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DOI: 10.4230/LIPIcs.FUN.2026.18

1038 A10s Fit into One A0

Authors: Noel Friedrich

Published in: LIPIcs, Volume 366, 13th International Conference on Fun with Algorithms (FUN 2026)

Abstract

The A-series paper sizes are specified in integer millimetres in ISO 216. Since the sizes are based on an irrational aspect ratio, rounding errors introduce small but cumulative discrepancies from their nominal areas. In this work, we prove that exactly 1038 sheets of ISO A10 can be packed without overlap into a single ISO A0 sheet, allowing only orthogonal (axis-aligned) placements. A lower bound is given by an explicit construction, while the upper bound is proved by a simple-to-verify computer-assisted certificate. Along the way, the dual certificates produce unexpectedly pretty weightmaps.

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Noel Friedrich. 1038 A10s Fit into One A0. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 18:1-18:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{friedrich:LIPIcs.FUN.2026.18,
  author =	{Friedrich, Noel},
  title =	{{1038 A10s Fit into One A0}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{18:1--18:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-417-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{366},
  editor =	{Iacono, John},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2026.18},
  URN =		{urn:nbn:de:0030-drops-257379},
  doi =		{10.4230/LIPIcs.FUN.2026.18},
  annote =	{Keywords: rectangle packing, pallet loading problem, rounding effects, ISO 216}
}

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1038 A10s Fit into One A0

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