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 genius of democracies is seen not only in the great number of new words introduced but even more in the new ideas they express.”
—Alexis de Tocqueville (1805–1859)
“It is always possible to bind together a considerable number of people in love, so long as there are other people left over to receive the manifestations of their aggression.”
—Sigmund Freud (1856–1939)
“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)