{"schema":"vela.problem-packet.v0.1","problem":1084,"statement":"Let $f_d(n)$ be minimal such that in any collection of $n$ points in $\\mathbb{R}^d$, all of distance at least $1$ apart, there are at most $f_d(n)$ many pairs of points which are distance $1$ apart. Estimate $f_d(n)$.","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A045945","name":"Hexagonal matchstick numbers: a(n) = 3*n*(3*n+1).","terms":"0,12,42,90,156,240,342,462,600,756,930,1122,1332,1560,1806,2070,2352,2652,2970,3306,3660,4032,4422,4830,5256,5700,6162,6","url":"https://oeis.org/A045945"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}