23 14:05:55');
INSERT INTO forumpost VALUES (1659,231,7,'Re: Another Newbie here!','You don\'t need to post it in 5 different spots... We can see in the other post... \r
\n\r
\nAnd didn\'t you read the instructions... Don\'t post problems here!',1626,'Gamer','2003-08-23 14:32:26');
INSERT INTO forumpost VALUES (1660,245,7,'Re: math puzzles i need help please!!','I think you could find the answer to all of these or how to solve them on the site somewhere... (including one of them exactly!) You just need to not be lazy and actually LOOK!\r
\n\r
\nDidn\'t you read the rules? No posting problems to the forum? I won\'t answer these questions and would encourage others not to either.',1626,'Gamer','2003-08-23 14:33:48');
INSERT INTO forumpost VALUES (1661,246,4,'Group Duplicate Problems','The problem has come in the queue. that many problems that have the same \"rules\" but different \"input\" are posted.\r
\n\r
\nFor example, the Number Machine problems had the same instructions, and so did most of the Word Meld problems and the Letter Cube puzzles.\r
\n\r
\n(In other words, many word meld problems had the same instructions on how to solve, while only changing the starting and ending word.)\r
\n\r
\nI am wondering what we should do about these such problems. In my opinion we should group them together. This is another way to cut down on the queue, and it helps solvers have more than one problem to work on. Plus, it would cut down on typing and reading.',1626,'Gamer','2003-08-23 14:40:36');
INSERT INTO forumpost VALUES (1662,245,7,'Re: math puzzles i need help please!!','gee thanx alot you were probably one of those people that told on kids in school for cheating...this is summer im not supposed to have work!!!',3208,'dea','2003-08-23 15:13:31');
INSERT INTO forumpost VALUES (1663,245,7,'Re: math puzzles i need help please!!','Then don\'t do the puzzles... You can be one of the people that doesn\'t do their work. :)\r
\n\r
\nAre you in southern hemisphere where it\'s starting to be summer now? It just is ending for me, and I don\'t really know much about these global season things! :)\r
\n\r
\nAnyway, one such puzzle you could find if you searched for hat (it\'s the top one) was More hats! here',1626,'Gamer','2003-08-23 15:30:45');
INSERT INTO forumpost VALUES (1664,246,4,'Re: Group Duplicate Problems','I think it definitely depends on the problem. Especially for problems where each has one definite answer that doesn\'t warrant any further discussion, such as \'Sequence and Pattern Exam,\' the \'Number Machine\' problems, or groups of simple riddles, I agree. Simply having the same set of instructions doesn\'t mean you should have to put five puzzles into one.\r
\n\r
\nMy full solution to each \'Letter Cubes\' problem is 120-150 lines long. It\'s possible to maybe solve each in a few minutes by scribbling on a piece of paper, but a complete solution with an explanation will take a bit of time to produce, I think.\r
\nThe \'Word Meld\' problems are the same way, while there may be a definite shortest method, you have to think about each and how to connect the words (unless you have a program that does all the work for you), and a single problem or pair of problems I think certainly carries enough discussion to last at least half a day. Also, the instructions for all of them are not the same, most of them are two puzzles in one already, and I have a few more different types of problems falling under the same series, still pending.\r
\n\r
\nI think it\'s sad (coming from the same people who posted ten \'Guessme\' problems) to have to defend series of problems that people seem to enjoy, to the point that any future problems will be \'shot on sight\' simply because the instructions are similar.\r
\n\r
\nSo, yes, simple problems could be combined to make them more interesting or involved, but I think that if you combined some of the more involved problems, as seen in \'Sequence and Pattern Exam,\' people would do a few that were obvious and ignore others altogether. and the discussion revolving around each would be lost. So, I\'ll reiterate, it ultimately depends on each problem.',1575,'DJ','2003-08-23 15:56:07');
INSERT INTO forumpost VALUES (1665,231,7,'Re: Another Newbie here!','No she wants us to answer them to get her homework done. Well dea I\'m not going to do your homeworf for you but if you go to search and type coins then A problem about coins and a scale will come up (like yours) it\'ll have a different number of coins but once you figure the concept and why the answer is what it is your 50 coin problem should become that much easier.',1072,'Alan','2003-08-24 10:59:43');
INSERT INTO forumpost VALUES (1666,245,7,'Re: math puzzles i need help please!!','By the way Dea you\'re saying its summer and you shouldn\'t have to work. Well It\'s my summer to so why should we have to work for you. Something to think about.',1072,'Alan','2003-08-24 11:01:46');
INSERT INTO forumpost VALUES (1667,246,4,'Re: Group Duplicate Problems','Yes this is something I brought up a long, long time ago and I called it \"problem condensing\" and talked about how people should group problems together. I see now that the response is \"what about sequel and prequel problems\". For this I love to use the pearls series. Every problem in that series has totally different concept and almost every problem in that series is submitted by a different author. This is how a sequence should be.\r
\n\r
\nIn conclusion I\'ll say this. Problems which are dupes in \"concept\" I shall simply start to TD. That\'s that.\r
\nthe only thing that could change would be if dupe concept problems were instead never shown on the front page and you could only access them from a link on the original concept. So letter cubes 2, 3, etc. would never appear on the front page but in letter cubes would be links to letter cubes 2,3,etc. also letter cubes 2,3,etc wouldn\'t appear in the listing as one is already there.\r
\n(Note: letter cubes is an example)',1072,'Alan','2003-08-24 11:08:26');
INSERT INTO forumpost VALUES (1668,247,7,'Submitting Problems','I\'m really keen to move my way up the user levels, but the only thing is that I don\'t know how long it\'s going to take for my submitted problems to get approved. What kind of lag time can I expect here?\r
\nCheers,\r
\nDave',3136,'Popstar Dave','2003-08-24 12:13:38');
INSERT INTO forumpost VALUES (1669,246,4,'Re: Group Duplicate Problems','That\'s a good idea... I don\'t really like getting rid of duplicates like word ladders, letter cubes, and logic problems (Especially if there\'s a new twist) because each one can be solved... Although they are duplicates, you can solve each one individullly :)\r
\n',1626,'Gamer','2003-08-24 17:38:23');
INSERT INTO forumpost VALUES (1670,247,7,'Re: Submitting Problems','Well, right now there are a little more than 400 problems in queue, and we post two problems a day (only one one weekends), besides the ones that get voted down and deleted. There are 10 problems in the \"active\" queue at any time, that are being discussed and voted on. Just to give you the heads up, the most recent problem currently in the queue was submitted July 18. So, it looks like the wait time is down to around a month or a month and a half (compared to almost three months, not too long ago).',1575,'DJ','2003-08-24 17:40:07');
INSERT INTO forumpost VALUES (1671,247,7,'Re: Submitting Problems','Be careful that what you have submitted isn\'t a duplicate of another problem already on the site... We have many of the \"classic\" duplicates...\r
\n\r
\nTechnically 400 problems in the queue means about half a year of waiting. The only difference is the queue weight, which brings the wait down to around 2 months... :) Yay queue weight!',1626,'Gamer','2003-08-24 17:57:28');
INSERT INTO forumpost VALUES (1672,247,7,'Re: Submitting Problems','Each person\'s problems are assigned a \'queue weight.\' Their earliest two problems have a queue weight of 1, the next two have a value of 2, and so on. The idea is that everyone\'s QW 1 problems are looked at before any of the QW 2 problems, so if you are just submitting a problem, you won\'t have to wait for every one of 50 problems submitted by someone else (meaning, you won\'t have to wait for all 400 of the current problems to be sorted out before we look at yours).\r
\n\r
\nAnd yes, Gamer makes a good point; there are hundreds of problems already on the site, and pretty much all of the more common puzzles are on here, so look around. If you see a problem on the site after you have already submitted the same one, there is the option to delete the problem yourself (and save us the trouble; we of course won\'t post duplicate problems anyway). Riddles and lateral thinking problems are also discouraged in favor of more math- and logic-based puzzles.',1575,'DJ','2003-08-24 18:46:42');
INSERT INTO forumpost VALUES (1673,231,7,'Re: Another Newbie here!','And if you search on \"hats: you should be able to find help for the last puzzle.',2839,'FatBoy','2003-08-25 09:17:11');
INSERT INTO forumpost VALUES (1674,246,4,'Re: Group Duplicate Problems','Here\'s the problem as I see it. Very few people ever go and browse the archives to look at older problems. Especially, if they are not on the front page in their respective categories. That\'s just web user mentality for you. (In fact I plan to have a proposal with reguard to this a little later.)\r
\n\r
\nSo the idea of \"concept dupes\", as annoying as it is to the regulars such as us, may not be so bad where visitors are concerned. I am against \"condenced\" problems, because they do not solve the concept dupe issue - you still get a lot of repetitions to do, and you get them all at once. Not only that, but the problem becomes long (text wise) and the longer a problem is, the less likely somebody is to read it and become interested.\r
\n\r
\nSo my idea on the subject is a \"dunk\" feature. If a problem comes up that\'s similar to one recently posted, it can go through the voting process, and then \"dunked\" - which would have its submission date made later by a month, effectively putting it further back in the queue. The problem would then re-surface in about 30 days, when the concept is not fresh in everyone\'s mind anymore.\r
\n\r
\nI\'m not sure how the actual voting would happen - perhaps anyone who votes TU on a problem will be able to mark it dunkable, and then once it has +3, a scholar can dunk it if at least 2 other people thought it should be dunked... Or to make it easier, we could have a problem become dunkable at +2, and leave it to the scholars\' discression - others could still voice their opinions by placing notes on the problem.',1,'levik','2003-08-25 12:18:40');
INSERT INTO forumpost VALUES (1675,248,5,'Comment editing','Not sure if anyone noticed, but as of today, Stunents and up can now edit their comments. (The \"edit\" link appears next to the \"Reply\" link under the comment.\r
\n\r
\nFor now, only the editing of the comment body (not subject or \"marker\") is allowed.\r
\n\r
\nThank DJ for requesting this much needed addition.',1,'levik','2003-08-25 19:19:05');
INSERT INTO forumpost VALUES (1676,246,4,'Re: Group Duplicate Problems','Well they main reason I brought up \"dupe concepts\" was because I wanted the queue to be depleted that much quicker. I really want to start seriously plowing throughout that queue. A lot of times I think to myself \"hey that would be a great idea for a problem\" but the idea of the queue being so long really prevents me from posting it. I really hate looking at my problem seeing it move 0 spots in queue position from day to day so I prevent myself the trouble of seeing it go nowhere by not submitting it.',1072,'Alan','2003-08-25 22:18:13');
INSERT INTO forumpost VALUES (1677,248,5,'Re: Comment editing','I am unsure comment editing is such a good thing. Suppose someone changes their comment so they have the right answer? Other things could come up too. I would suggest putting something editted in later in italics or something else distinguishable but not distracting.',1626,'Gamer','2003-08-25 22:37:21');
INSERT INTO forumpost VALUES (1678,246,4,'Re: Group Duplicate Problems','What I do is I submit it anyway. Not submitting it at all will take an infinite time to get it posted (I suppose so, since someone has to eventually have the same idea as you Any queue wait where there are less than an infinite amount of problems (a million isn\'t infinite! :D), you post it faster.\r
\n\r
\nWhy does the queue\'s length prohibit you from posting a problem? If you aren\'t looking for a rank change based on problems, it would seem like however long is good enough to hold out on the discussion. I don\'t know though :)',1626,'Gamer','2003-08-25 22:52:51');
INSERT INTO forumpost VALUES (1679,248,5,'Re: Comment editing','Right now, the last edit date is appended to the end of the comment after editing. I believe that since this is only open to Students and up, there should not be too much immature behavior. After all, comments don\'t really count for much in the way of granting privileges on the site, so in the end run, is it really horrible for the site if somebody goed and fixes their solution after reading an official one?',1,'levik','2003-08-26 00:02:01');
INSERT INTO forumpost VALUES (1680,246,4,'Re: Group Duplicate Problems','It will please you guys to know that I have problems sitting in the queue myself (they\'re getting close though!) - so by all means, do contribute yourgood ideas.\r
\n\r
\nAdditionally, the queue is over a hundred problems slimmer today than it was a short while ago, so the throughput times are going to start declining.\r
\n\r
\nIf this continues, we may run out of problems to post altogether! :)',1,'levik','2003-08-26 00:04:57');
INSERT INTO forumpost VALUES (1681,248,5,'Re: Comment editing','Yeah, if you\'re just going to append something to a comment, you might as well post another comment. The editing allows us to fix problems with the <pre> tag and the preview box, as we have seen troubles with lately, without having to post a string of comments correcting typos or other small errors.\r
\nSomeone can\'t do any more than they could in posting a comment normally; the worst I can see happening is a new user changing their incorrect solution after the official one is posted or something, and even then there is the edit date.\r
\n\r
\nIf that worries you, perhaps to make sure that the feature is used only to correct errors, etc, you could only allow problem editing for 12 hours after it\'s posted or something.\r
\n\r
\nOne thing, though, I would suggest that the \'Edited date/time stamp\' not be added if the problem has just been submitted, for half an hour or an hour or something, to allow people to fix display problems with their comments and not have it looks as if a solution was fixed later or something (although the actual time/date of the change will show otherwise, I imagine that will be overlooked a lot of the time). I can see using it quite often in place of the preview comment box, since that often doesn\'t work the way it should, but then a newly posted comment looks as if it was changed after it was posted. That\'s the only further suggestion I have.',1575,'DJ','2003-08-26 09:12:00');
INSERT INTO forumpost VALUES (1682,249,7,'Ok.. I have no Idea.. But I\'m new.. lol','Cool.. hrm what x-actually goes on in this place??',3258,'AmE','2003-08-27 08:38:58');
INSERT INTO forumpost VALUES (1683,249,7,'Re: Ok.. I have no Idea.. But I\'m new.. lol','Welcome AmE!\r
\n\r
\nI\'m pretty new too but I\'ll tell you what I have figures out...\r
\nYou log on navigate around and solve or comment on puzzles. Good place for it as the puzzles are of generally high quality with few repeats.\r
\n\r
\nYou can also submit puzzles for posting which apparantly entitles you to complain about how long it si taking for your puzzles to be posted. This seems to be a major source of entertainment. I\'ve only submitted three adn tehy are not that good so I don\'t feel entitled to gripe.\r
\n\r
\nThere are also apparantly a series of levels or ranks you can attain by commenting on, solving and posting puzzles. Each rank apparantly gives you enhanced privilidges. I\'m a student now but figure I will eventually attain \"Jedi Knight\" status or whateve (perhaps not after that snarky remark).\r
\n\r
\nTo fingd out your level click on \"Your Information\" next to your login name. THere is also a link that explains the various levels.\r
\n\r
\nYou can also wander the message furums. SOme are fairly interesting. If you want to irritate folks than put a puzzle in a forum, its against the rules really bugs the power structure.\r
\n\r
\nIgnore my snottiness as I am a big grump. iTs really a cool site if your into puzzles. If not, I can not imagine why you would have come here.\r
\n\r
\n\r
\n',2839,'FatBoy','2003-08-27 09:29:34');
INSERT INTO forumpost VALUES (1684,249,7,'Re: Ok.. I have no Idea.. But I\'m new..','Wew, nicely put, FatBoy :) Maybe I should put your little rant on the \"about\" page instead of the current \"blah\" copy that\'s on there :)\r
\n\r
\nWelcome to the site AmE.',1,'levik','2003-08-27 10:24:46');
INSERT INTO forumpost VALUES (1685,249,7,'oooopps, busted by da man','I didn\'t type a word of it, and even if I did it was not my fault, I had a bad childhood, \r
\n\r
\nand anyway I do not recall anything about it, I was visiting realtives in another state at the time',2839,'FatBoy','2003-08-27 13:00:26');
INSERT INTO forumpost VALUES (1686,249,7,'Re: Ok.. I have no Idea.. But I\'m new.. lol','Haha.. that was great. I don\'t know about replacing the \"about\" page, you know, encouring delinquent behavior and all. And I\'m sure that if that had been up when I first came, I\'d be sorely disappointed to learn that solving puzzles could not make me a Jedi knight.\r
\n\r
\n..Perhaps we can take suggestions for new rank titles?',1575,'DJ','2003-08-27 13:08:36');
INSERT INTO forumpost VALUES (1687,249,7,'Re: Ok.. I have no Idea.. But I\'m new.. lol','Hi \r
\n\r
\nI am new to all of this but i have a problem i cant solve and maybe you guys can help it goes like this \r
\n\r
\n\r
\nThere are three switches in front of you, A, B and C. One controls a light\r
\nbulb in another room, far far away. The others do nowt. You can do\r
\nwhatever you want with these switches, but you have to at some point leave\r
\nthem and go to the room with the light bulb in. When you are there, you\r
\ncannot return to the switches, and you must say with certainty which switch\r
\ncontrols the light bulb.\r
\n\r
\nHow do you do it?',3273,'Darren Winchester','2003-08-28 08:54:40');
INSERT INTO forumpost VALUES (1688,249,7,'Re: Ok.. I have no Idea.. But I\'m new.. lol','Well, we\'re not going to do your homework or whatever it is for you, but please, if you have a puzzle to submit, do so by clicking \'Submit a Puzzle\' on the front page. Also, look around first, to make sure that the problem you\'re trying to submit isn\'t already on here. I think you\'ll find your answer if you just search a bit...',1575,'DJ','2003-08-28 10:32:21');
INSERT INTO forumpost VALUES (1689,250,3,'Money making Idea...','Hey,\r
\n\r
\nI was thinking.\r
\n\r
\nIt seems like every week or so we get someone trying to get their homework done for them.\r
\nJudging from the responses I see to the tough math problems, there is enough brain power regularly loggin\' in here to kick major math/logic butt.\r
\n\r
\nHere\'s my notion. Start a seperate section called \"I\'m to lazy to do my own flippin\' homework\" then folks can log in, pay a fee and post their pleas for help.\r
\n\r
\nTHen whoever knows the answer can jot a quick response. Prophets from this endeeavor could be used to pay for equipment needed to host the site (I am assuming someone must own teh hardware) or maybe go to buy levik a new car.\r
\n\r
\nI\'ll leave the deatils for others to figure out. Take this all as a suggestion since the only help I would be is if some prospective client posted a request that said: \"Hey, my teacher assigned me the task of coming up with some snotty sarcastic remarks.\"\r
\n\r
\nIn any case, what about it you scholars and directors, sounds like a chance to rake in a little extra green. (yes, I realize that you all have jobs and are doing just fine, but c\'mon who couldn\'t use a little extra scratch?)',2839,'FatBoy','2003-08-28 15:42:46');
INSERT INTO forumpost VALUES (1690,249,7,'Re: Ok.. I have no Idea.. But I\'m new.. lol','This is indeed a duplicate... Look at the puzzle (and the solution) by searching for \"Light Bulb\" in the Search box',1626,'Gamer','2003-08-28 18:10:52');
INSERT INTO forumpost VALUES (1691,250,3,'Re: Money making Idea...','That\'s not a bad idea, in writing... I don\'t know, though; even if we do find some prophets from this little venture, I don\'t know if they would do much more than predict that levik will get a new car, since they tend to live in solitude and relative poverty and all.\r
\n\r
\nYou are right, however, about the little scratch. Right in the middle, where I can\'t reach, just below my shoulder blades...',1575,'DJ','2003-08-28 22:31:43');
INSERT INTO forumpost VALUES (1692,250,3,'Re: Money making Idea...','The scheme is brilliant, but has a fatal flaw. Levik (who for the duration of this post decided to refer to herself in the third person - and a female) does not have a driver\'s license. She was just too damn busy programming the site to go for a road test. \r
\n\r
\nNo license - no car. No car - no point in propheting. As you see, it\'s a whole big domino effect we have going.\r
\n\r
\nSeriously though, I think it\'s great enough that people are willing to help out in the day to day operations of this site (commenting, submitting problems, approving them). To expect that people will do somebody else\'s homework to fatten my wallet would be silly of me and highly presumptuous.\r
\n\r
\nBesides... Let them do their own damn homework',1,'levik','2003-08-28 22:48:26');
INSERT INTO forumpost VALUES (1693,250,3,'Re: Money making Idea...','Sheesh.. levik is going to give people worse gender confusion than Ravi, but hey, she brought it upon himself.\r
\n\r
\nI find humor in site like Eli\'s Math and Logic Page that expect me to pay for a solution to problems that are on this site, where I can get them for free. But hey, if someone wants to pay me, I won\'t object.\r
\n\r
\nAlso, I heard a prophecy that levik would give me her car if he got one. So, I\'ll do other people\'s homework to buy levik a car...',1575,'DJ','2003-08-29 00:58:23');
INSERT INTO forumpost VALUES (1694,251,4,'Easy problems','Occasionally, a problem in the queue receives one or more TD\'s simply because it is relatively easy for us puzzle reviewers to solve. I try to look past that and see what problem solving skills were required to solve it. Sometimes it can be a fine line between being simple and being trivial, but if the answer isn\'t a complete no-brainer, I give it a TU, figuring that is what the D1 and D2 designations are for. \r
\n\r
\nDo others feel easy problems (perhaps most appropriate for young teens) should or should not have a home on Flooble Perplexus?\r
\n\r
\nIncidentally, when I see a simple problem, I make a point of not giving the answer when it posts so that newer/younger puzzle solvers can be first. ',1567,'Bryan','2003-08-29 12:25:38');
INSERT INTO forumpost VALUES (1695,250,3,'Re: Money making Idea...','Actually the idea of making the solution less readily available is a pretty good one. I was thinking of placing an intersticial ad in front of solutions - so that if somebody wanted to see one, they would have to sit through a 5-7 second advertisiment.\r
\n\r
\nI may still do it some time...',1,'levik','2003-08-29 12:32:38');
INSERT INTO forumpost VALUES (1696,251,4,'Re: Easy problems','I believe easy problems are ok, as long as they are interesting. You are right that that\'s what the lower difficulties are there for. However if the problem is simple arithmetics, perhaps it would fit in better on a \"homework excercises for fun\" site :)\r
\n\r
\nI do think thta easy problems ought to be pushed in the morning, so they don\'t occupy the \"primetime\" slots.',1,'levik','2003-08-29 12:35:01');
INSERT INTO forumpost VALUES (1697,249,7,'Re: Ok.. I have no Idea.. But I\'m new.. lol','Darren you cheating so and so. You could have asked me for the answer rather than trying to give the impression of answering it yourself.',3274,'Dacre','2003-08-29 12:55:51');
INSERT INTO forumpost VALUES (1698,252,5,'The Flooble \'get out the links\' Drive','So here\'s a plea for help of sorts... \r
\n\r
\nRight now, a lot of new blood we get here comes from Google - people searching for \"logic puzzles\" or \"brainteasers\" and the like. The other major source is from little links in the Chatterbox. However, precious little other places on the web link here, and I believe that with a few strategically placed links, we could really draw in the crowds - the kind of people we would like to see. \r
\n\r
\nSo I am appealing to the visitors of this site to help me promote it by spreading the word. Wether you place a link on your site, tell a friend who may be interested or put perplexus in your signature on some forum, whatever you can do to help will be sure to attract interesting people to the site. And I think everyone knows that the more interesting people there are on a site, the better it becomes.\r
\n\r
\nYou can link to the homepage (http://www.flooble.com/perplexus/) one of the categories, or even to individual problems.\r
\n\r
\nI believe this to be one of the best places on the web to go for puzzles - and it\'s you guys that have helped make it this way. So why not help it be more recognized as such?',1,'levik','2003-08-29 15:31:45');
INSERT INTO forumpost VALUES (1699,251,4,'Re: Easy problems','I say every so often do an easy problem. Maybe 1 or 2 every week? I think there are young people who might not know as much, and it\'s good to have the same solution 15 times because then we know we have at least 15 visitors on the site. :D\r
\n\r
\nI try to make all mine more than 1/5 difficulty so that I don\'t contribute to this...',1626,'Gamer','2003-08-29 16:07:09');
INSERT INTO forumpost VALUES (1700,250,3,'Re: Money making Idea...','Yeah, but waiting five seconds is a whole lot better than shelling out five bucks a problem. On some sites, higher-level users don\'t have to deal with the ads, is this site like that? I think it\'s a good idea, since people who have the ranks most likely ignore all the ads anyway, and the traffic comes from the passers-by.\r
\nSomeday, I\'ll get around to writing some problems and join all you big wigs..',2912,'Talon5000','2003-08-29 17:05:45');
INSERT INTO forumpost VALUES (1701,250,3,'Re: Money making Idea...','Actually, you could just hide the solutiong until someone comments on a problem, so they at least try it? That might work..',2912,'Talon5000','2003-08-29 17:07:09');
INSERT INTO forumpost VALUES (1702,253,7,'hi there','I just joined this week (first as catherine, then I modified my nick to cat) and am already addicted. My only regret is that there are not more logic puzzles (I especially love the liars and knights variety). I\'ve done the new ones that dont yet have solutions and am waiting impatiently for more! Meanwhile I\'m going over some of the solved ones and seeing if i can get them right without looking at anyone\'s comments or the solutions. But it\'s much more fun getting to post a solution. Anyway, great site. Thanks to all who are responsible.',3241,'cat','2003-08-29 20:40:48');
INSERT INTO forumpost VALUES (1703,213,5,'Re: Slow server?','I\'m experiencing intermittent slowness this week (I only just joined). I installed cookie pal yesterday and wondered if that was causing it. Anyone else also having this problem at the moment?',3241,'cat','2003-08-29 20:45:45');
INSERT INTO forumpost VALUES (1704,250,3,'Re: Money making Idea...','That would just lead to having a bunch of \"filler\" comments people would post just so they could look at the solution.\r
\n\r
\nAbout the ads... There is no differentiation by rank, but logged in users get much less popups than do casual visitors.',1,'levik','2003-08-30 09:19:38');
INSERT INTO forumpost VALUES (1705,249,7,'Re: Ok.. I have no Idea.. But I\'m new..','I take it you two know each other? :)',1,'levik','2003-08-30 09:21:26');
INSERT INTO forumpost VALUES (1706,253,7,'Re: hi there','Welcome to the site, Cat, and I am glad you are enjoying it.\r
\n\r
\nJust because a puzzle has a solution posted, you should not feel like you can no longer comment on it! (Often discussion springs up around older puzzles, and we sometimes even come up with newer and better ways to solve them!)',1,'levik','2003-08-30 09:23:11');
INSERT INTO forumpost VALUES (1707,253,7,'hi there','Hey thios is my first time at this site I got it hrough New Mon It\'s really cool. Although if you want a suggestion it could b a little more organized but on the long run i really like it. Although for the brain teasers Where do you post the sollution?',NULL,'kitten*meow','2003-08-30 10:26:24');
INSERT INTO forumpost VALUES (1708,254,7,'No Subject','Sorry this is meant to be on a new thread not the first one:\r
\n Hey thios is my first time at this site I got it hrough New Mon It\'s really cool. Although if you want a suggestion it could b a little more organized but on the long run i really like it. Although for the brain teasers Where do you post the sollution? \r
\n',NULL,'Kitten*Meow','2003-08-30 10:27:24');
INSERT INTO forumpost VALUES (1709,255,7,'myself','Welcome to my thread. I came here to solve everything and be on my way. I am a computer engingeering student and this site came highly recommended. I believe logic expands your understanding of everything by way of making you see things from other angles. Bottom line, I enjoy the hell out of puzzles like this, I\'m trying to keep this short, good luck all. ',3323,'Nicholas','2003-09-01 19:39:09');
INSERT INTO forumpost VALUES (1710,255,7,'Re: myself','Hi, nice thread you have here... =)\r
\nI was a computer engineering student too, for two years; this year I switched to software engineering because I\'m more interested in implementation and programming than the design and circuit-related stuff we had been doing.\r
\nAnd I agree, logic and reasoning puzzles are really good, and I think the set here is one if not the best on the Internet.\r
\nSee you around!',1575,'DJ','2003-09-01 21:03:52');
INSERT INTO forumpost VALUES (1711,256,4,'Solution Strategy','When I submit a problem, I don\'t submit the solution because I figure that\'s a way for me to check on the difficulty and solution of the problem (because I have usually forgotten it) This helps me make sure it\'s a good problem, but I recently have had a problem with this in the solution for \"Knight\'s Tour\" because I have forgotten the reason why As must be done before Bs and didn\'t specify it enough when I did know it. Do others think this is a good strategy or not?',1626,'Gamer','2003-09-04 17:48:39');
INSERT INTO forumpost VALUES (1712,256,4,'Re: Solution Strategy','I wouldn\'t think this to be the best of strategies... Perhaps if you excercise a little self restraint and don\'t look at your own submitted solution once you submit it, you will have achieved the same effect without the risk of the solution being lost :)',1,'levik','2003-09-04 19:09:05');
INSERT INTO forumpost VALUES (1713,256,4,'Re: Solution Strategy','If I had to retype the solution twice it would get less useful (mainly for larger problems)... I don\'t really understand what you are saying....',1626,'Gamer','2003-09-04 19:30:25');
INSERT INTO forumpost VALUES (1714,257,3,'not a puzzle...','but maybe it should be.',2839,'FatBoy','2003-09-05 09:45:05');
INSERT INTO forumpost VALUES (1715,257,3,'Re: not a puzzle...','Imagine if someone had posted this puzzle thress months ago.\r
\n\r
\nWhat do former body builder Arnold Schwarzenager\r
\nformer child TV star Gary Coleman\r
\nand pornographer Larry Flynt have in common?\r
\n\r
\nWould anyone possibly have come up with. THey will all soon be candidates for governor of California??',2839,'FatBoy','2003-09-05 09:48:14');
INSERT INTO forumpost VALUES (1716,256,4,'Re: Solution Strategy','I tend to write the solutions once I know that the problem\'s going to get posted (unless the solution is short) because I hate it when I\'ve typed out a really long solution only to get the problem rejected.',1919,'Lewis','2003-09-05 15:21:40');
INSERT INTO forumpost VALUES (1717,258,3,'Avatars!','OK, everyone, I would like to announce that the site will now support avatars from my other (new) venture - Avatarity. You can set your avatar in by going to your profile page - it will be visible in your profile, and in the forums.',1,'levik','2003-09-05 17:14:34');
INSERT INTO forumpost VALUES (1718,258,3,'Re: Avatars!','I am surprised to find that bust a move dude on there! I love playing Bust a move and was so surprised to see it! :D',1626,'Gamer','2003-09-05 18:34:08');
INSERT INTO forumpost VALUES (1719,258,3,'Re: Avatars!','How do you set it from your profile? I am still confused as to that part.',1626,'Gamer','2003-09-05 18:36:50');
INSERT INTO forumpost VALUES (1720,258,3,'Re: Avatars!','To set up your avatar for perplexus, go to your perplexus profile, and where it says \"Avatar\" click \"pick\"\r
\n\r
\nThat will take you over to Avatarity and give instructions on exporting the avatar back to Perplexus',1,'levik','2003-09-05 19:44:03');
INSERT INTO forumpost VALUES (1721,258,3,'Re: Avatars!','When I clicked on \"Your information\" and \"Edit your info\" I couldn\'t find that avatar thing anywhere.',1626,'Gamer','2003-09-05 21:41:29');
INSERT INTO forumpost VALUES (1722,258,3,'Re: Avatars!','Sorry for the confusion - you don\'t need to click \"Edit your info\" - onece you are looking at your user profile, the avatar and a link to change it should appear on the upper-right.',1,'levik','2003-09-05 22:34:11');
INSERT INTO forumpost VALUES (1723,258,3,'Re: Avatars!','It doesn\'t appear there though... I don\'t know if I am not looking in the right spot, but all I see is the normal stuff.\r
\n',1626,'Gamer','2003-09-06 09:45:34');
INSERT INTO forumpost VALUES (1724,258,3,'Re: Avatars!','(This is levik again)\r
\n\r
\nIt works for me under my test accounts as well. Click \"Your Information\", and see the blank avatar in the top-right corner.\r
\n\r
\nIf you\'re logged in, you should also see a \"Pick\" link under there. Does it not show up for you?',2,'art','2003-09-06 13:46:28');
INSERT INTO forumpost VALUES (1725,258,3,'Re: Avatars!','Here is my test account, and it works here, but it doesn\'t work for Gamer... I don\'t know why...',3373,'Test_Gamer','2003-09-06 14:24:12');
INSERT INTO forumpost VALUES (1726,258,3,'Re: Avatars!','What I did was typed in the same link that I got from Test Gamer in when I was signed in as Gamer, and chose my spinning Bust-A-Move dinosaur dude... :) It still doesn\'t show up in my user profile that that\'s what I have selected though.',1626,'Gamer','2003-09-06 14:27:11');
INSERT INTO forumpost VALUES (1727,258,3,'Re: Avatars!','Its the same for me...',3374,'Test_Lewis','2003-09-06 16:22:02');
INSERT INTO forumpost VALUES (1728,258,3,'Re: Avatars!','Testing avatar',1919,'Lewis','2003-09-06 16:23:10');
INSERT INTO forumpost VALUES (1729,258,3,'Re: Avatars!','HOORAY! I just did the same as Gamer and it worked OK.',1919,'Lewis','2003-09-06 16:23:43');
INSERT INTO forumpost VALUES (1730,258,3,'Re: Avatars!','I got it working, but they\'re right, the link is only showing up on newly-created accounts. The selection, as I\'m sure you\'re painfully aware, is somewhat limited.. but how about just including all the smiley face avatars on the flooble forum? That would be an easy big step, I think, to expanding the choices..',1575,'DJ','2003-09-06 17:35:13');
INSERT INTO forumpost VALUES (1731,258,3,'Re: Avatars!','I had no problem. Really Simple. Thanks Gamer and Lewis for helping levik work out the bugs. :)',153,'TomM','2003-09-06 19:19:24');
INSERT INTO forumpost VALUES (1732,258,3,'Re: Avatars!','I don\'t really mind the selection... there are \"enough\" for me... Some of the ones on there are cool (I haven\'t seen the puzzle bobble before so that struck me by surprise)',1626,'Gamer','2003-09-06 21:07:48');
INSERT INTO forumpost VALUES (1733,258,3,'Re: Avatars!','I\'m not sure what exactly you guys were missing - If you tell me which link didn\'t show up for your old accounts, I will try to fix this.\r
\n\r
\nAlso, DJ, I really didn\'t understand what you were saying about smileys and the forums.\r
\n\r
\nJust to be clear, you DO NOT NEED to sign up on avatarity to use one of the avatars on perplexus. The only limitation is the 64x64 pixel dimensions, which rules out most of the Street Fighter animations...',1,'levik','2003-09-06 23:32:51');
INSERT INTO forumpost VALUES (1734,258,3,'Re: Avatars!','The problem for me is that link for the avatar isn\'t at all on my account. It\'s there for my new account, but not for this one. I think it might be account specific too. I can see both levik\'s and TomM\'s avatars when I go to their \"about\" page, but not anyone else\'s. (including my own)\r
\n',1626,'Gamer','2003-09-07 08:30:03');
INSERT INTO forumpost VALUES (1735,258,3,'Re: Avatars!','Maybe it is specific to your browser. I see nothing wrong. I\'m using Netscape 7.01.\r
\n\r
\nLet levik know what browser you are using, and then maybe he can repeat the problem, and find a solution.',153,'TomM','2003-09-07 08:43:59');
INSERT INTO forumpost VALUES (1737,258,3,'Re: Avatars!','I can only see TomM\'s and levik\'s too',1919,'Lewis','2003-09-07 08:46:32');
INSERT INTO forumpost VALUES (1738,258,3,'Re: Avatars!','Oh, and levik -- what I think DJ was talking about: one of the ads that\'s been appearring lately in the right-hand column is for animated smiley icons. He may have thought that that was another venture of yours.',153,'TomM','2003-09-07 08:52:24');
INSERT INTO forumpost VALUES (1739,258,3,'Re: Avatars!','I see about a bazillion smiley icons ads a day... the ones that say \"Free smileys for your email\" like the ones at smileycentral ;)',1626,'Gamer','2003-09-07 09:08:10');
INSERT INTO forumpost VALUES (1740,258,3,'Re: Avatars!','Seems to have been some weird problem with IE. I changed the HTML for the avatar box a bit, so hopefully it will now work for everyone. Do let me know if that\'s not the case.',1,'levik','2003-09-07 10:30:42');
INSERT INTO forumpost VALUES (1741,258,3,'Re: Avatars!','On another note, I\'m thinking of making avatars show up in problem comments as well... Any thoughts? (Are you TU or TD on this idea, and where would be a better place?)',1,'levik','2003-09-07 10:34:14');
INSERT INTO forumpost VALUES (1742,258,3,'Re: Avatars!','problem comments and forum, and public profile all get TU from me. Anyways levik does our avatar have to be from avatarity.com? or is it possible to find our own sprites?',1072,'Alan','2003-09-07 10:38:05');
INSERT INTO forumpost VALUES (1743,258,3,'Re: Avatars!','Btw: avatarity is a very nice site. I wonder if i could help. I may be able to locate some sprites and send them to you. (mostly video game sprites but thats pretty much what everyone has)',1072,'Alan','2003-09-07 10:41:08');
INSERT INTO forumpost VALUES (1744,258,3,'Re: Avatars!','Personally, I think avatars would be too much of a distraction in the comments.',1301,'Charlie','2003-09-07 11:30:31');
INSERT INTO forumpost VALUES (1745,258,3,'Re: Avatars!','I agree with charlie on the comments bit.',1919,'Lewis','2003-09-07 12:31:16');
INSERT INTO forumpost VALUES (1746,258,3,'Re: Avatars!','Right now you have to pick an avatar through Avatarity - however if you want to use your own, you can sign up with Avatarity and submit the avatar there. If you don\'t wish to share it with others, you can make it private.\r
\n\r
\nAs far as comments and avatars go, I was thinking of only showing one avatar of the poster of the comment you are currently looking at (since comments are shown one at a time.\r
\n',1,'levik','2003-09-07 12:48:06');
INSERT INTO forumpost VALUES (1747,258,3,'Re: Avatars!','I don\'t like avatars in the comments... seems like they aren\'t needed there as much...',1626,'Gamer','2003-09-07 14:20:59');
INSERT INTO forumpost VALUES (1748,258,3,'Re: Avatars!','The cool thing is all your comment\'s avatars change when you change your avatar... See I changed to cloud now... :)',1626,'Gamer','2003-09-07 14:25:36');
INSERT INTO forumpost VALUES (1749,258,3,'Re: Avatars!','Yeah, the avatars are completely dynamic.\r
\n\r
\nAbout the comments, I disagree with you - we have a lot of members, and keeping track of who\'s who is difficult. Associating somebody with a visual representation of any kind helps you to remember that person - you come to associate the picture with some sort of reputation. This should work fairly well for comments.\r
\n\r
\nI was actually thinking of adding a feature where it wouldn\'t allow you to use a particular avatar if it was already in use by somebody who is Journeyman+... Not sure yet though.',1,'levik','2003-09-07 15:16:12');
INSERT INTO forumpost VALUES (1750,258,3,'Re: Avatars!','Personally, it would be harder to remember people\'s avatars than people\'s names. I think it would be just memorization for me to remember whose aviatars were what... For example, I don\'t look like a cloud or a dinosaur, and except for when you are groaning that Marbles Bonanza isn\'t going to the top of the queue, you probably don\'t look like your avatar either :)',1626,'Gamer','2003-09-07 15:34:17');
INSERT INTO forumpost VALUES (1751,258,3,'Re: Avatars!','The point though isn\'t for you to look like your avatar. It\'s just to have some visual cue that gets associated with the person - using a different part of the brain than what would be responsible for storing a combination of letters that is your name. \r
\n\r
\nOur brains are wired in such a way that recognizing an graphical icon would be be easier for them than recognizing a name.',1,'levik','2003-09-07 16:58:40');
INSERT INTO forumpost VALUES (1752,258,3,'Re: Avatars!','\"Our brains\"? It has always seemed to me that associating words with a person is easier to me than to associate a graphic with a person... particularly if the graphic doesn\'t make sense with the person.\r
\n\r
\nThis may be because when I refer to a person, I use the screen name rather than the avatar (or something else identifying)...',1626,'Gamer','2003-09-07 17:32:11');
INSERT INTO forumpost VALUES (1753,258,3,'Re: Avatars!','Hmmm... Maybe I am unique in this, but it always seems that in online forums I start recognizing people much quicker by their avatars than by their screen names. Perhaps it\'s because I don\'t have a very good memory for names...\r
\n\r
\nOne thing I am sure of is that a different part of the brain is used for \"memorizing\" something visual like one\'s avatar than for some bit of text or sound. As such, I don\'t think it would hurt if the comments provided an additional queue for people to associate with the poster.',1,'levik','2003-09-07 19:08:42');
INSERT INTO forumpost VALUES (1754,258,3,'Re: Avatars!','I posted this earlier, but for some reason it\'s not showing up -- probably I just forgot to hit the \'Post\' button.\r
\n\r
\nAnyway, I know the difference between an ad banner and the rest of the page..I\'m talking about the flooble forum (there\'s only one - http://forum.flooble.com); when you sign up there are a hundred twenty-something smiley face avatars you can pick from. I was just suggesting that you make those available on Avatarity (and, in turn, on here). It would be an easy, quick way to add a good number of images to the listing (plus there\'s one there that I really like)..\r
\n\r
\nI like the idea of showing the avatar in problem comments, especially since many people don\'t visit the forums or other people\'s info pages, and as levik said, it\'s a good way to visually associate people. Obviously, you would still refer to people by their screen name, but the pictures are nice, and if we\'re going to have them, you can be sure that they\'ll be seen more in problem comments, than anywhere else. The only other place, maybe, is next to the author of a problem that you\'re looking at, as well as the author of the comment you are viewing, but anything more than that might be overkill.\r
\n\r
\nI also like the idea of \'reserving\' icons in use by Journeymen and up (since I fit into that category), because there are not an overwhelming number of us, and I think it will make it easier to recognize the people who are always around and always contributing, or at least prevent any confusion.',1575,'DJ','2003-09-07 23:17:27');
INSERT INTO forumpost VALUES (1755,258,3,'Re: Avatars!','Sorry, DJ. I didn\'t know about the avatars on forum.flooble.com, and since levik seemed not to recognize your reference, I thought it might be the ad banner. My bad.\r
\n\r
\n',153,'TomM','2003-09-08 06:07:57');
INSERT INTO forumpost VALUES (1756,259,7,'another new guy','hey all, im a 21 year old cook. live in Vancouver BC,(best place in the world, IMHO) just kinda stumbled on this site. i love logic and reason puzzles. play lots of strategy games and regularily whip my friends.(i lose too, but not often. trying to stretch my brain after a few too many years of sleep.',3397,'aaron','2003-09-08 13:33:03');
INSERT INTO forumpost VALUES (1757,258,3,'Re: Avatars!','No need to apologize.. I\'m just surprised that levik didn\'t know what I was talking about.',1575,'DJ','2003-09-08 14:08:04');
INSERT INTO forumpost VALUES (1758,258,3,'Re: Avatars!','I think I would like to change my avatar if there were better avatars that were made available, or I just wanted a change of scenery, however I don\'t want to have to bump someone off another avatar or not be permitted to use someone else\'s avatar.\r
\n\r
\nOther than this reason I think that would be good to avoid confusion and association, but I don\'t see any way around my above idea.\r
\n\r
\nIf others want avatars in comments I don\'t care, but I still think they would be more of a distraction. (at least to me)',1626,'Gamer','2003-09-08 15:58:39');
INSERT INTO forumpost VALUES (1759,258,3,'Re: Avatars!','DJ: I set up that forum over a year ago, and the avtars on it came canned with the software. I never really paid much attention to them which is why I initially didn\'t understand you. Yes, I too sometimes get lost in the complexities of all things flooble.\r
\n\r
\nGamer: My idea would only ban someone from switching to an avatar in use by a high ranking member. If you as a high ranking member wanted to switch your avatar to something that\'s already used by a novice, it would not affect anyone (the novice doesn\'t get kicked, but perhaps you get notified that someone else is using the avatar of your choice)',1,'levik','2003-09-08 17:31:09');
INSERT INTO forumpost VALUES (1760,260,3,'Methinks the rate should increase !','How about upping the rate at which problems are posted? This notion that only 12 comes out per week (assuming two/weekday and one/weekend-day) is terribly slow and prevents new people from seeing their problems enter quickly.
\r
\nAt the time of this writing, there are approximately 400 problems in the queue. I understand that most of these are from the same people, but there are at least 25 (probably more) people with various problems (even at queue weight one).
\r
\nEven if half of the remaining problems are not approved, there are still 200 problems (taking more than a month to get out).
\r
\nThanks for your consideration,
\r
\n--- SilverKnight',3172,'SilverKnight','2003-09-08 18:10:49');
INSERT INTO forumpost VALUES (1761,260,3,'Re: Methinks the rate should increase !','I don\'t... Some problems just get brushed aside when they aren\'t on the digest (like Knight\'s tour) and if we increase the rate, people with 9 of the same problem will just put them in 9 different problems instead of just one problem... so the queue will increase this way.\r
\n\r
\nIt also takes time for debating about problems, changing them, and giving them thumbs up. As of now, there are only 3 problems with +3 or more which means only 3 possible problems could go on the site.\r
\n\r
\nAnyway, if you are looking for a submitted problem to go onto the site, look in the chatterbox for the conversation about this.',1626,'Gamer','2003-09-08 18:19:53');
INSERT INTO forumpost VALUES (1762,260,3,'Re: Methinks the rate should increase !','I don\'t understand why someone with 9 of the same problem will put them in 9 different problems.... but even if they did.... the OTHER people\'s problems would jump (I think and hope) in front of the seven problems with queue weights greather than one, thus solving that \"problem\".
\r
\nI\'m guessing that (I don\'t have the privilege yet to know) the reason why only 3 problmes have +3 or more is for two reasons:
\r
\n(1) Not enough people with the permission to give thumbs up, come on regularly to cast a vote, and
\r
\n(2) Those people can see only 10 (rather than, say 30) at a time.
\r
\nSo, how long does something stay in the top 10 without getting pushed?
I\'m not sure I have a good understanding of how exactly this queue thing works... but what if the top 10 all have +1 (and nothing reaches +3)?
\r
\nCheers',3172,'SilverKnight','2003-09-08 18:35:31');
INSERT INTO forumpost VALUES (1763,260,3,'Re: Methinks ... (it can\'t!)','Two a day is plenty; any more and each problem wouldn\'t get the exposure it [usually] deserves. Many people can only get on once a day, for a short time. Really, there\'s no rush. The queue has diminished by about 20% from only a month ago, and as long as the rate of posting and deletion outdoes the rate of submission, we\'re gaining all the time.\r
\n\r
\nWe don\'t need a ton of problems to be approved, waiting to be posted. There are more than plenty active voters, and the problems in the voting queue that aren\'t approved are waiting for changes by the author, or are simply still being debated. 10 problems is enough, also; I think some problems get too much \"pre-live exposure\" as it is. If there were 30 in there, sure, there\'d be more approved, but people with access to the queue would have full solutions weeks before a problem was live on the site.\r
\n\r
\nMuch of the fun of this site for a lot of people, something it seems you\'ve missed, is just putting out ideas and solving a problem collaboratively (not rushing to be the first and only person to post an answer). If problems sit in queue too long, that idea gets killed when someone posts a mile-long solution five minutes after the problem goes live; and if problems were to come any faster, there wouldn\'t be much or any discussion to any of them, as many fewer people would see each problem. Most visitors only ever look at the current latest problem when they come here.\r
\n\r
\nThere are always a few problems with +3 in queue, ready to be posted. If not (something that hasn\'t happened yet), levik can always push a problem manually.\r
\n\r
\n=)',1575,'DJ','2003-09-08 19:12:43');
INSERT INTO forumpost VALUES (1764,260,3,'Methinks... (Discussing is good!)','I would agree with most of what DJ says... You can always comment more on a problem... New ideas you have missed, or new ideas for problems can usually be found to comment on... For example, How many moves would it take Towers of Hanoi with x discs and y poles? Now prove the formula you got. Or even trying to find a simpler way to solve a problem, whether it be \"Know who your friends are\" or \"School shelves\"...\r
\n\r
\nJust talking about the problem (like talking in crypto speech, and coming up with new and fun \"How many letters are in this question\" answers) is usually more fun than knowing the answer.\r
\n\r
\nOnce a problem is gone from \"Latest problem\" it lowers the amount of people who look at it, so more problems means less input.',1626,'Gamer','2003-09-08 20:47:29');
INSERT INTO forumpost VALUES (1765,258,3,'Re: Avatars!','Ok... I see what you mean; I think that would be good to implement.',1626,'Gamer','2003-09-08 20:48:43');
INSERT INTO forumpost VALUES (1766,259,7,'Re: another new guy','Welcome to the site. I hope you enjoy your stay. Do holler if you need anything ;)',1,'levik','2003-09-08 21:21:59');
INSERT INTO forumpost VALUES (1767,260,3,'Re: Methinks the rate should increase !','You should TRY it before you dismiss is as \"more problems means less input\".
\r
\nAnother possibility would be to have more than one \"latest\" problem (perhaps all the problems posted that day) showing up on the front page.... And it could be made more obvious how to get to the newest problems, or perhaps more \"flashy\" so more people will click on it.
\r
\nAs for your \"not rushing to be the first... to post an answer\"... are you suggesting that if I have a solution, I should post only a short answer, not show one way to solve it, and not explain how I came to the solution? Or are you perhaps making reference to my earlier comments?
\r
\nCheers
\r
\nP.S. I\'ve had my first two submitted problems (queue weight = 1) \"stuck\" around 41 for more than a week. I was under the impression that they would move down roughly at a speed corresponding to the speed problems are getting posted from the \"top 10\".... but that doesn\'t seem to be the case. Am I misunderstanding how this works? That is, why might problems not move much, even though problems are being posted?',3172,'SilverKnight','2003-09-08 22:10:05');
INSERT INTO forumpost VALUES (1768,260,3,'Re: Methinks the rate should increase !','Not that I know anything, being that I\'m a newbie, but I think SilverKnight\'s idea of having more, but having them all up just as titles in a \"flashier\" form, might make sense. If I see the titles to todays five puzzles, and lower down to yesterday\'s five puzzles, I\'d might be more inclined to go through them. \r
\n\r
\nAlso, just a question, why two on weekdays and one each on the weekends? Surely people have more time to go through puzzles on weekends, rather than less time. Even if having two on weekends is kept, perhaps there could be three on weekends?',3372,'sam','2003-09-08 22:39:28');
INSERT INTO forumpost VALUES (1769,258,3,'AAAAAAA CHHOOOOOO !!!','I just found out that I\'m allergic to avatars... *sigh*\r
\n\r
\nP.S. I think dynamic loading of one\'s own 64x64 pixel image (checked to make sure that it\'s not bigger than say... 1024 bytes or something) would be really cool. Then one could guarantee a unique avatar (well almost... I suppose someone could copy it and change a pixel or something).',3172,'SilverKnight','2003-09-09 03:01:34');
INSERT INTO forumpost VALUES (1770,260,3,'Re: Methinks the rate should increase !','It\'s simple statistics. The site gets at least 40% less visiotrs on weekends than on weekdays. Therefore, to assure roughly the same \"number of eyeballs\" reach a problem while it\'s the top one, we decrease the rate of posting by a half.\r
\n\r
\nI am not sure why everyone is so anxious to go and see all the new problems right away. This site has an archive of over 650 problems sitting and waiting for you to look at. Now I bet most of them are \"new\" for you. You don\'t have to read their solutions, and nobody would think worse of you for commenting on something a year old (in fact discussions like these sometimes bring old problems back into the limelight).\r
\n\r
\nIf the reason you want the rate upped is only so that you can see YOUR problems on the site faster, consider that most people rarely \"click through\" to the older puzzles. Would you wish your own to become \"old\" after only an hour or so?',1,'levik','2003-09-09 07:46:22');
INSERT INTO forumpost VALUES (1771,258,3,'Re: Avatars!','If you wish to have your own, you can submit it to Avatarity as a \"private\" avatar - then use it on this site.',1,'levik','2003-09-09 07:47:55');
INSERT INTO forumpost VALUES (1772,260,3,'Re: Methinks the rate should increase !','Well... I can speak for only myself regarding the \"old\" problems... but I\'ve gone through almost all of them. If I think I know the answer, I confirm it by verifying it against the posted solution (or perhaps against another\'s answers). I rarely post anything to those \"old\" problems unless I have something new to add (and I generally check all the messages). I still don\'t see the point to show people that \"I solved it too!!!!\". Sometimes, I don\'t know the solution, and sometimes it\'s (IMHO) yet ANOTHER logic problem that we can all work through with a logic square, or some similar tedious (IMHO) problem that I don\'t really wish to trudge through.
\r
\nSo, to address your question... I *would* like to see my problems faster. And I *would* like to see \"new\" problems more often.
\r
\nAnd I\'m sure you\'re right about the statistic that roughly 40% fewer people come on weekends.... And I\'m sure there are those who do not search the archives. But perhaps this site would attract more attention and KEEP more attention if there were more new problems, more often.
\r
\n--- SK',3172,'SilverKnight','2003-09-09 11:08:19');
INSERT INTO forumpost VALUES (1773,139,7,'Re: caio','hi are you there?\r
\n',NULL,'leslie','2003-09-09 14:10:47');
INSERT INTO forumpost VALUES (1774,260,3,'Re: Methinks the rate should increase !','I would disagree with you on the last point... It has kept my attention even when we only had 1 problem per day. (We DID try raising the problems, so I am pretty sure I know what would happen.)\r
\n\r
\nI don\'t understand why less people would come here on weekends as that is where I come here more often.\r
\n\r
\nFlooble is a journey, not a destination... In general, I think a problem won\'t be noticed as much if it appears less. People will just brush aside problems that they would work on otherwise.\r
\n\r
\nI think what DJ means about posting a solution together is this... Working together and using teamwork to solve problems is a good idea.',1626,'Gamer','2003-09-09 15:59:27');
INSERT INTO forumpost VALUES (1775,216,3,'Re: Order of Posting','I don\'t know a scholar\'s experiences, but should a problem be pushed that just appeared in the queue that day? It seems wierd to do something like that.',1626,'Gamer','2003-09-09 17:09:24');
INSERT INTO forumpost VALUES (1776,216,3,'Re: Order of Posting','I thought that it was odd, too...when there are problems that have been sitting approved in queue for a week or better. On the one hand, there is very little exposure to that problem, so all attempts will be \'fresh\' approaches, but on the other hand, those other problems will sit and stagnate even longer. No matter, it was approved that quickly, and there\'s not much point fussing over it now...',1575,'DJ','2003-09-09 17:33:09');
INSERT INTO forumpost VALUES (1777,216,3,'Re: Order of Posting','I am just saying we shouldn\'t do that with many (if any) more problems... :)',1626,'Gamer','2003-09-09 18:20:05');
INSERT INTO forumpost VALUES (1778,260,3,'Re: Methinks the rate should increase !','jeez Gamer.... a sample size of ONE... well... can\'t argue with that.
\r
\nBut seriously... this place has kept MY attention as well... even with the slow problem rate (wow! sample size of TWO!).
\r
\nBut that\'s not what I said. Even if the AVERAGE time spent on a particular problem goes down (perhaps because many people only want to deal with the last one or two), you may get many more people, and much more attention. It\'s only your own prejudice to spend lots of time on one or two problems that leads you to that conclusion. I say this, because certainly there are people who would prefer to see more NEW problems at any given time. (Sample size = one... me... actually TWO since SAM, above, seems to agree :-)
\r
\nProbably, people use this place as a diversion from work, which is why they come during weekdays. And they\'re all out sailing and camping on the weekends.
\r
\nAnd lastly, please tell me how you changed the rate before and what you observed.',3172,'SilverKnight','2003-09-09 21:27:04');
INSERT INTO forumpost VALUES (1779,216,3,'Re: Order of Posting','As levik mentions above, \"I generally DO post the first one that\'s in the queue and eligible (making it Ravi\'s if he has one)\" \r
\n\r
\nbut also modified by levik\'s comment in the Library Forum:\r
\n\r
\n<
\nBecause only one problem goes up per day on the weekends, it should be a moderately interesting one. \r
\n\r
\nI believe that we should try and avoid a situation where two consecutive problems are from the same person or in the same category - the site looks more diverse if there are no \\\"streaks\\\" of similar problems, or problems from one user. \r
\n\r
\nI believe the problem to be pushed should be the highest one in the queue that qualifies under the above. Exceptions can be made for good problems that have hung around the bottom of the queue for a long time. >>\r
\n\r
\nThe posting of Ravi\'s problem, in the top slot in the queue, and with the three previously pushed problems not being either Ravi\'s or in the same category, made Ravi\'s problem the one of choice.\r
\n',1301,'Charlie','2003-09-09 21:47:37');
INSERT INTO forumpost VALUES (1780,216,3,'Re: Order of Posting','Of course it\'s subjective as to how long \"a long time\" is in hanging around the bottom of the queue.',1301,'Charlie','2003-09-09 21:49:45');
INSERT INTO forumpost VALUES (1781,216,3,'Re: Order of Posting','I would personally prefer to try to get them out in the order in which they had received their third thumbs up, or give a priority to some that have already achieved more than just 3 thumbs up. However, such priority is, as mentioned above, an exception.',1301,'Charlie','2003-09-09 21:51:32');
INSERT INTO forumpost VALUES (1782,216,3,'Re: Order of Posting','Yeah, that\'s what I try to generally do, since the order in the queue is the order in which they are submitted, not the order in which they entered the queue (and of course not the order in which they were approved). Alternatively, I try to push problems that have just been sitting in queue for a long time, even if they haven\'t had 3 TU the whole time or even for a long time, so as to minimize the \'pre-exposure\' each problem has before going to the main page.',1575,'DJ','2003-09-09 22:12:56');
INSERT INTO forumpost VALUES (1783,258,3,'Re: Avatars!','cool... you\'re a step ahead of me, then.',3172,'SilverKnight','2003-09-09 23:18:28');
INSERT INTO forumpost VALUES (1784,258,3,'Re: Avatars!','Yup.. that\'s what I did (isn\'t it great?) :-p',1575,'DJ','2003-09-09 23:25:54');
INSERT INTO forumpost VALUES (1785,260,3,'Re: Methinks the rate should increase !','To add to the sample pool...\r
\n\r
\nI\'m one of the 60% \"diversion from work flooblers\" and I spend most of my weekends covered in oil under a car. I usually have a look in the morning when I start to find a problem to keep me amused during the morning and again at lunchtime for the afternoon, so two new problems per day suits me fine. \r
\n\r
\nI find it particularly interesting when the discussion around a problem spawns other problems or when there is more than method of solution. (eg the number square problem that\'s currently live). I agree with previous posts that if the number of problems per day increased that some of this discussion would be lost as people instead looked to solve the next problem rather than looked to expand or put an alternative view on a current problem.\r
\n\r
\nHowever, there are occasions when I find the two per day rate frustrating. For example, when there are riddles or knights & liars type problems that usually take all of 30 secs to solve; or when there are several pure maths (eg calculus) problems that I\'ve no hope of solving. It\'s at these times I wish that the problems were more frequent.\r
\n\r
\nI\'m sure though that this is just a matter of taste and that some of our fellow flooblers find hours of amusement in calculus problems (or find some of the logic based problems tedious). So when the latest problem doesn\'t suit my taste I either look elsewhere or pick a random problem and try to come up with something new for it.\r
\n\r
\nOn balance, I\'d rather have to go elsewhere occasionally for my distractions than lose some of the banter that comes out through problems being \'current\' for longer. There\'s also the inevitable problem that once the current reserve is substantially reduced, then the issue of quantity vs quality arises. From what I\'ve seen on my searches elsewhere many sites promote quantity over quality and there is a lot of dross to filter before reaching a gem.',1183,'fwaff','2003-09-10 05:05:34');
INSERT INTO forumpost VALUES (1786,260,3,'Re: Methinks the rate should increase !','Here\'s awhat I found to hold from my limited experience with running sites.\r
\n\r
\nPeople like to be \"in touch\" with what\'s going on in a community they belong to. That is, if there are new problems appearing, regular visitors will wish to be aware of all of them. If they don\'t feel as though they can keep up, they will get frustrated and leave. Sometimes it\'s not even a fully concious decision - the people are simply no longer \"comfortable\" in a community that they can\'t keep up with. (In this case it would require them to log in 5 times a day, or spend a lot of time in the evening to re-view the posted problems)\r
\n\r
\nI believe that if we have 5 problems posted every day, only a small percentage of people will be able to follow them all - especially given that a large number read us from work (and may have to duck and run whenever the boss approaches).\r
\n\r
\nI know that there are exceptions to every rule, but this is something that I have seen happen in web communities before. ',1,'levik','2003-09-10 07:49:10');
INSERT INTO forumpost VALUES (1787,139,7,'Re: caio','Welcome, \r
\nlots of good logic problems here, but beware some of them are murder.\r
\nLots of dead brutal math stuff as well.\r
\n',2839,'FatBoy','2003-09-10 09:27:26');
INSERT INTO forumpost VALUES (1788,139,7,'Re: caio','Haha fatboy... such violence...\r
\nMy personal opinion is that this is the best collection of puzzles in a public forum on the web. They tend to be more challenging, but I think that\'s more fun than the trivial problems you find everywhere else. So, enjoy the site (there are hundreds of old problems to look at once you go through the ones on the front page), and we\'ll see you around!\r
\n\r
\n=)',1575,'DJ','2003-09-10 10:00:53');
INSERT INTO forumpost VALUES (1789,260,3,'Re: Methinks the rate should increase !','Hmmmm... I must admit... a well worded (and somewhat convincing) argument.\r
\nHow \'bout THREE? :-) (particularly when the first two for that day are tedious/easy problems)',3172,'SilverKnight','2003-09-10 18:37:50');
INSERT INTO forumpost VALUES (1790,260,3,'Re: Methinks the rate should increase !','I don\'t think that should be the case... Usually the second problem of the day SHOULD be harder problems or problems that don\'t just have one solution (like the problem of today)\r
\n\r
\nI agree with levik... I have ditched a few forums because people in there talk TOO much... I don\'t want to spend all my time there or catch up on a zillion posts.',1626,'Gamer','2003-09-10 20:05:09');
INSERT INTO forumpost VALUES (1791,261,4,'Scav game','Hi all. I\'d like to offer you a bit of a sneak peek at my newest venture. \r
\n\r
\nBefore I do so, I\'d like to ask for your help. You see, it\'s not fully done yet, and as such I want your thoughts and comments, but what I don\'t want is for you to tell anyone else about this. (Hence this forum). I want to get any input I can from you guys, then when the game (which it is of sorts) is ready, unleash it on the world :)\r
\n\r
\nNow it\'s a pretty unusual game - more like a scavenger hunt meets a hacking contest. But perhaps I should just give you the link... \r
\n\r
\nhttp://www.flooble.com/scav/ \r
\n\r
\nYou have to register to play, and right now there\'s only seven \"challenges\" with no congratulations after you are done. Let me know how yuo like it - you can post your thoughts here. I know I can count on you not to disclose the solutions. Also, once again, please tell nobody else of this, since I will be sure to make changes based on feedback, and would hate to show an unfinished version to more than the trusted few.\r
\n\r
\nThanks in advance for your help, and I am eagerly waiting for comments.\r
\n',1,'levik','2003-09-10 20:15:53');
INSERT INTO forumpost VALUES (1792,261,4,'Re: Scav game','Are we allowed to talk about disclosed solutions here? I don\'t know what the \"rules\" are.\r
\n\r
\nI think it looks cool, although I am not sure I like the concept of a timer... I always get nervous when I am timed! :)\r
\n\r
\nWhy is it called a scavenger game... does it all have to do with the idea of the first solution?',1626,'Gamer','2003-09-10 22:21:30');
INSERT INTO forumpost VALUES (1793,261,4,'Re: Scav game','You\'re only timed so you can compare how long it took you versus others. Also maybe so I can see which challenges are easier than others.\r
\n\r
\nAs far as scavenging, it\'s because you are looking for clues that were dropped by me, the game\'s creator.',1,'levik','2003-09-10 22:45:34');
INSERT INTO forumpost VALUES (1794,261,4,'Re: Scav game','And of course I would ask you not to disclose the solutions\' particulars - though discussing their difficulty is welcome.',1,'levik','2003-09-10 22:46:36');
INSERT INTO forumpost VALUES (1795,260,3,'Re: Methinks the rate should increase !','That\'s a good point.. I already come here like I have OCD, and it takes a bit of time to keep up with things even at the current \'slow\' rate of posting. Any more and I might have to drop out of school to keep pace..',1575,'DJ','2003-09-10 23:01:16');
INSERT INTO forumpost VALUES (1796,261,4,'Re: Scav game','Pretty cool, although doing these in classes, my times have suffered quite a bit. It does seem, though that the timings are off; one of mine was 45 minutes, I think I was doing something else for ten or fifteen.\r
\nI put \'easter eggs\' like this into my weblog, but after a year and a half, I think only two have ever been found, even when I tell people to look for them...\r
\n\r
\nStuck on number 8 right now.\r
\n\r
\n=)',1575,'DJ','2003-09-11 13:26:07');
INSERT INTO forumpost VALUES (1797,262,4,'Top 10','I have been seeing problems bounce in and out of the 10 problems eligible to be voted on in the queue. I assume this is from recalculating queue weights regularly. To prevent this in the future, I recommend when recalculating the queue, the \"top 10\" are frozen in their places. When a problem leaves the top 10 (by being posted or deleted) then problem #11 can be moved in.',1920,'Brian Smith','2003-09-11 14:46:00');
INSERT INTO forumpost VALUES (1798,262,4,'Re: Top 10','While I agree that this would be a good idea, I have to be honest that I am not quite certain as to the best way to implement it with current setup - and I do not think that this is worth making database changes over.\r
\n\r
\n',1,'levik','2003-09-11 14:50:15');
INSERT INTO forumpost VALUES (1799,262,4,'Re: Top 10','If the queue weights could be recalculated as soon as a problem is either posted or rejected, rather than waiting until midnight, this would not happen. I don\'t know how feasible that is, but it presumably would not require database changes.',1301,'Charlie','2003-09-11 14:55:47');
INSERT INTO forumpost VALUES (1800,262,4,'Re: Top 10','Perhaps two queues would solve the problem. One queue contains the 10 problems being debated and the other contains all the pending problems. When the top 10 queue needs a new problem, it can just grab one from the pending problems queue.',1920,'Brian Smith','2003-09-11 14:57:16');
INSERT INTO forumpost VALUES (1801,261,4,'Re: Scav game','So any comments? Changes? \r
\n\r
\nAre any of them too easy? Too difficult?',1,'levik','2003-09-11 17:10:15');
INSERT INTO forumpost VALUES (1802,262,4,'Re: Top 10','I know this has been a problem in the past forums, and I would like to see this happen, but I didn\'t know how to do it.',1626,'Gamer','2003-09-11 17:22:56');
INSERT INTO forumpost VALUES (1803,261,4,'Re: Scav game','I don\'t know about number 4... I don\'t know javascript yet, and thus can\'t proceed.',1626,'Gamer','2003-09-11 17:30:31');
INSERT INTO forumpost VALUES (1804,261,4,'Re: Scav game','Can you make it so the server remembers what challenges I completed? I don\'t want to have to remember websites or start back at 1.\r
\n',1626,'Gamer','2003-09-11 17:31:05');
INSERT INTO forumpost VALUES (1805,261,4,'Re: Scav game','Ditto that, some kind of interface that remembers what the last one you completed was. Also, maybe even a system where, each \'challenge page\' opens in a new browser window, and you type your \'answer\' into a little box on the main page, maybe. Typing wrong things into the address bar and having to backtrack is kind of a pain.\r
\n\r
\nFor the two problems I needed to use an image editor for, ms paint worked much better than photoshop or some more complicated editing program would have been, in my opinion.\r
\n\r
\nThe only one I have trouble with, not that it was even hard, but #5, when you put the one thing into the address, it opens the file in dreamweaver or frontpage or whatever webpage editor is installed, and getting the \'code\' from there is easy, just opening the program is a little bothersome when you\'re doing something else (say, working in .NET on a c++ project)..\r
\n\r
\nI\'m still on #8, and converting to binary or using a \'tricky code\' methodology (as the directory name would suggest) hasn\'t gotten me anywhere. The others took only a minute or two, so this is a grand step harder, at least to me at first glance..',1575,'DJ','2003-09-11 18:59:04');
INSERT INTO forumpost VALUES (1806,261,4,'Re: Scav game','Hmmmm... Are you telling me you didn\'t even hit any wrong URLs until #8?\r
\n\r
\nI kinda thought this trail of challenges would be a bit more difficult than that...\r
\n\r
\nBut do you think a game like this is fun? (Assuming I make it go to where you left off from the front page)',1,'levik','2003-09-11 20:55:52');
INSERT INTO forumpost VALUES (1807,261,4,'Re: Scav game','No, I meant that I hit several wrong URLs for most of them, and it\'d be a little easier to just type it into a box and have it tell me if I\'m right or not. Also, I didn\'t think they were too easy, I just meant that #8 is very much harder by comparison. And yes, I think it\'s really fun (too fun.. I was doing it instead of schoolwork all day), haha.\r
\n\r
\nI put little \'easter eggs\' like this into my weblog, but in a year and a half I think only two have ever been found, even when I tell people to look for them..\r
\n\r
\n=)',1575,'DJ','2003-09-11 21:10:41');
INSERT INTO forumpost VALUES (1808,262,4,'Re: Top 10','I can\'t think of any \'neat\' ways to do this, but with the current setup, I have an idea that I think would work. When a problem first enters the \'top 10\' queue, just change its time/datestamp to the current date, one year ago. That way, all the problems would be listed in the order that they appeared in the queue (assuming that we are not backlogged by more than a year), and when queue weights are recalculated every night, the current problems in the active voting queue would still be the oldest QW1 problems, and remain in the queue. It\'s a little sloppy, but it could work..',1575,'DJ','2003-09-11 21:15:26');
INSERT INTO forumpost VALUES (1809,261,4,'Re: Scav game','I think the first few were useful because it\'s like \"what now?\"\r
\n\r
\nI still need to know if I need to learn partial java to continue on number 4... I don\'t know what the ?tra1ler or whatever does.',1626,'Gamer','2003-09-11 22:04:49');
INSERT INTO forumpost VALUES (1810,261,4,'Re: Scav game','you just need to know how the source of a script is linked to. . just like an image. i don\'t think that gives away too much..',1575,'DJ','2003-09-11 23:10:08');
INSERT INTO forumpost VALUES (1811,261,4,'Re: Scav game','Yeah - you don\'t need to know the actual JS code, just how it can be included into a page.',1,'levik','2003-09-12 00:57:54');
INSERT INTO forumpost VALUES (1812,176,5,'Re: Problem flooding revisited','All... this problem flooding is ridiculously frustrating to new users. In the last two weeks, I think my first submitted problem (and it\'s a good one) has gone down 2 or three in the queue order. It\'s still at 40.\r
\n\r
\nYou MUST be kidding me.\r
\n\r
\nI understand the desire to reward people who submit a lot of problems, but because of the queue weighting system, it takes only 5-7 people who submit a lot of problems (and I can see that there are more people than that by analysis of the posted problems/submitters) to put a virtual stranglehold on newer members\' problems making it to the top 10 to be voted on. (D\'ya like my dangling preposition?)\r
\n\r
\nWith the current backlog on some of these users\' submissions, almost everytime a problem is pushed live, another problem from QUEUE WEIGHT TWO comes in to take its place, of course jumping in front of most of the other QUEUE WEIGHT ONEs.\r
\n\r
\nAnyway, I want to make clear my level of frustration here, and impress upon Levik the need to come up with a method of getting these problems through the queue more quickly.\r
\n\r
\nI would ALSO like to impress upon all you Journeymen the need to cull some of the chafe out. I am certainly not able to look at the queue (but I hope to in a YEAR OR SO!!!!), because I haven\'t had the requisite number of problems posted, but from the discussion here, it seems that some of you are reluctant to give a TD to poor problems. Get over it! Let\'s clear the queue, and let the cream come to the top.\r
\n\r
\nI *am* glad to see in the couple of weeks, fewer of yet ANOTHER liars and knights problem, or the same old \"solve by creating a logic matrix\"--matching up rows and columns, or crypto problems that seem to continuously get below 3 ratings....\r
\n\r
\nI\'d like to encourage you to consider giving TU *ONLY* to those problems that you think will get 4-5 ratings... (remember 1-3 isn\'t particularly good).\r
\n\r
\nWell, thanks for taking the time to read this, and allowing me to vent.\r
\n\r
\n --- SK',3172,'SilverKnight','2003-09-12 09:26:30');
INSERT INTO forumpost VALUES (1813,176,5,'Re: Problem flooding revisited','I agree and have said in the past that we need to be more discriminate in the problems that we let through to the site, and the only way to clear the queue with a fixed rate of posting is to TD more problems, and people are often reluctant to give a mediocre problem a vote down.\r
\nHowever, I think you have crossed the line and are being very much overcritical. Fine, you don\'t like L&K problems, or deductive logic problems, or cryptography problems -- but lots of people do.\r
\n\r
\nAs far as the queue backlog, Ravi still has problems coming into the queue from February, and the rest of the active voting queue is composed of problems submitted in June and July. It\'s great that you\'ve submitted problems, and I\'m sure they\'re good ones, but above all you need to learn the same patience that everyone else has. It\'s not a stranglehold on new members; people that are really interested and will stick around for a few months will see their problems (pending approval) make it onto the site.\r
\n\r
\nI\'m sure that once you\'ve been around for more than three weeks, if your problems are as good as you suggest, you\'ll become privy to the voting queue and company car and all the wonderful benifits of being a flooble journeyman. In the meantime, please try to realize that the purpose of the site is to post interesting, challenging problems for a lot of people, and while we don\'t want to go the way of other sites in promoting quantity over quality and ridiculously easy problems, we want a variety of problem types and difficulties. Generally, the \'regular\' users are the ones who vote on each problem, it seems, and the simpler ones also seem to generally recieve a lower score. That doesn\'t necessarily mean that they are bad problems. Also, a good problem can seem ridiculously easy once the solution is known, but that doesn\'t mean that it wasn\'t reasonably challenging to begin with. Just some things to consider as you [patiently] await voting on your problems...',1575,'DJ','2003-09-12 12:22:24');
INSERT INTO forumpost VALUES (1814,262,4,'Re: Top 10','On second thought, that in general may not be a favorable solution anyway. While fewer problems would get the \'pre-exposure\' of being in the voting queue for a long time, there would only be one or two new problems in the active queue a day, if none are deleted. That means, if a number of problems are pending and being debated and being edited, then we may see the situation arise where none of the problems have been approved. The current situation, while being a side effect of the nightly queue wieght recalculations, actually allows us to continue to move problems through voting and onto the site (or into the dumpster) while debating others.',1575,'DJ','2003-09-12 12:30:04');
INSERT INTO forumpost VALUES (1815,176,5,'Re: Problem flooding revisited','Well, thanks for your comment, DJ. I hope that others will take the time to also comment.\r
\n\r
\nBut to reply to your note:\r
\n\"It\'s not a stranglehold on new members\"\r
\n -- and --\r
\n\"people [who] stick around for a few months will see their problems...\"\r
\nare mutually exclusive.\r
\n\r
\nThat one MUST wait significant fractions of years to see their problems come through *is* a stranglehold. What\'s more... if people \"learn\" from this, to post massive amounts of problems, the problem will only continue to get worse.\r
\n\r
\nI am admittedly an impatient person. (And that\'s as much out of me as you\'re getting! ;-). It is (IMHO) absurd to have problems dating from February jumping in front of newer members first postings. What *is* the point of this queue weight if it can be circumvented by mass postings, as this is? Really, the only difference here is that as long as we have at least 5 different submitters with at least 2 problems each, then a person can have at most 2 people in the \"top 10\" at any given time... apart from that... this is basically a FIFO queue. In other words, the \"reward\" for early submission of problems is too great.\r
\n\r
\n(And, btw, the notion of limiting an individuals problem submissions to 2/day, does not really address this problem, as they could submit 120 in two months, and then a new member is still following those 120. And what\'s more... why would you want to discourage people from posting problems?)\r
\n\r
\n--- SK',3172,'SilverKnight','2003-09-12 12:45:38');
INSERT INTO forumpost VALUES (1816,176,5,'Re: Problem flooding revisited','It\'s easy to complain without having a solution. What would you suggest be done? I haven\'t taken mass submission to the extreme that Ravi has, but I have a number of problems waiting, each of which I honestly think is a fairly good one. Are you suggesting that only the first two problems I ever submitted should have QW1, and once those are posted, the weights should never be recalculated? That\'s the only way for what you suggest should happen could happen, that a new user could come in and submit a problem that magically jumps to the front of the queue in front of problems that people who have been here for months submitted months ago. And, once your first two problems have been laid to rest, I think you\'ll agree that that\'s not exactly the best way to go either.',1575,'DJ','2003-09-12 12:53:29');
INSERT INTO forumpost VALUES (1817,176,5,'Re: Problem flooding revisited','I do agree DJ. And it is fair that you call me on \"just complaining\" and not giving a solution.... But, to be sure, I have \"petitioned\" already and made a suggestion or two. If you (and others) think it is appropriate, I will happily post to a public forum, some possibilities that might solve this problem.\r
\n\r
\nAdditionally, I agree with you about the latter not being the best way to go either. As Levik has mentioned to me (and I infer from your comments), their SHOULD be reward for early submission as well as quality of the problem.\r
\n\r
\n--- SK',3172,'SilverKnight','2003-09-12 12:59:22');
INSERT INTO forumpost VALUES (1818,176,5,'Re: Problem flooding revisited','I, for one, like L&K and deductive reasoning and crypto and stupid riddles for that matter. As I\'ve already stated elsewhere I especially like those \"who is in the green house?\" grid problems that seem to be so loathed by the kids who sit at the cool table.\r
\nFor the record I have been waiting ( I believe longer than SK) for the posting on my first three problems. They are not great massive mindblowing mots of mathematical mastery but they are cute and amusing (like me in my wife\'s estimation) and I made them up myself rather than cribbing them from somewhere else. That being said, I have a message for any scholars reading. If you find the fatboy\'s offerings lame, please do not hesitate to vote them down. I will not be offended (well, maybe a little, but not so much it\'ll show). I\'d rather have everything I ever submit turned down than lower the quality level of the site.\r
\nBUT, dear scholars, please do not be brow beaten into restricting any particular types of problems. Yes, a site made up entirly of word melds would probably drive some folks away, but don\'t turn the site into some sort of number theory text book either.\r
\nI LIKE the site as it is. I think you\'ve got a good mix. Keep up the good work.\r
\n\r
\nPS I second DJ\'s thought about scholars commenting right away. Give us regular folk a shot, huh? Thanks ',2839,'FatBoy','2003-09-12 13:18:28');
INSERT INTO forumpost VALUES (1819,176,5,'Re: Problem flooding revisited','I assume you and DJ are implying that a Scholar has been thinking about the problem in advance, before others who haven\'t seen the problem, and therefore is \"using an unfair advantage\".\r
\n\r
\nIf my assumption is wrong, that why would a solver\'s being a scholar have anything to do with commenting right away, or at all?\r
\n\r
\nWhat\'s more... FatBoy, you seem to be posting all over the site even if there ARE solutions already posted (and I\'m sure you are welcome to do so). So again, what is the issue here?',3172,'SilverKnight','2003-09-12 13:44:22');
INSERT INTO forumpost VALUES (1820,176,5,'Re: Problem flooding revisited','One thought that I have had regarding the turnover of top-10 spots is the idea of not changing any QW 2 to QW 1 until all the QW 1\'s were depleted (that is until there are only 9 QW 1). I don\'t know the statistics of how many submitters there are (and so how many QW 1\'s there are at any given time), and so I don\'t know if this would unduly harm the heavy-hitting posters. If there are dozens of QW 1\'s to get through, it could be a long time between pairs of offerings from the top few submitters, with resulting needlessly long waits for them. But if there are only a few QW1\'s then it might not be onerous, especially if some turn out to be easily thumbed down.\r
\n\r
\nRegarding the early solution post, I misread the time since posting. I\'ll have to be more careful, especially on fridays when levik sleeps in for a while.',1301,'Charlie','2003-09-12 15:35:00');
INSERT INTO forumpost VALUES (1821,176,5,'Re: Problem flooding revisited','Charlie, that\'s actually very similar to one suggestion I made directly to Levik (via petition). And the drawback is exactly what you brought up... that pairings from the same submitters would necessarily wait for those introduced by seldom-submitting-users.\r
\n\r
\nI bet if we posted this issue (with some useful constraints) on Flooble as a problem.... we\'d get some pretty good ideas! :-)',3172,'SilverKnight','2003-09-12 16:02:16');
INSERT INTO forumpost VALUES (1822,176,5,'Re: Problem flooding revisited','I think your scholar idea is much of the same idea as the \"long feet make you smarter\" Better solvers are more likely to stay with the site and eventually become journeymen (and maybe even scholars)\r
\n\r
\nI think it\'s hard to weed out problems, because many of the problems we see ARE good... there aren\'t too many that should be weeded out.\r
\n\r
\nMy solution to the \"problem submitted\" thing is just to make it so that a user can only submit one problem a day. This would disperse the problems, and also make it so that some people *cough* can\'t post lots of problems in one day.\r
\n\r
\nI really think that the queue position needs to be more \"accurate\", but I don\'t know a solution so I can\'t complain too much .',1626,'Gamer','2003-09-12 16:10:09');
INSERT INTO forumpost VALUES (1823,176,5,'Re: Problem flooding revisited','I believe that I have just as good problems as anyone else, so I am unsure if my problems (which were submitted well before some new person\'s) should come after somebody else\'s whose problems were submitted after mine.',1626,'Gamer','2003-09-12 16:11:58');
INSERT INTO forumpost VALUES (1824,176,5,'Re: Problem flooding revisited','Gamer,\r
\n\r
\nI think that your suggestion of \"more accurate\" description of queue position would go a long way to remove misunderstandings. Unfortunately, given the current workings of the system (at least as I understand them), it is indeterminate where exactly your problem lies. (In other words, it sort of depends on which problems that people post and discard in the future, and can\'t be uniquely determined at any given time.) So an estimate would have to continue to be calculated.\r
\n\r
\nAs for you likening the \"scholar idea\" to the \"long feet make you smarter\".... what scholar idea are you talking about? Are you advocating that scholars should be able to freely post to problems?\r
\n\r
\n--- SK',3172,'SilverKnight','2003-09-12 16:58:05');
INSERT INTO forumpost VALUES (1825,176,5,'Re: Problem flooding revisited','I think you were talking about scholars solving problems while they were still in the queue?\r
\n\r
\nMany scholars don\'t even figure out the problem until it appears on the site, as a way to be fair to others. Anyone might be able to see a sequence and after little solving come up with the answer.\r
\n',1626,'Gamer','2003-09-12 17:40:13');
INSERT INTO forumpost VALUES (1826,176,5,'Re: Problem flooding revisited','I think you are confusing comments that DJ and FatBoy made with comments that I made.\r
\n\r
\nCharlie solved this problem earlier today very quickly.\r
\n\r
\nI commended him on it. But DJ and FatBoy criticized his answering so quickly. I was backing up a scholar\'s right to answer quickly. And I agree with your analysis that scholars are better problem solvers because they have larger feet.\r
\n\r
\n--- SK',3172,'SilverKnight','2003-09-12 17:54:56');
INSERT INTO forumpost VALUES (1827,176,5,'Re: Problem flooding revisited','Oh, then sorry! I meant \"You all...\" not you personally! :) I think Charlie\'s ability to see things like that is great... I personally was baffled by it, which is why I wondered about 5/5 but didn\'t question it.',1626,'Gamer','2003-09-12 19:20:45');
INSERT INTO forumpost VALUES (1828,263,5,'Retired problem types','I found a few \"tricks\" problems that I submitted, but with the new queue \"better problems\" idea, I don\'t know if trick problems are good to submit anymore mainly because putting a puzzle in \"tricks\" usually makes it much easier to solve.\r
\n\r
\n(Also, did we decide what to do with many concept duplicates, like word meld for instance.)',1626,'Gamer','2003-09-12 19:25:10');
INSERT INTO forumpost VALUES (1829,176,5,'Re: Problem flooding revisited','Man - this is a great discussion we have here (brough back from inactivity)\r
\n\r
\nLet me weigh in on some things.\r
\n\r
\n1. The queue mechanism currently offers a \"benefit\" for early submission. This benefit is lessened by the QW mechanism, but is not eliminated. Nor should it be. It has been suggested on a few occasions that to encourage new posters, their problems should be given top priority (even to the extreme of placing a person\'s first problem onto the head of the queue immediately). I disagree with such suggestions for the reason that statistically, people\'s first problems are not the best submissions we get on the site. Once a person gets posting priviliges (by becoming a Student) they are often so eager to submit that they do not bother to dupe check their problem, or figure out if it belongs on the site at all. Those who have not had access to the queue would be surprised to see the kinds of submissions we sometimes get - from ridiculously easy arithmetics problems to riddles that totally do not work once put down on \"paper\".\r
\n\r
\nI find that statistically (no offense to SilverKnight whose problems I\'m sure are very good) the more a person has been submitting to the site, the better suited their problems are for posting. Of course exceptions to these occur at both ends of the spectrum.\r
\n\r
\n2. The purpose of the site is not to see your problem on the front page. It is to serve as a place to come in order to solve interesting, brain-stimulating puzzles. I believe that the site as it is now is serving this purpose really well, to great credit of everyone who has ever submitted a problem here, as well as those who make sure that these problems are up to par.\r
\n\r
\nI know that seeing your problem on the front page is more satisfying than seeing somebody else\'s - especially if it\'s an interesting and thought provoking one. However, this is not the site\'s primary goal, and while it may be frustrating to have to wait two to three months to have your problems show up, I believe that it\'s worth it to maintain the great quality of the material this site is seeing.\r
\n\r
\n3. Journeymen and Scholars get to see problems before anyone else. They are always asked to not try too hard to solve a problem before it going live, since usually just seeing it is enough to determine whether if fits the site well. However, some problems are really easy, and others are just too darn interesting to hold off on.\r
\n\r
\nI have full confidence, that people who have reached these ranks on the site know better than to tak e advantage of them - especially since they recognize more than anyone else that this is not a competition to show yourself in the best light. As such, if any Journeyman or Scholar posts a solution to the site shortly after a problem goes \"live\", I fully trust that they were able to solve the problem on their own after it having been posted. (In particular Charlie\'s ability to solve even the most difficult problems quickly and correctly has been well demonstrated even before he reached the Journeyman rank.)\r
\n\r
\n4. This site has over 650 problems as of right now. Most of the great classics that people tell each other at parties have been submitted in the early days - and it\'s a pitty that more people do not go browsing the archives for them. I believe that commenting on them (be it to post your solution, or just correct someone else\'s) is great since it brings them into the visible list of puzzles with new comments, and thus allows newer members to experience them perhaps for the first time. Much like this thread surfaced after 3 months of inactivity, I believe re-visiting old problems to be healthy for this site (also keeps the number of dupes down, freeing the queue for more new problems to come through quickly).\r
\n\r
\nWell - that looks like it, sorry for the long rant :) - And thanks for caring enough to read this whole thread :) ',1,'levik','2003-09-13 16:08:18');
INSERT INTO forumpost VALUES (1830,176,5,'Re: Problem flooding revisited','I was enlightened by Levik\'s above reminder on the purpose of this site, and how we are doing on meeting it. Given his arguments, I am less inclined to mess with the current system, but I would like to make a suggestion I think others have made before: What if puzzle submitters had only one QW1 puzzle each, instead of two? \r
\n\r
\nThis would ensure that multiple submissions from a single author (such as myself) would be more spread out, as only one would appear in the top-ten queue at a time. I\'m sure I don\'t see all the ramifications of making this change, but it seems like an improvement to me.',1567,'Bryan','2003-09-14 00:06:43');
INSERT INTO forumpost VALUES (1831,176,5,'Re: Problem flooding revisited','I was actually thinking of doing this same thing lately. Anyone see any issues with it? This would be the second time we mess with QW since its introduction... I don\'t reember any adverse effects from when we switched it from 3 per user to 2, but if anyone does, please speak up...',1,'levik','2003-09-14 02:53:07');
INSERT INTO forumpost VALUES (1832,176,5,'Re: Problem flooding revisited','First, special thanks for the consideration that Levik showed to the quality of my first few submitted problems.... Levik OBVIOUSLY took a sneak peak and was impressed by the underlying creativity. :-) Okay... enough silliness.\r
\n__________________\r
\n\r
\nYes, I see an issue with it. Because... ALL this does... is change the required number of mass \"problem polluters\" to 10, from 5.\r
\n\r
\nActually... the term polluters is probably too strong. But it does not change the issue at hand. Levik wrote \"This benefit is lessened by the QW mechanism, but is not eliminated.\"\r
\n\r
\nWell, this is a true statement. But I would like to make clear that this benefit is only barely modified by the QW mechanism. Under the current system if the same 5 people (and there are more than that number of \"big submitters\") push a lot into the queue, they will ALL remain in the top 10... until the first one of them has problems run out (pushed or rejected). This is true with or without the QW system. So, I want to make clear that the QW system really does very little in terms of helping newer members\' problems get posted earlier.\r
\n\r
\nThe switch from 3 to 2 was before my time, but if my analysis holds, it really did very little.... it would have changed the minimum number of submitters in the top 10 from 3.3 (really 4) to 5. Now, if you change the number of problems for each user in the top 10 from 2 to 1, you\'ll be changing the minimum number of submitters in the top 10 from 5 to 10. And that\'s about it.\r
\n\r
\nSo, yes, I think that would be an improvement. But again, it doesn\'t really change (or fix) the issue.\r
\n\r
\nNow, with all that being said.... and with more insight from having read (and posted) many messages regarding this subject, particularly those from Levik... I am convinced that this issue is not considered a fault or problem of the system. And I think I understand that perspective.\r
\n\r
\nSo, unless it is somehow considered bad that older problems almost necessarily are in the top 10 before newer ones get there no matter how many are submitted by one person, then the underlying system should not change significantly.\r
\n_________________\r
\n\r
\nWow! That\'s a long one... \"What does it boil down to?\" you may ask....\r
\n\r
\nMy vote is for changing the max problems for a user in QW1 to one, and that\'s all.\r
\n\r
\nCheers!\r
\n\r
\n --- SK',3172,'SilverKnight','2003-09-14 03:31:43');
INSERT INTO forumpost VALUES (1833,176,5,'Re: Problem flooding revisited','Silver Knight--\r
\n\r
\nThere are two conditions affecting your analysis for which you are assuming the worst case (in terms of a non-mass-submitter getting through the queue fairly quickly), while the truth is that while not at the best case positions, these conditions are much better than your assumptions.\r
\n\r
\nFirst, those journeymen and scholars with the hacking abilities to check it out have assured us that there are only five or six über-submitters, which means that once levik reduces QW1 to one question per submitter, there are still six or seven \"top ten\" spots for those with less submissions. (Because of QW re-calc-ing, there are usually 12 or thirteen problems which have been exposed in the \"top ten\" and recieved comments and/or votes.)\r
\n\r
\nSecond, even most of the über-submitters did not submit all of their problems at the same time. This means that there may well come a time that their oldest problem is newer than enough other QW1 problems that it does not make the \"top ten\" for a few days, or possibly even for a week or more. (Granted it\'s not likely it will stay out of the running that long, but it does have to face the same competition that your problem submitted on the same day does.',153,'TomM','2003-09-14 10:18:23');
INSERT INTO forumpost VALUES (1834,176,5,'Re: Problem flooding revisited','I think the QW 1 problem thing would be a good idea. I don\'t think there are more than 4 or 5 major contributors. I think that would \"allow\" more newcomers to submit their problems, naturally rather than by admin power because most of the queue now is made up by \"major contributors\". Plus, problems from a particular creator are spaced out anyway. :)\r
\n\r
\nAlthough I submit problems in spurts at a time, I don\'t think many others do, and I have seen what TomM describes in the queue.',1626,'Gamer','2003-09-14 12:33:03');
INSERT INTO forumpost VALUES (1835,176,5,'Re: Problem flooding revisited','TomM,\r
\n\r
\nWith all due respect, I addressed both of your points earlier.\r
\n\r
\nFirst, I am happy to hear that there are only 5 or 6 über-submitters. But all this means is that the \"system\" works PROVIDED we are fortunate enough to continue to have the number of über-submitters stay below 10 (or 11 or 12 with the re-calculating). If this site should, unfortunately ;-) , get popular enough to attract a few extra über-submitters, then this issue returns. (Note that I didn\'t use the term problem.)\r
\n\r
\nAnd second, the notion of an über-submitter\'s problems being older than a newbie\'s submissions remains with or without QW (as I mentioned in a previous posting).\r
\n___________________\r
\n\r
\nSo, again, with respect to the two conditions affecting [my] analysis for which [I am] assuming the worst case, the \"worst case\" (as you put it), for the first condition, WILL occur eventually, so we are just postponing dealing with it (if indeed we wish to deal with it).\r
\n\r
\nAnd your second condition has almost nothing to do with QW.',3172,'SilverKnight','2003-09-14 17:20:02');
INSERT INTO forumpost VALUES (1836,80,7,'Re: Hello, First time here','Kenny, welcome I am new here too. Can you plese help me with a problem\r
\n',3461,'cassie','2003-09-14 18:11:22');
INSERT INTO forumpost VALUES (1837,80,7,'Re: Hello, First time here','the problem is to get gas heat and water to all 3 houses without crossing lines. My teacher said the clue isthe think #-D, and use the bak of the paper\r
\n',3461,'cassie','2003-09-14 18:14:07');
INSERT INTO forumpost VALUES (1838,80,7,'Re: Hello, First time here','I mean think 3-D not #-d',3461,'cassie','2003-09-14 18:15:02');
INSERT INTO forumpost VALUES (1839,80,7,'Re: Hello, First time here','k, do you know the answer',3461,'cassie','2003-09-14 18:15:48');
INSERT INTO forumpost VALUES (1840,80,7,'Re: Hello, First time here','ok bye',3461,'cassie','2003-09-14 18:16:29');
INSERT INTO forumpost VALUES (1841,80,7,'Re: Hello, First time here','cassie, the solution is not too hard...\r
\n\r
\nBasically you go from the gas straight to house number 1, then you go from heat to number 1, and then you go from water to number 1. Then you draw a line and sorta curve it around from gas to house number 2 and cycle number 3 from water just barely by heat to house number 3. Once you finish that line, just draw from water counterclockwise around gas to house number 2. Now, at this point you\'d WANT to go straight from heat to house number 3, but clearly you can\'t. So, draw a line from gas parallel to the previous line, but perpendicular to the first line. You\'ll notice that if you juxtapose the two lines, the lane between them becomes apparent And of course the remaining two lines to be drawn are relatively obvious, and they are left as an exercise to the reader.\r
\n\r
\n--- SK',3172,'SilverKnight','2003-09-14 23:06:10');
INSERT INTO forumpost VALUES (1842,261,4,'Re: Scav game','Levik, do not be led astray by those who are saying this is an easy one. I\'ve spent several minutes on the first page and can get absolutely nowhere. There may be an issue of internet illiteracy (close to half the total time ive spent on the internet, in my entire life, has been spent on your site), or some other brain block, but i did put in a solid effort to no avail.',775,'Cory Taylor','2003-09-15 12:11:24');
INSERT INTO forumpost VALUES (1843,176,5,'Re: Problem flooding revisited','I don\'t know what constitutes a so-called \"über-submitter,\" but there is one person with more than 100 pending problems, only three with more than 50, and only four with more than 30 (cumulatively). The simple fact of the matter is, the problems in the current voting queue, from 7 or 8 different authors, were submitted months ago.\r
\n\r
\nAlso, when a problem from a particular user is held up in queue, either due to a need for editing, disagreement in the voting, questions about its content/solvability, or simply because it is a \'morning,\' \'evening,\' or \'weekend\' problem, oftentimes a second problem from the same user is able to bypass the \'stuck\' problem. If only one problem per user is allowed into the active queue, then that person\'s problems would be pretty much put on hold, and I don\'t in all fairness think that a single problem being debated should be enough to stop them altogether.\r
\n',1575,'DJ','2003-09-15 12:58:00');
INSERT INTO forumpost VALUES (1844,176,5,'Re: Problem flooding revisited','DJ,\r
\n\r
\nThose are good points.\r
\n\r
\nAccording to your description then, even when several users gradually (as opposed to all at once) submit problems... one or two per week.... you can see that they can easily mass a backlog of 50+ problems. It might get worse as the site becomes more popular. And perhaps... that\'s okay.\r
\n\r
\nOne partial suggestion to address the point you make, is to change the \"order by\" from submission date to some other number (let\'s call it SW, submission weight). Perhaps the submission date can strongly influence the initial SW, and then, for example, if a paricular problem gets held up for one of various reasons, one can simply do a +10 (or whatever is appropriate), to slide it a little away from the front of the list, thereby allowing other problems (even by the same author) to slide down.\r
\n\r
\nAnd perhaps the SW could be influenced by the number of other pending problems the user has, etc.\r
\n\r
\n--- SK',3172,'SilverKnight','2003-09-15 13:27:27');
INSERT INTO forumpost VALUES (1845,261,4,'Re: Scav game','Thanks, Cory :)\r
\n\r
\nThe game does require you to have some knowelege of how the Web works - that\'s the fun of it - I wanted to make a puzzle for the web-literate.\r
\n\r
\nFor the first challenge, I should say that the source of the answer is not immediately visible...',1,'levik','2003-09-15 16:06:52');
INSERT INTO forumpost VALUES (1846,176,5,'Re: Problem flooding revisited','I modified the statictical screen for the site so we can now see the top 10 queue placeholders.\r
\n\r
\nHave fun with the full disclosure. (I lament the loss of page views that people have generated in the past jumping from one user info screen to another to obtain this same information. :)',1,'levik','2003-09-15 16:11:30');
INSERT INTO forumpost VALUES (1847,80,7,'Re: Hello, First time here','You aren\'t really supposed to answer solutions in the questions as it encourages them to break the rules and post in the forum.',1626,'Gamer','2003-09-15 19:44:03');
INSERT INTO forumpost VALUES (1848,80,7,'Re: Hello, First time here','The problem has been proven impossible to solve in a single plane, and honestly, SK, I don\'t understand what you\'re trying to say.\r
\n \r
\nIf you think three dimensionally, just draw all the straight lines, and pretend all the gas lines are at ground level, the water lines are two feet below the surface, and the gas lines are buried four feet deep. That way, none of them will ever cross..',1575,'DJ','2003-09-15 19:49:34');
INSERT INTO forumpost VALUES (1849,80,7,'Re: Hello, First time here','But yes, Gamer is right, although I don\'t think we\'ll ever see that problem on here..',1575,'DJ','2003-09-15 19:56:49');
INSERT INTO forumpost VALUES (1850,261,4,'Re: Scav game','He\'s right.. the first one took me the longest to figure out, as I didn\'t know what to do at all.. the longest, that is, until this eighth one, four days and counting..',1575,'DJ','2003-09-15 19:58:24');
INSERT INTO forumpost VALUES (1851,261,4,'Re: Scav game','Actually I knew how to do the first one from another site I figured it out on ;)\r
\n\r
\nI don\'t really know \"how it can be included in a page\", but I will look anyway.',1626,'Gamer','2003-09-15 20:00:46');
INSERT INTO forumpost VALUES (1852,80,7,'Re: Hello, First time here','Holy #@!$% guys (Gamer and DJ)... did you actually READ my answer? (and *sigh* yes the problem is impossible in a single plane).... sometimes... the literal-mindedness of otherwise smart people is amazing....',3172,'SilverKnight','2003-09-16 09:16:52');
INSERT INTO forumpost VALUES (1853,80,7,'Re: Hello, First time here','Yes, I read your answer, but unless someone is picturing exactly what you are, \"draw a line and sorta curve it around from gas to house number 2 and cycle number 3 from wateallost barely by heat to house number 3\" doesn\'t really mean a whole lot.',1575,'DJ','2003-09-16 09:29:10');
INSERT INTO forumpost VALUES (1854,80,7,'Re: Hello, First time here','c\'mon DJ... EXACTLY... there\'s no way to interpret this as meaningful. That\'s kinda the point.',3172,'SilverKnight','2003-09-16 10:04:01');
INSERT INTO forumpost VALUES (1855,80,7,'Re: Hello, First time here','It\'s obvious that that\'s true, but it\'s not as obvious that being meaningless was your point in leaving a comment; it just looked like someone trying to describe what they had drawn on paper..',1575,'DJ','2003-09-16 10:17:40');
INSERT INTO forumpost VALUES (1856,80,7,'Re: Hello, First time here','Gee DJ... you\'re a frequent contributor to this community... You must have seen some of my solutions to problems, such as this one. Am I not, generally, very precise (if not complete) in my answers?\r
\n\r
\nI would hope that those members who \'know\' flooble as of late, would get it.\r
\n\r
\n--- SK',3172,'SilverKnight','2003-09-16 11:52:41');
INSERT INTO forumpost VALUES (1857,80,7,'Re: Hello, First time here','I will admit I read the first half and that is a perfectly genuine way to go about this problem. You have gotten so good at solving problems that you explained an impossible problem too well! :)',1626,'Gamer','2003-09-16 17:22:24');
INSERT INTO forumpost VALUES (1858,261,4,'Re: Scav game','Well i got stuck on the very first challenge. And I get a strange feeling i had to modify the web address (i tried various things). I did find it fun even though i got nowhere. All in all perhaps providing solutions somewhere would help.',1072,'Alan','2003-09-16 17:50:36');
INSERT INTO forumpost VALUES (1859,264,7,'HELLO','Hello\r
\nMy name is Andrew.\r
\nIm new to the site, and i yould like to say a big HELLO to all of you...\r
\nI promise that i will post the best riddles, quizes, tricks and stuff I can find!!!!\r
\n\r
\nSO......\r
\nHI!!!!!!!!!!!!!!!!!!1',3495,'Andrew','2003-09-17 07:53:34');
INSERT INTO forumpost VALUES (1860,265,5,'I propose a new problem category...','How about a category title,\r
\n\"Problems which require absolutely no critical thought at all\"?\r
\n\r
\nThis would contain problems such as Old MacDonald Had a Sequence, Words in Common 5, The Famous Horse, and Metaphysics...\r
\n\r
\nAnd perhaps we could even \"push\" problems to this category on a separate schedule, so as not to impact the rate at which problems, which require a modicum of actual thought, actually get posted.\r
\n\r
\nAny thoughts (sarcastic or otherwise)?\r
\n\r
\n --- SK',3172,'SilverKnight','2003-09-17 12:35:34');
INSERT INTO forumpost VALUES (1861,265,5,'Re: I propose a new problem category...','If there is a new category created, the problems in it need a good common thread like cryptography or algorithms. The problems you listed dont have very much in common with each other.',1920,'Brian Smith','2003-09-17 14:20:32');
INSERT INTO forumpost VALUES (1862,265,5,'Re: I propose a new problem category...','LOL.... Brian you crack me up.\r
\n\r
\nBTW, I think the title exactly describes the theme that they all share.',3172,'SilverKnight','2003-09-17 14:24:21');
INSERT INTO forumpost VALUES (1863,265,5,'Re: I propose a new problem category...','Ummm... if no critical thought means easyness of the puzzles, only the famous Horse would work.\r
\n\r
\nThe easy problems are designated by their difficulty, and are pushed as stated.',1626,'Gamer','2003-09-17 17:00:07');
INSERT INTO forumpost VALUES (1864,265,5,'Re: I propose a new problem category...','An interesting point... but no I was not referring to the difficulty rating of the problems. As I mentioned in a thread on one of those problems:\r
\nI can come up with an equally difficult problem of sequencing.... such as the third letter of the prime numbers starting from 13 and going up. But really... is that worth while?\r
\n\r
\n...very difficult, virtually impossible to solve, and definitely not worth the attention it might get on this site.',3172,'SilverKnight','2003-09-17 17:13:16');
INSERT INTO forumpost VALUES (1865,265,5,'Re: I propose a new problem category...','Be careful, I am reading your definition as \"bad problems\", and I feel that all above problems are fine.\r
\n\r
\nAs long as journeymen continue to remember that problems which are very obscure aren\'t good without proper hints, I don\'t think we will need that catergory.',1626,'Gamer','2003-09-17 18:16:35');
INSERT INTO forumpost VALUES (1866,265,5,'Re: I propose a new problem category...','SK, I admit that Old MacDonald Had a Sequence is not a very good puzzle. I suppose I submitted it out of amusement that the sequence (derived from a sequence of numbers less esoteric as your proposed \"third letter of primes starting at 13\", but I see what you mean) resembled the children\'s song. \r
\n\r
\nHowever, your criticism of WIC 5 as requiring no critical thought is demonstrably false. I included \"horizontal\" to help puzzlers look beyond simple letter substitutions, which are often the key to solving such puzzles, and in fact Happy used the word \"midday\" to figure out the solution, resulting in an \"AHA!\" experience. This is definitely not a you-either-get-it-or-you-don\'t puzzle.\r
\n\r
\nIf you find such problems \"very difficult, virtually impossible to solve\", maybe you will be happier sticking to puzzles that are more obviously left-brained. You\'ll be happy to know my next submission is more analytical in nature. However, it must be obvious to you from the comments of others that some people enjoy these problems, so I ask you kindly not to be a spoilsport.\r
\n\r
\nBTW, love your avatar -- very aggro.',1567,'Bryan','2003-09-18 13:12:12');
INSERT INTO forumpost VALUES (1867,265,5,'Re: I propose a new problem category...','wow.... aggro... good word!\r
\n\r
\nInteresting that that\'s how you interpret it... :-) That\'s certainly not how it was intended.\r
\n____________\r
\n\r
\nNot to be contrary (okay... maybe a little), but just \'cause there is an AHA experience, which I agree Happy probably had, doesn\'t mean there is any significant critical thought involved. Similarly, \"George & Gracie\" problems where we \"AHA! they must be fish!\" or \"AHA! the cabin on the mountain is a PLANE cabin that crashed there\" produces a similar experience, and yet again, no significant critical thought.\r
\n____________\r
\n\r
\nIf by \"obviously left-brained\" you mean \"requires critical thought\", well... then... of course, that\'s exactly what I am talking about.\r
\n____________\r
\n\r
\nAnd to be sure, one can find a plethora (another word of the day) of people who like any kind of problem... even mind-numbing silliness that requires no significant critical thought. (Heck, there are even people who sit and stare at MTV all day.)',3172,'SilverKnight','2003-09-18 14:34:54');
INSERT INTO forumpost VALUES (1868,265,5,'Re: I propose a new problem category...','Other than \"absolutely no critical thought at all\", what would the problems in this new category have in common?',1920,'Brian Smith','2003-09-18 15:06:04');
INSERT INTO forumpost VALUES (1869,265,5,'Re: I propose a new problem category...','isn\'t that enough? ;-)',3172,'SilverKnight','2003-09-18 15:28:49');
INSERT INTO forumpost VALUES (1870,265,5,'Re: I propose a new problem category...','In my opinion, we can always stick one of those problems in another catergory. It seems only problems that don\'t have a catergory and are piling up would do well to find a new catergory.\r
\n\r
\nI don\'t think comparing flooble problems to lateral-thinking problems is a good idea because lateral-thinking problems aren\'t allowed here.',1626,'Gamer','2003-09-18 17:18:24');
INSERT INTO forumpost VALUES (1871,265,5,'Re: I propose a new problem category...','Problems where the answers come from \"Aha! Maybe George & Gracie are fish\" or \"Aha! Maybe it\'s a plane\" or, often, \"Aha! Ice must be involved,\" had always been told to me under the general heading of Minute Mysteries. I personally have the same reaction to you, since a) the answer could always be one of two hundred things, but that the same time b) once you realise the sort of brain that is behind them the answer is usually quite easy. My question is why don\'t we stick all these under the heading Minute Mysteries, since we\'re looking for a more specific category name. (A more defined definition for these puzzles could be \"could you list more than 437 possible answers to your question?)\r
\n\r
\nOtherwise just ban the lot of them as Gamer suggests. Start with anything involving ice.\r
\n',3372,'Sam','2003-09-18 20:20:28');
INSERT INTO forumpost VALUES (1872,265,5,'Re: I propose a new problem category...','Sam: LOL!\r
\n\r
\nP.S. The cabin one is ON FLOOBLE and so is the the \"George and Gracie\"problem. And this cops and robbers is another perfect example...\r
\n\r
\nAnd Sam... here\'s an ice one, and here\'s <A HREF=\\\"http://flooble.com/perplexus/show.php?pid=429\\\"another ice\n\r
\nGamer... what do you mean these aren\'t allowed here?',3172,'SilverKnight','2003-09-18 20:49:17');
INSERT INTO forumpost VALUES (1873,265,5,'Re: I propose a new problem category...','whoops... maybe Levik can correct the previous post/typo for me... (and delete this one at the same time...)',3172,'SilverKnight','2003-09-18 20:50:00');
INSERT INTO forumpost VALUES (1874,265,5,'Re: I propose a new problem category...','Oh, I forgot, you aren\'t a journeyman so you might not know about the reasons I heard there recently.\r
\n\r
\nWe haven\'t passed many new lateral-thinking problems recently because they don\'t qualify as the sort of problems we want. (Sam\'s two reasons are approximately why) I don\'t know how the old problems were passed, not being a journeyman at the time they were passed (maybe some knowledgible scholar like TomM knows why) but I have seen that the consensus of these problems (including the severed arm one) was that they got TD because they were lateral thinking problems. If you look at the pid of them, you will notice they were submitted early on to the site. Over 500 problems were submitted between when the last lateral thinking problem you listed went on the site and now.\r
\n\r
\nI don\'t think people think the lateral-thinking problems (some of them at least) are bad problems, but they are just not what flooble is after.',1626,'Gamer','2003-09-18 21:23:42');
INSERT INTO forumpost VALUES (1875,265,5,'Re: I propose a new problem category...','Y\'know... you Journeymen (and Levik) are some of the most PC muther#$@#~@# I\'ve ever met. (I\'m not sure if that\'s a good thing or not.)',3172,'SilverKnight','2003-09-19 01:29:15');
INSERT INTO forumpost VALUES (1876,265,5,'Re: I propose a new problem category...','SK, are you sarcastic or intentionally disrespectful? 8)\r
\n\r
\nThe Old MacDonald sequence makes sense. Sure, you could come up with another sequence, but you would still have to match it up with a song, wouldn\'t you?\r
\n\r
\nThere was another sequences puzzle submitted a week ago which featured letter-to-numbers (still isn\'t solved by the way). Why does this one require more critical thought than the Old MacDonald? I\'m not implying that the latter puzzle is bad. Personally, I enjoyed both of them.\r
\nThe only problem I have with Old MacDonald is, that it\'s not a difficulty-4-problem. ',1220,'abc','2003-09-19 11:24:11');
INSERT INTO forumpost VALUES (1877,265,5,'Re: I propose a new problem category...','Sarcastic.... very sarcastic... with a little facetiousness thrown in there.\r
\n\r
\nI hope no one takes me so seriously that he gets offended or interprets it as disrespect.... (Of course... if one does... eh)\r
\n___________\r
\n\r
\nyeah... the Old MacDonald sequence matched the song... like a typical Karaoke singer matches the song he\'s singin\'. And I don\'t know to which problem you are referring (that perhaps required critical thought). But if it required no critical thought too, then it could also go the way of the dodo.',3172,'SilverKnight','2003-09-19 12:03:59');
INSERT INTO forumpost VALUES (1878,265,5,'Re: I propose a new problem category...','SK I don\'t care if you\'re sarcastic ro what not. Just stop beoing an asshole. seriously. I might as well come out and say it. Let me say this ONE simple thing. If you don\'t like the way this site is being run leave. Plain and simple. If you want to continue to act this way then I\'m sure levik will be more than happy to ban your I.P and any accounts you open and this one to. O yeah In case you say this.
