  We present a technique to identify the most probable dynamical formation
scenario for an observed binary or triple system containing one or more merger
products or, alternatively, to rule out the possibility of a dynamical origin.
Our method relies on an analytic prescription for energy conservation during
stellar encounters. With this, observations of the multiple star system
containing the merger product(s) can be used to work backwards in order to
constrain the initial orbital energies of any single, binary or triple systems
that went into the encounter. The initial semi-major axes of the orbits provide
an estimate for the collisional cross section and therefore the time-scale for
the encounter to occur in its host cluster. We have applied our analytic
prescription to observed binary and triple systems containing blue stragglers,
in particular the triple system S1082 in M67 and the period distribution of the
blue straggler binaries in NGC 188. We have shown that both S1082 and most of
the blue straggler binaries in NGC 188 could have a dynamical origin, and that
encounters involving triples are a significant contributor to blue straggler
populations in old open clusters. In general, our results suggest that
encounters involving triples could make up a significant fraction of those
dynamical interactions that result in stellar mergers, in particular encounters
that produce multiple star systems containing one or more blue stragglers.
