Rotation Of "T"- Shapes Clockwise

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Rotation Of “T”-Shapes Clockwise

I shaded “T”-shapes on all the girds from 5 by 5 to 10 by 10, so that I could make a sequence and then find the formulae for all the grids. I rotated the “T”-shapes 90° clockwise until I had made a full rotation, (refer to diagram 1A) but did not change the “T”-number as I rotated the “T”-shapes.

 I then drew tables to show the “T”-numbers and the “T”-totals for the grids.

 Once I had drawn the tables and calculated the “T”-totals for all the grids I realised that there is a difference of 7 between the differences of “T”-totals as the grid size increases by one. E.g. In the 5 by 5 grid there is a difference of 42 between the “T”-totals of the “T”-totals of the first rotation and in the 6 by 6 grid there is a difference of 49 between the “T”-totals of the first rotation. 49-42 = 7 (refer to diagram 1B.) After I had found this sequence occurs between all the grids I came up with the formula “T”-total = pt + 7 where pt is the previous “T”-total in the sequence. However I found that this was not the correct formula because for example in the

5 by 5 grid the first “T”-total in the sequence is 30. 30 + 7 = 37, which is not equal to the next “T”-total in the sequence which is 72. I had had tried to include 7 in my formula, because it is the constant difference between one grid and the next.

 I found that there was a difference of 35 from the number I got from my formula (37)

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And the actual “T”-total I was trying to find. 72 – 37 = 35.

 So I tried to add this number instead, to the previous “T”-total. 30 +35 = 65> But it still did not give me the number I wanted (72). However there was only a difference 7. So I added 7 to the formula and came up with the formula “T”-total=pt + 35 + 7 for the first rotation in the 5 by 5 grid.  

“T”-total = pt + 35 + 7

               =30 + 35 + 7

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