Not mine:
If t1,t2,...tn are positive reals for some integer n and:
(t1+t2+...+tn)(1/t1 + 1/t2 +...+1/tn) < n^2+1
prove that any three distinct ti, tj, tk are side lengths of a triangle.
It's a good idea to look at the case n=3 first, since it's much more obvious and you can see how it works.
