Lines in the plane
Source: Greek Olympiad - 2010 ,senior today, problem - 4
February 27, 2010
combinatorics proposedcombinatorics
Problem Statement
On the plane are given k\plus{}n distinct lines , where is integer and is integer as well.Any three of these lines do not pass through the
same point . Among these lines exactly are parallel and all the other lines intersect each other.All k\plus{}n lines define on the plane a partition
of triangular , polygonic or not bounded regions. Two regions are colled different, if the have not common points
or if they have common points only on their boundary.A regions is called ''good'' if it contained in a zone between two parallel lines .
If in a such given configuration the minimum number of ''good'' regionrs is and the maximum number of these regions is , find and .
Babis