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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 start learning magic squares. Here one type exercise of 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 the 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 that the sum is 15 so to find the number in the middle we need to devide by 3.

15 : 3 = 5

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

 

            

            

            

5

 

 

 

 

         

        

And then I can make it easier by removing 5 of the numbers I need to use.

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

After this we see that five is at all of the 4 places for 3 numbers which 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

And now I need to find 4 sums of two numbers between 1 to 9 ( without 5 ) which cost 10
We have the numbers 1, 2, 3, 4, 6, 7, 8, 9.
You can try to write the sums before look at the answer. Here is it:

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

And now you know what to do. All the sums which cost 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 this sums in the magic square. It doesn't matter where you put each of the sums. 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 for them to learn more. Now, bye!