Three prisoners stand in a single file line facing a wall. They are shown 5 hats (3 black, 2 white) before being blindfolded. Each is given one hat, and the rest are hidden. P3 (back) sees P2 and P1. P2 (middle) sees P1. P1 (front) sees no one. P3 is asked if he knows his hat color and says 'No'. P2 hears this, is asked, and also says 'No'. P1 then correctly announces his hat color. What color is P1's hat?
Black.
P3 would only know his color if he saw two white hats in front of him. P3 saying 'No' means at least one of P2 or P1 has a black hat. P2 realizes that if P1 had a white hat, P2's own hat would have to be black for P3 to be unsure. Because P2 also said 'No', P1 deduces that his own hat cannot be white, so it must be black.
About this riddle
Logic riddles give you a few facts and ask what must be true. List what you know, cross out what cannot be, and see what is left.
Difficulty: Hard. More like this: Logic riddles with answers or try Einstein's Logic Grid for a different kind of puzzle.
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