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3 x 4 Connect-The-Dots Game


Best Answer witzar, 08 July 2013 - 04:01 PM

 

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Good idea but does that guarantee a win?

 

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Go to the full post


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#1 BMAD

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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?


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#2 bonanova

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Posted 07 July 2013 - 07:02 AM

Spoiler for first thoughts

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#3 witzar

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Posted 07 July 2013 - 05:06 PM

Spoiler for


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#4 Nins_Leprechaun

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Posted 07 July 2013 - 05:28 PM

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If we are playing this game, me three.
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#5 BMAD

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Posted 07 July 2013 - 05:48 PM

The trick that kids in my homeland soon discover is the rule of crossing. As long as the line runs tangent to another line (or itself) then it did not cross but did effectively cut off some of the board.

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.
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#6 BMAD

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Posted 07 July 2013 - 05:52 PM

I think you will discover many such winning lines, but now consider the line (or summation of line lengths), and try to find it/them that is/are needed to create the shortest guranteed win
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#7 witzar

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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?


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#8 BMAD

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Posted 07 July 2013 - 06:08 PM

Yes, if you have the skill. Which is hard for young kids cause violating the rules is an immediate lost. Now, given that it is hard to make such a line for a child, what is the shortest possible line they would have to make to gurantee victory?
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#9 bonanova

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Posted 08 July 2013 - 02:28 AM

To divde the plane requires a line segment of infinite length or a closed loop.
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?
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#10 witzar

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Posted 08 July 2013 - 02:45 AM

If I understand correctly, the following pattern is not considered "crossing":

__Ω_Ω_Ω_Ω_Ω__

 

The loops are closed, but it is "touching" not "crossing".


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