Abstract
from its initial position on an infinite chessboard are derived. The number of squares reachable in exactly k moves are 1, 8, 32, 68, and 96 for k = 0, 1, 2, 3, and 4, respectively, and 28k – 20 for k ≥ 5. The cumulative number of squares reach- able in k or fever moves are 1, 9, 41, and 109 for k = 0, 1, 2, and 3, respectively, and 14k-squared – 6k + 5 for k ≥ 4. Although these formulas are known, the proofs that are presented are new and more mathematically accessible then preceding proofs.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Publication Date
7-2013
Document Type
Article
Department, Program, or Center
School of Mathematical Sciences (COS)
Recommended Citation
A. Miller and D. Farnsworth, "Counting the Number of Squares Reachable in k Knight’s Moves," Open Journal of Discrete Mathematics, Vol. 3 No. 3, 2013, pp. 151-154. doi: 10.4236/ojdm.2013.33027.
Campus
RIT – Main Campus
