Number of Closed Tours
On an 8 × 8 board, there are exactly 26,534,728,821,064 directed closed tours (i.e. two tours along the same path that travel in opposite directions are counted separately, as are rotations and reflections). The number of undirected closed tours is half this number, since every tour can be traced in reverse. There are 9,862 undirected closed tours on a 6 × 6 board.
Read more about this topic: Knight's Tour
Famous quotes containing the words number of, number and/or closed:
“Can a woman become a genius of the first class? Nobody can know unless women in general shall have equal opportunity with men in education, in vocational choice, and in social welcome of their best intellectual work for a number of generations.”
—Anna Garlin Spencer (1851–1931)
“In proportion as our inward life fails, we go more constantly and desperately to the post office. You may depend on it, that the poor fellow who walks away with the greatest number of letters, proud of his extensive correspondence, has not heard from himself this long while.”
—Henry David Thoreau (1817–1862)
“Thus piteously Love closed what he begat:
The union of this ever-diverse pair!
These two were rapid falcons in a snare,
Condemned to do the flitting of the bat.”
—George Meredith (1828–1909)