Chess problem, by Wikipedia
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- This article uses algebraic notation to describe chess moves.
Hampstead and Highgate Express, 1905-06 (1st Prize)
A chess problem, also called a chess composition, is a puzzle set by somebody using chess pieces on a chess board, that presents 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 defense. A person who creates such problems is known as a composer. There is a good deal of specialized jargon used in connection with chess problems; see chess problem terminology for a list.
The term "chess problem" is not sharply defined: there is no clear demarcation between chess compositions on the one hand and puzzles or tactical exercises on the other. In practice, however, the distinction is very clear. There are common characteristics shared by compositions in the problem section of chess magazines, in specialist chess problem magazines, and in collections of chess problems in book form. Not every chess problem has every one of these features, but most have many:
- 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. Although a constraint on orthodox chess problems is that the original position be reachable via a series of legal moves from the starting position, most problem positions would not arise in over-the-board play.
- There is a specific stipulation, that is, a goal to be achieved; for example, to checkmate black within a specified number of moves.
- There is a theme (or combination of themes) that the problem has been composed to illustrate: chess problems typically instantiate particular ideas.
- The problem exhibits economy in its construction: no greater force is employed than that required to render the problem sound (that is, to guarantee that the problem's intended solution is indeed a solution and that it is the problem's only solution).
- The problem has aesthetic value. Problems are experienced not only as puzzles but as objects of beauty. This is closely related to the fact that problems are organized to exhibit clear ideas in as economical a manner as possible.
Problems can be contrasted with tactical puzzles often found in chess columns or magazines in which the task is to find the best move or sequence of moves (usually leading to mate or gain of material) from a given position. Such puzzles are often taken from actual games, or at least have positions which look as if they could have arisen during a game, and are used for instructional purposes. Most such puzzles fail to exhibit the above features.
 Types of problem
There are various different types of chess problems:
- 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 n moves against any defence, where n is some particular number greater than three.
- Helpmates: black to move first cooperates with white to get black's own king mated in a specified number of moves.
- Selfmates: white moves first and forces black (in a specified number of moves) to checkmate white.
- Reflexmates: a form of selfmate with the added stipulation that each side must give mate if it is able to do so. (When this stipulation applies only to black, it is a semi-reflexmate.)
- Seriesmovers: 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 seriesmover may take various forms:
- Seriesmate: a directmate with white playing a series of moves without reply to checkmate black.
- Serieshelpmate: a helpmate in which black plays a series of moves without reply after which white plays one move to checkmate black.
- Seriesselfmate: a selfmate in which white plays a series of moves leading to a position in which black is forced to give mate.
- Seriesreflexmate: a reflexmate in which white plays a series of moves leading to a position in which black can, and therefore must, give mate.
Except for the directmates, the above are also considered forms of fairy chess insofar as they involve unorthodox rules.
- Studies: an orthodox problem in which the stipulation is that white to play must win or draw. Almost all studies are endgame positions. Studies are composed chess problems, but because their stipulation is open-ended (the win or draw does not have to be achieved within any particular number of moves) they are usually thought of as distinct from problems and as a form of composition that is closer to the puzzles of interest to over-the-board players. Indeed, composed studies have often extended our knowledge of endgame theory. But again, there is no clear dividing line between the two kinds of positions.
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 legal, 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 fall into any of the above categories. Some of these are really coded mathematical problems, expressed using the geometry and pieces of the chessboard. A famous such problem is the knight's tour, in which one is to determine the path of a knight that visits each square of the board exactly once. Another is the eight queens problem, in which eight queens are to be placed on the board so that none is attacking any of the others.
Of far greater relation to standard chess problems, however, are the following, which have a rich history and have been revisited many times, with magazines, books and prizes dedicated to them:
- Retrograde analysis problems: such problems, often also called retros, typically present the solver with a diagram position and a question. In order to answer the question, the solver must work out the history of the position, that is, must work backwards from the given position to the previous move or moves that have been played. A problem employing retrograde analysis may, for example, present a position and ask questions like "What was white's last move?", "Has the bishop on c1 moved?", "Is the black knight promoted?", "Can White castle?", etc. (Some 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 subset of retro problems are:
- Shortest proof games: the solver is given a position and must construct a game, starting from the normal game array, which ends in that position. 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 smallest number of moves.
- Construction tasks: 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#); while all white moves are unique (see Beauty in chess problems below), the black ones aren't.
 Beauty in chess problems
The role of aesthetic evaluation in the appreciation of chess problems is very significant, and indeed most composers and solvers consider such compositions to be an art form. Vladimir Nabokov wrote about the "originality, invention, conciseness, harmony, complexity, and splendid insincerity" of creating chess problems and spent considerable time doing so. There are no official standards by which to distinguish a beautiful problem from a poor one, and such judgments can vary from individual to individual as well as from generation to generation. Such variation is to be expected when it comes to aesthetic appraisal. Nevertheless, modern taste generally recognizes the following elements to be important in the aesthetic evaluation of a problem:
- The problem position must be legal. That is to say, the diagram must be reachable by legal moves beginning with the initial game array. It is not considered a defect if the diagram can only be reached via a game containing what over-the-board players would consider gross blunders.
- 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 is judged to be unsound or defective. (Exceptions are problems which are composed to have more than one solution which are thematically related to one another in some way; this type of problem is particularly common in helpmates.)
- Ideally, in directmates, there should be a unique white move after each black move. A choice of white moves (other than the key) is a dual. Duals are often tolerated if the problem is strong in other regards and if the duals occur in lines of play that are subsidiary to the main theme.
- The solution should illustrate 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 not be obvious. 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 to which it could initially move (flight squares), but at the same time make available an equal or greater number of flight squares 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. In general, the weaker (in terms of ordinary over-the-board play) the key move is the less obvious it will be, and hence the more highly prized it will be.
- There should be no promoted pawns in the initial position. For example, if White has three knights, one of them must clearly have been promoted; the same is true of two light-square bishops. There are more subtle cases: if f1 is empty, a white bishop stands on b5 and there are white pawns on e2 and g2, then the bishop must be a promoted pawn (there is no way the original bishop could have got past those unmoved pawns). A piece such as this, which does not leave a player with pieces additional to those at the start of a game, but which nonetheless must have been promoted, is called obtrusive. The presence of obtrusive units constitutes a smaller flaw than the presence of more obviously promoted units. See, for example, the diagram at right.
- The problem should be economical. There are several facets to this desideratum. For one thing, 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. For another, the problem should not employ more moves than is needed to exhibit the particular theme(s) at its heart; if the theme can be shown in fewer moves, it should be.
 Example problem
Dubuque Chess Journal, 1889 (1st Prize)