How to solve chess problems

by Vlaicu Crisan
5/17/2021 – For many chess players, chess problems just look bizarre: the pieces on the board often seem to be randomly placed and the positions appear to to be utterly removed from anything that can happen in a practical game. However, solving chess problems can be fun - if you know how to approach them. Vlaicu Crisan has some advice.

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How to solve chess problems

During these days, it seems [online] solving chess compositions tournaments have become more popular. One possible explanation for this curious phenomenon is that there are still people enjoying the thrilling experience of solving chess problems. But what does it actually mean to solve a chess problem?

Apparently a chess problem is quite easy to define: an initial position, an aim – usually mate, a fixed number of moves for reaching the aim and a stipulation which governs the play. The most often encountered stipulation is named "direct", when White begins and achieves the aim against any Black move. However, in solving competitions you will also encounter two other stipulations. The first is called "help", when Black begins and collaborates with White in order to mate the black king. The second is called "self", when White begins and forces Black to mate the white king, while again Black opposes. In most cases, the solution of a chess problem is unique and, of course, well hidden.

Chess problems are generally created by the human mind and the artists who create such chess problems are called chess composers. Chess composers don’t like the term "puzzles" or "riddles" too much. They even prefer the term "chess composition" instead of chess problem when referring to their work. Did I mention before that chess composers are artists? OK, that explains why they also prefer using their own terminology which perhaps doesn’t immediately make sense for most chess player.

Still, solving a chess problem can be an enjoyable experience, for all chess players, whether beginner, intermediate or advanced. However, problems can’t be solved by thinking like the composers that first created them. Probably that’s why most of the books available on solving might not be very appealing for the average chess player, as they are often written by reputed chess composers. Such titles are: "Как решать шахматные задачи" (How to solve chess problems) by Aleksandr Pavlovich Gulyaev, published in 1936, "Решение шахматных задач" (Solving chess problems) by Evgenij Ivanovich Umnov, published in 1958 and "Как решать задачи и этюды" (How to solve problems and studies) by Yakov Georgievich Vladimirov, published in 1986. One of the best introduction of chess problems and studies to over-the-board players is "Solving in Style" by John Nunn, published in 1985.

How should an average chess player approach a composition in order to solve it? Some of them use a brute force approach, by trying all possible moves until they eventually reach the aim. This approach might be preferred by those who are good calculators. However, while this approach might work for shorter compositions, it will definitely be time-consuming for the longer ones. So, a "discovery project" approach would be better: ask yourself some good questions about the position and based on the answers gradually understand and deduce the solution based on logic.

This sounds a little bit complicated in theory, but in practice it is not. We shall give some examples in order to make the solving process of direct two movers easier to understand. When starting the analysis of the position, the first question is surprisingly "What is Black’s strongest move?" I can hear your protest: "Hey, wait a second: isn’t it White who is supposed to give mate and who makes the first move?! Then why should I waste my time looking for best Black move? That’s sheer nonsense!"

Let’s try again, this time by explaining how to look for Black’s strongest moves. Merely from Black’s perspective, the best moves are those that: a) run with the king from the original square; b) create one or more squares for the king to evade to and c) give check to the white king. Once you have properly identified these Black moves, you should look how White can immediately counter these moves by giving mate on the next move.

 

Let’s examine the position in diagram A. The preliminary investigation reveals that the black king can’t go anywhere: all the squares around the king are occupied by black pieces and h7 is controlled by the white king. Also no black piece can attack the white king. Black can create room for the king either on h5 by pushing the pawn or on g6 by moving the rook along the 6th rank. The first move can be immediately countered by White by capturing the pawn with the rook: 1...h4 2.Rxh4# However, White has nothing prepared against the second move, hence the next question: "How can we exploit the black rook move on the 6th rank in order to be able to mate on the next move?".

Now, let’s admit that there is no obvious answer to this question. So, it is better to ask an intermediate question first: "What weakness in Black’s position creates the rook move on the 6th rank?" Fortunately, this time the answer is easy: by moving away from g6, the black rook no longer defends black pawn on g5. Now we can ask the second intermediate question: "How can White exploit the weakness created by the black rook’s move?" Well, after an additional attack on g5, White would be able to capture the pawn g5 with the queen, delivering mate. In this way, step by step, we made some progress in understanding what White’s first move should do: attacking g5.

