They Do It With Mirrors

Miss Marple senses danger when she visits a friend living in a Victorian mansion which doubles as a rehabilitiation 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 Gilbrandsen, 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 Gilbrandsen's visit.