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 am going to find the relationship between the T-Total and the T-number on a 7x7 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 7x7 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-15+n-14+n-13+n-7
T= 5n-15-14-13-7
T= 5n-49
T= T-Total
n= T-number
The formula is T=5n - 49 for the 7x7 grid.
I will test this formula be using the T-shape below.
.
The T-total for this shape is 31 and the T-number is 16. I will use this to work out the formula for this grid.
31=5n-49
31=5x16-49
31=80-49
I will use this formula for another T-shape and see if it works for that T- number as well. I will test 17 for the T-number where the total is 36.
36=5n-49
36=5x17-49
36=85-49
The formula also works for this.
7x7 Grid formula to find the T-Total = 5n-49
6x6 Grid
I am going to find the relationship between the T-Total and the T-number on a 6x6 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 6x6 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-13+n-12+n-11+n-6
T= 5n-13-12-11-6
T= 5n-42
T= T-Total
n= T-number
The formula is T=5n - 42 for the 6x6 grid.
I will test this formula be using the T-shape below.
.
The T-total for this shape is 28 and the T-number is 14. I will use this to work out the formula for this grid.
28=5n-42
28=5x14-42
28=70-42
I will use this formula for another T-shape and see if it works for that T- number as well. I will test 15 for the T-number where the total is 33.
33=5n-42
33=5x15-42
33=75-42
The formula also works for this.
6x6 Grid formula to find the T-Total = 5n-49
The General Formula for different Grid sizes
I am going to find the relationship between the T-Total, the T-number and the grid size. I will try and find a formula to work out the T-Total from the T-number and the grid size.
The Formulas that I have gathered
Each of these formulas are
T=5n-x
x= The number that is subtracted
In all of these formulas I have noticed that each of the subtractions made is the grid size multiplied by 7. I.e. For a 6x6 grid use the number 6. E.g. 5n-(7x6)
Below is the formula that I have worked out for the general formula of different grid sizes.
T=5n-(7xG)
G= Grid size i.e. for a 6x6 grid use the number 6. E.g. 5n-(7x6)
Here are the results that I have gathered from the tests that I have done.
9x9
8x8
7x7
6x6
I will test this formula that I have worked out on each of the first T-numbers on each of the grid sizes.
9x9 grid
5x20-(7x9)= 37
The formula has worked for the 9x9 grid
8x8 grid
5x18-(7x8)=34
The formula has worked for the 8x8 grid
7x7 grid
5x16-(7x7)=31
The formula has worked for the 7x7 grid
6x6 grid
5x14-(7x6)=28
The formula has worked for the 6x6 grid
The general grid size formula to find the T-Total = 5n-(Gx7)
Relationships between the T-Total and the T-number using rotations of 180°
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, when the t-shape is rotated 180°.
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 73 and the T-number is 2. I will use this to work out the formula for this grid.
73=5n+63
73=5x2+63
73=10+63
I will use this formula for another T-shape and see if it works for that T- number as well. I will test 3 for the T-number where the total is 73.
78=5n+63
785x3+63
78=15+63
The formula also works for this.
9x9 Grid formula to find the T-Total = 5n+56
8x8 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, when the t-shape is rotated 180°.
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+15+n+16+n+17+n+8
T= 5n+15+16+17+8
T= 5n+56
T= T-Total
n= T-number
The formula is T=5n + 56 for the 8x8 grid.
I will test this formula be using the T-shape below.
.
The t-total for this shape is 66 and the T-number is 2. I will use this to work out the formula for this grid.
66=5n+56
66=5x2+56
66=10+56
I will use this formula for another T-shape and see if it works for that T- number as well. I will test 3 for the T-number where the total is 71.
71=5n+56
71=5x3+56
71=15+56
The formula also works for this.
8x8 Grid formula to find the T-Total = 5n+56
The General Formula for different Grid sizes
I am going to find the relationship between the T-Total, the T-number and the grid size when the t-shape is rotated 180°. I will try and find a formula to work out the T-Total from the T-number and the grid size.
The Formulas that I have gathered
Each of these formulas are
T=5n+x
x= The number that is added on
In all of these formulas I have noticed that each of the additions made is the grid size multiplied by 7. I.e. For an 8x8 grid use the number 8. E.g. 5n+(7x8)
Below is the formula that I have worked out for the general formula of different grid sizes.
