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Smart prisoners always get a break #2 (Posted on 2007-03-07) Difficulty: 4 of 5
Note: Read this problem carefully, because it's completely different from the original.

As before, 100 prisoners are put into solitary cells, and there's a room with a light bulb. (No prisoner can see the light bulb from his or her own cell.) Every night, the warden picks a prisoner at random, and that prisoner goes to the living room. While there, the prisoner can toggle the bulb if he or she wishes. but this time, the prisoner needs to assert that he knows, which prisoner was in the living room before him. If the assertion is false, all 100 prisoners will be shot. 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.

The prisoners are allowed to get together one night, to discuss a plan.

But, the prisoners know that after that night, when they will go back to their solitary cells. the warden will choose one prisoner secretly (and this time, not randomly) and will kill him.

What plan should they agree on, so that eventually, someone will make a correct assertion?

See The Solution Submitted by Assaf    
Rating: 4.1818 (11 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts re(2): only 99% sure | Comment 3 of 11 |
(In reply to re: only 99% sure by Charlie)

Of course the designated person A, could, after the specified number of days, refrain from turning on the light, and leave it to B, preventing the possibility of total extermination, but allowing for the possibility they will never get out, if B was the killed person, with the probability (0.01)*(0.99^d).

Then again, they could decide to transfer to C after a similar number of days.

  Posted by Charlie on 2007-03-07 11:38:57
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