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The only person on the island who knows how to repair the radio transmitter is the Skipper (Alan Hale Jr.). Unfortunately, the Skipper can only rememeber the instructions when he's asleep and dreaming. As the possibility of rescue in the form of the famous aviatrix "The Vagabond Lady" looms large, everyone does everything within their power to keep the Skipper in dreamland, with the Professor (Russell Johnson) working hardest of all as an amateur hypnotist.