## magic tourSuppose a chess piece makes a tour on an n
× n chessboard whose squares are numbered from 1 to n^{2}
along the path of the piece. The tour is a magic tour if the resulting arrangement
of numbers is a magic square, and is a semimagic
tour if the resulting arrangement of numbers is a semi-magic
square. Magic knight's tours aren't
possible on n × n boards if n is odd. They are
possible for all boards of size 4k × 4k for k
> 2, but are believed to be impossible for n = 8. Magic tours have been found in 4 × 4 × 4, 8 × 8 × 8, and 12 × 12 × 12 cubes, and on the surface of 8 × 8 × 8 cube. However, there are no known knight tours in hypercubes. [Thanks to Awani Kumar for corrections to and additional information for this entry.] ## Reference- Kumar, Awani. "In Search of Perfect Magic Tours of Knight on 12×12
Board."
*The On-line Journal for Mathematical Recreations*, Issue 26, April-June 2003.
## Related category• GAMES AND PUZZLES | |||||

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