>Awani Kumar sent me two 12x12 magic knight tours in which four of the
"broken" diagonals (i.e. those that folllow the line of a bishop move on the
torus) are magic. These are due to appear in the next G&P Journal issue.
Also he suggests looking into the possibilty of a pandiagonal solution.
Did Awani Kumar explain his method for building such tours ?
Searching for pandiagonal squares seems more feasible than enumerating magic
tours on 12x12 !
So I'll perhaps modify my program this week-end.
>It may be possible for knight lines on the torus also to be magic, but why
stop there? What about camel (1,3), zebra(2,3), giraffe (1,4) and so on?
Modifying the behaviour of the leapers is really easy (it takes no time at
all !).
Just give me the leapers and the board sizes for every leaper, and I'll
generate independent programs for these.
Of course, such programs can easily be distributed through manual
reservation, so we'll have to wait that Hugues has almost finished before
asking contributions.
>I e-mailed the mathworld site with some updates, and I've also corrected
the statement about 4x4k magic tours on the KTN "General theory" page.
There's a typo in the 8x12 tour as sent: one of the 84s should be 94.
Very good ! The link to your page was not up to date too.
Hugues' laptop confirmed my computation: a4-d4 has only 3 solutions (my
computation was abrutly stopped by a strange coredump of Windows 2000, due
to a failing network cable).
Thus, only 3 known solutions have not yet been 'rediscovered'. I think that
this confirms that my program is exhaustive !
JC
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Received on Thu Dec 04 14:24:18 2001
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