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)
“Black lady,
what will I do
without your two flowers?
I have inhabited you, number by number.
I have pushed you in and out like a needle.”
—Anne Sexton (1928–1974)
“Because you live, O Christ,
the spirit bird of hope is freed for flying,
our cages of despair no longer keep us closed and life-denying.
The stone has rolled away and death cannot imprison!
O sing this Easter Day, for Jesus Christ has risen!”
—Shirley Erena Murray (20th century)