# Number Grid

Extracts from this document...

Introduction

N ATWELL-MANSINGH

GCSE MATHS

COURSE WORK

Number 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 | 70 | 80 |

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

91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 90 | 100 |

Fig. A

To solve this problem I have broken down the table as much as possible starting with the first query given in the problem.

Ex (1) first box

Highlighted box: the product of the top right hand number and the bottom left hand

number minus the product of the top left hand number and the bottom right hand number

2*13= 26

12*3= 36

36-26= 10

Ex (2) second box

45*56=2520

55*46= 2530

2530-2520= 10

The product of the top right hand number and the bottom left hand number in each square of numbers minus the product of the top left hand number

Middle

I tried using the formula for what I have found before in table Fig. B below but this time I added more columns to the problem

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 | 70 | 80 |

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

91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 90 | 100 |

Fig. B

The first column grid only 7 columns were highlighted and the following was taken into consideration

6 first number is n

7 the second number is n +1

By trying to find the formula for the number of columns used I introduced c in the formula

Therefore when 7 columns were used

The number below n =n+c

The number next to is as n +c=1

Conclusion

Investigation 1:

The product of any square regardless of it’s location in the grid is 10.

Investigation 2:

n+c+1 (c being the number of columns) the answer is always equal to the number of columns used in the grid.

Investigation 3:

The total of numbers in the top row of a grid subtract the total of numbers below is always equal to the number of columns used in the grid multiply by ten (10) which is the product of any square.

In conclusion I found that the general formula for a grid with c columns multiply by the general formula in a square is equal to the sum of numbers in the grid square and grid column.

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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