Difference between revisions of "2006 USAMO Problems/Problem 2"
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== Problem == | == Problem == | ||
| − | For a given positive integer | + | |
| + | For a given positive integer <math> \displaystyle k </math> find, in terms of <math> \displaystyle k </math>, the minimum value of <math> \displaystyle N </math> for which there is a set of <math> \displaystyle 2k+1 </math> distinct positive integers that has sum greater than <math> \displaystyle N </math> but every subset of size <math> \displaystyle k </math> has sum at most <math>\displaystyle N/2 </math>. | ||
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== Solution == | == Solution == | ||
| + | |||
| + | {{solution}} | ||
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== See Also == | == See Also == | ||
| − | *[[2006 USAMO Problems]] | + | |
| + | * [[2006 USAMO Problems]] | ||
| + | * [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=490581#p490581 Discussion on AoPS/MathLinks] | ||
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| + | [[Category:Olympiad Combinatorics Problems]] | ||
Revision as of 19:24, 1 September 2006
Problem
For a given positive integer 
find, in terms of , the minimum value of 
for which there is a set of 
distinct positive integers that has sum greater than but every subset of size has sum at most 
.
Solution
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