Handbook of Cubik Math

A clear explanation of the mathematics that underlies Rubik's Cube, and how the cube can be used to grasp the fundamentals of group theory.

In thirty years, Rubik's cube, invented by Erno Rubik, has established itself as a neverending source of delight, frustration and intellectual stimulation to children and adults alike. There is a large literature on the subject, but one of the few books to have established themselves as offering a serious contribution to the subject is Alexander H. Frey's and David Singmaster's Handbook of Cubik Math, first published in 1982.

Frey and Singmaster were the first to offer an elegant mathematical solution to the cube, doing it in a form that enables readers to understand the processes that have been undertaken. As a result the book has proved readily accessible to generations of high-school maths students and more advanced college students of algebra.

The solution is intuitive, and does not require memorisation of formulae. The authors demonstrate how movements of the cube exemplify the fascinating but abstract field of mathematics known as group theory. Using the cube as a model they make comprehensible and concrete the hard-to-understand ideas of group theory. Their hypothesis that the maximum number of moves required for 'God's Algorithm' was in the low twenties was proved correct in 2008 by Tomas Rokicki, who showed that it was twenty-two.

In addition to showing how to solve Rubik's cube, the authors explain the theory involved, and its application to similar puzzles. They also show how the cube provides a physical example for many mathematical concepts where such examples are scarce, and the book therefore provides a useful teaching aid.

Alexander H. Frey, Jr has a Ph.D. in mathematics from the University of Washington and was a computer architect with IBM. He is now retired.