MathNet 2011 Question 59

All cells of a $9 \times 10$ board are colored red, blue, and green. In any row of the board the number of red cells is no smaller than the number of blue cells and no smaller than the number of green ones. In any column of the board the number of blue cells is no smaller than the number of red cells and no smaller than the number of green ones.
Find the greatest and the smallest possible number of green cells of the board.
(I. Voronovich)