Andy and Bob play a game using a long straight row of squares, alternating turns. When it’s Andy’s turn, he writes an A in one of the blank squares. When Bob takes a turn, he writes a B in some blank square. (Once a letter is written in a square, neither player can use that square again.) A player wins the game when his initial is written in 4 equally-spaced squares. For example, suppose the following board is the result of several turns: (below)
_ _ B B _ A B A _ _ _ A B _ _ A ^ |
Andy can win by writing A in the indicated square. (Four A’s with spacing 2) Bob can win by writing B in that same square. (Four B’s with spacing 3)
- If Andy goes first, find a strategy Andy can use that guarantees that he wins. How many moves must Andy make to get 4 in a row, no matter what moves Bob makes? (Can Andy always win in just 4 moves?) Justify your answer.
- How many squares are needed in the game board to allow Andy’s strategy to work?