# In my maths coursework I will be focusing on T-Numbers. I will be investigating the relationship between T-totals and T-numbers.

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Introduction

T-Numbers:

In my maths coursework I will be focusing on T-Numbers. I will be investigating the relationship between T-totals and T-numbers.

In my investigation I will also try and find out the relationships between the grid size and the transformations. The T-number is always the number at the bottom of

Middle

73

74

75

76

77

78

79

80

81

The total of the numbers inside the T-shape is 1+2+3+11+20=37 this is called the T-total.

The number at the bottom of the T-shape is called the T-number. For the t-shape in red the T-number for this T-shape is 20. When you take the other numbers in the T-Shape away from the T-Number you get something like this:

N-17 | N-18 | N-19 |

N-9 | ||

N |

When you get the T-shape like this you can see that the centre numbers always go up by 9’s because of the table size, with the table set out like this a formula can be worked out to find the formula to find any T-Total on this size grid. This can be achieved by using this below:

T-Total =A

T-Number =N

T-total = N-19+N-18+N-17+N-9+N

So the formula for this grid is: 5N-63

The Testing Process for grid 9x9:

Testing the formula can be done using the variables A and N.

T-Total =A

T-Number =N

(I have used the number 5 in the formula to multiply N because there are 5 grid boxes in one T shape on any grid)

(Example T-number = 20)

A = 5N-63

N = 20

A = 5x20

= 100-63 = 37

I will now test to see if this will work any were on the 9x9 grid.

N=43

A=5x43 24+25+26+34+43=152

24 | 25 | 26 |

34 | ||

43 |

A=215-63

## A=152

## ---------------------------------------------------------------------------------------------------------------------------

## N=49

A=5x49 30+31+32+40+49=182

A=245-63

30 | 31 | 32 |

40 | ||

49 |

Conclusion

T-Total = N-13+N-12+N-11+N-6+N

= 5N-42

The Testing Process for grid 6x6:

Testing the formula can be done using the variables A and N.

T-Total =A

T-Number =N

(I have used the number 5 in the formula to multiply N because there are 5 grid boxes in one T shape on any grid)

A = 5N-42

N = 14

A = 5x14

= 70-42 = 28

I will now test to see if this will work any were on the 6x6 grid.

N=22

A=5x22 9+10+11+16+22=68

9 | 10 | 11 |

16 | ||

22 |

A=110-42

## A=68

## ---------------------------------------------------------------------------------------------------------------------------

## N=35

A=5x35 22+23+24+29+35=133

A=175-42

22 | 23 | 24 |

29 | ||

35 |

A=113

## ---------------------------------------------------------------------------------------------------------------------------

## N=32

A=5x32 19+20+21+26+32=118

A=160-42

19 | 20 | 21 |

26 | ||

32 |

A=118

I have fully tested the formula for three different T-numbers and the formula works any were correctly on a 6 by 6 grid.

The full formula for this size grid is: A=5N-42

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

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