MathDB
There is a tri-blued unit square

Source: India TST 2016 Day 3 Problem 3

July 22, 2016
combinatoricssquare grid

Problem Statement

Let nn be an odd natural number. We consider an n×nn\times n grid which is made up of n2n^2 unit squares and 2n(n+1)2n(n+1) edges. We colour each of these edges either <spanclass=latexitalic>red</span>\color{red} <span class='latex-italic'>red</span> or <spanclass=latexitalic>blue</span>\color{blue}<span class='latex-italic'>blue</span>. If there are at most n2n^2 <spanclass=latexitalic>red</span>\color{red} <span class='latex-italic'>red</span> edges, then show that there exists a unit square at least three of whose edges are <spanclass=latexitalic>blue</span>\color{blue}<span class='latex-italic'>blue</span>.