Every child can see everyone's muddy face except their own — can they work it out?
Several children have been playing and some (at least one) have mud on their forehead. Each child can see everyone else's forehead but not their own, and no one may say who is muddy. An adult announces, truthfully, 'at least one of you has a muddy forehead,' then repeatedly asks 'do you know if your own forehead is muddy?' At first everyone says no. What happens as the question keeps being asked?
Reveal the answer
If exactly n children are muddy, all of them suddenly say yes, in unison, on the nth round of questioning, having said no every round before. Each muddy child is watching the other muddy children hesitate; if there had been only one fewer muddy face than they can see, that other child would already have answered yes. It's a classic illustration in epistemic logic of how publicly announcing a fact everyone already privately suspects can still create new 'common knowledge' that changes what everyone can deduce.