A chess problem is a puzzle set by a composer using chess pieces on a chess board, presenting the solver with a particular task to be achieved. For instance, a position might be given with the instruction that white is to move first, and checkmate black in two moves against any possible defence. There is a good deal of specialised jargon used in chess problems; see chess problem terminology for a list.
Exactly what constitutes a chess problem, is, to a degree, open to debate. However, the kinds of things published in the problem section of chess magazines, in specialist chess problem magazines, and in collections of chess problems in book form, tend to have certain common characteristics:
The position is composed - that is, it has not been taken from an actual game, but has been invented for the specific purpose of providing a problem.
There is a specific aim, for example, to checkmate black within a specified number of moves. This distinguishes problems from positions taken from games or game-like positions where the task is simply to find the best move.
There is a theme and the problem is aesthetically pleasing. A problem's theme is an underlying idea, giving coherence and beauty to its solution. It is this aesthetic element, as much as the challenge of actually solving the problem, which makes chess problems attractive to many people.
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There are various different types of chess problem:
Directmates - white to move first and checkmate black within a specified number of moves against any defence. These are often referred to as "mate in n", where n is the number of moves within which mate must be delivered. In composing and solving competitions, directmates are further broken down into three classes:
Two-movers - white to move and checkmate black in two moves against any defence
Three-movers - white to move and checkmate black in no more than three moves against any defence
More-movers - white to move and checkmate black in a given number of moves more than three against any defence
Helpmates - black to move first cooperates with white to get his own king mated via legal moves
Selfmates - white moves first and forces black to checkmate white's king against black's will
Reflexmates - a selfmate in which each player must give mate if they are able to do so on their turn. When this stipulation applies only to black, it is a semi-reflexmate.
Series-movers - one side makes a series of moves without reply to achieve a stipulated aim. Check may not be given except on the last move. A series-mover can be a:
Series-mate - a directmate with white playing a series of moves without reply to checkmate black
Series-helpmate - a helpmate in which black plays a series of moves without reply, and then white plays one move to checkmate black
Series-selfmate - a selfmate in which white plays a series of moves leading to a position in which black is forced to give mate
Series-reflexmate - a reflexmate in which white plays a series of moves leading to a position in which black can, and therefore must, give mate
All the above may also be found in forms of fairy chess - chess played with unorthodox rules, possibly using fairy pieces (unorthodox pieces).
In addition, there is the study, in which the stipulation is that white to play must win or draw. Almost all studies are endgame positions. Because the study is composed it is related to the problem, but because the stipulation is open-ended (the win or draw does not have to be achieved within any particular number of moves) it is usually thought of as separate from the problem. However, particularly long more-movers sometimes have the character of a study - there is no clear dividing line between the two.
In all the above types of problem, castling is assumed to be allowed unless it can be proved by retrograde analysis (see below) that the rook in question or king must have previously moved. En passant captures, on the other hand, are assumed not to be allowed, unless it can be proved that the pawn in question must have moved two squares on the previous move.
There are several other types of chess problem which do not follow the usual chess pattern of two sides playing moves towards checkmate. Some of these, like the knight's tour are essentially one-offs, but other types have been revisited many times, with magazines, books and prizes being dedicated to them:
Retrograde analysis - this is the act of working out from a given position, what previous move or moves have been played. A problem employing retrograde analysis may, for example, present a position and carry the stipulation "Find white's last move" or "Has the bishop on c1 moved?". Problems such as these in which retrograde analysis is the main point are commonly called retros. Retrograde analysis may also have to be employed in more conventional problems (directmates and so on) to determine, for example, whether an en passant pawn capture or castling is possible. The most important sub-set of retro problems are:
Shortest proof games - the solver must construct a game, starting from the normal initial position in chess, which ends with the position in a given diagram. The two sides cooperate to reach the position, but all moves must be legal. Usually the number of moves required to reach the position is given, though sometimes the task is simply to reach the given position in the shortest possible number of moves.
Construction task - no diagram is given in construction tasks; instead the aim is to construct a game or position with certain features. For example, Sam Loyd devised the problem: "Construct a game which ends with black delivering discovered checkmate on move four" (published in Le Sphinx, 1866; the solution is 1.f3 e5 2.Kf2 h5 3.Kg3 h4+ 4.Kg4 d5#). Some construction tasks ask for a maximum or minimum number of something to be arranged, for example a game with the maximum possible number of consecutive discovered checks, or a position in which all sixteen pieces control the minimum number of squares.
