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Corners Draw a grid 5 columns wide, with any number of rows above 2. Select a square of numbers, 2x2, e.g. 7,8,12,13 Multiply together the numbers in opposite corners of the square (e.g. 7*13=91, 8*12=96) 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 I shall now begin searching for patterns, and for rules that I will then prove and use to explain patterns. My first step shall be to make examples to compare Ex.1 7 8 12 13 7*13=91 8*12=96 13 14 18 19 13*19=247 14*18=252 The pattern in this case would seem to be a difference of 5. It may be a coincidence that 5 is the number of columns in the grid, and in order to test whether it is in fact a coincidence or not I shall introduce a new letter 'c' which will stand for the number of columns within the entire grid. Algebra n n+1 n+c n+c+1 n(n+c+1)=n²+nc+n (n+1)(n+c)=n²+nc+n+c n²+nc+n+c-(n²+nc+n) = n²+nc+n +c -(n²-nc-n) = c The difference is c, the number of columns within the grid. RULE d = c I shall extend this by varying the size of the square extracted from the grid. The...

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