ON A COMBINATORIAL PROBLEM . 11

Let M be a set and F a family of its subsets. F is said by E. W. MILLER [5] to possess property B if there exists a subset K of M so that no set of the family F is contained either in K or in K (K is the complement of K in M) . HAJNAL and 1 [2] recently published a paper on the property B and its generalisations . One of the unsolved problems we state asks : What is the smallest integer in (n) for which there exists a family F of sets A 1 , . . ., A ( „ ) each having n elements which does not possess property B? Throughout this paper A 1 will denote sets having n elements .