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Source: https://writers.stackexchange.com/a/6678
License name: CC BY-SA 3.0
License URL: https://creativecommons.org/licenses/by-sa/3.0/

Primarily, cheat by writing the story backwards. Start from the end revelation of the implicit story (the crime) and progress towards beginning, iteratively removing any simplicity.

Start with the outcome, the rather simple final set of events that is to be discovered. Then take it apart: tools, witnesses, methods, motives.

Take a look at each of them. Whenever you see something overly simple, replace it with something ambiguous, deceiving, non-obvious, or outright fake. Unlike the real wise guy, you don't have to limit yourself to things they can do. You can modify circumstances, personalities, environments to fit your convoluted needs.

Then, when you have the whole set of utterly corrupted clues, start writing the explicit story, what the readers will see. Distribute the clues throughout it, and then have the investigator come to the right conclusions, correctly recognize lies and deceits, and present the outcome as result of detailed analysis, a set of random pieces matching in the end, ingenious mind combining them, while in fact it was constructed from a kit of parts with a builder's manual you have created before starting on the explicit story, and only made the process seem unguided while you, the writer, were the guide.

(just to add: this is how math exercises are written. How do you get that complex equation to resolve to "2"? Start with "2", then keep multiplying by expressions that resolve to identity, add expressions that resolve to zero, square both sides, shift expressions between sides, divide by some red herring, and when your equation looks mangled enough, write it down as the subject of the exercise.)

Original score: 14