Ray Steiner wants to know if all numbers of intersection points are possible between n-1 and n(n-1)/2 if n>3 lines are arranged (in a plane or more generally?).
I don't know the answer, but thirty-odd years ago I worked on the dual question: for which k is it possible to arrange n points in the plane so that the number of lines they determine is k? A classic result is that k cannot be strictly between 1 and n, and obviously k cannot exceed n(n-1)/2. A few other values are seen to be excluded, as well (e.g., I believe that a friend of mine showed that you can't get 8 lines from 7 points, as part of his project that took him to the finals of the Westinghouse Science Talent Search). So people looking at Steiner's question can look at this one as well. Jerry Grossman Oakland University