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How many rectangles can been seen in this 4×4 grid of squares (shown on the left)?
In fact there are exactly 100.
I made a much larger square grid with lines dividing it into little squares (a three-figure number of little squares, in fact) and I calculated the number of rectangles which could be seen in this new grid. I then cut the grid along one of the lines in order to make two rectangular pieces, and I calculated the number of rectangles visible in each of my two new pieces. The total of these two numbers was exactly two-thirds of the number visible in my original large square grid. What was the size of my original grid before I cut it? |