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Print24th Hellenic Mathematical Olympiad
Greece counting and probability
Problem
Each of the students of a class sent on Christmas period cards to exactly co-students. Prove that at least of the students each received the card of the other.
Solution
students determine different pairs. The cards sent are totally , a number greater than the number of different pairs. Hence at least the members of one pair received each the card of the other.
Techniques
Pigeonhole principle