IMC 2017 · Problem 4

Day 124th IMC · Blagoevgrad, Bulgaria

Statement

There are nn 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 SS of people such that at least n/2017n/2017 persons in SS have exactly two friends in SS.

Official solution

Hidden so you can work on the problem first.

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