TITLE:
Knight’s Tours on 3 x n Chessboards with a Single Square Removed
AUTHORS:
Amanda M. Miller, David L. Farnsworth
KEYWORDS:
Knight’s Tour; Hamiltonian Cycle; Forced Edge; Extender Board
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.3 No.1,
January
29,
2013
ABSTRACT: The following theorem is proved: A knight’s tour exists on all 3 x n chessboards with one square removed unless: n is even, the removed square is (i, j) with i + j odd, n = 3 when any square other than the center square is removed, n = 5, n = 7 when any square other than square (2, 2) or (2, 6) is removed, n = 9 when square (1, 3), (3, 3), (1, 7), (3, 7), (2, 4), (2, 6), (2, 2), or (2, 8) is removed, or when square (1, 3), (2, 4), (3, 3), (1, n – 2), (2, n – 3), or (3, n – 2) is removed.