Question 9 with triangles
I am having a hard time finding a good way to visualize this. Maybe someone can make suggestions.
One thing I decided early on: A "best" set of N points (with a maximal number of dichotomies) has to be convex. If it is concave, make the point on the inside 1 and three points surrounding it +1 and it won't work.
Once the set is convex (maybe you can put them on a circle WLOG or some such), I _think_ I can guess the number that will force no breaking, but I don't have a clear argument.
