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        riddles >> medium >> n dots, m lines
        
(Message started by: Noke Lieu on Sep 10^th, 2008, 10:30pm)

Title: n dots, m lines
Post by Noke Lieu on Sep 10^th, 2008, 10:30pm

I've been thinking about circles being cut by chords.

It's pretty famous that given n chords you dissect a circle into m=(n²+n+2)/2 regions.

My question is though, given m-1 points, such that no 3 are colinear, can the circle be dissected by n chords such that each region has no more than one point?

Title: Re: n dots, m lines
Post by Grimbal on Sep 11^th, 2008, 12:35am

It seems to me that if the points are on a circle, with n chords, you cannot split the points in more than 2n groups.
For n=4, m=11, m-1=10, but you have max 8 pieces with points in it.