This game

Our variable groups are tenants and homeowners. Tenants: F G J K M Homeowners: P Q R S Rule 2 is saying that whoever the chairperson is, there must be exactly one other person from their group in, and the other three in must be from the other group. And, with rule one, we know that since each group has to have at least two, our only possible games are two tenants and three homeowners, or two homeowners and three tenants. If the chairperson is F, for example, we must have exactly one of G J K M in, and exactly three of P Q R S in.