2011 AIME I Problems/Problem 10
Problem
The probability that a set of three distinct vertices chosen at random from among the vertices of a regular n-gon determine an obtuse triangle is 
. Find the sum of all possible values of 
.
Solution
This is not complete and may not be correct.
triangle is obtuse 
there exists 
consecutive points that are not chosen. (i.e. all 3 points of the triangle are on the same half of the n-gon.
The probability of this happening is obviously lesser than 
, but 
. Thus there is no such possible n-gon?
