20.9. Ali, Borya, and Vasya played several games of chess, and each played the same number of games. Could it have turned out that Ali had the fewest losses, Borya had the most wins, and Vasya had the most points?
20.9. Answer: yes, it could. To construct a corresponding example, consider three types of tournaments with the following tables:

|  | Wins | Draws | Losses | Points |
| :---: | :---: | :---: | :---: | :---: |
| Alik | 0 | 4 | 0 | 2 |
| Borya | 1 | 2 | 1 | 2 |
| Vasya | 1 | 2 | 1 | 2 |


|  | Wins | Draws | Losses | Points |
| :---: | :---: | :---: | :---: | :---: |
| Alik | 1 | 2 | 1 | 2 |
| Borya | 1 | 2 | 1 | 2 |
| Vasya | 0 | 4 | 0 | 2 |


|  | Wins | Draws | Losses | Points |
| :---: | :---: | :---: | :---: | :---: |
| Alik | 0 | 1 | 1 | $1 / 2$ |
| Borya | 0 | 1 | 1 | $1 / 2$ |
| Vasya | 2 | 0 | 0 | 2 |

Let $a$ be the number of tournaments of the first type, $b$ - of the second, and $c$ - of the third. Then Alik has $b+c$ losses, Borya and Vasya have $a+b+c$ and $a$ losses. Borya has $a+b$ wins, Alik and Vasya have $b$ and $a+2c$ wins. Vasya has $2(a+b+c)$ points, Alik and Borya have $2a+2b+c/2$ points. Therefore, the inequalities $a>b+c$, $b>2c$, and $c>0$ must be satisfied. For example, we can take $c=1$, $b=3$, and $a=5$.