T-Totals and T-Numbers

T-Totals and T-Numbers

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This is a T-shape! It allows us to gather information into algebraic

formulas to explain the relationships between numbers.

[IMAGE]This is the T-Number. It is the central part of our research.

If you add up all the numbers in the T, you will find the T-Total! For

the T above, the T-Total will be

1 + 2 + 3 + 9 + 16 = 31.

2)

Using algebra, we can work out a formula for this T. On a 9x9 grid a T

would look like this:

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From this we can see that if:

T number = n

1 = a

2 = b

3 = c

11 = d

20 = n

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a = n-19 From this we can see that the T-Total

b = n-18 will equal:

c = n-17

d = n-9 1 + 2 + 3 + 11 + 20 = 37

e = n

Using the algebraic formula for each of the numbers we can see that:

T-Total = (n-19) + (n-18) + (n-17) + (n-9) + (n)

= 5n-63

We can see that if we apply this formula to a 9x9 grid we can find the

T-total, and we can prove this by testing it on 1 other T:

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T-Total = 4 + 5 + 6 + 14 + 23 = 52

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This number should = 5n - 63

T-Total = 5n - 63

= (5 x 23) - 63

= 115 - 63

= 52

We can see that the two T-Totals (shortened to TT's) are equal. I

shall next test this equation on a 10 x 10 graph to see if it works.

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TT = 1 + 2 + 3 + 12 + 22 = 39

&

TT = 5n - 63

= (5 x 22) - 63

= 110 - 63