The biggest fear of most GMs is to be considered a railroading GM. This is a particular problem with mysteries when you have a single plot hook and a single correct answer to the mystery.
There are two big names in investigative games, Cthulhu and Gumshoe.
Gumshoe uses a very linear approach to each scene that contains a clue, and you follow the trail from hook to crook picking up the clues in a sequence. It sounds very much like a railroad. It certainly isn’t for everyone.
I like to offer at least three, but normally three, pretty obvious different ways to approach an investigation. Right from scene one, the players have options. They are all going to eventually lead to mostly the same clues, the same evidence exists regardless of how the players approach the mystery, but they have these different ways to carry out their investigation.
If your clues turn out to be completely opaque to the players and they hit a wall, they have the option to try a different approach.
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