MathDB
Special Rectangular Grids

Source: Romania TST 2019 Day 5 P3, based on Rioplatense 2010 Level 2

March 5, 2022
combinatoricsgridcolouring

Problem Statement

Given an integer n2,n\geq 2, colour red exactly nn cells of an infinite sheet of grid paper. A rectangular grid array is called special if it contains at least two red opposite corner cells; single red cells and 1-row or 1-column grid arrays whose end-cells are both red are special. Given a configuration of exactly nn red cells, let NN be the largest number of red cells a special rectangular grid array may contain. Determine the least value NN may take over all possible configurations of exactly nn red cells