ANSWERS: 2
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A split screen was used when the "cousins" had to appear in the same scene.
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As Perryman said, split screen was used most of the time, but I also found this: The dual role for Duke challenged special effects for its time, considering television special effects were rare in the early 1960s, particularly for a sitcom. When special effects weren't practical, child actress Rita McLaughlin was used as Duke's double (almost always seen only from behind).[2] Ironically, McLaughlin's hair was bright red while Duke was a brunette. This proved not to be a problem for the show since the two actresses' hair shades appeared the same in monochrome.
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