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Diagonal Differences
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| Submitted: Thu Jul 11 2002
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Diagonal Differences Diagonal Differences Examples I will try a 2X2, 3X3, 4X4 and 5X5 square in a 5X5 grid 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 2X2 square = 2X6=12, 1X7=7 12-7=5 3X3 square = 3X11=33, 1X13=13 33-13=20 4X4 square = 4X16=64, 1X19=19 64-19=45 5X5 square = 5X21=105, 1X25=25 105-25=80 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 2X2 square = 12X16=192, 11X17= 187 192-187=5 2X2 square = 4X8=32, 3X9=27 32-27=5 I noticed that no matter where in the grid the 2X2 square was the diagonal difference was always 5. This is equal to the number of rows. Once I noticed this I realised that the 3X3 grids diagonal difference was equal to the number of rows X4. Also the number of rows in the 4X4 square are timed by 9 And in a 5X5 square the rows are timed by 16. I then noticed that if you take the number of rows in the square and take away one and square the answer you can times this by the number of rows in the grid...
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