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Extremely Difficult Ending Study

White to move and win. This has a high difficulty level.

1B6/8/n1KPP1p1/4k1p1/6Q1/3p4/8/1q6 w - - 0 1

I have yet to fully convince myself this study is sound, but it is endlessly fascinating to me, and I want to know what the other readers think of it. I will later show my analysis once they have.

V-1

1.Bc7 Nb8+
2.Bxb8 Qxb8
3.Qxg5+ Kxe6
4.Qxg6+ Ke5
5.Qg5+ Kd4
6.d7 Qa8+
7.Kd6 Qb8+
8.Ke7 Qc7
9.Ke8 Qb8+
10.d8=Q+ Qxd8+
11.Kxd8 Kc3
12.Qc1+ Kd4
13.Qd1
It's a win for white.

V-2

1.Bc7 Qc1+
2.Kb5 Nxc7+
3.dxc7 d2
4.e7 Qb2+
5.Qb4 Qxb4+
6.Kxb4 d1=Q
7.e8=Q+ Kf4
8.Qf7+ Kg3
9.c8=Q Qb1+
10.Qb3+ Qxb3+
11.Qxb3
It's a win for white.

V-3

1.Bc7 Qc1+
2.Kb5 Kd5
3.Qg2+ Kxe6
4.Qe4+ Kf7
5.Qd5+ Kg7
6.Ba5 d2
7.Qd4+ Kf7
8.Bxd2 Qf1+
9.Kb6 Nb8
10.Qd5+ Kf8
11.Qa8 Qf2+
12.Kb7 Qxd2
13.Qxb8+ Kg7
14.Qc7+ Kh6
15.d7 Qd5+
16.Qc6 Qd4
17.Kc8 Qg4
18.Qh1+ Kg7
19.Qd5 Kh8
20.Kb7 Qb4+
21.Kc6 Qc3+
22.Qc5 Qf6+
23.Qd6 Qc3+
24.Kd5 Qb3+
25.Ke5 Qe3+
26.Kf6 Qf3+
27.Ke7 Kg7
28.Qd4+ Kh7
29.d8=Q
It's a win for white.

But I'm not sure that there is no variation leading to a draw.

The main line is 1. Bc7 Qc2! That is where the true beauty here lies- there are some amazing mutual zugzwang positions that arise.

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