The lady, the tiger, and two contradicting signs
A king's dungeon has two doors. Behind one waits a lady; behind the other, a hungry tiger. Door One reads: "IN THIS ROOM THERE IS A LADY, AND IN THE OTHER ROOM THERE IS A TIGER." Door Two reads: "IN ONE OF THESE ROOMS THERE IS A LADY, AND IN ONE OF THESE ROOMS THERE IS A TIGER." The king says exactly one of the two signs is true. Which door should the prisoner open to find the lady?
Reveal the answer
Door Two. If Door One's sign were true, Door Two's sign would automatically be true as well, but only one sign may be true, a contradiction. So Door One's sign is false, meaning Door One holds the tiger and the lady waits behind Door Two. It's one of the opening puzzles in Raymond Smullyan's 1982 collection, itself a nod to Frank R. Stockton's 1882 short story of the same name.
— Raymond M. Smullyan, The Lady or the Tiger? and Other Logic Puzzles — Alfred A. Knopf, 1982