Final answer:
The narrator is surprised by Dupin's highly effective yet unorthodox problem-solving methods, which confound the police and allow him to solve a perplexing case.
Step-by-step explanation:
The narrator is surprised by Dupin for several reasons, particularly because of Dupin's unique approach to solving problems and his ability to outwit the Parisian police. Dupin's methods are unorthodox, relying heavily on psychological insight and a deep understanding of the human character, which often confounds his contemporaries. His use of ratiocination to analyze the Minister and predict his actions showcases not only his intelligence but also his practical application of knowledge to solve what appeared to be a perplexing case for the police.
The surprise is evident when the Prefect is absolutely thunder-stricken after Dupin produces the letter that they had all been searching for. This astonishment stems from Dupin's capability to resolve the issue in such a straightforward yet unexpected manner, challenging the conventional police methods and expectations of the Prefect and others. Dupin's actions exemplify his outstanding analytical skills and deft maneuvering within the intricate social and political machinations of Paris.