分类计数、分步计数原理是排到组合的理论基础, 涂色问题就可以直接应用这两个计数原理来解决．例1 用n种不同颜色为下列两块广告牌着色(如图1、2),要求在①、②、③、④四个区域中相邻(有公共边界)的区域不用同一种颜色． (1)若n=6,为图1着色时共有多少种不同的方法? (2)若为图2着色时共有120种不同方法,求n. The principle of classification counting and step counting is the theoretical basis for arranging and combining. The problem of coloring can be solved directly by applying these two counting principles. Example 1 Coloring the following two billboards with n different colors (as shown in Figure 1, 2) requires that the adjacent (with common boundary) regions in the four regions 1, 2, 3, and 4 do not have the same color. (1) If n=6, how many different methods are there for coloring in Figure 1? (2) If there are 120 different methods for coloring in Figure 2, find n.