A chess puzzle is a

puzzle A puzzle is a game, problem, or toy that tests a person's ingenuity or knowledge. In a puzzle, the solver is expected to put pieces together ( or take them apart) in a logical way, in order to find the solution of the puzzle. There are differe ...

in which knowledge of the pieces and rules of chess is used to logically solve a chess-related problem. The history of chess puzzles reaches back to the

Middle Ages In the history of Europe, the Middle Ages or medieval period lasted approximately from the 5th to the late 15th centuries, similarly to the post-classical period of global history. It began with the fall of the Western Roman Empire and ...

and has since evolved. Usually the goal is to find the single best, ideally aesthetic move or a series of single best moves in a chess position, that was created by a

composer A composer is a person who writes music. The term is especially used to indicate composers of Western classical music, or those who are composers by occupation. Many composers are, or were, also skilled performers of music. Etymology and def ...

or is from a real game. But puzzles can also set different objectives. Examples include deducing the last move played, the location of a missing piece, or whether a player has lost the right to

castle A castle is a type of fortification, fortified structure built during the Middle Ages predominantly by the nobility or royalty and by Military order (monastic society), military orders. Scholars usually consider a ''castle'' to be the private ...

. Sometimes the objective is antithetical to normal chess, such as helping (or even compelling) the opponent to

checkmate Checkmate (often shortened to mate) is any game position in chess and other chess-like games in which a player's king is in check (threatened with ) and there is no possible escape. Checkmating the opponent wins the game. In chess, the king is ...

one's own king.

Chess problems

While a ''chess puzzle'' is any puzzle involving aspects of chess, a ''chess problem'' (or ''chess composition'') is a crafted position with a specified task to be fulfilled, such as White mates in ''n'' moves. Chess problems are divided into orthodox and heterodox types, both covering a variety of genres. ''Orthodox problems'' employ the standard rules of chess and involve positions that can legally arise from actual gameplay. The most common form of orthodox problem is the directmate, which stipulates checkmate in ''n'' moves, usually two or three. The positions are often dissimilar to positions from actual play, sometimes to the extent of being outlandish in comparison. The move is usually counter-intuitive. Despite their unusual stipulations, helpmates and selfmates are usually considered orthodox problems, as they use standard chess rules. Likewise, retrograde analysis problems are usually considered orthodox. ''Heterodox problems'', also called fairy chess problems, involve altered rules, such as different boards and pieces not used in standard chess.

Tactical puzzles

Chess puzzles can also be regular positions from actual games, usually meant as tactical training positions. They can range from a simple "Mate in one" combination to a complex attack on the enemy king. Solving tactical chess puzzles is a very common chess teaching technique. They are helpful in pattern recognition.

Example 1

240px, Puzzle 1: Black to play and win The solution is 1...Qf2, attacking the f1-rook; 2.Rxf2 would incur a back-rank checkmate after 2...Rd1+. If 2.Rg1, 2...Bc5 sets up a targetting g1, where White can stop checkmate only by moving the c1-bishop to . Since the only two squares available to the bishop are controlled by the black queen, loss of the bishop is unavoidable. White's best try is 2.Be3, giving up the bishop immediately and leaving Black an easily .

Example 2

240px, Puzzle 2: White to play and win The solution is 1.Ne6+, unblocking White's h4-bishop and g1-rook. Black's f-pawn must guard the g6-bishop, preventing ...fxe6 in almost all variations; thus, if the black king moves after 1.Ne6+, then 2.Qxf6 leaves Black down a piece and in a . 1...Kh7 and 2...Rhg8 defending the bishop allows for 3...fxe6, but White's attack is insurmountable, with prospects of opening the h-file with Bg5 and of Bxe6. White can force mate in less than 13 moves against any alternative to 1...Qxe6, which sacrifices material to blunt White's attack.

Mathematical chess problems

Some chess problems, like the eight queens puzzle or the knight's tour problem, have connections to mathematics, especially to

graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...

and

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...

. Many famous mathematicians have studied such problems, including

Euler Leonhard Euler ( ; ; ; 15 April 170718 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential ...

, Legendre, and

Gauss Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, Geodesy, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observat ...

. Besides finding a solution to a particular puzzle, mathematicians are usually interested in counting the total number of possible solutions, finding solutions with certain properties, and generalization of the problems to ''n''×''n'' or rectangular boards.

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