Problem

Source: IX International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade

Tags: table, combinatorics, Coloring, combinatorics unsolved



The cells of a table m x n, $m \geq 5$, $n \geq 5$ are colored in 3 colors where: (i) Each cell has an equal number of adjacent (by side) cells from the other two colors; (ii) Each of the cells in the 4 corners of the table doesn’t have an adjacent cell in the same color. Find all possible values for $m$ and $n$.