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As part of my coursework I have chosen number grid.

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Introduction

As part of my coursework I have chosen number grid.

According to the task, I followed four steps in 10   10 grid

  1. A box is drawn round four numbers.
  2. Find the product of the top left number and the bottom right number.
  3. Do the same with the top right and bottom left number.
  4. Calculate the difference between these numbers.

The results are noted in the table below.

BOX

MULTIPLIED NUMBER

PRODUCT

DIFFERENCE

4          5

4       15

60

10

14       15

5      14

70

26       27

26     37

962

10

36       37

27     36

972

81       82

81     92

7452

10

91      92

91     82

7462

From the worked examples I find that the difference between the product found for the diagnol square in the 10      10  is 10.

From these results I predict that the difference between the next products in a diagnol square of 2    2 will be 10in 10    10 grid.

BOX

MULTIPLIED NUMBER

PRODUCT

DIFFERENCE

31     32

31     42

1302

10

41     42

32     41

1312

66     67

66     77

5082

10

76     77

67     76

5092

89     90

89     100

8900

10

99     100

90     99

8910

...read more.

Middle

4     37

148

90

24    25    25    26

7     34

238

34    35    36    37

21    22    23    24

31    32    33    34

21     54

1134

90

41    42    43    44

24     51

1224

51    52    53    54

56    57    58    59

66    67    68    69

56     89

4984

90

76    77    78    79

59     86

5074

86    87    88     89

The results show that the difference between the products in 4    4 square is 90.It is five times to the difference in 3    3 square.I predict that it will be true for next squares in 4    4 square in 10    10 grid.

BOX

MULTIPLIED NUMBER

PRODUCT

DIFFERENCE

7      8       9     10

17    18    19    20

7     40

280

27    28    29    30

10     37

370

90

37    38    39    40

33    34    35    36

43    44    45    46

33     66

2178

53    54    55    56

36     63

2268

90

63    64    65    66

46    47    48    49

56    57    58    59

46     79

3634

90

66    67    68    69

49     76

3724

76    77    78    79

The results show that the prediction was right.

What would be the difference in 5    5 square in this grid ?

BOX

MULTIPLIED NUMBER

PRODUCT

DIFFERENCE

4      5      6      7      8

14     15   16    17    18

24    25    26    27    28

4    48

192

160

34    35    36    37    38

8     44

352

44    45    46    47    48

11   12    13     14    15

21    22    23    24    25

31    32    33    34    35

11     55

605

160

41    42    43    44    45

15     51

765

51    52    53    54    55

26    27    28    29    30

36    37    38    39    40

46    47    48    49    50

26     70

1820

56    57    58    59    60

30     66

1980

160

66    67    68    69    70

The difference between the products is 160.

...read more.

Conclusion

THE SEQUENCE OF NUMBERS:  10, 40, 90, 160,

Position Number

1

2

3

4

Term

10

40

90

160

Difference

30

50

70

2nd Difference

20

20

The 2nd difference between the succesive terms is (+)20.So the nth term will be

DINO

Nth term = 20n – 10

               =10

4th term  = 20     4 – 10

              = 80 –10

             = 70

5th term = 20    5 – 10

                = 100 – 10

                = 90

10th term =  20    10 – 10

               = 200 – 10

                = 190

BOX

MULTIPLIED NO

PRODUCT

DIFFERENCE

x              x + 1

x(x + 11)

x + 11

10

x + 10       x + 11

(x + 1) (x + 10)

x + 10x + x +10

3    3 SQUARE

x            x + 1       x + 2

x(x + 22)

x + 22x

x + 10    x +11      x + 12

(x + 2) (x + 20)

x +22x +2x + 40

40

x +20    x + 21     x + 22

4    4  SQUARE

x           x + 1      x + 2   x + 3  

x + 10   x + 11    x + 12  x + 13

x(x + 33)

x + 33x

x + 20   x + 21    x + 22  x + 23

(x + 3) (x + 30)

x +30x + 3x + 90

90

x + 30   x +31     x + 32   x + 33

x         x + 1      x + 2     x + 3     x + 4

x +10  x + 11    x + 12    x + 13   x + 14

x(x + 44)

x + 44x

x +20   x +21   x + 22     x + 23  x + 24

(x + 4) (x +40)

x + 40x +4x + 160

160

x + 30   x + 31   x + 32   x + 33   x + 34

x +40   x + 41   x + 42    x + 43   x + 44

...read more.

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