In my gambling years, between the ages of eight and 12, I played roulette, poker, blackjack and any other game that had a three-cent ante. One of my favorite games, though, was one we called "Bluffhead." Each person takes a card from a shuffled deck and holds it, face out, to his or her forehead. In other words, players see everyone else's cards but not their own. The best card wins. Ace is high and suits don't matter, so ties are possible.
This puzzle has to do with inferring information about the cards people hold by hearing what the players say. To be concrete, suppose that we have three players. Caroline always speaks first, then David, then Jordan, and back to Caroline and so on. Each player makes one of the statements listed at the bottom right of this page. Assume the players are perfect logicians and reveal information only through these phrases; also, they say the strongest thing they can--that is, they choose the statement that is true and highest on the list.
This article was originally published with the title Bluffhead.