# T-Total. In order to find the relationship between the T-number and the T-total I need to show the numbers in the T algebraically

Extracts from this document...

Introduction

James Benson 11sb

T-Total

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 | 77 | 78 | 79 | 80 | 81 | 82 |

Highlighted in yellow are 5 numbers in a shape of a T. If I add these five numbers I get the T-total, e.g. 1+2+3+11+20=37

Highlighted in yellow and coloured redis what is called the T-number.

Middle

N-19

N-18

N-17

N-9

N

This is worked out with the grid size because how you get one square up is by taking 9 because it is a 9*9 grid. If I move left I +1 and if you move right you -1. If I add all the numbers together in the diagram above you get 63 and that is the same wherever the T is on a 9*9 grid.

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 | 77 | 78 | 79 | 80 | 81 | 82 |

T-total= 37

+5

T-total=42

+5

T-total=47

Every time the T moves right the T-total is +5 so this means all the t-totals have a relationship with the 5* table.

So if I * the T-number by 5 I get 100 and then if we go back to diagram that showed T algebraically and use 63 that I worked out from it. Then if I -63 from 100 I get 37 and that is the t-number.

So if I put that in a formula it looks something like this N=T+63

5

The relationship between the T-number, T-total and the grid size

The examples I used in the first section only worked for a 9*9 size grid and to find so to find the relationship between the grid size I have to try the same thing with different grid sizes and then notice a pattern.

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

N-9 | ||

N |

This is the T is written algebraically for a 9*9 size grid add all the numbers in the T up I get 63

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |

9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |

17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |

1st 3 rows of a 8*8 grid

N-17 | N-16 | N-15 |

N-8 | ||

N |

Conclusion

That is only to work out how to get from the first N(N1) to the second N(N2) what I need to find out is how to get from the N1 to the second T-total(T2). So if we put the translation into a formula to find T2 from N1 this is what it looks like. T2=5[(n+x)+(wY)]-(7w)

Replacing the letters for numbers in the example I should be able to work it out like this T2=5[(20+4)+(3*9)]-(7*9)

=5[24+27]-63

=5[51]-63

=255-63

=192

so now to find out if my formula is correct I will work out T2 by adding the numbers in the T, 32+33+34+42+51=192

That concludes my maths coursework…

Maths coursework

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

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