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 Post subject: New type of Magic Puzzles: The "Möbius Magics"!
PostPosted: Sat Jan 27, 2007 5:07 am 
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Here I present the final "chapter" regarding single closed loop magics magics with standard stringing.

After making the odd numbered tile Magic Myths and then separating all magics into two types (A and B), I thought I had covered all possible standard stringing cases, and actually I had. But what I have covered in the past was regarding those magics which had TWO sides! You know... front side and back side. And even the magic myths (which are odd tiled) have two sides, but in their case, it is in three dimensions (the same goes with the type B magics).

Now imagine a magic puzzle which only ONE side, i.e. it was connected in the same way as a Möbius Strip:

Image
(the image above was taken from this nice website which is in French and has a LOT of information for the Möbius Strip)


You may say... "Oh no! Wouldn't the strings of the magic be stretched too much and then break???"
The answer here is a very surprising "NO!!!" ;)
"But how?" You may reply....

First a little bit of theoretical stuff. You probably know the normal 8-tile Rubik's, as well the the 8-tile "Frame" puzzle (e.g. Flexible Tetragon). The normal puzzle and the Frame are different in that one tile is connected differently than the rest, i.e. it has a half turn in both sides. That creates a parity difference between the two puzzles making them different. Or you may call them type A and type B as I defined them in the past.

But what if, only one side of the tile was connected differently? Then we would have a "half parity" (don't know if that makes sense LOL), or in other words a half turn which is the way a Möbius Strip is made!

So lets go to the stringing part! While stringing the tiles, the most tricky part is obviously the last step. It is the step where you must make the half turn twist to give the puzzle the Möbius Strip form. But after understanding how the last part should be connected (to close the loop) and by moving two tiles on the other side (which *does not* affect the final form of the puzzle), voila! Now, the final stringing can be easily done, without any stretching whatsoever.

In other words, if we have a magic puzzle in a Möbius Strip form, the stringing of the puzzle allows flat shapes to be formed too! So why string it in the (sometimes overstretched) Möbius Strip form? Using the equivalent flat shape to string it is much easier! Of course, it's supposed to have the shape of a Möbius Strip, and we want to see it right? Well, we can't easily see it on an 8-tile magic (big angles between very few tiles), but we can certainly do so on a 24-tile magic!!! (in fact, the more the tiles, the smaller the angles between the tiles to reach the Möbius Strip form).

So here, after the Magic Myths, I present a new type of magics, the Möbius Magics!!! Note that, for consistent standard stringing, (i.e. to avoid any sort of bandaging) we are forced to use an *even* number of tiles.
(which is definitely *not* a bad thing!). Odd numbered-tile Möbius Magics can also be made (and they are different too in their own respect), but they just have another form, which has a few movement limitations if the tiles are seven or less.

Firstly, I present the "Magic Line", an 8-tile magic, which has Mr Escher's ant theme (as seen in the animated pictures above).



Image
The flat state which is allowed by the tile movement. No need to stretch anything to build it!!!
(but the stringing can still be very tricky!)



Image
The other side of the puzzle... I mean it's the same side, but... hmmm....nevermind! LOL



Image
It is possible to reach the Möbius Strip form with 8 tiles, but some serious stretching is required!



A few more (scrambled) possible shapes:
Image
Image
Image
Image




Image
In the above picture, it is easy to see the differences between all those three magics. The Rubik's Magic (top), can take the form of a circle with no "extensions". The Flexible Tetragon (bottom right), can have an internal extension (+) and and internal extension (-), which preserves the "flatness" of the magic. And finally, the Magic Line (bottom left), which has a single extension. Now believe me, ALL closed loop 8-tile shapes with any other number of extensions can be transformed to one of those three magics. The reason is, each of the magics above is always equivalent with any other magic which has an additional even number of either external extensions or internal extensions. After understanding this, it is easy to make a fast check that covers all possibilities. ;-)

By adding extra half turns, we will still end up with Type A Magics, Type B Magics, or Möbius Magics.



************************************************************
************************************************************


And I also present the "Magic Strip", which also has the ant theme, and whose 24 tiles allow it to take its "natural" Möbius Strip form.



Image
The stringing movement allows it to take many shapes without stretching the strings.



Image
With 24 tiles in our disposal and less angle problems, it is easy to see now its Möbius Strip form! :-)
(and there is no need to even hold it!!!)



