6. Several cells on a $14 \times 14$ board are marked. It is known that no two of the marked cells are in the same row and the same column, and also that a knight can, starting from any marked cell, reach any other marked cell via marked cells. What is the maximum possible number of marked cells?
Answer: 14.

Sketch of the solution.

Estimate. In each row, there is no more than one marked cell (field), and therefore no more than 14 cells are marked.

Example in the image.

![](https://cdn.mathpix.com/cropped/2024_05_06_f259ce87565f6e7a499dg-3.jpg?height=503&width=507&top_left_y=1188&top_left_x=865)