MathDB

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 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.

Problem Statement