When written as a decimal, the fraction m/n (with m < n, both positive integers) contains the consecutive digits 2, 5, 1 (in this order). Find the smallest possible n.
4 point 26
5 Small=9999
10 for T=2 to 5000
20 for M=1 to int(T/2)
30 N=T-M
40 F=str(M/N)
45 Ix=instr(F,"251")
50 if Ix>0 and Ix<len(F)-8 and N<=Small then print M;N;left(F,69):Small=N
60 next
70 next
finds
num den decimal
1 127 0.007874015748031496062992125984251968503937007874015748031496062992
2 127 0.015748031496062992125984251968503937007874015748031496062992125984
4 127 0.031496062992125984251968503937007874015748031496062992125984251968
5 127 0.039370078740157480314960629921259842519685039370078740157480314960
8 127 0.062992125984251968503937007874015748031496062992125984251968503937
10 127 0.078740157480314960629921259842519685039370078740157480314960629921
16 127 0.125984251968503937007874015748031496062992125984251968503937007874
19 127 0.149606299212598425196850393700787401574803149606299212598425196850
20 127 0.157480314960629921259842519685039370078740157480314960629921259842
25 127 0.196850393700787401574803149606299212598425196850393700787401574803
27 127 0.212598425196850393700787401574803149606299212598425196850393700787
32 127 0.251968503937007874015748031496062992125984251968503937007874015748
33 127 0.259842519685039370078740157480314960629921259842519685039370078740
38 127 0.299212598425196850393700787401574803149606299212598425196850393700
40 127 0.314960629921259842519685039370078740157480314960629921259842519685
47 127 0.370078740157480314960629921259842519685039370078740157480314960629
50 127 0.393700787401574803149606299212598425196850393700787401574803149606
51 127 0.401574803149606299212598425196850393700787401574803149606299212598
54 127 0.425196850393700787401574803149606299212598425196850393700787401574
61 127 0.480314960629921259842519685039370078740157480314960629921259842519
63 127 0.496062992125984251968503937007874015748031496062992125984251968503
64 127 0.503937007874015748031496062992125984251968503937007874015748031496
66 127 0.519685039370078740157480314960629921259842519685039370078740157480
73 127 0.574803149606299212598425196850393700787401574803149606299212598425
76 127 0.598425196850393700787401574803149606299212598425196850393700787401
77 127 0.606299212598425196850393700787401574803149606299212598425196850393
80 127 0.629921259842519685039370078740157480314960629921259842519685039370
87 127 0.685039370078740157480314960629921259842519685039370078740157480314
89 127 0.700787401574803149606299212598425196850393700787401574803149606299
94 127 0.740157480314960629921259842519685039370078740157480314960629921259
95 127 0.748031496062992125984251968503937007874015748031496062992125984251
100 127 0.787401574803149606299212598425196850393700787401574803149606299212
102 127 0.803149606299212598425196850393700787401574803149606299212598425196
107 127 0.842519685039370078740157480314960629921259842519685039370078740157
108 127 0.850393700787401574803149606299212598425196850393700787401574803149
111 127 0.874015748031496062992125984251968503937007874015748031496062992125
117 127 0.921259842519685039370078740157480314960629921259842519685039370078
119 127 0.937007874015748031496062992125984251968503937007874015748031496062
122 127 0.960629921259842519685039370078740157480314960629921259842519685039
123 127 0.968503937007874015748031496062992125984251968503937007874015748031
125 127 0.984251968503937007874015748031496062992125984251968503937007874015
126 127 0.992125984251968503937007874015748031496062992125984251968503937007
so the answer is 127.
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Posted by Charlie
on 2009-01-05 15:52:08 |
computer solution
