In 1962, Sheila Webb, a typist-for-hire at a secretarial firm, arrives at her afternoon appointment to find a well-dressed corpse surrounded by six clocks, four of which are stopped at 4:13. When a blind woman enters the house, Sheila runs screaming into the street and into the arms of Colin Lamb, who plays a key part in the investigation that follows.
It is while visiting Wilbraham Crescent that agent Colin Lamb finds Sheila running into his arms. He is there investigating areas connected with crescents or the moon while following up a clue to the route by which classified information is leaving the country. The clue left by a fellow agent, Hanbury, before his death, reads “61 W” and a crescent shape.
At 19 Wilbraham Crescent an investigation begins into the murder. The corpse has a business card in its pocket suggesting that he was an insurance salesman called “R. H. Curry”. This proves to be a false lead, since neither the Insurance Company nor the salesman existed.
Miss Martindale, at Sheila’s agency, gives the background to her attendance at the house of the blind lady, Miss Pebmarsh. Apparently Miss Pebmarsh had telephoned and asked for Sheila personally to come to her, and to enter the house if she had not returned. Miss Pebmarsh, however, denies having done anything of the sort.
A colourful group of neighbours is interviewed by Inspector Dick Hardcastle with Lamb in attendance. At 18 Wilbraham Crescent, Miss Waterhouse tells them about the other neighbours. At 20 Wilbraham Crescent, Mrs. Hemmings lives in a house full of cats. At 61 Wilbraham Crescent, behind 19, Mr. and Mrs. Bland have recently inherited money from an overseas relative of Mrs. Bland. At 62 Wilbraham Crescent, Mrs. Ramsay looks after two sons who are always getting into trouble; her husband, an engineer, is frequently overseas.
Things begin to look bleaker for Sheila when her aunt, Mrs. Lawton, is interviewed. It seems that Sheila’s other forename is Rosemary, the name on a leather travel clock that has been found at the scene of the murder but which has subsequently been stolen, quite possibly by Sheila herself. Moreover, Sheila has some question regarding her birth, since she apparently believes herself to be an orphan: in reality, her father’s identity was never known and her mother is presumed to be still living somewhere. Frustrated, Colin approaches Hercule Poirot, an old friend of his father, to investigate the case, challenging him to do so from his armchair as he had always claimed was possible. He leaves Poirot with detailed notes on the investigation thus far.
After the inquest, Edna Brent, one of Sheila’s fellow secretaries, is confused by something said in evidence, and attempts to draw it to Hardcastle’s attention but he is too busy to speak to her. On the day of the murder she is known to have broken the heel of her shoe when she went to lunch. Later, she is found dead in a telephone box on Wilbraham Crescent, strangled with her own scarf.
A woman, Merlina Rival, comes forward to identify the corpse of “Mr. Curry” as that of her estranged husband, whom she has not seen for fifteen years. The husband, known to her as Harry Castleton, made a profession of conning women out of their savings. Later, however, she adds to her identification the seemingly corroborative evidence that her husband had a small scar behind his ear. Hardcastle, however, discovers that the scar is too new for her to have seen it. After he challenges her with this fact, she telephones the person for whom she has given the false identification, threatening to admit the truth. She subsequently becomes the third victim.
Colin makes an important discovery when he finds a ten-year-old girl, Geraldine Brown, who has been observing the events at Wilbraham Crescent with a pair of opera glasses while confined to her room. She reveals that a new laundry service delivered a heavy basket of laundry on the day of the murder. Colin also clears up one area of confusion: Mrs. Ramsay’s husband has defected beyond the Iron Curtain, but she is not otherwise implicated.
Poirot’s explanation is based on his inference that since the appearance of complexity must conceal quite a simple murder. The clocks are therefore a red herring, as is the presence of Sheila and the confusion about the corpse’s identity. What Edna realised, having returned early to the secretarial bureau due to the damage to her shoe, is that Miss Martindale never took any telephone call that arranged Sheila to visit Miss Pebmarsh’s house. Miss Martindale, one of the conspirators to the murder, is secretly the sister of Mrs. Bland, who is Mr. Bland’s second wife. The first wife was heiress to the overseas fortune, but when news of it reached the Blands they decided that Mrs. Bland must pose as the heiress in order to obtain the fortune. When, however, Quentin Duguesclin, who knew the Canadian Mrs. Bland, decided to look her up in England, a plan was laid to murder him and relocate the body to Miss Pebmarsh’s house. Miss Martindale had picked up Sheila’s “Rosemary” clock and found it easy to add another confusing detail to an already literary puzzle; in fact, she took the entire idea from an unpublished book idea by one of the authors for whom the bureau provided secretaries.
During the explanation, Poirot also gives Colin a hint to the mystery of Hanbury’s clue. Hanbury had written it upside down on hotel headed notepaper; it really read “M [crescent] 19”, Miss Pebmarsh’s house. At the end of the novel, Colin visits Miss Pebmarsh and reveals to her that she is about to be raided by Special Branch. He knows that all along she has been using Braille as a means to sending information abroad, but it is willing to give her two hours’ head start since he intends to marry Sheila, whom he has correctly recognised as her daughter. Miss Pebmarsh admits to being the long lost mother, but refuses to run away and the two are left intransigently facing one another until the authorities arrive.