When Raymond Smullyan was teaching probability at Princeton, he told one class about the birthday paradox — the fact that if there are 23 people in a room, the chances are greater than 50 percent that at least two of them share a birthday. There were only 19 students in the classroom, so he said that the chance that two of them shared a birthday was quite small.

One boy said, “I’ll bet you a quarter that two of us here have the same birthday.”

Smullyan thought about that for a moment and said, “Oh, of course! You know the birthday of someone else here as well as your own!”

The boy said, “No, I give you my word that I don’t know the birthday of anyone here other than my own. Nevertheless I’ll bet you that there are two of us here who have the same birthday.”

Smullyan took the bet and lost. Why?

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