Given is a planar set of 25 points such that among any three there exists a pair at the distance less than 1. Prove that there exists a circle of radius 1 that contains at least 13 of the given points.

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Copyright © 1996-2018 Alexander BogomolnyGiven is a planar set of 25 points such that among any three there exists a pair at the distance less than 1. Prove that there exists a circle of radius 1 that contains at least 13 of the given points.

Pick arbitrarily one point A out of the given 25 and consider a circle

Else, there is a point B that lies outside

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Copyright © 1996-2018 Alexander Bogomolny