The only white piece which can attack g5 again is the white rook e4. There are two different ways to accomplish that: 1.Re5 or 1.Rg4. Which of these moves is correct? After 1.Re5 we no longer have a mate after 1...h4 as the rook left the fourth rank. After 1.Rg4 White can still mate after the advance of the Black h-pawn, but the black pawn can capture the white rook! Fortunately enough, after this capture White mates with 1...hxg4 2.Qh2# After carefully checking all these possibilities once again, we can safely conclude that 1.Rg4! is the only white move leading to the solution.

 

In our next problem, a close examination of the position doesn’t reveal any prominent strong move for Black. How should we proceed in this case – shall we try all possible White moves? No! We should examine what moves Black could possibly play, what weaknesses these moves would create and how can White exploit these weaknesses in order to mate at the next move.

Let’s look at them systematically. A random move with the black rook (1...Rb6~) doesn’t create any apparent weakness, and White is unable to deliver mate afterwards. After a random move with the black bishop (1...Ba4~) White has 2.Qa1#. A random move with the black knight (1...Nc5~) again doesn’t create any apparent weakness. After 1...d5 the black pawn on d6 no longer controls e5, and White can mate with the bishop: 2.Be5#. Finally, the move 1...b3 doesn’t create any apparent weakness.

In view of the many moves Black has, so we could try placing the queen on the 8th rank: 1.Qa8. The idea is simple: any move of the white knight will deliver a mate by discovery check. But after 1...Ne6 the black knight can interfere on f8 after White gives a check. So, what to do now?

We will find the right move when we ask how White actually mates after a random move of the black bishop. The black bishop blocks the access of the queen to a1 where the queen would mate. What if we could arrange something similar for the other black pieces? After a careful look we will soon find the right square: a5. So the first move is 1.Qa5!. After 1...Rb6~ White has 2.Qd8#. After 1...Ba4~ we have 2.Qa1#. After 1...Nc5~ White mates with 2.Qh5#, and after 1...b3 White mates with 2.Qc3#.

 

One crucial question that helps to solve chess compositions is to ask what the white pieces are doing. The white queen controls the square g2, the white rook f4 controls the squares f2 and h4, the white rook a4 controls the square f4, the white bishop c8 controls the square h3. But there are two white pieces for which the initial role can’t be figured out: the white bishop on b8 and the white knight on e5. Curiously enough, the black king on g3 stands on the same diagonal as these two white pieces. That means the black king would be exposed to a discovered check once the white rook f4 goes away.

But where should the white rook on f4 go to? As both f2 and h4 must be kept under control, the white rook must move along the f-file: to f6, f7 or f8.

After 1.Rf6, White threatens to mate with 2.Nf7 but the problem is that the white rook on f6 can be captured by the black pawn g7: 1...gxf6 after which White has no mate.

But what can Black do after 1.Rf7? After 1...Bg2 the black bishop blocked a potential escape square and White mates with 2.Nc6#. However, 2.Nf3 does not work because Black’s king can now escape to f2. After 1...Bh3 mates with 2.Nd7#. But not 2.Ng4+ because Black’s king will then escape to h4. After 1...h4 the black pawn blocked the third potential escape square, and White mates with 2.Nc4#. Again, 2.Ng4 is ruled out because it creates an escape square on h3. But after 1...Nf2 White has no mate because 2.Nf3 creates an escape square on g2.

So, White should play 1.Rf8! Now, everything works as above and after 1...Nf2 White has 2.Nf7#.

 

In example D, 1...Bxd2 by Black would create two escape squares for the black king: c1 and e1. And 1...Qxb3 would create an escape square for the black king on c2.

The key question in such cases is: "Assuming the white pieces have teleportation power, where do they mate after 1...Qxb3?" If you look closely, you will see that White has only one way to mate after 1…Qxb3 2.Qxc1#. And the white queen has only one square from which it can reach c1 and mate: a1.

So, to parry Black’s threat of 1…Qxb3 White only has 1.Qa1!. After 1...Bxd2 White has 2.Qxb1#. And after 1...Qxb3 White mates with 2.Qxc1#. End of story? Not yet. After 1...Qxa1+ has the surprising countercheck 2.c3#. And after 1...Qb2+ the black bishop is pinned by the white queen and White mates with 2.Bc3#. And after 1...Bb2+ the black queen is pinned by the white queen and White again has 2.c3#. All other moves by Black (1...Qa2, 1...Qxc2 or 1...Ba3) also lead to mate.

