# Number grids

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Introduction

In this assignment I am going to investigate about the number grid. I am going to use two different types of formula to find out the correct answers one is numerical formula and second is algebra. In numerical way I am going to multiply the top left number with right bottom number and the top right number with bottom left number and than I am going to find the difference between the products. The difference of product is going to be same as the size of a grid (in width) in 2 x 2 size. In 3 x 3 size the difference going to be four times bigger than a grid (width) size. I will also use the 5 x 5 grid, 6 x 6 grid and 7 x 7 grid to see how it works. E.g. 5 x 5 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 20 x 24 = 480 19 x 25 = 475 Difference between these products is 5. In algebra I am going to use different formula to find out the correct answer. This is the formula that I am going to use: n = Top left corner n + 1 = Top right corner n + 5 = Bottom left corner n + 6 = Bottom right corner (n + 1) (n + 5) - (n) (n + 6) n2 + 5n + n + 5 - n2 - 6n (n2 cancel out with - n2, 5n + n cancel out with - 6n) 5 left over This is the product difference of 2 x 2 in a 5 x 5 grid. 8 x 8 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 ...read more.

Middle

n2 + 16n + 2n + 32 - n2 - 18n (n2 cancel out with - n2, 16n + 2n cancel out with - 18n) 32 left over This is the product difference of 3 x 3 in an 8 x 8 grid. 9 x 9 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 22 x 38 = 836 20 x 40 = 800 Difference between these products is 36. n = Top left corner n + 2 = Top right corner n + 18 = Bottom left corner n + 20 = Bottom right corner (n + 2) (n + 18) - (n) (n + 20) n2 + 18n + 2n + 36 - n2 - 20n (n2 cancel out with - n2, 18n + 2n cancel out with - 20n) 36 left over This is the product difference of 3 x 3 in a 9 x 9 grid. 10 x 10 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 43 x 61 = 2623 41 x 63 = 2583 Difference between these products is 40. ...read more.

Conclusion

106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 28 x 46 = 1288 24 x 50 = 1200 Difference between these products is 88. n = Top left corner n + 4 = Top right corner n + 22 = Bottom left corner n + 26 = Bottom right corner (n + 4) (n + 22) - (n) (n + 26) n2 + 22n + 4n + 88 - n2 - 26n (n2 cancel out with - n2, 22n + 4n cancel out with - 26n) 88 left over This is the product difference of 5 x 3 in an 11 x 11 grid. 11 x 11 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 11 x 100 = 1100 1 x 110 = 110 Difference between these products is 990. n = Top left corner n + 10 = Top right corner n + 99 = Bottom left corner n + 109 = Bottom right corner (n + 10) (n + 99) - (n) (n + 109) n2 + 99n + 10n + 990- n2 - 109n (n2 cancel out with - n2, 99n + 10n cancel out with - 109n) 990 left over This is the product difference of 11 x 10 in an 11 x 11 grid. Yasir Ghayas ...read more.

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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