Studies in Tours of Knight on Rectangular Boards
Awani Kumar
TL;DR
This paper explores the construction and enumeration of knight's tours with magic properties on rectangular boards, revealing the existence and quantity of such tours on specific 4 x n and 6 x n boards.
Contribution
It introduces new methods for constructing and counting magic knight's tours on 4 x n and 6 x n boards, providing extensive enumerations and existence proofs.
Findings
Discovered 47,456 magic tours on 4 x 28 boards
Found 4,904 magic tours on 6 x 26 boards
Magic tours exist on all 4 x 2k and 6 x 4k boards for certain k
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsArtificial Intelligence in Games