# Brainteaser #10- The Prisoners' Hats -

Four inmates are cleaning up a littered beach as part of a prisoner work program. The warden, who happens
to be overseeing the work, decides to play a little game with the prisoners. He tells them that if they
win the game he will let them go free! He then proceeds to bury each prisoner up to his neck in
sand as shown below.

There is a wall between prisoners C and D (which cannot be seen through or around). Prisoner A can
see prisoners B and C (by moving his head to the side). Prisoner B can see prisoner C. Prisoners C and D
see only the wall.

The prisoners are immobilized in the ground and can't twist their body to see the person behind them. The
warden shows them two black hats and two white hats and then puts the hats in a bag to conceal them.
He then stands behind each prisoner, chooses a hat from the bag, and puts it on their head. The color of
each prisoner's hat is shown in the image above.

The rules are simple. If any prisoner can figure out the color of the hat on his head, all four prisoners
will be set free. But they must be sure, if one of them simply guesses and is wrong, they will all be shot
dead! The prisoners are not allowed to talk to each other and they have 10 seconds.

The warden counts down "ten, nine, eight, seven". All four prisoners are silent. The warden smiles,
knowing that he put the hats on in such a way that no prisoner could possibly know the color of the hat
they had on. He continues "six, five, four, thr.."

"I know the color of my hat!" one of the prisoners finally blurts out.

Which prisoner called out and why is he 100% certain of the color of his hat?

PS: This is not a trick question.

**ANSWER**:

*Prisoner B.*
**EXPLANATION**: If prisoners B and C had the same color hat on, prisoner A would have know
immediately that his hat was the other color (there are only two hats of each color). Since prisoner A
was silent, prisoners B and C must have different colored hats. Prisoner B realized this and knew that
his hat was not the same color as prisoner C, therefore his hat must be black!

Do you have a

suggestion for this puzzle (e.g. something that should
be mentioned/clarified in the question or solution, bug, typo, etc.)?