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TR-MO 2014 Problem 1

    In a bag there are 10071007 black and 10071007 white balls, which are randomly numbered 11 to 20142014 . In every step we draw one ball and put it on the table; also if we want to, we may choose two different colored balls from the table and put them in a different bag. If we do that we earn points equal to the absolute value of their differences. How many points can we guarantee to earn after 20142014 steps?

    Dataset text AI-MO AoPS. Quoted with source.

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