Given a finite subset $A$ of an abelian group $G$, we study the set $k \wedge A$ of all sums of $k$ distinct elements of $A$. In this paper, we prove that $|k \wedge A| \geq |A|$ for all $k \in \{2,\dots,|A|-2\}$, unless $k \in \{2,|A|-2\}$ and $A$ is a coset of an elementary $2$-subgroup of $G$. Furthermore, we characterise those finite sets $A \subseteq G$ for which $|k \wedge A|=|A|$ for some $k \in \{2,\dots,|A|-2\}$. This result answers a question of Diderrich. Our proof relies on an elementary property of proper edge-colourings of the complete graph.