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,
otherwise it is open. The exact number of open tours on an 8x8
chessboard is still unknown. The knight's tour problem is the
mathematical problem of finding a knight's tour. Creating a
program to find a knight's tour is a common problem given to
computer science students. Variations of the knight's tour
problem involve chessboards of different sizes than the usual 8
× 8, as well as irregular (non-rectangular) boards. The knight's
tour problem is an instance of the more general Hamiltonian path
problem in graph theory. The problem of finding a closed
knight's tour is similarly an instance of the Hamiltonian cycle
problem. Note, however, that unlike the general Hamiltonian path
problem, the knight's tour problem c