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Re: Random rook's tour of a rectangle

  • To: mathgroup at
  • Subject: [mg50297] Re: Random rook's tour of a rectangle
  • From: Paul Abbott <paul at>
  • Date: Wed, 25 Aug 2004 03:36:09 -0400 (EDT)
  • Organization: The University of Western Australia
  • References: <cggs1h$gb3$>
  • Sender: owner-wri-mathgroup at

In article <cggs1h$gb3$1 at>, "DIAMOND Mark R." <dot at> 

> I wondered if anyone might know of an algorithm for generating a random
> "rooks's tour" of a (not necessarily square) chessboard. I have looked in
> the literature on self-avoiding walks tours of chessboards but not found
> what I seek. (Knight's tour obviously gets a lot of attention).
> I have found some exhaustive enumeration algorithms which cope with
> relatively small chessboards, but none that find a random paths, and none
> that would manage with, say, a 1000*1000 chessboard.
> Any hints, algorithm, reference, suggestions for modifying an existing
> algorithm (etc.) would be most appreciated.

Not sure if this will help but Chapter 6 of Computational Recreations in 
Mathematica by Ilan Vardi (Addison-Wesley, 1991) has a chapter on "The 
n-Queens Problem" that mentions non-attacking rooks on an n x n chess 
board. Perhaps Ilan Vardi or Igor Rivin would be able to help.


Paul Abbott                                   Phone: +61 8 9380 2734
School of Physics, M013                         Fax: +61 8 9380 1014
The University of Western Australia      (CRICOS Provider No 00126G)         
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Crawley WA 6009                      mailto:paul at 

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