API · no tools. This is the prompt and response recorded for this attempt; a full solution may not have been returned.
Return a single integer only. The problem has been revised so that no final answer is an irrational number, a parameterized expression, a range, a proof, a drawing, a graph, a locus equation, or a region description.
Let . Choose four distinct vertices of a regular -gon uniformly at random. Let be the probability that the quadrilateral whose vertices are the four chosen points contains the center of the polygon in its interior. If in lowest terms, find .
The probability that a randomly chosen quadrilateral from a regular 9-gon contains the center is . In lowest terms, and , so .
\boxed{12}
Comparative Analysis (P3) (Average across runs)
Averages use reported measurements only. Missing usage is not treated as zero.