Prove existence of 5 non-attacking rooks

Question

Problem: There are $41$ rooks on a $10\times10$ chessboard. Prove that there must exist $5$ rooks, none of which attack each other.

---

I could only observe that at least one of rows and at least one column must contain at least 5 rooks. Please help!!

Answer 1

HINT: Divide the board into diagonals. Here’s an example of what I mean on a small board:

$$\begin{array}{|c|c|c|} \hline 1&2&3\\ \hline 3&1&2\\ \hline 2&3&1\\ \hline \end{array}$$