Studies in Tours of Knight on Rectangular Boards
General Mathematics
2018-12-07 v2
Abstract
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.
Cite
@article{arxiv.1802.09340,
title = {Studies in Tours of Knight on Rectangular Boards},
author = {Awani Kumar},
journal= {arXiv preprint arXiv:1802.09340},
year = {2018}
}
Comments
30 pages, 55 figures and 2 tables