Riddle by Jeff Rosenspan

[JeffRosenspan]

Three men sit in chairs (#1, #2, and #3), in a straight line, all facing north, one behind another. Each man will have a hat placed on his head. No one can see his own hat at any time. The man in Chair #1 is in the front, he cannot see anyone else. The man in Chair #2 is behind Chair #1 and he can only see the man in Chair #1. The man in Chair #3 is behind Chair #2 and he can see both men in Chairs #1 and #2.

On the table, there are three blue hats and two white hats. Each of the three men will be randomly given one of those five hats and two will be discarded. No one will know the color of the discarded hats or the color of his own hat. The first person to use logic to determine what color hat is on his own head wins.

After five minutes, the man in Chair #1 stands up and says, "I win. I know the color of my hat."

The riddle is: What color was it, and how did he figure it out?

- Jeffrey Rosenspan

[Fou-Lu]

Blue.

This is a classic put yourself in their shoes logic riddle. Even without vocal (which is the more common of the approaches: #3 says I'm not sure, #2 says the same; #1 could even be blind as what they can see wouldn't matter to the riddle) the implied logic from chair #1 is that neither #2 nor #3 can accurately gauge their correct color.
For this to happen, with 3x blue and 2x white, we know what #3 can only see that #2 and #1 wear either:

1. #2 blue, #1 blue
2. #2 white, #1 blue
3. #2 blue, #1 white

#3 can only determine their colour if both #2 and #1 were wearing white. Therefore we know that both #2 and #1 are not wearing white.

Using the same implied logic, since #2 also cannot determine their colour, and #2 knows that #3 can only see one of the possible combinations above, the only possible colour that #1 can be wearing so #2 can accurately determine their colour is option number 3. Since #2 also cannot determine their colour, this therefore results in #1 wearing blue.

This is one of my favorite riddles as it is difficult to determine until you put yourself in their shoes one at a time.