Problem

Source: 9.4 of XX Geometrical Olympiad in honour of I.F.Sharygin

Tags: Combi Geo, geo, geometry



For which $n > 0$ it is possible to mark several different points and several different circles on the plane in such a way that: — exactly $n$ marked circles pass through each marked point; — exactly $n$ marked points lie on each marked circle; — the center of each marked circle is marked?