The detectives arrive at the scene of the crime to find the victim lying on the floor with a pistol in his right hand and a fatal wound behind his left ear. Poirot detects an odour in the air and examines the handkerchief stuffed up the victim's sleeve. The key missing from the lock is evidence that the crime was a murder, not a suicide.
The housekeeper points out that a couple named Parker were staying at the house the night before; their presence was not pleasing to Mr. Protheroe. A tramp comes forward and reveals that he heard Mr. Protheroe arguing with Mr. Parker the night before. It is further revealed that Protheroe's named was really Wendall and he had been involved with the sinking of a naval vessel years ago. Mr. Parker was blackmailing him to this effect.
Poirot summons the housekeeper to his room where he accuses her of setting up Mr. Parker. It turns out that Mrs. Clegg was in love with her boss. She realized that he killed himself because he was despairing about Mr. Parker's blackmailing. Therefore, she switched the gun, putting it in the wrong hand to make it look like a murder rather than a suicide.