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T-Total. In order to find the relationship between the T-number and the T-total I need to show the numbers in the T algebraically

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Introduction

James Benson 11sb

T-Total

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Highlighted in yellow are 5 numbers in a shape of a T. If I add these five numbers I get the T-total, e.g. 1+2+3+11+20=37

Highlighted in yellow and coloured redis what is called the T-number.

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Middle

N-19

N-18

N-17

N-9

N

This is worked out with the grid size because how you get one square up is by taking 9 because it is a 9*9 grid. If I move left I +1 and if you move right you -1. If I add all the numbers together in the diagram above you get 63 and that is the same wherever the T is on a 9*9 grid.

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T-total= 37

                      +5

T-total=42

                      +5

T-total=47

Every time the T moves right the T-total is +5 so this means all the t-totals have a relationship with the 5* table.

So if I * the T-number by 5 I get 100 and then if we go back to diagram that showed T algebraically and use 63 that I worked out from it. Then if I -63 from 100 I get 37 and that is the t-number.

So if I put that in a formula it looks something like this N=T+63

                                                                                                  5

The relationship between the T-number, T-total and the grid size

The examples I used in the first section only worked for a 9*9 size grid and to find so to find the relationship between the grid size I have to try the same thing with different grid sizes and then notice a pattern.

N-19

N-18

N-17

N-9

N

This is the T is written algebraically for a 9*9 size grid add all the numbers in the T up I get 63

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  1st 3 rows of a 8*8 grid                                                                  

N-17

N-16

N-15

N-8

N

image00.png

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Conclusion

That is only to work out how to get from the first N(N1) to the second N(N2) what I need to find out is how to get from the N1 to the second T-total(T2). So if we put the translation into a formula to find T2 from N1 this is what it looks like. T2=5[(n+x)+(wY)]-(7w)

Replacing the letters for numbers in the example I should be able to work it out like this T2=5[(20+4)+(3*9)]-(7*9)

            =5[24+27]-63

            =5[51]-63

            =255-63

            =192

so now to find out if my formula is correct I will work out T2 by adding the numbers in the T, 32+33+34+42+51=192

That concludes my maths coursework…

image02.png

Maths coursework

...read more.

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