Four Players, Three Colors: Possible Strategy

For this to work, we need to treat the hat colors as numbers 0,1,2.

All math below (additions and subtraction) is done modulus 3 (so the result is always 0 or 1 or 2).

There could be a way to guarantee two are right, but this makes sure that at least one person guesses their own hat color correctly.

  • Person 1 adds the hat colors of Person 2 and Person 4 and makes that their own guess.
  • Person 2 adds the hat colors of Person 1 and Person 3, and then subtracts that from zero and makes that their own guess.
  • Person 3 subtracts the hat color of Person 4 from the hat color of Person 2 and makes that their own guess.
  • Person 4 subtracts the hat color of Person 1 from the hat color of Person 3 and makes that their own guess.

    This makes it so that either one person guesses right or all four do.








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