Evil Under the Sun

A female hiker finds a dead woman on the North York Moors in England. The strangled victim is identified as Alice Ruber.
Four months later, an insurance company asks detective Hercule Poirot to examine an expensive diamond belonging to millionaire Sir Horace Blatt. Poirot identifies it as a fake, but is assured by Sir Horace that the original was purchased at Tiffany’s in New York for his mistress, actress Arlena Stuart Marshall; she apparently returned a paste replica after their split. Poirot agrees to meet Arlena at an exclusive hotel on an island in the Adriatic Sea to probe the mystery. The hotel was the King of Tyrania's summer palace, gifted to his former mistress, ex-actress Daphne Castle.
Arlena is on holiday with Kenneth, her new husband. She is emotionally abusive to her stepdaughter, Linda, and flirts openly with Patrick Redfern, who is holidaying on the island with his wife, Christine. Kenneth turns to his old friend, Daphne for support. She is horrified by how Arlena treats Kenneth and Linda and reveals that Arlena arranged for Patrick to be on the island. Also at the resort are theatrical producers Odell and Myra Gardener, who are experiencing financial hardship because Arlena left a major show of theirs and is refusing a role in another. Likewise, Arlena is causing trouble for writer Rex Brewster, who has already spent his advance royalties for Arlena's tell-all biography, which she now refuses to approve for release.
Early on the third morning, Arlena goes by paddle-boat to Ladder Bay for an assignation with Patrick. He arrives by powerboat with Myra, and, upon approaching Arlena, calls out to Myra that Arlena has been strangled.
Poirot begins to investigate the murder, but all of the guests have an alibi. Kenneth claims to have been in his room typing at the time of the crime. Christine was with Linda at Gull Cove, and did not leave until 11:55 for a 12:30 tennis match. Sir Horace argued with Arlena at Ladder Bay and returned the fake diamond at 11:30, with Arlena promising an explanation that evening; his alibi is confirmed by both his yacht crew and Daphne. Poirot found the bauble in a grotto when examining the crime scene. Patrick left the hotel with Myra minutes before 12:00 PM, seeing Sir Horace's yacht approaching, and hearing the commemorative noon cannon firing. Rex met the swimming Linda when entering Gull Cove at noon, and reports that a bottle flung from the top of a cliff nearly hit him. Odell was seen reading by Daphne and her staff. He claims low water pressure hindered his 12:15 wash before tennis, but nobody admits to bathing at that time.
Assembling the suspects together, Poirot accuses the Redferns of the crime. He asserts that Christine knocked out Arlena and hid her in the grotto (where he had detected Arlena's perfume in the air), then donned her outfit and applied makeup to simulate a suntan and posed as Arlena's body for Myra to see. After Myra went for help, Patrick strangled Arlena and placed her body on the beach.
Poirot calls Christine's alibi into question by proposing that she set Linda's watch twenty minutes ahead, suggested the girl wear a swim cap to muffle the sound of the noon cannon, and corrected the watch before leaving to attack Arlena. Once Myra left the beach, Christine still would have had time to toss away the lotion bottle—which almost hit Rex—and wash off her "tan"—accounting for the drop in water pressure—before the tennis match. The Redferns scoff at Poirot's accusations, and taunt that he has provided neither motive, nor proof.
Patrick pays for his hotel stay by cheque, signing the "R" in "Redfern" in a distinctive way that Poirot recognises as being the same way "Felix Ruber", husband of the well-insured Yorkshire moor victim, signed his name. Poirot states that sending for pictures will prove this, as well as that the hiker who found the body, at a time when the husband had an alibi, was Christine. Exposed, Patrick does not resist when Poirot removes a pipe, which he never actually smokes, from his lips, empties its bowl, and reveals the real diamond. Redfern then punches Poirot before he and Christine are arrested and taken away from the island by boat. Daphne informs Poirot that he will be rewarded by the Kingdom of Tyrania for his work before he and the others depart the island.