Four Men in Hats

I stumbled upon a brain teaser today called the Four Men in Hats Puzzle (aka the Prisoners and Hats Puzzle). Here’s the 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. Between A and B is a brick wall which 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 know where the other three men are buried.

In order to avoid being shot, one of them must call out to the executioner the color of their hat. If they get it wrong, everyone will be shot. 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.

Question: Which one of them calls out? Why is he 100% certain of the color of his hat?

Keep reading if you want to know the answer.

My answer was a little more general than the answer given on Mycoted, because it didn’t assume that the hats in the drawing were the actual colors of the hats the men were wearing. Here’s my answer:

D can see the hats of both B and C. If D sees either 2 white hats or 2 black hats, he will immediately know that his hat is the opposite color and will call out. Since it took a minute for someone to call out, it must not have been D. Therefore, B and C are wearing different colored hats.

C can see which hat B is wearing. Since he knows he is wearing a different colored hat than B, C calls out the color that is not the color of B’s hat.

This, of course, assumes that none of the men want to be shot. 😉