2012/01/02 by Awani Kumar, Kumar, Awani
Computer Science · Mathematics · #05C20 #Artificial Intelligence in Games #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph Labeling and Dimension Problems #cs.DM #math.CO #msc:05C20
paper · pdf · doi:10.48550/arxiv.1201.0458
12 pages, 10 figures
arxiv created 2012/01/02 · openalex publication_date 2012/01/02 · arxiv updated 2012/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 × 4 × 2n-2 is the smallest cuboid (n ≥ 2) and 4 × 4 × 4n-2 is the smallest cube in which knight's tour is possible in n-dimensions (n ≥ 3). Magic knight's tours are possible in 4 × 4 × 4 × 4 and 4 × 4 × 4 × 4 × 4 hypercube.