46 lines
949 B
Python
46 lines
949 B
Python
from fractions import Fraction
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from itertools import combinations
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def mul(xs):
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r = 1
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for x in xs:
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r *= x
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return r
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def mul_inv(xs):
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r = 1
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for x in xs:
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r *= (1 - x)
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return r
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def sub_odds(n_blue, n_total):
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""" Computes the odds for getting exactly n_blue out of n_total blue discs.
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"""
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total_odds = 0
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odds = [Fraction(1, n) for n in range(2, 2 + n_total)]
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odds_set = set(odds)
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for odd in combinations(odds, n_blue):
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odd_inv = tuple(odds_set.difference(set(odd)))
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total_odds += mul(odd) * mul_inv(odd_inv)
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return total_odds
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def euler_121():
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n_turns = 15
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n_to_win = n_turns // 2 + 1
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odds = 0
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for n_blue in range(n_to_win, n_turns + 1):
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odds += sub_odds(n_blue, n_turns)
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price = int(1 / odds)
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return price
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if __name__ == "__main__":
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solution = euler_121()
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print("e121.py: " + str(solution))
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assert(solution == 2269)
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