silverknight said \"I hope no one takes me so seriously that he gets offended or interprets it as disrespect.... (Of course... if one does... eh)\"
you think that clears you from calling us motherfukkers? No it doesn\'t. You can either shape up or shut up.\r
\n',1072,'Alan','2003-09-19 18:59:30');
INSERT INTO forumpost VALUES (2331,312,5,'Re: Base 1 and Base 0','There can\'t be a numbering system in base 0 because the place value of each position to the left of the units position would be 0 times the one on the right, meaning no value at all.\r
\n\r
\nThere is a terminology of \"zero-based\", meaning that counting starts at zero instead of one, so that the first item is item 0, the second is 1, etc., as opposed to 1-based which is the usual counting scheme of 1,2,3,4, etc.\r
\n\r
\nAs a number base, base 1 is as said in the chatterbox, 1, 11, 111, 1111, etc.',1301,'Charlie','2003-11-18 21:37:14');
INSERT INTO forumpost VALUES (2332,312,5,'Re: Base 1 and Base 0','I think that most n-based number systems can\'t have a value higher than n-1 in a single digit. Base 1 is forced to break this rule for non-zero values. It seems to me that since it already broke this rule, there is more than one way to notate any one value. For example, 3 could equal 111, 120, 300, 201, etc. Of course, for just one notation for each number, counting 1,11,111... will do.\r
\n\r
\nI\'m thinking that base 0 is impossible because each digit would be multiplied by 0^3,0^2,0^1,etc. and cannot equal anything other than 0. Also, for some reason or another, 0^0 is considered undefined. I\'m not sure quite why, but I know that not everyone agrees on it. 0 raised to a negative power is obviously undefined because it is dividing by 0.',3558,'Tristan','2003-11-19 01:24:38');
INSERT INTO forumpost VALUES (1881,265,5,'Re: I propose a new problem category...','I personally don\'t understand why you would say something like that out of context... Even when you are not on as good footing as others (this was on a \"these are bad problems\" thread)\r
\n\r
\nIt is a great skill to say things in a nicer way, rather than \"Gamer, what do you mean???\" you could say \"I don\'t understand how lateral thinking problems are being filtered. I found a few problems which I would consider lateral thinking, but they are on the site. Can you explain more fully your reasons?\"\r
\n\r
\nI personally am very lacking in that skill, but I see it and appreciate it in others, and it adds one mark under \"good person\"\r
\n\r
\nAlthough I wouldn\'t tell you to take a hike, maybe a little walk wouldn\'t hurt... :)',1626,'Gamer','2003-09-19 19:28:26');
INSERT INTO forumpost VALUES (2335,312,5,'Re: Base 1 and Base 0','This is why I was confused in the chatbox earlier between saying 1, 11, 111 and 0, 00, 000. But 000 abviously makes no sence, as that would just be 0.\r
\n\r
\nI think that the reason base-1 is strange is that really isn\'t equivalent to the other bases. This is because in the others, each digit represents the number of (x ^ n)\'s, which always increase as you go to the left. In base 1 they don\'t increase, as 1^0 = 1^99. A 1 is a 1 no matter where in the row it is.',3372,'Sam','2003-11-19 09:45:58');
INSERT INTO forumpost VALUES (1883,265,5,'Re: I propose a new problem category...','Alan,\r
\n\r
\nIn context, I called you guys PC (as in politically correct). The \"muther#$@#~@#\" was added for emphasis.\r
\n\r
\nOf course, in the future, I will definitely refrain from referring to you as PC.\r
\n\r
\nAs far as your assumption that I don\'t like the way the site is run, you couldn\'t be more wrong. The site is well run, and (from what I\'ve seen) the best of its kind on the net--by far. I appreciate Levik\'s comments and quick responses very much, and he has been very helpful.\r
\n\r
\nAnd frankly, so have most of the journeymen (and other community members).\r
\n\r
\nOf course Levik can ban my IP or my account or any such thing... he could always do that... to anyone. Is there any other obviousness you wish to spout?\r
\n\r
\n(Gamer, point taken, and I hope you\'ll continue to forgive my lapses into coarseness.)\r
\n\r
\nAlan, I make my attempts to provide helpful suggestions, and I do so, often sarcastically. I generally do so to see of whom I can easily get a rise. Enough said ;-)',3172,'SilverKnight','2003-09-20 04:00:25');
INSERT INTO forumpost VALUES (1884,265,5,'Re: I propose a new problem category...','OK, let\'s everyone take a deep breath :)\r
\n\r
\nNobody is getting banned, but let\'s all remember that we\'re grownups here, and as such there\'s no need to add words like \"motherfuckers\" or \"asshole\" for emphasis.\r
\n\r
\nAs to the charge of being politically correct, I refer you to the fact that with 679 problems live on the site (from the statistics page), the ID of the latest problem is 1359. If you do some quick math here, you\'ll realize that this means MORE THAN HALF (by a margin of one) the problems that got submitted didn\'t pass muster. So don\'t think we don\'t vote out problems that don\'t belong. But when we do, we sure don\'t say to people \"That\'s a dumb problem and you\'re dumn for having submitted it\" - if that makes us PC, than maybe it\'s not such a bad thing. Kinda helps retain users if nobody feels insulted for being new and uninformed.\r
\n\r
\nAs far as the existing lateral thinking problems they\'re primarily the reason why no more are being accepted - we saw that such problems don\'t work well in the context of a web site where you can\'t ask clarifying questions.',1,'levik','2003-09-20 11:00:32');
INSERT INTO forumpost VALUES (2334,312,5,'Re: Base 1 and Base 0','Tristan\'s point was that in base 1, then theoretically even 1 has no meaning, just as in base 2, 2 has no meaning. Personally I think we can stretch to allow the digit 1 in base 1, but putting higher digits in there is just stretching it too far.',1301,'Charlie','2003-11-19 09:20:27');
INSERT INTO forumpost VALUES (2333,312,5,'Re: Base 1 and Base 0','I really should not get involved in these theoretical math discussions but, as someone once told me, I seem to have an insaiable desire to draw attention to myself.\r
\nTristan, you said: For example, 3 could equal 111, 120, 300, 201, etc. but in a one based numbering system the symbols \"3\" and \"2\" would have no meaning. The simply are symbols to which you are assigning values (i.e. 11 = 2, 111 = 3). You are using base 10 numbers as your symbols in base one. this makes no more sense than using the accepted hexidecimal symbol \"a\" in a base 10 number. \r
\n\r
\n',2839,'FatBoy','2003-11-19 07:01:12');
INSERT INTO forumpost VALUES (1887,267,7,'how are uz?','lo all...just another n00b....i wish i was 1337....anwayz...hope to get ta no u peepz...if not well...',3559,'Kyle Jung','2003-09-20 13:20:21');
INSERT INTO forumpost VALUES (1889,267,7,'Re: how are uz?','ya got ta comint on da pr0bl3ms an r3ad 4umz... ta git 2 no us peepz... ;)\r
\n\r
\n(If that sounds coherent, it\'s just because I am not good at typing like that yet)',1626,'Gamer','2003-09-20 14:05:30');
INSERT INTO forumpost VALUES (1890,268,7,'Hi, everybody!','Hi! I just became a novice the other day, but I\'ve been looking at this site for a little while. I found that it\'s part of a webring called the puzzle ring. The puzzle ring was actually part of a category of rings focusing on puzzles. The puzzle ring seemed to be the biggest and best of all the others. I didn\'t look at all the sites on it (there were over a hundred) but I think I could confidently say that this site is the best and most organized site. I couldn\'t stand not being able to post myself, so I just had to sign up.',3558,'Tristan','2003-09-21 11:24:17');
INSERT INTO forumpost VALUES (1891,268,7,'Yet another new boy on the block!','Hi! I\'m an old guy who likes puzzles. I found the site by typing in logic puzzles in Google OK? You can have a laugh at my first but not last mistake very shortly.',3571,'Denis Cronin','2003-09-21 19:45:25');
INSERT INTO forumpost VALUES (1892,268,7,'Re: Hi, everybody!','Welcome both of you, glad to see fresh faces around here :)\r
\n\r
\nI hope you enjoy your stay.',1,'levik','2003-09-22 10:38:03');
INSERT INTO forumpost VALUES (1893,269,5,'problem with submitting','I was finished typing up a problem I wanted to submit and I pressed the preview button. A notice appeared saying I had to be logged on to submit, which I thought I was, but I typed it in anyway. Afterwards, I went to the problem submitting screen, but it was blank, with a blank preview on top. I checked to see if it was already in queue by trying to edit my puzzles, but it said I hadn\'t submitted any. What happened? Before I try typing it again I\'d like to know a few things. To what extent can we edit puzzles already submitted? Is there anyway to save a draft without it going into queue? If there isn\'t, maybe there should be. Though, I suppose that I could save it on a document and paste it on later...',3558,'Tristan','2003-09-22 21:20:10');
INSERT INTO forumpost VALUES (1894,269,5,'Re: problem with submitting','If you thought you were logged in, but it turned out that you weren\'t, I would guess that there\'s a problem with your browser settings in accepting cookies. Make sure that cookies are enabled, and try it again.. and if you ever get a message that implies that you\'re not logged on, you probably aren\'t. As a student, once you have submitted a problem, you can edit its text and difficulty, but not the category. There\'s no way to save a draft.. I usually just type my probelms up in notepad and submit the completed version. That way, too, if something goes wrong, all my work isn\'t lost. Hope this helps.\r
\n\r
\n=)',1575,'DJ','2003-09-22 23:29:14');
INSERT INTO forumpost VALUES (1895,270,5,'recently solved','Is there a way to see the problems that have been recently solved?\r
\nIf an official solution to a problem is posted, it disappears from the \"unsolved\" list and is forgotten. I can\'t keep track of all the unsolved puzzles.',1220,'abc','2003-09-23 07:44:46');
INSERT INTO forumpost VALUES (1896,270,5,'Re: recently solved','I don\'t think so, but that is actually a really good idea. I would also like to see the unsolved problems arranged chronologically.',1920,'Brian Smith','2003-09-23 09:23:11');
INSERT INTO forumpost VALUES (1897,176,5,'Re: Problem flooding revisited','better problems. more categories, especially verbal... probs solved. pat/sat',3430,'pat','2003-09-23 13:09:24');
INSERT INTO forumpost VALUES (1898,269,5,'Re: problem with submitting','I\'m not sure what happened the first time, but the second time I tried, the preview worked and nothing disappeared. I\'m pretty sure that my browser is accepting cookies. Maybe the internet temporarily disconnected on me? I hope it doesn\'t happen again, but I\'ll write my puzzles somewhere else first anyway.\r
\n\r
\nAnyway, I still didn\'t post my puzzle because I couldn\'t figure out how to put large spaces in it. They just wouldn\'t appear on the preview. Coincidently, someone using the same name as mine seemed to have a similar problem and posted it on the chatterbox. Unfortunately, he seemed to have figured it out and only said that it was like html, and I\'m not sure what he meant. ',3558,'Tristan','2003-09-23 20:05:07');
INSERT INTO forumpost VALUES (1899,269,5,'Re: problem with submitting','Writing the phrase (br) but using a less than sign at the beginning and a greater than sign at the end of the br instead of paretheses will give a break, like you pressed return. :)\r
\n\r
\n
Two enters. :)',1626,'Gamer','2003-09-23 20:11:01');
INSERT INTO forumpost VALUES (1900,269,5,'Re: problem with submitting','Unfortunately you can\'t do it here apparently because it recognizes html codes',1626,'Gamer','2003-09-23 20:11:46');
INSERT INTO forumpost VALUES (1901,269,5,'Re: problem with submitting','The major problem, which you are probably having (or had), is/was that when you are logged on, and don\'t do send anything back to the site (such as when the only thing you are doing is typing the submission into the text box), there is a time limit after which you are automatically logged out. The site doesn\'t actually push a new screen at you when this happens; it just says you\'re not logged on the next time you press a button, such as Preview or Submit.\r
\n\r
\nOne solution as mentioned above is to type your text into notepad and transfer to the flooble text box with a copy and paste, so if anything goes wrong you can do that again.\r
\n\r
\nAnother solution is, before you hit the review or submit button, highlight the whole text in the text box and put the text onto the clipboard via Edit...Copy, or cntrl-C, or the old-fashioned way: cntl-insert. Then if something bad happens you can log on again and paste the text in since its still on the clipboars (edit...paste, cntrl-V or shift-insert).',1301,'Charlie','2003-09-23 21:09:42');
INSERT INTO forumpost VALUES (1902,271,3,'New answer to Zeno\'s Paradox','Hey, I don\'t know if this is the right place to post these sorts of topics, but I thought you all might be interested in this.\r
\n\r
\nA previously unknown, not-college educated physisist has recently made huge waves with his new theory on time. He has written two srticles on it and one of them deals directly with Zeno\'s paradox. The solution that we had all been told (Zeno was wrong \'cause he didn\'t know calculus) may well be wrong, and it could just be that we have an incorrect view of time. Lynds, the guy, says that it simply doesn\'t make sense to ask where something is at a specific moment in time, because time doesn\'t have any \"moments\" in it, and things that are moving aren\'t in any specific position at any specific time.\r
\n\r
\nAnyways, just thowing that out there, as so many paradoxes and logic puzzles seem to be based on the fact that we can ask where something is at any time.\r
\nhttp://philsci-archive.pitt.edu/archive/00001197/02/Zeno_s_Paradoxes_-_A_Timely_Solution.pdf',3372,'Sam','2003-09-24 00:24:38');
INSERT INTO forumpost VALUES (1903,269,5,'Re: problem with submitting','One way I believe you can I avoid being kicekd out like this is by clicking \"remember me\" on the login form when you first sign in. It\'s kept me logged in for months.',1,'levik','2003-09-24 07:34:35');
INSERT INTO forumpost VALUES (1904,272,7,'First timer','I\'ve been floating around for a few days and decided to write a \"hello!\" type thing. I am a philosophy lecturer in scotland (specializing in Logic), so I tend to spend a good bit of time playing around with logic puzzles, etc. I am looking forward to finding a lot of new puzzles here, and also to sharing one or two of my own creations (not to brag, but I once shared one of my puzzles with the Master of Knights and Liars himself, Raymond Smullyan, and his first comment was \"That\'s solvable?\"- Of course, a moment later he saw the general idea behind the solution). Anyway, I am going to control the urge to post puzzles here, and will just have to wait until the powers that be decide to honour me with the oh-so-coveted student status so that I can post puzzles. Solving other people\'s (o at least trying) will keep me entertained for awhile.',3546,'RoyCook','2003-09-24 11:25:29');
INSERT INTO forumpost VALUES (1905,271,3,'Re: New answer to Zeno\'s Paradox','That relates to the Heisenberg Uncertanty Principle and the fact that the mathematical models used to describe the physical world do not match it perfectly. (E.g. Newton\'s laws are close enough in most cases, but there are situations in which they \"break down\" and you need to switch to Relativity or Quantum Mechanics). \r
\n\r
\nMost puzzles and paradoxes are based on the mathematical models, or on \"pure mathematics. Real Physics, especially on the Quantum Mechanics level need to take Heisenberg into consideration: if you pin down one parameter too closely, there is a paired parameter which can vary far too greatly. The most common of such paired parameters are time and position (location in space): the same two parameters that your synopsis indicates. \r
\n\r
\nAt the moment I am on a library computer and cannot read *.pdf files. I\'ll take a look at the article from my own computer later.',153,'TomM','2003-09-24 12:19:28');
INSERT INTO forumpost VALUES (1906,273,3,'brain teasers',' _ 5 _ _\r
\n + _ _ _ 5\r
\n----------\r
\n_ _ 6 _ _\r
\n\r
\n\r
\nuse the numbers 0-9 to make a true equation',3601,'Tammy Skaggs','2003-09-24 13:18:46');
INSERT INTO forumpost VALUES (1907,273,3,'Re: brain teasers','What number names a plant?\r
\n',3601,'Tammy Skaggs','2003-09-24 13:19:07');
INSERT INTO forumpost VALUES (1908,273,3,'Re: brain teasers',' 9587
\r
\n+6045
\r
\n 15632
\r
\nBut we should discourage you from posting here... In the future, please submit the problem to the site, so that it can be categorized, stored, and rated appropriately.\r
\n\r
\n--- SK',3172,'SilverKnight','2003-09-24 14:00:37');
INSERT INTO forumpost VALUES (1909,269,5,'Re: problem with submitting','I think that Charlie is right. Someone needed to use the computer urgently while I was in the middle of typing. That was probably enough time for me to log out. Thanks for the help.',3558,'Tristan','2003-09-24 20:03:53');
INSERT INTO forumpost VALUES (1910,273,3,'Re: brain teasers','I won\'t say the correct answer is IV (ivy) because you really shouldn\'t post problems here. Please submit the problems like anyone else. :)',1626,'Gamer','2003-09-24 20:34:29');
INSERT INTO forumpost VALUES (1911,272,7,'Re: First timer','The Student status is not all that coveted - nor is it hard to achieve. Moreover, you will be disappointed to know that the \"powers that be\" you have referred to are actually embodied in a PHP script that runs nightly :)\r
\n\r
\nAnyway, welcome to the site - I hope to see your puzzles in the queue (though as others will no doubt warn, they will take A WHILE to trickle through and show up on the site\'s public areas)',1,'levik','2003-09-24 21:50:27');
INSERT INTO forumpost VALUES (1912,273,3,'Re: brain teasers','Hahaha...\r
\n\r
\nWay to discourage, guys :)',1,'levik','2003-09-24 21:52:20');
INSERT INTO forumpost VALUES (1913,272,7,'Re: First timer','*sigh*... yeah...\r
\n\r
\nI\'ve been on this site for almost ten years... and my puzzles haven\'t reached the front yet. (And I\'m prone to slight exaggeration.)',NULL,'Aspiring Novice','2003-09-24 23:28:31');
INSERT INTO forumpost VALUES (1914,273,3,'Re: brain teasers','Yeah, Gamer.... c\'mon dude.',3172,'SilverKnight','2003-09-24 23:32:23');
INSERT INTO forumpost VALUES (1915,272,7,'Re: First timer','Aspiring Novice, I should point out that posting under multiple personalities is generally frowned upon here. Ask anyone the sad tale of Tim Axoy...',1,'levik','2003-09-25 07:50:51');
INSERT INTO forumpost VALUES (1916,271,3,'Re: New answer to Zeno\'s Paradox','Indeed, with most puzzles of this sort to mathematical answer is the one expected, as it\'s rather a bore when know-it-alls start telling you \"you can\'t split quarks\" or whatever when dividing things by infinity.\r
\nIn this case though it\'s interesting because people say, Zeno\'s paradox seems to make sense, so why *does* Achillies pass the Tortois? At which point people normally bring in calculus as the real-world answer. This answer, though, is instead telling us that the entire question makes no sense, as is is a contradiction in terms to say \"where is Achillies at time T?\"',3372,'Sam','2003-09-25 11:50:46');
INSERT INTO forumpost VALUES (1917,273,3,'Re: brain teasers','thank you for the help ok will submit to the site next time ',3601,'Tammy Skaggs','2003-09-25 12:00:36');
INSERT INTO forumpost VALUES (1918,271,3,'Re: New answer to Zeno\'s Paradox','I read that and I have a lowcomprehending of what was being said/portrayed (I did understand a good portion of it though) and I must say that was very interesting to read. I just must ask this. Was one of the concepts that was being portrayed that nothing is relative to any other thing? Or that space and time can\'t be relative to eachother.',1072,'Alan','2003-09-25 16:12:01');
INSERT INTO forumpost VALUES (1919,273,3,'Re: brain teasers','Hey! I stated that I wouldn\'t state the answer, where as you said you would say the answer! :)',1626,'Gamer','2003-09-25 17:16:27');
INSERT INTO forumpost VALUES (1920,269,5,'Re: problem with submitting','I\'ve never been automatically timed out or logged out, after weeks and months, let alone a few minutes, so make sure you have the \'remember me\' box checked (if it\'s on your own computer). Also, editing in notepad or copying the text or any of the other suggestions are good safeguards.\r
\n\r
\nAnyway, as far as formatting, you can\'t just push enter for a line break like you can in here or in comments. You have to type in <p> for a paragraph (two lines) or <br> for a single line break.\r
\n\r
\nFor example, typing:\r
\n\r
\nsomething here<br>something else<br>another something<p>finally this\r
\n\r
\nwill show up as:\r
\n\r
\nsomething here\r
\nsomething else\r
\nanother something\r
\n\r
\nfinally this\r
\n\r
\nHope that helps.',1575,'DJ','2003-09-25 18:12:58');
INSERT INTO forumpost VALUES (1921,271,3,'Re: New answer to Zeno\'s Paradox','Though I can\'t pretend I understood it all myself, I think that\'s it\'s neither of those things. Rather I think he is saying that there is no such thing as an instance in time, only intervals, and that if it were a series of instances, motion would be impossible:\r
\n\r
\n\"Time enters mechanics as a measure of interval, relative to the clock completing the measurement. \r
\nConversely, although it is generally not realized, in all cases a time value indicates an interval of time, rather than a precise static instant in time at which the relative position of a body in relative motion or a specific physical magnitude would theoretically be precisely determined. \r
\n...\r
\n[if that were not so] the relative position of a body in relative motion or a specific physical magnitude, although precisely determined at such a precise static instant, it would also by way of logical necessity be frozen static at that precise static instant. Furthermore, events and all physical magnitudes would remain frozen static, as such a precise static instant in time would remain frozen static at the same precise static instant: motion would not be possible.\"',3372,'Sam','2003-09-25 19:03:38');
INSERT INTO forumpost VALUES (1922,273,3,'Re: brain teasers','lol! touché!',3172,'SilverKnight','2003-09-26 11:47:52');
INSERT INTO forumpost VALUES (1923,272,7,'Re: First timer','Well... *I\'m* dying of curiousity .... whatever happened to Tim Axoy?',3172,'SilverKnight','2003-09-26 15:48:22');
INSERT INTO forumpost VALUES (1924,272,7,'Re: First timer','Hehe, im also a first timer too, and I\'m very addicted to scottish ppol right now, not in a \"lusty\" way :)...it\'s just that, Im reading books about them, and it\'s interesting to see if wat i read is exactly how they act/talk, etc...\r
\nur probably wondering, wat the heck im talking about...I just happen to read that Roy is from scotland(though, not necessarily scottish)...which reminded me of my interest for scotland...anyway, back to puzzles and logic, i love solving both of them, but im not a \"fast thinker\", nor a \"philosopy proffesor\"...so im pretty intimidated with all of the ppol here...but, i guess i can learn to think things in a systematic way, by hanging out with u guys...\r
\npls dont butcher this mssg, coz i also noticed, that a lot of people(esp. the scholars), here are burning the novices...so pls be nice...im not doinga nything wrong, am i? :D',3624,'aydontknow','2003-09-26 18:35:10');
INSERT INTO forumpost VALUES (1925,271,3,'Re: New answer to Zeno\'s Paradox','Like the two of you, I can\'t pretend to have understood it all, but what I got out of it was that Zeno was trying to point out the difference between the real world and a mathematical model of the world by showing that the mathematical model could not explain motion.\r
\n\r
\nThe invention of calculus allowed the mathematical model to catch up with the real world (thus creating the science of Physics). \r
\n\r
\nBut Quantum Mechanics returns us to Zeno\'s old questions, but with a twist. The mathematics (calculus) are there to accomodate motion, but the experimental \"real-world\" data is what seems to be denying it now.',153,'TomM','2003-09-26 19:00:17');
INSERT INTO forumpost VALUES (1926,272,7,'Re: First timer','To SilverKnight,\r
\nIt shows Tim Axoy\'s story in the reference forum, second thread.',3558,'Tristan','2003-09-26 19:11:30');
INSERT INTO forumpost VALUES (1927,272,7,'Re: First timer','hey... thanks, Tristan.',3172,'SilverKnight','2003-09-26 20:41:27');
INSERT INTO forumpost VALUES (1928,274,7,'hello there!!','hi! im from cavite, Philippines. im very interested to your site i just browsed it on google. what is this site all about? are the users of this site came from different countries? is this site made for progammers? for students? or for anyone who wants to be a part of this site? im glad to one of its part. and to find lots of friends from here.',3636,'karen anne','2003-09-26 23:12:43');
INSERT INTO forumpost VALUES (1929,176,5,'Re: Problem flooding revisited','I\'ve been reading this long thread and I picked the best ideas(I think) out of it. The backlog seemed like a great idea, but the idea needs to be worked on, maybe in a new, shorter thread. I also liked the idea of students being able to edit categories, but not titles. I bugged, I mean petitioned, Levik on it. \r
\n\r
\nI also liked the idea of limiting the problems per day per user. I, for one, write my problems elsewhere first, edit them, then submit them if I think they\'re good. It may take a few days, but what\'s that compared to the time they\'re in queue? I don\'t mind the long wait, but others are less patient then I am.\r
\n\r
\nThat digest page Levik mentioned in the beginning... Is there any way to get there besides through this thread? As for the QW system, I don\'t understand enough of it to say anything about it.',3558,'Tristan','2003-09-27 16:47:42');
INSERT INTO forumpost VALUES (1930,176,5,'Re: Problem flooding revisited','The link on the home page for the digest page is just below the link for the forums and is labelled \"Newest Problems.\"\r
\n\r
\n',153,'TomM','2003-09-27 19:02:31');
INSERT INTO forumpost VALUES (1931,274,7,'Re: hello there!!','Welcome to the site. Anyone who is interested in solving puzzles is welcome here, and yes, we do have people from all over the world.\r
\n\r
\nEnjoy your stay.',1,'levik','2003-09-27 19:55:29');
INSERT INTO forumpost VALUES (1932,176,5,'Re: Problem flooding revisited','Oh, I thought it might be labelled \"Digest\". I don\'t see why people shouldn\'t use it.\r
\n\r
\nLevik told me that the reason students can\'t edit categories is because we might misplace it. That makes sense, though I didn\'t think of it at first. There ought to be a help page telling us all this information. Though, maybe it\'s better in some cases if the new users have to figure it out for themselves... Maybe giving certain information might cause people to send in better quality problems.',3558,'Tristan','2003-09-28 12:45:11');
INSERT INTO forumpost VALUES (1933,176,5,'Re: Problem flooding revisited','I\'m all for such a page, but unfortunately I am so familiar with the site (having programmed it and all) that I think I take a lot of things for granted that should really be explained.\r
\n\r
\nI suggest we strart a help thread, where peole can point out areas of the site that need explanation for either myself, or anyone knowelegable enough to answer. Then I will compile it all into some sort of an FAQ and make a separate page of it.\r
\n\r
\nCome to think of it, that\'s a good idea. I\'m off to start that thread.',1,'levik','2003-09-28 15:00:25');
INSERT INTO forumpost VALUES (1934,275,5,'The FAQ WIP','OK, As I mentioned here, we should have an FAQ section - but since I am way too familiar with the site to know what areas are (gasp!) less than inguitive, I am going to ask people for help in this reguard.\r
\n\r
\nPlease submit things you think should be covered in an FAQ for this site - and either myself or someone else who knows the answer will provide it. I will then take the wealth of knoledge we accumulate and make it into an FAQ page for easy reading.',1,'levik','2003-09-28 15:03:02');
INSERT INTO forumpost VALUES (1935,272,7,'Re: First timer','For aydontknow:\r
\n\r
\nI am actually not Scottish, but am from the USA. I have lived in Bonny Scotland for 3 years or so now, and it is lovely. I do not know that much about Scottish history or anything, but have picked up a bit about day to day life.\r
\n\r
\nAs far as your ability to solve puzzles and such go- I think you have the right attitude- after years of teaching math and logic (and that\'s really what most of the puzzles here amount to) I have found that the only real way to learn the stuff is by constantly working with it. So just try some of the puzzles- even if you do not come up with anything that you think is good enough to post in the comments section at first, you will most likely quickly become better at figuring them out as time goes on. Eventually, you will end up solving some.\r
\n\r
\nRoy',3546,'RoyCook','2003-09-28 15:03:12');
INSERT INTO forumpost VALUES (1936,272,7,'Re: First timer','I would also advise new users if you don\'t feel you are getting anywhere, just narrow down individual cases. Why can\'t you use this answer? for problems like 4-digit number. When I use the same reason 10 or so times, I begin to evaluate it. ;)\r
\n\r
\nUsually when you don\'t think you are getting anywhere you just haven\'t seen the big picture. It\'s like working on a jigsaw puzzle of unknown dimensions. You might get mad if you have the two sides done but can\'t hook them in the middle, but you may only need 1 or 2 pieces to do so.',1626,'Gamer','2003-09-28 15:42:00');
INSERT INTO forumpost VALUES (1937,275,5,'Re: The FAQ WIP','When will my puzzles show up? This is probably the most important question in my opinion. Others could include:\r
\n\r
\nHow come nobody is talking in the chatterbox?\r
\nWhere\'s the digest?\r
\nWhen does my solution show up on the page?\r
\nHow do I get an avatar? (Unless there were instructions I missed somewhere)\r
\nHow come there are 400 (or some number) problems in the queue, but my problem\'s approximate queue position is 200 (or some such number) right after its submission?\r
\nHow important is a solution to a problem I submit?\r
\n\r
\nI think all of these questions can be easily answered when you know the site, but newcomers minght not know ;)\r
\n\r
\nDo we want to include other questions that are already on the site if people are too lazy to look around?',1626,'Gamer','2003-09-28 15:48:56');
INSERT INTO forumpost VALUES (1938,275,5,'Re: The FAQ WIP','A quick peruse of the chatterbox thread gives the following FAQ type questions...\r
\n\r
\nHow do I submit a problem?\r
\nHow do I submit an answer?\r
\nWhy is the problem still showing unsolved when there are correct answers in the comments?\r
\nHow do I format my solution/comment/problem? (probably a link to the HTML forum would be sufficient here)\r
\nWhy shouldn\'t I post problems in the chatterbox or forums?\r
\n\r
\nI think it would also be useful to make some comment as to the types of problems you wish to see submitted for posting. For example, I only just found out that you\'d taken a policy decision to TD lateral thinking problems.',1183,'fwaff','2003-09-29 04:20:01');
INSERT INTO forumpost VALUES (1939,275,5,'Re: The FAQ WIP','>>Do we want to include other questions that are already on the site if people are too lazy to look around? \r
\n\r
\nWell, yes. The point is that these answers are going to be included in a FAQ file page. If it is a question that newcomers frequently ask, it should be included.\r
\n\r
\nSome of the more basic questions would include:\r
\n\r
\nQ. How do I submit a solution to a problem?\r
\nA. Click on the \"Post a comment\" link. You must be logged on (Registration is easy and free.) If you are reading the latest puzzle on the home page, you will have to click to the puzzle\'s own page first.\r
\n\r
\nQ. I submitted my solution, and it is up on the page, but the puzzle still says \"No Solution.\" What\'s going on?\r
\nA. Most puzzles have an \"official\" solution, usually submitted by the person who submitted the puzzle. It is revealed a day or two later than the puzzle itself. It could also indicate that the original submitter did not include an \"official\" solution.\r
\n\r
\nQ. Why can\'t I submit a puzzle to this site?\r
\nA. In order to submit a puzzle, you must be registered and have a rank of \"Student\" or better. \r
\n\r
\nQ. What is rank?/How do I get promoted to a new rank?/etc.\r
\nA. Ranks/User Levels are explained here [link to http://www.flooble.com/perplexus/levels.php]',153,'TomM','2003-09-29 04:23:59');
INSERT INTO forumpost VALUES (1940,275,5,'Re: The FAQ WIP','>> I think it would also be useful to make some comment as to the types of problems you wish to see submitted for posting. For example, I only just found out that you\'d taken a policy decision to TD lateral thinking problems. \r
\n\r
\nOne problem is that it is not usually a blanket \"policy,\" but rather the consensus of the currently active Journeymen and Scholars. Anothr problem is that there are at least three types of \"banned\" problems -- those which we\'ve decided are not approriate for Flooble, those which too closely duplicate puzzles already on the site, and those whose type we\'ve recently been getting a glut of, and the regulars are getting a little tired of. \r
\n\r
\nIn most cases, the disqualification is done on an individual basis, and there is often not a clear consensus as to whether it should be banned, or why. ',153,'TomM','2003-09-29 04:40:48');
INSERT INTO forumpost VALUES (1941,275,5,'Re: The FAQ WIP','heres two more.
Why was my problem deleted?
Whats html? (this way people could always have a page listing the html to look to rather than look at that one thread in the forums.',1072,'Alan','2003-09-29 15:29:34');
INSERT INTO forumpost VALUES (1942,275,5,'Re: The FAQ WIP','Here\'s a few more. If they don\'t seem frequently asked, that\'s because I can\'t think of many more.\r
\n\r
\nHow long do we stay logged on?\r
\nHow often are problems posted?\r
\nHow many problems are rejected?\r
\nWhat is the objective of this site?\r
\nWhat\'s the rest of Flooble about, besides perplexus?\r
\nWhat do QW, TD, and TU all mean?\r
\nWhy is the power to change category withheld from students?\r
\nWhat are the policies on posting unofficial solutions and other comments? Does it matter whether we repeat a solution or anything?',3558,'Tristan','2003-09-29 19:11:19');
INSERT INTO forumpost VALUES (1944,276,7,'Re: No Subject','I couldn\'t agree more!',3172,'SilverKnight','2003-09-30 09:54:15');
INSERT INTO forumpost VALUES (1945,276,7,'Re: No Subject','You know, SK, I think maybe you are off-base on this one...',2839,'FatBoy','2003-09-30 13:30:49');
INSERT INTO forumpost VALUES (1946,276,7,'Re: No Subject','I think it\'s supposed to be funny, not neccesarily mean. (though with SK we do wonder)',1626,'Gamer','2003-09-30 16:58:01');
INSERT INTO forumpost VALUES (1947,276,7,'Re: No Subject','what?',1575,'DJ','2003-09-30 19:34:45');
INSERT INTO forumpost VALUES (1948,277,5,'Problem flooding re-revisited','Rather than extend the previous thread even more... it occurred to me that I might start another thread... so....\r
\n________________\r
\n\r
\nHere\'s a first stab at making some (public) suggestions.\r
\n\r
\nI assume that we wish to find the best problems the quickest (even if we choose to post only one of the best, and pair a not-so-best with it, on a given day).\r
\n\r
\nIt stands to reason, that the best problems are not in the \"front 10\"... when there are many more than 10 in the total queue. (...working on the assumption that we didn\'t, for example, happen to submit them in decreasing order of goodness).\r
\n\r
\nTo find those best problems quickest, we need some mechanism to go through more problems quicker.\r
\n\r
\n(By \"find\" I mean that scholars/journeymen are able to peruse it and rate it.)\r
\n\r
\nNow, one obvious mechanism (which I am *not* advocating) is to allow them to see the whole queue, rather than just the \"top 10\". I think this might be somewhat unwieldy... and I will defer others\' judgement, since I am not yet a journeyman.\r
\n\r
\nAnother mechanism, that might be more wieldy, would be to increase the range from 10 to 20 problem simultaneously.... and further create at least one new queue.... as follows:\r
\n\r
\nI assume (someone correct me here as needed), that if a problem gets three Thumbs Down (TD), then it gets \"deleted\"... it is deemed not worthy of Flooble and is taken out of the potentially-posted-problems list.\r
\n\r
\nI suggest that there be at least three choices of voting... TU, TD, and TH \"thumb-horizontal, flat palm?\"... the third choice indicating that it is worthy of being posted on Flooble, but there may be some more interesting/relevant problems that might take precedence.\r
\n\r
\nThis would carry a weight of zero (not impacting the TU/TD weight), but if a problem gets 3-5 of these, it can be moved to this new queue (an \'alternate\' list)... This queue may contain a whole bunch of problems, ALL of which have been deemed flooble-worthy, and could at any time be posted.\r
\n\r
\nThis new alternate queue, though, would generally grow, as there would likely be more problems placed on this queue than are taken off (much as the current queue is now). At least, it would grow if we continue to have the pace of submission that we\'ve seen as of late.\r
\n\r
\nAnd then, of course, when posting, problems could be pushed from the \"top 10-20\", or from the front of the alternate queue.\r
\n_________________\r
\n\r
\nYou may ask... if we do this, haven\'t we simply moved from one queue to another? No! ...at least not quite. Because what we\'ve done is... reviewed far more of the flooble problems. Therefore, the better ones get to the front faster, while still granting a reward to those who submit earlier. (e.g., all of Ravi\'s 100+ submissions from February, will be reviewed before anyone\'s from September)\r
\n\r
\nAnd lastly, you may think this would be a lot of work on Levik\'s part.... but I have faith in Levik\'s abilities... and I\'m sure it wouldn\'t take much time. ;-)\r
\n\r
\nCriticisms? Compliments? Concerns? Amendments?\r
\n\r
\n --- SK',3172,'SilverKnight','2003-10-02 17:36:41');
INSERT INTO forumpost VALUES (1949,277,5,'Re: Problem flooding re-revisited','So you are advocating a \"Voting queue\" and a \"OK for now\" queue?\r
\n\r
\nI think it woud be good to say \"Top 10 queue\" PLUS any queue problems which have notes are automatically in the queue.',1626,'Gamer','2003-10-02 17:59:07');
INSERT INTO forumpost VALUES (1950,277,5,'Re: Problem flooding re-revisited','Gamer, I\'m not sure I understand what you\'re saying. Would you please be more detailed?',3172,'SilverKnight','2003-10-02 18:31:06');
INSERT INTO forumpost VALUES (1951,277,5,'Re: Problem flooding re-revisited','To stop problems from going in and out of the queue, any problem that has a note on it will stay in the queue. This may result in the queue being over 10 problems, but that\'s OK ;)',1626,'Gamer','2003-10-02 18:39:49');
INSERT INTO forumpost VALUES (1952,277,5,'Re: Problem flooding re-revisited','This \"alternate queue\" sounds suspiciously like the backlog idea in the other thread. I\'m glad that this idea came up again, though it\'s really more for journeymen and scholars to discuss.\r
\n\r
\nAll these thumbs pointing in every direction, would any of them cancel each other out? Do they currently cancel each other out? Could gamer explain what he\'s talking about?',3558,'Tristan','2003-10-02 18:42:14');
INSERT INTO forumpost VALUES (1953,277,5,'Re: Problem flooding re-revisited','Oh, you posted an explanation while I was typing. The problem with that is that we can easily enough post notes on our own problems. I wouldn\'t want to lose this power. I think separating into 2 queues is better because it seems more organized. How would this result in more than 10 problems?',3558,'Tristan','2003-10-02 18:46:50');
INSERT INTO forumpost VALUES (1954,277,5,'Re: Problem flooding re-revisited','Yes Tristan, this is why I proposed 3-5 TH before it gets sent to the alternate queue. No \"auto-sending\" your own problems.\r
\n\r
\nAs for the thumbs cancelling each other out.... as I addressed already... 1 TU cancels 1 TD... +1, -1. But you still need a minimum TH before you can be deemed at least flooble-worthy.\r
\n\r
\nSo, to be absolutely clear: one would not be able to place one\'s own problems in the alternate queue.',3172,'SilverKnight','2003-10-02 18:51:14');
INSERT INTO forumpost VALUES (1955,277,5,'Re: Problem flooding re-revisited','Gamer, to address your mention of the queue being over 10 problems... I assume you mean the alternate queue... and yes, to quote my first message (up top):\r
\n\r
\nThis new alternate queue, though, would generally grow, as there would likely be more problems placed on this queue than are taken off (much as the current queue is now). At least, it would grow if we continue to have the pace of submission that we\'ve seen as of late.',3172,'SilverKnight','2003-10-02 18:53:03');
INSERT INTO forumpost VALUES (1956,277,5,'Re: Problem flooding re-revisited','I am saying my idea of saying if a problem has a note by someone else (like a journeyman or scholar or such) it would have been in the queue at some time. Then the problems wouldn\'t jump around.\r
\n\r
\nI am talking about a quick fix, if Levik doesn\'t want to spend all his time with an alternative queue.\r
\n\r
\nIn my opinion, the queue works good enough for me, but I don\'t know how new people might feel.',1626,'Gamer','2003-10-02 19:51:34');
INSERT INTO forumpost VALUES (1957,277,5,'Re: Problem flooding re-revisited','There are a couple of points that you are overlooking.\r
\n\r
\nFirst, we want to minimize exposure to problems before they are posted or made live on the main site. Having a regular queue of ten problems and then a growing \'alternate\' queue would be counterproductive in this respect.\r
\n\r
\nAlso, who says that the \'best\' problems need to come out before anything else? If all the proverbial cream floats to the top, in the end you\'re stuck with a lot of skim milk, if you can follow that. I would say, homogenize. =P\r
\nOften, what one would consider a \'better\' problem is one that is more involved, and would require much more time to solve, and generally will receive discussion for several days after it has been posted. If we put up a complex problem every day, several days in a row, each problem would not get the attention it may merit.\r
\nTo cite an example, my problem \"Lumber Netters\" was never solved (although someone prematurely posted the solution on me), because the next few problems, \"Marbles Bonanza,\" \"Square Sequence,\" and \"Primes,\" brought up a lot of discussion, and the earlier problem was ignored.\r
\nThat is not to say, of course, that having more \'trivial\' problems is a good thing, but if a problem is deemed siteworthy, it should have the same priority as any other. There\'s the general rule of thumb that simpler problems are posted in the mornings and on weekends, and \'better\' problems are posted weeknights, and it balances out pretty well. Ordering the problems in the order they were submitted is not only fairer to everyone, it\'s a good, relatively random way to keep the problems mixed up so that we get a good variety of problems at any given time.\r
\n\r
\nIn my opinion, the alternate queue would be much more trouble than it\'s worth, as the problems still need to be looked at, edited if necessary, and voted on, and that happens at about the same rate as they are pushed onto the site. Ocassionally there is a problem that immediately receives 3 TU or 3 TD, but for the most part they need some deliberation or modification. Your alternate queue will probably not grow as quickly as you seem to think, and I doubt that it would change the problems being put onto the site very much at all.',1575,'DJ','2003-10-02 21:16:06');
INSERT INTO forumpost VALUES (1958,277,5,'Re: Problem flooding re-revisited','I think the queue has been cutting down due to the less amount of problems being submitted. Although I am unsure why it is, I don\'t think there were as many duplicate/lesser good problems getting TD now than there were when the problems were flooding.\r
\n\r
\nI know that my recent logic problems haven\'t got much exposure, showing that even less discussion stirring problems can slow down the discussion on a good problem.\r
\n\r
\nI think DJ has a good point which I overlooked as well, the fact that we don\'t want all our \"good\" problems (come to think of it, what makes up a \"good\" problem anyway... they are ususally controversial) in one scoop.',1626,'Gamer','2003-10-02 21:27:29');
INSERT INTO forumpost VALUES (1959,277,5,'Re: Problem flooding re-revisited','Gamer: Please be more precise with your explanations (at least for my benefit), because I\'m having trouble understanding exactly what you\'re trying to say.\r
\n\r
\nI think what you are saying (and I CERTAINLY don\'t want to put words in your mouth) is that the queue is shrinking rapidly because a lot of problems are getting TD\'d. And that the quality is going up.\r
\n\r
\nIf by \"much exposure\" you mean a lot of discussion... then yeah... I think the reason why these logic problems (I think you mean the suspender problems) aren\'t generating much discussion is because it\'s, for the most part, the same problem revisited each time. So, whomever gets there first is pretty much the only one who cares to write a solution. Everyone else looks at it... and says... \"okay another logic grid\". Nevertheless, the problems must have received three TU... so... apparently enough people wanted to see them again. I won\'t argue that point.\r
\n______________________________\r
\n\r
\nAs for the \"good\" problems all coming out in one fell swoop... I will quote from my original (up top) comment:\r
\nI assume that we wish to find the best problems the quickest (even if we choose to post only one of the best, and pair a not-so-best with it, on a given day).\r
\n\r
\nAnd it is exactly that... the point is not necessarily to post the best problems sooner rather than later... but to IDENTIFY the best problems sooner rather than later. And if Levik so chose, you could even put a third best-of-queue to push the problems that the journeymen really liked a lot (received 7+ TU, for instance)! You could post one or two of those on Fridays... and make Friday the best-of-flooble day... :-)\r
\n\r
\n',3172,'SilverKnight','2003-10-03 02:02:01');
INSERT INTO forumpost VALUES (1960,278,3,'Can anyone recap my memory','Does anyone remember that brainteaser involving four soldiers buried neck down in the sand with a wall separating three of them from the one. 2 are wearing red helmets and 2 are wearing blue????????\r
\n\r
\nseriously desperate to remember............',3717,'SK','2003-10-03 05:48:01');
INSERT INTO forumpost VALUES (1961,278,3,'Re: Can anyone recap my memory','???????????????????????????????',3717,'SK','2003-10-03 05:54:15');
INSERT INTO forumpost VALUES (1962,278,3,'Re: Can anyone recap my memory','COME ON....U GUYS ARE SUPPOSED TO B KINGS AT RECOGNISING BRAINTEASERS',3717,'SK','2003-10-03 06:54:54');
INSERT INTO forumpost VALUES (1963,277,5,'Re: Problem flooding re-revisited','By exposure, I mean problems that have been sitting around the voting queue for days or weeks before making it onto the site. That usually happens (getting into the \'weeks\' range is rare) when a problem is being debated or modified; the way the queue is running now, problems are generally posted shortly after they are approved. That\'s a good thing. There\'s no reason to have an extra queue of approved problems waiting around to be pushed, when we\'re not short on problems to push as it is. I also fail to see what wondrous good \'identifying\' the best problems sooner is going to do.\r
\n\r
\nThe rate of posting isn\'t increasing, so having all these ridiculous queues is, first, not going to change as much as you seem to think, and second, just going to mean that the voters are looking at more problems sooner. That\'s what I mean by [over-]exposure, and that\'s bad, not good.\r
\n\r
\nGetting discussion on the main page is good, which wouldn\'t happen (as I noted in my previous overlooked comment) if we posted an extrememly challenging puzzle every day, several days in a row.\r
\n\r
\nAlso, if we did that, the queue wouldn\'t keep up; frankly, we don\'t generally see five \'exceptional\' puzzles submitted a week, so we\'d eventually be cutting off our own legs.\r
\n\r
\nSo, I propose that your assumption is misplaced. There is no reason to even find the \'best\' problems more quickly, as they won\'t be posted any more quickly; they\'re assorted more or less randomly as is, so that the problems are distributed roughly evenly with regard to \'goodness.\'',1575,'DJ','2003-10-03 08:13:45');
INSERT INTO forumpost VALUES (1964,277,5,'Re: Problem flooding re-revisited','Hmmm.... Well, DJ they *could* be posted more often/quickly. You simply state that they won\'t be posted any more quickly.\r
\n\r
\nSo, I agree with you... sort of.... If you (and others) refuse to make better/different decisions with additional information, then yes, having that additional information is \"ridiculous\".\r
\n\r
\nHowever, if you choose to take advantage of the additional information, then having it is not ridiculous.',3172,'SilverKnight','2003-10-03 08:31:11');
INSERT INTO forumpost VALUES (1965,278,3,'HEY!!!','Levik... didn\'t I copyright SilverKnight, silverknight, SK, sk, SilverK, and SKnight for this site? This character\'s infringing on my copyright! :-D',3172,'SilverKnight','2003-10-03 08:36:27');
INSERT INTO forumpost VALUES (1966,277,5,'Hey Gamer','By the way, I just worked white suspenders and really liked it\r
\n\r
\nThanks\r
\nFatboy',2839,'FatBoy','2003-10-03 10:34:39');
INSERT INTO forumpost VALUES (1967,277,5,'Re: Problem flooding re-revisited','Thanks FatBoy, it was fun to create. :)',1626,'Gamer','2003-10-03 15:52:03');
INSERT INTO forumpost VALUES (1968,278,3,'Re: Can anyone recap my memory','Guess what? We are also kings at recognizing annoying people who barge in here had use 3 posts to say 1 lame message. Plus, you are asking about a problem ON THE FORUM, which is a mistake, and you are asking about a problem that is already on the site in a different form',1626,'Gamer','2003-10-03 15:57:23');
INSERT INTO forumpost VALUES (1969,277,5,'Re: Problem flooding re-revisited','Do we have to go back to the reason we don\'t have more than 2 problems per day, AGAIN? I thought we had covered that already.\r
\n\r
\n(Actually what I was saying above was there are LESS TDs than there were before... It\'s not as important to the discussion.)\r
\n\r
\nI really don\'t see any problem with the current queue other than problems jumping in and out of it due to queue weight. I don\'t think there is as many problems as when this thread was started.',1626,'Gamer','2003-10-03 17:11:26');
INSERT INTO forumpost VALUES (1970,277,5,'Re: Problem flooding re-revisited','Even though there aren\'t as many problems being submitted now, there may be another flood by the time everyone is finished arguing. None of you seem to know the cause of less problem submissions or more problem submissions, so you can\'t really predict it. At the rate this is going, a dozen threads and a yearcould be used up before you all agree (maybe a little exaggerated).\r
\n\r
\nTo DJ,\r
\nHow would the fact that journeymen are looking at \"more problems sooner\" result in overexposure before posting? \r
\n\r
\nTo SK, \r
\nMaybe you assumed to much when you said \"I assume that we wish to find the best problems the quickest\". You may need to rethink this assumption, based on what these people are saying.',3558,'Tristan','2003-10-03 18:20:07');
INSERT INTO forumpost VALUES (1971,59,5,'AHA!','I have finally found it! The thread that explains QW! There\'s so much in the forums, I knew it would be somewhere. \r
\n\r
\nI\'m posting this because QW may have changed since the time this was up at the top. I know that by now the number of QW 1\'s is only two, so there may have been other changes. \r
\n\r
\nI\'d also like to have more details. My first puzzle first appeared in the upper 60\'s. Does this mean that there are 60 other problems with QW 1? The way QW is described here, it seems to be flawed. Logically, if QW 1s ALL come before higher QWs, wouldn\'t puzzles from people like Ravi and Gamer never appear until there are less then 10 QW 1 puzzles? How would calculating QW every night change anything? Aren\'t puzzles the same QW for their whole queue time?\r
\n\r
\nPeople may respond here and/or that FAQ page',3558,'Tristan','2003-10-03 23:21:07');
INSERT INTO forumpost VALUES (1972,59,5,'Re: Re-calculating QW','>>Logically, if QW 1s ALL come before higher QWs, wouldn\'t puzzles from people like Ravi and Gamer never appear until there are less then 10 QW 1 puzzles? How would calculating QW every night change anything? Aren\'t puzzles the same QW for their whole queue time? \r
\n\r
\nAssume that Ravi has 10 puzzles in the queue. The first two are QW1, etc. One gets 3 Thumbs-up and is pushed, the other is determined to be a duplicate of a puzzle already posted, gets three thumbs down and is dropped. They are replaced in the queue by the next two QW1 puzzles (which are not Ravi\'s). Call them P1 and P2. These new puzzles get a couple of votes and other comments. \r
\n\r
\nThen mid-night comes along (or whatever time levik schedules the re-calc). Ravi\'s two oldest remaining problems are now given QW1. Call them R1 and R2. If R1 is older than P1, it moves ahead of it in the queue, forcing P2 back into obscurity. If R2 is also older than P1, P1 also gets \"bumped.\r
\n\r
\nThat\'s why there are usually really 12 or 13 puzzles in the \"top ten\" of the queue -- the ten (plus) puzzles available to be commented on and voted for. ',153,'TomM','2003-10-04 00:52:20');
INSERT INTO forumpost VALUES (1973,59,5,'Re: What is','I see, I must have missed a few points. I thought that the QW 1 puzzles were the first puzzles submitted, not the first ones submitted, still in the queue! (that would really create problems). And so also, the puzzles with same QW are sorted by age. It all makes sense now.',3558,'Tristan','2003-10-04 10:28:30');
INSERT INTO forumpost VALUES (1974,275,5,'Re: The FAQ WIP','Sorry for letting this slip for a while - I\'ve been a bit under the weather, and short of time. Promise to step up on this thing once I have a chance.\r
\n\r
\nHonest ;)',1,'levik','2003-10-04 12:36:00');
INSERT INTO forumpost VALUES (1975,277,5,'Re: Problem flooding re-revisited','The issue of changing the posting rate has been discussed and, I thought, closed not too long ago. We could go into it again, but I think any pertinent questions were brought up and addressed in the previous thread.\r
\nI stated that we\'re not going to increase the posting rate simple because, well, we\'re not, at least not any time soon.\r
\n\r
\nI also don\'t think, as I stated before, that putting all the best problems on the site as soon as we can is necessarily a \'better\' decision. Sure, we\'d have good problems for a while, but none of them would get the viewer attention it probably warrants (especially so if the posting rate were to increase as well), and eventually we\'d end up with a long run of \'mediocre\' problems. Given SK\'s idea, we\'d put all the \'great\' problems on the site first, and when those ran out, we\'d go back to the alternate queue and push the \'okay\' problems. I think it\'s plain enough that this isn\'t the most favorable situation, unless you alternate posting problems from the \'good\' queue and the \'alternate\' queue -- which in essence is what happens now, but with limits as to the number of problems that are being examined at any given time.\r
\n\r
\nThere are two underlying ideas you are overlooking.\r
\nThe first is longevity; there\'s no reason to assume that the ratio of good to okay problems is increasing when they are being subitted, so there\'s no reason to increase that ratio in the problems that are being posted now.\r
\nThe second idea is the primary purpose of this site; if the point were to give people as many puzzles as quickly as possible, we would just go through the entire queue, post the problems with the solutions as soon as we could, and let people just browse through the puzzles. There are a lot of sites that do that, which is fine. The way this site is set up, however, with the comment system, holding back the solutions, even the aesthetics of highlighting a few porblems at a time on the main page, is geared to show good puzzles, but also to foster the sense of a web community, putting out ideas even if you don\'t have a full solution to the problem, that sort of thing.\r
\n\r
\nI think that, while the current set up is not flawless, it is very close to ideal, in that:\r
\nProblems are able to be sorted, filtered, or edited as necessary before they are posted.\r
\nWe see a good mix of problems, by category, difficulty, length (of problem and solution), discussion, etc, posted to the site throughout the week (I don\'t know what you want to change as far as this goes, but if we start pulling problems from farther than farther back in the queue, the imbalance will eventually catch up to us).\r
\nThe way levik has determined the posting should be done (weekday, weeknight, and weekend problems) is very good to allow front page time and exposure to the problems that most warrant it.\r
\nProblems move through the active voting queue relatively quickly, so that they are generally not \'overexposed\' to the scholars and journeymen who review them, before the problems are pushed live to the main site (this is the biggest thing that your suggestion would probably affect, detrimentally, and I don\'t really see the benefits as far as anything else is concerned in the long run).\r
\n\r
\n****\r
\n\r
\nTo Tristan: I\'m not sure what you are asking. If we look at more problems sooner, as SK is suggesting, without upping the rate of problem posting, then it would have to follow that we are seeing problems for longer before they are pushed onto the site, and more of them at that. Now, of course we have to see the problems in order to approve/disapprove them, request any necessary changes, etc. Ideally, we want them posted, once they\'re approved, fast enough so that they\'re still relatively new to us when they hit the main site, and so that we don\'t have a slew of voters with pre-typed solutions before anyone else even sees the problem.\r
\nPersonally, I won\'t attempt to solve a problem that\'s in voting; there are some problems for which the solution comes immediately upon reading the problem, but that\'s often an idication that it\'s too easy or trivial for the site. Other people do figure out the solutions in voting, or at least insofar as to emsure that one exists and is satisfying (we have come across, in the past, a few problems that could not be solved or were indeterminate, or just weren\'t as good as the problem itself sounded), which is good and sometimes needed.\r
\nAnyway, that\'s what\'s meant by preexposure to the problems in queue, and why we try to minimize it.',1575,'DJ','2003-10-04 13:22:50');
INSERT INTO forumpost VALUES (1976,277,5,'Re: Problem flooding re-revisited','DJ and Tristan,\r
\n\r
\nI\'m gratified that you both actually read what I wrote, and addressed my points even if you don\'t necessarily agree with them (and also obviously spent time to write clear responses.)\r
\n\r
\nBut to be clear to all: I am *not* advocating we \"put all the the \'great\' problems on the site first\". I am advocating that we have the information to do so, and then choose to distribute the \'great\' problems as appropriate. As it is, the journeymen can not... because they have only 10 (or a few more) to look at at any given moment.\r
\n\r
\nThanks!',3172,'SilverKnight','2003-10-05 18:38:51');
INSERT INTO forumpost VALUES (1977,277,5,'Re: Problem flooding re-revisited','As DJ said, the goal isn\'t to distribute \"great\" problems more appropriately; it\'s to distibute all the problems at an appropriate time. While occassionally there is a situation where none of the problems ready to be pushed are (for example) \"weekend\" problems, and a \"morning\" problem has to be pushed on Saturday, this really does not happen all that often. If it does start happening more frequently, the other, forgotten part of your suggestion, increasing the \"top ten\" to the \"top twenty\" (or even only \"top fifteen\") would probably be sufficient to cure it. ',153,'TomM','2003-10-05 22:59:39');
INSERT INTO forumpost VALUES (1978,277,5,'Re: Problem flooding re-revisited','Once again I feel behind times here, having just read this whole thread from start to end. You see I was down with a flu, and this is all new to me :)\r
\n\r
\nMy thoughts: I absolutely agree with DJ, Tom and Gamer about the fact that we should not put an emphasis on the \"BEST\" problems. (Also I agree about not changing the posting rates, which may be moot since they were largely instituded at my urging :)\r
\n\r
\nOne point I have not seen brought up yet, which I think is very important is that a lot of people have very different ideas of what a \"best\" problem is. Some people love geometry, others - crypto stuff. Others yet think that lateral thinking puzzles are the best thing since sliced bread (lately we direct these people to google). So while it\'s fairly easy to spot a puzzle that isn\'t good enough or hard enough for flooble (and rest assured such puzzles get spotted and ruthlessly voted down) - distinguishing between good and better is much trickier. \r
\n\r
\nOf course there are puzzles that rise above the rest in everyone\'s eyes, but these are SO rare that we can consider their distribution to be random and therefore uniform.\r
\n\r
\nThe bottom line is that after all of these lengthy discussions, with a lot of elaborate ideas proposed, I think most of them would not really help improve the overall quality of problems posted on the site. In fact the queue is inherently limited by the speed of problem posting, which I think is there for a good reason, and contributes to the community feel of the site.\r
\n\r
\nIn fact the one area where I will admit significant improvements can be made is the ability by empowered third parties (scholars and journeymen) to alter the submitted problem or at least to bring requested changes to the attention of the submitter in a more obvious way. (I am currenlty considering an alert box that will direct the user to go look at any new problem comments they may have received.)',1,'levik','2003-10-06 13:56:21');
INSERT INTO forumpost VALUES (1979,279,5,'Help (Stupid question)','Dear all,\r
\n\r
\nI was submitting a problem and could not figure out how to get it to skip a line between paragraphs (I hit return twice, as one would do, but the preview showed it all as one single paragraph). The problem I was writing up will really look better if I can figure out how to do this. I realize that this is a silly thing not to be able to figure out, but any help would be appreciated.\r
\n\r
\nRoy',3546,'RoyCook','2003-10-06 14:16:30');
INSERT INTO forumpost VALUES (1980,279,5,'Re: Help (Stupid question)','All you need to do is put a
to skip one line. I also had the same problem about a week ago. If this is somehow not enough, you can look at the thread called \"problem with submitting\".',3558,'Tristan','2003-10-06 14:21:12');
INSERT INTO forumpost VALUES (1981,279,5,'Re: Help (Stupid question)','Darn, I wasn\'t expecting the html codes to work here. Well, to explain again, <p.> is to skip two lines and <br.> is to skip one. Don\'t include the periods if you actually want the codes to work.\r
\n',3558,'Tristan','2003-10-06 14:23:22');
INSERT INTO forumpost VALUES (1982,280,7,'ratings vs. difficulty level','Hi. I\'m new to flooble and I\'ve been poking around the site some every now and then. I think if I\'m understanding correctly, a problem\'s rating and difficulty are NOT the same thing. Is this correct? When I go to rate a problem, am I grading how hard I think it is or how good I think it is?\r
\n\r
\nThanks\r
\nGreg',1112,'Greg','2003-10-06 18:35:13');
INSERT INTO forumpost VALUES (1983,280,7,'Re: ratings vs. difficulty level','The rating is based on how you enjoyed the problem. There is a link on the front page for the highest rated problems. It is sort of a \"best of Flooble\" page. There should be problems of all different difficulty levels.\r
\n\r
\n',153,'TomM','2003-10-06 20:31:10');
INSERT INTO forumpost VALUES (1984,280,7,'Re: ratings vs. difficulty level','Yes, that is a distinction that is very important to make. Well, the ratings themselves aren\'t that important; there\'s no prize for writing the best problems or anything. However, it does seem that people tend to rate the easier problems much less favorably, and the same for very complex problems.\r
\n\r
\nIn general, you shouldn\'t rate a problem until you have at least tried to solve it; I would take that a step farther and say don\'t rate a problem until you know what the author\'s intended answer is. Some very good problems look very trivial, stupid, or even impossibly complex at first glance, causing a low rating, but the actual solution invokes some clever point that many people don\'t immediately see. In my opinion, such problems are great, but often people will look at it for a few seconds, decide it\'s not worth the bother, and then just hit \'1\' for a rating. For example, on the current front page problem, Charlie\'s Fifth Thursdays - somebody gave the problem a \'1\' rating before it has even received any comments! I think that\'s abominable practice, and the problem looks like a very good one, although I haven\'t had time enough to do anything with it just yet (nor anyone else, apparently).\r
\n\r
\nThat\'s perhaps a bit long-winded, but you brought up a good point I wished to elaborate on -- an easy problem is not necessarily a \'bad\' one, and always wait to see what the author had in mind, before deciding one way or the other on a problem.\r
\n\r
\nAlso, if a problem seems really easy, but you see that it has a difficulty of 1, it\'s supposed to be fairly easy. Along the same lines, if a puzzle seems impossibly difficult, and its difficulty level is 5, then it should be pretty hard. Rate the problem based on how much you enjoyed it (and to be sure, wait until you know what the author intended).\r
\n\r
\nOne last point.. you can change your vote after you make it. Say you give a problem a low rating because you figured it out and it didn\'t seem all that great, but then you saw the clever trick that someone found to get the answer. Or, suppose you thought a problem was really good, until someone pointed out a trivial point, or you saw the official solution and just said, \'Oh, that\'s stupid,\' you can simply go click on a new rating. It\'s not like voting again; it actually changes your original vote to the new value. So, voting \'early\' is find, but be aware that your opinion of the problem is very likely to change when you see how the author solved the problem.',1575,'DJ','2003-10-07 01:31:12');
INSERT INTO forumpost VALUES (1985,279,5,'Re: Help (Stupid question)','To be more neat, put <p> for a paragraph (2 lines) and <br> for a line break. Selected HTML codes work in all the text-entry boxes (comments, forums, problems, and solutions) on the page, but only the comments and forums automatically convert your carriage returns into line breaks. In a problem or solution, you have to insert them manually.\r
\nFor example, typing:\r
\nsomething<br>other thing<p>whee!\r
\nwill show up as:\r
\nsomething\r
\nother thing\r
\n\r
\nwhee!\r
\n\r
\nOther codes work, such as bold (<b>bold</b>), italics(<i>italics</i>), and underline (<u>underline</u>). See the HTML thread in the forum for more, and there will soon be a FAQ page with all these codes (and the answer to questions like this), on the site.\r
\nHope that helps.\r
\n=)',1575,'DJ','2003-10-07 01:41:05');
INSERT INTO forumpost VALUES (1986,279,5,'Re: Help (Stupid question)','Thanks for the help. I am one of these people who teaches courses proving that Turing machines (i.e. digital computers) can and cannot in principle do certain things, yet I am ignorant of how to actually get real life examples of such machines to do very simple things like this! So thanks again.',3546,'RoyCook','2003-10-07 10:04:35');
INSERT INTO forumpost VALUES (1987,279,5,'Re: Help (Stupid question)','Question for DJ: How do you type in the hytml codes here all normal? I haven\'t succeeded, they all end up
looking like this instead.',1626,'Gamer','2003-10-07 17:22:21');
INSERT INTO forumpost VALUES (1988,281,7,'Hi! New guy','Hi. I am new here. \r
\nOnce a friend of mine gave me a problem to solve. It took me some time to do it. I liked it so much that I started to look for some more to do. Then when I met him again I asked where we found the problem so he told me about the flooble.\r
\nThat\'s it. I am sure I will love this.\r
\n\r
\nThanks for your time!\r
\n',3778,'Marcelo','2003-10-07 17:52:59');
INSERT INTO forumpost VALUES (1989,143,3,'Re: Best puzzle for the masses','I\'m a bit late coming to this thread, but I\'d like to present an alternative view of the burning ropes puzzle: namely, that the puzzle is flawed, and the solution would not necessarily work. In fact, there is a hidden assumption, without which there is no purely deductive solution.\r
\n\r
\nThe problem lies with the assertion that a \'1 hour\' rope lit at both ends will burn up in 30 minutes. Consider the following rather weird piece of rope.\r
\n\r
\nA->->->->->->C<-<-<-<-<-<-B\r
\n\r
\nIgnite at A, the flame takes 20 minutes to reach C, and a further 40 minutes to reach B.\r
\n\r
\nIgnite at B, the flame takes 20 minutes to reach C, and a further 40 minutes to reach A.\r
\n\r
\nThis is consistent with the puzzle statement.\r
\n\r
\nHowever, if we ignite the rope at A and B simultaneously, the flames meet at C after only 20 minutes!\r
\n\r
\nYou may ask why a rope should burn faster in one direction than the other. Strictly speaking, of course, the reason is irrelevant; the puzzle is already broken. But there are plausible reasons for a preferential burn direction. Perhaps the rope is resting on a mound, so that it is easier for a flame to progress upward than downward.\r
\n\r
\nOr maybe the ends of the \\\">\" and \"<\" symbols, in the diagram above, represent frayed strands of rope, preferentially sticking out to the left on the left hand side of the rope, and to the right on the right hand side of the rope. They may allow a flame to progress faster by more easily igniting the frayed strands from one direction.\r
\n\r
\nThe bottom line is that there is no purely deductive solution. We need to know something about the physical properties of the rope. That is, unless we add to the puzzle statement the hidden assumption I referred to above. It is this: in each section of rope, the rate of burning is the same in either direction.',3735,'Nick Hobson','2003-10-07 19:37:36');
INSERT INTO forumpost VALUES (1990,143,3,'Re: Best puzzle for the masses','Nick,\r
\n\r
\nWhile what you say is technically true, I don\'t think it is particularly useful, because you introduce something to the problem which is, IMHO, safely assumed away.\r
\n\r
\nI also made a hidden assumption that the rope isn\'t in a box with the oxygen slowly getting used up, slowing the burning process down (in which case I would need to know the rate of oxygen consumption and its affect on the burn rate).\r
\n\r
\nI\'m sure there are plenty of different scenarios that imply other hidden assumptions, but how useful is this?',3172,'SilverKnight','2003-10-07 20:06:12');
INSERT INTO forumpost VALUES (1991,279,5,'Re: Help (Stupid question)','Hmmmm..... I think it\'s SCHOLAR POWER! ;-)',3172,'SilverKnight','2003-10-07 20:07:42');
INSERT INTO forumpost VALUES (1992,279,5,'Re: Help (Stupid question)','It\'s been a while since I coded HTML by hand for more than an occasional bold or font, but as I recall, if you want to include a tag as text rather than as an HTML instruction, you simply \"escape\" it by preceeding it with the proper character (Which specific character, I forget). Alternatively, you could use the ISO character codes for the beginning bracket (<): instead of typing the bracket, type either its ascii code #60 or its ISO description lt between an ampersand (&) and a semicolon (;). Testing: (the left side of the = contains a white space which breaks the ISO code) & #60; = < < ; = < ',153,'TomM','2003-10-07 20:30:18');
INSERT INTO forumpost VALUES (1993,279,5,'Re: Help (Stupid question)','Hmm.. That last equation should read & lt; = < Apparently in the second attempt, where I put the space at the end, the code was complete except for the semicolon, and levik\'s parser added that \"forgotten\" semicolon onto the end. Nice detail under normal circumstances, but a little confusing in this context.\r
\n\r
\nBTW the \"lt\" is lower-case LT: it stands for less than.',153,'TomM','2003-10-07 20:37:28');
INSERT INTO forumpost VALUES (1994,279,5,'Re: Help (Stupid question)','Yeah, there\'s nothing special about being a scholar, really, just a little HTML manipulation. To make the < show up, I type in <. Then, to make the ampersand (&) show up in <, I type in &. I\'ve never heard of an escape character for HTML tags, but that of course doesn\'t mean that one can\'t exist. That\'s usually how tags are written out; the opening < is replaced by <.\r
\n\r
\nNow I just hope this whole message shows up the way I want it to.',1575,'DJ','2003-10-08 02:04:28');
INSERT INTO forumpost VALUES (1995,281,7,'Re: Hi! New guy','There\'s a search box on the front page that you can use to find the problem that your mate gave you. Have a look through the comments for the problem to see how others solved it and if you came up with anything different then add a comment of your own.\r
\n\r
\nHappy floobling.',1183,'fwaff','2003-10-08 05:39:26');
INSERT INTO forumpost VALUES (1996,282,5,'Advertising','Ads that get into your computer and change your homepage should be illegal, but more importantly shouldn\'t be attached to this site. The amount of pop-up and intrussive advertising on this site far exceedes just about any other site I know, and when you are going around, looking and people\'s solutions and opening new pages, you easily end up with fifteen or twenty pages of ads in the background (some of which try to change your homepage...).\r
\n\r
\nI realise that you put a lot of effort into this site, and the rest of us are getting it for free, so obviously you need some sort of revenue to make it worth your while. I just wonder if we can think of something that\'s less intrusive that fifteen pages worth of pop-ups. Perhaps individual ads would pay more if a single ad was shown for five seconds before you get to the solution page, or something.',3372,'Sam','2003-10-08 08:52:43');
INSERT INTO forumpost VALUES (1997,279,5,'Re: Help (Stupid question)','Speaking of Escape characters, it seems that sometimes when a double quote character is entered in a solution or comment, the system puts an untyped backslash in front of it, apparently thinking it needs this as an escape character, but it just shows up on the solution or comment.',1301,'Charlie','2003-10-08 09:09:46');
INSERT INTO forumpost VALUES (1998,282,5,'Re: Advertising','Yes, It started some time last week: an ad that persistently changed the home page of my browser, just by starting up flooble, before having a chance to log in on my computer at work. Now I even have put \"remember me\" on at the office computer, to avoid excess advertising, particularly of the noxious kind that changes one\'s home page, sometimes including images not suitable for an office environment.',1301,'Charlie','2003-10-08 09:13:26');
INSERT INTO forumpost VALUES (1999,282,5,'Re: Advertising','Let me put in a vote too.\r
\nThis is a great site and very well run.\r
\nI love it, but one particular add (the one that changes the home page to one with inappropriate images) has made me seriously consider not coming back.\r
\nIts not that I\'m a prude but I, like many others, check the site on my lunch break at work and inaapropriate images could get me in deep trouble.\r
\nI\'ll say it again, this is a great site and I know that there is no free lunch but if it is at all possible to avoid that specific type of advertising I\'d be very grateful.',2839,'FatBoy','2003-10-08 13:33:59');
INSERT INTO forumpost VALUES (2000,282,5,'Re: Advertising','I am new to flooble. I saw the site over the summer, but just recently started consistently reading and trying problems. I am annoyed also by the pop-ups, but I have dealth with it. Now that I realize that the problems are posted throughout the day, I have tried to read them at lunch...the only problem is I teach high school and CAN NOT have anything remotely inappropriate on my computer at school. I don\'t mind too much at home, but usually by then several people have commented on an posted solutions. Fortunately, I have not come across the pop up that tries to set my homepage for me yet...but this thread makes me nervous. I also understand the expense to design and operate a site like this, so I\'ll be thinking of some alternate suggestion (if you are interested).\r
\nGreg',1112,'Greg','2003-10-08 14:43:30');
INSERT INTO forumpost VALUES (2001,279,5,'Re: Help (Stupid question)','When that happens, I think it\'s not because the escape character is needed in the display on the page, but rather in the PHP string used to store the entry. Such problems are rare, as the slashes are generally stripped from a string before posting (PHP has a built-in stripslashes() function to handle that), but I have noticed that happening a few times on this site.',1575,'DJ','2003-10-08 14:59:43');
INSERT INTO forumpost VALUES (2002,146,6,'Re: sequences','Just another note...\r
\nYou mentioned \"I was under the impression that a sequence relied upon some mathematical or computational \"rule\" to progress from one term to the next\"\r
\nThere are certain TYPES of sequences that do rely on a computational rule. The two most basic ones are\r
\nArithmetic Sequence {10,15,20,25,30,35} (add the same thing each time)\r
\nGeometric Sequence {10,20,40,80,160,320}(multiply by the same thing each time)\r
\n',1112,'Greg','2003-10-08 18:01:06');
INSERT INTO forumpost VALUES (2003,282,5,'Re: Advertising','If you have trouble with your home page, set it to one of your favorites. Then, whenever the home page changes, hold down the mouse on the link on your favorites menu and drag your original home page to the home page icon. This is an easy way to fix it, but it doesn\'t get rid of the ads. The homepage changing ads don\'t come up often, at least not to me.\r
\n\r
\nIf you\'re logged on to Flooble, less pop-ups appear (or so I heard from a thread at the bottom of the general forum). I think the pop-ups can be annoying, but what\'s more annoying is that lottery ad that sometimes appears and makes music, and it\'s not a pop-up I can just close.',3558,'Tristan','2003-10-08 19:25:04');
INSERT INTO forumpost VALUES (2004,282,5,'Re: Advertising','That\'s why I\'ve muted the volume on my office computer.',1301,'Charlie','2003-10-08 22:21:47');
INSERT INTO forumpost VALUES (2005,282,5,'Re: Advertising','Tristan,\r
\nyou are the MAN!!\r
\nSeriously, thanks your tip will save me tons of hassle in the future. I never realized that I had become one of those old guys who couldn\'t figure out the basic shortcuts but I guess I am.\r
\n\r
\nTo Everyone,\r
\nHave you started to get a little pop-up that is labled something like \"data protection\" It looks like a fairly convincing windows dialog box and it asks for your windows password.\r
\n\r
\nI just wanted to know if this is another advertising thing or if it means my IT people have jsut installed something new on my system.',2839,'FatBoy','2003-10-09 07:24:29');
INSERT INTO forumpost VALUES (2006,282,5,'Re: Advertising','I\'ve recently had one that looked exactly like the file download window that claimed to be from the system administrator. The message was something to do with updating my security policy. That may be the same thing. FWIW I always close any windows I haven\'t knowingly opened on the basis that if it\'s something important then the sysadmin will send an e-mither.\r
\n\r
\nCuriously I\'ve noticed a marked reduction recently in the number of pop-ups that appear. I now only get one when I log on (usually either a fit-inducing flashing box telling me I\'m the 1,000,000,000,000th visitor or the offer of magic beans that will make me look better in a bikini). I\'ve not had any that change my homepage and I\'ve not seen anything inappropriate.',1183,'fwaff','2003-10-09 09:13:53');
INSERT INTO forumpost VALUES (2007,282,5,'Re: Advertising','Hmmm... That\'s not good - I will try to look over the ads served on this site and make sure nothing that intrusive is getting through. \r
\n\r
\nIn all, as the site gets more traffic I am hoping to be able to show more high quality ads instead of that sort of junk.\r
\n\r
\nIt\'s unfortunate that this type of advertising is neccessary to provide free sites nowadays.',1,'levik','2003-10-09 10:08:11');
INSERT INTO forumpost VALUES (2008,282,5,'Re: Advertising','Can anyone point out the exact ad that causes the homepage change? I would prefer that to having to track it down, since I usually browse with Firebird - a browser that I heartily recommend not only for its speed but the ability to very precisely block only the unwanted popups.',1,'levik','2003-10-09 10:10:35');
INSERT INTO forumpost VALUES (2009,282,5,'Re: Advertising','Levik,\r
\nI don\'t know the specific ad but the home page it re-directs me to is called something along the lines of \"pass this On\"\r
\nThe page itself is often deceptive: sometimes it offers adult photos (annoying but not that scary as it is easy to recognize and get rid of) and the scarier message that say something like: click here to get an important security bulletin. (MOre scary since I might actually press a button for security info(although I as yet have not been fooled))\r
\n',2839,'FatBoy','2003-10-09 12:30:26');
INSERT INTO forumpost VALUES (2010,282,5,'Re: Advertising','But if we all used Firebird what would be the point in the pop-ups? You wouldn\'t get any revenues anyways!\r
\n\r
\nSeriously though, the Onion sometimes has you sit in front of a five second ad before you get to their page and, while it\'s a bit of a bore, I think it\'s better than pop-ups, and they must pay much more. If you had one of those before the solutions page or something, that might generate the same revenues as twenty-odd pop-ups that noone will ever click.',3372,'Sam','2003-10-09 12:40:16');
INSERT INTO forumpost VALUES (2011,275,5,'Re: The FAQ WIP','There - I promised I\'d get to it eventually :) \r
\n\r
\nCheck it out here',1,'levik','2003-10-09 12:41:58');
INSERT INTO forumpost VALUES (2012,282,5,'Re: Advertising','Unfortunately the reality of todays internet marketplace is such that I cannot employ a sales force to actively seek out people to buy that type of ad on my site, so no high-enough quality ads of this type are available.\r
\n\r
\nFor full disclosure, one company does offer them, but they don\'t let me customize the ad pages, which make it impossible to make them look like they\'re part of the site. I am afraid that as a result, people would leave thinking they clicked on the wrong link or something.',1,'levik','2003-10-09 12:45:24');
INSERT INTO forumpost VALUES (2013,275,5,'Re: The FAQ WIP','Looks pretty good so far; there are a few things that could be added, but just about everything I can think of has already been mentioned in this thread. What\'s there covers the basics, at least.\r
\n\r
\nI did notice one spelling/grammar error.. in the first FAQ listing, \"click it\'s name\" should read \"click its name.\"',1575,'DJ','2003-10-09 14:58:55');
INSERT INTO forumpost VALUES (2014,275,5,'Re: The FAQ WIP','Good catch :)\r
\n\r
\nYou\'re not an editor for a living, are you?',1,'levik','2003-10-09 15:04:17');
INSERT INTO forumpost VALUES (2015,143,3,'Re: Best puzzle for the masses','It\'s true there are many possible factors that could influence the validity of the solution. However, this is a *logic* puzzle. When a logic puzzle posits a rope which does not burn at a uniform rate, a *closely related* question is: does it burn at the same rate in both directions? It is also a relevant question, as any solution depends upon the answer. Therefore it seems likely that the poser omitted any mention of directional burn rate either because: a) he/she overlooked it; or b) it would be too big a hint.\r
\n\r
\nEither way, in my opinion, we have a flawed logic puzzle.',3735,'Nick Hobson','2003-10-09 15:25:53');
INSERT INTO forumpost VALUES (2016,143,3,'Re: Best puzzle for the masses','Nick you are wrong. The rate at which the rope burns is irrelevant all that matters is that it takes one hour to burn.',1072,'Alan','2003-10-09 17:41:47');
INSERT INTO forumpost VALUES (2017,275,5,'Re: The FAQ WIP','Where can I see a complete list of html? (for the faq)',1072,'Alan','2003-10-09 17:43:47');
INSERT INTO forumpost VALUES (2018,143,3,'Re: Best puzzle for the masses','Alan, then how do you explain the counter-example rope in my October 7th post, above?\r
\n\r
\nLight either end of this rope and it burns out in 60 minutes. Simultaneously light both ends and it would burn out in 20 minutes.',3735,'Nick Hobson','2003-10-09 17:53:21');
INSERT INTO forumpost VALUES (2019,143,3,'Re: Best puzzle for the masses','There\'s no reason to assume that any rope would burn at different rates depending on the direction, and the wording of the problem clearly implies that either end of the rope may burn at different rates, but that rate is constant for the given half. (\"half the rope may burn in one minute, and the other half will take 59 more minutes to burn\"). That precludes the possibility that either half would have two different rates associated with it, depending on which end was lit.',1575,'DJ','2003-10-09 18:05:30');
INSERT INTO forumpost VALUES (2020,275,5,'Re: The FAQ WIP','There is a check it out here link above, in addition to FAQ on the main page.\r
\n\r
\nI would recommend making the questions in a larger font and in a more contrasting color. Right now they are hard to read, and if you don\'t know the question the answer doesn\'t help much.\r
\n',1626,'Gamer','2003-10-09 18:13:07');
INSERT INTO forumpost VALUES (2021,143,3,'Re: Best puzzle for the masses','DJ, on the contrary the assumption that a rope will always burn at the same rate in either direction is in need of justification. Practically, I believe it is quite likely that any given rope will have sections that burn at different rates depending on the direction. Logically, it is possible.\r
\n\r
\nThe complete statement of the puzzle premise is: \"You have two ropes. You know that each rope takes one hour to burn from one end to the other, but that the burning does not take place at a constant rate (i.e. half the rope may burn in one minute, and the other half will take 59 more minutes to burn).\"\r
\n\r
\nIt seems to me the second sentence is saying that burning does *not* take place at a constant rate. It then gives a numerical example to reinforce the fact that the first half (by length) of the rope need not burn in 30 minutes. It doesn\'t imply that each half burns at a constant rate. And it certainly doesn\'t preclude the possibility that sections of the rope may burn at a different rate in either direction.',3735,'Nick Hobson','2003-10-09 18:39:18');
INSERT INTO forumpost VALUES (2022,275,5,'Re: The FAQ WIP','Nevermind about the contrast thing (although bigger still would be good), the colors I was viewing with were messed up resulting in the text being much darker than it should.',1626,'Gamer','2003-10-09 18:42:15');
INSERT INTO forumpost VALUES (2023,275,5,'Re: The FAQ WIP','Something that could be added to the \"Ooh! Ooh! I know the solution - how do I post it?\" query - no, you do not gain any \"points\" for answering correctly, or first, nor will it raise your rank. I think a lot of people, including myself, had that question at first. Might also be the reason that some questions have forty-two identical solutions all lined up one after the other...',3372,'Sam','2003-10-09 20:59:34');
INSERT INTO forumpost VALUES (2024,275,5,'Re: The FAQ WIP','One important point you forgot to mention in the FAQ is:\r
\n\r
\nIf one posts to a problem with no new information (e.g., restating a solution essentially identical to an earlier post), then his rank is lowered.\r
\n\r
\n:-)',3172,'SilverKnight','2003-10-09 22:04:18');
INSERT INTO forumpost VALUES (2025,275,5,'Re: The FAQ WIP','Yes, we wish that could be implemented so we don\'t just see the same solution over and over and over with no explanation, but levik hasn\'t agreed to that. :D',1626,'Gamer','2003-10-09 22:57:39');
INSERT INTO forumpost VALUES (2026,143,3,'Re: Best puzzle for the masses','I am confused as to how a rope could burn differently in two different directions from a practical stand point.\r
\n\r
\nAlso, I think the wording of the puzzle states how a certain half would burn in x minutes and how a certain half would burn in y minutes. It says x doesn\'t need to equal y, but x will always equal x.',1626,'Gamer','2003-10-09 23:01:14');
INSERT INTO forumpost VALUES (2027,143,3,'Re: Best puzzle for the masses','What I mean by my first comment is wouldn\'t the frayed strands no matter what burn in the same length? Even if they ignited, wouldn\'t the rope still burn at the same rate?\r
\n\r
\nAnyway, I would feel like adding \"frayed\" strands to the problem is really trying to find SOME way to make the problem wrong. The whole point of the puzzle is to assume that the rope is normal, no frayage, no \"different burning in other directions\", and no dousing in gasoline half way through. In my opinion, if the rope is just pure rope, it isn\'t possible to have it burn in another way.',1626,'Gamer','2003-10-09 23:06:02');
INSERT INTO forumpost VALUES (2028,283,5,'Previewing pi','I was writing a problem and I used the html codes for pi. They worked just fine, and little pi signs replaced my html codes in both the preview and the word box. When I made a few corrections and previewed it again, all my pi signs had changed to some new sign I had never seen. It only seems to happen when submitting problems, not when editing them. It\'s kind of a minor error, something I assume Levik can quickly fix, and if not, it\'s not too hard to get around.',3558,'Tristan','2003-10-10 00:29:47');
INSERT INTO forumpost VALUES (2029,143,3,'Re: Best puzzle for the masses','Gamer,\r
\n\r
\nTo answer your question... (and I think Nick kinda made mention to this earlier)... what if I laid a rope over an inverted \'V\'.\r
\n\r
\nSo, the middle of the rope was higher than either end.\r
\n\r
\nThen, if I ignite only one end, the flame may go \'up\' the rope to the middle in 20 minutes, but going down the other side would be much slower and take, say, 40 minutes. So, the rope burns in one hour.\r
\n\r
\nHowever, if I begin burning both ends at the same time, then both flames go \'up\' towards the middle, and the rope burns completely in 20 minutes.\r
\n\r
\nAlternatively, I imagine it would be possible to treat a rope chemically, or fashion it via a special weave, or some other method, such that it could cause differing burn rates in opposing directions.\r
\n________________________________\r
\n\r
\nIt really boils down to whether or not you think a *closely related* question is: does it burn at the same rate in both directions?. I do not. Nick, on the other hand, does.\r
\n________________________________\r
\n\r
\nNow all that said, I sincerely hope (but don\'t expect) that we can put this discussion to rest.\r
\n\r
\n--- SK',3172,'SilverKnight','2003-10-10 03:18:04');
INSERT INTO forumpost VALUES (2030,282,5,'Re: Advertising','Following on from Tristan\'s comment above I logged out of Flooble yesterday so that this morning I appeared as a guest (when I first joined I ticked the \'remember me\' box so I\'ve never been a guest since). It may be coincidence, but as the site was loading 3 pop-ups came with it rather than the usual 1 I get when I\'m logged on. 2 extra pop-ups, no great problem, except that one of them was for a porn site and contained some very explicit photos in the ad, to make matters worse clicking the \'X\' button to close it opened up several other pages of similar material. Some of these new windows closed no problem, a couple of them then opened up more of the same. I guess that in total there were about a dozen pages to shut down.\r
\n\r
\nAs with Fatboy, I\'m no prude, but that kind of advertising is totally inappropriate for this site for multitudinous reasons, not least of which is that you\'re getting a growing following from schools as this is seen as a well run site with a good community and an excellent library of puzzles. This kind of advertising will destrtoy that hard built reputation very quickly.\r
\n\r
\nIt appears it\'s possible to avoid that particular set of pop-ups by using the \'remember me\' option, but that only helps those that are already members. Anybody coming in cold from Google or through recommendation is possibly going to close it down and never come back especially if they are in an environment where that kind of advertising is not appropriate (eg schools, offices, etc).\r
\n\r
\nI fully appreciate that you must have a revenue source to fund this, but advertising porn is not the way to do it.\r
\n\r
\nLevik you need to act quickly on this or all your hard work will have been wasted.',1183,'fwaff','2003-10-10 04:04:40');
INSERT INTO forumpost VALUES (2031,283,5,'Re: Previewing pi','This happens when submitting problems. If you noticed in the comments, whenever you typed in an actual sign (copy and pasted froma previous post) instead of using the html thing, it would come up wierd. Because the preview button changes the things from the pi-html to pi, and submitting it changes pi to wierd-pi, you will end up with wierd-pi on the page.',1626,'Gamer','2003-10-10 07:15:42');
INSERT INTO forumpost VALUES (2032,143,3,'Re: Best puzzle for the masses','Nick, I believe you are nit picking. The assumption about a rope is that it will burn, do so uniformly and at the same rate in both directions. In our case, the rope does NOT burn uniformly, so we specify that conditions. All the other regular rope \"defaults\" still apply. \r
\n\r
\nI don\'t believe anyone would think of the solution and then discard it on the basis of ropes burning at different rates each way, and as such, specifying that they burn the same reguardless of direction is not strictly neccessary. It would however provide a hint that I belive the problem is more interesting without.',1,'levik','2003-10-10 07:46:08');
INSERT INTO forumpost VALUES (2033,282,5,'Re: Advertising','Thanks fotr the tip _ will look into it. The problem is that there are a few networks rotating ads on the server, so figuring out which one it is to shut it down won\'t be the easiest thing in the world. But I will try.',1,'levik','2003-10-10 08:05:51');
INSERT INTO forumpost VALUES (2034,282,5,'Re: Advertising','It it helps, it was one that was added recently. I quite often until recently did not tick the \"remember me\" box, and didn\'t have the home-page-switcher come up. It is only last week that I had to tick that box even at my office computer to prevent unseemly sites from popping up, and worse, becoming a home page.',1301,'Charlie','2003-10-10 09:07:22');
INSERT INTO forumpost VALUES (2035,282,5,'Re: Advertising','The problem is, as I said, that I don\'t deal with advertisers directly. I join \"networks\" which act as intermediaries between web publishers such as myself, and people who want to buy ad space. These networks get new advertisers all the time which I do not get to approve. I can assure you I have not added any new advertiser or network in well over a year, so the problem most likely lies with a bad apple advertiser joining one of these places. \r
\n\r
\nNow generally, networks themselves have policies against the types of ads you speak of, but unfortunately, they are not always able to enforce them with sufficient success... If the offender is tracked down and reported, they generally cancel their account.\r
\n\r
\nI have added some debug code to the bottom of every page, which details what popup network gets called. I have run through the site a couple of times myself without getting hit with anything too difficult to close, objectionable or any type of installer. However, if you run into them, I would greatly appreciate it if you could just scroll to the bottom of the page and let me know what it says there for \"Last Ad\" and \"This Ad\". This will allow me to figure out which network the offenders are coming from so that I could take the issue up with their management.\r
\n\r
\nI also increased the effectiveness of cookies that ensure that you should not see repeat popups too many times - this is something I should have done a long time ago, and was actually sure that I *HAD* done it. Ah, the blissful ignorance of browsing with Firebird...',1,'levik','2003-10-10 10:32:47');
INSERT INTO forumpost VALUES (2036,282,5,'Re: Advertising','Levik,\r
\nI don\'t know when you increased the effectiveness of the cookies, but I have seen a definite improvement today.',2839,'FatBoy','2003-10-10 12:50:26');
INSERT INTO forumpost VALUES (2037,284,3,'Hey, DJ','DJ, \r
\nI\'ve just gotten around to working the letter cubes problems. I really like them, thanks.\r
\nI saw that you got them from all-star puzzles. I went over there and have been looking around for more and can\'t find any. Is there some specifc category that they are under?\r
\n\r
\nThanks\r
\nthe Corpulent One',2839,'FatBoy','2003-10-10 14:38:53');
INSERT INTO forumpost VALUES (2038,275,5,'Re: The FAQ WIP','In the question \"I submitted a problem. When will it be poste don the site?\", \"poste don\" s/b \"posted on\".',1301,'Charlie','2003-10-10 16:47:32');
INSERT INTO forumpost VALUES (2039,143,3,'Re: Best puzzle for the masses','In many problems you can find ways to make the solution wrong. For example, one problem might include plurals where the answer was singular, or you might answer in base 5 when the question doesn\'t say anything about bases. For every good solution there is an equal and opposite person who validates their solution by finding something wrong with the posted solution.',1626,'Gamer','2003-10-10 17:07:52');
INSERT INTO forumpost VALUES (2040,143,3,'Re: Best puzzle for the masses','levik,\r
\n\r
\nWhen I first heard this puzzle, maybe five years ago, I was disappointed with the purported solution for the very reason you suppose nobody would be! But I agree that, with the directional assumption, the solution is elegant.\r
\n\r
\nI understand your idea of regular rope \"defaults.\" Were we dealing with a completely regular rope, I could almost agree it would not be necessary to specify that burn rate is independent of direction. But when you introduce a rope where one half might burn 59 times faster than the other half, I\'m afraid all bets are off, as far as I\'m concerned. Then it is quite legitimate to question the directional burn rate. Indeed, I strongly suspect such a rope *would* have sections that burn faster in one direction.\r
\n\r
\nHere is the basis for an abstract solution that does not assume the burn rate is independent of direction. It requires the use of a knife.\r
\n\r
\nChop the rope in half and simultaneously ignite both left ends. (Without reorienting either section, of course.) If they both burn out at the same time, we have measured 30 minutes. If not, instantaneously chop the unburnt portion of rope in half and ignite the non-burning left end. And so on, ad infinitum... \r
\n \r
\nSince, at any given time, we have two pieces of rope burning *in the same direction*, once the entire rope burns out, we have measured 30 minutes! \r
\n \r
\nIf we treat this as a logic problem, and conceptualise the burning rope as a line segment with point(s) moving along it, this approach offers some advantages over the standard solution. Firstly, as already mentioned, it does not implicitly assume a unidirectional burn rate. This appeals (to me) aesthetically. Secondly, it can immediately be generalised to yield a way of measuring 60/n minutes, where n is a positive integer.\r
\n \r
\nAs a solution to a physical problem, it may or may not be more accurate than the standard solution, depending upon the nature of the rope. (You would, of course, chop the rope only a few times.)',3735,'Nick Hobson','2003-10-10 17:42:42');
INSERT INTO forumpost VALUES (2041,143,3,'Re: Best puzzle for the masses','Gamer,\r
\n\r
\nTrue, but I think you need to distinguish between trivial and substantive objections.',3735,'Nick Hobson','2003-10-10 17:57:17');
INSERT INTO forumpost VALUES (2042,283,5,'Re: Previewing pi','Well, that\'s pretty much what I thought. Still, the wierd-pi doesn\'t look anything like pi to me. It\'s kind of a minor error, but maybe that means it\'s a minor thing to fix it. ',3558,'Tristan','2003-10-10 17:58:37');
INSERT INTO forumpost VALUES (2043,282,5,'Re: Advertising','You could be seeing the effects of the cookies, or potentially the networks cracked down on the offenders. Most likely it\'s a combination of the two factors.',1,'levik','2003-10-10 18:43:33');
INSERT INTO forumpost VALUES (2044,143,3,'Re: Best puzzle for the masses','Ok nick now i think i understand the rope burning in 40 minute thing but maybe i don\'t but now here the thing. The question asks \"how can u measure out 45 minutes\" So If you put the rope in such a way or hold it up in a direction that causes it to burn \"improperly\" then you simply didn\'t solve the problem. You are wrong because you didn\'t solve the problem. the problem is not wrong because you found a way to come up with an incorrect answer. What I\'m trying to say is If you do the things you\'re talkin about that come up with an incorrect solution, well then you\'re incorrect, plain and simple. hers the solution. Lie both ropes flat down on any surface (Please don\'t argue abou surfaces now) and light two ends of one rope and one end of the other. Next when one rope burns out light the end of the other rope. the solution does not say put the rope in an inverted v so it burns in 40 minutes now does it say hold the rope in an upward direction causing it to burn un-uniformly.',1072,'Alan','2003-10-11 13:32:11');
INSERT INTO forumpost VALUES (2045,143,3,'Re: Best puzzle for the masses','sorry for the spelling mistakes but I think everyone can understand what i\'m trying to say. In my last sentence it should say nor not now.',1072,'Alan','2003-10-11 13:35:29');
INSERT INTO forumpost VALUES (2046,143,3,'Re: Best puzzle for the masses','Alan,\r
\n\r
\nPlacing a rope on an inverted V-shape is just one example of how it may burn faster in one direction than the other.\r
\n\r
\nAnother possibility is that the rope construction itself could confer a bidirectional burn rate, and over this the puzzler has no control. Whether this takes the form of an asymmetrical construction, or frayed ends, or is a consequence of a very inhomogenous structure (one half of which may burn *59 times* faster than the other), it is a distinct physical possibility, and a definite logical one.\r
\n\r
\nTherefore we cannot reasonably deduce that a \'1 hour\' rope, lit at both ends, will burn out in 30 minutes.',3735,'Nick Hobson','2003-10-11 20:10:37');
INSERT INTO forumpost VALUES (2047,143,3,'Re: Best puzzle for the masses','But with a normal rope, is any of this possible? You are to assume the rope is normal except for anyting stated.\r
\n\r
\nSure you could tie the rope into many knots and it would burn faster, or you could put it into other formations which would make it burn differently. The point of the problem is to note how such a rope would function under normal circumstances.\r
\n\r
\n',1626,'Gamer','2003-10-11 21:00:11');
INSERT INTO forumpost VALUES (2048,13,5,'Re: Problems in forums','I think that is precisly right and agree all users should be aware that problems should not be subbmitted in forums.\r
\n\r
\nGoodbye and good day.',3835,'rachel','2003-10-12 05:31:22');
INSERT INTO forumpost VALUES (2049,143,3,'Re: Best puzzle for the masses','Ok lets take this one hour rope and work with it ok? first lets take this rope and light one end. According to the rule it should burn out in one hour. Now lets \"revive\" this rope back to its original state. And light the other end. Note that this time it would also take one hour to burn in order to up hold the rule of it being a one hour rope. if the rope burns \"faster\" in one direction then there fore it is no longer a one hour rope, and using that rope would not constitute it as a part of any solution to that problem. As we can see the the problem clearly states \"If one end of the rope is lit then the rope will burn out in one hour\" the existence of this statement prevents the rope from taking more than one hour to burn in either direction. Now that we see every rope burns one hour both ways we can deduce that one both ends are lighted it will take half an hour to burn. And with simple logic we see the rest of the solution that is on flooble right now is correct.',1072,'Alan','2003-10-12 14:20:17');
INSERT INTO forumpost VALUES (2050,143,3,'Re: Best puzzle for the masses','Gamer,\r
\n\r
\nIt\'s not a normal rope, though, is it? It\'s a rope one half of which can burn dozens of time faster than the other. Given such a weird rope, surely a natural question is: does it burn at the same rate in both directions? It\'s a question that relates to burn rate (mentioned in the puzzle), and it\'s a question that is relevant to the solution.\r
\n\r
\nAlan,\r
\n\r
\nThe counter-example rope in my October 7th post, above, lit from *either* end, *does* burn out in one hour. Parts of it burn faster left to right; other parts burn faster right to left. They balance out, so that the rope takes one hour to burn out, in either direction. Yet, if you light both ends, it burns out in 20 minutes. So it cannot be a matter of simple logic that, if both ends of a \'1 hour\' are lighted, it will take half an hour to burn.',3735,'Nick Hobson','2003-10-12 16:51:50');
INSERT INTO forumpost VALUES (2051,143,3,'Re: Best puzzle for the masses','But it is a normal rope other than that aspect! When you don\'t see anything to the contrary, you are to assume it burns like a normal rope. The only thing you see is that it doesn\'t burn evenly across. The other stuff you have to assume is even unless otherwise satement. And one thing different isn\'t that wierd is it? Haven\'t you found many other things to do to the rope to make it burn in all sorts of obscure fashions?',1626,'Gamer','2003-10-12 18:26:33');
INSERT INTO forumpost VALUES (2052,143,3,'Re: Best puzzle for the masses','Gamer,\r
\n\r
\nI\'m willing to let it rest at that! As SilverKnight remarked in an earlier post: \"It really boils down to whether or not you think a *closely related* question is: does it burn at the same rate in both directions? I do not. Nick, on the other hand, does.\" It spoils the puzzle, for me.',3735,'Nick Hobson','2003-10-12 19:51:39');
INSERT INTO forumpost VALUES (2053,143,3,'Re: Best puzzle for the masses','OK... I am not as perceptive... I am rather closed minded and would never think of frayed edges or different rope postions so it is good for me. :)\r
\n\r
\nI think its an interesting puzzle, and helps remind us to be more specific in our wording. :)',1626,'Gamer','2003-10-12 21:28:37');
INSERT INTO forumpost VALUES (2054,73,7,'HELLO','umm...HI...im neW and i dont get wats the diffrence between xanga and this....but anywaz...hi?',3850,'Arthur Huang','2003-10-13 01:31:23');
INSERT INTO forumpost VALUES (2055,284,3,'Re: Hey, DJ','No, there were only two problems of the type there, which are #3 and #4 on this site. They are listed under the logic problems, and you might have to go through a few pages to find them.',1575,'DJ','2003-10-13 13:20:50');
INSERT INTO forumpost VALUES (2056,73,7,'Re: hello!','I don\'t get what is at all similar about xanga and this, other than the fact that they are both webpages..',2561,'Aaron','2003-10-13 23:35:39');
INSERT INTO forumpost VALUES (2057,284,3,'Re: Hey, DJ','THanks\r
\n',2839,'FatBoy','2003-10-14 08:11:46');
INSERT INTO forumpost VALUES (2058,284,3,'Re: Hey, DJ','Oh.. I just noticed that problems #1 and 2 also say that they are from that site, but they\'re not, if that\'s what you were looking for. The erroneous citation was added after the problem was already posted.',1575,'DJ','2003-10-14 09:09:24');
INSERT INTO forumpost VALUES (2059,285,7,'Help me with this','hi ppls im new, but id like some help with a problem, so if anybody is there, please respond\r
\n',3880,'brian harrison','2003-10-14 17:44:26');
INSERT INTO forumpost VALUES (2060,285,7,'Re: Help me with this','You can look in the archives. That is often how things are solved here. ;)\r
\n\r
\nWe aren\'t allowed to give the problems\' solutions because that\'s against the rules, and you shouldn\'t post any problems to the site as well. They are likely already on the site.',1626,'Gamer','2003-10-14 17:52:07');
INSERT INTO forumpost VALUES (2061,278,3,'Re: Can anyone recap my memory','Zzzzzzzzzzzzzzz- not very helpful are u\r
\n\r
\nNEXT............',3802,'SK','2003-10-15 06:00:50');
INSERT INTO forumpost VALUES (2062,278,3,'Re: Can anyone recap my memory','you go gamer.\r
\nI can\'t believe he didn\'t get it.',2839,'FatBoy','2003-10-15 07:31:54');
INSERT INTO forumpost VALUES (2063,278,3,'Re: Can anyone recap my memory','I think I remember the puzzle you are asking about. It is a variation of the puzzle \"Colored Hats\" on this site. Gamer has provided a link to \"Colored Hats\" in his comment.',1920,'Brian Smith','2003-10-15 09:41:31');
INSERT INTO forumpost VALUES (2064,278,3,'Re: Can anyone recap my memory','Although.. I don\'t see what\'s the problem about asking for help finding a problem in the forum - where should someone ask?',1575,'DJ','2003-10-15 12:05:25');
INSERT INTO forumpost VALUES (2065,285,7,'Re: Help me with this','Rather, you shouldn\'t post a problem in the forum, chatterbox, or in comments to another problem and ask for the solution.\r
\nMore often than not, the problem you are trying to solve is already on the site anyway, so use the search box on the main page to try to find it. The search looks for exact phrases, not multiple words, so something like \"hats color person\" probably won\'t find anything. Try looking for single keywords, and use the \'Search body\' checkbox for better results.\r
\nOn the other hand, if you have a problem that you found interesting, you know the solution to, and want to share, feel free to submit the problem to the site once you have become a student and are more familiar with what goes on here.\r
\nLastly, the site is not here to get people to solve your homework problems, and as there are always quite a few problems waiting to be posted, submitting a problem you don\'t know the answer to will probably not very useful to you in a few months\' time anyway.',1575,'DJ','2003-10-15 12:27:07');
INSERT INTO forumpost VALUES (2066,278,3,'Re: Can anyone recap my memory','My guess is if you type in key words it\'s either hit or miss, so finding a problem either will happen by using common sense words or it won\'t work at all. Even the problem suggested which was a more major change might have been found.\r
\n\r
\nAnyway, if the person was asking about where to find a problem (which could be just an excuse for someone to solve it for them... Being the less polite person that he was I would guess this is the case) and really wanted to find it, it would be fine in my opinion. \r
\n\r
\nHowever, a major issue here (and what I said in my first sentence) was being rude. We don\'t need to use 3 posts, we don\'t need to insult the people you are trying to get help from, and we don\'t need to use caps and wierd language.',1626,'Gamer','2003-10-15 18:00:53');
INSERT INTO forumpost VALUES (2067,286,5,'Changing Categories','Fooligh question: Is it possible to change the category of a puzzle once it has been submitted? I thought I remembered seeing a \"change category\" button in the edit problem page, but now can\'t find it (if it ever was there).\r
\nThanks!',3372,'Sam','2003-10-20 12:09:13');
INSERT INTO forumpost VALUES (2068,286,5,'Re: Changing Categories','You don\'t get that option until you become an apprentice.',1301,'Charlie','2003-10-20 14:25:03');
INSERT INTO forumpost VALUES (2069,286,5,'Re: Changing Categories','If you believe the category should be changed, and cannot do it yourself, you can always petition asking me to do it. I will change it if I find the new category more appropriate.',1,'levik','2003-10-20 14:38:44');
INSERT INTO forumpost VALUES (2070,286,5,'Re: Changing Categories','If nothing else works, just delete and resubmit your problem if you submitted it within the last two or three days.',1920,'Brian Smith','2003-10-20 15:27:22');
INSERT INTO forumpost VALUES (2071,286,5,'Re: Changing Categories','I always found that annoying, and that is why Strawberries! is in Logic and not Liars and Knights, but if others don\'t want to change that, it\'s fine :)',1626,'Gamer','2003-10-20 16:41:41');
INSERT INTO forumpost VALUES (2072,287,7,'Hey, yet another newbie!!','Hey, I\'m new here.\r
\n\r
\nI found this site by posting on another site. One of the boxes was down the bottom. I had always wanted to join, didn\'t know how...\r
\n\r
\n\r
\nIf you want to know anything about me, just ask!!\r
\n\r
\nAlso, how many Australians are there on here?? \'cause nearly everywhere I go there are hardly any!!\r
\n\r
\n\r
\nlove nashie',3785,'Ashlee','2003-10-21 05:45:03');
INSERT INTO forumpost VALUES (2073,287,7,'Re: Hey, yet another newbie!!','Welcome, nashie,\r
\nWe had a discussion about the international represnetation and I think we have a few folks loggin in from down under. If not then spread the word.\r
\nDon\'t worry, if we do have some australians you are sure to hear form them.\r
\nAs many have noted, female newbies always seem to garner a lot of response in the forums.\r
\nFatboy',2839,'FatBoy','2003-10-21 07:28:45');
INSERT INTO forumpost VALUES (2074,288,7,'D&D Riddle anyone?','What is blind, deaf and dumb but always tells the truth?\r
\n\r
\nBlickQuickly',3966,'Rock','2003-10-21 11:51:06');
INSERT INTO forumpost VALUES (2075,288,7,'Re: D&D Riddle anyone?','Please do not post puzzles or riddles in the forums.',1920,'Brian Smith','2003-10-21 11:52:31');
INSERT INTO forumpost VALUES (2076,287,7,'Re: Hey, yet another newbie!!','From pedants corner it\'s worth pointing out that it is newbies with female sounding names or those claiming to be female that garner (good word Fatboy, not just a pretty face after all) the most responses. Of course it\'s impossible to KNOW what sex anybody is in floobland - I followed the link through to Charlie\'s homepage and I\'m still not sure whether \'Charlie\' is short for Charles or Charlotte! For all we know Ashlee could be a highly trained koala or maybe a even a new lifeform that evolved from that piece of old corned beef in the back of my fridge.\r
\n\r
\nThe point is that out here everybody can be whatever they want to be, which is probably why it appears that there aren\'t any Welsh flooblers.',1183,'fwaff','2003-10-21 11:58:17');
INSERT INTO forumpost VALUES (2077,287,7,'Re: Hey, yet another newbie!!','Actually, that might be due the crack about whales I made a while back.. I hope I didn\'t offend anyone from the homophonic country..',1575,'DJ','2003-10-21 12:21:19');
INSERT INTO forumpost VALUES (2078,289,3,'Riddle for you all...','What is blind deaf and dumb but always tells the truth?',3966,'Rock','2003-10-21 14:55:18');
INSERT INTO forumpost VALUES (2079,289,3,'Re: Riddle for you all...','Please stop posting riddles in the forums.',1920,'Brian Smith','2003-10-21 14:59:44');
INSERT INTO forumpost VALUES (2080,289,3,'Re: Riddle for you all...','Maybe we need to make that \"Don\'t post things on the forum\" in big letters or something :)',1626,'Gamer','2003-10-21 17:20:15');
INSERT INTO forumpost VALUES (2081,287,7,'Re: Hey, yet another newbie!!','I would also like to point out that although Gamer looks like Garner, they aren\'t the same word.',1626,'Gamer','2003-10-21 17:21:52');
INSERT INTO forumpost VALUES (2082,289,3,'Re: Riddle for you all...','Hmmm...Funny you must comprehend these lines different than me:\r
\n\r
\nForums > General Discussion\r
\nThis is a forum for discussing anything and everything.\r
\n\r
\n So where DO I post this? Frankly, I\'m just trying to get an answer to a riddle and if no one here wants to help, fine, I\'ll find it somewhere else. I got this site from a yahoo search. No big whoop.',3966,'Rock','2003-10-21 19:28:37');
INSERT INTO forumpost VALUES (2083,282,5,'Re: Advertising','Levik, I am a newbie at web design...I\'m toying around with my first site right now. It is a classified advertising site for my local area. It\'s not big enough to draw real advertisers yet, but I have several \"affiliate\" programs that are just banner ads but no pop-ups. They all pay a % of the sale, or some variation. \r
\n\r
\nI noticed you have banner ads too and I assume they are they same type of thing. Have you not had any luck with these? Though banner ads are somewhat annoying, I think we can all respect your need to make some income to pay for the site. BUT, I\'ll take 10 banner ads per page instead of pop-ups...there\'s just something about those pop-ups that make my skin crawl (not yours, just pop-ups in general).\r
\n\r
\nSince my site is virtually brand new, I can\'t really give any testimony to the success of my banner ads...I\'m just trying to continue to stir the conversation.\r
\n\r
\nI\'ve also seen some sites have a \"donation\" link where users can simply donate to the site. I\'d bet you\'d be suprised how many regular users would donate $5 or $10. Heck, I\'m a cheap school teacher who makes virtually nill but I\'d be happy to donate $5, or maybe even $10 per year. (I know that\'s not much, but I GUARANTEE it\'s more than you\'ll make on me with pop-ups, or even banner ads for that matter.) It\'s probably not enough to make a salary on this site, but if I\'m not mistaken, this is an \"on the side\" for you and your just trying to have it pay for iteself. I\'m sure your familiar with Paypal.com...you can easily setup a donation link on your site through paypal so you don\'t pay a monthly fee, only a small transaction fee.\r
\n\r
\nWell, that\'s enough rambling for now. Keep up the good work. \r
\nNew Floobler,\r
\nGreg Williams',1112,'Greg','2003-10-21 20:01:08');
INSERT INTO forumpost VALUES (2084,289,3,'Re: Riddle for you all...','I think we got into this with Tim Axoy. Anyway, when you clicked \"New Thread\", just above the place you type that reads \"Notice: About to post a problem to the forum? Please don\'t. (Here\'s why)\", with a link to a relevant thread. I know that was added to the site because of so many people who thought the same way you did.\r
\n\r
\nIf you want to wait 2 or so months for \"official judgement\" on your riddle, you can submit it to the queue. Otherwise I would reccommend going somewhere else. Thanks! :)',1626,'Gamer','2003-10-21 20:15:46');
INSERT INTO forumpost VALUES (2085,287,7,'Re: Hey, yet another newbie!!','Homophonic? Does that mean that everyone sounds the same? Or is it that everyone sounds a bit camp?',1183,'fwaff','2003-10-22 04:01:59');
INSERT INTO forumpost VALUES (2086,287,7,'Re: Hey, yet another newbie!!','Homophone- a word with the same sound as another. - [The Australian school dictionary]\r
\n\r
\nHere\'s a bit more about me. Not that anyone would want to know.\r
\n\r
\nName- Ashlee, I preferred to be called Nashie though.\r
\nNick names- Nashie, Nash, Nashter and Cinderella.\r
\nGender- I\'m female, 100%\r
\nAge- 13, It\'s great to be young\r
\nYear- 8\r
\nState- SA\r
\n\r
\nI have a photo, but it\'s old and I hate it...',3785,'Ashlee','2003-10-22 05:03:17');
INSERT INTO forumpost VALUES (2087,287,7,'Re: Hey, yet another newbie!!','Nashie,\r
\nNot to sound like your grumpy old Uncle, but you might want to be careful about sharing too much on the net.\r
\nDon\'t get me wrong, I think that it is great that you are open and want to get to know people, and (from what I\'ve seen) the folks on Flooble seem to be decent enough. But you never can tell who is out there. There are predators everywhere.\r
\nEnough of my sermon, I\'ll stop now,\r
\nFatboy',2839,'FatBoy','2003-10-22 08:25:09');
INSERT INTO forumpost VALUES (2088,287,7,'Re: Hey, yet another newbie!!','I don\'t tell anyone anything more than that...unless I know then REALLY well, like Max and Chris and...yeah, you get what I mean.',3785,'Ashlee','2003-10-23 03:23:55');
INSERT INTO forumpost VALUES (2089,282,5,'Re: Advertising','Levik,\r
\nI just got the offending popup and it changed my homepage\r
\non the bottom of my flooble screen where you put teh telltales is says\r
\nLastAd:ExitFuel This Ad:FastClick\r
\nI am not 100% sure but I think that ExitFuel is an ad I have seen listed when I have ahd other problems.\r
\n\r
\nI hope that this helps.\r
\nKeep fughting the good fight',2839,'FatBoy','2003-10-23 09:24:37');
INSERT INTO forumpost VALUES (2090,286,5,'Re: Changing Categories','Thanks all. The puzzle is about 32nd in the queue, so I won\'t resubmit it. Levik, I\'ll petition you (what\'s the difference between writing it here and formally petitioning? Never mind, no matter).',3372,'Sam','2003-10-24 11:02:29');
INSERT INTO forumpost VALUES (2091,287,7,'hey fwaff','Check out Charlie\'s homepage again.\r
\nI think me mus have read your message as he has posted a picture.\r
\nAlso, thanks for mentioning that you had gone to it. It inspired me to. I found it interesting a challenging. Its cool to get a window into our fellow Flooblers\r
\n',2839,'FatBoy','2003-10-24 14:43:29');
INSERT INTO forumpost VALUES (2092,287,7,'Re: Hey, yet another newbie!!','My picture was there before fwaff\'s comment. But fwaff sure must have missed it.',1301,'Charlie','2003-10-25 00:01:29');
INSERT INTO forumpost VALUES (2093,286,5,'Re: Changing Categories','The petition is specifically designed to request levik to do something, fix a bug, add a feature, clean up a \'mess\' we made, etc. The forums are for discussion of whatever, for everyone, and if levik is busy, he may not get to the forums at all. A petition is a way to make sure that something that you need done will be looked at.\r
\n\r
\nOn a side note, I think the reason \'lower\' users are not allowed to change the category of their puzzles is to prevent switching puzzles for another, mass submission, submitting blank puzzles to \'hold\' a spot in the queue, that sort of thing. At least, I can\'t think of any other reason. If that\'s the case, I would propose that maybe we be allowed to change the category of puzzles, but not their titles.. that would also (and probably more effectively) prevent that sort of \'sneaky submission.\' The other reason I would say that is, the things most often needed to change about a problem, especially by newer members, are the category and the difficulty. Very rarely does a valid puzzle need a name change, and if such a case arose, it would be quite simple to petition levik to do it. It would still be much less frequent than we are asking him to change puzzle categories currently.\r
\n\r
\nIf anyone has any other ideas, or even insight as to some other reason the category changes are disallowed, I\'d like to hear it.',1575,'DJ','2003-10-25 10:53:49');
INSERT INTO forumpost VALUES (2094,287,7,'Re: Hey, yet another newbie!!','Even just look at the address of his site... I don\'t know any girls that go by \'Chas\' as a nickname, either.',1575,'DJ','2003-10-25 10:56:51');
INSERT INTO forumpost VALUES (2095,290,3,'Languages','Hey. I was pretty bored so I just made this out of curiosity. How many languages do you know? I only know english (and after 9 years of freanch still know nothing) and I\'m taking cantonese classes and have high hopes of learning to speak it.',1072,'Alan','2003-10-25 21:27:09');
INSERT INTO forumpost VALUES (2096,291,7,'New here - HELP ME!','I\'m from Brasil. Hey, I\'m new here. I don\'t know much about this site yet. I like to try to solve probles. I want to find some neat problems... If you can help me!',4023,'Romulo','2003-10-25 23:57:08');
INSERT INTO forumpost VALUES (2097,291,7,'Re: New here - HELP ME!','Depends what you like. There\'s a lot. On the home page you can find all catagories. Have a look in each one to find out which one you like the most',3785,'Ashlee','2003-10-26 02:30:37');
INSERT INTO forumpost VALUES (2098,286,5,'Re: Changing Categories','That is not the reason. Levik told me that it was because he didn\'t want people to wrongly categorize their own puzzles. If they wanted to change the categories of their puzzles, they can consult Levik, and he would change it if he agrees. Then, the person is not allowed to change it back. In short, you can change your category, as long as Levik agrees with your change.',3558,'Tristan','2003-10-26 09:58:38');
INSERT INTO forumpost VALUES (2099,286,5,'Re: Changing Categories','\"The\" reason? I don\'t think there is any one reason for how it\'s used. Although one of those may have been why it was used in the first place, both reasons make sense for why it was there.\r
\n\r
\nThis also shows a lesser known \"reason\" for queue weight, namely that if someone wants to become a journeyman, it will take time to submit 6 good problems.',1626,'Gamer','2003-10-26 14:46:54');
INSERT INTO forumpost VALUES (2100,291,7,'Re: New here - HELP ME!','Look at this forum thread here where there was talk about what were the best problems.\r
\n\r
\nOf course I think most of my problems are good, but I am likely biased. :)',1626,'Gamer','2003-10-26 15:36:45');
INSERT INTO forumpost VALUES (2101,291,7,'Re: New here - HELP ME!','By the way, you can stop reading about half the way down when Nick Hobson joins, because then the thread takes a turn and talks about picky stuff in the Burning Ropes problem.',1626,'Gamer','2003-10-26 15:39:43');
INSERT INTO forumpost VALUES (2102,292,4,'How did Puzzle Strips appear?','Puzzle Strips is a puzzle still on the queue, but now shows up as having been posted. It shows up as having no previous puzzle, and shows that the next puzzle after it is Burning Ropes, though it shows a date of 2003-19-26. It has one comment already: by SilverKnight.\r
\n\r
\nHow did this happen?',1301,'Charlie','2003-10-26 18:06:22');
INSERT INTO forumpost VALUES (2103,292,4,'Re: How did Puzzle Strips appear?','I\'m seeing it show up absolutely fine... Meaning live on the site, with today\'s post date, no \"next\" puzzle, and the correct \"previous\" one (Lotsa Sequences)\r
\n\r
\nI also don\'t see it in the queue. Are you still observing this anomalie, Charlie?',1,'levik','2003-10-27 10:51:34');
INSERT INTO forumpost VALUES (2104,292,4,'Re: How did Puzzle Strips appear?','OK, never mind that last one, I see that the problem was somehow duplicated with 2 different IDs. My hypothesis is that DJ somehow re-submitted it, and checked \"Make it live immediately\"\r
\n\r
\nDid you DJ?\r
\n\r
\nAnyway, I deleted the double, so everything should be back to normal\r
\n',1,'levik','2003-10-27 10:57:56');
INSERT INTO forumpost VALUES (2105,290,3,'Re: Languages','English/French/Arabic\r
\nbut my knowledge of Arabic is fairly specialized and related directly to my work.',2839,'FatBoy','2003-10-27 11:00:04');
INSERT INTO forumpost VALUES (2106,290,3,'Re: Languages','English, Spanish, BASIC, C, C++, HTML, Java, javascript, prolog, perl, PHP ...',1575,'DJ','2003-10-27 12:12:45');
INSERT INTO forumpost VALUES (2107,290,3,'Re: Languages','Russian and English. That\'s right, English is my second language. (Anyone who\'s been hanging around here long enough has surely suspected this for quite some time)',1,'levik','2003-10-27 14:21:18');
INSERT INTO forumpost VALUES (2108,217,3,'Re: NEED HELP!','Hi, could I add a question. My daughter has a logic question in her math class they are allowed to ask others for help, so we\'re not cheating.\r
\n\r
\nit is . ________ then it has a backwards 2 or a u on its side (not sure which) out\r
\n So it is a period, a line, a backwards 2 or a u on its side then the word out\r
\n\r
\nMy email address is tmb@yellowbananas.com, its due friday, Oct 31,03',4051,'Tracy Bowser','2003-10-27 16:49:02');
INSERT INTO forumpost VALUES (2109,217,3,'Re: NEED HELP!','Sorry, I don\'t know this one, and you shouldn\'t post problems.',1626,'Gamer','2003-10-27 17:00:49');
INSERT INTO forumpost VALUES (2110,293,7,'NEWBIE','Hi yall. My name\'s Victor and I\'m a newbie. I\'m proud of it! Woo. lol. Anyway, how\'s everyone doing. a/s/l to all and hope all yas have a great day coz i am (u see i\'m usually perky heh)\r
\n\r
\n15\r
\nmale\r
\nnew york',3386,'Victor Zapana','2003-10-27 21:17:34');
INSERT INTO forumpost VALUES (2111,290,3,'Re: Languages','english spanish korean very very very lil french and ....\r
\nwow.. DJ so programmer fluent :)\r
\n',3386,'Victor Zapana','2003-10-27 21:19:58');
INSERT INTO forumpost VALUES (2112,289,3,'Re: Riddle for you all...','not to sound abrupt, rude, or otherwise\r
\n\"What Gamer\'s saying is that whatever Gamer says is true and you should follow Gamer.\" :-P',3386,'Victor Zapana','2003-10-27 21:21:56');
INSERT INTO forumpost VALUES (2113,217,3,'Re: NEED HELP!','hmmm elementary math be my guide. what was the set terminology fr the side U, that shud help u',3386,'Victor Zapana','2003-10-27 21:24:22');
INSERT INTO forumpost VALUES (2114,290,3,'Re: Languages','English is the only one I am competent in, but in school I took Spanish, French and Latin (it was required, and I guess I\'m showing my age). I retain just enough to pick out a hint of what a written paragraph in most Romance languages is about. Can\'t follow spoken languages, tho.\r
\n\r
\nAlso I can sort of read and write (if given enough time and good resourses to review the basics and cheat from) in HTML, Basic and Fortran-4 (but not any later versions) and can recognize but not really follow C and its derivative languages.',153,'TomM','2003-10-28 01:05:42');
INSERT INTO forumpost VALUES (2115,294,7,'I love Google!','That\'s how I found this site - I love Google. Now if I could only find my way around a little better...',4063,'Delta','2003-10-28 15:15:48');
INSERT INTO forumpost VALUES (2116,290,3,'Re: Languages','I think there was some major clue I remember that led me to think you were Russian.\r
\n\r
\nI am mainly English, and more of an algorithmer than a programmer as I am less cognizant of programming languages.',1626,'Gamer','2003-10-28 16:32:43');
INSERT INTO forumpost VALUES (2117,294,7,'Re: I love Google!','Hey, welcome to the site. We love google too, since it brings us a lot of quality members.\r
\n\r
\nIf you run into trouble on this site, just ask in the forums, and somebody (maybe even me!) will help you out. We\'re a fairly hospitable bunch.',1,'levik','2003-10-28 17:23:53');
INSERT INTO forumpost VALUES (2118,290,3,'Re: Languages','I feel so alone. Programmer language scares me lol.',3386,'Victor Zapana','2003-10-28 20:39:38');
INSERT INTO forumpost VALUES (2119,294,7,'Re: I love Google!','Hey Delta. try to get Alpha, Beta, Gamma,....etc. on the site too. :)\r
\nSorry, but I was just trying to say that you can recommend this site to some of your friends and other people too and ask them to become a member. :)#\r
\n',979,'Ravi Raja','2003-10-29 05:56:53');
INSERT INTO forumpost VALUES (2120,295,4,'Queue Placement?','I noticed a jump in the queue, but I don\'t see why. I think Ravi\'s problems are staying at the same amount, as are many of the other submitters (including me)',1626,'Gamer','2003-10-29 06:10:17');
INSERT INTO forumpost VALUES (2121,295,4,'Re: Queue Placement?','n00bs? :)',1,'levik','2003-10-29 13:34:05');
INSERT INTO forumpost VALUES (2122,296,4,'Scholars - edit queue problems','As was requested by DJ a couple of weeks ago, I just added the ability for scholars to edit others\' problems that are in the queue.\r
\n\r
\nI trust this feature will be used responsibly, and not abused to make changes that dramatically alter a problem. Also, if a user is active on the site and able to make adjustments themselves, I would ask that you leave it to them as a matter of common courtesy.\r
\n\r
\nOther than that, enjoy :)',1,'levik','2003-10-29 13:38:37');
INSERT INTO forumpost VALUES (2123,275,5,'Re: The FAQ WIP','O I know this is a bit foolish but i just found out today that levik responds to the petitions we send him. D\'oh Anyways in the faq it could say \"Why haven\'t i recieved and answer to my petition?\" and then it would say \"This is because either Levik has yet to look at it or you have not clicked the \"see my petitions button\"(or something like that)',1072,'Alan','2003-10-29 16:21:57');
INSERT INTO forumpost VALUES (2124,275,5,'Re: Re: The FAQ WIP (from Alan)','lol nice one ALan',3386,'Victor Zapana','2003-10-29 19:22:55');
INSERT INTO forumpost VALUES (2125,275,5,'Re: The FAQ WIP','Somebody\'s put a fake email into the system. I added a \"feature\" that will email any person whose petition I reply to with a link directly to where they can view the answer.\r
\n\r
\nI\'m not sure i want to put anything petition-related in a FAQ, since most people don\'t really need to post petitions - they have questions that belong in the forums.',1,'levik','2003-10-29 23:45:57');
INSERT INTO forumpost VALUES (2126,245,7,'Re: math puzzles i need help please!!','Dea try to think of the question outside of the square and maybe you will get the answer. All i mean is you should go through every aspect of the question, you should try \"trial and error\". \r
\n\r
\nAnd alan there is nothing to think about your question, you are just asking why we have to work for dea. Well dea is one of the members of the website and otheres are supposed to help or give hints on how to solve a problem or problems.',4093,'Nithin','2003-10-30 03:36:17');
INSERT INTO forumpost VALUES (2127,297,7,'Getting problems posted...','Once I\'ve got a problem in the queue and it\'s been given three thumbs up, how long does it usually take to get posted? \r
\nI\'m just really keen to get my stuff out there for you guys! \r
\nCheers, \r
\nDave',3136,'Popstar Dave','2003-10-30 06:48:13');
INSERT INTO forumpost VALUES (2128,297,7,'Re: Getting problems posted...','From a small statistical universe (I\'ve only had one posted) It took less than a day ',2839,'FatBoy','2003-10-30 08:21:58');
INSERT INTO forumpost VALUES (2129,297,7,'Re: Getting problems posted...','Things are misorienting here. It may seem like your problem gets voted on quickly, but it usually for new people it takes much longer between when it was voted on and when it will actually come out.',1626,'Gamer','2003-10-30 12:46:15');
INSERT INTO forumpost VALUES (2130,295,4,'Re: Queue Placement?','Actually, I don\'t remember you as having 93 problems, but if it wasn\'t you, it must have been someone else..',1575,'DJ','2003-10-30 13:33:21');
INSERT INTO forumpost VALUES (2131,297,7,'Re: Getting problems posted...','Its possible that because my puzzles are (apparantly) pretty darn easy. They get posted quickly to fill the \"less interesting\" morning slot. But seriously, this morning Bang Bang Kiss kiss had only two thumbs up and next thing I knew it was posted.',2839,'FatBoy','2003-10-30 15:32:44');
INSERT INTO forumpost VALUES (2132,295,4,'Re: Queue Placement?','I have submitted 5 to 10 problems, but all I know is about a month ago, I was a distant third. Now I am a high first, and I definitely didn\'t submit enough problems for that to happen; the answer lies with where the problems I already submitted were instead.',1626,'Gamer','2003-10-30 20:05:52');
INSERT INTO forumpost VALUES (2133,297,7,'Re: Getting problems posted...','hmmm...\r
\nthis is besides the point.\r
\nhmm is that avatar of urs fatboy from metal slug? lol\r
\nalso. none of my problems are getting voted.. guess i shud be patient.',3386,'Victor Zapana','2003-10-30 20:50:36');
INSERT INTO forumpost VALUES (2134,298,6,'???','question: is there any other way to get the area of a square without using the regular K= 1/2 Bh, K = 1/2 ab sin C, or Heron\'s formulae?',3386,'Victor Zapana','2003-10-30 20:52:47');
INSERT INTO forumpost VALUES (2135,298,6,'Re: ???','er... sry bout that not square.. triangle heh',3386,'Victor Zapana','2003-10-30 20:53:31');
INSERT INTO forumpost VALUES (2161,302,7,'hello!','hi! anyone majoring in math?\r
\n\r
\ntalk to me, anyone? =) ',4122,'Hazel','2003-11-01 21:16:42');
INSERT INTO forumpost VALUES (2162,300,5,'Re: Scavenger Hunt','Um... Indeed. Almost a year and a half of diligent work, day after day behind my computer. \'Course, I started puzzle 1 just two days ago. Wretched worm holes.\r
\n<sigh>',3372,'Sam','2003-11-01 22:51:31');
INSERT INTO forumpost VALUES (2165,303,5,'Posting solutions to your problems','If I\'ve had a problem recently posted and it\'s been solved in the comments, is it up to me to post the official solution? If so, how?\r
\nCheers,\r
\nDave',3136,'Popstar Dave','2003-11-02 19:05:38');
INSERT INTO forumpost VALUES (2137,290,3,'Re: Languages','English, Italian, French, some Spanish and Portugese, and a little Swahili.',3372,'Sam','2003-10-30 23:22:44');
INSERT INTO forumpost VALUES (2138,300,5,'Scavenger Hunt','Hmmm... So I\'m completely befuddled on the very first hurdle in Flooble\'s \"scavanger\" hunt (http://flooble.com/scav). Do I have to be a major league hacker? Do I have to know PHP? Oh well, I\'m not looking for any actual answers, more like a \"it\'s easier than you think, stupid! Why don\'t you use your brain for once??\" or something along those lines... Anyone here solved the puzzles?',3372,'Sam','2003-10-30 23:48:26');
INSERT INTO forumpost VALUES (2139,300,5,'Re: Scavenger Hunt','I wish we could edit posts. That way it wouldn\'t look like I was making fun of Levik\'s spelling of \"scavenger\" by my putting it in quotes and then spelling it wrong myself...',3372,'Sam','2003-10-30 23:50:05');
INSERT INTO forumpost VALUES (2140,297,7,'Re: Getting problems posted...','I really don\'t know where it came from originally.\r
\nI saw it on the avatar page and it seemed to suit my screen name.',2839,'FatBoy','2003-10-31 07:35:36');
INSERT INTO forumpost VALUES (2141,300,5,'Re: Scavenger Hunt','dang im having trouble with even the first one lol',3386,'Victor Zapana','2003-10-31 10:29:09');
INSERT INTO forumpost VALUES (2142,300,5,'Re: Scavenger Hunt','im thinking mebe has to do sumthing with the spelling error of surprize but dunno',3386,'Victor Zapana','2003-10-31 10:29:32');
INSERT INTO forumpost VALUES (2143,297,7,'Re: Getting problems posted...','coz i remember a game called metal slug with almost that exact character model.',3386,'Victor Zapana','2003-10-31 10:31:34');
INSERT INTO forumpost VALUES (2144,301,3,'WOOHOO!!!','I\'m no longer a flooble virgin!
