names_in_boxes.py

"""
The names of 100 prisoners are placed in 100 wooden boxes, one name to a box, and the boxes are
lined up on a table in a room. One by one, the prisoners are led into the room; each may look
in at most 50 boxes, but must leave the room exactly as he found it and is permitted no further
communication with the others.
The prisoners have a chance to plot their strategy in advance, and they are going to need it,
because unless every single prisoner finds his own name all will subsequently be executed.
Find a strategy for them which which has probability of success exceeding 30%.
"""

import random

def game():
    labeling = range(100)
    random.shuffle(labeling)

    for prisoner in range(100):
        next = prisoner
        found = False
        for n in range(50):
            cur = labeling.index(next)
            if cur == prisoner:
                found = True
            next = cur
        if not found:
            return False

    return True


TRIES = 1000
counts = {True: 0, False: 0}
for i in range(TRIES):
    counts[game()] += 1
print counts[True] / float(TRIES)