The police soon get a tip-off about the man linked to the murders – Alexander Bonaparte Cust, an epileptic traveling salesman, who suffers from memory blackouts and constant agonizing headaches as the result of a head injury during the First World War. Cust flees his apartment, but collapses upon arriving at the Andover police station, where he is taken into custody. Apart from claiming that a stocking firm hired him, he lacks any memory of committing the murders, but believes he must be guilty of them – he had been at the cinema when the last murder occurred, and found blood on his sleeve and a knife in his pocket after he had left. The police learn that the firm in question never hired Cust. Their search of his room turns up an unopened box of ABC railway guides, and the typewriter and fine paper used in A.B.C.'s letters, while the knife is discovered in the hallway outside his room where he dropped it. Poirot doubts Cust's guilt because of his memory blackouts, and especially because he had a solid alibi for the Bexhill murder.