100 people are in a room.   All 100 of them are perfect logicians. They are told that at least one person in the room has blue paint on their forehead. They are told that once you deduce that you have blue paint on your forehead, the next time that the lights are turned off, leave the room.   All 100 people have actually had their foreheads painted blue (but of course, each of them don’t know this at this point – they can only see the other people’s foreheads).  The light is turned off, then on, then off, on, etc.  What happens?     Answer: So each person sees…

There are 3 people placed in a room.  They all have perfect logic.  The 3 people are told by a host that a number has been written on each of their foreheads.  Each of the 3 numbers are unique, they are all positive, and they relate to each other such that A + B = C (i.e. one is the sum of the other two).  In the room, each person can only see the other two people’s numbers, as they cannot see their own foreheads.   Suppose you are one of the 3 and you see one person with “20” on their forehead and the other person with “30.”  The…