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Investingating L-totals

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Introduction

Practice coursework

INVESTIGATING “L” TOTALS

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An 8x8 grid is a grid that is 8 rows across by 8 rows down. The numbers go up in sequences of 1.

The “L” total is the total of all of the numbers in the L shape. The “L” shape is the shape below. Its name comes from the shape that it is.

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9

17

18


=45

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10

18

19


=49

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11

19

20

=53

4

12

20

21

=57

I have found that my numbers go up in sequences of 4 if add them together

To identify where I placed my “L” on the grid I am going to use the bottom left number

E.g.

34

42

50

51


=177

I am going to come up with a table of results for different numbers

THESE ARE MY RESULTS FOR THE L NUMBER BEING 17 GOING UP TO 24.

L NUMBER

L TOTAL

17

45

18

49

19

53

20

57

21

61

22

65

23

69

24

73

I have found that my totals increase in sequences of 4

I am now going to miss a few out and carry on at number 33

First off I am going to predict that number 33’s L total is 109

17

25

33

34

33+34+17+25 = 109

I have found that however much further up the table that you go then they still go up in 4’s. It is also always going to be an odd number.

L-16

L-8

L

L+1

L+1+L+L-8+L-16

4L-24+1

4L-23

...read more.

Middle

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I am going to add 1+2+11+20

=This total equals 34

I am now going to add 2+3+12+21

This total equals 38

I am now going to add 3+4+13+22

This total equals 42

The formula for this is 4l+3g-1

I am now going to flip the “L” shape so that it is the other way around – this “L” shape will be coloured blue. The “L” number is the one in the top right. It is highlighted blue

I am now going to add 2+11+20+19

The total of this is 52

I am now going to add 3 +12+21+20

This total is 56

I am concluding that this is increases in sequences of four

The formula for this box is 4L+3g-1. This is the same as the sequence above. This means that their totals will be the same

I am now going to see what happens to the sequences if I increase the size of the table so that it is 9X9. This means that it will be nine squares across and 9 squares down

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I am now going to add up the numbers in the “L” shape. The “L” number is the one highlighted in yellow

1+10+19+20 = 50

I am now going to add the next lot of numbers

2+11+20+21 = 54

I am now going to, again add the next sequence of numbers

3+12+21+22 = 58

I am going to make a table of results to show you what I mean

“L” number

Total

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50

20

54

21

58

I am concluding that this sequence also goes up in fours. This surprised me however because I would expect it to go up in fives because I have added one more column of numbers onto the table. The total is always an even number.

The algebra of this sequence is:

L-18

L-9

L

L+1

...read more.

Conclusion

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L-25

L-24

L-16

L-17

L-8

L-7

L-6

L-5

L

L+1

L+2

L+3

I have worked out that this formula is:

12L-107+6

12L-101

12L-6G+6

I am going to try to work out the total of the numbers in the box

I have added 1+2+9+10+17+18+19+20+25+26+27+28

This total equals 202

I am now going to add 2+3+10+11+18+19+20+21+26+27+28+29

This total equals 214

I am now going to add 3+4+11+12+19+20+21+22+27+28+29+30

This total equals 226

I have concluded that it goes up in sequences of 12

I am now going to try to adjust the size of my “L” so that it is 5 down and 5 across

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I am going to try to work out the total of the numbers in the box

I am going to add 1+2+9+10+17+18+25+26+27+28+29+33+34+35+36+37

The total of this is 367

I am now going to move the “L” shape along one space so now I am going to add 2+3+10+11+18+19+26+27+28+29+30+34+35+36+37+38

The total of this is 383

I am now going to move the “L” shape along one space so now I am going to add 3+4+11+12+19+20+27+28+29+30+31+35+36+37+38+39

The total of this is 399

I have concluded that the totals go up in sequences of 16

If I have an L, shape like this:

L-32

L-31

L-24

L-23

L-16

L-15

L-8

L-7

L-6

L-5

L-4

L

L+1

L+2

L+3

L+4

I have worked out a formula for this:

16L-168+4

16L-164

Or:

16L-8g+6

...read more.

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