 

In our last example, Black has no strong move. Moreover, no matter what Black plays, White has a mate. When the rook on d8 moves along the eighth rank (1...R~8) White has 2.Qd7#. After 1...Rd6 White has 2.c6# and after 1...Bb7 White mates with 2.Qxb7#. 1...Bc6 blocks a potential escape square for the black king and White mates with 2.Qc4#. And after a random move of the black bishop on f6 (1...Bf6~) White has 2.Ne7#. After 1...Bxd4 mates with 2.c4#. Finally, after 1...g4 White finishes the game with 2.Nf4#.

But what should White do in such cases? If possible, he should play a move that doesn’t destroy any of these possible mates. Here, the only white piece not involved in the mating positions is the white king. So, let’s check where White’s king can go to!

After 1.Ka4 Black plays 1...Bc6 pinning the queen and preventing 2.Qc4#. After 1.Kb4 Rb8 the white queen is again pinned and White no longer has 2.Qd7#. But what about 1.Kb2? Well, when Black plays 1...Bxd4, pinning the white pawn on c3 and preventing 2.c4#. The only correct move is 1.Ka2!, after which all the variations given above still work.

All these five beautiful chess compositions featured in the first round of a solving event organized last year by the German Chess Youth Association in collaboration with the German Association for Chess Composition "Die Schwalbe", targeting the young chess players aged under 27 years. The event proved to be a real success, with many chess amateurs taking part. Consequently, these associations decided to repeat the experience this year and launched the second edition of the solving tournament. Please have a look at the announcement and then try to solve the compositions from the first round. You will surely enjoy the experience!

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Vlaicu Crisan was born 26 August 1973 in Cluj-Napoca, Romania. He is an International Master of Solving (since 2007) and an International Master of Chess Composition (since 2016). His favorite genre in chess composition is fairies - particularly helpselfmates, which constitute the stipulation of the Romanian Tzuica Tourneys he organizes together with Eric Huber during the Chess Composition congresses of FIDE. He is currently the fairy editor of the Japanese chess problem magazine "Problem Paradise" and occasionally contributes to the ChessComposers blog which is maintained and updated by Eric Huber.

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Frits Fritschy Frits Fritschy 5/20/2021 01:25
Yeah, that's a point I didn't consider. I know a bit about problem composition, but clearly not everything.
JoshuaVGreen JoshuaVGreen 5/20/2021 01:04
@Frits Fritschy:

In the Osipov problem, 1. ... Ka3 has the set mate 2. Qa1#. Thus, taking away that flight isn't a great accomplishment for White, and I think the problem has a fair "give-and-take" key.
(FWIW, I first composed an inferior version of that problem, and that received 2nd Commendation in a thematic tournament focused on corner-to-corner moves. Later I improved my rendering to [a horizontal reflection of] the Osipove problem, and it was only after that was published that the anticipation was noted.)

Among my own compositions I only see one (other?) such move:
Joshua Green
Commended -- "StrateGems" -- October-December 1999
White to play and stalemate Black in 6 moves
Frits Fritschy Frits Fritschy 5/19/2021 02:25
Nice one! However, a key taking away (okay, and giving one in return) two flight squares...? Hope you have done better.
JoshuaVGreen JoshuaVGreen 5/19/2021 12:45
@Frits Fritschy, my comments were with respect to the article. Your suggestion to consider Queen moves to corners is reasonable, and I'll offer another nice example (albeit one which unfortunately anticipated my own composition[s]).

G. Osipov, 3rd HM — Concours Shakhmatnogo Kliga "Trudov reserv"
1985-86

White to play and checkmate Black in 2 moves
JoshuaVGreen JoshuaVGreen 5/19/2021 12:32
@talmage, those steps are excellent when solving game positions and tactical exercises. In composed problems like these they tend to be less useful as composers aim for keys that are more surprising (to players, not necessarily to other problemists).
Frits Fritschy Frits Fritschy 5/19/2021 10:40
Talmage,
It's just the other way around: the answer is usually NOT one of those. Look at position D.
Frits Fritschy Frits Fritschy 5/19/2021 10:31
Joshua, I didn't even notice my point was already proven in problem D... By the way, I've also seen others noting the predilection of problemists for queen-to-corner moves in two-movers. Not so strange either: an important aspect of good problems is surprise value - and what is usually the worst square for a queen? But it has been used so many times that for some that doesn't work anymore - they should be tricked by, say, a white queen on a1 that can go to a8, h8 and h1, and only one of those moves is right (or none of them), as in adbennet's problem below.
A good strategy for solving problems is to try thinking like the problemist.
adbennet adbennet 5/19/2021 09:14
@FritsFritschy - You mean like this?



