A serial-sided polygon is a polygon with side-lengths equal to $1,2,\dotsb,n$ in a random order. For a given positive integer $n$, what is the probability that a serial-suded polygon has an angle between $30^°$,$60^°$?
I've only been able to try the complex-plane representation of polygons that has lead to absolutely nothing. The only fact I have is the trivial statement that any of the polygons that don't satisfy the condition shall have numerous angles more that 60 since they can't have all of their angles less then 30. (As said, trivial)
Any help would be appreciated!