Chess Problem - Types of Problem

Types of Problem

Solution: 1.Rcc7! (threatening 2.Nc3):
1...Nxb3 2. Qd3#
1...Nb5 2.Rc5#
1...Nc6 2.Rcd7#
1...Ne6 2.Red7#
1...Nf5 2.Re5#
1...Nf3 2.Qe4#
1...Ne2 2.Qxh5#
1...Nc2 2.b4#
1...Rxa4 2.Rc5#
1...Rc5 2.Rxc5#
When a black knight moves to the maximum number of eight squares like this, it is known as a knight wheel.

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. A unique problem is: "Construct a game with black b-pawn checkmating on move four" (from Shortest construction tasks map in External links 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 (from Moves that determine all the previous moves in External links section).