mate in 2
https://chessimprover.com/what-say-you-the-1-minute-challenge-44/
talmage talmage 5/19/2021 04:03
Step 1. Evaluate the position noting material differences, and any pins or pieces en prise. Step 2. Consider checks, takes, and attacking moves (in that order). The answer is usually one of those.
JoshuaVGreen JoshuaVGreen 5/19/2021 01:37
There's nothing wrong with identifying Black's "strongest moves," but in good problems moves of type (a) and (c) (and possibly [b]), if they exist, will tend to already have mates set for them. As a primary means of solving problems, such searching will likely only be sufficient against "block" positions in which most (if not all) of Black's moves already have set mates and White need only complete or maintain the block. Against threat problems -- which aren't represented in this collection -- this will only take you so far, and against mutates and block-threats one will be positively deceived.

The weakness of a Black move that allows a mate to work is known as its "error." In diagram A you correctly note an error of Rook moves -- they unguard g5 -- but you ignore the conceivably equally relevant error of unguarding g7. I don't consider it fair to so skip to the right answer without explaining how the wrong one was dismissed. I consider it similarly unfair in example D to ignore (say) 1. Qb2 -- a move which also parries 1. ... Qxb3 while attacking the bBc1 -- while jumping straight to 1. Qa1!.

Against diagram C I'd say it's clear that either the wBb8, wNe5, or wRf4 should make the key as otherwise the wBb8 won't be relevant, but I don't see how to directly go from there to assuming that the wRf4 must move.

In short, I think much of the particular logic shown here is strongly motivated by already knowing the solutions and/or assuming that Black will be in zugzwang after the keys.
Frits Fritschy Frits Fritschy 5/18/2021 10:59
Another advice that works fine: if the white queen can move to a corner, that will be the key in more than 50% of the twomovers, especially when it's a 'long' move.
JoshuaVGreen JoshuaVGreen 5/18/2021 02:04
"Solving in Style" is great. About the only complaint I have against it concerns a comment Nunn makes on page 126 in order to motivate the reflexmate genre:

"Readers may have noticed that selfmates often have ugly, congested positions. This is an inevitable consequence of the need to control the freedom of both kings. ..."

While that description may be true of many selfmates, it's certainly not true of the ones that he's presented up to that point (diagrams 160-165), nor does it clearly hold for the exercises.
JoshuaVGreen JoshuaVGreen 5/18/2021 01:25
@ChrisHolmes, in good problems Black's checks will already have mates set for them. In some of those White will have to replace those set mates with new ones.
JoshuaVGreen JoshuaVGreen 5/18/2021 01:23
I remember when ChessBase showed these problems last year but omitted the bNh1 from the Ellermann position.
ChrisHolmes ChrisHolmes 5/17/2021 11:43
I think you should emphasize a basic principle of 2-movers that I've taught my 7 year old grandson & he always uses.

First verify whether Black to move can give check. If so then White's first move must usually give check.

It's elementary, but for novice solvers it needs saying.
adbennet adbennet 5/17/2021 11:17
I love two-movers, but I use them as _training_. So my method is completely different from what is proposed here. Step 1 - look for the crazy move that might work. This is to train my intuition. So in the Martindale problem, the first move that popped into my head was 1.Rh4. Brief consideration of the drawbacks of this move led directly to the correct solution, but that was more a random feature of the problem rather than a general benefit of my method. Step 2 - Assuming step one was a wrong guess (which it usually was), list all the legal moves and work through them methodically. This is to train my candidate moves. And it actually is quite hard to work through all the candidates, because (a) in a problem there are so many of them, (b) the mind likes to jump around instead of sticking to the task at hand, and (c) even when told to look at everything, the mind likes to edit out certain moves for mysterious reasons of its own. An example is
; Mansfield; #2;
where despite numerous iterations through "all" (sic) white's moves, I consistently failed to consider any wK to e-file moves. And didn't even realize I had done that, multiple times! But eventually I figured it out.

I agree the brute force method is not so good for longer problems. But even for three-movers it can be used to train visualization. So, with a three-mover, you look at each legal move for white, *clearly* visualize the resulting position, and then see if a "mate-in-two" (but with black moving first) jumps out immediately. Surprisingly often it does. So much thought goes into the key move that I find the mate-in-two with black to move is actually easier than the (one-ply-shorter) mate-in-two with white to move. Anyway, the clear visualization is the point of the training, so even if the problem can't be solved this way it's still good to try.
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