A complicated answer of 1 is given for the below question after using modulo arithmetic. Wouldn't the easiest solution strategy be for all three of them to agree to always say either "Red, "Green" or "Blue"? Someone must be wearing the Blue (etc.) hat which implies that the probability=1.
Alice, Bob, and Charlie are each wearing a hat, and each hat is either red, green, or blue. They can all see each other's hats, but cannot see their own. At the same time, the three people guess their hat color. They win if any of them correctly guesses their hat color. With a perfect strategy, what is the probability they win the game?