Question 5
One of the numbers $1$, $2$, ..., $n$ is written in each cell of a $17 \times 17$ table for a certain $n \in \mathbb{N}$; all of these numbers are used. If a row contains two cells $C_1$ and $C_2$ with equal numbers $k$ and $C_1$ is to the left of $C_2$ then there are no numbers $k$ in the column of $C_1$ that are above $C_1$. Determine the minimal $n$ for which such a table exists.