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Claim. For every prime $p$, every $A\subseteq\mathbb F_p\setminus\{0\}$ of size $p-2$, and $\mathbb F_p\setminus\{0\}$ itself, has an ordering whose partial sums are distinct, the question of Problem 475 for the two largest sizes. The paper's result is Theorem 2 (printed p. 4) of J.-P. Bode and H. Harborth, Directed paths of diagonals within polygons: "Conjecture 1 is true for $t=n-2$", where Conjecture 1 is Alspach's conjecture in the paper's language of directed diagonals of an $n$-gon. In the problem's notation, for every $n$ every $(n-2)$-subset of $\mathbb Z_n\setminus\{0\}$ with nonzero sum has an ordering whose partial sums are distinct and nonzero: by an explicit directed cycle through all $n-1$ lengths, with one diagonal deleted, for odd $n$, and by an induction on the missing length for even $n$. For $n=p$, every $(p-2)$-subset $\mathbb Z_p\setminus\{0,x\}$ has sum $-x\ne0$, so each has an ordering with distinct, nonzero partial sums, which is more than the problem asks. Appending $x$ gives a valid ordering of $\mathbb Z_p\setminus\{0\}$, by the step in the proof of the Archdeacon--Dinitz--Mattern--Stinson implication (Costa and Pellegrini, Arch. Math. 115 (2020), p. 7 of the arXiv version); the odd-$n$ cycle, read as on the result page, gives the same ordering directly. The paper's Theorem 1, for the size $n-1$, is vacuous for odd $n$, since the only $(n-1)$-subset then has sum $\binom n2\equiv0$. Hicks, Ollis and Schmitt report both sizes from this paper on their p. 2 and reprove its odd case as their Theorem 4.3, attributed to it (their claim page). Read depth: Theorem 2 and the odd-$n$ half of its proof are checked; the even-$n$ induction (pp. 5--9), carried by the paper's figures, is read for structure only.

Covers. Every prime $p$: every subset of size $p-2$, and $\mathbb Z_p\setminus\{0\}$ itself. The latter is Graham's case $t=p-1$, whose proof no cited source prints.

Depends on. Nothing in this wiki: the result is the paper's own, filed on its library result pages.

Acceptance. Refereed publication: Discrete Mathematics 299 (2005), 3--10, DOI 10.1016/j.disc.2005.05.006, available online 10 August 2005, which dates this page. The site credits the range $p-3\le t\le p-1$ through Hicks, Ollis and Schmitt and the references therein, but its label DECIDABLE leaves the problem open, so that credit is not reviewed evidence.