Arseniy GameTheory

import math

def f(m, n = 20, turn = 0):
    if n+m<=40 and (turn == 2 or turn == 4):  # Набрали меньше 40 ровно на 3
        return True
    elif n+m<=40 and turn < 4:  # Набрали меньше 40 до 3
        return False
    elif n+m>40 and turn == 4:  # Не набрали 40 на 3
        return False
    if turn%2 == 1:
        return f(m-1, n, turn+1) or f(math.ceil(m/2), n, turn+1) \
               or f(m, n-1, turn+1) or f(m, math.ceil(n/2), turn+1)
    else:
        return f(m-1, n, turn+1) and f(math.ceil(m/2), n, turn+1) \
               and f(m, n-1, turn+1) and f(m, math.ceil(n/2), turn+1)

def Check2(m, n = 20, turn = 0):
    if n+m <= 40 and turn == 2:  # Набрали меньше 40 ровно на 3
        return True
    elif n+m <= 40 and turn < 2:  # Набрали меньше 40 до 3
        return False
    elif n+m > 40 and turn == 2:  # Не набрали 40 на 3
        return False
    if turn % 2 == 1:
        return Check2(m-1, n, turn+1) or Check2(math.ceil(m/2), n, turn+1) \
               or Check2(m, n-1, turn+1) or Check2(m, math.ceil(n/2), turn+1)
    else:
        return Check2(m-1, n, turn+1) and Check2(math.ceil(m/2), n, turn+1) \
               and Check2(m, n-1, turn+1) and Check2(m, math.ceil(n/2), turn+1)


for s in range(20, 100):
     if f(s) and not Check2(s):
         print(s)