Moschopoulos II

A nice magic square results from a different method by Moschopoulos, where we move across the square like a knight while playing chess. The second method by Moschopoulos presented here works for all odd squares. If the order n is not divisible by three, even pandiagonal magic squares are created.

• Place the first number in the center cell on the top row.
• Determine the next cell by going one row to the right and two columns down like a knight.
• After exactly n steps, you reach an already occupied cell. Then perform an intermediate step that cyclically takes you four rows down from the last occupied cell.
• Whenever you are leave the square at one end, continue at the opposite side of the square.

Let's take a closer look at the algorithm for order n=5. At the beginning, we write the number 1 in the center cell of the top row and make the first four knight moves.

Now the 5 is entered and after a further knight move for the number 6 will determine a cell, which is already occupied by the number 1. At this point, the specified move sequence must be interrupted with a special intermediate move, simply by moving down four rows from the last occupied cell.

You can continue with these moves until the entire square is filled with the numbers 1, 2, 3, … , n2. The resulting magic square in this case is a pandiagonal magic square.

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