Problem

Source: Ukraine TST 2014 p6

Tags: combinatorics, Coloring



Let n3 be an odd integer. Each cell is a n×n board painted in yellow or blue. Let's call the sequence of cells S1,S2,...,Sm path if they are all the same color and the cells Si and Sj have one in common an edge if and only if |ij|=1. Suppose that all yellow cells form a path and all the blue cells form a path. Prove that one of the two paths begins or ends at the center of the board.