# Greece National Olympiad Problem 1

On the plane are given $$k+n$$ distinct lines , where $$k>1$$ is integer and $$n$$ is integer as well.Any three of these lines do not pass through the same point . Among these lines exactly $$k$$ are parallel and all the other $$n$$ lines intersect each other. All $$k+n$$ lines define on the plane a partition of triangular , polygonic or not bounded regions. Two regions are called different, if they don't have common points or if they have common points only on their boundary. A region is called ''good'' if it is contained in a zone between two parallel lines .

If in a such given configuration the minimum number of ''good'' regions is $$176$$ and the maximum number of these regions is $$221$$, find $$k+n$$.This problem is part of this set.

×