Problem 7
Source: All-Russian Olympiad 2019 grade 10 Problem 7
April 24, 2019
combinatoricsset theory
Problem Statement
students attend a mathematical circle. For any team consisting of students, the teacher considers it to be either GOOD or OK. For the tournament of mathematical battles, the teacher wants to partition all the students into teams of students each. May it happen that every such partition contains either GOOD teams or exactly one GOOD team and both options are present?