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Problem26.py
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Problem26.py
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"""
@author: mces58
Problem 26
A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:
1/2 = 0.5
1/3 = 0.(3)
1/4 = 0.25
1/5 = 0.2
1/6 = 0.1(6)
1/7 = 0.(142857)
1/8 = 0.125
1/9 = 0.(1)
1/10 = 0.1
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.
Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.
Answer: 983
"""
# Returns the length of the recurring cycle in the decimal representation of 1/n.
def recurringLength(n):
remainders = {} # dictionary to store the remainder and its position
remainder = 1
position = 0
while remainder not in remainders:
remainders[remainder] = position
remainder = (remainder * 10) % n
position += 1
if remainder == 0:
return 0 # no recurring cycle
else:
return position - remainders[remainder]
maxLength = 0
maxDenominator = 0
for d in range(2, 1000):
cycleLength = recurringLength(d)
if cycleLength > maxLength:
maxLength = cycleLength
maxDenominator = d
print(maxDenominator)