A. 629. An infinite number of points have been marked in the square grid in such a way that no circle contains more than 2014 marked points. Show that there is a circular disk of diameter 100 (in the plane of the grid) that does not contain any marked point in its interior.
Proposed by: Péter Ágoston, Zoltán Gyenes and Bálint Hujter
Deadline expired on 12 January 2015.