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3 x 4 Connect-The-Dots Game
Posted 06 July 2013 - 09:14 PM
There is a simple game that I used to play as a kid in my home country. Here is a simplified version. There is a game board with 4 dots on three levels setup as follows:
* * * *
* * * *
* * * *
One player moves first (usually the youngest) and both follow the same rules. Connect one dot to any other dot. When connecting two dots you may not cross over another dot, you may not cross a line made from a prior connection, nor can you cross over your own line. Dots that are already connected are 'off limits' from reuse. Dots may be connected using any type of line (curve, straight, etc.) as long as it is continuous. The player that cannot make a move is the loser.
Assuming that the youngest person goes first, which player has the winning strategy to guarantee victory?
Posted 07 July 2013 - 05:48 PM
This distinction may not exist in English, and I am sorry if it confused anyone. I once got in a heated discussion with someone over what the word cross means. As my friend meant touching is the same as crossing, but for my people, crossing requires the passage over (beyond) the line.
Posted 07 July 2013 - 05:52 PM
Posted 07 July 2013 - 06:03 PM
So you can win instantly in first move connecting two dots and cutting off each of the remaining dots with a loop around it?
Posted 07 July 2013 - 06:08 PM
Posted 08 July 2013 - 02:28 AM
A closed loop would require starting and ending on the same point, or a line segment that crosses itself.
Both cases seem prohibited by OP.
So, somewhere in one of those statements is what I am missing?
Vidi vici veni.
Posted 08 July 2013 - 02:45 AM
If I understand correctly, the following pattern is not considered "crossing":
The loops are closed, but it is "touching" not "crossing".
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