Gomoku, is it possible to not be able to make a legal move?

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

1 Answer

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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