9.69 In a $7 \times 7$ grid, 19 cells are painted red. A row or a column is called red if it contains at least 4 red cells. How many red rows and columns can there be in the grid at most?
[Solution] First, we point out that the number of red rows and columns is no more than 8. Otherwise, if there are at least 9 red rows and columns, then there must be at least 5 red rows or 5 red columns, let's assume the former. Since each red row contains at least 4 red cells, it follows that there are at least 20 red cells on the board, which contradicts the given information.

Second, when we color all 16 cells of a $4 \times 4$ square in the table red, we get 4 red rows and 4 red columns, totaling 8. This shows that with 19 red cells, it is indeed possible to have 8 red rows and columns. Therefore, the maximum number sought is 8.