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arXiv · 2408.00903

Permutation Wordle

Samuel A. Kutin·Lawren M. Smithline
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Abstract

We introduce a guessing game, permutation Wordle, in which a guesser attempts to recover a hidden permutation in $S_n$. In each round, the guesser guesses a permutation (using information from previous rounds) and is told which entries of that permutation are correct. We describe a natural guessing strategy, which we believe to be optimal. We show that the number of permutations this strategy solves in $k+1$ rounds is the Eulerian number $A(n,k)$. We also describe an extension to suited permutations: the setter chooses a permutation in $S_n$ and also a coloring of $[n]$ using $s$ colors. We generalize our strategy, give a recurrence for the number of suited permutations solved in $k+1$ rounds, and relate these numbers to the Eulerian numbers. In the case of two suits, or signed permutations, we also relate these numbers to the Eulerian numbers of type B.

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Samuel A. Kutin, Lawren M. Smithline. 2024-08-01. Permutation Wordle. https://arxiv.org/abs/2408.00903

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