2. In a school checkers tournament, each participant played against every other participant once. 2 points were awarded for a win, 1 point for a draw, and 0 points for a loss. There were 9 times fewer girls than boys, and the boys together scored 4 times more points than the girls together. How many points did the girls score?
Answer: 18 points.

Solution. Let $x$ be the number of girls participating in the tournament. Then there were $10 x$ participants in total, and they scored $10 x(10 x-1)$ points. According to the problem, the ratio of the number of points scored by girls to the number of points scored by boys is 1:4. Therefore, the girls scored one-fifth of the points, which is $2 x(10 x-1)$ points, meaning each girl won all $10 x-1$ games she played. If there were two girls among the participants, they would have had to both win their game against each other, which is impossible. Therefore, only one girl participated in the tournament; she scored 18 points.

Comment. The expression for the total number of points is written - 1 point, the expression for the number of points scored by girls is written - 2 points, the conclusion about the number of wins by girls is made - 2 points, the conclusion about the number of girls and the answer is obtained - 2 points. Points are summed.