The episode begins with Conan, Ran, and Kogoro visiting a vintage clock tower set for demolition. A wealthy collector is found dead inside the mechanism room—strangled by a broken gear chain. The victim left a dying message: a broken pocket watch stopped at 7:35. The suspects include the collector’s assistant, a clockmaker, and a local historian. Conan deduces that the time actually points to a mirrored number (5:37 on a 24-hour dial) to reveal a hidden safe.