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Names in Boxes (Posted on 2017-04-09) Difficulty: 3 of 5
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!

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.7500 (4 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re(2): This is not possible - further thoughts.broll2017-04-12 16:09:14
re(3): LoopsCharlie2017-04-12 14:41:51
re(2): LoopsJer2017-04-12 13:27:25
re(2): LoopsBrian Smith2017-04-12 13:08:19
reference and solutionxdog2017-04-12 12:42:48
re: LoopsCharlie2017-04-12 10:54:02
SolutionLoopsBrian Smith2017-04-12 10:11:43
Some Thoughtsre: This is not possible.broll2017-04-12 02:36:48
SolutionThis is not possible.Math Man2017-04-11 08:20:11
Some ThoughtsThoughtsJer2017-04-10 15:31:03
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