{"schema":"vela.problem-packet.v0.1","problem":1045,"statement":"Let $z_1,\\ldots,z_n\\in \\mathbb{C}$ with $\\lvert z_i-z_j\\rvert\\leq 2$ for all $i,j$, and\\[\\Delta(z_1,\\ldots,z_n)=\\prod_{i\\neq j}\\lvert z_i-z_j\\rvert.\\]What is the maximum possible value of $\\Delta$? Is it maximised by taking the $z_i$ to be the vertices of a regular polygon?","status":"open","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)"}