24. In a $100 \times 100$ square table, some cells are shaded. Each shaded cell is the only shaded cell either in its column or in its row. What is the maximum number of cells that can be shaded?

## 10th grade
75.24. Answer: 198. Let's mark for each shaded cell the line in which it is the only one. Then among the marked lines - not all columns, otherwise there would be no more than 100 shaded cells. Similarly, not all rows are marked. Therefore, the number of marked lines is no more than 198. On the other hand, if we shade all cells in any row and in any column, except for the cell at their intersection, we get the required coloring with 198 cells.