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:
“The world is so full of a number of things,
I’m sure we should all be as happy as kings.”
—Robert Louis Stevenson (1850–1894)
“Cultivated labor drives out brute labor. An infinite number of shrewd men, in infinite years, have arrived at certain best and shortest ways of doing, and this accumulated skill in arts, cultures, harvestings, curings, manufactures, navigations, exchanges, constitutes the worth of our world to-day.”
—Ralph Waldo Emerson (1803–1882)
“No other creative field is as closed to those who are not white and male as is the visual arts. After I decided to be an artist, the first thing that I had to believe was that I, a black woman, could penetrate the art scene, and that, further, I could do so without sacrificing one iota of my blackness or my femaleness or my humanity.”
—Faith Ringgold (b. 1934)