Prisoner’s Hat Puzzle

Four prisoners are caught and are to be punished. The judge allows them to be freed if they can solve a puzzle. If they do not, they will be hanged. They all agree.

The four prisoners are lined up on some steps (shown below). They are all facing in the same direction. A wall separates the fourth prisoner from the other three.

To summarize:-
Man 1 can see men 2 and 3.
Man 2 can see man 3.
Man 3 can see none of the others.
Man 4 can see none of the others.

The prisoners are wearing hats. They are told that there are two white hats and two black hats. The men initially don’t know what colour hat they are wearing. They are told to shout out the color of the hat that they are wearing as soon as they know for certain what colour it is.

They are not allowed to turn round or move.
They are not allowed to talk to each other.
They are not allowed to take their hats off.
Who is the first person to shout out and why?

5 Responses

1. Anonymous says:

man 1

2. Anonymous says:

Man 2

• Anonymous says:

Yes, because Man 1 could see that 1 hat in front of him was black, and one was white. That means that the hat on his head could be either white or black because there are 2 of each colour. Man 2 must have noticed that Man 1 did not speak up, because if Man 2 had the same coloured hat as Man 3, black, then he would do so because that meant that the two other hats would have to be white. Since he did not say anything, Man 2 knew that his hat was white.

3. Anonymous says:

Here’s why:

– Man 3 and 4 can’t see the other hats.
– Man 1 sees a white hat and a black hat and knows his hat can be black or white.
– Man 2 sees one black hat , but if he is also wearing a black hat, it would be obvious to Man 1 that he is wearing a white hat. Since Man 1 did not shout out, Then Man 2 concluded that he himself is wearing a white hat.

4. Anonymous says:

what happen to man 1 and 4? how do they get out?