The Tower of Hanoi Myths and Maths 2nd Edition by Andreas Hinz, Sandi Klavzar, Ciril Petr ISBN 3319737791 9783319737799

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ISBN 10:      3319737791
ISBN 13: 978-3319737799
Author:      Andreas M. Hinz, Sandi Klavzar, Ciril Petr

The Tower of Hanoi Myths and Maths 2nd Table of contents:

Chapter 0: The Beginning of the World

• 0.1 The Legend of the Tower of Brahma – A historical or mythological introduction to the Tower of Hanoi.
• 0.2 History of the Chinese Rings – Exploring the origins and mathematical structure of the Chinese Rings puzzle.
• 0.3 History of the Tower of Hanoi – A deep dive into the origins and development of the Tower of Hanoi puzzle.
• 0.4 Sequences – Focus on mathematical sequences:
  • 0.4.1 Integers
  • 0.4.2 Integer Sequences
  • 0.4.3 The Dyadic Number System
  • 0.4.4 Finite Binary Sequences
• 0.5 Indian Verses, Polish Curves, and Italian Pavements – Likely an exploration of the intersections between puzzles and cultural/mathematical concepts.
• 0.6 Elementary Graphs – Introduces basic graph theory concepts.
  • 0.6.1 The Handshaking Lemma
  • 0.6.2 Finite Paths and Cycles
  • 0.6.3 Infinite Cycles and Paths
• 0.7 Puzzles and Graphs – Graph-theory applications to puzzles.
  • 0.7.1 The Bridges of Königsberg
  • 0.7.2 The Icosian Game
  • 0.7.3 Planar Graphs
  • 0.7.4 Crossing Rivers without Bridges
• 0.8 Quotient Sets – Focus on equivalence relations, group actions, and Burnside’s Lemma.
  • 0.8.1 Equivalence
  • 0.8.2 Group Actions and Burnside’s Lemma
• 0.9 Distance – Likely about distances in graphs or puzzles.
• 0.10 Early Mathematical Sources – Historical context for the development of these puzzles.
  • 0.10.1 Chinese Rings
  • 0.10.2 Tower of Hanoi
• Missing Minimality, False Assumptions, and Unproved Conjectures – A discussion on puzzle-solving and conjectures in the early stages of mathematical research.
• The Reve’s Puzzle – Possibly an introduction to a related puzzle or its mathematical significance.
• The First Serious Papers – Exploration of early formal treatments of these puzzles.
• Psychology, Variations, Open Problems – Discusses cognitive aspects and unsolved challenges in the puzzles.
• 0.11 Exercises – A collection of problems for the reader to engage with.

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Chapter 1: The Chinese Rings

• 1.1 Theory of the Chinese Rings – An exploration of the mathematical structure and solving strategy of the Chinese Rings.
• 1.2 The Gros Sequence – Possibly a sequence related to the puzzle.
  • The Greedy Square-Free Sequence – Likely discussing a specific type of sequence used in the puzzle.
• 1.3 Two Applications – Applications of the Chinese Rings puzzle in other contexts:
  • Topological Variations
  • Tower of Hanoi Networks
• 1.4 Exercises – Problems related to the Chinese Rings.

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Chapter 2: The Classical Tower of Hanoi

• 2.1 Perfect to Perfect – Focusing on the concept of “perfect” states and solutions in the Tower of Hanoi.
  • Regular States and Legal Moves
  • The Optimal Solution – Likely introducing a formal way to solve the puzzle optimally.
  • 2.1.1 Olive’s Algorithm – A specific algorithm for solving the Tower of Hanoi.
  • 2.1.2 Other Algorithms – Additional solving algorithms.
• 2.2 Regular to Perfect – Another phase or step in solving the puzzle.
  • Noland’s Problem
  • Tower of Hanoi with Random Moves
• 2.3 Hanoi Graphs – Using graph theory to model the Tower of Hanoi.
  • The Linear Tower of Hanoi
  • Perfect Codes and Domination
  • Symmetries
  • Spanning Trees
• 2.4 Regular to Regular – A focus on specific solutions.
  • The Average Distance on Hn3
  • Pascal’s Triangle and Stern’s Diatomic Sequence
  • Romik’s Solution to the P2 Decision Problem
  • The Double P2 Problem
• 2.5 Exercises – Related exercises to solidify the concepts from the chapter.

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Chapter 3: Lucas’s Second Problem

• 3.1 Irregular to Regular
• 3.2 Irregular to Perfect
• 3.3 Exercises

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Chapter 4: Sierpiński Graphs

• 4.1 Sierpiński Graphs Sn3
• 4.2 Sierpiński Graphs Snp – A detailed look at these fractal-like graphs and their properties.
  • Distance Properties
  • Other Properties – Symmetry, Domination-type invariants, Planarity, Connectivity, Colorings, etc.
  • Sierpiński Graphs as Interconnection Networks
• 4.3 Connections to Topology – Connections between these graphs and topological concepts.
  • Sierpiński Spaces
  • Sierpiński Triangle
  • Cantor Sets
  • Connections to Sierpiński and Hanoi Graphs
• 4.4 Exercises

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Chapter 5: The Tower of Hanoi with More Pegs

• 5.1 The Reve’s Puzzle and the Frame-Stewart Conjecture
• 5.2 Frame-Stewart Numbers
• 5.3 Numerical Evidence for The Reve’s Puzzle
• 5.4 Even More Pegs
  • Strong Frame-Stewart Conjecture (SFSC)
• 5.5 Bousch’s Solution of The Reve’s Puzzle – Focus on solving the puzzle with new techniques.
  • Some Two-Dimensional Arrays
  • Dudeney’s Array
  • Frame-Stewart Numbers Revisited
  • The Reve’s Puzzle Solved
  • The Proof of Theorem 5.38
• 5.6 Hanoi Graphs Hnp
• 5.7 Numerical Results and Largest Disc Moves
  • Path Algorithms
  • Largest Disc Moves
• 5.8 Exercises

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Chapter 6: Variations of the Puzzle

• 6.1 What is a Tower of Hanoi Variant?
• 6.2 Ambiguous Goal
• 6.3 The Tower of Antwerpen – A specific variation.
  • Little Tower of Antwerpen
  • Twin- and Triple-Tower Problems
  • Linear Twin Hanoi
  • Classical-Linear Hybrid Problem
• 6.4 The Bottleneck Tower of Hanoi
• 6.5 Exercises

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Chapter 7: The Tower of London

• 7.1 Shallice’s Tower of London
• 7.2 More London Towers
• 7.3 Exercises

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Chapter 8: Tower of Hanoi Variants with Restricted Disc Moves

• 8.1 Solvability
• 8.2 An Algorithm for Three Pegs
  • The Cyclic Tower of Antwerpen
• 8.3 Undirected Move Graphs on More Than Three Pegs
  • Stockmeyer’s Tower
  • 3-Smooth Numbers
  • Bousch’s Proof of Stockmeyer’s Conjecture
  • Stewart-Type Algorithms
  • The Linear Tower of Hanoi
• 8.4 The Cyclic Tower of Hanoi
• 8.5 Exponential and Sub-Exponential Variants
• 8.6 Exercises

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Chapter 9: Hints, Solutions and Supplements to Exercises

• This chapter appears to provide hints and solutions to exercises from the previous chapters.

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Chapter 10: The End of the World

• Likely a conclusion or reflection on the Tower of Hanoi and its broader mathematical and puzzle-related context.

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