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.


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

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – 6005, Mark Viola, Clément Guérin, tired, A.P.
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ 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