Alice, Bob, and Charlie are playing a game with hats. Each is wearing a hat that is either red, yellow, or blue. Though there are three possible hat colors, they might not be distinct - perhaps there are three red hats, or two blue and one yellow.
Alice, Bob, and Charlie each look at the other two hats and simultaneously guess their own hat color. They must guess, and cannot convey any other information.
Before they don their hats, they can agree on a strategy. Is there a strategy that guarantees exactly one of them will guess correctly?