Number grid coursework

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Number Grid Coursework.

For this coursework I shall investigate and explain thoroughly the
patterns, rules and formulae found in a number grid when placing a
square at any point in the grid, multiplying the top left and bottom
right corners and the top right and bottom left corners and finding
the difference. In the beginning of my investigation I’d like to write the main purpose of it. I want to find one common formula that would help me to find difference on any x by x square on 10 by 10 number grid. Let’s start the investigation!

I have a 2 by 2 square in a 10 by 10 number grid.

I am going to investigate it and find the difference.

 

First I shall find the product of the top left number and the bottom right number in the square.

I shall find the product of the top right and bottom left numbers.

Now I shall find difference between these products.

Let’s now move the square and do same calculations.

The product of the top left number and the bottom right number in the square is:

The product of the top right and bottom left numbers is:

Difference between these products is:

I have noticed a pattern from the two squares that I have done. There has been a difference of 10. I predict that there should be a difference of 10 for the next square in the number grid.

Join now!

Let’s check if my prediction was correct.

The product of the top left number and the bottom right number in the square will be:

The product of the top right and bottom left numbers will be:

Difference between these products will be:

Conclusion:

My prediction was correct. There was a difference of 10. This may mean that it doesn't matter which 2 by 2 square you select within a 10 by 10 number grid the difference will still be 10.

As I see, where ever we move the square there ...

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