Mrs. Ariadne Oliver, a famous crime novelist and longtime friend of Belgian detective Hercule Poirot, attends a literary luncheon in London. Afterward, a domineering stranger named Mrs. Burton-Cox corners her and reveals that her son, Desmond, intends to marry Mrs. Oliver's goddaughter, Celia Ravenscroft. She poses a startling question: Can Mrs. Oliver find out whether Celia's mother killed her father, or her father killed her mother? She is referring to a tragedy roughly 12 years earlier in which Sir Alistair Ravenscroft, a retired general, and his wife, Lady Ravenscroft, were found shot dead on a cliff near their home, a revolver between them. The case was treated as a probable double suicide, but no motive was ever established. Mrs. Oliver, shocked and offended, escapes the conversation.
Mrs. Oliver visits Poirot to discuss the encounter. She recalls that the Ravenscrofts appeared to be a happy couple with no financial or health difficulties, and no explanation for their deaths was ever found. Poirot advises her to do nothing, but her curiosity proves stronger. She proposes seeking out "elephants," her term for people from the past who, like elephants, never forget. She will track down anyone who knew the Ravenscrofts and learn what they remember. Poirot agrees to make his own inquiries through retired police contacts.
Mrs. Oliver locates Celia, now in her mid-twenties and living in London. Celia confirms she and Desmond are considering marriage and that she dislikes his mother. She was away at school in Switzerland when the tragedy occurred and has no firsthand knowledge. Yet the uncertainty has become a constant burden: She thinks about her parents' deaths "nearly all the time," and Desmond feels the same.
Poirot meets with retired Chief Superintendent Garroway, who originally investigated the Ravenscroft case. Garroway recalls that it had all the hallmarks of a double suicide, yet something felt wrong. The couple were affectionate, healthy, and financially secure. No motive was ever found. Garroway suspects the cause lay buried in the distant past and confirms the Ravenscrofts had a dog that accompanied them on walks.
Mrs. Oliver embarks on her elephant hunt, visiting a series of elderly acquaintances. Julia Carstairs remembers Lady Ravenscroft and mentions she wore several wigs. Mrs. Matcham, Mrs. Oliver's childhood nanny, recalls a sister of Lady Ravenscroft who had been institutionalized after harming a baby. This sister was released and married but later caused another incident involving a child and was placed in care again. Mrs. Buckle, a former cleaning woman for the Ravenscrofts, confirms the couple were happy and mentions Lady Ravenscroft's multiple wigs and a troublesome relative who visited.
When Mrs. Oliver reports her findings, recurring details catch Poirot's attention: four wigs, stories of mental illness in the family, a twin sister confined to institutions, and violence against children. One informant said the family dog was devoted to Lady Ravenscroft; another said the dog bit her. Poirot finds both the wigs and the dog's contradictory behavior especially suggestive.
Desmond Burton-Cox visits Poirot independently. He reveals that Mrs. Burton-Cox adopted him after her own child died. Distressed by her interference, he wants to uncover the truth about the Ravenscroft deaths. He suggests two people who may help: Mademoiselle Rouselle, called "Maddy," a former governess to the Ravenscroft children, and Mademoiselle Meauhourat, called "Zélie," a later companion who was at Overcliffe, the Ravenscroft home, at the time of the tragedy.
Poirot's investigation deepens. From Garroway, he learns that Lady Ravenscroft, born Margaret Preston-Grey and called Molly, had an identical twin sister, Dorothea, called Dolly. Dolly had a history of serious mental illness and a particular hostility toward children. She had been institutionalized and released several times. Critically, Dolly had been staying at Overcliffe about three weeks before the double suicide. She reportedly walked in her sleep, fell from the cliff, and died in what appeared to be a separate accident.
Poirot visits Dr. Willoughby, the son of the psychiatrist who treated Dolly, and learns she was genuinely dangerous and responsible for at least one child's death. Dr. Willoughby also reveals that Alistair Ravenscroft originally fell in love with Dolly but transferred his affections to Molly and married her instead, a source of enduring jealousy. Molly was always devoted to protecting her troubled twin.
Mrs. Oliver visits Mrs. Rosentelle, a retired wig supplier, who confirms that a French companion ordered two additional wigs for Lady Ravenscroft just weeks before the tragedy, bringing the total to four.
When Mrs. Burton-Cox encounters Poirot at Mrs. Oliver's flat, she is evasive and nervous, leaving abruptly. Poirot concludes she does not actually want a thorough investigation. He employs Mr. Goby, a specialist information gatherer, to investigate her background. The results reveal that Desmond is the biological son of Kathleen Fenn, a former mistress of Mrs. Burton-Cox's first husband. Fenn became a wealthy actress and recently died, leaving her entire fortune to Desmond, who will inherit at age 25. Desmond, unaware of his biological mother's identity, has presumably made a will favoring Mrs. Burton-Cox. If he marries and redirects his inheritance to Celia, Mrs. Burton-Cox loses everything. Her motive for discouraging the marriage is purely financial.
Poirot asks Garroway about the dog biting Lady Ravenscroft and learns of recent bites. He remarks that the dog was "perhaps a very intelligent dog": It knew by scent that the woman in the house was not its true mistress.
Poirot travels to Switzerland. Maddy, the former governess, confirms Dolly seemed disturbed when she first knew the family. Zélie, the former companion, has been expecting Poirot and agrees to come to England after he persuades her that the truth is necessary for Celia and Desmond's future.
The final gathering takes place at the now-empty Overcliffe. Poirot, Mrs. Oliver, Celia, Desmond, and Zélie assemble on the grounds. Poirot presents his deductions: Four wigs were excessive because two extra were needed for a second woman to impersonate the first. The dog bit its supposed mistress because the woman wearing Molly's clothes and wig was not Molly. The nearly blind housekeeper could not tell the identical twins apart. Dolly killed Molly by attacking her during a walk.
Zélie confirms and completes the account. She and General Ravenscroft found Molly dying on a cliff ledge, battered with rocks. With her last words, Molly begged them to protect Dolly, to never let her be arrested or imprisoned, out of lifelong love for her twin. They honored the wish by hiding Molly's body and staging the death as Dolly's sleepwalking accident. Dolly was then disguised as Molly using her clothes and wig and brought back to the house. General Ravenscroft told Zélie that Dolly could not live free because she would harm more children, yet she must not face the law. He would shoot Dolly and then himself, making it appear a double suicide. He sent Zélie to Switzerland before carrying out the plan.
Poirot frames the events as encompassing murder, execution, suicide, and tragedy. Dolly murdered Molly. The General executed Dolly to protect future victims. He killed himself to pay for what he had done. Two people who loved each other died because of that love. Celia responds with relief, viewing her parents as brave and loving. Desmond declares they will marry. Zélie, having finally unburdened herself, is embraced warmly by Celia. Mrs. Oliver reflects that while elephants can remember, "mercifully human beings can forget."