2006 CMO 第 5 题

Suppose $X$ is a set with $|X| = 56$ . Find the minimum value of $n$ , so that for any 15 subsets of $X$ , if the cardinality of the union of any 7 of them is greater or equal to $n$ , then there exists 3 of them whose intersection is nonempty.

假设 $X$ 是一个包含 $|X| 的集合= 56 美元。求$n$的最小值，使得对于$X$的任意 15 个子集，如果其中任意 7 个子集的并集基数大于或等于$n$ ，则存在 3 个交集非空的子集。