# The hat puzzle

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 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. 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?๐

## Replies

• anuragh27crony
dude..pics are not visible..plz check the links
• Mayur Pathak
anuragh27crony
dude..pics are not visible..plz check the links
๐กI know. I'm trying to fix the problem. Just wait for some time.
• Mayur Pathak
Biggie fixed it. Check now?
• anuragh27crony
srry dude...for making you angry :smile:
yeah it's fixed
• Differential
Second Man after waiting for sometime will shout first and say right answer. Here is why....
Had M2 and M3 have got same color, M1 would have easily figured out his own color and shouted. But He's not doing so, means M2 (myself) and M3 have got different colors. Now I can see what M3 has got. So my hat-color is diff than what M3 has got.

--Differential
• anuragh27crony
@Differential....
The solution is not complete.....
Let's go by yor words.... then it leaves M1 in confused state whether my hat is Black or White..... and so as the position of M3..

1. If M1 has shouted worng (White Hat)...... since two blacks are left then M3 and M4 shouts Black...
2. If M1 has shouts right (Black Hat)...... since one black and one white.. which leaves M3 and M4 confused...
so..on goes with M4 if M3 speaks right or wrong....
• Differential
anuragh27crony
@Differential....
The solution is not complete.....
Let's go by yor words.... then it leaves M1 in confused state whether my hat is Black or White..... and so as the position of M3..

1. If M1 has shouted worng (White Hat)...... since two blacks are left then M3 and M4 shouts Black...
2. If M1 has shouts right (Black Hat)...... since one black and one white.. which leaves M3 and M4 confused...
so..on goes with M4 if M3 speaks right or wrong....
๐
The solution is based on an assumption that all of the men are intelligent and no one lies.

Also its asked that who will shout first, not about all of them !!!

Who is the first person to shout out and why?
--Differential
• Norvicute
Any body can shout first ๐ its a matter of decision. yeah lets assume all men are intelligent.

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

Man 1 is not shouting yet because he is confused on what he sees he seing white and black hat.

If man 1 is not shouting yet man 2 he thinks that if man 3 wearing black and he is wearing black as well then man 1 would shout it fast that he is wearing white hat but he didnt. therefore man 2 can conclude that he is wearing white hat.

Therefore man 2 shout first the right color of hat he is wearing.

๐
• Mayur Pathak
Let me declare. Differential's and norvicute's arguments are correct. ๐
• gohm
All the hats have brims and the brim would be the same color as the cap part of the hat. You can see the brim while wearing the hat without moving while wearing a hat so therefore they all would shout out... ๐
• Sanjeevjmt1

not any man can shout anything .. its a matter of their life

You are reading an archived discussion.

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