Find the number of all paths of shortest possible length that a knight on a chessboard can use to go from the lower left corner to the upper right corner.
A chessboard is a square grid of \(8\times8\).
Details and assumptions
At each step of the path, a knight is allowed to move two squares in one of the four directions (up, down, right or left) and one square in the perpendicular direction. So, for example, it can go two squares to the right and one square up, or two squares to the right and one square down, or two squares up and one square to the left (or right), and so on. Of course, after each move, the knight has to stay on the chessboard (which is a square grid of size 8-by-8).