The Question of Hats Is a Life or Death Issue

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Problem

Three inmates are serving life sentences in a prison in a faraway part of South America. The guards decide to play a game with the inmates as a way to keep the inmates occupied.

In the trunk, they show the inmates three black hats and two white hats, showing that there are five total hats in the trunk. Guards force the inmates to sit in chairs and line them up in a three-row row so that the inmate at one end of the line can see two inmates in front of him, while the inmate at the other end can only see the wall of the prison.

The guards put a hat on each of the prisoners’ heads and blindfold them. They then remove the blindfolds and tell the inmates that if they correctly identify the colour of the hat they are wearing, they will be released—but if they guess incorrectly, they will be shot dead. As a result, the inmates are unable to tell what colour hat they are wearing.

There is an initial question for each inmate: “What colour hat do you wear?” He claims to be clueless. The man in the middle is also stumped when pressed with the question. The prisoner at the head of the line is freed when the guards ask him what colour hat he is wearing.

In what way did he know the colour of the hat he was wearing?

Hint

Assume the role of the prisoner at the end of the queue. Look around. Then act like you’re the one in the middle of the line, with no one to help you out.

Solution

So, what colour is the inmate’s cap now that he’s free? Black. Here’s how he found out.

Begin with the first inmate who responds. He’s in the rear of the line, with a clear view of the two inmates in front of him, yet he has no idea what colour hat he’s wearing. There are three black hats and only two white hats, thus he would have realised he was wearing a black hat if he had seen white hats on both of the convicts in front of him. As a result, we can deduce that he does not notice the two white hats in front of him.

The fact that the first prisoner failed to solve the riddle informs the second prisoner in line, who is in the middle of the line, that he and the man ahead of him cannot both be wearing white hats. There are three alternatives left.

 

A) He and the man in front of him both wear black caps.

B) The man in front of him wears a white hat, whilst he wears a black one

C) He is wearing a white hat whereas the man in front is wearing a black one.

If the man in the middle had seen the man in front of him wearing a white hat, he would have recognised that option B was accurate, proclaimed that he was wearing a black hat, and went away. We know he must see a black hat in front of him because he can’t figure out what colour hat he’s wearing since he can’t figure out what colour hat he’s wearing (choices A and C are both possibilities).

Consider the three options from the standpoint of the man in the lead. He has no idea which of the other options, A or C, is correct. He must, however, be wearing a black hat in both scenarios. He is set free, but the other two remain incarcerated. It’s a harsh and chilly world out there.

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ANSWER: I AM THE BEGINNING OF THE END RIDDLE SOLVED!