Enigma Number 1769 Crossing lines

摘要

I have drawn a number of straight lines across a large sheet of paper, each extending from edge to edge on the paper, so that each line crosses all the other lines. One of the intersections is between three lines, all the others are between just two lines, and none of them are on the edge of the paper. I counted the number of non-overlapping areas formed that did not touch the edge of the paper and found that this was exactly three times the number of non-overlapping areas that did touch the edge of the paper, How many lines did I draw?