# Squares

**Discrete Mathematics**Level 4

You have a \(10 \times 10\) grid containing the numbers 1 - 100 as shown below, all in order, except that 13 is switched with 40, (in red).

Now for the question...

How many ways can you pick two different \(3 \times 3\) groups of 9 numbers (like the one in green above) such that the sum of the 9 numbers inside is the same for both of them?