I\'ve had my first problem posted!
Bartender, a round for everyone... on me!',3172,'SilverKnight','2003-10-31 10:46:45');
INSERT INTO forumpost VALUES (2145,300,5,'Re: Scavenger Hunt','Here\'s a quote I found on a calendar. It works here too. \r
\n\r
\n\"When problems happen and take their course, always remember to consider the source.\"',1626,'Gamer','2003-10-31 10:51:58');
INSERT INTO forumpost VALUES (2146,297,7,'Re: Getting problems posted...','Yeah, it\'s from metal slug.\r
\nI only know that because I saw it in the categories levik first put on avatarity..',1575,'DJ','2003-10-31 12:07:48');
INSERT INTO forumpost VALUES (2160,300,5,'Re: Scavenger Hunt','wow sam.\r
\n\r
\nSam - Challenge 3 (4m) \r
\nSam - Challenge 2 (11669h 39m) \r
\n\r
\nchallenge 2 took u that long? lol',3386,'Victor Zapana','2003-11-01 19:40:26');
INSERT INTO forumpost VALUES (2163,302,7,'Re: hello!','Hi Hazel\r
\n\r
\nI am not majoring in math. but I have taught it.\r
\nTom',4125,'Tom','2003-11-02 01:30:00');
INSERT INTO forumpost VALUES (2164,302,7,'New Guy','Hello all. I found this great site while looking for some logic exercises for my students.',4125,'Tom','2003-11-02 01:33:21');
INSERT INTO forumpost VALUES (2150,300,5,'Re: Scavenger Hunt','Phhttbb! Stupid me. Ok passed it.',3372,'Sam','2003-10-31 13:56:48');
INSERT INTO forumpost VALUES (2151,300,5,'Re: Scavenger Hunt','That page doesn\'t have any ads as far as I remember. The only ads are before you get to the site.',1626,'Gamer','2003-10-31 13:59:16');
INSERT INTO forumpost VALUES (2152,300,5,'Re: Scavenger Hunt','I was going to try the scavenger hunt, but it didn\'t work. Do we have to sign up separately on the forum home page to try it?',3558,'Tristan','2003-10-31 17:20:29');
INSERT INTO forumpost VALUES (2153,300,5,'Re: Scavenger Hunt','Never mind, I just signed up on it and I see why I needed to. But now I\'m stumped on the first page.',3558,'Tristan','2003-10-31 18:34:59');
INSERT INTO forumpost VALUES (2154,300,5,'Re: Scavenger Hunt','hmmm... gamer thx fr the advice. and tristan follow his advice its very helpful... hell the answer is sumwhere here lol. dang now im stuck on the gif image on 2. thinking it got sumthing to do with the pic so im editing it on my photo editor right now lol',3386,'Victor Zapana','2003-10-31 20:22:57');
INSERT INTO forumpost VALUES (2155,300,5,'Re: Scavenger Hunt','I already saw the code Sam mentioned, and I\'m pretty sure it has something to do with the hunt, but I still can\'t figure out what to use it for. I hope it doesn\'t involve more html knowledge, because I had to research to figure out how to get to the source.',3558,'Tristan','2003-10-31 23:06:52');
INSERT INTO forumpost VALUES (2157,300,5,'Re: Scavenger Hunt','I can\'t get past the fourth one because I don\'t know how to use javascript.',1626,'Gamer','2003-11-01 09:11:41');
INSERT INTO forumpost VALUES (2158,297,7,'Re: Getting problems posted...','Cheers for the help guys. It got posted. \r
\nCheck it out, it\'s called \"A group of letters\". \r
\nI reckon that the hardest part of submitting a problem is thinking of a good title, that doesn\'t give too much away about the solution.',3136,'Popstar Dave','2003-11-01 10:40:41');
INSERT INTO forumpost VALUES (2159,300,5,'Re: Scavenger Hunt','That\'s where I am right now. I passed the third one in about three minutes - once you get the idea they go rather fast (he says, before having even tried out number four...).',3372,'Sam','2003-11-01 15:40:58');
INSERT INTO forumpost VALUES (2166,303,5,'Re: Posting solutions to your problems','No, just make sure that you have a solution submitted. After two days of the problem being live on the site, the solution becomes visible to the Journeymen and Scholars, and we can review the solution and leave comments if anything needs to be added or fixed.\r
\nAlso, since many people don\'t know or bother to check the comments on their problems\' solutions, Scholars are able to manually edit them, but only if suggestions or corrections have been made to the author and not addressed.\r
\n\r
\nAfter the problem has been on the site for four days, Scholars can push the problem live onto the site. Journeymen are able to post the solutions to their own problems at any time.',1575,'DJ','2003-11-02 21:22:25');
INSERT INTO forumpost VALUES (2167,300,5,'Re: Scavenger Hunt','First one was ok. I\'ve not a clue what to do with the second. I\'ve played around with the image in MS Paint and Photo Editor and nothing new has magically appeared. I\'m in desparate need of a burst of inspiration.',1183,'fwaff','2003-11-03 05:46:46');
INSERT INTO forumpost VALUES (2168,300,5,'Re: Scavenger Hunt','The sign is telling you everything - it\'s telling you where you need to be. There are no coded messages in the image.',3372,'Sam','2003-11-03 14:34:23');
INSERT INTO forumpost VALUES (2169,300,5,'Re: Scavenger Hunt','Don\'t you mean the signs?',1626,'Gamer','2003-11-03 15:01:40');
INSERT INTO forumpost VALUES (2170,300,5,'Re: Scavenger Hunt','Nope, wrong puzzle.',3372,'Sam','2003-11-03 17:46:29');
INSERT INTO forumpost VALUES (2171,304,7,'Looking for the name of a puzzle','This puzzle looks like 5 bricks. You have to draw a continuous line through each wall. I am looking for a solution and name of the puzzle. How would I search this site for it not knowing the name?\r
\n\r
\n',4156,'Jim Collins','2003-11-03 18:59:10');
INSERT INTO forumpost VALUES (2172,304,7,'Re: Looking for the name of a puzzle','I would need more information to help out with the puzzle. :(',1626,'Gamer','2003-11-03 19:01:44');
INSERT INTO forumpost VALUES (2173,304,7,'Re: Looking for the name of a puzzle','\r
\n\r
\n Two brick on top. Three on the bottom. Line must pass thru each connecting wall. 16 walls. Can only go thru a wall one time.\r
\n \r
\n\r
\n 9 8\r
\n ---------------------------------------------\r
\n 1| | |\r
\n | 14 | | 7 \r
\n |----10--------11---------12---------13------\r
\n 2| | | |\r
\n | |15 |16 | 6\r
\n ---------------------------------------------\r
\n\r
\n 3 4 5',4156,'Jim Collins','2003-11-03 19:11:17');
INSERT INTO forumpost VALUES (2174,304,7,'Re: Looking for the name of a puzzle','Sorry. My lines all shifted. Jim\r
\n\r
\n',4156,'Jim Collins','2003-11-03 19:11:51');
INSERT INTO forumpost VALUES (2175,300,5,'Re: Scavenger Hunt','I found that when I log off the Scavenger hunt, I also log off Flooble, and when I log back on to Flooble, I log back onto the scavenger hunt. Since I normally check off the remember me button, I\'m gonna be logged onto the hunt the whole time. That means I\'ll probably have a longer time finishing the challenges than Sam on challenge 2. I wonder if the computer recognized my username or something. Or maybe it\'s the cookies. Oh well, not like the time matters...',3558,'Tristan','2003-11-03 19:21:34');
INSERT INTO forumpost VALUES (2176,300,5,'Re: Scavenger Hunt','OK, gang, let\'s be more careful about spoilers. (I already had to delete one)\r
\n\r
\nAnd since now the first person to finish all the challenges will get a free flooble T-shirt (see the game page for details) that should spur you guys on to try a little harder ;)\r
\n\r
\nI am thinking that if this proves popular, we will enable additional \"trails\" of challenges, perhaps even user-submitted ones.',1,'levik','2003-11-03 19:23:30');
INSERT INTO forumpost VALUES (2177,304,7,'Re: Looking for the name of a puzzle','The puzzle should look like:\r
\n\r
\r
\n 9 8\r
\n ---------------------------------------------\r
\n 1| | |\r
\n | 14 | | 7 \r
\n |----10--------11---------12---------13------\r
\n 2| | | |\r
\n | |15 |16 | 6\r
\n ---------------------------------------------\r
\n\r
\n 3 4 5\r
\n
\nI\'m pretty sure the puzzle is not on this site, as problems are generally submitted just as text, there are only a few that rely on an image.\r
\n\r
\nThis problem is impossible, anyway. There are three regions with five sides, and two regions with four sides (it does not matter that some of the walls are shared between regions). If you have a region with an odd number of sides, the line must begin or end in that region. Since the continuous line will have only two endpoints, it\'s impossible to solve this puzzle.\r
\n\r
\nThere is still a poor guy trying to solve it, if you look here.',1575,'DJ','2003-11-03 20:56:44');
INSERT INTO forumpost VALUES (2178,304,7,'Re: Looking for the name of a puzzle','My sentence that got cut off in the previous post (stupid pre tag) said, most problems are submitted as text, and there are only a few that rely on images, and I\'m fairly sure that we haven\'t seen this problem.',1575,'DJ','2003-11-03 20:57:58');
INSERT INTO forumpost VALUES (2179,304,7,'Re: Looking for the name of a puzzle','It\'s a pretty good problem. I think the one where you have to draw that diagram with only 3 strokes is good too. (This one is impossible too)',1626,'Gamer','2003-11-03 21:26:35');
INSERT INTO forumpost VALUES (2180,304,7,'Re: Looking for the name of a puzzle','The top result from a Google search on Euler puzzle rooms is this .',1301,'Charlie','2003-11-03 22:17:03');
INSERT INTO forumpost VALUES (2181,300,5,'Re: Scavenger Hunt','Yes yes indeed. My apologies for bringing up something that would obviously start to generate spoilers. I need to be more careful with my tongue in future (some say I should start to use my fingers for typing, but pshaw...).\r
\nMultiple trails seems like a good idea, though. It\'s a bore to get stuck on one and not be able to go anywhere (wretched challange four...).',3372,'Sam','2003-11-03 23:09:42');
INSERT INTO forumpost VALUES (2182,287,7,'Re: Hey, yet another newbie!!','So it\'s true then, Americans don\'t understand irony.\r
\nDiscuss.',1183,'fwaff','2003-11-04 03:59:12');
INSERT INTO forumpost VALUES (2183,300,5,'Re: Scavenger Hunt','Oh well, I give up.\r
\nLooks like I\'ll have to fork out $25 (which I think is equivalent to about 16 Guineas or 8 pints of Boddies) if I want to be the only island monkey with a flooble t-shirt.',1183,'fwaff','2003-11-04 05:08:02');
INSERT INTO forumpost VALUES (2184,300,5,'Re: Scavenger Hunt','Damn you, Challenge 4! You will be the bane of my procrastination. How am I supposed to avoid study when I can\'t even get past that level. \r
\n\r
\nLevik,\r
\nIs there any way to run some sort of Scav forum, with some tips (NOT spoilers)? Maybe divided up into challenge levels. It\'s just REALLY annoying to be stuck on a challenge and have absolutely no idea how to get through it. When, just maybe, a little prodding it the right direction by a fellow Floobler (hey, I like that word!) could get you going. ',3136,'Popstar Dave','2003-11-04 05:22:20');
INSERT INTO forumpost VALUES (2185,287,7,'How terribly unfair!','We sure do understand irony Miss Smartypants.\r
\nIn fact, I never drink the water from the well down home cause it tastes way to irony.',2839,'FatBoy','2003-11-04 07:23:01');
INSERT INTO forumpost VALUES (2186,287,7,'Re: Hey, yet another newbie!!','or Mr. Smartypants as the case may be...',2839,'FatBoy','2003-11-04 07:23:44');
INSERT INTO forumpost VALUES (2187,300,5,'Re: Scavenger Hunt','My tip for challenge 4 is that in my experience, it\'s harder on the users on Internet Explorer than other browsers.',1,'levik','2003-11-04 07:41:22');
INSERT INTO forumpost VALUES (2188,275,5,'Re: The FAQ WIP','In response to questions that I think should be in the FAQ... I think something needs to be said about publically posting solutions to your own problems. Once your problem get\'s posted, you kinda lose control over it (as a \"Student\" anyway... and it gets a little confusing as to who\'s job it is to allow people to see the official solution. \r
\n\r
\nMy two cents.',3136,'Popstar Dave','2003-11-04 07:45:04');
INSERT INTO forumpost VALUES (2189,287,7,'Re: Hey, yet another newbie!!','sarchasm: (sa:kaz\'m) n. The gulf between a witty remark and a person that fails to understand it. (see Atlantic)\r
\n\r
\nIt\'s actually Dr Smarty-Pants, but thank-you anyway for attempting to address me formally. ',1183,'fwaff','2003-11-04 08:28:24');
INSERT INTO forumpost VALUES (2190,300,5,'Re: Scavenger Hunt','Hmmm... sitting here in IE6, that\'s not making e feel good.\r
\n\r
\nCheers for the advice tho. I\'ll have to check up on how IE differs from other browsers.',3136,'Popstar Dave','2003-11-04 08:40:57');
INSERT INTO forumpost VALUES (2191,300,5,'Re: Scavenger Hunt','tip for levik\'s tip (not really that spoilish)
\nhttp://www.webreference.com/js/column75/',3386,'Victor Zapana','2003-11-04 10:26:47');
INSERT INTO forumpost VALUES (2192,287,7,'Re: Hey, yet another newbie!!','Sarcasm: Doctor Smarty-Pants needs to leave the building.',3386,'Victor Zapana','2003-11-04 10:28:21');
INSERT INTO forumpost VALUES (2193,287,7,'Re: Hey, yet another newbie!!','America knows irony. Comeon they\'re making this new TV Show where like 6 guys are gonna fight for a girl\'s hand in marriage, and then at the altar, the \"lucky\" guy will find out that the girl is GUY -gasp- lol. this is an AMERICAN show . :_>',3386,'Victor Zapana','2003-11-04 10:29:30');
INSERT INTO forumpost VALUES (2194,287,7,'Re: Hey, yet another newbie!!','so what if i\'m a newbie soooooo r uuuuuu!!!!\r
\n',4167,'Patricia','2003-11-04 11:00:19');
INSERT INTO forumpost VALUES (2195,304,7,'Re: Looking for the name of a puzzle','huh.....??????........???....?',4167,'Patricia','2003-11-04 11:07:45');
INSERT INTO forumpost VALUES (2196,294,7,'Re: I love Google!','I like google tooooo. it is the greatest search engine in the world\r
\n',4167,'Patricia','2003-11-04 11:09:08');
INSERT INTO forumpost VALUES (2197,86,7,'Re: Problems','i dont know\r
\n',4167,'Patricia','2003-11-04 11:10:01');
INSERT INTO forumpost VALUES (2198,264,7,'Re: HELLO','hi Andrew i will try to do that toooooo.',4167,'Patricia','2003-11-04 11:10:57');
INSERT INTO forumpost VALUES (2199,302,7,'Re: hello!','i am not but i am going to take pre-cal this year and i\'m only in 10th grade.',4167,'Patricia','2003-11-04 11:12:27');
INSERT INTO forumpost VALUES (2200,276,7,'Re: No Subject','????????????????...................?',4167,'Patricia','2003-11-04 11:13:14');
INSERT INTO forumpost VALUES (2201,245,7,'Re: math puzzles i need help please!!','my head hurts now',4167,'Patricia','2003-11-04 11:16:43');
INSERT INTO forumpost VALUES (2202,293,7,'Re: NEWBIE','HI!!! Victor!!! I\'m proud to be a newbie too.! And thank you I am having a great day.\r
\n\r
\n15\r
\nfemale\r
\nHouston Texas',4167,'Patricia','2003-11-04 11:19:45');
INSERT INTO forumpost VALUES (2203,291,7,'Re: New here - HELP ME!','i\'m new too i can\'t help you',4167,'Patricia','2003-11-04 11:21:06');
INSERT INTO forumpost VALUES (2204,300,5,'Re: Scavenger Hunt','Err.. I don\'t see how that\'s helpful at all, Victor. Though I didn\'t read the whole column, I did glance thorough the table of contents, and the topics discussed are far more in depth than what is required for challenge 4.\r
\n\r
\nTo solve it you need to know the most basic Javascript, as well as how it can be included into a page.',1,'levik','2003-11-04 11:29:33');
INSERT INTO forumpost VALUES (2205,304,7,'Re: Looking for the name of a puzzle','Thanks for the help. One of my co-workers had this puzzle stuck in his mind by an elementry teacher. Drove him crazy. \r
\n\r
\nJim',4156,'Jim Collins','2003-11-04 13:42:52');
INSERT INTO forumpost VALUES (2206,305,4,'A problem','Ok now I just checked my e-mail today and found out that dancing 2 was deleted. No I am not going to complain and say it was siteworthy, but I will say this. The reasons for which it were deleted really got me angry. Why? Well when the problem was submitted into the queue some people viewed it and said change the wording. I did. After I changed the wording It sat in the queue for about a week with no new comments. Then I posted in the chatterbox please look at dancing 2. So did another person (I think it was gamer?) Still no comments. This went on for about a month. Now over the past 2 days people may have made comments but coincidentally i did not log on those 2 days because I just got hooked on an internet game I just found (The game is Gunbound for those who care) and for the two days I was away my problem suddenly gets deleted because people think the wording still needs to be changed. Now would it have killed anyone at all to actually look at my problem and post that you STILL thought the wording was not good enough. No. This suddenly emerged in the two days I was away. And instead of being given a 1 week chance to change the wording (for a second time but nevertheless change the wording the way new users get to) It was immediately deleted because nobody could be bothered at all to look at my problem and say \"hey, Here is the reason I will not give it a Thumbs up\" or \"hey, the wording is STILL unclear to me\"
\n\r
\nroflmao',3172,'SilverKnight','2003-11-04 21:00:33');
INSERT INTO forumpost VALUES (2211,300,5,'Re: Scavenger Hunt','I don\'t know what problem there was with IE..or how the browser would have even mattered for that one...',1575,'DJ','2003-11-04 21:54:02');
INSERT INTO forumpost VALUES (2212,300,5,'Re: Scavenger Hunt','I\'m using IE 6.0... and I don\'t want to \'give it away\', but I agree with Levik... there is something about IE that makes that one harder (IMHO).',3172,'SilverKnight','2003-11-04 22:03:41');
INSERT INTO forumpost VALUES (2213,294,7,'Re: I love Google!','Google and Yahoo (for my emails) my 2 favorite sites lol',NULL,'Aspiring Novice','2003-11-04 22:51:03');
INSERT INTO forumpost VALUES (2214,294,7,'Re: I love Google!','the aspiring novice is me i frgt to log on lol',NULL,'Victor Zapana','2003-11-04 22:51:28');
INSERT INTO forumpost VALUES (2215,276,7,'Re: No Subject','I think Silverknight can read the guy\'s mind. Nice telepathic skills, SK! lol',3386,'Victor Zapana','2003-11-04 22:58:10');
INSERT INTO forumpost VALUES (2216,300,5,'Re: Scavenger Hunt','lol this scavenger hunt is now one of the biggest forum topics currently lol now with ... 36 posts. hm.. anyone want to change to subject?',3386,'Victor Zapana','2003-11-04 23:02:16');
INSERT INTO forumpost VALUES (2217,276,7,'Re: No Subject','I just assumed that he could relate to the new guy\'s name. SK wishes he had a bigger part to play here at perplexus, hence \"aspiring\", yet he really hasn\'t been around all that long, hence \"novice\".',3136,'Popstar Dave','2003-11-05 09:42:33');
INSERT INTO forumpost VALUES (2218,241,3,'Re: Blackout','i was in a meeteing and as soon the meeting finished it started : all our eqipment was turned down',4186,'nick','2003-11-05 12:32:51');
INSERT INTO forumpost VALUES (2219,305,4,'Re: A problem','I know what you\'re saying.. but really, you\'re overreacting. There were quite a few comments on that problem saying that the wording needed to be cleared up, and while you made some changes, there were still a lot of questions as to what was intended (and that\'s just from the journeymen and scholars, let alone everyone else who visits the site). Now, I know what your problem was referring to because I know the video game, and you answered people\'s questions in the problem comments, but the wording was still rather unclear. Nobody posted a new comment probably because the problem wording didn\'t change to address the old questions, but that\'s just speculation.\r
\nEven disregarding that, the problem sat in queue for more than a month, and only one person was interested enough to give a TU. Whether or not a problem is interesting or not to the voters is certainly relevant to our voting decisions .. chances are, if we don\'t find a problem interesting (particulary if it\'s on the grounds of being too complex or hard to understand), few other people will either. I\'m not saying it wouldn\'t make a good problem, but as it were, most casual visitors would have spent about five minutes trying to understand it and then gone looking somewhere else. As someone put in the comments, good writing is part of a good problem.\r
\n\r
\nNow, I know what you\'re feeling, as far as what you consider to be a good problem being voted down. For example, my recent submission, \"Sorry, We\'re Closed\" was deleted (actually, I just deleted myself after reading the comments) on the grounds that the concept of a set being closed under multiplication is \"too advanced mathematical theory for this site.\" Now, I certainly don\'t think that that is the case, set closure is a relatively basic idea in my opinion, but if that\'s the viewpoint of the other voters, there\'s not much point in trying to push the problem. If you have to work to convince everyone that yours is a great problem, it probably isn\'t.',1575,'DJ','2003-11-05 12:33:30');
INSERT INTO forumpost VALUES (2220,305,4,'Re: A problem','Yes DJ but i wasn\'t so much complaining about my problem as I was using it as an example. All I really wanted to say is this. if a problem is going nowhere perhaps another post about what is still wrong with it is needed.
Or if you look at a problem avtually post a comment. If it doesn\'t interest you then td it and perhaps say why it doesn\'t interest you.',1072,'Alan','2003-11-05 14:37:01');
INSERT INTO forumpost VALUES (2221,306,4,'New category','After hearing about djs problem sorry were closed being deleted I realized there may have been or may be many more problems that deal with advanced theory. Well I propose a new problem category.
\r
\ntheoretical(is that right)
\r
\nAny problems that deal with thearoy or is to unknown can go here. because it is theoretical. DJ\'s problem could go into this category. I may submit a problem such as \"What is 5 divided by 0 times 0? (answer 5, Theory: when you start off witha number if u divide then multiply by the same amount you will end up with the same amount.) Or if noone really likes this idea why not just have a page in the site called \"theories\" and it would have theories on quantum mechanics, relativity, string theory, etc.',1072,'Alan','2003-11-05 14:44:09');
INSERT INTO forumpost VALUES (2222,300,5,'Chalange Four','What???? That was the very first thing I tried to do, like four days ago. Wretched stupid ugly smelly IE.\r
\n\r
\nOk, passed 4.',3372,'Sam','2003-11-05 14:51:58');
INSERT INTO forumpost VALUES (2223,300,5,'Re: Scavenger Hunt','Spelling \"Challenge\" right is certainly a challenge...\r
\nNumber eight looks mighty difficult, but it has to stop now. Must do real work. Sigh.',3372,'Sam','2003-11-05 15:59:32');
INSERT INTO forumpost VALUES (2224,306,4,'Re: New category','I am unusre that they couldn\'t go somewhere else instead. If we already have a catergory for them (other than \"general\") then I don\'t think we need another one.\r
\n\r
\nAs to dividing 0 times 0, that hasn\'t been proven yet. Same way as squaring the square root of a negative number.',1626,'Gamer','2003-11-05 16:38:50');
INSERT INTO forumpost VALUES (2225,305,4,'Re: A problem','I agree with DJ. Although I TU your dancing problem, I will say everyone has a problem TD once in a while, and the whole idea of the queue is to make problems that everyone can solve, not one that might pertain to only a certain people.',1626,'Gamer','2003-11-05 16:54:40');
INSERT INTO forumpost VALUES (2226,294,7,'Re: I love Google!','You can find anything in google. Thats how I found this place.',4188,'GimmeKat','2003-11-05 18:45:24');
INSERT INTO forumpost VALUES (2227,294,7,'Re: I love Google!','Google is okay, but I\'d rather Yahoo or Msn...I love msn...\r
\n\r
\nI found this site from a forum that I go to...',3785,'Ashlee','2003-11-06 02:58:39');
INSERT INTO forumpost VALUES (2228,300,5,'Re: Scavenger Hunt','Agreed...\r
\n\r
\nAll the previous ones seemed to have something directly to work with, and number eight is more subtle. I\'m stumped! (Boy that was difficult for me to say.) :-)',3172,'SilverKnight','2003-11-06 09:46:40');
INSERT INTO forumpost VALUES (2229,306,4,'Re: New category','√-25 = ±5i, and (±5i)± = -25',1301,'Charlie','2003-11-06 11:33:47');
INSERT INTO forumpost VALUES (2230,306,4,'Re: New category','Make that \r
\n√-25 = ±5i, and (±5i)² = -25',1301,'Charlie','2003-11-06 11:35:50');
INSERT INTO forumpost VALUES (2231,300,5,'Re: Scavenger Hunt','Yeah.. the first seven didn\'t take more than a few minutes, and I\'ve been stuck on eight for a while..',1575,'DJ','2003-11-06 12:29:46');
INSERT INTO forumpost VALUES (2232,300,5,'Re: Scavenger Hunt','hmmm im not up to eight but mebe u spell challenge in an AIM screenname style like... ch@113ng3 or something of the sort.',3386,'Victor Zapana','2003-11-06 21:27:02');
INSERT INTO forumpost VALUES (2233,306,4,'Re: New category','Gamer, I know it hasn\'t been proven yet. Thats why its theoretical. Its a theory. NOT a theorem. On top of that you said You\'re pretty sure they could fit somewhere else. Well then why was that problem deleted \"sorry we\'re closed\". Because it was to (advanced/questionable?) theory for the site. This is why I propose this new category. Remember theory\'s don\'t have to be proven. In fact anything can be a theory. Its just that it has to be logical and makes sense for it to be accepted into society.',1072,'Alan','2003-11-06 21:46:25');
INSERT INTO forumpost VALUES (2234,306,4,'Re: New category','Hmmm... This sounds suspiciously similar to (and I don\'t know if you guys have been here long enough to remember this) the theories about the result of a division by zero being infinity. I believe Dulanjana was posting them, but I may be wrong.',1,'levik','2003-11-06 22:07:01');
INSERT INTO forumpost VALUES (2235,294,7,'Re: I love Google!','Really? What forum is that? It\'s always interesting when people link to us.',1,'levik','2003-11-06 22:08:05');
INSERT INTO forumpost VALUES (2236,306,4,'Re: New category','No it wasn\'t, it\'s the same reason we don\'t have a lateral thinking catergory. Most people felt that it wouldn\'t work well on this site. At least that\'s what I saw.',1626,'Gamer','2003-11-07 07:07:54');
INSERT INTO forumpost VALUES (2237,294,7,'Re: I love Google!','You can also look here :)',1626,'Gamer','2003-11-07 09:53:42');
INSERT INTO forumpost VALUES (2238,300,5,'Congratulations to lo0ol!...','... I see that (s)he solved challenge 8. Can you give us any tips?',3172,'SilverKnight','2003-11-07 10:49:16');
INSERT INTO forumpost VALUES (2239,300,5,'Re: Scavenger Hunt','I don\'t think lo0ol is even a member of this site :)\r
\n\r
\nHe asked me for a hint to challenge 1 a couple of weeks back on a webmaster forum. Now I almost wish I hadn\'t given it to him :) Well, now he gets the t-shirt, so the prize is gone. But at least we know that the game is beatable with no prior knowledge.\r
\n\r
\nThis is what lo0ol emailed me: \r
\nEgad that last challenge took me forever. I was going into Photoshop, inverting things, frantically working in NotePad... made it more complicated than it needed to be. :)',1,'levik','2003-11-07 12:58:20');
INSERT INTO forumpost VALUES (2240,294,7,'Re: I love Google!','i found this site by google too :)\r
\n\r
\ni\'m a newbie here ;)',4208,'nobrain','2003-11-07 13:05:55');
INSERT INTO forumpost VALUES (2241,307,7,'a new newbie','i am the newb miester :D\r
\n\r
\njust introducing myself:)',4208,'nobrain','2003-11-07 13:07:24');
INSERT INTO forumpost VALUES (2242,217,3,'Re: NEED HELP!','so tara...what was the question? :)',4208,'nobrain','2003-11-07 13:10:13');
INSERT INTO forumpost VALUES (2243,300,5,'Re: Scavenger Hunt','Rats, challenge 8 was the last one? So near and yet so far! Goodbye, sweet t-shirt! I\'ll miss you!\r
\n\r
\nNah, just kidding. Some of us started this puzzle long before any of you young \'uns needed to be bribed with such worldly treasures (about a day before, to be precise)... The thrill of the chase was enough for me!\r
\n\r
\nI\'d challenge SilverKnight and DJ for first over the last hurdle, but I expect that they have far more time that me to work on it than me... It\'s not because I\'m not good enough, I swear - it\'s a time issue. Just time!\r
\n;)',3372,'Sam','2003-11-07 14:21:28');
INSERT INTO forumpost VALUES (2244,300,5,'Re: Scavenger Hunt','Well... I must admit that I sure am lucky that my full time employer gives me all the time I want to surf the web!\r
\n\r
\nActually, I asked Levik to set up the system to e-mail and page me every time a new problem is posted. That way I can generally get to them before anyone else. It sure is helpful! Thanks again Levik!\r
\n\r
\n:-)',3172,'SilverKnight','2003-11-07 14:26:59');
INSERT INTO forumpost VALUES (2245,307,7,'Re: a new newbie','Welcome to the site, I hope you enjoy your stay.',1,'levik','2003-11-07 15:26:41');
INSERT INTO forumpost VALUES (2246,308,5,'The new Scavenger Thread','So, as you know the scavenger game was beaten by a non-floobler (which ought to be humbling to us :)\r
\n\r
\nI\'m still kinda interested to see which of the members will be the first to get past challenge 8. To tell you the truth, I was beginning to doubt myself for the last couple of days, thinking that it was too difficult or trivial, but since somebody actually managed to beat it, I think the people here can do it too.\r
\n\r
\nI\'ll stress again that I don\'t believe that the solution requires any specialized knowledge of in-depth programming, though you have to know some HTML, image editing and javascript basics and concepts. (I think that those who have made it to challenge 8 would agree that this is a fair assessment of the previous challenges as well).\r
\n\r
\nSince games like this are not exactly re-playable any more than the puzzles on this site, I am interested in adding more challenge trails to the game. I would be very interested to know if you guys found this an entertaining excercise, and would like to see more such puzzles.',1,'levik','2003-11-07 15:50:46');
INSERT INTO forumpost VALUES (2247,308,5,'Re: The new Scavenger Thread','Levik, it was very entertaining, and I\'d love to see more of them.\r
\nI especially like the ones that are rather more involved, like the dotMAC puzzle (I belive it was number 6 or 7), which required you to actually think a little bit more in depth. It would be good if the scavanger hunt involved more of the thinking that this site fosters (yes, I\'m assuming puzzle eight requires that sort of thinking. Working on it, I swear!).\r
\n\r
\nPerhaps people could submit ideas for new trails in the game? Perhaps either by making an actual webpage, or just emailing the idea. Of course, it would mean that your particular puzzle would be no challange for you if it were accepted, but if the different trails were long enough, with perhaps multiple branches coming off from each other, it wouldn\'t be a problem.\r
\nJust thinking out loud...',3372,'Sam','2003-11-07 20:25:26');
INSERT INTO forumpost VALUES (2248,308,5,'Re: The new Scavenger Thread','Interesting you should suggest that, Sam, since I was thinking in that direction as well. I would happily accept email with suggestions for future challenges, be they actual HTML and images, or just descriptions.\r
\n\r
\nHowever, I do not wish these challenges to be purely logical, since such puzzles can be submitted to this site directly. As you undoubtedly saw in the challenges you were able to solve, there is always some grounding in the practical setup of the way the web works. Nothing fancy, requiring in-depth knowledge, but if it forced somebody to give a tutorial a cursory look, so much the better in my book :)',1,'levik','2003-11-07 20:55:37');
INSERT INTO forumpost VALUES (2249,306,4,'Re: New category','The only new category that I think could be usefull is some sort of \"category\" category. (Bear with me)\r
\nThis would only be a sub-category of \"General\" or something and would be appropriate for all problems of the type:
\r
\nSome of these could fit into \"Number Problems\" or \"Word Problems\", but they are still all have one important thing in common. Can you work out what it is? (hehehe...)',3136,'Popstar Dave','2003-11-07 23:04:32');
INSERT INTO forumpost VALUES (2251,294,7,'Re: I love Google!','Anyone ever played the \"What does Google think?\" game? You put in the first half of a sentance in quotation marks, run it through google and see what sentances you come up with. I had a procrastination session with it on my blog. You can see what I came up with here.',3136,'Popstar Dave','2003-11-07 23:29:37');
INSERT INTO forumpost VALUES (2252,307,7,'Re: a new newbie','Have a good time... You might want to work on that nick-name if you\'re going to get the answers correct! =P',3136,'Popstar Dave','2003-11-07 23:31:45');
INSERT INTO forumpost VALUES (2253,217,3,'Re: NEED HELP!','Tracy,\r
\nGamer\'s right... this isn\'t the place for problems, but since it\'s already there, I believe that the answer is \"Inside Out\". \r
\nThe period, line and \'n\' rotated 90 deg, anti-clockwise represent \"in\" on it\'s \"side\". Then \"out\".\r
\n\"Inside Out\" QED',3136,'Popstar Dave','2003-11-08 00:20:38');
INSERT INTO forumpost VALUES (2254,308,5,'Re: The new Scavenger Thread','>> As you undoubtedly saw in the challenges you were able to solve, there is always some grounding in the practical setup of the way the web works\r
\n\r
\nIndeed, that\'s why I liked the dotMAC puzzle so much, since it was the right kind of thinking, but put into a webpage structure.\r
\nAlso, your comment has given me new hope about challenge eight. Maybe I\'m trying to hard to see the shape representing some sort of code - one that could mean anything at all!! I think this was what SilverKnight was referring to in the other forum, the challenge doesn\'t seem to have any footholds like the others do. But of course, once we solve it we\'ll kick ourselves for not having seen what was right in front of us, I\'m sure.',3372,'Sam','2003-11-08 02:48:48');
INSERT INTO forumpost VALUES (2255,298,6,'Re: ???','Hehehe... I\'m sitting here reading your first post thinking, \"Hmmm... what freaky maths books were you reading as a kid?!\"\r
\nAs for triangles... I\'m really not sure, nothing comes to mind as I type this, but I\'ll have a think about it and let you know if I come up with anything.',3136,'Popstar Dave','2003-11-08 04:57:11');
INSERT INTO forumpost VALUES (2256,309,5,'Where does Flooble live?','I was just curious as to where Flooble is based. \r
\n \r
\nI\'ve noticed that you\'re running 16 hours behind me (here in Melbournem, Australia) so I\'m guessing west coast, USA somewhere. \r
\nI guess that\'s why there\'s not much action here most of the time that I\'m usually online (3am - 6am Flooble time)!!',3136,'Popstar Dave','2003-11-08 08:57:33');
INSERT INTO forumpost VALUES (2257,37,5,'Re: Names','Now that there\'s another Charlie posting, I\'m thinking of adding a last name. But I notice if I do that, my old postings still have my old name and that would be the same as the new Charlie\'s name.',1301,'Charlie','2003-11-08 09:41:50');
INSERT INTO forumpost VALUES (2258,37,5,'Re: Names','Maybe it does make sense to put avatars on the comments.',1301,'Charlie','2003-11-08 09:42:21');
INSERT INTO forumpost VALUES (2259,37,5,'Re: Names','I sypathize with Charlie... best to prevent people from using the same name. I would suggest the first one to pick a name keeps it, and the latter people are forced to pick a new name.\r
\n\r
\nAnd best to \"separate\" the name from the login name as two different issues (unless you\'re going to change the system to ONLY use/show logins, rather than names).\r
\n\r
\n--- SK',3172,'SilverKnight','2003-11-08 09:51:46');
INSERT INTO forumpost VALUES (2260,309,5,'Re: Where does Flooble live?','New York City, baby :) (Actually the server is technically in Jersey)',1,'levik','2003-11-08 11:34:49');
INSERT INTO forumpost VALUES (2261,37,5,'Re: Names','I think it\'s better to have a screen name and an actual name. Many people come up with something really bizarre to be their screen name, and would have an actual name that is better. Maybe you could only make it so that the first person to get a name makes it unique.',1626,'Gamer','2003-11-08 17:43:39');
INSERT INTO forumpost VALUES (2262,37,5,'Re: Names','I agree with SK. Cross checking and making sure that one person\'s name can\'t be the same as another persons login seems like a strange solution. Just making sure that the are no duplicate logins and no duplicate names would seem to solve the problem.\r
\nI\'m worried, \'cause there\'s bound to be another Sam coming along soon..!',3372,'Sam','2003-11-08 22:15:03');
INSERT INTO forumpost VALUES (2263,309,5,'Re: Where does Flooble live?','u shuda just kept in nyc lol. NEW YORK CITY PRIDE lol.',3386,'Victor Zapana','2003-11-09 09:24:00');
INSERT INTO forumpost VALUES (2264,217,3,'Re: NEED HELP!','dang popstar ur brain sees things my brain cant lol',3386,'Victor Zapana','2003-11-09 10:14:05');
INSERT INTO forumpost VALUES (2265,17,6,'FLOOBLE SCROLLBAR!!!!!','HELP!!! How DO YOU FREAKING CHANGE THE COLOR OF THE FLOOBLE CHATTERBOX\'S SCROLLBAR!??!?!? PLEASE TELL ME!!!!!!',NULL,'ZoKeSpaDe','2003-11-09 14:23:05');
INSERT INTO forumpost VALUES (2266,37,5,'Re: Names','I found out that there\'s another Tristan already! If this is changed, would people be asked to change their names?',3558,'Tristan','2003-11-09 17:21:00');
INSERT INTO forumpost VALUES (2267,204,7,'Hi there','Well, guess I\'m the newest here, but I\'ll try to keep you entertained.',4241,'Vinod','2003-11-10 12:44:54');
INSERT INTO forumpost VALUES (2268,217,3,'Re: NEED HELP!','Well if what Tracy means is what i think it is.... then it is a notation in set theory that stands for \'is a subset of\', meaning that the set that preceded the symbol contains all the elements of the set on the right hand side of the symbol. ',4241,'Vinod','2003-11-10 12:56:35');
INSERT INTO forumpost VALUES (2269,217,3,'Re: NEED HELP!','what is TARA\'s problem neways ... ??',4241,'Vinod','2003-11-10 12:59:40');
INSERT INTO forumpost VALUES (2270,204,7,'wilkomen, bienvenue weeeeelllllllooome','c\'mon in\r
\nhave a seat,\r
\nmake yourself t\'home\r
\n\r
\nWelcome to your new puzzling home away from home.\r
\nCheck out the digest for the latest puzzles.\r
\nIf there is a particular kind of puzzle you like (i.e. logic puzzles) click the link in the upper half of your screen with the appropriate name and get a list of those kinds of problems.\r
\nIf you wnat to say something about the puzzle, or tell how you would solve it post a comment. \r
\n\r
\nIf you have questions about how the sight works check out the commons forum it has lots of interesting strands. OR hit teh DAQ button for some quick canned responses to common questions.\r
\n\r
\nWe are all friends here, so if someone says something to you that rubs you teh wrong way, don\'t let it get you down. They probably did not mean to be rude.\r
\n\r
\n',2839,'FatBoy','2003-11-10 16:05:55');
INSERT INTO forumpost VALUES (2271,204,7,'Re: wilkomen, bienvenue weeeeelllllllooo','FB, you\'ve been practicing that spiel for a while haven\'t you?\r
\n\r
\nQuote from Oceans\'s Eleven (The new one):\r
\nBrad Pitt: \"Why do this?\"\r
\nGeorge Clooney: \"Because the house always wins. Unless, when that perfect hand comes along, you bet big, and then you take the house.\"\r
\nBP: \"You\'ve been practicing that speech, haven\'t you?\"\r
\nGC: \"A little bit. Did I rush it? It felt like I rushed it.\"\r
\nBP: \"No, it was good. I liked it.\"\r
\n\r
\nHehehehe...',3136,'Popstar Dave','2003-11-10 19:04:58');
INSERT INTO forumpost VALUES (2272,308,5,'Re: The new Scavenger Thread','Can someone just give me one tip. Do I need to know anything about US politics to do challenge 4. Because if not, I\'ve just been going off on a tangent for the past few days... bugger.',3136,'Popstar Dave','2003-11-10 19:10:56');
INSERT INTO forumpost VALUES (2289,308,5,'Re: The new Scavenger Thread','Gamer, you fool! I Can\'t believe you unwittingly posted the answer to CH4 :)\r
\n\r
\nI had to delete it to avoid spoilage.',1,'levik','2003-11-11 23:26:27');
INSERT INTO forumpost VALUES (2274,308,5,'Re: The new Scavenger Thread','Gamer, as mentioned in the previous thread. Don\'t use I.E. on #4.',3172,'SilverKnight','2003-11-10 21:15:33');
INSERT INTO forumpost VALUES (2275,308,5,'Re: The new Scavenger Thread','Popstar, none of them assume any actual knowledge. Everything is always right there. And use Netscape.',3372,'Sam','2003-11-10 22:06:36');
INSERT INTO forumpost VALUES (2276,308,5,'Re: The new Scavenger Thread','There we go... It wasn\'t the IE/Netscape thing. It was just that I\'d been going in entirely the wrong direction for about a week. But once I got through challeng 4, check out my progress...\r
\n\r
\npopstar - Challenge 6 (0m) \r
\npopstar - Challenge 5 (0m) \r
\npopstar - Challenge 4 (169h 17m)',3136,'Popstar Dave','2003-11-11 02:08:06');
INSERT INTO forumpost VALUES (2277,308,5,'Re: The new Scavenger Thread','I got all gee\'ed up and now I\'m stuck on challenge 7. I\'ve got the word (you\'ll know what I mean) and I\'ve got \"DOTmac\" (and an idea as to what it means), but now I just can\'t seem to put them together. Now I know only 10 people have passes challenge 7, but I\'m also assuming that most of them read this forum from time to time. So if you\'ve got a word or two to push me along, I\'d love to hear from you! (I\'d rather not have a week next to a challenge again!)',3136,'Popstar Dave','2003-11-11 07:32:23');
INSERT INTO forumpost VALUES (2278,301,3,'Re: WOOHOO!!!','I\'m still a little confused as to when problems get posted. \r
\nI have a puzzle that has gone from queue position 29 to 27 in two weeks. Does this mean that in those two weeks only two puzzles from the front of the queue were used? Does this mean that all the others have been pushed from further back? \r
\nAnd what does it mean that my puzzle that\'s in the 90s seems to be going backwards? Are more and more puzzles beeing inserted between it and the front of the queue?',3372,'Sam','2003-11-11 11:55:36');
INSERT INTO forumpost VALUES (2279,217,3,'Re: NEED HELP!','test\r
\ntest\r
\nPlease delete this post.',3172,'SilverKnight','2003-11-11 12:56:35');
INSERT INTO forumpost VALUES (2280,301,3,'Re: WOOHOO!!!','Sam,\r
\n\r
\nHere\'s why a problem will go backwards.... Some NEW person just submitted their first one or two problems... and therefore, those problems become queue 1 (and get sorted ahead of your, and my, queue 2 problems). But don\'t worry, it\'s pretty meaningless.\r
\n\r
\nI know what you mean about the queue position. I\'ve had a problem at number 16 for about two weeks as well.\r
\n\r
\nThere are some other threads regarding this, and I think a little info in the FAQ, but the system is IMHO inherently confusing.\r
\n_________________\r
\n\r
\nIn general, if someone submits a BUNCH of problems ahead of you... they ALL will get placed in front of your problems... even though they have a higher \"queue position\". The reason is... the queue number means very little.\r
\n\r
\nEach person can have only two problems at each queue weight. And ALL problems with queue weight 1 are reported before all problems with queue weight 2... and all with 2 are reported before 3, etc....\r
\n\r
\nThe catch is... that if someone\'s Queue 1 problem gets posted (or rejected), then a queue 2 problem will JUMP in front of all the other queue 2 problems (and most/many queue 1 problems) to take the missing problems place.\r
\n\r
\nIn short, the queue number is almost meaningless.... The best indication of when a problem will be posted/rejected is the DATE when it was first SUBMITTED.\r
\n________________________\r
\n\r
\nAs you\'ve probably noticed (as of 2003-11-11, at the time of this posting), let\'s look at the last two weeks of posting (this incudes 23 problems):\r
\n\r
\n6 - Gamer\r
\n5 - PopstarDave\r
\n5 - Ravi Raja\r
\n4 - DJ\r
\n1 - Lewis\r
\n1 - FatBoy\r
\n1 - SilverKnight\r
\n\r
\nIt is not a coincidence that this is heavily weighted to only 4-5 different submitters.\r
\n\r
\nSince TWO problems can be at queue weight one at any given time... this generally means that the FIVE earliest, most prolific posters will each have two problems in the \"top ten\" to be review/posted.\r
\n\r
\nA SIXTH person can \"sneak\" in there slowly because when one or two problems gets posted in a day, the next queue weight 1 problem will slide up (and it can\'t be one of the 5 people\'s problems).\r
\n\r
\nBut when midnight comes around... the automatic RESORTING occurs... and any queue weight one problems posted/removed get replaced by queue weight two problems (if they exist, and they usually do). So, all the other queue weight one problems... remain ahead of ALL of your problems, and queue weight two problems jumped ahead.\r
\n________________________\r
\n\r
\nI hope this has been helpful to you (and to others).\r
\n\r
\n--- SK\r
\n\r
\nP.S. Perhaps Levik can link to this posting for the FAQ. :-)',3172,'SilverKnight','2003-11-11 13:03:20');
INSERT INTO forumpost VALUES (2281,301,3,'Re: WOOHOO!!!','It seems that the point of the queue weighting is so that the same person\'s/people\'s problems to not show up too close to each other, and that we see a selection of puzzles from as wide a selection of people as possible on any given week. If this is really the intent, it seems that the weighting system is inherently flawed, as, as you noticed, the same people\'s puzzles show up day after day.\r
\nWhy doesn\'t the system instead prioritize things in order of submission, as it does, but arrange it\'s week such that as many people as possible are reviewed (with the same number of problems being reviewed, of course), while selecting from a set of puzzles below a certian rank.\r
\n\r
\nFor instance, an easier example with just a three day turn over instead of seven day\r
\n\r
\nOrder submitted (by person): ABAACD BEFABG ABHIJC JKLIJK\r
\nEight people have submitted 18 puzzles\r
\n\r
\nOrder posted:\r
\nThe program selects 6 puzzles for the first three days, selecting from the first twelve submitted:\r
\n1: A, B\r
\n2: C, D\r
\n3: E, F\r
\n\r
\nRemaining: AABABG ABHIJC JKLIJK\r
\n\r
\nThe program again selects six from twelve:\r
\n4: A, B\r
\n5: G, H\r
\n6: I, J\r
\n\r
\nRemaining: AABABC JKLIJK\r
\n\r
\nDitto again:\r
\n7: A, B\r
\n8: C, J\r
\n9: K, L\r
\n\r
\n\r
\n\r
\nOk, so that was a little more complicated than I meant it to be. But the system still works. The people that have submitted a huge number of problems still get their\'s shown more frequently. However, the this system works in such a way that the time between their puzzles is increased, which means that a wider selection of puzzles are shown each week.\r
\n\r
\nEven if you find to be this system confusing, the point is still that the queue weighting doesn\'t seem to be doing what it is supposed to be doing, I assume, which is to try and get a wider selection shown over a given time period. In the example above, noone was posted twice in a three day cycle, where as the weighting system would have had A\'s puzzles be posted much more frequently towards the beginning.',3372,'Sam','2003-11-11 17:12:57');
INSERT INTO forumpost VALUES (2282,301,3,'Re: WOOHOO!!!','Sam,\r
\n\r
\nIf you\'re not already aware... the automated process just kicks the problems up to the \"top ten\".... Once the problems are there, HUMANS (Scholars and Journeymen) vote plus or minus... to determine whether each is ELIGIBLE for posting or if it should be rejected. Then, I believe, only a scholar can \"push\" it live.\r
\n\r
\nI think you described an automatic way for posting problems, but I\'m sure we don\'t want to see every problem ever submitted (there\'s gotta be a lot of junk amid the pearls).\r
\n\r
\nSo, I think the issue is:\r
\nUnder the current algorithm, as long as there are \"many\" submitters of problems, then if we sample any, say, month-long period, we will find that it is heavily skewed to about 5 people\'s submissions.\r
\n\r
\nSam, I will direct you and others to this previous thread for much more discussion about this subject.\r
\n\r
\n--- SK',3172,'SilverKnight','2003-11-11 17:59:13');
INSERT INTO forumpost VALUES (2283,301,3,'Re: WOOHOO!!!','I didn\'t read through these last two comments, as I figured they were mostly directed to each other...\r
\n\r
\nThe problem with the queue now is that we have 5 submitters that are already submitting puzzles. This has filled up the queue, such that any problems submitted after 8-18 (as of today) likely won\'t get posted. (pid of less than 1500)\r
\n\r
\nThe point of queue weighing is so that in the queue we don\'t see all of Ravi\'s puzzles; as he somehow submits 40 puzzles at one time. Or for example, we don\'t see all of my of anyone else\'s in a big clump. This can be seem because there are 340 problems submitted by the top 8 submitters.\r
\n',1626,'Gamer','2003-11-11 18:09:32');
INSERT INTO forumpost VALUES (2284,301,3,'Re: WOOHOO!!!','SK\'s probably right. This discussion should continue in that other thread. When I found out how QW worked, I thought it might somehow be flawed, and I still have my doubts. \r
\n\r
\nBack to the original reason for this thread, I really liked your puzzle, SK. I only wish the ones I submitted were as good... Yeah, my first puzzle has been QW 42 for like a month now, not that the number truly means anything. Then again, 42 is the answer to everything (according to a certain author).',3558,'Tristan','2003-11-11 18:53:51');
INSERT INTO forumpost VALUES (2285,301,3,'Re: WOOHOO!!!','Thanks Tristan, I\'m flattered.\r
\n\r
\nWell... hopefully, you\'ll like some of my other ones (if they ever get posted :-). I look forward to seeing yours.\r
\n\r
\n--- SK\r
\n\r
\nP.S. Douglas Adams rocked!',3172,'SilverKnight','2003-11-11 19:05:20');
INSERT INTO forumpost VALUES (2286,301,3,'Re: WOOHOO!!!','sigh... i feel slightly saddened. i give 23 problems and like only 3 of them are queue 100-. mebe they suck too much. -sigh-',3386,'Victor Zapana','2003-11-11 19:31:59');
INSERT INTO forumpost VALUES (2287,308,5,'Re: The new Scavenger Thread','I just finished challenge 8! I\'ll say nothing more than the fact that it was rather satisfying!\r
\n\r
\nWhatever you\'re doing, Dave, it sounds like you\'re in the right direction. It\'s probably more obvious than you think.\r
\n\r
\nThat scavenger hunt was very exhilarating! We should definitely have more.',3558,'Tristan','2003-11-11 19:45:03');
INSERT INTO forumpost VALUES (2288,301,3,'Re: WOOHOO!!!','I think you just submitted them too late.\r
\n\r
\nI think pid is an important factor too. A recently submitted problem had a pid of 1788. Since all problems in the queue have a pid of less than 1500, it takes a while for your problems to get into the queue without queue weight, and because of so many \"many problem submitters\" have many problems inside that range, (I have 25 that haven\'t been in the queue yet that have a pid of less than 1500), it\'s hard for many submitters to get them in.\r
\n\r
\nIf you submit problems then wait for a while they will be there! :)',1626,'Gamer','2003-11-11 20:50:39');
INSERT INTO forumpost VALUES (2290,308,5,'Re: The new Scavenger Thread','Oh, and also, congratulations, Tristan. \r
\n\r
\nI\'m glad that you were able to beat the challenge. Surely this ough to shame everyone else into following ;)',1,'levik','2003-11-11 23:29:21');
INSERT INTO forumpost VALUES (2291,308,5,'Re: The new Scavenger Thread','Yes I feel suitably shamed. Yes I feel suitably humbled. Yes I\'m still stuck on challenege 2.\r
\n\r
\nI\'ve tried everything I can think of that\'s obvious. I\'ve tried everything I can think of that\'s obscure. I\'ve even tried random URLs. All to no avail.\r
\n\r
\nI can\'t sleep. I can\'t eat. I can\'t think about anything else.\r
\n\r
\nAAAAAAARRRRRRGGGGGGGGGGGGHHHHHHHHHHHHHHHHHHHHHHHHHHH!!!!!!!!!!!!!!!!',1183,'fwaff','2003-11-12 03:13:46');
INSERT INTO forumpost VALUES (2292,204,7,'Re: No Subject','Popstar,\r
\nNo, not practicing but I haev types a few postings along these lines before. I wwas remembering being a new Floobler and feelling like I did not know my way around and decided to add a welcome to Billie. \r
\nOf course, now I look a lttle closer at his original post and see he wrote it way back in September. Then I checked his info ans see that he hasn\'t even logged in since then....... oh well, so I\'m a dope.\r
\n',2839,'FatBoy','2003-11-12 07:32:22');
INSERT INTO forumpost VALUES (2293,204,7,'Re: No Subject','Hehehe... oh yeah. I didn\'t notice that either! \r
\nObviously you weren\'t welcoming enough!! =P
',3136,'Popstar Dave','2003-11-12 09:10:15');
INSERT INTO forumpost VALUES (2294,308,5,'Re: The new Scavenger Thread','well fwaff, at least you made it to #2!!! I couldn\'t even get through number one. I believe this qualifies as a \"double AARRGGHH!!\"',775,'Cory Taylor','2003-11-12 11:30:14');
INSERT INTO forumpost VALUES (2295,308,5,'Re: The new Scavenger Thread','Cory... try VIEW SOURCE, then scroll to the bottom...',3172,'SilverKnight','2003-11-12 11:40:55');
INSERT INTO forumpost VALUES (2296,308,5,'Re: The new Scavenger Thread','fwaff... pay careful attention (in general on these problems) to ANY REFERENCE to something NOT on the page itself (HTML provides many ways to reference things not on the page).',3172,'SilverKnight','2003-11-12 11:43:08');
INSERT INTO forumpost VALUES (2297,308,5,'Re: The new Scavenger Thread','Well, looks like more and more people are beating the challenge trail!',1,'levik','2003-11-12 19:25:18');
INSERT INTO forumpost VALUES (2298,308,5,'Re: The new Scavenger Thread','SK, maybe give a tip... not a walkthrough.\r
\nNo one wants to be spoon-fed.',3136,'Popstar Dave','2003-11-12 20:26:58');
INSERT INTO forumpost VALUES (2299,308,5,'Re: The new Scavenger Thread','actually Dave... I met this one guy... this one time.... and he actually DID want to be given the answer...\r
\n\r
\nBut, in any case... since I certainly didn\'t give fwaff a walkthrough on any of them, I assume you are referring to the problem #1 \"hint\" I gave to Cory....\r
\n\r
\nSince Levik (who obviously saw it... he posted afterwards) thought it appropriate for the first problem... and since no one seemed to mind (until you choose to honor us with your opinion), I think it\'s okay to give such a tip.\r
\n\r
\nBut, you keep posting!',3172,'SilverKnight','2003-11-12 20:54:43');
INSERT INTO forumpost VALUES (2300,301,3,'Re: WOOHOO!!!','SK, of course I realize that humans check them - it would be terrible if they didn\'t. I guess instead of looking at my system above as posting the problems, look at it as offering six puzzles to the voters.\r
\n\r
\nI guess the system can be explained much more simply:\r
\n\r
\nTake a bound of, say, 50 puzzles.\r
\nArrange set by order of posting.\r
\nRearrange so that no submitter in that set has two problems without every other submitter having a problem in between, if possible.\r
\nShow top ten to humans.\r
\n\r
\nSo shown, with a bound of 8 and top 4 shown:\r
\n\r
\nABCADEFBAGHI submitted in order\r
\n\r
\nBound (left side):\r
\n\r
\nABCADEFB | AGHI\r
\n\r
\nRearanged:\r
\n\r
\nABCDEFAB | AGHI\r
\n\r
\nOffered for judging:\r
\n\r
\nABCDEF | ABAGHI\r
\n\r
\nA, B get posted (if their good enough).\r
\n\r
\nRestart. New set in original order:\r
\n\r
\nCADEFBAGHI\r
\n\r
\nBound, then rearrange:\r
\n\r
\nCADEFBGA | HI\r
\n\r
\nand so on...\r
\nDoes that make sense? No queue weights, and if the set is large enough, you will have much more space between the same submitters puzzles.',3372,'Sam','2003-11-12 21:49:04');
INSERT INTO forumpost VALUES (2301,308,5,'Re: The new Scavenger Thread','People that beat challange eight in 15 and 6 minutes. Does it really only take them that long, or are they getting the anser and restarting?\r
\n\r
\nJust wondering... If someone can get it in six minutes I must be really dumb! :)',3372,'Sam','2003-11-12 21:56:43');
INSERT INTO forumpost VALUES (2302,301,3,'Re: WOOHOO!!!','Sam, I think you\'ve got to retry your scenario with the following possibility (more like what Flooble has really seen.....)\r
\n\r
\nsubmitted order:\r
\nAAAAAABBBABBBBBAAAAAAACCCCBBBBBBBAAAAAAAAAAAAAAAADDDDDDEFGAAAAABBBBHIJKAAAAA\r
\n\r
\nNow, try your algorithm again.... what happens?\r
\n\r
\nAnd to quote Levik:\r
\n\"The queue mechanism currently offers a \"benefit\" for early submission.... statistically, people\'s first problems are not the best submissions we get on the site.\"\r
\n____________________________\r
\n\r
\nSam, please understand, I\'m playing Devil\'s Advocate here.... I\'m not a big fan of the current system, and if you check the link I\'ve given you, you\'ll see I\'ve already presented similar arguments.... :-)\r
\n\r
\nThat being said, I *AM* a big fan of this site, and all in all, I think it is run extremely well.',3172,'SilverKnight','2003-11-13 00:27:15');
INSERT INTO forumpost VALUES (2303,310,4,'Perplexus-etiquette','As your latest Journeyman, I\'m just curious as to what Perplexus-etiquette there is relating to the added responsibilities that go with being a Journeyman. I want to do my bit, but I don\'t want to step on anyone\'s toes while I\'m here!',3136,'Popstar Dave','2003-11-13 00:41:04');
INSERT INTO forumpost VALUES (2304,301,3,'Re: WOOHOO!!!','I see your point, though with a large enough initial set the problem would be slightly alleviated. Your posting above, for instance would be rearanged as:\r
\n\r
\nABCDEFGHIJKABCDABCD.....\r
\n\r
\nand since the set is recalculated once the two or three are taken off the end each day, you won\'t ever reach the point where it sarts going ABCABCABC...\r
\n\r
\nHere is it in the very simplest terms: \r
\nIf someone\'s puzzle in in the set, say the top 50, then this system would guarantee that that puzzle is seen by the judges before anyone elses puzzle is seen twice.\r
\nDoes that make sense?\r
\n\r
\nAnyways, obviously I am saying this because I\'m a great fan of the site, not inspite of it. If I didn\'t think that it was brilliant and very well run, I wouldn\'t spend my time trying to improve it :D',3372,'Sam','2003-11-13 02:08:06');
INSERT INTO forumpost VALUES (2305,301,3,'Re: WOOHOO!!!','Sam,\r
\n\r
\nI really think you should read through the thread/link I referenced above... not that this isn\'t a valuable discussion, but it\'s really rehashing points already made. (Your suggestion that the set be enlarged is virtually identical to a point I, and perhaps others, made before.) :-)\r
\n\r
\n--- SK\r
\n\r
\n',3172,'SilverKnight','2003-11-13 02:42:42');
INSERT INTO forumpost VALUES (2306,310,4,'Re: Perplexus-etiquette','I think that you will find that most Journeymen are horribly prickly, and try to screw each other over at every turn. This is of course nothing compared to what the Scholars are like :)\r
\n\r
\nI\'m kidding of course. \r
\n\r
\nI don\'t think that there\'s much to getting along with everyone, reguardless what level you\'re at. You seem to be doing just fine.\r
\n\r
\nCongratulations on your promotion, and thanks for participating in the site.',1,'levik','2003-11-13 10:38:26');
INSERT INTO forumpost VALUES (2307,301,3,'Re: WOOHOO!!!','Well, I had indeed read that other thread, and really didn\'t think that the system I was proposing was the same as the two queues idea you had, but since I\'ve explained my system fully now I guess I don\'t need to rehash it. My one line synopsis in my last post said it best, I think.',3372,'Sam','2003-11-13 15:55:13');
INSERT INTO forumpost VALUES (2308,310,4,'Re: Perplexus-etiquette','Just know to vote on problems fairly, and don\'t be afraid to give your opinion. :)\r
\n\r
\nThis morning the only thing to push was Not Another One! so we could use another journeyman :)',1626,'Gamer','2003-11-13 16:11:45');
INSERT INTO forumpost VALUES (2330,312,5,'Base 1 and Base 0','Well... I mentioned it in the chatterbox and many people answered... but not with base 0. so can anyway give me what base 0 is? or if anyone wanna comment on base 1... please... i dun like bases under binary.',3386,'Victor Zapana','2003-11-18 20:36:39');
INSERT INTO forumpost VALUES (2310,308,5,'Re: The new Scavenger Thread','blah i feel sad i cant get past challenge 2',3386,'Victor Zapana','2003-11-13 19:23:12');
INSERT INTO forumpost VALUES (2318,146,6,'Re: sequences','I need to know the anser to the following sequence - anyone help?\r
\n\r
\n17 _ _ _ 67 87\r
\n\r
\nalexepson@hotmail.com',4338,'alex epson','2003-11-16 09:12:58');
INSERT INTO forumpost VALUES (2317,308,5,'Re: The new Scavenger Thread','OK, guys, I had to delete some of Victor and SK\'s posts - too many clues for my tastes... \r
\n\r
\nLet\'s all be a bit more careful.',1,'levik','2003-11-14 21:14:11');
INSERT INTO forumpost VALUES (2314,308,5,'Re: The new Scavenger Thread','o.. wow... that took me a while thanks sk. now ew... hu the hell made that crappy pic in CH3. eww...',3386,'Victor Zapana','2003-11-13 21:33:19');
INSERT INTO forumpost VALUES (2315,308,5,'Re: The new Scavenger Thread','hmm.. can i ask... (all of this is for CH3)
\nis the picture there just as a picture, and it involves the HTML ..
