Answer to Last Week’s Brain Teaser

Brain Teaser If the first prisoner had seen two black hats on the other two prisoners, he would have know that he was wearing a white hat as there were only two black hats to begin with. As he didn’t know what color hat he had, this means the other two prisoners must either have been both wearing white hats or one wearing a white hat and the other a black one.

The second prisoner would know this once the first prisoner is unable to say what color his hat is, i.e. the second prisoner now knows that either both he and the blind prisoner are wearing white hats or one of them is wearing white and the other black. So if the blind prisoner was wearing a black hat, the second prisoner would know that he must be wearing a white hat.

As the second prisoner couldn’t work out what color of hat he was wearing, this told the blind prisoner that he must be wearing a white hat (if the blind prisoner was wearing a black hat, the second prisoner would have been able to deduce that he was wearing a white hat). The question: If you missed the question last week, here it is… The Blind Prisoner There were 3 prisoners in the King’s dungeon. Two of them had perfect vision but the third prisoner was completely blind.

One day the King gathered the prisoners together and said to them, “I have 5 hats. 2 of the hats are black and 3 are white. I will blindfold each of you and then put one of the hats on each of your heads. I will then put the remaining two hats in another room. Next, I will remove your blindfolds. At this point you may look at your fellow prisoners but may not speak to them. The person that can tell me the color of the hat on his head will go free. Do not insult me by guessing, however, for if you guess and are wrong, you shall be executed.”

The hats were then placed on the prisoners’ heads and the blindfolds were removed. The King then spoke to the first prisoner, a fully sighted man. “What is the color of the hat on your head” The prisoner looked around carefully but finally, not wanting to risk death by guessing, said that he did not know.

The King then spoke to the second prisoner, the other fully sighted man. “What is the color of the hat on your head” This prisoner also looked carefully at the hats upon the heads of the other two prisoners, but finally admitted that he also did not know. At this point the King turned and began to walk away, assuming that the third prisoner who was blind could not know possibly the answer to the riddle.

But then the blind man spoke. “Excuse me, my lord,” he said, “but I am certain my hat is white.”

Surprised, the King turned around. He saw that the blind man was correct and ordered him to be freed at once.

How did the blind prisoner know the color of his hat?