Number Grids Coursework

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Number Grids Coursework

Introduction

In the following piece of coursework, I intend to investigate taking a square of numbers from a 10 x 10 grid, multiplying the opposite corners and then finding the difference between the two products.

I was first asked to take a 2 x 2 square from a 10 x 10 grid, multiply the opposite corners and then find the difference. This is the result I received;

2x2 squares

5

6

25

26

Square 1

5 x 26 = 390

6 x 25 = 400

Difference = 400 - 390 = 10

Here I found that the difference was 10, to find out if the difference was the same for every 2 x 2 square, I decided to test another 3 squares, and here are the results I received;

Square 2

8

9

28

29

8 x 29 = 522

9 x 28 = 532

Difference = 532 - 522 = 10

Square 3

32

33

42

43

32 x 43 = 1376

33 x 42 = 1386

Difference = 1386 - 1376 = 10

35

36

45

46

Square 4

35 x 46 = 1610

36 x 45 = 1620

Difference = 1620 - 1610 = 10

After calculating the differences between the products of four 2 x 2 square grids, I can conclude that the difference is always 10, and I predict that the difference will always remain 10 for 2 x 2 square grids. I then decided to look at a 3 x 3 square on a 10 x 10 grid, to see if the difference would be 10, or anything different, and here is the result;

32

33

34

42

43

44

52

53

54

3 x 3 squares

Square 1

32 x 54 = 1728

34 x 52 = 1768

Difference = 1768 - 1728 = 40

Here, however I found that the difference was 40 to find out if the difference was the same for every 3 x 3 square, I decided to test another 3 squares, and here are the results I received;

35

36

37

45

46

47

55

56

57

Square 2

35 x 57 = 1995

37 x 55 = 2035

Difference = 2035 - 1995 = 40

38

39

40

48

49

50

58

59

60

Square 3

38 x 60 = 2280

40 x 58 = 2320

Difference = 2320 - 2280 = 40

62

63

64

72

73

74

82

83

84

Square 4

62 x 84 = 5208

64 x 82 = 5248

Difference = 5248 - 5208 = 40

After calculating the differences between the products of four 3 x 3 square grids, I can conclude that the difference is always 40, and I predict that the difference will always remain 40 for all 3 x 3 square grids. I then decided to look at 4 x 4 squares on a 10 x 10 grid to find their differences; I also decided to look at 5 x 5 squares to see if there was any particular pattern, and here are the results

2

3

4

1

2

3

4

21

22

23

24

31

32

33

34

4 x 4 squares

Square 1

x 34 = 34
Join now!


4 x 31 = 124

Difference = 124 - 34 = 90

5

6

7

8

5

6

7

8

25

26

27

28

35

36

37

38

Square 2

5 x 38 = 190

8 x 35 = 280

Difference = 280 - 190 = 90

5

6

7

8

5

6

7

8

25

26

27

28

35

36

...

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