T-Total and T-Number - page 5
Keywords: T-Total and T-Number
By Grant867 on 07/12/2008
Level: GCSE Key Stage 4 (Years 10-11)
Page Number: 5 of 6 pages: 1 2 3 4 5 6
t-total and we get this
5tn - (7*9) + 70 = t-total
5*41-63+ 70 = 212
The formula has worked. We now want to work out the difference in the t-total of the first t-shape we started with to the rest of the other six t-shapes. The next two are the below t-shapes.
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
The blue t-shapes t-total is a difference of 126 to the original t-shape that had a t-total of 142.
Formula
5tn – (7*G) + 126 = t-total.
5*41-(7*9) + 126 = 268
The red t-shape therefore will be
5tn – (7*G) + 56 = t-total
5*41- (7*9)+ 56 = 198
The next four t-shapes are just the same apart from you – the (7*G)
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
Red t-shape
5tn- (7*G)+7= t-total
5*41 – 63+7 = 149#
Blue t-shape
5tn- (7*G) + 119 = t-total
5* 41 –63+ 119 =261
The last two t-shapes
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
Red t-shape
5tn- (7*G) + 133 = t-total
5* 41 –63+ 133= 275
Blue t-shape
5tn- (7*G) -7 = t-total
5*41-63-7 = 135
W now have a formula for seven different rotations. The number at the end of the formula we plus by or in one case minus buy again are divisible by seven. You could say that the magic number for this piece of coursework is seven. Like they have a magic number in the bible that is 12.
If there are formulas for rotation then surly there is for reflection. Here I have simply only done one type of reflection just to prove that reflection actually works. Here is the formula 5tn+ (12gm) = t-total. How do we get this formula is what we need to know.
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
The answer to this is that you need to think of what you are doing to each of the numbers in the t-shape from the blue t-shapes t-number. For the number 29 we have a grid movement of one so we get (tn+gm). For the number 38 we have a grid movement of two so we get (tn+2gm). For the numbers 46, 47 and 48 we have a grid movement of three and a total of three numbers, se we get 3(tn+3gm). The total of all of them together is (5tn +12*gridsize) = t-total.
This formula should be tested. The t-total of the blue t-shape is 37 and the t-total of the red t-shape is 208.
Formula
5tn+(12*gridsize)= t-total
5*20+ 12* 9 = 208
The formula has worked.
CONCLUSION
In this project we have found out many ways in which to solve the problem we have with the t-shape being in various different positions
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