Willoughby, is also a psychiatrist and has run the institute for several years.

The room in which he was found hadn't been used for years. Poirot investigates the death of a friend's father, a semi-retired psychiatrist who is found bound and floating in a hydrotherapy bathtub in the psychiatric institute he founded. With the help of a wigmaker, the evidence of a clever dog, and a French connection to the Ravenscroft case, Poirot is able to penetrate the fog of memory to uncover the truth of two long-ago deaths, and how that tragic story inspired the present-day killer whom he himself has been hunting. When Poirot realizes that his investigation is inextricably linked with Mrs Oliver's, the two join forces. However, the memories of the people Ariadne interviews are not as reliable as she has hoped, and soon the investigation takes a sinister turn when Desmond's life is threatened by an unknown entity. So Ariadne sets out to solve the Ravenscroft affair herself, with the mantra that 'elephants can remember' - no matter how much time has passed and how much people who were acquainted with the Ravenscrofts have aged, memories remain unchanged. When she turns to Poirot for assistance, however, she finds him already preoccupied investigating the murder of an elderly psychiatrist who was the father of a personal friend. Were they murdered, or was it a suicide pact? If they were murdered, who shot whom? Despite being insulted by the woman's impertinence, Ariadne is nevertheless drawn to the cold case by curiosity, and resolves to find out the truth when she is persuaded by Celia herself.

But Mrs Burton-Cox will not give her blessings to the match until she learns the truth of the deaths of Celia's parents, who were found shot to death on the grounds of their estate a decade before. Some fairly engaging sub-plots too, esp Hastings and his car (if it wasn't his car it would be golf.) and Miss Lemon's love-life.Ariadne Oliver is accosted by the unpleasant Mrs Burton-Cox, whose son Desmond has hopes of marrying Ariadne's beautiful goddaughter Celia Ravenscroft. Not entirely obvious who it is and there are a few good red herrings along the way. From Mr Graves' testimony, it appears that the main suspect is Mario Ascanio, an Italian gentleman who appeared to be the Count's blackmailer. Mr Graves had previously mentioned to Poirot that the Count may be interested in using his services, as he was being blackmailed. Meanwhile, Miss Lemon is dating the Count's valet, Mr Graves. Hastings recognises the Count from the Italian car dealer where he just bought his car. The doctor and Poirot race to the Count's flat to find him murdered, bludgeoned to death. Poirot is having dinner with a doctor friend when a patient, Count Foscatini, phones to say he has been attacked. A murder is committed and Poirot, Hastings and Miss Lemon are all independently connected to the victim in some way.