Magic squares are fascinating mathematical creations. Essentially, they are grids populated with numbers, typically integers, that share a remarkable feature: the sum of the numbers in every row, column, and diagonal is the same, resulting in a singular, enchanting constant.

If you haven’t already checked, try 3×3 magic square first. Once you know how to make a 3×3 magic square, understanding 5×5 magic square becomes easier.

Materials required

– Grid paper

– A pencil

Directions

Take a grid paper. If you don’t have one, you can also draw a 5×5 square grid on a paper.

Next, mark blue squares outside the magic square grid as shown in the picture below.

Write numbers 1 to 25 in a specific pattern; starting with number 1, write numbers in diagonals as shown below.

To solve the magic square, let’s first focus on the 3×3 center square (highlighted in red border below). Draw the arrows as shown. The arrow directs where the numbers from the blue boxes needs to be moved in the center 3×3 square. For example, number 5 needs to be placed in the 4th row, 3rd column (between 12 and 18); number 21 will go between 8 and 14; and so on.

Does your grid look as shown in the picture below?

Next, let’s focus on the outer squares of the 5×5 grid. One at a time, move numbers from blue boxes to orange boxes as shown below. For example, number 16 should be placed between 3 and 9; number 22 should be moved between 9 and 15; and so on.

Once all the numbers from blue boxes are moved to orange boxes, you get the 5×5 magic square.

Check the sum of numbers in each row, each column and each diagonal. They all add to 65, for example 3+16+9+22+15=65, 3+20+7+24+11=66. Let’s check diagonal- 11+12+13+14+15=65. This is true for each row, each column and diagonals. The magic constant for 5×5 square created with numbers 1-9 is 65. What would it be if you were to create a 7×7 square?

Activity Extension

• You have tried 3×3, 5×5, 7×7 squares. Do you notice a pattern?
• If you use the same trick for even numbered magic square such as 4×4, would it work? Think and check if you come up with a similar 4×4 magic square as we got.
• Is it possible to create a magic square of a number greater than 100?

More Magic Squares

3×3 magic square

4×4 magic square

Magic square book