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A knight's tour is a sequence of moves of a knight on a chessboard such that the knight visits every square exactly once. If the knight ends on a square that is one knight's move from the beginning square (so that it could tour the board again immediately, following the same path), the tour is closed (or re-entrant); otherwise, it is open.
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.
A Hamiltonian cycle on the knight's graph is a (closed) knight's tour. [1] A chessboard with an odd number of squares has no tour, because the knight's graph is a bipartite graph (each color of squares can be used as one of two independent sets, and knight moves always change square color) and only bipartite graphs with an even number of ...
The game structure and nature of chess are related to several branches of mathematics. Many combinatorical and topological problems connected to chess, such as the knight's tour and the eight queens puzzle, have been known for hundreds of years. Mathematicians Euler, Legendre, de Moivre, and Vandermonde studied the knight's tour.
The longest uncrossed (or nonintersecting) knight's path is a mathematical problem involving a knight on the standard 8×8 chessboard or, more generally, on a square n×n board. The problem is to find the longest path the knight can take on the given board, such that the path does not intersect itself.
Makes any number of consecutive knight moves on an octagonal (almost circular) path. It may move either clockwise or counterclockwise: going along a sequence of numbers 1-2-3-4-3-2-1 in a circle on the diagram demonstrates one possible move of the rose. For example, it may travel along the following path: i8–g9–e8–d6–e4–g3–i4–j6–i8.
When the attacker is a knight the tactic is often specifically called a knight fork. Some sources state that only a knight can give a fork and that the term double attack is correct when another piece is involved, but this usage is rare. [5] Forsyth–Edwards Notation A standard notation for describing a particular board position of a chess game.
The knight (♘, ♞) is a piece in the game of chess, represented by a horse's head and neck.It moves two squares vertically and one square horizontally, or two squares horizontally and one square vertically, jumping over other pieces.