Closed Knight’s Tour on Ring Boards (n,n,1)

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Ratinan Boonklurb
Punyaporn Sapworarit
Wasupol Srichote


Let  m, n be odd integers such  that m, n gif.latex?\geq 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 gif.latex?\geq 11 and k gif.latex?\geq  0 and if it exists, then an algorithm for finding a closed knight’s tour on that board is given.

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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
Research Article


[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.