Magic Tour

Let a chess piece make a Tour on an Chessboard whose squares are numbered from 1 to along thepath of the chess piece. Then the Tour is called a magic tour if the resulting arrangement of numbers is a MagicSquare. 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. The Magic Constant for the Chessboard is 260.

Magic Knight's Tours are not possible on boards for Odd, and are believed to beimpossible for . The ``most magic'' knight tour known on the board is the Semimagic Square illustratedin the above left figure (Ball and Coxeter 1987, p. 185) having main diagonal sums of 348 and 168. Combining two half-knights'tours one above the other as in the above right figure does, however, give a Magic Square (Ball and Coxeter 1987,p. 185).

The above illustration shows a closed magic Knight's Tour (Madachy 1979).

A magic tour for king moves is illustrated above (Coxeter 1987, p. 186).

References

Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 185-187, 1987.

Madachy, J. S. Madachy's Mathematical Recreations. New York: Dover, pp. 87-89, 1979.

• Interval Order
• Intrinsically Linked
• Intrinsic Curvature
• Intrinsic Equation
• Invariant
• Invariant Density
• Invariant (Elliptic Function)
• Invariant Manifold
• Invariant Point
• Invariant Subgroup
• Inverse Cosecant
• Inverse Cosine
• Inverse Cotangent
• Inverse Curve
• Inverse Filter
• Inverse Function
• Inverse Hyperbolic Cosecant
• Inverse Hyperbolic Cosine
• Inverse Hyperbolic Cotangent
• Inverse Hyperbolic Functions
• Inverse Hyperbolic Secant
• Inverse Hyperbolic Sine
• Inverse Hyperbolic Tangent
• Inversely Similar
• Inverse Matrix