Formula = 5n – 63
I tested that when:
n = 80
T = 265
Below is a t-shape, and in each cell how the number is connected with n on a 9x9 grid
I will know check the formula
(n)+(n-9)+(n-19)+(n-18)+(n-17)
= 5n – 63
so this is correct
10x10 Grid
Formula = 5n – 70
I tested that when:
n = 88
T = 370
Below is a t-shape, and in each cell how the number is connected with n on a 10x10 grid
I will now check the formula
(n)+(n-10)+(n-20)+(n-19)+(n-21)
=5n-70
so this is correct
Now I will show how to work out the formula of any Grid
Let GxG = Grid Size
Let G = Length/width of grid
I will now construct part of a random GxG Grid and then prove my Formula of 5n-7G
32 Is my T-Number
N = 32
5n = 160
G = 15
7G = 105
I now have enough data to prove that my formula works
5n - 7G
160 – 105 = 55
So my Formula works because T = 55
I am now going to translate my T shape 2 to the right on a 10x10 grid
10x10 Grid
n=22
T=50
I will now work out a general T, that has been translated 2 to the right, for any grid size because I can see the connection with a translation 2 to the right and the grid.
((n-2G)+1) +((n-2G)+2) + ((n-2G)+3)
I will now get a formula by drawing part of a GxG grid and using a T-shape that has been translated x times to the right.
n=32
T=85
Let x = number of times/squares translated to the right
I will now work out a general T that has been translated x times to the right
I will now try to prove that my formula works
Let y = Number of times/squares translated down
I will now do all the same things as I did translating the T shape across, but now I am going to Translate it down, which means I will be finding a general T-shape that has been moved y times down for any grid size and a general formula.
Then I will combine both Moving the T shape Across And moving it down, which will enable me to get a general formula for a general T shape that has been moved x times right and x times down.
10x10 grid
n=22
T=140
Bradley Robertson™ 10R Page of