It's a Kind of Magic: Mathematical Magic Tricks Explained

It's a Kind of Magic offers a large assortment of number tricks, mind reading tricks, and card tricks, along with mathematical explanations of what makes them work. Of course, the mathematician will realize that there is nothing magic about the tricks at all, but rather that these tricks exploit properties of numbers and patterns in a way that surprises an unsuspecting audience. This book will appeal to mathematicians and mathematics teachers who want to use the tricks to illustrate topics in number theory and also to magicians who want to add tricks to their repertoires.

The book is organized with descriptions of how to perform the tricks, grouped by type of trick, with a second section describing why the tricks work. As a mathematician and not a magician, I found myself much more interested in the explanations of the tricks than the tricks themselves. Often the explanations are simply a sequence of algebraic manipulations that reveal why the trick works, but a few cases offer more hearty fare. For example, there are a few tricks that rely on the Chinese Remainder Theorem, with details about the theorem in an appendix.

I might have preferred that the descriptions of the tricks were immediately followed by their explanations, because I found myself flipping back and forth between the descriptions and explanations, but this reveals my bias toward the mathematics and not the "magic" of the trick. For my use, it might also have been helpful if the tricks were organized by type of mathematics used rather than type of trick, but again, that's my bias.

I expect the book could be of great use for teachers in K-12 classrooms. College courses that prepare teachers, as well as undergraduate number theory courses, would also find valuable problems to support topics covered in those classes.

Elizabeth A. Burroughs, is an assistant professor of mathematics education in the Department of Mathematical Sciences at Montana State University.