Why can’t the police openly pursue Minister D––?

The police cannot simply arrest Minister D–– because of the delicate nature of the letter he stole. Minister D–– steals the royal lady’s letter because it implicates her in something that would be considered treasonous, meaning that he can use it for blackmail. If the police arrest Minister D––, they would have no choice but to reveal the letter’s existence to everyone, compromising the royal lady in the process.

Why is it significant that Minister D–– is both a poet and a mathematician?

The implication that Minister D–– is both a poet and a mathematician means that he, like Dupin, is capable of both logic and creativity. He has both the logic to understand what the rationally clever move would be, like a mathematician, and the creativity to do something unexpected instead, like a poet. Therefore, he understands the steps the police are likely to take to search for the letter, and so instead of hiding the letter in a logical spot, like hidden in a small place, he hides it in plain sight.

How do the police search for the letter?

The police thoroughly and methodically search for the letter using the most contemporary scientific methods. They undertake a grid search for the letter, making sure every inch of the apartment has been searched. They look for tiny hiding spaces in bed posts, books, and other small locations. They search under the carpets, behind the wallpaper, and even dig up the cellar floor. They also use a magnifying glass, referred to as a microscope, to search for any signs that something has been drilled into to create a hiding spot.

Where is the purloined letter?

Minister D–– hides the letter in plain sight in the rack where his visitors leave their calling cards. He disguises the letter by adding a new wax seal of a different size and color, writing a different address on it in very different handwriting, and refolding the letter in the opposite direction. However, Dupin notices how these superficial differences are complete opposites from the missing letter and considers the sheer enormity of those differences suspicious.

Why does Dupin make a duplicate of the letter?

Dupin uses the duplicate of the letter so as not to alert Minister D–– that he has been outwitted, and Dupin can safely leave the apartment. However, Dupin also uses the duplicate to engineer Minister D––’s downfall. If Minister D–– thinks he still has the letter, he will continue to attempt to blackmail the royal lady. However, as the royal lady has possession of the letter, she can ruin Minister D––. Dupin considers Minister D––’s downfall revenge. He politically sympathizes with the royal lady, but Dupin also has a personal hatred for Minister D–– because of an undescribed slight Minister D–– once gave him.