Question

Five prisoners are arrested in a crime. But the jail is full and the police has nowhere to place them. So he comes up with this solution. He will give them a puzzle. If they succeed, all of them go free; otherwise they are transferred to another jail in another state. The police sets the 5 of them into a line and puts a hat on each one of them. He explains to them that there are exactly 3 black hats and 3 white hats. The rule for the puzzle is simple. If at least two of the prisoners can figure out the color of their own hat in 45 seconds, all of them can go free. Prisoner A can see prisoners B, C, D, and E. Prisoner B can see prisoners C, D, E. Prisoner C can see prisoners D and E. Prisoner D can only see prisoner E. Prisoner E cannot see anyone. And none of them can see their own hat. After 15 seconds one of the prisoners blurts out “I know the color of my 1 hat”. After another 15 seconds, another prisoner blurts out the same words. Which two prisoners are they and how do they find out?

Answer 1

Given :

There are five prisoners name A,B,C,D,E and six hats 3 black color and 3 white color

Prisoner A can see color of 4 hats of 4 prisoner B, C, D, E

Prisoner B can see color of 3 hats of 3 prisoner C, D and E

Prisoner C can see color of 2 hats of 2 prisoner D, E

Prisoner D can see color of 1 hats of 1 prisoner E

Prisoner E can not see anyone

Solution :

Prisoner A can see 3 hats of exact color

suppose 3 hats which Prisoner A can see are white then

Probability of white hat = P(white) + P(black)

                                      = 3/3 + 1/3  

                                      =1+1/3

It means Prisoner A knows the color of his own hat is exactly opposite of that 3 same color hats

now by hearing Prisoner A's answer

Prisoner B can know the color of 4 hats

Prisoner A, C, D, E i.e Prisoner B can see 3 hats of exact color

suppose 3 hats which Prisoner B can see are black then

Probability of Black hat =P(white) + P(Black)

                                     =1/3 + 3/3

                                    =1/3 + 1

Ans: Prisoner A and Prisoner B can answer their hats color