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41 lines
912 B
Python
41 lines
912 B
Python
#!/usr/bin/python3
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# mari wahl @2014
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# marina.w4hl at gmail
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'''
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A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:
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1/2 = 0.5
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1/3 = 0.(3)
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1/4 = 0.25
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1/5 = 0.2
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1/6 = 0.1(6)
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1/7 = 0.(142857)
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1/8 = 0.125
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1/9 = 0.(1)
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1/10 = 0.1
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Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.
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Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.
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Answer: 983
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'''
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def recurring_cycle(n, d):
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for dd in range(1, d):
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if 1 == 10**dd % d:
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return dd
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return 0
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def main():
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n = 1
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limit = 1000
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longest = max(recurring_cycle(n, i) for i in range(2, limit+1))
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print [i for i in range(2, limit+1) if recurring_cycle(n, i) == longest][0]
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if __name__ == '__main__':
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main()
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