Knight's Tour

The Knight's Tour ismathematical problem involvingknight onchessboard. The knightplaced onempty board and, moving according toruleschess, must visit each square once.

Thereseveral billion solutions toproblem,which about 122,000,000 haveknight finishing onsame square on whichbegins.

Many variations on this topic have been studied duringcenturies:

• differently sized boards
• two-player games based on this idea
• problems using slight variations onwayknight moves.

The knight's tour probleman instance ofmore general hamiltonian path problemgraph theory, whichNP-complete. The problemgettingclosed knight's toursimilarly an instance ofhamiltonian cycle problem. See Howsolveknight's tourinstructions on solvingknight's tour problem. Note however that, unlikegeneral hamiltonian path problem,knight's tour problem can be solvedlinear time (Conrad et al 1994).

The pattern made byKnight's Tour has often been used asliterary constraint. The earliest instancethisfoundRudrata's Kavyalankara written during9th century.

In20th centuryOulipo groupwriters usedamong many others. The most notable example is10x10 Knight Tour which setsorder ofchaptersGeorges Perec's novel La Vie mode d'emploi.

External links

• The knight's tour
• Knight's tour notes