Problem 4.2. In class 4A, each child has no fewer than 11 classmates and no fewer than 13 female classmates. What is the smallest number of children that can study in this class?
Answer: 26.

Solution. It is not difficult to verify that a class consisting of 12 boys and 14 girls satisfies the condition of the problem. Now let's prove that it cannot be less.

It is clear that there are both boys and girls in the class. Each boy in the class has at least 11 classmates, so there must be at least 12 boys in total. Each girl in the class has at least 13 female classmates, so there must be at least 14 girls in total. Therefore, there are at least $12+14=26$ children in the class.