Hats Problem

4 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 hung. They agreed. The 4 criminals are lined up on some steps (shown in picture). They are all facing in the same direction. A wall seperates the fourth man from the other three.

To Summarise

• 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. 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 colour 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.

Now the question is "Who is the first person to shout out and why?

Answer)

Man 1 will shout first. If Man1 will not shout then Man 2 surely shouts.

Reason: Man 1 can see the other two criminals? hats. If the hats are same color then he told his hat is opposite color of remaining two hats. So he shouts first. If Man 1 does not shout, it means that the hats of Man 2 and Man 3 are of different color. So Man 2 sees the color of Man 3 hat and he tells that the color of his hat is opposite to the color of Man 3 Hat.