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

Extracts from this document...

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

## 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

## 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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