The Behting study is sound
By John Nunn
Back in August, ChessBase published the famous Behting study, which is often used as a demonstration that computers can’t solve all positions.
K. K. Behting, Baltische Schachblätter 1908
White to play and draw
The intended solution is 1 Kc6! g1Q 2 Nxh4, followed by 3 Nhf3, with a positional draw as Black cannot make progress.
However, I suggested that there might be an alternative solution to this study, and this provoked several people to look at the position more closely. The proposed alternative ran 1 Ng7+ Kg5 2 Nf3+ Kg4 3 Nf5 h3 4 Ke4 g1Q 5 Nxh6+ Kh5 6 Nxg1 h2 7 Nf3 h1Q 8 Nf5 Kg4, reaching a key position.
It isn’t easy to see how Black can break down White’s fortress, but to definitely resolve the issue, endgame tablebase expert Marc Bourzutschky constructed the seven-man tablebase with Q+P vs 2N+P. This showed that Black can break down the defence, and while the winning line isn’t especially deep, there are some surprising features. One important point is that while the ending of Q vs 2N is generally drawn, if the knights are badly placed defending one another then the queen can often win – indeed the queen may still win even if the defender has an extra pawn.
There was then a discussion involving several endgame experts, such as Noam Elkies, Harold van der Heijden and John Beasley, before it was discovered that the key winning idea had already been given by Arapd Rusz in 2010. Finally, Peter Stephenson sent some detailed analysis giving the win in more depth. The analysis which follows is based on these contributions, but any mistakes are my responsibility.
From the diagram position, one side line runs 9 N5d4 Kg3 10 Ke3 (10 Ne2+ Kf2 11 Ned4 Kg2 and 10 Nf5+ Kf2 11 N5d4 Kg2 transpose to the main line below) 10...Qh6+ 11 Ke4 Qf4+ 12 Kd5 Qf7+ 13 Ke5 Qe7+ 14 Kf5 Qa7 15 Ke5 Qa8 and now White is in an unpleasant zugzwang. His king must move, allowing ...Kf4 followed by ...Ke4, and Black’s king penetrates.
The main line runs 9 Ne3+ Kg3 10 Nf5+ Kf2 11 N5d4 and this is where the key idea comes in.
11...Kg2!! This is the move I had missed when I first looked at the position. Black’s surprising triangulation, which in addition unpins the knight, leaves White without a good reply:
12 Nf5 Qb1+ 13 Kf4 Kf2 14 Ng5 Qb8+ 15 Kg4 Ke2 16 Ne4 Qf8 17 Kf4 Kd3 and Black’s king enters.
12 Kf4 Qh7 13 Ke3 (13 Nf5 Kf2 14 N5d4 Qd3 15 Ke5 transposes) 13...Qd3+ 14 Kf4 Kf2 15 Ke5 c3 16 dxc3 Ke3 wins, since Black’s king enters and the white knights are badly placed.
12 Ke3 Qb1! 13 Kf4 Qh7 14 Ke3 Qd3+ transposes to line 2.
12 Ne5 Kg3+ 13 Ndf3 Qb1+ 14 Ke3 Qf1 15 Kd4 Kf4 16 Kc3 Qb1 17 Kxc4 Ke4 is similar.
12 Kd5 Kg3 13 Kxc4 is perhaps the most surprising line. Black simply gives up his pawn in order to activate his pieces. Although White doesn’t appear too badly off, he cannot save the game and the tablebase shows that Black can now mate in 50 moves. The main line starts 13...Qf1+ 14 Kd5 Kf4 15 Ne5 Qg2+ 16 Ndf3 Qg8+ 17 Kd4 Qa8 18 Kc4 Ke4 and again we have the typical penetration by the king, while the knights are paralysed since they can only defend each other.
Thus Behting’s 1908 study has, after just over a century, been proved correct and ChessBase can continue to use it to humiliate computers until the day dawns when they can finally solve it.
GM Dr John Nunn is a director of Gambit Publications, one of the world’s leading chess publishers. Gambit was founded in 1997, and in the past 15 years has published over 170 chess books in English and more than 50 in German. Several of its titles have won awards in different countries, most recently the English Chess Federation Book of the Year Prize for Nunn’s Chess Endings Volume 1 and Volume 2. Nunn’s recently published Understanding Chess Middlegames is already a bestseller and has been reprinted after only two months on sale.
Gambit has exciting plans to bring its books to a wider audience by means of electronic publishing. There are already 15 Gambit titles available for the Kindle e-book reader, with more to follow in the coming months. Additionally, Gambit will be producing an app, initially for the iPad, which will enable readers to play over electronic versions of Gambit books on-screen.
John is also an avid amateur astronomer, as you can see from the latest images he sent us recently. He made them using a remote telescope of iTelescope.net.
This image, captured by John in a 70-minute exposure using the T21 telescope of iTelescope.net, is a rather difficult target, as all the galaxies are quite faint. The galaxies in this cluster are believed to be about 200 million light-years away, a figure based on the red shift of the galaxies involved. You can click on the image to get a larger version, and then endeavor to count the number of galaxies.
John has labelled the more prominent members in the above picture. "I don't recall having seen the odd double galaxy NGC750/751 before," he says, "and could only find very few good amateur pictures on the Internet. The best I could locate is here, an image using a lengthy exposure of some 20 hours. Is this two galaxies in the process of merging, or is it something else? Maybe some of our readers can help by finding more images or information?"
Addendum: Appeals for assistance on our news page are always answered, including the most obscure ones. Jeremy Treadwell of Bakersfield, CA, wrote: "The two galaxies are said to be connected by luminous filaments. You can find more info on them here (PDF file). These types of double-galaxies are actually common, though I understand the term is highly subjective. For something really cool, look up WILD's triple system.
To which John Nunn writes:
It is interesting to see a paper from 1956 (the year after I was born) and
the comparison between an image (left) taken with the Palomar
200-inch telescope, the largest in the world at the time, and one taken
with a modern 12.5 inch RCOS telescope, a high-end amateur instrument costing
just about $20,000.