The Prisoners and the Hats

Dec 26, 2020

RAY: The warden admits three prisoners into his chambers. He tells them, "One of you fellas is going to have a chance to get out. Here's the dealI'm going to blindfold all of you, then I'm going to put hats on your heads. I have three white hats and two black hats. Each of you is going to get a hat. You have to figure out which color hat you have to get released."

He blindfolds them and puts a hat on each prisoner. They're led out of the room in single file. When the blindfolds are removed, the guy in the back can see the two people in front of him, the guy in the middle can see the one guy in front of him, and the guy in front can see nobody.

They can't turn around and they have to walk around the prison in this order. And they walk around the prison, stopping outside the warden's office. The warden says to the fellow in back, who can see the two people in front of him, and their hats, "Can you tell me what color your hat is?

Don't forget, there are three white hats and two black hats available. The fellow in back says nothing. He doesn't know.

The fellow in the middle is asked the same question. He is unable to answer.

The guy in the very front, who can see no hats, knows. He says, "I can identify the color of my hat."

How does he know?



RAY: His hat was white. He knew because the other two guys didn't know what color hats they were each wearing. Because the back prisoner said nothing, he must have seen either two white hats or a black and a white hat in front of him.

Now, if the prisoner in the middle had seen a black hat in front of him, he would have known that he was wearing a white hat. Why's that? Because if he had a black hat on, then the guy who was in the back would have known that his own hat was white, and he would have spoken up when he had his chance.

Because the prisoner in the back and the middle didn't say anything, then the prisoner in the front knew he had a white hat.

Get the Car Talk Newsletter