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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