A puzzle that involves figuring out what happened with regard to a certain incident through analyzing clues and deducing conclusions.
A mystery puzzle is a puzzle that involves figuring out the exact details of an incident or a specific desired detail, given limited relevant information. Mystery puzzles usually take the form of solving a crime, often murder. Such puzzles are a subset of the word-problem genre.
Please be careful that your mystery puzzle is not a situation riddle, in which only a situation is given with no context or evidence. Those problems require active question-asking on the part of the participant to answer. Make sure that the correct answer is clearly deducible given your problem statement alone.