MathDB
4 colors for each point of a right triangle

Source: Portugal OPM 1996 p5

May 18, 2024
Coloringcombinatoricscombinatorial geometry

Problem Statement

Consider a right-angled triangle whose legs are 11 cm long. Suppose that each point of the triangle was assigned a color from the set of Brown, Blue, Green and Orange colors. It proves that, whatever way this was done, there is at least one pair of points of the same color at a distance equal to or greater than 222-\sqrt 2 cm from each other.