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Number Grid Investigation In this investigation, I am using a 10x10 number grid, with numbers 1 to 100. I am going to take 2x2 sections of this grid, and calculate the differences between the products of the top-left and bottom-right numbers, and the bottom-right and top-left numbers. Once I have found a pattern, I will attempt to write a generalisation using algebra. After I have done this, I investigate larger sections taken from the grid, 3x3, 4x4 and so on. I will then try to find a general rule for the numbers in any size grid using algebra. 2x2 Sections 12*23=276 13*22=286 286-276=10 65*76=4940 66*75=4950 4950-4940=10 29*40=1160 30*39=1170 1170-1160=10 The difference is ALWAYS 10 Generalisation: x x+1 x+10 x+11 x*(x+11) = x²+11x (x+1)(x+10) = x²+11x+10 (x²+11x+10) - (x²+11x) = 10 Therefore: (x+1)(x+10) - x(x+11) = 10 3x3 Sections 13*35=455 15*33=495 495-455=40 27*49=1323 29*47=1363 1363-1323=40 65*87=5655 67*85=5695 5695-5655=40 The difference is...

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