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Mathematical chess problem. A mathematical chess problem is a mathematical problem which is formulated using a chessboard and chess pieces. These problems belong to recreational mathematics. The most well-known problems of this kind are the eight queens puzzle and the knight's tour problem, which have connection to graph theory and combinatorics.
Eight queens puzzle. The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other; thus, a solution requires that no two queens share the same row, column, or diagonal. There are 92 solutions. The problem was first posed in the mid-19th century.
Domination (chess) In chess, and particularly in endgame studies, domination occurs when a player controls all movement squares of an enemy piece. [1] This article uses algebraic notation to describe chess moves.
Biconnected, Hamiltonian. Table of graphs and parameters. In mathematics, a queen's graph is an undirected graph that represents all legal moves of the queen —a chess piece —on a chessboard. In the graph, each vertex represents a square on a chessboard, and each edge is a legal move the queen can make, that is, a horizontal, vertical or ...
Bishop's graph. In mathematics, a bishop's graph is a graph that represents all legal moves of the chess piece the bishop on a chessboard. Each vertex represents a square on the chessboard and each edge represents a legal move of the bishop; that is, there is an edge between two vertices (squares) if they occupy a common diagonal.
The domination number of a graph is the minimum cardinality among all dominating sets. On the rook's graph a set of vertices is a dominating set if and only if their corresponding squares either occupy, or are a rook's move away from, all squares on the m × n board. For the m × n board the domination number is min(m, n). [24]
De ludo scachorum ('On the Game of Chess'), also known as Schifanoia ('the "Boredom Dodger"'), [1] is a Latin-language manuscript on the game of chess written around 1500 by Luca Pacioli, a leading mathematician of the Renaissance. Created in the times when rules of the game (especially the way queen and bishop move) were evolving to the ones ...
t. e. A chess problem, also called a chess composition, is a puzzle set by the composer using chess pieces on a chess board, 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.