In this paper I propose to deal with some difficulties in Sophocles' Oedipus Tyrannus, of which some have been noticed before, others I think have not. I am going to propose an unorthodox explanation, not through any love of unorthodoxy, but in the spirit of Oedipus himself, who when faced with a puzzle could not resist following a fact to its logical conclusion. The Sphinx's riddle was not, after all, a very hard one; and Oedipus doubtless grew tired of being praised for ingenuity. My thesis too disclaims that dubious quality. Ingenuity is what many of us have been using all our lives to explain difficulties in this play which may after all be insoluble.