  The properties of the one-dimensional $SU(3)$ population-imbalanced fermions
are discussed. The system is assumed to be in the two-body resonance where all
two-body scattering lengths diverge, and the only interaction between fermions
that is taken into account is the short-range three-body one. In particular, we
consider the situation when only one `flavor' of fermions is macroscopically
occupied, and there are exactly two atoms of two others. This system supports
the trimer and the medium-induced dimer states studied here in detail and shows
evidence of color superfluidity.
