Question 127
There are 100 students in a summer camp, with exactly 2024 pairs of mutual friends. We need to divide them into 50 groups of 2 students each. Prove that:
1. It's possible to group them such that at most 20 groups contain mutual friends;
2. It's possible to group them such that at least 23 groups contain mutual friends;
3. It's possible to group them such that exactly 22 groups contain mutual friends.
1. It's possible to group them such that at most 20 groups contain mutual friends;
2. It's possible to group them such that at least 23 groups contain mutual friends;
3. It's possible to group them such that exactly 22 groups contain mutual friends.