A.Y. of evnin

2000 people registered on a new website. Each of them invited 1000 people to be their friends. Two people are considered friends if and only if each of them invited the other to be a friend. What is the minimum number of pairs of friends that could have formed?
Evaluation. A total of 2,000,000 invitations were sent, while the number of pairs on the site is $1000 \cdot 1999 = 1999000$. There are 1000 more invitations than pairs, so within at least 1000 pairs, two invitations were sent. Therefore, at least 1000 pairs were formed.

Example: Place everyone at the vertices of a regular 2000-gon, and let each person invite the next 1000 people in a clockwise direction. Then, friends will only be those located at opposite vertices.

## Answer

1000 pairs.