Undergrad @CMU

hat problem

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Say the king is bored and decides to play a game with 10 people. The king has 10 types of hat and randomly gives those hat to those 10 people (the number of each type of hat is not fixed, so everyone could have same or distinct hats). The goal of the game is for at least one person to guess their own hat type but before the game starts, they are allowed to communicate a strategy. After they have decided their strategy, they are then taken into a room where hats will be assigned and any sort of communication will be disallowed (including moving around, signling, etc). The king then waits a bit and after a short period of time snaps his finger, when all 10 people need to declare their guesses at the exact same time.

Now, what is the strategy to guarantee a victory (at least one person gets the right guess)?

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