Relationship between T-total and T-number I am going to investigate T-totals and T-numbers on a 9x9 grid.

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Relationship between T-total and T-number

I am going to investigate T-totals and T-numbers on a 9x9 grid.

The T-total is when a T-shape is placed on a grid and the numbers in the T-shape are added up to give a total.

My aim is to find a relationship between T-totals and T-numbers.

I am going to translate the T-shape 5 times on a 9x9 grid and then do the same on various sized grids.

T total = 1 + 2 + 3 + 11 + 20 = 37 [All numbers added together]

T number = 20 [number at the bottom of the T shape]

I am going to translate the T shape across the 9x9 grid.

 

T total = 1 + 2 + 3 + 11 + 20 = 37

T number = 20

T total = 2 + 3 + 4 + 12 + 21 = 42

T number = 21

T total = 3 + 4 + 5 + 13 + 22 = 47

T number = 22

I have translated the T shape across the 9x9 grid 3 times. So far I have noticed that when the T number increases by one, the T total increases by 5. I predict that if I move the T shape across once more I will get a T total of 52. I am going to do 2 more T shapes to confirm my prediction.

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T total = 4 + 5 + 6 + 14 + 23 = 52

T number = 23

T total = 5 + 6 + 7 + 15 + 24 = 57

T number = 24

I have tested my prediction and have found that my prediction was right. Now I am going to see what the relationship is between the T total and T number when I translate the shame down the grid.

T total = 1 ...

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