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3

Part of 1989 India National Olympiad

Problems(1)

problem 3 of Indian Mathematical Olympiad 1989

Source: Combinatorics (box principle)

9/1/2009
Let A A denote a subset of the set {1,11,21,31,…,541,551} \{ 1,11,21,31, \dots ,541,551 \} having the property that no two elements of A A add up to 552 552. Prove that A A can't have more than 28 28 elements.
combinatorics unsolvedcombinatorics