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 Who will win? (Posted on 2005-01-10)
There are 2n cards labeled 1, 2, ..., 2n respectively, and the cards are distributed randomly between two players so that each has n cards. Each player takes turns to place one card, and you win if you put down a card so that the current sum of all the played cards is divisible by 2n+1.

For example, if n=10, and the previously placed cards are 5, 8, 9, 19, then if player A now places 1, he wins since 5+8+9+19+1 = 42 is divisible by 2*10+1=21.

Assuming both players want to win, what strategy should one adopt in order to win? Following the strategy, is there a consistent winner of this game?

 See The Solution Submitted by Bon Rating: 2.0000 (1 votes)

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 Solution | Comment 1 of 9
Player 2 will win.  On each of his turns, he has (k+1) choices, only k of which can lead to winning moves for Player 1 on his next turn.  So Player 1 never has a winning move as long as Player 2 makes such a move.  On the other hand, if the game goes to the last move, Player 2's last move wins him the game.
 Posted by David Shin on 2005-01-10 17:22:13

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