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一、问题的提出例1将n种颜色涂在三角形三边a,b,c上,相邻边不同色,求不同的涂色方法种数.分析涂a边共有n种方法,涂b边共有n-1种方法,涂c边共有n-2种方法,则涂色方法数为n(n-1)(n-2)种.这是一道较为简单常规的涂色问题,作为我校的一道基础年段模块测试题出现,得分率较高.作为任意选修课的素材,我让同学将其类比至其它n边形,看是否可以得到一系列具有共性的结论,并加以证明,下面是师生课堂上的类比.
First, the problem raised Example 1 n kinds of colors painted on the triangular sides a, b, c, adjacent sides of different colors, find a different method of coloring species. A total of n-1 kinds of methods, coated c edge of a total of n-2 kinds of methods, then the number of coloring method for the n (n-1) (n-2) species.This is a simpler conventional coloring problem, as my school As a material for any elective course, I asked my classmates to compare them to other n-polygons to see if you can get a series of common conclusions and prove that the following Is the teacher and student class analogy.