Monochromatic Edges in Complete Multipartite Hypergraphs

Consider the following problem. In a school with three classes containing n students each, given that their genders are unknown, find minimum possible number of triples same-gender students—not all which from same class. Muaengwaeng asked this question and conjectured scenario occurs when boys, girls half-and-half. paper, we solve many generalizations problem including has more than classes, replaced by groups larger sizes, different gender is other non-binary attributes.