2018/02/19 by Awani Kumar, Kumar, Awani
Computer Science · Mathematics · #05-02 #Artificial Intelligence in Games #FOS: Mathematics #General Mathematics (math.GM) #math.GM #msc:05-02
paper · pdf · doi:10.48550/arxiv.1802.09340
30 pages, 55 figures and 2 tables
openalex publication_date 2018/02/19 · arxiv created 2018/12/06 · arxiv updated 2018/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The author has constructed and enumerated tours of knight having various magic properties on 4 x n and 6 x n boards. 16 magic tours of knight have been discovered on 4 x 18 board, 88 on 4 x 20 board, 464 on 4 x 22 board, 2076 on 4 x 24 board, 9904 on 4 x 26 board and 47456 on 4 x 28 board. Magic tours exist on all boards of size 4 x 2k for k > 8. Quasi-magic tour exists on 6 x 11 board. 8 magic tours of knight have been discovered on 6 x 12 board and magic tours exist on all boards of size 6 x 4k for k > 2.