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Cups and downs. (English) Zbl 1273.00016

Summary: Martin Gardner wrote about a coin-flipping trick, performed by a blindfolded magician. The paper analyses this trick, and compares it with a similar trick using three cups flipped in pairs. Several different methods of analysis are discussed, including a graphical analysis of the state space and a representation in terms of a matrix. These methods can also solve a more general problem about inverting \(n\) cups \(m\) at a time, whose answer is surprisingly complicated.

MSC:

00A08 Recreational mathematics
05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
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