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Introduction

Number Grid Investigation I was first given A 10x10 grid, counting from 1-100. Inside the grid was A 2x2 box surrounding the numbers, 12, 13, 22 and 23; 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 I was asked to; * Find the product of the top left number and bottom right number in the box. * Do the same with the top right and bottom left numbers n the box. * Calculate the difference between these numbers. ...read more.

Middle

= M Top of box = N Side of grid = X Bottom of grid = Y Difference = L I now had to start by trying to work out the sequence of the numbers: M = 2 3 4 5 L = 10 40 90 160 30 50 70 20 20 To work out A sequence, we first see how many times we have to look for an equal difference, in this case we have to go look twice, this means that M will be squared; M2 We next look at the difference, in this case 20, we halve it, this will be multiplied by M; M2 x 10 This should be the formula, I will test it; 42 x 10 = 160 This is clearly wrong, as this is the answer for the next part, but I can see what's wrong, so I can fix it. The problem is that I am going to have to take 1 away from M before it is multiplied by 10 to get the correct formula; (M - 1)2 x 10, or factorised, 10(M - 1)2 This will now work, (4 ...read more.

Conclusion

86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 I will not write here all of my working, as it would take up too much space, so I will just write the results; N x M = L 2x2 = 10 3x2 = 20 4x2 = 30 5x2 = 40 6x2 = 50 There is A certain pattern here, as each time we add 1 to N, the difference goes up by 10. Instead of taking M to be the variable in this formula, I will use N as it is the one changing; N --> 2 3 4 5 6 L --> 10 20 30 40 50 10 10 10 10 As I only had to look once for A common difference, N will not have to be squared. The formula turned out like this: 10 (N - 1) I tested this for the 7th part of the 'sequence', 10 (7 - 1) = 60, which, as you can see from the numbers above, is the next part of the sequence, I have found A formula for rectangles where M = 2. ...read more.

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