T- Total Investigation

Authors Avatar
T- Total

2

3

4

5

6

7

8

9

0

1

2

3

4

5

6

7

8

9

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

Look at the T-shape drawn on the 9 by 9 number grid.

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 theT-number.

The T-number for this T-shape is 20.

T

If you take the other numbers in the T-Shape away from the T-Number you get a T-Shape like this.

T-17

T-18

T-19

T-9

T

You will notice that the centre column of the T-Shape is going up in 9's because of the table size. With the table set out like this a formula can be worked out to find any T-Total on this size grid. This is done in the working below:-

T-total = T-19+T-18+T-17+T-9+T

= 5T-63

Now to test this formula to see if it works

For T-Total I will use the letter X

For the T-Number I will use the letter T

So X = 5T-63

T = 20

X = 5x20-63

= 100-63

= 37

Now I will do two more to check to see if it will work anywhere on the grid.

T=43

X=5x43-63 24+25+26+34+43=152

X=215-63

X=152

T=49

X=5x49-63 30+31+32+40+49=182

X=245-63

X=182

I have tested the formula for three different T-numbers and the formula works for a 9 by 9 grid.

The full formula for this size grid is:- X=5T-63

When trying to fine out the T-Total in a 6 by 6 number grid,

2

3

4

5

6

7

8

9

0
Join now!


1

2

3

4

5

6

7

8

9

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

If you take the other numbers in the T-Shape away from the T-Number you get a T-Shape like this.

T-13

T-12

T-11

T-6

T

This time the centre column of the T-Shape is going up in 6's because of the ...

This is a preview of the whole essay