The Games and Puzzles Journal, #15 - Mayhematics

THE GAh{ES ANID PLIZZI.ES JOTIRhIAL
Knight's Tour htrotes
King Tours
One of the main characteristics of 'Celtic Art' during its later period is the use of intsrlace patterns
depicting a ribbon passing alternately over and under itself. No doubt such pattems derived originally
from depictions of real interlacings, as in the plaiting of hair, rope-making (where several strands are
woven together to gtve greater strength), lace fastenings for boots, leggings or coats, or in the passes
and stitches used in weaving, tapestry and embroidery.
Many of the interlacings can be represented graphicall-v by a
path of king moves on a lafiice of squares, the cross-overs being
made by diagonal moves of the king, though this does not
necessarily imply that they \,\.ere designed this way. I give here
horvever two diagrams which it seems to me almost certainl-v
derive from underlylng king-tour patterns. It may be noted that
these king tours avoid sharp turns (of 45') since this would result
in small interstitial arsas: not allowing room for the definite !\.idth
of the ribbon.
A nearly square king tour underlies the design of a panel from the Saint Madoes stone, Perthshire.
The illustration below left is reduced from George Bwn, Celtic Art: The Methods of Construction,
195I,p.46. This is a20x24 king tour" which can be formed by'doubling' a simpler king tour 10x12
(inset) and altering some links to tum the pseudotour into a true tour.
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