# Prisoner’s and hats interview puzzle

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Suppose there are 4 prisoners named W, X, Y, and Z. Prisoner W is standing on one side of a wall, and prisoners X Y and Z are standing on the other side of the wall. Prisoners X, Y, and Z are all standing in a straight line facing right – so X can see prisoner Y and Z, and Y can see prisoner Z. This is what their arrangement looks like:

W(cann’t see anything) || X(can see both Y&Z) Y(can see z) Z(cann’t see anything)
Where the “||” represents a wall. The wall has no mirrors. So, prisoner W can see the wall and nothing else.

There are 2 white hats and 2 black hats. Each prisoner has a hat on his head. Each prisoner can not see the color of his own hat, and can not remove the hat from his own head. But the prisoners do know that there are 2 white hats and 2 black hats amongst themselves.

The prison guard says that if one of the prisoners can correctly guess the color of his hat then the prisoners will be set free and released.

Question :Figure out which prisoner would know the color of his own hat?

Note that the prisoners are not allowed to signal to each other, nor speak to each other to give each other hints. But, they can all hear each other if one of them tries to answer the question. Also, you can assume that every prisoner thinks logically and knows that the other prisoners think logically as well.

anikam Expert Asked on 22nd August 2015 in

Clearly prisoners W and Z can not immediately know anything since neither of those prisoners can see any of the other prisoners. So, let’s instead focus on prisoners X and Y.Suppose we have the following scenario with the arrangement of different hat colors:

W(B) || X(B) Y(W) Z(W)

In the scenario above, prisoner X will clearly see that Y and Z both have white hats, and logically deduce that he must have a black hat since there are 2 white hats and 2 black hats all together – and he would be correct. Very simple! And this simple logic would also apply to this scenario as well:

W(W) || X(W) Y(B) Z(B)

But let’s consider another example:

W(B) || X (W) Y(B) Z(W)

In this case Z cann’t say what colour hat he is wearing .Y also knows that if the colour’s of Y and Z hats were same he would have shouted immediately.So he will guess that he and Z are wearing opposite color hats..So Y will wait till the time is about to over and then he will shout the opposite colour which Z is wearing.

pnikam Expert Answered on 22nd August 2015.

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