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# The puzzle of the black and white hats

Four men are lined up on some steps. They are all facing in the same direction. A wall seperates the fourth man from the other three.
So 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 men are wearing hats. They are told that there are two white hats and two black hats. The men initally 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.

They are not allowed to talk to each other.

So the question is -
Who is the first person to shout out and why?

Solution

The man who calls out is Number 2.
Why? Well, I'll tell you.

After a short time, Number 1 has not shouted out what colour hat he is wearing. Because of this number 2 knows that he cannot be wearing the same colour hat as the person in front of him. If he was then number 1 would see two black hats and would therefore know that his hat must be white.

Armed with the knowledge that :-

He isn't wearing the same colour hat as the man in front.
The man in front is wearing a black hat.
number two can confidently shout out that the hat he is wearing is white.
Easy wasn't it!