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Caravel Forum : Other Boards : Forum Games : Devilish Mazes (An interesting Go-related puzzle)
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stigant
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icon Devilish Mazes (+4)  
I ran into this puzzle on the demos page for Wolfram's Mathematica player:

http://demonstrations.wolfram.com/DevilishMazes/

You'll need to install the Mathematica player to view and interact with it, but I'll post screen shots and explain the puzzle here.

There are three puzzles. Each is played on a Go board. The board starts with a sort of maze of walls created from black stones and a white stone at the center. The white player is trying to connect his stone to the outside while black is trying to completely contain the white group (just like in Go). The catch is that white gets to play 2 stones each turn while black only gets to play 1. The question is, with best play, who wins in each situation?

Here are the initial positions:




Edit:
I should be more specific about the win conditions for white:
In maze 1, white wins if he connects his center stone to one of the white stones on the perimeter of the black wall.
In mazes 2 and 3, white wins if he connects his center stone to a stone clear of the black maze.

My answers (so far):
Click here to view the secret text


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[Last edited by stigant at 02-07-2014 03:17 PM]
02-07-2014 at 03:14 PM
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stigant
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icon Re: Devilish Mazes (0)  
AH! I think I got it now:
Click here to view the secret text


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02-07-2014 at 03:56 PM
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Someone Else
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icon Re: Devilish Mazes (+1)  
Click here to view the secret text

02-07-2014 at 04:01 PM
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stigant
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icon Re: Devilish Mazes (0)  
Actually:
Click here to view the secret text


Edit: no, I agree with you again. Argh.


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[Last edited by stigant at 02-07-2014 04:18 PM]
02-07-2014 at 04:09 PM
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The spitemaster
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icon Re: Devilish Mazes (+1)  
Click here to view the secret text


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02-07-2014 at 04:50 PM
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stigant
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icon Re: Devilish Mazes (0)  
Ok, I think you're correct, but I'll play black. Your move:


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02-07-2014 at 05:33 PM
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TripleM
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icon Re: Devilish Mazes (0)  
Fascinating puzzle. I'm leaning towards black at this stage, but without any concrete proof.
02-07-2014 at 09:42 PM
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Nuntar
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icon Re: Devilish Mazes (0)  
I haven't looked at #3 yet, but here's a simple proof for White win in #1:
Click here to view the secret text


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02-07-2014 at 09:59 PM
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Someone Else
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icon Re: Devilish Mazes (0)  
For #3, labelling the lone white stone as the origin, I think a fairly complete solution is:
Click here to view the secret text

02-07-2014 at 11:42 PM
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stigant
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icon Re: Devilish Mazes (0)  
Click here to view the secret text

Ah, but
Click here to view the secret text


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02-08-2014 at 12:02 AM
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TripleM
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icon Re: Devilish Mazes (0)  
Agreed - the (+-3,+-3) squares seem crucial squares for both sides to play on early.
02-08-2014 at 01:50 AM
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The spitemaster
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icon Re: Devilish Mazes (0)  
My solution
Click here to view the secret text


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02-08-2014 at 06:35 AM
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TripleM
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icon Re: Devilish Mazes (0)  
The spitemaster wrote:
My solution
Click here to view the secret text

I'm not convinced at all even that position is a win for white, but change black's last move to (0,-3) (and you may as well change his early moves from (2,0) to (3,0) and (0,2) to (0,3)) and that's an easy win for black.
02-08-2014 at 07:23 AM
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The spitemaster
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icon Re: Devilish Mazes (0)  
I will continue then while changing all of blacks responses to the intersections:
Click here to view the secret text


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02-08-2014 at 07:41 AM
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The spitemaster
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icon Re: Devilish Mazes (0)  
I do however have to retract the bit about an infinite board. That is not true to my knowledge.

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I wish that man would stay away
02-08-2014 at 07:44 AM
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The spitemaster
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icon Re: Devilish Mazes (0)  
And for the variant of black changing to (0,-3) at the indicated time.
Click here to view the secret text


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Last night upon a stair
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He wasn't there again today
I wish that man would stay away
02-08-2014 at 07:48 AM
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TripleM
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icon Re: Devilish Mazes (0)  
You're right, sorry, I was looking at the wrong thing. Still, as mentioned earlier, black playing in the center early doesn't seem to be a great strategy compared to some others, so that doesn't prove anything regarding who wins.
02-08-2014 at 07:57 AM
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Tim
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icon Re: Devilish Mazes (0)  
I think that
Click here to view the secret text


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02-08-2014 at 08:14 AM
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The spitemaster
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icon Re: Devilish Mazes (0)  
Here is an alternate
Click here to view the secret text


Here is the problem that I am having a hard time to convey; what the goal of white is. Really it is not too escape, first it is to have two stones on different 3 distance rows that are unblocked to the exit after blacks turn. This is because this will meant victory two turns later. So, how is white to achieve this? Well, having three different exits going into blacks turn. Then we can count that as White's victory as well. To pull it back yet another turn (or two depending on blacks choice), we can see that if white has one exit starting it's turn and then has a corner that it can get to on it's turn then it also wins.

To Tim's Variant:
Click here to view the secret text


As a side note: White keeps changing due to: perhaps an improvement on my part, or to an easier to demonstrate method.

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Last night upon a stair
I met a man that wasn't there
He wasn't there again today
I wish that man would stay away
02-08-2014 at 02:44 PM
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The spitemaster
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icon Re: Devilish Mazes (0)  
I've been thinking about this all day, and I am now convinced I am in error. I will be back when I can prove black wins regardless.

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Last night upon a stair
I met a man that wasn't there
He wasn't there again today
I wish that man would stay away
02-08-2014 at 11:06 PM
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