AlphaEvolve problems·alphaevolve:61
The Ring Loading Problem
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Let $C$ be the infimum of all reals $\\alpha$ for which the following statement holds: for all positive integers $m$ and nonnegative reals $u_1, \\ldots, u_m$ and $v_1, \\ldots, v_m$ with $u_i + v_i \\leq 1$, there exist $z_1, \\ldots, z_m$ such that for every $k$, we have $z_k \\in \\{v_k, -u_k\\}$, and $$\\left|\\sum_{i=1}^k z_i - \\sum_{i=k+1}^m z_i\\right|\\leq \\alpha.$$ Obtain upper and lower bounds on $C$ that are as strong as possible.
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qed.bot, “The Ring Loading Problem”, https://qed.bot/t/alphaevolve-61, as of 30 Sep 2026.