diff --git a/project_euler/problem_129/__init__.py b/project_euler/problem_129/__init__.py new file mode 100644 index 000000000..e69de29bb diff --git a/project_euler/problem_129/sol1.py b/project_euler/problem_129/sol1.py new file mode 100644 index 000000000..8afe82df1 --- /dev/null +++ b/project_euler/problem_129/sol1.py @@ -0,0 +1,57 @@ +""" +Project Euler Problem 129: https://projecteuler.net/problem=129 + +A number consisting entirely of ones is called a repunit. We shall define R(k) to be +a repunit of length k; for example, R(6) = 111111. + +Given that n is a positive integer and GCD(n, 10) = 1, it can be shown that there +always exists a value, k, for which R(k) is divisible by n, and let A(n) be the least +such value of k; for example, A(7) = 6 and A(41) = 5. + +The least value of n for which A(n) first exceeds ten is 17. + +Find the least value of n for which A(n) first exceeds one-million. +""" + + +def least_divisible_repunit(divisor: int) -> int: + """ + Return the least value k such that the Repunit of length k is divisible by divisor. + >>> least_divisible_repunit(7) + 6 + >>> least_divisible_repunit(41) + 5 + >>> least_divisible_repunit(1234567) + 34020 + """ + if divisor % 5 == 0 or divisor % 2 == 0: + return 0 + repunit = 1 + repunit_index = 1 + while repunit: + repunit = (10 * repunit + 1) % divisor + repunit_index += 1 + return repunit_index + + +def solution(limit: int = 1000000) -> int: + """ + Return the least value of n for which least_divisible_repunit(n) + first exceeds limit. + >>> solution(10) + 17 + >>> solution(100) + 109 + >>> solution(1000) + 1017 + """ + divisor = limit - 1 + if divisor % 2 == 0: + divisor += 1 + while least_divisible_repunit(divisor) <= limit: + divisor += 2 + return divisor + + +if __name__ == "__main__": + print(f"{solution() = }")