Number Grid

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Number Grid For this task I will first be looking at a number grid from 1 to 100, like the one below : 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 will start my investigation by looking at 2 by 2 squares. I will draw a square around 4 numbers, find the product of the bottom left and top right numbers and the product of the top left and bottom right numbers, then calculate the difference between the 2 products. I will see if there are any patterns and if so I will try to work it out algebraically. I will then look at changing the size of the squares to see if there are any patterns. I will try looking at 3 by 3 squares, 4 by 4 squares and 5 by 5 squares; I will do the same with these squares as I have with the 2 by 2 squares, I will find the products of the top left and bottom right and the bottom left and top right numbers then calcula... ... middle of paper ... ... Product Difference Right Left Yellow Rectangle : 1 44 44 41 4 164 120 Green Rectangle : 16 59 944 56 19 1064 120 Purple Rectangle : 52 95 4940 92 55 5060 120 I have noticed that the difference of the products in each square is always one hundred twenty. I have worked out the formula for this pattern below: N N+3 N+40 N+43 N(N+43) - (N+3)(N+40) = D N2 + 43N - N2 - 40N - 3N - 120 = D -120 = D Difference = 120 This shows that the difference between the two products in each rectangle is always -120; I have shown the difference as 120 rather than -120 as I am only interested in the number and not the sign in front of it (+/-).

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