Puzzle thread? Puzzle thread.

[Darkmatters]

D'oh!!! Actually you did say they both took some time: "After some time, the first man says that he does not know. Some more time passes, and the second man says that he does not know, either." I assumed that was an important detail. You're right the first guy could only know his if the other 2 are blue, so you can't eliminate all 3 being red until after the 2nd guy answers - I should have said the first guy proves the other 2 aren't both wearing blue and the second proves that there's only 1 blue fez in play. Also of course my answer depends on them knowing how many red and blue hats were in the box, which you never stated.