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1 Rxf8+ Kxf8 2 Ne6+ Kg8 3Qe8+ Kh7 4 Qxe7+ Kg6 5 Qg7+ Kf5 6 g4+ Ke4 7 Qg6+ Nf5 8Qxf5#
Rxf8+ Kxf8
Ne6+ Kg8
Qe8+ Kh7
Qxe7 Nf7
Qxf7+ Kh6
Qg7+ Kh5
g4+ Kh4
Qh6++
Rxf8+ Kxf8
Ne6+ Kg8
Qe8+ Kh7
Qxe7 Kg4
Qg5+ Kf7
Qg7+ Ke8
Qf8+ Kd7
Qd8++
Rxf8+ followed by Qf7
Woops forgot about the knight. Rxf8 Kxf8 Ne6+
rxf8 kxr ne7+ kg8 qe8 kh7 qxn+ and its over
1. Rf8 if Kf8
2. Ne6 Kg8
3. Qe8 Kh7
4. Qe7 Kh8 or Kg8
5. Qg7 #
or in move one:
1. Rf8 Kg7
2. Ne6 Kh7
3. Rf7 Kg8 (if 3. … Kh8 4. Qh6 Qh7 ( 4. … Kg8 5. Qg7#) 5. Qh7##)
4. Rg7 Kh8
5. Qh6 Qh7
6. Qh7#
1. Rf8 mate in 8
with both 1…Kf8
or 1…Kg7
followed by 2.Ne6
1.Rxf8+ Kxf8 2.Ne6+ Kg8 3.Qe8+ Kh7 4.Qxe7+ Kg6 5.Qg7+ Kf5 6.g4+ Nxg4 7.hxg4+ Ke4 8.Qg6#.
Jorg, at first, I made the exact same mistake, but 1. Rf8 is the winner.
1. Rf8 Kf8 (Kg7 below)
2. Ne6 Kg8
3. Qe8
Really the only move possible since Qg5+ allows black’s queen to join the defense. Continuing:
3. …..Kh7
4. Qe7 Kg6 (Kg8 5.Qg7#; Nf7 below)
5. Qg7
Force black into the picket fence:
5. …..Kf5 (Kh5 6.Qg5#)
6. g4 Ng4 (Ke4 7.Qg6 Nf5 8.Qf5#)
7. hg4 Ke4
8. Qg6#
At move 4 above, black is still mated after Nf7:
4. …..Nf7
5. Qf7 Kh6
6. Qg7 Kh5
7. Qg5#
And, at move 1, black clearly can’t decline the rook:
1. …..Kg7
2. Ne6 Kh7
3. Rf7 Kg8 (Kh8 4.Qh6 # next move)
4. Rg7 Kh8
5. Qh6 with mate on the next move.
Rxf8+ Kg6 Ne6+ Kh7 Rf6+ Kg8 Rg7+ Kh8 Qxh6+ Qh6 QxQ
1.Rxf8+
I)1…Kxf8 2.Ne6+ Kg8 3.Qe8+ Kh7 4.Qxe7+ Kg6 5.Qg5+ Kf7 6.Qg7+ Ke8 7.Qf8+ Kd7 8.Qd8 mate
II)1…Kg7 2.Ne6+ Kh7 3.Rh8+ Kxh8 4.Qxh6+ Qh7 5.Qf6+ Kg8 6.Qf8 mate
After the rook sac on f8 black has two choices:
a) run and b) take the rook. Let’s look at a) first.
1.Rxf8+ Kg7
2.Ne6+ Kh7
3.Rf7+ Kh8
4.Qxh6+ Qh7(Kg8, 5.Qg7#)
5.Qxh7#
3.Rf7+ Kg8
4.Rg7+ Kh8
5.Qxh6+ Qh7
6.Qxh7#
Now let’s look at option b):
1.Rxf8+ Kxf8
2.Ne6+ Kg8
3.Qe8+ Kh7
4.Qxe7+ Kg6(Kg8 or h8, 5.Qg7#)
(Nf7 5.Qxf7 Kh6 6.Qg7+ Kh5 7.Qg5#)
5.Qg5+ Kf7(Kh7 6.Qg7#)
6.Qg7+ Ke8
7.Qf8+ Kd7
8.Qd8#
1.Rxf8+ Kxf8
2.Ne6+ Kg8
3.Qe8+ Kh7
4.Qxe7+ Kg6
5.Qg7+ Kf5
6.Qg5+ Ke4
7.Ke3+ Kf5
8.g4+ Kf6
9.Kxh6+ Kf7
10.Qf8+ Kg6
11.Qg7#
Checkmate follows in other variations to like if Black decides to sacrifice knight after 8.g4+ Nxg4 9.Kxg4 10.Qg5#
Rxf8+,Kxf8
Ne6+,Kg8
Qe8+,Kh7
Nf8+,Kg7 or Kg8 inviting perennial check stalemate…
Ne6+,Kf6
Qf8+,Nf7
Qg7+,Kf5
Qh7+,Ng6
Qxf7+,Kd4 runs but cant hide..
Qg6++ final waterloo!!
actually mo complicated like it seems, and once d white queen veers of its trajectory to keep the check going, the black knight could easily block the f-file and threatening the white king in reverse… i go with my earlier submission as enumerated. tanx! -john.