Difference between revisions of "2006 USAMO Problems/Problem 2"

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== Problem ==
 
== Problem ==
For a given positive integer '''k''' find, in terms of '''k''', the minimum value of <math>N</math> for which there is a set of <math>2k+1</math> distinct positive integers that has sum greater than <math>N</math> but every subset of size '''k''' has sum at most <math>\frac{N}{2}</math>.
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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 ==
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{{solution}}
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== See Also ==
 
== See Also ==
*[[2006 USAMO Problems]]
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* [[2006 USAMO Problems]]
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* [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 $\displaystyle k$ find, in terms of $\displaystyle k$, the minimum value of $\displaystyle N$ for which there is a set of $\displaystyle 2k+1$ distinct positive integers that has sum greater than $\displaystyle N$ but every subset of size $\displaystyle k$ has sum at most $\displaystyle N/2$.

Solution

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See Also

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