Relationships with the T-shapes, the T-total and the position of the stair shape on the grid.

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T- Total

By Gary Holmes

Introduction:

                In this investigation in which I am presenting, I am going to look at the relationships with the T-shapes, the T-total and the position of the stair shape on the grid. I will be observing patterns and I will look at the other stairs to see if I can notice other formulas for these. Finally, I hope to be able to find the formula for any size grids and any T-total

Look at the T-shape drawn on the 9 by 9     number grid.

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

This is called the T-total.

The number at the bottom of the T-shape is called theT-number.

The T-number for this T-shape is 20.

If you take the other numbers in the T-Shape away from the T-Number you get a T-Shape like this.

You will notice that the centre column of the T-Shape is going up in 9's because of the table size. With the table set out like this a formula can be worked out to find any T-Total on this size grid. This is done in the working below:-

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

= 5T-63

Now to test this formula to see if it works

For T-Total I will use the letter X

For the T-Number I will use the letter T

Join now!

So X = 5T-63

T = 20

X = 5x20-63

= 100-63

= 37

Now I will do two more to check to see if it will work anywhere on the grid.

T=43

X=5x43-63 24+25+26+34+43=152

X=215-63

X=152

T=49

X=5x49-63 30+31+32+40+49=182

X=245-63

X=182

I have tested the formula for three different T-numbers and the formula works for a 9 by 9 grid.

The full formula for this size grid is:- X=5T-63

When trying to fine out the T-Total in a 6 by 6 number grid,

If you take the other numbers in the T-Shape away from the T-Number you get a ...

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