Chess problem: Difference between revisions

Revision as of 12:38, 12 January 2023

Revision as of 21:45, 18 March 2023

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Not every chess problem has every one of these features, but most have several:

* The position is <em>''composed</em>'' – 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 <em>''stipulation</em>'', that is, a goal to be achieved; for example, to checkmate Black within a specified number of moves.

* There is a <em>''theme</em>'' (or combination of themes) that the problem has been composed to illustrate: chess problems typically instantiate particular ideas.

* The problem exhibits <em>''economy</em>'' 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 <em>''aesthetic value</em>''. Problems are experienced not only as puzzles but as objects of beauty. This is closely related to the fact that problems are organised to exhibit clear ideas in as economical a manner as possible.

==Tactical puzzles==

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* 1...Rxa4 2.Rc5#

* 1...Rc5 2.Rxc5#

(When a black knight can move to the maximum number of eight squares like this, it is known as a <em>''knight wheel</em>''.)}}

}}

{{Chess diagram

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*'''[[Selfmate]]s''': White moves first and forces Black (in a specified number of moves) to checkmate White.

*'''[[Helpselfmate]]s''': White to move first cooperates with Black to get a position of selfmate in one move.

*'''[[Reflexmate]]s''': a form of selfmate with the added stipulation that each side <em>''must</em>'' give mate if it is able to do so. When this stipulation applies only to Black, it is a <em>''semi-reflexmate</em>''.

*'''[[Seriesmover]]s''': 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.

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*'''[[Endgame study|Studies]]''': an orthodox problem in which the stipulation is that White to play must win or draw. Almost all studies are [[Chess endgame|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 <em>''not</em>'' to be legal, unless it can be proved that the pawn to be captured 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 chess problem|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 puzzle|eight queens]] problem, in which eight queens are to be placed on the board so that none is attacking any of the others.

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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|Retrograde analysis problems]]''': such problems, often also called <em>''retros</em>'', 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.<ref>{{cite book |author=Smullyan, R. |year=1994 |title=Chess Mysteries of Sherlock Holmes: Fifty tantalizing problems of chess detection |publisher=Random House |series=Puzzles & Games |ISBN=978-0-8129-2389-6}}</ref> 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 actually a promoted pawn?", "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:

**'''[[Proof game|Shortest proof game]]s''': 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 <em>''Beauty in chess problems</em>'' below), the Black ones are not. A unique problem is: "Construct a game with black b-pawn checkmating on move four" (from <em>''Shortest construction tasks map</em>'' in <em>''External links</em>'' section; the unique solution is 1.d4 c6 2.Kd2 Qa5+ 3.Kd3 Qa3+ 4.Kc4 b5#). Some construction tasks ask for a maximum or minimum number of effects 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. A special class are games uniquely determined by their last move like "3...Rxe5+" or "4...b5#" from above.

Across most of the above genres, there is great interest in exploring [[fairy chess]], in which non-standard boards, pieces or rules apply.

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*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 <em>''key move</em>'' or <em>''key</em>'') must be unique. A problem which has two keys is said to be <em>''cooked</em>'' and is judged to be <em>''unsound</em>'' 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 <em>''each</em>'' Black move. A choice of White moves (other than the key) is a <em>''dual</em>''. 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 (<em>''flight squares</em>''), 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 [[promotion (chess)|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 {{chessgloss|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 gotten 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 <em>''obtrusive</em>''. The presence of obtrusive units constitutes a smaller flaw than the presence of more obviously promoted units.

