Question 128
In each of the cells of an $n \times m$ table is written one of the letters $a$, $b$, or $c$. The corresponding letter in every two rows, respectively every two columns of the table, coincide in at most $k \ge 0$ positions. Determine $m$, $n$ and $k$, if
$$
\frac{2mn + 6k}{3(m + n)} \ge k + 1.
$$
$$
\frac{2mn + 6k}{3(m + n)} \ge k + 1.
$$