  We consider a physical system comprising discrete massive particles on the
real line whose trajectories interact via perfectly inelastic collision, also
known as sticky particles. It turns out that polygons formed in a convex
"cumulative momentum diagram" of the initial conditions allow us to easily
predict how many particle clusters form as time $t\to\infty$. We explore an
application of this to a unit mass system with $\pm 1$ velocities, which has
ties to simple symmetric random walks and lattice path counting.
