View source for G285 2021 MC-IME II

==Problem 1==
Let <math>20</math> points lie in the interior of the circumcircle of regular decagon <math>ABCDEFGHIJ</math>. If each point is connected to the second farthest point away from itself by a line, find the maximum number of regions created by the intersections of lines.

[[G285 2021 MC-IME II|Solution]]

==Problem 2==
Suppose <math>\phi(n)</math> denote the number of integer <math>k</math> where <math>1 \le k < n</math> such that <math>\gcd(k,n)=1</math>. If <cmath>\sum_{p=1}^{n} \frac{1}{2^p \phi(p)}</cmath> can be represented as <math>\phi(n) \cdot l</math> for some constant <math>l</math>, find <math>l \mod 1000</math>