Skip to main content
Submitted by Niki on

Introduction:
Hi again! Today I am again with an easy thing, but actually easy.

The task with the solution:
Today I am starting to learn magic squares. Here is one type of exercise for magic squares:

Complete the magic square using the numbers 1 to 9. Each number can be used only once. The sum of the numbers in every row, column, and diagonal must be 15.

 

            

            

            

 

 

 

 

 


That is the task for today. An interesting thing about magic squares is that the number in the middle multiplied by 3 is the sum of the numbers in every row, column, and diagonal. In this exercise, I see the sum is 15, so to find the middle number, we need to divide by 3.

15 : 3 = 5

So the number in the middle is five. Let's write it:

 

            

            

            

5

 

 

 

 

         

        

Then I can make it easier by removing 5 from the numbers I need to use.

1 , 2 , 3 , 4 , 6 , 7 , 8 , 9

After this, we see that five is in all of the 4 places for 3 numbers whose sum needs to be 15:

Do you know how to continue? I will show my way to continue. We know that all the sums will look like this:

_ + 5 + _ = 15

Now, if we look at this like an equation, it will be solved like this:

_ + 5 + _ = 15 
_ + _ = 15 - 5
_ + _ = 10

Now I need to find 4 sums of two numbers between 1 and 9 (without 5) that equal 10. 
We have the numbers 1, 2, 3, 4, 6, 7, 8, 9.
You can try to write the sums before looking at the answer. Here it is:

1 + 9
2 + 8
3 + 7
4 + 6

And now you know what to do. All the sums that equal 15 are:

1 + 5 + 9
2 + 5 + 8
3 + 5 + 7
4 + 5 + 6

The last thing that we need to do is to put these sums in the magic square. It doesn't matter where you put each sum. I will put them like this:

8

    1      

     6      

     3      

5

7

4

9

2

The end:
This is one of the exercises for magic squares. You can open the other lessons, like Magic squares - unknown in the square, to learn more. Now, bye!