Write number like this:
As in the calendar; mark four numbers in a square and find the difference of diagonal products. Is it the same for all squares of four numbers?
Explain why this is so, using algebra.
Instead of a square of four numbers, take a square of nine numbers and mark only the numbers at the four corners.
What is the difference of diagonal products? Explain using algebra.
In the multiplication table made earlier, take a square of nine numbers, instead of four, and mark the numbers at the four corners:
What is the difference of diagonal sums?
Explain using algebra, why this difference is the same for all such squares.