Challenge Level

Take an addition table from $1$ to $10$ (or any other that you like better!):

Now take a $3\times 3$ square of numbers on it, such as this
red one:

Now multiply the two diagonally
opposite corner numbers together:

And then find the difference between the two answers:

$5 \times 9 = 45$

$7 \times 7 = 49$

$49 - 45 = 4$

Now try the numbers in the green
square:

What is the answer?

Investigate other $3\times 3$ squares.

What do you notice?

Can you explain it?

Now try with $2\times 2$ squares and $4\times 4$
squares.

Can you predict your answers? What is happening?