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....
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