5. Ten football teams conducted two tournaments over two years. Each year, the results of the tournament were recorded in a table, listing the teams from first to tenth place. A team is considered stable if there is at least one other team that ranks lower than it in both tables. What is the minimum and maximum number of stable teams that can result from the two tournaments? Solution. According to the results of the two tournaments, there cannot be ten stable teams in the tables, as there will be no team that ranks lower than all ten teams in any table. The maximum number of stable teams is nine, and the minimum number of stable teams is zero. We will provide examples of team placements in the tables. Nine stable teams can be achieved if the same team finishes in tenth place in both tournaments. Then, for each of the remaining nine teams, the stability condition will be met.

Zero stable teams can be achieved with the following two tables for the two years:

| Place | Team Number |
| :--- | :--- |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| $\ldots$ | $\ldots$ |
| 9 | 9 |
| 10 | 10 |


| Place | Team Number |
| :--- | :--- |
| 1 | 10 |
| 2 | 9 |
| 3 | 8 |
| $\ldots$ | $\ldots$ |
| 9 | 2 |
| 10 | 1 |

Reversing the order of the teams results in no team having a lower-ranked team in the first year for the second year.
Answer: The minimum number is 0 stable teams, the maximum number is 9 stable teams.