Dodge Ball

    From The Heart Of Mathematics by Burger and Starbird

    Dodge ball is a game for 2 people: player 1 and player 2. Each player has a special game board as shown.

Player 1
1            
2            
3            
4            
5            
6            
           
Player 2
1 2 3 4 5 6
         

    Player 1 begins by filling in the first row of his board with a run of X's and O's. Then player 2 places either an X or an O in the first square of her board. The game continues with player 1 filling in the next row of his board and player 2 marking the next square in her board. This continues until the board is filled; player 1 has filled in 6 rows with X's and O's and player 2 has filled in the 6 squares on her board. Player 1 wins if any of his rows exactly matches player 2's row (player 1 matches player 2). Player 2 wins if none of player 1's rows match her row (player 2 dodges player 1).

    Would you rather be player 1 or player 2? Who has the advantage? If possible, devise a strategy for either player that will always result in a victory. Generalize the game to n rows of length n for player 1 and n squares for player 2.