Question

4 prisoners are all going to be shot in 60 seconds unless one of them correctly calls out the colour of his own hat. If he's right everyone is free, but everyone gets shot if he's wrong. They are standing in the below configuration. They know how they are positioned and they know there are 2 black hats and 2 white hats. But they don't know the configuration of the hats. They can't communicate, they can't turn around and they can't see the colour of their own hat. So prisoner 1 can see 2 and 3. Prisoner 2 can see 3. Prisoner 4 is behind a wall so nobody can see him or be seen by him. No shadows, reflections, etc. After 45 seconds, someone calls out the correct colour of his hat. Who is it and how does he know he is right?

Answer 1

Hey there!

There are 4 prisoners in all. And each of them is wearing a hat.
There are 2 black hats and 2 white hats in all.

Prisoner 1 can see 2 , 3 prisoners hats but not his own .

Prisoner 2 can see only hat of 3 , Prisoner 4 can't see anyone.

Now, The person who would probably say the answer is Prisoner 2 .

Reason : If The prisoner 2 & 3 are wearing same hats ( Either of black or white) , Prisoner 1 can determine his hat and say aloud. But It is given after 45 seconds, a person told.

So, If prisoner 1 could have determined, He would have told before 45 seconds.

So, One conclusion Prisoner 2 can make is that Prisoner 3 & him are wearing different hats.

As he can see the colour of hat on Prisoner 3 head, he will say the other colour as the colour of his hat.

Hence, Each of them would be safe

Answer 2

Given:

4 prisoners

2 black hats

2 white hats

Prisoner 1 can see prisoners 2 and 3.

Prisoner 2 can see prisoner 3.

Prisoner 4 is behind a wall and so nobody can see him.

The prisoner should identify the color of the hat he is wearing correctly so that everybody is saved or everybody will be shot in 60 seconds if he is wrong.

Conditions:

No communication.

Solution:

• Prisoner 1 can determine the color of his hat and say aloud if  prisoners 2 and 3 are wearing same hats.

If not,

• Assuming that he and prisoner 3 wearing different hats, Prisoner 2 will answer the color that is opposite to prisoner 3's hat.

So, prisoner 2 calls out the correct color of his hat.