\section*{Problem 1 - 101211}

In a parent-teacher meeting, exactly 18 fathers and exactly 24 mothers were present, with at least one parent of each student in the class attending.

Of exactly 10 boys and exactly 8 girls, both parents were present for each. For exactly 4 boys and exactly 3 girls, only the mother was present, while for exactly 1 boy and exactly 1 girl, only the father was present.

Determine the number of all those children in this class who have siblings in the same class! (There are no children in this class who have step-parents or step-siblings.)
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According to 3., 1 or 2 single fathers were present, so 16 or 17 fathers (out of the 18 present) were with the mother (4).

According to 2., at most 7 mothers were alone, so out of the total 24 mothers, at least 17 mothers were with the father (5).

From these two statements (4) and (5), it follows that there are exactly 17 parent couples, thus one single father and 7 single mothers remain (6).

According to 1., both parents are present for 18 students, meaning 17 parent couples (6) belong to 18 children, so one of them must be a pair of siblings (7). Now, one single father remains for 2 children according to 3. and (4), so these children are also siblings. Therefore, there are 2 pairs of siblings in the class, which means 4 children have siblings in the class.

\section*{Adopted from \([5]\)}