T Total Investigation Essay

4228 words - 17 pages

T-Total Investigation

PART 1

I am investigating the relationship between the T-total and T-number
on a 9 x 9 grid by using a variety of T-Shapes

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34 (+5)

= 39 (+5)

= 44

Formula = 5T - 56

I tested that when:

T = 63

n = 259

259 = 5T - 56

259 = (5 x 63) - 56

259 = (315) - 56

259 = 259

Formula works.

Below is a t-shape, and in each cell how the number is connected with
T on an 8x8 grid

T-17

T-16

T-15

T-8

T

Check the formula:

(T-17) + (T-16) + (T-15) + (T-8) + (T)

= 5T - 56

So this is correct

9x9 Grid

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T-number = 20

Numbers:

1 2 3 11 20

20-1 20-2 20-3 20-11 20

T-19 T-18 T-17 T-9 T

T-total = 37

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20

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T-number = 21

Numbers:

1 2 3 11 20

21-1 21-3 21-4 21-11 21

T-19 T-18 T-17 T-9 T

T-total = 42

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21

(T-19) + (T-18) + (T-17) + (T-9) + (T)

= 5T - 63

Let T-number = T

Let T-total = n

T

n

20

21

22

I have realised the pattern of the sequence goes up by 5 each time as
does the 8 x 8 grid.

37 +(5)

= 42 +(5)

= 47

Formula = 5T - 63

I tested that when:

T = 80

n = 337

337 = 5T - 63

337 = (5 x 80) - 63

= (5 x 80 = 400) - 63

= 400 -63

= 337

337 = 337

Formula works.

Below is a t-shape, and in each cell how the number is connected with
T on a 9x9 grid

T-19

T-18

T-17

T-9

T

Check the formula:

(T-19) + (T-18) + (T-17) + (T-9) + (T)

= 5T - 63

So this is correct

10x10 Grid

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