# Task 1. (2 points)

In a class, each student has either 5 or 6 friends (friendship is mutual), and any two friends have a different number of friends in the class. What is the smallest number of students, greater than 0, that can be in the class?
Answer: 11

## Solution:

Let's look at some person. Suppose he has five friends. Then each of these five people has six friends. Similarly, there are at least another 6 people with five friends each. In total, there are 11 people.

It is quite easy to construct an example: two groups of 5 and 6 people, people from different groups are friends with each other, but not within the same group.

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