Players A and B play a game with N ≥ 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, . . . by the following rules:
• On every move of his B passes 1 coin from every box to an adjacent box.
• 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 chosen coin to an 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.
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, . . . by the following rules:
• On every move of his B passes 1 coin from every box to an adjacent box.
• 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 chosen coin to an 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.
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