White to move and win. How should White proceed?
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Very nice!
1. h7 g5 2. Nd4! Rxd4 3. c3+ Kxc3 4. h8=Q, now 4. … Rh4+ is not possible because the rook is pinned!
c3+ looks like a winner. Rxc3+ Kg2;Kxc3 g7;Ka3(or a4 b5) nd4
H7 looks good to me
1. Nb3-d2, with the Knight heading towards f3, the idea being preventing the black rook from reaching the h-file with any kind of support from the black pawn currently on g6.
–br
1.h7 g5 2.Nd4! Rxd4 3.c3+ Kxc3 4.h8=Q with threat of Qa8, white wins
1.h7 g5 2.Nd4 Rxd4 3.c3+ Kxc3 4.h8Q
This looks trivial. Just advance the h pawn. If checks come in move king to g5 where the knight defends a rook check. Once the pawn is queened it looks easy to help the a pawn to queen.
with no posts listed. Deep,Dark and Dummy says h7 with 2. N-d4 does the trick
1.h7 g5 (1…Rc3 2.Kg4 Rc4 3.Kg5 wins) 2.Nd4! Rxd4 3.c3 Kxc3 4.h8Q and the rook on d4 is pinned, so White wins.
The direct way h7-h8 doesn’t work because of:
1. h7 g5
2. h8=Q Rh4+
So the challenge is to stop the rook from reaching h4.
1. h7 g5
2. Nd4 Rxd4
3. c3+ Kxc3
4. h8=Q
And the rook cannot move.
Extension:
After h8=Q, white has to play Qa8 or Qb8 followed by Qxa7. After h8=Q, black plays Kc4, which is followed by Kb5 and Kxa6, if white is careless.
Is this win so clear, though?
1. h7 g5 2. Nd4 R:d4 3. c3+ K:c3 4. h8Q Kc4 5.Qa8 Kb5 6. Q:a7 Ra4 leaves us in one of those Q vs. R+P endings where there are a lot of drawing ideas for the inferior side.
. h7 g5 2. Nd4! Rxd4 3. c3 Kxc3 4. g8Q Kc4 5.Qa8 Kb5 6. Qa7 Ra4 7. Qc7 Ka6 and there’s no way for the white king to go to the queenside, specially on the c-file, because the rook will guard the c-file whatever happens. And the white king is very far from the queenside. The g5 pawn is an added burden to both white king and queen. Black can play g4+, b5 and Rc4.
h7 g5 2. Nd4! Rxd4 3. c3 Kxc3 4. g8Q Kc4 5. Qg7 Rd3+ 6. Kg4 Ra3 7. Qxc7+ Kb5 8.Qa7 Ra6 and and Black must secure the c-file for his rook and it’s a clear draw because there’s no way for the white king to penetrate on the queenside and queen alone is not enough to win the game. And the black king must stay around the b pawn.
1. h7 g5
2. Nd4 Rxd4
3. c3+ Kxc3
4. h8Q Kc4
5. Qg7 Rd3+
6. Kg4 Ra3
7. Qxc7+ Kb5
8. Qxa7 Rxa6 and here, the quickest win, accordind to the 6-men tablebase, is
9. Qd7+
But it is clearly an inhuman endgame. Practically, Black has very good chances to draw.
Anyway, the position here is much harder than the original study from
Kalinin, Magyar Sakkélet, #536, 1964
wKh3,Nb3,Pa4,c2,h6/bKb4,Rc4,Pa7,c7,g6
And, without the pawn b6 and a much more defensible white a-pawn on a4 instead of a6, the endgame is much easier to win for White!