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T-Total Investigation

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Firstly I looked at how the T-shapes would overlap each other   -

Then I experimented with a 9X9 grid and realized

the following points;

  1. Sum of T2=T+5
  2. Difference between T-total and

T-number goes up in 4

  1. Difference between each T-total is 5

I thought of an equation that would be able to tell a person the T-total of

the second T just by using the first T.

T is made up of 5 squares and moves across 1 to make T2

Squares in T X Movement = 5 ∆ Second T = T + 5

ST X M = 5 ∆T2 = T + 5

This proved to be unnecessary in my investigation

...read more.

Middle

This table shows that when 20 is taken from any T-number and then the answer is multiplied by 5 and 37 is added, you will get the T-total. I had to test this method with a few other numbers to check that it worked.

I could now make an equation to summarize my work on task 1

5(n-20)+37

This can be simplified to: 5n-63

Now I had completed task1 I felt I had more of a feel to the investigation and was confident in successful completion. I would now begin to experiment with different grid sizes and investigate the relation of this alteration to the T-total and T-number.

...read more.

Conclusion

2n+2+(n+2)+6(you add six because the top bar of the T will always be 1,2 and 3 which equal six when added together)

Because there are so many digits scattered everywhere you can simplify this equation to:

3n+10 (where n equals grid size)

I had already found a formula using the 7X7 grid so I began using the 11X11 grid; I decided to draw a table as I had done for the other grid sizes to make my investigation easier.

T-number

T-total

Difference (between T-totals)

24

43

+ 1st total

25

48

5

26

53

5

27

58

5

28

63

5

29

68

5

In every table I had looked at, the difference between T-totals was always 5.

...read more.

This student written piece of work is one of many that can be found in our GCSE T-Total section.

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