Difference between revisions of "2010 USAMO Problems/Problem 6"
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Revision as of 07:56, 19 April 2012
Problem
A blackboard contains 68 pairs of nonzero integers. Suppose that for each positive integer at most one of the pairs and 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 of points that the student can guarantee to score regardless of which 68 pairs have been written on the board.
Solution
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See Also
2010 USAMO (Problems • Resources) | ||
Preceded by Problem 5 |
Followed by Last question | |
1 • 2 • 3 • 4 • 5 • 6 | ||
All USAMO Problems and Solutions |