100 prisoners each have a number 1-100. In a room are 100 boxes, each containing one number. Each prisoner may open 50 boxes trying to find their number. They can't communicate after entering. If ALL prisoners find their number, all go free. Otherwise, all die. What strategy gives them the best chance?
Hints
Don't search randomly—follow the number chains.
Answer
Each prisoner opens the box matching their number, then opens the box with the number they found, continuing this chain for 50 attempts. This 'cycle-following' strategy gives approximately 31% success rate versus 1/2^100 for random search.