1. Rh8+ Bxh8 2. Rxh8+ Ng8 (Kg7 Qh6#) 3. Qxd6+ Kg7 (Ke8 Rxg8+ Rf8 Qe7#) 4. Qxe5+ Kf8 (Rf6 Qe7#, Kg6 Qh5+ Kf6 Qe5+) 5. Qd6+ Kg7 6. Qe5+ seems to be a draw. If here is something better, I have missed it.
Avoiding the plan Rxg8+, Nxe7+ and Qxb6, black should in that case simply be up with a rook.
For me, this one was very hard to see. I got the first three moves correct, but couldn’t see how to complete the mate attack (i.e., 4. Qxd6+). And there is another subtlety where the black king must be driven back to the 8th rank so that the white rook can capture the knight at g8 and force the black rook off the 7th rank. Complicated! Fritz found the winning completion after move 3. Here’s the full analysis. [FEN “1r3k2/4nrb1/1qNpQ3/3Pp3/p4p2/P1p2P1R/8/K6R w – – 0 0”] 1. Rh8+ Bxh8 2. Rxh8+ Ng8 (2… Kg7 3. Qh6#) 3. Qh6+ Rg7 (3… Ke8 4. Rxg8+ Kd7 5. Qe6+ Kc7 6. Qxf7#) 4. Qxd6+ Kf7 (4… Re7 5. Qxe7# {Black knight at g8 is pinned.}) (4… Ke8 5. Rxg8+ Kf7 6. Qe6#) 5. Qe6+ Kf8 {White queen forces black king back to 8th rank as a preliminary to forcing the black rook off the 7th rank.} 6. Rxg8+ Rxg8 {Since the king is in check and has nowhere to go, the black rook must capture the white rook. Now it is safe to move the white queen to e7. Previously, white could not do that.} 7. Qe7#
An alternative line where black responds with Ng8 rather than Bxh8: 1… Ng8 2. Qxd6+ Ke8 3. Rxg8+ Bf8 4. Rxf8+ Rxf8 5. Qe7#
Some not so great ideas: 1. Nxb8 Kg8 2. Qg4 Qb2# {Black wins.}
I guess my mistake was to play 3. Qxd6+ one move too early. Here must be inserted 3. Qh6+ Rg7 for the purpose to deprive king of the escape field g7. Then 4. Qxd6+ works better.
1 Rh8+ B:h8
(If 1 … Ng8
2 Q:d6+ Ke8
3 R:g8+ Bf8
4 R:f8+ R:f8
5 Qe7#)
2 R:h8+ Ng8
3 Qh6+ Rg7
(If 3 … Ke8;
4 Qe6+ Kf8;
5 R:g8+ R:g8
6 Qe7#)
4 Q:d6+ Ke8
(If 4 … Kf7
5 Qe6+ Kf8
6 R:g8+ R:g8
7 Qe7#)
5 R:g8+ Kf7
(If 5 … R:g8
6 Qe7#)
6 Qe7+ Kg6
7 Q:g7+ Kf5
8 Qg6#
(or 7 … Kh5
8 Qg5#)
1. Rh8+ Bxh8
2. Rxh8+ Ng8 (Kg7 Qh6#)
3. Qxd6+ Kg7 (Ke8 Rxg8+ Rf8 Qe7#)
4. Qxe5+ Kf8 (Rf6 Qe7#, Kg6 Qh5+ Kf6 Qe5+)
5. Qd6+ Kg7
6. Qe5+
seems to be a draw.
If here is something better, I have missed it.
Avoiding the plan Rxg8+, Nxe7+ and Qxb6, black should in that case simply be up with a rook.
1. Rh3-h8+
–br
No idea. Too difficult.
1. Rh8+ wins
If 1….Ng8
2. Qxd6+ Ke8
3. Rxg8+ Bf8
4. Rxf8+ Rxf8
and mate next move
If 1… Bxh8
2. Rxh8+ Ng8
3. Qh6+ Rg7
4. Qxd6+ Kf7
5. Qe6+ Kf8
and mate follows
1.Rh8+ Bxh8
2.Rxh8+ Ng8 (if 2…Kg7 3.Qh6 mate)
3.Qh6+! Rg7
4.Qxd6+ Ke8
5.Rxg8+ Rxg8
6.Qe7 mate!
Kamalakanta
The best I can see is a draw by perpetual check:
1. Rh7+ Ng8
2. Rxg8+ Kxg8
3. Nxe7+ Kf8
4. Ng6+ Kg8
5. Ne7+ etc.
But note that if Black responds with 1. … Bxh8, it’s a win for White:
2. Rxh8 Ng8 (Kg7 Qh6#)
3. Qxd6+ Ke1 (Re7 Qxe7#)
4. Rxg8+ Rf8
5. Rxf8#
For me, this one was very hard to see. I got the first three moves correct, but couldn’t see how to complete the mate attack (i.e., 4. Qxd6+). And there is another subtlety where the black king must be driven back to the 8th rank so that the white rook can capture the knight at g8 and force the black rook off the 7th rank. Complicated! Fritz found the winning completion after move 3. Here’s the full analysis.
[FEN “1r3k2/4nrb1/1qNpQ3/3Pp3/p4p2/P1p2P1R/8/K6R w – – 0 0”]
1. Rh8+ Bxh8
2. Rxh8+ Ng8
(2… Kg7 3. Qh6#)
3. Qh6+ Rg7
(3… Ke8 4. Rxg8+ Kd7 5. Qe6+ Kc7 6. Qxf7#)
4. Qxd6+ Kf7
(4… Re7 5. Qxe7# {Black knight at g8 is pinned.})
(4… Ke8 5. Rxg8+ Kf7 6. Qe6#)
5. Qe6+ Kf8 {White queen forces black king back to 8th rank as a preliminary to forcing the black rook off the 7th rank.}
6. Rxg8+ Rxg8 {Since the king is in check and has nowhere to go, the black rook must capture the white rook. Now it is safe to move the white queen to e7. Previously, white could not do that.}
7. Qe7#
An alternative line where black responds with Ng8 rather than Bxh8:
1… Ng8
2. Qxd6+ Ke8
3. Rxg8+ Bf8
4. Rxf8+ Rxf8
5. Qe7#
Some not so great ideas:
1. Nxb8 Kg8
2. Qg4 Qb2# {Black wins.}
1. Nb4 c2
2. Nxc2 Qb2# {Black wins.}
I guess my mistake was to play 3. Qxd6+ one move too early. Here must be inserted 3. Qh6+ Rg7 for the purpose to deprive king of the escape field g7. Then 4. Qxd6+ works better.