Jump to content


Welcome to BrainDen.com - Brain Teasers Forum

Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account.
As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends.

Of course, you can also enjoy our collection of amazing optical illusions and cool math games.

If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top.
If you have a website, we would appreciate a little link to BrainDen.

Thanks and enjoy the Den :-)
Guest Message by DevFuse
 

Photo
- - - - -

Pairing points


Best Answer k-man, 03 June 2014 - 07:07 PM

Spoiler for clarification with the drawing
Go to the full post


  • Please log in to reply
7 replies to this topic

#1 bonanova

bonanova

    bonanova

  • Moderator
  • PipPipPipPip
  • 5887 posts
  • Gender:Male
  • Location:New York

Posted 01 June 2014 - 06:06 AM

Take a red pen and touch a sheet of paper with it at n randomly chosen points.

Now add n random points with a blue pen, for a total of 2n points, no three of

which lie on a straight line.

 

Is it possible in every case to pair the points so that no two of the n lines that

join each red point with its corresponding blue point will cross?


  • 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#2 k-man

k-man

    Advanced Member

  • Members
  • PipPipPip
  • 472 posts
  • Gender:Male

Posted 02 June 2014 - 08:04 PM

It's easy to show with n=2 that it's not possible with lines, so I will assume that you meant line segments connecting a red and a blue points.

 

Spoiler for combination of two methods

  • 0

#3 bonanova

bonanova

    bonanova

  • Moderator
  • PipPipPipPip
  • 5887 posts
  • Gender:Male
  • Location:New York

Posted 03 June 2014 - 05:00 AM

Sorry. 

That was a nice discussion, and I wasn't very clear.

 

Begin with n red points and n blue points randomly intermingled.

Can n (straight) line (segments) each join a red point to a blue point?

Once drawn they remain in place.

They may not cross.

 

Spoiler for There is a simple answer if the connecting line (segments) can be curved:


  • 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#4 k-man

k-man

    Advanced Member

  • Members
  • PipPipPip
  • 472 posts
  • Gender:Male

Posted 03 June 2014 - 03:48 PM

Maybe I wasn't clear, but my solution doesn't involve any curved lines. All straight line segments connecting a blue dot with a red dot and they don't cross.


  • 0

#5 k-man

k-man

    Advanced Member

  • Members
  • PipPipPip
  • 472 posts
  • Gender:Male

Posted 03 June 2014 - 07:07 PM   Best Answer

Spoiler for clarification with the drawing

  • 1

#6 bonanova

bonanova

    bonanova

  • Moderator
  • PipPipPipPip
  • 5887 posts
  • Gender:Male
  • Location:New York

Posted 03 June 2014 - 07:38 PM

Nice. bona_goldstar.gif

 

I misinterpreted "points contained by the hull" as "points within the hull."

You were saying perimeter; I thought interior.
 

BTW there is a very simple idea that does the job

 

Spoiler for Can you show that
.


  • 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#7 k-man

k-man

    Advanced Member

  • Members
  • PipPipPip
  • 472 posts
  • Gender:Male

Posted 03 June 2014 - 08:31 PM

Spoiler for Can you show that
.

 

Spoiler for first thoughts...


  • 0

#8 bonanova

bonanova

    bonanova

  • Moderator
  • PipPipPipPip
  • 5887 posts
  • Gender:Male
  • Location:New York

Posted 04 June 2014 - 06:11 AM

 

Spoiler for Can you show that
.

 

Spoiler for first thoughts...

 

 

That's it. I don't believe it's cyclic.

BTW your solution constructs a non-crossing pairing.

This observation proves that one exists, which is all that is asked, but does not construct it.


  • 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users