  We have analyzed populations of blue straggler stars (BSSs) in 24 Magellanic
Cloud star clusters using multi-passband Hubble Space Telescope images. We
compiled a homogeneous BSS database, containing both traditional and evolved
BSSs. We uncovered a sub-linear correlation between the number of BSSs in the
cluster cores and the clusters' core masses, characterized by a power-law index
of $0.51\pm 0.07$. For low stellar collision rates, the mass-normalized number
of BSSs depends only weakly (or perhaps not at all) on the collision rate,
implying that the binary-driven BSS formation channel dominates. Comparison
with simulations suggests that stellar collisions contribute less than 20\% to
the total number of BSSs formed. Further tests, including analysis of the BSS
specific frequencies and their population numbers at larger cluster radii,
suggest that binary interactions may be their main formation channel, hinting
at an anti-correlation between a cluster's binary fraction and its core mass.
