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Opposite Corners Investigation
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| Submitted: Wed Aug 27 2003
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Opposite Corners Investigation This investigation is about finding the difference between the products of the opposite corner numbers in a number square. There are three variables which I can change whilst doing my investigation, they are the size of the grid, the shape of the grid and the numbers inside the grid. I am going to start by looking only at number squares with consecutive numbers Consecutive Numbers 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 4 x 13 = 52 1 x 16 = 16 Difference = 36 0 3 12 15 0 x 15 = 0 3 x 12 = 36 Difference = 36 -2 1 10 13 1 x 10 = 10 -2 x 13 = -26 Difference = 36 The difference seems to be the same, for these 3 the answer is 36 but this isn't proof. Let X stand for the start number which can be any real number. X X + 3 X + 12 X + 15 (X + 3) (X + 12) = X2 + 3X +...
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