- #1
ehrenfest
- 2,020
- 1
Homework Statement
http://math.stanford.edu/~vakil/putnam07/07putnam5.pdf
I am having trouble with Sample 2.
I am trying a proof by induction (the case n = 1,2 are easy). So if it is true for n=k and you have k+1 of each colors, you can take out any red-blue pair and get the desired line segments for the remaining ones.
So somehow I need to show that we can find a pair to take out that will not intersect the line segments drawn between any of the other ones.
So, can we just take the red point with the largest y coordinate and the blue point with the largest y coordinates?
Hmmm...that seems like it would work.
EDIT: on second thought, I do not think that will work because you could have something like this
red
red
blue
blue
EDIT 2: It isn't showing the spaces. Does anyone know why?
Homework Equations
The Attempt at a Solution
Last edited: