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#Post#: 49--------------------------------------------------
pandiagonal magic tours
DIR By: gsgs
Date: May 14, 2026, 5:16 am
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Here is a link, where you can read about the problem
of pan-magic tours :
HTML http://www.jsbeasley.co.uk/vchess/vc57.pdf
HTML http://www.jsbeasley.co.uk/puzzles/knightstours.pdf
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I found 88 fully "pan-magic" 2-knight tours on the
8x8 torus. With different panmagic constants for
even and odd diagonals, as described at the above links.
HTML http://magictour.free.fr/8x8-p88.csv
I only searched symmetric tours, since this sort of
symmetry yields the magicity.
These are "2kts" since the middle-move is not a knight's
move in any of the 88.
I assume that there are no panmagic 1-knight tours on the
torus, but I can't prove it.
I found no similar 2kts for 12x12 or 16x16 with incomplete
search.
Below is one of the 88, which can be nicely shown
in an 8x10 diagram without doing visual swap-arounds.
It consecutively visits 16 squares and has a nice binary pattern
as seen in the Jaenisch-tour shown by John Beasley above.
--,61,02,05,58,45,18,21,42,--
01,--,57,60,19,04,43,46,--,22
62,--,06,03,44,59,20,17,--,41
--,00,63,56,07,16,47,40,23,--
--,55,08,15,48,39,24,31,32,--
09,--,49,52,27,12,35,38,--,30
54,--,14,11,36,51,28,25,--,33
--,10,53,50,13,26,37,34,29,--
61,02,05,58,45,18,21,42
22,57,60,19,04,43,46,01
41,06,03,44,59,20,17,62
00,63,56,07,16,47,40,23
55,08,15,48,39,24,31,32
30,49,52,27,12,35,38,09
33,14,11,36,51,28,25,54
10,53,50,13,26,37,34,29
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