[Magictour] Re: magictour project finished

Congratulations to everyone on completing the search for 8x8 magic =
tours. It's surprising perhaps that more were not found, but I suppose =
this shows how well the earlier workers on the subject did their work, =
in the pre-computer age.

It will take me a while to get all the related pages on the KTN website =
up to date with the new figures.

Thanks for dropping the "semi-magic" (meaning non-diagonally magic) =
terminology. It's not just my idea. "Magic" has been used in that sense =
with regard to tours from way back. It's those whose interest is purely =
in traditional "magic squares" who seem to be fixated on diagonal =
properties to the exclusion of others.

I tried the non-intersecting path problem proposed by JCM (from Ed =
Pegg's site) and found two 16-move solutions, one symmetric which I =
suppose is the intended answer, but the 17-move eludes me.

Awani Kumar also sends his congratulations. It seems the people he works =
for have sent him off to the backwoods somewhere, so he may not be able =
to participate in the search for 12x12 tours, but will try to keep in =
touch with developments.

Has anyone done a count of 4x8 semi-magic tours (in the sense of adding =
to the magic constant in all rows or all files but not both)? I find 66 =
magic in the 8-cell lines and 8 magic in the 4-cell lines (not counting =
reversals), but Murray (1917) claimed 67 of the first type.

GPJ




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Received on Thu Dec 04 14:24:18 2001