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t-totals. I will be doing three grids, a 10 x 10 grid, a 9 x 9 and an 8 x 8. Doing three will give me the evidence more than if I just did one or two

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Introduction

Maths Coursework – T-Totals

What I am trying to do in this coursework is trying to find a link between two parts of a T. The two parts are the T number (the bottom number) and the T total (all the numbers in the T added together). I will now try and find a connection and hopefully be successful. I will be doing three grids, a 10 x 10 grid, a 9 x 9 and an 8 x 8.  Doing three will give me the evidence more than if I just did one or two and would make sure that I was right.

The first grid I did was the 10 x 10:

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11 + 12 + 13 + 22 + 32 = 90

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12 + 13 + 14 + 23 + 33 = 95

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13 + 14 + 15 + 24 + 34 = 100

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14 + 15 + 16 + 25 + 35 = 105

T-Total and T-Number grid

T-Number

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35

T-Total

90

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100

105

I have done 4 T’s so that I can be sure of the pattern I come across.

...read more.

Middle

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4 + 5 + 6 + 14 + 23 = 52

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5 + 6 + 7 + 15 + 24 = 57

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6 + 7 + 8 + 16 + 25 = 62

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7 + 8 + 9 + 17 + 26 = 67

T-Total and T-Number grid

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T-Total

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67

I have come across the same formula in this grid that I did before of:

T Total = 5N +?

N is the T Number.

This is a formula which I believe is the true pattern but I needed to do the 8 x 8 gird to be sure. I also think that I have come across a new formula which can only be proven if the next formula goes down 7 in its T total. The last two have been:

5t -70 = 10 x 10 grid

5t -63= 9 x 9 grid

...read more.

Conclusion

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Where N is 16 then the T Total will be equal to 5N-7G =5 x 16 – 7 x 7

                                                                                        =80 – 49

                                                                                        =31

Also this can be worked out by adding the number 1+2+3+9+16=31. As I demonstrated this works.

Conclusion

From the very first grid, I found the right sum but everything that is found out still needs to be checked unless 100% right. I had made a prediction and I turned that into an answer after looking at two more grids. After completing the three grids (10x10, 9x9 and 8x8), I found that every time that the T-Number goes up 1, the T-Total will go up by 5. I have also worked the general rule:

  • 5t-70= 10x10 grid
  • 5t-63= 9x9 grid
  • 5t -56= 8x8 grid

So I can work out any T Total in any sized grid which gives a T number.

...read more.

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