\nor does the picture actually need manipulation to get the answer? ',3386,'Victor Zapana','2003-11-13 21:44:52');
INSERT INTO forumpost VALUES (2316,308,5,'Re: The new Scavenger Thread','you can ask... (and if Dave will permit me to say), it all seems to involve the html to some degree or other.',3172,'SilverKnight','2003-11-13 21:48:22');
INSERT INTO forumpost VALUES (2319,146,6,'Re: sequences','first, its bad to post problems on forums. :-<
\n\r
\nThis could be written as a bunch of formulas, even as a quadratic function (like (3(term^2))/2 (7(term))/2 + 24/2))',1626,'Gamer','2003-11-16 14:25:30');
INSERT INTO forumpost VALUES (2321,146,6,'Re: sequences','woah Gamer howd u get that quadratic function out that sequence? dang ',NULL,'Victor Zapana','2003-11-16 16:36:03');
INSERT INTO forumpost VALUES (2322,146,6,'Re: sequences','Easy, he just closed his eyes and visualized the graph of, um, that long equation. For fun he then multiplied it by 1/pi and created some beautiful images with the interference patterns created by the two graphs, but couldn\'t show them \'cause his mental printer was out of blue ink. Oh well.',3372,'Sam','2003-11-16 20:07:59');
INSERT INTO forumpost VALUES (2323,146,6,'Re: sequences','Well, I do that sometimes, but for this particular one I was lazy and used quadratic regression. You can do this by setting up a system of equations, and then solving them by lots of \"linear\" combination, or by setting up inverse matrices. I am sure the smarties of this forum know plenty of other ways I don\'t :) ',1626,'Gamer','2003-11-16 20:20:12');
INSERT INTO forumpost VALUES (2324,146,6,'Re: sequences','Really? I\'d like to hear them. My self-taught methods don\'t work very well there. And this is the reference forum. How fitting.',3558,'Tristan','2003-11-16 20:49:30');
INSERT INTO forumpost VALUES (2325,311,3,'need solution,HELP','with marble walls as soft as silk lined with jelly crystals, the folls break in and steal the gold: there is no door 2 this. what is it ?',4355,'AJ','2003-11-17 03:56:25');
INSERT INTO forumpost VALUES (2326,311,3,'Re: need solution,HELP','with marble walls as soft as silk lined with jelly crystals, the fools break in and steal the gold: there is no door 2 this. what is it ? \r
\n',4355,'AJ','2003-11-17 03:57:07');
INSERT INTO forumpost VALUES (2327,311,3,'Re: need solution,HELP','AJ, we\'ve got this little policy here about not posting problems to the forums. You may have noticed this on the screen while you were typing your post:\r
\n\"Notice: About to post a problem to the forum? Please don\'t. (Here\'s why)\"\r
\nThat link goes to a forum post by Levik (The Director of Perplexus) who\'ll explain it all to you a whole lot better than I can.\r
\nCheers,\r
\nDave',3136,'Popstar Dave','2003-11-17 07:22:00');
INSERT INTO forumpost VALUES (2328,80,7,'You have a coool name','I like your name it is sweet.',4358,'Noodlez','2003-11-17 12:57:03');
INSERT INTO forumpost VALUES (2329,80,7,'Re: Hello, First time here','ur names so edible. i like it lol',3386,'Victor Zapana','2003-11-17 16:41:18');
INSERT INTO forumpost VALUES (2336,312,5,'Re: Base 1 and Base 0','I don\'t think Bases 1 or 0 are real bases, because in base 0 there are 0 digits. This means numbers don\'t exist!\r
\n\r
\nIn base 1, you have 0, 00, 000 and so on. This also doesn\'t work.\r
\n\r
\nAlso, to answer the question about 0^0 being undefined, some people say this argument: If going up 1 exponent is the same as multiplying the base (if 4^3 = 64, then 4^(3+1) = 64 * 4) then subtracting 1 must be the same as dividing by the base. (so if 4^3 = 64, then 4^(3-1) = 64 / 4)\r
\n\r
\nWhen such an argument is reached, you can see that if 0^1 = 0, then 0^(1-1) = 0 / 0. But what is 0 / 0? :)',1626,'Gamer','2003-11-19 15:34:07');
INSERT INTO forumpost VALUES (2337,313,7,'Finally got here','Well I guess I could say I\'m new here.. After 73 years searching on the Internet(well not really that long)I think I may have found a good site.\r
\nLater I would like to make a comment on a \"Riddle\" that I have read on this site.',4396,'Fred','2003-11-19 16:45:16');
INSERT INTO forumpost VALUES (2338,314,3,'Riddle... \"Brothers & Sisters\"','On 12/30/2002 a riddle.. Brothers & Sisters\" was posted by cyes.. I would like to make a old version of this..\r
\nWhen I was in Navy during the Korean war, we would fly way into North Korean behind emeny lines.. Generally there was five or six of us pilots flying bombing missions. Going to the bombing sites we would keep radio silence(no cummunications whatsoever) until we made our bombing runs. Then if we all were safe and no one got shot down, we could tell a \"riddle\" on the way back to the aircraft carrier. The riddle would take your mind off the war and calm you down.. Here is my riddle that no one solved.\r
\nI quote..\r
\n\"Two men walking down a sidewalk next to a building that had a county jail on the second floor.. A man in a second story window behind bars waves. The man next to the building side, waves back at the person in the jail window. The other man says, \"who was that man?\"..\r
\nThe other man says, \"Brothers and Sisters I have none, that man\'s father is my father son\"\r
\nWho was the man behind bars?',4396,'Fred','2003-11-19 17:05:30');
INSERT INTO forumpost VALUES (2339,314,3,'Re: Riddle...','Fred,\r
\nWe do not normally post puzzles in the forums and solving them here is also frowned on. In this case though, I ca refer you to the original Trivial Persuit game which included that specific puzzle as a quesiton. Ask the next three trivial persuit players you meet, one of them is sure to answer.\r
\nSOrry to be a jerk abuot not answering here, but I am a slave to peer pressure.',2839,'FatBoy','2003-11-19 17:41:50');
INSERT INTO forumpost VALUES (2340,314,3,'Re: Riddle...','Actually (and FatBoy is correct), Fred didn\'t really post a new problem here.\r
\n\r
\nHe is relating an anecdote in which he told the riddle to his peer pilots.\r
\n\r
\nIf you click the link, you\'ll see the problem that Fred is referencing, already exists on the site, almost verbatim.\r
\n\r
\n--- SK',3172,'SilverKnight','2003-11-19 17:47:51');
INSERT INTO forumpost VALUES (2341,312,5,'Re: Base 1 and Base 0','Well, about 0^0, I first had my doubts because my math teacher said, \"You can\'t take a 0 and a 0 and make a 1, so it\'s undefined.\" I thought such an argument was unsatisfactory. Searching on the internet, I found this place, and google just said it was 1. It has to do with l\'hopital\'s rule, which I\'m sure everyone here but me understands.\r
\n\r
\nMy problem with the argument you gave (I know it\'s not really yours) is that you could say that 0^(2-1) is undefined too. My problem with what I understand of the l\'hopital\'s rule is that making 0^0 undefined interrupts x^0=y as much as making it defined interrupts 0^x=y. Well, I can\'t make a good argument there without enough knowledge of calculus.',3558,'Tristan','2003-11-19 18:33:04');
INSERT INTO forumpost VALUES (2342,313,7,'Re: Finally got here','Hiya Fred and welcome. To post a comment on a \"Riddle\" click \"Post a Comment\" :).',3386,'Victor Zapana','2003-11-19 20:05:59');
INSERT INTO forumpost VALUES (2343,313,7,'Re: Finally got here','Hey Fred,\r
\n\r
\nSorry for misunderstanding your other post.\r
\nWelcome to flooble and since, as your other post indicates, you are one of those who has put it all on the line for the U.S. overseas, thank you.',2839,'FatBoy','2003-11-20 07:44:28');
INSERT INTO forumpost VALUES (2344,312,5,'Re: Base 1 and Base 0','Tristan, l\'Hopitals rule doesn\'t equate numbers, it equates limits, which is the reason that in some cases it appears that 0/0=1. In other cases 0/0=4 or 0/0=-7 etc. The driving factor in the differences here is that the zero in question here is not actually zero, it is in fact something approaching zero. I\'m sure that I\'m not really clearing things up for you, but I\'ll attempt to give an example. Due to many years since formal math instruction and a lack of reference texts, it\'ll be unfinished but the idea will be there.\r
\n\r
\nAssuming that you understand the basic trig functions sin and cos;\r
\n\r
\nsin(0)=0 and cos(0)=1\r
\n\r
\nwhat happens when you take sin(0)/0?\r
\nhow about (cos(0)-1)/0?\r
\n\r
\nwell, these both look like 0/0 cases to me, and so we use l\'hopitals rule and create limits from the two equations. In the first we equate the answer to the limit of [sin(x)/x] as x approaches 0 (similarly in the secong we equate the answer to the limt of [(cos(x)-1/x) as x approaches 0). Now we see that the answer is ~approaching~ 0/0 (it is not equal to 0/0 - this is a property of limits that is very important). Since this is the case (as it would have also been if approaching inf./inf. or -inf./-inf) we can further evaluate using l\'hopitals rule.\r
\n\r
\nNow assuming that you\'re familiar with basic calculus, if you\'re not you\'ll have to take me at faith;\r
\n\r
\nThe original limits are described by the derivatives of the original numerators divided by the derivatives of the original denominators. This means that sin(0)/0 simplifies to inf/1, or just infinity, while the (cos(0)-1)/0 simplifies to 0/1, or zero. Two different cases of 0/0 providing different answer depending on the various initial condition - this shows that the term 0/0 is undefined (and this means something different fomr infinity).\r
\n\r
\nI\'ll finalize with the clarification that there is likely some flaws in the math I\'ve produced (I expected the sin(x)/x to reduce to 1 somehow...) and I\'m sure that others will come along to clean it up a little, but hopefully you see the catch here is that l\'hopitals rule doesn\'t deal with quantities, it derals with limits of equations, and these behave somewhat differently that the quantities they evaluate to.',775,'Cory Taylor','2003-11-20 10:22:03');
INSERT INTO forumpost VALUES (2345,312,5,'Re: Base 1 and Base 0','doh - thats some bad math. Of course the derivative of sin is cos, producing the sin(x)/x -> 1 that I was expecting. Not really sure what I was thinking there...\r
\n\r
\ncleaning the egg of my face...',775,'Cory Taylor','2003-11-20 10:24:16');
INSERT INTO forumpost VALUES (2346,312,5,'Re: Base 1 and Base 0','To illustrate what Cory is saying, here\'s some spreadsheet output showing how, when x approaches zero, the corresponding quantities change:\r
\n\r
\r
\n X(RAD) SIN(X) SIN(X)/X COS(X)-1 (COS(X)-1)/X\r
\n 1 0.841471 0.841471 -0.4597 -0.4597\r
\n 0.1 0.099833 0.998334 -0.005 -0.04996\r
\n 0.01 0.01 0.999983 -.00005 -0.005\r
\n 0.001 0.001 1 -.0000005 -0.0005\r
\n
\nso as x approaches zero, sin(x)/x approaches 1 while (cos(x)-1)/x approaches zero.',1301,'Charlie','2003-11-20 14:35:44');
INSERT INTO forumpost VALUES (2347,313,7,'Re: Finally got here','At last! What kept you? You\'re dinner\'s cone all cold, but we can always heat it up again. No worries.',3372,'Sam','2003-11-20 16:22:17');
INSERT INTO forumpost VALUES (2348,312,5,'Re: Base 1 and Base 0','In truth, I don\'t really know much basic calculus (except the definitions of derivative and integral), which is probably why I didn\'t understand l\'hopital\'s rule in the first place. But I think I understand what you\'re saying.\r
\n\r
\nSo I suppose the equation x^y has impossible limits for point (0,0)?',3558,'Tristan','2003-11-20 19:11:55');
INSERT INTO forumpost VALUES (2349,315,7,'In a slight pickel',' Thanks for taking a moment for this...\r
\n\r
\nI just got this problem that i wish someone could help me with, but i also just signed up ....you see my dilema.\r
\n\r
\nI understand that i cant post it here, so i must ask how does one obtain a higher rank and therefore be allowed to post?\r
\n\r
\nIm in a bit of a rush so if you see this and know the answer post and/or IM me at supermansamdr (aim) or supermansam15 (yim)\r
\n\r
\nThanks a heap for your help\r
\n\r
\nSorry for any potential misspelled words im in a hurry.....',4425,'Sam','2003-11-21 02:09:57');
INSERT INTO forumpost VALUES (2350,312,5,'Re: Base 1 and Base 0','The method of approach to (0,0) must be specified. If you consider the function y=0^x as x approaches 0, the answer will be 0, as zero raised to even a tiny amount above zero is zero. If you consider the function y=x^0 as x approaches 0, the answer will be 1, as any tiny number (above zero) raised to the zero power is 1.',1301,'Charlie','2003-11-21 08:17:15');
INSERT INTO forumpost VALUES (2351,315,7,'Re: In a slight pickel','All the info about levels and what each of them allows, can be found here.',3136,'Popstar Dave','2003-11-21 08:54:07');
INSERT INTO forumpost VALUES (2352,312,5,'Re: Base 1 and Base 0','There are 10 types of people in this world...those who understand binary code, and those who don\'t.',1112,'Greg','2003-11-21 09:37:30');
INSERT INTO forumpost VALUES (2353,315,7,'Re: In a slight pickel','Also, if this is a homework-type problem or something, I would wager that pretty nearly all of the more common logic problems, riddles, whatever, are already on the site. Use the search box on the main page (it does an exact search, so try using a single relevant keyword) and check the \"Search body\" box to see if there is anything here that could help you out.\r
\n\r
\nIf that fails, perhaps one of us that has been around for a while could help point you in the right direction, either by locating a problem on the site or giving a hint, but this isn\'t really a homework-answering service..',1575,'DJ','2003-11-21 10:49:42');
INSERT INTO forumpost VALUES (2354,282,5,'Re: Advertising','Apparently porn is still showing up. Helen posted this url in the chat box, and I\'m posting it here:\r
\nhttp://204.177.92.193/pt/affpp/dlotherway_datefor_newerror_c_pbd.html\r
\n',3372,'Sam','2003-11-21 12:11:41');
INSERT INTO forumpost VALUES (2355,315,7,'Re: In a slight pickel','Posting the puzzle by submitting it doesn\'t require much, but you\'re likely to wait a couple of months. If you\'re looking for a fast solution, posting a way to contact you is the best thing to do, so it\'s nice that you did that.',3558,'Tristan','2003-11-21 22:00:40');
INSERT INTO forumpost VALUES (2356,315,7,'Re: In a slight pickel','Arghh! Another Sam! I told you just a few days ago that the time would come. Perhaps I should sell my serices as a prophet... \r
\nDid we ever decide on anything re multiple logins?',3372,'Sam','2003-11-22 01:49:45');
INSERT INTO forumpost VALUES (2357,315,7,'Re: In a slight pickel','Oh... and welcome. Like other\'s said, your probably best off using the search funtion. Chances are it\'s been posted here before.',3372,'Sam','2003-11-22 01:51:12');
INSERT INTO forumpost VALUES (2358,316,7,'Hey all','Good morning evryone(besides the fact that its 19:10 here)\r
\n\r
\nMy names Greg Smith, live in South Africa, and am a 18 year old student.\r
\nGot onto the site when I typed in \"riddles with solutions\" in googles search engine.\r
\n\r
\nMain reason was to find the answer to a riddle thats got me confused...but we\'re not supposed to post riddles in the forums are we? So how does a novice post his riddle here anyway?\r
\n\r
\nIve tried looking for it with no luck, maybe Im just looking in the wrong places.\r
\n\r
\nAnyone care to give advice?',4447,'Greg','2003-11-22 12:09:49');
INSERT INTO forumpost VALUES (2359,317,7,'New here','Hi I am new here and thought that I would say Hi. I found this site because I was looking for riddles and brainteasers.',4452,'Lisa','2003-11-22 20:39:53');
INSERT INTO forumpost VALUES (2360,316,7,'Re: Hey all','Well my piece of advice would be to look at every riddle (seems like you\'ve already done that) then perhaps try logic and general. If that doesn\'t work you could always submit the problem because that means the site doesn\'t have it.',1072,'Alan','2003-11-22 22:02:35');
INSERT INTO forumpost VALUES (2361,316,7,'Re: Hey all','Greg,\r
\nIf you really need to find answer to the riddle, you could try posting your email address and and letting anyone who\'s willing to help email you. As a start you could email it to me and I\'ll see if I can help!\r
\nCheers,\r
\nDave',3136,'Popstar Dave','2003-11-22 22:16:45');
INSERT INTO forumpost VALUES (2362,317,7,'Re: New here','welcome lisa and i hope u enjoy ur stay. remember many of us are ready to help (and eager) you if we can.',3386,'Victor Zapana','2003-11-22 22:17:26');
INSERT INTO forumpost VALUES (2363,317,7,'Re: New here','Well Lisa,\r
\nWelcome to Perplexus. Have a good time looking round and if you have any questions about how this place works, check out the FAQ or just ask in the forums, we\'re all nicee people here!\r
\nCheers,\r
\nDave',3136,'Popstar Dave','2003-11-22 22:20:03');
INSERT INTO forumpost VALUES (2364,317,7,'Re: New here','ehy all i\'m new here too and i was wondering where all the philosophical brainteasers are ( chicken or egg, tree falling in the woods, etc.).\r
\noh by the way i found this site while visiting a frat. house during a party',4453,'muzo','2003-11-23 00:23:32');
INSERT INTO forumpost VALUES (2365,317,7,'Re: New here','Hmmm... Frat House Party & Brain Teasers and logic problems. \r
\nA bit different to the parties I\'m used to! =P',3136,'Popstar Dave','2003-11-23 01:18:24');
INSERT INTO forumpost VALUES (2366,317,7,'Re: New here','Indeed, doesn\'t sound like any frat parties I know of..! I\'m not sure if you\'ll find problems of that sort, though. Except for a few paradoxes, most questions here are the sort that have answers.',3372,'Sam','2003-11-23 02:33:20');
INSERT INTO forumpost VALUES (2367,146,6,'Re: sequences','i dont know about any of you but when i try gamers function it does not work???\r
\nhelp?',4450,'drew','2003-11-23 13:30:58');
INSERT INTO forumpost VALUES (2368,146,6,'Re: sequences','\r
\n\r
',1626,'Gamer','2003-11-23 14:54:40');
INSERT INTO forumpost VALUES (2369,146,6,'Re: sequences','this is not self explanetory\r
\n1 3/2 7/2 24/2 17 \r
\n2 __ \r
\n3 __ \r
\n4 __ \r
\n5 75/2 35/2 24/2 67 \r
\n6 108/2 42/2 24/2 87 \r
\n
\nplease explain\r
\nhow do you get 87 from 67',4450,'drew','2003-11-23 18:11:21');
INSERT INTO forumpost VALUES (2370,146,6,'Re: sequences','If it doesn\'t go down, maybe you could try the only other option and go across! Surely you have read my formula for the sequence or you couldn\'t be confused about that! You also must have read the 17,?,?,?,67,87 sequence or you couldn\'t be confused about that!\r
\n\r
\nI am just showing that it DOES work, even though you said it didn\'t :)\r
\n\r
\nThe term numbers are on the left, each part is in the middle, and their sum are on the right.',1626,'Gamer','2003-11-23 18:46:01');
INSERT INTO forumpost VALUES (2371,146,6,'Re: sequences','All, in an effort to put this to rest... let me simply restate what Gamer has said, perhaps in a more easy to read format:\r
\n\r
\nF(x) = 0.5 * (3x² + 7x + 24)\r
\n\r
\nF(1) = 17\r
\nF(2) = 25\r
\nF(3) = 36\r
\nF(4) = 50\r
\nF(5) = 67\r
\nF(6) = 87\r
\n\r
\n- SK',3172,'SilverKnight','2003-11-23 19:00:01');
INSERT INTO forumpost VALUES (2372,146,6,'Re: sequences','thanx !SilverKnight! !you! helped alot.\r
\nlol',4450,'drew','2003-11-23 22:31:36');
INSERT INTO forumpost VALUES (2373,282,5,'Re: Advertising','Sorry that I have neglected this thread for a while... \r
\n\r
\nGreg, the unfortunate truth is that even were I able to have 10 paid banners on this page (which no advertiser would agree to in the first place), they would still not bring in as much money as a single popup. The advertising market is pretty bad right now, and people dislike paying money unless they make it.\r
\n\r
\nI would like to see a count of hands of people who have clicked on a banner on this site, and went and bought something as a result.\r
\n\r
\nAs far as Exitfuel goes, I *AM* seeing a lot of problem ads from them lately, and while they do end up removing them, they do so slower than I\'d like. Over the next few months, I will be looking into wether or not running their ads is worth the trouble. \r
\n\r
\nI will reiterate that if you are kept logged in to the site, you should be seeing *significantly* less popups - I don\'t want to annoy the people that help make the site a good place to be. \r
\n',1,'levik','2003-11-24 12:30:32');
INSERT INTO forumpost VALUES (2374,318,5,'Do we need a chat?','So I built a chat engine for avatarity (the site you go to to get avatars for here).\r
\n\r
\nIt seems to work OK, with no need for Flash or Java (all you need is a relatively modern browser)\r
\n\r
\nI am considering adding such a thing to perplexus as well. The way it works right now is you open the window, and just keep it open. It will focus itself when a new user enters the chatroom. You would need to be logged in to use it.\r
\n\r
\nI\'m not sure how much interest there is in a thing like that - people are constantly trying to use chatterbox for an insta-chat, but unlike chatterbox a chatroom doesn\'t show you any messages typed in prior to your arrival. ',1,'levik','2003-11-24 12:46:53');
INSERT INTO forumpost VALUES (2375,318,5,'Re: Do we need a chat?','I think that would be great!\r
\n\r
\nI\'m curious... if no java or flash, is this going to \"auto-refresh\" every 5 seconds or something....? If so, aren\'t you at all worried about network/server load?\r
\n\r
\n- SK',3172,'SilverKnight','2003-11-24 13:27:21');
INSERT INTO forumpost VALUES (2376,318,5,'Re: Do we need a chat?','I agree, it would be a great addition.\r
\n\r
\nWhy no java? Almost all browsers support it nowadays, don\'t they? Or is it more of a programming issue?',3372,'Sam','2003-11-24 14:15:27');
INSERT INTO forumpost VALUES (2377,318,5,'Re: Do we need a chat?','I personally would enjoy a chat engine that is more useful then chatter box. I know if i try to talk to somone online they never see the message in the chatter box. If programming is an issue i could help you there but i would prefer that you do not do this in java since the schools computers do not support it.',4450,'drew','2003-11-24 14:25:59');
INSERT INTO forumpost VALUES (2378,318,5,'Re: Do we need a chat?','I personally would enjoy a chat engine that is more useful then chatter box. I know if i try to talk to somone online they never see the message in the chatter box. If programming is an issue i could help you there but i would prefer that you do not do this in java since the schools computers do not support it.',4450,'drew','2003-11-24 14:26:51');
INSERT INTO forumpost VALUES (2379,318,5,'Re: Do we need a chat?','oops i guess it posted twice???\r
\ncould be the crappy school computers.',4450,'drew','2003-11-24 14:27:37');
INSERT INTO forumpost VALUES (2380,319,3,'Herons formula','Out of curiosity has anyone derived herons formula?',4450,'drew','2003-11-24 14:31:01');
INSERT INTO forumpost VALUES (2381,319,3,'Re: Herons formula','yeah.... Heron did.',3172,'SilverKnight','2003-11-24 14:35:48');
INSERT INTO forumpost VALUES (2382,319,3,'Re: Herons formula','You can find a proof of Heron\'s formula at:\r
\nhttp://mathforum.org/library/drmath/view/54957.html, and\r
\nhttp://planetmath.org/encyclopedia/ProofOfHeronsFormula.html',3172,'SilverKnight','2003-11-24 14:42:09');
INSERT INTO forumpost VALUES (2383,80,7,'Re: Hello, First time here','Hi-2-Every-1,\r
\nSeems like the done thing to introduce oneself.\r
\nFound this place by accident while looking for something to keep and old brain from seizing up.\r
\n',4469,'John','2003-11-24 14:49:14');
INSERT INTO forumpost VALUES (2384,318,5,'Re: Do we need a chat?','It seems like java is the thing to use on web pages, but it looks fine; levik doesn\'t seem to need help.\r
\n\r
\nI think anything we want done we could do on the forums pertaining to perplexus. That way everyone could see the equestions asked and we wouldn\'t have to answer the same questions over and over.',1626,'Gamer','2003-11-24 15:11:20');
INSERT INTO forumpost VALUES (2385,318,5,'Re: Do we need a chat?','Well, at least everybody sees a chatterbox on most pages - you\'d have to actually go into the chat page in order to see the messages.\r
\n\r
\nIt would be better if you want to have a conversation, but not any better for sending a message to somebody.\r
\n\r
\nI personally think Java applets are clunky (I love java on the server side, and work with it on the daily basis as part of my job). Feel free to check out the avatarity chat - it\'s doing a form of refreshes, but I think the overhead should be minimal and not noticable.',1,'levik','2003-11-24 15:14:19');
INSERT INTO forumpost VALUES (2386,80,7,'Re: Hello, First time here','lol accidents or otherwise, welcome John to our humble abode of puzzle mischief and people who want to help you if we can.',3386,'Victor Zapana','2003-11-24 17:00:25');
INSERT INTO forumpost VALUES (2387,319,3,'Re: Herons formula','smary answer sk... Heron did... well i have the paper of deriving it... but im too lazy to scan it or type it up here lol',3386,'Victor Zapana','2003-11-24 17:01:30');
INSERT INTO forumpost VALUES (2388,319,3,'Re: Herons formula','hmm.. i cant spell (to above post) smart*',3386,'Victor Zapana','2003-11-24 17:01:47');
INSERT INTO forumpost VALUES (2389,319,3,'Re: Herons formula','Can someone derive Stewart\'s Theorem for me? i forgot how to... just for those who don\'t know what i mean its the MAN + DAD = BMB + CNC with the cevian and the triangle... sorry for being so nondescriptive.',3386,'Victor Zapana','2003-11-24 17:03:56');
INSERT INTO forumpost VALUES (2390,319,3,'Re: Herons formula','another question for curiosity was heron the guys name or what?',4450,'drew','2003-11-24 20:16:48');
INSERT INTO forumpost VALUES (2391,319,3,'Re: Herons formula','to silver knight those proofs are mean anyone got some that does not use the law of cosines?\r
\n',4450,'drew','2003-11-24 20:20:32');
INSERT INTO forumpost VALUES (2392,319,3,'Re: Herons formula','oh yah i forgot to ask if anyone has created a program that factors equations for a graphing calculator. No i am not in algebra 2........ i wont cheat',4450,'drew','2003-11-24 20:23:15');
INSERT INTO forumpost VALUES (2393,80,7,'Re: Hello, First time here','does this forum allow us to use html???? I hope no one minds if i try to find a way arround an html blocker if there is one.\r
\n<marquee>hey guys<marquee>',4450,'drew','2003-11-24 20:36:54');
INSERT INTO forumpost VALUES (2394,80,7,'Re: Hello, First time here','shoot,\r
\nanyone wanna help me get around this html thing????\r
\nsorry if i dont know the correct wording.\r
\n\"<html><html><body><marquee>hi<marquee>\r
\nif this doesnt work then it seems that this forum is more complex then the ones i am used to .',4450,'drew','2003-11-24 20:38:48');
INSERT INTO forumpost VALUES (2395,319,3,'Re: Herons formula','hold on til tomorrow drew i have the paper in my locker in my school. it has the derivation to the herons formula using no trig rule. so wait. patience is a virture',3386,'Victor Zapana','2003-11-24 21:07:24');
INSERT INTO forumpost VALUES (2396,319,3,'Re: Herons formula','ok thnx i take it my other questions will not be awnsered?',4450,'drew','2003-11-24 21:56:58');
INSERT INTO forumpost VALUES (2397,320,6,'.5!','I was using my TI-83 plus to graph y=x!. To my deep surprise, the calculator said that there is a .5! Wow! Besides that, it also seemed that there was a solution for (-.5)! and every other multiple of 1/2 above these. The calculator gave irrational numbers for all of them. I\'ve been puzzling over this over the last few days. Can someone explain why you can take the factorial of halves, or, in the likeliness that it is much too complex, verify that it isn\'t just a bug in the calculator or my mind playing tricks on me?',3558,'Tristan','2003-11-25 01:41:23');
INSERT INTO forumpost VALUES (2398,320,6,'Re: .5!','Given that the definition of n! is 1x2x3x...xn, then 0.5! is undefined. What answer did your calculator give? If the calculator gave 0.5 as the answer, then it could be working on the basis of 0.5! = (1/2)! = 1!/2! = 1/2 (=0.5) What solutions does it give for other multiples of 1/2? eg does 2.5! = 60 (=5!/2!)\r
\n\r
\nYou could always have a look at the instructions to see if it gives any clue.',1183,'fwaff','2003-11-25 06:28:33');
INSERT INTO forumpost VALUES (2399,320,6,'Re: .5!','I\'ve got a TI-83 as well, and for me I\'m getting:\r
\n(1/2)! = 0.8862269255 (x)\r
\n(3/2)! = 1.329340388 (y)\r
\n(5/2)! = 3.32335097 (z)\r
\nAs a note:\r
\nx/y = 2/3\r
\ny/z = 2/5\r
\nx/z = 4/15\r
\nSo, yeah...\r
\n\r
\nAs for factorials of negatives, I get an error for all negative integer values and negative fractional values EXCEPT:\r
\n(-1/2)! = 1.772453851\r
\nUsing the values calculated above, this value of (-1/2)! is double the value for (1/2)!. \r
\n\r
\nI\'m stumped.',3136,'Popstar Dave','2003-11-25 07:01:23');
INSERT INTO forumpost VALUES (2400,320,6,'Re: .5!','The version of factorials extended to the real domain (and even the complex domain) exists in the Gamma function. For integers, n! = Γ(n+1). A graph of the Gamma function can be found at Mathworld. So the calculator in this instance is giving you Γ(n+1). As (n-1)! = n!/n, (-1/2)!, defined in this manner, is (1/2)!/(1/2), or 2 (1/2)!.',1301,'Charlie','2003-11-25 08:32:16');
INSERT INTO forumpost VALUES (2401,320,6,'Re: .5!','And of course the factorials for negative integers do not exist, as -1! would be 0!/0, or 1/0.',1301,'Charlie','2003-11-25 08:50:09');
INSERT INTO forumpost VALUES (2402,80,7,'Re: Hello, First time here','You can use HTML in the forums, but use is restricted to some of the more basic tags like bold and italics.',1920,'Brian Smith','2003-11-25 09:40:37');
INSERT INTO forumpost VALUES (2403,320,6,'Re: .5!','The exact value of (1/2)! = Gamma(3/2) = (sqrt(pi))/2\r
\n\r
\nThe exact value of (-1/2)! = Gamma(1/2) = (Gamma(3/2))/(1/2) = sqrt(pi)\r
\n',1920,'Brian Smith','2003-11-25 09:49:57');
INSERT INTO forumpost VALUES (2404,282,5,'Re: Advertising','Levik, since you asked...\r
\n\r
\nI can\'t even imagine looking at a pop-up or banner, let alone buying things advertised on them. I close pop-ups with the right click on the task bar - therefore never even seeing the graphics, and banners I just ignore (but at least must show on the active page).',775,'Cory Taylor','2003-11-25 09:56:53');
INSERT INTO forumpost VALUES (2405,282,5,'Re: Advertising','I agree with (and do) what Cory said.',1301,'Charlie','2003-11-25 10:08:29');
INSERT INTO forumpost VALUES (2406,282,5,'Re: Advertising','I don\'t know if it has anything to do with it but when I started closing the pop-ups the way Cory describes was when I stopped encountering that darn one that changes your home page to the porno site.',2839,'FatBoy','2003-11-25 12:57:32');
INSERT INTO forumpost VALUES (2407,321,5,'algorithm problems','In particular, this problem I submitted seems to be disliked. I\'m curious as to why.\r
\n\r
\nI can understand that people who aren\'t familiar with programming languages may not understand it or be able to address the problem, but does that make it bad? Or are there other reasons that people don\'t like it?\r
\n\r
\n- SK',3172,'SilverKnight','2003-11-25 13:09:02');
INSERT INTO forumpost VALUES (2408,321,5,'Re: algorithm problems','For me, it was that the concept was far too advanced for many of the people who usually come on this site. If you can\'t explain it in the problem, it\'s likely to be too hard. (See how DJ explained complex numbers in the problem itself.)\r
\n\r
\nI don\'t know that it\'s a bad problem, just as many problems that are TDed in the queue. It\'s just that it might not get good reviews if people don\'t understand it and the problem doesn\'t explain it.',1626,'Gamer','2003-11-25 14:51:42');
INSERT INTO forumpost VALUES (2409,321,5,'Re: algorithm problems','Gamer,\r
\n\r
\nPerhaps... but with respect to DJ\'s The Powers that Be, he specified how to represent a complex number, but he didn\'t show how to add or multiply two complex numbers, let alone how to exponentiate them.\r
\n\r
\nThat being said, I think DJ wrote it just fine.... It is to complex an issue to describe in his problem. But similarly, what verbage could I have used to simplify this problem, or make it more available to those who aren\'t familiar with pointer-supporting computer languages?\r
\n\r
\n- SK',3172,'SilverKnight','2003-11-25 14:57:52');
INSERT INTO forumpost VALUES (2410,321,5,'Re: algorithm problems','I agree with gamer in that the problem is probably too advanced for people on this site. I have percieved (sk) that you are an old guiser (sorry for spelling) and you probably are better and know more programming languages than anyone on the planet. if you would like to find a problem that people will like go back before you were an expert programmer and create a problem that you would have been able to solve. I also agree that you may not have enough space to explain the problem to dufuses(like me) who cant understand your problem so what i suggest, which you did a pretty good job with on your last problem is that you post a refrence site for people interested in solving the problem with very little know how. At least now i know what an algorithim is and one of those link list thingies. thanx for helping.',4450,'drew','2003-11-25 15:35:21');
INSERT INTO forumpost VALUES (2411,321,5,'Re: algorithm problems','*sigh*... okay... I\'m outta college... (is that an \"old geezer\"?) How old do you think I am?!? :-)',3172,'SilverKnight','2003-11-25 15:43:54');
INSERT INTO forumpost VALUES (2412,321,5,'Re: algorithm problems','Hey - no geezer bashing. I too have been in the workforce for over 4 years. :)',1,'levik','2003-11-25 18:14:00');
INSERT INTO forumpost VALUES (2413,320,6,'Re: .5!','I thought it might be related somehow to advanced calculus! As long as it\'s not a bug, I\'m happy. Thanks!',3558,'Tristan','2003-11-25 18:15:59');
INSERT INTO forumpost VALUES (2414,282,5,'Re: Advertising','Cory - the beauty of pops is that the advertiser pays for each one that was loaded. Even if it was never actually the top window on your screen, the advertiser will pay out the cost of the impression. So they are kind of there for the webmasters whose visitors never buy anything :)\r
\n\r
\nThough of course the ad company\'s thinking is that if they barrage you with ads, sooner or later you\'ll end up buying, and I prefer not to argue with them on that.\r
\n\r
\nI *am* a bit discomforted by the amount of ads you guys say you are seeing - as I said, I try to minimize the advertisement shown to logged in users. Are you really getting hit that much even when logged in? If so, this is something I need to work on.',1,'levik','2003-11-25 18:19:48');
INSERT INTO forumpost VALUES (2415,318,5,'Re: Do we need a chat?','So has anybody (other than Gamer) had the chance to check out the chat feature on avatarity? If so, let me know if something like that would be useful for flooble. Most of the code is already done, so migrating would not be too much trouble, but I don\'t want to bloat the site with yet another means of communication if nobody\'s gonna use it.',1,'levik','2003-11-25 18:21:16');
INSERT INTO forumpost VALUES (2416,80,7,'Re: Hello, First time here','Any forum allowing you to put a BODY tag inside of a post is asking for trouble...',1,'levik','2003-11-25 18:22:40');
INSERT INTO forumpost VALUES (2417,282,5,'Re: Advertising','I only get one pop-up when I come on, while logged in. I don\'t think that\'s much.',3558,'Tristan','2003-11-25 18:27:04');
INSERT INTO forumpost VALUES (2418,320,6,'Re: .5!','I can\'t figure out why they\'d limit the fractional possibilities to multiples of 1/2 though.',1301,'Charlie','2003-11-25 18:38:28');
INSERT INTO forumpost VALUES (2419,320,6,'Re: .5!','You mean in the calculator? I was wondering that too. Maybe the real bug in calculator is that it can\'t calculate the factorial of smaller fractions. lol',3558,'Tristan','2003-11-25 19:12:09');
INSERT INTO forumpost VALUES (2420,282,5,'Re: Advertising','I don\'t really care. Once I get in the habit of clicking, It\'s good. Sometimes I get a laugh from the way they market these. For example\r
\n\r
\nGet your free DVD player! Just click here! (OF COURSE it\'s not that easy)\r
\n\r
\n(after clicking here there or anywhere, it doesn\'t matter) Just type in your name here! And your Address! And your e-mail address! And your first grade teacher\'s maiden name! And your third cousin twice removed\'s favorite gerund!\r
\n',1626,'Gamer','2003-11-25 19:47:47');
INSERT INTO forumpost VALUES (2421,321,5,'Re: algorithm problems','lol\r
\ni think old guys are much smarter then i am\r
\nbesides in china being called old is a matter of respect(i am not chinese)\r
\nwhen somone is called old it means that they are wise and make good decisions. By making good decisions it means you are a good member of the community and that you are happy. You dont wanna be happy?=(\r
\nlol',4450,'drew','2003-11-25 20:18:46');
INSERT INTO forumpost VALUES (2422,318,5,'Re: Do we need a chat?','Levik, personally, I think the value comes from knowing who is on the site... and being able to \"pop up\" a message to that person. Of course, then the person should be able to indicate whether or not he is willing to receive such popups... better yet.... have an explicit grant list, explicit deny list, and an all the rest (on/off)... but now we\'re pretty much talking about reproducing ICQ :-)\r
\n\r
\nIf one has to go to a separate page... I think it will be a novelty, but not used much.\r
\n\r
\n(All that said, I haven\'t yet looked at it on Avatarity.)',3172,'SilverKnight','2003-11-25 20:22:10');
INSERT INTO forumpost VALUES (2423,282,5,'Re: Advertising','for all yall who dont know mozilla is an excellent we browsing tool. (www.mozilla.com or org i cant remember) it closes all popups, i am not sure if it still paysthe website by advertisers but i love it. no matter what it closes all popups. its free too. it has a button on the bottom right corner that if you click the popup will open. So if you need to see some popup then you can click there.',4450,'drew','2003-11-25 20:22:47');
INSERT INTO forumpost VALUES (2424,321,5,'Re: algorithm problems','umm... yeah... :-)\r
\n\r
\nso how old do you think I am?!? :-)',3172,'SilverKnight','2003-11-25 20:23:11');
INSERT INTO forumpost VALUES (2425,318,5,'Re: Do we need a chat?','yah i agree with silver knight we should have a way of contacting. maybe we could have a mail letter popup in the top left corner so that if you are trying to read somthing you arent interupted. maybe if the person clicks on it it opens a window that could chat, and you could also have an X to close it.\r
\nmaybe?????',4450,'drew','2003-11-25 20:26:46');
INSERT INTO forumpost VALUES (2426,80,7,'Re: Hello, First time here','lol\r
\nthey were some cheap forums and they used javascript\r
\ni know but levik do you know how i can put marquees in the forums?',4450,'drew','2003-11-25 20:32:15');
INSERT INTO forumpost VALUES (2427,318,5,'Re: Do we need a chat?','If people check their e-mail, we can just do it that way instead. No need to clutter the flooble systems! :)',1626,'Gamer','2003-11-25 20:56:20');
INSERT INTO forumpost VALUES (2428,321,5,'Re: algorithm problems','Everyone pretty much knows that if i = square root (-1), you can just leave that there and multiply. :) So I don\'t think that\'s a problem.\r
\n\r
\nThe idea of the problem was to say if such a thing to another power would make sense.',1626,'Gamer','2003-11-25 20:58:14');
INSERT INTO forumpost VALUES (2429,282,5,'Re: Advertising','One thing I have on my computer is pop-up blocker. Quality control at its very BEST. Any and every pop-up is closed. if pop-up blocker blocks a popup you want to open you just hold control and click again. Trust me.',1072,'Alan','2003-11-25 20:58:43');
INSERT INTO forumpost VALUES (2430,318,5,'Re: Do we need a chat?','One thing to note is that the chat ability should be restricted to either the second or third rank. i don\'t want nubs saying \"yo sup\" to me and trying to find about my personal life.',1072,'Alan','2003-11-25 21:02:24');
INSERT INTO forumpost VALUES (2431,318,5,'Re: Do we need a chat?','Alan, that\'s why I wrote earlier the person should be able to indicate whether or not he is willing to receive such popups... better yet.... have an explicit grant list, explicit deny list, and an all the rest (on/off).......\r
\n\r
\nSeems better than only allowing 2nd/3rd rank from using it.',3172,'SilverKnight','2003-11-25 21:06:20');
INSERT INTO forumpost VALUES (2432,318,5,'Re: Do we need a chat?','Hmmm... I doubt we need something that advanced here. For a while, I was considering an email-like system (similar to PMs on many forums)\r
\n\r
\nBut eventualy it kinda got lost in among the more neccessary features.',1,'levik','2003-11-26 08:04:54');
INSERT INTO forumpost VALUES (2433,282,5,'Re: Advertising','OK, I\'ll start counting my pop-ups and get back to you...',775,'Cory Taylor','2003-11-26 09:36:31');
INSERT INTO forumpost VALUES (2434,287,7,'Re: Hey, yet another newbie!!','I love nev',NULL,'Caroline Creese','2003-11-26 11:52:27');
INSERT INTO forumpost VALUES (2435,315,7,'Re: In a slight pickel','No luck for me.\r
\n\r
\nIts not homework and i understand that this isnt a homework answering service\r
\n\r
\nIts a very odd problem that one of my teachers gave me just to mess with my head...\r
\n\r
\nim really not even sure theres an answer to it.\r
\n\r
\nso if anyone reads this and is curious as to what it is cough*levik*cough you can always just manually promote me....heh heh heh.....just kidding\r
\n\r
\nand sam.....its nice to see that theres another one....one day were gonna take over\r
\n\r
\noh......yeah....one more thing.....i realize that i misspelled pickle and im goning to have to live with that shame.....',4425,'Sam','2003-11-26 13:29:16');
INSERT INTO forumpost VALUES (2436,315,7,'Re: In a slight pickel','Sam, you can submit a problem (like EVERYONE else) right now... and it will have to take its time to go through the queue.\r
\n\r
\nUnless the process changes in the near future... it will almost certainly take more than 3 months to get to the \'front\' position where it may or may not be posted by the aristocracy :-). Given the size of the queue, 4 months is probably more accurate.\r
\n_________________\r
\n\r
\nDon\'t post it here, because it\'s not allowed. Levik will probably delete it soon after you post it. And it would be bad form for you to do so. Even though someone MAY see it, and POST A SOLUTION before Levik has a chance to delete it, do NOT post it here. You might get your answer that way. And people might see the problem, and perhaps like it. And even after someone POSTS A SOLUTION to your problem, Levik will likely just remove it... so don\'t POST YOUR PROBLEM here... ok?!?',3172,'SilverKnight','2003-11-26 14:10:08');
INSERT INTO forumpost VALUES (2437,282,5,'Re: Advertising','I downloaded a dedicated pop-up blocker, but hated it because I couldn;t even try to open pages in a new window without it blocking them. I\'m now using the Google Toolbar, however, which works much better.\r
\n\r
\nAt what point does the block occur? Do the ads know that they\'ve been blocked? Does Levik still get money from them even if they\'ve been blocked? My guess is unfortunately no, but it would be nice were it so.',3372,'Sam','2003-11-26 14:11:34');
INSERT INTO forumpost VALUES (2438,282,5,'Re: Advertising','Last vist to flooble was ~25 minutes, four pop-ups, including the log-on one.',775,'Cory Taylor','2003-11-26 14:13:51');
INSERT INTO forumpost VALUES (2439,318,5,'Re: Do we need a chat?','I believe that i would like to contact silver knight right now but i have no way. It would be good if I would be able to IM him but he is online and i am online and i cant contact him',4450,'drew','2003-11-26 14:15:16');
INSERT INTO forumpost VALUES (2440,318,5,'Re: Do we need a chat?','WHEW!!!! Thank goodness for anonymity! :-)',3172,'SilverKnight','2003-11-26 14:16:14');
INSERT INTO forumpost VALUES (2441,282,5,'Re: Advertising','with mozilla if you try to open in new window it allows you to. and even bettter you can open new window in a tab and it wont open a window but will put a tab that you click on. It is an excellent feature',4450,'drew','2003-11-26 14:18:01');
INSERT INTO forumpost VALUES (2442,321,5,'Re: algorithm problems','I have no clue as to anyones age but i can make fun of people by calling them older simply because i am still in highschool and i am a sophmore and i started school early which means the chances that i am younger then you are really high\r
\ni assume you are 40-50???\r
\njust from your knowledge level so dont get mad if i made you seem older then you already are.',4450,'drew','2003-11-26 14:20:11');
INSERT INTO forumpost VALUES (2443,321,5,'Re: algorithm problems','I\'m happy to say I\'m MUCH younger than that ;-)',3172,'SilverKnight','2003-11-26 14:21:40');
INSERT INTO forumpost VALUES (2444,321,5,'Re: algorithm problems','is much younger like 3 yrs???',4450,'drew','2003-11-26 14:25:41');
INSERT INTO forumpost VALUES (2445,321,5,'Re: algorithm problems','no. :-) much younger would have to be... oh... I dunno.... at least 10...',3172,'SilverKnight','2003-11-26 14:27:33');
INSERT INTO forumpost VALUES (2446,318,5,'Re: Do we need a chat?','lol\r
\nbe mean to the high schooler will you???\r
\nit would be cool if i could talk to somone smarter then me because i have been trying to find a proof for herons formula that is efficient and that i can understand. People have yet to awnser my request. At least if I could bug the hell i mean heck out of Sk i might get an awnser',4450,'drew','2003-11-26 14:27:42');
INSERT INTO forumpost VALUES (2447,321,5,'Re: algorithm problems','lol i thought you were out of college?\r
\nyes i do have a good memory',4450,'drew','2003-11-26 14:28:18');
INSERT INTO forumpost VALUES (2448,322,5,'Chat with SK(herons formula cont.)','you see i need to talk to SK or anyone who found a proof to heros formula that i can understand...(3rd grade level {lol})',4450,'drew','2003-11-26 14:30:26');
INSERT INTO forumpost VALUES (2449,318,5,'Re: Do we need a chat?','More evidence for the need of an explicit \"do not contact me\" list! :-)\r
\n\r
\n(And you\'re probably barking up the wrong tree if you\'re lookin\' for a smart guy.)\r
\n\r
\nAs to Heron\'s formula... one generally should have a good understanding and foundation of trigonometry before tackling that one.... I\'m guessing that you have not yet completed that course. If I\'m correct, pick up a good trigonometric text and do a little self-studying... it\'ll provide those answers.',3172,'SilverKnight','2003-11-26 14:31:06');
INSERT INTO forumpost VALUES (2450,318,5,'Re: Do we need a chat?','I found a proof that uses no trig... but i cant understand it it uses higher mathematics oh good at least i can spell. Anyway i am in Algebra II and we only go over a touch of trig. dont tell me its not out there. its the internet thats what we made it for. besides I think you are flat outt wrong...You are a smart guy.',4450,'drew','2003-11-26 14:33:19');
INSERT INTO forumpost VALUES (2451,322,5,'Re: Chat with SK(herons formula cont.)','As I mentioned in the other thread... you\'ll need a good founding in trigonometry (at least I think that will be your easiest route for an understanding of a proof of Heron\'s formula).',3172,'SilverKnight','2003-11-26 14:34:13');
INSERT INTO forumpost VALUES (2452,322,5,'Re: Chat with SK(herons formula cont.)','Now wouldnt this be easier if we could have this conversation in a chat room??\r
\ncheck the other thread i have an update',4450,'drew','2003-11-26 14:35:01');
INSERT INTO forumpost VALUES (2453,318,5,'Re: Do we need a chat?','I\'m guessing you found a solution involving matrices.... but you\'ll find that matrices actually can be interpreted as encoded vectors, rotations, angles, etc... so they are sortuv another way of doing trigonometry (and much more).\r
\n\r
\nEither way, I think trigonometry and analytic geometry (and vector calculus) will help a lot towards your understanding.',3172,'SilverKnight','2003-11-26 14:36:27');
INSERT INTO forumpost VALUES (2454,321,5,'Re: algorithm problems','I mean at least 10 years YOUNGER than 40-50 years old... (not at least 10 years old)... and yes, I\'m outta college... though I\'m STRONGLY desiring to go back in... life is hard.',3172,'SilverKnight','2003-11-26 14:37:53');
INSERT INTO forumpost VALUES (2455,318,5,'Re: Do we need a chat?','no matricies\r
\ni which i could show you the site i had\r
\nit had a formula which was algebra 2 level but it made a jump that confused me a little bit and i was trying to find an easier one. I believe there is one and i think i will just have to proove it myself to proove to youk',4450,'drew','2003-11-26 14:38:39');
INSERT INTO forumpost VALUES (2456,318,5,'Re: Do we need a chat?','you could, uh, like, uh, provide a link...er.. or something...',3172,'SilverKnight','2003-11-26 14:39:24');
INSERT INTO forumpost VALUES (2457,321,5,'Re: algorithm problems','yes it is infact my dad went back to college he works for boeing and i think thats where i got my math skills\r
\n(in case you are wondering i am jus over 15 yrs old like 2 weeks and you arent 20 are you?)',4450,'drew','2003-11-26 14:40:34');
INSERT INTO forumpost VALUES (2458,318,5,'Re: Do we need a chat?','i told you i cant oh wait hold on next post will have link.',4450,'drew','2003-11-26 14:41:44');
INSERT INTO forumpost VALUES (2459,318,5,'Re: Do we need a chat?','www.newton.dep.anl.gov/newton/askasci/1993/math/MATH002.HTM',4450,'drew','2003-11-26 14:43:22');
INSERT INTO forumpost VALUES (2460,321,5,'Re: algorithm problems','No, I\'m somewhere between 21 and at least 10 years less than 40.',3172,'SilverKnight','2003-11-26 14:44:39');
INSERT INTO forumpost VALUES (2461,321,5,'Re: algorithm problems','oh\r
\ni see so 30 yrs old???\r
\nwanna cont. this conversation in chatter box???',4450,'drew','2003-11-26 14:45:30');
INSERT INTO forumpost VALUES (2462,318,5,'Re: Do we need a chat?','At first glance, this looks correct, and you\'re right... assuming you take for granted the Pythagorean Theorem, then this solution works without introducing trigonometric functions.\r
\n\r
\nWhat do you take issue with?',3172,'SilverKnight','2003-11-26 14:50:45');
INSERT INTO forumpost VALUES (2463,321,5,'Re: algorithm problems','uh... perhaps... and\r
\nno, sorry.',3172,'SilverKnight','2003-11-26 14:51:52');
INSERT INTO forumpost VALUES (2464,315,7,'Re: In a slight pickel','It takes about 3 to 4 months for a problem to make it through the queue. I submitted a problem on Sept 10, and now (Nov 26) it is hovering around position 26. Just be patient. If you really want a challenge to occupy your time, I recommend tackling one of the problems in the unsolved list.',NULL,'Brian Smith','2003-11-26 15:22:33');
INSERT INTO forumpost VALUES (2465,282,5,'Re: Advertising','Cory - you mean you got hit with 4 popups upon returning after a 25 minute absense? That should never happen. Can you give me the details?\r
\n\r
\nMozilla\'s is the best blocker I saw - I use mozilla myself, which is why I am not as in touch with various pop-related issues. Feel free to use it. I don\'t get paid for the popups it blocks, but it\'s more important that you guys are not annoyed by them, since you are the reason the site is worth coming to in the first place.',1,'levik','2003-11-26 17:07:34');
INSERT INTO forumpost VALUES (2466,319,3,'Re: Herons formula','hmm ok.. sry for doing this so late. yesterday i was slightly ill.. so i dint have the strength to do it yesterday but today is fine.
\nThere is a triangle, with sides a, b, c. The altitude h is made so that a is the base. Altitude h splits a into parts p and q. c is to the left of the altitude, and so it p. b is the right of the altitude, and so is q. Thats the triangle and all the sides needed to prove Herons formula
\nh= c^2 - p^2 = b^2 - q^2 (important equation needed to be used later)
\n- p^2 = b^2 - q^2 - c^2
\nq^2 - p^2 = b^2 - c^2 = (q + p)(q - p)
\nq + p = a (because p and q are the 2 parts that make up side a)
\nb^2 - c^2 = a(q - p)= aq - ap (now leave alone for just a second)
\na^2 = a(p + q) = ap + aq
\na^2 + b^2 - c^2 = 2aq (important equation needed to be used later)
\n(Area of Triangle) K= (1/2)(a)(h)
\nK^2 = (1/4)(a^2)(h^2)
\n16K^2 = (16)(1/4)(a^2)(h^2)
\n = 4(a^2)(h^2)
\n = 4(a^2)(b^2 - q^2) (this is from above equation)
\n = 4(a^2)(b^2) - 4(a^2)(q^2)
\n = (2ab + 2aq) (2ab - 2aq)
\n = (2ab + a^2 + b^2 - c^2) (2ab - a^2 - b^2 + c^2) (from above equation)
\n = (a^2 + 2ab + b^2 - c^2) (c^2 - a^2 + 2ab - b^2)
\n = ((a + b)^2 - c^2) (c^2 - (a - b)^2) (Now factor)
\n16K^2 = (a + b + c)(a + b - c)(c + a - b)(c - a + b)
\nK^2 = [(a + b + c)(a + b - c)(c + a - b)(c - a + b)]/16
\nK^2 = [(a + b + c)/2] [(a + b - c)/2] [(c + a - b)/2] [(c - a + b)/2]
\nLets say s = [(a + b + c)/2] (semi-perimeter)
\nK^2 = (s)(s - c)(s - b)(s - a)
\nK = sqrt[s(s - c)(s - b)(s - a)]
\nThere ya go. enjoy :) ',3386,'Victor Zapana','2003-11-26 17:13:13');
INSERT INTO forumpost VALUES (2467,322,5,'Re: Chat with SK(herons formula cont.)','heh if u want the proof look in ur old post from another group the other herons formula post',3386,'Victor Zapana','2003-11-26 17:17:45');
INSERT INTO forumpost VALUES (2468,322,5,'Re: Chat with SK(herons formula cont.)','er. when i mean group i mean forum',3386,'Victor Zapana','2003-11-26 17:17:59');
INSERT INTO forumpost VALUES (2469,322,5,'Re: Chat with SK(herons formula cont.)','It would be better if you didn\'t have this chat at all. I don\'t believe much was accomplished here that couldn\'t have been done by some search engines instead. But if you want to ask \"interesting\" questions that is your choice, and I suppose we need chat rooms to accommodate people.\r
\n\r
\nThe point is you won\'t understand it until you understand its basics. I think if you looked around on the web you could get as much help here. However, if you want to keep asking such questions, it would be easier to get a chat box to cut down on such questions.',1626,'Gamer','2003-11-26 20:46:53');
INSERT INTO forumpost VALUES (2470,318,5,'Re: Do we need a chat?','I do believe that\'s what e-mail is for, as I have said before. That\'s a way to contact people! That\'s where you could have continued this ranting on! I think it\'s fine to keep 2 e-mails, so you could have 1 for people on the web and 1 for other people.',1626,'Gamer','2003-11-26 20:50:29');
INSERT INTO forumpost VALUES (2471,318,5,'Re: Do we need a chat?','well.... actually... don\'t you think this would be a good one for the reference forum (rather than the commons forum? Either way, I do.',3172,'SilverKnight','2003-11-26 23:03:25');
INSERT INTO forumpost VALUES (2472,318,5,'Re: Do we need a chat?','I find e-mail relatively slow. Many people don\'t check their e-mail very often. Also, on my e-mail at least, I\'d have to log off and on to receive new messages. Many of us wouldn\'t like to put the effort into making another e-mail account. I don\'t get enough e-mail to come close to filling my first e-mail account. While e-mail might be fine for you, it\'s not necessarily the best way for everyone. And that doesn\'t mean they wouldn\'t like to chat, it just means they wouldn\'t want to use e-mail to chat.',3558,'Tristan','2003-11-27 01:05:27');
INSERT INTO forumpost VALUES (2473,282,5,'Re: Advertising','I\'ve recently downloaded the new Google toolbar 2.0 which has a built in pop up blocker. I\'ve never used blocker software to compare it to, but it works fine for me. It also has a google search bar, and an autofill feature for web forms.\r
\n\r
\nLevik, what did you think about the \"donation\" idea I posted earlier? Also, what do the rest of you think? Would you be willing to donate $5 or $10 to help cover the cost of this site (and perhaps to help reduce the pop-ups)?',1112,'Greg','2003-11-27 01:28:32');
INSERT INTO forumpost VALUES (2474,282,5,'Re: Advertising','If a contribution as Greg suggests (and as others have suggested before) will stop the porn pop-ups then I\'m all for it. I\'ve no problem with the other pop-ups and occasionally \'play\' with them as Gamer described above, but the porn pop-up makes this a site I\'m very wary of viewing on my work PC (since porn-surfing is a sackable offence) and although I\'ve printed off a couple of the simpler problems for my sons\' amusement/education I\'ve not let them into the site themselves due to the potential \'embarassment factor\' (and also their mum would kill me!!)\r
\n\r
\nIf flooble becomes a subscription site then one thing that needs careful thought is how much access is free, it needs to be enough to encourage people to join, but not so much that it gives the joining fee no added value.\r
\n\r
\nOne alternative would be to charge people a dollar to submit problems, in that way Levik can pay for the site and the queue will drop to below a decade!',1183,'fwaff','2003-11-27 02:48:22');
INSERT INTO forumpost VALUES (2475,282,5,'Re: Advertising','Of course one of the best factors of this site would be its freeness. I think I would just do a \"flooble deluxe\" plan, where the only perk you get from subscribing is to get rid of ads for while you are subscribed.',1626,'Gamer','2003-11-27 10:55:13');
INSERT INTO forumpost VALUES (2476,282,5,'Re: Advertising','I agree that it is important that, on some level at least, this site remains free. I\'d think both the donating idea or the Subscriber = No Ads idea are good ones.',3372,'Sam','2003-11-27 11:20:12');
INSERT INTO forumpost VALUES (2477,319,3,'Re: Herons formula','er my bad the first equation is h^2 = blah blah blah, not h = blah blah blah, now the proof makes sense',3386,'Victor Zapana','2003-11-27 11:20:41');
INSERT INTO forumpost VALUES (2478,319,3,'Re: Herons formula','could you make it any longer?\r
\n',4450,'drew','2003-11-27 11:24:05');
INSERT INTO forumpost VALUES (2479,282,5,'Re: Advertising','Yes i am poor and i have no money i dont have the money to subscribe i would apretiate it if the site could remain free. I am not sure what other people will do but if the site begins charging i would leave\r
\n',4450,'drew','2003-11-27 11:30:47');
INSERT INTO forumpost VALUES (2480,318,5,'Re: Do we need a chat?','I agree with Tristan. I would feel uncomfortable giving my email to people on the web (especially all of the porn emails I would get from SK) I would also not like to make a new email because it would be to much of a hassle. SK i have finally found a proof that i can understand so i am good. ',4450,'drew','2003-11-27 11:34:51');
INSERT INTO forumpost VALUES (2481,322,5,'Re: Chat with SK(herons formula cont.)','Thats why i hate you gamer. You sit there on your chair at home like a super genious unconnected to the outside world. I am just a highschooler and i have tried the internet thing. I have found many proofs but none that were at all easy in any way. I wanted to derive it myself but it was tooo diifficult. This is wwhy in the other forum i have argued for a new chat room.',4450,'drew','2003-11-27 11:37:42');
INSERT INTO forumpost VALUES (2482,321,5,'Re: algorithm problems','=P',4450,'drew','2003-11-27 11:38:32');
INSERT INTO forumpost VALUES (2483,301,3,'Re: WOOHOO!!!','Woohoo² !!!\r
\n\r
\nI\'ve had my 3rd (and 4th) problem posted.... I\'m an Apprentice!',3172,'SilverKnight','2003-11-27 12:36:42');
INSERT INTO forumpost VALUES (2484,323,5,'Happy Thanksgiving fellow flooblers !!!','Gotta run and cook my turkey !\r
\n\r
\nEnjoy your turkey-day!',3172,'SilverKnight','2003-11-27 12:37:48');
INSERT INTO forumpost VALUES (2485,282,5,'Re: Advertising','So it might be best to have the option of paying something and get no ads but still leave the choice of getting the ads but not paying.',1301,'Charlie','2003-11-27 13:47:28');
INSERT INTO forumpost VALUES (2486,301,3,'Re: WOOHOO!!!','I really don\'t think you need to say either of those things; we can see that your problems have been posted; especially to the people who posted them.',1626,'Gamer','2003-11-27 20:46:37');
INSERT INTO forumpost VALUES (2487,315,7,'Re: In a slight pickel','Sigh... Seems to me, SK, that you were confusing the other Sam for someone that could recognize a hint when dropped on him from a great height...\r
\nWe need to get a better class of Sams around here.\r
\n;-)\r
\n(no worries Sam, only joking)',3372,'Sam','2003-11-27 20:49:30');
INSERT INTO forumpost VALUES (2488,319,3,'Re: Herons formula','lol... u wanted it without trig so here. it cant be shortened me thinks',3386,'Victor Zapana','2003-11-27 23:25:06');
INSERT INTO forumpost VALUES (2489,315,7,'Re: In a slight pickel','To Sam (the original): lol!',3172,'SilverKnight','2003-11-28 00:26:03');
INSERT INTO forumpost VALUES (2490,301,3,'Re: WOOHOO!!!','Wow! Imagine the tongue-lashing I\'d get from Gamer had I gone with my initial impulse and started a NEW thread to announce that I\'m a newly made Apprentice... jeez....',3172,'SilverKnight','2003-11-28 00:37:16');
INSERT INTO forumpost VALUES (2491,324,7,'hi everyone','hi',4530,'Benjamin','2003-11-28 01:04:29');
INSERT INTO forumpost VALUES (2492,19,4,'Re:','I know when there is a twist in the logic problem it seems fine, like we thought of on the Word Meld problems. Even though they are similar, each has its own distinct twist. :)',1626,'Gamer','2003-11-28 19:26:01');
INSERT INTO forumpost VALUES (2493,301,3,'Re: WOOHOO!!!','Congratulations SK, what is your secret?\r
\n\r
\nYeah Gamer, why ya gotta rain on his parade?',3351,'Eric','2003-11-29 04:02:31');
INSERT INTO forumpost VALUES (2494,301,3,'Ethics','I haven\'t seen this referenced directly, but I was wondering if different posters felt obliged to cite where they got their problems from, if they simply varied them or just wrote them from scratch. Do some people care if the poster actually makes a problem up?',3351,'Eric','2003-11-29 04:06:34');
INSERT INTO forumpost VALUES (2495,301,3,'Re: WOOHOO!!!','Well, besides my rapier-like wit, my incredible good looks, my mind-boggling intellect, and my unbelievable humility...\r
\n\r
\n...as the FAQ and levels pages will tell you, it\'s mostly just a matter of submitting enough approved problems for the site.',3172,'SilverKnight','2003-11-29 04:14:06');
INSERT INTO forumpost VALUES (2496,325,4,'Screen difference','For some reason the site looks without any divider-lines at all. Is there a reason for this, or is the computer just acting up?',1626,'Gamer','2003-11-29 06:58:06');
INSERT INTO forumpost VALUES (2497,325,4,'Re: Screen difference','I get that some times when there is a lot of netlag and my browser gives up before downloading all of the page. I usually also lose the ads column, and occassionally the chatterbox.',153,'TomM','2003-11-29 10:24:00');
INSERT INTO forumpost VALUES (2498,301,3,'Re: Ethics',' I haven\'t seen this referenced directly, but I was wondering...<\\i><\\b>\r
\n\r
\nThere is a whole thread devoted to this very question, and I was going to link to it, but when I found it, it turned out to be in the Library (with the lead pipe), which means that it is only visible to higher-ranking members. Sorry.\r
\n\r
\nThe consensus we arrived at is that we would prefer that you submit original puzzles. If you submit recycled puzzles, we would prefer \"classics\" to new ones. Give credit whenever you can, and never steal copyrighted material. \r
\n\r
\n',153,'TomM','2003-11-29 10:44:35');
INSERT INTO forumpost VALUES (2503,301,3,'Re: WOOHOO!!!','P.S. If you wish, re-post your comment, and I will delete the original one - I *DO* have a deletion tool *GRIN*',1,'levik','2003-11-29 19:38:24');
INSERT INTO forumpost VALUES (2500,301,3,'Re: WOOHOO!!!','shhh... don\'t tell Gamer... but there is another status change!',3172,'SilverKnight','2003-11-29 14:54:58');
INSERT INTO forumpost VALUES (2501,325,4,'Re: Screen difference','TomM, what you are seeing at those times is caused by chatterbox lag. The chatterbox server is overloaded, and takes a very long time to respond. Your browser waits on it to resume drawing the page, and the ad column, which appears after chatterbox in the code is not drawn until the chatterbox is.\r
\n\r
\nI have moved the chatterbox to a new server last week, which will hopefully eliminate the problems we have been having with the lag.\r
\n\r
\nNot at all sure how to account for what Gamer is seeing though.',1,'levik','2003-11-29 19:33:48');
INSERT INTO forumpost VALUES (2502,301,3,'Re: WOOHOO!!!','Tom - Sorry, but the backslashes will have to stay - at least until I make a post-editing tool. \r
\n\r
\nChanging backslashes to forward slashes in pure SQL is not fun :) Besides, your post is perfectly readable.',1,'levik','2003-11-29 19:37:22');
INSERT INTO forumpost VALUES (2504,325,4,'Re: Screen difference','I don\'t know. The Dark Grey bars (Bonus... latest... search) were all omitted in what I saw. I don\'t understand why, but it\'s fine now.',1626,'Gamer','2003-11-30 11:19:05');
INSERT INTO forumpost VALUES (2505,301,3,'Re: WOOHOO!!!','so u could delete this post if u wanted to?',3386,'Victor Zapana','2003-11-30 11:58:16');
INSERT INTO forumpost VALUES (2506,301,3,'Re: WOOHOO!!!','I don\'t care, we have enough problems in the queue already! :) You should see the amount of unapproved solutions out there!\r
\n\r
\nAs for the submitting old puzzles, I think Penny gave you enough of a thrashing there! :) I think old puzzles (like the rope and the lovelorn snail) are good because they stood the test of time.\r
\n\r
\nAm I the only one hearing levik cackling with power? :D',1626,'Gamer','2003-11-30 16:46:28');
INSERT INTO forumpost VALUES (2507,326,4,'About Penny','I would bet that I am one of the few who have had too much contact, so I don\'t think much should be done based on my opinion. But things are really getting out of hand with the insults. It\'s more than just an argument now right?',1626,'Gamer','2003-11-30 18:41:47');
INSERT INTO forumpost VALUES (2508,301,3,'Re: WOOHOO!!!','I hear him to, but I stand to defy it (please dont hurt me levik lol).',3386,'Victor Zapana','2003-11-30 19:01:33');
INSERT INTO forumpost VALUES (2509,326,4,'Re: About Penny','I just looked into it and yes saw that penny is a problem and will continue to be. She goes on and on in an argument and then when when she gets beaten it just goes back to her superstrong boyfriend. Anyways I say a threaten to ban her is in good order. Oh yeah heres some clever things we can do to shut her up.\r
\n1. When she posts a problem in her comment just tell her to submit her problems as opposed to post them in the comments. That will not only shut her up but be extremely amusing :).\r
\n2. Whenever she says sylvester can wipe you in the real world just be like \"To bad this isn\'t the real world\"\r
\n3. Any comments about intelligence can easily be countered by simply saying she has no social intelligence and using the evidence her position on this site is in danger.',1072,'Alan','2003-11-30 21:22:45');
INSERT INTO forumpost VALUES (2510,326,4,'Re: About Penny','Once she stops insulting people she will be fine. Of course, that\'s about 2/3 of her character, but it is true! :)\r
\n\r
\nBe careful about insulting her. I realized that isn\'t really worth it, she will just say personal attacks are immature, and that will just lead to more pyscopath behavior! I would go through the calm route of elders like TomM and Charlie; anything they do is good to mirror and learn from our elders! :)',1626,'Gamer','2003-11-30 21:52:37');
INSERT INTO forumpost VALUES (2511,326,4,'Re: About Penny','Penny appeared soon after Dan disappeared (was banned?)... Dan was offended because he made a fool of himself. I would bet they are one and the same (the insults and phrasing are extremely similar too).\r
\n________________________________\r
\n\r
\nThat being said, TomM, if this comment was an attempt to help smooth things over, then I would just as soon do without your help.\r
\n\r
\nYour comment equates any disagreements I\'ve had with others and my previous behavior with what Penny is doing, and I am offended.\r
\n\r
\nWhile, I don\'t doubt that I \"upset some of the old-timers so much that levik was asked to ban\" me (and perhaps Gamer did the same, I don\'t know), I did not insult for the sake of insulting... nor, did I ever answer problems without providing a solution (at least not intentionally, or without making it obviously humorous/sarcastic)... nor, did I submit problems in comments to other problems.\r
\n\r
\nYour comment, further, provides only more ammunition for Penny\'s ridiculousness.',3172,'SilverKnight','2003-11-30 23:19:13');
INSERT INTO forumpost VALUES (2512,301,3,'Re: WOOHOO!!!','PAH! I laugh in the face of Levik\'s almighty power. His deletion tool cannot harm me, my posts are like a shield of steel.',1183,'fwaff','2003-12-01 03:20:26');
INSERT INTO forumpost VALUES (2513,326,4,'Re: About Penny','Calm down chaps, this is exacly the kind of response Penny is hoping for. It sounds like you\'re genuinely offended by the \'insults\' she\'s throwing around?!? Instead of steaming in with a counter-insult take a step back and look at what\'s being said. If she was using \'foul-language\' to abuse you and your family then I\'d be in full agreement with you about getting her banned. But what she\'s saying is little more than play-ground insults along the lines of \'if brains were chocolate you couldn\'t fill a smartie\' and hardly something to throw the toys out of the pram about.\r
\n\r
\nWhen it comes to it she\'s not causing much harm to the site, just a small fly in the ointment. It\'s not as if she\'s another Tim Axoy that posted problems and solutions all over the place. BTW am I the only one that doesn\'t believe that \'Tim\' is only 9 years old?',1183,'fwaff','2003-12-01 04:57:13');
INSERT INTO forumpost VALUES (2514,326,4,'Re: About Penny','fwaff... I assume you\'re speaking to others, since I haven\'t (yet) called for anything to be done about anyone.\r
\n\r
\nI won\'t speak for anyone else, but *I* am not in the slightest offended by Penny\'s comments. I\'m more amused by them and find, as Alan hinted, that she says more about herself with these comments than anyone else. But I do think Penny\'s (or Dan\'s) comments are very disruptive to the flow of the site. They are generally negative, and she repeatedly performs ad hominem attacks.\r
\n\r
\nWhat\'s more, they clearly discourage newbies from posting or staying at this site.\r
\n\r
\nI don\'t understand why you focus on \'foul-language\' as a significant criterion, as the (rather sad) intent of her messages comes through... she seeks to diminish/insult others.\r
\n\r
\nI\'m sure we all have taken a step back and looked at what\'s being said. And the vast majority of the Penny\'s intent is insulting and condescending. Again, I\'d have to respect Penny\'s opinion or intellect to be at all offended by her comments, and ... well... I\'ve seen no reason to respect either.\r
\n\r
\n(Penny\'s posting of problems in comments is almost incidental, but clearly violates the community\'s rules.)',3172,'SilverKnight','2003-12-01 05:15:36');
INSERT INTO forumpost VALUES (2515,326,4,'Re: About Penny','SK: I was \'speaking\' more to Gamer and Alan since the tone of their comments implies to me that they are genuinely offended by Penny.\r
\n\r
\nI do agree that her comments cause some disruption, however I don\'t believe that they are that bad compared to some we\'ve had previously. I believe that there is the possibility (although I do concede that this is not necessarily a likelihood) that her intent is misconstrued and that perhaps all she\'s guilty of is slightly overstepping the line with regard to playful banter. What may be needed is a quiet word to truly understand her intent rather than firing back insults and compounding the problem. From her comments there is clearly some degree of intelligence and reasoning there (which cannot be said of Tim), so there is presumably a chance of her developing into a constructive floobler.\r
\n\r
\nIt\'s not that long since that a relatively new floober posted the following comment:\r
\n\r
\n\"How about a category title, \r
\n\"Problems which require absolutely no critical thought at all\"? \r
\nThis would contain problems such as Old MacDonald Had a Sequence, Words in Common 5, The Famous Horse, and Metaphysics... \"\r
\n\r
\nwhich he then followed up with...\r
\n\r
\n\"Y\'know... you Journeymen (and Levik) are some of the most PC muther#$@#~@# I\'ve ever met.\"\r
\n\r
\nwhich prompted some rather angry responses from existing flooblers, including:\r
\n\r
\n\"I don\'t care if you\'re sarcastic or what not. Just stop being an asshole.\"\r
\n\r
\nEventually Levik stepped in to calm the waters. Since the person who kicked off that particular thread now appears to be considered a respected member of floobland, then I assume that either his initial comments were misconstrued or he has now learned where the boundary is between acceptable and unacceptable in this particular reality.\r
\n\r
\nNeed I say more?',1183,'fwaff','2003-12-01 06:20:36');
INSERT INTO forumpost VALUES (2516,326,4,'Re: About Penny','OK, well then we both thought you were not talking to me.\r
\n__________________________\r
\n\r
\nYour point is well taken. But your comparison is, IMHO, limited only to the notion that I offended some flooblers (which is apparently quite easy to do), and is hardly applicable to the situation at hand.\r
\n\r
\nAs I mentioned above w/r/t TomM\'s comment, while I may have offended, I answered (and stuck to) issues at hand. I did not insult for the sake of insulting, and putting the comment back in context, one will see that I was not literally calling anyone a muther#$@#~@#.\r
\n\r
\nWhat\'s more, I think I responded to well thought out responses, quite well.\r
\n\r
\nI did not do what Penny (and Dan) do/did.\r
\n_________________________________\r
\n\r
\nI am surprised that you are at all impressed with Penny and think \"there is clearly some degree of intelligence and reasoning there\". I see consistent regurgitation of knowledge learned by rote with little analysis or synthesis.',3172,'SilverKnight','2003-12-01 06:50:25');
INSERT INTO forumpost VALUES (2517,301,3,'Re: WOOHOO!!!','Where I go you go Hugo Agogo!!!!!!',2839,'FatBoy','2003-12-01 09:35:45');
INSERT INTO forumpost VALUES (2518,326,4,'Re: About Penny','Three points and then I\'ve had my two pen\'orth.....\r
\n---------------------------\r
\nFirstly, the insulter always knows exactly what is meant - ie the degree of venom/offence/sarcasm/wit/humour that is intended - whereas the insultee is always left guessing. In a one-dimensional medium such as text, where there is no benefit of tone of voice or facial expression to help, it\'s all too easy for the insultee to receive a different message from the one intended by the insulter. So whilst there is an onus on the insulter to be careful not to cause offence, there is also an onus on the insultee to show some lenience/tolerance and not immediately assume the worst.\r
\n------------------------------------\r
\nSecondly, have a read through all the comments for the \'Burger Buddies\' problem and wherever you see the word \'Penny\', replace it with Fatboy, or some other floobler with whom you normally associate a tongue-in-cheek response - of course you\'ll have to imagine a few extra typos if you\'re going to imagine Fatboy ;-) What you\'ll find is a pretty good job of finding and explaining the solution(s), some constructive help for Victor (who made an error in his posted solution) and a bit of a pun-fest once Charlie posted that he\'d written one of his famous programs that proves the problem has multiple solutions. The only slightly contentious part is after Charlie points out an error in Penny\'s solution to the revised problem that she makes light of it by breaking the flooble code and posting a problem in the comments. It was this thread that led me to the conclusion that she does have some degree of intelligence and reasoning, but it would take far more than that for her to impress me.\r
\n-----------------------------------\r
\nFinally, as far as first impressions go SK, you aren\'t as far removed from Penny as you may think...\r
\n\r
\nwho said: \"I *am* glad to see in the couple of weeks, fewer of ... the same old \"solve by creating a logic matrix\"--matching up rows and columns problems\"\r
\n\r
\nand who said: \"You just draw a few tables, eliminate possibilites, etc. No real insight or higher intelligence is required.\"\r
\n\r
\n...and by drawing out this likeness I am only trying to re-iterate the point that first impressions can be very wrong.\r
\n-----------------------------------\r
\nI must admit that with each comment she posts the chances of her redemption grow less. The only certainty is that if we respond to every little jibe with a bigger jibe then there is no chance of her ever changing her stripes.\r
\nOver and out.',1183,'fwaff','2003-12-01 09:41:26');
INSERT INTO forumpost VALUES (2519,326,4,'Re: About Penny','Fwaff,\r
\n\r
\nI\'m ALMOST :-) at a loss for what to say to you.\r
\n\r
\nI said those things. And I stand by them. I would say them again. I appreciate you saying that you have a better opinion of me than you once did... but that\'s not the point, nor does it really matter.\r
\n\r
\nI STILL think those things.\r
\n\r
\nYou won\'t (unless you become a journeyman) see the fact that I represent those thoughts in my voting and comments on problems. And I\'d prefer that I\'m frank and up front about it.\r
\n______________________\r
\n\r
\nYou are far too forgiving w/r/t Penny, and it is clear to me exactly what the intent of the THREAD of her posts is trying to achieve.\r
\n\r
\nI would guess (and I hope others will comment) that why people might have been forgiving towards me (since you keep drawing inaccurate parallels between me and Penny), is because I generally backed my statements up with at least some kind of reasonable, well thought out argument, and that the intent of my THREADS was never to go out of my way and insult Gamer, or DJ, or anyone else here.\r
\n\r
\n(I only wish I had had access to the queue discussions in THIS forum earlier this year.... it would have saved me many questions, much time, and much debating.)\r
\n\r
\nBut again, this \'likeness\' that you are drawing... is ill-fitting. Even the quotes you bring out are not naming people... and degrading the puzzle submitters.\r
\n\r
\nBottomline... if everyone (i.e., Levik) wants me to leave... I\'ll go.... relatively quietly, but enough with the inaccurate comparisons.',3172,'SilverKnight','2003-12-01 09:58:24');
INSERT INTO forumpost VALUES (2520,301,3,'Hey, SK','SK,\r
\n\r
\nKudos on being the bigger man and stopping that bloodbath over in the comments on \"flawless.\" Sometimes it\'s harder just to walk away, you deserve credit for doing it.\r
\n
\n\r
\nAnd you can complain to me all you want! (I probably deserve it! :-)... not that I\'ll be able to do anything about it.)',3172,'SilverKnight','2003-12-01 11:35:24');
INSERT INTO forumpost VALUES (2522,326,4,'Re: About Penny','First, fwaff, are you Canadian? Smarties here don\'t have any chocolate in them..\r
\n\r
\nSecond, I don\'t think Penny is Dan, or vice-versa. Dan was blatantly bashing people for no reason; Penny at least appears to be trying to make some sense (if largely unsuccessfully).\r
\n\r
\nI missed the heat of the threads in question, to my slight dismay, but that may have been for the best in the long run. I\'m not going to join in now, anyway.\r
\n\r
\nFrom an objective view, it seems like she\'s just pushing buttons because it\'s working. A lot of my friends have little brothers and sisters, and nearly all of them will invariably attack me on sight and try to wrestle. They don\'t do that to my sister.. because she doesn\'t fight back. Now, an onlooker might see that and think that little kids must hate me or something, but it\'s all good-natured. Further, they only do that because I\'ve given them the idea that playing around is okay. Granted, Penny has a little more venom than my friend\'s six-year old brother, but the concept appears to be the same. Penny was trying to be witty and appear smart, and when you guys come back with insults in suit, she\'s gonna keep going. I think she started out with a little less malintent than everyone seems to be assuming, and it\'s escalated as much as it has because:\r
\na) she doesn\'t know as much as she thinks and refuses to admit it, so she keeps pasting dr math. even his citations. in that case, i would just drop it.\r
\nb) she doesn\'t have a boyfriend, and refuses to admit that too. the more you mention it, the more she\'s going to mention \'him.\' i would just drop that subject too.\r
\nc) she ran out of witty insults. if you keep up, she\'s gonna keep asking google for more, so your best bet is probably to drop that too.\r
\n\r
\nIn short, problems shrink when they lose attention.\r
\n\r
\nTo SK: I\'m fairly certain no one wants you to leave now. There was a thread in this private forum regarding that, which I asked levik to delete not too long ago, because whatever annoyance or problem you may have once posed doesn\'t exist any more. There is similar thread for Tim Axoy, which still exists somewhere I believe, and he\'s no longer here because the problem didn\'t stop. Whatever happened with Gamer, I wasn\'t around to see it, but it\'s of little concern to me because he\'s now a valuable member of this \'society.\' Maybe there was similar talk when I first came here, I can only imagine, but that\'s of little consequence now as well. I\'m not sure of fwaff\'s judgment in bringing that up when he did, especially considering\'s Penny\'s response to such information, but I think you should construe it as an attempt to warn Penny, not any attack against yourself.\r
\n\r
\nThere may be a little merit to what fwaff is saying, and such comments about certain types of puzzles that people seem to enjoy (indeed, have explicitly asked to see more of them) are a little out of place. And I\'ll admit, my initial reaction to seeing the perfect numbers posted as a sequence (in my absence) was similar to Penny\'s, although my comment to that effect would have been considerably less pointed. In any case, it\'s still safe to say that the little red laser sight dots are not on you (has anyone seen The Recruit?) right now.',1575,'DJ','2003-12-01 13:45:56');
INSERT INTO forumpost VALUES (2523,326,4,'Re: About Penny','I would (seriously) LOVE to see the deleted thread you mentioned.... Levik... if you\'re reading this.... I *know* you didn\'t TRULY delete it... not permanently... can I see?\r
\n_______________________\r
\n\r
\nAs for perfect numbers as a sequence... well, clearly it\'s mathematics, but it was an attempt at a little misdirection, and a (poor) case can be made that the problem is in fact looking for a sequence of numbers.\r
\n_______________________\r
\n\r
\nAs for the difference in Dan/Penny... I noticed that difference too... I think (though I\'m not sure) that they\'re one and the same, and he\'s decided to change his tactics a bit, \'cause actually posting content led him to produce too many mistakes (as can be seen in the history, case in point).\r
\n\r
\nThat\'s what happens when one is in a hurry to post, and Penny is in a BIG hurry to post... :-) When she \"gets in to it\"... she also makes lots of mistakes/changes... as is evident by the high percentage (more than half) of her postings that have been modified after the initial submission.\r
\n\r
\nBut... I could be wrong. :-)',3172,'SilverKnight','2003-12-01 14:13:45');
INSERT INTO forumpost VALUES (2524,326,4,'Re: About Penny','Nah, I think people wouldn\'t have said what they said about you if the thread wasn\'t going to be deleted. Look how much we are talking about Penny.\r
\n\r
\nAlthough I think I would like to know if such an argument went out about me, I believe in the same policy; people won\'t express their true opinions if they think others will see them.',1626,'Gamer','2003-12-01 16:57:15');
INSERT INTO forumpost VALUES (2525,326,4,'Re: About Penny',':-) I would.\r
\n\r
\n(I don\'t say anything about anyone that I wouldn\'t say to one\'s face.)',3172,'SilverKnight','2003-12-01 17:13:42');
INSERT INTO forumpost VALUES (2526,326,4,'Re: About Penny','By the way, I have noticed the traffic that\'s gone on with penny. I can\'t say I followed this rule, but someone commenting on this said to just ignore her. Is that fine? I will try to do this (although I haven\'t been doing it!) because I think it\'s effective :)',1626,'Gamer','2003-12-01 17:25:00');
INSERT INTO forumpost VALUES (2527,326,4,'Re: About Penny','I have a feeling that Penny can\'t log on anymore... I would be very surprised if he/she stopped so abruptly out of choice. But, it\'s probably good advice, regardless.',3172,'SilverKnight','2003-12-01 17:35:43');
INSERT INTO forumpost VALUES (2528,301,3,'Re: WOOHOO!!!','Me too... I get caught up in arguing lots of times, especially if I am winning! :)\r
\n\r
\nIt also means SK can help us tame the solution queue and vote on some of these problems!',1626,'Gamer','2003-12-01 18:40:51');
INSERT INTO forumpost VALUES (2529,326,4,'Re: About Penny','Whoa... (again)...\r
\n\r
\nThis keeps happening. Try and have a social life for a day or two, and up springs a cool new thread you wish you\'d gotten on the ground floor of.\r
\n\r
\nFirstly, I have yet taken no action against Penny. At a cursory glance she does bear some strong similarities to Dan. She signed up about 5 days after I banned him, she uses an AOL account (making IP banning pretty much out of the question), and of course she posts a lot of insults for no apparent reason. However the tone does seem to be slightly different, and not as immediately problematic as was the case with Dan. (Whose account I closed, but whom nothing is stopping from creating a new one.)\r
\n\r
\nI did email Penny asking her to stop insulting people, but have yet received no reply.\r
\n\r
\nOh, and SK, I really DID delete the thread. Everything on the site is deleted permanently.',1,'levik','2003-12-01 19:58:05');
INSERT INTO forumpost VALUES (2530,301,3,'Re: WOOHOO!!!','You\'re so lucky, you get to see the library forum. The total number of new comments in all the forums probably makes sense to you now... unless there\'s something else that\'s messing up that number.',3558,'Tristan','2003-12-01 21:04:21');
INSERT INTO forumpost VALUES (2531,301,3,'Re: WOOHOO!!!','hmm big meanies... have to resort to a library forum, away from the public eye.. i was wondering why there were only 5 new posts in the forums but it sed there were 20 new posts on the link to the forums. gr... let us hear your private squabbling.',3386,'Victor Zapana','2003-12-01 22:20:04');
INSERT INTO forumpost VALUES (2532,301,3,'Re: WOOHOO!!!','wahhh i wanna be journeyman :P',3386,'Victor Zapana','2003-12-01 22:22:17');
INSERT INTO forumpost VALUES (2533,326,4,'Re: About Penny','Well Silverknight since the case is up i guess I shall come clean. I had originally been the creator of that topic and inquired the question \"What should we do with him\" This was slightly after the most PC **********ing comment. I was still slightly on the defensive side for flooble after Tim Axoy. I believe I also created the Tim Axoy thread I\'m not to sure. Rest assured Silverknight I do think of you now as a true member of the flooble community. As for penny, i guess after the e-mail we\'ll just all have to see what happens next.\r
\n\r
\nO yes SK how careless of me. In case you were wondering the general gist of that thread was \"He\'s ok but has some respect problems\" Which was primarily based off of \"the comment\" Now I\'m sure everyone\'s opinion has changed.\r
\n\r
\nAnd one final thing while I\'m at it. levik, I simply make the request that threads not be deleted for the simple reason that it will be an archive of knowledge for us and new flooblers to look at and learn from. With the exception of \"Tim Axoy threads\"(pointless threads)',1072,'Alan','2003-12-01 22:45:40');
INSERT INTO forumpost VALUES (2534,326,4,'Re: About Penny','Sorry for the laziness in my last thread. Ya know. With my paragraphs going in no logical order or anything. See this is the kind of stuff holding me back from scholar.',1072,'Alan','2003-12-01 22:47:02');
INSERT INTO forumpost VALUES (2535,301,3,'Re: WOOHOO!!!','hm.. i feel strangely uncomfortable. im the 2nd most problem giver according to site statistics.',3386,'Victor Zapana','2003-12-01 22:50:01');
INSERT INTO forumpost VALUES (2536,327,3,'hitchhike to the dark side of the moon','I was just wondering if there were any Douglas Adams or Pink Floyd fans out there fans out there.',4300,'Minion123','2003-12-02 00:25:43');
INSERT INTO forumpost VALUES (2537,327,3,'Oh and...','I submitted a problem and I\'m not sure how I see where it stands in the line of other problems',4300,'Minion123','2003-12-02 00:28:03');
INSERT INTO forumpost VALUES (2538,326,4,'Re: About Penny','DJ: No I\'m not Canadian - there is a whole other world outside North America ;-)\r
\n\r
\nDJ - Re my judgement: I\'ve only made reference to a likeness in first impressions between Penny and SK in this library forum where Penny can\'t see it (yet) and thus can\'t use it as ammunition.\r
\n\r
\nSK: Calm down mate, nobody\'s asking you to leave - (and even if I was, who\'s going to listen to me?!?). The only parallel I\'m drawing between you and Penny is with regard to the impression you both create in the first half dozen lines of text you each left here (I\'m taking the Burger problem thread as my first impression of her), where IMHO you both appear as slightly cocky know-it-alls with a grasp of sarcasm. Subsequently you\'ve shown (as you point out above) that you have the substance to back up your claims and everyone now knows that any sarcasm is directed towards humour rather than insult. Unfortunately all Penny has shown (or had the opportunity to show) subsequently is the ability to return insults (here I\'m referring to the Flawless Series thread). \r
\n\r
\n',1183,'fwaff','2003-12-02 03:56:09');
INSERT INTO forumpost VALUES (2539,327,3,'Re: hitchhike to the dark side of the mo','yes and yes',3172,'SilverKnight','2003-12-02 07:25:49');
INSERT INTO forumpost VALUES (2540,327,3,'Re: hitchhike to the dark side of the moon','Pink Floyd is okay. I like Animals or Dark Side of the Moon better than the Wall (which I think suffered from overplaying). Douglas Adams is also fun but I prefer the Discworld books by Terry Pratchett. If you have not read them, give \'em a try. Small Gods is my personal favorite.\r
\n\r
\nTo see where your problem stands, log in and then look in that same area where you just typed your name and password. There will be a link there to a page that has info about your problems.',2839,'FatBoy','2003-12-02 08:41:11');
INSERT INTO forumpost VALUES (2541,301,3,'Re: WOOHOO!!!','If you become #1, you win a T-shirt... or a flooble pin... or a baseball cap... or a frisbie or something... actually... I\'m not sure.',3172,'SilverKnight','2003-12-02 08:50:00');
INSERT INTO forumpost VALUES (2542,327,3,'Re: hitchhike to the dark side of the moon','I wnet out and checked and got more info...\r
\nUnder teh \"logout\" button there are three links \r
\nthe first says \"your information\" (but this is not the one you want now)\r
\nbelow that it says \"x problems pending\" yours probably says 1 problem pending.\r
\nthis is the one you want to click. It takes you to a screen with a list of your pending problems. Next to the name of your puzzle are two links one that allows you to edit the puzzle and one that allows yo to edit the solution. Click the puzzle one and then go down to the bottom of the screen. It will tell you what position your puzzle is in the list in a box thats called something like \"notes and votes\"',2839,'FatBoy','2003-12-02 08:54:00');
INSERT INTO forumpost VALUES (2543,326,4,'Re: About Penny','fwaff - I know that, but the only place I\'ve seen chocolate Smarties is in Canada.',1575,'DJ','2003-12-02 13:43:05');
INSERT INTO forumpost VALUES (2544,40,6,'Re: perfect squares','Another dumb question - sorry its not related to the forum title, but since I\'ve got one here already I figured I\'d continue my trend...\r
\n\r
\nI don\'t recall the rigorous definition of a \"prime\" number, just the everyday definition that a prime is a number with only two factors - one and itself. Now this serves as a very adequate definition, but,\r
\n\r
\nwhat about -1? Does the rigorous definition exclude this or is this in fact a prime number?',775,'Cory Taylor','2003-12-02 14:45:27');
INSERT INTO forumpost VALUES (2545,40,6,'Re: perfect squares','the definition requires it (and the factors) be positive...\r
\n\r
\notherwise 3 is evenly divisible by -1, 1, -3, and 3.',3172,'SilverKnight','2003-12-02 14:47:17');
INSERT INTO forumpost VALUES (2546,40,6,'Re: perfect squares','and techincally thats why 1 can\'t be prime either. if it included negative factors, 1 would have 1 and -1, making it prime. However, prime numbers don\'t include negative, that\'s why 1 isn\'t prime.',3386,'Victor Zapana','2003-12-02 20:25:18');
INSERT INTO forumpost VALUES (2547,40,6,'Re: perfect squares','Actually, if we included negative numbers, -1 and 1 would be the only numbers with exactly two integral factors, while other \'normal\' primes would each have four. Every integer is considered a multiple of 1 and a factor of 0.\r
\n\r
\nThe \'rigorous\' definition is simple enough: a prime number is an integer with exactly two positive integral factors.',1575,'DJ','2003-12-02 22:42:15');
INSERT INTO forumpost VALUES (2548,40,6,'Re: perfect squares','i agree.',3386,'Victor Zapana','2003-12-02 22:50:56');
INSERT INTO forumpost VALUES (2549,326,4,'Re: About Penny','Check this out:\r
\nhttp://www.flooble.com/perplexus/show.php?pid=1517&cid=10118\r
\nalong with the following two posts....\r
\n\r
\nI\'ll bet GOOD money, that \"plextor\" is Penny! :-) (Newly created account in the hopes of me arguing the technicalities...) Then, when I didn\'t bite, the following post, making fun of my earlier point.\r
\n\r
\n:-) any takers?',3172,'SilverKnight','2003-12-02 22:56:06');
INSERT INTO forumpost VALUES (2550,327,3,'Re: hitchhike to the dark side of the moon','Douglas Adams is so cool, but it\'s been a while since I\'ve read his books. I ought to read those books again, I hardly remember any of it except the last two books I read, which weren\'t in the Hitchhiker\'s trilogy. I\'ve heard Dark Side of the Moon once or twice, but that was it. I thought Money was the best one because it\'s in seven.',3558,'Tristan','2003-12-02 23:30:05');
INSERT INTO forumpost VALUES (2551,328,6,'Testing','There are often times when I want to use a mathematical symbol from the HTML character codes that isn\'t included in the system font, at least on any machine I have viewed this page on. I\'m just testing the hexadecimal (☺, etc) codes to see which ones show up..\r
\n\r
\nΓ Δ Θ Λ Ν Ξ Π Σ Φ Ψ Ω β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ ς σ τ υ φ χ ψ ω † ‡ • … ‰ ‹ › ‼ ₣ ₤ ₧ ₪ ₫ € ℅ ℓ № ™ Ω ℮ ⅓ ⅔ ⅛ ⅜ ⅝ ⅞ ← ↑ → ↓ ↔ ↕ ↨ ∂ ∆ ∏ ∑ − ∕ ∙ √ ∞ ∟ ∩ ∫ ≈ ≠ ≡ ≤ ≥ ∂ ∂ ∂ ∂ ∂ ⌂ ⌐ ⌠ ⌡ ─ │ ┌ ┐ └ ┘ ├ ┤ ┬ ┴ ┼ ═ ║ ╒ ╓ ╔ ╕ ╖ ╗ ╘ ╙ ╚ ╛ ╜ ╝ ╞ ╟ ╠ ╡ ╢ ╣ ╤ ╥ ╦ ╧ ╨ ╩ ╪ ╫ ╬ ▀ ▄ █ ▌ ▐ ░ ▒ ▓ ■ □ ▪ ▫ ▬ ▲ ► ▼ ◄ ◊ ○ ● ◘ ◙ ◦ ☺ ☻ ☼ ♠ ♣ ♥ ♦ ♪ ♫ ',1575,'DJ','2003-12-02 23:33:06');
INSERT INTO forumpost VALUES (2552,328,6,'Re: Testing','Wow, better than I thought. Now, if I try the other system fixed-width font (by surrounding the same code with <tt> and </tt> tags), I think it will be even better:\r
\n\r
\n\r
\nΓ Δ Θ Λ Ν Ξ Π Σ Φ Ψ Ω β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ ς σ τ υ φ χ ψ ω † ‡ • … ‰ ‹ › ‼ ₣ ₤ ₧ ₪ ₫ € ℅ ℓ № ™ Ω ℮ ⅓ ⅔ ⅛ ⅜ ⅝ ⅞ ← ↑ → ↓ ↔ ↕ ↨ ∂ ∆ ∏ ∑ − ∕ ∙ √ ∞ ∟ ∩ ∫ ≈ ≠ ≡ ≤ ≥ ∂ ∂ ∂ ∂ ∂ ⌂ ⌐ ⌠ ⌡ ─ │ ┌ ┐ └ ┘ ├ ┤ ┬ ┴ ┼ ═ ║ ╒ ╓ ╔ ╕ ╖ ╗ ╘ ╙ ╚ ╛ ╜ ╝ ╞ ╟ ╠ ╡ ╢ ╣ ╤ ╥ ╦ ╧ ╨ ╩ ╪ ╫ ╬ ▀ ▄ █ ▌ ▐ ░ ▒ ▓ ■ □ ▪ ▫ ▬ ▲ ► ▼ ◄ ◊ ○ ● ◘ ◙ ◦ ☺ ☻ ☼ ♠ ♣ ♥ ♦ ♪ ♫ ',1575,'DJ','2003-12-02 23:34:24');
INSERT INTO forumpost VALUES (2553,327,3,'Thanks',' I really like Pink floyd. I like The Wall, but I like the more instrumental songs like Dark Side and my favorite song (depending on my mood) would probably be Shine On You Crazy Diamond from Wish You Were Here. I also like some of their stuff before Barrett left. \r
\n I just started to read Douglass Adams\' novels a year ago and have finished the Hitchhikers series. I\'m now reading the Dirk Gently series. I\'m not sure if I want to get the Salmon of Doubt because I\'ve heard that it isn\'t very good.\r
\n And thanks Fatboy for the help.',4300,'Minion123','2003-12-02 23:41:45');
INSERT INTO forumpost VALUES (2554,328,6,'Re: Testing','Okay, here\'s the whole list, if this works:\r
\n\r
\nΓ Γ
Δ Δ
Θ Θ
Λ Λ
Ν Ν
Ξ Ξ
Π Π
Σ Σ
Φ Φ
Ψ Ψ
Ω Ω
β β
γ γ
δ δ
ε ε
ζ ζ
η η
θ θ
ι ι
κ κ
λ λ
μ μ
ν ν
ξ ξ
ο ο
π π
ρ ρ
ς ς
σ σ
τ τ
υ υ
φ φ
χ χ
ψ ψ
ω ω
† †
‡ ‡
• •
… …
‰ ‰
‹ ‹
› ›
‼ ‼
₣ ₣
₤ ₤
₧ ₧
₪ ₪
₫ ₫
€ €
℅ ℅
ℓ ℓ
№ №
™ ™
Ω Ω
℮ ℮
⅓ ⅓
⅔ ⅔
⅛ ⅛
⅜ ⅜
⅝ ⅝
⅞ ⅞
← ←
↑ ↑
→ →
↓ ↓
↔ ↔
↕ ↕
↨ ↨
∂ ∂
∆ ∆
∏ ∏
∑ ∑
− −
∕ ∕
∙ ∙
√ √
∞ ∞
∟ ∟
∩ ∩
∫ ∫
≈ ≈
≠ ≠
≡ ≡
≤ ≤
≥ ≥
⌂ ⌂
⌐ ⌐
⌠ ⌠
⌡ ⌡
─ ─
│ │
┌ ┌
┐ ┐
└ └
┘ ┘
├ ├
┤ ┤
┬ ┬
┴ ┴
┼ ┼
═ ═
║ ║
╒ ╒
╓ ╓
╔ ╔
╕ ╕
╖ ╖
╗ ╗
╘ ╘
╙ ╙
╚ ╚
╛ ╛
╜ ╜
╝ ╝
╞ ╞
╟ ╟
╠ ╠
╡ ╡
╢ ╢
╣ ╣
╤ ╤
╥ ╥
╦ ╦
╧ ╧
╨ ╨
╩ ╩
╪ ╪
╫ ╫
╬ ╬
▀ ▀
▄ ▄
█ █
▌ ▌
▐ ▐
░ ░
▒ ▒
▓ ▓
■ ■
□ □
▪ ▪
▫ ▫
▬ ▬
▲ ▲
► ►
▼ ▼
◄ ◄
◊ ◊
○ ○
● ●
◘ ◘
◙ ◙
◦ ◦
☺ ☺
☻ ☻
☼ ☼
♠ ♠
♣ ♣
♥ ♥
♦ ♦
♪ ♪
♫ ♫\r
\n',1575,'DJ','2003-12-02 23:42:30');
INSERT INTO forumpost VALUES (2555,326,4,'Re: About Penny','I doubt it, plextor just seems like a typical passer-by with an original solution and no reference at all to the previous posts. Penny\'s just mad that she didn\'t come up with it..',1575,'DJ','2003-12-03 00:16:56');
INSERT INTO forumpost VALUES (2556,326,4,'Re: About Penny','Important question!!\r
\n\r
\nI was mentioning the above post to my wife and we are both completely stumped. (We\'re from Canada). What are in the U.S. smarties if not chocolate?????',775,'Cory Taylor','2003-12-03 10:14:43');
INSERT INTO forumpost VALUES (2557,326,4,'Re: About Penny','The original Smarties, which were first created in England in 1932, are little sugar tarts sold in rolls. When the company moved to the US in 1949, they only registered the trademark for the name in the US. A bigger company, Nestlé, later started marketing M&Ms-like chocolate candies in Canada, capitalizing on the Smarties name, which was not registered as a trademark north of the border. \'Real\' Smarties are now sold in Canada under the name \'Rockets.\'\r
\nOverseas, I don\'t know which candies are called what.',1575,'DJ','2003-12-03 12:05:25');
INSERT INTO forumpost VALUES (2558,326,4,'Re: About Penny','Wow, DJ... I\'m impressed with your erudition on the trivia of confectionary history.\r
\n\r
\nMaybe if I ever decide to make a candy history site I will auto-scholar you :)',1,'levik','2003-12-03 18:16:26');
INSERT INTO forumpost VALUES (2559,326,4,'Re: About Penny','PS. Plextor is not Penny apparently. Penny uses AOL to connect, while Plextor came from another ISP.',1,'levik','2003-12-03 18:17:38');
INSERT INTO forumpost VALUES (2560,326,4,'Re: About Penny','I only knew the basics.. the details came from the FAQ at smarties.com, heh.',1575,'DJ','2003-12-03 18:17:54');
INSERT INTO forumpost VALUES (2561,326,4,'Re: About Penny','I\'m gonna go create an account on my friend\'s AOL account to PROVE that it\'s not me. :-P',3172,'SilverKnight','2003-12-03 18:19:18');
INSERT INTO forumpost VALUES (2562,321,5,'Re: algorithm problems','SK, I haven\'t read the Forums in weeks and just saw your query ...\r
\n\r
\nI didn\'t (couldn\'t) enjoy the problem in question because I am not a programmer, and so it meant as little to me as Sanskrit. This is not an indictment of the problem; I just couldn\'t understand the puzzle or the world it was coming from. If I recall correctly, rather than give it a TD I simply did not vote on it and left it to the EECS-minded to decide its worth.\r
\n\r
\nIn general, I would recommend to everyone that they submit puzzles that don\'t require much beyond a high school education, simply so that the puzzle has the potential to be appreciated by the largest audience. Sure, many of us have educations that far exceed this level and, case in point, your puzzle seemed to draw keen interest from some fellow Flooblers. The problem IMHO with submitting specialized problems such as computer programming is that they turn off those who don\'t have the background to even understand what is being asked. I\'ve thought of five or six really cool puzzles that I haven\'t submitted because the contingent of readers lacking a degree in Mechanical Engineering are going to feel cheated that my puzzle took the place of something else they could participate in. \r
\n\r
\nSabes?',1567,'Bryan','2003-12-03 18:55:03');
INSERT INTO forumpost VALUES (2563,279,5,'Re: Help (Stupid question)','YEah
is good to work with',4628,'steven','2003-12-03 19:32:41');
INSERT INTO forumpost VALUES (2564,324,7,'Re: hi everyone','HEllo how are you',4628,'steven','2003-12-03 19:34:29');
INSERT INTO forumpost VALUES (2565,316,7,'Re: Hey all','Hello and welcome to the site all the way from south africa',4628,'steven','2003-12-03 19:35:38');
INSERT INTO forumpost VALUES (2566,321,5,'Re: algorithm problems','Thanks, Bryan, for the valuable thoughts.\r
\n\r
\nWhat do people think about making a (sub)category for problems that require computer solutions (either because the problem deals with programming languages or computer related-issues, or because the solution domain can\'t be minimized and therefore, a computer must be used to evaluate it \"brute force\")?\r
\n\r
\nPerhaps another (sub)category to deal with (mechanical) engineering issues?',3172,'SilverKnight','2003-12-03 20:15:39');
INSERT INTO forumpost VALUES (2567,316,7,'Re: Hey all','Perhaps Silver Knight Might have a suggestion, he has had thoughts on similar cases in the past.',2839,'FatBoy','2003-12-04 07:55:51');
INSERT INTO forumpost VALUES (2568,321,5,'Re: algorithm problems','Another consideration is that all problems, regardless of category, show up on levik\'s Problem of the Day on other sites that link to it. A problem should be of general interest. I think the problems shouldn\'t be esoteric in the sense of being solely computer-related. That is, so long as the algorithm has a tie-in with either the real world or the world of puzzles, the computer algorithm or verbal algorithm description will have interest. I think the difficulty of the one problem about linked lists is the fact that it was computer-related concerning a solely-computer-related problem, rather than computer-related concerning a real-world or puzzle-world problem. You\'d probably get the same, not so enthusiastic response if you discussed queues and stacks, unless you framed the queuing problem in terms of queues (lines to us Americans) at bank teller windows, etc.',1301,'Charlie','2003-12-04 08:46:29');
INSERT INTO forumpost VALUES (2569,316,7,'Re: Hey all','I think FatBoy is referring to an earlier comment I made. (If not, then I have no idea what he means....)\r
\n\r
\n',3172,'SilverKnight','2003-12-04 09:34:01');
INSERT INTO forumpost VALUES (2570,327,3,'Re: hitchhike to the dark side of the moon','The best Pink Floyd song is definitely \"Coming back to Life\" on the Division Bell..... but their songs are all really good!',3992,'Jane Doe','2003-12-04 10:18:01');
INSERT INTO forumpost VALUES (2571,329,5,'A Homework Forum?????','This issue has been discussed before, I apologize for bringing it up again but I think I might have a useful suggestion.
\r
\nA couple of months ago, I suggested (jokingly) that we should have a “pay for help with your homework” feature on Flooble. I think its time to resurrect the idea (only without the money part.)
\nLately it seems we are getting more and more of visitors to Flooble who are looking for help with a puzzle rather than puzzles to work. We’ve all seen them, they show up in the chatterbox or one of the other forums. The response to them tends to be in one of three forms: 1) ignoring them (which while it might be effective really isn’t very nice); 2) explaining that we do not do homework for people and gently suggesting that they look around Flooble for answers (also effective but has engendered negative feedback); and 3) attempts to help the supplicant clandestinely (or at least quickly before their request can be removed [you know who you are]) This is the nicest option but it involves scorning the social contract and history shows that a rule that is ignored is worse than no rule at all.
\r
\nI understand and agree with the thought behind not helping students cheat but I think that there is some middle ground. Saying “the answer is yellow” would be cheating the classmates of the student who asked as well as the student himself. On the other hand, saying “don’t just think about what color hats the man can see but think about what he learned from the answer of the man next to him” would be a more legit way to give someone a hand.
\r
\nSome of these folks are just lazy but some are legitimately trying. Who knows a small hint from us might be the difference between someone becoming the king of person who joins the math club verses the kind of person who beats up members of the math club.
\nHere is what I suggest. We petition The Great One (his Levikness) to create a forum called “help with homework” (or something like it). Then when we get someone looking for help we can send them over to the forum where they will be allowed to post their questions (with the express caveat that it is not an “official Flooble posting.”)
\nParticipation in the forum would be voluntary. No one would be compelled to go in and help, but I\'ve watched you folks, you love a challenge and I bet lots of flooblers will take the time to lend a hand. I imagine the hints provided would be along the lines of: “There’s a problem like this in Liars and Knights, you should look there”; or “Don’t just think in base 10” or even “you should do a web search on maraschino primes (I know that’s not what they are called, I’m trying [weakly] to be witty).\r
\nThis seems like a win-win situation (or even win-win-win). The students win because they get some help. Flooblers win because there will be fewer of these annoying “I gotta problem where do I get an answer” postings in other places and Flooblers win again because on days when you are bored because you found the problem that got posted in the morning too easy, you can have fun giving cryptic clues to inquiring minds.
\nLet me close by saying this is not a selfless suggestion on my part. I hope to see the explanations that Flooblers post. I find the insights on Flooble both amusing and instructive. I keep a probability tree diagram that DJ posted in a comment back in October on my bulletin board. It explains a lot for a guy like me who never took prob and stats.
\r
\nSo, think about it. If folks think it’s a silly idea, so be it. If Levik thinks it is ill-advised, that’s the way the cookie crumbles. On the other hand, if we like the idea, it could be fun.\r
\n',2839,'FatBoy','2003-12-04 11:16:09');
INSERT INTO forumpost VALUES (2572,329,5,'Re: A Homework Forum?????','Fatboy wrote:\r
\nSome of these folks are just lazy but some are legitimately trying. Who knows a small hint from us might be the difference between someone becoming the king[sic] of person who joins the math club verses the kind of person who beats up members of the math club.\r
\n\r
\nI\'m not sure which kind of person you\'re advocating.... :-)\r
\n___________________________\r
\n\r
\nBut seriously... this is a nice suggestion, but you\'re essentially saying if you post problems here, you won\'t have to wait the months it would otherwise take to get the \"flooble community\" to see and answer it.\r
\n\r
\nThe opportunity for abuse may be too great.',3172,'SilverKnight','2003-12-04 11:37:18');
INSERT INTO forumpost VALUES (2573,329,5,'Re: A Homework Forum?????','\".. becoming the KIND of person...\"\r
\n\r
\nJeez, one typo and they beat you over the head...\r
\nat least I made SOME effort to proof read it.\r
\nThats more than I normally do.\r
\n\r
\nand speaking of opportunity for abuse... watch what you call that kettle, mr. pot.',2839,'FatBoy','2003-12-04 12:18:19');
INSERT INTO forumpost VALUES (2574,329,5,'Re: A Homework Forum?????','no Fatboy... I wasn\'t makin\' fun of the typo... I was wondering which kind of person (those who are IN the math club... or those who beat up those in the math club) you were saying is preferable.\r
\n\r
\nI wasn\'t callin\' any kettles black!',3172,'SilverKnight','2003-12-04 12:26:55');
INSERT INTO forumpost VALUES (2575,329,5,'Re: A Homework Forum?????','I was a band geek.
\nWe used the math club guys as diversions so that WE wouldn\'t get beat up.',2839,'FatBoy','2003-12-04 12:33:29');
INSERT INTO forumpost VALUES (2576,329,5,'Re: A Homework Forum?????','<a href=\\\"http://www.flooble.com/perplexus/forum.php?fid=6&tid=17\\\"\nmaybe this\'ll work',2839,'FatBoy','2003-12-04 12:44:09');
INSERT INTO forumpost VALUES (2580,316,7,'Re: Hey all','WoHOOO!\r
\neveryday in everyway things get better and beter',2839,'FatBoy','2003-12-04 12:44:59');
INSERT INTO forumpost VALUES (2581,329,5,'Re: A Homework Forum?????','I think it\'s a great idea, but I agree with SK\'s point regarding the potential for it to be abused to bypass the proper submission process. If it\'s to go ahead then there\'ll need to be a fair amount of thought and programming goes into it, because it will not work if it\'s just another forum.\r
\n\r
\nIn principle the problems posted to the homework forum will be ones where the poser needs the answer and is also not particularly bothered about it generating discussion/interest/amusement for the flooble community. Whereas the problems in the proper queue are posted by people who want to show off their superior intellect, have their name on the front page and collect promotion points.\r
\n\r
\nIf the homework forum was constructed in a similar way to the current problem submission process then it could separate the bewildered from the egotists. The way I see it possibly working is that problems posted in the homework forum are only visible to the submitter and a select band of homework helpers (cf the voting queue). The helpers would give their cryptic hints in the same way as Journeymen et al put notes on problems in the queue and in the same way the submitter can ask for further clarification.\r
\n\r
\nThis way the problem isn\'t visible to the wider flooble community (so it doesn\'t detract from the official problems and isn\'t a short-cut to front-page fame) and the submitter gets the answer she wanted (without having to wait four months, by which time his assignment is 3 months overdue). There could be the added feature that if the helpers believe that the problem is worthy of becoming an official problem then it can be added to the official queue, at which point it goes through exactly the same process as any other problem - ie wait for hell to freeze over before an argument about grammar.\r
\n\r
\nSo that the burden doesn\'t fall on those responsible for maintaining the standards of the official problems then maybe the official queue is restricted to just the Scholars and it is the Journeymen who look after the homework forum. ',1183,'fwaff','2003-12-04 12:59:22');
INSERT INTO forumpost VALUES (2582,329,5,'Re: A Homework Forum?????','If the official queue were restricted to just the scholars we\'d never get enough votes to get anything posted.',1301,'Charlie','2003-12-04 13:08:52');
INSERT INTO forumpost VALUES (2583,329,5,'Re: A Homework Forum?????','fwaff,\r
\n\r
\nOn behalf of those of us who want to show off their superior intellect, have their name on the front page, and collect promotion points, I thank you for looking out for our interests.\r
\n\r
\n:-)',3172,'SilverKnight','2003-12-04 13:14:21');
INSERT INTO forumpost VALUES (2584,321,5,'Re: algorithm problems','The notion of all problems, regardless of category, showing up on Levik\'s problem of the day is remedied (trivially) by adding/modifying a SQL WHERE clause.',3172,'SilverKnight','2003-12-04 14:44:08');
INSERT INTO forumpost VALUES (2585,330,4,'ICQ','Is anyone else here interested in using ICQ to do instant messaging?\r
\n\r
\nI figure it might be useful to have journeymen/scholars, at least, being able to discuss something sometimes... perhaps to resolve something quickly.',3172,'SilverKnight','2003-12-04 18:58:18');
INSERT INTO forumpost VALUES (2586,330,4,'Re: ICQ','well my number is 217095419 if your interested. Anyways sure its a great idea.',1072,'Alan','2003-12-04 20:03:28');
INSERT INTO forumpost VALUES (2587,330,4,'Re: ICQ','I suppose this is what a chat on the site could be used for. Anyway I am for that. :)',1626,'Gamer','2003-12-04 20:25:21');
INSERT INTO forumpost VALUES (2588,330,4,'Re: ICQ','I don\'t use ICQ anymore, mainly because no one else does, and the program itself uses more system resources than AIM, MSN, and Y!M put together. So, I have those three (my sn is xrestassuredx on all three)',1575,'DJ','2003-12-04 20:47:38');
INSERT INTO forumpost VALUES (2589,329,5,'Re: A Homework Forum?????','Maybe each thread should disappear after a certain amount of time.\r
\n\r
\nBTW, FatBoy, I think that you missed the > sign on your links. Also, some of those slashes appear to be backwards. Furthermore, you need the hyperlink text and a closing tag. I think (but am not sure) that if you\'re linking to another site on perplexus, you only need the url that comes after \"http://flooble.com/perplexus/\" Let me test: this thread',3558,'Tristan','2003-12-04 21:15:44');
INSERT INTO forumpost VALUES (2590,329,5,'Re: A Homework Forum?????','Excellent. It works.',3558,'Tristan','2003-12-04 21:16:34');
INSERT INTO forumpost VALUES (2593,330,4,'Re: ICQ','mine is 94030430, if you add me, please identify who you are, so I don\'t reject it....',3172,'SilverKnight','2003-12-04 22:28:48');
INSERT INTO forumpost VALUES (2594,327,3,'?','Did Syd Barrett sing \"Coming back to Life\"?',4300,'Minion123','2003-12-04 23:10:22');
INSERT INTO forumpost VALUES (2595,329,5,'Re: A Homework Forum?????','Charlie: OK, I have no idea how many scholars there are or how many are needed to manage the queue. Two possibilities then present themselves (assuming that you agree that the homework helpers should be a distinct group from the official problem quality controllers): either promote more scholars (in this way the quality control is down to people appointed to the task, rather than those who merely have the patience to wait long enough to have 6 problems posted); or appoint a few willing apprentices that have been around for long enough to show that they aren\'t total muppets (eg Fatboy).\r
\n\r
\nSK: Harsh but fair? I agreed with you, surely you don\'t expect me to be complimentary as well?!? Pah, some people want the moon on a stick. ;-)\r
\n\r
\nOn a separate note, are there any legal ramifications to this homework helper idea? Particularly with regard to a service that is based on 18+ males (perhaps another gross generalisation, but I think most \'senior\' flooblers are) giving helpful advice to minors.',1183,'fwaff','2003-12-05 03:22:58');
INSERT INTO forumpost VALUES (2596,327,3,'Re: hitchhike to the dark side of the moon','Pink Floyd, Terry Pratchet, Douglas Adams, likes puzzles...\r
\n...and the final two questions before you are deemed a true maths-spod: \r
\n1. Have you ever played Dungeons and Dragons or Warhammer?\r
\n2. Do you know by rote the dead parrot sketch or the Spanish Inquisition sketch?\r
\n\r
\nI\'nt stereotypes brilliant.\r
\n',1183,'fwaff','2003-12-05 03:32:53');
INSERT INTO forumpost VALUES (2597,329,5,'Re: A Homework Forum?????','If we make it so the less senior flooblers can see it I think it would work. The only problem I would have is people just putting their problem there and not checking to see if it was already on the forum. I worry that the people in charge will have to answer the same questions (like the ones that are classic problems) over and over again.',1626,'Gamer','2003-12-05 06:54:40');
INSERT INTO forumpost VALUES (2598,327,3,'Re: hitchhike to the dark side of the moon','I know hte dead parrot sketch but can\'t do the spanish inquisition. On the other hand, I know \"Dead Bishop on the Landing\" down pat, can do most of the Holy Grail and often sing a stirring rendition of \"Always look on the bright side of Life\" from LOB. Can I still play with you all?',2839,'FatBoy','2003-12-05 07:20:43');
INSERT INTO forumpost VALUES (2599,329,5,'Re: A Homework Forum?????','Folks,
I was thinking of something a lot simpler: just a forum like the others with the difference that you would be allowed to post puzzles there for the purpose of getting hints/help with them. I’m afraid that if you limit responses to certain people you create an added burden on them. Charlie is a fairly patient guy but how often is he going to feel like typing “hey, bozo, there is a problem JUST like this one over in the “just math” list, look there.” On the other hand, if everybody shares the burden it seems less burdensome. Heck, I might help somebody just for the chance to show off that I have learned how to put links in my posts. (small things make me so proud.)
\r
\nfwaff, SilverKnight, Charlie, I see your concerns that people might use a homework forum to get around the submission process and I think it is legitimate but I think it will also be self-correcting. To paraphrase fwaff, most of the folks who want to get around the submission process want to do so for one of three reasons: 1)ego, they desire to see there name or puzzle on the sites front page; 2)ego (part 2) they want their peers (other flooblers) to tell them how clever they are (i.e. “wow, little snively, what a neato puzzle that was.); or 3) to earn points toward promotion. None of these three desires will be fed by posting in the homework forum. No points would be awarded and the problem would appear not up front but locked back in the forums. As for the second point, anyone who posts a problem there and then reveals the answer to show how clever they are will only wind up looking like a dope and (knowing flooblers the way I do) probably facing a bit of ‘good natured’ derision. The way I see it, the only one who loses is the one who tries to get around the system.
\r
\nThe one problem that concerns me is what happens if someone actually starts posting good problems in the homework forum that deserve to be on the front. This would be a shame, as Levik has pointed out, because the good problems would then not get the attention that they deserve. All I can say is, if that happens Levik can always dump the forum and we can go back to how we do it now.
