Dupin (Poe) reminds me of a depressed and drinking Sherlock Holmes. Despite his drinking and his brusque demeanor, Poe does have the ability to notice details and connect the dots, so to speak. It seems to me that there is not one clear moment when he has the entire puzzle figured out, but there are a series of small discoveries beginning with the first which lead to a quick solution. That moment is when he discovers how close the apartment building is to the building next door. From there, it all begins to fall into place for him.