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 n = 11 when square (1, 3), (2, 4), (3, 3), (1, n – 2), (2, n – 3), or (3, n – 2) is removed.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Publication Date
1-2013
Document Type
Article
Department, Program, or Center
School of Mathematical Sciences (COS)
Recommended Citation
A. Miller and D. Farnsworth, "Knight’s Tours on 3 x n Chessboards with a Single Square Removed," Open Journal of Discrete Mathematics, Vol. 3 No. 1, 2013, pp. 56-59. doi: 10.4236/ojdm.2013.31012.
Campus
RIT – Main Campus
