This is my favourite brain teaser, and one of the most difficult that I know. I apologize if it has been posted before and I missed it.
A team of 15 takes part in a contest. They know each other and all the rules of the contest, and they have time to make their strategy before the actual contest starts.
The rules of the contest are:
1. The players sit in a circle, so that everybody sees everybody. Then the players are blindfolded.
2. On each player's head, either a red or a blue cap