{"schema":"vela.problem-packet.v0.1","problem":1129,"statement":"For $x_1,\\ldots,x_n\\in [-1,1]$ let\\[l_k(x)=\\frac{\\prod_{i\\neq k}(x-x_i)}{\\prod_{i\\neq k}(x_k-x_i)},\\]which are such that $l_k(x_k)=1$ and $l_k(x_i)=0$ for $i\\neq k$.Describe which choice of $x_i$ minimise\\[\\Lambda(x_1,\\ldots,x_n)=\\max_{x\\in [-1,1]} \\sum_k \\lvert l_k(x)\\rvert.\\]","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)"}