Enter Your Reply The Comment You're Replying To Joe Joyce wrote on Tue, Oct 5, 2010 05:02 PM UTC:The problem of the slippery king - the king that can keep evading your attacks - has 'probably' existed since the beginnings of chess. It becomes very evident in higher dimensional chess, 4D being enough to require some drastic measures, and 3D mates are not a cakewalk. We likely fail to recognize how difficult mate is even in FIDE. Even there, special assistance is required, in the form of a small board with straight edges. Consider how difficult it would be to mate a bare king on an infinite board. Minimum force needed would be a K, Q, and N vs a lone k. K _ _ _ _ Q _ _ _ _ _ k _ _ _ _ _ _ _ _ _ _ _ N _ . . . And how do you get to that position? I would suspect at least one more piece was required. Going to 3D makes the problem more interesting. Using standard 2D FIDE pieces extrapolated to 3D lets the king move to 26 cells in a 3x3x3 cube. This is a good bit harder to cover, even with 3D queens. David Paulowich made the point that there was no demonstration of minimum required force for bare king checkmate in Raumschach not all that long ago. Has the situation changed? Going to 4D just explodes the problem. Even limited 4D like Hyperchess gives far too many ways to escape to make mate practical without some specific rule(s) for that purpose. That is, unless you make the pieces so powerful the king cannot escape, which brings its own set of problems, but does allow easy checkmate. Ben Reiniger's TessChess, using all the higher-D diagonals for movement, is an excellent piece of work exploring this area. Without question, king and queen can mate bare king. I don't know about other piece combinations, but he has done beautiful extrapolations of the standard FIDE pieces to higher dimensions. And I, with excellent help, am happy to report that the minimum requirement to force mate in Hyperchess is demonstrated to be any 2 'major' pieces and king vs bare king [the major pieces in this specific case being queen and bishop.] For a very simple, linear approach to 4D chess, this is actually a good result. It's nice to know that, after years of effort, your game is not only playable but winnable. Well, I think it's playable. And it is the easiest 4D chess game that gives you both chess and 4D, by a lot. :) Further, there are probably 5 or 10 people in the world who agree with me. Lol, it's still a good game. May all 6 of you enjoy it! Edit Form You may not post a new comment, because ItemID Slippery King does not match any item.