# T-Total Investigation

Extracts from this document...

Introduction

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 |

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

Then I experimented with a 9X9 grid and realized

the following points;

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

T-number goes up in 4

- 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

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.

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.

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

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