1988 IMO 第 5 题

(CZS 2) ${ }^{\mathrm{IMO} 2}$ Let $n$ be an even positive integer. Let $A_{1}, A_{2}, \ldots, A_{n+1}$ be sets having $n$ elements each such that any two of them have exactly one element in common while every element of their union belongs to at least two of the given sets. For which $n$ can one assign to every element of the union one of the numbers 0 and 1 in such a manner that each of the sets has exactly $n / 2$ zeros?

(CZS 2) ${ }^{\mathrm{IMO} 2}$ 令 $n$ 为偶正整数。设 $A_{1}、A_{2}、\ldots、A_{n+1}$ 为分别具有 $n$ 个元素的集合，其中任意两个元素恰好有一个共同元素，而它们并集的每个元素都属于至少两个给定集合。对于哪个 $n$ ，可以将数字 0 和 1 之一分配给并集的每个元素，使得每个集合都恰好有 $n / 2$ 个零？