Number Grid Investigation

Number Grid Investigation

In numerical way I am going to multiply the top left number with right

bottom number and the top right number with bottom left number and

than I am going to find the difference between the products. The

difference of product is going to be same as the size of a grid (in

width) in 2 x 2 size. In 3 x 3 size the difference going to be four

times bigger than a grid (width) size. I will also use the 5 x 5 grid,

6 x 6 grid and 7 x 7 grid to see how it works.

E.g.

5 x 5 Grid

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

20 x 24 = 480

19 x 25 = 475

Difference between these products is 5.

In algebra I am going to use different formula to find out the correct

answer.

This is the formula that I am going to use:

n = Top left corner

n + 1 = Top right corner

n + 5 = Bottom left corner

n + 6 = Bottom right corner

(n + 1) (n + 5) - (n) (n + 6)

n2 + 5n + n + 5 - n2 - 6n (n2 cancel out with - n2, 5n + n cancel out

with - 6n)

5 left over

This is the product difference of 2 x 2 in a 5 x 5 grid.

8 x 8 Grid

1

2

3

4

5

6

7

8

9

10

11

12

13