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!
(In reply to Loops
by Brian Smith)
The solution to Fatal Guess involved rearranging the boxes in the room. Here we're not allowed to do that.
You say "The only way for the prisoners to fail is if there is a loop with more that 50 names.", but what if the first box he chooses is in the wrong loop? There's no guarantee his name will be in the loop that has his numbered code name label or position. There is no way around MathMan's objections.
Posted by Charlie
on 2017-04-12 10:54:02