The n-knights problem

Given just a description of an 8x8 chess board and the rules for how a
knight can move, I want to write a Prolog program to compute, through logic
alone, the maximum number of knights that can be placed on the board such
that no knight attacks any other. I don't care about specific
configurations (as in the classical 8-queens problem), but would like a
"proof" that the number it comes up with is correct.

I figure that first, the program would need to deduce that knights can only
threaten squares of the opposite color. The program would then "realize"
this property applies no matter how many knights there are on the same
color of square. Then it'd come up with the answer: 32. There'd
undoubtedly be more steps, but that's the gist of it. Part of the "proof"
I'd like to see is those deductions it comes up with.

It sounds easy enough, but I've no idea how to even start. Any ideas of
how to set this up?
.

Relevant Pages

  • Re: The n-knights problem
    ... }> Given just a description of an 8x8 chess board and the rules for ... need to deduce that knights can}> only threaten squares of the ... I peeked ahead in "Prolog ... knights only threaten squares of the opposite color. ...
    (comp.lang.prolog)
  • Re: The n-knights problem
    ... knight can move, I want to write a Prolog program to compute, through ... the program would need to deduce that knights can ... only threaten squares of the opposite color. ...
    (comp.lang.prolog)
  • Re: The n-knights problem
    ... alone, the maximum number of knights that can be placed on the board such ... the program would need to deduce that knights can only ... threaten squares of the opposite color. ...
    (comp.lang.prolog)
  • Re: The n-knights problem
    ... Lash Rambo wrote: ... }> Given just a description of an 8x8 chess board and the rules for how a ... the program would need to deduce that knights can ... but maybe not Prolog -- would be an exhaustive search. ...
    (comp.lang.prolog)