Question 129
We call a coloring of an $m \times n$ table ($m, n \ge 5$) in three colors a *good coloring* if the following two conditions are satisfied:
1) Each cell has the same number of neighboring cells of two other colors;
2) Each corner cell has no neighboring cells of its color.
Find all pairs $(m, n)$ ($m, n \ge 5$) for which there exists a good coloring of $m \times n$ table.
1) Each cell has the same number of neighboring cells of two other colors;
2) Each corner cell has no neighboring cells of its color.
Find all pairs $(m, n)$ ($m, n \ge 5$) for which there exists a good coloring of $m \times n$ table.