# T- Total Investigation

Extracts from this document...

Introduction

T- Total 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 Look at the T-shape drawn on the 9 by 9 number grid. The total of the numbers inside the T-shape is 1+2+3+11+20=37 This is called the T-total. The number at the bottom of the T-shape is called theT-number. The T-number for this T-shape is 20. T If you take the other numbers in the T-Shape away from the T-Number you get a T-Shape like this. T-17 T-18 T-19 T-9 T You will notice that the centre column of the T-Shape is going up in 9's because of the table size. With the table set out like this a formula can be worked out to find any T-Total on this size grid. This is done in the working below:- T-total = T-19+T-18+T-17+T-9+T = 5T-63 Now to test this formula to see if it works For T-Total I will use the letter X For the T-Number I will use the letter T ...read more.

Middle

60 X=5X33-42 (20+21+22+27+33=123 X=165-42 X=123 Now I have worked the formula out for the T-Shape in the one position, I am going to translate the T-Shape to different positions and investigate the relationships between the T-Total, the T-number and the grid size. The other T-Shape's that I can find a formula's are shown below:- A 3 by 3 grid can be used for the other 3. 1 2 3 4 5 6 7 8 9 T T+G T+2G+1 T+2G T+2G-1 T T+G T+2G T+2G-1 T+2G+1 7G+5T X=7G+5T=7x3+5x2 =21+10 (2+5+7+8+9=31) =31 I will now try this new formula on a 4 by 7 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 7G+5T x=7x4+5x10 (17+18+19+14+10=78) =28+50 =78 I will now try it on a 8 by 3 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 7G+5T x=7x9+5x2 (19+20+21+11+2=73) =56+10 =73 I have tried this new formula for an inverted T and it works, the formula is: 7G+5T 1 2 3 4 5 6 7 8 9 T-1-G T-2 T-1 T T-2+G T T-1 T-2 T-2-G T-2+G 5T-7 X= 5T-7=5x6-7 =30-7 (1+4+7+5+6=23) ...read more.

Conclusion

5 25 67 42 6 33 82 49 Goes up in 7's 7 41 97 56 _________________________________________________________________________________ 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 Now I will rotate it again 180� from it's original place T- Number = 12 Purple T-Total = 25 Grey T-Total = 95 a difference of 70..... The formula 5T - 7G + 70 Now I'm going to see what happens on a 6 by 6 width 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 T- Number = 14 Purple T = 28 Grey T = 112 a difference of 84..... The formula 5T - 7G + 84 7 by 7 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 T- Number = 16 Purple T-Total = 31 Grey T-Total = 129 a difference of 98....The formula 5T - 7G + 98 Table of Results Now I will rotate it again 270&de ...read more.

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