The Amazing “Knight’s Tour” (Semi-) Magic Square

Quick Background/Review:

A magic square is a square array (of any size) of consecutive counting numbers where all the rows, columns, and diagonals add to the same number.  A simple 3 x 3 example is shown to the right.

 

 

An 8 x 8 Square with an Incredible Feature:

Look at the 8 x 8 square below.  Technically, it’s not quite a ‘magic square’ (all 16 of the rows/columns add to the same number, but the diagonals don’t), so it’s called a Semi-Magic Square.

Now take a knight from a chessboard and place in on the number 1 (upper left-hand corner).  Moving as a knight does, proceed to square #2 (3rd row, 2nd entry), then square #3 (2nd row, 4th entry), and so forth.

Proceeding in that fashion (using knight’s moves) the knight can visit each square on the chessboard exactly once by following the numbers in sequence !!