Given are $n$ different concentric circles on the plane.Inside the disk with the smallest radius (strictly inside it),we consider two distinct points $A,B$.We consider $k$ distinct lines passing through $A$ and $m$ distinct lines passing through $B$.There is no line passing through both $A$ and $B$ and all the lines passing through $k$ intersect with all the lines passing through $B$.The intersections do not lie on some of the circles.Determine the maximum and the minimum number of regions formed by the lines and the circles and are inside the circles.
Problem
Source: 2013 Greek TST,Pr.4
Tags: combinatorics, counting, circles, lines
silouan
03.08.2016 16:44
Let's try this problem! Up! Up!
soryn
29.12.2018 14:12
Interesting problem..
ThE-dArK-lOrD
29.12.2018 15:30
I don't understand the problem. What is $k$ in "all the lines passing through $k$ intersect with all the lines passing through $B$," and what "regions formed by the lines and the circles and are inside the circles" means?
adityaguharoy
29.12.2018 15:47
@ThE-dArK-lOrD maybe in the former phrase $k$ is a typo for $A$ !
adityaguharoy
29.12.2018 15:48
And for the latter I think it means the number of regions inside the circles which are formed by the lines.
soryn
30.12.2018 00:55
Yes,I think...
soryn
31.12.2018 16:21
Any idea?