nayuki/Project-Euler-solutions

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 # # Solution to Project Euler problem 33 # Copyright (c) Project Nayuki. All rights reserved. # # https://www.nayuki.io/page/project-euler-solutions # https://github.com/nayuki/Project-Euler-solutions # import fractions def compute(): # Consider an arbitrary fraction n/d: # Let n = 10 * n1 + n0 be the numerator. # Let d = 10 * d1 + d0 be the denominator. # As stated in the problem, we need 10 <= n < d < 100. # We must disregard trivial simplifications where n0 = d0 = 0. # # Now, a simplification with n0 = d0 is impossible because: # n1 / d1 = n / d = (10*n1 + n0) / (10*d1 + n0). # n1 * (10*d1 + n0) = d1 * (10*n1 + n0). # 10*n1*d1 + n1*n0 = 10*d1*n1 + d1*n0. # n1*n0 = d1*n0. # n1 = d1. # This implies n = d, which contradicts the fact that n < d. # Similarly, we cannot have a simplification with n1 = d1 for the same reason. # # Therefore we only need to consider the cases where n0 = d1 or n1 = d0. # In the first case, check that n1/d0 = n/d; # in the second case, check that n0/d1 = n/d. numer = 1 denom = 1 for d in range(10, 100): for n in range(10, d): n0 = n % 10 n1 = n // 10 d0 = d % 10 d1 = d // 10 if (n1 == d0 and n0 * d == n * d1) or (n0 == d1 and n1 * d == n * d0): numer *= n denom *= d return str(denom // fractions.gcd(numer, denom)) if __name__ == "__main__": print(compute())