Puzzle: Four Men in Hats
Shown above are four men buried up to their necks in the ground. They cannot move, so they can only look forward. In between A and B is a brick wall that cannot be seen through. They all know that between them they are wearing four hats – two black and two white – but they do not know what color they are wearing. Each of them knows where the other three men are buried.
In order that someone comes to help them get out of the ground, one of them must correctly yell out the color of their hat. If they get it wrong, then they stay stuck in the ground. They are not allowed to talk to each other and have 10 minutes to fathom it out.
After one minute, one of them calls out. Which one?
D is the only one who can see two hats – B & C. If D saw that both B and C were wearing hats of the same color, then D would know the color of D’s hat. Since D didn’t yell out, C knows that D is seeing hats of two different colors. C sees that color of B’s hat is white, so C’s hat must be black.
