Prison Puzzle

[WilyTilt]

Hey, anyone heard of this one? I posted it on OOT but they told me to go here ...

This took me days to figure out. One of the best around, I think.

Here's the situation. An Arab sultan has arrested 50 men accused of plotting against him, and decided to imprison them for life unless they can figure out a puzzle. All 50 will be separated by day and will never see each other, but every night one of them will be randomly picked and placed in a special cell, where in the corner there is a light bulb. He can turn on or turn off the lightbulb as he likes, and it will remain in that state until the next night. There's no other way to leave any message in the room. The prisoners are allowed one night to discuss a plan before they are separated and the puzzle starts.

The sultan tells them that when one of them can tell him for certain that every single prisoner has been in the room at least once, and can explain why, all of them will be freed. If he's wrong, then all of them will be executed.

Please post answers in white. Enjoy.

[gharp]

An obfuscated version of this was a Car Talk puzzler maybe a couple years ago. Pretty cool problem -- when I first heard it I remember spending a lot of time thinking about it.

[Stephen H]

The follow up question is how long, on average, will it take them to get out? [img]/images/graemlins/smile.gif[/img]

[dmk]

answer:

<font color="white">the first person turns the lightbulb on. each following night, if you are in the cell for the first time, burn your fingerprint onto the lightbulb. when there are 50, you win</font>

[sighing]

[ QUOTE ]
The follow up question is how long, on average, will it take them to get out? [img]/images/graemlins/smile.gif[/img]

[/ QUOTE ]
Answering that question gives a hint to the answer, but I'd say that the main problem with the solution is that some of them will die of natural causes during the process.

<font color="white">About 10 years</font>

(yes, I've seen this puzzle before)

[durron597]

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