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 Post subject: Paragon of Atlantis (9-tile magic Secret of Atlantis sequel)
PostPosted: Sat Mar 31, 2007 6:44 am 
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This puzzle is a 9-tile magic myth with a more elegant theme than the well known maze theme. It is based on the greek key pattern, which was very commonly used in ancient times. It has two solved states:

(1) a spread triangle state (black background with cyan lines) which looks like a stand, and
(2) a pyramid state (yellow, green and red colors).


Both solved states require the line to be continuous, going through consistent colors, and no line leads to a dead end. The design makes the puzzle extremely hard, much harder than the
Secret of Atlantis puzzle.
In fact, before even finding the pattern, someone must practice ways to find the appropriate shapes first! ;-)


Not many photos are presented at this stage because of the difficulty in finding the solutions!!!!

Image
Spread triangle solved state.


Image
The pyramid form is correct, but the puzzle is still unsolved as the lines do not match.


Image

And as stated before, the spread triangle state, can serve as an ideal stand for the Memory Cube!!!

;-)



Pantazis

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Last edited by kastellorizo on Mon May 05, 2008 1:00 pm, edited 1 time in total.

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 Post subject:
PostPosted: Sat Mar 31, 2007 6:47 am 
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Another great Magic!
Now we wait for the next one.... :lol:

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 Post subject:
PostPosted: Sat Mar 31, 2007 6:57 am 
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Pembo wrote:
Another great Magic!
Now we wait for the next one.... :lol:


Thanks Pembo! :)

For the 9-tile magic myths, there will be a last one to conclude the "Atlantis Trilogy". I have already prepared half of the design for the third part, so it should be ready in a couple of weeks. But currently I have a very big problem solving the Paragon... between the spread square and pyramid solved states, there is some sort of semi-parity(??? - I don't know how to even call that LOL) problem.



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 Post subject:
PostPosted: Sat Mar 31, 2007 7:10 am 
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Do the strings tangle?

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 Post subject:
PostPosted: Sat Mar 31, 2007 8:17 am 
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Pembo wrote:
Do the strings tangle?


Stringing is consistent and all tiles swap strings the same way like any rubik's magic. There is absolutely no blocking or tangling.

This is the main reason odd-tile magics are forced to be three dimensional. ;)





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 Post subject:
PostPosted: Sat Mar 31, 2007 8:47 am 
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So what is this parity then?

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 Post subject:
PostPosted: Sat Mar 31, 2007 9:59 am 
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Pembo wrote:
So what is this parity then?



Good question because it is a very funny case. I will put it this way:


With an odd numbered magic, you can get magic shapes that have some parity difference. This cannot happen with even numbered magics.

Image
EQUAL TO
Image



Image
NOT EQUAL TO
Image





However, those shapes heavily depend on the position of the paper tiles.

That is, although you may get different shapes, that doesn't mean you can get those shapes starting from whichever tile you want.

Of course, I might also be wrong with that. But so far, this is what I have experienced.



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Last edited by kastellorizo on Mon May 05, 2008 1:03 pm, edited 1 time in total.

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 Post subject:
PostPosted: Sat Mar 31, 2007 10:18 am 
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Very nice try mate.....i am feeling jealous .......


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 Post subject:
PostPosted: Sat Mar 31, 2007 11:18 am 
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I understand now.
I know the 8 tile can't make a frame, because of the number of 'turns' the strings make.

I think I know what you mean about starting at only certain tiles.
Is it because of where the string loops start/end?

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 Post subject:
PostPosted: Sat Mar 31, 2007 12:51 pm 
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Pembo wrote:
Is it because of where the string loops start/end?


That is what I also thought and confused me, but I just found out that this is not the case.

You can still achieve the shape you want with the paper tiles at the position you want. But that doesn't mean you will get the correct orientation of the paper tiles. Therefore, it is not about where the stringing starts, it is all about the paper orientation.


;)



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 Post subject:
PostPosted: Sat Mar 31, 2007 2:13 pm 
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?
So your puzzle has orientation?

I never knew Magics were so indepth.

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 Post subject:
PostPosted: Sat Mar 31, 2007 2:35 pm 
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Pembo wrote:
?
So your puzzle has orientation?

I never knew Magics were so indepth.



Take a four tile magic for example. It has two types of transformations. After doing any combination of those transformations, the shape remains always the same, but you may end up with 4 different ways of tile orientation. If we include the other 4 different ways of orientation, this time for the mirror image with regard to the tile positions, then we have the total of eight combinations.

And yes, magics are much more mysterious and complex than many people think.

:)



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 Post subject:
PostPosted: Sat Mar 31, 2007 2:35 pm 
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Pembo wrote:
I never knew Magics were so indepth.


No one did... Until Pantazis started thinking perpindicular to accepted reality.

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 Post subject:
PostPosted: Sat Mar 31, 2007 9:43 pm 
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Puzzlemaster42 wrote:
Pembo wrote:
I never knew Magics were so indepth.


No one did... Until Pantazis started thinking perpindicular to accepted reality.


LOL You are absolutely right, everything started when I realised "perpendicular stringing" was what enabled the existence of regular stringed closed-loop odd numbered tile magics (I know the name is too long, but I am trying to be succinct!!!).

And the Paragon just showed that we can use angles of other degrees too (e.g. 120 or 60 degrees), depending on the number of tiles...! And if there is symmetry between the angles throughout the magic, stability is guaranteed!

Based on this, I just want to underline, that any 9-tile magic myth is extremely stable when used as a stand for the Memory Cube. It just seems so natural when and the cube feels like it is "floating"!


:)



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 Post subject: nice puzzle!
PostPosted: Fri May 18, 2007 6:59 am 
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can u explain how to make this puzzle ? - is it much different from a regular magic ? i'd really like to make this puzzle - or some variant of it :P

..i imagine (from the first solved state, it's just a loop connected - with 3 tiles batched together as normal) ? except.. if there's an odd amount, does that mean that the 'overlap' with stringing is 2 tiles rather than the usual 1 ? ..meaning you used.. 18 strings ? ..

also maybe a diagram of how the pictures on one side are oriented / paired with the pictures of the other ?


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 Post subject: Re: nice puzzle!
PostPosted: Fri May 18, 2007 9:30 am 
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wittkamp wrote:
can u explain how to make this puzzle ? - is it much different from a regular magic ? i'd really like to make this puzzle - or some variant of it :P

..i imagine (from the first solved state, it's just a loop connected - with 3 tiles batched together as normal) ? except.. if there's an odd amount, does that mean that the 'overlap' with stringing is 2 tiles rather than the usual 1 ? ..meaning you used.. 18 strings ? ..

also maybe a diagram of how the pictures on one side are oriented / paired with the pictures of the other ?


Hi Mark!

Since you are in Perth, you may visit me anytime you want at my Uni office. I always have with me one Secret of Atlantis and I can answer all the above. In fact, the puzzle will do all the talking LOL

Let me know, and I will send you my email/mobile to make a time to meet.

:)



Pantazis


PS I apologise for not much happening with the puzzle club, this semester had been too busy for me!

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