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T-Shape investigation.  

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T-Shape Firstly, I am going to look at the relationship between the t-number and the t-total. I am going to refer to these terms using the letters N and Z: n = t-number z = -total I will take the first t-shape at the top left of a 9 x 9 size grid. 1 2 3 4 10 11 12 13 19 20 21 22 28 29 30 31 37 38 39 40 I predict that if I move the t-shape to a different location the t-total will be the t-number + 17 (n+17) 1 2 3 4 5 6 7 10 11 12 13 14 15 16 19 20 21 22 23 24 25 28 29 30 31 32 33 34 37 38 39 40 41 42 43 If my prediction is correct, t-total should equal 40 (23 + 17 = 40) Z = 4+5+6+14+23=52 My prediction is not correct. I will move the t-shape to the right and tabulate my results to see if there is a pattern. n 20 23 26 z 37 52 67 The t-total is in creasing by 15. Using first differences I will try to find a formula. n 20 23 26 15n 300 345 390 -263 -293 -323 z 37 52 67 I cannot find a formula for this. However, I have noticed that my n value is increasing by 3 every time. I will re-tabulate...

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