Part sudoku, part investigation. You get a floor of the castle drawn as a grid, a handful of statements, and nothing else. Everything you are told is true, and the trick is working out what it rules out. Every puzzle is machine-checked before it ships: exactly one arrangement fits, and it can always be reasoned out step by step. You will never need to guess.
Seven rooms, six prefects, one way out for the basilisk.
A basilisk came out of one of the rooms last night. The prefects were standing at their posts and saw nothing, which means the snake never crossed a room they were watching. There are seven rooms and only six prefects, so one room was left without a post. Put every prefect back where they stood and the empty room gives itself away.