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4 out of 15 points, vertices of equilateral 2018 Malaysia OMK Intermediate A3

Source:

September 19, 2021
combinatoricscombinatorial geometry

Problem Statement

On each side of a triangle, 55 points are chosen (other than the vertices of the triangle) and these 1515 points are colored red. How many ways are there to choose four red points such that they form the vertices of a quadrilateral?