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1. Ra6 … and the black Queen has no suitable squares for retreat
I think its a draw by Perpetual check.
After Ra8+ Kf7
Nd8+ Kg7
Ne6+ Kh7 1/2-1/2
After Ra6, white wins the queen in every variations, but the pawn will reach on “h” line the last square h1=Q, black wins!
1.Ra6! Kf7 2.Nd8+ Kg7 3.Rxh6 Kxh6 4.d6! exd6 5.Nf7+ Kh5 6.Nxd6 Kg4 (h3 7.Ne4 h2 8.Ne2)
7.Kd1 h3 8.Ne4 and white wins
A very difficult task!
After 1.Ra6 the queen has no place to go to avoid being captured by a fork of some kind.
So Black might as well give up the queen for the rook in the hope of promoting the h-pawn afterwards.
1…Kf7 2.Nd8+ Kg7 3.RxQ KxR
Now White seems to be unable to stop the h-pawn as knight and king are too far away.
But 4.d6! enables the knight to go to better squares and is able to stop the h-pawn now.
1.Ra6!! Does the dirty on black.
1. Ra6 forces the queen to move off the 6th rank because otherwise the N moves with check. No diagonal move is safe, so it must go to h8, h8, or h5.
1…Qh8 2. Ra8+ wins.
1…Qh5 2. Ng7+ wins.
1…Qh7 2. Ra8+ Kf7 (Kd7 3. Rd8#)3. Ng5+ wins.
So it appears that 1. Ra6 Kf7 2. Nd8+ Kg7 3. R:h6 K:h6 is best. Now the N must catch the h-pawn.
4. Nc6 h3 5. N:e7 h2 6. Nf5+ and 7. Ng3 does that, so Black must use his King to try to ward off the knight. 4… Kg5 seems to do that, so perhaps white should try another tack.
4. d6 ed 5. Nf7+ simplifies the ending; the N can easily get back via d6, e4, and f2 to guard h1. if black’s king tries to get in place to ward off the knight, the white king can easily get to e2 to guard the pawn and allow the N to occupy f2 safely.
So 1. Ra6 Kf7 2. Nd8+ Kg7 3. R:h6 K:h6 4. d6 ed 5. Nf7+ and 6. N:d6 seems to win.
1 Ra8+ Kf7 (if 1…Kd7 2 Rd8 mate)
2 Rf8+ Kg6 (forced)
3 Nf4+ Kg5 (if 3…Kg7 4 Ne6+ repeats)
hmmm… now I am stuck 🙁
Ra6
Ra6 and the queen is lost
Va6
Ta6 winning the queen
1. Ra6! and black can’t avoid losing the Queen … e.g.,
1. … Qh5
2. Ng7+
1. … Qh7
2. Ra8+ Kf7
3. Ng5+
1. … Qh7
2. Ra8+ Kd7
3. Nf8+
1. … Qh8
2. Ra8+
1. … Qg6
2. Ra8! Kd7?
3. Rd8# mate
1. … Qf6 (best move)
2. Ra8! Kf7
3. Rf8+ Kg6
4. Nf4+ Kf5
5. Rxf6+ Kxf6
6. Kd1 Kf5
7. Nd3 Ke4
8. Ke2 Kxd5 and black may have some drawing chances.
1. Ra6 Qf6 2. Ra8+ Kf7 3. Rf8+ Kg6 4. Rxf6+ Kxf6 5. Nd4 Ke5 (5… h3 6. Nf3 Kg6
7. Kd1 Kh5 8. Ke2 Kg4 9. Kf2 Kf5 10. Kg3 h2 11. Nxh2 Ke4 12. Ng4 Kxd5 (12…
Kd4 13. Ne3 Ke5 14. Kf3)) 6. Nf3+ Kf5 7. Ne5 (7. Nxh4+) *