T totals
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GCSE Math's
Investigation
Introduction
In this investigation I'm going to investigate the relationship between the T-total and the T-number. What I'm going to do is use different sizes of grids for example 9*9, 8*8, 7*7, 6*6, 5*5 and 4*4. To compare the answers I will have to investigate each grid for a few times for example 9*9 grid will be investigated for at list three times. I will have to make predictions for each of the grids. I will also have to translate and compare different positions of the T-shape and the T-numbers. After I have finished the investigation I will then evaluate and compare the relationships between different sizes of grids.
The first grid I will investigate will be the 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 76
77 78 79 80 81
1 2 3
11
20
T-number = 20
T-Total = 1+2+3+11+20=37
T20=37
n-19 n-18 n-17
n-9
n
T-number = n
T-Total = n+n-9+n-17+n-18+n-19
Tn = 5n-63
T-number = 20
Tn = 5n-63
20 * 5 = 100
-63
37
Here is another 9*9 grid I will use the similar method just like the one on the first page and see what I gate for this second one. The difference between these is that the numbers this time are all different.
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
3 4 5
13
22
T-number = 22
T-Total = 3+4+5+13+22=47
T20=47
n-19 n-18 n-17
n-9
n
T-number = n
T-Total = n+n-9+n-17+n-18+n-19
Tn = 5n-63
T-number = 22
Tn = 5n-63
22 * 5 = 110
-63
47
As you can see this is another 9*9 grid though this is the final one which will bring as to the final conclusion on whether my prediction was write or wrong...