T=5n+(7xG)
G= Grid size i.e. for a 9x9 grid use the number 9. E.g. 5n+(7x9)
Here are the results that I have gathered from the tests that I have done.
9x9
I will test this formula that I have worked out on each of the first T-numbers on each of the grid sizes.
9x9
8x8
I will test this formula that I have worked out on each of the first T-numbers on each of the grid sizes.
9x9 grid
5x2+(7x9)= 66
The formula has worked for the 9x9 grid
8x8 grid
5x2+(7x8)=73
The formula has worked for the 8x8 grid
The general grid size formula to find the 180°
T-shape T-Total = 5n+(Gx7)
Relationships between the T-Total and the T-number using rotations of 90° Clockwise
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, when the t-shape is rotated 180°.
The table below shows the results that I have gathered from the T-shapes on the 9x9 grid above.
I have worked out the formula as shown below:
The formula is T=5n + 7 for the 9x9 grid.
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, when the t-shape is rotated 90° Clockwise.
The table below shows the results that I have gathered from the T-shapes on the 8x8 grid above.
I have worked out the formula as shown below:
The formula is T=5n + 7 for the 8x8 grid.
The General Formula for different Grid sizes
I am going to find the relationship between the T-Total, the T-number and the grid size when the t-shape is rotated 90° clockwise. I will try and find a formula to work out the T-Total from the T-number and the grid size.
The Formulas that I have gathered
The Formula for all of the grid sizes is 5n+7
The general grid size formula to find the clockwise 90°
T-shape T-Total = 5n+7
Relationships between the T-Total and the T-number using rotations of 90° Anti-Clockwise
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, when the t-shape is rotated 90° anti-clockwise.
The table below shows the results that I have gathered from the T-shapes on the 9x9 grid above.
I have worked out the formula as shown below:
The formula is T=5n - 7 for the 9x9 grid.
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, when the t-shape is rotated 90° anti-clockwise.
The table below shows the results that I have gathered from the T-shapes on the 8x8 grid above.
I have worked out the formula as shown below:
The formula is T=5n - 7 for the 8x8 grid.
The General Formula for different Grid sizes
I am going to find the relationship between the T-Total, the T-number and the grid size when the t-shape is rotated 90° anti-clockwise. I will try and find a formula to work out the T-Total from the T-number and the grid size.
The Formulas that I have gathered
The Formula for all of the grid sizes is 5n-7
The general grid size formula to find the anti-clockwise 90°
T-shape T-Total = 5n-7
Relationships between the T-Total and the T-number using rotations of 45° Clockwise
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, when the t-shape is rotated 45° clockwise.
The table below shows the results that I have gathered from the T-shapes on the 9x9 grid above.
I have worked out the formula as shown below:
The formula is T=5n - 56 for the 9x9 grid.
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, when the t-shape is rotated 45° clockwise.
The table below shows the results that I have gathered from the T-shapes on the 8x8 grid above.
I have worked out the formula as shown below:
The formula is T=5n-49 for the 8x8 grid.
The General Formula for different Grid sizes
I am going to find the relationship between the T-Total, the T-number and the grid size when the t-shape is rotated 45° clockwise. I will try and find a formula to work out the T-Total from the T-number and the grid size.
The Formulas that I have gathered
Each of these formulas are
T=5n-x
x= The number that is added on
In all of these formulas I have noticed that each of the additions made is the grid size minus 1 multiplied by 7. I.e. For an 8x8 grid use the number 7. E.g. 5n-7(8-1)
Below is the formula that I have worked out for the general formula of different grid sizes.
T=5n-7(G-1)
G= Grid size i.e. for a 9x9 grid use the number 9. E.g. 5n-7(9-1)
I will test this formula that I have worked out on each of the first T-numbers on each of the grid sizes.
9x9 grid
5x28-7(9-1)= 84
The formula has worked for the 9x9 grid
8x8 grid
5x25-7(8-1)=49
The formula has worked for the 8x8 grid
The general grid size formula to find the clockwise 45°
T-shape T-Total = 5n-7(G-1)
A Table of Formulas that I have found
By Luke Scowcroft 10-0