Around a round table, 10 boys and 15 girls sat down. It turned out that there were exactly 5 pairs of boys sitting next to each other.

How many pairs of girls sitting next to each other are there?

#
How many groups of boys sitting next to each other are there at the table?

## Solution

Groups of boys sitting next to each other alternate with groups of girls sitting next to each other. Let the number of groups of boys sitting next to each other be $k$. Then the number of groups of girls sitting next to each other is also $k$. In a group of $n$ boys sitting next to each other, there are exactly $n-1$ pairs of boys sitting next to each other. Since we have a total of 10 boys and $k$ groups, there are $10-k$ pairs of boys sitting next to each other. According to the problem, $k=5$. Therefore, the number of pairs of girls sitting next to each other is $15-5=10$.

## Answer

10 pairs.