Schoolchildren living in four cities
Source: Tuymaada 2010
August 7, 2010
combinatorics unsolvedcombinatorics
Problem Statement
In a country there are schoolchildren living in four cities. At the end of the school year a state examination was held in 9 subjects. It is known that any two students have different marks at least in one subject. However, every two students from the same city got equal marks at least in one subject. Prove that there is a subject such that every two children living in the same city have equal marks in this subject.Fedor Petrov