\nI had not thought about the fact that we would have a bunch of grown men offering help to school age folk (including young females). It does have a certain “ick-factor” to it, but I don’t think any of us are really the “aqualung” types. Its something to think about.\r
\n\r
\n\r
\nPS a few willing apprentices that ... total muppets (eg Fatboy). \r
\nfwaff you are making the fat one blush\r
\n',2839,'FatBoy','2003-12-05 09:10:29');
INSERT INTO forumpost VALUES (2600,330,4,'Re: ICQ','I tried to sign into ICQ, but it\'s been like four years and I don\'t have an account anymore. My new number is 347452294..',1575,'DJ','2003-12-05 11:43:47');
INSERT INTO forumpost VALUES (2601,330,4,'Re: ICQ','BTW, apologies to anyone trying to reach me during the day (ICQ is blocked at work), so I could only be on in the evening... (American time) :-)',3172,'SilverKnight','2003-12-05 13:57:30');
INSERT INTO forumpost VALUES (2602,308,5,'Re: The new Scavenger Thread','i feel stupid, i can\'t get past Challenge 1 -_-',4659,'Edwin Hong','2003-12-05 18:36:32');
INSERT INTO forumpost VALUES (2603,328,6,'Re: Testing','♫',NULL,'Aspiring Novice','2003-12-05 20:12:59');
INSERT INTO forumpost VALUES (2604,328,6,'Re: Testing','♫\r
\n',NULL,'Aspiring Novice','2003-12-05 20:13:09');
INSERT INTO forumpost VALUES (2605,327,3,'What?','What are you two talking about?',4300,'Minion123','2003-12-05 22:19:20');
INSERT INTO forumpost VALUES (2606,330,4,'Re: ICQ','Don\'t remember my number, but you can find me as \"levik\". (I signed on with them in \'96 or so, so my number is one of the few 6 digit ones still in use.)\r
\n\r
\nHowever, I am logged in at work and nowhere else - so I never log off from my work account. This means that I\'m always online, but only truly \"there\" 10-5:30 Monday through Thursday.\r
\n\r
\nBy the way, anyone who\'s still not using it, should get Trillian - an amazing piece of software that lets you use MSN, Yahoo, ICQ, AIM and IRC all from the same IM interface. Just set up all your accounts in it, and you\'re good to go. I believe it takes less resources than any one of the \"offical\" clients. But that\'s just speculation.',1,'levik','2003-12-06 13:37:40');
INSERT INTO forumpost VALUES (2607,330,4,'Re: ICQ','I don\'t do ICQ (as yet... I really should get Trillian). But if anyone wants to catch me on MSN, just go with:\r
\ndavidcheetham82 AT hotmail DOT com',3136,'Popstar Dave','2003-12-07 02:07:49');
INSERT INTO forumpost VALUES (2608,330,4,'Re: ICQ','I found you, levik, by your last name .. but your number has seven digits, not six (5222704). my old icq number was only 7 digits, as well, but my account has been recycled; i couldn\'t sign in with it when i tried a few days ago. the program has a lot less overhead than it used to, which is nice.\r
\n\r
\nalso, i found trillian a year or two ago, and used it for a while, but there were a few little features that i found annoying, such as the lack of support for sending font colors and styles in messages. there probably is a new version that i will have to look at especially since i am now running four messaging clients (aim, y!m, msmgs, and icq) instead of two as i have been. also, i like the ability to create your own skins for trillian, besides the fact that having all your contacts in one program is a whole lot simpler. although, there are some features of the latest deadaim that i\'ve grown to rely on.. i\'ll have to see if trillian supports them..',1575,'DJ','2003-12-07 02:33:21');
INSERT INTO forumpost VALUES (2609,330,4,'Re: ICQ','actually, lev, if you couldn\'t remember your number.. it\'s on your website',1575,'DJ','2003-12-07 02:35:04');
INSERT INTO forumpost VALUES (2610,327,3,'Brits','Well, yes to all those, except D&D. But I lived in England for a while (and in Italy most of the rest of my life), and Monty Python is pretty much required watching over there, so I guess it doesn\'t have quite the same connotations as it does over here.\r
\n\r
\nInteresting, actually. Douglas Adams, Terry Pratchet, Tolkien, Monty Python, Red Dwarf... what is it about English culture that turns it into \"geek culture\" in the States?',3372,'Sam','2003-12-07 03:20:14');
INSERT INTO forumpost VALUES (2611,327,3,'Re: hitchhike to the dark side of the moon','More important than Dead Parrot or Spanish Inquisition, can anyone do the Latin Grammer scene from Life of Brian? :)',3372,'Sam','2003-12-07 03:21:35');
INSERT INTO forumpost VALUES (2612,331,4,'Hiding one\'s previous comments/solutions','I just observed (sure enough it had to be Penny)... the following occurence:\r
\n\r
\nPenny submitted this post, titled Solution (No computer program used).\r
\n(at 16:22 server time).\r
\n\r
\nEthan submitted this post, titled Solution at 16:38 server time).\r
\n\r
\nThen at 16:39, server time, Penny\'s submission is updated to reflect identically what Ethan had submitted (as can be seen by the notation at the end).\r
\n_____________________________\r
\n\r
\nI didn\'t see Penny\'s original posting, so I can only guess that it did not previously agree with Ethan\'s post, but does this seem odd to any of you? Or even in some way, wrong?\r
\n_____________________________\r
\n\r
\nI think it\'s great that we can edit our posts, but I think at least a full history should be kept. So, that we can see what the previous comment was, and, in this instance, give Ethan \"credit\". (Yes, I know we\'re not here for ego or solving points... I\'m not talking about that.)\r
\n\r
\n\r
\n\r
\nAny thoughts?\r
\n\r
\n',3172,'SilverKnight','2003-12-08 17:16:15');
INSERT INTO forumpost VALUES (2613,331,4,'Re: Hiding one\'s previous comments/solutions','I think that\'s fine. I too noticed what Penny has done, and she has editted many of her posts as well.\r
\n\r
\nEven if a history isn\'t kept on the site, at least keeping it offline (like so levik can read it or something) is a good idea. :)',1626,'Gamer','2003-12-08 18:53:37');
INSERT INTO forumpost VALUES (2614,331,4,'Re: Hiding one\'s previous comments/solutions','In answer to SK\'s questions: it only seems odd in the sense that it wasn\'t Dr Math\'s answer that she copy/pasted; yes, I think it\'s wrong.\r
\n\r
\nEssentially she\'s abusing a functionality that was created to help people eliminate typos and daft errors without having to create another post along the lines of \"In my previous comment I meant hamster, not toothbrush\".\r
\n\r
\nAlthough I agree that keeping the history will work in the case of plagarism, I don\'t think it\'s a workable solution for the other 99% cases where it\'s a genuine error that\'s being corrected. IMHO if people used the preview function to properly proof-read their submissions then the edit function becomes redundant.\r
\n\r
\nOne possibility that may work is that when a comment is edited the time-stamp in the comments-list is revised to show the edit time, rather than leaving it as the original submission time. Basically this is deleting the original comment and adding a new one. For example, in the case SK outlined above, Penny\'s revised comment would show as 16:39 rather than 16:22 so that since Ethan\'s comment was submitted at 16:38 then it would leapfrog Penny\'s comment to become first on the list (or rather Penny\'s comment is demoted to second on the list) - thus giving him the credit for being the first to come up with the correct solution.',1183,'fwaff','2003-12-09 05:28:18');
INSERT INTO forumpost VALUES (2615,332,4,'Good job, everybody','Over the last couple of weeks it seems voting on the queue has improved: more people getting involved, lively discussions with people unafraid to put their TU or TD out there, and yet moving the puzzles through in a timely maner (with a few notable exceptions). I think the recent comments on \"Jars and Pencils\" are a good example of the approval process working well, in spite of and because of differing opinions. Well done! \r
\n\r
\nNow, if we can just get the problems with 15+ comments to reach 3TU or 3TD, we\'ll be cookin\'.',1567,'Bryan','2003-12-09 11:30:19');
INSERT INTO forumpost VALUES (2616,331,4,'Re: Hiding one\'s previous comments/solut','(I should have been more clear about what I mean by a history and how it would be used, and I\'m not a big fan of deletion of any sort, which is the current situation as well.)\r
\n\r
\nfwaff... what do you think of the following?\r
\n\r
\nProposal:\r
\nThe edit function works (no time limit still) as it does today. But if there is at least one comment-update, then a little \"history icon\" shows up... and one can click it, and see all the \"previous incarnations\" of the comment. So, if someone wants to use it (in 95% of the cases) to edit the comment, one still can. (Yes, the typo will be available if someone wants to see it, but who cares?)\r
\n\r
\nAnd the up/down (next previous) functionality doesn\'t give you access to the the \"historical comments\"... only the \"front\" one.\r
\n\r
\nDoes all this make sense? I think with an HTML GUI, this would be very intuitive.',3172,'SilverKnight','2003-12-09 13:03:25');
INSERT INTO forumpost VALUES (2617,331,4,'Re: Hiding one\'s previous comments/solutions','I like Fwaff\'s idea better. If something is editted, it is moved. This would mean that newer posts that are editted (and should be paid attention to) are noticed as well. :)',1626,'Gamer','2003-12-09 15:39:05');
INSERT INTO forumpost VALUES (2618,331,4,'Re: Hiding one\'s previous comments/solut','... what it doesn\'t prevent is \"deletion\" or \"intentional permanent hiding\" of one\'s previous posts... ',3172,'SilverKnight','2003-12-09 15:50:09');
INSERT INTO forumpost VALUES (2619,331,4,'Re: Hiding one\'s previous comments/solutions','\"IMHO if people used the preview function to properly proof-read their submissions then the edit function becomes redundant.\"\r
\n\r
\nThe ability to edit comments was implemented [fairly recently] because the preview comment function is severely crippled and in most cases all but useless. It seems that it is implemented using the GET rather than POST method of reading the form, so comments more than a few lines long won\'t be read at all, and the <pre> tag, often the main reason for needing to preview the comment, isn\'t support by the preview box at all. So, for a post of any considerable length or where one wants to ensure that pre-formatted text is showing up correctly, submitting the problem and then editing it (if necessary) become the only option.\r
\n\r
\nI think that is is safe to say that 99% of edits (actually, probably those from all but one user thus far) are \'valid\' corrections to formatting or typos in a comment. I would also venture that it is safe to say that most of those edits are performed immediately after the comment is submitted.\r
\n\r
\nThat being said, I will revert to my original suggestion when the comment-editing was first implemented - allow comments to be edited for only a short time, say ten or fifteen minutes, after it was first submitted. That would be a good deal easier to implement than the full history, and with a lot less unnecessary overhead (some of my comments go through six or seven iterations before I am satisfied - moreso with the lengthier ones). Also, simply changing the timestamp of the comment could be bothersome if, say, someone replies to comment that is subsequently edited; the reply will show up first! As that could potentially happen quite often, I\'m not sure that is the best solution either.\r
\n\r
\nWhile it is possible that someone may want to correct something in their comment after a substantial amount of time has passed, it seems that that would be the situation in which to post a new comment, either clarifying what was previously said or adding a new idea to the discussion. In that way, the edit functionality would be used only to correct a comment upon its first submission, and most closely mimic its purpose, to be able to preview comments and make sure they are displayed correctly.',1575,'DJ','2003-12-09 16:09:47');
INSERT INTO forumpost VALUES (2620,327,3,'Re: hitchhike to the dark side of the moon','Minion,\r
\nyou may have picked this up from Sam\'s post but just in case you did not, the things I mentioned were preformances by the defunct BRitish comedy troupe \"Monty Python\". They were very funny. If you already nkow about them then ignore the rest as my being a boreing condescending old guy (most folks here already ignore me for just that reason.) You should give python a try if you haven\'t already. You will already recognize John Clease and probably Eric Idle. I think the definitive introduction would have to be Monty Python\'s Holy Grail. others may disagree ',2839,'FatBoy','2003-12-10 07:30:50');
INSERT INTO forumpost VALUES (2621,308,5,'Re: The new Scavenger Thread','A number of small hints were in the first scavenger thread:\r
\nhttp://flooble.com/perplexus/forum.php?fid=5&tid=300\r
\n',3372,'Sam','2003-12-10 13:43:59');
INSERT INTO forumpost VALUES (2931,375,5,'Re: Rich edit control','Hmmm... I was actually thinking of doing away with the view source. At least that way I could be sure that whatever\'s posted has all the tags closed. \r
\n\r
\nAssuming pre and tt functionality is provided via the GUI what would you need to edit source for?',1,'levik','2004-01-20 00:53:37');
INSERT INTO forumpost VALUES (2624,327,3,'Re: hitchhike to the dark side of the moon','I have heard of Python. I just wasn\'t sure how we came to start talking about that.',4300,'Minion123','2003-12-10 21:20:20');
INSERT INTO forumpost VALUES (2625,327,3,'sorry','i didnt mean to have those two posts there\r
\n',4300,'Minion123','2003-12-10 21:21:22');
INSERT INTO forumpost VALUES (2626,331,4,'Re: Hiding one\'s previous comments/solut','I\'m gonna have to agree with Fwaff on this one. It seems to solve all of the problems. The comment will end up time-stamped at the time when you\'re finally happy with it, and it solves the kind of problem that we\'ve had with penny et. al. I also think that this would be a bit easier to implement on Levik\'s behalf. Anyway, that was just my 2c.',3136,'Popstar Dave','2003-12-11 02:24:24');
INSERT INTO forumpost VALUES (2627,331,4,'Re: Hiding one\'s previous comments/solutions','But how does that offer more information to the reader than the current time-stamp as part of the comment itseld, the latest one being uneraseable until the next one is made?',1301,'Charlie','2003-12-11 15:46:18');
INSERT INTO forumpost VALUES (2628,331,4,'Re: Hiding one\'s previous comments/solut','I agree (w/Charlie)... one musn\'t eliminate (or have the ability to eliminate) the previous comment, as it will make threads incoherent -- we\'ll end up with responses to comments that aren\'t there.',3172,'SilverKnight','2003-12-11 15:54:32');
INSERT INTO forumpost VALUES (2629,308,5,'Re: The new Scavenger Thread','Welp, I\'m now on CH8 and completely stuck, but at least it looks like I\'m not alone. Btw, the page title for CH6 is mistitled as CH4.',122,'Happy','2003-12-11 16:40:37');
INSERT INTO forumpost VALUES (2630,331,4,'Re: Hiding one\'s previous comments/solutions','Charlie: I agree that no more information is provided in the sense that the date of the last edit appears in the comment. However, I think the point is one of perception in that in the situation SK originally outlined, because Ethan\'s comment is second in the list then it appears he was the second one to answer the question correctly irrespective of what the edit time is that appears within the body of Penny\'s comment.\r
\n\r
\nDJ: Thanks for the clarification. I didn\'t realise that the edit mode was put in place to overcome problems with the preview mode.\r
\n\r
\nBy the sound of it we\'re all pretty much agreed that the edit function should only really be used to make corrections in wording/typos etc to ones own solutions and shouldn\'t be used to fundamentally change answers or include/delete flames - ie it should only be used as a preview mode. (I think DJ\'s last para sums it up pretty well)\r
\n\r
\nSo assuming that it\'s easier to change the functionality on the edit mode than it is to correct the preview functionality, how about only allowing comments to be edited for a short period (as per DJ\'s suggestion) and making the timestamp on the comment the same as the final edit time (\"The comment will end up time-stamped at the time when you\'re finally happy with it\" to quote popstar). \r
\n\r
\nThis effectively makes the edit mode a preview mode but the only difference is that the unedited version can be seen by everybody. Unless there\'s some way of only making comments live (ie visible to all) once the edit time has elapsed. If this isn\'t possible then at least there\'s only a short time window for editing which should mean that there aren\'t many instances of comments and replies getting out of sequence. \r
\n',1183,'fwaff','2003-12-12 04:44:21');
INSERT INTO forumpost VALUES (2631,327,3,'Re: hitchhike to the dark side of the moon','Minion: my fault I guess. The stereotypical maths-spod (at least on the island) reads Adams and Pratchett, listens to Floyd, plays D&D and is an avid fan of Monty Python. From the comments above it appears to be a fair summary.\r
\n\r
\nFatboy: Even if you weren\'t a boring, condescending old guy then we\'d still ignore you! ;-)\r
\n\r
\nFWIW I think that \'The Meaning of Life\' is the funniest Python film, but there\'s funnier stuff in the Flying Circus episodes.',1183,'fwaff','2003-12-12 04:56:32');
INSERT INTO forumpost VALUES (2632,331,4,'Re: Hiding one\'s previous comments/solut','So what kind of \"short time\" do you mean? 10 minutes? 15? The idea seems OK, even though I generally disagree with crippling functionality for all the users because of misdeeds of one.\r
\n\r
\nI wonder if denying Penny the edit button wouldn\'t solve the current problem better.',1,'levik','2003-12-12 09:08:25');
INSERT INTO forumpost VALUES (2633,331,4,'Re: Hiding one\'s previous comments/solutions','Yes, I was thinking something on the order of ten or fifteen minutes, enough time to sufficiently correct any visual problem with a comment, but not so much that one could go back and change it based on responses by other people. In my opinion, if someone wants to change what they said after a significant amount of time has elapsed, then they should add another comment anyway. As fwaff said, that effectively makes the edit mode a preview mode, which was indeed why it was added in the first place.\r
\n\r
\nAntoher option would be to make the preview button similar to those in problem submission, etc, such that the person could preview the problem, on the page, exactly as it will appear, but still be able to make changes before the final submission. That actually makes the most sense to me; people are able to preview the comments properly, on the page instead of in the popup window, and there will never be a need to edit a comment after it has been posted. It also seems that that kind of a preview would be relatively easy to implement, but that\'s just speculation..\r
\n\r
\nWhat does everyone else think?',1575,'DJ','2003-12-12 11:00:35');
INSERT INTO forumpost VALUES (2634,331,4,'Re: Hiding one\'s previous comments/solutions','I know that on one occasion I posted a comment to the completely wrong puzzle. It was not caught until noticed by SilverKnight. I\'m sure hours went by before I noticed SK\'s catch, at which time I transferred it to the proper puzzle and left a note of explanation in place of the original comment under the wrong puzzle. It would have looked silly still staying there under the wrong puzzle.',1301,'Charlie','2003-12-12 12:17:42');
INSERT INTO forumpost VALUES (2635,331,4,'Re: Hiding one\'s previous comments/solutions','While such things could happen, I\'m sure they occur infrequently enough that one could \'bug levik\' if need be, and the vast majority of the time there will be no need to edit a comment once it has been posted and you are sure that it looks as it should.',1575,'DJ','2003-12-12 12:46:27');
INSERT INTO forumpost VALUES (2636,331,4,'Re: Hiding one\'s previous comments/solut','Just to chime in again:\r
\n\r
\nI agree with the latest few comments... particularly because we are considering it along with the necessary effort on Levik\'s part....\r
\n\r
\nThe major pros:\r
\n
\r
\n
\n
\n
\nAnd achieving all of those would be great.\r
\n_________________________________________________\r
\n\r
\nNow, if Levik\'s effort wasn\'t an issue (and hey... it\'s HIS time not mine, right? :-), then if he were to implement the notion of history, then we still get all these PROS plus the following two PROS:\r
\n
',3172,'SilverKnight','2003-12-12 15:01:10');
INSERT INTO forumpost VALUES (2637,333,4,'didn\'t mean to ignore ya!','Gamer,\r
\n
\n
\n\r
\nRegarding your comment, I completely missed your comment to say these are the only five that fit this rule. When did you submit it?\r
\n\r
\nGenerally, I don\'t like ambiguities in the problem (unless the point of the problem *is* the ambiguity). And I wish I had added something to the effect of these being the only five to fit the rule.\r
\n\r
\nAs for your second paragraph.... Dan/Penny already knows this... He\'s trying to be difficult... why bother? :-)\r
\n\r
\n- SK',3172,'SilverKnight','2003-12-12 15:50:51');
INSERT INTO forumpost VALUES (2638,333,4,'Re: didn\'t mean to ignore ya!','I was thinking I put that in there because you don\'t have enough information with a ? for all 5 comments. I was thinking I suggested saying there are exactly 5 sets of that. I was actually the one that pushed this problem so it is also my fault for not making sure the changes were made. :)\r
\n\r
\nWhy bother? is a good question. I hope others aren\'t mad (at all, not necessarily real mad) that I restated that; it helps me to remember. Also, some of the other things are just ground rules; obvious things like the additive property of equality and reflexive property. Of course Penny isn\'t logical as you have noted numerous times, so I suppose that wasn\'t as useful as it is in other cases.\r
\n\r
\nAbout saying where your perfect-number explanation was, I really didn\'t remember your posts, so I had no idea if Penny was lying or what. I imagine there\'s SOME problem out there with an unrelated title.',1626,'Gamer','2003-12-12 21:21:40');
INSERT INTO forumpost VALUES (2639,334,7,'bored & sleepy','hey people just join this thing what do you recommend i do first?',4786,'winnie','2003-12-13 16:05:06');
INSERT INTO forumpost VALUES (2640,335,7,'How I got here...','How did I find this site? I googled a problem that has been bugging me: besides angry and hungry, what other English word ends in -gry? Anyway, that search led me here and I enjoy the puzzles!',4788,'corey','2003-12-13 16:41:57');
INSERT INTO forumpost VALUES (2641,331,4,'it\'s up to levik','Well as you can tell by the title of my post this decision would rest solely on levik because it woukld take a lot of work on his part implement. What if you could spell/grammar check a post before posting it? Then the edit button used for these purposes will no longer be needed except for the use of pre tags which could easily be fixed if the preview window has the same x column y row setup as the post itself would have.',1072,'Alan','2003-12-13 22:03:38');
INSERT INTO forumpost VALUES (2642,336,4,'help me make a problem?','Okay Now firstly I know that posting problems in the forums is forbidden but is posting problem concepts? I\'ve just come up with a great problem concept but can\'t quite seem to make up good problems that fit into it. Anyways the problem concept is down lower. If you don\'t wanna see it/participate in making the problems for it then don\'t scroll down. If you think i shouldn\'t be posting here then scroll down really quickly towards the bottom where you can post a comment. Also please don\'t thin I\'m lazy for doing this. I just really think that everyone in Flooble could contriute their own and this way we won\'t take up pace in the queue and the other people\'s word breaks (thats what the problems are called) will get posted faster.
Anyways spoilers below.\r
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\nIn Word breaks, you are given a line of letters with a blank in the middle. You\'re job is to eliminate all the letters by inserting a word letter by letter into the blank. Whenever the letter inserted forms a word you can eliminate that word as shown here.
Puzzle: stefo_eveven
\r
\nSolution:nine\r
\n
\r
\nThe n from nine comes in and eliminates the word one.
\r
\nstefoneveven
\r
\n\r
\nLetters and words are eliminated in this way
\r
\nstefiveven\r
\n
\r
\nstenven
\r
\nseven\r
\n
\nDifficulty will slowly get harder.\r
\n\r
\nSo can anyone help me think up some word breaks. I do have some of my own but I\'m not quite clever enough to come up with ones that have two solutions or conceal a message. Also If you do post one then could you please put the respective diffculty beside its name.(Which you think it has) ',1072,'Alan','2003-12-13 22:30:08');
INSERT INTO forumpost VALUES (2643,336,4,'Re: help me make a problem?','I think the problem with these kind of puzzles will be coming up with unique solutions. For example, if you picked \'ode\' istead of \'one\' first in your example, you get \'dine,\' which is another perfectly valid solution. It\'s a neat concept, but a lot of work will need to go into creating puzzles with only one solution.',1575,'DJ','2003-12-13 23:08:02');
INSERT INTO forumpost VALUES (2644,335,7,'Re: How I got here...','The -gry puzzle is a wording riddle gone horribly awry. The original message is supposed to read as follows:\r
\n\r
\n\"Think of words ending in -GRY. Angry and hungry are two of them. There\r
\nare only three words in the English language. What is the third word? The\r
\nword is something that everyone uses every day. If you have listened\r
\ncarefully, I have already told you what it is.\"\r
\n\r
\nNow, given that version of it, ignore the first two sentences. Get it now?',1575,'DJ','2003-12-13 23:12:39');
INSERT INTO forumpost VALUES (2645,334,7,'Re: bored & sleepy','Unless you have a particular type of puzzle that you like, your best be would be to check out the highest rated problems. They\'ll give you a good idea about the kind of thing that we like and you\'re likely to find on perplexus. \r
\nIf you do have a specific type of problem that you like (e.g. logic, math, word problems, etc.) all the problems on this site are divided into these sort of categories that you can get to from the home page. \r
\nEnjoy!',3136,'Popstar Dave','2003-12-14 01:36:08');
INSERT INTO forumpost VALUES (2646,336,4,'Re: help me make a problem?','Or, a solution of \'wine\' will use \'owe\'... \r
\nMaybe the challenge could be to come up with more than one completely independant solutions. \r
\nBy completely independant I mean that (in this exapmple) none of the words: one, five, ten or seven can be used. \r
\nI don\'t know... just a thought for a different spin on it.',3136,'Popstar Dave','2003-12-14 01:47:38');
INSERT INTO forumpost VALUES (2647,326,4,'Re: About Penny','(I did warn in the problem comments, before Proof of Anything was pushed live, that exactly this sad discussion would occur. That\'s my \"I told ya so\".)\r
\n\r
\nWell... I haven\'t commented at all regarding Dan/Penny, in the last three problems, namely Shapely Figures, Nothing But Flowers, and Proof of Anything.\r
\n\r
\nSo, except for the fact that I submitted the first one... I didn\'t feed any of Dan/Penny\'s recent comments.\r
\n\r
\nThe site has become an actively hostile place if one posts anything at all in the problem comments. The discussion in those comments is, too often, not about the problem, but about having to defend oneself and prior comments along with ad hominem attack. It\'s one thing to challenge what someone else said, briefly, concisely, and respectfully (which I think my comments with Brian Wainscott in The Amazing Stamp demonstrate), but how many of these counter examples should we expect to see?\r
\n\r
\nI think this has been allowed to continue too long--there\'s much to be said about \"nipping it in the bud\".',3172,'SilverKnight','2003-12-14 05:44:54');
INSERT INTO forumpost VALUES (2648,326,4,'Re: About Penny','SK, be careful what you say about \"nipping it in the bud\"... if there\'d been too much of that going on a few months ago, you might not be here right now.',3136,'Popstar Dave','2003-12-14 09:37:44');
INSERT INTO forumpost VALUES (2649,335,7,'Re: How I got here...','alot of people dont believe me when i say \"language\" is the answer... ',4799,'gee','2003-12-14 18:13:04');
INSERT INTO forumpost VALUES (2650,326,4,'Re: About Penny','Then you shoulda done that then... Again, I\'m sick of your B.S. comparison between what I did/said and what Dan/Penny does/says....\r
\n\r
\nIf I was ever like this, then Levik should have banned me.',3172,'SilverKnight','2003-12-15 00:27:13');
INSERT INTO forumpost VALUES (2651,326,4,'Re: About Penny','What\'s this? Is Penny turning over a new leaf? She actually admitted that she was wrong. \r
\nHmmm... maybe people can change.',3136,'Popstar Dave','2003-12-16 05:50:19');
INSERT INTO forumpost VALUES (2652,326,4,'Re: About Penny','It\'s not the first time.',3172,'SilverKnight','2003-12-16 07:19:37');
INSERT INTO forumpost VALUES (2653,335,7,'Re: How I got here...','I googled for logic problems online and other puzzles and this site popped up. I think I\'ve visited before but know I\'ve never registered before...',4828,'Jennifer','2003-12-17 00:03:27');
INSERT INTO forumpost VALUES (2654,337,4,'lack of levik','Guys, sorry I haven\'tbeen around at all this past week - I\'m currently down with the flu, and my fever goes up anytime I near a computer.\r
\n\r
\nSo please bear with me - all the petitions, requests and such will be lookd at once I come back.',1,'levik','2003-12-17 08:37:04');
INSERT INTO forumpost VALUES (2655,337,4,'Re: lack of levik','No worries, I don\'t think we\'ve broken too much while you\'ve been having fun with phlegm.\r
\n\r
\nGet well soon :-)',1183,'fwaff','2003-12-17 11:13:12');
INSERT INTO forumpost VALUES (2656,333,4,'Re: didn\'t mean to ignore ya!','Gamer, why bother? :-)\r
\n\r
\nAnd to address your earlier concern, I\'m not mad at all... but Dan/Penny\'s valueless posting seems to serve no purpose other than to draw out your (or similar) responses.',3172,'SilverKnight','2003-12-17 15:11:41');
INSERT INTO forumpost VALUES (2657,336,4,'Re: help me make a problem?','well see thats why i really put this here. I always think I have a great problem and then there is something I never thought of. but another idea of mine is to have themes. like in my example the theme was numbers so every word (Both solution and ones made) must be a number. So anyways will anyone still wanna contriute actual word breaks or ideas still?',1072,'Alan','2003-12-17 15:38:37');
INSERT INTO forumpost VALUES (2658,336,4,'Re: help me make a problem?','You mean like:\r
\n\r
\nAJAMST_AULVEOMSTHUR\r
\n\r
\nTheme: Guys names\r
\n\r
\n\r
\n\r
\n\r
\n\r
\nAnswer: PETER\r
\n\r
\nStages:\r
\nPaul\r
\nstEve\r
\nTom\r
\njamEs\r
\naRthur',3136,'Popstar Dave','2003-12-17 19:03:39');
INSERT INTO forumpost VALUES (2659,335,7,'Re: How I got here...','I searched for riddles and paradoxes. Here I am. I enjoy these puzzles. Thanks so much for having this website.',4844,'Linda Malone','2003-12-17 20:33:41');
INSERT INTO forumpost VALUES (2660,338,5,'God and Flooble','Okay folks,
\r
\nHere comes another of the Fatboy\'s busybody suggestions.
\r
\n\r
\nIt seems there is a brouhaha brewing (but no one is haha-ing) over in the comments to \"proof of anything\". This has happened before (in the puzzle \"can or can not\") and led to the thread \"the existence of God.\"
\r
\n\r
\nThe thing about these two dustups is that they both could easily been avoided. Both of the puzzles could have been posted in a manner that would not have changed them substantially but would have not brought about so many ill will. \"Can or Can not\" could (and I suspect probably originally was referred to \"an omnipotent being\" instead of \"God\" and Proof of anything could have been written with a different broadly accepted statement \"If S is true then the Pope is Polish\".
\r
\n\r
\nI would respectfully suggest that in the future those reviewing problems consider suggesting changes to avoid unneeded, distracting controversy.
\r
\n\r
\nI\'m not suggesting that we ban any topics or that we avoid controvery all together. But in cases where the controversial elements do not particulaly add to the puzzle\'s interest (as I think was the case in these two puzzles) we should consider doing without it.
\r
\n\r
\nI know that this seems needlesly PC of me but I think it would keep discussion in the comments more centered and what flooble is best at: puzzles and puzzling.
\r
\n\r
\nIn the interest of full disclosure, When I was a newer floobler, I argued the otherside of this issue saying: whats wrong with a little free exchange of ideas? or something like that. Charlie set me strait then and while I did not agree at first, I have begun to see that this kind of debate really doesn\'t add to flooble.\r
\n ',2839,'FatBoy','2003-12-18 08:49:04');
INSERT INTO forumpost VALUES (2661,338,5,'Re: God and Flooble','Good suggestion, FatBoy.\r
\n\r
\nDuring the review process, I don\'t think anyone suggested changing the predicate to avoid a reference to God (or his existence). I, certainly, didn\'t think anything was wrong with the problem as it stood. In fact, I still don\'t... but as FatBoy states (and has been reiterated several times), this kind of debate really doesn\'t add to Flooble.\r
\n\r
\nSo, in the interest of avoiding this type of unnecessary debate, I will, and hope we all will, endeavor to point it out ahead of time (in the review process).',3172,'SilverKnight','2003-12-18 13:58:53');
INSERT INTO forumpost VALUES (2662,338,5,'Re: God and Flooble','Well....\r
\n\r
\nSure I\'ll agree that this type of religeous back and forth is not in the \'heart\' of flooble, but I don\'t see it as a bad thing regardless. Lifes greatest opportunities for growth happen when unexpected circumstances arise, or different (and therefore often challenging) views or opinions are brought to bear. Obviously, I know that I\'ll be in the minoroity here, but I thought I\'d express my opinion anyways.\r
\n\r
\nAnd, (poor grammar there) I think the argument being about the existence of God was the best way to go with this puzzle, though any choice would\'ve worked. The reason that I think this topic was best suited was precisely because you can\'t use knowledge or logic to conclude anything about the topic in general. Obviously, the puzzle was not ~about~ theology, but I think it was properly suited to ~include~ theology. Maybe a better choice would\'ve been to relate it to some other \'religeon\', say like proving that Zues did indeed use a demon to kill prometheus...\r
\n\r
\nI find it most interesting to see how both sides of heavily ~opinionated~ people react to these theological disagreements, and would miss it wherever it turned up, flooble or otherwise.\r
\n\r
\n',775,'Cory Taylor','2003-12-18 15:07:06');
INSERT INTO forumpost VALUES (2663,338,5,'Re: God and Flooble','I think we don\'t need to talk about it. If we do, I don\'t know it\'s terrible, but I think it could only stir up madness because neither side will be willing to give up ground.\r
\n\r
\nAlso, flooble is more about logic. There is even a catergory named after it, and religion becomes science once it\'s proven or logical.\r
\n\r
\nLastly, I think religious comments should be avoided if they can. The consequent of that statement could be \"I am a monkey\" or some other statement. In the Prometheus question and the Can or Can not (although this could have been avoided) religion is the base of the question.',1626,'Gamer','2003-12-18 18:29:13');
INSERT INTO forumpost VALUES (2664,336,4,'Re: help me make a problem?','precisely',1072,'Alan','2003-12-18 19:34:26');
INSERT INTO forumpost VALUES (2665,339,7,'it\'s just me and me is good','first things first....call me chic. ofcourse that is not who i am but that really doesn\'t matter. next in line, i am forever looking for something to make me think. something more than which of the 31 flavors. so that is me and what i am all about. so we will see you guys round like a donut.',4778,'chic','2003-12-18 23:24:50');
INSERT INTO forumpost VALUES (2666,338,5,'Re: God and Flooble','A fundamental of religion is faith - ie believing in something without proof.\r
\n\r
\nA fundamental of logic problems is a definitive answer - ie deriving a proven solution.\r
\n\r
\nErgo religion and flooble do not fit together. QED\r
\n\r
\nThat said, I do agree with Corey\'s last point in that I\'ll miss the amusement of watching otherwise rational people trying to construct reasoned arguments that justify their personal beliefs, despite the fact that the \'debate\' is as pointless as arguing about what is the perfect thing to spread on toast. After all everybody knows that it\'s Marmite, so what is there to discuss?',1183,'fwaff','2003-12-19 04:58:22');
INSERT INTO forumpost VALUES (2667,338,5,'Re: God and Flooble','Marmite\'s okay, if you ignore the smell, flavor and texture, but for toast give the fatboy some apple butter or, better yet, leave the toast alone and rustle up a mess o\' biscuits with sausage gravy and/or fried apples.',2839,'FatBoy','2003-12-19 07:30:13');
INSERT INTO forumpost VALUES (2668,65,5,'ignore this','\r
\r
\n
\n
\n
\n
\n',2839,'FatBoy','2003-12-19 09:30:54');
INSERT INTO forumpost VALUES (2669,339,7,'Re: it\'s just me and me is good','Welcome chic (I\'ll assume that is pronounced shiek and not chick),
\r
\n\r
\nWe are all looking for something to make us think so let me offer you this list of the top ten (or so) entertaining things to do on flooble.
\r
\n\r
\nTen most entertaining things to do on Flooble.
\n\r
\r
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n\r
\n
\n\r
\n
let em say in closing mmmmmm, donuts.....ghghghghhghhg',2839,'FatBoy','2003-12-19 09:44:28');
INSERT INTO forumpost VALUES (2670,339,7,'Re: it\'s just me and me is good','Fatboy, you forgot #12, reading your post above! Ok, I guess you couldn\'t have put that in there, cause the post wasn\'t there yet when you were writing it, but that was very funny.',775,'Cory Taylor','2003-12-19 10:12:39');
INSERT INTO forumpost VALUES (2671,339,7,'Re: it\'s just me and me is good','lol (at list)... :-D',3172,'SilverKnight','2003-12-19 10:42:05');
INSERT INTO forumpost VALUES (2672,336,4,'Re: help me make a problem?','I think if the letters removed spelled a question, it would be cool. Then the problem would have an answer.',1626,'Gamer','2003-12-19 14:56:14');
INSERT INTO forumpost VALUES (2673,338,5,'Re: God and Flooble','Why do people use \"QED\" when they never said what they were going to prove in the first place?',1575,'DJ','2003-12-19 15:20:42');
INSERT INTO forumpost VALUES (2674,339,7,'Re: it\'s just me and me is good','lol\r
\nI want to do that last one now.',3558,'Tristan','2003-12-20 12:59:26');
INSERT INTO forumpost VALUES (2675,340,7,'Submitting problems','Well, I\'m not really a new user, but I do have a question.\r
\nI saw a problem in something. I figured out the answer. I changed the numbers around a bit and submitted a different problem with the same concept. Do I have to put a note saying, \"concept received from this organization?\"',2130,'ethan','2003-12-20 21:41:01');
INSERT INTO forumpost VALUES (2676,341,7,'I Found You...','I found you from a site and I clicked on the I want a chatter-box thing. This is the website that I found it on: http://annie666.proboards26.com\r
\n\r
\nWell, I will tell about myself. My name is Andrea and I am 8 years old. I am in 3rd grade right now and my teacher\'s name is Ms. Rossman.\r
\n I have a website for magic. It is a school. It has nothing to do with Harry Potter or Hogwarts. For more information go to: http://witchwizard.proboards25.com\r
\n\r
\nI hope you will join!',4899,'Andrea','2003-12-21 16:38:35');
INSERT INTO forumpost VALUES (2677,287,7,'Re: Hey, yet another newbie!!','Oh well. I\'m new! Can you check out my website? http://witchwizard.proboards25.com',4899,'Andrea','2003-12-21 16:41:41');
INSERT INTO forumpost VALUES (2678,338,5,'Re: God and Flooble','LOL DJ, because it makes us people feel clever and think that we know how to do proper sciency stuff. I was \'proving\' the chubby one\'s God and Flooble Don\'t Mix Theorem, besides I can\'t spell quod erat demonstrandum.',1183,'fwaff','2003-12-22 03:35:21');
INSERT INTO forumpost VALUES (2679,342,7,'??','??????????',4904,'WanD','2003-12-22 03:53:37');
INSERT INTO forumpost VALUES (2680,343,4,'Ya tune out for one weekend and...','I was disappointed that a recent puzzle of mine (starfield simulator) recently got rejected out of hand. I am guessing that it posted over the weekend, since I never saw it through Friday, and on Monday I got the flooble e-mail of death.\r
\n\r
\nI\'ve had puzzles rejected before and it\'s not a very big deal, but this was different. I feel I have a track record at Flooble for creating pretty decent puzzles, and yet three (or more) peers TD\'d it without giving me a chance to address their concerns. The puzzle was an algorithm that was not as straight-forward as it might first appear, and that fact was implied in the verbage of the question, yet the puzzle was rejected for being \"too like a homework problem\". Can anyone who saw the puzzle in the queue (whether you TD\'d it or not) give me some feedback? And would you agree that established Flooblers deserve a couple days to respond to questions before axing their work? (I still advocate the use of an edit backlog for just such problems.)',1567,'Bryan','2003-12-23 01:03:53');
INSERT INTO forumpost VALUES (2681,344,7,'Introducing myself','Hi I was asked to introduce myself so here goes.\r
\n\r
\nIm Dragon King.........I post under this name in a few Rugby League forums downunder.\r
\n\r
\nActually that is how I came to be here cos I needed ideas for our kwik kwiz section and here I am.\r
\n\r
\nI have read one of the propblems that is on offer regards pennies and I thought I had the solution.........being 16 however I havent seen an answer yet.\r
\n\r
\nI have always been keen on brain food and have a feeling I will be spending a fair bit of time here.\r
\n\r
\nCheers all and look forward to getting to know u all better.',4916,'Ian','2003-12-23 04:56:31');
INSERT INTO forumpost VALUES (2682,344,7,'Re: Introducing myself','Welcome to the site, Ian. I hope you get all the brainfood you want :)',1,'levik','2003-12-23 08:05:05');
INSERT INTO forumpost VALUES (2683,343,4,'Re: Ya tune out for one weekend and...','I wasn\'t aware that it got axed; I thought it moved to the queue end. I don\'t think it was ready to be rid of, but it needed some work, and some explanation.\r
\n\r
\nI was thinking it seemed too much like a work problem than an actual problem, but I didn\'t know if you felt that way; we should at least get some feedback for a problem like this if the person is actually here.',1626,'Gamer','2003-12-23 11:55:43');
INSERT INTO forumpost VALUES (2684,344,7,'Re: Introducing myself','Thanks Levik, most appreciated.\r
\n\r
\nMay I wish you and all the other members a very happy festive season.',4916,'Dragon King','2003-12-23 17:48:01');
INSERT INTO forumpost VALUES (2685,339,7,'still me and still good','hey again you guys! really appreciate all the advice. i\'m on a mission. a personal one @ that. can you help. to all the ones who read my first post i think you might know what i am needing. a fight.',4778,'chic','2003-12-26 19:32:35');
INSERT INTO forumpost VALUES (2686,327,3,'monty python','monty python films are wonderful. sick and twisted ... i suppose it takes one to know one. have anyone of you ever heard of the dancing outlaw? simply hilarious!',4778,'chic','2003-12-26 20:04:43');
INSERT INTO forumpost VALUES (2687,345,3,'United States football','All this talk about logic and math wheres my brain out.\r
\nSo (forgive me for straying from the purpose of the site) but if anyone has any comments on the NFL, put them here.\r
\n\r
\n',2130,'ethan','2003-12-27 00:26:52');
INSERT INTO forumpost VALUES (2688,345,3,'Re: United States football','Does anyone agree with me? That no team from the NFC should go to the playoffs, save maybe KC?',2130,'ethan','2003-12-27 00:30:14');
INSERT INTO forumpost VALUES (2689,304,7,'Re: Looking for the name of a puzzle','I believe there was an article in \"Scientific American\" many years ago that presented this problem and explained why there is no solution (as DJ did so well above). I was first exposed to this problem by my seventh grade math teacher years ago. I wasted many, many hours, as did everyone else in my class, trying to find the solution to this unsolvable puzzle. At least it kept us busy and out of trouble!',4954,'Richard Wohlers','2003-12-27 03:39:10');
INSERT INTO forumpost VALUES (2690,346,7,'Just Registered - Newbie','Hi everyone. Finally registered after lurking for several days because I think I have the solution for one of the problems. It was a piece of cake...really. I came upon this site when I clicked on an unknown icon at beerlovercam.com (great site, have to check out Beer Drinking Troubleshooting Chart. It\'s hilarious). I\'ve always loved science and math, as well as puzzles and brainteasers. I plan on visiting frequently. Thanks for having me!',4954,'spunky','2003-12-27 03:55:27');
INSERT INTO forumpost VALUES (2691,346,7,'Re: Just Registered - Newbie','Cool :) Remember that you don\'t get anything for submitting yet another solution to a problem if it\'s the same solution; but if you want to do so go ahead :)',1626,'Gamer','2003-12-27 07:42:50');
INSERT INTO forumpost VALUES (2692,347,4,'Algorithms versus Homework?','In order to prevent problems like with Starfield Simulator to occur, I think we need to decide what exactly is an algorithm, and what is just a \"homework programming problem\";\r
\n\r
\nI think if a problem can be much more easily stated as an algorithm (or can\'t be stated at all), it shouldn\'t appear. Algorithms should be for people who can think LIKE a programmer in my opinion.\r
\n',1626,'Gamer','2003-12-27 12:09:55');
INSERT INTO forumpost VALUES (2693,347,4,'Re: Algorithms versus Homework?','I missed the Starfield Simulator problem... would someone please post the text of it, here...?',3172,'SilverKnight','2003-12-28 02:16:04');
INSERT INTO forumpost VALUES (2694,347,4,'Re: Algorithms versus Homework?','Perhaps it would help to go back to the thread at the institution of the algorithms category: <a href=\\\"http://flooble.com/perplexus/forum.php?fid=3&tid=111>Computer/Programming puzzles started by levik. \r
\n\r
\nThe question of homework vs. puzzle has come up in other categories also, and I think it has more to do with how \"interesting\" a problem is. Of course interest is in the mind of the observer, and so is not something that can be objectively categorized.',1301,'Charlie','2003-12-28 09:51:25');
INSERT INTO forumpost VALUES (2695,347,4,'Re: Algorithms versus Homework?','Whoops. Didn\'t close my quote: Computer/Programming puzzles.',1301,'Charlie','2003-12-28 09:52:50');
INSERT INTO forumpost VALUES (2696,348,7,'new addict loggin on....','hi hello! :)\r
\nabsolutely love the site!\r
\ngot to solve around 5 already in one night!\r
\n:) :)\r
\nfeels great to solve them!\r
\nhi! i\'m jo-anne, new addict logging on...',4967,'Jo-Anne','2003-12-28 10:44:54');
INSERT INTO forumpost VALUES (2697,348,7,'Re: new addict loggin on....','Welcome. Yes, it can be addictive.',1301,'Charlie','2003-12-28 16:06:50');
INSERT INTO forumpost VALUES (2698,349,7,'Just Flew In from the Internet...','And boy, are my jokes tired. I\'ve actually been visiting this forum for a while, having found it through google. Figured out the answer to one of the word problems, and here I am. If you feel like worshipping me, for any reason, that\'s perfectly understandable. I accept tribute in the form of works of art, fine wine, and large sacks of cash.',4970,'Jack the Reaper','2003-12-28 18:29:17');
INSERT INTO forumpost VALUES (2699,327,3,'Hey, Minion','I jsut thought that I\'d tell you that you inspired me. My wife adn I were trying to think of gifts for my young neices for Christmas and I remembered your post adn got one \"Hitchhiker\'s Guide\" and the other \"Restaraunt at the End of the Universe\" \r
\nMaybe I can create to new Math-Spods for the world',2839,'FatBoy','2003-12-29 07:06:10');
INSERT INTO forumpost VALUES (2700,348,7,'Re: new addict loggin on....','Good to hear that you\'re enjoying yourself... \r
\nIf you\'ve solved five problems already, try heading over to the Unsolved Problems, and see how you go there!\r
\nYou might teach the rest of us a few lessons!',3136,'Popstar Dave','2003-12-29 08:18:19');
INSERT INTO forumpost VALUES (2701,350,3,'Here\'s something you don\'t see every day','The \"bonus\" problem',1575,'DJ','2003-12-29 11:08:33');
INSERT INTO forumpost VALUES (2702,245,7,'Re: math puzzles i need help please!!','The answer to #1 is 100 tries, #2 is 9 students, I\'m not sure about #3, and #4 is that the man in front observed that there were only 2 white hats and that the rest were black, and he learned that his own hat was white and that the man\'s hat behind him was also white, so the man\'s hat in back must have been black.',4986,'D.','2003-12-29 20:18:19');
INSERT INTO forumpost VALUES (2703,204,7,'Re: No Subject','Sorry, Vinod, I just started today.',4986,'Dom','2003-12-29 21:13:35');
INSERT INTO forumpost VALUES (2704,273,3,'Re: brain teasers','Here\'s a brain teaser:JUST144ICE',4986,'Dom','2003-12-29 21:21:34');
INSERT INTO forumpost VALUES (2705,289,3,'Re: Riddle for you all...','Helen Keller',4986,'Dom','2003-12-29 21:22:55');
INSERT INTO forumpost VALUES (2706,350,3,'Re: Here\'s something you don\'t see every day','What the heck? thats all I have to say.',1072,'Alan','2003-12-29 22:25:18');
INSERT INTO forumpost VALUES (2707,289,3,'Re: Riddle for you all...','Levik should change the description of general discussion to discuss anything and everything here except for unposted problems.',1072,'Alan','2003-12-29 22:27:01');
INSERT INTO forumpost VALUES (2708,351,7,'How much education?','I\'m just wondering how much formal training some of the regs here have. Me personally, I\'m a senior math major, with theoretical classes such as Mathematical Structures and Proofs, Modern Algebra, and Mathematics and Philosophy, as well as some more concrete stuff such as Statistics, Crypotolgy, three levels of Calculus, and Operations Research :)\r
\n\r
\n--Graatz',4925,'Jeff','2003-12-30 17:38:27');
INSERT INTO forumpost VALUES (2709,352,7,'Hi people!','Hi. I\'m new to all this. \r
\n\r
\nJust saw your site while looking for math problems in Google. From the looks of it, I\'m going to have fun in this site. :)\r
\n\r
\nThanks guys for putting something like this together.',4999,'Lou','2003-12-30 20:36:48');
INSERT INTO forumpost VALUES (2710,289,3,'Re: Riddle for you all...','If what goes up, must come down, then what went up in the first place?',5003,'E=MC2','2003-12-31 11:56:13');
INSERT INTO forumpost VALUES (2711,353,3,'Happy New Year!','Happy new year, everyone!\r
\n\r
\nI hope the coming year will be good and healthy for all.\r
\n\r
\nI\'ll be out of town for a couple of days, so see you all when I get back.',1,'levik','2003-12-31 13:39:21');
INSERT INTO forumpost VALUES (2712,276,7,'Re: No Subject','what is the subject of this no subject thread?',5009,'Eduardo Pensado','2004-01-01 22:59:38');
INSERT INTO forumpost VALUES (2713,354,7,'Hello, I\'m new','Hi everyone! My name is Erin, and I\'m new to this site. Is there anything I should know? otherwise, just let\'s chat or sumthin...',5020,'*Erin*','2004-01-02 20:34:09');
INSERT INTO forumpost VALUES (2714,327,3,'Fatboy','I know your niece will love the books.',4300,'Minion123','2004-01-04 02:26:53');
INSERT INTO forumpost VALUES (2715,355,4,'The (BIG) solutions push','OK, I just went to the statistics page to see that we had close to 80 problems on the site with no solutions... Which seemed a bit excessive, so I went through the solution queue, and pushed all the available solution which nobody had any objections to or which the existing objections seemed to have been addressed. (I saw a couple where people were waiting for somebody to come along and solve them, but these were a couple of months old, and seemed like a lost cause). In all, I was able to get the unsolved count down to about 45 problems.\r
\n\r
\nA few times I saw people post things like \"I have a solution but will post it later\" (SilverKnight comes to mind, but I\'m sure there were others). \r
\n\r
\nI believe that one of the nice things about this site is the ready availability of solutions to the vast majority of the problems. Seeing and understanding a solution, even if not worked out by themselves, usually gives people a sense of satisfaction.\r
\n\r
\nAs such, I am asking anyone who still \"owes\" us a solution to try and deliver one. I will try and go through a list again sometime in a week or two to pick up any stragglers.\r
\n\r
\nThanks for your help.',1,'levik','2004-01-04 12:51:38');
INSERT INTO forumpost VALUES (2716,355,4,'Re: The (BIG) solutions push','My prime sequence problem hasn\'t been solved; maybe there isn\'t a way to find the constant difference or first term. The solution that\'s there only answers the first part of the question.\r
\n\r
\nAs for Square sequence and Another square sequence, I would like someone else to look over it and push it.',1626,'Gamer','2004-01-04 14:54:15');
INSERT INTO forumpost VALUES (2717,354,7,'Re: Hello, I\'m new','iii iam new here... soo nice to meet uu all',NULL,'demonrez','2004-01-04 15:13:14');
INSERT INTO forumpost VALUES (2718,356,7,'novice standing','i first stumbled onto this site about 2 weeks ago. i was under the impression that one advances to student after a couple of days. is two weeks more accurate, or will i still be waiting in two months?',4909,'Brian','2004-01-04 20:15:06');
INSERT INTO forumpost VALUES (2719,356,7,'Re: novice standing','You have to rate at least one problem (in addition to the comments, which you have already done), as explained here, when you click on a \"what does this mean\" when looking at a given standing.',1301,'Charlie','2004-01-04 20:55:28');
INSERT INTO forumpost VALUES (2720,357,5,'How long until I move ahead?','I am a novice on flooble :: perplexus. I have rated 2 problems and commented about 10 times. How long will I have to wait to become a student? Or is there some other criteria which must be fulfilled?',5033,'Captain Paradox','2004-01-04 21:26:43');
INSERT INTO forumpost VALUES (2721,357,5,'Re: How long until I move ahead?','It should happen overnight, when the software recognizes the criteria.',1301,'Charlie','2004-01-04 22:52:00');
INSERT INTO forumpost VALUES (2722,273,3,'Re: brain teasers','I\'d be doing the problem submission process a gross injustice if I were to answer that problem, so I won\'t. Please use the official channels in future.',1183,'fwaff','2004-01-05 03:35:37');
INSERT INTO forumpost VALUES (2723,358,3,'Queue weighting','I realize that this topic has been discussed again and again, but I have an idea. If there are any problems with this idea, feel free to state them here.\r
\n\r
\nI think it would work if instead of a queue weighting system, we could just have a round-robin type of system. This is how it would work. First the people with the most problems submitted would get a problem viewed by journeymen and the scholars. Next the people with the most problems submitted after that would get a problem viewed, and so on until everyone with a submitted problem has had a problem viewed. Then the process would start over. This way everyone will get the same number of problems viewed.\r
\n\r
\nWhen people see that their only problem submitted has stayed in the 80\'s for its Apprx. Queue Pos., they might get discouraged and/or bored with the site and stop coming here altogether. This system would give them something to check every day, to see if their problems have votes or have been posted, and they would come to this great site regularly.\r
\n\r
\n',2130,'ethan','2004-01-05 17:33:19');
INSERT INTO forumpost VALUES (2724,359,7,'Anyone know 20 questions type of riddles','I\'ve just signed up. Really like the site - found it on Google when I searched for \'Logic Riddles\' - - - I am interested in riddles of deduction (usually involving crimes, motives, assumptions, etc.) whereby you \'play\' with another person in a 20 questions type format. All questions have to be yes or no questions (I usually play with no limit). Does anyone know of a group of these somewhere on this site? I have several I can post if there is an interest. Feel free to email me: shelly@pacificintermedia.com',5059,'Shelly','2004-01-05 17:51:42');
INSERT INTO forumpost VALUES (2725,351,7,'Re: How much education?','I am not yet a regular but can tell you my background is art, art history and architecture - quite a different background than you - though I have always loved math and science.',5059,'Shelly','2004-01-05 17:56:17');
INSERT INTO forumpost VALUES (2726,359,7,'Re: Anyone know 20 questions type of rid','Shelly,\r
\n\r
\nNot to rain on your parade, but the consensus seems to be that those kind of \"question and answer\" riddles don\'t work well here... when the author/riddler isn\'t available in real time to answer the questions.\r
\n\r
\nSo, this site prefers to see questions that \"stand on their own\", without further elucidation.\r
\n\r
\n--- SK\r
\n\r
\nP.S. Elucidation was the \"word of the day\".',3172,'SilverKnight','2004-01-05 18:39:43');
INSERT INTO forumpost VALUES (2727,360,3,'hi','hey\r
\ni am new to this site \r
\ni love it though for the help with the problems it has given me\r
\nthanks \r
\n-Steve',5062,'Steve','2004-01-05 19:42:10');
INSERT INTO forumpost VALUES (2728,361,7,'i am new','hi everyone\r
\ni am new\r
\ni joined to maybe get some help with my grade 12 geometry and discrete math course.\r
\ni hope to be able to post some questions eventually once i get to student status\r
\n-Steve',5062,'Steve','2004-01-05 19:47:33');
INSERT INTO forumpost VALUES (2729,356,7,'Re: novice standing','so all we have to do is rate a question and post some comments to become a student rather than a novice?',5062,'Steve','2004-01-05 19:51:05');
INSERT INTO forumpost VALUES (2730,359,7,'Re: Anyone know 20 questions type of riddles','If you search for \"lateral thinking puzzles\", you may be able to find them on google. We don\'t usually do that here; this is more of a logic site -- if the answer fits than it must be right.',1626,'Gamer','2004-01-05 20:42:44');
INSERT INTO forumpost VALUES (2731,362,7,'Looky here.......video games.','Any know about SUPER MARIO SUNSHINE?',5065,'Darryl','2004-01-05 22:36:07');
INSERT INTO forumpost VALUES (2733,363,7,'Helloooooooooooo','My names Darryl.I just signed up.',5065,'Darryl','2004-01-05 22:38:29');
INSERT INTO forumpost VALUES (2734,344,7,'Re: Introducing myself','Welcome Ian,feel free to talk 2 me any time.',5065,'Darryl','2004-01-05 22:49:16');
INSERT INTO forumpost VALUES (2735,64,7,'Re: Twin chat','r u talking 2 ur self?',5065,'Darryl','2004-01-05 22:59:38');
INSERT INTO forumpost VALUES (2736,349,7,'Re: Just Flew In from the Internet...','All hail Jack the Reaper.',5065,'Darryl','2004-01-05 23:06:20');
INSERT INTO forumpost VALUES (2737,362,7,'Re: Looky here.......video games.','That was a good game, and it had really good graphics and music too. I can hear the main theme now. It\'ll probably be stuck in my head for a while now.',3558,'Tristan','2004-01-06 19:15:58');
INSERT INTO forumpost VALUES (2738,362,7,'Re: Looky here.......video games.','Oh, right, and um, welcome to Flooble! Explore the puzzles and read the FAQ page if you haven\'t already.',3558,'Tristan','2004-01-06 19:17:58');
INSERT INTO forumpost VALUES (2739,357,5,'Re: How long until I move ahead?','Thanks, Charlie. It sure did. I guess wishes do come true. If you don\'t mind me asking, how long have you been on flooble? I just started.',5033,'Captain Paradox','2004-01-06 21:05:59');
INSERT INTO forumpost VALUES (2740,357,5,'Re: How long until I move ahead?','I started on Flooble almost a year ago now--last January.',1301,'Charlie','2004-01-06 22:49:20');
INSERT INTO forumpost VALUES (2741,357,5,'Re: How long until I move ahead?','Wow. Have you submitted any problems? Or are you strictly a reader?',5033,'Captain Paradox','2004-01-07 17:44:20');
INSERT INTO forumpost VALUES (2742,180,5,'Re: The riddle problem','I agree with Alan. Perhaps the riddle option could be moved up to Apprentice or (if it\'s really bad) Journeyman. This could also apply to other categories that someday become swamped.\r
\n
\nRiddles should be reserved for those who already know how to make a good puzzle.',5033,'Captain Paradox','2004-01-07 17:54:44');
INSERT INTO forumpost VALUES (2743,364,5,'How old is flooble?','I\'ve noticed that many threads begin in 2003. How old is flooble? Or the flooble forums, if they weren\'t started at the same time.',5033,'Captain Paradox','2004-01-07 18:02:59');
INSERT INTO forumpost VALUES (2744,364,5,'Re: How old is flooble?','Well, if you went to http://flooble.com/perplexus/show.php?pid=1, the first problem on Flooble, you would see that it was posted on March 28, 2002.\r
\n\r
\nSo... gettin\' close to 2 years old.',3172,'SilverKnight','2004-01-07 18:25:16');
INSERT INTO forumpost VALUES (2745,364,5,'Re: How old is flooble?','Thanks, Silverknight.',5033,'Captain Paradox','2004-01-07 22:05:15');
INSERT INTO forumpost VALUES (2746,356,7,'Re: novice standing','Well, almost. As Charlie told me, the site needs to process the information, so try to be patient with the server (unlike I was!).',5033,'Captain Paradox','2004-01-07 22:31:24');
INSERT INTO forumpost VALUES (2747,365,7,'Membership','Hi all, do you pay to register for this site?? I want to register and chat now and then but I don\'t want to pay...',NULL,'Acid - Non member','2004-01-08 04:42:49');
INSERT INTO forumpost VALUES (2748,365,7,'Re: Membership','Never mind this site seem to suck anyway because it looks like I am the only person that visied this site today...\r
\n\r
\nCheers\r
\n',NULL,'Aspiring Novice','2004-01-08 05:36:49');
INSERT INTO forumpost VALUES (2749,366,7,'Hi','Hi All,\r
\n\r
\nI was just searching for teasers and puzzles and i stumbled upon flooble ! But a very good site indeed !\r
\n\r
\nsee you later !\r
\n\r
\n\r
\n',5106,'justin','2004-01-08 09:56:54');
INSERT INTO forumpost VALUES (2750,357,5,'Re: How long until I move ahead?','Just to get to apprentice level requires having had 3 problems published on the site, and then Journeyman needs another 3. Scholars come up through the Journeyman level, so have at least 6 problems on the site. I do have a couple more in the queue. If you click on anyone\'s name, as a link, you can see what puzzles on the site were submitted by that person, as you can do with my name.',1301,'Charlie','2004-01-08 10:12:44');
INSERT INTO forumpost VALUES (2751,357,5,'Re: How long until I move ahead?','I know friedlinguini only had 6 problems, and then was done. I have many problems, so I am flowing constantly. :)',1626,'Gamer','2004-01-08 16:17:06');
INSERT INTO forumpost VALUES (2752,365,7,'Re: Membership','Membership to flooble perplexus is free and quick. There is a sign-up link below the two white boxes in the upper right of your screen. Just click that and you can sign up! No money involved.\r
\nAspiring Novice - don\'t think that just because you seemed to be the only one on the site that day doesn\'t mean it\'s a sucky site. There were people on before and after that time . . . me included.',5033,'Captain Paradox','2004-01-08 20:43:09');
INSERT INTO forumpost VALUES (2753,365,7,'Re: Membership','Oops! Scratch that second second don\'t.\r
\nSorry about that.',5033,'Captain Paradox','2004-01-08 20:44:16');
INSERT INTO forumpost VALUES (2754,205,7,'Re: Hi. I\'m new at this.','That\'s right, Lewis. It\'s not a chat room.',5033,'Captain Paradox','2004-01-08 20:45:09');
INSERT INTO forumpost VALUES (2755,205,7,'Re: Hi. I\'m new at this.','hi',5126,'melanie','2004-01-09 19:42:19');
INSERT INTO forumpost VALUES (2756,367,7,'chloe flowers anyone no me????','yo yo yo peeps anyone no me even if ya dont plz talk to me plz plz am new at this so help me\r
\nlove ya all love from \r
\nchloe flowers oh yeh asl?????????',5148,'chloe flowers','2004-01-11 11:34:54');
INSERT INTO forumpost VALUES (2757,368,7,'Logging in for the first time!','Hi all,\r
\n\r
\nI am the new kid on the block. I found this site while seaching the net to get brainteasers to sharping up my brain. what is it like in here? I cant wait to start cracking the puzzlezzzzz. WHERE ARE THE PUZZLESSSS????????',5157,'Ben Beauty','2004-01-12 10:41:34');
INSERT INTO forumpost VALUES (2758,328,6,'Re: Testing','it won\'t work unless you add the semicolon .. ♫ (♫) as opposed to just ♫',1575,'DJ','2004-01-12 12:34:03');
INSERT INTO forumpost VALUES (2759,328,6,'Re: Testing','Also, some of the characters will only show up between the <tt> and </tt> tags:\r
\n\r
\n♫ = ♫\r
\n\r
\n<tt>♫</tt> = ♫',1575,'DJ','2004-01-12 12:36:40');
INSERT INTO forumpost VALUES (2760,364,5,'Re: How old is flooble?','I know levik is the administrator of flooble but did he create it as well?',5062,'Steve','2004-01-12 19:07:10');
INSERT INTO forumpost VALUES (2761,364,5,'Re: How old is flooble?','And Levik looked upon the chaos and saw that it was lacking of order. And Levik said \"Let There Be Flooble\". And so Flooble was. And Levik looked upon his creation. And Levik saw that it was good.\r
\n\r
\nWithin his creation, He spawned aspiring novices which prospered in this Eden. And to sustain them, He provided conundrums. But the novices flailed around miserably, lacking direction and wasting much of their idle time. So Levik created unto them a path of righteousness, for which they now had purpose. And they could begin the traversal of the path, being students. And Levik saw that it was good.\r
\n\r
\nBut they floundered in their inability to recategorize their submissions. And Levik bestowed upon a few this power. And He called them apprentices. And Levik saw that it was good.\r
\n\r
\nLevik wondered at his creation with much love. And He spent much time tending to the submissions. And He saw that his creatures longed to take part in the ritualistic judgement of the submissions. And He desired to focus His attention on other endeavors, to share His gifts. So Levik confered a select few the ability to foresee submissions with an oracle-like ability to judge those submissions that were Flooble-worthy. He called these few journeymen. And Levik saw that it was good.\r
\n\r
\nAgain, Levik looked down from on high. He found that he still spent much time improving his creation. Levik chose to remove from himself the duty of excessively nurturing his children. And He saw several exceptional journeymen to whom he would grant the capability to spawn those enigmas that the journeymen deemed Flooble-worthy, only those that would provide great nourishment. To these extraordinary few beings, Levik gave the name scholars. And the scholars would help with minor administrative duties, tending to and encouraging the lesser creatures.\r
\n\r
\nAnd He saw that it was good.',3172,'SilverKnight','2004-01-12 19:50:17');
INSERT INTO forumpost VALUES (2762,364,5,'Re: How old is flooble?','Amen',1,'levik','2004-01-12 21:19:49');
INSERT INTO forumpost VALUES (2763,301,3,'Re: WOOHOO!!!','Question . . . can you see the top 10 in each category while voting, or are all the puzzles pooled into one queue?',5033,'Captain Paradox','2004-01-12 21:43:35');
INSERT INTO forumpost VALUES (2764,301,3,'Re: WOOHOO!!!','... all pooled into one queue (so Journeymen can see only 10...), but the proposed problem category, given by the submitter, is shown.',3172,'SilverKnight','2004-01-12 21:47:11');
INSERT INTO forumpost VALUES (2930,374,5,'Re: Blast it!','It\'s not as much an aristocracy as it is more of a duplicate prevention tool. There\'s pretty many problems on the site and it\'s easy to miss some. Your idea is right, however due to the massive number of all the problems on the site, it will take 2-3 months usually to see it in the queue/ see it on the site (if fine); my advice is to submit the problem even if the wait is long because as long as you don\'t die in the next 2-3 months, you will see it get voted on eventually :)\r
\n\r
\nGenerally if it\'s already on the site in some form it won\'t get put on again.',1626,'Gamer','2004-01-19 21:46:02');
INSERT INTO forumpost VALUES (2929,374,5,'Re: Blast it!','so to get a question posted you have to submit it and then the higher ups of this wonderful site decide whether it is good enough to make it or not?',5062,'Steve','2004-01-19 20:31:43');
INSERT INTO forumpost VALUES (2928,364,5,'Re: How old is flooble?','enough of all this algorith junk, levik does exist right it isn\'t just some guy who posts as someone else too?',5062,'Steve','2004-01-19 20:26:11');
INSERT INTO forumpost VALUES (2927,375,5,'Re: Rich edit control','Thanks DJ. I see now that the \"view source\" also allows editing source, and the shift-return works as well, just as you say.',1301,'Charlie','2004-01-19 20:22:42');
INSERT INTO forumpost VALUES (2926,375,5,'Re: Rich edit control','To charlie: hitting return inserts a paragraph (<p>). To get a single line break (<br>), use shift-return. If you want to use <pre> tags (or any other HTML) you need to click the \'view source\' button at the bottom to see the underlying code.',1575,'DJ','2004-01-19 19:00:05');
INSERT INTO forumpost VALUES (2925,375,5,'Re: Rich edit control','I think it looks pretty good. The font style, font, and size boxes could be replaced with just a button (like the buttons for bold or italics) to use a fixed-width font, and text highlighting could probably be removed (to preserve the current format of the site). Also, the box automatically replaces repeated spaces with the character, which is nice. The \'view source\' button is a must. Buttons for subscript and superscript would be very useful as well.',1575,'DJ','2004-01-19 18:57:53');
INSERT INTO forumpost VALUES (2924,375,5,'Re: Rich edit control','Charlie - not sure what you mean. Are you listing the problems with the control?\r
\n\r
\nSK - sorry, but the insert image function will be disabled before this is implemented :)',1,'levik','2004-01-19 15:23:29');
INSERT INTO forumpost VALUES (2923,372,7,'Re: Hello','Hey! I have no idea what to talk about! I havent tried any of the puzzles to know what to talk about them either. Thank you so much for talking to me!!! You can pick what you want to talk about!',5199,'Sarah','2004-01-19 11:36:40');
INSERT INTO forumpost VALUES (2922,375,5,'Re: Rich edit control','suuuwwwweeeeetttt !',3172,'SilverKnight','2004-01-19 11:34:54');
INSERT INTO forumpost VALUES (2921,375,5,'Re: Rich edit control','Within the text box the words are double (at least) spaced. The <pre> values get converted to the < symbology. The formatting looks good.',1301,'Charlie','2004-01-19 11:30:05');
INSERT INTO forumpost VALUES (2920,375,5,'Rich edit control','So after getting a number of formatting-related requests, I decided it was time to simplify the process of posting rich-text comments/problems/solutions/forum posts. To that end, I have done some research on the topic, and found this:\r
\n\r
\nhttp://www.kevinroth.com/rte/demo.htm\r
\n\r
\nLet me know if this souped up text area works in your browser, and what you think about me making it a standard on the site.',1,'levik','2004-01-19 11:04:59');
INSERT INTO forumpost VALUES (2919,374,5,'Re: Blast it!','DJ is right - I haven\'t posted a problem in a while... You know why? Because my single solitary problem is in the queue for the last 3 months! \r
\n\r
\nStupid slow queue. :)\r
\n\r
\nHm..... Anyway, it should be known by now that the problem posting on this site is exclusively the achievement of the submitters, Journeyman voters and Scholar pushers.\r
\n\r
\nI have been simply hovering in the wings observing the wonders of this democratic process for a while now :)',1,'levik','2004-01-19 11:02:59');
INSERT INTO forumpost VALUES (2918,374,5,'Re: Blast it!','Also, lots of Ravi\'s problems are either based on a previous problem he submitted or too easy. It gets confusing once you have submitted so many.',1626,'Gamer','2004-01-19 08:33:42');
INSERT INTO forumpost VALUES (2917,374,5,'Re: Blast it!','Most of the \"classic\" problems have been posted -- in fact they were most likely posted early in the site\'s run (Fall of 2002 or earlier), so it is not likely \"your\" classic puzzle was missed. That is why approximately 1 in 3 of Ravi\'s submissions gets a quick rejection.',153,'TomM','2004-01-19 00:14:43');
INSERT INTO forumpost VALUES (2916,374,5,'Re: Blast it!','If is was a problem that levik posted, I don\'t think he \'just\' did it -- he hasn\'t posted a new problem to the site since last (2003) October ...',1575,'DJ','2004-01-18 22:50:17');
INSERT INTO forumpost VALUES (2915,374,5,'Blast it!',' Alas, my pending problem was not to be, for Levik just happened to post another version before mine was viewed. Doggone it. But he presented it better than I did, so I guess it was for the good of flooble.',5033,'Captain Paradox','2004-01-18 22:15:41');
INSERT INTO forumpost VALUES (2914,364,5,'Re: How old is flooble?','How about this:\r
\n\r
\nT: if T is false, Levik does not exist.\r
\n\r
\nWell, that doesn\'t work either. Charlie, where are you?',5033,'Captain Paradox','2004-01-18 16:03:18');
INSERT INTO forumpost VALUES (2913,372,7,'Re: Hello','Sarah,\r
\n\r
\nGo ahead, what would you like to talk about?\r
\nPuzzles are always a good topic around here, but I\'m wiling to talk abotu just about anything and if I know the other flooblers I\'m sure they\'ll start chiming in.',2839,'FatBoy','2004-01-16 09:13:01');
INSERT INTO forumpost VALUES (2912,372,7,'Re: Hello','yay! i wanna talk!',5199,'Sarah','2004-01-15 18:22:23');
INSERT INTO forumpost VALUES (2911,364,5,'Re: How old is flooble?','Proof of the inexistance of Levik:\r
\n\r
\nS: If S is true, Levik does not exist\r
\nLogically, S must be either True or False...\r
\n...\r
\n\r
\n\r
\n:)',3372,'Sam','2004-01-15 12:03:29');
INSERT INTO forumpost VALUES (2910,372,7,'Re: Hello','Welcome, Welcome, Welcome....',2839,'FatBoy','2004-01-15 10:08:17');
INSERT INTO forumpost VALUES (2909,371,4,'Re: 136 new forum posts','\"IE 5 on WinNT 4\" could just be an old computer. I still have a computer with IE 2 on Win95!',1920,'Brian Smith','2004-01-15 09:23:21');
INSERT INTO forumpost VALUES (2908,371,4,'Re: 136 new forum posts','OK... I deleted all the posts with empty bodies, plus made it so you can\'t post an empty post.\r
\n\r
\nWhich doesn\'t circumvent a potential attack, but at least will prevent accidental spiderings such as this one may have been (although the User Agent on those requests was IE 5 on WinNT 4 which looks pretty fake in this day and age)',1,'levik','2004-01-15 02:50:24');
INSERT INTO forumpost VALUES (2893,371,4,'136 new forum posts','Did a non-member (with WAY too much time on their hands) actually go and drop a blank comment onto each thread in the Reference and New Users forums? Or was that some sort of bug in the way the forums are coded? Coz that would\'ve taken a mighty long time!',3136,'Popstar Dave','2004-01-13 05:10:15');
INSERT INTO forumpost VALUES (2894,364,5,'Re: How old is flooble?','Careful SK, or Charlie and DJ might start arguing about whether or not Levik exists.',1183,'fwaff','2004-01-13 05:13:18');
INSERT INTO forumpost VALUES (2895,364,5,'Re: How old is flooble?','It\'s ok, Charlie\'s already written an algorithm that shows that he does exist.',3136,'Popstar Dave','2004-01-13 07:03:42');
INSERT INTO forumpost VALUES (2896,371,4,'Re: 136 new forum posts','It looks like Aspiring Novice (not logged in--so black letters) used some automated program to post them within seconds of one another.',1301,'Charlie','2004-01-13 08:43:31');
INSERT INTO forumpost VALUES (2897,78,7,'Re: Hello all','hey everyone i am new here i dont really get this hole thing. But if someone could kindly fill me in. that would be great! One! the only BaybeGirl round!',5173,'Lori','2004-01-13 08:45:10');
INSERT INTO forumpost VALUES (2898,371,4,'Re: 136 new forum posts','I would put money on that it was simply a robot (web crawler) that was checking out links.... and this one did Form \"POST\" operations, to see what it could see. (But I suppose someone COULD have written a program to do this.... wouldn\'t be too hard.)',3172,'SilverKnight','2004-01-13 15:44:03');
INSERT INTO forumpost VALUES (2899,371,4,'Re: 136 new forum posts','Levik,\r
\n\r
\nCan you easily write a script that deletes all forum postings that occurred around 4am last night (give or take 20 minutes)...? That should get rid of these postings.\r
\n\r
\n- SK',3172,'SilverKnight','2004-01-13 16:03:13');
INSERT INTO forumpost VALUES (2900,371,4,'Re: 136 new forum posts','SK, what\'s the difficulty level on that? And shouldn\'t it be in \"Algorithms\", instead of being posted in a forum?!\r
\n=P',3136,'Popstar Dave','2004-01-14 09:00:24');
INSERT INTO forumpost VALUES (2901,364,5,'Hey, Charlie!!!','Cool,
\r
\nLets see if we can get him to post it.
\r
\nIf he can prove that Levik exists, can he prove that there is really only one Tim Axoy and the others exist only in pontentie??\r
\n\r
\n',2839,'FatBoy','2004-01-14 11:55:22');
INSERT INTO forumpost VALUES (2902,372,7,'Hello','Hi folks, just joined and announcing my presence to all.',5193,'Mike McGowan','2004-01-14 13:01:53');
INSERT INTO forumpost VALUES (2903,372,7,'Re: Hello','Hi, me too',5197,'Bob','2004-01-14 16:37:02');
INSERT INTO forumpost VALUES (2904,373,3,'I dont know what to do.','Um, i dont know what to do on this, it is my first time, i just want some people to read my blog: www.captianjacksparrow.blogspot.com I know i spelled captain wrong. sorry! ',5199,'Sarah','2004-01-14 18:31:36');
INSERT INTO forumpost VALUES (2905,372,7,'Re: Hello','ok, then i will to!',5199,'Sarah','2004-01-14 18:45:18');
INSERT INTO forumpost VALUES (2906,371,4,'Re: 136 new forum posts',':) But then wouldn\'t it take too long to come up in the queue?\r
\n',1626,'Gamer','2004-01-14 21:27:33');
INSERT INTO forumpost VALUES (2907,371,4,'Re: 136 new forum posts','This one was even simpler - it converted all the forms into GET formatted links.\r
\n\r
\nI really screwed up here - will need to add code to disallow empty posts.',1,'levik','2004-01-15 02:45:59');
INSERT INTO forumpost VALUES (2934,375,5,'Re: Rich edit control','While the GUI is nice, it doesn\'t do everything. One of the biggest shortcomings in not being able to edit the source directly is with the special characters (see my testing thread), which I use quite often -- the existing buttons for the HTML codes are rather lacking, and very limited in selection.\r
\n\r
\nAlso, having to enter every comment using the GUI would be extremely annoying. First, I don\'t ever enter a comment directly into the box on the site, I type it up first in notepad (for many problems, the ability to search/replace text is invaluable) and paste it in. If that were pasted into the GUI, I might as well have not done anything.\r
\n\r
\nIf you\'re worried about closed tags, the script for the text-edit box automatically closes any tags that are left open anyway (if you type in \"<i>hello\", it will output \"<i>hello</i>\").',1575,'DJ','2004-01-20 10:27:40');
INSERT INTO forumpost VALUES (2935,377,4,'Rich Edit Control (continued)','I started a new thread just to avoid making this suggestion in the public forums -- but maybe the \"view source\" button (on the rich text-edit box, see <a herf=\\\"http://www.flooble.com/perplexus/forum.php?fid=5&tid=375\\\">this thread if you don\'t know what i\'m talking about) could be restricted for journeymen+ to use?\r
\n\r
\nI\'m just so used to typing and doing everything via the keyboard, that to have to leave the keyboard and use the mouse to do anything would be a great annoyance. I imagine that there are other people who share the same sentiment.. ',1575,'DJ','2004-01-20 11:43:31');
INSERT INTO forumpost VALUES (2936,375,5,'Re: Rich edit control','The text editor is rather nice. I like it. Much better than parsing my writeups and inserting all the line breaks, < and > codes, etc.',1920,'Brian Smith','2004-01-20 12:28:48');
INSERT INTO forumpost VALUES (2937,328,6,'Re: Testing','<em>em tags<em>\r
\ni tags',1920,'Brian Smith','2004-01-20 12:30:18');
INSERT INTO forumpost VALUES (2938,375,5,'Re: Rich edit control','I found an inconsistancy between flooble and the editor. The editor uses EM (embellishment) tags for italics, but flooble requires I tags for italics.',1920,'Brian Smith','2004-01-20 12:32:43');
INSERT INTO forumpost VALUES (2939,377,4,'Re: Rich Edit Control (continued)','I don\'t like having to switch over because my mouse is \"far away\" from my keyboard. Having to move back and fourth many times when I am writing would certainly add up.',1626,'Gamer','2004-01-20 12:50:46');
INSERT INTO forumpost VALUES (2940,378,4,'uh... like, uh...','As much as I like my problems posted in the afternoon... :-)\r
\n\r
\nSquare Challenge was posted in the afterrnoon... and A Better Mousetrap was posted in the morning.\r
\n\r
\nSince the easy one should be posted in the morning, and the harder ones in the afterrnoon, shouldn\'t these have been reversed?\r
\n _/_/_/ _/ _/
\r
_/ _/ _/ _/
_/ _/ _/
_/_/_/ _/_/_/ _/_/
_/ _/ _/
_/ _/ _/ _/
_/_/_/ _/ _/
\r
\n
\n',3172,'SilverKnight','2004-01-20 14:11:44');
INSERT INTO forumpost VALUES (2941,375,5,'Re: Rich edit control','Flooble requires nothing - unfortunately the whole set of functions for these things are REALLY old and must be replaced. All it does is filter out most tags except for the allowed ones. I imagine I will still have to worry about somebody slipping in a rouge IMG ont he sly, but the rich textarea looks to be a good solution on the side of allowing users to do more.\r
\n\r
\nDJ, if you are right about the auto closing of tags, that might work.\r
\n\r
\nI\'m planning to devote some serious time to perplexus over the next few weeks, so hopefully I\'ll be able to get this done. (No small task mind you. Text areas are used in many different places, and their functionality is always slightly different.)',1,'levik','2004-01-20 16:02:53');
INSERT INTO forumpost VALUES (2942,378,4,'Re: uh... like, uh...','hey, we all make mistakes. I think thats the case here. All we can do is just keep it in mind for next time.',1072,'Alan','2004-01-20 19:04:59');
INSERT INTO forumpost VALUES (2943,378,4,'Re: uh... like, uh...','okay... my bad... I wasn\'t tryin\' to be a #$@!... thought I mighta been misunderstandin\' policy.',3172,'SilverKnight','2004-01-20 20:26:18');
INSERT INTO forumpost VALUES (2944,378,4,'Re: uh... like, uh...','There isn\'t that many problems we can push. It may have been the case that A Better Moustrap just got its third TU and so the person that did it decided to push it.',1626,'Gamer','2004-01-20 21:48:47');
INSERT INTO forumpost VALUES (2945,379,5,'Candy machine system?',' I assume that ten problems of any category are posted at a time. While this works, some categories move slower than others. Here is my proposition (although I don\'t know squat about programming, so it might not be able to work).\r
\n\r
\nTHE CANDY MACHINE SYSTEM\r
\n\r
\n At any given time, one problem from each category is up for review. In a candy machine, you don\'t just buy whichever ten types of candy are in the front . . . you can pick any one of each type of candy, and none are duplicated. \"Liars and Knights\" and \"Weights and Scales\" might have seperate sections from \"Logic Problems\", or they might all be together. This way all the problem queues would move at relatively the same speed.\r
\n Once a problem is pushed through to floobledom, a new problem of its category will fill its slot. Only a certain number of problems for each category would be available at a time. (Candy machines do not have infinite supplies.) Once a problem type is exhausted, you have to wait until the next day when all the types are \"refilled\" and ready for viewing. This way, no certain category would move too fast or too slow.\r
\n\r
\n Again, this system is just theoretical. I have absolutely no clue how it would or could work. Just a suggestion.',5033,'Captain Paradox','2004-01-20 22:00:42');
INSERT INTO forumpost VALUES (2946,379,5,'Re: Candy machine system?','I like it... But I think it\'s gonna take Levik at least 3 hours to code this... :-)',3172,'SilverKnight','2004-01-20 22:04:02');
INSERT INTO forumpost VALUES (2947,379,5,'Re: Candy machine system?',' Yeah . . . if it even can work at all. Remember, I can\'t program squat.',5033,'Captain Paradox','2004-01-21 07:41:41');
INSERT INTO forumpost VALUES (2948,364,5,'Re: How old is flooble?','Okay, my last proof of levik:\r
\n\r
\nPROOF OF LEVIK\r
\nU: if and only if U is false, levik does not exist.\r
\n\r
\nIf U is false, then a true statement would be\r
\nV: if and only if U is false, levik does exist\r
\n\r
\nIf U is true, then levik does exist, because he can\'t not exist.',5033,'Captain Paradox','2004-01-21 08:34:45');
INSERT INTO forumpost VALUES (2949,379,5,'Re: Candy machine system?','I think if this plan were implemented, certain types of problems like Algorithms and Calculus would wind up moving to the front much faster than the more numerous types like Numbers or Logic simply beacuse there are fewer of one kind of puzzle over another.',1920,'Brian Smith','2004-01-21 10:43:01');
INSERT INTO forumpost VALUES (2950,375,5,'Re: Rich edit control','The reason I\'m familiar with the one you suggested is that the same basic control is used on xanga.com, where I have a weblog. Other nice features that are that the key commands ctrl-i, -b, and -u work for formatting as they normally would within a word processor.\r
\n\r
\nI prefer to just type in the HTML tags; I imagine most people will prefer the GUI. As far as rogue tags, as you put it, I\'m sure you could change the existing filtering method to get rid of any <img> or <embed> or other potentially abusive tags, rather than delimiting the tags that you specifically want to allow. There are very good preexisting codes to do this on the PHP website, and since PHP is server-side, you can run all those checks after the control form is submitted. To me, that seems like the best way to allow full use of the test-edit box and still prevent abuse.',1575,'DJ','2004-01-21 12:02:18');
INSERT INTO forumpost VALUES (2951,368,7,'Re: Logging in for the first time!','Hi!\r
\nMe too!\r
\nA friend recommended this site, and it\'s very good indeed!',5273,'Asi','2004-01-21 12:26:46');
INSERT INTO forumpost VALUES (2952,379,5,'Re: Candy machine system?',' What if . . . only a certain number of problems were in the candy machine at a time? Then five or so Algorithms or Calculus puzzles could be reviewed until the machine ran out. It could be replenished daily.\r
\n But this might add another hour of programming. I wouldn\'t know.',5033,'Captain Paradox','2004-01-21 19:25:09');
INSERT INTO forumpost VALUES (2953,368,7,'Re: Logging in for the first time!',' Ben Beauty, just click on a category in the center of the home page that interests you, and you can start cracking those puzzles.\r
\n And have fun!',5033,'Captain Paradox','2004-01-21 19:56:20');
INSERT INTO forumpost VALUES (2954,379,5,'Re: Candy machine system?','ahhhhh.... Levik\'s pretty good at this stuff... it\'d probably only take him 30 minutes.',3172,'SilverKnight','2004-01-21 20:28:10');
INSERT INTO forumpost VALUES (2955,379,5,'Re: Candy machine system?','\"While this works, some categories move slower than others.\"\r
\n\r
\nWhy do you think this is the case? Certainly there are fewer problems in some categories than in others, but yes, we see 10 problems of all types, and they are reviewed, voted upon, and pushed in about the same order as they enter the queue, which is in turn the order in which they were submitted. If one of every fifty problems is a calculus puzzle, then one of every fifty problems we look at is a calculus problem.\r
\n\r
\nThe FIFO system is not only the simplest, but in my opinion, a better model than some complex category-based method of selecting problems for review, not to mention fairer to the people submitting problems. The changes would not only be messy to implement, but as Brian noted, would mess up the order in which problems move forward.',1575,'DJ','2004-01-21 20:31:50');
INSERT INTO forumpost VALUES (2956,380,7,'Hi....','Hi...\r
\n\r
\nI\'m a new user... found this site from a search engine.... \r
\nFound this site interesting cos puzzles recently arosed my interest.. \r
\nAs i\'m new to this site i need assistance from all...\r
\nRgds\r
\nSiva',5283,'Sivaprasad','2004-01-22 07:23:13');
INSERT INTO forumpost VALUES (2957,380,7,'Re: Hi....','Welcome Siva,\r
\nIf you want help, there\'s no shortage of folks here willing to put their two cents in.\r
\n\r
\n',2839,'FatBoy','2004-01-22 08:37:29');
INSERT INTO forumpost VALUES (2958,375,5,'Re: Rich edit control','Just so you guys don\'t think I\'ve been slacking off at this, check out the work in progress... I substituted the color picker for symbol selector, and got rid of a bunch of things we\'d never use. In the process, I managed to break keyboard handling, so I\'ll have to go back and see what it was that I did wrong.',1,'levik','2004-01-23 13:31:19');
INSERT INTO forumpost VALUES (2959,375,5,'Re: Rich edit control','Wow, that looks very good! \r
\nGlad to see that you still love us after all this time... ;)',3372,'Sam','2004-01-23 13:48:56');
INSERT INTO forumpost VALUES (2960,381,3,'Cryptography Question','Ciphers and codes are of great importance during times of warfare. Consulates regularly exchange information with their governments in coded messages. The solution of the Enigma cipher led to Hitler\'s defeat in WWII. There is a large branch of research devoted to this study especially with issues of privacy on the Internet and its relation to cryptography. The simplest cipher is a substitution of one letter for another. For example:\r
\n SYSTEMS ANALYSIS\r
\nbecomes\r
\n BKBXYLB RQRSKBPB\r
\n\r
\nwith a simple substitution of B for S, K for Y, etc. To make the following English message a bit harder to decode, the words are run together and the letters are grouped in blocks of five. punctuation has been added to help.\r
\n\r
\nFMFPW HFNAN SMFTF TFZAS MNDNQ PZUPB TFIZJ\r
\nQFW.MZ JXTSS XZQRP ZKWPB WQXTP BPWNH HNPWF\r
\nPZFZS GWNAT AUZQH NPTZA FMFPW HFDQZ LSWH.P\r
\nBWISN FFTFN SFZXQ TPTAK TAPWA FTGW,H NRTAK\r
\nPBWIZ JQFWU QJFPQ NPTAK, WAKNK TAK,NA CIBNS\r
\nSWAKT AK.WAE ZMHWW PTAKZ PBWQF PJCWA PF.\r
\n\r
\nwhat is the coded message?\r
\n\r
\n\r
\ni have absolutely no clue as to what the answer is, so don\'t ask. my friend gave this to me and after staring at it for an hour my head hurts, i thought i\'d ask you all and see what you could make of it.',1928,'The Mighty Puck','2004-01-23 15:49:09');
INSERT INTO forumpost VALUES (2961,372,7,'Re: Hello','Hi there, I found you by searching for \"logic problems\" it\'s a great site. I wanted to know if submitted problems went through some sort of review process before they were approved for posting. Also, is there some time frame for posting an official solution to a problem?',5267,'cogitater','2004-01-24 04:05:33');
INSERT INTO forumpost VALUES (2962,372,7,'Re: Hello',' Usually, if somebody submits a problem, it will appear on the site before its solution. The solution follows after a few days.\r
\n Yes, puzzles are reviewed everyday by journeymen and scholars (two higher ranks of flooble) or by levik, the director. Ten problems are able to be voted on per day, but only one or two are posted daily.\r
\n Keep submitting problems, and watch any by yours truly!',5033,'Captain Paradox','2004-01-24 14:30:23');
INSERT INTO forumpost VALUES (2963,372,7,'Re: Hello',' \'Scuse me. There\'s supposed to be a \"for\" between \"watch\" and \"any\". Oops.',5033,'Captain Paradox','2004-01-24 14:31:45');
INSERT INTO forumpost VALUES (2964,372,7,'Re: Hello','Yes they do, but it\'s usually not for testing for a solution (though that happens sometimes);\r
\n\r
\nYour problem may take a while to get to the queue. During that time, check out the other problems here and make sure it\'s not a duplicate of anything! :)',1626,'Gamer','2004-01-24 18:58:18');
INSERT INTO forumpost VALUES (2965,372,7,'Re: Hello',' Yes. It\'s kind of disheartening, but I got over it.\r
\n(Sob!',5033,'Captain Paradox','2004-01-24 22:00:36');
INSERT INTO forumpost VALUES (2966,381,3,'Re: Cryptography Question',' You\'ve probably figured this out by now, but try making all the \"B\"\'s \"S\"\'s, like in the first message. Try this for all the letters in the first message. It may help.',5033,'Captain Paradox','2004-01-25 10:50:23');
INSERT INTO forumpost VALUES (2967,381,3,'Re: Cryptography Question','I beilieve I\'ve seen this before. It was part of a message incoded on some famous cryptogropher\'s stone (Not to sure what type of stone, commemoration, tombstone etc) And to this day leading experts in the world have only decoded the first part. Then again I could be wrong and be thinking of something else.',1072,'Alan','2004-01-25 18:22:21');
INSERT INTO forumpost VALUES (2968,382,7,'Any genetic puzzlers?','Hey everyone (what an original comment), I\'m obviously new here and wondered if anyone else here is into the idea of solving problems by using genetic algorithms? I enjoy genetic programming and am continuosly looking for problems (particularly game strategy problems) suitable for solving using GAs. Anyways... Cheers :)',5345,'Rawlyn','2004-01-26 20:23:23');
INSERT INTO forumpost VALUES (2969,382,7,'Re: Any genetic puzzlers?','Can you give us an example of a logical puzzle that could be solved using a GA? I\'ve used GAs a lot, but only in AI research for modeling evolutionary systems. I\'d be interested if you had a flooble-like puzzle that could be solved with one.',3372,'Sam','2004-01-27 11:34:36');
INSERT INTO forumpost VALUES (2970,382,7,'Re: Any genetic puzzlers?','I\'m not well versed with GAs... but my (admittedly limited) understanding is that they are not well suited to find the (guaranteed) best solution to something, but rather, they are well suited to finding a very good answer to something, when we are looking for a \'close to perfect\' solution.\r
\n\r
\nI suppose they might help with the well known traveling salesman problem, but I doubt they\'d be efficient at finding the solution to On Average, Alphanumeric Ambiguity, or Truncated Cone....\r
\n\r
\n(Not to mention, I don\'t think GAs generally provide a proof that the solution *is* the best solution).',3172,'SilverKnight','2004-01-27 11:43:48');
INSERT INTO forumpost VALUES (2971,383,7,'No Subject','hi everyone.',5361,'Sandeep','2004-01-27 14:17:31');
INSERT INTO forumpost VALUES (2972,372,7,'Re: Hello','Thanks Captain and gamer for the helpful information. I\'ve only had time to do a couple of logic problems. One was gamer\'s \" timely manner\". It was enjoyable and challenging. As I was doing it I wondered if a reviewer checked how much thought and care went into the phrasing of the submitted problems. Gamer\'s use of the words \"notice\", \"know\" and \"came in\" (as opposed to \"went in\") were critical to my initial determination that B had to have personally observed the order of arrival from inside and therefore had to be either first or second to arrive. If someone submitted a problem with less precise clues, would a reviewer\'s catch it? In other words when we start a problem, are we assured that there are sufficient precise clues to lead us to the solution, or could we get stuck working on a problem in which the given clues would be insufficient to allow us to reach a correct answer?',NULL,'cogitater','2004-01-27 16:41:40');
INSERT INTO forumpost VALUES (2973,372,7,'Re: Hello','Cogitater,\r
\n\r
\nIn answer to your questions, I will direct you to this earlier post.\r
\n\r
\nIt is an excerpt, from the the book of Levikus, beginning at chapter 2, verse 1.\r
\n\r
\nI encourage you to read it carefully.',3172,'SilverKnight','2004-01-27 17:16:15');
INSERT INTO forumpost VALUES (2974,381,3,'Re: Cryptography Question','I don\'t have an hour to spend staring at it right now, but a basic cryptography course suggests you deal with substitution codes by counting the number of each of the letters in the message. It\'s been a while, so I\'ve forgotten the statistics, but research has shown that certain letters are used a certain % of the time, ie e is used more than any other letter. t, a, s are high on the list. There is a chart setting all letters forth in their order of usage. After you\'ve counted the letters in your message you attempt to correlate them with the statistical data. I.e. if z was used the most times, it is the likely substitute for e. You set up two parallel lines, the top one being the alphabet in its normal order and the second being the probable substitutions. The simplest codes involve shifting the second line right or left or reversing the alphabet etc. Book codes are more difficult unless you have some clues as to what lines in what book are used as a substitute alphabet. Completely random codes are the most difficult and are usually solved by trial and error process. Now that you are armed with all of this unrequested wisdom, go forth and solve your problem.',5267,'cogitater','2004-01-28 02:40:21');
INSERT INTO forumpost VALUES (2975,372,7,'Re: Hello','hi, all............i\'m new to the site\r
\n',5341,'bacchus','2004-01-28 16:58:11');
INSERT INTO forumpost VALUES (2976,372,7,'Re: Hello','guess now is probably not a good time as no one seems to be around. will try you all later tonite\r
\n',5341,'bacchus','2004-01-28 17:01:29');
INSERT INTO forumpost VALUES (2977,382,7,'Re: Any genetic puzzlers?','As you point out SilverKnight, a GA will never come up with a proof. Their basic usage is in optimization (a la Travelling Salesman), and so far the only flooble puzzle I\'ve set a GA to work on is your own \"How many points?\" post. It quickly gave a 17 point solution (each \"gene\" containing 17 real valued numbers) but obviously there is no point continuing... I\'ve also used GA\'s to come up with a winning stratgy for the Prisoner\'s Dilemma. In that it was a case of evolving an optimised set of rules to play by.\r
\n\r
\nI understand that GA\'s a far from suitable for most flooble puzzles, but I\'m not interested in most - only the ones that can be used to hone my GA skills :P\r
\n\r
\nPeace,\r
\nRawlyn.',5345,'Rawlyn','2004-01-28 20:16:01');
INSERT INTO forumpost VALUES (2978,375,5,'Re: Rich edit control','Thanks for the hard work Levik. Another one of these FREE rich edit controlers for text area can be found at\r
\n\r
\nhttp://www.interactivetools.com/products/htmlarea/\r
\n\r
\nI\'ve never used it specifically, but their other products are wonderful. Just wanted to give you a choice in case one was harder to implement/modify than the other.',1112,'Greg','2004-01-29 01:39:45');
INSERT INTO forumpost VALUES (2979,384,4,'\"newest problem\" addition','As I check Flooble throughout the day, I find myself often wondering... \"How many new comments have been posted, since the last time I logged on?\".\r
\n\r
\nAs you probably know, the scope of \'new\' comments is 24 hours. So, I might be logged on at 3:00pm and notice that there are 23 \'New Comments\'. Then I might come back at 5:00pm and I see that there are 21 \'New Comments\'. I cannot immediately tell if 2 comments \'fell out of scope\' or, perhaps, 4 comments \'fell out of scope\' but 2 new comments were submitted.\r
\n\r
\nWell, we\'ve discussed the difficulty that Levik would have to implement that kind of change (storing for each user, the last time he looked at comments, for example, and performing the calculation every time the user checks for \'new\' comments). This seems overkill.\r
\n\r
\nBut, one thing that might be easy for Levik to implement is a display that shows \'new comments for the day\'. And this would always just calculate the number of new comments since midnight. This would not be keyed to any user. But what it *would* give is the ability to see, at a glance, if new postings exist.\r
\n\r
\nSo, to go back to my earlier example.... at 3:00pm, I might see that there are 23 \'New Comments\' and there are 15 \'Comments Submitted Today\'. Then when I come back at 5:00pm, I see that there are 21 \'New Comments\' and there are 18 \'Comments Submitted Today\'.\r
\n\r
\nI would immediately know that there have been 3 comments submitted since I last logged on.\r
\n\r
\n(If I cared to calculate it... and I remembered the number of \'new comments\' from earlier, I would realize that 5 comments went \'out of new scope\'... but this is incidental.)\r
\n\r
\nOne nice thing about it, is that it would be relatively easy for Levik to implement (so he tells me).\r
\n________________________________\r
\n\r
\nP.S. I would think this would be in addition to the \'New Comments\' button... it could be another button or just a display somewhere.',3172,'SilverKnight','2004-01-29 02:31:02');
INSERT INTO forumpost VALUES (2980,382,7,'Re: Any genetic puzzlers?','You may want to take a look at \"Fill the Grid\".',1920,'Brian Smith','2004-01-29 10:00:31');
INSERT INTO forumpost VALUES (2981,384,4,'Re:','Or, in the parentheses just put the number of new comments in the past 24 hours, and then the number since midnight, like New Comments(7/4) or something similar. The same kind of thing could be done to the Forums link on the main page. Plus, it doesn\'t seem like that would be much more difficult to implement (maybe even easier) than finding all comments in the past 24 hours.',1575,'DJ','2004-01-29 12:28:02');
INSERT INTO forumpost VALUES (2982,384,4,'Re:','Sounds like a good idea. I think it would also be useful to show the system time so that it\'s clear when midnight was.',1183,'fwaff','2004-01-30 08:01:45');
INSERT INTO forumpost VALUES (2983,384,4,'Re:','good point... (Levik, btw, it appears the system time is a few minutes off... based on times of submissions.)',3172,'SilverKnight','2004-01-30 08:17:14');
INSERT INTO forumpost VALUES (2984,384,4,'Re:','Yes, It\'s now 8:50 EST and the last problem posted notation says that 8:10 was 30 minutes ago.',1301,'Charlie','2004-01-30 08:41:32');
INSERT INTO forumpost VALUES (2985,381,3,'Re: Cryptography Question','The most commonly used letters in American English are, (mostly)in order E, T, A, O, I, N, S, H, R, D, L, U.\r
\n\r
\nFor years the more \"in the know\" contestants who made it to the end of show bonus puzzle on Wheel of Fortune would choose as their \"five consonants and a vowel\" T, N, S, R, L (or occassionally D) and E. Later, those letters would become a given.',153,'TomM','2004-01-31 01:20:07');
INSERT INTO forumpost VALUES (2986,385,7,'Hey!','Hi everyone, just thought I\'d give my brain a workout every once in a while and this seems like a nice place to do it :)',5420,'Orfeus','2004-01-31 10:45:14');
INSERT INTO forumpost VALUES (2987,375,5,'Re: Rich edit control','I think I spotted that one while I was looking for a suitable candidate. However I didn\'t want to use it since it was IE only...\r
\n\r
\nIn any case, I made some more tweaks to the one I likned before - you can now see the result of a submission. I would appreciate it if you guys could test it out with some of your more interesting comments to see if it works well or not.\r
\n\r
\nLet me know if you run into any weirdness. If not, hopefully I will start putting it into the site around next weekend.',1,'levik','2004-01-31 12:15:13');
INSERT INTO forumpost VALUES (2988,38,7,'Re: New forum','Hi,Levik\r
\nI am a new to your site and most likely will stay as an active member. At present time I solve a lot of archive problems and comment now and then to the new ones. I also have quite a lot of my own at various level of difficulty.\r
\n\r
\n While noting the ambiguity around your question \"..how did you find this site? \" I could not resist sending you the following item:\r
\n\r
\nWaiter: And how did you find our steak, Sir? \r
\nCustomer: Well, I just browsed between the mashed potatoes and there it was..\r
\n\r
\n\r
\nPray tell ..and how did you find this joke?\r
\n\r
\nady',5285,'Ady TZIDON','2004-01-31 19:32:32');
INSERT INTO forumpost VALUES (2989,375,5,'Re: Rich edit control','In the posted comment, the strong and em tags show up with their surrounding angle brackets instead of producing bold and italic. The already-set-up bold shows as bold and the bulleted list shows up fine, rather than with unorderd list tags. So it comes out partly as if it were showing source (just for the newly entered bold and italic).',1301,'Charlie','2004-01-31 23:06:47');
INSERT INTO forumpost VALUES (2990,381,3,'Re: Cryptography Question',' Forgive me if I\'m wrong, TomM, but I read somewhere that the most common letters in the English language are: E, T, A, O, N, R, I, S, H. Of course, they mnay be already outdated.',5033,'Captain Paradox','2004-02-01 13:55:15');
INSERT INTO forumpost VALUES (2991,38,7,'Re: New forum','I\'ve been trying to rate problems to become a student but it won\'t let. Am i rating them wrong?',NULL,'Nick','2004-02-01 17:06:04');
INSERT INTO forumpost VALUES (2992,375,5,'Re: Rich edit control','Hmm... On my mozilla it uses SPAN for all the styling, so I didn\'t bother \"allowing\" STRONG and EM. \r
\n\r
\nI\'m going to enable them now, let me know if the results come out any better.',1,'levik','2004-02-01 18:05:46');
INSERT INTO forumpost VALUES (2993,375,5,'Re: Rich edit control','In the spirit of disclosure, there is a list of allowable tags, some of them must be closed, some don\'t need to be. For every tag that must be closed (such as PRE) the validator will keep count of the open and closed tags in the submitted text. If at the end they don\'t match up, a required number of closing tags will be appended.\r
\n\r
\nHere are the allowed tags as of now (Must close tags with a \"*\"):\r
\n\r
\nA*\r
\nB*\r
\nBR\r
\nI*\r
\nTT*\r
\nP\r
\nPRE*\r
\nLI\r
\nUL*\r
\nOL*\r
\nSPAN*\r
\nSTRONG*\r
\nEM*\r
\nDIV* (just realized that DIV is used for indentation)',1,'levik','2004-02-01 18:15:59');
INSERT INTO forumpost VALUES (2994,375,5,'Re: Rich edit control','It looks good for the bold and italic, except that clicking on a button such as that (to precede typing bold/italic -- or non-bold after bold/italic) most of the time removes the focus from the text box, rather than allow continuation of the typing in the new face. When swiping previously typed text this isn\'t too important, but if one is going along typing, and wants to prepare for bold by clicking the button, having the focus lost from the text box is disconcerting.\r
\n\r
\n(By the way, the title bar says Rich Tect Edit Demo rather than Rich Text Edit Demo.)',1301,'Charlie','2004-02-01 19:43:58');
INSERT INTO forumpost VALUES (2995,370,7,'Re: We\'d love to know how you found us!','I found this site by typing the word \" Logic \" on the address locator or keyword and I followed a lot of links that ultimately brought me to this page where I\'m writing right now .That\'s how I found it. Why I found you?...Now that\'s a different angle of arguement. If you email ( KuyaArdy@aol.com ) me I\'m more that willing to discuss the whys.',5448,'Florentino','2004-02-02 06:29:02');
INSERT INTO forumpost VALUES (2996,38,7,'Re: New forum','That depends, Nick. How have you been rating them?\r
\n\r
\nThe standard method for rating problems is to go to the problems page (if you can read the problem and you\'re not on the home page, you\'re there...) then click the rating that you think the problem is worth (i.e. if you loved it, give it 5; if you loathed it, give it 1). \r
\n\r
\nI think you\'ll be able to work it out!',3136,'Popstar Dave','2004-02-02 07:10:51');
INSERT INTO forumpost VALUES (2997,38,7,'Re: New forum','Be sure you are logged in, in order to see the Rate this problem: 1 2 3 4 5 notation where you can click on one of the numbers. I notice your name appears in black rather than blue on this forum, indicating you weren\'t logged in for the forum posting; perhaps you weren\'t logged in for the puzzle viewing.',1301,'Charlie','2004-02-02 08:42:01');
INSERT INTO forumpost VALUES (2998,381,3,'Re: Cryptography Question','Well there is a method to solving this and cogitater mentioned the beginning, but that is usually not enough. Like in the case of the code above it is usual that two or even three letters in the code are represented equally so further analysis is needed (F and W here) - you see how often are they around other letters, make a table really because for example letter E can appear before or after any other letter really, while consonants like T rarely appear before or after B, D, G, J. Also once you are fairly certain which letter represents E you can see by looking which letter is most common before but almost never after E, that would represent H. Then it is more like guessing the words for starters, more difficult in this case since they have been grouped in fives.',5420,'Orfeus','2004-02-02 10:10:30');
INSERT INTO forumpost VALUES (2999,375,5,'Re: Rich edit control','You could also include <sup> and <sub>. Also, while <ol> is allowed, you removed that button from the toolbar..',1575,'DJ','2004-02-02 10:48:01');
INSERT INTO forumpost VALUES (3000,386,4,'Congratulations to our newest Apprentice','Welcome Tristan!',3172,'SilverKnight','2004-02-02 10:49:26');
INSERT INTO forumpost VALUES (3001,381,3,'Re: Cryptography Question','Also the difficulty is much increased is the person deliberately misspelled the message. Simple substitutions like \"taht\" for \"that,\" or throwing in a few numbers for letters, make automated decryptors very sad.',3372,'Sam','2004-02-02 14:28:08');
INSERT INTO forumpost VALUES (3002,386,4,'Re: Congratulations to our newest Apprentice','Surprise! Did you know this board existed? It\'s where we talk about secret things :)\r
\n\r
\nWelcome anyway! I suppose you will become a journeyman soon with the problems you are putting out. :)',1626,'Gamer','2004-02-02 15:02:05');
INSERT INTO forumpost VALUES (3003,375,5,'Re: Rich edit control','Charlie - I changed the behavior to \"focus-back\" on the edit area after one of the buttons is pressed - hopefully it will work, let me know if there are other \"behavioral\" issues.\r
\n\r
\nDJ - good catch on the ***script tags. Will go add them now. About the OL, I didn\'t think it needed a button. UL is by far the more used, and anyone needing OL will probably know what they\'re doing enough to go and add one manually. Like you :)',1,'levik','2004-02-02 23:49:48');
INSERT INTO forumpost VALUES (3004,387,5,'Recently Posted Solution','Not sure if anyone has noticed, but there is now a list of 5 problems with the most recently posted solutions shown on the bottom of the front page.\r
\n\r
\nThis was a feature someone has requested (I forget who it was) and I thought was a very good idea. \r
\n\r
\nComments?',1,'levik','2004-02-03 14:00:31');
INSERT INTO forumpost VALUES (3005,387,5,'Re: Recently Posted Solution','I give it a \'thumbs up\'. But you\'re right, I hadn\'t noticed.... I don\'t often have occasion to scroll down that far.',3172,'SilverKnight','2004-02-03 15:04:21');
INSERT INTO forumpost VALUES (3006,387,5,'Re: Recently Posted Solution','Well, hopefully this will give some people more of an incentive to scroll down and check out any new problems they may have missed. \r
\n\r
\nAlso, maybe this will speed up the rate of solution postings.',1,'levik','2004-02-03 16:34:36');
INSERT INTO forumpost VALUES (3007,386,4,'Re: Congratulations to our newest Apprentice','The existence of this board had come to my knowledge before, but nobody really said what you discussed in here! How exciting it will be to find out right now!',3558,'Tristan','2004-02-03 18:31:01');
INSERT INTO forumpost VALUES (3008,386,4,'Re: Congratulations to our newest Apprentice','Wow! This is even more exciting than I thought!',3558,'Tristan','2004-02-03 19:15:55');
INSERT INTO forumpost VALUES (3009,387,5,'Re: Recently Posted Solution','Yes, I do think it\'s a very good feature.\r
\n\r
\nBTW, The solution to two of my puzzles are ready, but they haven\'t been posted. I doubt they will create much more discussion weeks after their posting. I was wondering if I have the power to post the solutions, and I just don\'t know it. If I do, telling us all would also speed up the rate of solution postings.',3558,'Tristan','2004-02-03 19:37:17');
INSERT INTO forumpost VALUES (3010,387,5,'Re: Recently Posted Solution','I believe you have the ability to push them. If you go to the problem page of a problem you submitted, there should be a link there that lets you edit the solution. On that page you should see an option to make the solution public.',1,'levik','2004-02-03 20:07:25');
INSERT INTO forumpost VALUES (3011,387,5,'Re: Recently Posted Solution','I can\'t find it. Are you sure that\'s not just a journeyman feature?',3558,'Tristan','2004-02-03 20:18:21');
INSERT INTO forumpost VALUES (3012,387,5,'Re: Recently Posted Solution','You know what, you\'re right. My bad :)\r
\n\r
\nLet me go take a look at those solutions of yours then :)',1,'levik','2004-02-03 22:13:57');
INSERT INTO forumpost VALUES (3013,387,5,'Re: Recently Posted Solution','Er, you posted the solutions to the latest two puzzles. I was really referring to the earliest two puzzles (\"Extraterrestrial Primes\" and \"Game of Luck\").',3558,'Tristan','2004-02-03 23:15:24');
INSERT INTO forumpost VALUES (3014,387,5,'Re: Recently Posted Solution','Whoa... I\'m really showing some crappy webmastering right here...\r
\n\r
\nI just fixed that... sorry for the premature exposure.',1,'levik','2004-02-04 09:58:56');
INSERT INTO forumpost VALUES (3015,314,3,'Re: Riddle...','Just for the heck of it, the man behind bars was his son.
