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1. f6
The threat is 2. Qh6 followed by 3. Qg7#.
1. .. Kh7 2. Rf5
The threat is 3.Rxh5# Kg8 4. Qh6 followed by 5. Qg7#.
2. .. gxf5
(2. .. Qxf5 3. Bxf5 gxf5 4. Qg5 Rg8 5. Qxh5#)
3. Qg5 Rg8 4. Qxh5#
Lucymarie Ruth (with the assistance of Grind-master Lenya Gristmilli)
1.f6 Kh7
(1…Qg4 2.Qh6)
(1…Kh8 2.Qh6+ Kg8 3.Qg7#)
(1…g5 2.Qxg5+ Kh8 3.Qg7#)
2.Rf5 Qxf5
(2…gxf5 3.Qg5 Rfe8
(3…Rg8 4.Qxh5#)
4.Qg7#)
3.Bxf5 Rae8
(3…gxf5 4.Qg5 Rg8 5.Qxh5#)
4.Be4 Rh8 5.Qg5 c4 6.Qxh5+ Kg8 7.Qg5 Rh5 8.Qg4 Kh8 9.Bxg6 Rh6 10.Bf5 Rg8 11.Qe2
I could not see any alternative to 1. f6.
I didn’t want to look at other plans, and after some thinking I made it work!
1. f6 Kh7
Enforced to avoid Qh6-Qg7#, and now there is a beautiful pin on g6!
2. Qg5!
Black has nothing against Qxh5+.
f6 fairly screams out in this position to threaten Qh6 and Qg7#:
1. f6 Kh7
If there is another defense to 2.Qh6, I am not seeing it. Now, I had to look at this position a long while before I found the winning line. My first idea was 2.Qg5 to threaten Qxh5 (the bishop pins g6 to the king), but black can defend with Qg4, and I could not find a way forward that wasn’t a big edge for black. Then I looked at pawn pushes on the kingside, but they all looked losing. Also, the bishop sacrifice at g6 is just flat out losing. I finally looked at Rf5 in detail, and felt really stupid for not seeing this works much earlier. It has the same plan as Qg5, but now black can’t play Qg4, but I misjudged a key feature initially that caused me to ignore this move at the beginning:
2. Rf5! Qf5
Any other move, and black gets mated: [2. …Qe6 3.Rh5 Kg8 4.Qh6]; or [2. …gf5 3.Qg5! Rg8 4.Qh5#]; or [2. …Rh8 3.Rh5 Kg8 4.Rh8 Kh8 5.Qh6 with mate to follow.] Continuing:
3. Bf5
And the this is the thing I missed- black can’t take the bishop without getting mated starting with Qg5 and ending with either Qg7 or Qh5#. White has a fairly easily won ending.
f6 Kh7
Rf5 gf5
Dg5 Rg8
Dxh5#
f6 Kh7
Rf5 Dd6
Rxh5+ Kg8
Rh8+ Kxh8
Dh6+ Kg8
Dg7#