Question 85
We call $n$ lines in the plane three-way if they can be separated into three nonempty sets, $X, Y, Z$, such that every two lines from the same set are parallel to each other, no two lines from different sets are parallel to each other, and no three lines intersect at a point.
By $S_n$ we denote the maximum number of regions into which $n$ three-way lines can divide the plane. As a region we consider a connected part of the plane, not necessarily finite, whose boundaries are defined by three-way lines.
What is the largest $n$ for which $S_n \lt 128$?
(Konstantin Delchev)
By $S_n$ we denote the maximum number of regions into which $n$ three-way lines can divide the plane. As a region we consider a connected part of the plane, not necessarily finite, whose boundaries are defined by three-way lines.
What is the largest $n$ for which $S_n \lt 128$?
(Konstantin Delchev)