# t-totals. I will be doing three grids, a 10 x 10 grid, a 9 x 9 and an 8 x 8. Doing three will give me the evidence more than if I just did one or two

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Introduction

Maths Coursework – T-Totals

What I am trying to do in this coursework is trying to find a link between two parts of a T. The two parts are the T number (the bottom number) and the T total (all the numbers in the T added together). I will now try and find a connection and hopefully be successful. I will be doing three grids, a 10 x 10 grid, a 9 x 9 and an 8 x 8. Doing three will give me the evidence more than if I just did one or two and would make sure that I was right.

The first grid I did was the 10 x 10:

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 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 | 90 |

91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 |

11 | 12 | 13 |

22 | ||

32 |

11 + 12 + 13 + 22 + 32 = 90

12 | 13 | 14 |

23 | ||

33 |

12 + 13 + 14 + 23 + 33 = 95

13 | 14 | 15 |

24 | ||

34 |

13 + 14 + 15 + 24 + 34 = 100

14 | 15 | 16 |

25 | ||

35 |

14 + 15 + 16 + 25 + 35 = 105

T-Total and T-Number grid

T-Number | 32 | 33 | 34 | 35 |

T-Total | 90 | 95 | 100 | 105 |

I have done 4 T’s so that I can be sure of the pattern I come across.

Middle

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

4 | 5 | 6 |

14 | ||

23 |

4 + 5 + 6 + 14 + 23 = 52

5 | 6 | 7 |

15 | ||

24 |

5 + 6 + 7 + 15 + 24 = 57

6 | 7 | 8 |

16 | ||

25 |

6 + 7 + 8 + 16 + 25 = 62

7 | 8 | 9 |

17 | ||

26 |

7 + 8 + 9 + 17 + 26 = 67

T-Total and T-Number grid

T-Number | 23 | 24 | 25 | 26 |

T-Total | 52 | 57 | 62 | 67 |

I have come across the same formula in this grid that I did before of:

T Total = 5N +?

N is the T Number.

This is a formula which I believe is the true pattern but I needed to do the 8 x 8 gird to be sure. I also think that I have come across a new formula which can only be proven if the next formula goes down 7 in its T total. The last two have been:

5t -70 = 10 x 10 grid

5t -63= 9 x 9 grid

Conclusion

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 |

Where N is 16 then the T Total will be equal to 5N-7G =5 x 16 – 7 x 7

=80 – 49

=31

Also this can be worked out by adding the number 1+2+3+9+16=31. As I demonstrated this works.

Conclusion

From the very first grid, I found the right sum but everything that is found out still needs to be checked unless 100% right. I had made a prediction and I turned that into an answer after looking at two more grids. After completing the three grids (10x10, 9x9 and 8x8), I found that every time that the T-Number goes up 1, the T-Total will go up by 5. I have also worked the general rule:

- 5t-70= 10x10 grid
- 5t-63= 9x9 grid
- 5t -56= 8x8 grid

So I can work out any T Total in any sized grid which gives a T number.

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

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