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forum.virtualchallengemeets.com • View topic - 2010 USAMO 6

2010 USAMO 6

Pose Olympiad-level questions to the monkeys in the peanut #.

2010 USAMO 6

Postby stupidityismygam » Wed May 05, 2010 6:07 am

A blackboard contains 68 pairs of nonzero integers. Suppose that for each positive integer [unparseable or potentially dangerous latex formula] at most one of the pairs [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] is written on the blackboard. A student erases some of the 136 integers, subject to the condition that no two erased integers may add to 0. The student then scores one point for each of the 68 pairs in which at least one integer is erased. Determine, with proof, the largest number [unparseable or potentially dangerous latex formula] of points that the student can guarantee to score regardless of which 68 pairs have been written on the board.
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