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Found problems: 1

2009 USAMO, 2
Let $n$ be a positive integer. Determine the size of the largest subset of $\{ -n, -n+1, \dots, n-1, n\}$ which does not contain three elements $a$, $b$, $c$ (not necessarily distinct) satisfying $a+b+c=0$.
oron wang orz inequalities induction pigeonhole principle ceiling function combinatorics symmetry casework floor and ceiling functions greedy algorithm mathematical induction number theory parity