A week after the nurse is hired to care for Louise, the latter is found dead in her room, the victim of a blow by a blunt instrument. Dr. Reilly examines the body and establishes a time line, concluding that it was an inside job. He calls in Hercule Poirot, travelling in Iraq at the time, to solve the crime. Poirot determines that it must be someone from the expedition who is guilty of the murder. The murderer must have entered the victim's bedroom from the inside of the house as the bedroom window is barred. However, after one round of questioning it appears that everyone has an airtight alibi.
Nurse Leatheran tells Poirot the story of Louise's young brother in law, William, who was fifteen years younger. She points out that Louise always craved the attention of men. Poirot suspects that William, or even Frederick himself might be part of the expedition as Frederick's identity was never proven on the train wreck. Poirot warns Nurse Leatheran that she might be a future target of the murderer but she still insists on attending Louise's funeral.
After the funeral, Nurse Leatheran and Miss Johnson are up on the roof and the latter points out how someone could enter the house without being seen. Later Miss Johnson is poisoned: someone substituted hydrocholoric acid in her water glass, through her window.. Poirot solves the crimes, but has no proof.
It turns out Mrs. Leidner and Miss Johnson were murdered by Dr. Erich Leidner. Poirot determines that Leidner is really the long lost husband, Frederick who really didn't die in the crash. Leidner did die and he has stolen his identity. Frederick remarried his wife who, after 15 years, didn't recognize him. He was the one who sent her the letters to discourage her from engaging in relationships with other men. He discovered that his wife was falling in love with his friend, Richard Carey, and he murdered her in a jealous rage. Miss Johnson figured it out and he in turn murdered her.
On the night of the crime, Louise heard a noise up on the roof. Unbeknowst to her it was her husband sorting pottery. She opened her bedroom window to investigate only to be knocked out by a stone quern. In the meantime, Frederick removed the bloodstained rug and closed the window before calling the nurse. With the nurse on the scene, she could vouch for the time of death. Frederick tried to make Miss Johnson's death appear a suicide; however, Poirot points out that hydrolic acid is an incredibly painful way to kill oneself.