Given two billion distinct points on a plane such That no three are collinear. I color any half of them red and the Remaining blue. Is it always possible for you to join each red point to one (and Only one) blue point by means of line segments such that no two line segments Intersect?

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john

  • Jul 10th, 2005
 

hai , 
 
can the answer be a regular fig like a circle on which only two points r collinear i.e ends of diameter nd all the other conditions can also satisfied.....if any one knows the answer kindly post the ans to me 
 
Truly 
john

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raj_893

  • Aug 8th, 2005
 

Hi folks!!!!!!!!!!!! 
 
given that joining is by line segments..... 
a circle can be drawn from any 3 non-collinear points. but once the no. of points crosses 3 ,drawing a cirle is possible only under special conditions.... I think joining by lines is not always possible. only if every two blue lines ( joining two points) are parellel. only then all points can still lie in one plane and still not intersect.................... 
 
truly 
 
raj.

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Vasanth

  • Aug 10th, 2005
 

The question does not say that each red point has to be joined to a distinct blue point, atleast to my understanding. 
 
If that is the case, we can pick any single blue point and join all red points to that single blue point by lines and none of them would intersect. 
 
They would not intersect because all these line segments originate from one single point and hence they cannot intersect but can only overlap if any three points are collinear, which is not the case either.

manojthesingham

  • Dec 4th, 2009
 

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if the points are like this..., then draw as many straight lines between every consecutive red and blue

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