Problem

Source: 2017 Romania JBMO TST 5.4

Tags: combinatorial geometry, combinatorics, Coloring



Consider an m×n board where m,n3 are positive integers, divided into unit squares. Initially all the squares are white. What is the minimum number of squares that need to be painted red such that each 3×3 square contains at least two red squares? Andrei Eckstein and Alexandru Mihalcu