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T-Shapes

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The T-Shaped numbers of the different grids, 5 by 5, 6 by 6, 7 by 7, up to a grid of 12 by 12. 5 by 5 Grids: Calculations / Findings: 1. 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 TN = 12 TT = 1+2+3+7+12 = 25 2. 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 TN = 13 TT = 2+3+4+8+13 = 30 3. 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 TN = 14 TT = 3+4+5+9+14 = 35 Results: Result No.: TN: TT: 1. 12 25 2. 13 30 3. 14 35 The regular interval between the T-Totals (TT) is 5, as seen above, 25, 25 + 5 = 30, 30 + 5 = 35. Conclusions: The Algebraic Expression: N - 11 N - 10 N - 9 N - 5 N So, TN = N TT = (N - 11) + (N - 10) + (N - 9) + (N - 5) + N = N - 11 + N - 10 + N - 9 + N - 5 + N = N + N+ N+ N+ N - 11 - 10 - 9 - 5 = 5N - 35 6 by 6 Grids: Calculations / Findings: 1. 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 TN = 14 TT = 1+2+3+8+14 = 28 2. 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 TN = 15 TT = 2+3+4+9+15...

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