There is a lever in room A, which is connected to two lights in room B. Depending on how one pulls on the lever, it will either make a red light or a green light goes up in room B. The game proceeds as follows. Each prisoner in room A will take turn going up and examine the 26 jars away from the sight of his fellow prisoners. He can not rearrange or modify the jar in any way, shape, or form. He then must pull the level and make either a red light or green light goes up in room B. If he attempts to communicate any other information besides those two bit of information (i.e. waiting a certain amount of time before pulling the lever, pulling the level more than once, not pull the level at all, etc. ) all prisoners will be executed immediately. The order in which the prisoners take their turn at the jar is randomly determined by the warden.
If the prisoner in room B can reconstruct the arrangement of balls inside the jars in room A at the end of 31 turns, all prisoners will live. However, there's a catch. The warden will randomly intercept the communication of 1 prisoner from room A to room B and flip it. For example, suppose that the warden choose to flip prisoner 16's communication. Let's say that number 16 examines the jar and choose to make the green light goes up, the warden would intercept the electronic signal and make the red light goes up instead. Likewise, if number 16 were to choose to make the red light goes up, the warden would make the green light goes up instead.
The 32 prisoners are informed of this game the night before, so they know that the communication of exactly 1 random person will be compromised during the game. They have 1 night to prepare.
Is there a strategy to guarantee the survival of all prisoners? Describe it.
Edited by bushindo, 01 June 2009 - 06:06 AM.