What is the color of my hat?

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The principles of coding theory can be demonstrated with so-called hat problems: participants put on either a black or red hat without looking, so that they can see the color of everyone else's hats (or possibly just some subset), but not of their own. Then, based on certain premises, they try to deduce the color of their own hat. These puzzles lend themselves nicely to activities, but using playing cards which students hold to their foreheads. These problems were taken from a Math Horizons article by Ezra Brown and James Tanton.