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China Mathematical Olympiad 1989 problem5

Source: China Mathematical Olympiad 1989 problem5

October 29, 2013
combinatorics unsolvedcombinatorics

Problem Statement

Given 19891989 points in the space, any three of them are not collinear. We divide these points into 3030 groups such that the numbers of points in these groups are different from each other. Consider those triangles whose vertices are points belong to three different groups among the 3030. Determine the numbers of points of each group such that the number of such triangles attains a maximum.