We have a stick of length $g$ which is dropped and is broken into $n$ pieces. The choice of the $n-1$ breaking points are chosen randomly and independently on the stick.
What is the probability that with $n$ breaks some number of triangles $x$ can be formed?
Note that we say that a triangle can be formed if some three lengths we choose satisfy the triangle inequality. A piece can be used in multiple triangles.
I'm not expecting a perfect solution but if you have any cases or something that'd be great.