Question

This is a famous Prisoners and Hats Puzzle.,4 prisoners are caught and are to be punished. The Judge allows them to be freed if they can solve a puzzle. If they do not, they will be hung. They agreed.,The 4 prisoners are lined up on some steps (as shown). They are all facing in the same direction. A wall separates the fourth man from the other three.,So to summarize:- Prisoner 1 can see Prisoners 2 and 3. Prisoner 2 can see Prisoner 3. Prisoner 3 can see none of the others. Prisoner 4 can see none of the others.,The prisoners are wearing hats. They are told that there are two white hats and two black hats. The men initially don't know what colour hat they are wearing. They are told to shout out the color of the hat that they are wearing as soon as they know for certain what colour it is.,They are not allowed to turn round or move. They are not allowed to talk to each other. They are not allowed to take their hats off.,Who is the first person to shout out and why?

Answer 1

This answer actually depends. Prisoner 1 can see both 2 and 3, as well as their hats. Meaning that if both of them are wearing the same colour, his is definitely the opposite colour. In this case prisoner 1 is the first to shout out.

On the other hand, if 2 and 3 are wearing different hats, 1 can say nothing. In such a case, 2 can deduce that he and 3 are wearing different hats (judging by 1's silence). In this way, 2 can look at 3's hat and conclude that he's wearing the opposite colour. So in this case, prisoner 2 shouts out first.

Answer 2

Answer:

This is a famous Prisoners and Hats Puzzle.,4 prisoners are caught and are to be punished. The Judge allows them to be freed if they can solve a puzzle. If they do not, they will be hung. They agreed.,The 4 prisoners are lined up on some steps (as shown). They are all facing in the same direction. A wall separates the fourth man from the other three.,So to summarize:- Prisoner 1 can see Prisoners 2 and 3. Prisoner 2 can see Prisoner 3. Prisoner 3 can see none of the others. Prisoner 4 can see none of the others.,The prisoners are wearing hats. They are told that there are two white hats and two black hats. The men initially don't know what colour hat they are wearing. They are told to shout out the color of the hat that they are wearing as soon as they know for certain what colour it is.,They are not allowed to turn round or move. They are not allowed to talk to each other. They are not allowed to take their hats off.,Who is the first person to shout out and why?