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T-Shapes.  

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T-Shapes I am going to investigate the T-Shapes grid. I will be first looking at the 9 x 9 grid. I will then show how many T-shapes I would be able to make, by only moving the shapes across only once each time. Once I have done this I will add up all the T-Shapes to find out the T-Total. The last number at the bottom of the T-Shape is called the T-number. The T-total for this T-shape is: 1 + 2 + 3 + 11 + 20 = 37 37 = T-Total 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 The T-number for this T-shape is 20. 1 2 3 11 T = 20 If you take the other numbers in the T-Shape away from the T-Number you get a T-Shape like this. T-17 T-18 T-19 T-9 T You will notice that the centre column of the T-Shape is going up in 9's because of the table size. With the table set out like this a formula can be worked out to find...

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