Existence of monochromatic triangle
Source: 2023 Grosman MO, P7
September 8, 2023
combinatorical geometryColoringEquilateral Trianglecombinatoricsgeometry
Problem Statement
The plane is colored with two colors so that the following property holds: for each real there is an equilateral triangle of side length whose vertices are of the same color.Prove that for any three numbers for which the sum of any two is greater than the third there is a triangle with sides , , and whose vertices are of the same color.