Caskets and suitors
Back when Bellini and Cellini, the casket-makers, were just starting to become famous and before their children were yet born, an Italian noble wanted to test his daughter's suitor. He commissioned two caskets and put a golden ring in one of them. If the suitor could find the golden ring, he could marry the daughter.
As always, Bellini puts only true inscriptions on his caskets, and Cellini puts only false inscriptions on his.
The suitor was confronted with two beautiful golden caskets. The noble gave his sworn word of honor that the golden ring was in exactly one of them.
Casket A read: The golden ring is in this casket.
Casket B read: Exactly one of these two caskets was fashioned by Cellini.
To win the noble's daughter, which casket should the suitor choose?
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Assume the statement on casket B is true. Then it was fashioned by Bellini, and so casket A must be the exactly one casket fashioned by Cellini.
Now assume the statement on casket B is false. Then it was fashioned by Cellini. Therefore, casket A cannot be made by Bellini, because that would make the statement on casket B true, so A was made by Cellini.
So in either case, A was fashioned by Cellini. So the statement on A is false. Therefore, the ring is in casket B.