Putnam 1981 A2

Two distinct squares of the $8\times8$ chessboard $C$ are said to be adjacent if they have a vertex or side in common. Also, $g$ is called a $C$ -gap if for every numbering of the squares of $C$ with all the integers $1, 2, \ldots, 64$ there exist twoadjacent squares whose numbers differ by at least $g$ . Determine the largest $C$ -gap $g$ .