맥소날드

0 - so.py

#!/usr/bin/env python

import itertools

NR_OF_MARIOS = 4
def mario_test(n):
    marios = range(NR_OF_MARIOS)

    all_cases = [p for p in itertools.product(marios, repeat = n)]

    def succeed_at_last(case):
        init = set(case[:-1])
        return case[-1] not in init and len(init) == NR_OF_MARIOS - 1

    successful_cases = filter(succeed_at_last, all_cases)

    nr_all     = len(all_cases)
    nr_success = len(successful_cases)

    print "%2d: %10d / %10d (%s)" % (n, nr_success, nr_all, nr_success / float(nr_all))

for i in range(4, 13):
    mario_test(i)

1 - result.txt

 4:         24 /        256 (0.09375)
 5:        144 /       1024 (0.140625)
 6:        600 /       4096 (0.146484375)
 7:       2160 /      16384 (0.1318359375)
 8:       7224 /      65536 (0.110229492188)
 9:      23184 /     262144 (0.0884399414062)
10:      72600 /    1048576 (0.0692367553711)
11:     223920 /    4194304 (0.0533866882324)
12:     684024 /   16777216 (0.0407710075378)