Difference between revisions of "2010 USAMO Problems/Problem 6"
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Revision as of 12:45, 4 July 2013
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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
