{
  "abstract": "We introduce a guessing game, ``Permutation Wordle,'' in which a guesser attempts to recover a setter's hidden permutation of the set $\\{1, \\ldots, n\\}$. In each round, the guesser submits a word over the alphabet $\\{1, \\ldots, n\\}$, and, as in the game Wordle, learns which entries are correct. We describe a natural strategy and prove that it is optimal in a strong sense: for every $r$, it solves at least as many secrets within $r$ rounds as any possible strategy. The number of permutations it solves in exactly $k+1$ rounds is the Eulerian number $A(n,k)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01874",
  "author_total": 3,
  "authors": [
    {
      "name": "Samuel Kutin"
    },
    {
      "name": "Lawren Smithline"
    },
    {
      "name": "Vincent Vatter"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0q2zgesyswbwb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01874",
  "fulltext_url": null,
  "id": "0q2zgesyswbwb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01874",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.01874",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0q2zgesyswbwb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.01874",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01874"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Permutation Wordle",
  "title_text": "Permutation Wordle",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/0q2zgesyswbwb",
  "venue": "arXiv",
  "versions": []
}