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2player game with 2019 coins (2019 Auckland MO J5)

Source:

November 14, 2021
gamecombinatoricswinning strategy

Problem Statement

20192019 coins are on the table. Two students play the following game making alternating moves. The first player can in one move take the odd number of coins from 1 1 to 9999, the second player in one move can take an even number of coins from 22 to 100100. The player who can not make a move is lost. Who has the winning strategy in this game?
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