Journal of Integer Sequences, Vol. 29 (2026), Article 26.1.7

Experimenting with Permutation Wordle


Aurora Hiveley
Department of Mathematics
Rutgers University
Piscataway, NJ 08854
USA

Abstract:

Consider a game of permutation wordle in which a player attempts to guess a secret permutation in Sn in as few guesses as possible. In each round, the guessing player is told which indices of their guessed permutation are correct. How can we optimize the player's strategy? Kutin and Smithline proposed a strategy called cyclic shift in which all incorrect entries are shifted one index to the right in successive guesses, and they conjectured its optimality. We investigate this conjecture by formalizing what a "strategy" looks like, performing experimental analysis on inductively constructed strategies, and examining the coefficients of an inductive strategy’s generating function.


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(Concerned with sequences A000295 A023548 A046739 A284843 A385588.)


Received September 17 2025; revised version received February 17 2026; March 1 2026; March 9 2026. Published in Journal of Integer Sequences, March 9 2026.


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