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  • Level: GCSE
  • Subject: Maths
  • Word count: 1894

T-total Investigation

Extracts from this document...

Introduction

Lewis WrightMaths Coursework     16th May 2001

Introduction:

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T-number

The T-total is all the        

numbers in the T added together.                                                                

Lewis WrightMaths Coursework     16th May 2001

9x9 Grid

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T-Shape

T-number

T-total

Red

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37

Blue

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177

Purple

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317

Green

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57

Yellow

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197

Grey

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337

        In my Research I have found that in all of my T’s if you take the number above the T-number and add 9 you will get the same number as the T-number, and if you take the one above that and add 18 you get the T-number, and if you take the one to the left of that one and add 19 you get the T-number, and if you take the number furthest to the right and add 17 that also adds up to the same amount as the T-number.

+19=T

+18=T

+17=T

+9=T

    T

          To find out the formula I have used algebra.  

...read more.

Middle

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T-Shape

T-number

T-total

Red

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73

Blue

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213

Purple

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353

Green

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93

Yellow

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233

Grey

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373

        In my Research I have found that all you have to do is change the minus sign in the formula to add and I can find out the formula for the upside down T’s  

T

+9=T

+17=T

+18=    

+19=T

          To find out the formula I have used algebra

 T-total=T+T+9+T+18+T+17+T+19=5T+635T+63=T-total

8x8 Grid Upside down

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    T

 +8=T

+15+T

 +16=T

+17=T

T-Shape

T-number

T-total

Red

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             66

Blue

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           266

Purple

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             91

Green

            21

           161

Yellow

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291

Formula for 8x8 grid

T-total=T+T+8+T+16+T+15+T+17=5T+56                                       5T+56=T-total

7x7 Grid Upside down

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    T

 +7=T

+13=T

+14=T

+15=T

T-Shape

T-number

T-total

Red

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59

Blue

             30

199

Purple

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                      49

Green

34

                    219

Formula for 7x7 grid

T-total=T+T+7+T+14+T+13+T+15=5T+49                                   5T+49=T-total

6x6 Grid Upside down

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    T

 +6=T

+11=T

+12=T    

+13=T

T-Shape

T-number

T-total

Red

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52

Blue

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           142

Purple

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           127  

Formula for 6x6…

T-total=T+T+6+T+12+T+11+T+13=5T+42                               5T+42=T-total

5x5 Grid Upside down

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    T

 +5=T

   +9=T

 +10=T

+11=T

T-Shape

T-number

T-total

Red

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45

Blue

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105

Formula for 5x5…

T-total=T+T+5+T+10+T+9+T+11=5T+35                              5T+35=T-total

9x9 Grid to the Right

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T-Shape

T-number

T-total

Red

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53

Blue

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           193

Purple

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333

Green

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Yellow

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           246

Grey

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353

         In my research I have found that as you decrease the grid size there is no change to the formula. I will therefore only do three grid sizes to prove my point.

+11=T

 +2=T    

+1=T

  T

+7=T

...read more.

Conclusion

+7=T

    T    

+1=T

+2=T

+11=T

          To find out the formula I have used algebra  

T-total=T+T+1+T+7+T+2+T+11=5T+7                                             5T+7=T-total

8x8 Grid to the left

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+6=T

    T

 +1=T

+2=T

+10=T

T-Shape

T-number

T-total

Red

9

            52

Blue

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            252

Purple

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              77

Green

            28

             147

Yellow

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277

Formula for 8x8 grid

T-total=T+T+1+T+2+T+6+T+10=5T+7                                       5T+7=T-total

7x7 Grid to the left

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+5=T

    T

 -1=T

 -2=T  

-9=T

T-Shape

T-number

T-total

Red

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Blue

            36

          187

Purple

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            67

Green

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          207

Formula for 7x7 grid

T-total=T+T+1+T+2+T+5+T+9=5T+7                                      5T+7=T-total

Final all round Formula:

         After all my extensive research I have found the formula that will change any T- number in to it’s T-total…

                                         T-total = T+ (T-9) + (T-18) + (T-19) + (N-17)

                                                       =5T-63

...read more.

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