Problem

Source: 2017 Romania JBMO TST 5.4

Tags: combinatorial geometry, combinatorics, Coloring



Consider an $m\times n$ board where $m, n \ge 3$ 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 $3\times 3$ square contains at least two red squares? Andrei Eckstein and Alexandru Mihalcu