• Corpus ID: 200294

Magic Knight's Tours in Higher Dimensions

  title={Magic Knight's Tours in Higher Dimensions},
  author={Awani Kumar},
A knight's tour on a board is a sequence of knight moves that visits each square exactly once. A knight's tour on a square board is called magic knight's tour if the sum of the numbers in each row and column is the same (magic constant). Knight's tour in higher dimensions (n > 3) is a new topic in the age-old world of knight's tours. In this paper, it has been proved that there can't be magic knight's tour or closed knight's tour in an odd order n-dimensional hypercube. 3 \times 4 \times 2n-2… 
4 Citations

The Closed Knight Tour Problem in Higher Dimensions

The solution of existence of closed knight tours for rectangular chessboards for rectangular boards for n-dimensional rectangular boards is given.


  • Marco Ripà
  • Computer Science
    Journal of Fundamental Mathematics and Applications (JFMA)
  • 2021
An optimization problem related to the extension in k-dimensions of the well known 3x3 points problem by Sam Loyd is considered, thanks to a variation of the so called “clockwise-algorithm”, it is shown how it is possible to visit all the 3^k points of the k-dimensional grid given by the Cartesian product of (0, 1, 2).

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A magic square of dimension п-Ъу-п is a square divided into n2 congruent cells in which numbers are placed in such a way that the sums of the numbers in all rows and columns, as well as both

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(1991). Which Rectangular Chessboards Have a Knight's Tour? Mathematics Magazine: Vol. 64, No. 5, pp. 325-332.

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