MathDB
coloring 1x1 in a nxn array

Source: 2023 Czech-Polish-Slovak Match Junior, individual p4 CPSJ

May 5, 2024
combinatoricsColoring

Problem Statement

Each field of the n×nn \times n array has been colored either red or blue, with the following conditions met: \bullet if a row and a column contain the same number of red fields, the field at their intersection is red; \bullet if a row and a column contain different numbers of red cells, the field at their intersection is blue. Prove that the total number of blue cells is even.