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The knight's tour is a chess problem in which a knight is placed on an empty chessboard and, moving consistent with the rules of chess, must visit each square exactly once. Although the tour is most often completed by chess players, especially at expositions whilst blindfolded, and was renownedly solved by The Turk, a chess-playing automaton hoax, it is most often studied as a mathematical problem, an instance of a general Hamiltonian path problem in graph theory which can be solved in linear time. Under the most restrictive conditions, those requiring that the knight finishes on a square whence it attacks its starting square (closed) and that the knight begin on a specified square (producing a directed path), there are exactly 26,534,728,821,064 solutions to the problem; many other solutions are not bound by the former constraint and are known as open tours (example pictured).
