Numbers inside T shape
GRID-9
Numbers inside T shape
GRID-10
Numbers inside T shape
Above are the grids and the formula, which go into those grids. I am going to pick any number from the grids and use the formula to check if the formula works.
CHECKING
GRID- 5
GRID 6
GRID 7
GRID 8
GRID 9
GRID 10
I have done the checking and it shows that I have put in the correct formula that goes in each grid.
I am going to investigate the pattern in formula and find the common number from the grids formula. Below are the T-Number and T-Total and the numbers.
GRIDS – 5
Numbers inside T shape
GRID-6
Numbers inside T shape
GRID 7
Numbers inside T shape
GIRD-8
Numbers inside T shape
GRID-9
Numbers inside T shape
GRID 10
Numbers inside T shape
FORMULAS
GRID 5 = 5N - 35
GRID 6 = 5N - 42
GRID 7 =5N - 49
GRID 8 = 5N – 56
GRID 9 = 5N – 63
GRID 10 =5N – 70
PATTERN = 35, 42, 49, 56, 63, 70
This shows that is it going up by 7 and it a multiple of 7.
COMMON = 5N because they all start with 5N and it the difference is 5 as well.
All the grids above formula begin with 5N because that how many numbers inside the T-shape. Number 7 links the endings of each formula because all the grids I have done its T-Total are multiples of 7.it also gives me the last part of the formula. Which I shown above.
FORMULA THAT GOES IN EACH GRID
I have found the formula that will help me find T-Total of any grid.
FORMULA = 5N – 7W
(N = T NUMBER)
(W = WIDTH OF GRID)
I will show you working out of each grid using the formula above, which will give me the T-Total of any grid.
WORKING OUT: -
GRID - 5
5 X 14 = 70
7 X 6 = 42
70 – 42
T-TOTAL = 25
GRID - 6
5 X 14 = 70
7 X 6 = 42
70 – 42
T-TOTAL = 28
GRID 7
5 X 16 = 80
7 X 7 = 49
80 – 49
T-TOTAL = 31
GRID 8
5 X 18 = 90
7 X 8 = 42
90 – 42
T-TOTAL = 34
GRID 9
5 X 20 = 100
7 X 9 = 63
100 – 63
T-TOTAL = 37
GRID 10
5 X 22 = 110
7 X 10 = 70
110 – 70
T-TOTAL = 40
As you can see above. That my calculation prove that I have found the
T-Total of any number using the formula (5N – 7W).
MOVING THE T UPSIDEDOWN
GRIDS – 5
Numbers inside T shape
GRID-6
Numbers inside T shape
GRID 7
Numbers inside T shape
GIRD-8
Numbers inside T shape
GRID-9
Numbers inside T shape
GRID-10
Numbers inside T shape
FORMULAS
GRID 5 = 5N +35
GRID 6 = 5N + 63
GRID 7 =5N + 49
GRID 8 = 5N + 56
GRID 9 = 5N + 63
GRID 10 =5N + 70
I have turned the T-shape upside down. I have the formula above for each of the grid that l am investigating. The only difference in the formula is that instead – (negative) which l got from the first T Shape. Know l have got a + (positive) number for my second T-Shape.
T SHAPE TURNED LEFT
GRID 5
Numbers inside T shape
GRID 6
Numbers inside T shape
GRID 7
Numbers inside T shape
GRID 8
Numbers inside T shape
GRID 9
Numbers inside T shape
GRID 10
Numbers inside T shape
T SHAPE TURNED RIGHT
GRID 5
Numbers inside T shape
GRID 6
Numbers inside T shape
GRID 7
Numbers inside T shape
GRID 8
Numbers inside T shape
GRID 9
Numbers inside T shape
GRID 10
Numbers inside T shape
USING ALGEBRA IN T SHAPE
T SHAPE
GRID 5
N + N-11 + N-10 + N-9 + N-5 (FORMULA= 5N – 35)
GRID 6
N + N-6 + N-12 + N-11 +N-13 (FORMULA= 5N –42)
GRID 7
N + N-7 +N-14 + N-13 + N-15 (FORMULA= 5N-45)
GRID 8
N + N-8 + N-16 +N-15 + N-17 (FORMULA=5N-56)
GRID 9
N + N-9 + N18 + N-17 + N-19 (FORMULA=5N-63)
GRID 10
N + N-10 + N –20 + N-19 + N + 21(FORMULA=5N-70)
TURNING T UPSIDE DOWN
GRID 5
N + N+5 + N+10 + N+19 + N+11 (FORMULA=5N+35)
GRID 6
N + N+6 + N+12 + N+11 + N+13 (FORMULA= 5N+42)
GRID 7
N + N+7 + N+14 + N +13 + N+15 (FORMULA=5N+49)
GRID 8
N + N+8 + N+16 + N+15 + N+17 (FORMULA=5N+56)
GRID 9
N + N+9 + N+18 + N+19 + N+17 (FORMULA=5N+63)
GRID 10
N + N+10 + N+20 + N+21 + N-19 (FORMULA=5N+70)
TURNING T LEFT
GRID 5
N + N-1 - N-2 - N-7 + N+3 (FORMULA=5N-7)
GRID 6
N + N-1 - N-2 – N –8 + N+4 (FORMULA=5N-7)
GRID 7
N + N-1 - N-2 – N-9 + N+5 (FORMULA=5N-7)
GRID 8
N + N-1 - N-2 – N-10 + N+6 (FORMULA=5N-7)
GRID 9
N + N-1 - N-2 – N-11 + N+7 (FORMULA=5N-7)
GRID 10
N + N-1 - N-2 – N-12 + N+8 (FORMULA=5N-7)
TURNING T RIGHT
GRID 5
N + N+1 + N+2 + N+7 – N-3 (FORMULA=5N+7)
GRID 6
N + N+1 + N+2 + N+8 – N-4 (FORMULA=5N+7)
GRID 7
N + N+1 + N+2 + N+9 – N-5 (FORMULA=5N+7)
GRID 8
N + N+1 + N+2 + N+10 – N-6 (FORMULA=5N+7)
GRID 9
N + N+1 + N+2 + N+11 – N-7 (FORMULA=5N+7)
GRID 10
N + N+1 + N+2 + N+12 - N-8 (FORMULA=5N+7)
In the grids above I have used algebra in the T shape to show that I can do working out in algebraic form. The difference was that T shape was + (positive) and when T shape was turned upside-down was – (negative).
When I turned T shape left and then right I found the formula that goes into both of the shapes was 5n-7.the only differences was that T shape which was turn left had a – (Negative) and the one turned was + (positive).
FINDING THE W BY W GRID
T SHAPE
N – N-W – N-2W – N-2W-1 – N-2W+1
TURNING T UPSIDE DOWN
N+ N+W + N+2W + N+2W+1 + N+2W-1
I have found that T shape and upside-down shape have the same w-by w formula that will give 5n-7w.Doing that formula I can work out and any number when I draw T shape and when I turn it up side down.
TURNING T LEFT
N + N-1 + N-2 + N+2+W + N-2+W
TURNING T RIGHT
N + N+1 + N+2 + N+2 – W + N+2+W
