Knight's Tour Notes
Compiled by George Jelliss © 2000 – 2023

A version of these Knight's Tour Notes [September 2019] is now available on the publications page in the form of twelve PDFs. Those new to the subject may like to see some selected Highlights. I have also reproduced here an older essay Introducing Knight's Tours since I have found it was cited in several sources. For a record of changes to this website and a history of this work on knight's tours see the Archive Page. Asterisked pages (*) outside the magic knight section also include magic or semimagic results. [2022] notes recent updates.


HISTORY
Early History of Knight's Tours
Rediscovery of the Knight's Problem
Rhombic Tours and Roget's Method
History of Magic Knight's Tours *
Indian Tours
Representation of Knight's Tours
Cryptotours

Chronology: Before 1800
Chronology: 1800 to 1899
Chronology: 1900 to 1999
Chronology: 2000s
Biobibliography
Links [2023]

THEORY
Theory of Moves and Pieces
Theory of Journeys
Shortest Path Problem
Knight-Move Geometry
Symmetry in Knight's Tours
Simple-Linking of Pseudotours
Theory of Magic * [2022]
Theory of Magic Knight's Tours *

OBLONG BOARDS
3×N Knight Tours Open
3×N Knight Tours Closed
4×N Knight Tours
4×N Semi-Magic Knight Tours *
Knight Tours of Larger Oblongs * [Jan 2023]
Knight Tours 6×7 Extra Diagrams [Jan 2023]
Oblong Magic Knight Tours *

SQUARE BOARDS
Odd Square Boards

6×6 Symmetric Knight Tours
6×6 Asymmetric with 4 or 12 Slants
6×6 Asymmetric with 6 or 10 Slants
6×6 Asymmetric with 8 Slants
6×6 Semi-Magic Knight Tours *

8×8 Board: Counting Tours [2022]
8×8 Rhombic Tours with 4 Slants
8×8 Graphical Tours: Lines
8×8 Collinian Tours
8×8 Crosspatch Tours
8×8 Octonarian Tours
8×8 Vandermondian Tours
8×8 Mixed Quaternary Symmetry
8×8 Symmetric Tours
8×8 Rhombic Halfboard Tours
8×8 Symmetric Rhombic Tours
8×8 Quaternary Pseudotours
10×10 Board *
Even Larger Square Boards *

MAGIC TOURS
8×8 Magic Knight's Tours
Catalogue of 8×8 Magic Kt Tours
Catalogue: The 8×8 Rhombic Tours
Catalogue: The 8×8 Beverley Tours
Catalogue: The 8×8 Irregular Tours
12×12 Magic Knight Tours
16×16 Magic Knight Tours
Larger Square Magic Knight Tours

FIGURED TOURS [2022]
History of Figured Tours [Jan 2023]
Dawsonian Figured Tours
The Onitiu Problem

SHAPED AND HOLEY BOARDS [2022]
Smallest Open Tours
Smallest Closed Tours
Octonary
Quaternary - Biaxial
Quaternary - Birotary, Shaped
Quaternary - Birotary, Holey
Binary - Open Tours
Binary - Axial Closed Tours
Binary - Rotary Closed Tours
Asymmetry
Non-Intersecting Paths
-- with high symmetry

WALKER TOURS [2022]
Labyrinths and Knots
Wazir Tours
King Tours *
Rook Tours *
Queen Tours *
Crossover & Hopper Tours

AUGMENTED KNIGHTS [2022]
Emperor Tours (N+W) *
Empress Tours (N+R) *
Princely Tours (N+B)
Amazonian Tours (N+Q) *

THE BIG BEASTS [2022]
Leapers at Large *
Fiveleaper *
Double-Pattern Leapers *
Multimovers: Four by Four Squares *
Multimovers: Larger Squares *
Multimovers: Oblongs *

OTHER BOARDS
Bent Boards (Cylinder, Torus) *
Space Boards (3D, 4D etc) *
Honeycomb Boards


Comments, queries, new work or other information on knight's tours are always welcome
and I always endeavour to reply by return if possible. email (remove spaces): george . jelliss @ btinternet . com


© 2000 - 2023 Copyright G. P. Jelliss and contributing authors.