100 prisoners and the Light Bulb Puzzle
This is a very good interview puzzle.Good in the sense that it requires good amount of thinking if you haven’t already heard this problem.Here’s the Puzzle:
Puzzle : There are 100 prisoners are in solitary cells, unable to see, speak or communicate in any way with each other. There’s a room with one light bulb, the bulb is initially off. No prisoner can see the light bulb from his own cell. Everyday, the warden picks a prisoner at random, and that prisoner goes to the that room. While there, the prisoner can toggle the bulb if he wishes. Also, the prisoner has the option of asserting the claim that all 100 prisoners have been to the living room. If this assertion is false (that is, some prisoners still haven’t been to the living room), all 100 prisoners will be shot for their stupidity. However, if it is indeed true, all prisoners are set free. Thus, the assertion should only be made if the prisoner is 100% certain of its validity.
Before the random picking begins.All the prisoners are allowed to get together to discuss a plan.
Note that each prisoner can be selected any number of times and the process will continue till the assertion is not made.
Question: What plan should they agree on, so that eventually, someone will make a correct assertion ?
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