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

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Guest Message by DevFuse

Started by bonanova, Jun 01 2014 06:06 AM

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

Spoiler for clarification with the drawing

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7 replies to this topic

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 2

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?

*A leader's credentials do not hang on his wall. They are written by the lives of the people he has led.*

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

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

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:

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.

Posted 03 June 2014 - 07:07 PM Best Answer

Spoiler for clarification with the drawing

Posted 03 June 2014 - 07:38 PM

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

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Posted 03 June 2014 - 08:31 PM

Spoiler for Can you show that.

Spoiler for first thoughts...

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.

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