3[ Examples and counterexamples. Constructions]

In the cells of a $5 \times 5$ square table, the numbers 1 and -1 are arranged. It is known that the number of rows with a positive sum is greater than the number of rows with a negative sum.

What is the maximum number of columns in this table that can have a negative sum?
Let's consider one of the possible examples (see the table). The sum of the numbers in each of the three upper rows is positive, while the sum of the numbers in each column is negative.

| 1 | 1 | 1 | -1 | -1 |
| :---: | :---: | :---: | :---: | :---: |
| 1 | -1 | 1 | -1 | 1 |
| -1 | 1 | -1 | 1 | 1 |
| -1 | -1 | -1 | -1 | -1 |
| -1 | -1 | -1 | -1 | -1 |

## Answer

5 columns.

Problem