Combinatorics · Pigeonhole principle · Double counting · Directed graphs · Out degrees
In a group of \(20\) people, every person chooses ten of the other nineteen and sends one letter to each of them. Prove that there are two people who sent a letter to each other.
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Serbian Republic Competition (Republicko takmicenje) 2003, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source