2001 AIME II Problem 5

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?

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.