Poirot and Captain Hastings, at the suggestion of Inspector Japp, have gone to stay with him for the weekend in the small countryside town of Market Basing (which is not far from the small village where Jane Marple resides). Sitting in their inn and enjoying Sunday breakfast, the three are interrupted when the local constable requests Japp's help with a problem. Walter Protheroe, the reclusive owner of a local large mansion, has been found dead in his house, supposedly by suicide, but the local doctor states that this is impossible.
The three go to Leigh House as requested and meet Dr. Giles who was called in by Miss Clegg, the housekeeper of some fourteen years, when she was unable to raise her master in his bedroom. Constable Pollard also arrived at the same moment and he and the doctor broke down the oak door. Inside they found Protheroe, shot through the head and his pistol clasped in his right hand. The problem is that the bullet has been fired in behind the left ear and such a shot is impossible. As they examine the room Hastings is puzzled as to why Poirot sniffs the air so keenly and also why he examines so carefully a handkerchief lodged up Protheroe's right sleeve. Hastings can smell nothing in the air, nor can he see anything on the handkerchief.
The key is missing from the lock of the door and Japp supposes that this is the murderer's one big error in trying to make a murder look like suicide. Staying in the house are a couple called Parker who according to Miss Clegg have not stayed in the house before and whose arrival did not seem to please Protheroe. She knew that he kept a pistol, although she has not seen it for some time, but she cannot state why the windows of the room were locked and bolted when they were usually open at night.
The inquest takes place two days later and a tramp comes forward who states that he heard Protheroe and Parker rowing about money at midnight on the night of the death. It comes to light that Protheroe's true surname was Wendover; he had been involved with the treacherous sinking of a naval vessel some years earlier and Parker was blackmailing him over this. On the suspicion of killing Wendover and making it look like suicide, Parker is arrested.
At the inn, Poirot receives Miss Clegg who was summoned there by him. He has guessed that Wendover did in fact kill himself – but with his left hand holding the gun – and that Miss Clegg found him in the morning. In love with her employer and knowing Parker to be the cause, she changed the pistol to his right hand to throw suspicion on the blackmailer in an effort to bring him to some sort of justice; however, she neglected the change the handkerchief up the right sleeve over to the left sleeve as well. She also locked and bolted the windows to prevent it looking like a potential murderer escaped by that method, therefore indicating that the murderer was someone in the house, but as the fireplace grate was full of smoked cigarettes, the air should not have been as fresh as it was, and Poirot deduced that the windows of the room must have been open that night, otherwise the air would have smelled smoky and the tramp could not have overheard the conversation he did.