ABC Murders

Poirot receives typed letters from a serial murderer, ABC, explaining where and when the next murder will be.   Alice Ascher is a tobacco shop owner killed in Andover.  Betty Barnard is a flirtatious waitress killed in Bexhill.  Carmichael Clarke is a wealthy man killed in his manor in Churston.  ABC leaves a railway guide with each victim.  Poirot wonders:  "Why would ABC write to him instead of Scotland Yard or any reputed newspaper?" and "Why did a meticulous man like ABC misspell Poirot's address on the Churston letter?"

The murder mystery is unravelled by Captain Hastings who talks about Cust, travelling salesman and Great War veteran, who suffered from epilepsy due to a war injury.  He is prone to memory blackouts and headaches.  Also involved in the investigation are Inspector Crome, who doubts Poirot's investigative abilities, and Dr. Thomson who profiles the serial killer.

Poirot notices a similarity among all three murders.  A stockings salesman visited each home before the murder, selling a pair of stockings to the first two victims, but being turned away by the third.  ABC sends a fourth letter, this time directing everyone to Doncaster where a famous horse race will take place.  But ABC strikes in a cinema where he kills George Earlsfield, instead of Roger Downes, the logical victim sitting only two seats away.  The salesman, Cust, who had suffered a blackout, later slips out of the theatre unnoticed.  Cust finds the murder weapon in his pocket and blood on his sleeve.

Cust, tipped off that the police are after him, flees but collapses at the Andover police station.  Cust, who can't remember the murder, fears that he is guilty.  Cust's room contains many incriminating items:  silk stockings, lists of clients, the fine paper used to type the letters to Poirot, an unopened box of ABC railway guides, and in the hall lies the bloodied knife from the most recent murder.  It is revealed that Cust was never hired by the stocking company and that the letters to Poirot were indeed typed on Cust's typewriter, the one he claimed the company gave him.  Poirot meets with Cust who has no recollection of any of the murders.  He has a solid alibi, however, for the Bexhill murder.

Poirot categorically explains how Cust could not have committed the murders.  Then he points the finger at Franklin Clarke, the brother of Sir Carmichael Clarke, the third victim.  Sir Carmichael was heir to a fortune and a member of Cust's legion.  The third letter, which contained an error, was meant to lead the reader astray.  Franklin had feared that, with Lady Clarke's death imminent, his brother would marry his young beautiful assistant.  When Sir Carmichael died, his wealth would go to his new wife and any children they had.  Franklin's meeting with Cust in a pub served as inspiration for his serial murder plot, with Cust serving as the stalking horse.

Franklin laughs off the accusations until Poirot states that the former's fingerprint was found on Cust's typewriter key.  Further Franklin has been recognized by Milly Higley, a coworker of the deceased Betty Barnard.  Franklin tries to shoot himself but Poirot is one step ahead of him and has emptied the bullets from his gun.  Poirot reveals to Hastings that the fingerprint on the typewriter key was a bluff.  Cust, meanwhile, has an offer from the press to sell his story,  

The ABC Murders, published in 1936, courtesy 

http://www.agathachristie.com/stories/the-abc-murders.