MathDB
Problem 7

Source: All-Russian Olympiad 2019 grade 10 Problem 7

April 24, 2019
combinatoricsset theory

Problem Statement

2424 students attend a mathematical circle. For any team consisting of 66 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 44 teams of 66 students each. May it happen that every such partition contains either 33 GOOD teams or exactly one GOOD team and both options are present?