Consider a pentagram (see picture below). There are five disjoint triangles initially. Just count the five ‘caps’ above the pentagon, do not count the larger triangles formed by using three of the five vertices, for those ‘triangles’ have lines going through them. By adding just two lines, you can go from five to 10 disjoint triangles. How?
Submitted by Bruce Lin, from friends at MIT, who got it from Andrew Russell, a graduate student in EE at MIT, who either made it up or got it from…?