The superlatively analytical Inspector Hemingway is confronted by a murder that seems impossible – no one was near the murder weapon at the time the shot was fired. Everyone on the scene seems to have a motive, not to mention the wherewithal to commit murder, and alibis that simply don't hold up. The inspector is sorely tried by a wide variety of suspects, including the neglected widow, the neighbour who's in love with her, her resentful daughter, and a patently phony Russian prince preying on the widow's emotional vulnerability and social aspirations. And then there's the blackmail plot that may – or may not – be at the heart of the case ...