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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 29, 2018
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Take a look at this link, and see if you can get an idea:

https://math.stackexchange.com/questions/227451/number-of-distinct-centroids-of-triangles-formed-by-40-equally-spaced-points-on

smileysmiley

 Jun 29, 2018

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