K+N v K (lone)

Yep, impossible not enough material to mate.

Best a king can do is limit an opposing king to rank. Best a knight can do is attack two squares on a diagonal, which means if the knight can put the king in check, it can always move to a free square.

Only Swiss Gambit can mate with a lone N. 😛

-Removed-

Originally posted by ChessPraxis
Only Swiss Gambit can mate with a lone N. 😛

Originally posted by woodypusher
R J can force mate with lone bishop v king...in the opposite-colored corner, through faith.

Originally posted by woodypusher
Checkmate is also impossible to force with K+N+N v K

Originally posted by moonbus
This was thought to be impossible until a computer program worked it out. It requires more than 30 moves, however, so, according to tournament rules, this would be a draw. I doubt any human could reproduce the moves.

Wiki has a good article on mate with 2 knights: it is possible if the opposing K is poorly placed.

https://en.wikipedia.org/wiki/Two_knights_endgame#CITEREFSeirawan2003

Originally posted by moonbus
This was thought to be impossible until a computer program worked it out. It requires more than 30 moves, however, so, according to tournament rules, this would be a draw. I doubt any human could reproduce the moves.

FEN	8/8/5N2/8/8/7p/5K1k/8 w - - 0 1

• 8
• a
• 7
• b
• 6
• c
• 5
• d
• 4
• e
• 3
• f
• 2
• g
• 1
• h

1.	Ng4	Kh1
2.	Kf1	h2
3.	Nf2

+2

Invert BoardPGNHeaders

[FEN "8/8/5N2/8/8/7p/5K1k/8 w - - 0 1"]
1. Ng4+ Kh1 2. Kf1 h2 3. Nf2

Originally posted by moonbus
This was thought to be impossible until a computer program worked it out. It requires more than 30 moves, however, so, according to tournament rules, this would be a draw. I doubt any human could reproduce the moves.

Wiki has a good article on mate with 2 knights: it is possible if the opposing K is poorly placed.

https://en.wikipedia.org/wiki/Two_knights_endgame#CITEREFSeirawan2003

There are also checkmate positions with the inferior side's king on the edge of the board (instead of the corner), but again they cannot be forced. (my bold)

Originally posted by SwissGambit
The article you quoted doesn't agree with your statement. 😛

There are also checkmate positions with the inferior side's king on the edge of the board (instead of the corner), but again [b]they cannot be forced. (my bold)

[/b]

I vaguely recall an article in an IT journal, not a chess journal, some years ago, claiming that the K+2N vs K problem had been solved. Alas, I can find no reference to this on the Internet. As I recall, the program ran for several days (well over tournament time limit) and the mate required many more moves than the 50-move draw-limit, of which all but the last few moves were not recognizable to humans as having made any progress. I wish I could find that article again... shucks. Anyway, no human could reproduce the sequence, and no tourney director could be expected to adjudicate whether the superior side had made any progress after 50 moves. Given that even Karpov and Annand have landed in K+2N vs K+P endings and made mistakes (drawing in won positions), we mere mortals may accept that K+2N vs K is drawn.

Originally posted by moonbus
I vaguely recall an article in an IT journal, not a chess journal, some years ago, claiming that the K+2N vs K problem had been solved. Alas, I can find no reference to this on the Internet. As I recall, the program ran for several days (well over tournament time limit) and the mate required many more moves than the 50-move draw-limit, of which all but the l ...[text shortened]... nd made mistakes (drawing in won positions), we mere mortals may accept that K+2N vs K is drawn.

Originally posted by ChessPraxis
Thanks for clarifying your other post.

Originally posted by moonbus
It is furthermore useful to distinguish impossible, possible, and forced. Checkmate with K+2N vs K is possible, though not forced (for humans within tourney limits), whereas checkmate w/ K+B or K+N vs K is impossible.