Japp and Dr. Thompson visit Poirot at home, informing him that Cust’s trial will be soon. Cust has an alibi for the Bexhill murder but is pleading insanity, which Japp dismisses as mere legal strategy. Dr. Thompson admits that Cust does not strike him as a person with a mental health condition at first glance but that those with epilepsy can commit crimes they do not remember, though the letters are an indicator the crimes were not spontaneous. Cust does not explain the letters, which fails to satisfy Poirot: “Until I get at the reason for those letters being written to me, I shall not feel that the case is solved” (221). Thompson suggests that Cust is delusional because of his names, which reference the great emperor Bonaparte and the world conqueror Alexander.

After Thompson leaves, Japp reports that Cust’s alibi comes from a mining engineer whom he met in the hotel and played dominoes with until well after the Barnard murder was committed. Japp cannot see a way to break the alibi and exhorts Poirot to try. Poirot asks Hastings if he is satisfied, and Hastings cites the evidence. Poirot is excited by this, arguing that motive is still key.