A father tells his children, a boy and a girl, to play in the backyard without getting dirty, but they play in the mud anyway. Both children get mud on their foreheads. The father says, “at least one of you has mud on his or her forehead, which I asked you not to do. I’m going to take away desert tonight, but I’ll give you a chance to get your desert back.” He tells them he will ask the following question twice: do you know if you have mud on your forehead? Each child must answer honestly and simultaneously each time the question is asked. Each child can see the other’s forehead but not his or her own. If both children can correctly tell whether or not they have mud on their foreheads, they can have desert that night. What should the children do?
The solution is here.