[Magictour] Re: Pandiagonal 7x7 magic torus

JCM:
>I tested this program on every N<=29.
>It gave pandiagonal torus tours for N=7, 11, 13, 17, 19, 23 and 29 (and
also
>non-pandiagonal magic tours on 5x5 and 25x25).

GS:
these are only the (linear) pandiagonal graeco-latin torus knight tours,
I assume you didn't check all pandiagonal torus knight tours.
Now, it seems that there are linear pandiagonal graeco-latin torus knight
tours ,
iff n is prime and n>6. But then ... some solutions popped up for n=49 !

>Although it seems that there is a relation between these values (since
there
>are 16 values for every N !), I was unable to find it. Perhaps someone may
>have an idea ?

we have the 16 symmetries, so this is just one symmetry-class
of knight tours. I assume, it's just the one from my previous post,
the rhombus wrapped around the torus , adapted for other n.
I also noticed, that the 4 values have only 2 possible determinands,
suming to n : 3+4,2+9,5+8,7+10,4+15,9+14,6+23

>A 25*25 pandiagonal tour using this method is not possible, but it's
perhaps
>impossible to find a 25x25 pandiagonal torus tour ???

this seems to be unsolved. Is there any nonlinear pandiagonal
magic square ? I didn't find this, or maybe I didn't read careful enough.

>I attached the C source-code.

thanks.It compiles with GCC, but is a bit slow for n=49


Guenter


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Received on Thu Dec 04 14:24:18 2001