One more puzzle Dots and Boxes

6 replies. Last post: 2015-05-05

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One more puzzle
  • al_ef13 at 2015-04-11

    I forgot to post another interesting position from the earlier game:

    http://littlegolem.net/jsp/game/game.jsp?gid=1690407&nmove=22

    Player 1 to move and win. In the game purgency played 23.f5 which loses both nimstring and the game, so I was extremely lucky.

    You can probably guess which move has a chance to be winning, but the next move of P1 in the principal variation is not straightforward.

    The solution does not require any complicated brute force search, but rather a beautiful idea which is typical in endgames with close score..

  • Carroll at 2015-04-13

    You did not tell what P2 answer would be to P1 23th “obvious” winning move...

  • al_ef13 at 2015-04-13

    Well, I did not say “obvious”, but it’s quite natural move to consider.

    OK, let’s make it more precise. The winning move is the double sacrifice 23. j7. This move is natural to consider because it’s the only way to win nimstring. Now the most reasonable response by P2 is 24. d9 (~e8). For convenience, here is the link to the resulting position with P1 to move and win:
    http://www.trmph.com/dnb/board#5,f3h9k8i8h11f1h1h3k2j5j3i6f11f9i4k4d3c4d7c8g10e10i10c6b7j7j9k6d9e8

  • Carroll at 2015-04-14

    Agreed on 25.e8, but I think another move which makes sense is 25.c2 making a threat for three chains and making P1’s chains shorter.

    Then from a nimstring point of view, north (including the small-chain) is *0  and bottom chain is *0 too as one chain will be made and can not be prevented in four waiting moves.
    The central part is a strange animal of value *2 as first player can chose the number of waiting moves between 2 (playing in the center) or 1 by sacrificing a square in south-east corner.
    So if nimstring is winning P1 should play the waiting move in the central region.
    To check it is winning is a bit complex as the chains will be short and a quad may form in the center, plus P1 being in control will lose short chain battle.

    I guess it is better to lose control and make a quad plus 3-chains.

  • al_ef13 at 2015-04-14

    I am sorry but I don’t completely understand what you mean.

    I assume you mean 24. e8 (not 25. e8).
    Also, I assume that you mean 24. c2 (not 25. c2).

    I assume that your discussion of nimstring applies to the position after move 24. e8 (~d9), hence to the above-linked position. But  then the waiting move in the center (that is, 25.f5 or 25. g6)  does not win nim, because it makes the value of the central region to be 1 (moreover, this move obviously loses the game).
    The only move that wins nim is the sacrifice 25.g4 (~h5), but the point is that this move loses the game, and this observation is the first step towards the solution.



  • Sean_Hettenbach at 2015-05-05

    I love it, nice post here ef. You guys should help me to learn and understand nim when I get back from my leave. Not too much longer I hope. I hope to be able to contribute to these puzzles and such!

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