Solutions to chess problems and astronomical dilemmas

31st World Chess Problem Solving Championship

The World Chess Problem Solving Championship took place from October 16th-17th 2007 in Rhodes, Greece. This was one of the strongest solving championships ever held, and was won by Dr John Nunn and by the team of Great Britain. Nunn’s score was unusually high and his winning margin was also exceptional. This is the second time he has been world champion, the previous occasion being in 2004. In 2005 and 2006 he finished third.

The world championship consists of six timed papers, each consisting of three problems or studies. The six papers cover two-movers, three-movers, studies, helpmates, moremovers (mates in more than three moves) and selfmates. Five points are awarded for each position, according to how complete the solver’s solution is, so 15 points is the maximum score for each of the six rounds.

In our previous report we brought you a sample of the chess problems that were used in the competition. Here, today, are the solutions, annotated by John Nunn.

Solutions to the chess problems

All Black's available moves are already provided with a white mate, for example if the b5-knight moves, then Nd4#, or if the d6-knight moves, then Qe4#. Thus if White had a pure waiting move, then the problem would be solved. However, there is no pure waiting move, for example 1 Bb3 would give Black the extra possibility of 1...a2. The solution is 1.Qd1 Black is again in zugzwang, but some of the mates are different. If the d6-knight moves, then instead of Qe4# we have Qxd7#. Likewise, 1...g3 is met by 2 Qh5# (rather than 2 Qxh3#) and 1...Bg2 by 2 Qxg4# (rather than 2 Qh5#).

[Click to replay]
Note that in the replay window you can click on the notation to follow the analysis.

Here is a more complex problem. In a solving event, to get full marks you have to not only give the key move, but also all the variations leading to mate. When there are several variations, it is easy to miss one and thereby drop a point or half-point. 1.Qa3 The threat is 2 Qxc5+ Be5 3 Qxe5+. 1...Bd6 [1...Be5 2.Rg5+ Kf6 3.dxe5#; 1...Be4 2.Bg4+ Rxg4 3.hxg4#; 1...Re4 2.Rg5+ Kf6 3.R8g6#; 1...Rxd4 2.Qe3 threat Qg5# 2...Bf4 (2...Rf4 3.Qxc5#) 3.Bg4#; 1...cxd4 2.Qxe7 and Black cannot meet the many threats of mate in one] 2.Qc1 threat 3 Qg5# 2...Bf4 [2...Rg4 3.hxg4; 2...Rf4 3.Ng3#; 2...Rh5 3.Qxb1#] 3.Qxb1# My first idea was indeed to play 1 Qa3, but for a long time I couldn't see how to mate after 1...Re4. I then tried some other first moves, and after wasting some time I suddenly realised that this blocked off the bishop on b1 to allow a mate on g6 after 2 Rg5+ Kf6 3 R8g6#. [Click to replay]

In this problem, the key move is far from obvious. Black will play ...hxg1 and will have a choice of four promotion pieces; note especially the choice of a rook, by which Black attempts to stalemate himself. The key idea is to focus on the most awkward promotion and see if that helps to determine the key move. To start with I looked at the rook promotion, but it turned out that there were several ways to cope with this. Then I looked at the knight promotion, and realised that the threats of ...Nxe2 and ...Nxh3, freeing the g1-square, meant that this was the promotion which White must take most care about. The possibility of 1...hxg1N, 2...N somewhere and 3...Kg1 suggested that the final mate would be by Nf3#, and this led to me to suppose that the key was 1.d5 to free d4 for a knight. This key is surprising as if Black promotes to a queen or bishop, then there will be a check after a capture on f2. Then the variations could be worked out one by one, although there were still some tricky moves to find, such as 1...hxg1R 2 Qb1!, lifting the stalemate. 1...hxg1Q [1...hxg1R 2.Qb1 Kxe2 3.Nd4+ Kd2 (3...Kf1 4.Qd3#) 4.Qc2#; 1...hxg1B 2.Nbc3 Bgxf2+ (2...Bh2 3.Nb1 or (3.Ne4) ) 3.Qd4 Bxc3 4.Qxf2#; 1...hxg1N 2.Ned4 Nxh3 or any other move 3.Qe2+ Kg1 4.Nf3#] 2.Nbd4 Qh2 [2...Qxf2 3.e7] 3.Nb3 and 4 Nd2#. The large number of complex variations caused several solvers to drop points on this problem. [Click to replay]

