2007 USAMO 第 3 题

Let $S$ be a set containing $n^2+n-1$ elements, for some positive integer $n$. Suppose that the $n$-element subsets of $S$ are partitioned into two classes. Prove that there are at least $n$ pairwise disjoint sets in the same class.

对于某个正整数 $n$，令 $S$ 为包含 $n^2+n-1$ 元素的集合。假设 $S$ 的 $n$ 个元素子集被划分为两类。证明同一类中至少有 $n$ 成对不相交集。