The Prisoners Problem

100 condemned men are given a chance for reprieve by a mathematically oriented warden. The integers from 1 to 100 are written down three times on three sets of 100 placards, one number per placard. The first set is used to label 100 identical boxes, one label per box. The boxes are in a closed room. Unseen by the prisoners, the warden distributes the second set randomly among the 100 boxes, one card placed inside each box. Each prisoner gets a number from the remaining set. The warden explains that each prisoner will enter the room with the boxes with the warden witnessing, but no other prisoner present. Each prisoner may open up to fifty boxes. If a prisoner reads his own number in one of the boxes he opens, he personally has passed the test. If every prisoner passes the test they all live. If even one fails the test they all die. The prisoners are allowed one strategy meeting before they go one by one into the room with the warden, but they are not allowed to communicate with each other in any way after that strategy meeting. For example they cannot move the boxes, and they don't get to see or hear each other after they've been in the room. What's a good strategy, and for that strategy, what is the probability of all going free?

Eva's Home Page

Jean-Claude Chetrit heard this problem and solution at a conference 
and shared it with the Brooklyn Go Club email list little by little in a 
way that promoted enjoyable back and forth.

 Last Revised August 15, 2007