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The T Number.

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Introduction

Introduction

In this experiment I will be using a 10x10 grid.  In a regular T, the T Number is the number at the bottom of the T.

In order for me to try and establish a relationship, I am going to draw a table, which shows T Number with T total and try to work out the difference and see whether a pattern emerges

1st T-Total (Normal 5 square T)

I am going to try and establish a relationship between the T

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Middle

86

360

274

94

400

306

98

420

322

n

5n-70

As you can see from the table above, I have been unable to establish a relationship between the T Number and the T Total using this method.  I am going to use another method in order to try and find a relationship. I will substitute the numbers in a regular T with relevant values of n and try and establish an algebraic link between T Number and T Total. I worked the values relevant to n as shown below and this helped my progress.

n-21

n-20

n-19

n-10

n

Using this T, I am now able to work out an algebraic T Total for a regular T.  It would be n-21+n-20+n-19+n-10+n which simplifies to 5n – 70.  I can check that this is correct by putting the T number of any T into this equation and then work it out.

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Conclusion

N

N+10

N+19

N+20

N+21

I can now work out an algebraic T total for this T.  The formula would be n+n+10+n+19+n+20+n+21, which amounts to 5n+70 as opposed to the 5n-70 that I obtained from the previous experiment. Putting the T number of any T should now give me the right T Total if I put it into the equation.  I will use 22 as the n and because I already know that a T total for a T where N=22 is 22+32+41+42+43=180. Putting it into my formula – 5n+70 then 5*22=110 and 110+70 =180 so this proves my formula works.  Just to confirm it I am going to draw the graph of y=5n+70 and see if when I look the T number 22, I get 180.

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