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1. Nf2+ Kh4 (1…Kg3 2. g7 and the pawn queens with check) 2. g7 R:c6 3. g8R (if g8Q, ….Rg6+ 4. Q:g6 is stalemate) R:c2 4. Rg2 and now if …R:a2, 5. Rh2+ forces the black K to a dark square, and Ne4+ discovers an attack on the rook with an easy win.
How about: 1.Nf2+ … 2. g7. 1….Kh3 seems the only hopeful response for Black. Black might try 2….Rc3 or 2….Rc5 with an eye on 3….Rg3+ or 3…Rg5+. But White can respond 3.Kh2 and 3.Ne4 respectively.
1. Nf2+ defends g4 from Black’s rook, but after 1. … Kh4 2. g7 Rxc6, promotion to a rook is necessary (3. g8(Q) Rg6+ 4. Qxg6 stalemate). 3. g8(Rook) Rxc2 4. Rg2 Rc1+ (4. … Rxa2 5. Rh2+ Kg5 6. Nh3+ or 5. … Kg3 6. Ne4+) 5. Kh2. There is some play left, but White has a material advantage with protection on a2 and an extra piece to capture on a3 and guide the pawn to promotion.
Hmm, the first thing that comes to mind is 1.Nf2+ Kh4! 2.g7 Rxc6 3.g8(Q) Rg6+! 4.Qxg6 stalemate. That presumably is not the solution.
Since black can play Rg4 with check, then I think white cannot push the g-pawn on the first and win:
1. g7 Rg4
2. Kf1 Rg7
3. Nf2 Kh4 (Kg3 looks ok, too)
4. Nd3 Rg4 (Rc7 5.Nb4 likely =)
5. Ke2 Rc4
6. Kd2 Rc6
7. c3 Kg3 (Kg4?? knight fork)
8. Kc2
Here, Nb4 doesn’t seem to be better, but I am not sure. Continuing:
8. ….Rc8
Required because of the knight fork that arises on Kf3. Continuing:
9. Kb3 Kf3
And I tried everything to win the a-pawn while retaining the c-pawn, but I just can’t find a winning line for white. The “obvious” idea of Nb4 and Nc2 doesn’t quite work:
10.Nb4 Ke3
11.Nc2 Kd3 and the c-pawn is doubly attacked, now. I really don’t see a winning line with g7 as the first move. Back to the drawing board.
I see Frederick has already started to discuss the 1.Nf2 line. I think he misses something, though:
1. Nf2 Kh4
2. g7 Rc6
And, as Frederick points out, g8Q is met by Rg6 followed by a stalemate. However, we can underpromote to a rook:
3. g8(R) Rc2 (forced)
Of course, now, white needs to find a way to save the remaining pawn. All I can think of is to try:
4. Rg2
And now, if black captures at a2
4. …..Ra2??
5. Rh2 Kg5 (Kg3 6.Nh1+-)
6. Nh3 with a mortal discovered attack. So, at move 4, black must try something else. I have things to do, so I can’t really devote the time to finish this, but if 1.Nf2 is the right beginning, then that underpromotion is critical.
1. Nf2+ Kh4
2. g7 Rxc6
3. g8=R Rxc2
4. Rh8+ Kg3/5
5. Rh2 1-0 as white can now save the a2 pawn!
Yes, Nf2 is the right first move:
1. Nf2 Kh4 (Kg3 2.g7+-)
2. g7 Rc6
Here, Rc3 loses more surely: [2. …Rc3 3.g8Q Rg3 4.Qg3 Kg3 5.c7+-]. Continuing:
3. g8R Rc2
Here, if black doesn’t take the pawn immediately, white will just attack the a3 pawn with Rg3 and win a simple ending. Continuing:
4. Rg2
For me, the hardest move to find. The underpromotion sort of suggests itself once you realize the queen stalemates from g6 at move 4 in that line. Finding the following maneuver isn’t so obvious. Continuing:
4. …..Rc1 (Ra2 5.Rh2 Kg5 6.Nh3+-)
5. Kh2 Rc3
If there is anything better for black than these moves at 4 and 5, I will eat a hat. For the moment, white needs to untangle his men and advance on the a3 pawn. This is mostly just careful technique, and. I would do it as follows:
6. Rg4
To drive the black king back a rank. Continuing:
6. …..Kh5
7. Ne4 Rc2
Here, Kg4 is a lost endgame: [7. …Kg4 8.Nc3 Kf3 9.Nb1 Ke3 10.Na3 Kd3 11.Nb1 Kc4 (11. …Kc2 12.a4+-) 12.Kg2 and the white king will prove decisive. Even if the black king could approach the pawn, a3 would provide the correct disposition of a knight protecting it’s pawn from behind so that the knight is indirectly protected by the threat of the pawn running away from the enemy king]. Continuing:
8. Rg2 Rc4
9. Nd6 Rd4
10.Nb5 Rd3 (Ra4 11.Rg3 Rb4 12.Na3)
11.Kg1 Kh4
12.Kf2 Kh3 (Rd2 13.Kf3 Rd3 14.Ke4)
13.Rg8! Kh4
Here, [13. …Rd2 14.Kf3 Kh4 (to deal with mate threat) 15.Nc3 Rd3 16.Kf4! Kh3 (to deal with the mate threat) 17.Rc8 Kg2 18.Ke4 Rd2 19.Ra8! and the a-pawn falls].
14.Ke2 Rd5
15.Rb8
Not Na3 which is a draw after Ra5. Continuing:
15. ….Kg3
16.Na3 Ra5
17.Rb3