Repetition in Permutation Wordle

TL;DR

This paper analyzes strategies in permutation Wordle, focusing on how information is gained and repeated, and introduces algorithms to construct permutations that lead to inefficient repetition, challenging existing conjectures.

Contribution

It provides new algorithms and proofs for constructing permutations that cause strategic inefficiencies, advancing understanding of information repetition in permutation Wordle.

Findings

Algorithms successfully induce inefficient repetition in strategies.

Proofs demonstrate the effectiveness of these algorithms.

Analysis offers insights into information gain and repetition in the game.

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.