The Tower of Hanoi – Myths and Maths

Andreas M. Hinz is Professor at the Department of Mathematics, University of Munich (LMU), Germany. He has worked at the University of Geneva (Switzerland), King's College London (England), the Technical University of Munich (Germany), and the Open University in Hagen (Germany). His main fields of research are real analysis, the history of science, mathematical modeling, and discrete mathematics. Sandi Klavzar is Professor at the Faculty of Mathematics and Physics, University of Ljubljana, Slovenia, and at the Department of Mathematics and Computer Science, University of Maribor, Slovenia. He is an author of three books on graph theory and an editorial board member of numerous journals including Discrete Applied Mathematics, European Journal of Combinatorics, and MATCH Communications in Mathematical and in Computer Chemistry. Uros Milutinovic is Professor at the Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia. His main fields of research are topology and discrete mathematics. Ciril Petr is a researcher at the Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia.

Foreword by Ian Stewart.- Preface.- 0 The Beginning of the World.- 1 The Chinese Rings.- 2 The Classical Tower of Hanoi.- 3 Lucas's Second Problem.- 4 Sierpinski Graphs.- 5 The Tower of Hanoi with More Pegs.- 6 Variations of the Puzzle.- 7 The Tower of London.- 8 Tower of Hanoi Variants with Oriented Disc Moves.- 9 The End of the World.- A Hints and Solutions to Exercises.- Glossary.- Bibliography.- Name Index.- Subject Index.- Symbol Index.

"The Tower of Hanoi isn't just a recreational problem, it is also a substantial area worthy of study, and this book does this area full justice. ... I haven't enjoyed reading a 'popular mathematics' book as much for quite some time, and I don't hesitate to recommend this book to students, professional research mathematicians, teachers, and to readers of popular mathematics who enjoy more technical expository detail." (Chris Sangwin, The Mathematical Intelligencer, Vol. 37, 2015)

"This book takes the reader on an enjoyable adventure into the Tower of Hanoi puzzle (TH) and various related puzzles and objects. ... 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 ... and some proofs of the theorems or statements inthe main text. ... As such, the book will be an enjoyable read for any recreational mathematician ... ." (Andrew Percy, zbMATH, Vol. 1285, 2014)

"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)