Although there is only a single line of play, and Black's moves are almost all forced, this problem defeated a number of solvers, including former champion Jonathan Mestel. Black is in stalemate, so White's first move must allow the black king to move. Then, to prevent Black's pieces coming out, White must immediately force the king back to c5. The question is how White can make progress while keeping Black bottled up. I realised that the g5-pawn is the key feature of the problem. Why is it on the board? The answer must be that White starts with 1 Rh8 and 2 Rh4+, the g5-pawn being present to prevent the alternative 1 Rg8 and 2 Rg4+ (problems must have a unique solution). This logic allowed me to ignore possibilities such as 1 Bd5 and 1 Nd6, which don't work and on which I could have wasted a lot of time. 1.Rh8 Kd4 2.Rh4+ Kc5 With two moves determined, it is now much easier although some imagination is still necessary to see the conclusion. 3.Rh6 Kd4 4.Rd6+ Kc5 The transfer of the rook from d8 to d6 means that the bishop is no longer required to defend c6, and so White can sacrifice it. 5.Be2! dxe2 6.d4#. [Click to replay]

In this problem White must force Black to deliver mate in 5 moves (White starts). Long selfmates can be very difficult to solve but a good start is to spot a possible final mating position. Here Black has only three legal moves, and after 1...Bxb7 I saw the plausible line 2 something exf3 3 Qd3+ Rc3 4 something Rxd3 5 Bd5+ Rxd5#. The obvious problem here is that there are three unknown White moves, which have to be used up somehow. Then the idea occurred to me of moving the b8-rook on the first move. After 1 Rb8-somewhere Bxb7 2 Rb8 exf3 3 waiting move Qd3+ it all works as planned, and the surprising fact that there is only one waiting move, namely 3 Ng7, led me to believe that this idea was correct. It only remained to work out where the b8-rook should move to, and this was determined by the line 1...Bb5 2 b8Q exf3 3 Qxc4+ Kxc4 4 Nd2+ which works after 4...Kc5 5 Qb6+ cxb6#, provided only that the black king cannot move to d3. This shows that 1 Rd8! was the key, and it only remained to tidy up the loose ends to provide the full solution: 1.Rd8 exf3 [1...Bb5 2.b8Q exf3 transposes to the main line; 1...Bxb7 2.Rb8 exf3 3.Qd3+ Rc3 4.Ng7 Rxd3 5.Bd5+ Rxd5#] 2.b8Q+ Bb5 [2...Bb7 3.Qd3+ Rc3 4.Rc8 Rxd3 5.Bd5+ Rxd5#] 3.Qxc4+ Kxc4 4.Nd2+ Kc5 5.Qb6+ cxb6#. [Click to replay]

The Grandmaster and Astronomy

At 52 John Nunn, once a world-class player, has retired from competitive chess. But he has been far from idle. Apart from his work as director of Gambit Publications and his successes in problem-solving, he has also taken up an interest in astronomy. He writes:

My current interest in astronomy dates back a long time. When I was about six years old, my brother had a small telescope (2.5 inch refractor) and I was able to use it from time to time. Unfortunately, such a small telescope did not afford particularly interesting views, especially as I was living in London. At the time the air in London was very polluted and this, coupled with the myriad lights shining into the sky (creating what is called light pollution) made any real observational astronomy difficult.

In fact I didn’t use the telescope much; what I enjoyed most was taking advantage of any visits to the countryside by lying on my back and just looking up at the stars. I could enjoy the heavens like this for hours, or at least until I was told that it was too cold and I should come in now. Despite the problems with the practical side of astronomy, I found the subject interesting and read a great deal about it. Round about this time, planetary science was being transformed by space probes travelling to Mars and Venus, and the new discoveries further excited my youthful enthusiasm.

Despite this early start, I didn’t progress much further with the subject. I was spending an increasing amount of time playing chess and studying mathematics, so the astronomy got dropped when I was about 11. During the next 35 years I did not own a telescope, but I still followed astronomical news and took an interest in the exploration of the solar system by robotic probes as they visited every planet from Mercury to Neptune.

