Repetition in Permutation Wordle

Abstract

In a game of permutation wordle, a player attempts to guess a secret permutation in the fewest number of guesses possible. Previously, Samuel Kutin and Lawren Smithline (arXiv:2408.00903) introduced this game and proposed a strategy called cyclic shift, which they conjecture performs optimally. We continue our investigation of this conjecture by considering how information is obtained and, at times, repeated during a game of permutation wordle using an arbitrary strategy. This analysis includes several algorithms to construct a secret permutation which prompts inefficient repetition according to the player's strategy, as well as proofs of their efficacy.