• Corpus ID: 200294

Magic Knight's Tours in Higher Dimensions

@article{Kumar2012MagicKT,
  title={Magic Knight's Tours in Higher Dimensions},
  author={Awani Kumar},
  journal={ArXiv},
  year={2012},
  volume={abs/1201.0458}
}
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… 
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References

SHOWING 1-10 OF 27 REFERENCES

Which Chessboards have a Closed Knight's Tour within the Cube?

TLDR
In this paper necessary and sufficient conditions for the existence of a closed knight's tour for the cube are proven.

Which Chessboards have a Closed Knight's Tour within the Rectangular Prism?

TLDR
In honor of the upcoming twentieth anniversary of the publication of Schwenk's paper, this article extends his result by classifying thei\times j\times k$ rectangular prisms that admit a closed knight's tour.

Mathematics and Chess.

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

Which Rectangular Chessboards Have a Knight's Tour?

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

A History of Chess

Have you ever played chess? Did you know that chess is the oldest skill game in the world? Chess can tell you a great deal about the way people lived in medieval times. If you look at the way a

The Fourth Dimension Simply Explained

THERE are few fallacies which have done more to mislead the unscientific public than the misconception known as the fourth dimension. The use of this term is calculated to convey the false

Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning

Who were the five strangest mathematicians in history? What are the ten most interesting numbers? Jam-packed with thought-provoking mathematical mysteries, puzzles, and games, Wonders of Numbers will

Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension

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Extra Dimensions

For explanation of terms used and discussion of significant model dependence of following limits, see the " Extra Dimensions Review. " Limits are expressed in conventions of of Giudice, Rattazzi, and