• it works only if n is odd.

• Place a 1 in the middle of the bottom row.
• After k has been placed in the (i, j) square,
• place k+1 into the square to the right and down, wrapping around the borders.

However,

• if the square to the right and down has already been filled,
• or if you are in the lower right corner,
• then you must move to the square straight up instead.

Here's the 5x5 square that you get if you follow this method:

 11  18  25   2   9
 10  12  19  21   3
  4   6  13  20  22
 23   5   7  14  16
 17  24   1   8  15 

• whose input is the number n and
• whose output is the magic square of order n if n is odd.