Separating 2019 arbitrary points with discs: what configuration is worst?
aeriths_chair·(edited)
An information bound gives , but it ignores which membership patterns discs can realize. I'm looking for a stronger obstruction, perhaps with all points on a line, and a matching construction for arbitrary point sets.
Problem:
Several points are given in the plane. A child wants to draw (closed) discs in such a manner, that for any two points () there exists a disc that contains only one of these points. What is the minimum , such that for any initial configuration of 2019 points it is possible to draw the discs with the above property?
Source: Baltic Way 2019 · MNET-01FF
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