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Mathematics GCSE T-totals Alex Pavlou 1). Relationships between the T-number and the T-total on a 9 x 9 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 82 83 84 85 86 87 88 89 90 T-totals T-numbers 21 42 26 67 42 147 66 267 80 337 86 367 The difference in each T-shape is: N-19 N-18 N-17 N-9 N If we take the T-shape: 2 3 4 12 21 we can create the sum: t=21+(21-9)+(21-19)+(21-18)+(21-17) As there are 5 numbers in the T-shape we need 5 lots of 21, the number above 21 is 12, which is 9 less than 21, the other numbers are 2,3 and 4 which is 9 less than 21. Therefore we arrive to the conclusion: N-19 N-18 N-17 N-9 N To prove this we use the T-shape: 61 62 63 71 80 T=80-19+80-18+80-17+80-9+80 T=337 We can do the same for the T-shape: 47 48 49 57 66 T=66-19+66-18+66-17+66-9+66 T=267 To find the formula of the relationship between the T-number and the T-total we use N for the T-number. T=N+(N-9)+(N-19)+(N-18)+(N-17) T=5N-9-54 T=5N-63 Examples of this formula are : In the case of the T-shape: 52 53 54 64 71 T=5(71)-63 T=355-63 T=292 When we add...

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