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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?
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    Welcome to math.SE: since you are a new user, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are so far; this will prevent people from telling you things you already know, and help them write their answers at an appropriate level.2012-04-19
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    @ZevChonoles: (+1) I think this sort of proactive communication with new users is helpful. I realize a moderator can't and shouldn't be expected to do this in every instance. But, I wanted you to know that at least one regular user is appreciative of such efforts.2012-04-19
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    It appears that the original question about a game has been completely overwritten with a question about putting spheres in spheres.2012-04-20
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    @Greg, I rolled it back and flagged it for moderator attention.2012-04-20
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    @Blue Eyes, if you want to ask another question, use "ask question" on top; do not edit this question.2012-04-20

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