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.
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.
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:
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