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:
“In this world, which is so plainly the antechamber of another, there are no happy men. The true division of humanity is between those who live in light and those who live in darkness. Our aim must be to diminish the number of the latter and increase the number of the former. That is why we demand education and knowledge.”
—Victor Hugo (1802–1885)
“After a certain number of years our faces become our biographies. We get to be responsible for our faces.”
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“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.”
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