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Case Description: Creon was seriously sweating it before Oedipus came along. See, Creon had been left in charge of Thebes, while his brother-in-law, King Laius, went on a walk-about. Just about that same time, a giant lion with the head of woman showed up who called herself the Sphinx. Her favorite thing to do was sit on a rock near Thebes and ask people riddles. When they couldn't answer, she ate them. This wasn't good news for Creon, but things got worse when the word came that Laius had been murdered by some highwayman. Creon totally freaked out and declared that whoever could solve the riddle of the Sphinx could get married to his sister, Jocasta, and have the throne of Thebes. Creon was completely relieved when a dude named Oedipus came along, solved the riddle, got rid of the Sphinx, married Jocasta, and took the throne of Thebes off his hands.
Addendum: Giving Oedipus the throne turned out to be a major headache for Creon, because unbeknownst to anybody, Oedipus was actually the son of Laius and Jocasta. That means Creon married his sister off to her own little boy.