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:
“That country is the richest which nourishes the greatest number of noble and happy human beings.”
—John Ruskin (1819–1900)
“The two great points of difference between a democracy and a republic are: first, the delegation of the government, in the latter, to a small number of citizens elected by the rest; secondly, the greater number of citizens and greater sphere of country over which the latter may be extended.”
—James Madison (1751–1836)
“On a flat road runs the well-trained runner,
He is lean and sinewy with muscular legs,
He is thinly clothed, he leans forward as he runs,
With lightly closed fists and arms partially raised.”
—Walt Whitman (1819–1892)