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BALTIC-WAY 2019 Problem 10

    There are 20192019 points given in the plane. A child wants to draw kk (closed) discs in such a manner, that for any two distinct points there exists a disc that contains exactly one of these two points. What is the minimal kk , such that for any initial configuration of points it is possible to draw kk discs with the above property?

    Dataset text AI-MO AoPS. Quoted with source.

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