Besides, there are lots of ways to word this particular riddle. I once heard it as a man looking at a Wanted poster who spoke the rhyme to another man questioning as to who it was.
The simple way to think about this riddle is to realize that since he has no brothers or sisters, then the part that stated \"is my father\'s son,\" can be reworded to \"is me.\" I always liked that riddle. Sorry if I wasn\'t supposed to say anything, but this is my first forum posting.',5407,'Ashley','2004-02-04 11:21:47');
INSERT INTO forumpost VALUES (3016,373,3,'Re: I dont know what to do.','I\'m kinda new to this site as well, but I\'ve come to realize that the general purpose of Flooble allows you to read and solve challenging trivia questions, riddles, and the occasional joke. You can rate them and post comments as well as submit your own problems for other people to answer once you increase your rank once.
I\'ll check out your blog later since I\'m actually in third period and I need to get back to the assignment, lol.',5407,'Ashley','2004-02-04 11:29:01');
INSERT INTO forumpost VALUES (3017,38,7,'Re: New forum','Hey guys\r
\n',5487,'Peter Lunts','2004-02-04 19:37:10');
INSERT INTO forumpost VALUES (3018,38,7,'Re: New forum','I wanted to ask what do you have to do to reply to problems and be able to post your own. If anybody knows please tell me.',5487,'Peter Lunts','2004-02-04 19:39:25');
INSERT INTO forumpost VALUES (3019,388,3,'No Subject',' My pending problems (4) have stayed at their queue postition for two weeks or so, except for 2 which have moved back.\r
\n This is really me asking for an inside surveillance job. Have you Journeymen noticed if the rated problems are making it through to flooble kind of slowly? I (being a Student) don\'t have the position to check.\r
\n Also, what on earth is the queue weight about?',5033,'Captain Paradox','2004-02-04 19:56:55');
INSERT INTO forumpost VALUES (3020,38,7,'Re: New forum','Also, how do you know if you\'ve rated a problem correctly or rated it at all?',5487,'Peter Lunts','2004-02-04 19:57:10');
INSERT INTO forumpost VALUES (3021,38,7,'Re: New forum','If you want to post comments, click on the \"post a comment\" link next to the heading \"Comments.\" If you want to post a puzzle, you first have to post three comments and rate a puzzle to become student rank. We prefer that your comments don\'t include other puzzles or insults. \r
\n\r
\nWhen you submit a puzzle, you will most likely wait a couple of months because so many submitted puzzles are waiting in queue. Be patient and use the extra time to make sure the puzzle isn\'t a repeat or to submit more puzzles.\r
\n\r
\nTo rate a problem, look at Charlie\'s above comment. You know you rated a problem when the words \"Rate this problem\" stop shimmering. Also, if you click on your name, you can see how many puzzles you\'ve rated. You apparently rated one already.',3558,'Tristan','2004-02-04 20:13:07');
INSERT INTO forumpost VALUES (3022,38,7,'Re: New forum','Thanks Tristan. I have a few Q\'s though. When you say \"puzzle\" do you mean any type of problem or only a problem that falls into the \"Puzzle\" category? Also, can I take my problem/puzzle of the queue list? ',5487,'Peter Lunts','2004-02-04 20:27:12');
INSERT INTO forumpost VALUES (3023,388,3,'Re: No Subject','Queue weight, or QW was also asked about here. Basically, all puzzles are sorted first by QW, and puzzles with the same QW are sorted by date submitted. Each person has QW1 for the earliest submitted two puzzles, QW2 for the next 2 and so on. \r
\n\r
\nThe way the \"approximate queue position\" is calculated, the numbers don\'t really tell that much. It does not show the speed, just the position (it might jump forward some days and move back others). The speed is slow because the QW makes your puzzle seem further than it really is sometimes. Also, we limit the number of puzzles by two per weekday, one per day on weekends. \r
\n\r
\nThis topic has been thoroughly discussed. Just look at the long thread here or the even longer thread here.',3558,'Tristan','2004-02-04 20:31:07');
INSERT INTO forumpost VALUES (3024,38,7,'Re: New forum','How many times can you rate a specific problem and how do you know if you\'ve already rated it or not?',5487,'Peter Lunts','2004-02-04 20:32:43');
INSERT INTO forumpost VALUES (3025,386,4,'Re: Congratulations to our newest Apprentice','If you think this is exciting then you need to get out more. ;-)',1183,'fwaff','2004-02-05 07:55:08');
INSERT INTO forumpost VALUES (3026,389,4,'Problem precision','\"Thirty two barbarians\" has had a lot of discussion. Unfortunately, most of it has been misdirected (and hence less valuable than it could have been).\r
\n\r
\nBecause of the lack of precision in the problem, and more importantly the lack of responses and clarity when questions were asked in the discussion, many apparently valid solutions occur.\r
\n\r
\nI see in Gamer\'s proposed solution, that \'11\' is the desired answer, but clearly cases can be made for fewer (or more) than that.\r
\n\r
\nWith some problems, ambiguity is a key component. This is not one of those problems. It is potentially very good, and with better wording it would have been.\r
\n\r
\nI encourage all Journeymen+ to be more critical about pushing problems live before they are well stated.',3172,'SilverKnight','2004-02-05 12:58:01');
INSERT INTO forumpost VALUES (3027,389,4,'Re: Problem precision','I agree .. but there seem to be many people jumping to say \"good enough,\" especially when the author is absent/slow to make corrections ..',1575,'DJ','2004-02-05 17:55:31');
INSERT INTO forumpost VALUES (3028,389,4,'Re: Problem precision','Hmmm... your \"many people\" includes me.\r
\n\r
\nI\'ll endeavor to use a more critical eye too.',3172,'SilverKnight','2004-02-05 17:59:08');
INSERT INTO forumpost VALUES (3029,389,4,'Re: Problem precision','There\'s just way too many things to say in my opinion. None of them have curvy bodies. None of the barbarians suddenly get muscle spasms. None of their gun\'s bullets split apart; none disintegrate. None of the villagers suddenly gets hit by lightning; none of them are smaller or stooped over.\r
\n\r
\nI don\'t want my problems to turn into crazy math theoroms; we take about a page to explain something we could say in a few words just because of all the people that will say aha! here\'s a loophole. Everyone knows that lining up isn\'t \"around\"; whether or not you stand behind a strange definition that\'s out of context. I haven\'t found a solution that\'s less than 11 without having about a zillion barbarians lining up, instead of around. I don\'t think there was anything else a problem except I didn\'t use a super-solid definition of around; I assumed everyone knew what \"around\" meant.\r
\n\r
\nOriginally I had said the bullets flew over people which was a mistake on my part; I should have caught that :) Other than that, I don\'t think anything else was too vague.\r
\n\r
\nI was unsure if 11 was the minimum; I had no way to prove it; that is why I haven\'t pushed the solution. Should I go ahead and put the diagram in?',1626,'Gamer','2004-02-05 19:04:47');
INSERT INTO forumpost VALUES (3030,389,4,'Re: Problem precision','Muscle spasms, lightning, and splitting bullets have nothing relevant to impart. Only the relevant information need be incorporated. But it *should* be incorporated. \r
\n\r
\nWhat\'s more, you ignored questions, specifically asking for answers and additional clarification. That they were reasonably asked is a sign of a poorly worded problem. That they were ignored... well... I don\'t understand why you ignored the questions.\r
\n_______________________\r
\n\r
\nAs for the solution, you can post it... but with your current wording, 3 is the minimum, not 11. And if you change the wording (which you may choose to do), well, then you pretty much invalidate the comments up to this point.',3172,'SilverKnight','2004-02-05 19:19:38');
INSERT INTO forumpost VALUES (3031,389,4,'Re: Problem precision','Perhaps if you say that the bullets only went over villagers\' heads, and not barbarians\'? I\'m not quite sure what you meant either.\r
\n\r
\nI think that the only people who look for loopholes like that when they shouldn\'t are people like Dan (and perhaps Penny). But I agree that it is very hard to eliminate ambiguity. As shown in my puzzles, I\'m not very good at it, but I try. It really depends on the puzzle though.',3558,'Tristan','2004-02-05 21:19:51');
INSERT INTO forumpost VALUES (3032,390,7,'hi','hey im new here...soo excited bout this site.. i juz wanna ask how do i post the puzzle a day or the tricks on my website??',5496,'Allie','2004-02-06 10:44:55');
INSERT INTO forumpost VALUES (3033,389,4,'Re: Problem precision','Like I said before, I don\'t see anything else besides lines that are a problem. Penny\'s solution was the only one under 11 that actually had barbarians somewhat around the city. (as I understood it)\r
\n\r
\nLining up in a line outside the city isn\'t going around the city. I guess I needed a rigid, confusing definition of around.',1626,'Gamer','2004-02-06 15:17:13');
INSERT INTO forumpost VALUES (3034,389,4,'Re: Problem precision','Like I said before,\r
\n\r
\nyou HAD a \"confusing definition\".... what you needed was an unconfused definition (of the problem).\r
\n_________________\r
\n\r
\nThe bottom line is... the difficulty of the problem (as you intended) seems to be that you wanted people to think \"oh... the villagers must be shot\" requiring 4-villager-lines, rather than 3-villager-lines. And I *guess* this is why you ignored the questions/issues in the comments. (You haven\'t addressed why you did this.)\r
\n\r
\nThen you wanted people to interpret \"position themselves around the city\", as at least 4 or 5 different directional points (as seen from the center of the city).\r
\n\r
\nClearly (well it\'s clearer now), ambiguity is what you were RELYING on for this problem.\r
\n\r
\nSo, to quote a comment from the problem itself: \"if that is the case, the problem should be in \'tricks\'...\".',3172,'SilverKnight','2004-02-06 15:45:55');
INSERT INTO forumpost VALUES (3035,384,4,'Re:','oh... perhaps this is obvious... but it would be useful to have the same \"new postings today number\" for forums as well.',3172,'SilverKnight','2004-02-06 18:16:32');
INSERT INTO forumpost VALUES (3036,312,5,'Re: Base 1 and Base 0','I was reading recently about working with pure sets, that is, sets of sets of set etc of nothing. Would this count as a base-0 system?\r
\n\r
\nAlso, surely the easy way to explain base-1 is the word \"tally\"?\r
\n\r
\nPeace,\r
\nRawlyn.',5345,'Rawlyn','2004-02-06 18:17:12');
INSERT INTO forumpost VALUES (3037,391,5,'Question about submitting puzzles','I wonder if someone can tell me a bit about how the system of submitting a problem works. I saw an interesting little bit of algebra recently and thought it might be of interest to the group. Only thing is this - I don\'t have a solution, and if there is a solution, it\'s more of a question of philosophy than math, yet the problem is mostly in the form of equations.\r
\n\r
\nAnyways, which category should I post the problem to, and does it matter that it\'s just a good starter for debate rather than a solveable \"puzzle\"?\r
\nAlso, I don\'t want to post something that\'s been posted before - will someone check this when I submit?\r
\n\r
\nPeace,\r
\nRawlyn.',5345,'Rawlyn','2004-02-06 18:23:44');
INSERT INTO forumpost VALUES (3038,391,5,'Re: Question about submitting puzzles','Rawlyn,\r
\n\r
\nWe can always change the category in the queue (and we sometimes do, if necessary), so don\'t give it too much thought.\r
\n\r
\nAs for posting something that\'s been posted before... well... the combined memory of the Journeymen+ is pretty effective at weeding these out, but nevertheless, you could save yourself a LOT of unnecessary waiting, and save us some time if you go through Flooble\'s archives. (Not to mention, you\'ll probably come across some pretty decent problems.)\r
\n\r
\nAs for the way the system works... I would suggest you read through the forums starting right here, then read this... and then you can graduate to this.\r
\n\r
\nAnd hopefully, you\'ll soon be making your own contributions.\r
\n\r
\n- SK',3172,'SilverKnight','2004-02-06 18:41:04');
INSERT INTO forumpost VALUES (3039,388,3,'Re: No Subject','The QW was instituted after one member submitted a huge pile of puzzles at once. It allowed all of the other problems to slip past some of his, so that it would not take a year or more for other posters\' problems to appear.\r
\n\r
\nUnfortunately, other heavy submitters\' puzzles began to back up as well. Since their oldest puzzles are now far older than any others, most of thi time the queue has eight to ten puzzles by the same five or six \"super-contributors\" and everyone else\'s are almost as stagnant as before QW was instituted. If your approximate queue position is over fifty, you should probably add another 100-150 for the QW 2+ puzzles that will jump ahead during the nightly re-calcs before your puzzle approaches the \"hot ten\" ',153,'TomM','2004-02-06 22:09:13');
INSERT INTO forumpost VALUES (3040,388,3,'Re: No Subject','Yes indeed... My closest problem (QW 1) has been sitting at 59 for well over two weeks now - it\'s mighty frustrating. There have been many discussions on whether the current system is the best possible one, but it\'s very difficult to change the status quo so I doubt anything can be done. You just have to be patient.',3372,'Sam','2004-02-07 00:55:36');
INSERT INTO forumpost VALUES (3041,392,7,'Hello!','Thats right !!\r
\nKeep your way!!\r
\nBye!!',5531,'kodi','2004-02-07 09:26:40');
INSERT INTO forumpost VALUES (3042,391,5,'Re: Question about submitting puzzles','If you mailed your problem to someone, maybe they could tell you if it is already on the site or not. Otherwise it will take a while in the queue, but still be worth it.',1626,'Gamer','2004-02-07 13:53:44');
INSERT INTO forumpost VALUES (3043,393,7,'Logic Puzzle Got Me Stumped','Need help solving a logic puzzle, any suggestions',5541,'Gary','2004-02-07 20:59:43');
INSERT INTO forumpost VALUES (3044,393,7,'Re: Logic Puzzle Got Me Stumped','You can mail it to someone, me included, but please don\'t post it here. :)\r
\n',1626,'Gamer','2004-02-08 18:03:32');
INSERT INTO forumpost VALUES (3045,394,7,'I am New Hello','Hello I am new just wanted to say hi and hope I can make some friends here!\r
\n',5557,'Cheryl Barcus','2004-02-09 01:29:27');
INSERT INTO forumpost VALUES (3046,395,6,'four times???','Can you make 13 by using 4 four times, no power(except 4,4) you can use brackets.',5571,'frank','2004-02-10 01:56:48');
INSERT INTO forumpost VALUES (3047,396,7,'hello','Hello every one, where can i submit some questions and can some one please give the steps\r
\n\r
\n\r
\nmany thaanks!',5571,'frank','2004-02-10 02:01:44');
INSERT INTO forumpost VALUES (3048,395,6,'Re: four times???','The forums are not for posting puzzles. Click on Submit a Problem on the Home page of this site.',1301,'Charlie','2004-02-10 08:37:03');
INSERT INTO forumpost VALUES (3049,395,6,'Re: four times???','This puzzle is well known enough that typing \"four 4\" into google brings up pages with the solutions for 1 to 100.',1920,'Brian Smith','2004-02-10 11:12:29');
INSERT INTO forumpost VALUES (3050,397,7,'I HAVE A PROBLEM!!!!!!!!! LOL','CAN YOU PLEASE HELP ME WITH THIS ..\r
\nIM STUMPED AS STUMPED CAN BE :S\r
\n\r
\n\r
\nThere are three words in the English language that end in \"gry\". \r
\nONE is angry and the other is hungry. Everyone knows what the third ONE means and what it stands for. Everyone uses them everyday, and if you listened very carefully, I\'ve given you the third word. \r
\n\r
\nWhat is it? _______gry? \r
\n',5577,'sammie','2004-02-10 17:00:13');
INSERT INTO forumpost VALUES (3051,397,7,'Re: I HAVE A PROBLEM!!!!!!!!! LOL','BTW I FOUND THIS SITE OFF OF ASK.COM\r
\nI TYPED IN RIDDLES AND WENT TO RIDDLES AND PUZZLES ON THE RIGHT MENU\r
\nAND WENT TO YOUR SITE FROM THERE ;)',5577,'sammie','2004-02-10 17:01:25');
INSERT INTO forumpost VALUES (3052,397,7,'Re: I HAVE A PROBLEM!!!!!!!!! LOL','Sammie, in the future, please do not post problems in the forums. However, this is a common problem, and is all over the internet.\r
\n\r
\nCheck out this link and be sure to read the WHOLE page... \r
\n _/_/_/ _/ _/
',3172,'SilverKnight','2004-02-10 17:55:11');
INSERT INTO forumpost VALUES (3053,395,6,'Hmmm','Hmmm, I can\'t say I agree with the answer though...\r
_/ _/ _/ _/
_/ _/ _/
_/_/_/ _/_/_/ _/_/
_/ _/ _/
_/ _/ _/ _/
_/_/_/ _/ _/
\r
\n
\nIf the only power that is allowed is 4^4, why on earth is Sqrt allowed? Square root is mearly short hand for 4^(1/2), no? Are cube roots allowed, fifth roots?\r
\n\r
\nUmmmm... not that I\'m discussing a puzzle in the forum. I wouldn\'t do that.',3372,'Sam','2004-02-10 19:42:05');
INSERT INTO forumpost VALUES (3054,397,7,'Re: I HAVE A PROBLEM!!!!!!!!! LOL','This has already been mentioned in the forums on this site as well, check it out here.\r
\n\r
\nAlso, you have misquoted the puzzle in a way that makes it impossible to answer. The real version reads as follows:\r
\n\r
\n\"Think of words ending in -gry. Angry and hungry are two of them. There are only three words in the English language. What is the third word? The word is something that everyone uses every day. If you have listened \r
\ncarefully, I have already told you what it is.\"\r
\n\r
\n(then try ignoring the first two sentences)',1575,'DJ','2004-02-10 20:10:52');
INSERT INTO forumpost VALUES (3055,395,6,'Re: four times???','The point is that no numeral (other than the four 4\'s) is used in the expression. 4^4 uses two of the 4\'s but no other numeral. 4^3 uses a forbidden 3. The radical symbol can be used, but only for Square root (which is the symbol alone) or Quartic root (which uses up one of the 4\'s)',153,'TomM','2004-02-11 14:26:52');
INSERT INTO forumpost VALUES (3056,397,7,'Re: I HAVE A PROBLEM!!!!!!!!! LOL','ok let me start off by saying ...\r
\n I SORRRRRRRRRRRRRRRRRRRRY :D:D\r
\nand now the TYYYYYYYYY part lol\r
\ni was going nuts .. ive not heard that before and was pulling my hair out ..\r
\nyes seriously ... \r
\nok now can i ask what is allowed to be posted here? \r
\n:) Sammie',5577,'sammie','2004-02-12 03:43:10');
INSERT INTO forumpost VALUES (3057,397,7,'Re: I HAVE A PROBLEM!!!!!!!!! LOL','Sammie,\r
\n\r
\nThe various forums have various generic topics, but I suggest you start by reading the FAQ.\r
\n\r
\n- SK',3172,'SilverKnight','2004-02-12 04:11:31');
INSERT INTO forumpost VALUES (3058,384,4,'Re:','It was only obvious once DJ had mentioned it, but thanks anyway for the extra clarification!\r
\n;-)',1183,'fwaff','2004-02-12 06:17:02');
INSERT INTO forumpost VALUES (3059,384,4,'Re:','FWIW my previous post was at 11.27am GMT so the system\'s about 10mins behind.',1183,'fwaff','2004-02-12 06:18:07');
INSERT INTO forumpost VALUES (3060,389,4,'Re: Problem precision','Going back to SK\'s original point: is this a sign that maybe the power to vote on problems is something that should be specifically awarded to individuals rather than something that happens by default once a user has 6 problems posted?',1183,'fwaff','2004-02-12 06:30:52');
INSERT INTO forumpost VALUES (3061,384,4,'Re:','Isn\'t THAT what Charlie wrote? (thanks for the extra clarification!) :-P',3172,'SilverKnight','2004-02-12 10:15:36');
INSERT INTO forumpost VALUES (3062,398,3,'Yes!',' Two of my pending problems have just moved up after a month or two! I feel ten feet tall.\r
\n Thanks to all you Journeymen, Scholars, and Directors for voting in some new material!',5033,'Captain Paradox','2004-02-15 10:33:43');
INSERT INTO forumpost VALUES (3063,384,4,'Re:','OK - here are my thoughs on this (as I have already mentioned them to SK)\r
\n\r
\nThe problem with implementing a dual \"new comment\" count is that it would be confusing. Right now the number next to the new comments link is how many comments you will see once you click the link. (This is unfortunately not so with the forums due to the access restrictions) If there were to be two numbers, one of them would be \"wrong\" from that standpoint, unless there were also two links - which I don\'t think is really needed.\r
\n\r
\nIf the majority consensus decides that the daily number is more useful than the 24h number, I can change the behavior of these links, but would rather there be one rule. The site is pretty complicated to use as it is. (Well, that\'s mostly due to the queue)',1,'levik','2004-02-15 13:00:17');
INSERT INTO forumpost VALUES (3064,399,4,'early access','give it a twirl @ perlexus.info \r
\n\r
\nlet me know what you think - please keep the URL from getting out for now.',1,'levik','2004-02-15 13:32:50');
INSERT INTO forumpost VALUES (3065,384,4,'Re:','Well.... since you asked :-) ...\r
\n\r
\nI think the \"new forum postings\" should reflect whether or not you have the access. In other words, if we\'re not logged in, or we\'re not apprentice+, then don\'t even \'count\' the postings in the library in the tally.\r
\n\r
\nAlso, one might consider putting the \"daily\" numbers in a different location either just as information, or as another button/link. Rather than trying to combine the two figures with a slash or something....\r
\n\r
\n- SK',3172,'SilverKnight','2004-02-15 16:36:51');
INSERT INTO forumpost VALUES (3066,399,4,'Re: early access','Looks good... the only think I\'ve noticed is that it seems to be using a new color scheme (style sheet?), and, of course, has a different top level domain.\r
\n\r
\nDid I miss any new functionality?\r
\n\r
\n- SK\r
\n\r
\nP.S. I noticed a few problems (including those I created images for) no longer \"meld\" with the background color, because you changed it... such as:\r
\nSphere Cube.',3172,'SilverKnight','2004-02-15 16:42:00');
INSERT INTO forumpost VALUES (3067,399,4,'Re: early access','I also added the rich text editor to comment posting/editing. I did see the color differences you spoke of, but they seem minor enough, and most of the other problem images have a border on them to begin with so it\'s not a huge issue.\r
\n\r
\nI thought that perplexus should have its own domain, and now seemed like a good time to do it. Unfortunately, .com and .net were taken :)',1,'levik','2004-02-15 16:54:25');
INSERT INTO forumpost VALUES (3068,399,4,'Re: early access','Also, most of the links people put in comments go to flooble.com/perplexus.',3558,'Tristan','2004-02-15 18:43:06');
INSERT INTO forumpost VALUES (3069,399,4,'Re: early access','ahhh.... very good point!',3172,'SilverKnight','2004-02-15 19:19:37');
INSERT INTO forumpost VALUES (3070,384,4,'Re:','The daily number would be more valuable than the 24h number, but we still need markers on the 24h forum posts, to see what\'s new if we had not logged in since well before midnight.',1301,'Charlie','2004-02-15 19:43:16');
INSERT INTO forumpost VALUES (3071,399,4,'Re: early access','I think at flooble is fine too. :) The grey background is kind of boring :N',1626,'Gamer','2004-02-15 21:02:17');
INSERT INTO forumpost VALUES (3072,399,4,'A question and a problem','What is the \"Formatting\" pulldown for? I didn\'t change it to anything. Is that why I got:\r
\n\r
\nYou have an error in your SQL syntax. Check the manual that corresponds to your MySQL server version for the right syntax to use near \'s the significance of this comment?\r
\n\r
\nActually, this is g\r
\nWarning: Cannot modify header information - headers already sent by (output started at /home/projects/perplexus/htdocs/show.php:286) in /home/projects/perplexus/htdocs/show.php on line 287\r
\n\r
\n',1301,'Charlie','2004-02-16 10:23:12');
INSERT INTO forumpost VALUES (3073,399,4,'Re: early access','Parts of the above were what I was typing. I had pressed enter twice between paragraphs, but backspaced away one of them, before continuing to type \"Actually, ...\"',1301,'Charlie','2004-02-16 10:25:13');
INSERT INTO forumpost VALUES (3074,399,4,'Re: early access','Interesting... I\'ll have to look into that.',1,'levik','2004-02-16 10:45:38');
INSERT INTO forumpost VALUES (3075,399,4,'Re: early access','Ah... I think the error was caused by a bug that forgot to escape the single quotes in the new code. See if the comment will work now...',1,'levik','2004-02-16 10:50:50');
INSERT INTO forumpost VALUES (3076,377,4,'Re: Rich Edit Control (continued)','Oh, having looked at the \"allowed\" tags, I decided to keep the button there for everybody, and instead of being lazy, implement a \"tag closing\" function - it will try and figure out every tag you used, and if a tag requires to be closed (such as PRE) but isn\'t, the closing tag is appended at the very end.\r
\n\r
\nAs such I deemed it safe... :)',1,'levik','2004-02-16 10:54:11');
INSERT INTO forumpost VALUES (3077,399,4,'Re: early access','Yes, that fixes the problem.\r
\n\r
\nBut the question remains as to what the pull-down for \"Formatting\" is, with choices \"normal\" and \"pre-formatted\".',1301,'Charlie','2004-02-16 10:59:48');
INSERT INTO forumpost VALUES (3078,399,4,'Re: early access','I don\'t really understand what it does, but they change some of the symbols. Looking at the source, \"normal\" uses &itP> and &it/P> tags. \"Pre-formatted\" uses pre tags.',3558,'Tristan','2004-02-16 14:30:01');
INSERT INTO forumpost VALUES (3079,399,4,'Re: early access','Right, I capitalize the I. That was &ItP> and &It/P>.',3558,'Tristan','2004-02-16 14:34:43');
INSERT INTO forumpost VALUES (3080,399,4,'Re: early access','That didn\'t work either, but you get the idea. I meant <',3558,'Tristan','2004-02-16 14:35:18');
INSERT INTO forumpost VALUES (3081,399,4,'Re: early access','No need to explain, I know what I did wrong. It\'s l not I or i.',3558,'Tristan','2004-02-16 14:37:28');
INSERT INTO forumpost VALUES (3082,399,4,'Re: early access','I tried producing a comment in Notepad and then pasting in the new window, including some \'s at the beginnings of lines, but no matter what selection I chose they appeared as typed rather than as spaces, except when pasted in a view as source; then I didn\'t get any paragraphing. So I had to return to the flooble perplexus to edit my comment. Does the pre-formatting, which then appears the better way to go than non-breaking spaces, apply to sections as you type them, or the whole post?',1301,'Charlie','2004-02-16 15:36:57');
INSERT INTO forumpost VALUES (3083,186,6,'Exponent more than 100','How to solve a problem with the exponent of more than 100?\r
\n e.g \r
\n 156 with exponent 100\r
\nhow to solve it\r
\n',NULL,'allan','2004-02-16 21:12:48');
INSERT INTO forumpost VALUES (3084,399,4,'Re: early access','Pre formatting puts \"PRE\" around the section. Or that\'s what it\'s supposed to do. You should be able to use spaces to format stuff in the new editor, Charlie...',1,'levik','2004-02-17 17:24:50');
INSERT INTO forumpost VALUES (3085,399,4,'Re: early access','The new replies link doesn\'t seem to be working.',3558,'Tristan','2004-02-17 18:25:10');
INSERT INTO forumpost VALUES (3086,186,6,'Re: Log?','You can always tell a computer to do it, or do it by hand. I don\'t know that there\'s any other super way. There\'s other ways to tell things about it, but if you just want to know the whole big long number you will be stuck.',1626,'Gamer','2004-02-17 19:02:10');
INSERT INTO forumpost VALUES (3087,399,4,'Re: early access','Thanks for pointing this out - it\'s now fixed.\r
\n\r
\nCharlie, to expland on my answer to you, the new rich text editor (at least on my Mozilla browser) will convert consecutive spaces into NBSPs automatically, making it easier to format stuff (that is you shouldn\'t need to post NBSP codes on your own anymore)',1,'levik','2004-02-18 09:51:48');
INSERT INTO forumpost VALUES (3088,399,4,'Re: early access','Anyway, I\'m thinking of \"throwing the switch\" this weekend (this will include updating as many links as possible, and including a redirect URL on all the pages of the old site)\r
\n\r
\nLet me know if you guys think there are issues to be ironed out before then. (Especially with the rich text editor, and anything in the way of missing files I forgot to copy, like the replies search that Tristan caught)\r
\n\r
\nIf no more problems surface in relation to the rich text edit box, I will start adding it to more areas of the site in a couple of weeks (forums would probably be first)',1,'levik','2004-02-18 11:48:56');
INSERT INTO forumpost VALUES (3089,400,5,'Queue Weighting','I\'ve just submitted a couple of problems, and then checked their status, one as a queue weight of 1, the other of 5, what does this mean? and who decides?\r
\n\r
\nBTW great site!!!!',5352,'Phil','2004-02-19 20:30:50');
INSERT INTO forumpost VALUES (3090,401,3,'For Frederico Kereki...','I don`t know how to send messages and I don`t know in which forum to post this, so... apologies to anyone who thinks this is Spam.\r
\n\r
\nNow to the subject.\r
\nI have a friend whose father is called so. Mr Kereki, do you have a daughter called Andreea?',5530,'Sandu-Dragu Vlad','2004-02-20 06:51:22');
INSERT INTO forumpost VALUES (3091,400,5,'Re: Queue Weighting','In order to prevent a few submitters from tying up the queue, so as to allow newcomers a better opportunity to advance their problems, the first two puzzles a given person has in the queue at a given time are given QW 1. The rest, I understand, have QW 2. I hadn\'t heard of QW 5. Also I don\'t know why both are not QW 1, unless there is a temporary queue weight assigned on the day you enter the puzzle. Are they the same today?\r
\n',1301,'Charlie','2004-02-20 09:07:03');
INSERT INTO forumpost VALUES (3092,400,5,'Re: Queue Weighting','BTW, the way the QW is supposed to help is that even though others may have many puzzles ahead of yours in the queue, only the ones with QW 1 appear in the voting queue, eligible for posting. As each one is posted or rejected, subsequent ones become QW 1 for that submitter, but again, only two can be such at a time for each submitter.',1301,'Charlie','2004-02-20 09:09:43');
INSERT INTO forumpost VALUES (3093,400,5,'Re: Queue Weighting','Charlie: I\'ve just checked again, they are both QW1 now, thanks for the explanation.',5352,'Phil','2004-02-20 10:03:23');
INSERT INTO forumpost VALUES (3094,394,7,'Re: I am New Hello','hi, i\'m new too. :)',NULL,'Aspiring Novice','2004-02-20 17:47:56');
INSERT INTO forumpost VALUES (3095,394,7,'Re: I am New Hello','hi everybody!',NULL,'elizabeth','2004-02-20 17:50:51');
INSERT INTO forumpost VALUES (3096,402,4,'Snooping around','I guess I really do have too much time on my hands (as fwaff observed), because I read the whole library forum. Well, I might have skipped over the more technical parts, or any paragraphs with more than 5 lines. I think I should learn to split my comments into a bunch of short paragraphs; it makes it look easier to read.\r
\n\r
\nWell anyway, what most kept me interested was the part about a certain 9 year old and a certain hacker. It was kind of like old Flooble lore, or a detective story of some kind (well, maybe not that exciting...).\r
\n\r
\nI was sort of intrigued, so I went to look for luvya\'s user information. I found it a little inconsistent with the story that he/she had last logged on only 52 days ago and his/her last comment was last July, when it really should have been April.\r
\n\r
\nSo I\'m a little disappointed because it\'s like some movie with a big plot hole here. I\'m thinking that maybe I looked at the wrong user or something and the name and log-in are just a coincidence... or maybe he/she purposely copied the username of the person I saw...',3558,'Tristan','2004-02-20 18:00:05');
INSERT INTO forumpost VALUES (3097,402,4,'Re: Snooping around','Ah... Well, so it happens that luvya emailed me explaining the whole situation - if memory serves, apparently her brother found her logged-in account on a computer they shared, and used it to look around the site, getting to know who the regulars are. He then tried a few passwords until he hit on one. Hilarity ensued. In cany case I decided to quitely allow luvya back on the site :)\r
\n\r
\nI guess she eventually lost interest and left.',1,'levik','2004-02-21 12:20:23');
INSERT INTO forumpost VALUES (3098,403,5,'perplexus dot info','I would like to introduce everyone to perplexus dot info.\r
\n\r
\nPerplexus has been so successful as part of flooble over the last couple of years that I have decided it should have its own domain. I believe that flooble\'s classification as a weblog site, and not having its own domain was holding perplexus back from reaching its true potential.\r
\n\r
\nHopefully, the new site will just work, but as with any major change, bugs can easily creep in - please feel free to bug me if anything seems amiss.\r
\n\r
\nThe first of the new features on the new site is the use of Rich Text editor for posting and editing problem comments - if you have IE 5.5 or later, or Mozilla 1.3 or later (including Firebird/Firefox after 6.1) you should be able to use the new rich text edit forms.\r
\n\r
\nLet me know what you think.',1,'levik','2004-02-21 15:31:51');
INSERT INTO forumpost VALUES (3099,403,5,'Re: perplexus dot info',' Levik - love the new look! The logo is pretty nice too. How long did it take to program all of this new stuff?\r
\n Keep on truckin\'!',5033,'Captain Paradox','2004-02-21 22:12:51');
INSERT INTO forumpost VALUES (3100,403,5,'Re: perplexus dot info','Wow - great job!!\r
\nTyping flooble.com/perplexus has gotten so well hard-wired in my motor cortex that it\'ll take me a few weeks to be able to write perplexus.info, but I\'m sure I\'ll get there in the end...',3372,'Sam','2004-02-22 03:01:24');
INSERT INTO forumpost VALUES (3101,403,5,'Re: perplexus dot info','tell me about it :)\r
\n\r
\nI pretty much only put a in link to the equivalent page on the new domain into the header of the old site for my own use :) But you\'re welcome to take advantage of it too :)',1,'levik','2004-02-22 04:06:55');
INSERT INTO forumpost VALUES (3102,404,5,'Changing problems:','In \"looking for n\", the problem was (in my opinion at least) to easy, so it was spiced up and made harder. However, this wasn\'t the submitter\'s intent. I think that it should be listed somewhere that your problem can get changed, and will if the problem\'s too easy, too hard, or the wording is hard.',1626,'Gamer','2004-02-22 19:40:31');
INSERT INTO forumpost VALUES (3103,404,5,'Re: Changing problems:','I don\'t know which problem you\'re talking about.',3558,'Tristan','2004-02-22 22:39:56');
INSERT INTO forumpost VALUES (3104,404,5,'Re: Changing problems:','(Shouldn\'t this discussion have gone in the library, since not everyone can see the waiting Queue? On second thought, no. It is better here, so all submitters can have a say in the discussion of what happens to their puzzles.)\r
\n\r
\nAs I recall, the ability to change someone else\'s puzzle was added in order to allow a good puzzle that was poorly worded to be \"fixed\" when the original poster has not been around. \r
\n\r
\nThat ability should be used sparingly. If the owner of the puzzle is around, suggest changes or improvements but leave the actual changes to him. \r
\n\r
\nEven on those occassions where it is necessary to go in and fix it, it should not be changed into a different problem altogether. The person whose name is on the puzzle, the one who will be blamed if the solution is now incomplete, or does not make sense, should still be able to recognize it. ',153,'TomM','2004-02-23 00:09:35');
INSERT INTO forumpost VALUES (3105,399,4,'Re: early access','What about search engines?! Typing \'perplexus\' into a search engine finds a pointer to the old site, but not the new one.',1920,'Brian Smith','2004-02-23 10:18:31');
INSERT INTO forumpost VALUES (3106,399,4,'Re: early access','I *think* there is a metatag... that indicates to webcrawlers... that a site is moving to another URL... I wish I could remember what it is.\r
\n\r
\n(But, supposedly, you update the old page, and resubmit... or wait for crawlers to come by again.)',3172,'SilverKnight','2004-02-23 10:47:05');
INSERT INTO forumpost VALUES (3107,404,5,'Re: Changing problems:','Gamer, you trivialized the problem I had submitted, but your proposed solution to my original problem didn\'t measure up. It was my impression that the reason for me (the author) to see feedback on the problem was so that the reviewers could suggest changes and discuss concerns with my problem, not to rewrite my problem because you don\'t understand it.\r
\n\r
\nAs to the solution for the specific problem, you can\'t prove anything using prime factorization (a multiple of a prime may contain any number of factors of that prime - and by the way, four is not prime).\r
\n\r
\nI think it should be listed somewhere for the people with the permissions to change problems only to do so when the author is absent, and suggestions have been made, or perhaps if the change is minor (spelling/grammatical). As TomM said, I\'m responsible for the solution and for the puzzle being submitted on my name. You said, \"if we change your problem, your solution doesn\'t have to cover it! Although it may seem like it, if we change the problem, we probably know the answer so you don\'t have to.\" Are you going to throw away my solution as well as my puzzle? How about just taking my name off it and putting your own on; wouldn\'t that be easier? That way, when you can\'t prove what you proposed, people will look to you for the answer instead of the unwitting author of the original problem.\r
\n\r
\nI\'m glad that I saw your changes before they were approved; I was never notified of the change, and you certainly never asked my (or anyone\'s) opinion, even in comments. A little discretion might be wise to apply in the future, and I will thank you to do so.',2561,'Aaron','2004-02-23 11:12:55');
INSERT INTO forumpost VALUES (3109,404,5,'Re: Changing problems:','I have to side with Aaron and TomM on this one. The scholar edit feature does request that only neccessary and publically accepted changes are made, and I certainly never intended it to be used to alter problems in a dramatic way.\r
\n\r
\nI\'m sure however that no harm was meant, and this is a simple misunderstanding, so let\'s just change the problem back to its original form, and think about how we can prevent this in the future...',1,'levik','2004-02-23 13:10:09');
INSERT INTO forumpost VALUES (3110,399,4,'Re: early access','I\'m not sure if this is what you meant by a \'redirect URL,\' but in lieu of simply replacing the old pages with one bearing a link to this site, you could use PHP to capture the variables (tid, pid, fid, whatever) from the URL and generate a script that automatically sends the person to the corresponding page on the new site. At the very least, the PHP (server-side) could create a link to the page they were trying to get to, instead of just a generic link to perplexus.info.. just a thought.',1575,'DJ','2004-02-23 13:59:03');
INSERT INTO forumpost VALUES (3111,399,4,'Re: early access','Here\'s a PHP script that does just that (you\'ll have to add individual variables as necessary):\r
\n\r
\r
\n<?php\r
\n$url=\"http://perplexus.info/forum.php\";\r
\n$c=0;\r
\nadd($fid, \"fid\", $c, $url);\r
\nadd($pid, \"pid\", $c, $url);\r
\nadd($tid, \"tid\", $c, $url);\r
\n\r
\nfunction add($var, $name, &$c, &$url) {\r
\n if ($var!=\"\") {\r
\n $url .= ($c==0 ? \"?\" : \"&\");\r
\n $url .= \"$name=$var\";\r
\n $c++;\r
\n }\r
\n}\r
\n?>\r
\n
\nAssuming the code shows up correctly, of course, that will take each variable from the URL of the current page and form a URL to the corresponding page on the new site. For instance, if I am at http://www.flooble.com/perplexus/forum.php?fid=4&tid=399#3110, it will make a link to http://perplexus.info/forum.php?fid=4&tid=399#3110. The \"forum.php\" part is hard-coded, but you can make a different version for each page. Or, you could use the $_ENV to extract the page name, but that\'s probably overkill.\r
\n\r
\nAnyway, I was bored this afternoon, if you couldn\'t tell .. my point is that you can dynamically link or redirect from one site to the other based on the URL of the old page they are trying to access. That way, any links from search engines or other sites, to the main site or to specific pages, will still take the user to the corresponding \'new\' page they want to see.',1575,'DJ','2004-02-23 14:42:16');
INSERT INTO forumpost VALUES (3112,399,4,'Re: early access','Oops, forgot about the <pre> thing .. here\'s what that paragraph said:\r
\n\r
\nAssuming the code shows up correctly, of course, that will take each variable from the URL of the current page and form a URL to the corresponding page on the new site. For instance, if I am at http://www.flooble.com/perplexus/forum.php?fid=4&tid=399#3110, it will make a link to http://perplexus.info/forum.php?fid=4&tid=399#3110. The \"forum.php\" part is hard-coded, but you can make a different version for each page. Or, you could use the $_ENV to extract the page name, but that\'s probably overkill. \r
\n',1575,'DJ','2004-02-23 14:42:52');
INSERT INTO forumpost VALUES (3113,399,4,'Re: early access','DJ, not sure if you noticed, but such a link already appears on every flooble.com/perplexus page.\r
\n\r
\nI will keep it this way for a while at least, to make the URL change as publically disclosed as possible. Eventually, the old pages will be replaced though, with either a redirect such as the one you mention, or an empty page with nothing on them but a link to the new site\'s equivalent of the same page.\r
\n\r
\nThere is still the matter of re-pointing all the links in any problems, comments or forum posts - I hope to get that done sometime this coming weekend.',1,'levik','2004-02-23 14:52:01');
INSERT INTO forumpost VALUES (3114,372,7,'Re: Hello','Hello! I am Mitch and you need to know two things:\r
\n1. I love to do and make puzzles, riddles, etc. and\r
\n2. I love the colour green!',5751,'Mitch Mullings','2004-02-23 17:09:54');
INSERT INTO forumpost VALUES (3115,399,4,'Re: early access','Heh .. I actually haven\'t looked around the old page at all since the move, but the generated link is basically what I had in mind. My original suggestion, though, was to have each page automatically redirect to the new site, rather than having people navigate the old site with a link at the top (something like <body onload=window.open(\'<?=$newurl?>\',\'_top\')>). Of course, that may not be practical for all browsers, especially with some types of \"ad-blocking\" software that disable just that kind of script.. anyway, what you have works just fine, if people read it..',1575,'DJ','2004-02-23 18:05:33');
INSERT INTO forumpost VALUES (3116,405,3,'SilverKnight\'s Lovelorn Snail','Can you post the solution to this problem......please',5352,'Juggler','2004-02-24 20:11:35');
INSERT INTO forumpost VALUES (3117,405,3,'Re: SilverKnight\'s Lovelorn Snail','Ask and ye shall receive.',3172,'SilverKnight','2004-02-24 20:24:05');
INSERT INTO forumpost VALUES (3118,405,3,'Re: SilverKnight\'s Lovelorn Snail','Fanks Very Much',5352,'Juggler','2004-02-24 20:26:52');
INSERT INTO forumpost VALUES (3119,399,4,'Re: early access','Another note: I just became journeyman today (Yay!) and I clicked on the journeyman link to get to the rank descriptions, but the link doesn\'t seem to be working.',3558,'Tristan','2004-02-24 20:47:13');
INSERT INTO forumpost VALUES (3120,386,4,'Congratulations to our newest JOURNEYMAN','Congratz Tristan!',3172,'SilverKnight','2004-02-24 22:58:03');
INSERT INTO forumpost VALUES (3121,399,4,'Re: early access','I don\'t think it is related to your access... the link on the new site is just broken. (I don\'t think the page is there to receive the browser\'s request.) I\'m sure Levik will fix it soon.',3172,'SilverKnight','2004-02-24 22:59:17');
INSERT INTO forumpost VALUES (3122,405,3,'Re: SilverKnight\'s Lovelorn Snail','SK: Can I have an Aston Martin Vantage...... please',1183,'fwaff','2004-02-25 03:30:25');
INSERT INTO forumpost VALUES (3123,405,3,'Re: SilverKnight\'s Lovelorn Snail','lol !',3172,'SilverKnight','2004-02-25 03:32:24');
INSERT INTO forumpost VALUES (3124,405,3,'Re: SilverKnight\'s Lovelorn Snail','Hopefully you\'re laughing with the joy of giving. I can\'t wait to get home and have a look in my garage!\r
\n',1183,'fwaff','2004-02-25 04:15:58');
INSERT INTO forumpost VALUES (3125,405,3,'Re: SilverKnight\'s Lovelorn Snail','If fwaff gets an Aston Martin, can I get a Mercedes Benz CLK55?',1920,'Brian Smith','2004-02-25 09:21:58');
INSERT INTO forumpost VALUES (3126,399,4,'Re: early access','Ah, thanks for finding this - it\'s been fixed. (Just a file I forgot to copy over...)\r
\n\r
\nAlso, I updated all the urls in problem, solution and comment bodies to reference the new domain name of the site (pretty much a standard search and replace)\r
\n\r
\nNot sure if I should do the same on forums...',1,'levik','2004-02-25 10:45:42');
INSERT INTO forumpost VALUES (3127,399,4,'Re: early access','I would think so... what are the cons in updating the forums links?',3172,'SilverKnight','2004-02-25 10:52:08');
INSERT INTO forumpost VALUES (3128,399,4,'Re: early access','you know... I\'m not quite sure... :) I had some reservations when I was actually doing it, but they now elude me.',1,'levik','2004-02-26 08:10:20');
INSERT INTO forumpost VALUES (3129,386,4,'Re: Congratulations to our newest Apprentice','Woohoo! I just made my first comment on one of the pending problems, but I feel hesitant to vote before seeing a few more problems in the queue. I\'d ask what the unwritten \"policy\" is, but I\'ve seen enough forum to know I wouldn\'t get more than \"do whatever you want.\" Well, enough speech, I wouldn\'t want to bore you.',3558,'Tristan','2004-02-26 19:01:03');
INSERT INTO forumpost VALUES (3130,386,4,'Re: Congratulations to our newest Appren','Hey, I still get to say \"Do whatever you want\" :)\r
\n\r
\nThe idea is that you\'ve been around long enough to make up your mind as to what works and what doesn\'t - so your opinion is now worth as much as everyone else\'s.\r
\n',1,'levik','2004-02-26 19:36:23');
INSERT INTO forumpost VALUES (3131,384,4,'Re:','So are you saying to make it by calendar day for \"new problem comments\" and by 24 hour period for \"forum posts\"?\r
\n\r
\nI\'m not sure I understand. My position is that there should only be one number, either or for each of these. (And I guess it would be better if they were consistent)',1,'levik','2004-02-26 19:39:59');
INSERT INTO forumpost VALUES (3132,406,3,'Area of Segment','I believe that I found a problem some months ago on this site where certain info was given and the area of the segment of a circle was required. I\'ve used relevant keywords (eg:area, segment, chord) to search the database, but the required problem does not appear. Can someone point me in the right direction, has it been removed for some reason, or did I find it elsewhere?',1253,'brianjn','2004-02-26 19:56:36');
INSERT INTO forumpost VALUES (3133,406,3,'Re: Area of Segment','Are you thinking of Circular Logic?',3172,'SilverKnight','2004-02-26 20:22:46');
INSERT INTO forumpost VALUES (3134,386,4,'Re: Congratulations to our newest Appren','(actually... a little more than some ;-)',3172,'SilverKnight','2004-02-26 20:24:40');
INSERT INTO forumpost VALUES (3135,384,4,'Re:','I think Charlie is saying the daily number is (in general) more valuable. But that doesn\'t mean we can do without the 24h forum posts (we don\'t have a 1, 2, or 6 hour recent postings).\r
\n\r
\nI think that goes for the regular comments too.',3172,'SilverKnight','2004-02-26 20:26:45');
INSERT INTO forumpost VALUES (3136,384,4,'Re:','Right; both formats are useful for both areas.',1301,'Charlie','2004-02-27 07:44:32');
INSERT INTO forumpost VALUES (3137,399,4,'Re: early access','I tried using the square root symbol in the new editor, but got garbage when the post was actually made to the site (it looked good in the editor). I also tried viewing source and pasting in the ampersand code for phi, but that didn\'t work either.',1301,'Charlie','2004-02-27 11:12:39');
INSERT INTO forumpost VALUES (3138,384,4,'Re:','I don\'t see what benefit the 24h count gives in any of this. I may be missing something (which is highly possible), but given that this facility is for regular flooblers logging in daily then there are two scenarios to take into account:\r
\n\r
\nFirstly, as per SK\'s original example, the two times that the user logs on are during the same system day. In which case there is no (worthwhile) information gained from the 24h count since it\'s the increase in \'Comments Submitted Today\' from 15 to 18 that tells us that there are three new comments. \r
\n\r
\nSecondly, as per Charlie\'s point, the two times the user logs on span a system midnight. Suppose that the first time the user logs on they see \'last 24h\' = 19, \'new today\' = 14. They then log on the following system day and see \'last 24h\' = 22, \'new today\' = 10. From the latest log-on info they know that there are 10 new comments from today and 12 of yesterday\'s still within the 24h window. Putting this info together with yesterday\'s info give\'s nothing at all in terms of how many comments were posted yesterday between the last log-in and system midnight, therefore no info is gained on exactly how many new comments there have been since last log on.\r
\n\r
\nTo paraphrase what SK said at the start, the ideal solution would be to have a personalised \'how many comments have there been since I last logged on\', but the work involved in this probably outweighs the benefits. In my view the best value solution is to make the simple change to \'new today\' rather than the current \'new in last 24h\', which addresses SK\'s point but not Charlie\'s.\r
\n\r
\nTo overcome Charlie\'s problem then the second count needs to be \'Comments Posted Yesterday\' rather than the \'last 24h\' count. So that for example, if yesterday I saw \'new today\' = 15, \'yesterday\' = 26 and today I saw \'new today\' = 12, \'yesterday\' = 24, then I know that there are 12 new comments to read from today and 9 (=24-15) that I missed yesterday. ie a total of 21 since last log on.\r
\n\r
\nSK please can you add some extra clarification as required ;-) ..... oh and btw, where\'s my Aston?',1183,'fwaff','2004-02-27 13:15:22');
INSERT INTO forumpost VALUES (3139,384,4,'Re:','LOL... wow! I appreciate all the detail... (and to think I thought that *I* was the only one anal retentive enough to spew 6+ paragraphs in a posting ;-).\r
\n\r
\nI agree with almost everything fwaff said. My only addition/issue is regarding as of the last period. Since we don\'t have a \"how many comments have there been since I last logged on\"... I regularly use the \"last 2 hours\" or \"last 4 hours\" (of course... to make the last 4 hours... I just edit the URL directly). I would *not* want to lose that. I find it convenient (if not a little bit redundant) to have the number in the last period.\r
\n\r
\nPlease note that this facility is useful - whether or not we span a midnight.\r
\n\r
\n(And it *is* true... that the convenience I am describing is different than reporting how many postings have occurred in the last 24 hour period. Those two are just associated in the same link!)\r
\n\r
\nP.S. fwaff, didn\'t you get the Aston already? Hmmm.... it must\'ve gotten lost in the mail',3172,'SilverKnight','2004-02-27 14:05:09');
INSERT INTO forumpost VALUES (3140,399,4,'Re: early access','See also my first two comments on \"Like Clockwork\".',1301,'Charlie','2004-02-27 14:47:11');
INSERT INTO forumpost VALUES (3141,407,5,'Rich editor problems','Looks like the \"symbols\" toolbar in the new rich editor is causing some issues - at least some of the characters (namely \"Theta\") don\'t work as they should. Technically speaking, it looks like the browser is submitting the actual character instead of the character\'s code, and that is causing the error to occur.\r
\n\r
\nI\'m going to try and figure out a way to get around that, hopefully sometime this weekend.',1,'levik','2004-02-27 19:04:14');
INSERT INTO forumpost VALUES (3142,399,4,'Re: early access','Charlie - looking into those symbol problems. I also added FONT to the list of allowed tags, so you should be able to use them in the future without problems.',1,'levik','2004-02-27 19:06:25');
INSERT INTO forumpost VALUES (3143,407,5,'Re: Rich editor problems','I\'m having a lot of difficulty copying and pasting to the new editor too... is anyone else experiencing that? (Mozilla Firefox)\r
\n\r
\nOften, it simply won\'t let me paste. And I can\'t use the arrow keys to move forward and backward, or up and down.',3172,'SilverKnight','2004-02-27 19:25:46');
INSERT INTO forumpost VALUES (3144,406,3,'Re: Area of Segment','Thank you, but no. The graphic in that is useful to describe what I was thinking about. I had thought that the puzzle offered a \'similar\' graphic, but with only the segment shaded. ',1253,'brianjn','2004-02-27 20:51:19');
INSERT INTO forumpost VALUES (3145,407,5,'Re: Rich editor problems','I had these issues - they seem to be more related to Mozilla\'s implementation of rich editing than to the code itself, since restarting mozilla usually fixes things.',1,'levik','2004-02-28 12:59:04');
INSERT INTO forumpost VALUES (3146,406,3,'Re: Area of Segment','The other circle problem I remember is <a href\\\"http://www.flooble.com/perplexus/show.php?pid=92\\\">Diagonal Length, and there was also Circular Logic II',1626,'Gamer','2004-02-28 14:22:55');
INSERT INTO forumpost VALUES (3147,406,3,'Re: Area of Segment','Diagonal Length',1626,'Gamer','2004-02-28 14:23:33');
INSERT INTO forumpost VALUES (3148,406,3,'Re: Area of Segment','Thanks, but again, no. I must have seen it somewhere else (it involved being given the radius and one other attribute (arc length, chord or included angle).\r
\n\r
\nThanks SK and Gamer, I\'ll look elsewhere.',1253,'brianjn','2004-02-28 20:58:54');
INSERT INTO forumpost VALUES (3149,408,5,'A NEWTONIAN ARMAGEDDON','I have found several perfect engine cycles and wrote them down at http://www.thewebspert.com/cresswell/. They appear to be Quantum devices.',5849,'Alan Cresswell','2004-02-29 08:52:10');
INSERT INTO forumpost VALUES (3150,409,7,'Hi','HI I\'m a new user \r
\n\r
\nand I hope you can welcome me to your group \r
\n\r
\nI found this site while searching the net and i like this site so i joined',5857,'hunter','2004-03-01 06:20:15');
INSERT INTO forumpost VALUES (3151,407,5,'Re: Rich editor problems','I had underlining that looked good in the rich text editor, but got posted with the html tags showing rather than the underlining, in my first comment (comment #2) to Move the 3, Triple the Number.',1301,'Charlie','2004-03-01 10:56:21');
INSERT INTO forumpost VALUES (3152,407,5,'Re: Rich editor problems','I had trouble pasting from notepad into the editor.. all my double spaces (null lines) were removed, making the paragraphs run into each other. Also, I had the same trouble with underlining. I had written the underline as <u> (lowercase), but the editor changed it to <U> (uppercase), which wasn\'t allowed before. Is the old filter still disabling different tag forms (<em> vs <i>, <U> vs <u> .. )?',1575,'DJ','2004-03-01 11:56:01');
INSERT INTO forumpost VALUES (3153,407,5,'Re: Rich editor problems','I suggest that you give the ability (in our profile) to use the old system of submitting problems, since some browsers (notably Mozilla - Firefox/Firebird) don\'t seem to use it much.\r
\n\r
\nThe \'default\' behavior can (and probably should) be to use the rich text editor, but I think I would use the old system (with the preview method, which I liked very much).\r
\n\r
\n- SK',3172,'SilverKnight','2004-03-01 12:15:28');
INSERT INTO forumpost VALUES (3154,399,4,'Re: early access','Ajusting the \"Character Set\" in my browsers\' settings (when available) seems to help, so might it relate to using older Charecter Sets instead of Unicode?',153,'TomM','2004-03-01 19:30:01');
INSERT INTO forumpost VALUES (3155,399,4,'Re: early access','TomM, could you elaborate? Adjusting it from what to what, and at what point? When posting the comment? When looking at it?\r
\n\r
\nIf we can find the \"encoding sweet spot\", I can just specify it for the needed pages, and that will be that...',1,'levik','2004-03-02 07:59:33');
INSERT INTO forumpost VALUES (3156,407,5,'Re: Rich editor problems','Well, the problems are still being submitted by the old system - so I\'m sure you mean comments...\r
\n\r
\nAs far as the underline tag, I simply forgot to add it to the allowed list (which has now been fixed).\r
\n\r
\nWill look into the stripping off of the empty lines...\r
\n',1,'levik','2004-03-02 08:07:09');
INSERT INTO forumpost VALUES (3157,71,3,'Re: Hey!','Hi! wuzzup!?',5866,'paurusan','2004-03-02 09:49:20');
INSERT INTO forumpost VALUES (3158,71,3,'Just wondering....','im new and dont know nothing for the moment.....just wondering if you \"knowledgable\" people have any tips for a newbie or any nifty ANIME sites for me here....?',5866,'paurusan','2004-03-02 09:51:25');
INSERT INTO forumpost VALUES (3159,409,7,'Yo','im new too and found the site similarly.\r
\n\r
\nso now, you\'re probably experienced.\r
\n\r
\nhelp me out.',5866,'paurusan','2004-03-02 09:53:52');
INSERT INTO forumpost VALUES (3160,409,7,'P.S.','please',5866,'paurusan','2004-03-02 09:59:17');
INSERT INTO forumpost VALUES (3161,409,7,'Re: Hi','I\'m not new but I haven\'t been around much lately.\r
\nFlooble is a great and wonderful place for those who love to think.\r
\ngo to the home page and look at the puzzles listed there.\r
\nAre they to your liking? If yes, solve them. Then, if no one else has posted your answer, post it and feel that warm glow of pride. If someone else has already posted your answer, you can post it anyway but people will complain. One trick commonly tried is to take credit for coming up with an anser without actually posting it by posting something like, \"I came up with the same thing\" This will irritate the same people who don\'t like double posted answers but they will be less likely to complain.\r
\n\r
\nIf you don\'t like the puzzles on the front page but do like other kinds of puzzes, look up at the top there is a list of categories. If you like Liars and Knights Puzzles click on logic then on Liars and Knights, VIOLA! you ahve tons to choose from. If you like non-linear thinking puzzles, click on Riddles but don\'t tell anyone you did this as they will think less of you. If you reallyn DIG number theory and such click on just math but don\'t tell me about what you find as it will only confuse me.\r
\n\r
\nIF you are not in the mood to solve puzzles but want to read about them, go to the forums (you\'ve obviously already found your way here). \r
\n\r
\nIF you want to create a puzzle, you can do that too. Once you have commented on a couple of folks puzzles you will have the \"submit a puzzle\" option clikc the link and have at it. One suggestion though, before you type in your puzzle you\'d be wise to look around and see if its already here as they will not post repeats. Then just be patient, there are lats of Flooblers submitting puzzles and only a few posted each week so it will take your puzzle a while to work its way through the system. Everyone faces this so you are not being singled out.\r
\n\r
\nIn teh eman time look around participate in forums. THere are lots of interesting and smart folks, many of whom are famously willig to share their opinions.\r
\n\r
\nOne last thing. You should check your posts for spelling errors and typos otherwise people will think you are lazy and careless like me.',2839,'FatBoy','2004-03-02 10:21:17');
INSERT INTO forumpost VALUES (3162,407,5,'Re: Rich editor problems','Yes, I meant comments.\r
\n\r
\nI hope you still include a \"preview\" mode (perhaps NEXT to the submit button). This will prove invaluable if we do some more esoteric formatting or edit the html directly.\r
\n\r
\nAnd, ideally, this will work perfectly with FireFox (thought it doesn\'t now).',3172,'SilverKnight','2004-03-02 13:07:13');
INSERT INTO forumpost VALUES (3163,399,4,'Re: early access','I found more link problems.\r
\n\r
\nAt the top of the screen, the links to fun stuff and the flooble pad don\'t work.',3558,'Tristan','2004-03-02 22:19:11');
INSERT INTO forumpost VALUES (3164,409,7,'Re: Hello','hi,\r
\n\r
\ni\'m a new user of the site & i found the site\r
\n\r
\nwhile searching for some good puzzles.\r
\n\r
\ni\'m still a kid in the site so pls assist me\r
\n\r
\n\r
\n\r
\n\r
\n\r
\n\r
\n\r
\n\r
\n\r
\n\r
\n\r
\n\r
\n\r
\n\r
\n\r
\n\r
\n\r
\n\r
\n\r
\n',5875,'balu','2004-03-02 23:04:58');
INSERT INTO forumpost VALUES (3165,399,4,'Re: early access','Also, the link to scav (on the petition page) doesn\'t work either',1575,'DJ','2004-03-02 23:56:46');
INSERT INTO forumpost VALUES (3166,71,3,'Re: Hey!',' Parusan - welcome to the site! You will like flooble a lot. What are your interests? Just go to flooble.com and pick a category. If you have any questions, just put them in the forum!\"',5033,'Captain Paradox','2004-03-03 15:32:36');
INSERT INTO forumpost VALUES (3167,399,4,'Re: early access','Ah - thanks for spotting this, guys - relative links tend to break when the domain is changed :) \r
\n\r
\nShould be OK now...\r
\n\r
\nTomM - I still hope you can elaborate on the encoding issue, since it may be the key to making the Rich Editor work as it should (at least for the special characters)',1,'levik','2004-03-03 21:54:42');
INSERT INTO forumpost VALUES (3168,399,4,'Re: early access','Here\'s another link which needs fixing:\r
\n\r
\nThe perplexus link on scav page points to the old perplexus.',1920,'Brian Smith','2004-03-04 15:05:38');
INSERT INTO forumpost VALUES (3169,320,6,'Re: .5!','The reason that the TI-83 and probably others allows for increments of .5 is that it is required to calculate the Probability Density function for a t-distribution. In the formula one encounters both (n/2)! and [(n-1)/2]! Where n can be any positive integer. So of the two expressions in the factorials must be of the form #.5 and thus the TI wants to know that value and to allow people to calculate it if they have to. As was mentioned previously the Gamma function is what we use to extend the factorial and Gamma(n+1)=n!. Hope this helps.',NULL,'Professor K at MCC','2004-03-04 19:19:15');
INSERT INTO forumpost VALUES (3170,407,5,'Re: Rich editor problems','I notice in the drop-down list for Formatting>>, when you choose Normal or Pre-formatted, neither replaces the word Formatting in the associated text area.',1301,'Charlie','2004-03-05 09:30:53');
INSERT INTO forumpost VALUES (3171,410,4,'Congratz to our newest Journeyman!','Welcome, Aaron.',3172,'SilverKnight','2004-03-05 10:10:32');
INSERT INTO forumpost VALUES (3172,409,7,'Re: Hi','Does anyone know any sites where I can get answers for krypto?\r
\nThe problem is 23 24 1 11 12 to equal 8. It might not work.',NULL,'Nick','2004-03-05 22:20:01');
INSERT INTO forumpost VALUES (3173,411,7,'looks like fun','I stumbled across this site and it looked like fun, so here I am!! Hello to all. ',5920,'mary esterhammer-fic','2004-03-06 00:22:03');
INSERT INTO forumpost VALUES (3174,409,7,'Re: Hi','Nevermind. I figured it out. Its sqrt(24+12)+(23-1)divided by 11',NULL,'Nick','2004-03-07 22:28:55');
INSERT INTO forumpost VALUES (3175,409,7,'Re: Hi','Sorry I\'m putting problems in the forum.',NULL,'Aspiring Novice','2004-03-07 22:29:47');
INSERT INTO forumpost VALUES (3176,409,7,'Re: Hi','By the way, I\'m Nick, not aspiring novice.',NULL,'Nick','2004-03-07 22:30:41');
INSERT INTO forumpost VALUES (3177,410,4,'Re: Congratz to our newest Journeyman!','And, wow! A hidden forum! There\'s all sorts of neat stuff to be found here (where\'s the mini bar?)...',2561,'Aaron','2004-03-09 10:15:28');
INSERT INTO forumpost VALUES (3178,410,4,'Re: Congratz to our newest Journeyman!','Here\'s your very own key to the executive washroom!',3172,'SilverKnight','2004-03-09 10:41:54');
INSERT INTO forumpost VALUES (3179,409,7,'Re: Hi','Hey all... New here. Hoping to find some real challenges. I have some challenges too, but perhaps they\'re too tough...\r
\n\r
\nWe\'ll see.\r
\n\r
\nPhil\r
\n',5962,'Phil','2004-03-09 11:56:03');
INSERT INTO forumpost VALUES (3180,412,7,'y0','Hello everyone. I\'m new here. I thought this might be an interesting place to look at a large range of different Puzzles. I found this place by looking on Google for \"logic puzzles\".',5963,'Vincent','2004-03-09 13:19:10');
INSERT INTO forumpost VALUES (3181,410,4,'Re: Congratz to our newest Journeyman!','Now you get to face the problem of the zillion probles in the solution queue! :) Plus, you can read the boring queue chatterbox :)',1626,'Gamer','2004-03-09 14:56:51');
INSERT INTO forumpost VALUES (3182,413,7,'I want to submit a problem, but...','Hi,\r
\nI love this site!\r
\nI want to submit a problem, but I have a question. If I submit the solution at the same time, will it be posted immediately for all to see? Or will I be able to control later what \"solution\" gets posted. Or do the directors post the official solution? ',5384,'Larry','2004-03-09 20:56:47');
INSERT INTO forumpost VALUES (3183,413,7,'Re: I want to submit a problem, but...','You may submit the solution (and interestingly... even the Journeymen don\'t get to see the solution until about two weeks after your problem is made public), and you have control later to determine when to display your solution.',3172,'SilverKnight','2004-03-09 21:10:58');
INSERT INTO forumpost VALUES (3184,413,7,'Re: I want to submit a problem, but...','Journeymen and scholars can post the solutions to their own problems, but everyone else has to wait for scholars to push the solution. Don\'t worry, by the time they push it, you\'ll probably be begging for it to be posted. :-)\r
\n\r
\nSK, I believe you meant scholars?',3558,'Tristan','2004-03-09 22:43:35');
INSERT INTO forumpost VALUES (3185,413,7,'Re: I want to submit a problem, but...','Thanks',5384,'Larry','2004-03-09 23:02:03');
INSERT INTO forumpost VALUES (3186,413,7,'Re: I want to submit a problem, but...','No, I meant Journeymen.... look around, Tristan. ;-)',3172,'SilverKnight','2004-03-10 00:14:41');
INSERT INTO forumpost VALUES (3187,413,7,'Re: I want to submit a problem, but...','Levik did that on purpose, didn\'t he?!',3558,'Tristan','2004-03-10 20:00:55');
INSERT INTO forumpost VALUES (3188,413,7,'Re: I want to submit a problem, but...','SK, Two weeks? ... did you mean two days?',1301,'Charlie','2004-03-11 09:58:52');
INSERT INTO forumpost VALUES (3189,413,7,'Re: I want to submit a problem, but...','No... I believe it is one or two weeks before the proposed solution is made available for us (Journeymen) to view (and comment). I don\'t check it very often, so I could be mistaken.\r
\n\r
\nPerhaps the Scholars can view it sooner.',3172,'SilverKnight','2004-03-11 13:09:36');
INSERT INTO forumpost VALUES (3190,413,7,'Re: I want to submit a problem, but...','Most of the solutions in the \"recently posted solutions\" section were posted round about ten days after the problem.',NULL,'Aspiring Novice','2004-03-11 14:24:54');
INSERT INTO forumpost VALUES (3191,413,7,'Re: I want to submit a problem, but...','It\'s actually visible two days after it\'s posted, and two days after it\'s visible is when it can be posted.\r
\n\r
\nBy the way, we can bug levik if we really have questions about a solution, so do put one in instead of waiting. That way levik can see if the solution is good or not if we have questions.',1626,'Gamer','2004-03-11 16:50:44');
INSERT INTO forumpost VALUES (3192,320,6,'Re: .5!','I always thought it went like this:\r
\n\r
\n4,5! = 4,5 * 3,5 * 2,5 * 1,5 * (0,5)!\r
\n\r
\nThe (0,5)! could be replaced with either (sqrt(ð))/2 or just 0,886226925 if you wanted.\r
\n\r
\nð = pi so you don\'t confuse it with n.',NULL,'Grade 11 student','2004-03-12 12:07:36');
INSERT INTO forumpost VALUES (3193,414,7,'I\'m Stumped!!! HELP!','3 guys walk into a hotel. The price for the room they want to share is $30.00. Each one puts down $10.00. (3 X 10) The manager tells them that since its Friday they can have the room for $25.00. He can\'t divide the $5.00 change evenly so he gives each man $1.00 and \"pockets\" $2.00 (3X1 + 2 = $5.00) \r
\n\r
\nIf each man now paid $9.00 ($10 - $1.00 refund)that equals $27.00 (3 X 9). And the manager \"pockets\" $2.00 which now equals $29.00. Where did the other dollar go?',5995,'barbara','2004-03-12 19:47:34');
INSERT INTO forumpost VALUES (3194,414,7,'Re: I\'m Stumped!!! HELP!','This is like the puzzle \"missing dollar\".\r
\n\r
\nYou\'re not supposed to post puzzles in the forums. If you need any more help with puzzles, give some way for people to contact you.',3558,'Tristan','2004-03-12 19:55:51');
INSERT INTO forumpost VALUES (3195,355,4,'Re: The (BIG) solutions push','Well, the unsolved list keeps growing. It is at 89 now. Most of the problems have solutions in the comments already. Perhaps we should allow higher ranking members of perplexus to submit official solutions to problems on the unsolved list if the problem has been \'abandoned\' for some peroid of time.',1920,'Brian Smith','2004-03-15 15:26:26');
INSERT INTO forumpost VALUES (3196,381,3,'Re: Cryptography Question','Try to find a logic realation between the letters have in your mind that in cryptography everything can be raplaced for exaple even space can be replaced with A.\r
\nTry to find some of the most common words in english in there and get the letters you need for exaple and, the, is e.t.c\r
\nI will try to find the answer and come back to you soon',6038,'Chris','2004-03-16 10:38:18');
INSERT INTO forumpost VALUES (3197,415,7,'NEW ONE','HELLO EVERYONE I SCANNED THIS SITE BECAUSE I AM A LOGIC FIEND AND WHEN I WAS HERE AT WORK I THOUGHT BUT NI BETTER WAY THAN TO SEE IF THE COMPUTER HAS LOGIC PUZZLES AND HERE I AM I HOPE TO SEE A LOT MORE PEOPLE JION SO WE CAN HELP ONE ANOTHER',6041,'DANIELLE','2004-03-16 13:12:35');
INSERT INTO forumpost VALUES (3198,355,4,'Re: The (BIG) solutions push','I\'ve been working on it, actually, for the past few days. I don\'t like to push a solution just for the sake of pushing it, if I feel that it could be improved on. But, two or three at a time, the unsolved problem queue is shrinking ...',1575,'DJ','2004-03-16 13:59:02');
INSERT INTO forumpost VALUES (3199,355,4,'Re: The (BIG) solutions push','I have been working too, but I don\'t like to push my own solutions, take the point out of the queue idea.\r
\n\r
\nMany of those problems actually are actually having something left to solve, so it\'s not like all of them need work. :)',1626,'Gamer','2004-03-16 20:33:50');
INSERT INTO forumpost VALUES (3200,415,7,'Re: NEW ONE','I would like to post a problem',6049,'ben','2004-03-17 00:44:46');
INSERT INTO forumpost VALUES (3201,415,7,'Re: NEW ONE','Ben, you need to go to the home page of the site, on the right of the \"categories\" box there is another menu, select \"submit a problem\" click on this and bob\'s your uncle.\r
\n\r
\nRemember to check other problems that have already been posted so you are not repeating existing puzzles.\r
\n\r
\nJuggler',5352,'Juggler','2004-03-17 08:56:14');
INSERT INTO forumpost VALUES (3202,414,7,'Re: I\'m Stumped!!! HELP!','9 dollars paid by each of the guys make 9 * 3 = 27\r
\neach man got one dollar back so 1*3 = 3\r
\nnow they make a total of 30 dollars. the two dollars the manager pockets are actually from the 27 dollars paid by the three guys. so u cant add the pocketed 2 dollars to the already paid 27 dollars.',5894,'Chandrakant','2004-03-17 13:57:13');
INSERT INTO forumpost VALUES (3203,277,5,'Re: Problem flooding re-revisited','Seems like if we combine our problems together it would make the queue smaller. If the bulk of the information is the same, the problems should be clustered together. Also, if it isn\'t pulling them apart is likely better (as I have observed)',1626,'Gamer','2004-03-17 21:06:06');
INSERT INTO forumpost VALUES (3204,277,5,'Re: Problem flooding re-revisited','I believe a preference (amounting to priority) should be given to original problems.',5285,'Ady TZIDON','2004-03-18 05:17:49');
INSERT INTO forumpost VALUES (3205,282,5,'Re: Advertising','I\'ve received a \"Trojan Program Found\" warning several times from my Virus Shield when this site opens pop ups. I\'m not sure if this is the same one as I\'ve had in the past, but here is the latest one:\r
\n\r
\nDownloaded File: INDEX[1].HTM\r
\nTrojan Name: VBS/Psyme\r
\n\r
\nLast Ad: ExitFuel; This Ad: PopUpTraffic (under)\r
\n\r
\nAbout four pop ups opened, though, so I can\'t swear it was either of these two ads.\r
\n\r
\n\r
\nOn a related note, about one time out of three when browsing this site without being logged in a pop up tries to load that takes so long it freezes everything, forcing me to Ctrl-Alt-Del my way out of Perplexus. Currently the computer beside me is frozen (I\'m in a computer lab), and is trying to load an ad from media.fastclick.net. This happens quite regularly, on a number of different (fast) computers, and seems to happen whether or not a pop up blocker is installed.',3372,'Sam','2004-03-18 10:31:55');
INSERT INTO forumpost VALUES (3206,282,5,'Re: Advertising','Should have added: I\'m using IE 6.0, Win XP Professional',3372,'Sam','2004-03-18 10:34:46');
INSERT INTO forumpost VALUES (3207,355,4,'Re: The (BIG) solutions push','Gamer, are you still using the old site (at flooble.com)? Is there any special reason for this (other than not liking the colors)\r
\n\r
\nIs the rich text editor THAT horrible? :)\r
\n\r
\nIn any case, can you make sure that if you post links to comments in the solution, that these links go to the NEW site, not the old one? (Just replace \"www.flooble.com/perplexus\" with \"perplexus.info\" in the URL).',1,'levik','2004-03-18 15:44:06');
INSERT INTO forumpost VALUES (3208,355,4,'Re: The (BIG) solutions push','actually... Levik, have you noticed that when people put links in the comments with the rich text editor... that they seem to be messed up? is <A HREF> being \'caught\' ?',3172,'SilverKnight','2004-03-18 15:57:56');
INSERT INTO forumpost VALUES (3209,355,4,'Re: The (BIG) solutions push','I will start doing that. I do dislike the colors, so I used flooble instead.',1626,'Gamer','2004-03-18 17:20:56');
INSERT INTO forumpost VALUES (3210,416,7,'Hello','I\'m new. I don\'t really know what is going on.',6081,'Ashley','2004-03-18 18:59:54');
INSERT INTO forumpost VALUES (3211,407,5,'Re: Rich editor problems','I have just discovered that the items in the drop-down list for Formatting work exactly like the pushbuttons, for, say, bold face. That answers my perplexity as to this drop-down list\'s use.\r
\n\r
\nBut why can\'t the two items in there just be push buttons, thereby indicating their use? I had previously wondered why the chosen item did not appear in the text portion of what seemed to be a combo box; now I see the items are push buttons masquerading as list items.\r
\n\r
\nNow of course I see that I can set highlighted areas to pre or set the new typing to be pre\'ed or not. But this is not obvious when, first, one doesn\'t realize that the view is changing in the text area to match what you have chosen, and second, one is worried about experimenting with actual postings.',1301,'Charlie','2004-03-19 11:34:52');
INSERT INTO forumpost VALUES (3212,407,5,'Re: Rich editor problems','Also, as push buttons, there\'d be only one click, rather than the two needed now.',1301,'Charlie','2004-03-19 11:35:35');
INSERT INTO forumpost VALUES (3213,416,7,'Re: Hello','im new too. could someone please tell us whats going on???',6088,'amy cooper','2004-03-19 12:53:40');
INSERT INTO forumpost VALUES (3214,417,7,'the site','how do you put other puzzles onto the site',6109,'hamish thompson','2004-03-20 23:39:45');
INSERT INTO forumpost VALUES (3215,417,7,'Re: the site','Once you become a student you can submit your own puzzles. Puzzles that are submitted take an average of a couple months to get posted because of the length of the queue, and have to be accepted to be put up. The usual reason for a puzzle not being posted is that it already exists on the site.\r
\n\r
\nEverything is in the FAQ that can be found on the main page.\r
\n',3372,'Sam','2004-03-21 02:19:51');
INSERT INTO forumpost VALUES (3216,355,4,'Re: The (BIG) solutions push','SK: The A HREF tag is allowed, however there was some weirdness with escaping quotes for insertion into mysql. This has hopefully been fixed (I was able to do a test link)\r
\n\r
\nGamer: Sorry for the color issue. I have to disappoint you that pertty soon the flooble version of the pages will not be available anymore (I will just have them redirect to their new versions automatically)',1,'levik','2004-03-21 10:22:04');
INSERT INTO forumpost VALUES (3231,423,7,'PUZZLES','There are seven houses each containing seven cats.Each cat kills seven mice and each mouse would have eaten seven ears of spelt.Each ear of spelt would have produced seven hekats of grain.What is the total of all these?\r
\n\r
\n\r
\nWhat number must be added to 100 and 20 (the same number to each) so that the sums are in the ratio 3:1?',6168,'sanjay','2004-03-24 14:25:54');
INSERT INTO forumpost VALUES (3234,282,5,'Re: Advertising','A number of you have expressed interest in donating to remove ads. In trying to figure out how feasible that would be, I\'d like to know if you would want the pops to disappear, or the banners/skyscrapers as well.\r
\n\r
\nPersonally, I don\'t really notice them, and believe the pages would look naked/ugly without the ad \"trimming\", but I understand others may be of a different opinion.\r
\n\r
\nClearly removing just the pops would be cheaper than getting rid of everything so I\'d like to know what you think. $10/year for no pops? (You\'d have to be logged in though)',1,'levik','2004-03-24 22:40:29');
INSERT INTO forumpost VALUES (3235,413,7,'Re: I want to submit a problem, but...','<big><a href=http://u-covered-india-foo.da.ru/>angelina jolie vs sylvia saint<big>',NULL,'Aspiring Novice','2004-03-25 00:25:22');
INSERT INTO forumpost VALUES (3223,282,5,'Re: Advertising','Update:\r
\n\r
\nMy computer at home undortunately does not have a virus shield that catches evil pop up trojans being downloaded, hijacking my homepage and installing spyware on my computer. I have Norton antivirus, a ZoneAlarm firewall and Google\'s pop up blocker, but that I guess isn\'t good enough.\r
\n\r
\nThis past week I\'ve found a very clear correlation between visiting Perplexus and having my homepage hijacked to http://default-homepage-network.com, an evil site that advises you to download their Spyware remover (Ha! That\'s like the thief stopping half way through robbing your house and suggesting you buy his burglar alarm...). My own Spyware program, Ad-Aware, finds thirty-odd new malicious programs everytime this happens.\r
\n\r
\nI know perfectly well that the net these days is no place to be walking around without adequate protection. I also know that it\'s almost impossible to control what comes in through pop-ups, especially when they\'re run by a third party, so I doubt that it would be possible to stop this from happening (these trojans are all over the web, Perplexus isn\'t alone in any way). I\'m just thinking that maybe we should revitalize the old idea putforward above somewhere above that, for instance, donation = no ads, or some such similar possiblity.\r
\n\r
\n\r
\nIn the meantime, until I start wearing proper protection at home I\'ll be visiting Perplexus from the safty of the Virus-Shielded lab computers. Also, I\'d suggest that anyone who frequents sites with a lot of pop ups downloads and regularly uses a reputable Spyware remover.',3372,'Sam','2004-03-22 22:42:35');
INSERT INTO forumpost VALUES (3224,205,7,'Re: Hi. I\'m new at this.','sorry. not ignoring you. I was reading some paradoxes. I just stumbled on to the sight, passing time',6145,'Ryan','2004-03-23 00:07:28');
INSERT INTO forumpost VALUES (3225,422,4,'Rejecting puzzles','Every now and then we will hear from someone complaining his puzzle came up in the queue and was rejected before he was aware. I\'m not talking about people who lost interest in the site, but those who check every day. (Gamer\'s Towers of Hanoi II is the latest.)\r
\n\r
\nI know that we are trying to do something about the huge backlog so that we don\'t lose too many new people too often, and sometimes a problem is unusable and unfixable (or more likely, a duplicate) and should be rejected. But whenever feasible, shouldn\'t we allow it to remain long enough for the owner to see the discussion? It\'s gotten to the point that, although I\'ll leave a negative \"note,\" I almost never thumbs down a problem.\r
\n\r
\n**Gamer: You did ask for an algorithm to solve a generalized Towers of Hanoi problem, which the original did not ask for, but most of the answers discussed the general problem, and then applied the algorithm to the five disc problem presented.',153,'TomM','2004-03-23 06:53:48');
INSERT INTO forumpost VALUES (3226,422,4,'Re: Rejecting puzzles','This quick-rejection phenomenon is especially prevalent when the top ten includes many +2\'s and -2\'s with nothing available to post. Perhaps levik can reduce some of the urgency for seeing new puzzles in the top-10 if it were expanded (maybe only temporarily, while there are many +2\'s and -2\'s) so that old candidates need not be removed so fast in order to see new ones.\r
\n\r
\nI know an alternative is to vote just for the sake of voting, even though one may have no interest in a particular puzzle (such as the recent comment that there are no riddle journeymen around to vote on the riddles in the queue), but that has its own problems, related to the one TomM mentions.',1301,'Charlie','2004-03-23 08:47:29');
INSERT INTO forumpost VALUES (3233,282,5,'Re: Advertising','Wow... This was pretty bad. I tracked the ads down to Exitfuel, and that was the last straw. Exitfuel is OUT.\r
\n\r
\nI truly apologize to everyone for any inconvenience this may have caused. I have had problems with them in the past, but at this point, they\'ve clearly become not worth bothering with.\r
\n\r
\nPlease let me know if something like this happens again (such an occurence definitely warrants submitting a personal request, so that it\'s addressed faster.)',1,'levik','2004-03-24 22:37:00');
INSERT INTO forumpost VALUES (3229,326,4,'Re: About Penny','Now that Penny has calmed down, here comes yo to slime up the site, ironically targeting Penny. Levik, can you clean out yo\'s comments?',1301,'Charlie','2004-03-23 15:09:52');
INSERT INTO forumpost VALUES (3232,423,7,'Re: PUZZLES','49 cats and 7 houses\r
\n343 mice\r
\n2401 ears of spelt\r
\nand 16807 hekats of grain \r
\n\r
\n20 is the number to be added. to get 120 and 40. ratio is 3:1\r
\n',6172,'mike','2004-03-24 16:46:36');
--
-- Table structure for table 'forumthread'
--
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threadId int(10) unsigned NOT NULL auto_increment,
forumId int(10) unsigned NOT NULL default '0',
subject varchar(100) default NULL,
authorId int(10) unsigned default NULL,
authorName varchar(40) default NULL,
started datetime default NULL,
updated datetime default NULL,
posts int(10) unsigned NOT NULL default '1',
PRIMARY KEY (threadId)
) TYPE=MyISAM;
--
-- Dumping data for table 'forumthread'
--
INSERT INTO forumthread VALUES (1,3,'Forums!',1,'levik','2002-11-30 12:18:55','2003-04-13 02:58:19',8);
INSERT INTO forumthread VALUES (2,4,'This is for?',746,'Raveen','2002-11-30 19:10:24','2003-03-06 17:51:39',6);
INSERT INTO forumthread VALUES (3,3,'Suggestions',746,'Raveen','2002-11-30 19:25:54','2003-03-23 18:16:39',11);
INSERT INTO forumthread VALUES (4,5,'Broken Link =D',746,'Raveen','2002-11-30 22:21:00','2002-12-01 05:47:58',2);
INSERT INTO forumthread VALUES (5,5,'Latest Comments Numbering..',746,'Raveen','2002-12-02 04:54:50','2003-03-06 06:16:40',7);
INSERT INTO forumthread VALUES (6,4,'So...',227,'Dulanjana','2002-12-04 13:57:06','2002-12-04 21:46:14',2);
INSERT INTO forumthread VALUES (7,3,'mystery Water Problem',879,'Anthony','2002-12-06 15:02:37','2003-04-17 11:22:49',9);
INSERT INTO forumthread VALUES (8,6,'Meanings...',746,'Raveen','2002-12-07 01:52:13','2004-01-13 04:08:04',6);
INSERT INTO forumthread VALUES (9,3,'Ratings.',1,'levik','2002-12-09 05:57:56','2003-01-14 06:30:09',10);
INSERT INTO forumthread VALUES (10,6,'Another meaning...',227,'Dulanjana','2002-12-10 01:33:47','2004-01-13 04:08:04',5);
INSERT INTO forumthread VALUES (11,5,'Forum thread suggestion',103,'friedlinguini','2002-12-11 10:04:23','2002-12-12 11:42:28',5);
INSERT INTO forumthread VALUES (12,4,'The queued limitation',227,'Dulanjana','2002-12-11 18:47:45','2002-12-12 01:41:05',2);
INSERT INTO forumthread VALUES (13,5,'Problems in forums',1,'levik','2002-12-13 05:47:32','2003-10-12 05:31:22',4);
INSERT INTO forumthread VALUES (14,6,'Any difference',227,'Dulanjana','2002-12-17 15:41:24','2004-01-13 04:08:03',10);
INSERT INTO forumthread VALUES (15,6,'sinh, cosh, tanh whats this?',227,'Dulanjana','2002-12-19 00:17:53','2004-01-13 04:08:04',3);
INSERT INTO forumthread VALUES (16,5,'Arrow icons',1,'levik','2002-12-23 08:43:46','2002-12-24 10:17:32',4);
INSERT INTO forumthread VALUES (17,6,'HTML codes for use on the site',1,'levik','2002-12-24 07:40:18','2004-01-13 04:08:02',82);
INSERT INTO forumthread VALUES (18,5,'Problem Rating',227,'Dulanjana','2002-12-26 16:00:04','2002-12-27 01:56:28',2);
INSERT INTO forumthread VALUES (19,4,'\"Inappropriate\" problems',1,'levik','2002-12-30 05:19:40','2003-11-28 19:26:01',4);
INSERT INTO forumthread VALUES (20,3,'LOGIC problems?',1,'levik','2003-01-07 06:30:49','2003-04-09 14:49:59',12);
INSERT INTO forumthread VALUES (21,3,'Puzzles',1145,'tom','2003-01-12 07:17:12','2003-04-17 11:24:07',22);
INSERT INTO forumthread VALUES (22,5,'problem acceptance comments',775,'Cory Taylor','2003-01-14 06:19:01','2003-01-14 06:51:59',2);
INSERT INTO forumthread VALUES (23,3,'Two a day?',1,'levik','2003-01-26 06:35:50','2003-04-09 14:52:29',13);
INSERT INTO forumthread VALUES (24,3,'Top-rated Problems',1072,'Alan','2003-01-27 10:45:32','2003-01-27 18:10:25',5);
INSERT INTO forumthread VALUES (25,5,'Scholar Level',1072,'Alan','2003-01-28 03:14:38','2003-01-29 01:44:53',3);
INSERT INTO forumthread VALUES (26,5,'Small request',103,'friedlinguini','2003-01-29 06:26:47','2003-01-29 18:14:37',5);
INSERT INTO forumthread VALUES (27,5,'Solution too early?',1,'levik','2003-01-30 01:49:31','2003-01-30 22:37:20',4);
INSERT INTO forumthread VALUES (28,3,'Brainteasers: The Aftermath',103,'friedlinguini','2003-01-31 04:37:42','2003-01-31 04:37:42',1);
INSERT INTO forumthread VALUES (29,3,'300 Problems!!!!',1,'levik','2003-02-09 18:18:19','2003-02-10 02:57:31',2);
INSERT INTO forumthread VALUES (30,5,'Browsers and Chatterboxes?',103,'friedlinguini','2003-02-20 18:07:59','2003-02-21 05:21:47',5);
INSERT INTO forumthread VALUES (31,4,'Riddles',1072,'Alan','2003-02-21 10:47:06','2003-02-24 18:20:55',10);
INSERT INTO forumthread VALUES (32,5,'Sorry to bug you again levik',1072,'Alan','2003-02-21 10:49:42','2003-02-21 10:49:42',1);
INSERT INTO forumthread VALUES (33,4,'Flooding',1,'levik','2003-02-22 19:57:51','2003-03-09 18:29:34',22);
INSERT INTO forumthread VALUES (34,4,'Queue ranking',1,'levik','2003-02-24 06:14:55','2003-03-07 10:47:30',28);
INSERT INTO forumthread VALUES (35,5,'Problem flagging',1072,'Alan','2003-02-27 14:24:39','2003-02-28 11:49:27',4);
INSERT INTO forumthread VALUES (36,4,'New QW thread',1,'levik','2003-03-01 08:36:28','2003-05-01 07:16:00',20);
INSERT INTO forumthread VALUES (37,5,'Names',1072,'Alan','2003-03-02 08:13:29','2003-11-09 17:21:00',16);
INSERT INTO forumthread VALUES (38,7,'New forum',1,'levik','2003-03-03 14:57:02','2004-02-04 20:32:43',38);
INSERT INTO forumthread VALUES (39,5,'Notifications?',1,'levik','2003-03-03 16:48:11','2003-03-05 10:51:16',10);
INSERT INTO forumthread VALUES (40,6,'perfect squares',775,'Cory Taylor','2003-03-06 05:08:36','2004-01-13 04:07:53',9);
INSERT INTO forumthread VALUES (41,5,'Ratings (appoximately)',1,'levik','2003-03-06 05:59:59','2003-03-06 05:59:59',1);
INSERT INTO forumthread VALUES (42,3,'Problems from Webring partners?',1301,'Charlie','2003-03-06 10:53:03','2003-03-06 14:14:48',2);
INSERT INTO forumthread VALUES (43,4,'Stalemates',103,'friedlinguini','2003-03-07 02:10:48','2003-03-07 02:10:48',1);
INSERT INTO forumthread VALUES (44,3,'Search Results',979,'Ravi Raja','2003-03-09 03:34:57','2003-03-09 05:05:21',3);
INSERT INTO forumthread VALUES (45,4,'How a Puzzle is Voted On.',1301,'Charlie','2003-03-09 07:44:17','2003-03-16 21:26:37',9);
INSERT INTO forumthread VALUES (46,4,'Hat down in apology',1299,'Anoop','2003-03-10 06:00:35','2003-03-10 06:39:38',3);
INSERT INTO forumthread VALUES (47,5,'Your info. in your words',1,'levik','2003-03-11 05:52:11','2003-03-11 05:52:11',1);
INSERT INTO forumthread VALUES (48,5,'Unsolved problem order',1072,'Alan','2003-03-13 12:20:40','2003-03-14 15:16:35',6);
INSERT INTO forumthread VALUES (49,4,'Solved Unsolved Puzzle',1301,'Charlie','2003-03-17 04:05:01','2003-05-13 13:28:45',14);
INSERT INTO forumthread VALUES (50,5,'Chatterbox',1183,'fwaff','2003-03-18 21:50:37','2003-06-24 12:02:15',14);
INSERT INTO forumthread VALUES (51,3,'Submitter\'s view of pending puzzles.',1301,'Charlie','2003-03-19 09:55:37','2003-03-19 09:55:37',1);
INSERT INTO forumthread VALUES (52,5,'truncated comments',1301,'Charlie','2003-03-19 16:27:45','2003-03-21 08:44:54',3);
INSERT INTO forumthread VALUES (53,5,'Submitter\'s view of pending puzzles.',1301,'Charlie','2003-03-20 04:02:12','2003-03-20 04:34:28',2);
INSERT INTO forumthread VALUES (54,5,'Suggestion for more problem ratings',103,'friedlinguini','2003-03-21 09:16:33','2003-03-21 09:16:33',1);
INSERT INTO forumthread VALUES (55,3,'Anything and everything',1660,'Tim Axoy','2003-03-23 07:10:24','2003-03-30 07:02:47',3);
INSERT INTO forumthread VALUES (56,7,'Tim Axoy',1660,'Tim Axoy','2003-03-23 07:15:34','2004-01-13 04:08:48',10);
INSERT INTO forumthread VALUES (57,3,'No,no,no',1660,'Tim Axoy','2003-03-23 09:15:57','2003-04-11 09:54:56',10);
INSERT INTO forumthread VALUES (58,4,'Forum puzzle trap',1072,'Alan','2003-03-23 14:45:16','2003-03-24 02:00:48',3);
INSERT INTO forumthread VALUES (59,5,'What is',1637,'chris','2003-03-23 19:22:28','2003-10-04 10:28:30',7);
INSERT INTO forumthread VALUES (60,5,'Levik',1660,'Tim Axoy','2003-03-24 02:16:34','2003-03-24 02:16:34',1);
INSERT INTO forumthread VALUES (61,4,'Insta-posting Scholars',1,'levik','2003-03-24 06:13:53','2003-03-25 13:10:14',5);
INSERT INTO forumthread VALUES (62,6,'Primes',1660,'Tim Axoy','2003-03-24 07:32:23','2004-01-13 04:08:03',4);
INSERT INTO forumthread VALUES (63,3,'a/s/l anyone?',1637,'chris','2003-03-24 18:25:23','2003-07-14 02:28:44',35);
INSERT INTO forumthread VALUES (64,7,'Twin chat',1660,'Tim Axoy','2003-03-25 02:59:16','2004-01-13 04:08:08',3);
INSERT INTO forumthread VALUES (65,5,'!',1660,'Tim Axoy','2003-03-26 01:56:58','2003-12-19 09:30:54',5);
INSERT INTO forumthread VALUES (66,3,'Hey,dudes',1660,'Tim Axoy','2003-03-26 02:00:12','2003-03-28 13:04:44',3);
INSERT INTO forumthread VALUES (67,4,'QW change?',1072,'Alan','2003-03-26 10:47:05','2003-03-26 11:15:56',2);
INSERT INTO forumthread VALUES (68,4,'New colour?',1072,'Alan','2003-03-26 13:19:00','2003-03-27 07:48:24',4);
INSERT INTO forumthread VALUES (69,5,'New postings',103,'friedlinguini','2003-03-27 04:05:18','2003-03-30 11:35:25',3);
INSERT INTO forumthread VALUES (70,5,'Small update',1,'levik','2003-03-27 08:36:30','2003-03-27 08:36:30',1);
INSERT INTO forumthread VALUES (71,3,'Hey!',1660,'Tim Axoy','2003-03-28 06:18:20','2004-03-03 15:32:36',4);
INSERT INTO forumthread VALUES (72,5,'User levels...',1767,'Fernando','2003-03-28 09:45:17','2003-03-29 04:46:29',3);
INSERT INTO forumthread VALUES (73,7,'hello!',1819,'karla','2003-03-30 01:51:36','2004-01-13 04:08:23',16);
INSERT INTO forumthread VALUES (74,4,'New for you page',1072,'Alan','2003-03-30 15:33:08','2003-04-01 13:32:56',3);
INSERT INTO forumthread VALUES (75,6,'Director',1822,'Gladys','2003-03-31 03:06:42','2004-01-13 04:08:01',11);
INSERT INTO forumthread VALUES (76,4,'Tim Axoy',1,'levik','2003-04-01 04:25:48','2003-04-17 11:48:49',13);
INSERT INTO forumthread VALUES (77,4,'Congratulations to me',775,'Cory Taylor','2003-04-01 05:16:42','2003-05-15 15:02:32',15);
INSERT INTO forumthread VALUES (78,7,'Hello all',1854,'Manoj Nair','2003-04-03 03:08:23','2004-01-13 08:45:10',8);
