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Strategical Game with 2010 coins in a pile

Source: JBMO Shortlist 2010 Problem C1 (Combinatorics #1)

January 25, 2015
combinatorics unsolvedcombinatorics

Problem Statement

<spanclass=latexbold>ProblemC.1</span><span class='latex-bold'>Problem C.1</span> There are two piles of coins, each containing 20102010 pieces. Two players AA and BB play a game taking turns (AA plays first). At each turn, the player on play has to take one or more coins from one pile or exactly one coin from each pile. Whoever takes the last coin is the winner. Which player will win if they both play in the best possible way?