9.2. Around a round table, 15 boys and 20 girls sat down. It turned out that the number of pairs of boys sitting next to each other is one and a half times less than the number of pairs of girls sitting next to each other. Find the number of boy - girl pairs sitting next to each other.
Answer: 10.

Solution. Let's call a group several children of the same gender sitting in a row, with children of the opposite gender sitting to the left and right of the outermost ones. Let $X$ be the number of groups of boys, which is equal to the number of groups of girls sitting in a row. It is easy to see that the number of pairs of adjacent children in each group is one less than the number of children in that group, so the number of pairs of boys sitting next to each other is $15-X$, and the number of pairs of girls sitting next to each other is $20-X$. According to the condition, $3(15-X)=2(20-X)$, from which $X=5$. Therefore, the number of pairs of adjacent boys is 10, the number of pairs of adjacent girls is 15, and the number of mixed adjacent pairs is $15+20-(10+15)=10$.

Grading criteria. Noted that the number of pairs of adjacent children in each group is one less than the number of children in that group: 1 point. Noted that the number of pairs of boys sitting next to each other is $15-X$, and the number of pairs of girls sitting next to each other is $20-X$: 2 points. Noted that the number of groups of boys is equal to the number of groups of girls: 1 point.