## September 9, 2009

### Prisoners and hats puzzles

4 prisoners 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 prisoners are lined up on some steps (shown above). 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 prisoners 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?

Anu said...

The second one will shout first...
Because if he was also black the first one must have shouted...

L Downing said...

Ditto, Anu.

Anonymous said...

Man 2 shouts first.

As Man 3 and Man 4 can't see anybody else, they don't really have a chance of guessing the right color of their hat.

Man 1 can see Man 2 and Man 3 but he can't say for certain the right color that he has.

Man 2 shouts the right color because he can see Man 3 and say the opposite color.

Varun said...

Man 2

bcoz 3 and 4 can not shout....

and Man 2 can see that 3rd is wearing black.... so if color of his hat was also black then Man 1 should have shouted that he(man 1) is wearing white as we have only 2 black hats.....

as man 1 did not shout so man 2 interpret that he is not wearing black and then he says its white

Anonymous said...

2 followed by 3; 1 and 4 will never know

Anonymous said...

man because he can see that man 2 has a white one and man 3 has a black and man 4 is gay so he can just guess the balls out of the answer.

v.rahmatullah said...

Is there a way to know the correct answer?

Anonymous said...

man two answers white because man one did not know, so he must have a different color than man 3. man 3 knows that man 1 must have seen two colors and answers black, because man two is white. man 1 cannot answer correctly but feals the heat of the sun on his hat and correctly guesses black, man 4 answers white.

Anonymous said...

It's not true that man 2 will shout first because of man 1 not shouting
it makes no sense because then man 2 should also shout white just because he sees the opposite colour :')

Arodiski said...

Man 1 wears a black hat and he sees a white and black hat which means he could have a black OR white hat because there are 2 black hats & 2 white hats
Man 2 sees a black hat and this means he wears a black or white hat
the fact that man 1 didn't shout means Man 2 knows Man 1 saw 2 different colours so he shouts the opposite colour which is white
problem solved

Varun Rao said...

Problem not solved. First person to be shout is Man 2... who is the next person to shout???????????

Anonymous said...

no one because Varun Rao is an idiot. Re read it. They were only told to shout out the color of their hat but there was no rule that "every one" should shout out.