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.


                                                             

I predict that if I move the t-shape to a different location the t-total will be the

t-number + 17   (n+17)

        

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.

The t-total is in creasing by 15. Using first differences I will try to find a formula.

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 my results so it increases by 1 each time. This will make the numbers smaller and closer together and easier to spot a pattern.

Join now!

There is a definite pattern. The z value is increasing by 5 each time. I will try and find a formula.

I have found a formula that works this sequence perfectly

        5n – 63

I will check this by placing a T in the middle of the grid.

        

                               Z = 49+50+51+59+68= 277

My Formula is correct.

To further my investigation I wanted to ...

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