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The hypothesis is that fictional detectives are curious characters that illuminate the temperaments of their creators to some degree... though I can't "prove" that without researching about the respective creators. Something I will have to postpone till a later time.
(1) Sherlock Holmes by Sir Arthur Conan Doyle
The one that inspired many to follow. For the Jungians, a textbook example of INTJ.
(2) Adrian Monk, created by Andy Breckman
The obsessive-compulsive detective.
(3) Kudo Shinichi from Case Closed by Aoyama Gosho
High school student-detective trapped in a six-year-old's body.
(4) Shawn Spencer from Psych, created by Steve Franks
The self-proclaimed psychic with no psychic abilities, though with razor-sharp sense of observation and quick wit.