通过建立递归关系解决问题的方法,我们称之为递推方法,在解决与自然数n有关的问题上它可以发挥重要作用。例1 一块黄铜平板上装着三根金钢石细柱,其中一根细柱上套着64个大小不等环形金盘。大的在下小的在上,如图1所示。这些盘子可一次一个地从一根柱子转移到另一根柱子,但不允许较大盘子放在较小的盘子的上面,若把这64个金盘从一根柱子全部移到另一根柱子上至少须移动多少次? 这是一个古老的数学游戏。据说古代印度婆罗门教寺庙内的僧侣们玩着这一称为“河内宝塔问题”的游戏,认为如果一场游戏能玩到结束,就意味 By establishing a recursive relationship to solve the problem, we call it a recursive method, which can play an important role in solving problems related to the natural number n. Example 1 Three brass diamond columns were mounted on a brass plate, and one of the columns was covered with 64 ring plates of unequal size. The big ones are on the lower ones, as shown in Figure 1. The plates can be transferred one column at a time from one column to another, but no bigger plate is allowed on the smaller plate. If you move all 64 plates from one column to another column How many times must I move at least? This is an old math game. It is said that monks in ancient Indian Brahmin temples played this game called the “Hanoi Pagoda Problem” and thought that if a game could end, it would mean