国内外数学竞赛中有不少关于平面有限点集的试题,这类问题处理起来往往使人感到困难,常有不知从何做起的感觉。本文尝试着探讨解决这类问题的几种常见方法。一、“极端性”原则平面有限点集的元素是有限的,所以解决这类问题时,可以考虑从某些在数量上达到极端值(最大值或最小值)的元素作为分析问题的出发点,来寻求问题的答案。例1 给定平面上n(≥4)个点,其中无三点共线,证明:存在以已知点为顶点的三角形使得其余n-3个 There are many questions in the math contest at home and abroad on the limited set of planes. The handling of such problems often makes people feel difficult, and often there is a feeling that they do not know where to start. This article attempts to explore several common ways to solve this type of problem. 1. The “extreme” principle The elements of the finite set of planes are limited, so when solving such problems, it may be considered to start from the analysis of some elements that reach the extreme value (maximum or minimum) in quantity. Ask for answers to questions. Example 1 Given n (≥4) points on the plane, where there are no three collinear lines, it is proved that there are triangles with known points as their vertices, leaving the remaining n-3