# Prisoner's Dilemma

This brain teaser involves an evil prison warden with way too much time on his hands:

4 men are in thrown in prison for jaywalking. It must have been very blatant jaywalking, for their sentence is 80 years. Luckily for them, the warden is apparently not too attached to his job, because he offers them a chance to go free.

Each man will be taken into a room with 4 lockers in it. Inside each locker will be a key with a number on it. The man will first open one locker. If it contains the key corresponding to his cell, then he has succeeded. (The number on the key matches his cell number) If the locker does not contain his key, he must shut it and open one more locker. If this locker does not contain his key either, then he loses and the entire group fails. In order to be let free, each man must succeed in this task and find his key.

This is all done individually, each man will be taken to the room with all the lockers initially closed, and they can not leave each other signs or communicate in any way. The prisoners are put together and are given a half hour before the game begins to plan out their strategy.

Now clearly if these were run-of-the-mill criminals, they would have no strategy and be stuck with a 1/16 chance of freedom. However, these terrible jaywalkers happen to be brilliant mathematicians, and soon realize that their chances of winning are actually greater than 40%. What was their solution?