MathDB
RB coloring of a grid by 2n x 2n lines

Source: 2003 Romania District VII p3

August 15, 2024
combinatoricsColoring

Problem Statement

A grid consists of 2n2n vertical and 2n2n horizontal lines, each group disposed at equal distances. The lines are all painted in red and black, such that exactly nn vertical and nn horizontal lines are red. Find the smallest nn such that for any painting satisfying the above condition, there is a square formed by the intersection of two vertical and two horizontal lines, all of the same colour.