10.4. On the cells of an 8 by 8 board, chips are placed such that for each chip, the row or column of the board in which it lies contains only one chip. What is the maximum possible number of chips on the board?
Answer: 14.

Solution: Let's match each chip to the row or column of the board in which it is the only one. If it is the only one in both, we match it to the row. From the condition, it follows that different chips are matched to different rows and columns. If not all rows and columns are matched, then their total number does not exceed 14, in each of them there is no more than one chip, so the total number of chips does not exceed 14. If, however, all rows, say, are matched, then there is a chip in each row - a total of 8.

Example of placing 14 chips: all cells of the left column and the bottom row are filled, except for the bottom left corner cell.

Evaluation: 5 points. Example: 2 points. Any incorrect estimate with any reasoning - 0 points.