In This Article

The Question

The Intuition Trap: Why Independent Strategies Fail

The Loop Strategy: Following the Permutation Cycle

The Mathematical Proof

Python Simulation: 100,000 Trials

Business Application: Correlated Failure vs. Independent Risk

The Question

The director of a prison offers 100 prisoners on death row a chance to survive. A room contains a cupboard with 100 drawers. The director randomly places one prisoner's number — drawn from 1 to 100 — into each closed drawer, one per drawer, so that the assignment is a uniformly random permutation. The prisoners enter the room one at a time. Each prisoner may open and look into exactly 50 drawers in any order. After examining the drawers, the prisoner leaves the room and the drawers are all closed again. No prisoner may communicate with the others once the game has begun, and they may not leave any marks or signals.

The prisoners survive if and only if every single prisoner finds their own number among the 50 drawers they open.…