Example 2-1 There are $n$ disks of different sizes stacked on column $A$ in ascending order of their radii, as shown in Figure 2-1. Each move allows transferring only one disk to either column $B$ or column $C$, and it is not allowed to place a larger disk on top of a smaller one. The goal is to transfer all $n$ disks from column $A$ to column $C$. Please design a method and estimate how many moves are required. The problem provides three columns $A, B, C$ for use.