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  • Level: GCSE
  • Subject: Maths
  • Word count: 1262

Number Grids

Extracts from this document...

Introduction

Craig Fryer

Number Grids

My investigation I will carry out is on number grids of different sizes, for example 2x2, 3x3, 4x4 and so on.

To do this I will times the top left number in the grid with the bottom right number, then I will times the top right number with the bottom left number, after this I will take away both answers to work out the difference.

My hypothesis is that there will be a pattern in the difference for each grid size.

2x2 Grids

1.

12   13

22   23

12x23 = 276

13x22 = 286

The Difference is of 10 because 286 – 276

2.

23   24

33   34

23x34 = 782

24x33 = 792

The Difference is of 10 because 792 – 782

3.

34   35

44   45

34x45 = 1530

35x44 = 1540

The Difference is of 10 because 1540 – 1530

This shows me that a 2x2 grid will

...read more.

Middle

34x78 = 2652

74x38 = 2812

The Difference is 160 because 2812 – 2652

3.

45   46   47   48   49

55   56   57   58   59

65   66   67   68   69

75   76   77   78   79

85   86   87   88   89

45x89 = 4005

85x49 = 4165

The Difference is 160 because 4165 – 4005

This shows me that a 5x5 grid will always have a difference of 160 and if I continued doing a 5x5 grid sequence I would always get a difference of 160.

6x6 Grids

1.

15   16   17   18   19   20

25   26   27   28   29   30

35   36   37   38   39   40

45   46   47   48   49   50

65   66   67   68   69   70  

15x70 = 1050

20x65 = 1300

The Difference is 250 because 1300 - 1050

2.

23   24   25   26   27   28

33   34   35   36   37   38

43   44   45   46   47   48

53   54   55   56   57   58

63   64   65   66   67   68

73   74   75   76   77   78

23x78 = 1794

28x73 = 2044

The Difference is 250 because 2044 - 1794

3.

42   43   44   45   46   47

52   53   54   55   56   57

62   63   64   65   66   67

72   73   74   75   76   77

82   83   84   85   86   87

92   93   94   95   96   97

42x97 = 4074

47x92 = 4324

The Difference is 250 because 4324 - 4074

This shows me that a 6x6 grid will always have a difference of 250 and if I continued doing a 6x6 grid sequence I would always get a difference of 250.

7x7 Grids

1.

01   02   03   04   05   06   07

11   12   13   14   15   16   17

21   22   23   24   25   26   27

31   32   33   34   35   36   37

41   42   43   44   45   46   47

51   52   53   54   55   56   57

61   62   63   64   65   66   67

1x57 = 57

61x7 = 427

The Difference is 370 because 427 – 57

2.

12   13   14   15   16   17   18

22   23   24   25   26   27   28

32   33   34   35   36   37   38

42   43   44   45   46   47   48

52   53   54   55   56   57   58

62   63   64   65   66   67   68

72   73   74   75   76   77   78

12x78 = 936

18x72 = 1296

The Difference is 360 because 1296 – 936

3.

23   24   25   26   27   28   29

33   34   35   36   37   38   39

43   44   45   46   47   48   49

53   54   55   56   57   58   59

63   64   65   66   67   68   69

73   74   75   76   77   78   79

83   84   85   86   87   88   89

23x89 = 2047

29x83 = 2407

The Difference is 360 because 2407 – 2047

...read more.

Conclusion

 2 and it worked because with 10N2 it was one Nth term in front and when I took away one Nth term it left me with the correct answer.

I can now find the rest of the sequence with this formula here are 3 examples used with the formula

Here are my examples;

Nth Term

8x8 (8)

9x9 (9)

10x10 (10)

10(N-1) 2

490

640

810

Here is the evidence backing up my formula.

8x8 Grid.

22

29

92

99


22x99 = 2178

29x92 = 2668

This gives me the answer of 490 because 2669 - 2668

9x9 Grid

11

19

91

99

11x99 = 1089

19x91 = 1729

This gives me the answer of 640 because 1729 - 1089

10x10 Grid

01

10

91

100

01x100 = 100

10x91 = 910

This gives me the answer of 810 because 910 – 100

This shows that there is a sequence to the number grids, and it works with the formula I have found.

Also it shows my hypothesis was correct as each grid size had a pattern of a difference of ten.

...read more.

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