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arXiv · 2609.01874

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 $\{1, \ldots, n\}$. 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 $A(n,k)$.

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Samuel Kutin, Lawren Smithline, Vincent Vatter. 2026-09-01. Permutation Wordle. https://arxiv.org/abs/2609.01874

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