Cluny is an ancient town in France better known for its past then its present, in other words, the perfect place for tourists and travelers. When a local wine grower who provides accommodations for the better sort of English tourist in his villa decides to entertain his guests with a masked ball it promises to be a pleasant diversion. But the diversion turns to tragedy when two of the attendees are found dead in a locked room, apparently as a result of a duel. But, was it really a duel fought over the wife of one of the dead men, or can their deaths be attributed to something more sinister, murder? Fortunately, Chief Inspector Pointer is attending a conference in the neighborhood and is prepared to assist the local police, but only, of course, in the role of an observer. But can even the ever astute Pointer solve . . . The Cluny Problem?