Place a Knight from a chess set on the corner of a 3 by 3 square board:

It would need 4 usual Knight's moves to place it in the opposite corner. One possible set of moves is shown below:

- What would be the smallest number of moves needed to move from
one corner to the opposite corner of a 99 by 99 square board?

- What would be the smallest number of moves needed to move from
one corner to the opposite corner of an
*n*by*n*square grid?