INSERT INTO forumthread VALUES (79,5,'Time Zone',1301,'Charlie','2003-04-03 09:56:46','2003-04-04 10:53:20',3);
INSERT INTO forumthread VALUES (80,7,'Hello, First time here',1866,'kenny','2003-04-04 05:44:44','2004-01-13 04:08:18',29);
INSERT INTO forumthread VALUES (81,4,'New category',1072,'Alan','2003-04-04 10:13:36','2003-04-05 14:17:57',9);
INSERT INTO forumthread VALUES (82,5,'Am I going crazy?',1072,'Alan','2003-04-05 05:19:36','2003-05-22 09:49:42',16);
INSERT INTO forumthread VALUES (83,5,'blank comments',1575,'DJ','2003-04-05 06:25:58','2003-04-12 17:59:43',7);
INSERT INTO forumthread VALUES (84,6,'Check on divide by zero?',1626,'Gamer','2003-04-06 05:20:00','2004-01-13 04:08:03',10);
INSERT INTO forumthread VALUES (85,4,'Deletion of 3-Thumbs-Down Puzzles',1301,'Charlie','2003-04-06 07:29:01','2003-04-06 11:15:38',2);
INSERT INTO forumthread VALUES (86,7,'Problems',1637,'chris','2003-04-08 08:11:46','2004-01-13 04:08:22',16);
INSERT INTO forumthread VALUES (87,6,'Levik!',NULL,'Tim Axoy','2003-04-10 09:20:32','2004-01-13 04:08:02',4);
INSERT INTO forumthread VALUES (88,4,'problem difficulties',775,'Cory Taylor','2003-04-10 10:37:45','2003-05-31 15:35:32',21);
INSERT INTO forumthread VALUES (89,5,'Delete,delete,delete',1660,'Tim Axoy','2003-04-10 11:41:37','2003-04-19 08:19:21',6);
INSERT INTO forumthread VALUES (90,5,'Long Comments',1301,'Charlie','2003-04-11 04:35:58','2003-04-15 05:55:33',9);
INSERT INTO forumthread VALUES (91,4,'\"Borrowed\" puzzles',1567,'Bryan','2003-04-11 08:58:05','2003-04-11 23:32:57',3);
INSERT INTO forumthread VALUES (92,4,'Preferences?',1567,'Bryan','2003-04-11 12:47:19','2003-04-11 23:39:44',4);
INSERT INTO forumthread VALUES (93,3,'Homer\'s and Horace\'s personalities',1660,'Tim Axoy','2003-04-12 12:03:15','2003-04-14 03:52:14',6);
INSERT INTO forumthread VALUES (94,3,'Tim Axoy',1,'levik','2003-04-13 05:21:58','2003-04-13 07:47:37',2);
INSERT INTO forumthread VALUES (95,7,'Hey guys! New here.',1975,'iris','2003-04-13 13:12:23','2004-01-13 04:08:48',8);
INSERT INTO forumthread VALUES (96,5,'Guest users,who are you???',1660,'Tim Axoy','2003-04-14 02:47:51','2003-04-14 10:36:24',4);
INSERT INTO forumthread VALUES (97,5,'Pi',103,'friedlinguini','2003-04-16 06:02:10','2003-04-22 23:29:39',12);
INSERT INTO forumthread VALUES (98,5,'\"Back to problem\"',1567,'Bryan','2003-04-16 06:52:57','2003-04-16 10:55:23',4);
INSERT INTO forumthread VALUES (99,7,'Hi!',1994,'Tiffy','2003-04-16 16:17:11','2004-01-13 04:08:51',3);
INSERT INTO forumthread VALUES (100,4,'Discovered leviks login password',1567,'Bryan','2003-04-18 13:37:36','2003-05-21 13:12:57',36);
INSERT INTO forumthread VALUES (101,4,'any one affected',1567,'Bryan','2003-04-19 10:07:11','2003-04-19 22:59:24',2);
INSERT INTO forumthread VALUES (102,5,'How often do they...',1660,'Tim Axoy','2003-04-20 03:08:16','2003-04-21 09:36:12',3);
INSERT INTO forumthread VALUES (103,4,'Queue Disappeared',1301,'Charlie','2003-04-20 04:42:41','2003-04-22 01:51:53',7);
INSERT INTO forumthread VALUES (104,5,'can anyone delete his/her own comments?',2005,'Aamir Rashid','2003-04-20 13:31:02','2003-04-21 12:27:49',4);
INSERT INTO forumthread VALUES (105,4,'Uh, this is the REAL Bryan',1567,'Bryan','2003-04-20 19:01:20','2003-04-21 12:51:48',6);
INSERT INTO forumthread VALUES (106,4,'So what happened?',1,'levik','2003-04-21 04:36:11','2003-05-13 13:24:02',4);
INSERT INTO forumthread VALUES (107,5,'Passwords',1,'levik','2003-04-21 04:40:47','2003-04-21 04:40:47',1);
INSERT INTO forumthread VALUES (108,7,'Gladys',1660,'Gladys','2003-04-21 12:52:24','2004-01-13 04:08:40',6);
INSERT INTO forumthread VALUES (109,6,'Plurals as restrictions?',1626,'Gamer','2003-04-21 14:07:31','2004-01-13 04:08:02',18);
INSERT INTO forumthread VALUES (110,5,'Goner?',1660,'Tim Axoy','2003-04-23 02:49:14','2003-06-06 06:15:55',8);
INSERT INTO forumthread VALUES (111,3,'Computer/Programming puzzles',1,'levik','2003-04-23 08:34:35','2003-04-30 07:52:15',19);
INSERT INTO forumthread VALUES (112,4,'Politically Correct Police',775,'Cory Taylor','2003-04-23 08:47:57','2003-04-24 01:53:28',6);
INSERT INTO forumthread VALUES (113,5,'Who\'s Online',979,'Ravi Raja','2003-04-23 09:16:27','2003-04-25 07:07:11',7);
INSERT INTO forumthread VALUES (114,5,'From Liars and knights to Logic',1660,'Tim Axoy','2003-04-23 14:07:52','2003-04-27 09:36:27',13);
INSERT INTO forumthread VALUES (115,7,'Hi..',1983,'Ahmed','2003-04-24 01:05:37','2004-01-13 04:08:50',3);
INSERT INTO forumthread VALUES (116,4,'Blank Puzzles in the Queue',1301,'Charlie','2003-04-25 03:14:47','2003-04-25 08:19:47',7);
INSERT INTO forumthread VALUES (117,4,'Problem condensing',1072,'Alan','2003-04-25 10:29:53','2003-04-28 12:42:23',6);
INSERT INTO forumthread VALUES (118,4,'Solution posted?',1626,'Gamer','2003-04-25 15:25:34','2003-04-26 19:04:36',5);
INSERT INTO forumthread VALUES (119,5,'A figure within the problem',1983,'Ahmed','2003-04-26 22:16:27','2003-04-27 04:08:10',2);
INSERT INTO forumthread VALUES (120,3,'Posting Pictures',1947,'Jon','2003-04-29 09:46:59','2003-04-29 09:47:23',2);
INSERT INTO forumthread VALUES (121,5,'Deleting my own pending problems',1645,'luvya2003','2003-04-29 11:05:11','2003-05-02 02:04:45',13);
INSERT INTO forumthread VALUES (122,5,'Accomodating algorithms',1575,'DJ','2003-05-01 15:00:03','2003-05-01 15:03:35',3);
INSERT INTO forumthread VALUES (123,4,'queue change vote',1072,'Alan','2003-05-01 15:23:46','2003-05-05 13:13:20',8);
INSERT INTO forumthread VALUES (124,7,'A little french in the Flooble.com world',2117,'Grumph NOBIAK','2003-05-02 03:05:29','2004-01-13 04:08:44',5);
INSERT INTO forumthread VALUES (125,4,'Bait and switch',103,'friedlinguini','2003-05-02 03:46:15','2003-05-09 11:21:13',11);
INSERT INTO forumthread VALUES (126,7,'HK engineer',2131,'joe','2003-05-03 22:19:49','2004-01-13 04:08:47',4);
INSERT INTO forumthread VALUES (127,4,'auto-log out un-post',1072,'Alan','2003-05-04 13:44:48','2003-05-06 05:44:57',8);
INSERT INTO forumthread VALUES (128,3,'The existence of god',1072,'Alan','2003-05-04 13:53:44','2003-08-21 21:54:25',30);
INSERT INTO forumthread VALUES (129,7,'Greetings and ??',2171,'Hank Schutz','2003-05-07 12:17:44','2004-01-13 04:08:47',3);
INSERT INTO forumthread VALUES (130,7,'Newbie',2180,'Cara','2003-05-08 08:14:06','2004-01-13 04:08:43',5);
INSERT INTO forumthread VALUES (131,7,'Silly Jilly',2196,'Silly Jilly','2003-05-10 11:40:39','2004-01-13 04:08:43',6);
INSERT INTO forumthread VALUES (132,4,'When do I get to see the hidden forums?',1660,'Tim Axoy','2003-05-13 13:29:48','2003-05-14 16:06:02',8);
INSERT INTO forumthread VALUES (133,6,'Programming for 1000 digit numbers?',NULL,'Brian Smith','2003-05-14 06:01:55','2004-01-13 04:08:00',5);
INSERT INTO forumthread VALUES (134,4,'I have a question',1660,'Tim Axoy','2003-05-14 07:34:39','2003-05-22 11:14:19',7);
INSERT INTO forumthread VALUES (135,4,'Are we self running?',1,'levik','2003-05-15 12:02:08','2003-05-18 05:11:16',14);
INSERT INTO forumthread VALUES (136,4,'Duplicate solutions',1626,'Gamer','2003-05-15 15:08:58','2003-05-15 20:54:06',2);
INSERT INTO forumthread VALUES (137,7,'Hi all',2237,'swaroop','2003-05-15 20:03:56','2004-01-13 04:08:46',4);
INSERT INTO forumthread VALUES (138,7,'just came across.......',2246,'abhi','2003-05-16 23:36:39','2004-01-13 04:08:46',3);
INSERT INTO forumthread VALUES (139,7,'caio',2256,'Jackie','2003-05-18 06:40:41','2004-01-13 04:08:25',6);
INSERT INTO forumthread VALUES (140,4,'MAIN CHARACTER',1660,'Tim Axoy','2003-05-19 02:09:33','2003-06-04 14:01:21',10);
INSERT INTO forumthread VALUES (141,4,'LEV EPSHTEYN',1660,'Tim Axoy','2003-05-19 02:10:14','2003-05-19 13:10:42',2);
INSERT INTO forumthread VALUES (142,7,'Go fish!',NULL,'Go fish!','2003-05-19 05:21:05','2004-01-13 04:08:45',13);
INSERT INTO forumthread VALUES (143,3,'Best puzzle for the masses',1,'levik','2003-05-19 05:45:17','2003-10-12 21:28:37',55);
INSERT INTO forumthread VALUES (144,4,'Solutions queue',1,'levik','2003-05-19 13:13:17','2003-05-19 19:05:04',5);
INSERT INTO forumthread VALUES (145,4,'Journeyman Timothy',1660,'Tim Axoy','2003-05-20 13:02:32','2003-05-26 17:11:20',9);
INSERT INTO forumthread VALUES (146,6,'sequences',775,'Cory Taylor','2003-05-21 04:29:13','2004-01-13 04:07:54',19);
INSERT INTO forumthread VALUES (147,5,'Submitting Problems',1575,'DJ','2003-05-22 17:55:29','2003-05-23 06:07:58',3);
INSERT INTO forumthread VALUES (148,3,'A locked safe',2196,'Silly Jilly','2003-05-23 13:20:02','2003-05-28 14:29:52',2);
INSERT INTO forumthread VALUES (149,7,'No Subject',2290,'Fred','2003-05-23 17:50:46','2004-01-13 04:08:41',5);
INSERT INTO forumthread VALUES (150,4,'Discovered Silly Jilly\'s login password',1660,'Tim Axoy','2003-05-24 02:58:32','2003-05-24 06:11:03',5);
INSERT INTO forumthread VALUES (151,3,'Discovered Silly Jilly\'s login password',1660,'Tim Axoy','2003-05-24 03:00:10','2003-05-24 06:05:31',2);
INSERT INTO forumthread VALUES (152,7,'I am new.',2296,'Bob Jock','2003-05-25 03:39:43','2004-01-13 04:08:43',4);
INSERT INTO forumthread VALUES (155,4,'Solutions allowed?',1626,'Gamer','2003-05-30 16:19:53','2003-05-31 10:46:17',6);
INSERT INTO forumthread VALUES (154,3,'Google Puzzle Championship',1,'levik','2003-05-29 04:29:07','2003-06-04 02:33:09',16);
INSERT INTO forumthread VALUES (156,7,'Yo!',2341,'Pickels','2003-05-30 18:03:08','2004-01-13 04:08:41',3);
INSERT INTO forumthread VALUES (157,3,'Static Queque',2148,'Jayaram S','2003-05-30 19:13:54','2003-05-31 10:47:01',9);
INSERT INTO forumthread VALUES (158,5,'Order of things',1626,'Gamer','2003-05-31 06:20:10','2003-05-31 07:04:24',3);
INSERT INTO forumthread VALUES (159,3,'Knights and liars problems',1660,'Tim Axoy','2003-06-01 03:19:50','2003-06-09 13:29:57',6);
INSERT INTO forumthread VALUES (160,7,'hello',2355,'annastashya','2003-06-01 16:58:39','2004-01-13 04:08:39',4);
INSERT INTO forumthread VALUES (161,7,'Maybe I\'ll get smarter?',2356,'Stefanie','2003-06-01 21:33:49','2004-01-13 04:08:40',2);
INSERT INTO forumthread VALUES (162,7,'Maybe I\'ll get smarter?',2356,'Stefanie','2003-06-01 21:35:02','2004-01-13 04:08:39',3);
INSERT INTO forumthread VALUES (163,5,'New bugs?',1575,'DJ','2003-06-02 12:06:12','2003-06-04 11:22:48',5);
INSERT INTO forumthread VALUES (164,4,'Scholars',1660,'Tim Axoy','2003-06-03 05:59:36','2003-06-10 16:32:49',7);
INSERT INTO forumthread VALUES (165,4,'User search/list?',1,'levik','2003-06-03 17:32:46','2003-06-08 09:25:23',5);
INSERT INTO forumthread VALUES (166,4,'DJ or .?',1660,'Tim Axoy','2003-06-04 05:33:59','2003-06-06 06:17:26',3);
INSERT INTO forumthread VALUES (167,7,'What\'s new? Me!',2385,'Bradley A. Esparza','2003-06-07 02:01:57','2004-01-13 04:08:38',5);
INSERT INTO forumthread VALUES (168,6,'Cool.',NULL,'URGENTOOT','2003-06-08 02:42:13','2004-01-13 04:08:00',3);
INSERT INTO forumthread VALUES (169,3,'500!',1,'levik','2003-06-08 09:07:53','2003-06-25 08:30:31',12);
INSERT INTO forumthread VALUES (170,4,'Cool symbols',1072,'Alan','2003-06-08 16:24:04','2003-06-13 11:23:36',7);
INSERT INTO forumthread VALUES (171,3,'Partial goodbye',775,'Cory Taylor','2003-06-09 06:20:37','2003-06-09 10:30:59',5);
INSERT INTO forumthread VALUES (172,5,'Crypto',1,'levik','2003-06-09 08:48:41','2003-06-14 17:05:28',15);
INSERT INTO forumthread VALUES (173,6,'To Tim Axoy',1,'levik','2003-06-09 17:37:14','2004-01-13 04:07:57',23);
INSERT INTO forumthread VALUES (174,5,'Putting Pictures in Pending Problems',1919,'Lewis','2003-06-11 05:36:58','2003-06-12 02:00:51',3);
INSERT INTO forumthread VALUES (175,5,'a suggestion for comments',2256,'Jackie','2003-06-11 15:51:20','2003-06-12 09:07:32',4);
INSERT INTO forumthread VALUES (176,5,'Problem flooding revisited',1,'levik','2003-06-12 11:38:42','2003-09-28 15:00:25',66);
INSERT INTO forumthread VALUES (177,7,'S\'up?',2438,'Maryam','2003-06-13 11:48:48','2004-01-13 04:08:38',4);
INSERT INTO forumthread VALUES (178,5,'Submission bar raised to Student level',1,'levik','2003-06-16 07:31:29','2003-06-16 16:37:43',6);
INSERT INTO forumthread VALUES (179,5,'Aw fiddle, another riddle.',1919,'Lewis','2003-06-18 04:28:13','2003-06-18 05:05:22',2);
INSERT INTO forumthread VALUES (180,5,'The riddle problem',1072,'Alan','2003-06-18 10:42:56','2004-01-07 17:54:44',18);
INSERT INTO forumthread VALUES (181,5,'After submitting a problem...',1626,'Gamer','2003-06-19 16:03:15','2003-06-19 16:03:15',1);
INSERT INTO forumthread VALUES (182,7,'nope.',2436,'Chris','2003-06-20 05:20:04','2004-01-13 04:08:40',2);
INSERT INTO forumthread VALUES (183,7,'nope.',2436,'Chris','2003-06-20 05:58:28','2004-01-13 04:08:38',4);
INSERT INTO forumthread VALUES (184,5,'Problem Comments',1575,'DJ','2003-06-20 06:21:09','2003-06-20 11:27:23',2);
INSERT INTO forumthread VALUES (185,4,'The queue needs help now!',1567,'Bryan','2003-06-20 07:02:23','2003-06-20 16:27:20',4);
INSERT INTO forumthread VALUES (186,6,'Log?',1919,'Lewis','2003-06-21 09:57:57','2004-02-17 19:02:10',10);
INSERT INTO forumthread VALUES (187,7,'The Gong Problem',2513,'Dom','2003-06-22 17:19:12','2004-01-13 04:08:36',5);
INSERT INTO forumthread VALUES (188,7,'Hello!',2536,'Peter','2003-06-23 22:49:35','2004-01-13 04:08:37',3);
INSERT INTO forumthread VALUES (189,5,'Just a Suggestion...',2536,'Peter','2003-06-23 22:56:07','2003-06-23 22:56:07',1);
INSERT INTO forumthread VALUES (190,3,'Triangles?',2436,'Chris','2003-06-24 01:54:28','2003-06-24 01:59:45',2);
INSERT INTO forumthread VALUES (191,6,'Spacing in Problems',1626,'Gamer','2003-06-24 04:52:15','2004-01-13 04:08:01',9);
INSERT INTO forumthread VALUES (192,5,'Where\'s my problem?',1567,'Bryan','2003-06-24 05:04:48','2003-06-24 09:41:42',3);
INSERT INTO forumthread VALUES (193,7,'newbie',2545,'rajesh','2003-06-24 21:20:34','2004-01-13 04:08:36',4);
INSERT INTO forumthread VALUES (194,4,'the most commented on... or is it?',1072,'Alan','2003-06-25 15:30:13','2003-06-26 09:50:41',6);
INSERT INTO forumthread VALUES (195,5,'Queue Idea',1626,'Gamer','2003-06-28 04:28:11','2003-06-29 09:54:56',6);
INSERT INTO forumthread VALUES (196,5,'How do I',1072,'Alan','2003-07-01 07:51:34','2003-07-01 10:05:05',2);
INSERT INTO forumthread VALUES (197,7,'No Subject',2599,'amy','2003-07-02 08:34:16','2004-01-13 04:08:36',5);
INSERT INTO forumthread VALUES (198,7,'hey all',2604,'Koren','2003-07-02 14:48:08','2004-01-13 04:08:36',3);
INSERT INTO forumthread VALUES (199,5,'Vacation',1,'levik','2003-07-03 09:06:21','2003-07-03 12:28:36',3);
INSERT INTO forumthread VALUES (200,4,'Its working',1072,'Alan','2003-07-03 14:24:57','2003-08-08 14:52:17',19);
INSERT INTO forumthread VALUES (201,4,'Quick Switch',1626,'Gamer','2003-07-03 14:49:24','2003-07-12 08:07:38',5);
INSERT INTO forumthread VALUES (202,7,'Another first posting :)',2627,'Andrew','2003-07-05 17:30:21','2004-01-13 04:08:35',9);
INSERT INTO forumthread VALUES (203,4,'Can\'t understand',1072,'Alan','2003-07-06 08:09:06','2003-07-06 08:09:06',1);
INSERT INTO forumthread VALUES (204,7,'No Subject',2639,'Billie Freeman','2003-07-07 15:40:37','2004-01-13 04:08:10',8);
INSERT INTO forumthread VALUES (205,7,'Hi. I\'m new at this.',2639,'Billie Freeman','2003-07-07 15:42:55','2004-03-23 15:06:52',11);
INSERT INTO forumthread VALUES (206,3,'Favourite Puzzle',1919,'Lewis','2003-07-08 09:44:20','2003-08-11 05:07:15',12);
INSERT INTO forumthread VALUES (207,7,'Hey everyone',2653,'Lucy','2003-07-08 10:25:39','2004-01-13 04:08:34',4);
INSERT INTO forumthread VALUES (208,4,'Secret Forum!',1919,'Lewis','2003-07-11 01:38:07','2003-07-30 01:55:41',5);
INSERT INTO forumthread VALUES (209,4,'My Problems',1919,'Lewis','2003-07-11 12:13:09','2003-07-13 04:57:41',8);
INSERT INTO forumthread VALUES (210,4,'My Vacation',1072,'Alan','2003-07-11 16:16:31','2003-07-12 00:26:41',3);
INSERT INTO forumthread VALUES (211,5,'Back From vacation',1,'levik','2003-07-13 13:50:32','2003-07-14 08:17:00',10);
INSERT INTO forumthread VALUES (212,7,'Hey!',2728,'Amanda','2003-07-15 15:19:38','2004-01-13 04:08:34',2);
INSERT INTO forumthread VALUES (213,5,'Slow server?',1,'levik','2003-07-17 19:05:28','2003-08-29 20:45:45',6);
INSERT INTO forumthread VALUES (214,4,'Stealing Puzzles',1919,'Lewis','2003-07-18 11:04:12','2003-08-02 05:37:38',21);
INSERT INTO forumthread VALUES (215,4,'Duplicate problems',1626,'Gamer','2003-07-19 10:00:58','2003-07-21 20:49:00',8);
INSERT INTO forumthread VALUES (216,3,'Order of Posting',1626,'Gamer','2003-07-23 02:45:10','2003-09-09 22:12:56',15);
INSERT INTO forumthread VALUES (217,3,'NEED HELP!',2832,'Tara','2003-07-23 15:59:13','2003-11-11 12:56:35',13);
INSERT INTO forumthread VALUES (218,4,'queue weight (wait) info',775,'Cory Taylor','2003-07-24 17:43:07','2003-07-24 17:43:07',1);
INSERT INTO forumthread VALUES (219,7,'Hello',2855,'Kesia Ihle','2003-07-25 08:57:54','2004-01-13 04:08:32',3);
INSERT INTO forumthread VALUES (220,4,'Petition Director',1,'levik','2003-07-29 10:03:40','2003-08-07 07:36:03',13);
INSERT INTO forumthread VALUES (221,7,'Hi.',2912,'Talon5000','2003-07-29 13:10:07','2004-01-13 04:08:31',4);
INSERT INTO forumthread VALUES (222,7,'hi everyone',2919,'darpan jain','2003-07-30 02:27:23','2004-01-13 04:08:34',4);
INSERT INTO forumthread VALUES (223,4,'Pushing order',1,'levik','2003-07-31 06:26:03','2003-08-19 14:26:16',12);
INSERT INTO forumthread VALUES (224,7,'new here',2921,'Salem D','2003-08-01 17:21:10','2004-01-13 04:08:31',3);
INSERT INTO forumthread VALUES (225,7,'dorkdork & gina.. same person',2898,'dorkdork','2003-08-02 05:39:51','2004-01-13 04:08:31',3);
INSERT INTO forumthread VALUES (226,4,'No solution still OK?',1626,'Gamer','2003-08-02 10:16:44','2003-08-03 06:51:47',4);
INSERT INTO forumthread VALUES (227,7,'Howdy! I\'m new here y\'all',2968,'Rikki','2003-08-02 18:33:36','2004-01-13 04:08:30',2);
INSERT INTO forumthread VALUES (228,4,'Posting unapproved problems?',1567,'Bryan','2003-08-04 06:48:50','2003-08-06 11:00:42',9);
INSERT INTO forumthread VALUES (229,7,'Hi',2992,'Chan Wah','2003-08-04 15:19:40','2004-01-13 04:08:29',2);
INSERT INTO forumthread VALUES (230,5,'Possible weirdness in the days to come',1,'levik','2003-08-05 16:02:50','2003-08-09 12:19:29',7);
INSERT INTO forumthread VALUES (231,7,'Another Newbie here!',3005,'Mathcop','2003-08-05 16:06:12','2004-01-13 04:08:27',12);
INSERT INTO forumthread VALUES (232,7,'Newbie here...',3020,'Mikal','2003-08-06 16:22:44','2004-01-13 04:08:29',3);
INSERT INTO forumthread VALUES (233,4,'Combining puzzles',1567,'Bryan','2003-08-07 11:11:58','2003-08-07 13:30:27',3);
INSERT INTO forumthread VALUES (234,4,'Help with Algorithms',1919,'Lewis','2003-08-07 17:28:44','2003-08-07 21:29:02',4);
INSERT INTO forumthread VALUES (235,6,'Word lists',1567,'Bryan','2003-08-08 16:10:47','2004-01-13 04:08:00',8);
INSERT INTO forumthread VALUES (236,7,'The newest newbie',3075,'Daniel','2003-08-11 05:47:08','2004-01-13 04:08:29',5);
INSERT INTO forumthread VALUES (237,3,'A silly whim',2839,'FatBoy','2003-08-11 08:28:18','2003-08-14 19:10:20',8);
INSERT INTO forumthread VALUES (238,4,'New Scholar ability',1,'levik','2003-08-13 11:29:08','2003-08-13 22:37:02',5);
INSERT INTO forumthread VALUES (239,3,'good site',1637,'chris','2003-08-13 19:15:11','2003-08-14 17:36:37',3);
INSERT INTO forumthread VALUES (240,4,'Posting solutions prematurely',1567,'Bryan','2003-08-15 14:49:41','2003-08-16 20:20:56',9);
INSERT INTO forumthread VALUES (241,3,'Blackout',1,'levik','2003-08-16 01:49:18','2003-11-05 12:32:51',8);
INSERT INTO forumthread VALUES (242,4,'-3 Deletion',1626,'Gamer','2003-08-17 19:47:28','2003-08-18 10:52:21',3);
INSERT INTO forumthread VALUES (243,5,'I can\'t submit anything',2121,'Chaz','2003-08-18 12:34:01','2003-08-18 15:06:05',2);
INSERT INTO forumthread VALUES (244,7,'How are yez?',3155,'Harriet','2003-08-19 04:27:29','2004-01-13 04:08:28',2);
INSERT INTO forumthread VALUES (245,7,'math puzzles i need help please!!',3208,'dea','2003-08-23 14:05:55','2004-01-13 04:08:11',9);
INSERT INTO forumthread VALUES (246,4,'Group Duplicate Problems',1626,'Gamer','2003-08-23 14:40:36','2003-08-26 00:04:57',8);
INSERT INTO forumthread VALUES (247,7,'Submitting Problems',3136,'Popstar Dave','2003-08-24 12:13:38','2004-01-13 04:08:27',5);
INSERT INTO forumthread VALUES (248,5,'Comment editing',1,'levik','2003-08-25 19:19:05','2003-08-26 09:12:00',4);
INSERT INTO forumthread VALUES (249,7,'Ok.. I have no Idea.. But I\'m new.. lol',3258,'AmE','2003-08-27 08:38:58','2004-01-13 04:08:27',11);
INSERT INTO forumthread VALUES (250,3,'Money making Idea...',2839,'FatBoy','2003-08-28 15:42:46','2003-08-30 09:19:38',8);
INSERT INTO forumthread VALUES (251,4,'Easy problems',1567,'Bryan','2003-08-29 12:25:38','2003-08-29 16:07:09',3);
INSERT INTO forumthread VALUES (252,5,'The Flooble \'get out the links\' Drive',1,'levik','2003-08-29 15:31:45','2003-08-29 15:31:45',1);
INSERT INTO forumthread VALUES (253,7,'hi there',3241,'cat','2003-08-29 20:40:48','2004-01-13 04:08:26',4);
INSERT INTO forumthread VALUES (254,7,'No Subject',NULL,'Kitten*Meow','2003-08-30 10:27:24','2004-01-13 04:08:26',2);
INSERT INTO forumthread VALUES (255,7,'myself',3323,'Nicholas','2003-09-01 19:39:09','2004-01-13 04:08:26',3);
INSERT INTO forumthread VALUES (256,4,'Solution Strategy',1626,'Gamer','2003-09-04 17:48:39','2003-09-05 15:21:40',4);
INSERT INTO forumthread VALUES (257,3,'not a puzzle...',2839,'FatBoy','2003-09-05 09:45:05','2003-09-05 09:48:14',2);
INSERT INTO forumthread VALUES (258,3,'Avatars!',1,'levik','2003-09-05 17:14:34','2003-09-09 23:25:54',46);
INSERT INTO forumthread VALUES (259,7,'another new guy',3397,'aaron','2003-09-08 13:33:03','2004-01-13 04:08:25',3);
INSERT INTO forumthread VALUES (260,3,'Methinks the rate should increase !',3172,'SilverKnight','2003-09-08 18:10:49','2003-09-10 23:01:16',16);
INSERT INTO forumthread VALUES (261,4,'Scav game',1,'levik','2003-09-10 20:15:53','2003-09-16 17:50:36',19);
INSERT INTO forumthread VALUES (262,4,'Top 10',1920,'Brian Smith','2003-09-11 14:46:00','2003-09-12 12:30:04',7);
INSERT INTO forumthread VALUES (263,5,'Retired problem types',1626,'Gamer','2003-09-12 19:25:10','2003-09-12 19:25:10',1);
INSERT INTO forumthread VALUES (264,7,'HELLO',3495,'Andrew','2003-09-17 07:53:34','2004-01-13 04:08:21',3);
INSERT INTO forumthread VALUES (265,5,'I propose a new problem category...',3172,'SilverKnight','2003-09-17 12:35:34','2003-09-20 11:00:32',22);
INSERT INTO forumthread VALUES (312,5,'Base 1 and Base 0',3386,'Victor Zapana','2003-11-18 20:36:39','2004-02-06 18:17:12',15);
INSERT INTO forumthread VALUES (267,7,'how are uz?',3559,'Kyle Jung','2003-09-20 13:20:21','2004-01-13 04:08:25',3);
INSERT INTO forumthread VALUES (268,7,'Hi, everybody!',3558,'Tristan','2003-09-21 11:24:17','2004-01-13 04:08:25',4);
INSERT INTO forumthread VALUES (269,5,'problem with submitting',3558,'Tristan','2003-09-22 21:20:10','2003-09-25 18:12:58',9);
INSERT INTO forumthread VALUES (270,5,'recently solved',1220,'abc','2003-09-23 07:44:46','2003-09-23 09:23:11',2);
INSERT INTO forumthread VALUES (271,3,'New answer to Zeno\'s Paradox',3372,'Sam','2003-09-24 00:24:38','2003-09-26 19:00:17',6);
INSERT INTO forumthread VALUES (272,7,'First timer',3546,'RoyCook','2003-09-24 11:25:29','2004-01-13 04:08:24',11);
INSERT INTO forumthread VALUES (273,3,'brain teasers',3601,'Tammy Skaggs','2003-09-24 13:18:46','2004-01-05 03:35:37',11);
INSERT INTO forumthread VALUES (274,7,'hello there!!',3636,'karen anne','2003-09-26 23:12:43','2004-01-13 04:08:24',3);
INSERT INTO forumthread VALUES (275,5,'The FAQ WIP',1,'levik','2003-09-28 15:03:02','2003-11-04 07:45:04',22);
INSERT INTO forumthread VALUES (276,7,'No Subject',NULL,'Aspiring Novice','2003-09-30 09:06:26','2004-01-13 04:08:10',10);
INSERT INTO forumthread VALUES (277,5,'Problem flooding re-revisited',3172,'SilverKnight','2003-10-02 17:36:41','2004-03-18 05:17:49',24);
INSERT INTO forumthread VALUES (278,3,'Can anyone recap my memory',3717,'SK','2003-10-03 05:48:01','2003-10-15 18:00:53',10);
INSERT INTO forumthread VALUES (279,5,'Help (Stupid question)',3546,'RoyCook','2003-10-06 14:16:30','2003-12-03 19:32:41',13);
INSERT INTO forumthread VALUES (280,7,'ratings vs. difficulty level',1112,'Greg','2003-10-06 18:35:13','2004-01-13 04:08:23',4);
INSERT INTO forumthread VALUES (281,7,'Hi! New guy',3778,'Marcelo','2003-10-07 17:52:59','2004-01-13 04:08:23',3);
INSERT INTO forumthread VALUES (282,5,'Advertising',3372,'Sam','2003-10-08 08:52:43','2004-03-24 22:40:29',47);
INSERT INTO forumthread VALUES (283,5,'Previewing pi',3558,'Tristan','2003-10-10 00:29:47','2003-10-10 17:58:37',3);
INSERT INTO forumthread VALUES (284,3,'Hey, DJ',2839,'FatBoy','2003-10-10 14:38:53','2003-10-14 09:09:24',4);
INSERT INTO forumthread VALUES (285,7,'Help me with this',3880,'brian harrison','2003-10-14 17:44:26','2004-01-13 04:08:22',4);
INSERT INTO forumthread VALUES (286,5,'Changing Categories',3372,'Sam','2003-10-20 12:09:13','2003-10-26 14:46:54',9);
INSERT INTO forumthread VALUES (287,7,'Hey, yet another newbie!!',3785,'Ashlee','2003-10-21 05:45:03','2004-01-13 04:08:14',22);
INSERT INTO forumthread VALUES (288,7,'D&D Riddle anyone?',3966,'Rock','2003-10-21 11:51:06','2004-01-13 04:08:21',3);
INSERT INTO forumthread VALUES (289,3,'Riddle for you all...',3966,'Rock','2003-10-21 14:55:18','2003-12-31 11:56:13',9);
INSERT INTO forumthread VALUES (290,3,'Languages',1072,'Alan','2003-10-25 21:27:09','2003-10-30 23:22:44',9);
INSERT INTO forumthread VALUES (291,7,'New here - HELP ME!',4023,'Romulo','2003-10-25 23:57:08','2004-01-13 04:08:20',6);
INSERT INTO forumthread VALUES (292,4,'How did Puzzle Strips appear?',1301,'Charlie','2003-10-26 18:06:22','2003-10-27 10:57:56',3);
INSERT INTO forumthread VALUES (293,7,'NEWBIE',3386,'Victor Zapana','2003-10-27 21:17:34','2004-01-13 04:08:20',3);
INSERT INTO forumthread VALUES (294,7,'I love Google!',4063,'Delta','2003-10-28 15:15:48','2004-01-13 04:08:19',13);
INSERT INTO forumthread VALUES (295,4,'Queue Placement?',1626,'Gamer','2003-10-29 06:10:17','2003-10-30 20:05:52',4);
INSERT INTO forumthread VALUES (296,4,'Scholars - edit queue problems',1,'levik','2003-10-29 13:38:37','2003-10-29 13:38:37',1);
INSERT INTO forumthread VALUES (297,7,'Getting problems posted...',3136,'Popstar Dave','2003-10-30 06:48:13','2004-01-13 04:08:21',10);
INSERT INTO forumthread VALUES (298,6,'???',3386,'Victor Zapana','2003-10-30 20:52:47','2004-01-13 04:07:58',4);
INSERT INTO forumthread VALUES (302,7,'hello!',4122,'Hazel','2003-11-01 21:16:42','2004-01-13 04:08:21',5);
INSERT INTO forumthread VALUES (300,5,'Scavenger Hunt',3372,'Sam','2003-10-30 23:48:25','2003-11-07 14:26:59',45);
INSERT INTO forumthread VALUES (301,3,'WOOHOO!!!',3172,'SilverKnight','2003-10-31 10:46:45','2004-01-12 21:47:11',41);
INSERT INTO forumthread VALUES (303,5,'Posting solutions to your problems',3136,'Popstar Dave','2003-11-02 19:05:38','2003-11-02 21:22:25',2);
INSERT INTO forumthread VALUES (304,7,'Looking for the name of a puzzle',4156,'Jim Collins','2003-11-03 18:59:10','2004-01-13 04:08:13',12);
INSERT INTO forumthread VALUES (305,4,'A problem',1072,'Alan','2003-11-04 15:52:51','2003-11-05 16:54:40',4);
INSERT INTO forumthread VALUES (306,4,'New category',1072,'Alan','2003-11-05 14:44:09','2003-11-07 23:04:32',8);
INSERT INTO forumthread VALUES (307,7,'a new newbie',4208,'nobrain','2003-11-07 13:07:24','2004-01-13 04:08:18',4);
INSERT INTO forumthread VALUES (308,5,'The new Scavenger Thread',1,'levik','2003-11-07 15:50:46','2003-12-11 16:40:37',32);
INSERT INTO forumthread VALUES (309,5,'Where does Flooble live?',3136,'Popstar Dave','2003-11-08 08:57:33','2003-11-09 09:24:00',3);
INSERT INTO forumthread VALUES (310,4,'Perplexus-etiquette',3136,'Popstar Dave','2003-11-13 00:41:04','2003-11-13 16:11:45',3);
INSERT INTO forumthread VALUES (311,3,'need solution,HELP',4355,'AJ','2003-11-17 03:56:25','2003-11-17 07:22:00',3);
INSERT INTO forumthread VALUES (313,7,'Finally got here',4396,'Fred','2003-11-19 16:45:16','2004-01-13 04:08:16',5);
INSERT INTO forumthread VALUES (314,3,'Riddle... \"Brothers & Sisters\"',4396,'Fred','2003-11-19 17:05:30','2004-02-04 11:21:47',4);
INSERT INTO forumthread VALUES (315,7,'In a slight pickel',4425,'Sam','2003-11-21 02:09:57','2004-01-13 04:08:16',12);
INSERT INTO forumthread VALUES (316,7,'Hey all',4447,'Greg','2003-11-22 12:09:49','2004-01-13 04:08:15',10);
INSERT INTO forumthread VALUES (317,7,'New here',4452,'Lisa','2003-11-22 20:39:53','2004-01-13 04:08:19',7);
INSERT INTO forumthread VALUES (318,5,'Do we need a chat?',1,'levik','2003-11-24 12:46:53','2003-11-27 11:34:51',30);
INSERT INTO forumthread VALUES (319,3,'Herons formula',4450,'drew','2003-11-24 14:31:01','2003-11-27 23:25:06',17);
INSERT INTO forumthread VALUES (320,6,'.5!',3558,'Tristan','2003-11-25 01:41:23','2004-03-12 12:07:36',12);
INSERT INTO forumthread VALUES (321,5,'algorithm problems',3172,'SilverKnight','2003-11-25 13:09:02','2003-12-04 14:44:08',24);
INSERT INTO forumthread VALUES (322,5,'Chat with SK(herons formula cont.)',4450,'drew','2003-11-26 14:30:26','2003-11-27 11:37:42',7);
INSERT INTO forumthread VALUES (323,5,'Happy Thanksgiving fellow flooblers !!!',3172,'SilverKnight','2003-11-27 12:37:48','2003-11-27 12:37:48',1);
INSERT INTO forumthread VALUES (324,7,'hi everyone',4530,'Benjamin','2003-11-28 01:04:29','2004-01-13 04:08:16',3);
INSERT INTO forumthread VALUES (325,4,'Screen difference',1626,'Gamer','2003-11-29 06:58:06','2003-11-30 11:19:05',4);
INSERT INTO forumthread VALUES (326,4,'About Penny',1626,'Gamer','2003-11-30 18:41:47','2004-03-23 15:09:52',35);
INSERT INTO forumthread VALUES (327,3,'hitchhike to the dark side of the moon',4300,'Minion123','2003-12-02 00:25:43','2004-01-04 02:26:53',23);
INSERT INTO forumthread VALUES (328,6,'Testing',1575,'DJ','2003-12-02 23:33:06','2004-01-20 12:30:18',10);
INSERT INTO forumthread VALUES (329,5,'A Homework Forum?????',2839,'FatBoy','2003-12-04 11:16:09','2003-12-05 09:10:29',16);
INSERT INTO forumthread VALUES (330,4,'ICQ',3172,'SilverKnight','2003-12-04 18:58:18','2003-12-07 02:35:04',11);
INSERT INTO forumthread VALUES (331,4,'Hiding one\'s previous comments/solutions',3172,'SilverKnight','2003-12-08 17:16:15','2003-12-13 22:03:38',17);
INSERT INTO forumthread VALUES (332,4,'Good job, everybody',1567,'Bryan','2003-12-09 11:30:19','2003-12-09 11:30:19',1);
INSERT INTO forumthread VALUES (333,4,'didn\'t mean to ignore ya!',3172,'SilverKnight','2003-12-12 15:50:51','2003-12-17 15:11:41',3);
INSERT INTO forumthread VALUES (334,7,'bored & sleepy',4786,'winnie','2003-12-13 16:05:06','2004-01-13 04:08:15',3);
INSERT INTO forumthread VALUES (335,7,'How I got here...',4788,'corey','2003-12-13 16:41:57','2004-01-13 04:08:15',6);
INSERT INTO forumthread VALUES (336,4,'help me make a problem?',1072,'Alan','2003-12-13 22:30:08','2003-12-19 14:56:14',7);
INSERT INTO forumthread VALUES (337,4,'lack of levik',1,'levik','2003-12-17 08:37:04','2003-12-17 11:13:12',2);
INSERT INTO forumthread VALUES (338,5,'God and Flooble',2839,'FatBoy','2003-12-18 08:49:04','2003-12-22 03:35:21',8);
INSERT INTO forumthread VALUES (339,7,'it\'s just me and me is good',4778,'chic','2003-12-18 23:24:50','2004-01-13 04:08:13',7);
INSERT INTO forumthread VALUES (340,7,'Submitting problems',2130,'ethan','2003-12-20 21:41:01','2004-01-13 04:08:15',2);
INSERT INTO forumthread VALUES (341,7,'I Found You...',4899,'Andrea','2003-12-21 16:38:35','2004-01-13 04:08:14',2);
INSERT INTO forumthread VALUES (342,7,'??',4904,'WanD','2003-12-22 03:53:37','2004-01-13 04:08:13',2);
INSERT INTO forumthread VALUES (343,4,'Ya tune out for one weekend and...',1567,'Bryan','2003-12-23 01:03:53','2003-12-23 11:55:43',2);
INSERT INTO forumthread VALUES (344,7,'Introducing myself',4916,'Ian','2003-12-23 04:56:31','2004-01-13 04:08:08',5);
INSERT INTO forumthread VALUES (345,3,'United States football',2130,'ethan','2003-12-27 00:26:52','2003-12-27 00:30:14',2);
INSERT INTO forumthread VALUES (346,7,'Just Registered - Newbie',4954,'spunky','2003-12-27 03:55:27','2004-01-13 04:08:12',3);
INSERT INTO forumthread VALUES (347,4,'Algorithms versus Homework?',1626,'Gamer','2003-12-27 12:09:55','2003-12-28 09:52:50',4);
INSERT INTO forumthread VALUES (348,7,'new addict loggin on....',4967,'Jo-Anne','2003-12-28 10:44:54','2004-01-13 04:08:12',4);
INSERT INTO forumthread VALUES (349,7,'Just Flew In from the Internet...',4970,'Jack the Reaper','2003-12-28 18:29:17','2004-01-13 04:08:08',3);
INSERT INTO forumthread VALUES (350,3,'Here\'s something you don\'t see every day',1575,'DJ','2003-12-29 11:08:33','2003-12-29 22:25:18',2);
INSERT INTO forumthread VALUES (351,7,'How much education?',4925,'Jeff','2003-12-30 17:38:27','2004-01-13 04:08:09',3);
INSERT INTO forumthread VALUES (352,7,'Hi people!',4999,'Lou','2003-12-30 20:36:48','2004-01-13 04:08:10',2);
INSERT INTO forumthread VALUES (353,3,'Happy New Year!',1,'levik','2003-12-31 13:39:21','2003-12-31 13:39:21',1);
INSERT INTO forumthread VALUES (354,7,'Hello, I\'m new',5020,'*Erin*','2004-01-02 20:34:09','2004-01-13 04:08:09',3);
INSERT INTO forumthread VALUES (355,4,'The (BIG) solutions push',1,'levik','2004-01-04 12:51:38','2004-03-21 10:22:04',9);
INSERT INTO forumthread VALUES (356,7,'novice standing',4909,'Brian','2004-01-04 20:15:06','2004-01-13 04:08:06',5);
INSERT INTO forumthread VALUES (357,5,'How long until I move ahead?',5033,'Captain Paradox','2004-01-04 21:26:43','2004-01-08 16:17:06',7);
INSERT INTO forumthread VALUES (358,3,'Queue weighting',2130,'ethan','2004-01-05 17:33:19','2004-01-05 17:33:19',1);
INSERT INTO forumthread VALUES (359,7,'Anyone know 20 questions type of riddles',5059,'Shelly','2004-01-05 17:51:42','2004-01-13 04:08:09',4);
INSERT INTO forumthread VALUES (360,3,'hi',5062,'Steve','2004-01-05 19:42:10','2004-01-05 19:42:10',1);
INSERT INTO forumthread VALUES (361,7,'i am new',5062,'Steve','2004-01-05 19:47:33','2004-01-13 04:08:09',2);
INSERT INTO forumthread VALUES (362,7,'Looky here.......video games.',5065,'Darryl','2004-01-05 22:36:07','2004-01-13 04:08:07',5);
INSERT INTO forumthread VALUES (363,7,'Helloooooooooooo',5065,'Darryl','2004-01-05 22:38:29','2004-01-13 04:08:08',2);
INSERT INTO forumthread VALUES (364,5,'How old is flooble?',5033,'Captain Paradox','2004-01-07 18:02:59','2004-01-21 08:34:46',13);
INSERT INTO forumthread VALUES (365,7,'Membership',NULL,'Acid - Non member','2004-01-08 04:42:49','2004-01-13 04:08:06',5);
INSERT INTO forumthread VALUES (366,7,'Hi',5106,'justin','2004-01-08 09:56:54','2004-01-13 04:08:07',2);
INSERT INTO forumthread VALUES (367,7,'chloe flowers anyone no me????',5148,'chloe flowers','2004-01-11 11:34:54','2004-01-13 04:08:05',2);
INSERT INTO forumthread VALUES (368,7,'Logging in for the first time!',5157,'Ben Beauty','2004-01-12 10:41:34','2004-01-21 19:56:20',4);
INSERT INTO forumthread VALUES (369,6,'No Subject',NULL,'Aspiring Novice','2004-01-13 04:07:52','2004-01-13 04:23:01',2);
INSERT INTO forumthread VALUES (370,7,'No Subject',NULL,'Aspiring Novice','2004-01-13 04:08:05','2004-02-02 06:29:02',3);
INSERT INTO forumthread VALUES (371,4,'136 new forum posts',3136,'Popstar Dave','2004-01-13 05:10:15','2004-01-15 09:23:21',9);
INSERT INTO forumthread VALUES (372,7,'Hello',5193,'Mike McGowan','2004-01-14 13:01:53','2004-02-23 17:09:54',18);
INSERT INTO forumthread VALUES (373,3,'I dont know what to do.',5199,'Sarah','2004-01-14 18:31:36','2004-02-04 11:29:01',2);
INSERT INTO forumthread VALUES (374,5,'Blast it!',5033,'Captain Paradox','2004-01-18 22:15:41','2004-01-19 21:46:02',7);
INSERT INTO forumthread VALUES (375,5,'Rich edit control',1,'levik','2004-01-19 11:04:59','2004-02-02 23:49:48',23);
INSERT INTO forumthread VALUES (376,7,'Hi ! every1',5257,'Raza','2004-01-20 08:07:41','2004-01-20 08:07:41',1);
INSERT INTO forumthread VALUES (377,4,'Rich Edit Control (continued)',1575,'DJ','2004-01-20 11:43:31','2004-02-16 10:54:11',3);
INSERT INTO forumthread VALUES (378,4,'uh... like, uh...',3172,'SilverKnight','2004-01-20 14:11:44','2004-01-20 21:48:47',4);
INSERT INTO forumthread VALUES (379,5,'Candy machine system?',5033,'Captain Paradox','2004-01-20 22:00:42','2004-01-21 20:31:50',7);
INSERT INTO forumthread VALUES (380,7,'Hi....',5283,'Sivaprasad','2004-01-22 07:23:13','2004-01-22 08:37:29',2);
INSERT INTO forumthread VALUES (381,3,'Cryptography Question',1928,'The Mighty Puck','2004-01-23 15:49:09','2004-03-16 10:38:18',9);
INSERT INTO forumthread VALUES (382,7,'Any genetic puzzlers?',5345,'Rawlyn','2004-01-26 20:23:23','2004-01-29 10:00:31',5);
INSERT INTO forumthread VALUES (383,7,'No Subject',5361,'Sandeep','2004-01-27 14:17:31','2004-01-27 14:17:31',1);
INSERT INTO forumthread VALUES (384,4,'\"newest problem\" addition',3172,'SilverKnight','2004-01-29 02:31:02','2004-02-27 14:05:09',17);
INSERT INTO forumthread VALUES (385,7,'Hey!',5420,'Orfeus','2004-01-31 10:45:14','2004-01-31 10:45:14',1);
INSERT INTO forumthread VALUES (386,4,'Congratulations to our newest Apprentice',3172,'SilverKnight','2004-02-02 10:49:26','2004-02-26 20:24:40',9);
INSERT INTO forumthread VALUES (387,5,'Recently Posted Solution',1,'levik','2004-02-03 14:00:31','2004-02-04 09:58:56',9);
INSERT INTO forumthread VALUES (388,3,'No Subject',5033,'Captain Paradox','2004-02-04 19:56:55','2004-02-07 00:55:37',4);
INSERT INTO forumthread VALUES (389,4,'Problem precision',3172,'SilverKnight','2004-02-05 12:58:01','2004-02-12 06:30:52',9);
INSERT INTO forumthread VALUES (390,7,'hi',5496,'Allie','2004-02-06 10:44:55','2004-02-06 10:44:55',1);
INSERT INTO forumthread VALUES (391,5,'Question about submitting puzzles',5345,'Rawlyn','2004-02-06 18:23:44','2004-02-07 13:53:44',3);
INSERT INTO forumthread VALUES (392,7,'Hello!',5531,'kodi','2004-02-07 09:26:40','2004-02-07 09:26:40',1);
INSERT INTO forumthread VALUES (393,7,'Logic Puzzle Got Me Stumped',5541,'Gary','2004-02-07 20:59:43','2004-02-08 18:03:32',2);
INSERT INTO forumthread VALUES (394,7,'I am New Hello',5557,'Cheryl Barcus','2004-02-09 01:29:27','2004-02-20 17:50:51',3);
INSERT INTO forumthread VALUES (395,6,'four times???',5571,'frank','2004-02-10 01:56:48','2004-02-11 14:26:52',5);
INSERT INTO forumthread VALUES (396,7,'hello',5571,'frank','2004-02-10 02:01:44','2004-02-10 02:01:44',1);
INSERT INTO forumthread VALUES (397,7,'I HAVE A PROBLEM!!!!!!!!! LOL',5577,'sammie','2004-02-10 17:00:13','2004-02-12 04:11:31',6);
INSERT INTO forumthread VALUES (398,3,'Yes!',5033,'Captain Paradox','2004-02-15 10:33:43','2004-02-15 10:33:43',1);
INSERT INTO forumthread VALUES (399,4,'early access',1,'levik','2004-02-15 13:32:50','2004-03-04 15:05:38',41);
INSERT INTO forumthread VALUES (400,5,'Queue Weighting',5352,'Phil','2004-02-19 20:30:50','2004-02-20 10:03:23',4);
INSERT INTO forumthread VALUES (401,3,'For Frederico Kereki...',5530,'Sandu-Dragu Vlad','2004-02-20 06:51:22','2004-02-20 06:51:22',1);
INSERT INTO forumthread VALUES (402,4,'Snooping around',3558,'Tristan','2004-02-20 18:00:05','2004-02-21 12:20:23',2);
INSERT INTO forumthread VALUES (403,5,'perplexus dot info',1,'levik','2004-02-21 15:31:51','2004-02-22 04:06:55',4);
INSERT INTO forumthread VALUES (404,5,'Changing problems:',1626,'Gamer','2004-02-22 19:40:31','2004-02-23 13:10:09',6);
INSERT INTO forumthread VALUES (405,3,'SilverKnight\'s Lovelorn Snail',5352,'Juggler','2004-02-24 20:11:35','2004-02-25 09:21:58',7);
INSERT INTO forumthread VALUES (406,3,'Area of Segment',1253,'brianjn','2004-02-26 19:56:36','2004-02-28 20:58:54',6);
INSERT INTO forumthread VALUES (407,5,'Rich editor problems',1,'levik','2004-02-27 19:04:14','2004-03-19 11:35:35',11);
INSERT INTO forumthread VALUES (408,5,'A NEWTONIAN ARMAGEDDON',5849,'Alan Cresswell','2004-02-29 08:52:10','2004-02-29 08:52:10',1);
INSERT INTO forumthread VALUES (409,7,'Hi',5857,'hunter','2004-03-01 06:20:15','2004-03-09 11:56:03',10);
INSERT INTO forumthread VALUES (410,4,'Congratz to our newest Journeyman!',3172,'SilverKnight','2004-03-05 10:10:32','2004-03-09 14:56:51',4);
INSERT INTO forumthread VALUES (411,7,'looks like fun',5920,'mary esterhammer-fic','2004-03-06 00:22:03','2004-03-06 00:22:03',1);
INSERT INTO forumthread VALUES (412,7,'y0',5963,'Vincent','2004-03-09 13:19:10','2004-03-09 13:19:10',1);
INSERT INTO forumthread VALUES (413,7,'I want to submit a problem, but...',5384,'Larry','2004-03-09 20:56:47','2004-03-25 00:25:22',11);
INSERT INTO forumthread VALUES (414,7,'I\'m Stumped!!! HELP!',5995,'barbara','2004-03-12 19:47:34','2004-03-17 13:57:13',3);
INSERT INTO forumthread VALUES (415,7,'NEW ONE',6041,'DANIELLE','2004-03-16 13:12:35','2004-03-17 08:56:14',3);
INSERT INTO forumthread VALUES (416,7,'Hello',6081,'Ashley','2004-03-18 18:59:54','2004-03-19 12:53:40',2);
INSERT INTO forumthread VALUES (417,7,'the site',6109,'hamish thompson','2004-03-20 23:39:45','2004-03-23 15:14:32',3);
INSERT INTO forumthread VALUES (423,7,'PUZZLES',6168,'sanjay','2004-03-24 14:25:54','2004-03-24 16:46:36',2);
INSERT INTO forumthread VALUES (422,4,'Rejecting puzzles',153,'TomM','2004-03-23 06:53:48','2004-03-23 08:47:29',2);
--
-- Table structure for table 'problem'
--
CREATE TABLE problem (
probId int(10) unsigned NOT NULL auto_increment,
catId int(10) unsigned NOT NULL default '0',
status int(10) unsigned NOT NULL default '10',
authorId int(10) unsigned NOT NULL default '0',
probName varchar(100) default NULL,
probText text,
probSol text,
created date default '0000-00-00',
modified timestamp(14) NOT NULL,
modName varchar(255) default NULL,
difficulty int(10) unsigned NOT NULL default '3',
originality int(10) unsigned NOT NULL default '3',
queueWeight int(10) unsigned default '5',
score decimal(4,2) unsigned default '0.00',
posted timestamp(14) NOT NULL,
queuePosition int(10) unsigned default '0',
PRIMARY KEY (probId),
KEY problem_catid (catId),
KEY problem_uid (authorId)
) TYPE=MyISAM;
--
-- Dumping data for table 'problem'
--
INSERT INTO problem VALUES (1,2,2,1,'Burning ropes','You have two ropes. You know that each rope takes one hour to burn from one end to the other, but that the burning does not take place at a constant rate (i.e. half the rope may burn in one minute, and the other half will take 59 more minutes to burn).\r\n![](\"http://www.flooble.com/images/perplexus/problem/2books.gif\")
\r\nA bookworm can chew through a millimiter (mm) of paper or cardboard in half an hour. One day it encounters a particularly tasty treat: a two-volume edition of a large book standing on a shelf as shown. \r\n![](\"http://www.flooble.com/images/perplexus/problem/2books-sol.gif\")
\r\nThe trick to this problem is to realize that when the books are arranged in the manner shown, the back of the second book is actually in direct contact with the front of the first book. This is actually the normal way that books are displayed. The picture shows why this is true, but you can see for yourself by putting any two volumes together in order.\r\n\r\nP(n) = 1/n * (1 + P(n-1) + P(n-2) + ... + P(2))
\r\n(This problem does not make sense with less than 2 passengers. Also, it is easy to see that P(2) is 1/2)\r\n\r\nP(n-1) = 1/(n-1) * (1 + P(n-2) + P(n-3) + ... + P(2)\r\nP(n-1) * (n-1) = (1 + P(n-2) + P(n-3) + ... + P(2)\r\nP(n) = 1/n * (1 + P(n-1) + P(n-2) + ... + P(2))\r\n(P(n) * n) - P(n-1) = (1 + P(n-2) + ... + P(2))
So, \r\n(P(n) * n) - P(n-1) = P(n-1) * (n-1)\r\n(P(n) * n) - P(n-1) = (P(n-1) * n) - P(n-1)\r\n(P(n) * n) = (P(n-1) * n)\r\nP(n) = P(n-1)
\r\nThis shows us that the problem\'s answer does not change if we add one more passenger. Starting at 2 passengers with the anser of 1/2, we can add passengers indefinitely, and still arrive at the same answer. Thus for the instance with 100 passengers, the probability of the last one getting to their proper seat is also 1/2, or 50%.\r\n','2002-04-18',20030908232101,NULL,5,3,0,4.57,20020418000000,0);
INSERT INTO problem VALUES (15,7,2,1,'Move the 2 - double the number','A certain number ends with the digit 2. Moving the 2 from the end of the number to its front doubles it. Can you find this number? \r\n\r\n ..42\r\n+ ..42\r\n= ...4
\r\n(This is because you are doubling the first number to get the new one.) It will become obvious that the second to last digit of the new number (and third to last of the new one) is 8: \r\n ...842\r\n+ ...842\r\n= ....84
\r\nNote that for the next step, 8+8 will be 16, and so we will use the 6 as the third to last digit for the new number, but remember to carry over the 10 for the next time, when 6+6+1 will yield 13: \r\n ...6842\r\n+ ...6842\r\n= ...3684
\r\nIf you keep this up long enough (don\'t get discouraged, but be careful in your arithmetics) you will eventually get a valid equasion: \r\n 105263157894736842\r\n+ 105263157894736842\r\n= 210526315789473684
','2002-04-19',20030420232102,NULL,3,3,0,3.33,20020419000000,0);
INSERT INTO problem VALUES (16,7,2,1,'Changing Chameleons','At one point, a remote island\'s population of chameleons was divided as follows:\r\n\r\n
\r\nEach time two different colored chameleons would meet, they would change their color to the third one. (I.E. If Green meets Red, they both change their color to Blue.)\r\n![](\"/images/perplexus/problem/10trees-sol.gif\")
\r\nThe trick is that nobody said anything about the rows of trees having to be parallel.\r\n\r\n
','To win this game, a player must strive to leave the deck containing four cards for the other player. Then no matter how many cards the second player takes, the first player will win by taking the rest. \r\n900*100 + 90*2 + 9 = 2889
\r\ndigits to enumerate. Since we are dealing with less digits, there are no pages with numbers over 999, and thus all the pages after page 99 have three digits in their number.\r\n(2775 - 189) / 3 = 2586 / 3 = 862
\r\nTo 862 pages over 100, add the 99 pages before 100 to get a total of 961 pages.','2002-04-21',20030410232101,NULL,3,3,0,2.71,20020421000000,0);
INSERT INTO problem VALUES (19,2,2,1,'Bob and his brother','You are to meet with two brothers. You know that one of them, named Bob, has a very important package for you. Unfortunately, you never saw Bob or his brother, and don\'t know who is who.\r\n\r\n
\r\nAs you can see, when asked this question, any brother would say \"No\" if he is Bob, and say \"Yes\" if he is not.\r\n![](\"/images/perplexus/problem/flycube.gif\")
\r\nConsider the cube shown (assume for argument\'s sake that it\'s a perfect cube, contraty to what the picture may look like).\r\n\r\n
\r\nAs you see, a \"yes\" answer means Bob is truthful, and \"no\" means he is a liar.','2002-04-24',20040305232101,NULL,3,3,0,3.12,20020424000000,0);
INSERT INTO problem VALUES (24,7,2,1,'Division by three','What do you get as the result, and the remainder, if you divide eleven thousand eleven hundred and eleven by three?','If you write it down correctly, the number is actually\r\n11*1000 + 11*100 + 11 or 11000 + 1100 + 11 = 12111\r\n\r\n 1. B---------->H\r\n 2. B<--------H\r\n 3. B----->H
\r\nand so on.\r\n\r\n K-K-L-K-K-L-K-K-L ....
\r\nThis sequence repeated 15 times would yield all liars sitting between two Knights, and each Knight being between a Knight and a Liar.\r\n\r\n 042 043 044 045 001 002\r\n L K K L K K
\r\nBut the problem also states that two of the Knights were mistaken, and therefore each of the two was actually either sitting between two other Knights or two Liars.\r\n\r\n 042 043 044 045 001 002\r\n K L K K K K
\r\nCreating a situation where two extra Knights are sitting between two other Knights, and are also mistaken. (So we would get a total of 4 mistaken knights instead of two.)\r\n\r\n
\r\n\r\nUnfortunately, one of these people is not telling the truth. Who is it?','Assume A lied. Then the number does not have 2 digits. But it cannot have 1 digit, since then it could not be divisible by 25. Nor could it have more than 2 since the only suchnumber that is a divisor of 150 is 150 itself, and that\'s not it according to C. Thus it is impossible that A was the \"lone liar\".\r\n![](\"http://www.flooble.com/images/dot.gif\")
\r\n![](\"http://www.flooble.com/images/perplexus/problem/2shapes.gif\")
\r\n
\r\nWhere did the exra square in shape \"B\" come from?\r\n
\r\n(i) A equal B, A unequal C => the odd coin is in C
\r\n(ii) A unequal B, A equal C => the odd coin is in B
\r\n(iii) A unequal B, A unequal C => the odd coin is in A
\r\n
\r\nStudent 2 said \"the number is divisible by 2\",
\r\nand so forth...until
\r\nStudent 31 said \"the number is divisible by 31\".\r\n\r\n /\\/\\/\\
\r\nThe cut will pass through each of these edges at its midpoint: \r\n
\r\nforming the hexagon.\r\n','2002-05-03',20030823232101,NULL,4,3,0,4.00,20020503000000,0);
INSERT INTO problem VALUES (46,6,2,1,'A chain in payment','You must use a gold chain to pay a worker for seven days of service. The chain has seven links on it, and you agree on a price of one link per day.\r\n/\\/\\/\\\r\n
\r\n\r\nThe difference from the problem with the gold bar is that by cutting one link, you make 3 pieces of the chain, instead of 2.','2002-05-04',20031117232102,NULL,2,3,0,3.00,20020504000000,0);
INSERT INTO problem VALUES (47,2,2,1,'The three sages','On a hot summer day, tired by long discussions, three wise sages were slumbering inthe shade of a tree. A prankster was walking by, and couldn\'t pass up such an opportunity. He took a piece of charcoal, and put a black spot in the middle of each sage\'s forhead, careful not to wake them.\r\n
\r\nsin(A)/a = sin(B)/b, or
\r\nsin(90)/H = sin(30)/200 and
\r\n1/H = (1/2)/200, giving us
\r\nH = 400.\r\n\r\n
\r\nAt first, everything seems fine. But unfortunately, the farmer had 17 cows. And pieces of cows weren\'t any good to the sons. \r\n\r\n
\r\n\'But what about the neighbour,\' you may say. Well, since 9 + 6 + 2 is 17, the cow that was left over went back to the neighbour. \r\n\r\n A---B\r\n | |\r\n D---C
\r\nAs the clock starts, A begins crawling directly toward B, which goes to C, C goes to D and D to A.\r\n\r\n
\r\nThe Question Is: Who Owns the Fish?','\r\nHouse Number one:\r\nColour Yellow\r\nNationality Norwegian\r\nBeverage Water\r\nSmoke Brand Dunhill\r\nPet Cats\r\n\r\nHouse Number Two:\r\nColour Blue\r\nNationality Dane\r\nBeverage Tea\r\nSmoke Brand Blends\r\nPet Horse\r\n\r\nHouse Number Three:\r\nColour Red\r\nNationality Brit\r\nBeverage Milk\r\nSmoke Branc Pall Mall\r\nPet Birds\r\n\r\nHouse Number Four:\r\nColour Green\r\nNationality German\r\nBeverage Coffee\r\nSmoke Brand Rothmas\r\nPet \"FISH\"\r\n\r\nHouse Number Five:\r\nColour White\r\nNationality Swede\r\nBeverage Beer\r\nSmoke Brand Players\r\nPet Dog
','2002-05-08',20030326065623,NULL,4,3,0,4.00,20020508000000,0);
INSERT INTO problem VALUES (57,5,2,1,'What\'s the area?','![](\"http://www.flooble.com/images/perplexus/problem/2circles.gif\")
\r\nConsider the picture to the right. We have two concentric circles, one inside another. We do not know the radius for either one of them.\r\n\r\n (pi)R^2 - (pi)r^2
\r\nLet\'s call the point where the red line touches the inner circle \"P\", the center of the circle \"C\" and the red line\'s endpoints \"A\" and \"B\". C-P, is be the radius of the small circle, C-A and C-B - the radii of the large one, and A-B is known to be 10 inches long. \r\n\r\n r^2 + (5)^2 = R^2 or\r\n 25 = R^2 - r^2
\r\nMultiply both sides by pi and we get \r\n 25(pi) = (pi)R^2 - (pi)r^2
\r\nWhich was what we were looking for. So the area is 25(pi)','2002-05-08',20030901232101,NULL,4,3,0,4.25,20020508000000,0);
INSERT INTO problem VALUES (58,11,2,1,'10 equal sacks','You have 20 pounds of flour that must be distributed into 10 sacks of 2 pounds each. \r\n\r\n
','If you take the right angled triangle ABC (Where b is a right angle and C = x) then\r\n\r\nRemember this problem? The one where you had to find the area between two circles by only knowing the length of the tangent \"chord\" (the red line)?\r\n\r\n A = (pi)R^2 = (pi)(10/2)^2 = 25(pi)
','2002-05-10',20040225103947,NULL,4,3,0,4.00,20020510000000,0);
INSERT INTO problem VALUES (65,8,2,1,'3 cards','A dealer offers to you to play a game. He shows you three two-sided cards: one with both sides red, one red and black and the other black and black. He puts them in a hat, and randomly (no tricks here) takes out a card and puts it on the table.\r\n\r\n 6 1 8\r\n 7 5 3\r\n 2 9 4
\r\nThis is a \"magic\" square, in which the sum of all columns, rows and diagonals is 15. Incidentally these 8 combinations are all the ways to make 15 out of 3 different numbers in the range of 1 - 9.\r\n\r\n
','2002-05-14',20040215232105,NULL,3,3,0,3.00,20020514000000,0);
INSERT INTO problem VALUES (69,14,2,1,'From A to B','A car drives downhill with the speed of 90 m/h. On a level road, the same car goes 72 m/h, and uphill it goes \"only\" 60 m/h.\r\n\r\n1: X/60 + Y/72 + Z/90 = 5
\r\nComing back from B to A the equation will look like this:\r\n2: X/90 + Y/72 + Z/60 = 4
\r\nBy Subtracting (2) from (1) we get:\r\n3: X/180 - Z/180 = 1\r\n (X - Z)/180 = 1\r\n X - Z = 180\r\n X = 180 + Z
\r\nPlug this into (1) to get:\r\n4: (180+Z)/60 + Y/72 + Z/90 = 5\r\n 3 + Z/60 + Z/90 + Y/72 = 5\r\n 5*Z/180 + Y/72 = 2\r\n Y/72 = 2 - (5*Z/180)\r\n Y = 72*2 - 72*(5*Z)/180\r\n Y = 144 - (20*Z)/10\r\n Y = 144 - 2*Z
\r\nNow that we can express both X and Y in terms of Z, plug these expressions into the formula we need to find the value of:\r\n5: X + Y + Z =\r\n (180 + Z) + (144 - 2*Z) + Z =\r\n 324 + 2*Z - 2*Z = \r\n 324
','2002-05-15',20040204232103,NULL,5,3,0,4.10,20020515000000,0);
INSERT INTO problem VALUES (70,14,2,117,'Buying Books','Two friends, Alex and Bob, go to a bookshop, together with their sons Peter and Tim. All four of them buy some books. Each book costs a whole amount of shillings. \r\n\r\n 4 : 6, 11, 7\r\n 3 : 8, 4, 12\r\n ? : 10, 55, 15
\r\nExplain the scheme used.','The answer is \"8\". The title of each \"row\" is the sum of it\'s members divided by the first number in the row.\r\n![](\"http://www.flooble.com/images/perplexus/problem/triomino.gif\")
\r\nThis is a triomino piece:
\r\n(A 2 x 2 cell square with one of the corner cells removed)\r\n\r\n __\r\n | |_\r\n |____|
\r\n\r\n _________\r\n | | |_\r\n | A | B |\r\n |-----+-----|\r\n | C | D |\r\n |_____|_____|
\r\nThe area B will be the smaller shape, since it is a square with the side of 2^(n-1) with one cell removed from the corner. The other three areas, A, C and D can each fit the smaller shape, and still have one cell left over.\r\n \r\n[ 1 + 1/2(pi)n (1 + (4.066 10^-9)/n ^2 ) ] km ,
\r\nfor some positive integer n. \r\n','2002-05-29',20030403232102,NULL,3,3,0,3.78,20020529000000,0);
INSERT INTO problem VALUES (81,4,2,227,'Set A and B','Consider the following two sets:\r\n
\r\nSet B = { 2,5,7,9 }\r\n
\"If Prometheus is still alive at 2:00 pm, kill him!\" To the second one he said:\r\n
\"If Prometheus is still alive at 1:30 pm, kill him!\" And to the third:\r\n
\"If Prometheus is still alive at 1:15 pm, kill him!\"\r\n
\"Tell us which one of your demons killed Prometheus, so that we may punish him!\"\r\n\r\n3.9999... = X \r\n3.9999... * 10 = 39.9999.... = 10X \r\n10X - 3.9999... = 9X \r\n39.9999... - 3.9999... = 36 = 9X \r\n36 / 9 = 9X / 9 = 4 \r\ntherefore, X = 4
','2002-05-29',20031115232101,NULL,3,3,0,3.83,20020529000000,0);
INSERT INTO problem VALUES (87,7,2,117,'Tom\'s address','John is tryng to locate Tom\'s house. All he knows is that Tom lives on a street with houses numbered from 8 to 100.\r\n![](\"http://www.flooble.com/images/perplexus/problem/diagonal.gif\")
\r\n x^2 + (2x)^2 = 36\r\n 5 * x^2 = 36\r\n x^2 = 36/5\r\n x = 6/SQRT(5)
\r\nThe side of the square, being 2*x is then\r\n 12/SQRT(5)
\r\nThe main diagonal of a square is SQRT(2) * length of the square\'s side, so DB is \r\n 12*SQRT(2)/SQRT(5) =\r\n 7.59
','2002-06-02',20030822232101,NULL,4,3,0,3.80,20020602000000,0);
INSERT INTO problem VALUES (98,4,2,1,'Five doors','Locked in a dungeon, you are faced with five doors. One of them leads to freedom. The other four will lead you back to the starting room disoriented and confused, so that you will not remember which of the doors you have already tried and have to start again.\r\n\r\n N = 1 + 0.8*N\r\n 0.2*N = 1\r\n N = 5
\r\nYou will average 5 attempts before making it out.\r\n\r\n 2(pi)r = 132\r\n r = 132 / 2(pi)
\r\nThe area of this circle is\r\n (pi)r^2 =\r\n (pi)(132/ 2(pi))^2 =\r\n 132^2 / 4(pi) =\r\n 1386.56
\r\nThe minimum area is of course achieved by folding the string in two and is equal to zero.','2002-06-03',20031104232103,NULL,3,3,0,3.25,20020603000000,0);
INSERT INTO problem VALUES (96,5,2,227,'The Triangle','An equilateral triangle with one side 6cm is inscribed in a circle with its three vertices on the circumference. What is the diameter of the circle?','Label the triangle\'s vertices A, B and C. The center of the circle is O. Find the midpoint of AB, and call it M.\r\n\r\n cos(30) = (MB)/(OB)\r\n (OB) = (MB)/cos(30)\r\n (OB) = 3 / cos(30)\r\n (OB) = 3.46
\r\nThe diameter of the circle is then 2*(OB) or 6.92cm','2002-06-03',20031013232101,NULL,2,3,0,2.91,20020603000000,0);
INSERT INTO problem VALUES (97,14,2,227,'A couple of Logs','logy(x) + logx(y) = 43\r\n\r\n (.1^-2e3)! which is equal to\r\n ((One Tenth) to the negative 2000th power) factorial
\r\n','2002-06-06',20040225103933,NULL,3,3,0,4.38,20020606000000,0);
INSERT INTO problem VALUES (100,7,2,248,'Digits 1-9','Can you arrange the digits 1-9 in any order so that:\r\n
\r\n 64 + 81 + Sam = 2 p^2\r\n
\r\n
\r\nSam = 55
\r\nSue = 64
\r\nSally = 81\r\n\r\n x^2+xy+y^2=3 and\r\n y^2+yz+z^2=16\r\n A=xy+yz+zx
\r\nFind the maximum value of A.\r\nFind x, y and z when A=max value.\r\n(x, y, z) = (7/√31, 4/√31, 20/√31)\r\nand \r\n(x, y, z) = (-7/√31, -4/√31, -20/√31)\r\n
\r\nBrian Smith offers a three-part solution here, here, and here.','2002-06-19',20040225103933,NULL,3,3,0,3.29,20020619000000,0);
INSERT INTO problem VALUES (114,15,2,257,'Minimum Value','Given:\r\n x,y,z > 0\r\n xy+yz+zx <= 3/4
\r\nand\r\n P=x+y+z+(1/x)+(1/y)+(1/z)
\r\nFind the Minimum Value of P.\r\nFind x, y, and z when P = Minimum Value.\r\n','As it turns out this was correctly solved quite a while ago!\r\n\r\n log 2(3) = x
\r\nWhat is \r\n log 2(9) ?
','The problem is obviously asking for an answer expressed in terms of x. (Otherwise, you could just use a calculator.)\r\n![](\"http://www.flooble.com/images/perplexus/problem/triangle.gif\")
\r\nGiven that:\r\n\r\n AB = AC
\r\n\r\n AD\r\n DE\r\n EC\r\n BC
\r\nFind the measure of angle A.','Boy, was this a turbulent one. Well, a few solutions were offered by different people, all of them interesting, and all found in the comments section for this problem.\r\n\r\n a,b,c >0 and a+b+c=1 ;\r\n P=(1/a)+(2/b)+(3/c);
\r\n1)Find the minimum value of P;
\r\n2)Does P have maximum value ?\r\n','P*1 = (a+b+c)*(1/a+2/b+3/c);\r\nP*1=6+2a/b + 3a/c + b/a + 3b/c + c/a\r\n+ 2c/b\r\nP=6+(2a/b+b/a)+(3a/c+c/a)+(3b/c+2c/b)\r\nUse Cauchy\'s inequality for each :\r\nwe have :\r\nP >= 6+ 2*sqrt(2)+2*sqrt(3)+2*sqrt(6)\r\n\r\n\"=\" when a+b+c=1 and b=a*sqrt(2)\r\nc=a*sqrt(3)\r\n===>we can solve for a,b,c\r\nNo maximum value.','2002-06-20',20040229232101,NULL,4,3,0,3.60,20020620000000,0);
INSERT INTO problem VALUES (117,16,2,257,'Angle Trisection','How can you divide an angle into 3 equal angles? You may only use a straightedge and a compass to achieve this.\r\n
\r\n2. f(s\') = 2f(s). If f(s) is not divisible by 3, neither is f(s\').
\r\n3. f(s\') = f(s) - 3. No help here.
\r\n4. f(s\') = f(s). Still no change.\r\n
\r\nRegardless of whether he is a knight or liar, Richard would have to be be sat between a knight and a liar for this to happen.\r\n\r\n \"...?K(L)L?...\" or \r\n \"...?K(K)L?...\"
\r\nNow, for everyone else to have answered No:\r\n
Again, regardless of whether they are knights or liars, everyone else would have to be sat between two knights or between two liars.\r\n\r\n \"...LKLKLKLKLK(L)LLLLLLLLL...\" or \r\n \"...KKKKKKKK(K)LKLKLKLKL...\"
\r\nAs we can see, on both these options the left side and right side can never meet up at the other side of the circle as they have differing patterns.\r\n
This gives us 4 options: \r\n \"...?K(K)K?...\" or \r\n \"...?L(K)L?...\" or \r\n \"...?L(L)L?...\" or \r\n \"...?K(L)K?...\"
\r\nWe now note that Richard must have said No, he is not sitting between two Knights. This eliminates two of our options, leaving us with: \r\n \"...?L(K)L?...\" or \r\n \"...?K(L)K?...\"
\r\nWhat can we infer from the fact that everyone else answered Yes to the round of questioning?\r\n\r\n \"...KKLLKKLL(K)LLKKLLKK...\" or \r\n \"...LLKKLLKK(L)KKLLKKLL...\"
\r\nYou will notice in the first option, no matter how many people there are, to link together to form a circle there must be one more liars than knights in the circle\r\n
(e.g. \"L(K)L\", or \"KLL(K)LLK\", or \"LKKLL(K)LLKKL\", ...)\r\n\r\n (e.g. \"K(L)K\", or \r\n \"LKK(L)KKL\", or \r\n \"KLLKK(L)KKLLK\", ...)
\r\nThomas, knowing if his good friend Richard is a Knight or Liar (and thus being able to see already which of the above options is the correct one) now states that the Knights are outnumbered by the liars:\r\n\r\n
\r\nCase 2 is a consequence of the strategy. More precisely,\r\nif any point during your journey you take the same\r\npath twice, you will be stuck in a loop forever. moreover,\r\nif you take a certain path twice, it follows that youre\r\nprevious path was also taken twice, and so on until the\r\nfirst path you took from the beginning.\r\n\r\n
\r\nWhich can be rewritten as\r\n\r\n
\r\nWhere the exit path is like any other path except it connects\r\na junction to the exit. Now, consider that you have already\r\ntaken 1 path (this is your first path). Each possibility above\r\nis clearly equally likely, since each is represented by 1 path.\r\n\r\nSo, after your first path, there is 1/2 chance you\'ll escape and\r\n1/2 chance youll be stuck forever. At the start,\r\nthere is 0 chance that youll retake your first path and\r\n1/n chance that youll take the exit path, where n\r\nis the total number of paths. So\r\n P(escape) = (1/n * 1) + n-1/n * 1/2\r\n P(trapped) = (1/n * 0) + n-1/n * 1/2\r\n P(trapped) = 1 - P(escape)
\r\n\r\nn is approximately 3 * the number of junctions. as\r\nthe maze size increases the first term is neglibible\r\nand P(trapped) = P(escape) = 1/2\r\n
\r\n\"There is equal chance that youll either escape or be trapped forever.\"','2002-06-26',20030712232102,NULL,3,3,0,2.75,20020626000000,0);
INSERT INTO problem VALUES (132,7,2,227,'What\'s your age Granny?','A child said that his age in years was equal to the last two digits of his birthyear. The child\'s grandmother said the same thing. \r\n\r\n 16 = 2*(X-Y) [eq. 1]\r\n X - Y = 8\r\n 16 = 2*Z - (X-Y) [eq. 3]\r\n 16 = 2*Z - 8\r\n Z = 12\r\n 16 = 2*Y - Z [eq. 2]\r\n 16 = 2*Y - 12\r\n Y = 14\r\n X - Y = 8\r\n X - 14 = 8\r\n X = 22
\r\nSo the numbers of matches originally in the piles are 22, 14 and 12','2002-06-27',20031222232101,NULL,3,3,0,3.67,20020627000000,0);
INSERT INTO problem VALUES (134,2,2,304,'Old man - older problem','(Hopefully this one hasn\'t been posted\r\nit\'s a really old one I think\r\ndon\'t post a solution if you ALREADY know the answer\r\nI haven\'t posted the solution cause I want people to actually try and not just look at the question then giveup right away.)\r\n\r\n
','2002-06-28',20030805232102,NULL,2,3,0,3.25,20020628000000,0);
INSERT INTO problem VALUES (135,11,2,227,'Painter\'s Pesky Problem','A painter needed 6 pints of grey paint, so he mixed 4 pints of black paint with 2 pints of white paint. This turned out to be too dark a grey and he realised that what he really needs is a mixture that has 4 pints of white with 2 of black. \r\n![](\"http://www.flooble.com/images/perplexus/problem/triangle2.gif\")
\r\nIf \r\n
\r\nfind the length of AC.','\r\n DB = CB / 2 = 12 / 2 = 6\r\n MB = CB - CM = 12 - 11 = 1\r\n DM = DB - MB = 6 - 1 = 5\r\n DM^2 + AM ^2 = AD^2 (pythagorean), so\r\n 25 + AM^2 = 100\r\n AM = sqrt(75)\r\n CA^2 = AM^2 + CM^2 (pythagorean), so\r\n CA = sqrt(75 + 121) = sqrt(196) = 14
','2002-07-01',20040303215126,NULL,3,3,0,3.00,20020701000000,0);
INSERT INTO problem VALUES (137,14,2,257,'How long did I walk from the Airport ?','I was going to take a trip to my friend\'s house in San Jose by airplane. If my airplane had arrived on time as scheduled, my friend would drive out to pick me up from San Jose\'s airport. She would get to the ariport just as I would be leaving it, and drive me to her house. This way, I would come to her house at 12:00.\r\n
The hot tap similarly (when it is running).\r\n
The plug empties 1/4 of a bath-full every minute.\r\n
But, with only the cold tap running and the plug out, the bath loses: 1/4 - 1/6 = 1/12 every minute\r\n
So, over the first 5.5 minutes the bath fills by (3 * 1/12) - (2.5 * 1/12) = 1/24 of a bath-full.\r\n
At this point the tank is full once again, ready to restart this cycle.\r\n
For the next 3 minutes, both taps dispense water. We know this results in the bath filling by 1/12 every minute. \r\nSo, after 3 more minutes the bath is full!\r\n
\r\nb) approximate a numerical value','It is a general consensus among the members of this site that no unique solution can exist without the knoweledge of how thick a book Bascule is likely to be reading.\r\n![](\"http://www.flooble.com/images/perplexus/problem/shaded.gif\")
\r\n576 = 24 * 24
\r\n169 = 13 * 13
\r\n\r\n FORTY \r\n + TEN \r\n + TEN \r\n -------\r\n = SIXTY
\r\nIf each letter represents a digit and all ten digits are to be included in the above equation. Can you find the arrangement of digits that would satisfy the equation? \r\n\r\n(TEN does not mean T x E x N. It represents the places the digits take)\r\n\r\n','First, we have Y + N + N = Y and T + E + E = T. That means N and E must be 0 and 5. If N was 5, there would be a 1 carried over, and there is no solution for E then. So, N=0 and E=5.\r\n
\r\n(This is possible, if for example, the grid is a 1x1 grid). I this case A and B are the same height.\r\n
\r\nSince A comes from a group of people who are the tallest in their rows, A must be the tallest person in his row. Thus, if B is in the same row, A is taller.\r\n
\r\nSince B comes from a group of people who are the shortest in their respective columns, B must be the shortest in his column. Thus, if A is in the same column, A must be taller.\r\n
\r\nFor this case, imagene a person C, who is in the same row as A, and in the same column as B. C must be shorter than A, since A is the tallest in his row. C must be taller than B since B is the shortest in his column. Thus, since A is taller than C who is taller than B, A must be taller than B.\r\n
\r\na) The relation is only one way. Think of it like mother and son. The mother is the parent of the son, but the son is not the parent of the mother.\r\n
\r\nb) The first thing you need to do is to establish (just using property E) how to solve the puzzle (i.e. how do you know if a combination opens the lock?). Then use this information to solve the puzzle using properties A thru D.\r\n','Begin with some additonal notation:
\r\nX is the reverse of x; if x = 123, x = 321.
\r\na ~ b means a is related to b.\r\n
\r\nxx2 → 2XX → XX → xx → x
\r\nor
\r\nxx2 → 2XX → XX → X → x
\r\nThis gives the proof:\r\n\r\n2x2 ~ x\r\n92x2 ~ xx\r\n592x2 ~ XX\r\n1592x2 ~ 2XX\r\n51592x2 ~ xx2
\r\nTherefore, x must equal 51592, and this shows that the number 51592515922 relates to itself and therefor must open the safe.\r\nSimilarly:\r\n2x2 ~ x\r\n52x2 ~ X\r\n952x2 ~ XX\r\n1952x2 ~ 2XX\r\n51952x2 ~ xx2\r\nTherefore, x in this example is equal to 51952, and 51952519522 also relates to itself and opens the safe.\r\n
\r\nx2x2 → 2X2X → 2X → X → x
\r\nor:
\r\nx2x2 → x2 → 2X → X → x.
\r\nThese give the proofs:\r\n\r\n2x2 ~ x\r\n52x2 ~ X\r\n152x2 ~ 2X\r\n9152x2 ~ 2X2X\r\n59152x2 ~ x2x2\r\n
\r\nThat means that x must equal 5915, and 5915259152 relates to itself and must open the safe.
\r\nAnd the last proof:\r\n\r\n2x2 ~ x\r\n52x2 ~ X\r\n152x2 ~ 2X\r\n5152x2 ~ x2\r\n95152x2 ~ x2x2\r\n
\r\nThis last proof gives that x=9515, and 9515295152 also relates to itself and must open the safe.\r\n\r\n2y2 ~ y\r\n92y2 ~ yy\r\n
\r\nSo, for any repeated number yy, 92y2 is related to y. By property E, if yy opens the safe, 92y2 must also open the safe. The last two solutions, 9515295152 and 5915259152, both have the form yy, and can be made shorter:\r\n\r\n2951522 ~ 95152 \r\n92951522 ~ 9515295152 \r\n
\r\nand\r\n\r\n2591522 ~ 59152 \r\n92591522 ~ 5915259152\r\n
\r\nSince 92951522 relates to 9515295152, which opens the safe, it must also open the safe. Similarly, 92591522 relates to 5915259152, and must open the safe as well.\r\n
\r\n
Imagine a rectangular (or square) grid of any size, every square white. If the grid is \"x\" squares across and \"y\" squares high, what is the minimum number of squares (\"n\") that must be shaded so that no white square is adjacent to more than 2 other white squares?\r\n
(For this puzzle, diagonally adjacent squares are not considered to be adjacent)\r\n
\r\n
So, for example, if the grid is simply a 3x3 then the only square that needs shading is the centre one, then all others squares only touch two others - i.e. for x=3 y=3, n=1\r\n
\r\n
a) Is there an formula to calculate \"n\" that will work for all paired-values of \"x\" and \"y\"?\r\n
b) If not, what is \"n\" for a chessboard-sized x=8 y=8 (post your suggested minimum using a standard chess-like \"A7\" type of description for a list of all your shaded squares)?','Brian gave a good solution here','2002-07-22',20040225103933,NULL,5,3,0,4.00,20020722000000,0);
INSERT INTO problem VALUES (160,4,2,250,'Dice Game','I have set up a stall where you may play a fabulous game.\r\n
\r\n
Presented before you are 4 unusual 6-sided dice:\r\n
\r\n
has the numbers 5, 5, 5, 5, 1 and 1 on its sides\r\n
has the numbers 6, 6, 2, 2, 2 and 2 on its sides\r\n
has the numbers 6, 4, 4, 2, 2 and 1 on its sides\r\n
has the numbers 3, 3, 3, 3, 3 and 1 on its sides\r\n
\r\n
I inform those that are unaware that the average value they would roll with each of the 4 dice are (roughly) 3.66, 3.33, 3.17 and 2.67 respectively. All dice are fair and players find it impossible to cheat when rolling them.\r\n
\r\n
I request a $1 payment from you to play. You may choose any one die. Then I may choose any of the remaining dice. We then roll. If you roll more than or the same as me, I return your original $1 stake and a bonus $1 prize. If I score more than you, I keep your stake and you win nothing.\r\n
\r\n
What would be your strategy if you wanted to walk away from my stall with the most amount of money possible?\r\n
\r\n
(Thanks go to an old university professor would showed us something similar, which instantly intrigued me, in a Probability lecture)','Although the game seems geared towards the player winning, it simply isn\'t so.\r\n
\r\n
Misconception 1: I will pick the big red dice - it has the highest average, so I\'m more likely to win\r\n
Misconception 2: I win if I roll higher OR on a draw - winning on a draw gives me that extra edge\r\n
Misconception 3: I either lose $1 or gain $1 - combined with the above I\'m sure to make money in the long run!\r\n
\r\n
If the person running the stall knows the basic premise they will, on average, win more often than not:\r\n
\r\n
If the player picks the red die, the stall-owner should pick the yellow\r\n
If the player picks the yellow die, the stall-owner should pick the blue\r\n
If the player picks the green die, the stall-owner should pick the red\r\n
If the player picks the blue die, the stall-owner should pick the green\r\n
\r\n
If the stall-owner does this, regardless of which die the player picks, the stall-owner has a 20/36 chance (i.e. 55.55%) of winning due to the specific way the dice are numbered. The player\'s chances of winning are less than 50% - as the payout is only what the player would normally lose, the stall-owner will make money in the long run.\r\n
\r\n
So, in reply to the question: \"The only winning move is not to play\"\r\n
\r\n
(Also noteworthy, as noticed by TomM, is that Red beats Blue 24/36 times - so if forced to play, the best strategy is not to pick Blue - however, the best strategy is still not to play at all)','2002-07-24',20030725232102,NULL,3,3,0,3.71,20020724000000,0);
INSERT INTO problem VALUES (162,12,2,122,'Domestic Complications','
\r\nd/dx(f(x)) = f\'(x)\r\n
\r\nd/dx(x^2) = 2x\r\n
\r\nx^2 - Ax - B = 0,\r\n
\r\nx = A/2
\r\nA = 2x.\r\n
\r\n
\r\nthat add to a certain constant and
\r\nthen multiply by the number of pairs
\r\n(ie Gauss)
\r\n
\r\nn is even, the sum S:
\r\n
\r\nS = (2n-1 + 1) * (n / 2)
\r\nS = 2n * n/2 = n²
\r\n
\r\nout exactly, there is a remaining
\r\ncentral term. However note that this
\r\nterm occurs in the middle so it is
\r\nequal to 2n/2 = n.
\r\n
\r\nS = 2n * (n-1/2) + n (remember n is odd)
\r\nS = 2n * (n-1) + n
\r\nS = n² - n + n = n²
\r\n
\r\nFor any n, the sum is always a perfect square.\r\n
\r\nsquaring..
\r\ny² = 1 - x²
\r\nx² + y² = 1²
\r\n
\r\n
\r\n
\r\n
\r\netc.\r\n
\r\n2. What kind of school is this?
\r\n3. Why aren\'t the robbers in jail?
\r\n4. What on earth is going on here?
\r\n','1. They were shot with laser guns.\r\n\r\n F(0) = 1, \r\n F(1) = 1, and\r\n F(2) = 2
\r\nNow, let us think about a generic staircase with n steps.\r\n\r\n F(n) = F(n-1) + F(n-2)
\r\nThis is the equasion for the Fibonacci sequence. However, the Fibonacci sequence f(n) starts with \r\n f(1) = 1,\r\n f(2) = 1,\r\n f(3) = 2 etc...
\r\nTherefore, \r\n F(n) = f(n+1), and\r\n F(100) = f(101) \r\n F(100) = 5,731,478,440,138,170,84,101
\r\n(That\'s pretty big)','2002-09-05',20040125232104,NULL,3,3,0,3.50,20020905000000,0);
INSERT INTO problem VALUES (191,2,2,1,'Bus','![](\"http://www.flooble.com/images/perplexus/problem/bus.gif\")
\r\nFour.
\r\nTen letters.\r\n','The first player to make his move has a strategy that will assure him victory.\r\n\r\n C1 : 0, 1, 2, 3, 4, 5\r\n C2 : 0, 1, 2, 6, 7, 8
','2002-09-09',20040311232101,NULL,3,3,0,3.60,20020909000000,0);
INSERT INTO problem VALUES (197,8,2,213,'Simultaneous Chess','Two reasonably competent chess players are discussing chess in a bar. A duffer comes up and challenges them to simultaneous matches, with the duffer playing white on one game, and black on the other. He offers a substantial bet on the outcome. However, since he\'s inexperienced, he will win the bet unless the two experienced players as a whole do better than the duffer. (That is, two draws or one win and one loss will result in the duffer winning the bet.)\r\n\r\n
\r\nSo how many male residents of Smallvile can there be?','Assume Smallvile has N male residents. Because of the third condition, the maxumum number of hairs on the head of any of them must be N-1. Also, because of the first condition, each man has a different number of hairs on their head. For this to be true, for any number from 0 to N-1, there has to be a male resident with that many hairs on their head.\r\n
\r\nA PIN number
\r\nThe River Avon
\r\nMount Fuji-yama
\r\nA hot water heater','The La Brea Tar Pits (The The Tar Tar Pits)
\r\nA PIN number (A Personal Identification Number number)
\r\nThe River Avon (The River River)
\r\nMount Fuji-yama (Mount Fuji Mountain)
\r\nA hot water heater (well, you get the idea)
','2002-09-23',20040129232107,NULL,2,3,0,3.38,20020923000000,0);
INSERT INTO problem VALUES (207,8,2,251,'Tic Tac Toe','A computer science teacher poses his students a problem.\r\n
\r\nthem (4) must yield the same number of combinations.\r\n
\r\nT = 4(C + S + C\' + S\')\r\n\r\n X1, X2, X3 ... Xn
\r\nuntil it breaks. Then, if the egg breaks on some attempt number k, we will use the second egg to test floors from \r\n Xk-1 + 1 to Xk - 1.
\r\n\r\n X1 = 14\r\n X2 = X1 + 13 = 27\r\n X3 = X2 + 12 = 39\r\n X4 = X3 + 11 = 50\r\n X5 = X4 + 10 = 60\r\n X6 = X5 + 9 = 69\r\n X7 = X6 + 8 = 77\r\n X8 = X7 + 7 = 84\r\n X9 = X8 + 6 = 90\r\n X10 = X9 + 5 = 95\r\n X11 = X10 + 4 = 99
\r\nWith each consecutive range, the range\'s size is decresed by one, to balance the one extra attempt it will take to get to it. If the first egg fails to break from 99th floor, only one attempt will remain to test if a drop off 100th floor will break it.','2002-10-01',20030528232102,NULL,3,3,0,3.67,20021001000000,0);
INSERT INTO problem VALUES (211,6,2,213,'The Intrepid Ant','A rubber band is 1 meter long. An ant starts at one end, crawling at 1 millimeter per second. At the end of each second, the rubber band is instantaneously stretched by an additional meter. (So, at the end of the nth second, the rubber band becomes n+1 meters long.)\r\n
\r\n(Z + 1) = odd
\r\nn = integer\r\n
\r\nz^2 + 2z + 1 = 8n + 1\r\n
\r\nz^2 + 2z = 8n
\r\nsince z is even, it must be 2w where w is an integer\r\n
\r\n4w^2 + 4w = 8n
\r\n4*(w^2 + w) = 8n
\r\n4*[w*(w+1)] = 8n\r\n
\r\n[w*(w+1)]/2 = n
\r\n
\r\n3^2 = 8(1) + 1
\r\n5^2 = 8(3) + 1
\r\n7^2 = 8(6) + 1
\r\n9^2 = 8(10) + 1
\r\n11^2 = 8(15) + 1
\r\n.
\r\n.
\r\n.','2002-10-06',20040304232102,NULL,2,3,0,3.12,20021006000000,0);
INSERT INTO problem VALUES (212,7,2,153,'Stopping for lunch','Al, Bert, and Carl are on a road trip, and stop at a roadside picnic table for lunch. Al has five sandwiches. Bert has three sandwiches. Carl, who is a little absent-minded, realizes that he forgot to stop at the Deli that morning. He has the $8 that he was going to buy his sandwiches with and offers it to Al and Bert for some of their lunch.\r\n
\r\nNumber the bags 1 to 5.
\r\nfrom bag 1, take 1 pearl
\r\nfrom bag 2, take 2 pearls
\r\nfrom bag 3, take 4 pearls
\r\nfrom bag 4, take 8 pearls
\r\nfrom bag 5, take 16 pearls
\r\n
\r\nLet W = Weight of selected pearls (in grams)
\r\n
\r\nA. Convert yottabytes to bits:
\r\n
\r\n1 YB = 2^83 bits = 9671406556917033397649408 bitsB. Convert bits to inches:
\r\n
\r\n9671406556917033397649408 bits/124000 bpi = 77995214168685753206.8500 inchesA. Convert microns to inches:
\r\n
\r\n8.9 microns/25400 microns-per-inch = .0003503937007874 inchesB. Length * Width:
\r\n
\r\n77995214168685753206.8500 inches * .0003503937007874 inches = 27329031736271779.6669 square inchesπ * .25² = 0.1963495408493620 square inches
\r\n27329031736271779.6669 + 0.1963495408493620 = 27329031736271779.8633 square inches
\r\n√ (27329031736271779.8633 / π) = 186537942.3224 inches
\r\n186537942.3224 / 63360 inches-per-mile = 2944.0963 miles
\r\n(2 * (√((((2^83)/124000) * (8.9/25400)) + (π * ((0.5/2)²)) / π))) / 63360 = 2944.0963
','2002-10-13',20030903232101,NULL,3,3,0,2.80,20021013000000,0);
INSERT INTO problem VALUES (225,7,2,122,'Two numbers','
\r\nBob: I knew you couldn\'t.
\r\nAlan: Ok, now I know the numbers.
\r\nBob: Now I know them, too.\r\n\r\n
\r\nHowever, this being perplexus, we have to look a bit deeper. As soon as you admit that the third error exists, it stops being an error. \r\n
\r\n1. Because the notes for which they are noted are not noted for being musical notes.
\r\n2. Because Poe wrote on both.\r\n\r\n
','2002-10-27',20040225103933,NULL,5,3,0,3.50,20021027000000,0);
INSERT INTO problem VALUES (233,6,2,1,'Corner of a die','![](\"http://www.flooble.com/images/perplexus/problem/die.gif\")
![](\"http://www.flooble.com/images/perplexus/problem/shaded1.gif\")
\r\n![](\"http://www.flooble.com/images/perplexus/problem/circles7.gif\")
\r\n![](\"http://www.flooble.com/images/perplexus/problem/triangles.gif\")
\r\n
\r\ncos^2 x = BC^2/AC^2\r\n\r\n
\r\n\r\n(From - http://www.riddlenut.com/)','The next row is\r\n1113213211\r\nStarting with the second line, every line describes the line before it. In writing, it is:\r\n\r\n
','2002-11-11',20030901232101,NULL,3,3,0,4.30,20021111000000,0);
INSERT INTO problem VALUES (250,9,2,746,'Liar or not?','A man walks up to you and says:
\r\n\"Everything I say to you is a lie.\"\r\n
\r\n64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 =
\r\n204','2002-11-18',20040223232101,NULL,2,3,0,3.75,20021118000000,0);
INSERT INTO problem VALUES (260,5,2,227,'Circle perimeters','![](\"http://www.flooble.com/images/perplexus/problem/circles8.gif\")
\r\n
\r\nMeanwhile, Jane, wrote \"had had\", which the teacher liked better.\r\n
\r\n\"Harold, make this line shorter. You may not erase it in any way\".
\r\nHarold said
\r\n\"No problem your highness\".
\r\nAnd he made the line shorter.\r\n
\r\n5 * (S + 6) = M + 6
\r\n
\r\n5S + 30 = S + 27
\r\n4S = -3
\r\nS = -3/4 = -9 months!
\r\n
\r\n M
\r\n-----
\r\nL=A\r\n','Mona Lisa\r\n(M on a L is A)','2002-11-26',20030829232101,NULL,1,3,0,4.11,20021126000000,0);
INSERT INTO problem VALUES (273,14,2,806,'N-gonal numbers','![](\"http://www.flooble.com/images/perplexus/problem/ngon.gif\")
\r\nFor starters, I will explain that a triangle number is any number X, such that if X dots were aranged in a a shape the first row would have one dot, the second two dots, the third three and so on, forming a triangular shape. \r\n\r\n0 <= J < 10\r\n0 <= G < 10\r\nJ + G = 14\r\n10*J + G = (10*G + J) + 36\r\n
\r\nWe have 2 equations with 2 unknowns. Let\'s solve \'em.\r\n\r\nJ = 14 - G.\r\n10*(14-G) + G = (10G + 14 - G) + 36\r\n140 - 9G = 9G + 50\r\n90 = 18G\r\nG = 5\r\nJ = 14 - 5 = 9\r\n
\r\nSo George\'s digit is 5, and Jack\'s is 9.','2002-11-28',20031204232103,NULL,1,3,0,2.09,20021128000000,0);
INSERT INTO problem VALUES (281,12,2,103,'Unusual Month','This is an unusual month - Santa, snow, and so on. This is an unusual paragraph, too. How quickly can you find out what is so uncommon about it? It looks so ordinary that you may think nothing is odd about it until you match it with most paragraphs this long. If you put your mind to it and study it you will find out, but nobody may assist you; do it without any coaching. Go to work and try your skill at figuring it out - it\'s usually about half an hour. Good luck - and don\'t blow your cool.\r\n\r\n0= 2×0×0×3\r\n1= 20^(0×3)\r\n2= 2+00×3\r\n3= 20×0+3\r\n4= 20^0+3\r\n\r\n5= 2+00+3\r\n6= (2+00)×3\r\n7= 20^0+3!\r\n8= 2+003!\r\n9= (2+00!)×3\r\n\r\n10= 20÷(-(0!)+3)\r\n11= (2+0!)!-0!+3!\r\n12= (2+0!+0!)×3\r\n13= (2+0!)!+0!+3!\r\n14= 2×(00!+3!)\r\n\r\n15= ((2+0!)!-0!)×3\r\n16= 2^(00!+3)\r\n17= 20-03\r\n18= 20+0!-3\r\n19= 20-(0×3)!\r\n\r\n20= 20+0×3\r\n21= 20+(0×3)!\r\n22= 20-0!+3\r\n23= 20+03\r\n24= 20+0!+3\r\n\r\n25= 20-0!+3!\r\n26= 20+03!\r\n27= 20+0!+3!\r\n28= (floor √20)+(0!+3)!\r\n29= (ceil √20)+(0!+3)!\r\n\r\n30= (2+0!)!+(0!+3)!\r\n31= ceil [-2×(tan (0!+0!))÷sin 3]\r\n32= 2^(0!+0!+3)\r\n33= (2+0!)×floor [(tan (0!))÷(sin 3)]\r\n34= 2+0!+ceil [(tan tan (0!))÷(√3)]\r\n\r\n35= -2+floor [(tan tan (0!))÷(-(0!)+3)]\r\n36= (2+0!)!×(0+3)!\r\n37= ceil [cos 2+(tan tan (0!))÷(-(0!)+3)]\r\n38= floor [√2+(tan tan (0!))÷(-(0!)+3)]\r\n39= 2+floor [(tan tan (0!))÷(-(0!)+3)]\r\n\r\n40= 20×(-(0!)+3)\r\n41= -2+0+floor [(tan tan (0!))÷(√3)]\r\n42= ((2+0!)!+0!)×3!\r\n43= 2×0+floor [(tan tan (0!))÷(√3)]\r\n44= 20+(0!+3)!\r\n\r\n45= 2+floor [(tan tan (00!))÷(√3)]\r\n46= 2×(-(0!)+(0!+3)!)\r\n47= 2+ceil [(tan tan (0!))÷(tan (0!))]-3\r\n48= 2×(00!+3)!\r\n49= floor [2×(tan tan (0!))÷03]\r\n\r\n.\r\n.\r\n.\r\n.\r\n
','2002-11-29',20040225103933,NULL,4,3,0,4.00,20021129000000,0);
INSERT INTO problem VALUES (342,12,2,122,'Play on words','
\r\na table
\r\na saw
\r\na baseball bat
\r\na piano\r\n\r\n
\r\n\r\n2461289=18
\r\n
\r\n11029447=1
\r\n6332516=333561
\r\n412961044=4141
\r\n2234=23
\r\n357924242=222
\r\n139=9
\r\n4344199=?\r\n
\r\nMy solution below is short and sweet, but some of the others given are well thought out and appreciated.
\r\nBen owes one drink but has four coming, so he needs three.
\r\nGlen owes two and has one coming, so he owes one.
\r\nRhen owes three and has two coming, so he owes one.
\r\nSven owes four and has three coming, so he owes one.
\r\nI throw two of the items away. as there are day and night.
\r\nIf I add up all the values together,
\r\nas there are seasons.
\r\nas there are lunar months.
\r\nas there are weeks in the year.
I get the amount of days in a year (minus 1 for the two items I threw away.) \r\n
\r\nThrow the 2 jokers away.
\r\nI look at the side (one half) that has the unique patterns of numbers and suits.
\r\nDay and night – black and red.
\r\n4 seasons – 4 suits.
\r\n13 lunar months - A, 2, …,J, Q, K – 13 values.
\r\n52 weeks in the year – 52 cards (one in each group).
\r\nA=1,2=2, ……,10=10, J=11, Q=12, K=13 added together is 364. ','2002-12-20',20031111232103,NULL,2,3,0,3.64,20021220000000,0);
INSERT INTO problem VALUES (292,2,2,872,'The Letter','You receive a strange letter stating the following: \r\n
\r\nAll letters are in alphabetical order, but are doubled if you can write them without lifting your pencil off the page.
Of course this varies with individual writing stlye (or computer font types.)','2002-12-14',20030905232101,NULL,2,3,0,2.38,20021214000000,0);
INSERT INTO problem VALUES (301,7,2,873,'2 Letters','Can you work out the logic that is being used here, and find the two letters that can satisfy the final equation?
\r\nX – N = C
\r\n(K + R) / R = T
\r\n(B * W) + E = Y
\r\nR * N * A = H + X
\r\n(X / G) + F – K = ?
\r\n','Each letter should be replaced by the number of \"ends\" which each letter has.
\r\nD = 0, M = 2, T = 3.
\r\nSo the answer to the final equation (4 / 2) + 3 - 4 = 1.
\r\nSo the answer must be P (or Q, depending on your individual writing style or font type.)
\r\nThe answer is 1420.
\r\nLooking at the 11th-20th primes, we do the following:
\r\nMultiply the prime by the nth spot it holds,
\r\naverage the next two primes, and repeat.
\r\n31x11 (341), average 37 & 41 (39), 43x14 (602), average 47 & 53 (50), 59x17 (1003), average 61 & 67 (64), 71x20 (1420). \r\n
\r\n\r\nConsider a 5 by 5 Chess Board. Is it possible to place \r\n5 Queens on the board such that three pawns can safely \r\nbe placed on the board? (aka, by carefully choosing where \r\nto place the 5 queens, can you arrange it so that there \r\nare 3 squares on the board that none of the queens can \r\nattack)\r\n\r\n \r\n A B C D E \r\n1 \r\n2 \r\n3 \r\n4 \r\n5 \r\n\r\nOn \r\nTuesday \r\nofnext\r\nweekwethought \r\nifwewereexperienced \r\nenoughwecantryto \r\nstumptheclassineighth \r\ngradebecausetheysometimes \r\nrubitinourfacesevertime \r\nwecantsolveourworkisthatokay?
','The answer is 31.
\r\nEach word (or words pushed together) holds a secret letter.
\r\nThe letters are found by looking at the next prime
(2, 3, 5, 7, 11, 13, 17, 19, 23, 29).
\r\nYou must count the letters in the word until you get to the next prime.
\r\nWhen you pick out the letter you get NEXTPRIME? or Next prime?
The next prime is 31.
\r\n\r\nE = (F – I + R)
\r\nwhen does
\r\nF = (N * O)
\r\nH = (F + X)
\r\nI = (N + O)
\r\nN = 3
\r\n0 = 2
\r\nR = (N – O)
\r\nT = (X + Y)
\r\nU = (O + O)
\r\nW = (Y + R)
\r\n\r\n (T+H+I+R+T+E+E+N)-(T+H+R+E+E)\r\n ----------------------------- = (T+W+0) ?\r\n (N+I+N+E)-(F+O+U+R)
\r\n\r\n(All Os ARE the letter Os, not zeros)\r\n','Leave the X and Y alone (T and W too), those letters are just smokescreen.
\r\nUse the N & O to find F=6, I=5, R=1, and U=4.
\r\nUse F, I, R to fine E=2.
\r\nThat enough to know that N+I+N+E=13 and F+O+U+R=13.
\r\nNow you have 13-13=0 in the denominator. It will never work out. \r\n a=b\r\n a^2-ab=a^2-b^2\r\n a(a-b)=(a+b)(a-b)\r\n a=a+b\r\n a=a+a\r\n a=2a\r\n 1=2
\r\nWith such a proof, we can show that\r\n1=2, pi=E, 10000000000000=1, etc.... Can you spot the flaw?','The flaw, as many have pointed out, is in step 4, where both sides are \"simplified\", or divided by (a-b). Since we assumed that a = b, this expression is equal to zero. The proof hinges on the ability to divide both sides of the equation by zero. Since such division is illegal, the proof itself is invalid.','2002-12-20',20040210232104,NULL,2,3,0,2.82,20021220000000,0);
INSERT INTO problem VALUES (327,6,2,872,'Meet me at the lake','You and a friend are planning on hiking separately and meeting at a lake neither of you have ever been to before. The map shows it to be a hilly area, with plenty of streams and trees. \r\n
\r\nQA, Z, OK, M, WS, X, IJ, N, ED, C, UH, B, RF, V, YG, ________.\r\n','The answer is V.
\r\nThe pattern is found by looking at the diagonals (left then right) of a standard American QWERTY keyboard.
\r\n Only include the diagonals with three letters in them. (Leave out PL[,] ) \r\n
Thus, Wolves is running twice as fast as Dances.
The answer is 30 seconds.','2002-12-22',20031103232101,NULL,1,3,0,2.60,20021222000000,0);
INSERT INTO problem VALUES (312,14,2,873,'Products of 22','The sum of the elements of a set of positive integers is 22.
What is the greatest possible product of the integers in this set if:
\r\nB Duplicates are not allowed?
That is, use six 3’s and one 2.
The answer is 2916.
What is the smallest possible surface area of the resulting configuration?
Glue the cubes so that one face of the medium size cube is entirely contained in one face of the largest cube.
Then glue on the smallest cube so that two of its faces are entirely contained in the faces of the other two.
The resulting surface area is 126 – 2(4) – 2(1) – 2(1) = 114.
','2002-12-24',20031103232101,NULL,2,3,0,3.38,20021224000000,0);
INSERT INTO problem VALUES (315,19,2,873,'Brothers and Sisters','There is a man looking at someone\'s picture and says: \r\n
\r\nbut this man\'s father is my father\'s son. \r\n
\r\nf(x) = a cosh(x/a),
\r\nwhere cosh is the hyperbolic cosine function.
\r\nAnyway...\r\n\r\nNeither Chris nor Stacey serves chips (which are served while watching the Broncos).
','The PJ is your cousin who watches the Dolphins who didn’t serve cookies or carrot sticks (clue 3), or chips (Broncos, clue 1) or pizza (Bobbi, 5), so popcorn. The cookies weren’t served while watching the Packers or Raiders (2) so Cowboys. The carrot sticks (4) weren’t served during the Packers, so Raiders, thus the Packers fan serves pizza. Pat serves chips (1). Your brother (2) serves carrot sticks (4) as is named Stacey. Chris serves cookies. Your sister (4) serves cookies. Your uncle wasn\'t (5) serving pizza; he served chips. Your mother served pizza. \r\n\r\nThus: \r\nPat – Uncle – Chips - Broncos
\r\n\r\n This is an original problem. ','2002-12-31',20030527232102,NULL,3,3,0,2.67,20021231000000,0);
INSERT INTO problem VALUES (341,7,2,1,'Adjacent numbers','
Chris – Sister – Cookies - Cowboys
\r\nPJ – Cousin – Popcorn - Dolphins
\r\nStacey – Brother – Carrot Sticks - Raiders
\r\nBobbi – Mother – Pizza – Packers \r\n
\r\n \r\nA : 1 \r\n B : 2 \r\nC : 3 \r\nD : 4 E : 5 \r\nF : 6 \r\nG : 7 \r\nH : 8 \r\n \r\n A : 7\r\n B : 3 C : 1 D : 4\r\n E : 5 F : 8 G : 6\r\n H : 2
\r\n\r\nNote that this can be \"reflected\" either horizontally, or vertically or both and the solution will still be valid, since such transformations do not alter adjacency.','2003-01-09',20031224232100,NULL,3,3,0,3.25,20030109000000,0);
INSERT INTO problem VALUES (329,12,2,961,'Girlfriend\'s name','If JASON is a DJ on FM and AM, what is his girlfriend\'s name?','Notice the letters of Jason\'s name, proffession and air waves spell out 11 out of 12 months:\r\n
\r\nthe\r\n
\r\non\r\n
\r\nand\r\n
\r\naverage = safe hits/at bats, and is recorded to three decimal places (though announcers generally multiply this fraction by 1000 to give a integer value). A good players average will be between .300 and .350, with higher averages possible, but rare. For example a player gets 20 safe hits in 80 \"at bats\" then his average is .250\r\n','This situation can occur due to the proportional averaging. To illustrate, the following example satisfies the players dilemna.\r\n
\r\nWhat\'s in a star, but not in the moon. \r\n
\r\nOut of range, but still in sight?','I\'m the letter \"S\", of course!','2003-01-03',20040208232101,NULL,2,3,0,2.58,20030103000000,0);
INSERT INTO problem VALUES (337,18,2,1016,'Seconds in a year','How many seconds are there in one year?','12, why you ask? There is a second in Jan 2nd, February 2nd, March 2nd etc...\r\n','2003-01-06',20040107232101,NULL,2,3,0,3.18,20030106000000,0);
INSERT INTO problem VALUES (338,12,2,853,'The Five Airy Creatures','We are little airy creatures
\r\nAll of different voice and features
\r\nOne of us in \"glass\" is set
\r\nOne of us you\'ll find in \"jet\"
\r\nT\'other you may see in \"tin\"
\r\nAnd the fourth a \"box\" within
\r\nIf the fifth you should pursue
\r\nIt can never fly from \"you\"
\r\n
\r\nshe saw a policeman skipping rope;
\r\nshe saw a fire engine eating an ice cream;
\r\nshe saw a squirrel humming a tune;
\r\nshe saw a puppy climbing a tree;
\r\nshe saw two robins playing hopscotch;
\r\nshe saw an organ grinder and his monkey.\r\n
\r\nshe saw a policeman. Skipping rope,
\r\nshe saw a fire engine. Eating an ice cream,
\r\nshe saw a squirrel. Humming a tune,
\r\nshe saw a puppy. Climbing a tree,
\r\nshe saw two robins. Playing hopscotch,
\r\nshe saw an organ grinder and his monkey.','2003-01-07',20040109232104,NULL,2,3,0,1.75,20030107000000,0);
INSERT INTO problem VALUES (340,12,2,853,'Funny business at the fountain','At a hotel in Las Vegas, a lady rushed out of the Manager\'s office to get a drink at the water fountain in the lobby. a few minutes later she came out for another drink. this time she was followed by a man.\r\n
\r\nI was given a body, but not given life. \r\n
\r\nThey made me a mouth, but didn\'t give me breath. \r\n
\r\nWater gives me life and sun brings me death. \r\n
\r\nHe was given a body (of snow), but not given a life.
