OT: Five Hat Puzzle

[Maple Leafs]

In a small village in the middle of nowhere, three innocent prisoners are sitting in a jail. One day, the cruel jailer takes them out and places them in a line on three chairs, in such a way that man C can see both man A and man B, man B can see only man A, and man A can see none of the other men. The jailer shows them 5 hats, 2 of which are black and 3 of which are white. After this, he blindfolds the men, places one hat on each of their heads, and removes the blindfolds again. The jailer tells his three prisoners that if one of them is able to determine the color of his hat within one minute, all of them are released. Otherwise, they will all be shot. None of the prisoners can see his own hat, and all are intelligent. After 59 seconds, man A shouts out the (correct) color of his hat!

The Question: What is the color of man A's hat, and how does he know?

[QuikSand]

I hadn't see this variant before... but I love hat puzzles generally.

I don't know how to do invisible spoiler text on this board (and I guess that would depend on the skin you're using), so I'll just let it go.

[albionmoonlight]

My answer below





















If both A & B had black hats, then C would know that his is white and would shout that out. C, however, does not shout.

When C does not shout after a few seconds, A & B realize that at least one of them is wearing a white hat.

If A was wearing a black hat, therefore, B would know that his hat was white and shout that out. B, however, does not shout.

When B does not shout after a few seconds, A realizes that his hat must be white and he shouts that out at the last moment.