5. Several teams held a hockey tournament - each team played against each other once. 2 points were awarded for a win, 1 point for a draw, and no points for a loss. The team "Squirrels" won the most games and scored the fewest points. What is the minimum number of teams that could have participated in the tournament
Answer: 6 teams.

Solution. In a tournament with $n$ teams, the "Squirrels" scored less than the average number, i.e., no more than $n-2$ points. Therefore, some team must have scored more than the average, i.e., no less than $n$ points. For this, they had to win at least one match. Consequently, the "Squirrels" must have won at least two matches, i.e., scored no less than 4 points. Therefore, $n \geq 6$. An example for six teams is shown in the table.

| Team | $\mathbf{1}$ | $\mathbf{2}$ | $\mathbf{3}$ | $\mathbf{4}$ | $\mathbf{5}$ | Squirrels | Total |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| $\mathbf{1}$ |  | 1 | 1 | 1 | 1 | 2 | 6 |
| $\mathbf{2}$ | 1 |  | 1 | 2 | 1 | 0 | 5 |
| $\mathbf{3}$ | 1 | 1 |  | 1 | 2 | 0 | 5 |
| $\mathbf{4}$ | 1 | 0 | 1 |  | 1 | 2 | 5 |
| $\mathbf{5}$ | 1 | 1 | 0 | 1 |  | 2 | 5 |
| Squirrels | 0 | 2 | 2 | 0 | 0 |  | 4 |