| [ QuizWit ] in KIDS 글 쓴 이(By): guest (legacy) 날 짜 (Date): 1995년08월29일(화) 07시18분14초 KDT 제 목(Title): [A2]집합문제. Assume n>= 872, then choose one set A. For every element a in A, we define Ga = {X|a belongs to X, X is not A while is one of {An}}. From the last condition, at least two elements have non- empty Ga. At the same time, by the 2nd condition, |Ga| <= 29. (since in a given Ga all sets are disjoint but a while for a Y in Gb they have one common elements which is not b. (here a != b). Thus maximum is 29 at most.) Now combine all above. n <= 1+30*29 = 871. Hence, n < 872. |