Recurrent Problems 1.1 THE TOWER OF HANOI

1.1 THE TOWER OF HANOI

Let’s look first at a neat little puzzle called the Tower of Hanoi,
invented by the French mathematician Edouard Lucas in 1883. We are given
a tower of eight disks, initially stacked in decreasing size on one of three pegs

让我们首先看一下一个叫汉诺塔小困惑。它被法国数学家Edouard Lucas于1883年发现。先在每一个钉上面堆放少数磁盘，例如8个磁盘。

The objective is to transfer the entire tower to one of the other pegs, moving
only one disk at a time and never moving a larger one onto a smaller.

我们的目的是把一个塔上面的所有碟片移到另一个塔上面，每一次只能移动一个碟片，并且不要把大的放在小的上面。

Lucas [208] furnished his toy with a romantic legend about a much larger
Tower of Brahma, which supposedly has 64 disks of pure gold resting on three
diamond needles. At the beginning of time, he said, God placed these golden
disks on the first needle and ordained that a group of priests should transfer
them to the third, according to the rules above. The priests reportedly work
day and night at their task. When they finish, the Tower will crumble and
the world will end.

Lucas[208]杜撰了一个浪漫的传说，关于一个更大的
梵天塔据称有64个纯金磁盘放在三个
钻石针。在刚开始的时候，他说，神把这些黄金
磁盘放到第一针上并且受戒，一群牧师会根据上述规则把他们转移到第三根钉上。
祭司一天到晚工作去完成任务。当他们成功的时候，也就是世界末日。

It’s not immediately obvious that the puzzle has a solution, but a little
thought (or having seen the problem before) convinces us that it does. Now
the question arises: What’s the best we can do? That is, how many moves
are necessary and sufficient to perform the task?

这个困惑没有一个显而易见的解决方案，但是经过思考会证实这是可以完成的。

现在的问题是：我们最好应该怎么做？也就是说用最有效的方法去解决这个问题。