A Common Joke About Common Knowledge

If you enjoy this joke (which is discussed here, and comes from the folks at Spiked Math Comics) as much as I do, you might be a gearhead.

It illustrates one of the many surprising and subtle impacts of common knowledge. Yale's John Geanakoplos provides an even more perverse version of the bar cartoon, in this incredibly helpful chapter :

Imagine three girls sitting in a circle, each wearing either a red hat or a white hat. Suppose that all the hats are red. When the teacher asks if any student can identify the color of her own hat, the answer is always negative, since nobody can see her own hat. But if the teacher happens to remark that there is at least one red hat in the room, a fact which is well-known to every child (who can see two red hats in the room) then the answers change. The first student who is asked cannot tell, nor can the second. But the third will be able to answer with confidence that she is indeed wearing a red hat.