When a person walks into a party he will be given one of 3 hats. Each hat is either yellow, red or blue. Every person does not know the colour of their own hat but he can see the colour of everyone else's.
At this point in the party everyone is seated in a circle and must guess the colour of their own hat. If they do they get 100 dollars.
Every person can make a guess of yellow, red or blue and nothing else. Every person gets two such guesses but these can be made in any order. (That is one need not make both his guesses one right after the other.)
In order to win with one of your two guesses you must say the colour of your own hat. How can every person guarantee themselves the money? (How can they have a 100% chance of guessing the colour of their hat correctly?)
Going clockwise around the table for the first time everyone guesses the color of the hat that the person on their left is wearing. Most everyone will be wrong but the second time around they can make the correct guess and get the $100. The biggest flaw I see in this solution is that if they are capable of this sort of cooperation I suppose that prior to guessing they could just ask someone "What color is my hat?". With that in mind I'm not sure my solution qualifies.
3 Hats
