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T-Total Investigation I am going to look at and investigate the relationship between the T-total, R-number and grid size of a T-shape on a numbered grid. 1) Investigate the relationship between the T-total and the T-number drawn on a 9 by 9 number 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 There is a possibility of 196 different translations of T-shape on this grid. I am going to investigate on this grid the T-shape shown above. Here is a table with T-totals from the grid above: T-number T-total 20 (20+11+1+2+3) 37 21 (21+12+2+3+4) 42 22 (22+13+3+4+5) 47 23 (23+14+4+5+6) 52 24 (24+15+5+6+7) 57 To find a relationship between the T-total and T-number I used the difference method. T-Total T-number Difference 20 37 5 21 42 5 22 47 5 23 52 5 24 57 T = T-total The reason why the difference increases by 5 each time, is because there is 5 numbers in the T. As the T moves across the each number increases by one. Five times each one equals 5. T = 5n - X = (5 x 20) - X = 100 - X = 37 = 63 So, 5n -...

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