While passing by on a different train, Miss Marple witnesses the strangulation of a young woman in the opposite carriage. The local police dismiss her story as the ramblings of a senile and bored old woman, so, undaunted, she conducts her own investigation, and comes to the conclusion that the body must be buried on the grounds of Ackenthorpe Hall, which adjoins the railway line. Wheedling her way into a job as housemaid there, Marple copes with the pompous machinations of her difficult employer, Luther Ackenthorpe (James Robertson Justice), so she can search for the mysterious corpse, and eventually finds it while supposedly practicing her golf shots. As she begins collecting suspects, accompanied by her long suffering companion Jim Stringer (Stringer Davis), Marple finds herself faced with an increasingly devious and resourceful killer, who begins casting his shadow over Ackenthorpe's heirs...
The old and wealthy Mr. Enderby dies of a heart attack but the ever suspicious Miss Marple has her doubts. Who or what gave him a heart attack? Enderby's poor relatives gather at the The Gallop, a combined boarding-house and riding school. Miss Marple also gets there to find out if any of them had any particular reasons to see him dead.
Although the evidence appears to be overwhelming in the strangulation murder of a blackmailer, Miss Marple's sole 'not guilty' vote hangs the jury 11-1. She becomes convinced that the real murderer is a member of a local theatrical troupe, so she joins them in order to gather information. The clues lead back many years to a single disastrously unsuccessful 1951 performance of a dreadful play written by the group's hammy director, H. Driffold Cosgood. Although at that time, several of the current cast members were only children, more murders follow before Miss Marple ultimately exposes the killer.
The action takes places mainly on board an old wooden-walled battleship, HMS Battledore, which has been purchased by a Trust for the rehabilitation of young criminals, and intended by the founder to put backbone into young jellyfish. Shortly after joining the board of management of the Trust, Miss Marple witnesses the sudden death of a fellow trustee, who has just returned from a surprise visit to the ship. She manages to obtain a small sample of his snuff, which is found to have been poisoned. Against police advice, she visits the ship, much to the distress of the Captain and officers. On her first night on board, one officer is murdered - run through with a sword and then hanged. As the police investigation proceeds, the assistant matron is killed, apparently by a poisoned mousetrap.
