7

Can white force this position

    [Title "KN vs K"]
    [FEN "8/8/8/8/8/8/5k1N/7K w - - 0 1"]

into this position?

    [Title "KN vs K"]
    [FEN "k7/8/1K1N4/8/8/8/8/8 w - - 0 1"]

Background: Yesterday I finally figured out the KBN vs K after one year of trial and error. Solving endgame problems like this is like crack to my brain. The 'fifth' fundamental checkmate and next in line seems to be the KNN vs KP.

In this game, one of the Ns only play a passive role, with the other N and the K are doing all the moves, I started wondering if the same approach is possible in the KBN vs K: Force the king to the corner with only K and N, and then deliberately deliver the checkmate with on B's first move.

Any concrete suggestions that could lead to an answer will be greatly appreciated.

A related question: is there an engine that can search for such non-checkmate positions?

5

I am not aware of being able to use an engine to calculate the possibility of such moves and no it is not possible to do this with one knight.

The easiest way to figure this out is by backtracking the position by one or two moves. No matter in which position the white king or knight were before this situation arose, black was not obligated to move to the corner of the board.

1k6/8/K2N4/8/8/8/8/8 w - - 0 0

black can move to C7

8/k7/2KN4/8/8/8/8/8 w - - 0 1

black can move to A6

8/k1K5/3N4/8/8/8/8/8 w - - 0 1

black can move to A6 here as well

2k5/8/1K6/1N6/8/8/8/8 w - - 0 1

And Regardless of the position of the Knight the black king has a square on D8 to go to.

The only way to actually get this done is if the king was in the corner to begin with:

k7/8/1K6/1N6/8/8/8/8 w - - 0 1
  • Just saw this. It's not quite that simple. In the second position (Kc3,Nd6/Ka7) Black can in fact be trapped in the corner: 1 ... Ka6 2 Nb7 Ka7 3 Nc5 Ka8 4 Kd7 Kb8 5 Kd8 Ka8 6 Kc8 Ka7 7 Kc7 Ka8, and now White can shift the Knight to d6 with 8 Kb6 Kb8 9 Nb7 Kc8 10 Kc6 Kb8 11 Nd6 etc. – Noam D. Elkies Jan 1 at 4:08
1

No. If that were possible then KN could stalemate the lone King by force (WTM 1 Nb5, 2 Na7, 3 Nc6; BTM Kb7 2 Kc6 Ka8 3 Kb5! Ka7 4 Ka5 etc.), and I already checked (as reported in this answer) that stalemate cannot be forced in general.

0

If KNN vs KP is a win in some cases then white has to be able to corner the black king while the other knight blockades the pawn. After cornering the king the other knight releases the pawn and then moves over to do the mate. That was one end game that I did not bother memorizing. But logic says KN vs K can corner the king otherwise the mate would not be possible if the other knight can do it before the pawn can queen.

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