olymmath

MK-MO 2010 Problem 3

    A total of 20102010 coins are distributed in 55 boxes. At the beginning the quantities of coins in the boxes are consecutive natural numbers. Martha should choose and take one of the boxes, but before that she can do the following transformation finitely many times: from a box with at least 4 coins she can transfer one coin to each of the other boxes. What is the maximum number of coins that Martha can take away?

    Dataset text AI-MO AoPS. Quoted with source.

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