### Four prisoners wearing black and white hats

• There are four prisoners. All four prisoners will be freed, 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:

Can the four prisoners be freed? If so, how?

Do they get to discuss this beforehand? Why not just all say "white" (or all "black")?

Do the prisoners know the configuration of the other prisoners? 2 cannot use the silence of 1 as extra information unless 2 knows which way 1 is facing.

• 4 can't see the other three due to the wall so he can't guess. 3 also can't see due to the wall. I eliminate 4 and 3. For 2, he knows 3 is wearing white hat. But how could he knows he is wearing black? For 1, if 2 hat is white then 1 hat is black. But if 1's is black and 2's is white then, he would be able to know. If the two in front have white hats then, he will answer first and say 'Mine is black'. But properly, 2 is aware of 1's hesitation , 'Ah~ 1 is also white'.Then, 2 will answer 'Mine is black'. So the answer is 2.

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@Rubio accepted with no votes ... weird ...

@Randal'Thor Very weird indeed, especially since this is objectively a worse answer than the others, of Which I can confirm 2 of them say exactly this but better worded, and they also say more about the other possible configurations.

Nothing in the question suggests they can hear each others answers. In fact, given that they can't speak to each other, this would suggest that they have to answer silently, e.g. by writing their answer down and passing it to the jailer.