  Let G be an additive, finite abelian group. The critical number
$\mathsf{cr}(G)$ of $G$ is the smallest positive integer $\ell$ such that for
every subset $S \subset G \setminus \{0\}$ with $|S| \ge \ell$ the following
holds: Every element of $G$ can be written as a nonempty sum of distinct
elements from $S$. The critical number was first studied by P. Erd\H{o}s and H.
Heilbronn in 1964, and due to the contributions of many authors the value of
$\mathsf {cr}(G)$ is known for all finite abelian groups $G$ except for $G
\cong \mathbb{Z}/pq\mathbb{Z}$ where $p,q$ are primes such that
$p+\lfloor2\sqrt{p-2}\rfloor+1<q<2p$. We determine that $\mathsf {cr}(G)=p+q-2$
for such groups.
