
Re: Minimal number of move for a Knight to go on every square of the board
Posted:
Jan 20, 1999 8:46 AM


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 reentrant tour, in which the knight > on its 64th move could get back to its starting square...." > > Obviously, a reentrant tour can start on any square. > >  > Brian
Online 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.unitrier.de/pub/UsersCTVD/eccc/reports/1995/TR95047/Paper.ps
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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.univmrs.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.univmrs.fr/pub/EMIS/journals/EJC/Volume_3/Comments/v3i1r5.01.psÃÂÃÂ
Antreas

