<p>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:</p>

<pre><code>WWBBWWBBWWBB

BBWWBBWWBBWW

WWBBWWBBWWBB

BBWWBBWWBBWW
</code></pre>

<p>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.</p>

CC BY-SA 3.0
2011-11-02T12:10:32.757Z
2011-11-02T18:17:37.030Z
2011-11-02T18:17:37.030Z
Teofrostus
<p>On a 11 across 12 down Gomoku board with the following conditions:</p>

<ol>
<li>A player must make a move within 3 spaces of an opponent's piece.</li>
<li><strong>If a player can't make a move that player loses.</strong></li>
</ol>

<p>Is it possible to force the above, given the conditions?</p>

CC BY-SA 3.0
2011-11-01T16:12:54.513Z
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
CC BY-SA 3.0
2011-11-01T16:36:53.023Z
This sounds like a theoretical research question in [m,n,k-games](http://en.wikipedia.org/wiki/M,n,k-game). In which case, I'm not sure you will find a very satisfactory answer here.
ire_and_curses
<gomoku>
Gomoku, is it possible to not be able to make a legal move?
user1966
# Gomoku, is it possible to not be able to make a legal move?

(Asked by: username_0 on 2011-11-01)

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?

**Tags:** gomoku

> **Comments:**
> **username_1**: I have never heard of this rule, and an 11x12 board is a non-standard size. Do you have a reference for this rule?  
> **username_2**: This sounds like a theoretical research question in [m,n,k-games](http://en.wikipedia.org/wiki/M,n,k-game). In which case, I'm not sure you will find a very satisfactory answer here.  

---

## 1 answers

### Answer by username_3 on 2011-11-02. Score: 4 | Accepted 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.


---

