Doubly Even Squares in the dimension of 4n x 4n

Last week, the children explored odd ordered magic squares where every row, column and both diagonals has the same sum. 

This week we looked at an algorithm for even ordered squares that are multiples of 4 like 4x4, 8x8, 12x12, 16x16, etc. Use a ruler to create your diagonals.

Step 1: put dotted lines diagonally through each 4x4 square.

Step 2: Count from 1 to 16 going top to bottom and left to right but only record the numbers in the squares with diagonal lines.

Step 3: Again, count from 1-16 again but this time start with the bottom right square going right to left and bottom to top and only record numbers in which there are no diagonals. This step takes more concentration so touch each cell with your pencil as you count.

Remember, you are counting from the bottom row to the top and from right to left. 

Step 4: You now have a “potential” magic square but you should add up a row, a column and a diagonal to make sure you find the magic number.

1 + 15 + 14 + 4 = 34   a row

13 + 10 + 7 + 4 = 34 a diagonal

1 + 12 + 8 + 13 = 34 a column

The process for 8x8, 12x12 and so on is exactly the same but the diagonals have to hit every 4th vertex. Use a ruler to connect each vertex at a 45 degree angle through each square's vertex.

The pdf provided has blank squares as well as with the diagonals provided. If you choose to use the blank squares, use a ruler and be careful to connect every fourth vertex.

Start to look for number patterns in the squares.