Solution to Magic Squares

The stairway method for magic squares of uneven order. Follow the construction of a magic square of the third order, as shown opposite. First draw the empty square. Then write the number 1 in the box outside the square, above the centre of the first row. Next enter the number 2 one box lower and to the right (and thus inside the square). Then enter the number 3 one box lower and to the right, and thus outside the square. The next three numbers (4, 5 and 6) form a diagonal row sloping to the left from the first row. The numbers 7, 8 and 9 are entered below this. See animation. The numbers outside the square are now entered on the opposite side in the remaining open boxes.

In a square of the fifth order, each diagonal row is made up of five boxes and you enter the number 1 outside the square, two boxes above the centre of the first row. Then follow the same method as for the square of the third order.

Here is the solution for the pandiagonal magic square. If you add up the broken diagonals, the sum is still 34. Example 1: 1+13 and 12+8 = 34. Example 2: 13+16 and 2+3 = 34.

Here are the solutions for the magic square with fractions.