International Mathematics Competition
for University Students
2017

IMC2017: Day 1, Problem 4

4. There are $n$ people in a city, and each of them has exactly $1000$ friends (friendship is always symmetric). Prove that it is possible to select a group $S$ of people such that at least $n/2017$ persons in $S$ have exactly two friends in $S$.

Proposed by: Rooholah Majdodin and Fedor Petrov, St. Petersburg State University

Hint: Choose the set $S$ randomly.

  Solution