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3 colors (Posted on 2003-05-01) Difficulty: 3 of 5
Imagine that a painter went down to a mathematical plane and colored all of the points on that plane one of three colors.

Prove that there exist two points on this plane, exactly one meter apart, that have the same color.

See The Solution Submitted by Jonathan Waltz    
Rating: 4.1000 (10 votes)

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re(3): Could be right | Comment 12 of 27 |
(In reply to re(2): Could be right by Hank)

One does not have to prove that red is not on the circle. The point is that we can't prove that red IS on the circle, and further we can't prove that if the circle is made up of two colors that there must be two of the same, within 1 meter along the circumference. Remember which side has the burden of proof.
  Posted by Charlie on 2003-05-01 05:38:00

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