OFFSET
1,2
COMMENTS
The squares are numbered starting with 1 at the origin (0,0). The sequence is finite: when arriving on square number a(180) = 157, there is no free square within reach for the next move.
Shifting the knight only 1 square to the right leads to an infinite sequence. Similarly, shifting only 1 square up leads to an infinite sequence. More generally, if the knight jumps (1,n) spaces and is shifted m squares to the right, m > n leads to an infinite sequence.
LINKS
N. J. A. Sloane and Brady Haran, The Trapped Knight, Numberphile video (2019).
CROSSREFS
KEYWORD
nonn,fini
AUTHOR
Simon S. Gurvets, Apr 18 2021
STATUS
approved