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arXiv · 1201.0458

Magic Knight's Tours in Higher Dimensions

Awani Kumar
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Abstract

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 is the smallest cuboid (n \geq 2) and 4 \times 4 \times 4n-2 is the smallest cube in which knight's tour is possible in n-dimensions (n \geq 3). Magic knight's tours are possible in 4 \times 4 \times 4 \times 4 and 4 \times 4 \times 4 \times 4 \times 4 hypercube.

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Awani Kumar. 2012-01-02. Magic Knight's Tours in Higher Dimensions. https://arxiv.org/abs/1201.0458

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