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Knight And Pawn Endgames

For me one of the most difficult kinds of endgames to win are those with just knights and pawns.

K2n4/4k3/1P6/8/2N5/8/8/8 w - - 0 1

White to move and win. How quickly can you find white's plan in this position?

I spend an hour and a half to solve this problem. I will be reviewing my solution for a couple of days more for deeper understanding.

V-1

1.Kb8! Nc6+
2.Kc8 Nb4
3.b7 Na6
4.Nb2 Kd6
5.Nd3 Kc6
6.Nb4+ Nxb4
7.b8=Q
It's a win for white.

V-2

1.Kb8 Ne6
2.Ne5 Nc5
3.Ka8 Kd6
4.Nd3 Nd7
5.b7 Kc7
6.Ka7 Kc6
7.Ne5+ Nxe5
8.b8=Q
It's a win for white.

V-3

1.Kb8 Kd7
2.Ne5+ Kd6
3.Kc8 Ke7
4.Kc7 Ne6+
5.Kb8 Kd6
6.Ka7 Nc5
7.Nd3 Nd7
8.b7 Kd5
9.Nb4+ Kd6
10.Nc2 Kc5
11.Ne3 Ne5
12.Nf5 Nc6+
13.Ka8 Kd5
14.Ne7+ Nxe7
15.b8=Q
It's a win for white.

V-4

1.Kb8 Ne6
2.Ne5 Kd6
3.Ka7 Nc5
4.Nd3 Nd7
5.b7 Kd5
6.Nb4 Kc5
7.Na6+ Kd6
8.Ka8 Nb6+
9.Kb8 Nd7+
10.Kc8 Nb6+
11.Kd8 Nd7
12.Nc5 Kc6
13.Kc8 Nb6+
14.Kb8 Nc4
15.Ka7 Kxc5
16.b8=Q
It's a win for white.

The usual plan for thee endings is to keep offering the N to deflect the defending N from preventing the advance of the pawn. That requires using the K to keep the defending K from joining the fray. Alena's v2 is a good example of this.

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