Poirot makes a five-pound bet with Inspector James Japp that he can solve the mysterious disappearance of a rich banker in a week, without getting up from his chair. So Japp gives him the facts of the case. Mr. Davenheim walked away from his home one afternoon and has not been seen since. Suspicion falls on a business rival of his that visited the house on the day of his disappearance; there is some reason to believe that the rival has done away with Mr. Davenheim, but if so, where is the body? Will Poirot solve the case and win the bet?