There are no official standards by which to distinguish a beautiful problem from a poor one, and judgement varies from individual to individual as well as from generation to generation, but modern taste generally recognizes the following elements as being important if a problem is to be regarded as beautiful:
The problem position must be legal. That is to say, the diagram must be reachable via a legal chess game which begins from the standard opening position. It is not considered a defect if the diagram can only be reached via a game containing gross blunders. Chess problems, on the whole, are not created for the purpose of practical chess training.
The first move of the problem's solution (the key move or key) must be unique. A problem which has two keys is said to be cooked, and would not be published in any magazine. An exception is problems which intentionally have more than one solution, which compliment or contrast each other in some way - this type of problem is particularly common in helpmates.
Some would say that, ideally, there should only be one possible white move after every black move, although this is not nearly so important. A choice of white moves other than the first move is a dual. Duals are often excusable if the problem is strong in other regards.
The solution should be explicable in terms of a theme or themes, rather than emerging from disjointed calculation. Many of the more common themes have been given names by problemists (see chess problem terminology for a list).
The key move of the solution should be unobvious. Obvious moves such as checks, captures, and (in directmates) moves which restrict the movement of the black king, make for bad keys. Keys which deprive the black king of some squares it could move to (flight squares) but at the same time surrender an equal or greater number of flights are acceptable. Key moves which prevent the enemy from playing a checking move are also undesirable, particularly in cases where there is no mate provided after the checking move.
Every piece on the board should serve a purpose, either to enable the actual solution, or to exclude alternative solutions. Extra units should not be added to create "red herrings" (this is called dressing the board), except in rare cases where this is part of the theme. If the theme can be shown with fewer total units, it should be.
The problem should exhibit economy of moves. If the theme can be shown in fewer moves, it should be.
The following is a problem composed by T. Taverner in 1881. It is a directmate, with white to move and mate in 2:
The key move is Rh1. The key difficult to find, because it makes no threat -- instead, it put black in zugzwang, a situation where every move is worse than no move, but move he must! Each of black's nineteen legal replies allows an immediate mate. For example, if black defends with 1...Bxh7, the d5 square is no longer guarded, and white mates with 2.Nd5#. Or if black plays 1...Re5, he blocks that escape square for his king allowing 2.Qg4#. Yet if black could pass (i.e. make no move at all) white would have no way to mate on his second move.
The thematic approach to solving is then to notice that in the original position, black is already almost in zugzwang. If black were compelled to play first, only Re3 and Bg5 would not allow immediate mate. However, each of those two moves blocks a critical escape square for the black king (a flight square), and once white has removed his rook from h2 he can put some other piece on that square to deliver mate: 1...Re3 2. Bh2# and 1...Bg5 2.Qh2#.
The arrangement of the black rooks and bishops, with a pair of adjacent rook flanked by a pair of bishops, is known to problemists as Organ Pipes. This arrangement means the black pieces get in the way of each other: for example, consider what happens after the key if black plays 1...Bf7. White now mates with 2.Qf5#, a move which is only possible because the bishop black moved has got in the way of the rook's guard of f5 - this is known as a self-interference. Similarly, if black tries 1...Rf7, this interferes with the bishop's guard of d5, meaning white can mate with Nd5#. Mutual interferences like this, between two pieces on one square, are known as Grimshaw interferences. There are several Grimshaw interferences in this problem.
Andrei Frolkin and Gerd Wilts, Shortest Proof Games (1991) - a collection of 170 proof games (published in Germany, but in English)
Michael Lipton, R. C. O. Matthews and John Rice, Chess Problems: Introduction to an Art (Faber, 1963)
Jeremy Morse, Chess Problems: Tasks and Records (Faber and Faber, 1995, revised edition 2001) - concentrates on maximum tasks and records
John Nunn, Solving in Style (1985) - problems seen from the point of view of the solver
John Rice, Chess Wizardry: The New ABC of Chess Problems (Batsford, 1996) - a general overview of chess problems, including an extensive A-Z of themes and terms, and 460 problems. Widely regarded as the best single-volume work in English on the subject.