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I think it’s possible for white to win this. However, of course there are so many trees of moves. So it might not be possible to cover unless you use a computer engine which I do not want to. At least not yet.
I think the key is keeping the black king out of the queening box. At first I was thinking Kc7 but then the black knight can harass progress of the white pawn so it is not simple. So first move seems to have to be
1.b5
Of course there are many lines to choose from here. But in keeping with the trend of getting the black king to the queening square, I think one of the most trying lines is
1… Kd8
2.Kb7
White needs to keep the black king away.
2… Ne4
3.b6 Nd6+
4.Kc3 Nc8
5.b7 and white wins
3… Nc5+
4.Kc3 Na6
5.b7 Nb8+
6.Kb6 Ke8
7.Nc6 Nd7
8.Kc7 wins
etc…
White should win this.
After 1.b5 Kd8 2.b6 and 3.b7 white is winning (e.g. Kc8 3.b7+ Kb8 4.Nd7+). A better try seems 1.-Ne6 2.b6 Nd8+ 3.Kc7 Ne6+ 4.Kc8 Nc5 5.Nd3 Na6 (5.-Nxd3 6.b7) 6.b7, followed by 6.Nb4.
P.S.: After 1.b5 Ne6 2.b6 black has a better defense with 2.-Ke7! But I think, 3.Nd3 with the idea 4.Nc5 should still be winning.
The key here is to sac the white knight in order to get the king away from the pawn. That positions arises after the pawn has advanced a bit. One should watch for the forking moves that the black knight can do. The pawn is the queen here and must be protected at all cost…
D.
4k3/8/2K5/4N1n1/1P6/8/8/8 w – –
Black’s easiest path to a draw is to move the knight to e6 then d8. From d8 whites pawn cannot pass b7 without becoming food.
so the key for white is to prevent those moves.
moving the king to c7 allows the knight to go to c7 on the next move and prevent black from occupying the d8 square.
can black find another path around while whites pawn advances?
as I see it, if white moves to c7 thyen black’s knight can go to e4 and then to block whites advance by moving the knight to c5. So it looks like a draw. Can someone find a creative way for white to both advance and block black’s knight?