On September 9th, in the seaside town of Crowdean, Miss Katherine Martindale, principal of the Cavendish Secretarial and Typewriting Bureau, dispatches shorthand typist Sheila Webb to 19 Wilbraham Crescent for a three o'clock appointment. A woman identifying herself as Miss Millicent Pebmarsh telephoned at 1:49 to request Sheila by name, with instructions to enter the house and wait if Miss Pebmarsh is not home. Sheila has no memory of ever working for Miss Pebmarsh.
When Sheila enters the sitting room, she notices an unusual profusion of clocks, several showing a time roughly an hour ahead. As she rounds the sofa, she discovers the body of an elderly man, stabbed and dead. Miss Pebmarsh, the home's blind owner, walks in moments later. Sheila screams and flees.
Outside, she collides with Colin Lamb, who tells her he was passing by. Colin is actually an intelligence agent investigating espionage connected to the nearby Portlebury Naval Station. A deceased colleague's sketch, showing a crescent shape, the number 61, and the letter "M," has led Colin to search the area for a hidden operations center. He enters the house, confirms the body, and telephones his friend Detective Inspector Dick Hardcastle.
Hardcastle takes statements. Sheila confirms Miss Pebmarsh asked for her by name, but Miss Pebmarsh categorically denies making the call and insists she does not own a telephone. She also states the extra clocks are not hers. The fingerprint officer reports all four extra clocks are set to 4:13, none are wound, and two have been wiped clean. Among them is a leather travelling clock inscribed with the name "Rosemary." The dead man carries a card identifying him as Mr. R. H. Curry of a nonexistent insurance company at a nonexistent address.
As Sheila leaves, she runs back inside to retrieve her gloves. The next morning, the "Rosemary" clock has vanished. Either Miss Pebmarsh or Sheila had a brief opportunity to take it.
Hardcastle and Colin canvass the neighbours. At Number 18, Miss Waterhouse notes that Miss Pebmarsh turned toward the telephone box rather than the shops when she went out. At Number 20, a house called Diana Lodge, the eccentric Mrs. Hemming makes a striking remark: the dead man "came here to be murdered" (76). At Number 61, the builder Josiah Bland and his wife Valerie deny any knowledge; Mrs. Bland mentions her sister lives nearby. At Number 62, Mrs. Ramsay's sons show the police a Czech coin found in the garden of Number 19.
Hardcastle visits Mrs. Lawton, Sheila's aunt, and learns that Sheila's full name is Rosemary Sheila Webb, matching the clock's inscription. Mrs. Lawton reveals Sheila is not an orphan but the illegitimate daughter of her sister Ann, a schoolteacher who arranged for her sister to raise the child and then cut all ties.
Colin consults Hercule Poirot, a celebrated private detective and friend of the family, at Poirot's London flat. Poirot listens and declares it must be a very simple crime because it appears so complex. He instructs Colin to keep talking to the neighbours and the people at the Bureau, insisting that ordinary conversation always contains clues.
At the inquest, the police surgeon reveals the dead man was drugged with chloral hydrate, a powerful sedative, before being stabbed. Afterward, Edna Brent, a colleague of Sheila's from the Bureau, approaches a constable and says she needs to speak to Hardcastle: "I don't see how what she said could have been true" (154). Told to come back later, Edna drifts toward Wilbraham Crescent and is found shortly afterward, strangled with her own scarf in the telephone box.
More than 10 days later, the dead man is finally identified. Mrs. Merlina Rival, a former actress whose real name is Flossie Gapp, comes forward and identifies him as Harry Castleton, her husband, whom she married in 1948 and last saw around 1951. She later writes to Hardcastle mentioning a small scar behind the dead man's left ear as corroboration.
Colin returns from an intelligence assignment abroad and meets privately with Sheila. She confesses she took the Rosemary clock because it was hers: She has had it nearly all her life, had it repaired, and lost it a week before the murder. Seeing it at the crime scene terrified her. She also reveals a threatening postcard she received depicting the Old Bailey, London's central criminal courthouse, bearing the word "REMEMBER" and the number "4:13." She fears someone is deliberately trying to implicate her.
Canvassing again, Colin discovers Geraldine Brown, a sharp 10-year-old with a broken leg who has been watching Wilbraham Crescent through opera glasses from a flat across the road. Geraldine confirms that at 1:35, a van marked "Snowflake Laundry" delivered an unusually large basket to the back door of Number 19. Colin realizes the body was transported to the house in that basket.
Hardcastle confronts Mrs. Rival about the scar. Medical examination shows it is only five or six years old, meaning she could not have known about it if she last saw her husband in 1951. Afterward, Mrs. Rival telephones someone in distress, accusing them of deceiving her. The person offers money to keep her quiet. The next evening, Mrs. Rival is fatally stabbed in the rush-hour crowd at Victoria Station.
Poirot travels to Crowdean and presents his solution. He identifies the killer as Miss Martindale, working with her sister Mrs. Valerie Bland and brother-in-law Josiah Bland. The motive centers on fraud: Bland's first wife, the true heir to a large Canadian fortune from the Montresor family, died during the war. Bland then married Hilda Martindale, Miss Martindale's sister, who assumed the public identity of Mrs. Valerie Bland. When the inheritance arrived for "Mrs. Bland," the three claimed it fraudulently. The dead man was a Canadian acquaintance of the real heir's family who would have recognized the impostor. The victim was drugged, killed, and transported to Miss Pebmarsh's house in a laundry basket via a van bearing "Snowflake Laundry" markings.
Poirot explains that Miss Martindale fabricated the telephone call to the Bureau. No call ever came through. Edna Brent, who had returned early to the office because of a broken shoe heel, knew this and was killed to keep her silent. The scheme with the clocks was lifted from an unpublished plot outline by the late thriller writer Garry Gregson, for whom Miss Martindale had been secretary. Mrs. Rival was recruited to provide a false identification and was killed when she became a liability.
In a separate resolution, Colin confronts Miss Pebmarsh and reveals she is the espionage hub he has been seeking. She keeps intelligence on microdots, microscopic images used in espionage, encoded in Braille and passes information through Ramsay, who crossed between their gardens at night. Colin offers her a two-hour head start before Special Branch, the police unit assigned to arrest her, arrives, because he believes she may be Sheila's mother. Miss Pebmarsh neither confirms nor denies the relationship but says quietly, "I did the best I could for her" (294). She reaches for a concealed knife, but Colin disarms her. She refuses to flee, vowing to continue her ideological work even in prison.
In a closing letter, Hardcastle confirms Poirot's deductions. The dead man was Quentin Duguesclin of Quebec. His passport was found in Boulogne, where Bland had traveled. Boards reading "Snowflake Laundry" were found at Bland's building yard. Mrs. Bland confessed, and Miss Martindale was identified as the buyer of two of the clocks. Colin married Sheila Webb.