### Logic - The Perfect Logicians

**Problem:** Four persons who claim to be perfect logicians (that is their use of logic is impeccable) are given the following test. All four are placed in a room, but just before each enters the room a colored sticker is place on his forehead. While each colored sticker is visible to other members of the group, the person with the sticker has no idea about his own color. All four of the individuals are told that at least one person in the group will have a sticker that is blue in color. More than one may have a blue sticker, but at least one has a blue sticker. The participants are told that if by using their "perfect" logic, they can determine that their own sticker must be blue (even though they cannot see their own) then they must leave the room at the first opportunity. Once all the participants have entered the room, the group of four is given a couple of minutes to observe the colors of the stickers on the foreheads of the others and try to deduce whether their own sticker must be blue. After a couple of minutes, the moderator states, "If you have deduced that your sticker must be blue, then leave the room immediately!" The moderator then gives the remaining participants a couple of more minutes to see if anyone else can conclude that their sticker must be blue, and then repeats his command. He continues this process until all participants with blue stickers on their foreheads have left the room. In this particular test of perfect logic, there is one more fact that you need to know – all four participants were given blue stickers! Assuming that all four participants actually do possess perfect logic, at which call for participants who know that their sticker must be blue will the first participant leave the room? At which call will the last participant leave the room?