Re: Re: Re: Re: Combinatorica questions!!!
- To: mathgroup at smc.vnet.net
- Subject: [mg20797] Re: [mg20777] Re: [mg20733] Re: [mg20645] Re: [mg20499] Combinatorica questions!!!
- From: "Arnold Knopfmacher" <arnoldk at cam.wits.ac.za>
- Date: Sun, 14 Nov 1999 18:13:48 -0500 (EST)
- Organization: MS, University of the Witwatersrand
- Sender: owner-wri-mathgroup at wolfram.com
Perhaps more interesting is to consider the number of paths
that other chess pieces can use to cross an n-by-n chessboard
from position {0,0} to {n-1,n-1}. As with the rook we dont allow
moves that decrease either coordinates at any step.
On an 8-by-8 board, I get for a queen (or king) 48639 paths.
For a bishop there is only one path (down the diagonal)
and no ways for a knight.
For the bishop or knight, the problem becomes much more interesting
if we allow moves in positive or negative directions with the proviso
that the piece cant return to any square its already occupied
( or go off the board). This
avoids possible infinite loops of moves. For example for a 3-by-3 board there
are 2 paths for a knight. I dont know the answers under these conditions
for a standard 8-by-8 board.
Arnold Knopfmacher
Dept of Computational and Applied Maths
Witwatersrand University
Johannesburg 2050
South Africa
http://www.wits.ac.za/science/number_theory/arnold.htm
Fax: 2711-4039317
Phone: 2711- 7163353
email: arnoldk at gauss.cam.wits.ac.za