Set $A$ consists of disjoint subsets $a_1, a_2, ..., a_n$. Although you do not know the cardinality of set $A$ ($|A|$), and the cardinality of each of the subset, you do know the proportion of each subset in terms of set $A$, that is you know $\frac{|a_1|}{|A|}, \frac{|a_2|}{|A|}, ... \frac{|a_n|}{|A|}$. You are allowed to add elements into subsets of $A$, and observe the change in proportionality of the subsets.