A Surprising Magic Trick, Its Mathematical Background, and Some Generalizations

Recently, a magic trick not known to me before was presented in our magic circle.Footnote 1 Its mathematical background is interesting, and an analysis will give rise to several generalizations. We note that our results are formally related to Bob Hummer’s tricks of type “cut and turn over two” (CATO) (see, for example, [1, Chapter 2]). In those tricks, like the one under consideration here, the magician knows more than one would expect after a spectator has produced a seemingly chaotic constellation of cards by switching and shuffling.