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project_euler/problem_100/sol1.py
48 строк
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Maxim Smolskiy
Add Project Euler problem 100 solution 1 (#8175)
14 мар 2023, 08:39
Не верифицирован
14 мар 2023, 08:39
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""" Project Euler Problem 100: https://projecteuler.net/problem=100 If a box contains twenty-one coloured discs, composed of fifteen blue discs and six red discs, and two discs were taken at random, it can be seen that the probability of taking two blue discs, P(BB) = (15/21) x (14/20) = 1/2. The next such arrangement, for which there is exactly 50% chance of taking two blue discs at random, is a box containing eighty-five blue discs and thirty-five red discs. By finding the first arrangement to contain over 10^12 = 1,000,000,000,000 discs in total, determine the number of blue discs that the box would contain. """ def solution(min_total: int = 10**12) -> int: """ Returns the number of blue discs for the first arrangement to contain over min_total discs in total >>> solution(2) 3 >>> solution(4) 15 >>> solution(21) 85 """ prev_numerator = 1 prev_denominator = 0 numerator = 1 denominator = 1 while numerator <= 2 * min_total - 1: prev_numerator += 2 * numerator numerator += 2 * prev_numerator prev_denominator += 2 * denominator denominator += 2 * prev_denominator return (denominator + 1) // 2 if __name__ == "__main__": print(f"{solution() = }")