Newlyweds, the rich but vulgar Sir George and the beautiful, though dim-witted, Lady Stubbs arrive at a country house as a storm rages, falling a great tree. One year later, Poirot is en route to that same country house, Nasse, to answer Ariadne Oliver's plea for help. His driver gives two young foreign hitchhikers a ride to the nearby youth hostel.
At Nasse, Ariadne explains her summons: commissioned to create a murder hunt for the Stubbs' grand summer fete, replete with victims, suspects, motives and murderers, she has become convinced that a real murder is going to occur. Changes keep being made to her plans, such as the boathouse rather than the pavilion being the location of the corpse. Similarly, the intended victim changed her mind, choosing to play a fortuneteller; instead, a local girl, Marlene Tucker, is engaged to play the corpse. These and other changes have led Ariadne to feel that she's being manipulated for nefarious purposes.
The architect George Weyman complains that Sir George had made him build a folly in an absurd location, in the woods where a tree fell in the previous year's storm. Poirot also meets Amy Folliat, whose family originally owned Nasse. She shares her sad story: her husband died in the war and her older son was killed in active service, but her younger son took up aviation and was killed in a crash. She'd had to sell Nasse when faced with death duties, and took young Hattie (now Lady Stubbs) in her care. Amy now resides at her ancestral house, albeit as a tenant. Amy is a mother figure to the intellectually impaired Hattie, who had the great fortune to marry Sir George, especially in light of her deficiencies and the penury she would have suffered when her parents died bankrupt. But the housekeeper Miss Brewis tells Poirot that Hattie knows exactly what she's doing—no simpleton is she.
Scientist Alec Legge takes a break from sniping at his vapid wife to share with Poirot his disdain for his host and the other "simpleminded" revelers; he'd use his skill as a chemist to kill them all if he could. Sally blatantly flirts with Weyman. At the riverside, Poirot learns from the drunken ferryman, John Merdell, that Amy Folliat had trouble with her husband and sons, especially the younger one, who was wild. "Always be Folliat’s at Nasse," he tells Poirot meaningfully.
On the day of the fete, Hattie is further distressed to learn that her "wicked" cousin Etienne De Sousa is planning to arrive. A yacht, carrying Etienne, sails upriver. Soon, visitors arrive and murder hunters take clues from Ariadne. Sally slips away from fortuneteller duties in her tent for a rendezvous with Weyman in the folly. Etienne arrives and is greeted by George and Poirot, but no one can find Hattie. When Poirot and Ariadne look in the locked boathouse, they find not Lady Stubbs but Marlene, truly dead, murdered no more than an hour earlier.
Inspector Bland questions De Sousa, who came ashore at Nassecombe Quay, which took him by the boathouse, and Miss Brewis, who had taken refreshments to Marlene as per Lady Stubbs' orders. But Weyman contradicts this; Hattie, truly selfish, would never have ordered anything for Marlene. He lies, stating that he was at the pub all afternoon.
Poirot finds an exit in the rear of the fortuneteller's tent, which opens to a path through the bushes, leading to an old, disused pavilion. He finds a metal buckle on the floor. Continuing to the boathouse, he finds marginalia scrawled on Marlene's comics demonstrating that she was a secret observer. In the folly, he finds an airplane charm from Sally's fortuneteller bracelet and catches her trying to retrieve it.
When the police find Hattie's hat on the shore, they search Etienne's yacht and find Hattie's emerald ring in his jacket pocket. He claims innocence but they arrest him for Hattie's murder. Bland thinks she was dumped in the river.
Back in London, Poirot broods about his failure to solve the mysteries of Nasse and save the innocent Etienne, who will surely hang. He returns to Nasse to find Amy defeated, tired and with little to live for. Poirot is convinced she knows more and urges her to reveal all. Next he encounters Gertie, Merdell's granddaughter and Marlene's sister. She tells him that Merdell died when he slipped and knocked his head getting off his boat and reveals that he'd been angry at Marlene for her buying makeup with money she was given for keeping quiet about goings-on she'd seen in the woods. Poirot has sudden understanding of the mystery. He summons Ariadne and confirms that someone had switched the location of the corpse from the pavilion to the boathouse. Then he begs Bland to call Scotland Yard and tell them to release the innocent Etienne De Sousa.
He asks Folliat to meet him at the boathouse. There, he reveals the truth of her crimes: After inflicting an unspeakable crime on a 14-year-old girl, Amy's wayward, wild son Jack had been sent away to South Africa. Years later, she learned he'd been killed in a plane crash. But James secretly resurfaced, having faked his own death to escape pursuit by police. The ne'er-do-well then persuaded his mother to give him one more chance. Hattie, the mentally impaired girl in Amy's charge, was to inherit a huge fortune, but Amy hid this fact, saying Hattie's parents had lost it all. In light of her penury and for her own good, Amy arranged for Hattie to marry an older, enormously rich man when she came of age: George Stubbs…the new identity of the actually penniless James. With Hattie's fortune, they bought Nasse house, secretly restoring James to his ancestral home and positioning Amy to continue caring for Hattie. But what Amy didn't know was that James was already married to an Italian girl connected to the criminal underworld and determined to be reunited with her now-rich husband. The night that Hattie arrived at Nasse, she was bundled up and rushed upstairs without anyone seeing her face. George murdered her that night in her bed and replaced her with the fake Hattie, who took her identity. The body was buried under the concrete poured where the tree went down, and the folly was built above. The plan would have continued apace, with "Hattie" receiving treatment and eventually regaining her full faculties, had James not been recognized by John Merdell, the ferryman, and had the real Hattie's cousin not arrived.
Merdell made the mistake of sharing with his granddaughter Marlene the truth about George's identity; Marlene blackmailed George for her silence. Needing to dispose of their blackmailer and fearful that Etienne De Sousa would recognize that Hattie was an imposter and expose their deception, they arranged to kill Marlene, make Hattie disappear, and pin both crimes on Etienne, George planting Hattie's ring in Etienne's pocket when he greeted him.
Slipping into the fortuneteller's tent while Sally was breaking for tea, Hattie snuck to the pavilion and disguised herself as one of the foreign hitchhikers with clothes she'd kept in a rucksack. She unlocked and entered the boathouse, strangled Marlene, then rejoined her Dutch friend on the lawn and boarded the bus unnoticed. She would return to Italy, where after a time, James would reunite with her. In the meantime, he murdered John Merdell, making it look like an accident.
As the police demolish the folly to exhume the real Hattie's corpse, Amy requests to see her son one last time. Poirot and Ariadne, outside of Nasse, hear two gunshots, presumably Amy, tragically, taking her son's life and her own.