  The scramble number of a graph, a natural generalization of bramble number,
is an invariant recently developed to study chip-firing games and graph
gonality. We introduce the carton number of a graph, defined to be the minimum
size of a maximum order scramble, to study the computational complexity of
scramble number. We show that there exist graphs with carton number exponential
in the size of the graph, proving that scrambles are not valid NP certificates.
We characterize families of graphs whose scramble number and gonality can be
constant-factor approximated in polynomial time and show that the disjoint
version of scramble number is fixed parameter tractable. Lastly, we find that
vertex congestion is an upper bound on screewidth and thus scramble number,
leading to a new proof of the best known bound on the treewidth of line graphs
and a bound on the scramble number of planar graphs with bounded degree.
