MathDB
0323 coloring points 3rd edition Round 2 p3

Source:

May 9, 2021
combinatoricsColoring3rd edition

Problem Statement

Each point in the Euclidean space is colored with one of n2n \ge 2 colors, and each of the nn colors is used. Prove that one can find a triangle such that the color assigned to the orthocenter is different from all the colors assigned to the vertices of the triangle.