Narrative causality as a detection technique
If you watch TV detective shows (CSI, NCIS, Law & Order, ...) then very often you can figure out who did it - or who actually did it, that quite often only being fully revealed after a lot of effort chasing/questioning/prosecuting/etc the ‘obvious’ suspect - simply by knowing the conventions of the show - sometimes as simply as counting characters and figuring out that the only point of a particular character's presence is to be the guilty party.
My suggestion, then: a story about a detective who knows that some such set of conventions apply to the world they're in and can therefore use them to figure out whodunnit (though of course, they would still have to find and interpret evidence, use interrogation skills, etc to actually construct a winnable case) simply by applying these rules.
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I'm afraid that all I have is First Among Sequels and The Fourth Bear, but you can borrow them if you get that far :-).
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(And I'd have gotten away with them if it wasn't for those pesky kids.)
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Which is pretty much the plot of every episode of Columbo, although in his case he figures out the culprit by intuition rather than by knowing the rules of the genre.
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"What do you mean, Holmes? He has said nothing at all."
"Precisely, Watson. His player is not here for this session."
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"A typical episode begins with a crime, which is subsequently investigated by a team of FBI agents led by Don and mathematically described by Charlie ... The insights provided by Charlie's mathematics are always in some way crucial to solving the crime."
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Another consequence of the CSI formula is that there's not enough screen time for a courtroom scene, so each plot has to end with the guilty party waiving his or her rights under the fifth amendment and confessing, destroying any lingering shreds of plausibility.