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PreprintarXiv licencearXiv

Permutation Wordle

  • Samuel Kutin
  • Lawren Smithline
  • Vincent Vatter
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Abstract

We introduce a guessing game, ``Permutation Wordle,'' in which a guesser attempts to recover a setter's hidden permutation of the set {1, …, n}. In each round, the guesser submits a word over the alphabet {1, …, 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).

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Cite

BibTeXRIS
BibTeX
@misc{kutin2026permutation,
  title = {{Permutation Wordle}},
  author = {Samuel Kutin and Lawren Smithline and Vincent Vatter},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.01874},
  eprint = {2609.01874},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.01874},
}
RIS
TY  - UNPB
TI  - Permutation Wordle
AU  - Samuel Kutin
AU  - Lawren Smithline
AU  - Vincent Vatter
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.01874
UR  - https://arxiv.org/abs/2609.01874
AB  - We introduce a guessing game, ``Permutation Wordle,'' in which a guesser attempts to recover a setter's hidden permutation of the set {1, …, n}. In each round, the guesser submits a word over the alphabet {1, …, 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).
ER  -