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1. Nd7+ Kg8
2. Qe8+ Kh7
3. Qxf7+ Kh8
4. Qf8+ Kh7
5. Nf6#
Alena, here is a puzzle I am working on just this past day. I think I have a solution broadly worked out- at least I have an idea now of the strategy white has to use to win this, but there are lot of variations that I haven’t confirmed are actually drawn, so I am not sure there is a unique solution yet, though there should be at move 1. This was posted on Susan’s blog over 8 years ago, but no one at the time solved it- I found it while perusing the older puzzles from that year posted here.
3k4/8/1p1P4/1B6/7b/5K2/7P/8 w – – 0 1
I have tried to solve your problem but I’m not sure that I played the strongest moves for black. I saw the idea ( give the h pawn for the bishop) instantly but it was very difficult to fulfill it.
1. Ke4 Be1
2. Kd5 Bh4
3. h3 Bg5
4. Kc6 Be7
5. Ba4 Bh4
6. Kxb6 Bf6
7. Kc6 Kc8
8. Kd5 Kb7
9. Ke6 Bd8
10. Kd7 Bh4
11. Bc2 Bg3
12. Be4+ Kb6
13. Ke6 Bh4
14. Bc2 Kb5
15. d7 Bd8
16. Bg6 Kc6
17. Be8 Kc7
18. Kf5 Bh4
19. Kg4 Bd8
20. h4 Kd6
21. h5 Ke5
22. h6 Kf6
23. Bh5 Bb6
24. Kf4 Ke7
25. Bg4 Bd4
26. Kg5 Bc3
27. Kg6 Ba1
28. Kh7 Kd8
29. Kg8 Ke7
30. h7 Kd8
31. h8=Q bxh8
32. Kxh8 Ke7
33. Kg7 Kd6
34. Kf7 Kc7
35. Ke8 Kb6
36. d8=Q
I am pretty sure 1.Ke4 is wrong is wrong, and when I work out all the details, I will show why later, but I can give a bit of a hint by describing the way I approach a problem like this:
Your instinct is correct. The thing you have to keep in mind the entire way is that black has a trivial draw if he can get the bishop into position to cover d8 and get the king to h8 since the h8 square is the wrong color for white’s bishop and h-pawn. Indeed, the thing to note is the role of black pawn on b6- its only purpose in this composition is to make the position winnable for white- it makes the squares a5 and b6 useless to black’s bishop, and keeps the black king from getting out of the box until white has been forced to push d7 opening e7. Ideally, black would like to quickly get the bishop on e5 or f4, or g3 if white has already pushed h3 foolishly, attack the d6 pawn forcing white to play d7 giving the black king access to e7 and the kingside.
It isn’t easy to find the first move or the path the white king must take to keep black from eventually realizing his goal. In you line that starts with 1.Ke4, I would suggest you reconsider black’s third move. Like I wrote, I am pretty certain at this point that 1.Ke4 will only draw with best play, but it is enlightening to work it why it only draws.
To illustrate the problem white is facing, here is a hypothetical approach- the first one I investigated yesterday:
1. Kg4
The idea, of course, is to support an immediate h4:
1. …………..Bf6 (with the plan of coming to e5 attacking d6)
2. h4
I will try to cover the alternatives later today or tomorrow if I don’t have time later, but what I want to do is demonstrate black’s resources in this position. Continuing:
2. …………..Be5 (forcing an immediate d7 by white)
3. d7 Bc7 (covering d8 and freeing the black king)
4. Kf5
Black’s immediate threat is Ke7-Kf8-Kg8/g7-Kh8. I will discuss 4.h5 again in a moment. Continuing:
4. ………….Ke7
5. Kg6
To cut off g7 for the black king. White is planning to cut off g8 with the bishop and then advance the pawn, but there is a problem with this strategy………..
5. ………….Kf8 (the only move now)
6. Bc4
Or the black king reaches h8 safely with time to spare. Continuing:
6. ………….Ke7
I think this is again an only move for black since Bd8 costs black a critical tempo because the black bishop is no longer able to safely cover h8 from e5, but has to cover from f6. The point of 6. …Ke7, of course, is to threaten Kxd7 and a later Be5 forever covering h8. White’s only hope is to retreat the bishop, but that is going to repeat positions…..
7. Bb5 Kf8
Finally, for this comment, I want to discuss white’s fourth move alternative of h5. From the top:
1. Kg4 Bf6
2. h4 Be5
3. d7 Bc7
4. h5 Ke7 (again, the only draw)
5. h6 Kf8 (or Kf7)
And white has the same problem as before, but worse- the black king can’t be kept out of even g7 now.
I hope this helps, Alena. It helped me find the right first move, or at least I think it did.
Alena, I am beginning to suspect this study is, in fact, unsound. I apologize for wasting your time here, but will let you know what I find. It may be a drawn position with best play no matter what white does. Right now, my best possible plan just doesn’t gain the tempo white appears to need. I have taken a look at the proposed solution, and have already determined that one part of it is definitely wrong in that it has black making a clearly losing move late in the line when there are others that are definitely drawn- i.e. it is a position I can analyze using the Nalimov tablebase by deleting the black pawn which plays no role at that point. Here is the line of the composer’s proposed solution which is almost identical to the line I had been working on but have failed to find a final win:
1. Kf4 Bf6
2. Ke4 Be7
3. Ke5 Bg5
4. Ke6 Bh4
5. Kf5 Be1
6. Kg4 Bb4
7. d7 Ke7
8. h4 Bd6
9. Kg5 Bc7
10.Kg6 Kf8
11.Kh7 Bd8
12.h5
And here, the composer proposes that black does best with 12. …..Bh4, but shows how white defeats this move quite easily. When you put the position afer 12.h5 minus the b6 pawn into the Nalimov Tablebase, it shows black does lose with 12. …Bh4 as even I could demonstrate quite easily, but then it shows black draws with 12. Bc7/b6/a5 and Kf7 which is what I kept running into yesterday with every single starting move for white including this afternoon my carefully planned maneuver that I kept running into a wall. Right now, I can’t quite wrap my head around this- does the pawn on b6 matter in some way the composer has left hidden after move 12, or am I right- this is a bust? I have to think about this quite a bit more to convince myself I am not overlooking something here.
I can’t win too.
It looks like your study is right.