Number grids.

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Number grids.

By Nicole Highfield.

The aim of this investigation is to find the differences of N x N squares that are inside a 10 x 10 grid (shown bellow) then to see if there is a rule or pattern that will connect the size of the N x N to the size.

To be able to find the difference of an N x N square, I will start at the smallest one, which is 2 x 2. The corners have to be multiplied together in a diagonal way. My 2 x 2 square is: -

2 x 23 = 276

3 x 22 = 286

Then to find the difference I have to minus the smallest answer from the biggest one. This is the to find the differences in all squares.

286 - 276 = 10

Using 2 x 2 array (square) of number I have found a difference between the two corners, this is a difference of ten. I will check this by doing some more 2 x 2 arrays, and work my way to bigger squares so that the investigation does not get complicated.

88 89

98 99

88 x 99 = 8712

89 x 98 = 8722

8722 - 8712 = 10

55 56

65 66

55 x 66 = 3630

56 x 65 = 3640

3640 - 3630 = 10

72 73

82 83

72 x 83 = 5976

73 x 82 = 5986

5986 - 5976 = 10

From doing these three checks I have found that the difference in a 2 x 2array is ten, to be completely sure that it is ten in any place in the 10 x 10 grid I am going to put it into a N x N formula.
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X X+1

X+10 X+11

This box is called an x-box and it is going to produce my N x N formula, which will then tell me if the difference is ten, or not.

X X+1

X+10 X+11

In multiplying the diagonal corners I will get two formulas, these are then going to show the difference of the 2 x 2 array.

The brackets need multiplying out first.

X(X+11) = X +11X This is the 1st formula.

(X+1) (X+10) = X +10X+X+10 This is the 2nd formula.

The second formula ...

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