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## Homework Statement

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?

## Homework Equations

## 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 2

^{n}- 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 2

^{n}- 1 people at the party.