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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 $\triangle PQR$?

 Jun 28, 2018
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This is old, but...

(Derived from AoPS' Alcumus, thank you!)

 

You are very welcome!

:P

 Dec 22, 2018

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