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涂色问题是排列组合中的重要题型,这类题的特点是:思路新颖、解法灵活、技巧性强,同学们在解这类题时常感困难,经常出错误.为帮助同学们解决这个问题,本文举例说明涂色问题的解法,供同学们参考.例1要用四种颜色给河北、河南、山东、山西四省的地图上色(见中国地图),每一省一种颜色,只要求相领省不同色,问共有几种不同的上色方法?解法1(元素分析法)分两类,一类用四种颜色涂,有A44=24种不同的方法.第二类用三种颜色涂,选三种颜
Coloring problems are arranged in an important combination of questions, these questions are characterized by: new ideas, flexible solution, highly skilled, students often feel difficult to solve such questions, often mistakes. To help students solve this Problem, this paper gives an example to explain the problem of coloring solution, for the students to refer to.Example 1 To use four colors to Hebei, Henan, Shandong, Shanxi provinces map (see China map), each province a color, There is a total of 24 different methods, A44 = 24, and the second is to use the four colors Three colors painted, choose three colors