David sent in this quite neat explanation:The numbers that are diagonal to each other add up to make the same number because you're adding one that's lower or higher by 1, 2 or 3 to the number beside it.
For example, in a 3x3 square, the number in the top right is 2 more than the number in the top left. The number in the bottom left is 2 less than the number in the bottom right. So when we add the top left and bottom right, and the top right and bottom left, we get the same total.
Esther who is 8 used letters to stand for the numbers (we call this algebra) and shows why the totals are the same:I have found out that the sum of each diagonal pair in a square is always the same as the other in the same colour. We can write any square out like this:
Thank you Esther, that's a very clear way of explaining.
Even if you haven't met algebra, you can still use ordinary words as David did. Well done!