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forum.virtualchallengemeets.com • View topic - USAMO 2007 Problem 3

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USAMO 2007 Problem 3

Posted: Wed Apr 25, 2007 5:33 pm

by zefuri

Let [unparseable or potentially dangerous latex formula] be a set containing [unparseable or potentially dangerous latex formula] elements, for some positive integer [unparseable or potentially dangerous latex formula]. Suppose that the [unparseable or potentially dangerous latex formula]-element subsets of [unparseable or potentially dangerous latex formula] are partitioned into two classes. Prove that there are at least [unparseable or potentially dangerous latex formula] pairwise disjoint sets in the same class.