Question 5
A finite set of circles in the plane is called nice if it satisfies the following three conditions:
(i) No two circles intersect in more than one point;
(ii) For every point $A$ of the plane there are at most two circles passing through $A$;
(iii) Each circle from the set is tangent to exactly 5 other circles from the set.
Does there exist a nice set consisting of exactly
(a) 2006 circles?
(b) 2007 circles?
(i) No two circles intersect in more than one point;
(ii) For every point $A$ of the plane there are at most two circles passing through $A$;
(iii) Each circle from the set is tangent to exactly 5 other circles from the set.
Does there exist a nice set consisting of exactly
(a) 2006 circles?
(b) 2007 circles?