Let H⊂P(X) be a system of subsets of X and κ>0 be a cardinal number such that every x∈X is contained in less than κ members of H. Prove that there exists an f:X→κ coloring, such that every nonempty A∈H has a “unique” point, that is, an element x∈A such that f(x)=f(y) for all x=y∈A.(translated by Miklós Maróti) college contestsMiklos Schweitzerfunction