Hence 1.Ba6! Is the right move. Queen sac does not work! 1.Qxb7+?.Kxb7.2.c6+.Ka/b8!.3.c7.Kb7!.4.Ba6+!.Kxa6!.5.c8=Q+.Kxa5! And the black king escapes mating net. White will run out of checks shortly with black bishop covering key squares in the queenside to protect the king. Black will win with his extra 3 pieces and passed pawn!
1.Qxb7+ Kxb7 2.c3+, for example 2…Ka8 3.Ba6 Qh8 4.Bc7 Ng6 4.Bb7# 2…Kc8 3.Ba6+ Kb8 4.c7+ Ka8 5.c8=R# 2…Kb8 3.c7+ (3.Ba6?? Bd6) Kb7 4.Ba6+ Kxa6 5.c8=Q+ Kxa5 should be at least a draw for White
The Queen sacrifice at b7 is easy to see. Because Black’s Queen & other pieces are so much clustered and so far away from the King. 1.Qxb7+! KxQ 2.c6+ Kb8 (or 2…Ka8 3. c7 Kb7 4.Bc6+! KxB (or 4…Ka6 5.c8=Q+ KxB 6.Qb7 and mate follows) Continuing, 5.c8=Q+ Kd5 (5…Kb5 6.Qc5+ wins)6. Qb7+ Kc4 7.Qc6#) Continuing from 2…Kb8 further, 3.c7+ Kb7 4.Bc6+ and remaining as above.
1. Q:b7+ K:b7
2. c6+ Kb8 (2…Kc8 3. Ba6+ Kb8 4. c7+ Ka8 5. c8Q#)
Back to the main line.
3. c7+ Kc8
4. Ba6+ Kd7
5. c8Q+ Kd6
6. Qc7+ Kd5
7. Bb7#
Cute!
1. Ba6..bxa6 forced else 2.Qxb2#!
2. Qc6…Bd8 forced else 3.Qc7+.Ka8.4.Qc8#!
3. Qd6+.Kc8 if 3….Bc7.4.Qxc7+.Ka8.4.Qc8#!
4. Qxd8+.Kb7
5. Qc7+..Ka8
6. Qc8#!
If
3. Qd6+..Kb7
4. c6+…Ka/c8
5. Qxd8#
Hence 1.Ba6! Is the right move. Queen sac does not work!
1.Qxb7+?.Kxb7.2.c6+.Ka/b8!.3.c7.Kb7!.4.Ba6+!.Kxa6!.5.c8=Q+.Kxa5! And the black king escapes mating net. White will run out of checks shortly with black bishop covering key squares in the queenside to protect the king. Black will win with his extra 3 pieces and passed pawn!
C6?
Qxb7!!
1. Ba6 bxa6 (1. … b6 2. Qb7#) 2. Qc6 Bd6 (2. … Nd7 3. Qc7+ Ka8 4. Qc8+ Nb8 5. c6 followed by 6. Qb7#) 3. Qxd6+ Ka8 4. Qd8+ Kb7 5. Qc7+ Ka8 6. Qc8#
1.Qxb7+ Kxb7 2.c3+, for example
2…Ka8 3.Ba6 Qh8 4.Bc7 Ng6 4.Bb7#
2…Kc8 3.Ba6+ Kb8 4.c7+ Ka8 5.c8=R#
2…Kb8 3.c7+ (3.Ba6?? Bd6) Kb7 4.Ba6+ Kxa6 5.c8=Q+ Kxa5 should be at least a draw for White
1. Ba6 (threatening mate on b7) bxa6
2. Qc6 and mate is unavoidable
B a6
The Queen sacrifice at b7 is easy to see. Because Black’s Queen & other pieces are so much clustered and so far away from the King.
1.Qxb7+! KxQ 2.c6+ Kb8
(or 2…Ka8 3. c7 Kb7 4.Bc6+! KxB (or 4…Ka6 5.c8=Q+ KxB 6.Qb7 and mate follows)
Continuing, 5.c8=Q+ Kd5 (5…Kb5 6.Qc5+ wins)6. Qb7+ Kc4 7.Qc6#)
Continuing from 2…Kb8 further,
3.c7+ Kb7 4.Bc6+ and remaining as above.
Here I would first look at the Q sack and how much speed the c pawn may get:
1. Qxb7+!! Kxb7
2. c6+! Kb8/Ka8 (2. … Kc8 3. Ba6+ Kb8 4. c7+ Ka8 5. c8=R#)
3. c7(+) Kb7 (enforced)
Here some thinking is needed.
I looked at 4. Bc6+? Kc8! as rather unpleasant for white. The best rry seems to be:
4. Ba6+! Kxa6 (Kc6 c8=Q+ Kd5 Qb7#)
5. c8=Q+ Kxa5
6. Qc7+ Kb4
7. Qb7+ Ka5 (Kc4? Qb3#)
Here some more thinking is needed.
Now Qxa7+? looks drawish to me. What about:
8. Kb3! any
9. Kc4!
With the double threat of 10. Qc5# and 10. Qxa7#. No matter what black’s move #8 was, I don’t see how black’s move #9 prevents both mates!
So my guess now is that this is a mate in 10 moves.