  A countable structure is indivisible if for every coloring with finite range
there is a monochromatic isomorphic subcopy of the structure. Each indivisible
structure naturally corresponds to an indivisibility problem which outputs such
a subcopy given a presentation and coloring. We investigate the Weihrauch
complexity of the indivisibility problems for two structures: the rational
numbers $\mathbb{Q}$ as a linear order, and the equivalence relation
$\mathscr{E}$ with countably many equivalence classes each having countably
many members. We separate the Weihrauch degrees of both corresponding
indivisibility problems from several benchmarks, showing in particular that the
indivisibility problem for $\mathbb{Q}$ cannot solve the problem of finding a
monochromatic rational interval given a coloring for which there is one; and
that the Weihrauch degree of the indivisibility problem for $\mathscr{E}$ is
strictly between those of $\mathsf{RT}^2$ and $\mathsf{SRT}^2$, two widely
studied variants of Ramsey's theorem for pairs whose reverse-mathematical
separation was open until recently.
