  This contributed conference proceeding reviews some results about a system of
a few identical particles with spin trapped in one-dimensional potentials and
experiencing two-body interactions. The focus is on how symmetry,
integrability, and solvability depend on the trap shape, two-body interaction,
the number of particles, and the number of spin components. A series of
comments are presented that characterize the minimal symmetries possible for a
composite system constructed from interacting single particles, with special
focus on the contact interaction. For five and more particles with internal
components like spin, a kind of universality called algebraically solvability
is lost.
