Problem dossier · Geometry & Packing
Square packing in a square
Find the smallest square that contains n unit squares without overlap. Tilted packings beat axis-aligned ones surprisingly early.
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Status
Optimal only for small and perfect-square n; open even for n = 11 (best known side ≈ 3.877, Gensane–Ryckelynck).
Think you can crack this one? Read the playbook before you announce →
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The Angle of Attack
Continuous optimization over positions and angles for n = 11–100; verify or improve record packings; study when the first tilted square appears in optima.
Tags: packing · squares · optimization · records
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The Lab
No instruments built yet. When this problem gets tackled, its interactive instruments — explorers, searches, verifiers running in the browser — live here. See the Collatz dossier for what a fully tackled problem looks like.
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The Log
Empty. Work on this problem gets logged here as dated entries — constructions tried, code run, dead ends included. Dead ends are results.
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Related Problems
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