Oedipus destroyed the sphinx when he answered the question "What walks on four legs in the morning, two legs at noon, and three legs in the evening." The answer: man.
The sphinx threw herself to her death and Oedipus entered Thebes triumphant. There he was given Jocasta, Queen of Thebes, as his reward for ridding the city of the sphinx. And that's where the problems begin. (artist: Gustave Moreau, painting courtesy of artmagick.com).