If new physics contains new, heavy strongly-interacting particles belonging
to irreducible representations of SU(3) different from the adjoint or the
(anti)fundamental, it is a non-trivial question to calculate what is the
minimum number of quarks/antiquarks/gluons needed to form a color-singlet bound
state ("hadron"), or, perturbatively, to form a gauge-invariant operator, with
the new particle. Here, I prove that for an SU(3) irreducible representation
with Dynkin label $(p,q)$, the minimal number of quarks needed to form a
product that includes the (0,0) representation is $2p+q$. I generalize this
result to SU($N$), with $N>3$. I also calculate the minimal total number of
quarks/antiquarks/gluons that, bound to a new particle in the $(p,q)$
representation, give a color-singlet state, or, equivalently, the
smallest-dimensional gauge-invariant operator that includes
quark/antiquark/gluon fields and the new strongly-interacting matter field.
Finally, I list all possible values of the electric charge of the smallest
hadrons containing the new exotic particles, and discuss constraints from
asymptotic freedom both for QCD and for grand unification embeddings thereof.