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'Diagonal Sums' printed from http://nrich.maths.org/
Here is a $100$ square with some of the numbers shaded:
Look at the green square which contains the numbers $2, 3, 12$ and
What is the sum of the numbers that are diagonally opposite each
Do you notice anything?
Look at the pink square.
Does the same thing happen?
What about the yellow square?
You could try with other squares which have four numbers in
Why does this happen?
Look at the squares shaded red. They form the corners of a large
$3$ by $3$ square.
If you add the numbers diagonally opposite each other, what
What happens for squares of different sizes?
You may like to print off this 100 square
to try out
some different squares of numbers.