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Dupin meets the narrator at a library in Paris; the two become friends.
Dupin moves into the mansion that the narrator rents.
The two start spending their daylight hours reading and thinking inside and their nighttime hours strolling the streets of Paris making observations about other people who happen to be walking by.
Dupin is particularly good at this game, as he proves it one evening by guessing what the narrator is thinking after several minutes of silence.
After reading about the brutal killings of Madame L'Espanaye and her daughter, Dupin decides to investigate on his own (with the narrator in tow).
Dupin owes a favor to the current police suspect, Alphonse de Bon, so he pulls a few strings and gets in to the scene of the crime to try and get Le Bon off the hook.
At the scene, Dupin examines the corpses, the room, the house, and the larger neighborhood carefully.
After a day of contemplation, he tells the narrator that he has solved the crime.
He runs through his chain of reasoning to prove to the narrator that the killer is an escaped Ourang-Outang from Southeast Asia.
This ape came to Paris in the care of a sailor, Dupin says. (Our detective thinks so because he found a length of ribbon probably used to tie back long hair favored by sailors, at the scene of the crime.)
To draw out the sailor, Dupin has put an ad in the local paper advertising a found Ourang-Outang.
The sailor comes to meet Dupin and the narrator at their mansion to ask after the Ourang-Outang. Dupin takes this opportunity to ask him what he knows about the murders in the Rue Morgue.
The sailor, realizing that Dupin already knows everything, confesses. The ape is his, recently brought back from Borneo. It escaped from him one night with his razor in hand, climbed into the open window of the L'Espanaye apartment, used the razor to slash Madame L'Espanaye's throat, and strangled Mademoiselle L'Espanaye with its bare hands before fleeing through the still-open window.
All is exactly as Dupin had deduced from the appearance of the room.
He uses the sailor's evidence to get Le Bon off the hook.
Dupin also manages to irritate the police chief with his success against all odds.
Dupin laughs off the police chief's disapproval: the police chief is smart enough in his own way, but he's not capable of thinking as creatively as Dupin.