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This being a posed problem, my first thought was the queen sacrifice at h5, but it was pretty easy to see this was losing for white. If I had been playing this game, however, I definitely would have looked at Rh7 first (or I at least like to think I would):
1. Rh7 Kh7
2. Qe7 Kh6(alternatives transpose)
3. Qf8 Kh7 (Kg5 4.Qf4#)
4. Bg8 Kh8
5. Be6! Kh7
6. Qg8 Kh6
7. Qh8 Kg5
8. f4#
So, back at move 2, black had two alternatives- Kh8 and Rf7. Both lines transpose to the line above:
2. …..Kh8
3. Qf8 Kh7
4. Bg8 and the mate follows as before.
So, we are left with 2. …Rf7:
2. …..Rf7
3. Qf7 and both Kh6 and Kh8 transpose to the first line after 3.Qf8+.
I think the best move is
1.Rxh7+ Kxh7
2.Qe7+ Kh8
3.Qxf8+ Kh7
4.Qg8+ Kh6
5.Qh8+ Kg5
6.f4+ Kf5
7.Qe5+ Kg4
8.h3+ Rxh3
9.Qg5#
Any other reply by Black will accelerate the mate
It CNA”T be as easy as r#h7/ Qe7 check..Q#f8 check and Qf4 mate can it??
The position seems to beg for Qxh5+, then Rxh7+, but lets see if anyone else works it out.
1.Rxh7+ Kxh7
2.Qe7+ Rf7
[if ..Kh6 3.Qxf8+ Kh7 4.Qg8+ Kh6 5.Qh8+ Kg5 6.h4+ Kg4(..Kf5 7.Qf8+ Ke5/Kg4 8.Qf4#)7.Qc8+ Qf5 8.Bf3#]
3.Qxf7+ Kh6(..Kh8 4.Qg8#)
4.Qf8+ Kh7(..Kg5 5.Qf4#)
5.Qg8+ Kh6
6.Qh8+ Kg5
7.h4+ Kg4
[if ..Rxh4 8.Qxh4+ Kf5 9.Qf4#]
[if ..Kf5 8.Qf8+ Ke5/Kg4 9.Qf4#]
8.Qc8+ Qf5
9.Bf3# ..finally nailed the stubborn King. lol
1Rxpch 2Qe7+ & 3Qxr+ mates with B.
1. Rxh7+ Kxh7
2. Qe7+ Kh8
3. Qxf8+ Kh7
4. Bg8#
If 2. … Rf7
3. Qxf7+ Kh6
4. Qf8+ Kg5
5. f4+ Kg4
6. h3+ Rxh3
7. Be6+ Qf5
8. Bxf5+ gxf5
9. Qg7#
Mark
1. Rxh7+ Kxh7 2. Qe7+ Kh6 3. Qxf8+ Kh7
1…. Kg5 2Qf4#
4. Bg8+ Kh8 5. Be6+ Kh7 6. Qg8+ Kh6 7. Qh8+ Kg5 8. f4#
{NO WAY OUT of this mating net. The longest variation is given in bold
type. All the variations are similar. Black prolongs things just a bit in the long variation by interposing the elephant onto f7.} 1. Rxh7+ Kxh7 2. Qe7+ Rf7
(2. .. Kh6 3. Qxf8+ Kh7 (3. .. Kg5 4. f4+ Kg4 5. Bf3#) 4. Bg8+ Kh8 5. Be6+ Kh7 6. Qg8+ Kh6 7. Qh8+ Kg5 8. f4#)
(2. .. Kh8 3. Qxf8+ Kh7 4. Bg8+ Kh8 5. Be6+ Kh7 6. Qg8+ Kh6 7. Qh8+ Kg5 8. f4#) 3. Qxf7+ Kh6 (3. .. Kh8 4. Qg8#)
4. Qf8+ Kh7
(4. .. Kg5 5. f4+ Kg4 6. Bf3#)
5. Bg8+ Kh8 6. Be6+ Kh7 7. Qg8+ Kh6 8. Qh8+ Kg5 9. f4#
Lucymarie
1.Rxh7+ Kxh7
2.Qe7+ Kh6
3.Qxf8+ Kh7
4.Qg8+ Kh6
5.Qh8+ Kg5
6.f4+ Kf5
7.Qe5+ Kg4
8.Be6#