Problem
The Problem
100 prisoners are each assigned a number 1-100. A room has 100 boxes, each containing a slip with a number 1-100 (a random permutation). Each prisoner enters the room alone and can open up to 50 boxes. They cannot communicate afterward.
If every prisoner finds their own number, all are freed. If even one fails, all are executed.
What's the optimal strategy, and what's the probability of success?