In this classic dilemma, the director of a prison offers 100 prisoners, who have been assigned numbers from 1 to 100, a last chance at freedom. A room contains 100 boxes. The director randomly puts one prisoner’s number in each closed box. The prisoners enter the room, one after another. Each prisoner may open and look into 50 boxes in any order. The boxes are closed again afterwards. If, during this search, every prisoner finds his number in one of the boxes, all prisoners are pardoned and given $5000 each. If just one prisoner does not find his number, all prisoners are admonished and never get another chance with this dilemma.
Before the first prisoner enters the room, the prisoners may discuss strategy — but may not communicate once the first prisoner enters to look in the boxes. There’s no way for them to always win, but what is their best strategy?
This problem originally appeared in The Prisoner’s Dilemma in the 2021 Fall issue of the PMP Newsletter. Solutions will be accepted through 2022 May 27.