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  • Level: GCSE
  • Subject: Maths
  • Word count: 2820

T-Totals and T-Shapes

Extracts from this document...

Introduction

T-Totals and T-Shapes T-Totals and T-numbers 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 This is the 9 x 9 Grid displaying the first kind of T I shall be looking at, as with this T and all other T's I shall be trying to find out a formula with which will tell me how to work out the T-Total of a T-Shape. The Numbers that have been highlighted in Purple will make my first T-shape. The T number for this shape is 20, as it is the number at the tip if the T (highlighted in yellow). The T total for this shape is 37 as it is the result off all the numbers in the T added together (1+2+3+11+20 = 37) You will notice that as the T progresses downwards the number increases by 9 (2+9 = 11, 11+9 =20) as this is the width of the grid. In the formula I will show this Number will be known as G or grid size. To get the formula I constructed a similar T-Shape however looking at subtraction rather than addition. T in this Shape stands for the T-Number which in this case is 20. ...read more.

Middle

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-Number = 32 T-Total = 32+41+50+49+51 = 223 5T + 7G = T-Total 160 + 63 = 223 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-Number = 57 T-Total = 57+66+75+74+76 = 348 5T + 7G = T-Total 285 + 63 = 348 Now I will test my formula on different grid sizes 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 T-Number = 3 T-Total = 3+9+15+14+16 = 57 5T + 7G = T-Total 15 + 42 = 57 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 T-Number = 4 5T + 7G = T-Total T-Total = 4+15+26+25+27 = 97 20 + 77 = 97 I will now try to find the formula for a T shape rotated around 270 degrees. ...read more.

Conclusion

62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 T-6G-3 T-6G-2 T-6G-1 T-6G T-6G+1 T-6G+2 T-6G +3 T-5G T-4G T-3G T-2G T-G T As the numbers (not shown in the table) cancel each other out and there are 13T's and 57 -G's in the table, I would expect the formula to be 13T-57G = T-Total I will prove my formula my changing the position of the T on the 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-Number = 67 T-Total = 10+11+12+13+14+15+16+22+31+40+58 +67 = 358 13T - 57G = T-Total 871 - 513 = 358 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-Number = 78 T-Total = 21+22+23+24+25+26+27+33+ 42+51+60+69+78 = 501 13T - 57G = T-Total 1014 - 513 = 501 ...read more.

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