{"schema":"vela.problem-packet.v0.1","problem":91,"statement":"Let $n$ be a sufficiently large integer. Suppose $A\\subset \\mathbb{R}^2$ has $\\lvert A\\rvert=n$ and minimises the number of distinct distances between points in $A$. Prove that there are at least two (and probably many) such $A$ which are non-similar.","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A186704","name":"The minimum number of distinct distances determined by n points in the Euclidean plane.","terms":"0,1,1,2,2,3,3,4,4,5,5,5,6","url":"https://oeis.org/A186704"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}