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Multiplication Square Poster

Age 11 to 14
Challenge Level

For 2 by 2 squares, the difference between the diagonal sums is always 1

For 3 by 3 squares, the difference between the diagonal sums is always 4

For 4 by 4 squares, the difference between the diagonal sums is always 10

 

Why?

Say the top left corner of the square is on $a\times b$.

2 by 2 square:

 

3 by 3 square:

 

4 by 4 square: