BG-MO 1969 Problem 3
Some of the points in the plane are white and some are blue (every point of the plane is either white or blue). Prove that for every positive number :
(a) there are at least two points with different color such that the distance between them is equal to ; (b) there are at least two points with the same color and the distance between them is equal to ; (c) will the statements above be true if the plane is replaced with the real line?
Dataset text AI-MO AoPS. Quoted with source.
Solutions
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