Number Grids Investigation

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Number Grids Investigation

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

15

16

25

26

Square 1

15 x 26 = 390

16 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

18

19

28

29

18 x 29 = 522

19 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

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