[1]中给出了如下一个组合问题: 一个给定的凸n边形A_0A_1A_2…A_(n-1),用不在形内相交的对角线将它分成n-2个三角形,问有多少种不同的分法? 徐士英教授在[2]中指出[1]的解答是错误的,并且给出了一个正确解法。但徐教授的解法利用了“生成函数”这一高等工具,不便于中学生接受和理解。 The following combination problem is given in [1]: A given convex n-angle A_0A_1A_2...A_(n-1) is divided into n-2 triangles by a diagonal line that does not intersect within the shape. Different kinds of points? Prof. Xu Shiying pointed out in [2] that the answer to [1] is wrong and gives a correct solution. However, Professor Xu’s solution makes use of the “generative function” as an advanced tool, which is not easy for middle school students to accept and understand.