  In this paper we consider the hyperplane arrangement in $\mathbb{R}^n$ whose
hyperplanes are $\{x_i + x_j = 1\mid 1\leq i < j\leq n\}\cup \{x_i=0,1\mid
1\leq i\leq n\}$. We call it the \emph{boxed threshold arrangement} since we
show that the bounded regions of this arrangement are contained in an $n$-cube
and are in one-to-one correspondence with the labeled threshold graphs on $n$
vertices. The problem of counting regions of this arrangement was studied
earlier by Joungmin Song. He determined the characteristic polynomial of this
arrangement by relating its coefficients to the count of certain graphs. Here,
we provide bijective arguments to determine the number of regions. In
particular, we construct certain signed partitions of the set $\{-n,\dots,
n\}\setminus\{0\}$ and also construct colored threshold graphs on $n$ vertices
and show that both these objects are in bijection with the regions of the boxed
threshold arrangement. We independently count these objects and provide closed
form formula for the number of regions.
