Which Boards Have Tours
Schwenk proved that for any m × n board with m less than or equal to n, a closed knight's tour is always possible unless one or more of these three conditions are met:
- m and n are both odd; n is not 1
- m = 1, 2, or 4; n is not 1
- m = 3 and n = 4, 6, or 8.
Cull and de Curtins proved that on any rectangular board whose smaller dimension is at least 5, there is a (possibly open) knight's tour.
Read more about this topic: Knight's Tour
Famous quotes containing the word boards:
“Strange that so few ever come to the woods to see how the pine lives and grows and spires, lifting its evergreen arms to the light,—to see its perfect success; but most are content to behold it in the shape of many broad boards brought to market, and deem that its true success! But the pine is no more lumber than man is, and to be made into boards and houses is no more its true and highest use than the truest use of a man is to be cut down and made into manure.”
—Henry David Thoreau (1817–1862)