OFFSET
1,3
COMMENTS
A quasi-magic tour is a special type of semi-magic tour in which the non-magic lines add to only two different values. Such tours are of interest on boards where magic tours don't exist.
LINKS
G. P. Jelliss, Quasi-Magic Tours, The Games and Puzzles Journal #26, April-June 2003.
Awani Kumar, Studies in Tours of Knight on Rectangular Boards, arXiv:1802.09340 [math.GM], 2018.
EXAMPLE
Example of 4 X 14 quasi-magic knight's tour. All long lines sum to 399 and the short lines sum to either 112 or 126.
3 52 19 40 1 50 21 42 13 48 23 30 11 46
18 39 2 51 20 41 14 49 22 29 12 47 24 31
53 4 37 16 55 6 35 28 43 8 33 26 45 10
38 17 54 5 36 15 56 7 34 27 44 9 32 25
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Awani Kumar, Dec 17 2019
STATUS
approved