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I remember this problem very well. This is one where I literally never found the right beginning, and even having it pointed out to me by pht, still couldn’t find the line, though looking over my notes, I think I found an improvement this afternoon:
1. Qf6 Kg8
Threatens Qf7# while pinning the f-pawn. Kg8 is the only move that isn’t mate that I see. Continuing:
2. Qf7 Kh8
3. Qf6 Kg8
So, now what for white? I really want to take at f5, but as pht points out (in the comments he made when this problem was first posted a year or two back), a1Q mucks things up since it occurs with check and exchanges white’s queen off the board. Of course, white could have taken at f5 on move 2 instead, but a1Q is still check and gives black time to play Qg7 defending the king, and I don’t see a win for white, and I have looked at these two positions for a long while now. So, I am left with 4.Nf7 (which white could have played at move 2, I suppose) which threatens 5.Nh6+ and 6.Ng5#:
4. Nf7 Ng6
No other move can avoid mate. The only interesting alternative is Kh7, but white puts black back in the hole taking advantage of the pin on the bishop at move 7: [4. …Kh7 5.Qh6 Kg8 6.Qh8 Kf7 7.Qh7 Kf8 8.Ng5 with mate to follow on the next move regardless of what black does]. Continuing:
5. Nd8
I have looked at this for over a half hour- I see nothing better for white. Continuing:
5. …..Rf8!
And, when I first studied this problem, I couldn’t find a better continuation for white than to return the queen to a1 wiht 6.Qa1, and after some liquidating moves, I thought white probably had a decisive edge, though, even now, it isn’t all that clear to me. However, I think white does better to take at c4 on move 6, a move I don’t seem to have even considered previously, that takes advantage of the hanging piece at f5:
6. Bc4! Rf6 (what else?)
7. Nf6 Kf8
If black plays 7. …Kh8, then white can sacrifice at a2 for the pawn: [7. …Kh8 8.Ba2! Bd3! 9.Nf7! Kg7 10.Nh5! Kg8 11.Rf2 leaves white up a clean piece]. If black plays 7. …Kg7, white can get a similar edge with 8.Nh5: [7. …Kg7 8.Nh5! Kg8 9.Ba2! again winning a clean piece]. Continuing:
8. Ba2! Bd3 (any better?)
9. Ne6 Ke7
10.Rf2 and white is still a piece up by my count.
1.Qf6-He5
2.Qxh6-Kg8
3.Hf6#
1Qf6 wins
1. Qf6!
{ 1… hxg5
2. Nxg5 Kg8 ( 2… Bg6? 3. Ne6+! Kg8 4. Qg7#)
3. Qxf7+ Kh8
4. Rf4!! a1Q+ ( 4. Rxf5? a1Q+ 5. Kh2 Qg7 6. Qh5+ Kg8 7. Rf7 Ng6! 8. Rxg7+ Kxg7 9. Qh7+ Kf6! -+)
5. Bf1 Qg7 ( 5… Ng6? 6. Qh7#)
7. Rh4+ Bh7
8. Rxh7+ Qxh7
9. Qxh7#}
1…Kg8 ( 1…Ne5? Qxh6+ 2. Kg8 Nf6 # )
2. Qxf7+ Kh8
3. Rxf5! a1Q+ Kh2!
4. Qg7 Qxg7+
5. Rf7+ Kg6 ( 5… Kg8 6. Nf6+ Kh8 7. Rf7#) (5… Kh8 6. Rh7+ Kg8 7. Nf6+ Kf8 8. Rf7#)
6. Bh5+!! Kxh5
7. g4+ Kg6 (7… Kh4? 8. Nf3#)
8. Rf6+ Kg7
9. Rf7+ Kh8 (9… Kg6? 10. Rg7#) (9…Kg8 10. Nf6+ Kh8 11. Rh7#)
10. Rh7+ Kg8
11. Nf6+ Kf8
12. Rf7#
Marcelo
1. Qf6 Bg6
2. Ne6+ Kg8
3. Qg7#
1. Qf6 Ne5
2. Qxh6+ Kg8
3. Nf6#
Nf6 followed by multiple threats looks good.
It looks like White will win material with Qf6 but I don’t see a forced mate with best defence by Black!