T-Total. I can work out a formula to find the T-total on a 9 by 9 grid.

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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. T would represent this.

The 20 at the bottom of the T shape will be called the T-Number. N would represent this.

 

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 = N-19+N-18+N-17+N-9+N

T = 5N-63

Time for me to check if this formula works:

N means T-Number.

N = 20

T = 5x20-63

T = 100-63

T = 37

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

T = 112

T = 5x35-63

T = 175-63

T = 112

T = 272

T = 5x67-63

T = 335-63

T = 272

So now you know the formula for the 9 by 9 grid is T =5N-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 = 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 = N+N-5+N-9+N-10+N-11

T = 5N-35

N = 12

T = 5x12-35

T = 60-35

T = 25

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

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T = 60

T = 5x19-35

T = 95-35

T = 60

T = 80

T = 5x23-35

T = 115-35

T = 80

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

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

G = Grid Width

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

T = N+N-G+N-2G+N-2G-1+N-2G+1

T =5N-7G

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