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DE-BUNDESWETTBEWERB 2011 Problem 1

  • Round 1

Ten bowls are in a circle. They will go clockwise - starting somewhere filled with 1,2,3,...,91, 2, 3, ..., 9 or 1010 marbles. You can have two choices in every move . Add a marble to neighboring shells or from two neighboring shells - if both of them are not empty - remove one marble each. Can you achieve that after finally many moves in each bowl exactly 20112011 marbles lying?

Dataset text AI-MO AoPS. Quoted with source.

Official text: Bundeswettbewerb Mathematik 2011 official paper, page 1.

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