What does the detective value? Why is he or she trying to solve the mystery? Why does it matter to him or her if the mystery is solved?
What is the relationship between the detective and authority? Is the detective smarter than adults, smarter than his or her peers, smarter than the police? Is the detective trying to solve the mystery before the authorities, or along with authorities?
Who is the detective? Is there more than one? Is the detective the narrator? If not, how does the narrator feel about the detective?
How does the gender of the detective influence how he or she solves the mystery? How do other people in the mystery treat the detective?
How is punishment given out in the end? Does the detective or other authorities punish the criminal? What desires for retribution are fulfilled or denied? Who gets punished, and who gets to punish?
What crime is committed and who, or how many people, commit it? Are larger institutions impicated, or just single individuals? Is the detective guilty of anything?
Are we led to be active readers, solving the mystery ourselves, or do we place our trust in the author to reveal all the information? Do we trust that the author is going to tell us everything we need to know?
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[Answers to these questions will help you to start to categorize different types of mysterys and to read them more carefully].