\r\nHe has a mouth (of coal), but no breath.
\r\nWater gives him life (as snow is made up of water),
\r\nand sun brings him death (as snow melts in sun). ','2003-01-13',20031111232103,NULL,2,3,0,3.22,20030113000000,0);
INSERT INTO problem VALUES (349,2,2,1072,'2 guesses, 3 hats','When a person walks into a party he will be given one of 3 hats. Each hat is either yellow, red or blue. Every person does not know the colour of their own hat but he can see the colour of everyone else\'s.\r\n
\r\nMore evil than the devil,
\r\nThe poor have it,
\r\nThe rich need it,
\r\nAnd if you eat it, you\'ll die?
\r\n','The answer, as a lot of people may have heard elsewhere, is \"Nothing\".','2003-01-24',20040212232105,NULL,2,3,0,3.19,20030124000000,0);
INSERT INTO problem VALUES (393,17,2,885,'pH of water','
\r\nH2CO3 --> H(+1) + HCO3(-1)
\r\nHCO3(-1) <--> H(+1) + CO3(-2)
\r\n\r\n
Last Saturday morning, Mrs. Holly returned the Christmas gifts for her children that hadn\'t worked out to the mall stores where she bought them. As it turned out, there was one return for each of the five children, including Ben, with each being returned for a different reason to a different mall retailer, one to Eddie Bauer. Given the details of her trip below, can you determine the order 1st-5th in which Mrs. Holly made the returns: the store visited, the child whose gift was returned, the item returned, and the reason for the return? \r\n\r\n\r\n\r\n
\r\n(i) Each of the three logicians was told one letter of a certain word, so that each logician knew only one of the letters and so that no two logicians knew the same letter.\r\n
\r\n(n+1)(n-1)=n²-1
\r\nand
\r\nn²-1+9=n²+8
\r\nwill also be divisible by three.\r\n
\r\n 75 4566.94
\r\n 60 4511.63
\r\n 45 4459.29
\r\n 30 4438.84
\r\n 15 4427.73
\r\n 0 4421.12
\r\n-15 4417.46
\r\n-30 4416.59
\r\n-45 4420.09
\r\n-60 4439.36
\r\n-75 4409.84
\r\n-90 4322.13
\r\n
\r\n 75 2827
\r\n 60 3599
\r\n 45 4674
\r\n 30 5561
\r\n 15 6132
\r\n 0 6327
\r\n-15 6132
\r\n-30 5561
\r\n-45 4674
\r\n-60 3599
\r\n-75 2828
\r\n-90 2627
\r\n
\r\n2/16 3 folds
\r\n3/16 3 folds
\r\n4/16 2 folds
\r\n5/16 4 folds
\r\n6/16 2 folds
\r\n7/16 4 folds
\r\n8/16 1 fold
\r\n9/16 5 folds
\r\n10/16 4 folds
\r\n11/16 5 folds
\r\n12/16 2 folds
\r\n13/16 4 folds
\r\n14/16 3 folds
\r\n15/16 3 folds
','2003-02-12',20030326065623,NULL,2,3,0,4.17,20030212000000,0);
INSERT INTO problem VALUES (464,7,2,1299,'Remainder','Show that the remainder when 2^1990 (2 to the power of 1990) is divided by 1990 equals 1024.\r\n
\r\n
\r\nHere\'s a sequence of 2000 consecutive composite numbers - \r\n
\r\n\r\n2001! + 2, 2001! + 3, 2001! + 4,.........,2001! + 2001\r\n\r\n
\r\nconsists of all composite numbers. \r\n
\r\n
\r\nIn the sum 2001! + x, we can see that both 2001! and x are definitely divisible by x as long as x < 2001.\r\n
\r\n
\r\n\r\nNote- this can be used to create a sequence of N number of composite integers.','2003-03-05',20030411232102,NULL,3,3,0,4.00,20030305000000,0);
INSERT INTO problem VALUES (402,11,2,1231,'5 weights','An ancient balance was found along with 5 weights. \r\n
\r\nWhat is the diameter of the largest sphere that can pass through the gap between the wall, floor and the sphere ?','Check the solution posted by Charlie here','2003-09-13',20040225103933,NULL,3,3,0,3.33,20030913094137,0);
INSERT INTO problem VALUES (622,6,2,979,'Man\'s Best Friend','Five men and five dogs (each man owned a dog) went hiking. They encountered a river that was swift and deep. The only way to cross it was an abandoned boat, left ashore on their side. But it would only hold three living things. Unfortunately, the dogs were edgy and could not be near another person (not even momentarily) unless its owner was present. One of the dogs attended a highly advanced, highly specialized obedience school and therefore knew how to operate the boat -- the other dogs lack this skill.\r\n![](\"http://www.flooble.com/images/perplexus/problem/9dots.gif\")
\r\n![](\"http://www.flooble.com/images/perplexus/problem/9dots-sol.gif\")
\r\n
\r\nMohammad: We are of different types.\r\n
iy=ln(-1)
e^iy=-1
Brant: Everard and Fredo are both knights.
Cuthbert: Brant is a liar and Everard is a knight.
Derek: Amery and Brant are both liars.
Everard: Cuthbert and Derek are both knights.
Fredo: Derek is a liar and Amery is a knight.
Remember: only part of a logical AND statement needs to be false for the entire statement to be false.','Amery, Brant, and Fredo are liars, while Cuthbert, Derek, and Everard are knights.\r\n
\r\nHence, a = 1(1+1) = 2, b = 2(2+1) = 6, and so on.\r\nBreak the code to reveal a famous phrase and its author:
\r\nSeveral people posted good methods of deduction in the comments, and DJ posted a program here that solves the puzzle.','2003-11-20',20040316133715,NULL,3,3,0,3.00,20031120084044,0);
INSERT INTO problem VALUES (929,7,2,1626,'Squares Probability','Suppose you had number cards in a deck, such that you had 2 2s, 3 3s, 7 7s, and 8 8s. (and no other cards in that deck)\r\n
\r\nTo be or not to be; that is the question.
\r\n~William Shakespeare
\r\n\r\nSince squaring any ones place number never will give 2, 3, 7 or 8 (because 0 thru 9 don\'t give it), you can\'t ever have a perfect square that ends with 2,3,7 or 8. This means the answer is 0.\r\n','2003-06-19',20030923232102,NULL,4,3,0,3.50,20030619030324,0);
INSERT INTO problem VALUES (406,4,2,1072,'The Peanuts','Although some of the things in this problem aren\'t true in real life just assume they are in the question.\r\n
\r\nTwo in the afternoon,
\r\nAnd three in the evening?\r\n
1. How much longer (in seconds) is one day today than 100 years ago?
\r\n2. How long a period of time need go by for one complete rotation (day) to be missed using the original rotation rate as a standard?\r\n
Assume a constant negative acceleration.','1. The negative acceleration resulted in a loss of 60 seconds of time over 100 years. If the acceleration is constant, the average rotational difference of .6 seconds per year is half the current defect of rotational rate, so that is 1.6 seconds per year or 1.6/365.25 seconds per day. The answer to part 1 is 0.00438056 seconds or 1/228 of a second.
\r\n2. As the positional difference increases as the square of the time when the acceleration is constant and we want a time over which the accumulated difference is 1440 times what it is over 100 years (as there are 1440 minutes in a day), we need x centuries, where x²=1440. That\'s about 38 centuries or 3800 years.','2003-03-08',20030907232101,NULL,2,3,0,3.00,20030308000000,0);
INSERT INTO problem VALUES (535,2,2,979,'Round Table','Ten people sit at a round table. The sum of Rupees 10 is to be distributed among them so that each person receives the average of what each of his two neighbours receives. \r\n
\r\n[Given: 1 Rupee = 100 Paise]\r\n
\r\nIn the case of n=3, represented by the Venn diagram, for ease of discussion, call A(1), A; A(2), B; and A(3), C. We need to show that the central area, A AND B AND C is counted exactly once by the formula, and that for each other area, the adding in and subtracting out exactly cancel and add zero net to the total.\r\n
\r\nThe central area is initially counted three times as it is included in P(A), P(B) and P(C). It is then subtracted out three times in P(A OR B), P(A OR C), P(B OR C). It is then added back in once in P(A OR B OR C). The net is it is counted once.\r\n
\r\nNow we only need to show that on net, none of the other areas is counted at all in the formula:\r\n
\r\nFor pairwise, consider the area of A AND B AND NOT C. That area is counted twice initially as P(A) and again in P(B). But then it is subtracted out three times as it is included in P(A OR B), P(A OR C) and in P(B OR C). It is then added in once again as P(A OR B OR C). Thus it is added in a total of three times and subtracted out a total of three times. Similarly for the other ANDed pairs.\r\n
\r\nThe areas that contain only a single occurrence, such as A AND NOT B AND NOT C, are added in once as P(A), subtracted out twice as P(A OR B) and P(A OR C), and added back in as P(A OR B OR C), thus adding in twice to balance out being subtracted out twice. Similarly for the other two events.\r\n
\r\nThe area NOT A AND NOT B AND NOT C is not counted at all in the formula. QED.\r\n
\r\nThe case of n=10 is of course more complicated. The central area, of A(1) AND A(2) AND...AND A(10), is counted in 10 times as P(A(1)) through P(A(10)). It is subtracted out 10C2 times, and added in 10C3 times, and subtracted out 10C4 times, etc. To sum up it is 10C1 - 10C2 + 10C3 - 10C4 + 10C5 - 10C6 + 10C7 - 10C8 + 10C9 - 10C10 + 10C0, where nCr is the combinations of n taken r at a time. We see that the 10C10 cancels out the 10C1, the 10C9 cancels out the 10C1, etc. as they are oppositely signed but equal in absolute value to their partner. The only one left is 10C1 = 1 time that this area is counted on net.\r\n
\r\nThe pairwise ANDed areas are more complicated as they involve not only the probabilities of themselves but probabilities that include other than themselves: for example, the area that represents A(1) AND A(2) but not any of the others A(3) through A(10), is counted by A(1) OR A(2), and also by A(1) OR A(3), but not by A(3) OR A(4), for example. In fact the net times that that area is included is 2C1 - (2C2+2C1*8C1) + (8C1+2C1*8C2) - (8C2+2C1*8C3) + (8C3+2C1*8C4) - (8C4+2C1*8C5) + ... - (8C8+2C1*8C9), with 8C9 being zero. The rationale for one of these terms, say (8C2 + 2C1*8C3), is that in quadruple ORed sets A(1) OR A(2) OR A(i) OR A(j) will have 8C2 representatives (the i and j out of the remaining 8), while A(1) and A(2) can each be joined individually with 8C3 triplets drawn from the remaining 8. The total of this formula is 2-(1+2*8)+(8+2*28)-(28+2*56)+(56+2*70)-(70+2*56)+(56+2*28)-(28+2*8)+(8+2*1)-(1+0), which indeed comes out to zero.\r\n
\r\nThe other areas on the multi-dimensional Venn diagram, containing two positive and eight negative events similarly count to zero.\r\n
\r\nThe triples of events get more complicated still: Each is counted 3C1 = 3 times in the single event total, and is subtracted out (3C2+3C1*7C1) of the pairwise ORed totals, as they appear doubly in 3C2 compound events and in 3C1*7C1 where one of the three is paired with any one from the other seven. In the triples there is an additional term to be added: (3C3+3C2*7C1+3C1*7C2), as we can choose all three from the given set of three (in 3C3 = 1) way, or two from the three with one from the remaining seven (in 3C2*7C3 ways), or one from the set of three with 2 from the remaining seven (in 3C1*7C2 ways). From here on, the terms look similar to the third through tenth of the doublet terms, and we can write the remaining sum as Sigma{i=4 to 10} (-1)^(i-1)*(7C(i-3)+3C2*7C(i-2)+3C1*7C(i-1)). In fact, we can consider the entire sum as Sigma{i=1 to 10} (-1)^(i-1)*(7C(i-3)+3C2*7C(i-2)+3C1*7C(i-1)), if we consider 7C(-2) and 7C(-1) to be zero. This summation comes out to (0+0+3*1)-(0+3*1+3*7)+(1+3*7+3*21)-(7+3*21+3*35)+(21+3*35+3*35)-(35+3*35+3*21)+(35+3*21+3*7)-(21+3*7+3*1)+(7+3*1+0)-(1+0+0)=0.\r\n
\r\nWe can see as we consider volumes in the Venn diagram that contain the overlap of r positive areas, with 10-r negative areas, such as A(1)...A(r), ~A(r+1),...,~A(10), the sum of their probabilities per the formula to be proved, is Sigma{i=1 to 10} (-1)^(i-1) Sigma{j=1 to r}(rCj*(10-r)C(i-j)). For quadruples this comes out to (4*1+0+0+0)-(4*6+6*1+0+0)+(4*15+6*6+4*1+0)-(4*20+6*15+4*6+1*1)+(4*15+6*20+4*15+1*6)-(4*6+6*15+4*20+1*15)+(4*1+6*6+4*15+1*20)-(0+6*1+4*6+1*15)+(0+0+4*1+1*6)-(0+0+0+1*1)=0\r\n
\r\nThis formula does in fact produce 1 in the case of r = 10, and zero for all other r, proving the case for n = 10.\r\n
\r\n(1*1)-(1*9)+(1*36)-(1*84)+(1*126)-(1*126)+(1*84)-(1*36)+(1*9)-(1*1)=0\r\n
\r\n(2*1+0)-(2*8+1*1)+(2*28+1*8)-(2*56+1*28)+(2*70+1*56)-(2*56+1*70)+(2*28+1*56)-(2*8+1*28)+(2*1+1*8)-(0+1*1)=0\r\n
\r\n(3*1+0+0)-(3*7+3*1+0)+(3*21+3*7+1*1)-(3*35+3*21+1*7)+(3*35+3*35+1*21)-(3*21+3*35+1*35)+(3*7+3*21+1*35)-(3*1+3*7+1*21)+(0+3*1+1*7)-(0+0+1*1)=0\r\n
\r\n(4*1+0+0+0)-(4*6+6*1+0+0)+(4*15+6*6+4*1+0)-(4*20+6*15+4*6+1*1)+(4*15+6*20+4*15+1*6)-(4*6+6*15+4*20+1*15)+(4*1+6*6+4*15+1*20)-(0+6*1+4*6+1*15)+(0+0+4*1+1*6)-(0+0+0+1*1)=0\r\n
\r\n(5*1+0+0+0+0)-(5*5+10*1+0+0+0)+(5*10+10*5+10*1+0+0)-(5*10+10*10+10*5+5*1+0)+(5*5+10*10+10*10+5*5+1*1)-(5*1+10*5+10*10+5*10+1*5)+(0+10*1+10*5+5*10+1*10)-(0+0+10*1+5*5+1*10)+(0+0+0+5*1+1*5)-(0+0+0+0+1*1)=0\r\n
\r\n(6*1+0+0+0+0+0)-(6*4+15*1+0+0+0+0)+(6*6+15*4+20*1+0+0+0)-(6*4+15*6+20*4+15*1+0+0)+(6*1+15*4+20*6+15*4+6*1+0)-(0+15*1+20*4+15*6+6*4+1*1)+(0+0+20*1+15*4+6*6+1*4)-(0+0+0+15*1+6*4+1*6)+(0+0+0+0+6*1+1*4)-(0+0+0+0+0+1*1)=0\r\n
\r\n(7*1+0+0+0+0+0+0)-(7*3+21*1+0+0+0+0+0)+(7*3+21*3+35*1+0+0+0+0)-(7*1+21*3+35*3+35*1+0+0+0)+(0+21*1+35*3+35*3+21*1+0+0)-(0+0+35*1+35*3+21*3+7*1+0)+(0+0+0+35*1+21*3+7*3+1*1)-(0+0+0+0+21*1+7*3+1*3)+(0+0+0+0+0+7*1+1*3)-(0+0+0+0+0+0+1*1)=0\r\n
\r\n(8*1+0+0+0+0+0+0+0)-(8*2+28*1+0+0+0+0+0+0)+(8*1+28*2+56*1+0+0+0+0+0)-(0+28*1+56*2+70*1+0+0+0+0)+(0+0+56*1+70*2+56*1+0+0+0)-(0+0+0+70*1+56*2+28*1+0+0)+(0+0+0+0+56*1+28*2+8*1+0)-(0+0+0+0+0+28*1+8*2+1*1)+(0+0+0+0+0+0+8*1+1*2)-(0+0+0+0+0+0+0+1*1)=0\r\n
\r\n(9*1+0+0+0+0+0+0+0+0)-(9*1+36*1+0+0+0+0+0+0+0)+(0+36*1+84*1+0+0+0+0+0+0)-(0+0+84*1+126*1+0+0+0+0+0)+(0+0+0+126*1+126*1+0+0+0+0)-(0+0+0+0+126*1+84*1+0+0+0)+(0+0+0+0+0+84*1+36*1+0+0)-(0+0+0+0+0+0+36*1+9*1+0)+(0+0+0+0+0+0+0+9*1+1*1)-(0+0+0+0+0+0+0+0+1*1)=0\r\n
\r\n(10*1+0+0+0+0+0+0+0+0+0)-(0+45*1+0+0+0+0+0+0+0+0)+(0+0+120*1+0+0+0+0+0+0+0)-(0+0+0+210*1+0+0+0+0+0+0)+(0+0+0+0+252*1+0+0+0+0+0)-(0+0+0+0+0+210*1+0+0+0+0)+(0+0+0+0+0+0+120*1+0+0+0)-(0+0+0+0+0+0+0+45*1+0+0)+(0+0+0+0+0+0+0+0+10*1+0)-(0+0+0+0+0+0+0+0+0+1*1)=1\r\n
\r\nA similar proof works for any n substituted in Sigma{i=1 to n} (-1)^(i-1) Sigma{j=1 to r}(rCj*(n-r)C(i-j)). For example, for n = 4, 5 and 6:\r\n
\r\nN=4:\r\n
\r\n(1*1)-(1*3)+(1*3)-(1*1)=0\r\n
\r\n(2*1+0)-(2*2+1*1)+(2*1+1*2)-(0+1*1)=0\r\n
\r\n(3*1+0+0)-(3*1+3*1+0)+(0+3*1+1*1)-(0+0+1*1)=0\r\n
\r\n(4*1+0+0+0)-(0+6*1+0+0)+(0+0+4*1+0)-(0+0+0+1*1)=1\r\n
\r\n
\r\nN=5:\r\n
\r\n(1*1)-(1*4)+(1*6)-(1*4)+(1*1)=0\r\n
\r\n(2*1+0)-(2*3+1*1)+(2*3+1*3)-(2*1+1*3)+(0+1*1)=0\r\n
\r\n(3*1+0+0)-(3*2+3*1+0)+(3*1+3*2+1*1)-(0+3*1+1*2)+(0+0+1*1)=0\r\n
\r\n(4*1+0+0+0)-(4*1+6*1+0+0)+(0+6*1+4*1+0)-(0+0+4*1+1*1)+(0+0+0+1*1)=0\r\n
\r\n(5*1+0+0+0+0)-(0+10*1+0+0+0)+(0+0+10*1+0+0)-(0+0+0+5*1+0)+(0+0+0+0+1*1)=1\r\n
\r\nN=6:\r\n
\r\n(1*1)-(1*5)+(1*10)-(1*10)+(1*5)-(1*1)=0\r\n
\r\n(2*1+0)-(2*4+1*1)+(2*6+1*4)-(2*4+1*6)+(2*1+1*4)-(0+1*1)=0\r\n
\r\n(3*1+0+0)-(3*3+3*1+0)+(3*3+3*3+1*1)-(3*1+3*3+1*3)+(0+3*1+1*3)-(0+0+1*1)=0\r\n
\r\n(4*1+0+0+0)-(4*2+6*1+0+0)+(4*1+6*2+4*1+0)-(0+6*1+4*2+1*1)+(0+0+4*1+1*2)-(0+0+0+1*1)=0\r\n
\r\n(5*1+0+0+0+0)-(5*1+10*1+0+0+0)+(0+10*1+10*1+0+0)-(0+0+10*1+5*1+0)+(0+0+0+5*1+1*1)-(0+0+0+0+1*1)=0\r\n
\r\n(6*1+0+0+0+0+0)-(0+15*1+0+0+0+0)+(0+0+20*1+0+0+0)-(0+0+0+15*1+0+0)+(0+0+0+0+6*1+0)-(0+0+0+0+0+1*1)=1\r\n
\r\nThis actually shows particular values of n. The pattern is clear.
\r\n9 numbers are arranged in a 3 x 3 grid. They are arranged such that the top row plus the middle row gives the bottom row. What is a possibility for this grid if forms another such sum when:
\r\n\r\nA: When the grid is given a turn to the right?
\r\nB: When the grid is given a turn to the left?
\r\nC: When the grid is turned so it\'s bottom side is up?
\r\nD: When it\'s flipped up so tit\'s bottom side is up?','?','2003-10-01',20040324232101,NULL,3,3,10,0.00,00000000000000,289);
INSERT INTO problem VALUES (1618,4,2,3558,'Game of luck','4 people play a game of chance. They each take turns until everyone has taken a turn, then they begin a new round. They stay in the same order every round. Every time a player takes a turn, they have a certain chance of winning. When someone wins, the game ends. They all have even odds of winning a game. The chance of someone winning in any given round is 3/5.
\r\n2nd player: (3/20)/(17/20)=3/17
\r\n3rd player: (3/20)/(14/20)=3/14
\r\n4th player: (3/20)/(11/20)=3/11\r\nB 4771 0.016744\r\nE 36232 0.127157\r\nF 7167 0.025153\r\nL 9563 0.033562\r\nO 22486 0.078915
\r\nthat is, for each letter is shown the number of occurrences in the text and that number divided by the total of characters in the text.','First we calculate how many quasi-random 7-letter sequences can be gotten from the text. There is a choice of 284,939 places to start. There would be a choice of 284,939 places to end, except for the fact that the difference between the starting and ending position must be a multiple of 6. So there are 284,939*(284,939/6) combinations of valid beginning and ending pairs (in such a large number we can ignore the fact that the size is not exactly divisible by 6--we\'ve still got 6 significant digits). In general if the text length is L and the word length is W, the number of random sequences we have to choose from is L²/(W-1). In this instance we have about 13,531,705,620 seven-random-letter sequences to choose from.
\r\n\r\nThen we consider the probability that any given 7-letter sequence is FLOOBLE. We multiply together the relative frequencies at each position: .025153*.033562*.078915²*.016744*.033562*.127157. That product is 3.7567 x 10^-10. Then multiply that by 13,531,705,620, giving 5.08, so we’d expect 5 occurrences of FLOOBLE as an ELS in the text. As this is the result of a large number of chances each with small probability, we’d expect the result to be Poisson distributed so the probabilities of finding given numbers in the text are (if we use 5.08 instead of 5):\r\n
\r\n0 0.0062199
\r\n 1 0.0315971
\r\n 2 0.0802567
\r\n 3 0.1359014
\r\n 4 0.1725948
\r\n 5 0.1753563
\r\n 6 0.1484683
\r\n 7 0.1077456
\r\n 8 0.0684184
\r\n9 0.0386184
\r\n
\r\nA search program actually found 8 occurrences. The Poisson distribution gives a 14% chance of it being this many or higher. The shortest skip distance among these occurrences was 382 backward, in a downloaded text of Thomas Paine’s The Age of Reason, which had the length and letter frequencies mentioned.\r\n
\r\n\r\nStart: 3012 skip: 40916 \r\ndandunadulteratedbeliefoFonegodandnomoreeverynati\r\nightytoperfectionnonotonLybecausethepowerandwisdo\r\niteverwillbeinallthingscOnsistentwiththeeverexist\r\nnsanddescendantsofesauwhOarecallededomitesandalso\r\nthisnameismentionedintheBibleinalaterworkpainenot\r\nhoughattheriskoftheirownLivesfortheaccountsaysnev\r\nnewtestamentandshowedothErwritingsquitedifferentt\r\n
','2003-03-18',20030414232101,NULL,4,3,0,3.20,20030318000000,0);
INSERT INTO problem VALUES (439,2,2,979,'The Ten Statements','Which of the following statements is true? \r\n
\r\nStart: 44861 skip: 33729 \r\nversialandthegloominessoFthesubjecttheydwellupont\r\ntfromthesunandconsequentLymovesroundinacirclegrea\r\navethesamemerittheyhavenOwweretheyanonymousnobody\r\noughtdowntobc1056thatistOthedeathofsaulwhichwasno\r\nthisromanticbookofschoolBoyseloquencebendtothemon\r\nentthenewtestamenttheyteLlusisfoundedupontheproph\r\neumaugustinehavingentitlEdhisbookcontrafsustumman\r\n
\r\nStart: 57965 skip:-3363
\r\nsasifheweretosaythouknowEstnotsowellasibutsomeper\r\nencethatitdidnotmakeitseLfeverymanisanevidencetoh\r\nrstifthefirstquestionhadBeenanswerednegativelythe\r\nywhichtheheavenlybodiesmOvebutitwouldbesomethingw\r\nfthatagencysoastobeabletOapplyitinpracticewemight\r\nstobetterstudiestheschooLsofthegreekswereschoolso\r\nertomakeanexcusetohimselFfornotexecutinghissuppos\r\n
\r\nStart: 192146 skip:-26506
\r\nthedisagreementofthewritErsbutbecauserevelationca\r\nearthwasaglobeandhabitabLeineverypartwheretherewa\r\nnotforeseethatitcouldnotBemaintainedagainsttheevi\r\nsinourestimationbutanimpOsterastotheancienthistor\r\nustohavesaidsothenextdayOrthenextweekorthenextmon\r\nththevicissitudesofhumanLifeandbyturnssinkingunde\r\nndofthefalsepredictionsoFjeremiahishallmentiontwo\r\n
\r\nStart: 193730 skip:-15099
\r\ncivilitybutwithrespectthEkeeperoftheluxembourgben\r\nthewriterofthosebooksiwiLlaftermakingafewobservat\r\nrsbytheaccountgivenintheBookofjoshuaafterthechild\r\nichasthosebooksareanonymOusandasweknownothingofth\r\norrapinshistoryofenglandOrthehistoryofanyothercou\r\ndthejewstoreturntojerusaLemfromthebabyloniancapti\r\npeaceandwiththeburningsoFthyfatherstheformerkings\r\n
\r\nStart: 208825 skip:-13751
\r\nypersonwhodiedbeforetherEwasacongressintheonecoun\r\nestheinhabitantsofjerusaLemthechildrenofjudahcoul\r\ncountalsoisgiveninkingsaBoutelijahitrunsthroughse\r\nedinsciencewhichthejewssOfarfrombeingfamousforwer\r\nththewindinthissituationOfthingsisaiahaddresseshi\r\nnthecharacterofthemenstyLedprophetsintheformerpar\r\nloneweretherenootherissuFficienttoindicatethatthe\r\n
\r\nStart: 240759 skip:-28476
\r\nonofgodafterthesermonwasEndediwentintothegardenan\r\nthereforeisacharacteruseLessandunnecessaryandthes\r\nyunderstoodandintendedtoBeunderstoodthathehasbeen\r\ntheirexistencehintedatthOughaccordingtothebiblech\r\northislyingprophetandimpOsterisaiahandthebookoffa\r\neciallyliabletotheridicuLeofsuperficialreadersand\r\ndofbelievingthereismuchoFthatwhichiscalledwilfull\r\n
\r\nStart: 248258 skip:-382
\r\nngthepeoplethencallingthEmselveschristiansnotonly\r\nmunderthenamesoftheapostLesandwhicharesofullofsot\r\nedthatthesethingshavenotBeenwrittenbyhimselfnorby\r\nboulangerhasquotedthemfrOmthewritingsofaugustinea\r\ntheywerevotedtobethewordOfgodbuttheinterestofthec\r\nlhersaintstoworkonemiracLesincetherevolutionbegan\r\neeitwasvotedtobethewordoFgodthefollowingextractsa\r\n
\r\n∙4∙∙1
\r\n∙∙∙∙∙
\r\n∙∙∙∙∙
\r\n∙1∙∙4
\r\n(a) There are only 2 flowers (neither of which is Rose, Tulip or Daisy) and \r\n
\r\n(b)There are 3 flowers: One Rose, One Tulip and One Daisy.\r\n','2003-03-01',20031229232104,NULL,1,3,0,2.83,20030301000000,0);
INSERT INTO problem VALUES (442,7,2,979,'Too Old For Grandma','\"I\'ve always been 45 years older than your Dad\", said Grandma to young grandson.\r\n
\r\nLet the two digits be A and B. \r\n
\r\nThen (10A+B)-(10B+A) = 45 \r\n
\r\nor, 9(A-B)= 45. \r\n
\r\nThis gives A-B = 5. \r\n
\r\n7 and 2 are the only two prime numbers that satisfy the given conditions.\r\n
\r\nTherefore, Grandma\'s age is 72 years.','2003-02-28',20031217232102,NULL,2,3,0,2.71,20030228000000,0);
INSERT INTO problem VALUES (443,7,2,979,'Age Difference','Said Albert to Bertrand, \"The last time we met, our ages were both prime numbers, and when I was a quarter of the age I am now, you were that age plus half the age your father would have been thirty years previous to when he was six times the age you would have been when I was half your age\". \r\n
\r\nIf A and B are Albert\'s and Bertrand\'s present ages and a and b are their ages when Albert was half Bertrand\'s age then\r\n
\r\nB - 3A/4 = (A/4) + (6b - 30)/2\r\n
\r\nSince their ages have always had the same difference we have\r\n
\r\nB - A = 3b - 15 = b - a\r\n
\r\nand since 2a = b then a = 3 and b = 6. \r\n
\r\nSo their ages differ by 3. Since all primes except 2 are odd and differ by an even number we can only have 2 and 5, Bertrand being the older of the two. \r\n','2003-03-02',20030907232101,NULL,3,3,0,4.17,20030302000000,0);
INSERT INTO problem VALUES (682,20,2,1301,'Thirteen Words','List 13 words such that the first contains an anagram of the word ONE, the second contains an anagram of the word TWO, etc. The anagrammed words cannot be directly in the containing word, so that while \"ounce\", \"sonnet\" and \"enough\" are good for \"one\"; \"gone\" and \"toner\" are not.
\r\n\r\nEach letter of the alphabet is to be used once as either a first or last letter in one of the thirteen words\r\n
\r\nJOINER
\r\nOUTWALK
\r\nBERTHED
\r\nFORUM
\r\nVERIFY
\r\nUNISEX
\r\nAVENGES
\r\nLIGHTEN
\r\nQUEENING
\r\nZENITH
\r\nINTERLEAVE
\r\nWAVELET
\r\nPARENTHETIC
\r\npuzzlers.org/ub/wordlists/enable1.txt
\r\nand
\r\npuzzlers.org/ub/wordlists/mbsingle.txt
\r\nSuppose B had bananas, then we see that both the third and the fourth statements are true thus violating the given condition that only one of the given statements are true. Thus, A had bananas and not B.\r\n
\r\nIf now we assume that B had grapes, then once again we see that both the second and the fourth statements are true, once again violating the conditions of the problem. Thus our assumption that B had grapes is wrong. This implies B had apples and C had grapes.So, we have the final solution as follows:\r\n
\r\n\'A\' had \'BANANAS\'.\r\n
\r\n\'B\' had \'APPLES\'.\r\n
\r\n\'C\' had \'GRAPES\'.','2003-03-03',20031217232102,NULL,2,3,0,2.62,20030303000000,0);
INSERT INTO problem VALUES (706,14,2,979,'Non - Zero Digit','What is the last non - zero digit in (20!)!? (That is, factorial of 20 factorial).\r\n\r\n','The solution to this problem will be found on this site: http://www.mathpages.com/home/kmath489.htm\r\n\r\n (n!)\' = (2^(a2-a5))(3^a3)(7^a7)...\r\n
\r\nSince we\'ve divided out all powers of 10, the least significant\r\ndigit of this number is non-zero, as are the least significant digits\r\nof the factors. Thus we have\r\n\r\n L(n!) = L((n!)\') = L[ L(2^a2 - a5) L(3^a3) L(7^a7) ...]\r\n
\r\nFor any given integer n we can compute the exponent of any prime p\r\nin n! simply by summing the nearest integers to [n/p^j] for j=1,2,..\r\nFor example, the exponent of 3 in 89! is given by\r\n\r\n a3 = [89/3] + [89/9] + [89/27] + [89/81]\r\n
\r\nFurthermore, the least significant decimal digit of 3^k is cyclical\r\nwith the four values {1,3,9,7}, so it\'s easy to see that L(3^42) = 9.\r\n
\r\n = 29 + 9 + 3 + 1 = 42\r\n\r\n n\r\n 1 5 10 15 20 25 30 35 40 45\r\n\r\n L(n!): 1264 22428 88682 88682 44846 44846 88682 22428 22428 66264 ...\r\n
\r\nThus, if we know the value of L((5n)!) we automatically know the values \r\nof L((5n+j)!) for j=0,1,2,3,4. However, the pattern of the values \r\nL((5n)!) is not immediately apparent. If we tabulate these values we \r\nfind that they too come in fixed strings of five, so we only need to \r\nknow L((25n)!) to automatically know L((25n+5j)!) for j=0,1,2,3,4. \r\nContinuing in this way, we can tabulate the values of L((5^t n)!) as \r\nshown below\r\n\r\n n\r\n 1 5 10 15 20 25 30 35 40 45\r\n\r\nL( n!): 1264 22428 88682 88682 44846 44846 88682 22428 22428 66264\r\nL( 5n!): 2884 48226 24668 48226 48226 86442 24668 62884 24668 24668\r\nL( 25n!): 4244 82622 82622 28488 46866 64244 82622 82622 28488 46866\r\nL(125n!): 8824 68824 26648 68824 42286 26648 26648 42286 26648 84462\r\nL(625n!): 6264 22428 88682 88682 44846 44846 88682 22428 22428 66264\r\n etc.\r\n
\r\nNotice that the pattern of digits for L(625n!) is the same as for\r\nL(n!). In general it appears that the pattern for L((5^j n)!) is the\r\nsame as for L((5^(j+4) n)!). In addition, on each level there are\r\nprecisely four distinct blocks of 5 sequential digits, one block\r\nbeginning with each of the digits 0,2,4,6,8.\r\n\r\n Look-Up Table for L() Patterns\r\n ------------------------------\r\n k mod 4\r\n -------\r\n 0 06264 22428 44846 66264 88682\r\n 1 02884 24668 48226 62884 86442\r\n 2 04244 28488 46866 64244 82622\r\n 3 08824 26648 42286 68824 84462\r\n
\r\nThis table represents all we need to determine the value of L(n!) for\r\nany integer n. First we convert n to the base 5, so we have\r\n\r\n n = d_0 + d_1*5 + d_2*5^2 + ... + d_h*5^h\r\n
\r\nNow we enter the above table at the row h (mod 4) in the block whose\r\nfirst digit is 0 (because the coefficient of 5^(h+1) is zero), and\r\ndetermine the digit in the (d_h)th position of this block. Let this\r\ndigit be denoted by s_h. Then we enter the table at row h-1 (mod 4)\r\nin the block that begins with s_h, and determine the digit in the\r\n(d_(h-1))th position of this block. Let this digit be denote by\r\ns_(h-1). We continue in this way down to s_0, which is the least\r\nsignificant non-zero digit of n!.\r\n\r\n L(1592!) = L((2*5^4 + 2*5^3 + 3*5^2 + 3*5 + 2)!) = 4\r\n
\r\nTo streamline this process, let\'s define an array A(4,5,5) where the\r\nfirst index signifies the row (0,1,2,3), the second is the block\r\nselector (0,2,4,6,8) in that row, and the third is the digit number \r\n(0,1,2,3,4) in that block. If it\'s understood that the first index \r\nis to be taken modulo 4, and if we let dj denote the jth digit of the \r\nbase-5 representation of n, then the above evaluation be written in \r\nthe form\r\n\r\n A(4, 0, d4) = s4\r\n A(3, s4, d3) = s3\r\n A(2, s3, d2) = s2\r\n A(1, s2, d1) = s1\r\n A(0, s1, d0) = s0 = L((d4*5^4 + d3*5^3 + d2*5^2 + d1*5 + d0)!)\r\n
\r\nThis shows how we can easily determine the value of L(n!) by means of \r\nk look-ups (in a simple fixed 4x5x5 table) where k is the number of \r\nbase-5 digits of n. From this we can also rigorously determine the\r\ndistribution of digits, which the table\'s symmetry seems to imply\r\nmust be uniform. Just checking empirically, we find the following \r\ndistribution of the values of L(n!) for n from 2 to 10^t with t=4,5,6.\r\n(This excludes n=1 for which L(n!)=1.)\r\n\r\n 2 4 6 8\r\n ------ ------ ------ ------\r\n 10^4 2509 2486 2494 2510\r\n 10^5 25026 24999 24973 25001\r\n 10^6 249993 250013 250040 249953\r\n
\r\nNaturally a similar analysis can be performed with respect to the\r\nleast significant digit of n! in any other base. For example, in \r\nthe base 3, we find that the blocks on the even levels are 112 and\r\n221, and the blocks on the odd levels are 122 and 211. With this\r\ninformation we can construct the function table shown below.\r\n\r\n previous current\r\n output digit output\r\n -------- ------- ------\r\n 1 0 1\r\n 1 1 p+1\r\n 1 2 2\r\n 2 0 2\r\n 2 1 2-p\r\n 2 2 1\r\n
\r\nwhere \"p\" denotes the parity of the exponent of 3 for the current\r\ndigit. To illustrate, suppose we wish to determine the least \r\nsignificant non-zero base-3 digit of (139!). The number 139 written\r\nin the base 3 is 12011, so the exponent of 3 for the leading digit\r\nis 4, which has parity 0. Thus the parity string of the exponents\r\nis 01010. Beginning with the most significant digit, 1, and a\r\n\"previous output\" of 1 (which is always the initial \"previous output\")\r\nwe enter the table in the row 1 1 to find that the output is p+1,\r\nwhich equals 1 (because the current exponent parity is p=0). Then\r\nwe take this output and the next input digit, 2, and enter the table\r\nat the row 1 2 to get the output 2. Then we take this output and\r\nthe next input digit, 0, and enter the table in the row 2 0 to find\r\nthe output 2. Next we enter at 2 1 to find he output 2-p, and on\r\nthis level we have p=1, so the output is 1. Finally we enter the\r\ntable at row 1 1 to find the output p+1, and on this level we have\r\np=0, so the final output is 1.\r\n
\r\n\r\nThere are 4 positive integers in order from least to greatest, such that the first three make an aritmetic sequence, and the last three make a geometric sequence. If the difference between the largest and smallest term is 30, what are the terms?','One way to do this is to note that the second and fourth numbers both have to be perfect squares times a number. (the same number) So start out with the perfect squares for the second term and fourth term.\r\n
\r\n1 won\'t work as the second term or fourth term, because no integer below it is positive.\r\n
\r\nTrying 4 as the second term and 9 as the fourth term: 2 4 6 9. The difference between 2 and 9 is 7, and 7 is not a factor of 30.\r\n
\r\nTrying 4 as the second term and anything more than 9 for the fourth term will end up with the first term not being positive.\r\n
\r\nSo trying 9 as the second term and 16 as the fourth term: 6 9 12 16, and this will work because the difference between the first term and fourth term is 10, a factor of 30. So multiplying every term by 30/10 or 3 gives 18, 27, 36, 48, and 48 - 18 is 30 as the problem says, so 18, 27, 36, 48 is the solution.\r\n
\r\nOther possible sequences include:
\r\n3, 9, 15, 25, and 25 - 3 = 22
\r\n12, 16, 20, 25, and 25 - 12 = 13
\r\n8, 16, 24, 36, and 36 - 8 = 28
\r\n20, 25, 30, 36, and 36 - 20 = 16
\r\n30, 36, 42, 49, and 49 - 30 = 19
\r\n42, 49, 56, 64, and 64 - 42 = 22
\r\n56, 64, 72, 81, and 81 - 56 = 25
\r\n72, 81, 90, 100, and 100 - 72 = 28
\r\n
\r\nAll other combinations won\'t work because they will end up with first terms which aren\'t positive, or the difference between the first and last term will be greater than 30.
\r\n\r\nNone of these sequences have the difference between the first and last term being a factor of 30, so no other sequence is possible.','2003-09-23',20030927142701,NULL,3,3,0,4.50,20030923175339,0);
INSERT INTO problem VALUES (447,7,2,979,'Bus Number','While visiting a small town in some country, I lost my overcoat in a bus. When I reported the matter to the bus company I was asked the number of the bus. Though I did not remember the exact number of the bus, I did remember that the bus number had a certain peculiarity about it.\r\n
\r\nTherefore, 196 is the correct answer.','2003-03-04',20040227232102,NULL,3,3,0,2.50,20030304000000,0);
INSERT INTO problem VALUES (448,14,2,979,'Party and Glasses','My friend Andrew was throwing a very grand party and wanted to borrow from me 100 wine glasses. I wanted to send them through my neighbour’s servant Harry.\r\n
\r\nThen according to the problem, we have:\r\n
\r\n30G - 90B = 2400 -------- (1)\r\n
\r\nG + B = 100 -------- (2)\r\n
\r\nSolving the above two equations, we have:\r\n
\r\nB = 5 and G = 95.\r\n
\r\nTherefore Harry broke 5 glasses, which is the required solution.','2003-03-05',20040217232105,NULL,2,3,0,2.60,20030305000000,0);
INSERT INTO problem VALUES (449,7,2,979,'Counting Stamps','My friend Charles works in a post office and he sells stamps. One day a man walked in and slamming seventy five rupees on the counter requested, \r\n
\r\nThen from the problem, we have: \r\n
\r\n8x + 5y = 75 \r\n
\r\n8x = 5(15 - y)\r\n
\r\nIt is clear from the bove equation that \'x\' is a multiple of 5 and the value of \'y\' cannot be more than 14. Thus either x = 5 or x = 10, but x = 10 violates the condition of the problem by exceeding the total amount. Therefore, x = 5, giving y = 7.\r\n
\r\nTherefore, the required answer is:\r\n
\r\nThe number of stamps of each type purchased by the man is: 5 Two-Rupee stamps, 30 One-Rupee stamps and 7 Five-Rupee stamps.\r\n','2003-03-06',20030326065623,NULL,2,3,0,2.80,20030306000000,0);
INSERT INTO problem VALUES (450,14,2,979,'Cattle Selling','My friend who owns a farm nearby, has five droves of animals on his farm consisting of cows, sheep and pigs with the same number of animals in each drove. One day he decided to sell them all and sold them to 8 dealers. \r\n
\r\nNow, it can be found out that this number is equal to 120 and the following figures satisfy the conditions of the problem:\r\n
\r\n3 cows, 8 sheep and 109 pigs, which is the required answer.','2003-03-10',20030615232102,NULL,3,3,0,1.50,20030310000000,0);
INSERT INTO problem VALUES (451,14,2,979,'Sums and Products','The product of three consecutive numbers when divided by each of them in turn gives three quotients. The sum of these three quotients is equal to 74.\r\n
\r\nThen the sum of their resulting quotients when their product is divided by each of them is:\r\n
\r\nn(n+1) + (n+1)(n-1) + n(n-1)\r\n
\r\nwhich is equal to 74.\r\n
\r\nTherefore, we have:\r\n
\r\nn(n+1) + (n+1)(n-1) + n(n-1) = 74\r\n
\r\nWhich on simplification gives:\r\n
\r\n(n)^2 = 25 which implies n = (-5) or n = (+5)\r\n
\r\nThus, the three consecutive numbers are: (-6,-5,-4) or (4,5,6).','2003-03-12',20040108232102,NULL,2,3,0,2.60,20030312000000,0);
INSERT INTO problem VALUES (452,14,2,979,'Step By Step','A short man takes three steps to a tall man’s two steps. They both start out on the left foot. \r\n
\r\nThe method of working out this problem is to reverse the whole process (that is, working backwards) which goes as follows: multiplying 2 by 10, deducting 8, squaring the result and so on.','2003-03-14',20040108232102,NULL,1,3,0,2.25,20030314000000,0);
INSERT INTO problem VALUES (455,14,2,979,'Marble Counting','A box contains 12 marbles of three different colors – Green, Yellow and Blue – 4 of each.
\r\nFrom this information, we can find the proportion in which each of them spent their part of money, thus giving us the following relation:\r\n
\r\nWriters : Doctors : Dentists : Bank Employees = 5 : 4 : 3 : 4\r\n
\r\nAlso, it is given that 25 Writers, 20 Doctors, 18 Dentists and 12 Bank Employees together contribute Rupees 1330.\r\n
\r\nNow, from the above relations, we can easily calculate that:\r\n
\r\n20 Doctors = 25 Writers, 18 Dentists = 30 Writers and 12 Bank Employees = 15 Writers.\r\n
\r\nThus giving us the following:\r\n
\r\nThe amount paid by each Writer = 14 Rupees.\r\n
\r\nTherefore, the total amount paid by 25 Writers = (14 x 25) = 350 Rupees and from here we can calculate the remaining figures that are required.\r\n\r\n+ +r+ | \r\nq+ + +| \r\n+ K +h| \r\n + +r+| \r\n+bB +h| \r\n------ 1 \r\n+k+bH | \r\n + + R| \r\nQ + + | \r\n +r+ +| \r\n+ +hB | \r\n------ 2 \r\n+ Q + | \r\nb+ + K| \r\n+ +r+ | \r\n + +r+| \r\nBh+ +h| \r\n------ 3 \r\n+q+ + | \r\n + R +| \r\nB + +b| \r\nh+k+ H| \r\n+ + R | \r\n------ 4 \r\n+ + R | \r\n Q + +| \r\n+ +r+ | \r\nb+ + B| \r\nH K +h| \r\n------ 5 \r\n+ Q + | \r\nb+ + K| \r\n+ +r+ | \r\n R + +| \r\nH + Bh| \r\n------ 6\r\n
','2003-02-27',20030418232103,NULL,4,3,0,3.00,20030227000000,0);
INSERT INTO problem VALUES (461,4,2,1301,'2,000,000 Coin Tosses','If a coin is tossed 2,000,000 times, what is the probability that it will come up exactly 1,000,000 times each heads and tails?\r\n
\r\nln(x!)=x(x+.5) – x + 1/(12x) – 1/(360x^3) + 1/(1260x^5) + ln(2*pi)/2
\r\nand since ln(a/b)=ln(a)-ln(b) and ln(2^p)=p ln(2), the natural log of our answer is
ln(2,000,000!) – 2 ln(1,000,000!) – 2,000,000 ln(2) = 27017323.65031588 – 2 (12815518.38465817) – 2,000,000 (.6931471805599453) = −7.480120345950127\r\n
The natural anti-log of this is 0.000564189513564, or about 1/1772.\r\n
\r\nMethod 2: The binomial distribution is approximated by the normal distribution. The mean for 2,000,000 trials with p = 1/2 is 1,000,000 and the standard deviation is the square root of n*p*q or the square root of 2,000,000 * 1/2 * 1/2 . That square root is 707.1067811865476, so we want the central 1/707.1067811865476 of the bell curve, or from z-value −1/1414.213562373095 to + 1/1414.213562373095, which is 0.000564189536532, or about 1/1772.\r\n\r\n','2003-03-03',20031222232101,NULL,2,3,0,2.60,20030303000000,0);
INSERT INTO problem VALUES (462,2,2,834,'Lotsa statements','You talk to six people, and they each give you five statements. Your job is to figure out which statements are true and which are false.\r\n\r\n
\r\nBob says:\r\n\r\n
\r\nChuck says:\r\n\r\n
\r\nDavid says:\r\n\r\n
\r\nEric says:\r\n\r\n
\r\nFrank says:\r\n\r\n
\r\n
\r\n
-You each take turns shooting each other.\r\n
-The duel stops when one person hits the other.\r\n
-Both of you are honourable enough to not take shots out of your turn.\r\n
-The probability of one person hitting the other is 1/2 and is independent of the probability of the other person hitting you.\r\n
\r\n
Let P(n)=probability of hitting your rival on your nth turn if you shoot first.\r\n
P(1)=1/2\r\n
P(2)=(1/2)*(1/2)*(1/2)\r\n
The first 1/2 is you missing on your first try, the second is your rival missing, the third is you hitting him.\r\n
P(3)=(1/2)*(1/2)*(1/2)*(1/2)*(1/2)\r\n
...etc\r\n
In general, P(n)=(1/2)*((1/4)^(n-1))\r\n\r\n
\r\n
P(winning)=P(heads)*P(going 1st)+P(tails)*P(going 2nd)\r\n
=(1/3)*(2/3)+(2/3)*(1/3)\r\n
=4/9\r\n\r\n
\r\nTherefore, we see that everybody who was paid the money used the money and got 100 rupees worth of something and hence there are no losses/gains because the net loss/gain circles back on the author, thus canceling everything.\r\n
\r\nWe can also say that all the transactions carried out through the counterfeit note are invalid, and therefore everybody stands in relation to his/her debtor just where he/she was before I picked up the note.\r\n\r\n\r\n\r\n\r\n\r\n','2003-03-20',20031221232101,NULL,4,3,0,3.83,20030320000000,0);
INSERT INTO problem VALUES (471,2,2,979,'The Best Strategy','A box is filled with \'N\' slips of paper. On each slip of paper is written some positive integer (note that any positive integer may appear on the slips - not just the integers from 1 to \'N\'). The integers do not necessarily appear in any sequence or pattern. Each of the slips has a different integer on it, so there is just one slip with the greatest integer.\r\n
In Calendar cubes pt 2 You figured out how many months you could fit on two cubes.
\r\nNow in calendar cubes pt 3 you must figure out how many days of the year you can fit on two cubes. E.G one cube says mar(for march) and another says 5. so you could make the date march 5 and that would count as one date.
a) the first letter of that month
b) the first and second letter of that month
c) the first three letters of that months. So for january you could use either j, ja or jan to represent that month.
Also no two letters or letter combinations can represent the same month. So j cannot stand for june and july, but you can have j stand for june and ju stand for july. Also note that one month symbol (lets say au for august) can be on 1 face of 1 cube.','First lets start with the months. Although it may seem as though you may only have 6 it is possible to have more. Allow me to explain. First we could have the letter J for july and A for august. Well if on the dice they\'re both shown by having the dice on a diagonal you could have JA represent january. So that means that letter combination JA can represent july, august and January. Also letter combination MA can represent March, April, May. so on four faces of the cube it\'d be written across JAMA. At which point the remaining two faces can have any other two months on them, but for sakes of the solution they need to be september and december(explained later) This gives us 8 months.
\r\nSo he put the 3 men on a flight of stairs, A at the top of the flight of stairs followed by B in the middle and then C at the base of the stairs. They are made to stand such that A can see B and C, and B can only see C, but can\'t see A, and C can see none.\r\n
\r\n
\r\nThey were then blindfolded, and on each of their head, he put a coloured cap; the colour of the cap can only either be black or white. The only thing they know for certain is that not all three hats have the same colour.\r\n
\r\nSo the hangman wanted them to tell him what coloured hat is on their head within the next 5 seconds after he removed the blindfold. If any one who could guess his hat colour correctly, he would save the life of all 3 men. \r\n
\r\n
\r\nAfter 4 seconds of his removing their blindfolds, the one in the middle {B} answered the question, and it was correct.\r\n
\r\n
\r\nHow did he do it? \r\n
\r\nYou can assume that all the blindfolds were removed at the same moment.','B answered only in the 4th second, which means that, the one on top of the stairs A did not know the answer. \r\nA is on top and can see the hats of B and C; but still A does not know the colour of his hat. This means that the colour of the hat of the man in the center and foot of the stairs {B and C} are different. \r\n
For n=6, the expression simplifies to 36 + (pi-36)*5!/5! = pi.
The next term in this sequence (n=7) is
\r\nNow, we proceed step by step as follows:\r\n
\r\nNumber of coconuts before the First division = x\r\n
\r\nNumber of coconuts removed in the First division = [{(x - 1)/5} + 1]\r\n
\r\nRemaining number of coconuts after the First division = [4(x - 1)/5] = A (say)\r\n
\r\nNumber of coconuts before the Second division = A\r\n
\r\nNumber of coconuts removed in the Second division = [{(A - 1)/5} + 1]\r\n
\r\nRemaining number of coconuts after the Second division = [4(A - 1)/5] = B (say)\r\n
\r\nNumber of coconuts before the Third division = B\r\n
\r\nNumber of coconuts removed in the Third division = [{(B - 1)/5} + 1]\r\n
\r\nRemaining number of coconuts after the Third division = [4(B - 1)/5] = C (say)\r\n
\r\nNumber of coconuts before the Fourth division = C\r\n
\r\nNumber of coconuts removed in the Fourth division = [{(C - 1)/5} + 1]\r\n
\r\nRemaining number of coconuts after the Fourth division = [4(C - 1)/5] = D (say)\r\n
\r\nNumber of coconuts before the Fifth division = D\r\n
\r\nNumber of coconuts removed in the Fifth division = [{(D - 1)/5} + 1]\r\n
\r\nRemaining number of coconuts after the Fifth division = [4(D - 1)/5] = E (say)\r\n
\r\nOn simplification (getting the final expression in terms of x and y), we get for the two questions (the two parts of the problem) the following equations:\r\n
\r\n1024x - 15625y = 8404 for (b).\r\n
\r\nx (minimum) = 3121 for (b).\r\n
\r\n15621, 12496, 9996, 7996, 6396, 5116 for (a) and\r\n
\r\n3121, 2496, 1996, 1596, 1276, 1020 for (b).\r\n\r\n','2003-03-26',20030401041026,NULL,3,3,0,4.00,20030326000000,0);
INSERT INTO problem VALUES (485,13,2,979,'Strange Sequence','What are the next two numbers in the following sequence ?\r\n
\r\nP=[(365)(364)(363)……..[{365 – (N – 1)}] /[(365)^N]\r\n
\r\nor, P=(365/365)(364/365)(363/365)……..[{ 365 – (N – 1)}/365]\r\n
\r\n2) If you take the product of any 4 digits of n, then it divides n.\r\n
\r\nNote 1: The ruler doesn\'t have any marks, so it\'s no good for measuring. It\'s only good for joining 2 points by a line.\r\n
\r\nNote 2: The circle which circumscribes the polygon, such that the polygon lies entirely within the circle and all of whose vertices lie on the circumference of the circle is the circumcircle of the polygon. The radius of this circle is the circumradius of the circle.\r\n
\r\n10001, 100010001, 1000100010001, 10001000100010001, 100010001000100010001,....\r\n
\r\nShow that none of them are prime numbers.','Very clever solution by DJ! (I myself haden\'t thought of it). See it here.','2003-05-23',20040225103933,NULL,3,3,0,4.25,20030523081816,0);
INSERT INTO problem VALUES (810,2,2,1767,'The Party Shakers','As the people arrived at the party, they had to greet everyone they knew in the hall with a handshake. \r\n
\r\n- The number n has at least 2 digits.\r\n
\r\n- All digits of n are in ascending order, in base 10.\r\n
\r\nBlitzen behind Cupid and in front of Donder, Vixen and Dancer.\r\n
\r\nCupid in front of Comet, Blitzen and Vixen.\r\n
\r\nDonder behind Vixen, Dasher and Prancer.\r\n
\r\nRudolph behind Prancer and in front of Donder, Dancer and Dasher.\r\n
\r\nVixen in front of Dancer and Comet.\r\n
\r\nDancer behind Donder, Rudolph and Blitzen.\r\n
\r\nPrancer in front of Cupid, Donder and Blitzen.\r\n
\r\nDasher behind Prancer and in front of Vixen, Dancer and Blitzen.\r\n
\r\nDonder behind Comet and Cupid.\r\n
\r\nCupid in front of Rudolph and Dancer.\r\n
\r\nVixen behind Rudolph, Prancer and Dasher.\r\n
\r\nBlitzen is behind Cupid ------(2)\r\n
\r\nDonder is behind (Vixen, Dasher and Prancer) ------(3)\r\n
\r\nRudolph is behind Prancer ----------(4)\r\n
\r\nDancer is behind (Donder, Rudolph and Blitzen) --------(5)\r\n
\r\nDasher is behind Prancer -------(6)\r\n
\r\nDonder is behind (Comet and Cupid) ------(7)\r\n
\r\nVixen is behind (Rudolph, Prancer and Dasher) -------(8)\r\n
\r\nBlitzen is in front of (Donder, Vixen and Dancer) ---------(9)\r\n
\r\nCupid is in front of (Comet, Blitzen and Vixen) ----------(10)\r\n
\r\nRudolph is in front of (Donder, Dancer and Dasher) -------(11)\r\n
\r\nVixen is in front of (Dancer and Comet) -------(12)\r\n
\r\nPrancer is in front of (Cupid, Donder and Blitzen) ---------(13)\r\n
\r\nDasher is in front of (Vixen, Dancer and Blitzen) --------(14)\r\n
\r\nCupid is in front of (Rudolph and Dancer) -------(15)\r\n
\r\nPrancer - Rudolph – Comet\r\n
\r\nUsing (7) and (15) and (5), we have:\r\n
\r\nPrancer - Cupid - Rudolph - Comet - Donder - Dancer\r\n
\r\nSince Vixen is behind Rudolph (8) and in front of Comet (12), we have: \r\n
\r\nPrancer - Cupid - Rudolph - Vixen - Comet - Donder - Dancer\r\n
\r\nAlso we know Rudolph is in front of Dasher (11) and Dasher is in front of Vixen (14), we now have: \r\n
\r\nPrancer - Cupid - Rudolph - Dasher - Vixen - Comet - Donder - Dancer\r\n
\r\nSince Blitzen is in font of Vixen (9) and Dasher is in front of Blitzen (14), we have:\r\n
\r\nPrancer - Cupid - Rudolph - Dasher - Blitzen - Vixen - Comet - Donder - Dancer\r\n
\r\n\r\n
\r\n2nd: CUPID\r\n
\r\n3rd: RUDOLPH\r\n
\r\n4th: DASHER\r\n
\r\n5th: BLITZEN\r\n
\r\n6th: VIXEN\r\n
\r\n7th: COMET\r\n
\r\n8th: DONDER\r\n
\r\n9th: DANCER','2003-04-07',20040319232102,NULL,3,3,0,2.50,20030407014816,0);
INSERT INTO problem VALUES (493,7,2,979,'Zero - The Hero','Using “Only Four” ZEROS (0) and any Mathematical Operations/Symbols [for example: \'e\', \'pi\',.... etc., if necessary], obtain the number 24. \r\n
\r\n(a)The formula is not in here.\r\n
\r\n(b)The formula is in Envelope 2.\r\n
\r\n(a)The formula is not in Envelope 1.\r\n
\r\n(b)The formula is in Envelope 3.\r\n
\r\n(a)The formula is not in here.\r\n
\r\n(b)The formula is in Envelope 1.\r\n
\r\n(Since the problem states that : \"The statements on one of the envelopes are BOTH TRUE, the statements on the other envelope are BOTH FALSE and the remaining envelope has ONE TRUE and ONE FALSE statement\"). \r\n
\r\nB: I am pure.\r\n
\r\nC: I am applied.\r\n
\r\nD: I am sane.\r\n
\r\nA: C is pure.\r\n
\r\nB: D is insane.\r\n
\r\nC: B is applied.\r\n
\r\nD: C is sane.\r\n
\r\nApplied mathematicians lie about their beliefs. \r\n
\r\nSane mathematicians beliefs are correct. \r\n
\r\nInsane mathematicians beliefs are incorrect. \r\n
\r\nThen cross multiply.\r\n
\r\n(1-2x)(1+x) = 2x(2-x)\r\n
\r\n1-x-2(x^2) = 4x - 2(x^2)\r\n
\r\n1-x = 4x \r\n
\r\n5x = 1 \r\n
\r\nx = 1/5 \r\n
\r\nSo the first time they meet is 2/5 of the way from Vegas and the second time is 1/5 of the way to Reno.\r\n
\r\nThe easiest approach at this point is to just follow the two paths as the birds continue to fly and see where they meet. When \'v\' has traveled 2/5 of the distance between Vegas and Reno to a point 3x the distance from Reno \'r\' will have traveled 3/5 of this distance to 2x the distance from Reno. When \'v\' has traveled another 2/5 he will be exactly in Vegas. Conventiently this is also where \'r\' will be.\r\n','2003-04-14',20040116232103,NULL,4,3,0,3.67,20030414014322,0);
INSERT INTO problem VALUES (498,13,2,979,'Playing With Numbers','What are the next two numbersin the following sequence ?\r\n
\r\nand by day they are lost without being stolen. \r\n
\r\ny = (4/3)x and \r\n
\r\ny = -{(3)^(1/2)}x + (108)^(1/2)\r\n
\r\nSolving the two equations, we get:\r\n
\r\ny = 4.52 (approximately)\r\n
\r\nwhich is the required height.','2003-04-21',20040119232102,NULL,5,3,0,2.86,20030421082758,0);
INSERT INTO problem VALUES (504,9,2,979,'True Or False - Part 1','Which of the two following statements is True and which is False ?\r\n
\r\nThe previous statement is \"True\".','Let the First statement be True. Then according to our assumption, the second statement is True which says that the First ( Previous) one is False, a Contradiction. Therefore the First statement cannot be True.\r\n
\r\nFrom (a), we get:\r\n
\r\n2M = 3(F - D) -------- (1)\r\n
\r\nfrom (b), we get the following result:\r\n
\r\n2M = F + 4D - 2S -------- (2)\r\n
\r\nFrom (c), we get the following result:\r\n
\r\n2M = 2S + D + F -------- (3)\r\n
\r\nFrom (2) and (3), we get:\r\n
\r\n4S = 3D -------- (4)\r\n
\r\nFrom (1) and (2), we get:\r\n
\r\n2S + 2F = 7D\r\n
\r\nor, 4S + 4F = 14D\r\n
\r\nNow, using (4), we get:\r\n
\r\n4F = 11D -------- (5)\r\n
\r\nFrom (1), (4) and (5), we get:\r\n
\r\n8M = 21D -------- (6)\r\n
\r\nFrom all these, we get:\r\n
\r\nF : M : S : D = 22 : 21 : 6 : 8 -------- (7)\r\n
\r\n(22, 21, 6, 8), (44, 42, 12, 16), (66, 63, 18, 24), (88, 84, 24, 32),....and so on. But we see that (44, 42, 12, 16) is the only combination where one of their ages is a Perfect Square.\r\n
\r\nFather = 44 \r\n
\r\nMother = 42 \r\n
\r\nSon = 12 \r\n
\r\nDaughter = 16 \r\n','2003-04-25',20040119232102,NULL,4,3,0,3.50,20030425031517,0);
INSERT INTO problem VALUES (506,2,2,979,'Professor and Students','A Professor asked four students how long each of them had been studying. \r\n
\r\nGiven that their product is equal to 180.\r\n
\r\nAnd that the sum of their years of study is equal to the number of years the Professor has been teaching.
\r\nAll positive factors of 180 are 1,2,2,3,3 and 5. \r\n
\r\nWe can form groups of four numbers such that the product of the four numbers in each group is equal to 180. All possible groups (irrespective of the order of the numbers in each group) are given below along with the sums of the numbers in each of the groups:
\r\n2 + 3 + 5 + 6 = 16 \r\n
\r\n1 + 5 + 6 + 6 = 18 \r\n
\r\n2 + 2 + 5 + 9 = 18 \r\n
\r\n2 + 3 + 3 +10 = 18 \r\n
\r\n1 + 4 + 5 + 9 = 19 \r\n
\r\n1 + 3 + 6 +10 = 20 \r\n
\r\n1 + 3 + 5 +12 = 21 \r\n
\r\n1 + 2 + 9 +10 = 22 \r\n
\r\n2 + 2 + 3 +15 = 22 \r\n
\r\n1 + 3 + 4 +15 = 23 \r\n
\r\n1 + 2 + 6 +15 = 24 \r\n
\r\n1 + 2 + 5 +18 = 26 \r\n
\r\n1 + 3 + 3 +20 = 27 \r\n
\r\n1 + 1 +12 +15 = 29 \r\n
\r\n1 + 1 +10 +18 = 30 \r\n
\r\n1 + 1 + 9 +20 = 31 \r\n
\r\n1 + 2 + 3 +30 = 36 \r\n
\r\n1 + 1 + 6 +30 = 38 \r\n
\r\n1 + 1 + 5 +36 = 43 \r\n
\r\n1 + 2 + 2 +45 = 50 \r\n
\r\n1 + 1 + 4 +45 = 51 \r\n
\r\n1 + 1 + 3 +60 = 65 \r\n
\r\n1 + 1 + 2 +90 = 94 \r\n
\r\n1 + 1 + 1+180 =183\r\n
\r\n1 + 5 + 6 + 6 = 18 \r\n
\r\n2 + 2 + 5 + 9 = 18 \r\n
\r\n2 + 3 + 3 +10 = 18 \r\n
\r\n1 + 2 + 9 +10 = 22 \r\n
\r\n2 + 2 + 3 +15 = 22 \r\n
\r\nBut the moment he knows that one of the students is in double years of study, he can at once conclude that the four students have been studying for 2, 3, 3 and 10 years.\r\n','2003-04-28',20030502061535,NULL,4,3,0,0.00,20030428014456,0);
INSERT INTO problem VALUES (507,7,2,979,'Four-Digit Number','Find a four-digit number with four different digits, that is equal to the number formed by its digits in descending order minus the number formed by its digits in ascending order.\r\n\r\n 7641\r\n -1467\r\n --------\r\n 6174
','2003-04-26',20040319232102,NULL,4,3,0,3.25,20030426041605,0);
INSERT INTO problem VALUES (983,13,2,122,'Letter Sequence','What\'s the next letter in this sequence?\r\n
\r\n\"This sentence contains Seven words\".\r\n
\r\nThis sentence does not contain Seven words\".\r\n
\r\n7, 9, 11, 12 and 15. \r\n\r\n','2003-05-01',20040119232102,NULL,3,3,0,3.33,20030501085039,0);
INSERT INTO problem VALUES (515,2,2,979,'Least But Not The Last','Prove that every Non-Empty set of Positive Integers contains a \"Least Element\".\r\n
\r\nWe define a subset T by T = {x belongs to S : x is less than or equal to k}. Then T is a non-empty subset of {1,2,3,4,....,k}.\r\n
\r\nClearly, T is a finite subset of N and therefore it has a Least element, say m. Then, m is one of {1,2,3,4,....,k}.\r\n
\r\nWe now show that m is the least element of S. Let s be any element of S. \r\n
\r\nIf s > k, then the inequality m less than or equal to k implies m < s.\r\n
\r\nIf s is less than or equal to k, then s belongs to T; and m being the Least element of T, we have m less than or equal to s.\r\n
\r\nThus m is the least element of S.','2003-05-08',20030827232101,NULL,4,3,0,3.33,20030508015447,0);
INSERT INTO problem VALUES (516,2,2,979,'Love Me For A Reason','Four men and four women are shipwrecked on a deserted island. Eventually each person falls in love with one person and is loved by one person. You are given the following information: \r\n
\r\n(b)Arthur loves the girl who loves the man who loves Ellen. \r\n
\r\n(c)Bruce loves the girl who loves the man who loves Mary. \r\n
\r\n(d)Gloria does not love Bruce. \r\n
\r\n(e)Helen loves a man who does not love Gloria. \r\n
\r\nWho loves who? ','SOLUTION: \r\n
\r\n9 + 1 + 6 = 16 = (4)^2\r\n
\r\n9 + 16 = 25 = (5)^2\r\n
\r\n9 * (16) = 144 = (12)^2','2003-05-15',20040131232102,NULL,4,3,0,3.75,20030515014955,0);
INSERT INTO problem VALUES (723,16,1,979,'Equilateral Triangle','Suppose ABC is an equilateral triangle and P is a point inside the triangle, such that PA = 3 cms., PB = 4 cms., and PC = 5 cms.\r\n
\r\nThen find the length of the side of the equilateral triangle.','','2003-12-18',20040106232106,NULL,3,3,0,3.67,20031218082646,0);
INSERT INTO problem VALUES (523,6,2,979,'The Number Line','Of those numbers whose English representation in Capital Block Letters consists only of straight lines, only one number has a value equal to the number of straight line segments required to write it out. What number is this?\r\n
\r\nAnd written with three,\r\n
\r\nTwo letters there are,\r\n
\r\nAnd two only in me.\r\n
\r\nI\'m double, I\'m single,\r\n
\r\nI\'m black, blue, and gray,\r\n
\r\nI\'m read from both ends,\r\n
\r\nAnd the same either way.\r\n
\r\nWhat am I? ','The word: EYE','2003-05-16',20040304232102,NULL,2,3,0,2.07,20030516082413,0);
INSERT INTO problem VALUES (525,19,2,979,'Journey To St. Ives','While on my way to St. Ives,\r\n
\r\n(You meet someone when you both are travelling in opposite directions. So when I was going to St. Ives, everyone whom I met were coming from the opposite direction, that is from St. Ives and so were not going there).','2003-05-19',20040322232105,NULL,2,3,0,2.38,20030519015115,0);
INSERT INTO problem VALUES (527,14,2,979,'Friendly Planets','Given that each distinct letter of the alphabet represents a distinct digit, find the values of the different letters so that the given equation is satisfied:\r\n\r\n M A R S \r\n + V E N U S \r\n + U R A N U S \r\n + S A T U R N \r\n ----------------\r\n N E P T U N E \r\n ----------------
\r\n','A = 5, E = 0, M = 4, N = 1, P = 7, R = 9, S = 3, T = 8, U = 6, V = 2.\r\n
\r\nN = 1\r\n
\r\nV = 2\r\n
\r\nS = 3\r\n
\r\nM = 4\r\n
\r\nA = 5\r\n
\r\nU = 6\r\n
\r\nP = 7\r\n
\r\nT = 8\r\n
\r\nR = 9\r\n','2003-05-20',20030728232102,NULL,3,3,0,3.50,20030520075451,0);
INSERT INTO problem VALUES (528,14,2,979,'Too Old For Young','The ages of Old and Young total 48. Old is twice as old as Young was when Old was half as old as Young will be when Young is three times as old as Old was when Old was three times as old as Young. \r\n
\r\n9 when divided by 10;\r\n
\r\n8 when divided by 9;\r\n
\r\n7 when divided by 8; \r\n
\r\n6 when divided by 7;\r\n
\r\n5 when divided by 6;\r\n
\r\n4 when divided by 5;\r\n
\r\n3 when divided by 4;\r\n
\r\n2 when divided by 3; \r\n
\r\n1 when divided by 2 ?\r\n
\r\nCannot be heard, cannot be smelt.\r\n
\r\nIt lies behind stars and under hills,\r\n
\r\nAnd empty holes it fills.\r\n
\r\nIt comes first and follows after,\r\n
\r\nEnds life, kills laughter.\r\n
\r\nOf the last 5 numbers (23-27), only 23 is prime.\r\n','2003-06-27',20031009232105,NULL,4,3,0,3.50,20030627015928,0);
INSERT INTO problem VALUES (1332,20,2,1567,'Words in Common 5','What do the following words have in common?
\r\n\r\nThe pirates will try above all else to stay alive, even if it means accepting no coins. If they will stay alive either way, they would like the most coins possible. Also, the pirates have been on board the ship for a while and are getting tired with each other, so if faced with the decision to reject a plan or keep it, they will reject it if nothing else matters more to them.\r\n
\r\nWhat should Pirate 5\'s offer be?','?','2003-09-16',20040324232101,NULL,3,3,3,0.00,00000000000000,134);
INSERT INTO problem VALUES (561,14,2,979,'Gain or Loss','The minute and the hour hand of a watch meet every 65 minutes. \r\n
\r\n= 65.45 minutes \r\n
\r\n~ 65 minutes 27.16 seconds \r\n
\r\nBut in our case they meet after every 65 minutes means the watch is gaining approximately 27.16 seconds in the 65 minute interval.\r\n
\r\n2. B said he is confident that P will not win. \r\n
\r\n3. C said he is confident that neither S nor R will win.\r\n
\r\nWhen the result came, it was found that only one of the above three people had made a correct statement.\r\n
\r\n\r\nLook here for RoyCook\'s solution, look here for Gamer\'s solution, look here for mohan\'s solution.','2003-10-05',20040225103933,NULL,3,3,0,3.40,20031005112042,0);
INSERT INTO problem VALUES (573,2,2,979,'Three Surgeons and A Cook','Three surgeons and a clumsy cook go camping in the remote wilderness. The clumsy cook stumbles over the campfire as he is serving the surgeons, injuring himself and dumping hot stew on the hands of the surgeons.\r\n
\r\n2. Mr. East did not take the South Road. \r\n
\r\n3. Mr.West did not the South Road. \r\n
\r\n4. The West Road was not taken by Mr. East.\r\n\r\n S O M E \r\n + G O O D \r\n ---------- \r\n I D E A S \r\n ----------
\r\n
\r\n(It can be in any direction: Horizontally, Vertically or Diagonally).\r\n\r\n dgooddodgooddo\r\n odoogggdodgogg\r\n ogogdoodgooddd\r\n dgdoooggoogdgo\r\n ogdgogdgoggogd\r\n dddgddodoogdoo\r\n odgoggdooggood
','The second \'d\' of the third row, fourth \'o\' of the fourth row and the fifth \'g\' in the fifth row.','2003-07-31',20040121232101,NULL,3,3,0,3.00,20030731004230,0);
INSERT INTO problem VALUES (577,20,2,979,'Is It or Is It Not ?','Punctuate the following so it makes sense:\r\n
\r\nNow clearly, the next number should be 64. But all numbers in actual series are base 5 numbers So convert 64 to base 5 and that is 224.\r\n','2003-08-03',20031028232101,NULL,3,3,0,2.83,20030803045710,0);
INSERT INTO problem VALUES (1439,13,2,1626,'Square Sequence','When you add all the terms up from this sequence: x² + (x-1)² + 3(x-2)² + (x-3)² + (x-4)² + (x-5)² + 3(x-6)² + (x-7)² ... it will be equal to half of (x³ + x² - x) for any positive even integer x. Prove why this works.\r\n
\r\nExample: 12² + 11² + 10² + 10² + 10² + 9² +8² + 7² + 6² + 6² + 6² + 5² + 4² + 3² + 2² + 2² + 2² + 1² if x = 12.
\r\nNote: The coefficients go 1, 1, then 3, then 3 1s, then 3, then 3 1s. The coefficients go in this order, even if there are coefficients left when the sequence stops. For example, with 6, the coefficients would go 1,1,3,1,1,1.','Charlie gave a proof by induction here, and a way to prove it without knowing the forumla is supplied here.','2003-12-19',20040225103933,NULL,5,3,0,2.33,20031219120341,0);
INSERT INTO problem VALUES (1440,7,2,1626,'Another Square Sequence','If you subtract the sum of the first x numbers, squared, from the sum of the next x numbers, squared, (for example, 6² + 5² + 4² - 3² - 2² - 1²); you will get (x²)(2x+1) and also x²(x+1)² minus x^4. Prove why this works.','A proof by induction was supplied here and a simpler proof based on sum of squares was provided here','2003-12-23',20040225103933,NULL,4,3,0,3.00,20031223141115,0);
INSERT INTO problem VALUES (581,2,2,1,'Jury selection','In the jury selection phase of a murder trial, one of the attorneys asked a prospective juror:\r\n\r\n5 × 4 = 20\r\n20 + 4 = 24\r\n24 ÷ 4 = 6\r\n6 - 4 = 2\r\n2 × 4 = 8\r\n8 + 4 = 12\r\n12 ÷ 4 = 3\r\n3 - 4 = -1\r\n-1 × 4 = -4\r\n...\r\n
\r\nSo, the next number in the sequence is 8.\r\n ','2003-08-08',20030914232101,NULL,1,3,0,1.40,20030808142208,0);
INSERT INTO problem VALUES (587,14,2,979,'Wine and Barrels','A man is the owner of a winery who recently passed away. In his will, he left 21 barrels (seven of which are filled with wine, seven of which are half full, and seven of which are empty) to his three sons. However, the wine and barrels must be split so that each son has the same number of full barrels, the same number of half-full barrels, and the same number of empty barrels.( Note that there are no measuring devices handy).\r\n
\r\nEach son gets three full barrels, one half-full barrel, and three empty barrels. ','2003-08-07',20030813185232,NULL,1,3,0,1.75,20030807073213,0);
INSERT INTO problem VALUES (1468,6,2,1626,'The glass balls','Through a marksmanship contest, there are 4 strings of 4 glass balls hanging down from a horizontal post. Each bullet can only hit one glass ball at a time, so 16 shots need to be fired.
The only problem is if you shoot a glass ball that has a glass ball hanging below it (on the same string), it will fall off. So given the rule that you can\'t shoot a glass ball with a glass ball underneath it (and on the same string), how many ways can you shoot all the glass balls?','The solution I heard to this is a great one in my opinion.
\r\n\r\nThe idea is to plot out the order of the 16 balls getting shot down by strings and not by balls.\r\nThe 4 balls on the first string may take any of the 16C4 places. Then the 4 balls on the next string may take any of the remaining 12C4 places. Then the 4 balls on the next string may take any of the remaining 8C4 places, and the final string must take the remaining 4 places. When 16C4, 12C4 and 8C4 are all multiplied (C meaning _ combinations taken _ at a time), it comes out to 63,063,000.\r\n\r\n(from \"The Glass Balls\")','2004-01-30',20040209232106,NULL,2,3,0,4.00,20040130135814,0);
INSERT INTO problem VALUES (1479,12,2,2839,'Kiss kiss, Bang bang','What do these five famous actors have in common?
The title is relevant to the riddle.','They have all portrayed in films characters created by Ian Fleming.
taper, sped, miter, deal, astray, unformed, snaky, reined.
\r\nFill the 5 liter jug with the 8 liter jug, so that there are 3 liters remaining. Empty the 5 liter jug into the 12 liter jug. Now there are 9 liters in the 12 liter jug and 3 liters in the 8 liter jug. \r\n
\r\nPour the 3 liters from the 8 liter jug into the 5 liter jug. Now fill the 8 liter jug with water from the 12 liter jug, leaving 1 liter in the 12 liter jug. \r\n
\r\nFill the 5 liter jug (which already has 3 liters in it) from the 8 liter jug, leaving 6 liters in the 8 liter jug. \r\n
\r\nEmpty the 5 liter jug into the 12 liter jug. Now there are 6 liters in the 12 liter jug, 6 liters in the 8 liter jug, and the 5 liter jug is empty.\r\n\r\n 12 8 5\r\n------------\r\n 12 0 0\r\n 4 8 0\r\n 4 3 5\r\n 9 3 0\r\n 9 0 3\r\n 1 8 3\r\n 1 6 5\r\n 6 6 0\r\n
','2003-08-18',20040225103933,NULL,3,3,0,3.00,20030818074741,0);
INSERT INTO problem VALUES (600,6,2,979,'Six boxes','There are six boxes containing 5, 7, 14, 16, 18, 29 balls of either red or blue in colour. Some boxes contain only red balls and others contain only blue. \r\n
\r\n
\r\nTotal number of balls are odd. Also, there are the same number of red balls and blue balls are left out after selling one box. That can only happen if the remaining number of balls is even, so a box with odd number of balls in it must have been sold out (5, 7 or 29).
\r\n
\r\nNow using trial and error:
\r\n(89-29) /2 = 60/2 = 30
\r\nand
\r\n14 + 16 = 5 + 7 + 18 = 30
\r\n
\r\nMore checking reveals that this does not work for the 5- or 7-ball boxes.
\r\n
\r\n\r\nSo the box with 29 balls was sold out, leaving 16+14=30 of one color and 5+7+18=30 of the other.','2003-08-14',20031014232104,NULL,3,3,0,2.00,20030814135133,0);
INSERT INTO problem VALUES (602,4,2,979,'Roots Of The Equation','Let us consider the quadratic equation: ax² + bx + c = 0.\r\n
\r\nIn other words, saying that you do something \'x\' times when you are differentiating with respect to x cannot work.','2003-08-22',20031107232103,NULL,3,3,0,2.67,20030822080550,0);
INSERT INTO problem VALUES (605,2,2,979,'Doctor and Engineer','One of Mr. X, his wife, their son and Mr. X\'s mother is an Engineer and another is a Doctor. \r\n
\r\n1. If the Doctor is a male, then the Engineer is a male. \r\n
\r\n2. If the Engineer is younger than the Doctor, then the Engineer and the Doctor are not blood relatives. \r\n
\r\n3. If the Engineer is a female, then she and the Doctor are blood relatives. \r\n
\r\nCan you tell who is the Doctor and the Engineer?','Mr. X is the engineer and either his wife or his son is the Doctor.\r\n
\r\nFrom 3, then, if the engineer is a female, the doctor is a male. However, from 1, if the doctor is a male, then the engineer must be a male.
\r\nThus, there is a contradiction, and the engineer cannot be female (either Mr. X or his son is the engineer).\r\n
\r\nSo, from 2, Mr. X\'s son is not the engineer.\r\n
\r\nIt is not possible to determine anything further, or eliminate either of these possiblities.
\r\nAlso, it does not even mater (for statement 2) if Mr. X or his wife are younger or older, as either way they are not blood relatives.','2003-08-25',20030926232101,NULL,3,3,0,2.75,20030825084035,0);
INSERT INTO problem VALUES (1504,5,1,3182,'Bull\'s eye!','Two points have polar coordinates as follows: θ=130°,r=.35 (point A) and θ=70°,r=.6 (point B). There is a surrounding circle, r=1, that acts as a mirror, and you wish to send a light ray from point A to point B by bouncing it once off the circle. What two alternative directions could you send it in (use an angular measure paralleling the θ coordinate it would have if directed from the origin)?','Solution:\r\n\r\n37.0112112532 degrees and 18.0986438974 degrees\r\n','2003-11-22',20031202232103,NULL,3,3,0,3.60,20031122094129,0);
INSERT INTO problem VALUES (607,14,2,979,'The Deleted Number','A professor writes N consecutive natural numbers, beginning with 1, on the blackboard. One of the students in the class deletes one of the numbers (exactly one number), from that list.\r\n
\r\nNow, given that the average of the remaining N-1 numbers is 271/16.\r\n
\r\nCan you find out the number that has been deleted from the list ? ','19 was removed from the first 33 counting numbers.\r\n
\r\nAlso, DJ posted a general method for solving this problem given any value for the average; that can be found here.','2003-08-27',20040225103933,NULL,3,3,0,2.00,20030827150146,0);
INSERT INTO problem VALUES (608,14,2,979,'Natural Problem','The Natural Numbers are written successively as shown below:\r\n
\r\n12345678910111213141516..........., such that the 4th digit is \'4\' the 9th digit is \'9\' but the 11th digit is \'0\', the 15th digit \'2\', the 17th \'3\', and so on.\r\n
\r\nWhat is the 40,000th digit that appears in this list ?','The digit in question is 1.\r\n
\r\nDigits 10-189 come from the 2-digit numbers.
\r\nDigits 190-2889 come from the 3-digit numbers.
\r\nDigits 2890-38889 come from the 4-digit numbers.
\r\nDigits 38890-488889 come from the 5-digit numbers.
\r\n
\r\n33550336,
\r\n8589869056, and
\r\n137438691328.
\r\nThese are the first few elements of the perfect numbers. Perfect numbers are those positive integers that equal the sum of all their factors (not including themselves).
\r\nFor example,
\r\n6 = 1 + 2 + 3
\r\n28 = 1 + 2 + 4 + 7 + 14
','2003-11-29',20040104122011,NULL,3,3,0,3.12,20031129104452,0);
INSERT INTO problem VALUES (1514,4,1,3172,'I\'ve a broken stick','I\'ve a straight stick which has been broken into three random-length pieces.
\r\nWhat is the probability that the pieces can be put together to form a triangle?
\r\nIf you can answer this at this point, please do.
\r\nIf not, perhaps this will help: here are several methods to break the stick into the three random length pieces:\r\n\r\n
\r\nIf this clarifies the problem, please show how this affects your work.','I\'ll provide an answer later, but I gather (from a somewhat similar problem...) that this will generate some discussion and the correct answer!\r\n\r\nBTW, this came from The Colossal Book of Mathematics','2003-12-07',20040107232101,NULL,5,3,0,3.50,20031207115644,0);
INSERT INTO problem VALUES (610,6,2,979,'Bird Watching','A, B and C went bird watching. Each of them saw one bird that none of the others did. Each pair saw one bird that the third did not. And one bird was seen by all three. Of the birds A saw, two were yellow. Of the birds B saw, three were yellow. Of the birds C saw, four were yellow.\r\n
\r\n(b) How many non-yellow birds were seen in all? ','Three birds were seen by one person each, three were seen by each unique pair (A-B, A-C, and B-C), and one was seen by all three. So seven birds were seen in all, and each person saw a total of four. Hence, all of the birds C saw were yellow. These four birds are: (1) the one C saw alone, (2) the one C saw with A, (3) the one C saw with B, and (4) the one all three saw together. This accounts for both of the yellow birds A saw, and two of the three yellow birds B saw. The third yellow bird B saw could not have been the one A and B saw together, because A only saw two yellow birds; so the third yellow bird B saw must have been the one he saw alone.\r\n
\r\nB had his own coat, D\'s hat, A\'s gloves, and C\'s cane.
\r\nC had D\'s coat, his own hat, B\'s gloves, and A\'s cane.
\r\nD had C\'s coat, A\'s hat, his own gloves, and B\'s cane.\r\n
\r\nAs it turns out, at the beginning of this problem, a Canadian Dollar is worth exactly the same as the U.S. Dollar, and people are quite accustomed to using them interchangeably (including banks).
\r\nBut, alas, the U.S. Government and the Canadian government get in a spat. So, the U.S. \"devalues\" the Canadian dollar 10%, so now they will treat it as worth 90 cents (U.S. currency). In retaliation, Canada does the same and \"devalues\" the U.S. dollar 10%, so they treat it as worth 90 cents (Canadian currency).
\r\nEnter Charlie.
\r\nCharlie goes to Alan\'s bar and purchases a 1 dollar drink and pays with a 10 dollar bill (U.S.). He receives, in change, a 10 dollar bill (Canadian). He then walks across the border to Bob\'s bar and purchases another 1 dollar drink, paying with a 10 dollar bill (Canadian), and he receives, in change, a 10 dollar bill (U.S.).
\r\nCharlie proceeds to continue doing this until he finds himself quite intoxicated.
\r\nI think it obvious that Charlie is gaining on these transactions. The question is.... WHO (if anyone) is losing out on these transactions?','Answer:
\r\nThe respective bar owners are losing money. Just because the government says money is worth something doesn\'t make it so.
\r\n__________________________________
\r\nAs Popstar Dave mentioned in his comment, this does provide an arbitrage situation. (And he\'s correct in that it would not last long in a free floating currency environment, but this problem described an environment where the currency is NOT free floating, so it doesn\'t apply.)
\r\nAlan should give change of 9 American dollars, and Bob should give change of 9 Canadian dollars. (They should do this to avoid losing on the transaction.) And, as several have pointed out, they could keep the foreign currency and trade it (in the foreign country) for their own currency.
\r\nIf Alan gives change of 10 Canadian dollars (instead of 9 American dollars), he is giving up something that CAN purchase the full equivalent of 10 American dollars.
\r\nSimilarly, if Bob gives change of 10 American dollars (instead of 9 Canadian dollars), he is giving up something that CAN purchase the full equivalent of 10 Canadian dollars.
\r\n*** It is interesting to note, that it is for exactly this reason, among others such as the (in)stability and (high or) low devaluation of the currency, that in countries that don\'t allow the local currency to freely float, you find the citizens will hoard another country\'s currency (often U.S. dollars).
\r\nLastly, as Marc Meyer hinted at... in the long run, if a country\'s banks \'honor\' this arbitrage situation, then it is the country (tax payers) which pays for the loss.','2003-10-31',20040225232101,NULL,3,3,0,3.67,20031031083616,0);
INSERT INTO problem VALUES (1482,6,2,3136,'A group of letters','What do the following letters all have in common?BHSNTTSPAZ\r\n\r\nDILBTEAIRU\r\n\r\nDSLEATIEDW\r\n\r\nCAMUHIRLCZ\r\n\r\nCTAMASAHLY\r\n\r\nAWETOTNTEV\r\n\r\nEHSSLLRAOX\r\n\r\nDTERLEEBRW
\r\n\r\nHint: The answer to this question is a single word.','(General solution)\r\n\r\nAlphabetize the words, then read down columns 2 through 5. Then do it backwards alphabetical using the last letter.\r\n\r\nThe answer is 40','2004-03-21',20040321232102,NULL,3,3,0,4.00,20040321080659,0);
INSERT INTO problem VALUES (616,2,2,1465,'True Day','1. Bob tells the truth on only one day of the week.\r\n
\r\n2. One day he said: \"I lie on Mondays and Tuesdays.\"\r\n
\r\n3. The next day he said: \"Today is either Thursday, Saturday, or Sunday.\"\r\n
\r\n4. The next day he said: \"I lie on Wednesdays and Fridays.\"\r\n
\r\nWhat is the diameter of the largest ball that can pass through the gap between the spheres and the floor ?','','2003-09-24',20040322232106,NULL,3,3,0,2.50,20030924072733,0);
INSERT INTO problem VALUES (1959,16,0,1920,'A Point In A Square','There is a point M inside a square ABCD such that angle MAB is 60° and angle MCD is 15°. Find angle MBC.','Angle MBC is 30°.','2004-01-21',20040324232101,NULL,3,3,6,0.00,00000000000000,224);
INSERT INTO problem VALUES (632,14,2,1299,'Divisibility','In any set of 181 square integers, prove that one can always find a\r\nsubset of 19 numbers, the sum of whose elements is divisible by 19.\r\n
\r\n
\r\n\r\nHence there are only 10 possible values for the remainders. Since there are 181 remainders at least, one of them must repeat 19 times at least. Choose 19 numbers congruent to that remainder. This\r\nproves the result.','2003-03-14',20040108232102,NULL,4,3,0,3.25,20030314000000,0);
INSERT INTO problem VALUES (633,17,2,1072,'Solids are denser?','In general, when a pure substance or mixture goes from liquid to solid, the molecules in it get closer resulting in a higher density.\r\n
\r\nThe driver sees a milestone showing a 2-digit number. After travelling for an hour the driver sees another milestone with the same digits in reverse order.\r\nAfter another hour the driver sees another milestone containing the same two digits as in the first one but the two digits separated by a zero(0).\r\n
\r\nThe distance traveled so far is: (10y+x) – (10x+y) = 9(y – x)\r\n
\r\nThe distance traveled in the second hour is:
\r\n(100x+y) – (10y+x) = 9(11x – y).\r\n
\r\n9(11x – y) = 9(y – x)
\r\nThis gives y = 6x.\r\n
\r\nSince x and y are both digits, x must be 1 and y must be 6.\r\n
\r\n\r\n(a-b)=(a-b)
\r\n(a-b)=√((a-b)²)
\r\n(a-b)=√(a²-2ab+b²)
\r\n(a-b)=√(a²-2ab+b²+4ab-4ab)
\r\n(a-b)=√((a²+2ab+b²)-4ab)
\r\n(a-b)=√((a+b)²-4ab)
\r\n(a-b)=√(x²-4y)
','2003-10-04',20040324232101,NULL,2,3,11,0.00,00000000000000,304);
INSERT INTO problem VALUES (2024,6,0,1413,'Robbery report','You are listening to a police scanner when you hear a report. There is considerable static, but you definitely hear the following: \"One armed man ent--ed bank at 1:10 p-; three armed m-- entered b--k half a minute later. First man demanded money. Tellers coop--ated. Robbers threw down weapons and ran out with $10,000 in each hand.\" \r\n\r\nBased only on the information given, what is the minimum amount of money that the robbers carried out?','$40,000. There is a chance that a one-armed man and a three-armed man robbed the bank.\r\n\r\nAlternate solution: $40,000 -- there were four robbers, but each had only one arm. (It is even possible for a man with no arms to be \"armed\" with some clever hands-free weapon -- but someone should have hands if the group plans on carrying money out of the bank.)','2004-02-03',20040323232102,NULL,1,3,1,0.00,00000000000000,54);
INSERT INTO problem VALUES (788,18,2,1715,'Can 1 Dollar = 1 Cent','1 dollar = 100 cents = 10 cents * 10 cents = 1/10 dollar * 1/10 dollar = 1/100 dollar = 1 cent\r\n
\r\nFor example:
\r\n1=1
\r\n1+8=9
\r\n1+8+27=36','?','2003-10-14',20040324232101,NULL,4,3,13,0.00,00000000000000,329);
INSERT INTO problem VALUES (1637,14,1,3546,'Chickens, Pigs, and Cattle','You are sent to the market by your father with 800 dollars, and told to buy 100 animals. When you arrive at the market, you find out that pigs cost 8 dollars each, so it would be easy to follow your father\'s instructions.\r\n
21 pigs, 7 cows.','2004-02-19',20040315232104,NULL,2,3,0,2.00,20040219083900,0);
INSERT INTO problem VALUES (2059,13,0,2716,'Before and After','If all the irreducible fractions between 0 and 1, with denominators at most 99, are listed in ascending order, which two fractions would be before and after 11/21?\r\n\r\nDetermine which two fractions are adjacent to 34/87 in this listing.','This kind of sequence is called a Farey series, and given two fractions (a/b, c/d) in sequence, they satisfy bc-ad=1.
\r\n1, 101, 10101, ...','The numbers are (10^(2n)-1)/99 but 10^(2n)-1 = (10^n-1)*(10^n+1).\r\n
\r\nThis monkey has muscle relaxion syndrome, which means that as soon as he hears a loud noise (like your gun going off), he will let go of the tree branch without realizing it and fall down.
\r\n\r\nThe problem with this is the monkey will fall, and not be where it was before you shot the gun, so it will be in another spot when the bullet is next to the tree. How far below the spot where the monkey\'s tail is pre-shot should you aim so the monkey\'s tail will be hit regardless of it\'s \"letting go\" of the tree branch?','Because objects free-fall without matter to mass or horizontal velocity, you should aim directly at the monkey\'s tail in order to hit it.','2003-10-14',20040324232101,NULL,2,3,14,0.00,00000000000000,340);
INSERT INTO problem VALUES (2148,7,0,5799,'Power of Multiplication','A magic square for addition could be made as follows\r\n2 9 4 (row1)\r\n7 5 3 (row2)\r\n6 1 8 (row3)\r\nNote all rows/columns/diagonals sum to 15\r\nUsing any set of positive integers can you make a magic square for multiplication?','Take 2 or any # for that matter as the base and raise addition magic square as the exponents!!!','2004-02-26',20040323232102,NULL,3,3,1,0.00,00000000000000,75);
INSERT INTO problem VALUES (2149,21,0,5799,'Four Corners','On each corner of a square is a quarter. The goal is to make them all heads or all tails. You are blindfolded and may flip however many of them you want and then ask if you are done. This constitutes a turn. The square is then rotated an undisclosed number of times and you may take another turn. In how many turns can you be assured of being done.','Treat this as a state machine problem.\r\nThere are only 3 states 3-1,2-2 columns/rows and 2-2 diagonals.\r\nThere are only 3 flips flip 1 flip 2 rows/columns or flip 2 diagonals.\r\n\r\nIf you flip diagonals when it is aligned along diagonals you will solve it.\r\n\r\nAssume it is aligned 2-2\r\n1. Flip diagonals now either done or aligned along columns.\r\n2. Flip rows now either done or aligned along diagonals\r\n3. Flip diagonals now either done or started 3-1 and are now still 3-1\r\n\r\n4. Flip 1 now 2-2 \r\nrepeat steps 1-3\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n','2004-02-26',20040323232102,NULL,3,3,1,0.00,00000000000000,76);
INSERT INTO problem VALUES (2150,4,0,5799,'Let\'s Make a Deal','on let\'s make a deal you choose one door of 3. Hoping to get the prize instead of the junk behind the other 2 bad doors. The host then will always show you one of the doors that you didn\'t choose which is junk and ask if you want to change your answer, should you and what are the odds that you will win? ','The odds that your first choice is right is 1/3 and remains unchanged, the odds of the remaining unseen doors originally are 2/3 and this is now the odds of the unseen door so you should change.','2004-02-26',20040324232101,NULL,3,3,2,0.00,00000000000000,121);
INSERT INTO problem VALUES (1668,6,2,1920,'Open By Majority','A group of five people want to put a set of locks on a chest and distribute keys to the locks amongst themselves in such a way that all the locks on the chest could be opened only when at least three of them were present to open it.\r\n\r\nA:1 3 5 78 0\r\nB:1 456 89\r\nC:123 6 90\r\nD: 2 4567 0\r\nE: 234 789
','2004-03-03',20040315134238,NULL,3,3,0,4.00,20040303153059,0);
INSERT INTO problem VALUES (2178,2,0,5815,'Whodunit Part 2: Places, Places','it would be easier just to veiw this problem on a word docoment, so click here to go to it. Also, if you find you do not know how to solve these types of problems, click here to go to pennypress.com, where it will tell you how to solve (only read the 3rd page, the first 2 don\'t have anything useful on them)',' \r\nThere is no solution, but keep the info derived from this puzzle, for it will aid you in part 5, where you will try to figure out whodunit! \r\n \r\n \r\n \r\n','2004-03-02',20040323232102,NULL,4,3,1,0.00,00000000000000,82);
INSERT INTO problem VALUES (2225,9,0,5815,'Today, or tomorrow?','When you woke up this morning, it was today, right? When you go to school or work this morning and afternoon, it is today, right? When you go to bed tonight, it is still today, right? Well what is it when you wake up the next morning, is it today, or tomorrow?','It is today, because you don\'t wake up and say, \"why, what a lovely day this tomorrow\", you say, \"my, what a lovely day today\"','2004-03-22',20040324232101,NULL,2,3,3,0.00,00000000000000,164);
INSERT INTO problem VALUES (655,14,2,979,'Twin Trouble','Create the number 24 using only these numbers once each: 3, 3, 7, 7. You may use only the rules of addition, multiplication and division.','7 * [(3 + (3/7)] = 24\r\n','2003-10-21',20031104014653,NULL,3,3,0,3.80,20031021093821,0);
INSERT INTO problem VALUES (656,13,2,979,'Strange Series','What are the next two numbers in the following series?\r\n
B: If A is innocent, then C must be guilty.
C: If B was the killer, then D must have had nothing to do with the crime.
D: I am innocent.
\r\n\r\nIf a ray aimed at C started at D, it would have gone 1 inch before going through C, and would eventually go through A.
\r\n\r\nIf BC and AE are both 5 inches, what is the area of this pentagon?','If diagonal DA is constructed, it can be seen that two triangles are formed. Then, it can be shown that these triangles are congruent because their angles and one side of each (BC and AE) are the same length.\r\n
\r\nTo figure out AD and AB, an equation would need to be created.
\r\n\r\nAC^2 + BC^2 + AB^2
\r\n(AD-CD)^2 + 25 = AB^2
\r\n(AB-1)^2 + 25 = AB^2
\r\nAB^2-2AB+1+25=AB^2
\r\n26=2AB
\r\nAB=13
\r\n\r\nThen since AB = 13, AC must equal 12. Since 30 = 1/2 base x height, 30 = (AC x BC) /2, or (12 x 5)/2. Since there are two of these triangles, the total area is 60 square inches.','2003-10-24',20040324232101,NULL,3,3,18,0.00,00000000000000,384);
INSERT INTO problem VALUES (660,14,2,979,'Pizza Cut','What is the greatest number of pieces you form with n cuts of a pizza? ','With every cut you should cut through every previous cut. As long as you keep doing this you will always be able to do so again your next cut. The number of additional pieces formed on cut x will always be x. \r\n
\r\n21978 x 4 = 87912','2003-11-09',20031208100317,NULL,3,3,0,3.00,20031109081644,0);
INSERT INTO problem VALUES (2051,7,0,2716,'Kennels problem','I have twenty kennels in a row. I raise guard dogs, and I cannot place two dogs in kennels next to each other, for they will start trying to fight. Obviously, the most dogs I can place is 10, and the minimum is 0.
\r\n111111111111111111111111
\r\nas is the number formed by 24 1s followed by 26 0s:
\r\n11111111111111111111111100000000000000000000000000.\r\n
\r\n11111111111111111111111100111111111111111111111111
\r\nand if you replace the middle two digits with 13 (literally, add 13000000000000000000000000 to the number), the result will, again, still be a multiple of 13.\r\n
\r\nBy mistake, he interchanged the two digits, a & b, in one of these ten integers. As a result, his answer for the arithmetic mean was 1.8 more than what it should have been. \r\n
\r\nFind the value of b-a.','Let the sum of the first 9 numbers be X and the 10th number be of the form (10a + b). Then according to the problem, we have the following relation:\r\n
\r\n[{X + (10b + a)}/10] - [{X + (10a + b)}/10] = 1.8\r\n
\r\nor, [(10b + a) - (10a + b)]/ 10 = 1.8\r\n
\r\nor, 9(b - a) = 18\r\n
\r\nor, b - a = 2','2003-11-19',20040123232103,NULL,2,3,0,2.40,20031119082140,0);
INSERT INTO problem VALUES (672,9,2,1498,'The two blacksmiths','There\'s this town with two blacksmiths - one, a swordsmaker and the other, a shield maker. The swordsmaker\'s swords can slice through anything as a rule and the other guy\'s shields cannot be destroyed. Now they get cut up with each other for some reason and pit their wares against each other. What do you expect happens?\r\n \r\n
\r\nThe second blank should be 1050601.
\r\nCall the last number B and the second-to-last number A.
\r\nThe formula for the next number is A+10B.
\r\nFor example,101+10(1020)=10301.\r\n','2003-05-07',20030827232101,NULL,2,3,0,4.10,20030507082102,0);
INSERT INTO problem VALUES (685,6,2,834,'Believe it or not','Is the following sentence technically true or false? \r\n\r\nThe sun will rise tomorrow morning. \r\n \r\n','False. The sun doesn\'t rise. The earth spins around.','2003-03-25',20030401140027,NULL,2,3,0,3.50,20030325000000,0);
INSERT INTO problem VALUES (686,12,2,834,'Murder down the street','While walking down a country road near his home, Clem Kadiddlehopper saw a murder. \r\n
\r\nWhat were their house numbers ?','','2003-12-02',20040123232103,NULL,2,3,0,2.50,20031202090136,0);
INSERT INTO problem VALUES (695,4,2,1598,'Shuffled Cards','2 people each shuffle a deck of 52 playing cards thoroughly. \r\n
\r\n
\r\n1 4 5 9 0 5 4 6 2 7 0','... but you might be able to have your Pi!\r\n\r\nStart with the digit \'1\', and then the differences between each digit and its predecessor (mod 10) are:
\r\n3 1 4 1 5 9 2 6 5 3
\r\n
\r\nYou might recognize this as the first 10 digits of Pi, if we continue with the pattern...
\r\n
\r\n1 4 5 9 0 5 4 6 2 7 0 5 3 2 9
\r\n3 1 4 1 5 9 2 6 5 3 5 8 9 7 9
\r\n\r\n','2003-11-26',20040324232101,NULL,4,3,2,0.00,00000000000000,100);
INSERT INTO problem VALUES (1019,14,2,1920,'Reciprocal Equation #1','Find all sets of integers A, B, and C which satisfy the following: \r\n
![](\"http://www.flooble.com/images/perplexus/problem/dice12b.gif\")
\r\n\r\nEach side of the die is a regular pentagon, which have an interior angle of 108° and an exterior angle of 72°. Consider a pentagon with one edge at the bottom and the apex at the top, and set the length of one edge arbitrarily to 1 (regardless of size, all the angles remain the same anyway). If we draw a line parallel to the base, from the left shoulder of the pentagon to the right, then the distance D from the base to the parallel is\r\n![](\"http://www.flooble.com/images/perplexus/problem/dice12a.gif\")
\r\n![](\"http://www.flooble.com/images/perplexus/problem/4tangent.gif\")
\r\n
![](\"http://www.flooble.com/images/perplexus/problem/ducky.gif\")
![](\"http://www.flooble.com/images/perplexus/problem/difangle.gif\")
\r\n![](\"http://www.flooble.com/images/perplexus/problem/linked-circles.jpg\")
\r\nThree rings (planer circles) are \"linked\" together, but you\'ll notice that none is directly linked with another. ![](\"http://www.eohpunx.com/widgets/cylinderjugs.gif\")
![](\"http://www.flooble.com/images/perplexus/problem/quadrilateral-fun.jpg\")
![](\"http://www.flooble.com/images/perplexus/problem/sphere-cube.jpg\")
\r\n![](\"http://perplexus.info/images/perplexus/problem/chess_switch.gif\")
![](\"http://perplexus.info/images/perplexus/problem/rooks.gif\")
\r\n![](\"http://www.flooble.com/images/perplexus/problem/quicker-than-the-eye.jpg\")
\r\nAs you probably know... a given color of light can generally, be described by one number (e.g., the frequency of its wave length).\r\n\r\n
\r\n![](\"http://www.flooble.com/images/perplexus/problem/ricketysol.gif\")
\r\n![](\"http://www.flooble.com/images/perplexus/problem/landscape.gif\")
\r\n![](\"http://www.flooble.com/images/perplexus/problem/farmer_area.jpg\")
\r\nA farmer has an irregular plot of land that he wishes to leave to his four sons. It encompasses 2700 acres.![](\"http://www.flooble.com/images/perplexus/problem/farmer_area_sol.jpg\")
![](\"http://www.flooble.com/images/perplexus/problem/circle-square.jpg\")
![](\"http://www.flooble.com/images/perplexus/problem/3bugs_ani.gif\")
\r\nRemember ![](\"http://www.flooble.com/images/perplexus/problem/6bugs_ani.gif\")
\r\n\r\nRemember ![](\"http://perplexus.info/images/perplexus/problem/chords-and-chords.jpg\")
\r\nGiven a circle and two points on that circle, P and Q, draw the chord PQ, and label its midpoint M.![link to tree picture](\"http://wwww.geocities.com/qball123ca/maze.gif\"){kind=link}
![frieds maze link](\"http://www.geocities.com/qball123ca/friedmaze.gif\r\n\"){kind=link}
![Right here.](\"http://www.angelfire.com/blog/popstar_dave/images/shapes.gif\"){kind=link}
![The \"bonus\" problem](\"http://www.clarkson.edu/~broadbdj/xanga/noteveryday.gif\"){kind=link}
![See picture](\"http://perplexus.info/probimg.php?pid=1499&pic=odd-soccer-ball.gif\"){kind=link}