IMO Shortlist 2012 problem C4

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Dodao/la: arhiva
3. studenoga 2013.
Players A and B play a game with N \geq 2012 coins and 2012 boxes arranged around a circle. Initially A distributes the coins among the boxes so that there is at least 1 coin in each box. Then the two of them make moves in the order B,A,B,A,\ldots by the following rules:
(a) On every move of his B passes 1 coin from every box to an adjacent box.
(b) On every move of hers A chooses several coins that were not involved in B's previous move and are in different boxes. She passes every coin to and adjacent box.
Player A's goal is to ensure at least 1 coin in each box after every move of hers, regardless of how B plays and how many moves are made. Find the least N that enables her to succeed.
Izvor: Međunarodna matematička olimpijada, shortlist 2012