A separating family is a set of subsets in which each pair of adjacent elements are found separated, each in one of two disjoint subsets. The 26 letters of the alphabet can be separated by a family of 9, (a b c d e f g h i) | (j k l m n o p q r) | (s t u v w x y z) (a b c j k l s t u) | (d e f m n o v w x) | (g h i p q r y z) (a d g j m p s v y) | (b e h k n q t w z) | (c f i l o r u x). The minimal size of the separating family for an n-set is 0, 2, 3, 4, 5, 5, 6, 6, 6, 7, 7, 7, ... (OEIS A007600).

Katona's problem