Number Grids

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Number Gridss

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Use the following rule: Find the product of the top left number and the bottom right number in the square. Do the same thing with the bottom left and top right numbers in the square. Calculate the difference between these numbers.

INVESTIGATE!

To start this assignment I randomly selected an area in the matrix to put boxes of size; (2x2) (3x3) (4x4) (5x5) (6x6) up to (10x10) I repeated these in different areas.

Here are my results:

(2x2) every time gave a difference of 10

(It was -10 but as the question asked for a difference I changed this to a positive consistently)

(3x3) every time gave a difference of 40

(4x4) every time gave a difference of 90
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(5x5) every time gave a difference of 160

(6x6) every time gave a difference of 250

(7x7) every time gave a difference of 360

(8x8) every time gave a difference of 490

(9x9) every time gave a difference of 640

(10x10) every time gave a difference of 810

Next I tried to find a pattern; I saw that the differences had a difference between them going up in twenty's starting with 30 then 50 etc. but realized that it was not helping or going anywhere.

I then looked at the similarity ...

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