Difference between revisions of "2001 AIME II Problems/Problem 5"

 
m
Line 1: Line 1:
 
== Problem ==
 
== Problem ==
 +
A set of positive numbers has the <math>triangle~property</math> if it has three distinct elements that are the lengths of the sides of a triangle whose area is positive. Consider sets <math>\{4, 5, 6, \ldots, n\}</math> of consecutive positive integers, all of whose ten-element subsets have the triangle property. What is the largest possible value of <math>n</math>?
  
 
== Solution ==
 
== Solution ==
 +
{{solution}}
  
 
== See also ==
 
== See also ==
* [[2001 AIME II Problems]]
+
{{AIME box|year=2001|n=II|num-b=4|num-a=6}}

Revision as of 00:41, 20 November 2007

Problem

A set of positive numbers has the $triangle~property$ if it has three distinct elements that are the lengths of the sides of a triangle whose area is positive. Consider sets $\{4, 5, 6, \ldots, n\}$ of consecutive positive integers, all of whose ten-element subsets have the triangle property. What is the largest possible value of $n$?

Solution

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

See also

2001 AIME II (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions
Invalid username
Login to AoPS