The smallest n-uniform hypergraph with positive discrepancy

A two-coloring of the vertices X of the hypergraph H=(X, ε) by red and blue has discrepancy d if d is the largest difference between the number of red and blue points in any edge. A two-coloring is an equipartition of H if it has discrepancy 0, i.e., every edge is exactly half red and half blue. Let f(n) be the fewest number of edges in an n-uniform hypergraph (all edges have size n) having positive discrepancy. Erdo{combining double acute accent}s and Sós asked: is f(n) unbounded? We answer this question in the affirmative and show that there exist constants c ₁ and c ₂ such that {Mathematical expression} where snd(x) is the least positive integer that does not divide x.