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hardLogicBy the Think Fanny puzzle desk

Three wise people, red hats

Published , last checked . Re-solved cold against the published wording before it went live: how puzzles and answers are checked.

They can see others' hats. Who figures out their color, and how? From the free puzzle set on Think Fanny. Next try Three switches, one bulb.

Think Fanny brain teaser scene with selective focus chess pieces

The puzzle

Three perfect logicians sit where each can see the other two. Hats are red or blue. They all know that at least one hat is red. In fact, all three hats are red.

They are asked, repeatedly, whether they know their own hat color. At first everyone says no. Then, using the others’ answers, they all become sure.

What color do they announce, and what is the core idea?

Reading around the hat problems

Hat problems are a documented family, and the trick of extracting information from the other players failing to answer is the classic common-knowledge move:

If one of these contradicts the answer above, we would rather hear it than not. See how puzzles and answers are checked.