"The Unsolved Puzzle of the Man with No Face" is a short story from Dorothy Sayers' book, Lord Peter Views the Body.
Several passengers on a train are excitedly discussing a recent murder, in which a man was found on a beach, strangled, with his face cut off. Lord Peter Wimsey is among them, and cleverly deduces several facts about the case based on details mentioned by the passengers. A policeman, Inspector Winterbottom among them overhears the conversation and takes Lord Peter's calling card.
Shortly afterwards, newspapers announce that police have identified of the faceless victim as the studio manager of an advertising agency. The policeman from the train visits Wimsey and professes his theory that the murder was committed by an Italian over a love affair...