Suppose that we are given 40 points equally spaced around the perimeter of a square, so that four of them are located at the vertices and the remaining points divide each side into ten congruent segments. If $P$, $Q$, and $R$ are chosen to be any three of these points which are not collinear, then how many different possible positions are there for the centroid of $\triangle PQR$?

Guest Jun 28, 2018

#1**0 **

This is old, but...

(Derived from AoPS' Alcumus, thank you!)

You are very welcome!

:P

CoolStuffYT Dec 22, 2018