Experimenting with Permutation Wordle

TL;DR

This paper explores strategies for permutation Wordle, analyzing the effectiveness of the cyclic shift method through formalization and experimental analysis to determine its optimality.

Contribution

It formalizes permutation Wordle strategies, investigates the cyclic shift conjecture, and provides experimental insights into strategy effectiveness.

Findings

Cyclic shift strategy's effectiveness analyzed

Experimental results support or challenge the conjecture

Insights into strategy optimization for permutation guessing

Abstract

Consider a game of permutation wordle in which a player attempts to guess a secret permutation of length $n$ 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? Samuel Kutin and Lawren Smithline (arXiv:2408.00903) propose a strategy called "cyclic shift" in which all incorrect entries are shifted one index to the right in successive guesses, and they conjecture 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.