AI 中文总结
该数学研究确定了n×n棋盘上每个皇后最多或恰好攻击另一个皇后时的最大皇后数，解决了相关猜想并给出了明确的数值结论。
AI 中文摘要
设q(n)为可放置在n×n国际象棋棋盘上且每个皇后最多攻击另一个皇后的最大皇后数。我们证明，对于所有n≥6，q(n)=⌊4n/3⌋；对于n≤5，q(n)=n，这解决了一个此前被猜想的数值。作为推论，我们还解决了该问题的另一版本：当每个皇后恰好攻击另一个皇后时，答案为2⌊2n/3⌋，这同样是此前被猜想的结果。
英文摘要
Let $q(n)$ denote the largest number of queens that can be placed on an $n\times n$ chessboard so that no queen attacks more than one other queen. We prove that $q(n)=\lfloor4n/3\rfloor$ for every $n\geqslant6$, and that $q(n)=n$ for $n\leqslant5$, which settles a previously conjectural value. As a corollary, we also settle that, in the version of the problem where each queen attacks \emph{exactly} one other queen, the answer is $2\lfloor2n/3\rfloor$, again as previously conjectured.
Comments10 pages, 5 figures
