MathNet 2019-part-01 — 184 problems (EN–VI) Question 159

Cells of an $11 \times 11$ table are colored with $n$ colors (each cell is colored with exactly one color). For each color the total amount of the cells of this color is not less than $7$ and not greater than $13$.
Prove that there exists at least one row or column which contains cells of at least four different colors.