Author |
Topic: n dots, m lines (Read 975 times) |
|
Noke Lieu
Uberpuzzler
pen... paper... let's go! (and bit of plastic)
Gender: 
Posts: 1884
|
 |
n dots, m lines
« on: Sep 10th, 2008, 10:30pm » |
 Quote  Modify
|
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?
|
|
 IP Logged |
a shade of wit and the art of farce.
|
|
|
Grimbal
wu::riddles Moderator
Uberpuzzler
Gender:
Posts: 7527
|
|
Re: n dots, m lines
« Reply #1 on: Sep 11th, 2008, 12:35am » |
Quote Modify
|
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.
|
| « Last Edit: Sep 11th, 2008, 12:35am by Grimbal » |
IP Logged |
|
|
|
|
RIDDLES SITE
WRITE MATH!
Home 
Help 
Search 
Members 
Login 
Register
Reply
Notify of replies
Send Topic
Print