[Magictour] Re: Graeco-latin tours

for an (r,s) torus-leaper, I can find the following numbers of
graeco-latin-torus-tours
on an n*n board for n=1,..,9 .
Starting at a fixrd square, other symmetries disregarded

(1,2): 1,0,0,0,96,0,32,2112,0
(1,3): 1,0,0,0,96,0,32,0,+
(1,4): 1,0,0,0,0,0,32,0,0
(2,3): 1,0,0,0,0,0,32,2112,+
(2,4): 1,0,0,0,96,0,32,0,0
(3,4): 1,0,0,0,96,0,0,0,168


+ means, there are some but I didn't run it to completion.

This is a simple backtracking program, not checking the neighbors of a new
node
for dead ends, as in magictours.exe

So speed can be improved and maybe finding tours upto n=12 is possible.


Guenter


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Received on Thu Dec 04 14:24:18 2001