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Gomory's theorem: Removing any two oppositely-colored squares of a chessboard leaves a region that can be tiled by dominoes. The two removed squares partition a Hamiltonian cycle through the squares into one (left) or two (right) paths through an even number of squares, allowing the modified chessboard to be tiled by dominoes laid along the paths.
English: Gomory's theorem: Removing any two oppositely-colored squares of a chessboard leaves a region that can be tiled by dominos.The two removed squares partition a Hamiltonian cycle through the squares into one (left) or two (right) even-length paths, allowing the modified chessboard to be tiled by dominos laid along the paths.
A chessboard complex is a particular kind of abstract simplicial complex, which has various applications in topological graph theory and algebraic topology. [1] [2] Informally, the (m, n)-chessboard complex contains all sets of positions on an m-by-n chessboard, where rooks can be placed without attacking each other.
Chess initial position. The game of chess is commonly divided into three phases: the opening, middlegame, and endgame. [1] There is a large body of theory regarding how the game should be played in each of these phases, especially the opening and endgame.
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.
In graph theory, a rook's graph is an undirected graph that represents all legal moves of the rook chess piece on a chessboard. Each vertex of a rook's graph represents a square on a chessboard, and there is an edge between any two squares sharing a row (rank) or column (file), the squares that a rook can move between. These graphs can be ...
The wheat and chessboard problem (sometimes expressed in terms of rice grains) is a mathematical problem expressed in textual form as: If a chessboard were to have wheat placed upon each square such that one grain were placed on the first square, two on the second, four on the third, and so on (doubling the number of grains on each subsequent ...
Ordered by chess opening: . Albin Countergambit: Lasker Trap; Blackmar–Diemer Gambit: Halosar Trap; Bogo-Indian Defence: Monticelli Trap; Budapest Gambit: Kieninger Trap; Englund Gambit Trap
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