olymmath

OSN 2009 Problem 5

  • Day 2

In a drawer, there are at most 20092009 balls, some of them are white, the rest are blue, which are randomly distributed. If two balls were taken at the same time, then the probability that the balls are both blue or both white is 12\frac12 . Determine the maximum amount of white balls in the drawer, such that the probability statement is true?

Dataset text AI-MO AoPS. Quoted with source.

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