wu :: forums
        (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi)
      

        riddles >> easy >> Knights domination
        
(Message started by: Altamira_64 on Feb 6th, 2012, 4:40am)
Title: Knights domination
Post by Altamira_64 on Feb 6th, 2012, 4:40am
That's an old one but with a variation:
Try to arrange a minimum number of knights on a chess board such that no 2 knights attack each other but still dominate all 64 squares of the kingdom. All knights are of the same colour (and obviously threaten each other).
Title: Re: Knights domination
Post by Altamira_64 on Feb 6th, 2012, 4:42am
I know that the solution without the restriction that no knight should attack each other is 12.
I can very easily do it with 16 knights but I am pretty sure the correct answer is somewhere between 12 and 14.
Any ideas?
Title: Re: Knights domination
Post by Grimbal on Feb 6th, 2012, 2:42pm
It is not 12, because the solution with 12 is unique.  And the knights do attack each other.

Per computer I find no solution with 13, but a set of solutions with 14.  Here is one.
[hideb]
X . X . . . . .
. . . . . X . .
X . . . X X . .
X . . . . . . .
. . . . . . . X
. . X X . . . X
. . X . . . . .
. . . . . X . X
[/hideb]
Title: Re: Knights domination
Post by Altamira_64 on Feb 7th, 2012, 1:21am
Excellent!
Title: Re: Knights domination
Post by mcboogle on May 2nd, 2012, 5:00am
fantastico!


Powered by YaBB 1 Gold - SP 1.4!
Forum software copyright © 2000-2004 Yet another Bulletin Board