  A giant impact is commonly thought to explain the dramatic contrast in
elevation and crustal thickness between the two hemispheres of Mars known as
the "Martian Dichotomy". Initially, this scenario referred to an impact in the
northern hemisphere that would lead to a huge impact basin (dubbed the
"Borealis Basin"), while more recent work has instead suggested a hybrid origin
that produces the Dichotomy through impact-induced crust-production. The
majority of these studies have relied upon impact scaling-laws inaccurate at
such large-scales, however, and those that have included realistic impact
models have utilised over-simplified geophysical models and neglected any
material strength. Here we use a large suite of strength-including
smoothed-particle hydrodynamics (SPH) impact simulations coupled with a more
sophisticated geophysical scheme of crust production and primordial crust to
simultaneously investigate the feasibility of a giant impact on either
hemisphere of Mars to have produced its dichotomous crust distribution, and
utilise spherical harmonic analysis to identify the best-fitting cases. We find
that the canonical Borealis-forming impact is not possible without both
excessive crust production and strong antipodal effects not seen on Mars'
southern hemisphere today. Our results instead favour an impact and subsequent
localised magma ocean in the southern hemisphere that results in a thicker
crust than the north upon crystallisation. Specifically, our best-fitting cases
suggest that the projectile responsible for the Dichotomy-forming event was of
radius 500-750 km, and collided with Mars at an impact angle of 15-30{\deg}
with a velocity of 1.2-1.4 times mutual escape speed ($\sim$6-7 km/s).
