Task 2. In the Water Supply Cup football tournament, the teams "Pump", "Filter", "Pump", and "Gate" participated. Each team played against each other once (3 points were awarded for a win, 1 for a draw, and 0 for a loss). The team "Pump" scored the most points, and the team "Gate" scored the least. Could it have been that "Pump" outscored "Gate" by only 2 points? [4 points] (A. A. Zaslavsky)
Answer: Yes, it could. An example is provided in the table:

| team | P | F | N | S | p |
| :--- | :---: | :---: | :---: | :---: | :---: |
| Pump | - | 1 | 1 | 3 | 5 |
| Filter | 1 | - | 3 | 0 | 4 |
| Pump | 1 | 0 | - | 3 | 4 |
| Gate | 0 | 3 | 0 | - | 3 |

Notes. 1. Since "Pump" overtook "Filter," and "Filter" overtook "Gate," the difference in points between "Gate" and "Pump" cannot be less than two. It can be shown that all differences from 2 to 9 points between "Pump" and "Gate" are possible.