Imagine a windowless room with no mirrors or reflective substances of any kind. Just four walls of drywall. In the middle of the room are three desks set up one behind the other in single file. There is a man sitting at each desk. For reference purposes, we’ll label the men, from front to back, A, B, and C. Now, by the way they are positioned in the room, man A can’t see anybody, man B can see A but not C, and man C can see both A and B. Now…
…a fourth man walks into the room. He reaches in his bag presents the men with five hats, three of the hats are red, two of them are white. He tells the men,
“I’m going to blindfold all three of you, put one of these five hats on each of your heads, and then hide the remaining two hats in my bag.”
So he proceeds to do just that — he takes out three blindfolds, blindfolds all three men, puts one of the five hats on each of their heads, and then hides the remaining two hats. He then says to the men,
“I am going to remove your blindfolds. When I do, you are not allowed to turn around or talk to each other.”
He then removes the blindfolds and says,
“The first man that can stand up and tell me what color hat he has on his OWN head will get a million dollars. If you stand up and guess wrong, I’ll cut your head off. In other words, no guessing.”
After a few minutes of silence, man A stood up and stated what color hat he was wearing. He was correct.
What color hat was man A wearing, and how did he know?