The Tower of Hanoi – Myths and Maths

  • Andreas M. Hinz
  • Sandi Klavžar
  • Uroš Milutinović
  • Ciril Petr

Table of contents

  1. Front Matter
    Pages i-xv
  2. Andreas M. Hinz, Sandi Klavžar, Uroš Milutinović, Ciril Petr
    Pages 1-51
  3. Andreas M. Hinz, Sandi Klavžar, Uroš Milutinović, Ciril Petr
    Pages 53-69
  4. Andreas M. Hinz, Sandi Klavžar, Uroš Milutinović, Ciril Petr
    Pages 71-130
  5. Andreas M. Hinz, Sandi Klavžar, Uroš Milutinović, Ciril Petr
    Pages 131-140
  6. Andreas M. Hinz, Sandi Klavžar, Uroš Milutinović, Ciril Petr
    Pages 141-164
  7. Andreas M. Hinz, Sandi Klavžar, Uroš Milutinović, Ciril Petr
    Pages 165-209
  8. Andreas M. Hinz, Sandi Klavžar, Uroš Milutinović, Ciril Petr
    Pages 211-226
  9. Andreas M. Hinz, Sandi Klavžar, Uroš Milutinović, Ciril Petr
    Pages 227-239
  10. Andreas M. Hinz, Sandi Klavžar, Uroš Milutinović, Ciril Petr
    Pages 241-259
  11. Andreas M. Hinz, Sandi Klavžar, Uroš Milutinović, Ciril Petr
    Pages 261-263
  12. Back Matter
    Pages 265-335

About this book

Introduction

This is the first comprehensive monograph on the mathematical theory of the solitaire game “The Tower of Hanoi” which was invented in the 19th century by the French number theorist Édouard Lucas. The book comprises a survey of the historical development from the game’s predecessors up to recent research in mathematics and applications in computer science and psychology. Apart from long-standing myths it contains a thorough, largely self-contained presentation of the essential mathematical facts with complete proofs, including also unpublished material. The main objects of research today are the so-called Hanoi graphs and the related Sierpiński graphs. Acknowledging the great popularity of the topic in computer science, algorithms and their correctness proofs form an essential part of the book. In view of the most important practical applications of the Tower of Hanoi and its variants, namely in physics, network theory, and cognitive (neuro)psychology, other related structures and puzzles like, e.g., the “Tower of London”, are addressed.

Numerous captivating integer sequences arise along the way, but also many open questions impose themselves. Central among these is the famed Frame-Stewart conjecture. Despite many attempts to decide it and large-scale numerical experiments supporting its truth, it remains unsettled after more than 70 years and thus demonstrates the timeliness of the topic.

Enriched with elaborate illustrations, connections to other puzzles and challenges for the reader in the form of (solved) exercises as well as problems for further exploration, this book is enjoyable reading for students, educators, game enthusiasts and researchers alike.

Keywords

Chinese Rings Frame-Stewart conjecture Gray code History of puzzles Sierpiński triangle Tower of London algorithms cognitive tests combinatorics finite automata integer sequences

Authors and affiliations

  • Andreas M. Hinz
    • 1
  • Sandi Klavžar
    • 2
  • Uroš Milutinović
    • 3
  • Ciril Petr
    • 4
  1. 1.Faculty of Mathematics, Computer ScienceLMU MünchenMunichGermany
  2. 2., Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia
  3. 3., Department of MathematicsUniversity of MariborMariborSlovenia
  4. 4., Faculty of Natural Sciences and MathematUniversity of MariborMariborSlovenia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-0237-6
  • Copyright Information Springer Basel 2013
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-0348-0236-9
  • Online ISBN 978-3-0348-0237-6
  • About this book