Let a chess piece make a tour on an n×n chessboard whose squares are numbered from 1 to n^2 along the path of the chess piece. Then the tour is called a magic tour if the resulting arrangement of numbers is a magic square, and a semimagic tour if the resulting arrangement of numbers is a semimagic square. If the first and last squares traversed are connected by a move, the tour is said to be closed (or "re-entrant"); otherwise it is open. (Note some care with terminology is necessary. For example, Jelliss terms a semimagic tour a "magic tour" and a magic tour a "diagonally magic tour.")

chessboard | knight graph | magic square | semimagic square | tour