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 Names in Boxes (Posted on 2017-04-09)
The names of 100 prisoners are placed in 100 wooden boxes, one name to a box, and the boxes are lined up on a table in a room. One by one, the prisoners are led into the room; each may look in at most 50 boxes, but must leave the room exactly as he found it and is permitted no further communication with the others.
The prisoners have a chance to plot their strategy in advance, and they are going to need it, because unless every single prisoner finds his own name all will subsequently be executed.
Find a strategy for them which has probability of success exceeding 30%.

Comment: If each prisoner examines a random set of 50 boxes, their probability of survival is an unenviable 1/2100 ∼ 0.0000000000000000000000000000008. They could do worse—if they all look in the same 50 boxes, their chances drop to zero. 30% seems ridiculously out of reach—but yes, you heard the problem correctly!

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 reference and solution | Comment 6 of 10 |
http://puzzling.stackexchange.com/questions/16/100-prisoners-names-in-boxes

Check especially Anachor's explanation:  ". . . we just need to find the probability that there is a cycle of 51 or longer.

. . . the probability that there is a cycle of length 51 or longer is just
1/51+1/52+1/53+...+1/100≈0.688172
, so the probability of the opposite is 0.3118280.311828 which is above 30%."

 Posted by xdog on 2017-04-12 12:42:48

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