⛓️ 九连环Nine Linked Rings
在线九连环：中国古老的益智玩具，把一串环一个一个从横杆上解下来。规则很简单：最右边的第 1 环随时能上下；其它的环，只有它右边紧挨的那一环套在杆上、再往右的环全部解下时，才能套上或解下。可选 3～9 连环，标出最少步数，九连环要 341 步，还有“下一步”提示。Nine Linked Rings online — the ancient Chinese ring puzzle: take every ring off the bar one by one. Ring 1 at the right end can always go on or off; any other ring may move only when the ring just to its right is on the bar and every ring further right is off. Choose 3 to 9 rings; the fewest number of moves is shown (341 for nine rings) and there is a next-step hint.
点一个环让它套上或解下；能动的环是橙色的。Tap a ring to put it on or take it off; rings that can move are orange.
玩法说明与常见问题How to play & FAQ
「九连环」怎么玩？How do I play Nine Linked Rings?
从右往左把环编号为 1、2、3……开始时所有环都套在杆上，目标是把它们全部解下来。第 1 环随时可以套上或解下；第 k 环（k≥2）只有在第 k−1 环套在杆上、并且第 1 到第 k−2 环全部解下时才能动。所以要解下高位的环，常常得先把低位的环装回去，来来回回，这正是九连环的妙处。Number the rings 1, 2, 3 … from the right. All start on the bar and the goal is to take every one off. Ring 1 can always go on or off; ring k (k ≥ 2) can move only when ring k−1 is on the bar and rings 1 to k−2 are all off. To free a higher ring you often have to put lower rings back on first — that back-and-forth is the charm of the puzzle.
九连环最少要多少步？How many moves do nine rings take?
按本页一步动一个环的算法，n 连环最少要 (2ⁿ⁺¹−1)/3 步（n 为奇数）或 (2ⁿ⁺¹−2)/3 步（n 为偶数），九连环是 341 步。Counting one ring per move, n rings need (2ⁿ⁺¹−1)/3 moves for odd n or (2ⁿ⁺¹−2)/3 for even n — 341 for nine rings.
九连环和汉诺塔有什么关系？How is it related to the Tower of Hanoi?
两者都是“递归”的谜题：解 n 连环要先解 n−2 连环、动最高位的环、再装回 n−2 连环……数学上九连环的状态正好对应格雷码。Both are recursive: to clear n rings you clear n−2, move the top ring, put n−2 back, and so on. Mathematically the ring positions follow the Gray code.
「九连环」免费吗？需要下载吗？Is Nine Linked Rings free? Do I need to download anything?
完全免费，无需注册、下载或安装，打开网页就能玩，手机、平板和电脑都支持；游戏完全在你的浏览器本地运行，不会上传任何数据。It is completely free with no sign-up, download or install — just open the page on a phone, tablet or computer. The game runs entirely in your browser and nothing is uploaded.