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White takes advantage of the Black king’s cramped position:
1. Nc6+ as the only option.
1. … Kc8 of course not
1. … Ka8
2. Na5/d4+ Kb8
3. Nxb3 axb3
4. Bd1 +-
2. Bd5! Qxd3+
2. … Qxd5
3. Ne7+ +-
3. e4 Qxa6 Black has no checks and Be6 was threatening with mate.
3. … Kd7 4. Ne5+ and 5. Nxd3 +-
3. Be6+ Kb7
4. Bc4! and the queen has nowhere to go.
4. … Qxc4 5. Na5+ and Nxc4 +-
4. … Kxc6 5. Bxa6 +-
1. Nc6+
A-1…..Ka1/b2. 2.Na5+.and 3.Nxb3 wins easily!
B-1…..Kc8..2.Bd5!!threatening Be6#
B1-2….Qxd5.3.Ne7+..and 4.Nxd5 winning
B2-2….Qxd3+3.e4!!.Qxd5 (forced to to prevent mate with Be6 as in B1. 4.Ne7+..and 5.Nxd5 winning.
Black’s other choices are Qxe4+ or Qh3 both of which lose Queen for only a pawn!
Harry
1.Nc6+ Kc8
2.bd5 Qxd3+
3.e4 (threat 4.Be6+) Qxa6
3…… Qb3
4.Bxb3 axb3
5.Nxa7+ and the N will be able to stop b pawn from queening.
4.Bc4 Qxc6
5.Bd5 Qxd5
6.exd5 Ka6
7.d6 cxd6
8.cxd6 Kb6
9.kh6 h4
10.Kg5(better than Kh5) h3
11.gxh3 wins.
Continuing my solution, I had left out one interesting alternative which also wins for white.
1.Nc6+.Kc8 forced
2.Bd5..Qxd3+
3.e4!!.Qxa6!
4.Be6+.Kb7
5.Bc4!!
C-5…Qxc4.6.Na5+ followed by 7.Nxc4 winning
D-5…Qxc6.6.Bd5 pins and wins black queen for a easy white win.
E-other queen moves allow queen capture directly by Knight, bishop or pawn!
Harry
Nice analysis by others here on the line …Qxd3+… Qxa6, eliminating the immediate mate threat, which I overlooked completely. Some attention, however, must be paid to the idea that Black allows his Queen to be captured on b3 and White must be able to stop the pawn. For example, I presume that is the case (but haven’t fully worked it out in my head) ;after:
1)Nc6+ Kc8
2)Bd5! Qxd3+
3)e4 Qb3 an interesting try, preventing the Be6 mate by X-ray
4)Bxb3 axb3
and I presume 5) Na7+ followed by Nb5 gives White time to get back and stop the pawn. And presumably Black’s K doesn’t have enough time to move up and support his Pawn’s advance…- Craigaroo
Craigaroo’s idea is interesting.
However, black king has to (1) decoy b2 to force white knight to Nc3 (2) capture the white pawn at a6 by Kb8-Ka7-Kxa6 (2moves)(3)then navigate through Kb7-Kc6-Kc5-Kd4-Kxc3-b1=Q (6 more moves for a total of 8 moves. But white in the meantime will queen his e pawn in 5 moves!
Qb3 doesnot work!
Harry