The Tower of Hanoi - Myths and Maths

This is the first comprehensive monograph on the mathematical theory of the solitaire game The Tower of Hanoi. It comprises a survey of the historical development from its invention in 1883 by the French number theorist Édouard Lucas to recent research in mathematics and applications in computer science and psychology. For instance, the so-called Frame-Stewart conjecture is an open problem since almost 70 years and shows the timeliness of the topic. The book

From the reviews: "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)

From the reviews:"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)

From the reviews:

"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 offers a comprehensive review of the mathematical theory of the solitaire game The Tower of Hanoi, from its invention in 1883 by the number theorist Édouard Lucas to current research in mathematics and applications in computer science and psychology.

Andreas M. Hinz is Professor at the Institute for Mathematics, University of Munich (LMU), Germany. Sandi Klavžar is Professor at the Faculty of Mathematics and Physics, University of Ljubljana, Slovenia. Uroš Milutinović is Professor at the Department of Mathematics and Computer Science, University of Maribor, Slovenia. 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.