Enigma 1452: Crossed lines
11 March 2013
Posted by on
From New Scientist #2613, 21st July 2007
How many rectangles can be seen in this 4-by-4 grid shown above? 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?