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Table of Contents
Intro; Foreword; Preface; Myths; Prerequisites; Algorithms; Exercises; Contents; Educational aims; Feedback; Acknowledgements; Preface to the Second Edition; Contents; Chapter 0 The Beginning of the World; 0.1 The Legend of the Tower of Brahma; 0.2 History of the Chinese Rings; 0.3 History of the Tower of Hanoi; 0.4 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; 0.6 Elementary Graphs; 0.6.1 The Handshaking Lemma; 0.6.2 Finite Paths and Cycles
0.6.3 Infinite Cycles and Paths0.7 Puzzles and Graphs; 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; 0.8.1 Equivalence; 0.8.2 Group Actions and Burnside's Lemma; 0.9 Distance; 0.10 Early Mathematical Sources; 0.10.1 Chinese Rings; 0.10.2 Tower of Hanoi; Missing minimality, false assumptions and unproved conjectures; The Reve's puzzle; "No more articles on the Towers of Hanoi for a while."; The presumed minimal solution for The Reve's puzzle; The first serious papers; Psychology, variations, open problems
0.11 ExercisesChapter 1 The Chinese Rings; 1.1 Theory of the Chinese Rings; 1.2 The Gros Sequence; The greedy square-free sequence; 1.3 Two Applications; Topological variations; Tower of Hanoi networks; 1.4 Exercises; Chapter 2 The Classical Tower of Hanoi; 2.1 Perfect to Perfect; Regular states; Legal moves; The optimal solution; 2.1.1 Olive's Algorithm; More square-free sequences; 2.1.2 Other Algorithms; 2.2 Regular to Perfect; 2.2.1 Noland's Problem; 2.2.2 Tower of Hanoi with Random Moves; 2.3 Hanoi Graphs; 2.3.1 The Linear Tower of Hanoi; 2.3.2 Perfect Codes and Domination
2.3.3 Symmetries2.3.4 Spanning Trees; 2.4 Regular to Regular; 2.4.1 The Average Distance on Hn3; 2.4.2 Pascal's Triangle and Stern's Diatomic Sequence; 2.4.3 Romik's Solution to the P2 Decision Problem; 2.4.4 The Double P2 Problem; 2.5 Exercises; Chapter 3 Lucas's Second Problem; 3.1 Irregular to Regular; 3.2 Irregular to Perfect; 3.3 Exercises; Chapter 4 Sierpiński Graphs; 4.1 Sierpiński Graphs Sn3; 4.2 Sierpiński Graphs Snp; 4.2.1 Distance Properties; 4.2.2 Other Properties; Symmetries; Domination type invariants; Planarity; Connectivity; Colorings; Additional properties
4.2.3 Sierpiński Graphs as Interconnection Networks4.3 Connections to Topology: Sierpiński Curveand Lipscomb Space; 4.3.1 Sierpiński Spaces; 4.3.2 Sierpiński Triangle; Cantor sets; Connections to Sierpiński and Hanoi graphs; 4.3.3 Sierpiński Curve; Hanoi attractors; Lipscomb space; 4.4 Exercises; 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
0.6.3 Infinite Cycles and Paths0.7 Puzzles and Graphs; 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; 0.8.1 Equivalence; 0.8.2 Group Actions and Burnside's Lemma; 0.9 Distance; 0.10 Early Mathematical Sources; 0.10.1 Chinese Rings; 0.10.2 Tower of Hanoi; Missing minimality, false assumptions and unproved conjectures; The Reve's puzzle; "No more articles on the Towers of Hanoi for a while."; The presumed minimal solution for The Reve's puzzle; The first serious papers; Psychology, variations, open problems
0.11 ExercisesChapter 1 The Chinese Rings; 1.1 Theory of the Chinese Rings; 1.2 The Gros Sequence; The greedy square-free sequence; 1.3 Two Applications; Topological variations; Tower of Hanoi networks; 1.4 Exercises; Chapter 2 The Classical Tower of Hanoi; 2.1 Perfect to Perfect; Regular states; Legal moves; The optimal solution; 2.1.1 Olive's Algorithm; More square-free sequences; 2.1.2 Other Algorithms; 2.2 Regular to Perfect; 2.2.1 Noland's Problem; 2.2.2 Tower of Hanoi with Random Moves; 2.3 Hanoi Graphs; 2.3.1 The Linear Tower of Hanoi; 2.3.2 Perfect Codes and Domination
2.3.3 Symmetries2.3.4 Spanning Trees; 2.4 Regular to Regular; 2.4.1 The Average Distance on Hn3; 2.4.2 Pascal's Triangle and Stern's Diatomic Sequence; 2.4.3 Romik's Solution to the P2 Decision Problem; 2.4.4 The Double P2 Problem; 2.5 Exercises; Chapter 3 Lucas's Second Problem; 3.1 Irregular to Regular; 3.2 Irregular to Perfect; 3.3 Exercises; Chapter 4 Sierpiński Graphs; 4.1 Sierpiński Graphs Sn3; 4.2 Sierpiński Graphs Snp; 4.2.1 Distance Properties; 4.2.2 Other Properties; Symmetries; Domination type invariants; Planarity; Connectivity; Colorings; Additional properties
4.2.3 Sierpiński Graphs as Interconnection Networks4.3 Connections to Topology: Sierpiński Curveand Lipscomb Space; 4.3.1 Sierpiński Spaces; 4.3.2 Sierpiński Triangle; Cantor sets; Connections to Sierpiński and Hanoi graphs; 4.3.3 Sierpiński Curve; Hanoi attractors; Lipscomb space; 4.4 Exercises; 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