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Suppose each of x and y is a real number > 0

Find the minimum value of:

 
2x2+2y2+3xy+1
-------------
     x+y

Find the smallest whole number N such that N contains all of the digits from 0 through 9, and N² contains all of the digit pairs 00, 11, 22, ..., 99.

Determine all the numbers formed by three different and non-zero digits, such that the six numbers obtained by permuting these digits leaves the same remainder after the division by 4.

Arrange the integers from 1 to N in an order such that the sum of any two consecutive terms is a power of 2.

For what values of N do solutions exist?

Solve:
FOR = I x WAS
where W, A, and S represent consecutive digits.

Find all positive integers x such that ⌊x/5⌋-⌊x/7⌋=1.

The sides of a triangle are three consecutive integers and its inradius is 4. Find the circumradius.

What are the next two numbers in the following sequence ?
2,12, 2122, 1132, 211213, 312213, 212223, .........

A positive integer N contains each 2-digit combination exactly once:
00, 01, ..., 99.

(A) What is the smallest number of digits N could have?
(B) What is the largest number of digits N could have?
(C) What is the smallest possible value of N?
(D) What is the largest possible value of N?

(no leading zeros)

Consider a sequence generated by positive integer x where each term is of the form ⌊(2+√7)^x⌋. Prove that the sum of two consecutive terms will always be odd.