A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2014; you can also visit the original URL.
The file type is `application/pdf`

.

##
###
Counting the Number of Squares Reachable in k Knight's Moves

2013
*
Open Journal of Discrete Mathematics
*

Using geometric techniques, formulas for the number of squares that require k moves in order to be reached by a sole knight 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 reachable in k or fever moves are 1, 9, 41, and 109 for k = 0, 1, 2, and 3, respectively, and 14k 2 -6k + 5 for k ≥ 4. Although these

doi:10.4236/ojdm.2013.33027
fatcat:ko7cvetlbnc75beb6z2bqzuq6u