I've been asked to give an update on the progress of my work on knight's tours that I have been trying to put into book form. Back in October last year I reported having the material in the form of eight monographs each of about 100 pages. These soon combined to form four volumes, each of about 200 pages. The latest development is that these have spontaneously rearranged themselves to form three volumes each of around 260 pages.
Volume 1 covers History, consisting mainly of an update of the Chronological Bibliography that I produced in 1990, in 25-year stages, including diagrams of magic tours, separated by essays on methods of construction and ending with a catalogue of quaternary pseudotours.
Volume 2 is on Symmetry and Shape in Knight's Tours and consists of enumerations of tours on small boards, square, oblong or shaped, plus examples on larger boards. It includes a catalogue of all the tours on the 6x6 board, and an account of Mixed Quaternary Symmetry on 8x8 and 12x12 boards.
Volume 3 whose title is undecided is on Theory of Moves and of Magic Tours in general, together with catalogues of tours by Leapers from Wazir to Antelope, and Multi-Movers from King to Wizard. The later sections include Magic Squares using up to seven move types. An appendix lists all the 280 magic knight tours in arithmetical form.
This seems to have reached a stable configuration, so I am hopeful of completing it soon.
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