Making 4 x 4 Magic Squares

Magic Squares are covered in a lot more detail in Murderous Maths

Kjartan shows how this magic square can produce the target number in at least 24 different ways. These include the 4 horizontal and 4 vertical lines. The challenge is to see if you can recall at least 16 more ways from Kjartan's demonstration!

• Any "target" number can be chosen for the square, but it's best between 20 and 50.
• The numbers in grey squares remain the same.
• The numbers in yellow squares are dependent on the "target number".
• x = (the target number - 20). Therefore if the target is 39, x = (39-20) = 19.
• Fill in x and also (x-1), (x+1) and (x+2) in the indicated places.

This completed square adds up to 39 in just about every way you can think of. (Try dividing it into four 2x2 squares and see what the numbers in each square add to. Also mark out a square of any block of 3x3 squares then add the four numbers in the corners of the 3x3 square.)

8 11 19 1 18 2 7 12 3 21 9 6 10 5 4 20

Teacher Resource Page

The Murderous Maths Home Page