user
A class consists of 20 students. Each student knows at least one other student in the class. If any two students who know each other form a pair, what is the minimum number of pairs needed to ensure that every student knows someone else in the class? Explain your thought process.
assistant
Here's how we can think about this problem:

1. We want to minimize the number of pairs formed while ensuring that every student knows at least one other student.
2. To achieve this, we can form pairs such that each pair consists of two students who know each other and no additional connections between the pairs.
3. In this case, each student will only know their partner in the pair, and there will be no overlapping friendships.
4. Since there are 20 students in total, we can create 10 non-overlapping pairs (20 / 2 = 10).
5. Therefore, the minimum number of pairs needed to ensure that every student knows someone else in the class is 10.

Final answer: The minimum number of pairs needed is 10.