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MathNet 2011 Question 7

Math Olympiad Vault · MathNet 2011

Question 7

In the plane there are 2011 pairwise distinct points colored either blue or red.

a. Suppose that for every blue point the disk centered at that point with radius 1 contains exactly two red points. What is the largest possible number of blue points?

b. Suppose that for every blue point the circle centered at that point with radius 1 contains exactly two red points. What is the largest possible number of blue points?