[Magictour] Re: on Rectangles

Concerning the 8x10 case I have constructed a number of "quasi-magic"
examples which add to 324 in the 8-lines but use two different sums in the
10-lines. Four of these were given in Issue 26 of the Games and Puzzles
Journal towards the end of the page
(http://www.gpj.connectfree.co.uk/gpjh.htm).

On the 8x12 board it is very easy to construct hundreds of magic tours by
extending 8x8 tours by the braid method. I doubt if it's a viable project to
count them all, even should anyone want to. Here is one (the only published
example as far as I'm aware) that I gave in Variant Chess 1992 (issue 8
p.105)

01 46 71 76 05 44 67 78 07 42 65 80
72 75 02 45 68 77 06 43 66 79 08 41
47 70 73 04 37 12 83 62 39 10 81 64
74 03 48 69 84 61 38 11 82 63 40 09
49 84 23 28 13 36 59 86 15 34 57 88
24 27 50 93 60 85 14 35 58 87 16 33
95 22 25 52 29 20 91 54 31 18 89 56
26 51 96 21 92 53 30 19 90 55 32 17

These would only be of interest if they fulfilled some additional criterion.
(closed , symmetric, magic when cyclically renumbered, and suchlike).

The next major problem in magic knight's tours is to find some more
diagonally magic 12x12 tours (both diagonals also adding to the magic
constant 870). Awani Kumar found four recently (see the website above).
Perhaps he should be included in this mailing list. I've asked him if he
would be interested.

GPJ 26 June 2003



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Received on Thu Dec 04 14:24:18 2001