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Black Sandwich, Red Sandwich
The plot is one of having a selected card travel magically from between a pair of sandwiching black cards, like the Jacks, in one half of the deck, to appear between the red counterparts in the other half of the deck. The plot appears to be L. Vosburgh Lyons's, and appeared under the title above in The Jinx, No. 110, nd., p. 654. Milt Kort offered a simplified handling, keeping Lyons's title, in The Gen, Vol. 23 No. 3, July 1967, p. 62-63.
Larry Jennings's “Visitor” in Alton Sharpe's Expert Card Mysteries, 1969, p. 53-56, is a popular solution and seems to be the first handling to feature a two-way travel in which the selected card travels back to the original sandwich.