Types of number grids that I will be working with.
(2x2) = (2 rows x 2 columns) 4 numbers
(3x3) = (3 rows x 3 columns) 9 numbers
(4x4) = (4 rows x 4 columns) 16 numbers
I will begin my investigation by randomly selecting two (2x2) number grids. I will then multiply the top left by the bottom right of the (2x2) number grids and then multiply the top right by the bottom left, after that I will subtract the two totals to find the difference. if there is any pattern then I will randomly select a third number grid and try to predict the result. I will do the same thing again but instead of using a (2x2) number grid I will use a (3x3) and a (4x4) number grid.
(2x2) number grids
8 x 19 = 152
9 x 18 = 162
Difference = 10
33 x 44 = 1452
34 x 43 = 1462
Diffrence
I have noticed a pattern from the two number grids that I have done (highlighted in red) there has been a difference of 10 I predict that there should be a difference of 10 for the next number grid (highlighted in blue).
87 x 98 = 8526
88 x 97 = 8536
Difference = 10
My prediction was correct there was a difference of 10 that means it doesn't matter which (2x2) number grid you select within a (10x10) number grid the difference will still be 10.
I am now going to do the same thing that I did before but instead of a (2x2) number grid I an going to be using a (3x3) number grid.
(3x3) number grids
44 x 66 = 2904
46 x 64 = 2944
Difference = 40
68 x 90 = 6120
70 x 88 = 6160
Difference = 400
I have noticed a pattern with this type of number grid as well from the two number grids that I have done (highlighted in red) there has been a difference of 40 I predict that there should be a difference of 40 for the next number grid (highlighted in blue).
61 x 83 = 5063
63 x 81 = 5103
Difference = 40
My prediction was correct there was a difference of 40 that means it doesn't matter which (3x3) number grid you select within a (10x10) number grid the difference will still be 40.
So far I have done a (2x2) and a (3x3) number grid there has been a difference of 30 between the two results I am now going to do a (4x4) number grid to see if there is a pattern in the results. if there is a pattern then I will be able to predict the result for any number grid for example (7x7).
(4x4) number grid
4 x 37 = 148
7 x 34 = 238
Difference = 90
42 x 75 = 3150
45 x 72 = 3240
Difference = 90
I have noticed a pattern with this type of number grid as well from the two number grids that I have done (highlighted in red) there has been a difference of 90 I predict that there should be a difference of 90 for the next number grid (highlighted in blue).
57 x 90 = 5130
60 x 87 = 5220
Difference = 90
My prediction was correct there was a difference of 90 that means it doesn't matter which (4x4) number grid you select within a (10x10) number grid the difference will still be 90.