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Hat Colors (Chapter 4 tab 7)

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?

Note by A 1
2 months ago

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Also, since the picture might add some confusion, I added a note to clarify that it's not necessarily one of each hat. Jason Dyer Staff · 2 months ago

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Hi, it looks like you're interpreting the problem is that each hat color must occur once. The way the problem is phrased is that there could be red, green, or blue, but it doesn't have to be one of each; if all three are wearing green then a strategy where they all say "blue" would fail.

Also note in the future, if you have a report like this, if you click on the three dots (either on the top of the screen if you're on in the app, or below "hide solution" if you're in a browser) there is an option called "report problem" which is intended for things like this. It'll get to me faster. Thanks! Jason Dyer Staff · 2 months ago

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They must specify one color only. They can't say more than 1 color... Pi Han Goh · 2 months ago

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