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:
“Of all reformers Mr. Sentiment is the most powerful. It is incredible the number of evil practices he has put down: it is to be feared he will soon lack subjects, and that when he has made the working classes comfortable, and got bitter beer into proper-sized pint bottles, there will be nothing left for him to do.”
—Anthony Trollope (1815–1882)
“States strong enough to do good are but few.
Their number would seem limited to three.”
—Robert Frost (1874–1963)
“One man’s observation is another man’s closed book or flight of fancy.”
—Willard Van Orman Quine (b. 1908)