Prisoners’ Escape: Answer

So, have the prisoners escaped? I like to think they did.

But how did they maximise their chances?

If you haven’t seen it, read the original puzzle here; and get a hint here, if you need it.

Here’s what the prisoners should have decided: when the first prisoner goes in, they should open their number locker door – you never know, they may get lucky! If this doesn’t contain their number, open the locker door of the number on the piece of paper they’ve just seen. If that locker doesn’t contain their number, repeat. If they find their number within 50 locker openings, then they’ve accomplished what they set out to do. Each prisoner should open his/her own box first (unless that box has already been opened and plundered of its number, in which case they can start anywhere they want).

This strategy works because it means that, unless there’s a loop of over 50 numbers in the cycle that naturally forms, every prisoner will find their number.

For reference, if each prisoner opens boxes at random, their chance is approx. 0.0000000000000000000000000000008!

Look out for more puzzles soon!