flipflop.py

for player_count in range(1, 10000):
    got_to_play = set()
    direction = 1
    player = 0
    for n in range(1, 1000000):
        got_to_play.add(player)
        if got_to_play == set(range(player_count)):
            break
        if n % 7 == 0 and n % 8 == 0: # flip flop
            direction = -direction
            player += direction # skip 1 player
        elif n % 7 == 0: # flip
            player += direction # skip 1 player
        elif n % 8 == 0: # flop
            direction = -direction

        player += direction

        # wrap players in the circle:
        if player >= player_count:
            player = 0
        elif player < 0:
            player = player_count - 1

    did_not_get_to_play = sorted(set(range(player_count)) - got_to_play)
    if did_not_get_to_play:
        print('With {} players, these {} players played: {}'.format(player_count, len(got_to_play), sorted(got_to_play)))
    else:
        print('With {} players, ALL players played'.format(player_count))