2k5/2p5/8/4N1b1/5p2/8/8/5BK1 w – – 0 1
White to move. No computer please because you’ll take the fun out of it for yourself. Can White win this game?
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Interesting…White can lock the black king into the corner with 1. Ba6+ {if Kd8, then Nf7+ wins the bishop and white will win if knows B+N checkmate} Kb8 2. Nc6. Now, if the white king can work its way to c8, it’s Bb7#. The only problem is that white doesn’t have time to do that directly because the black f-pawn would queen. White gains time by aiming his king for a6 with bishop on c8. As long as the king remains in the square of the pawn, it is not a threat to queen, so the white king marches to c4. If the pawn still hasn’t moved, the king moves to b5 and Ka6 and Bb7 can’t be stopped. Therefore, black must begin to move the pawn before the white king gets to b5. Here is a line:
1. Ba6+ Kb8 {Kd8 loses to Nf7+}
2. Nc6+ Ka8 {forced}
3. Kg2 Bh4
4. Kf3 Bg3 {if the white king can capture either the pawn or bishop while the black king is trapped in the corner, game is over}
5. Ke4 Bh2 {forced}
6. Kd4 Bg3
7. Kc4 f3 {Marching the pawn is the only way to prevent immediate checkmate with Bc8, Ka6, and Bb7#, but white could try postponing it one move. Variation below.}
8. Kd3 f2
9. Ke2 Bh4
10. Kf1 Bg3
11. Kg2 Bh4
12. Kh3 f1=Q+
13. Bxf1 Kb7 {Black cannot move the bishop because 14. Ba6 locks the king in again}
14. Na5+ Kb6 {The only hope is to chase the knight and offer exchange of bishop for knight}
15. Nc4+ Kc5 {But the knight can now deliver check from a protected square. Adios black bishop!}
16. Kxh4 {And now it is game over, provided white has good enough technique to checkmate with bishop and knight}
Alternative attempt by black:
7. …Bh2
8. Bc8 f3 {black cannot postpone it another move}
9. Kd3 f2
10. Ke2 Bg3
11. Kf1 Bh4
12. Ba6 Bg3 {and we are back to the variation above at move 11. White wins.}
I saw that White can lock the Black king in the corner, but I haven’t found a way to pick off the f-pawn.
In the anonymous’s line above,
after
1. Ba6+ Kb8
2. Nc6+ Ka8
3. Kg2 Bh4
4. Kf3 Bg3
5. Ke4 Bh2
6. Kd4
what about
6. … Bg1+
now White doesn’t have enough time to move the K to a6,
e.g.
7. Kc4 Bb6
8. Kb5 f3
9. Bc8 f2
10. Ka6 f1Q
if
7. Ke4 Bh2 and White made no progress
To void being checked, white could
try
6. Kd3 g3 and Black just shuffles his Bishop along the g1-a7 diagonal since White can’t approach the pawn.
There must be some other trick to picking off the f-pawn.
To anonymous:
In your second variation, what do you do
if black plays 9. Bf4 (instead of f2) and keeps its bishop on the diagonal c1-h6?
I think this is the correct solution,
1. Ba6+ Kb8
2. Nc6+ Ka8
3. Kf2 Bh4+
4. Kf3 Bg3
5. Ke4 Bh2
6. Kd4! Bg3
7. Ke5! f3+
8. Kf5! f2
9. Kg4 f1Q
10. Bxf1
Now the black bishop is under attack.
If black moves it the white bishop
goes back to a6…
10 …. Kb7
11. Na5+ Kb6
12. Nc4+
and the next move white takes the bishop.
Oops… I checked with a computer (yeah I know) and it seems my solution as it stands is defeated by 9 … Bd6.
Really a devilish problem!
Michel, what do you play after 6. Bg1+? The bishop gets on the c1-e3 diagonal, and I no longer see a win.
In my view, the key to this position is based on the following: if the wK goes to f5 at the time when the bB is on g3 and the wB is on a6, then f3 loses to the fork Kg4.
The problem is that with the direct approach the bishop is on h2, instead of g3, when the wK can go to f5, so we need a way to transfer the move to black, without allowing the bishop to switch to the c1-e3 diagonal, where zugzwang themes are no longer possible. With this in mind, my solution is:
1. Ba6+ Kb8
2. Nc6+ Ka8
3. Kg2 Bh4
(2. … Bh6 3. Kf3 Bg5 4. Kg4 Bh6 5. Bc8 is zugzwang)
4. Kf3 Bg3
5. Bc8 Bh2
6. Kf2! Bg3+
7. Ke2! Bh2 (the desired triangulation)
(Be1 is not possible, and 7 … Bh4 8. Kf3 Bg3 leads to the same position as in the main variation)
8. Kf3 Bg3
9. Ba6 Bh2
10. Kg4 Bg3
11. Kf5 B moves
(11. … f3 12. Kg4 wins the f pawn due to the fork on the pawn and the bishop, while the wB controls f1)
12. Ke6 f3
13. Kd7 f2
14. Kc8 f1Q
15 Bb7 mate
(to Christian Vogler)
I think your solution is correct!. There are variations possible on the triangulation but the key idea is to do Kf5 when black has a pawn on f4 and a bishop on g3. Black has no good options then.
Very mice problem.
Interesting: what is the source of this one?
Study by J. Gunst 1949 ,in the initial position the white bishop must be on c4 and the white king on h1 but the solution is the same.
Chris Vogler:
nice solution, I didnt see it!
axel
Would somebody explain how the following wins:
1. Ba6+ Kd8
2. Nf7+ Kd7
3. what?
3. Nxg5 c8=Q
4. BxQ KxB and white has no material to mate
3. Ne5 Kd8 and we’re back where we started.
if, instead
3. Bb5+ Ke7
the Bishop is still verboten, the pawn threatens to queen, and the Knight is hanging, how to save everything?
If there is a win, please show me:
1. Ba6+ Kd8
2. Nf7+ Kd7
3. what?
Thanks all for the Kb8 analysis, without an analysis board, I could only see the black king trapped, but nothing further. Beautiful solution to 1. … Kb8.
Kerry,
Your 3… c8=Q is illegal. Black’s pawn can’t move backwards, much less promote. =)
Jolly,
That’s just unfair. I hate this game.
heh. Thanks for clearing that up….doh.
Christian,
and what if black in
11…f3
12.Kg4 f2!
13.Kxg3 f1=Q
14.Bxf1 Kb7!! (runs away and… long chasing ahead with problematic black pawn…)
ramark: After 14. … Kb7 15. Ne5 followed by 16. Nc4 and the c pawn is safely blockaded, so the white king can approach. As long as you know how to mate with bishop and knight, winning the resulting position is easy.