The Disappearance of Mr Davenheim

Hercule Poirot, Captain Hastings, and Insepctor Japp discuss the disappearance of a banker, Mr Davenheim, from his country house three days earlier. Poirot claims that he can solve the case in one week without leaving his chair, as long as the relevant facts are brought to him, and accepts a five-pound wager from Japp to do so.

Davenheim had left the house on Saturday afternoon to post some letters. He instructed that Mr Lowen, a visitor he was expecting, should be shown into the study to await his return. However, Davenheim never returned and no trace of him was found. The police were called on Sunday, and a safe hidden in his study was found broken open and emptied of its contents − cash, bonds, and jewels − on Monday. Lowen and Davenheim were known to be on bad terms with one another, and the police have Lowen under observation but have not arrested him.

Poirot takes interest in the fact that the property has a lake and boathouse, and also in a recent picture of Davenheim that shows him wearing long hair and a full beard and moustache. The next day, Japp brings word that the police have found Davenheim's clothes in the lake and arrested Lowen, based on a maid's statement that she saw him crossing the grounds towards the study on the day Davenheim vanished. Furthermore, a petty criminal named Billy Kellett has been arrested. He had picked up and pawned Davenheim's ring after a man threw it into a ditch, used the money to get drunk, and assaulted an officer. Poirot asks Japp to find out whether Davenheim and his wife sleep in separate bedrooms. Upon learning that they have done so for six months, he declares the case solved and urges Japp to withdraw any money he has deposited at Davenheim's bank. Soon afterwards, the bank's sudden collapse is reported in newspapers all over London and an astounded Japp pays the wager.

Davenheim had been systematically embezzling from the bank and converting some of the money into bonds and jewels for easier transport. Several months earlier, under the guise of going abroad on business, he created the identity of Kellett, changed his appearance, and committed a crime that earned him a three-month jail sentence. After being released, he had to wear a wig and false beard and sleep in a separate room from his wife to keep the deception hidden from her. He staged the safe break-in, fled with the contents before Lowen arrived in order to set him up, threw his usual clothes into the lake after changing at the boathouse, and got himself arrested as Kellett to avoid police scrutiny.