MathDB
2n + 1 students chooses a finite set of consecutive integers

Source: Switzerland - 2013 Swiss MO Final Round p5

December 30, 2022
combinatoricsconsecutivenumber theory

Problem Statement

Each of 2n+12n + 1 students chooses a finite, nonempty set of consecutive integers . Two students are friends if they have chosen a common number. Everyone student is friends with at least nn other students. Show that there is a student who is friends with everyone else.