James Bentley is arrested for the murder of old Mrs McGinty. It looks like an open and shut case, but Superintendent Spence is not convinced. He turns to Poirot for help, and together with Poirot's writer friend Ariadne Oliver they set out to find the real killer.

Three single girls share a London flat. The first works as a secretary; the second is an artist; the third, who comes to Poirot for help, disappears believing she is a murderer.

On holiday in Jerusalem, Poirot hears about an archaeological expedition to Syria led by the eccentric Lord Boynton and his son Leonard, who believe they are on the track of the head of St John the Baptist. Drawn to visit the dig, Poirot meets Boynton's dominating, fabulously rich, American-born second wife. However, events are overtaken by the discovery of Lady Boynton's dead body and revelations about her fortune.