发表机构
Center for Communications Research（通信研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出排列 Wordle 游戏，描述一种自然策略并证明其强最优性，其恰好在k+1轮内解决的排列数为欧拉数A(n,k)。
AI 中文摘要
我们引入了一种名为“排列 Wordle”的猜词游戏，其中猜题者试图恢复出题者隐藏的集合{1,…,n}的排列。每一轮，猜题者提交一个字母表{1,…,n}上的“单词”，并像 Wordle 游戏一样，获知哪些条目是正确的。我们描述了一种自然策略，并证明它具有强最优性：对于任意r，它在r轮内解决的秘密数量不少于任何可能的策略。它恰好在k+1轮内解决的排列数量为欧拉数A(n,k)。
英文摘要
We introduce a guessing game, ``Permutation Wordle,'' in which a guesser attempts to recover a setter's hidden permutation of the set $\{1, \ldots, n\}$. In each round, the guesser submits a word over the alphabet $\{1, \ldots, n\}$, and, as in the game Wordle, learns which entries are correct. We describe a natural strategy and prove that it is optimal in a strong sense: for every $r$, it solves at least as many secrets within $r$ rounds as any possible strategy. The number of permutations it solves in exactly $k+1$ rounds is the Eulerian number $A(n,k)$.
Comments19 pages
