Closed Knight’s Tour on Ring Boards (n,n,1)
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Published:
Dec 16, 2019
Keywords:
Closed knight’s tour, Ring boards
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Abstract
Let m, n be odd integers such that m, n 3, the ring boards (m, n, 1) is an m x n chessboard with the middle part of size 1 x 1 is missing. This article studies the conditions to guarantee the existence of a closed knight’s tour on the ring board (n, n, 1) and the ring board (m, m+4k, 1) for odd integers m such that m
11 and k
0 and if it exists, then an algorithm for finding a closed knight’s tour on that board is given.
Article Details
How to Cite
Boonklurb, R., Sapworarit, P., & Srichote, W. (2019). Closed Knight’s Tour on Ring Boards (n,n,1). Mathematical Journal by The Mathematical Association of Thailand Under The Patronage of His Majesty The King, 64(699), 64–79. Retrieved from https://ph02.tci-thaijo.org/index.php/MJMATh/article/view/203819
Section
Research Article
References
[1] Chia, G.L. and Ong, S.-H. (2005). Generalized knight’s tours on rectangular chessboards, Discrete Applied Mathematics, 150, p.80-98.
[2] Schwenk, A.L. (1991). Rectangular chessboards have a knight’s tour, Math. Magazine, 64, p.325-332.
[3] Wiitala, H.R. (1996). The knight’s tour problem on boards with holes, Research Experiences for Undergraduates Proceedings, p.132-151.
[2] Schwenk, A.L. (1991). Rectangular chessboards have a knight’s tour, Math. Magazine, 64, p.325-332.
[3] Wiitala, H.R. (1996). The knight’s tour problem on boards with holes, Research Experiences for Undergraduates Proceedings, p.132-151.