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.
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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 = 5So the number in the middle is five. Let's write it:
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And then I can make it easier by removing 5 of the numbers I need to use.
1 , 2 , 3 , 4 , 6 , 7 , 8 , 9After 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 + _ = 15Now if we look at this like an equation it will be solved like this:
_ + 5 + _ = 15
_ + _ = 15 - 5
_ + _ = 10And 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 + 6And now you know what to do. All the sums which cost 15 are:
1 + 5 + 9
2 + 5 + 8
3 + 5 + 7
4 + 5 + 6The 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!