1985 USAMO 第 4 题

There are $n$ people at a party. Prove that there are two people such that, of the remaining $n-2$ people, there are at least $\lfloor n/2\rfloor -1$ of them, each of whom knows both or else knows neither of the two. Assume that "know" is a symmetrical relation; $\lfloor x\rfloor$ denotes the greatest integer less than or equal to $x$.

聚会上有 $n$ 人。证明有两个人，在剩下的 $n-2$ 人中，至少有 $\lfloor n/2\rfloor -1$ 个，每个人都认识这两个人，否则都不认识这两个人。假设“知道”是对称关系； $\lfloor x\rfloor$ denotes the greatest integer less than or equal to $x$.