1. The problem statement, all variables and given/known data Santa has n types of presents. Every child can receive at most one present of each type and: a) every child has to get a present AND cannot receive the same set of presents as any other child. b) for every 2 children, there must be a present that both of the children get How many children can attend the Christmas party at most? 2. Relevant equations 3. The attempt at a solution Assuming my interpretation is correct: Every child getting at most one of each present type - is this a fancy way of saying injection? All sets of presents have to be different. There are 2n - 1 different sets of presents (we cannot count the empty set since every child has to have a present - we are not concerned if the children do not receive the same number of presents i.e the cardinalities need not be equal). Per every 2 children, they must have a common present - this is the troublesome bit. What does it mean, exactly? I am sure it doesn't mean that ALL of the chosen subsets need to have a common element. This seems to be the attendance limiter - otherwise I can have 2n - 1 people at the party.