from math import factorial
from itertools import combinations


def product(xs):
    r = 1
    for x in xs:
        r *= x
    return r


def sub_odds(n_blue, n_total):
    odds = [n for n in range(1, n_total + 1)]
    return sum(map(product, combinations(odds, n_total - n_blue)))


def euler_121():
    n_turns = 15
    n_to_win = n_turns // 2 + 1
    odds = sum([sub_odds(n_blue, n_turns)
                for n_blue in range(n_to_win, n_turns + 1)])
    return int(factorial(n_turns + 1) / odds)


if __name__ == "__main__":
    solution = euler_121()
    print("e121.py: " + str(solution))
    assert(solution == 2269)