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.

Thanks.