20.01 Теория игр

from functools import lru_cache


@lru_cache(None)
def f(first_heap, second_heap, third_heap, c=0):
    if first_heap + second_heap + third_heap <= 32:
        return 0
    if c > 4:
        return 123123
    moves = []
    if first_heap > 1:
        moves.append(f(first_heap - 1, second_heap, third_heap, c + 1))
        moves.append(f((first_heap + 1) // 2, second_heap, third_heap, c + 1))
    if second_heap > 1:
        moves.append(f(first_heap, second_heap - 1, third_heap, c + 1))
        moves.append(f(first_heap, (second_heap + 1) // 2, third_heap, c + 1))
    if third_heap > 1:
        moves.append(f(first_heap, second_heap, third_heap - 1, c + 1))
        moves.append(f(first_heap, second_heap, (third_heap + 1) // 2, c + 1))

    petya_win = [i for i in moves if i <= 0]
    if petya_win:
        return -max(petya_win) + 1
    else:
        return -max(moves)


count = 0
for i in range(11, 100):
    if f(11, 11, i) == 2:
        count += 1
print(count)