Sphinx

The Sphinx (Σφίγγα in Ancient Greek), also known as "The Master of Riddles," is a creature with the head of a woman and the body of a lion. She is considered an "Exampler Monster", Percy describes her as looking like his choir teacher, and that she "would be pretty, but she wore too much makeup."

History
The Sphinx is said to have guarded the entrance to the Greek city of Thebes, and to have asked a riddle of travelers to allow them passage. The exact riddle asked by the Sphinx was not specified by early tellers of the stories, and was not standardized as the one given below until late in Greek history.

It was said in late lore that Hera or Ares sent the Sphinx from her Ethiopian homeland (the Greeks always remembered the foreign origin of the Sphinx) to Thebes in Greece where she asks all passers-by the most famous riddle in history: “Which creature in the morning goes on four legs, at mid-day on two, and in the evening upon three, and the more legs it has, the weaker it be?” 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. By some accounts (but much more rarely), there was a second riddle: "There are two sisters: one gives birth to the other and she, in turn, gives birth to the first." The answer is "day and night" (both words are feminine in Greek).

Bested at last, the tale continues,that 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 affect the transition between the old religious practices, represented by the death of the Sphinx, and the rise of the new, Olympian gods.

The Sea of Monsters
A Sphinx is not seen, but it is said that Tyson was attacked by one on 72nd Street in New York.

The Battle of the Labyrinth
Percy, Annabeth, and Grover run into the Sphinx while navigating the labyrinth. She asks the group to play Answer That Riddle, a gameshow type trap where if they lose they will be eaten. Rather than the riddles however, the Sphinx asks a series of random trivia questions that at first confuses Annabeth as she wants to know what happened to the riddle about man. The Sphinx says that everyone knew the answer so she changed the questions. Annabeth gets fustrated because the questions are so easy, she feels they're an insult to her intelligence and refuses to answer the Sphynx's 'riddles.' The Sphinx then attacks them, but is trapped by Grover's woodland magic. What happens to her afterward is unknown, though it is very likely that she would have been suffocated by the plants. The last the group heard of her, she was wailing about all the test papers she would have to correct by hand as her grading machine had been destroyed.