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James Fung 11D 15thFebruary2001 Mathematics Coursework T-Total (1) The T-shape has been translated to four different positions as shown in the grid below. 1 2 3 4 5 6 7 8 9 T- number T-total 10 11 12 13 14 15 16 17 18 20 37 19 20 21 22 23 24 25 26 27 35 112 28 29 30 31 32 33 34 35 36 57 222 37 38 39 40 41 42 43 44 45 71 292 46 47 48 49 50 51 52 53 54 77 322 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 The T-total of any T-number is related the primitive T-shape with T-number 20 or related to any other T-shape with a given T-number. As observed from the above, we can see that the T-total 322 with the T-number 77 can be expressed in the following ways: 322 = 37 + (77-20) × 5 or 322 = 112 + (77-35) × 5 or 322 = 222 + (77-57) × 5 We can conclude that the T-total t of any T-shape under translation can be expressed in terms of its corresponding T-number n i.e. t = 37 + (n-20) × 5 ---------- (*) [where 37 and 20 are the T-total and T-number respectively of the first T-shape in the grid 9 by 9] or T-total = any T-total found + (increase in T-number ) × 5 T-total = any...

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