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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:

 1 2 3 11 20

T-number

The T-total is all the

numbers in the T added together.

Lewis WrightMaths Coursework     16th May 2001

9x9 Grid

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81

 T-Shape T-number T-total Red 20 37 Blue 48 177 Purple 76 317 Green 24 57 Yellow 52 197 Grey 80 337

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.

Middle

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 T-Shape T-number T-total Red 2 73 Blue 30 213 Purple 58 353 Green 6 93 Yellow 34 233 Grey 62 373

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

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64

 T +8=T +15+T +16=T +17=T
 T-Shape T-number T-total Red 2 66 Blue 42 266 Purple 7 91 Green 21 161 Yellow 47 291

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

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49
 T +7=T +13=T +14=T +15=T
 T-Shape T-number T-total Red 2 59 Blue 30 199 Purple 6 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

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 T +6=T +11=T +12=T +13=T
 T-Shape T-number T-total Red 2 52 Blue 20 142 Purple 17 127

Formula for 6x6…

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

5x5 Grid Upside down

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 T +5=T +9=T +10=T +11=T
 T-Shape T-number T-total Red 2 45 Blue 14 105

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

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81
 T-Shape T-number T-total Red 12 53 Blue 40 193 Purple 68 333 Green 16 73 Yellow 44 246 Grey 72 353

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

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

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64

 +6=T T +1=T +2=T +10=T
 T-Shape T-number T-total Red 9 52 Blue 49 252 Purple 14 77 Green 28 147 Yellow 54 277

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

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49
 +5=T T -1=T -2=T -9=T
 T-Shape T-number T-total Red 8 47 Blue 36 187 Purple 12 67 Green 40 207

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

This student written piece of work is one of many that can be found in our GCSE T-Total section.

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