There are 100 prisoners numbered 1 through 100. There is a room with 100 slips of paper numbered 1 through 100 and 100 boxes similarly numbered 1 through 100. Each slip of paper is placed in a box. There is exactly one slip of paper in each box (no empty boxes, no boxes with multiple slips of paper).
Each prisoner is allowed to open 50 boxes without changing the contents of any box. All the boxes will be closed once the prisoner leaves the room. The prisoners are allowed to discuss a strategy as a group beforehand, but they can't talk to each other in any way after the game has started. One at a time, a prisoner will enter the room and open up to 50 boxes.
If every prisoner finds their own number within the 50 boxes, all the prisoners are allowed to go free. If any prisoner fails to find their own number within 50 tries, all the prisoners will be executed.
The goal of this puzzle is to find a strategy that will give the prisoners at least a 30% probability of success. In the following pages, we'll look at some different possible strategies.
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