  A set $L$ of straight lines and a set $P$ of points in the Euclidean plane
define an arrangement $\mathcal{A}$ = ($L$, $P$) of construction lines and
registration marks, if and only if: (1) any point in $P$ is a point of
intersection of at least two lines in $L$, and (2) any two nonparallel lines in
$L$ have a unique point of intersection in $P$. This paper discusses the
following open problems regarding such arrangements. Suppose $k \geq 0$ number
of points are given in the plane. How many construction lines $k$ points must
determine? How many distinct slopes, or directions, are defined by construction
lines that $k$ points determine? How many distinct sets of construction lines
partition the plane, such that the lines meet at exactly $k$ points? Empirical
evidence is reported for small numbers of $k$, offering partial answers to the
three problems. A conjecture is also stated for the first problem, on the
number of construction lines, after examining a related problem about finite
linear spaces from incidence geometry.
