🗼 汉诺塔Tower of Hanoi
在线汉诺塔游戏：3–10 个圆盘可选，点击柱子移动圆盘，把整座塔从 A 柱搬到 C 柱；显示最少步数 2ⁿ−1，支持撤销和自动演示最优解。Play the Tower of Hanoi online with 3–10 disks: tap pegs to move disks and rebuild the tower from peg A on peg C. Shows the optimal 2ⁿ−1 moves, with undo and an animated auto-solve.
先点一根柱子拿起最上面的圆盘，再点目标柱子放下。键盘：123（或 ABC）选择柱子，U 撤销。Tap a peg to pick up its top disk, then tap the destination. Keyboard: 123 (or ABC) choose pegs, U undoes.
玩法说明与常见问题How to play & FAQ
「汉诺塔」怎么玩？How do I play Tower of Hanoi?
把 A 柱上从大到小叠好的圆盘全部移到 C 柱。每次只能移动一个最上面的圆盘，而且大盘不能压在小盘上面。n 个圆盘最少需要 2ⁿ−1 步。Move the whole stack from peg A to peg C. Only the top disk can move, one at a time, and a larger disk may never sit on a smaller one. With n disks the minimum is 2ⁿ−1 moves.
最优解法是什么？What is the optimal strategy?
递归思路：先把上面 n−1 个圆盘移到中间柱，再把最大的移到目标柱，最后把 n−1 个移回来。点「自动演示」可以看完整过程，也可以中途接着你的局面演示。Recursively: move the top n−1 disks to the spare peg, move the largest disk to the target, then move the n−1 disks on top. Auto-solve animates it — even from the middle of your own game.
10 个圆盘要多少步？How many moves for 10 disks?
最少 1023 步。每多一个圆盘，步数大约翻一倍。At least 1,023 moves — each extra disk roughly doubles the count.
适合用来教学吗？Is it good for teaching?
非常适合讲解递归和指数增长，3–4 个圆盘适合孩子入门。Yes — it is a classic way to explain recursion and exponential growth; 3–4 disks suit children.
「汉诺塔」免费吗？需要下载吗？Is Tower of Hanoi 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.