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笔者参加了1989年全国初中数学联赛湖北省试卷的阅卷工作,现就当时的有关记要进行整理,对第二试第三题予以详细分析,并将此题推广,从中可以得到一些数学竞赛题如何命题的启示。第二试第3题如下:设,A_1,A_2,A_3,A_4,A_5,A_6是平面上的6点,其中任何三点不共线,(1)如果这些点之间任意连接13条线段,证明:必存在4点,它们每两点之间都有线段连接;(2)如果这些点之间只连接有12条线段,请你画一个图形,说明(1)的结论不成立(不必用文字说明)。
The writer participated in the 1989 national Hubei junior high school mathematics league examination paper examination work, now on the relevant remarks at the time of finishing, the second test to give a detailed analysis of the third question, and the promotion of this question, from which you can get some math contest questions How Propositions Revelation. The second test of the second question is as follows: Let A_1, A_2, A_3, A_4, A_5, A_6 be 6 points on the plane, any three points are not collinear, (1) If 13 lines are randomly connected between these points, Proof: There must be 4 points, and they have line segment connections between every two points; (2) If there are only 12 line segments connected between these points, please draw a graph, indicating that the conclusion of (1) is not valid (do not use text Description).