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Claim. There are seven points in the plane in general position, no three on a line and no four on a circle, that determine six distinct distances such that, in a suitable order, the $i$-th distance occurs exactly $i$ times for $i=1,\ldots,6$. This is the result of I. Palásti, On the seven points problem of P. Erdős, Studia Sci. Math. Hungar. 22 (1987), no. 1–4, 447–448, as the zbMATH review (Zbl 0561.51001) states it; the paper has no online posting. In the notation of Problem 217, the answer is yes for $n=7$, the case Erdős's 1983 lecture left undecided. Burt, Goldstein, Manski, Miller, Palsson and Suh record that the example lies on the triangular lattice (card).

Covers. The instance $n=7$. The property of the problem does not pass to subsets, so nothing is claimed for any other $n$; the instances $n=5$, $6$ and $8$ are settled on Pomerance's, [[problems/distance_problems/E0217/claims/1989_01_01_palasti|Palásti's six-point]] and eight-point claim pages.

Depends on. Nothing in this wiki.

Acceptance. Refereed: Studia Scientiarum Mathematicarum Hungarica 22 (1987), no. 1–4, 447–448. The site's remarks credit the seven-point construction to this paper, but the site labels the problem OPEN, so that credit is commentary on an open problem and no reviewed evidence is listed.