Archdeacon–Dinitz–Mattern–Stinson distinct partial sums conjecture

Let $(G,+)$ be an abelian group, let $A\subseteq G$ have $|A|=k$, and, for an ordering $(a_1,\ldots,a_k)$ of $A$, define partial sums by $s_0=0$ and

$$s_j=\sum_{i=1}^j a_i\quad (1\leq j\leq k).$$

Archdeacon–Dinitz–Mattern–Stinson conjecture. For any cyclic group $\mathbb{Z}_n$ and any subset $A\subseteq\mathbb{Z}_n\setminus\{0\}$, there is an ordering of the elements of $A$ such that $s_i\ne s_j$ for $1\leq i<j\leq k$.

This is weaker than Alspach's conjecture because it does not require $s_k\ne0$ and does not compare the positive partial sums with $s_0$. It was verified computationally for $n\leq25$ and proved for $|A|\leq6$; its general validity remains open.