# 2010 UNCO Math Contest II Problems/Problem 10

## Problem

Let where . What is the maximum number of elements in a subset of , which has at least three elements, such that for all in ? As an example, the subset of has the property that the sum of any two elements is strictly bigger than the third element, but the subset does not since is greater than . Since there is no subset of size satisfying these conditions, the answer for is .