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On a 11 across 12 down Gomoku board with the following conditions:

  1. A player must make a move within 3 spaces of an opponent's piece.
  2. If a player can't make a move that player loses.

Is it possible to force the above, given the conditions?

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I have never heard of this rule, and an 11x12 board is a non-standard size. Do you have a reference for this rule? –  ghoppe Nov 1 '11 at 16:12
    
This sounds like a theoretical research question in m,n,k-games. In which case, I'm not sure you will find a very satisfactory answer here. –  ire_and_curses Nov 1 '11 at 16:36
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1 Answer 1

up vote 3 down vote accepted

Yes, it is possible for such a condition to happen, though I'm not sure what you mean by "force." It is possible because it is possible to create a board-state in which neither player has won the game, but the entire board is filled. A simple example of such a state is the following: imagine a filled 11x12 which follows the pattern:

WWBBWWBBWWBB

BBWWBBWWBBWW

WWBBWWBBWWBB

BBWWBBWWBBWW

Obviously, neither player has won the game, and since white and black each have an equal number of stones on the board, it is not impossible to reach such a board state. I have therefore shown that it is possible to reach a board-state in which one player cannot make a legal move. You can also show this for non-full boards by applying the rule of three and three and the rule of four and four.

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