Stewart, Ian Cups and downs. (English) Zbl 1273.00016 Coll. Math. J. 43, No. 1, 15-19 (2012). 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.) PDFBibTeX XMLCite \textit{I. Stewart}, Coll. Math. J. 43, No. 1, 15--19 (2012; Zbl 1273.00016) Full Text: DOI