During this period astronomy progressed at an amazing pace and the present time is really a kind of golden age for the subject. Technology has advanced enormously, with both ground-based telescopes and space observatories providing views of distant objects which were quite unimaginable in the 1960s. The robotic exploration of the solar system hasn’t advanced at the same pace, but there have been spectacular successes such as the Mars rovers Spirit and Opportunity, the Cassini mission to Saturn and the incomparable Voyager probes, launched in 1977 and still in contact with Earth from a distance of over 15.7 billion kilometres (Voyager 1) and 12.6 billion kilometres (Voyager 2). These 35 years have seen many important questions answered; for example, the age of the universe has been pinned down to 13.7 billion years (plus or minus 0.2 billion years) and over 200 planets have been discovered orbiting other stars. But there are still huge mysteries in many areas, especially those relating to dark matter and dark energy. And the big question about whether extra-terrestrial life exists remains unanswered.

When I decided to more or less retire from over-the-board play in 2003, a decision which became permanent in 2006, I looked around for other interests. While Gambit Publications was taking up quite a lot of my time, there was still some left over for other things. I decided to return to chess problem solving, which led to my winning the world championship in 2004 and 2007, and I also returned to astronomy.

When I was looking for a telescope, I was astonished at the advances made in amateur astronomy. I recall that to find even one interesting celestial object was quite a struggle back in the 1960s; it involved moving from star to star, while trying to look at a star map in the dark, eventually finding a barely visible fuzzy patch which might or might not have been M31, the Andromeda galaxy. Now you could get relatively inexpensive telescopes with a keypad where you just typed in the object you wanted and the motors would drive the telescope round to point at it.

I started off with a Meade ETX 125, a 5-inch Maksutov-Cassegrain telescope, which afforded views incomparably better than any I experienced as a youth. However, I quickly realised that North Surrey is not an ideal spot for astronomy. While atmospheric pollution is certainly less than in the 1950s and 1960s, light pollution is much worse, which restricts the type of object you can see. Objects which have a low surface brightness blend in with the background light in the sky, so that galaxies such as M33 and M101 are barely visible. Despite this limitation, there were plenty of other things to look at, such as planets, double stars, globular clusters, open clusters and planetary nebulae. After two years with the ETX, I upgraded to a Meade LX200 10-inch Schmidt-Cassegrain telescope.

Practically every clear evening I take my telescope out to look at the sky. My favourite types of object are the planets, open star clusters and planetary nebulae. Recently I decided to try some astrophotography. This picture shows the set-up, with a CCD camera attached to the telescope and a computer to record the images.

Although there seems to be a considerable learning curve here, I have managed a couple of pictures which, as a beginner, I am satisfied with.

M57, the Ring Nebula

NGC 7662, the Blue Snowball Nebula

Both objects are so-called planetary nebulae. These have nothing to do with planets, but are shells of gas thrown off into space by very old stars. Both of these are over 1,000 light-years from Earth, although the distance isn’t known to any great accuracy.

However, you don’t need elaborate equipment to take astronomical photographs. Here’s the moon taken with an ordinary Panasonic Lumix FZ-18 digital camera on a tripod. The Japanese have taken better shots, but their camera equipment was closer to the object.

Recently astronomers have been fascinated by the unexpected outburst of comet 17P Holmes. This normally unexceptional comet is currently between the orbits of Mars and Jupiter and is moving away from the sun. On October 23rd it suddenly increased in brightness, becoming a million times brighter in less than 24 hours. The reason for this is still unknown, but the result is that the comet became one of the brightest comets of recent decades and is clearly visible to the naked eye.

Comet 17P Holmes taken on November 4, 2007 at 20:23:29h with the Lumix FZ-18 at 28mm focal length and automatic 15-second exposure at ISO 100. Once again others have used better equipment to capture clearer images.

How long it will remain so bright is unknown. I have been observing it every night that conditions have permitted. The rapid expansion of the cloud around the comet is extraordinary – the change from one night to the next is clearly noticeable. Although the cloud now appears slightly less dense, its increased size means that the total luminosity has remained roughly constant for the past several days.

As to what happened to the comet, the most likely explanation is that while it was near the sun, solar heating caused gas pressure to build up inside the comet; finally the crust ruptured, and a large cloud of debris was expelled. Alternative explanations are that the comet was struck by a meteoroid, or (the one liked best by conspiracy theorists and the editors of this newspage) that some nation has conducted a test of an ‘asteroid buster’ device.