Let the king stand in the upper left corner on an 8x8 chessboard. How many options to get to the cell number $ (i,j), i,j \in \{1,2 \ldots 8\}$ if the king goes to each cell no more than once?
I do not know combinatorics very well, but I am very curious about the result. Sorry for not making any attempts.
p.s. it's not homework.
This problem is generally in NP class of complexity and cannot be solved only through numerical analysis. Check out Self-avoiding walk
P.S. If it was a homework, it would have taken 2 or 3 month to solve it!