Who is the one? A Puzzle

[Chennaiite]

I am not sure if this had appeared in this forum before.

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 as shown in the attachment. 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 criminals 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 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?

 

[somashekar]

All are criminals and know each other how cunning they are.
Man 2 shouts out correctly.
Since he waits and man 1 does not call a while, means he and man 3 have different color hats, and so man 1 is confused.
Man 3 has black and hence his must be white.

 

[SD Aaron]

Nice job. Given that logic, could man 3 then figure the same thing and knowing man 2's color call out his own?

 

[Mikishots]

I am not sure if this had appeared in this forum before.

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 as shown in the attachment. 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 criminals 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 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?

Man 3 and man 4 cannot shout yet because they cannot see any of the others.

Man 1 is not shouting yet because he sees one of each color in front of him. He cannot be sure of his own hat color.

Man 2 can see the black hat in front of him. Since Man 1 didn't call out, Man 2 correctly surmises that his own hat isn't black; it must be white.

Man 2 shouts it out: "My hat is white". Why? He doesn't want to be hung.

 

[Ninja]

Nice job. Given that logic, could man 3 then figure the same thing and knowing man 2's color call out his own?

After man 2 calls out "White", Man 3 can then call out "Black".

Since 2 can see a Black 3, and knows that 1 did not call out...2 knows his hat is not black...

Now that 3 knows 2's hat is white from the call out, he knows his hat is black using the same logic 2 used based on #1 not calling out.

Then it is just up to #1 who has a 50/50 shot at it...#4 ran away 20 minutes ago since no one could see him behind the wall...

 

[JasonG]

#4 ran away 20 minutes ago since no one could see him behind the wall...

Brilliant. Of course all of this assumes clever criminals and if they were that clever, how did they get caught in the first place?