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