*The problem should be economical.<ref>Iqbal, A. (2008). Evaluation of Economy in a Zero-sum Perfect Information Game, The Computer Journal, Oxford University Press, Vol. 51, No. 4, pp. 408–418, {{doi|10.1093/comjnl/bxm060}}. Online ISSN 1460-2067, Print ISSN 0010-4620. http://comjnl.oxfordjournals.org/content/51/4/408.abstract {{Webarchive|url=https://web.archive.org/web/20160608122007/http://comjnl.oxfordjournals.org/content/51/4/408.abstract |date=2016-06-08 }}</ref> 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 <em>''dressing the board</em>''), 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==

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The thematic approach to solving is to notice then 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 flight square for the black king, and once White has removed his rook from h2 White 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 rooks flanked by a pair of bishops, is known to problemists as [[Pipe organ|Organ Pipe]]s. This arrangement is designed to illustrate the effect of mutual Black interferences: 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 <em>''self-interference</em>''. Similarly, if Black tries 1...Rf7, this interferes with the bishop's guard of d5, allowing White to mate with Nd5#. Mutual interferences like this, between two pieces on one square, are known as [[Grimshaw (chess)|Grimshaw]] interferences, and are the theme of this problem. The problem exhibits four such interferences, on squares e6, e7, f6, and f7.

{{Chess diagram

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Although most problems call for straightforward (though possibly difficult) solution, occasionally a problem will involve a humorous trick or twist. The problem at right, shown in Norwegian broadcaster [[NRK]]'s airings from the World Championships in Dubai 2021, calls for White to move and give immediate checkmate in just a single move. The trick is to recognize that despite the arrangement of the Black men, the board is actually viewed from the White side (as shown by the Black king standing on a square of its own color, rather than on the opposite color as in the standard opening position). Thus the solution is 1 Nd3#; the Black pawns are moving <em>''down</em>'' the board and cannot capture the White knight.

==Abbreviations==

For reasons of space and internationality, various abbreviations are often used in chess problem journals to indicate a problem's stipulation (whether it is a mate in two, helpmate in four, or whatever). The most common are:

* <nowiki>"#"</nowiki> abbreviates <em>''checkmate</em>''

* "=" abbreviates <em>''stalemate</em>'' (occasionally "<em>''p</em>''", standing for "<em>''pat</em>''", the French for stalemate, is used instead)

* "h" abbreviates <em>''helpmate</em>''

* "s" abbreviates <em>''selfmate</em>''

* "r" abbreviates <em>''reflexmate</em>''

* "ser-" abbreviates <em>''series</em>''

These are combined with a number to indicate in how many moves the goal must be achieved. "#3", therefore, indicates a mate in three, while "ser-h=14" indicates a series help stalemate in 14 (i.e., Black makes 14 moves in a row such that White can subsequently make one move to deliver stalemate).

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==Tournaments==

Various tournaments (or <em>''tourneys</em>'') exist for both the composition and solving of chess problems.

===Composition tournaments===

Composition tourneys may be <em>''formal</em>'' or <em>''informal</em>''. In formal tourneys, the competing problems are not published before they are judged, while in informal tourneys they are. Informal tourneys are often run by problem magazines and other publications with a regular problem section; it is common for every problem to have been published in a particular magazine within a particular year to be eligible for an informal award. Formal tourneys are often held to commemorate a particular event or person. The [[World Chess Composing Tournament]] (WCCT) is a formal tourney for national teams organised by the [[Permanent Commission of the FIDE for Chess Compositions]] (PCCC).

In both formal and informal tourneys, entries will normally be limited to a particular genre of problem (for example, mate in twos, moremovers, helpmates) and may or may not have additional restrictions (for example, problems in [[patrol chess]], problems showing the [[Lacny]] theme, problems using fewer than nine units). Honours are usually awarded in three grades: these are, in descending order of merit, prizes, honourable mentions, and commendations. As many problems as the judge sees fit may be placed in each grade, and the problems within each grade may or may not be ranked (so an award may include a 1st Honourable Mention, a 2nd Honourable Mention, and a 3rd Honourable Mention, or just three unranked Honourable Mentions).

After an award is published, there is a period (typically around three months) in which individuals may claim honoured problems are <em>''anticipated</em>'' (that is, that an identical problem, or nearly so, had been published at an earlier date) or unsound (i.e., that a problem has cooks or no solution). If such claims are upheld, the award may be adjusted accordingly. At the end of this period, the award becomes final. It is normal to indicate any honour a problem has received when it is republished.

===Solving tournaments===