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 vertical and horizontal lines, each group disposed at equal distances. The lines are all painted in red and black, such that exactly vertical and horizontal lines are red.
Find the smallest 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.