The earliest known reference to the knight's tour problem dates back to the 9th century AD. This particular solution is closed (circular), and can thus be completed from any point on the board. History The knight's tour as solved by the Turk, a chess-playing machine hoax. Unlike the general Hamiltonian path problem, the knight's tour problem can be solved in linear time. The problem of finding a closed knight's tour is similarly an instance of the Hamiltonian cycle problem. The knight's tour problem is an instance of the more general Hamiltonian path problem in graph theory. The numbers on each node indicate the number of possible moves that can be made from that position. Theory Knight's graph showing all possible paths for a knight's tour on a standard 8 × 8 chessboard. Variations of the knight's tour problem involve chessboards of different sizes than the usual 8 × 8, as well as irregular (non-rectangular) boards. Creating a program to find a knight's tour is a common problem given to computer science students. The knight's tour problem is the mathematical problem of finding a knight's tour. 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. Mathematical problem set on a chessboard An open knight's tour of a chessboard An animation of an open knight's tour on a 5 × 5 boardĪ knight's tour is a sequence of moves of a knight on a chessboard such that the knight visits every square exactly once.
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