Three university maths students are taken from their lecture and sat in a room facing each other. The organiser comes in and tells them...
"I'm going to paint a red or a white dot on your forehead. If you see any red dots at all you must put your hand up. If you see only white dots, you must leave it down."
The winner is the first person to work out what dot they have on their forehead.
The organiser paints only red dots on their foreheads. They all see two red dots on the two foreheads opposite and consequently all put their hands up.
After a while for thought, one of them shouts out to the organiser and correctly tells her that he has a red dot on his forehead. How did he work it out?
There's no trick, no info I haven't told you, there is no mirror, nobody tells anybody, nobody saw their own dot, the red paint feels the same, nobody saw that the organiser only had one pot of paint or one brush, the individual just worked it out. All the info is there in the question.