Quick recap
An insurer sends Poirot to look into millionaire Sir Horace Blatt's fake diamond; Blatt blames his ex-mistress, actress Arlena Marshall. The trail leads to a hotel on an Adriatic island, where Arlena is vacationing with her new husband and flirting with Patrick Redfern, who's married to Christine. One morning Arlena is found strangled in a cove, and every guest has an alibi. Poirot takes Christine's apart: she knocked Arlena out, dressed as her to be seen as the body, and Patrick did the rest. Patrick's signature matches that of the husband of a woman killed months earlier in Yorkshire. The Redferns are arrested, and the real diamond turns up.
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