# 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>. | ||

+ | |||

== Solution == | == Solution == | ||

+ | |||

+ | {{solution}} | ||

+ | |||

== See Also == | == See Also == | ||

− | *[[2006 USAMO Problems]] | + | |

+ | * [[2006 USAMO Problems]] | ||

+ | * [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=490581#p490581 Discussion on AoPS/MathLinks] | ||

+ | |||

+ | [[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

*This problem needs a solution. If you have a solution for it, please help us out by adding it.*