The 33% Hat Problem

The Puzzle

Three people sit in a circle, each wearing a red, blue, or white hat. Each sees the other two hats but not their own. They agree on a strategy beforehand, then simultaneously guess their hat color. At least one must be correct. What strategy works?

Choose your answer:

Everyone guesses 'red'

Use modulo 3 arithmetic with assigned targets

Each person guesses the most common color they see

Random coordinated guessing

Need a Hint?

Solution

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