MathDB
Private hotel and its guests

Source: Baltic Way 2000 Problem 6

February 13, 2009
combinatorics unsolvedcombinatorics

Problem Statement

Fredek runs a private hotel. He claims that whenever n3 n \ge 3 guests visit the hotel, it is possible to select two guests that have equally many acquaintances among the other guests, and that also have a common acquaintance or a common unknown among the guests. For which values of n n is Fredek right? (Acquaintance is a symmetric relation.)