A Knight's Tour is a "puzzle" which has amused chess players throughout the ages. The goal of the Knight is to traverse around the board, landing on each square but once. There are numerous solutions. Here's one: 
Here's another one: 
The above two paths are known as "closed" or "reentrant" paths. The Knight, after completing its journey, lands on the 64th square, which is also the square that it started on. Thus, it can complete the journey again. This is considered much more of an elegant solution than the many "open" paths, one of which is shown here: 
As you can see, our galloping Knight still lands on each of the 64 squares. However, he isn't able to complete the journey a second time. In this tour, the Knight starts out here on the h8 square, but ends up on c6... more than a Knight's move away. 
Not only is this next example a
reentrant path, but it's considered a somewhat semi
"magic square!" Each of the columns add up to 260! 
However, this one must be considered
a SUPER magic square which I've been informed was
found/created by the mathematician Leonhard
Euler. 1) Each column adds up to 260! 2) Each row also adds up to 260! 
3) Each of the four
colored quadrants add up to 520! (1 + 48 + 31 + 50 + 30 + 51 + 46 + 3 + 47 + 2 + 49 + 32 + 52 + 29 + 4 + 45 = 520) 

4) Each row and each column in each of the four colored quadrants add up to 130! (1 + 48 + 31 + 50 = 130) 5) Each of the 16 colored quadrants shown add up to 130! (1 + 48 + 31 + 50 + 30 + 51 + 46 + 3 + 47 + 2 + 49 + 32 + 52 + 29 + 4 + 45 = 520) 

Many
thanks to Muhammad Malik who brought this
Super Knight's Tour/Magic Square to my attention!
I.A. Horowitz and
P.L.Rothenberg have stated the number of possible Knight's Tours lies somewhere between 122,802,512
and 168! / (105!)(63!) Whoa Nellie! 