Prisoner P4 is put behind a screen. The arrangement looks like this: The ‘||’ is the screen. The jailer tells them that there are two black hats and two white hats; that each prisoner is wearing one of the hats; and that each of the prisoners is only able to see the hats in front of them but not on themselves or behind.
Why are four prisoners wearing black and white?
A is in the same situation as B, where he can’t see anyone and can’t determine his own hat color. Since A, B, and D are silent, that leaves C. C knows he is wearing a black hat because if D saw that both B and C were wearing white hats, then he would have answered.
How are four criminals wearing black and white hats?
Since 1,3 and 4 are silent, that leaves 2. 2 knows he is wearing a White hat because if 1 saw that both 2 and 3 were wearing Black hats, then he would have answered. But since 1 is silent, 2 knows that he must be wearing a black hat as he can see that 3 is wearing a white hat. Loading…
How to deduce the color of a prisoner’s hat?
Likewise, if both 2 and 3 had black hats on, 1 would know he’s wearing a white hat. BUT, if 2 and 3 had different colored hats on, then 1 cannot logically deduce the color of his own hat. FROM THAT LOGIC ABOVE, 2 knows that the color of his own hat is different to the color worn by the person ahead of him (prisoner 3).
How to solve the black and white hats puzzle?
To make it more interesting three prisoners stand in a line facing a brick wall. The prisoner at the back, A, stands on a box and can see both of the prisoners in front of him, B and C. Prisoner B stands on a smaller box and can only see prisoner C, who in turn can only see the wall.
Who are the 3 prisoners and 5 hats?
There were three prisoners in certain jail, one of whom had normal sight, one of whom had only one eye, and the third of whom was completely blind. The jailer liked to play tricks on his prisoners, so one day he brought them all three out and had them stand in a line. He then showed them five hats, three white and two red, which he hid in a bag.
Are there two black hats and two white hats?
The jailer tells them that there are two black hats and two white hats; that each prisoner is wearing one of the hats; and that each of the prisoners is only able to see the hats in front of them but not on themselves or behind. Prisoner P1 can see P2 and P3. Prisoner P2 can see P3 only.
