What's in a name?

What do you notice about these squares of numbers? What is the same? What is different?

Problem

What's in a Name? printable sheet

Have a look at these two squares of numbers:

 

Image
A 3-by-3 grid of numbers. From left to right, the top row reads 1, 5, 7. The second row reads 3, 8, 2. The third row reads 4, 9, 6.
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A 3-by-3 grid of numbers. From left to right, the top row reads 8, 4, 7. The second row reads 6, 1, 2. The third row reads 5, 9, 3.

 

What do you see?

 

What is the same about the two squares? What is different?

'Magic' squares are square grids with a special arrangement of numbers in them. The arrangement is special because the numbers in each row, column and diagonal add up to the same total. (We could call this the 'magic total'.)

Looking at the left hand square above, if we add the top row of numbers, 1 + 5 + 7, we get a total of 13:

 

Image
A 3-by-3 grid of numbers. From left to right, the top row reads 1, 5, 7. The second row reads 3, 8, 2. The third row reads 4, 9, 6. The first row is crossed out and it says 1+5+7=13.

 

If we add the left hand column of numbers, 1 + 3 + 4, we get a total of 8.

So, we know already that this square is not a magic square as these two totals are different. 

Use the numbers 1 to 9 to create a magic square.

Can you find another way of doing it?

And another? And another? ...

What do you notice about your magic squares?