Allowable sequences
(Jeck here.) Consider an arrangement of $n$ lines on the plane, which do not necessarily need to be in general position. There are many combinatorial problems one can explore with such configurations: If no three lines are concurrent, the number of regions into which these lines divide the plane is given by $1+\binom{n+1}{2}$. If not all lines are concurrent, there is always at least one intersection point that is shared by exactly two lines.