A Nasty Problem: Solution Time!

Last week I published the following nasty problem:

V. Halberstadt, 1938

White to play and win

4N3/3nP3/1k6/8/1K6/8/8/8 w - - 0 1

I had found the problem looking through Karsten Muller & Frank Lamprecht's Fundamental Chess Endings, where they used this a five star (extremely difficult) exercise.

(Solution below the fold.)

 

The solution in the back identifies this as a study by V. Halberstadt, and that it shared the first & second prize in 1938 in Gros. 

The solution as given uses the Nunn Convention and runs as follows:

Did you use the method of exclusion? Otherwise the study was probably unsolvable as the winning line is far from obvious.

1.Ka3!! The only move to win. Other moves lead to a draw. [1.Nd6? Nf6! 2.Ne4 Nd5+= ; 1.Kc3? Kc5! 2.Nd6 Nf6! 3.Ne4+ Nxe4+!= ; 1.Kc4? Ne5+ 2.Kd5 Nc6= ; 1.Ka4? Nc5+ 2.Ka3 Ne4= ; 1.Kb3? Nc5+! 2.Kc4 Ne6! 3.Nd6 Nc7 4.Nb5 Nxb5= ]

1...Kc6

2.Ka2!! Kb6 [2...Kc5 3.Nd6! Nf6 4.Ne4+!+- ]

3.Nc7 Nf6 4.Nd5+!+- 1-0

What follows is a wordy explanation: if you got everything just from the variations, you can skip this part.

I found the first move of the solution by two separate methods. The second method I used is a proper method: I looked at all the possible first moves and calculated until I saw how they failed. 

Two of the Knight moves for White are obviously useless: 1 Nf6 gives the Knight away for nothing, and 1 Ng7 just puts the Knight too far from the action. 1 Nc6 fails as given above. Now the solution doesn't mention the clever attempt 1 Nc7 right away. This too fails to 1...Nf6 because 2 Nd5 allows Nxd5 with check. In other words, if the White King were on, say, h1, the solution would be easy!

Therefore we look at King moves with this newfound insight. It's easy to eliminate the four of the King's possible moves quickly: moves to the light squares allow Black to pick up a tempo with a Knight check, and the move to c3 means White can't move his Knight to e4 to dislodge the defender of e8 without giving up a critical check, as given in the solution. So by elimination, we get to 1 Ka3 as the necessary first move. 

And here I got stuck. I kept trying to make a Knight move work for White's second move after Black's move, and it just wouldn't work. The main trick in the solution above is to make Black move his King back to b6, thus 2 Ka2 follows 1...Kc6. White must make certain to not move his own King back onto a square the Black knight could reach, thus a2, fleeing the scene of the action. And after 2 Ka2 Black's King has run out of viable options besides b6: moving to a light square allows White's knight to move with check, queening the pawn the next move. 

So far so good. But what if Black tries a different square for his King on his first move? (The Black Knight can't move for obvious reasons.) Again, light squares besides c6 are out due to Knight checks. The c7 square is out because the White Knight covers it. 1...Kc5 fails to 2 Nd6 Nf6 3 Ne4+ and the pawn queens. If 1...Ka5, then 2 Nc7 Nf6 3 Kb3 leaves Black without a move that doesn't lose immediately: 3...Kb6 4 Nd5+.

This only leaves 1...Ka7. This is actually the move where I got stuck. I just couldn't visualize the positions clearly enough after this to work my way through to a solution. Run this position through Stockfish for a few minutes and it settles on 2 Kb3 as the best option. (No, I've never bothered to install table-bases on my computer.) And maybe it is, only someone with table-bases can tell me for sure. But that allows Knight checks and whatnot and gets difficult for me to visualize/calculate. Instead, after checking on my computer, I decided on the following line - it's certainly not the best, but I understand it: 2.Ka2 Kb8 3.Kb1 Ka7 4.Kc1 Kb8 5.Kd2 Ka7 6.Ke3 Kb8 7.Kd4 Ka7 8.Nd6 Nf6 9.Ke5 Nd7+ 10.Kf5. I just bring my King around the long way and take away the f6-square from the Black knight so it can't stop the pawn from queening. Unfortunately, I had to work this out with a board and then check it with Stockfish, so I get no credit for the solution. Bummer, dude!

And what was the first method I used to find the initial move? That was easy and required very little chess knowledge. No I did not look at the back of the book. Years ago I realized that the quick and dirty method for finding the first move in extremely difficult chess problems was to look for the move that appeared to be the least helpful move on the board that didn't lose, and choose that! It doesn't always work, but it does have a fairly high rate of success. In this case, we're looking at a King, Knight and pawn endgame. Famously, these ending have been described (by Botvinnik, I believe) as nothing more than pawn endings. In pawn endings one typically wants to move the King closer to the action, and closer to the Queening square in particular. In this case, that means finding the move that moves the King farthest away from that goal: thus, 1 Ka3. Simplicity itself....