Deduction by Human Behaviour and Psychology
What happened?
Dupin simply found that the letter was not hided in the secret area of the hotel; the Prefect had wrong assumptions of the location of the letter. The Prefect thought the purloined letter must be hidden since the theft did not want to disclose it, therefore, the police searched every inch in the hotel. The prefect did not lie, it is the common logic of human.
Use of Deduction by Human Behaviour and Psychology
Dupin tried to be empathetic to the theft, the Minister, who was a poet. Therefore, he noticed that somebody ingenious like him would have known that the police must search all the secret areas in the hotel. Then he could only hid the letter in a highly visible place. Dupin also explained his ratiocination with the story of The smart boy who was able to guess to number of marbles in his open’s hand. It was not merely because he was smart or lucky. It was because you had to know who was your opponent, a cunning one or an asinine one. Dupin would first determine the qualities and personalities of his opponent by observation. Then he may penetrate their patterns of committing crimes and motives so as to identify them.