I have been set the task to find formulas that I need to find t the "T-Total" which is explained below:

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Introduction

I have been set the task to find formulas that I need to find t the “T-Total” which is explained below:

Have a look at the T-shape highlighted on the nine by nine number grid above.

The total of the number in the T-shape is:  1+2+3+11+20=37

This is called the “T-Total” (which this time added up to 37).

The number at the bottom of the T-shape is called the “T-number”

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

        For the task that I have been set I have to translate the T-shape to different parts of the grid and work out the T-Total.  I have to find the relationships with the T-total and the T-number, and find out a formula.

        To take this task further I will use grids of different sizes. Translate the shapes to different positions.  Then I will work out the T-Total.  Then I will find the relationship between the T-Total, T-number and the grid size, and find out a formula.

        To take this task even further I will use grids of different sizes again.  Try other transformations and combinations of different transformations.  I will find the relationships between the T-Total, the T-numbers, the grid size and the transformations and find a formula.

Relationships between the T-Total and the T-number

9x9 Grid        

I am going to find the relationship between the T-Total and the T-number on a 9x9 grid and try and find a formula to work out the T-Total from the T-number.

        The table below shows the results that I have gathered from the T-shapes on the 9x9 grid above. 

 

        I will try and work out the formula by finding the difference of the numbers and producing a formula.

Here is an example:

Here is the example shown as a formula:

n= T-number

Below is my working out for the formula:

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

T= 5n-19-18-17-9

T= 5n-63

T= T-Total

n= T-number

The formula is T=5n - 63 for the 9x9 grid.

I will test this formula be using the T-shape below.

.

The t-total for this shape is 37 and the T-number is 20.  I will use this to work out the formula for this grid.

37=5n-63

37=5x20-63

37=100-63

I will use this formula for another T-shape and see if it works for that T- number as well. I will test 21 for the T-number where the total is 42.  

42=5n-63

42=5x21-63

42=105-63

The formula also works for this.

9x9 Grid formula to find the T-Total = 5n-63

8x8 Grid

I am going to find the relationship between the T-Total and the T-number on an 8x8 grid and try and find a formula to work out the T-Total from the T-number.

The table below shows the results that I have gathered from the T-shapes on the 8x8 grid above. 

 

        I will try and work out the formula by finding the difference of the numbers and producing a formula.

Here is an example:

Here is the example shown as a formula:

n= T-number

Below is my working out for the formula:

T= n+n-17+n-16+n-15+n-8

T= 5n-17-16-15-8

T= 5n-56

T= T-Total

n= T-number

The formula is T=5n - 56 for the 8x8 grid.

Join now!

I will test this formula be using the T-shape below.

.

The t-total for this shape is 34 and the T-number is 18.  I will use this to work out the formula for this grid.

34=5n-56

34=5x18-56

34=90-56

I will use this formula for another T-shape and see if it works for that T- number as well. I will test 19 for the T-number where the total is 39.  

39=5n-56

39=5x19-56

39=95-56

The formula also works for this.

8x8 Grid formula to find the T-Total = 5n-56

7x7 Grid

I ...

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