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RU-ALLRUSSIAN 2019 Problem 107

    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?

    Dataset text AI-MO AoPS. Quoted with source.

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