OFFSET
1,4
COMMENTS
A semi-magic knight's tour is a tour that adds to a constant sum in every line in one direction, but not in every line in the perpendicular direction. A near-magic tour is a special type of semi-magic tour in which the non-magic direction has the lines add to the magic constant and two other values. Such tours are of interest on boards where magic tours don't exist.
LINKS
G. P. Jelliss, Semi-Magic Knight's Tours.
Awani Kumar, Studies in Tours of Knight on Rectangular Boards, arXiv:1802.09340 [math.GM], 2018.
EXAMPLE
Example of 6 X 10 near-magic knight's tour. All short lines add to 183 and the long lines add to the magic constant 305 and 305 +- 6.
29 50 53 14 27 16 55 38 03 20
52 13 28 17 54 25 02 19 56 39
49 30 51 26 15 18 37 60 21 04
12 09 32 45 36 43 24 01 40 57
31 48 11 34 07 46 59 42 05 22
10 33 08 47 44 35 06 23 58 41
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Awani Kumar, Jan 18 2020
STATUS
approved