How did encounter with the sphinx save thebes?

According to Greek mythology, it was not a sphinx that saved Thebes, but it was the riddle of the Sphinx that was key to salvation of the city. The presence of the Sphinx outside Thebes posed danger to the city and its people as it challenged anyone who passed by to solve its cunning riddles.

The riddled propounded by the sphinx was: "What creature walks on four legs in the morning, two legs at noon, and three legs in the evening?"

Oedipus, a wanderer who was not aware of the Sphinx's torment resolved the riddle by answering "Man". As a crawling infant, man walks on four legs; as an adult, he walks upright on two legs; and in old age, he supports himself with a cane, effectively using three legs.

Upon correctly answering the riddle, the Sphinx was vanquished, and Thebes was relieved from its misery and threat.