La Chaux-de-Fonds · 31 December 1899

The Regulator

A master watchmaker is dead in his atelier. Every clock in the house keeps its own time, and one witness is lying.

Watch it as a 13-minute film, which stops to let you solve it before the reveal.

Read the inspector's note and the six interviews. Then use the bench to set each clock's error and to set aside the witness you think is lying, until the house runs true. Name the murderer and the true minute of the blow.

Inspecteur Léon Matthey, Sûreté de Neuchâtel

The case

Six interviews, taken between one and four in the morning

Interviews

Readings of clocks and watches are underlined. The interviews are in the order the inspector took them.

Your workbench

The bench

Every statement in the interviews is laid out here as a time on a named clock or watch. Set how far each timepiece ran fast or slow, and the bench converts every reading to true time and shows where the accounts disagree. When you think you know who lied, set that witness aside. If no disagreement remains, the house runs true.

Set aside

Disagreements

When the repeater sounded

The question

Accuse

Who struck Aurèle Monnier, and at what true time, to the minute?

The movement behind the dial

The caseback

The answer is Dr Casimir Vauthier, at 22:38.

The minute of the blow. The repeater sounded at the blow. Félix heard it at 10:18 by his watch, and at dinner his watch showed twenty to nine when the temple struck nine, so it runs twenty minutes slow (Odile and Félix both say so). The blow fell at 22:38. Félix counted ten low notes, so the repeater agrees on the hour.
The hall clock. In the atelier, Lina heard the Morbier strike ten when the regulator showed 9:48, and at ten the regulator agreed with the temple exactly. The Morbier runs twelve minutes fast, and it struck its eleven at 22:48 by the true time.
Rosa's clock. Rosa believes it runs a quarter of an hour fast. But she heard the Morbier strike eleven, at 22:48, when her clock showed 11:13, so that evening it was twenty-five minutes fast. Lina saw the master with that clock in his hands in the afternoon. Lina's walk confirms it: she left the atelier at 22:20 and went straight down, and Rosa's clock showed 10:47 when she arrived, which is 22:22.
The piano. It began at 10:58 by Rosa's clock, which is 22:33. Bastien's watch says the same. He came in at 10:46 by his watch, just as the Morbier, twelve fast, showed 11:02, so his watch runs four minutes slow. He heard the piano begin at 10:29 by it (22:33) and the bells from the master's window at 10:34 (22:38, the same minute Félix gives).
The lie. The doctor says he left the salon at a quarter to eleven by his watch, which runs two minutes fast (he and Lina both say so), so at 22:43. He and Odile agree that the piano began as he went out. The piano began at 22:33. His account seats him at the card table when the repeater sounded, and it cannot be true. Only the murderer lies, so the murderer is the doctor.
The rest fits. He left the salon at 22:33. Félix heard someone go up past the library at 22:35 and come down at 22:41. The doctor struck at 22:38, stopped the regulator and set its hands to five past ten, an hour when he had been at cards in plain sight. He was back in the salon at 22:46, when the piano stopped, and the Morbier struck its eleven a moment later.
The trap. Take Rosa at her word and the piano begins at 22:43, the minute the doctor says he left. His story then looks corroborated and Bastien's watch looks wrong. Set the kitchen clock to fifteen minutes on the bench to watch it happen.

Why it cannot be anyone else

A solver (z3) checked the formal case, which is every statement as constraints on clocks and moments. If any of the other five were the murderer, the accounts of the remaining people would contradict each other. For each of them, these are the shortest sets of statements that cannot all be true together, out of the minimal sets the solver found.

The true evening

The bench below is set to the true errors, with the doctor set aside.