# Opposite corner

Extracts from this document...

Introduction

Opposite Corner

Candidate Sheet

Opposite corner

Firstly i will investigate the difference between the products of the numbers in oppsite corners of any rectangle that can be drawn in a 100-sqaure grid. After that i will choose randomly some rectangles from the 100-sqaure grids. After that i will mutiply the top right corner with bottom left corner (which will be coloured in blue) then i will multiply the bottom right corner with the top left corner (which will be coloured in yellow). After that i will find the answer then i will subtract the smallest number with biggest number, which will give me the answer of the opposite corner.

This is a diagram of a 100-sqaure grid.

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |

21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |

31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |

41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |

51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 |

61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 |

71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 |

81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 | 90 |

91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 |

1) (A) From the 100 sqaure i will choose a rectangle sided 2 by 3 horizontally

4 | 5 | 6 |

14 | 15 | 16 |

The products of the number in the opposite corner of this rectangle are:

4x16 = 64

14x6 = 84

The difference between these products is

84-64=20

The difference is 20

8 | 9 | 10 |

18 | 19 | 20 |

The product of the number in the opposite corner of this rectangle is:

8x20=160

18x10=180

The differences between these products are:

160-180=20

Middle

5

6

7

14

15

16

17

The product of the number in the opposite corner of this rectangle is:

4x17=68

14x7=98

The difference between these products is:

68-98=30

The difference is 30

24 | 25 | 26 | 27 |

34 | 35 | 36 | 37 |

The products of the number in the opposite corner of this rectangle are:

24x37=888

34x27=918

The differences between these products are:

888-918=30

The difference is 30

Now i have found out that a rectangle sized 2 by 4 is on anywhere in a 100 sqaure grid the difference is always going to be 30

I am going to choose a rectangle from the 100-sqaure grids sided 2 by 5 horizontally

1 | 2 | 3 | 4 | 5 |

11 | 12 | 13 | 14 | 15 |

The products of the number in the opposite corner of this rectangle are:

1x15=15

11x5=55

The differences between these products are:

55-15=40

The difference is 40

21 | 22 | 23 | 24 | 25 |

31 | 32 | 33 | 34 | 35 |

The products of the number in the opposite corner of this rectangle are:

21x35=735

31x25=775

The difference between these products is:

735-775=40

The difference is 40

6 | 7 | 8 | 9 | 10 |

16 | 17 | 18 | 19 | 20 |

The products of the number in the opposite corner of this rectangle are:

6x20=120

16x10=160

The difference between these products is:

120-160=40

The difference is 40

Now i have found out that a rectangle sized 2 by 5 is on anywhere in a 100 sqaure grid it is always going to be 40

Now i am going to choose a rectangle from the 100-sqaure grids sided 2 by 6 horizontally

25 | 26 | 27 | 28 | 29 | 30 |

35 | 36 | 37 | 38 | 39 | 40 |

The product of the number in the opposite corner of this rectangle is:

25x40=1000

35x30=1050

The difference between these products is:

1000-1050=50

The difference is 50

85 | 86 | 87 | 88 | 89 | 90 |

95 | 96 | 97 | 98 | 99 | 100 |

The product of the number in the opposite corner of this rectangle is:

85x100=8500

95x90=8550

The difference between these products is:

8500-8550=50

The difference is 50

62 | 63 | 64 | 65 | 66 | 67 |

72 | 73 | 74 | 75 | 76 | 77 |

The product of the number in the opposite corner of this rectangle is:

62x77=4774

72x67=4824

The difference between these products is:

4824-4774=50

The difference is 50

Now i have found out that a rectangle sized 2 by 6 is on anywhere in the 100 sqaure grid the difference will always going to be 50

Now i have found out that if i go up by 1 horizontally (e.g. 2 by 7, 2 by 8, 2 by 9...) the answer will go up by 10.

From the 100-sqaure grids I will now choose a rectangle 2 by 3 vertically

1 | 2 |

11 | 12 |

21 | 22 |

The product of the number in the opposite corner of this rectangle is:

1x22=22

21x2=42

The difference of this product is:

42-22=20

The difference 20

9 | 10 |

19 | 20 |

29 | 30 |

Conclusion

82-42=40

The difference is 40

4 | 5 |

14 | 15 |

24 | 25 |

34 | 35 |

44 | 45 |

The product of the number in the opposite corner of this rectangle is:

4x45=180

44x5=220

The difference between these products is:

220-180=40

Now i have found out that a rectangle sized 2 by 5 vertically is on anywhere in the 100 sqaure grid the difference is always going to be 40

From the 100-sqaure grids I will now choose a rectangle 2 by 6 vertically

1 | 2 |

11 | 12 |

21 | 22 |

31 | 32 |

41 | 42 |

51 | 52 |

The product of the number in the opposite corner of this rectangle is:

1x52=52

51x2=102

The difference between these products is:

102-52=50

The difference is 50

41 | 42 |

51 | 52 |

61 | 62 |

71 | 72 |

81 | 82 |

91 | 92 |

The product of the number in the opposite corner of this rectangle is:

41x92=3772

91x42=3822

The difference between these products is:

3822-3772=50

The difference is 50

4 | 5 |

14 | 15 |

24 | 25 |

34 | 35 |

44 | 45 |

54 | 55 |

The product of the number in the opposite corner of this rectangle is:

4x55=220

54x5=270

The difference between these products is:

270-220=50

The difference is 50

Now I have found out that a rectangle sized 2 by 6 vertically is on anywhere in the 100 sqaure grid the difference is always going to be 50

Now I have found out that if i go up by 1 vertically (e.g. 2 by 7, 2 by 8, 2 by 9...) the answer will go up by 10.

Omar Ferdous 10a - -

This student written piece of work is one of many that can be found in our GCSE Number Stairs, Grids and Sequences section.

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