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 T-Shape like this.
This time the centre column of the T-Shape is going up in 6's because of the table size. The formula for this size grid is:-
T-Total = T-13+T-12+T-11+T-6+T
= 5T-42
Now to test this formula to see if it works, again
For the T-total I will use the letter X
For the T-Number I will use the letter T
So X = 5T-42
T = 14
X = 5x14-42
= 70-42
= 28
Now I will do two more to check to see if it will work anywhere on the grid.
T=22
X=5x22-42 9+10+11+16+22=68
=110-42
= 68
T=35
X=5x35-42 22+23+24+29+35=133
=175-42
=133
I have tested the formula for three different T-numbers and the formula works for a 6 by 6 grid.
The full formula for this size grid is:- X=5T-42
Below is a grid with parts of the formula in. I will use this to
figure out a formula for any T-Total on any width grid.
T-total = T-2G-1
T-2G
T-2G+1
T-G
T
X=5T-7G
If the Grid Width (= G), and the T-Number (= T), the T-Total (= X) is calculated by
X=5T-7G
Now I'm going to try the grid that I drew earlier i.e. G=9
The formula is X=5T-7G
Which changes to X=5T-7x9
X=5T-63
I will now try the formula on a 7 by 7 grid.
X=5X17-49 (2+3+4+10+17=36
X=85-49
X=36
I am now going to try this formula on a 3 by 5 grid.
X=5X8-21 (1+2+3+5+8=19
X=40-21
X=19
I am now going to try this formula on a 6 by 10 grid.
X=5X33-42 (20+21+22+27+33=123
X=165-42
X=123
Now I have worked the formula out for the T-Shape in the one position, I am going to translate the T-Shape to different positions and investigate the relationships between the T-Total, the T-number and the grid size.
A 3 by 3 grid can be used for the other 3.
T
T+G
T+2G
T+2G-1
T+2G+1
7G+5T
X=7G+5T=7x3+5x2
=21+10 (2+5+7+8+9=31)
=31
I will now try this new formula on a 4 by 7 grid.
7G+5T
x=7x4+5x10 (17+18+19+14+10=78)
=28+50
=78
I will now try it on a 8 by 3 grid.
7G+5T
x=7x9+5x2 (19+20+21+11+2=73)
=56+10
=73
I have tried this new formula for an inverted T and it works, the formula is: 7G+5T
T
T-1
T-2
T-2-G
T-2+G
5T-7
X= 5T-7=5x6-7
=30-7 (1+4+7+5+6=23)
=23
I will now try the new formula on a 4 by 4 grid
5T-7
X=5x11-7 (5+9+13+10+11=48)
=48
And on a 4 by 9 grid.
5T-7
x=5x19-7 (13+17+21+18+19=88)
=88
I have tested this new formula for a side ways T the formula works it is: 5T-7
T
T+1
T+2
T+2+G
T+2-G
5t+7
The formula is 5T+7
X=5T+7=5x4+7
=20+7 (3+6+9+5+4=27)
=27
I will now try the new formula on a 6 by 6 grid.
5T+7
X=5x15+7 (11+17+23+16+15=82)
=82
And on a 11 by 5 grid.
5T+7
X=5x28+7 (28+29+30+19+41=147)
=147
I have tested this new formula for a side ways T the formula works it is: 5T+7
The formula for a this way up is: X=5T-7G
The formula for a this way up is: X=7G+5T
The formula for a this way up is:X=5T+7
The formula for a this way up is: X=5T-7
____________________________________________________
I am now going to investigate the effect on the T-Total when the T-Shape is transformed, rotated 90°, both T-Shapes will have the same T-Number like this:
T- Number = 12
Purple T-Total = 25
Grey T-Total = 67 a difference of 42….. The formula 5T - 7G + 42
Now I'm going to see what happens on a 6 by 6 width Grid
T- Number = 14
Purple T-Total = 33
Grey T-Total = 82 a difference of 49….. The formula 5T - 7G + 49
7 by 7 width Grid
T- Number = 16
Purple T-Total = 41
Grey T-Total = 97 a difference of 56….. The formula 5T - 7G + 56
Table of Results
Now I will rotate it again 180° from it's original place
T- Number = 12
Purple T-Total = 25
Grey T-Total = 95 a difference of 70….. The formula 5T - 7G + 70
Now I'm going to see what happens on a 6 by 6 width Grid
T- Number = 14
Purple T = 28
Grey T = 112 a difference of 84….. The formula 5T - 7G + 84
7 by 7 Grid
T- Number = 16
Purple T-Total = 31
Grey T-Total = 129 a difference of 98….The formula 5T - 7G + 98
Conclusion: The amount of numbers in the T decide the number before N in my formula. The number before the W is found by
(T-total - 2T) divided by the top right number of the grid.
By Gary Holmes