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After playing around with both 1.Be4 (probably loses for white) and 1.Qd3 (draw by repetition probably best for white), you should eventually land on
1. Rd4!
The idea is that white is threatening Be4#. In retrospect, I should have seen this move immediately, but I had eyes only for 1.Be4 right from the start (and this move as move 2 in a line below also betrayed me!). Black cannot defend e4 with Nc5 since this allows Qf6#. So, black seems to have only g4 and moves of the bishop to open up f4 for the king. Let’s just play through all of the important lines to be sure they all lose for black:
1. …..Bh2
2. Be4 Kf4
3. Bh7
There seem to be other mating moves here, like Bf3 even, but none of them can be shorter, though they might all be the same length. Continuing:
3. …..Ke3
Or [3. ….Kf3 4.Qd5 Ke3 (or 4. …Kg3 5.Qg2#) 5.Qe4#]; or [3. …Kg3 4.Rd3 Kf4 (or 4. …Kh4 5.Qh6#) 5.Qd4#]. Continuing:
4. Rd3 Kf4
5. Qd4#
Or, at move 1:
1. …..Be3
2. Be4 Kf4
3. Bh7! Bd4 (Kf3 4.Qd5#)
4. Qd4 Kf3
5. Qe4#
Or, at move 1:
1. …..Be5
2. Be4 Kf4
3. Bh7 Ke3 (Kf3 4.Qd5 Ke3 5.Qe4#)
4. Re4 Kf3
5. Qd3#
Or, at move 1:
1. …..g4
Now, does 2.Be4 win here for white? You tell me. I spent a half hour working through it and could come to no firm conclusion. If I have time later today, I may try to finish that line out, but it turns out I wasted most of that time anyway since white has a nice sacrifice to cap this off very, very efficiently, and elegantly:
2. Rf4! Kf4 (Kg5 3.Rg4+-)
3. Qd4 Kf5 (Kg5 4.Qg4#)
4. Be4 Kg5 (Ke6 5.Qd6#; Kf4 5.Bd3)
5. Qe3 Kh5 (Kh4 6.Qh6#)
6. hg4 Kh4 (Kg4 7.Qg3 Kh5 8.Bf3#)
7. Qg3 Kg5
8. h4#
This is way too hard.
1Rd4 (threatens 2Be4#)
1…. g5 makes way for king
2h4 denies g5 for black K.
2…. g3 seeks escape square g4
3h3 denies g4 for black K.
Now black may delay matters by moving g2,then f1.After that Be4# is inevitable.If …. Nc5 at any stage Qf6#.
For those who like sacrifice
1Rd4 g4
2Rxf4+ Kxf4
3Qd4+ Kg5
4Qe3+ Kh5
6hxg4+ Kh4
7Qg3+ Kg5
8h4#
After about 15 minutes of being led down the rabbit whole with checks–1.Qd3,1.Be4–I moved on and discovered 1.Rd4. All that I see for black is moving the bishop or g pawn to allow his king to try to escape. I think every move with the bishop fails:
1.Rd4 Be5
2.Be4 Kf4
3.Bh7 Ke3 (that pin is killer)
4.Re4 Kf3
5.Qd3
OR
3…. Kf3
4.Qd5
Other lines….
1…. Be3
2.Be4 Kf4
3.Bg6 Bd4
4.Qd4 Kf3
5.Bh5
OR
1…. Bh2
2.Be3 Kf4
3.Bh7 Kg3
4.Rd3 Kh4
5.Qh6
Moving the g pawn delays a little bit, but I think the same idea still wins.
1…. g4
2.h4 g3
3.h3 g2
4.Kg2 g1
5.Kg1 And black is left with nothing else but the bishop moves that all fail.
1. Rd4, threatening Be4 checkmate
1…Be5 2.Be4 Kf4 3.Bf3!
3…Kf5 4.Bg4#
3…Kf3 4.Qd5 Ke3 5.Qe4#
3…Ke3 4.Re4 Kf3 5.Qd3#
1.Rd4 threatening Be4
1.Nd7 somewhere
2.Qf6#
1.Bxe5
2.Be4+ 2.Kf4
3.Bg3+ 3.Ke3
4.Re4+ 4.Kf3
5.Qe3#
3.Kf3
4.Qd4+ 4.Ke3
5.Qe4#
I didn’t put it on any board, so i may have missed something
BE4, KXB, QD3
My favorite variation in the complex problem that has a lot of variations is:
1. Rd4 g4
2. Rxf4+ Kg5
3. Rxg4+ Kh5
4. Rh4+ Kxh4
5. Qxh6#