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Maths Coursework

T-Total

1. 

Here is a 9 by 9 grid.

The total of the numbers within the T shape is 1+2+3+11+20=37

I will call this the T-total.

The 20 at the bottom of the T shape will be called the T-Number.

 

Here is the T shape by itself. As you can see the middle column is going down in 9’s because the grid size is 9 by 9.

Here is a converted version of the original. This is so I can work out a formula to find the T-total on a 9 by 9 grid.

T-Total=T-19+T-18+T-17+T-9+T

T-Total=5T-63

Time for me to check if this formula works:

T means T-Number.

T=20

T-Total=5x20-63

T-Total=100-63

T-Total=37

To make sure it is not a fluke, I will do 2 more checks on the same grid size.

T-Total=112

T-Total=5x35-63

T-Total=175-63

T-Total=112

T-Total=272

T-Total=5x67-63

T-Total=335-63

T-Total=272

So now you know the formula for the 9 by 9 grid is T-Total=5T-63

2.

I will now find the formula for a 5 by 5 grid.

Here is the 5 by 5 grid.

The total of all the numbers inside the T-shape is 1+2+3+7+12=25

As you can see, the middle column is going down in 5’s because of the grid size.

T-Total=25

Here is a converted version of the original. This is so I can work out a formula to find the T-total on a 5 by 5 grid.

T-Total= T+T-5+T-9+T-10+T-11

T-Total=5T-35

T=12

T-Total=5x12-35

T-Total=60-35

T-Total=25

To make sure it is not a fluke, I will do 2 more checks on the same grid size.

T-Total=60

T-Total=5x19-35

T-Total=95-35

T-Total=60

Join now!

T-Total=80

T-Total=5x23-35

T-Total=115-35

T-Total=80

So now you know the formula for the 5 by 5 grid is T-Total=5T-35

Now I will find a formula to solve any T-Total on any size table.

N=Grid Width

Here is the full formula to work when solving out the formula for the T-Shape on a certain grid size.

T-Total=T+T-n+T-2n+T-2n-1+T-2n+1

T-Total=5T-7n

Now lets try that formula on the 5 by 5 grid.

T-Total=5T-7n

T-Total=5T-7x5

T-Total=5T-35

That is the formula to work ...

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