Superintendent Spence informs Hercule Poirot of the case of Mrs McGinty, an elderly charwoman, apparently killed by her lodger, James Bentley, for her savings of £30, which she kept under a floorboard. Bentley is convicted and to be executed for the crime, but Spence does not think he is guilty. Poirot agrees to go to the town of Broadhinny and investigate the murder further. Poirot finds that Mrs McGinty often worked as a cleaner at the houses of people in the village. No one wants to talk to Poirot, and most believe Bentley is the killer.

During a search among Mrs McGinty's possessions, Poirot finds a newspaper from which an article has been cut out. The newspaper is dated a few days before the murder. He later discovers that the missing article is about women connected with famous murder cases, and includes photographs of them. He also discovers that Mrs McGinty had purchased a bottle of ink in a local shop shortly before her murder. He concludes that she had recognised one of the women in the article, and had written to the paper in question. Someone must have found out about it and then killed her to prevent her from talking. Poirot and Spence, using the ages of people in the town, conclude that someone is either Lily Gamboll, who committed murder with a meat cleaver as a child, or Eva Kane, who had been the love interest who inspired a man to murder his wife and bury her in a cellar. Another possibility is that someone is Evelyn Hope, the daughter of Eva Kane. Shortly afterwards, Poirot discovers the murder weapon, a sugar hammer, left around in plain sight at his boarding house and accessible to all the suspects. In an attempt to flush out the murderer, Poirot claims to know more than he does and is nearly pushed under an oncoming train. Poirot decides to show most of the suspects the photos at a party. Mrs Upward claims to have seen the photo of Lily Gamboll, but does not say where.