Problem

Source: All-Russian Olympiad 2019 grade 10 Problem 7

Tags: combinatorics, set theory



$24$ students attend a mathematical circle. For any team consisting of $6$ 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 $4$ teams of $6$ students each. May it happen that every such partition contains either $3$ GOOD teams or exactly one GOOD team and both options are present?