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Re: Minimal number of move for a Knight to go on every square of the board
Posted:
Jan 20, 1999 8:46 AM
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In article <36a89455.15687811@news.demon.co.uk>, brian@brisk.demon.co.uk
(Brian Skinner) wrote:
> "sbsrd92" <sbsrd92@sopra.com> wrote:
>
> > Of course, I assume there is only one piece on the board : the knight.
> > Does it depends on the square the Knight is starting?
>
> From the Oxford Companion to Chess:
>
> "KNIGHT'S TOUR, the tour of a knight over an otherwise empty board
> visiting each square once only. There is almost an infinity of ways of
> achieving this and more than 122,000,000 ways of performing the more
> restricted version known as the re-entrant tour, in which the knight
> on its 64th move could get back to its starting square...."
>
> Obviously, a re-entrant tour can start on any square.
>
> --
> Brian
On-line papers in .ps format:
1.
Martin Loebbing, Ingo Wegener: The Number of Knight's Tours Equals
33,439,123,484,294 -- Counting with Binary Decision Diagrams
ftp://ftp.informatik.uni-trier.de/pub/Users-CTVD/eccc/reports/1995/TR95-047/Paper.ps
======================================
2.
http://cs.anu.edu.au/people/bdm/papers/knights.ps.gz
http://cs.anu.edu.au/~bdm/papers/knights.ps.gz
http://cs.anu.edu.au/publications/eljc/Volume_3/Comments/v3i1r5.01.ps
http://cs.anu.edu.au/publications/eljc/Volume_3/Comments/v3i1r5.01.psÃÂÃÂ
http://cirm.univ-mrs.fr/EMIS/journals/EJC/Volume_3/Comments/v3i1r5.01.psÃÂÃÂ
ftp://ftp.maths.tcd.ie/pub/EMIS/journals/EJC/Volume_3/Comments/v3i1r5.01.psÃÂÃÂ
ftp://cirm.univ-mrs.fr/pub/EMIS/journals/EJC/Volume_3/Comments/v3i1r5.01.psÃÂÃÂ
Antreas
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