A typist named Sheila Webb arrives for an appointment at a quiet house in the seaside town of Crowdean and stumbles on the body of a well-dressed stranger, stabbed and lying among several clocks all stopped at the same odd hour. The blind woman who owns the house denies summoning her, denies owning most of the clocks, and cannot identify the dead man. Detective Inspector Hardcastle takes the case and finds almost nothing to grip: no name for the victim, no clear motive, and a tangle of small contradictions that refuse to settle. Running alongside the investigation is the first-person account of Colin Lamb, a young intelligence agent working a separate matter in the same neighbourhood, who happens to cross paths with Sheila on the day of the discovery. Convinced the puzzle is more than the police can manage, he carries the details to his old acquaintance Hercule Poirot. Poirot accepts a wager he has long invited: to untangle the affair by reason alone, without leaving his rooms, without meeting a single witness. As Hardcastle works the streets and Lamb chases his own quarry, Poirot turns the reported facts over in conversation, weighing the clocks, the timing, and the people who orbit the house until the shape behind them comes clear.