@abakcus
Incidentally, it depends on the parity of the number of squares in the side, for a general nxn grid. For example, in a 3x3 grid you can only hop around the outer ring, but never into the central square.
@abakcus
But... the knight does not start on that square, but two more to the right side. This way he can visit all the squares, but some of them more than once (to reach the starting point shown here).
@abakcus
This is an interesting path where a knight can visit each square on a chessboard exactly once by excluding squares that had already visited. It will be more interesting if this happens irrelevant the starting point.