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One month later, Dupin and the narrator are again sitting together when the prefect visits. The prefect admits that he cannot find the letter, even though the reward has increased. The prefect says that he will pay 50,000 francs to anyone who obtains the letter for him. Dupin tells him to write a check for that amount on the spot. Upon receipt of the check, Dupin hands over the letter. The prefect rushes off to return it to its rightful owner, and Dupin explains how he obtained the letter.
Dupin admits that the police are skilled investigators according to their own principles. He explains this remark by describing a young boy playing “even and odd.” In this game, each player must guess whether the number of things (usually toys) held by another player is even or odd. If the guesser is right, he gets one of the toys. If he is wrong, he loses a toy of his own. The boy whom Dupin describes plays the game well because he bases his guesses on the knowledge of his opponent. When he faces difficulty, he imitates the facial expression of his opponent, as though to understand what he thinks and feels. With this knowledge, he often guesses correctly. Dupin argues that the Paris police do not use this strategy and therefore could not find the letter: the police think only to look for a letter in places where they themselves might hide it.
Dupin argues that the Minister D–– is intelligent enough not to hide the letter in the nooks and crannies of his apartment—exactly where the police first investigate. He describes to the narrator a game of puzzles in which one player finds a name on a map and tells the other player to find it as well. Amateurs, says Dupin, pick the names with the smallest letters. According to Dupin’s logic, the hardest names to find are actually those that stretch broadly across the map because they are so obvious.
