*Knight's Tours Notes*book that I am still working on and hope to publish soon. The 'z' represents a Knot symbol. The page numbers preceding each section should be in bold type.

Contents in 24 Knots

z 1- Theory 5 Boards 6 Moves, Pieces 8 Freedom and Multiplicity 9 Mobility, Nets 11 Journeys 14 Shortest Path Problem 17 Two-move Journeys: Angles 18 Schuh's Theorem, 3-Move, 4- 6- and 8-Move Circuits 22 Tours and Pseudotours 23 Touring Tests 24 Simple Linking 26 Symmetry 29 Symmetry in Paths 31 Magic Tours 37 Natural Magic 38 Some History of Magic Squares.

z 2- Lateral Movers 41 Labyrinths 42 The Wazir 2×n 44 3×n, 4×n, 5×n 50 6×6 8×8, 10×10 and larger 53 Non-crossing Rook Tours 54 Figured Wazir Tours 55 Rook around the Rocks 57 Rooks, One-Rank Tours 58 Two-Move 59 Three-Move 60 Four-Move Magic, More-Move Rooks.

z 3- Diagonal Movers 62 Knots 64 King, 2×n, 69 3×n 70 4×n 72 5×n 6×n 73 7×n 8×8 74 Alternating, Figured 75 Magic 76 Diamagic, Biaxial 79 Axial 80 Larger 81 Two-Move Queens 82 Three-Move 84 Four-Move 85 More-Move Queens.

z 4- Knight-Move Geometry 87 Nets, Borders, Coding, Generic Moves 91 Central Angles, Triangles, Quadrilaterals, Polygons, Intersections, Formations 96 Slants, Eccentrics, Radials 98 Symmetry in Rectangles 100 Mixed Quaternary Symmetry 102 Existence Theorems.

z 5- Shaped Boards 103 Octonary 107 Birotary 124 Biaxial 132 Rotary 154 Axial 166 Unary.

z 6- Oblong Boards 191 3×n 194 3×4 196 3×8 199 3×9 204 3×10 207 3×12 209 3×14 211 3×16 213 4×n 221 4×8 Medieval 231 4×9, 4×10, 4×11 238 5×n 242 6×n 246 7×n 248 8×n 251 Larger

z 7- Odd Square Boards 254 5×5 258 7×7 260 9×9 261 11×11 262 13×13, 15×15.

z 8- Oddly Even Squares 263 The 6×6 Board, Quaternary, Binary, Centre angles, Slants, 3-slant open tours, Semimagic, Figured 311 The 10×10 Board 320 14×14 322 18×18 etc.

z 9- The 8×8 Board: History 324 The Earliest Full-Board Tours 326 Rediscovery 1725-1823 337 Squares and Diamonds 1823-48 345 The First Magic Knight Tours 1848-76 351 The Age of Magic Tours 1876-86 363 Taking Stock 1886-1986 368 Completing the Task 1986-2003.

z 10- The 8×8 Board: Magic Methods 371 Quartes 374 Contraparallel chains, X and N notation 377 Murray's Test Procedure 378 Catalogues: Historical 381 Geometric 388 Arithmetic

z 11- The 8×8 Board: Lettered Tours 403 Alphabetical 406 Cryptotours, Crossword Tours

z 12- The 8×8 Board: Figured Tours 414 History 416 Dawsonian 427 My Own Work.

z 13- The 8×8 Board: Graphic Tours 429 Angles Min and Max, Directions, Triangles, Polygons, Stars, Intersections, Slants, Eccentrics, 446 Pictorial, Monograms. 451 Enumerations

z 14- The 8×8 Board: Asymmetry 452 Synthetic Tours 454 Irregularity 455 Approx Symmetry 456 Octonary, Biaxial 459 Axial 463 Birotary 464 Bergholtian 465 Diagonal.

z 15- The 8×8 Board: Exact Symmetry 466 Historical Examples 474 Construction, Conversion of Pseudotours 478 Symmetrisation 479 A Complete Central Angle Collection

z 16- The 8×8 Board: Mixed Symmetry 489 Types h-j-k. Mixed Quaternary Tours with h = 1 493 MQ Tours with k = 3 511 MQ Tours with h >1 and k >3 515 Summary, Max Octonary.

z 17- The 8×8 Board: Compartmental 516 Enumeration of Double Halfboard Tours 518 Crosspatch Patterns and Tours 524 Enumeration of Rhombic Double Halfboard Tours.

z 18- The 8×8 Board: Octonary Pseudotours 530 Catalogue 532 Collinian Tours 535 Tours from Other Octonary Pseudotours 538 Catalogue of Symmetric Rhombic Fullboard Tours.

z 19- The 8×8 Board: Quaternary Pseudotours 550 Enumeration, Vandermondian, Jaenischian 553 Aladdin's Conundrum, Non-Crossing 555 Catalogue 608 Other Quaternary.

z 20- Larger Evenly Even Squares 612 Braids 613 12×12 628 16×16 635 Even Larger

z 21- Augmented Knights 642 Two-Move Knighted Pieces, Emperor, Empress, Templar, Prince, Hospitaller, Lancelot, Nightrider 653 Three-move Knights 663 Four-move Knights

z 22- The Big Beasts 666 Camel {1,3} 669 Shaped boards 671 C+ 672 Gnu 675 Giraffe {1,4} 677 G+ 680 {1,5} 681 {1,6} 682 {1,7} 683 Root 50 {1,8} Zebra {2,3} 686 Z-rider, Z+ 689 {2,5} 690{2,7} 691 Antelope {3,4} 692 Fiveleaper 698 A+ 699 {3,5}, {4,5} 700 {6,7}, Chimaeras 703 Root 65, Root 85 704 Triple Beasts 707 Multimovers, 7×9 Rectangle 708 Wizard.

z 23- Alternative Worlds 709 Non-Crossing Paths 716 Rider and Hopper tours 720 Bent Boards 723 Space Chess 732 Honeycomb Boards

z 24- End Pages 738 Puzzle Solutions 742 Bibliography 798 Name Index