Who Will Shout First?
Four criminals 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 agree.
The four criminals are lined up on some steps (shown in the picture). They are all facing in the same direction. A wall separates the fourth man from the other three.
So, 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 criminals are wearing hats, whose colors are depicted in the picture. They are told that there are two white hats and two black hats. The men initially do not know what color 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 color it is.
- They are not allowed to turn around 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?
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Relevant wiki: K-level thinking
If man 1 sees men 2 and 3 are wearing the same colour hats he would know the color of the hat he is wearing. For example, if man 1 see men 2 and 3 are wearing black hats, then he knows he can only be wearing white hat. Likewise, if he see men 2 and 3 are wearing white hats, he must be wearing a black hat. He does not shout because he sees men 2 and 3 are wearing different colour hats. Man 2 knows this fact -- that is men 2 and 3 are wearing different colour hats -- and he sees that man 3 is wearing black hat, he knows he is wearing white. Therefore, man 2 is the first to shout.