This page records the dates of changes made to the Knight's Tour Notes website,
and gives a biographical account of the compiler's work.
Record of Changes
- August 2009: New section on The Smallest Tourable Boards.
- February-March 2011 Knight's Tour Notes transferred to the 'Mayhematics' site.
- March 2011: The note on "Literary Tours" moved to the History section and split into two sections
- the first covering methods of Representation of Knight's Tours, the second on Cryptotours.
- The note on Non-intersecting knight paths moved into the Geometry section.
- The note on Smallest Knight-Tourable Boards put in the section Shaped Boards.
- The note on Magic Torus Tours put in a new section on Other Boards.
- New sections on Knight's Tours of Odd Square Boards and Larger Oblongs.
- April 2011: Section on Wazir tours revised to include diagrams of more tours, and a correction.
- The page on Wazir tours extended - five sections added, including Magic Rook Tours.
- A new page on King and Queen Tours added.
- A new page about tours on Hexagonal and Triangular Honeycomb boards added.
- May 2011: Section on King tours revised to include extra diagrams and tables.
- Section on "Theory of Magic" added, and Note on 4×4 Magic Square Tours added as Supplement to this section.
- June 2011: Older essay: "Introducing Knight's Tours" reposted. Chronology pages partly updated.
- November 2012: Note on Quasi-magic Knight Tours on 4×4 Torus added to Magic Torus Tours.
- Material on Rook and Queen tours, plus some results on Bishop tours, moved to new page on Rider Tours.
- CSS now used for consistent styling on new pages will be extended to others gradually.
- December 2012: A new Links page, separated from the 2000s page, and updated.
- January - April 2013: A radical rearrangement of the contents undertaken, with Geometry as a separate section.
The html files now all in one folder, but the images in several separate folders. Many of the files and images renamed.
A new page on Mixed Quaternary Symmetry introduced.
- May 2013. New page on Oblique Binary Symmetry in the Shaped and Holey Boards section,
including new work by Michael Creighton. Also new page on Smaller boards 13 to 18 cells.
- June 2013. New page on Direct Binary Symmetry. (I thought this had been put on the site long ago,
but somehow failed to notice its absence.) Smaller Boards page amalgamated with Smallest Boards page.
- July 2013. Pages on oblique quaternary symmetry revised, now one on shaped and one on holey boards.
Smallest Tourable Boards page revised, all tours now diagrammed, black tour on grey board style.
Completed new pages on Asymmetry on shaped boards, and on Imperial tours (Knight + Rook).
- March 2014. Page on Indian Tours added to the History section. Includes diagrams of all tours by Rajah of Mysore.
- May 2014. Sections on Progressive Rook Tours and Integral Point Tours added to Wazir page.
- June 2014. Page of diagrams of 6 by 7 tours of Bergholtian (19) and Sulian (266) symmetry added.
A section on 5 by n tours added to the Camel section of the longer leapers page.
- July 2014 Further Zebra, Giraffe and Antelope tours added to the longer leapers page.
Compound leaper tours (e.g. E. Huber-Stockar) added to Multileapers page. Princely Tours page added.
- March 2015 My new email address entered on index page, and page on non-intersecting paths with high symmetry.
- October 2015 Page on 8×8 symmetric tours added.
- February 2016 Page on 8×8 Squares and Diamonds Halfboard Tours added.
- March 2016 Page on 8×8 Symmetric tours of Squares and Diamonds type added.
- September 2016 Page on 8×8 Quaternary Pseudotours added.
- March 2018 Page on Oblong Magic Tours added.
- April 2019 Pages on Even Larger Boards and on Larger Magic tours expanded.
- October 2019 Page on Oblong Magic Tours expanded and completely reset (more new results by Awani Kumar).
- March 2021 Two new pages on Figured Tours, Part 1 History and Part 2 Dawsonian.
A Biographical Note
I have been interested in questions related to the geometry of the knight's move since the early 1970s.
I did part of a mathematics degree course in 1960-61 but failed to complete it due to illness,
and my attention then turned to mathematical recreations which I had discovered in books such as those by
W. W. Rouse-Ball, Maurice Kraitchik and H. E. Dudeney. My fascination with the subject was also enhanced
when I discovered the Fairy Chess column run by Anthony Dickins and later Cedric Sells (now Cedric Lytton)
in the chess problem magazine The Problemist, which also included generalised knights, known as
leapers (which are also mentioned briefly in Kraitchik's Mathematical Recreations).
Some of my results on knight's paths, particularly concerning Angles and Free Leapers, began to appear
in my little magazine Chessics which began in 1976 and ran until 1987, and subsequently in my larger
magazine The Games and Puzzles Journal which ran 1987-89 and 1996-2001 and online 2001-2006.
Some also in Variant Chess magazine. These are all now available online or as PDF downloads.
During the Chessics period, which I produced mainly while I was working in the Publications
Department of the Institution of Chemical Engineers in Rugby, I did a lot of research into the past work on
knight's tours by visiting libraries (principally the British Library in London and the university libraries
in Leicester, Oxford and Cambridge) and also corresponding with overseas libraries (principally the Cleveland
Public Library, Ohio, USA and the Koninklijke Bibliotheque at the Hague in the Netherlands) who were generous
in providing photocopies. Correspondence with individuals (particularly Ken Whyld and Donald Knuth) was also
Three issues of Chessics numbers 22 "Notes on the Knight's Tour", 24 "Theory of Leapers" and
26 "Magic Tours" published in 1985-86 summarised the results of my researches, and in 1990 I circulated a
draft Bibliography of the subject to selected correspondents. In 1991 I was also given access to some
previously unpublished manuscripts by H. J. R. Murray held by his daughter. These are now in the
Bodleian Library, Oxford, along with his other unpublished material.
I had planned to publish a book on the subject but having taken a course in 1999 on the use of HTML was
instead able to set up the Knight's Tour Notes website (which was at http://www.ktn.freeuk.com) on a
dial-up provider. However after a change to broadband connection I no longer had dial-up access and so was
unable to update the site, and in any case I was intentionally taking a break from knight's tour studies.
The KTN website on freeuk then (19 February 2011) vanished into the ether, so this section on my
www.mayhematics.com website was set up as a new home for my study of Knight's Tours. A thorough revision
of the pages was undertaken at the start of 2013, though there are still some subjects not fully covered.
I believe it is still the leading source of accurate information on this fascinating subject.
In March 2014 I began an effort to produce a book, or series of monographs, containing most of the significant material.
Where there is too much to include in the book reference would be to this website.
This work continued until September 2019, when a satisfactory arrangement of the material into 12 PDF volumes was achieved.
These can now be downloaded from the publications page.
Some errors (mainly unrevised cross references) have been detected, and new historical information has since come to light.
So a revised edition may be needed next year. I still hope to produce a (smaller) book, if a publisher can be found.