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A '''chess problem''', also called a '''chess composition''', is a [[Chess puzzle|puzzle]] created by the composer using [[chess piece]]s on a [[chessboard]], which presents the solver with a particular task. For instance, a position may be given with the instruction that White is to move first, and [[checkmate]] Black in two moves against any possible defence. A chess problem fundamentally differs from {{chessgloss|over-the-board}} play in that the latter involves a struggle between Black and White, whereas the former involves a competition between the composer and the solver. Most positions which occur in a chess problem are unrealistic in the sense that they are very unlikely to occur in over-the-board play.<ref name=oz>{{Cite web|url=http://www.ozproblems.com/home|title=OzProblems - Australian chess problem composition|website=www.ozproblems.com}}</ref> There is a
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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}} to be legal, unless it can be proved that the pawn to be captured must have moved two squares on the previous move.<ref name="Codex">{{
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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