Experimenting with Permutation Wordle

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.