Task 1. In the club, 36 schoolchildren are attending. If any 33 of them come to the lesson, then girls will always be more than half. But if 31 students come to the lesson, it may turn out that more than half of them are boys. How many girls are attending the club? (20 points)
Answer: 20.

Solution: Since among any 33 children, there are more girls than half, then boys among them are less than half, that is, no more than 16. Therefore, there are no more than 16 boys in total, because if there were at least 17, it could happen that 17 boys and another 16 students came, and the boys would already be more than half.

Since there is a group of 31 students in which there are more boys than half, there are at least 16 boys in this group. Therefore, there are exactly 16 boys in total. Then the number of girls is $36-16=20$.

Criteria: Only shown that there are no fewer than 16 boys - 4 points.

Only shown that there are no more than 16 boys - 8 points.