> GPJ: According to my notes M.Matsuda published a 47-move solution in J.Rec
> Maths 1969 (vol.2 no.3). Your note stimulated me to finish processing the
> article by Robin Merson that appeared in G&PJournal no.17 in 1999. This is
> now on the KTN website in the Recreations section at the bottom of the
index
> page. Direct access is: http://www.ktn.freeuk.com/2b.htm.
>
I was completely amazed by the results exposed on your page !
For example, the 11x11 cited by Ed Pegg:
http://www.mathpuzzle.com/leapers.htm
can be improved to 76 moves !
Also, the 18x18 in 235 moves reported by Pierre Berloquin can be done in 237
moves.
I've improved my non-crossing program a little bit (20% faster), and ran it
on several boards with an AthlonXP 1900+.
The 7x9 has been explored in 228 seconds, giving the unique solution of 35
moves:
c3 e2 d4 f3 e5 d7 f6 e8 g9 f7 g5 e6 f4 g2 e3 f1 d2 b1 a3 c2 b4 d3 c5 e4 d6
c8 e7 d9 b8 a6 c7 d5 b6 c4 a5 b3
I also ran the 8x9 case, and got 2 solutions of 42 moves in 7593 seconds:
d3 e5 c4 d6 b5 c7 a6 b4 a2 c1 b3 d4 c2 e1 f3 d2 e4 f6 d5 e7 c6 d8 b7 a9 c8
e9 d7 f8 e6 g7 f5 e3 g4 f2 h1 g3 h5 f4 g6 h8 f7 g9 e8
d2 b1 c3 a2 b4 c6 a5 b7 a9 c8 b6 d7 c5 b3 d4 c2 e3 d1 f2 h1 g3 e2 f4 d3 e5
c4 d6 e8 c7 d9 f8 e6 g7 f9 h8 g6 h4 f3 g5 e4 f6 d5 e7
(they should be equivalent ?)
Of course, these results were already known...
I expect the 9x9 case to be much slower. It's really impressive that Matsuda
found 47 moves for the 9x9 in 1969 !
>GPJ: I'm interested. It would be more interesting if you could select out
>some examples with special properties, say approaching pandiagonality, or
>showing H-supersymmetry (that is 7 cells in the shape of an H add to the
>constant).
Indeed, I tried to run the 7x7 using standard magic properties, and it seems
to be very slow.
Pandiagonality or other kind of patterns will reduce the computation a lot,
but since the program is generated, I need to build one version for every
program.
I'll work on these versions tonight.
JC
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Received on Thu Dec 04 14:24:18 2001
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