They Do It with Mirrors, Agatha Christie (audiobook)

Miss Marple senses danger when she visits a friend living in a Victorian mansion which doubles as a rehabilitation centre for delinquents. Her fears are confirmed when a youth fires a revolver at the administrator, Lewis Serrocold. Neither is injured. But a mysterious visitor, Mr Gulbrandsen, is less fortunate - shot dead simultaneously in another part of the building.
Pure coincidence? Miss Marple thinks not, and vows to discover the real reason for Mr Gulbrandsen's visit.