http://www.mast.queensu.ca/~peter/inprocess/prisoners.pdf

You may want to consider another puzzle whose solution depends on developing an upfront strategy:

“N > 1 people sit in a circle clearly seeing all others. They are going to be blindfolded and, while in this state, hats are put on their heads – one per person, naturally. On each hat there is written a number from 0 to N-1. The numbers may be different or some may be equal. Nothing is known about that, except that each is picked up from the set {0, 1, 2, …, N-1}. When blindfolds are removed the numbers are in full display: everyone sees all the numbers except one’s own. Each is tasked with guessing his number. They are not allowed to communicate in anyway. Each is given a piece of paper on which to write his guess. The papers are collected and the responses are examined. The team wins if there is at least one right guess.”

]]>