The Sphinx is said to have guarded the entrance to the Greek city of Thebes, and to have asked a riddle of travellers to allow them passage.

She asks all passersby the most famous riddle in history: "Which creature walks on four legs in the morning, two legs in the afternoon, and three legs in the evening?" She strangled and devoured anyone unable to answer.

Oedipus solved the riddle by answering: Man—who crawls on all fours as a baby, then walks on two feet as an adult, and then walks with a cane in old age.

There was a second riddle: "There are two sisters: one gives birth to the other and she, in turn, gives birth to the first. Who are the two sisters?"

The answer is "day and night" (both words are feminine in Greek). This riddle is also found in a Gascon version of the myth and could be very ancient.

Bested at last, the tale continues, the Sphinx then threw herself from her high rock and died. An alternative version tells that she devoured herself. Thus Oedipus can be recognized as a "liminal" or threshold figure, helping effect the transition between the old religious practices, represented by the death of the Sphinx, and the rise of the new, Olympian gods.

Find out more:
http://en.wikipedia.org/wiki/Sphinx#The_Riddle_of_the_Sphinx