KBNK
Posted: Wed Nov 19, 2014 6:23 pm
I was wondering, is KBNK a won end-game on any (even) size board, and perhaps even on an infinite board? There doesn't seem to be a faster-than-linear increase in the length of the longest mate, as one usually sees in end-games that at some point cease to be won (e.g. K+K vs K). For KBNK I find
6x6: 22
8x8: 33 (+11)
10x10: 47 (+14)
12x12: 64 (+17)
14x14: 78 (+14)
In KBNK you have one piece that outruns the King (Knight), and a slider that can always be positioned to restrain it in a single move. And although B+N probably cannot drive a bare King in a specific diagonal direction all by themselves, they can conceivably slow its progress in the opposite direction enough that their own King eventually can catch up. And the three of them could possibly do the job. So it could very well be that mate is possible on an infinite board (with one corner).
6x6: 22
8x8: 33 (+11)
10x10: 47 (+14)
12x12: 64 (+17)
14x14: 78 (+14)
In KBNK you have one piece that outruns the King (Knight), and a slider that can always be positioned to restrain it in a single move. And although B+N probably cannot drive a bare King in a specific diagonal direction all by themselves, they can conceivably slow its progress in the opposite direction enough that their own King eventually can catch up. And the three of them could possibly do the job. So it could very well be that mate is possible on an infinite board (with one corner).