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Level B · Reproducible Algorithms P-the-ring-loading-problem

The Ring Loading Problem

Let C be the infimum of all reals α for which the following statement holds: for all positive integers m and nonnegative reals u_1, …, u_m and v_1, …, v_m with u_i + v_i ≤ 1, there exist z_1, …, z_m such that for every k, we have z_k ∈ v_k, -u_k, and |Σ_i=1^k z_i - Σ_i=k+1^m z_i|≤ α.

From the catalogue. Imported from Georgiev, Gómez-Serrano, Tao, Wagner (Google DeepMind), AlphaEvolve repository of problems (CC-BY-4.0) — original. Nobody has started on it here yet: tasks are created as soon as someone asks for one or submits a claim.

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Cite 
@misc{cairn-the-ring-loading-problem,
  title        = {The Ring Loading Problem},
  author       = {{Cairn Commons contributors}},
  howpublished = {\url{https://cairn-commons.com/problems/the-ring-loading-problem}},
  year         = {2026},
  note         = {Open problem on Cairn Commons, CC BY 4.0. Accessed 2026-09-28}
}

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The problem

The problem

Let be the infimum of all reals for which the following statement holds: for all positive integers and nonnegative reals and with , there exist such that for every , we have , and Obtain upper and lower bounds on that are as strong as possible.

AlphaEvolve found a construction better than the previous record (at publication).

What counts as progress

  • A better construction or bound, with code that re-computes its value (reproducible) — ideally verified by an independent re-run.
  • A proof that a known construction is optimal, or a better bound on the other side.
  • Literature: earlier or newer records (literature claims).

Source and licence

Imported from the AlphaEvolve repository of problems (Georgiev, Gómez-Serrano, Tao, Wagner — Mathematical exploration and discovery at scale, 2025), commit 8f447457957d. Text under CC BY 4.0, code under Apache 2.0; reformatted for this page.