# 4 Hats and 4 Prisoners puzzle !

There are four prisoners. All four prisoners will be released, if at least one of them correctly guesses the color of the hat on his head.

They can’t speak to each other, and they can’t touch each other.

Number 1 sees number 2 and 3’s hats.
Number 2 sees number 3’s hat.
Number 3 sees only the wall.
Number 4 sees only the wall.

There are no mirrors.

They all know that there are 2 black hats and 2 white hats, and that there are four people.

They know their placement in this room is as follows:

How they will guess the color of the hat?

2 cases â€“
1. When P2 and P3 wearing same color hats.
– Easy Case , as P1 can see both P2 and P3 he can easily guess he is wearing the opposite color hat. If P2, P3 wearing white then P1 will be wearing Black. As there are 2 black and 2 white color hats.

2. When P2 and P3 wearing different color hats.
– Now P1 cannot guess the color of his hat as P2 and P3 wearing different color hats. So he will be silent.
– After Sometime P2 will realize as P1 is not shouting any color that means P2 and P3 are wearing different color hats. ( Otherwise like Case 1 he must have shouted )
– P2 can see P3 is wearing black color hat that means he is wearing white color hat.
– P2 will shout white color.

Prisoners Escaped â€“ puzzle solved!