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There is an infinite grid. Two players play a game. Player A places two black marbles in consecutive blocks in his turn, and player B places one white marble in any of the squares. Player A wins, if he gets 1000 black marbles together in a line. However, player B does not have any winning combination, that is even if 1000 whites occur in a row, player B does not win. Show that player A always has a winning strategy.

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closed as off-topic by 6005, Mark Viola, Clément Guérin, tired, A.P. Nov 4 '15 at 15:05

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  • $\begingroup$ Can you suggest a field to which this question might be related ? $\endgroup$ – BumbleBee Oct 29 '15 at 1:52
  • $\begingroup$ I don't really understand the game. If we have an infinite grid, the probability to have a winning grid is very small!? $\endgroup$ – hlapointe Oct 29 '15 at 1:58
  • $\begingroup$ Can you structure your question a way it will be easier to understand it. $\endgroup$ – hlapointe Oct 29 '15 at 1:59
  • $\begingroup$ My intuition: It takes player B two moves to block one of A's potential lines, while A can create many potential lines at once (for example, his first move starts 3 potential lines). I guess we need to show that A can continue to grow his potential lines and start new potential lines much faster than B can block them. $\endgroup$ – angryavian Oct 29 '15 at 2:21
  • $\begingroup$ For clarification, is the grid specifically two-dimensional? by "consecutive blocks" do you mean to say two orthogonally adjacent blocks? And finally, "1000 in a line" do you mean to be 1000 orthogonally adjacent blocks? $\endgroup$ – JMoravitz Oct 29 '15 at 2:36