Question

Let M be a set of points in the plane. O is called a partial center of symmetry if it is possible to remove a point from M such that O is a regular center of symmetry of what remains. How many partial centers of symmetry can a finite set of points in the plane have? 
V. Prasolov 

Difficulty level (1 very easy - 10 very hard): 6

Topics:
Combinatorics -> Combinatorial Geometry Proof and Example -> Constructing an Example / Counterexample Geometry -> Plane Geometry -> Symmetry
Sources:
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