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Maths coursework: January 2001. Aim: To investigate and discover an equation, numerically and algebraically. 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 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 Method: We experimented with different grid sizes, including 9 and 7. We found out the total of the numbers inside the t-shape. (Red) T = 1+2+3+11+10 = 37 If I move the T across I can investigate the relationship by comparing the various t-totals. 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 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 T= total G= grid size N= t number (e.g.) 20 N G T Difference 20 9 37 5 21 9 42 5 22 9 47 5 To try and find a formula for the red T, I used the difference, 5 and multiplied it by the N number. 5 x 20 = 100. However the number we need is T: 37. So to get 37 from 100 I need to subtract 63. So, we would then be able to write the formula as: T= 5N-63 5x20=100 100-63 = 37. (T) I now know this works for the Red T but I must prove that it works for both...

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