The Tower of Hanoi - Myths and Maths
From the reviews:“This research monograph focuses on a large family of problems connected to the classic puzzle of the Tower of Hanoi. … The authors explain all the combinatorial concepts they use, so the book is completely accessible to an advanced undergraduate student. … Summing Up: Recommended. Comprehensive mathematics collections, upper-division undergraduates through researchers/faculty.” (M. Bona, Choice, Vol. 51 (3), November, 2013)“The Tower of Hanoi is an example of a problem that is easy to state and understand, yet a thorough mathematical analysis of the problem and its extensions is lengthy enough to make a book. … there is enough implied mathematics in the action to make it interesting to professional mathematicians. … It was surprising to learn that the ‘simple’ problem of the Tower of Hanoi … could be the subject of a full semester special topics course in advanced mathematics.” (Charles Ashbacher, MAA Reviews, May, 2013)“Gives an introduction to the problem and the history of the TH puzzle and other related puzzles, but it also introduces definitions and properties of graphs that are used in solving these problems. … Thus if you love puzzles, and more in particular the mathematics behind it, this is a book for you. … Also if you are looking for a lifelasting occupation, then you may find here a list of open problems that will keep you busy for a while.” (A. Bultheel, The European Mathematical Society, February, 2013)"This book takes the reader on an enjoyable adventure into the Tower of Hanoi puzzle (TH) and various related puzzles and objects. While essentially self-contained, readers with an introductory understanding of discrete mathematics will be more comfortable as some concepts and notation, such as mathematical logic, are assumed. The style of presentation is entertaining, at times humorous, and very thorough. The exercises ending each chapter are an essential part of the explication providing some definitions (such as perfect codes in Ex 1.5) and some proofs of the theorems or statements in the main text. As such, the book will be an enjoyable read for any recreational mathematician but, as the authors point out, could also be used as a text book for a second course into a particular area of discrete mathematics or as an introduction for research into the various unsolved conjectures and the list of possible extension topics given in the final chapter.  Chapter 0 “The beginning of the world” begins with a detailed history of TH invented by Edward Lucas in 1883. We then move through a broad range of topics related to TH and its generalizations which equips and introduces the reader to what the book will achieve. Topics include Chinese rings, Fibonacci numbers, Arithmetic (Pascal’s) triangle, combinatorics, probability, Sierpinski triangles, graphs, paths, circuits and colourings, Stern’s diatomic arrays, equivalence and Burnside’s counting theorem. Chapter 0 concludes with a thorough literature review of TH and related puzzles (there are 352 references) and their application in psychological testing. The next eight chapters provide the mathematical detail supporting the statements and summary given in the introductory Chapter 0 and develop the known theory of TH and several generalizations. (...) [The last chapter] is followed by a generous Hints and Solutions to Exercises, a Glossary and three comprehensive Indexes all of which provide the reader with as much help as anyone might wish for in a mathematical text."(Andrew Percy, zbMath, February, 2014)