How does the author use foreshadowing in The Purloined Letter?

Although neither the narrator nor the Prefect picks up on it, Dupin gives them the solution to the case of the purloined letter twice before he explains how he does it. In the beginning, after the Prefect has introduced the mystery but before he has given any details, he says about his police force that "we have all been a good deal puzzled because the affair is so simple, and yet baffles us altogether." Dupin notes that "perhaps the mystery is a little too plain," "a little too self-evident," an idea that the Prefect finds laughable. However, Dupin is giving both the Prefect and the reader a clue as to the solution of this mystery. Dupin does this again at the end of this first visit, after he has heard all of the methods that the Prefect has used to try to find the letter. The Prefect, expecting some good advice, asks Dupin what he should do next, to which Dupin replies, "make a thorough research of the premises." The Prefect does not realize that Dupin is giving another clue to the mystery. Dupin knows that the Prefect has only concentrated on the secret areas of the Minister's home, so he tells the Prefect to check all of the areas, including the obvious ones.