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Level B · Reproducible Geometry P-block-stacking-problem

Block Stacking Problem

Let n ≥ 1. Let C(n) be the largest displacement that the n^th block in a stack of identical rigid rectangular blocks of width 1 can be displaced horizontally over the edge of a table, with the stack remaining stable.

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-block-stacking-problem,
  title        = {Block Stacking Problem},
  author       = {{Cairn Commons contributors}},
  howpublished = {\url{https://cairn-commons.com/problems/block-stacking-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 . Let be the largest displacement that the block in a stack of identical rigid rectangular blocks of width can be displaced horizontally over the edge of a table, with the stack remaining stable. More mathematically, is the supremum of where are real numbers subject to the constraints for all . What is ?

AlphaEvolve matched the known optimum or best construction.

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.