1. (13 points) What is the minimum number of participants that could have been in the school drama club if the number of fifth graders was more than $25 \%$ but less than $35 \%$, the number of sixth graders was more than $30 \%$ but less than $40 \%$, and the number of seventh graders was more than $35 \%$ but less than $45 \%$ (there were no participants from other grades).
Answer: 11. Fifth-graders -3, sixth-graders -4, seventh-graders - 4.

Solution. Let the required number of participants be

$$
n=a+b+c
$$

where $a$ is the number of fifth-graders, $b$ is the number of sixth-graders, $c$ is the number of seventh-graders. Note: $a<c$ and all three numbers constitute more than 0.25 and less than 0.5 of the total number of participants according to the condition. Consider all remaining cases of the sum $(*)$ taking into account these observations.

$5=1+2+2$. The condition for sixth-graders is not met.

$7=2+2+3$. The condition for sixth-graders is not met.

$8=2+3+3$. The condition for fifth-graders is not met.

$9=3+3+3$. The condition $a<c$ is not met.

$10=3+3+4$. The condition for sixth-graders is not met.

$11=3+4+4$. All conditions are met.

Evaluation criteria. Correct answer based on a complete enumeration without losing cases - 13 points. Correct answer, but not all possible cases are considered - 7 points. For the correct answer without explanation 2 points.