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American private eye Steve Martin flies to Cape Town at the behest of Wexler, a copper tycoon who fears that his life is in danger following the murder of his butler. Martin is met at the airport by Wexler's secretary, Helga, and almost immediately an attempt is made on their lives. The members of Wexler's household, all of whom attract suspicion, include Gina, the millionaire's sensual stepdaughter; Paul, his personal physician and his daughter's boyfriend; and Anderson, the manager of Wexler's copper mine. Also working on the case is philandering police chief Inspector Lean, who has discovered an old photograph of four prisoners of war, including Wexler and the murdered butler. Ostrich farmer Vanberger, also among the prisoners in the photograph, soon meets his death, and Wexler, too, is eventually murdered. The two sleuths discover that the man responsible for the crimes is Paul, whose father, the fourth man in the photograph, was murdered by Wexler many years ago after discovering a rich copper deposit. Paul falls to his death after a chase along the cliffs of Table Mountain, and Martin returns to the United States with Helga, whom he plans to marry.