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Claim. For every prime $p$, every $A\subseteq\mathbb F_p\setminus\{0\}$ with $|A|\le12$ has an ordering whose partial sums are distinct, the question of Problem 475 for the sizes $t\le12$. This is Proposition 4.2 of S. Costa and M. A. Pellegrini, Some new results about a conjecture by Brian Alspach: the G-ADMS conjecture, their Conjecture 1.2, which asks exactly for an ordering of $A\subseteq\mathbb Z_n\setminus\{0\}$ with distinct partial sums and which the paper attributes to Graham for prime $n$, holds for subsets of size $k\le12$ of cyclic groups of prime order. The proof applies Alon's Combinatorial Nullstellensatz, in the manner of Hicks, Ollis and Schmitt, to a polynomial of degree $k^2$ encoding an ordering of a $(k+1)$-set with distinct partial sums; for $k=11$ two coefficients are computed, with greatest common divisor $2^3$, so for every prime $p>2$ one of them is nonzero modulo $p$ (p. 6 of the arXiv version), the case $p=2$ being trivial. Corollaries 4.3 and 4.4 transfer the result to torsion-free abelian groups and to $\mathbb Z_n$ with all prime factors large. Read depth: claims checked for the statement in the arXiv version; the coefficient computation (Section 4.1 and the appendix) not replayed.

Covers. Every prime $p$ and every size $t\le12$. The sizes $t\le11$ were known before through Alspach's conjecture (the paper's references, Theorem 2.2 of Hicks, Ollis and Schmitt for $k\le10$ among them); the size $12$ is the paper's. Nothing about $13\le t\le p-4$ for a fixed prime.

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

Acceptance. Refereed publication: Archiv der Mathematik (Basel) 115 (2020), no. 5, 479--488, published online 29 August 2020 (Crossref record; the journal text is not held and was not compared with the arXiv version). The site's commentary credits the sizes $t\le12$ to this paper and its references, but the site's label DECIDABLE leaves the problem open and settles no part of it, so that credit is not reviewed evidence.