{"schema":"vela.problem-packet.v0.1","problem":958,"statement":"Let $A\\subset \\mathbb{R}^2$ be a finite set of size $n$, and let $\\{d_1,\\ldots,d_k\\}$ be the set of distances determined by $A$. Let $f(d)$ be the multiplicity of $d$, that is, the number of ordered pairs from $A$ of distance $d$ apart. Is it true that $k=n-1$ and $\\{f(d_i)\\}=\\{n-1,\\ldots,1\\}$ if and only if $A$ is a set of equidistant points on a line or a circle?","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}