T-Totals and T-Shapes
T-Totals and T-numbers
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This is the 9 x 9 Grid displaying the first kind of T I shall be looking at, as with this T and all other T's I shall be trying to find out a formula with which will tell me how to work out the T-Total of a T-Shape.
The Numbers that have been highlighted in Purple will make my first T-shape. The T number for this shape is 20, as it is the number at the tip if the T (highlighted in yellow). The T total for this shape is 37 as it is the result off all the numbers in the T added together (1+2+3+11+20 = 37)
You will notice that as the T progresses downwards the number increases by 9 (2+9 = 11, 11+9 =20) as this is the width of the grid. In the formula I will show this Number will be known as G or grid size.
To get the formula I constructed a similar T-Shape however looking at subtraction rather than addition. T in this Shape stands for the T-Number which in this case is 20.
T-2G-1
T-2G
T-2G+1
T-G
T
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To test the accuracy of my Formula I will try it other T's in the 9x9 Grid and then test with and altered grid size:
T-Number = 32
T-Total= 13+14+15+23+32 = 97
5T - 7G = T Total
160 - 63 = 97
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T-Number = 77
T-Total= 58+59+60+68+77 = 322
5T - 7G = T-Total
385 - 63 =322
This T-shape has been drawn on a 6x3 Grid, meaning G =6:
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T-Number = 14
T-Total= 1+2+3+8+14 = 28
T-Totals and T-numbers
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This is the 9 x 9 Grid displaying the first kind of T I shall be looking at, as with this T and all other T's I shall be trying to find out a formula with which will tell me how to work out the T-Total of a T-Shape.
The Numbers that have been highlighted in Purple will make my first T-shape. The T number for this shape is 20, as it is the number at the tip if the T (highlighted in yellow). The T total for this shape is 37 as it is the result off all the numbers in the T added together (1+2+3+11+20 = 37)
You will notice that as the T progresses downwards the number increases by 9 (2+9 = 11, 11+9 =20) as this is the width of the grid. In the formula I will show this Number will be known as G or grid size.
To get the formula I constructed a similar T-Shape however looking at subtraction rather than addition. T in this Shape stands for the T-Number which in this case is 20.
T-2G-1
T-2G
T-2G+1
T-G
T
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To test the accuracy of my Formula I will try it other T's in the 9x9 Grid and then test with and altered grid size:
T-Number = 32
T-Total= 13+14+15+23+32 = 97
5T - 7G = T Total
160 - 63 = 97
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T-Number = 77
T-Total= 58+59+60+68+77 = 322
5T - 7G = T-Total
385 - 63 =322
This T-shape has been drawn on a 6x3 Grid, meaning G =6:
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9
0
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T-Number = 14
T-Total= 1+2+3+8+14 = 28
