We study the following combinatorial search problem: Reconstruct an unknown partition of the set [n]={1,...,n} into at most K disjoint non-empty subsets (classes) by making queries about subsets $Q_i \subseteq [n]$ such that the query returns the number of classes represented in $Q_i$. The goal is to reconstruct the whole partition with as few queries as possible. We also consider a variant of the problem where a representative of each class should be found without necessarily reconstructing the whole partition. Besides its theoretical interest, the problem has practical applications. Paper \cite{SBAW-RECOMB97} considers a physical mapping method based on hybridizing probes to chromosomes using the FISH technology. Under some reasonable assumptions, the method amounts to finding a partition of probes determined by the chromosome they hybridize to, and actually corresponds to the above formalization.