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Nh7 followed by Nf6, Nd8 and Qg7
I like:
1. Qf6 hxg5
2. Qh6+ Kg8
3. Nf6#
or
1. … Bg6 (otherwise Qxf7#)
2. Ne6+ Kg8
3. Qg7#
At first glance, I saw a rather easy mate in 3, in only 2 variations. But there is of course a third line:
1. Qf6 Kg6
2. Qxf7+ Kh8
3. Rxf5! hxg5 (otherwise Qh7#)
4. Nf6/Nxg5 Nxf5 or any
5. Qh7#
Oops!
My previous comment ran into nonsense.
Rxf5 is of course prohibited due to a1=Q+.
1. Qf6 Kg8!
Has to be critical, hxg5 or Bg6 were mate in 3.
It’s surprisingly hard to find the right continuation here!
1Qf6
1. Qf6 Ne5 White was threatening Qxf7#
1. … Bg6/Be6
2. Ne6+ Kg8
3. Qg7#
2. Qxh6+ Kg8
3. Nf6#
How about:
1. Nh7+ Kg8
2. Nf6+ Kg7 (or Kh8)
3. Nxe8+ Kxh7 (or Kg8)
4. Qg7++
I have to thank pht. Qf6 was invisible to me. I spent a lot of time looking at various sacrifices on the first move with great frustration. I think pht is correct- 1.Qf6 Kg8 is the critical line:
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, 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 I have to admit that I am a bit stuck here. The best I can come up with here for white is the return to a1 with the queen and start liquidating the position:
6. Qa1 Be4!
7. Rf8 Nf8!
8. Bc4 Rd8
9. Qa2
This clearly leaves white moderately ahead in material. Probably ahead enough to have a decisive advantage. If the black pawns were on light squares, black might have a good chance of a draw, still white will have a lot of effort to finish this off. I simply have to be missing something stronger here around move 2-5 in this line.
The critical line is 1…Qf6 2. Kg8! Qf7:+ 3.Kh8 Qf6+ 4 Kg8 Ne6!! 5. B:e6 Qe6:+
6. Kh8 Qh6+ 7Kg8 Nf6+! 8Kf7 Qh7+ 9.Kf8 Nd7++# double check AND mate
The Queen maneuvers are necessary to place the imperiled
Majesty in mating position with checks because of the always looming threat of
a1=Q+