Image
Its (scrambled) form with an external extension (just like in the 8-tile case).



Image
Its form with an internal extension! (they *are* the same puzzle! - but with LOTS of combinations)



Image
And finally, the Magic Strip in a much more compact form.



Summarising, the Möbius Magics belong to a new style magic series (which have many combinations and are extremely confusing to play with), different from the normal Rubik's (Type A) or the ones with a parity difference (Type B). The stringing of the square tiles may be based on the rubiks magics, but the concept is unique.



I hope you have survived reading all the the above! :P



Pantazis

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Last edited by kastellorizo on Sun Jan 28, 2007 12:02 am, edited 1 time in total.

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 Post subject: Re: New type of Magic Puzzles: The "Möbius Magics"
PostPosted: Sat Jan 27, 2007 5:43 am 
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Hey pantazis, once again you did it! That's a lovely creation! It's so extremelly fascinating! I don't know how the hell are you able to have so interesting ideas but man, they always gets me shocked! Absolutelly clever idea man! Well done!

I really DO hope that it wasn't your last creation, as you claimed.

I am still not able to understand how you can scramble it. Could you please explain the differences between being scrambled or not? I can't manage to imagine it.

It's really amazing how it can be twisted to (amost) normal positions. I mean, I wouldn't notify that it was not a normal stringing just by watching some of your posted pics! Awesome!

Anyway, and I want to say it again, I really love it man! You're Magic God! (POG)

Keep the hard work dude!

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 Post subject: Simple 2x2x5 idea
PostPosted: Sat Jan 27, 2007 9:21 am 
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This was something I was thinking of a couple of days ago:

Materials: 3 Rubik's 4x4x4 (if you have wood to make extensions with, one)

Similar to the 2x2x6, you would round two tetrads of centers. Then, use the easy method of creating a 2x2x3, except the piece that would go over a center isn't there but is instead rounded and attached to the rounded center. Then, do the exact same thing as you would for the 2x2x6 to make the last layer, except with more pieces because we want to preserve cube cubies.

Has anyone tried this? (Obviously, the shape-changing 2x2x6 is far more interesting, even if the cubies are rectangular)

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 Post subject:
PostPosted: Sat Jan 27, 2007 12:20 pm 
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very nice the 24 tile one is stabler then the 8 tile one so it would be easier to
play with the 24 tile one :) .

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 Post subject: Re: New type of Magic Puzzles: The "Möbius Magics"
PostPosted: Sat Jan 27, 2007 1:59 pm 
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rastarubik wrote:
You're Magic God! (POG)


Could you please tell me POG stands for I'm lost.

Looks awesome. Nice puzzle. I love M.C. Eschers work


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 Post subject: Re: New type of Magic Puzzles: The "Möbius Magics"
PostPosted: Sat Jan 27, 2007 10:38 pm 
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rastarubik wrote:
I really DO hope that it wasn't your last creation, as you claimed.


Thanks for the kind words David! :)

And no, it is not my last creation. But it seems that I have covered completely the theoretical part. I mean, any magic (with one side or two side single closed loop) is either type A, type B, or Möbius. Fortunately or unfortunately, there are no more standard stringing possibilities. Of course, now I may do more complex things LOL

rastarubik wrote:
I am still not able to understand how you can scramble it. Could you please explain the differences between being scrambled or not? I can't manage to imagine it.


The solved state is shown in the first three photos. Being a Möbius Magic, it has only one solved state. But there *could* be a second solved state which I have a great difficulty to reach. That is, to change it into another Möbius form where all ants have half of the body with different color than the other half. I will tell you if I achieve this... this 8-tile magic is already too complex!!!





Swordsman Kirby wrote:
Materials: 3 Rubik's 4x4x4 (if you have wood to make extensions with, one)
Similar to the 2x2x6, you would round two tetrads of centers. Then, use the easy method of creating a 2x2x3, except the piece that would go over a center isn't there but is instead rounded and attached to the rounded center. Then, do the exact same thing as you would for the 2x2x6 to make the last layer, except with more pieces because we want to preserve cube cubies.
Has anyone tried this? (Obviously, the shape-changing 2x2x6 is far more interesting, even if the cubies are rectangular)


Are you talking about combining magics with cubes??? LOL
(just kidding!!! I know it was accidentally sent to the wrong thread)

but I *do* have plans for some cubic magics... hehehe :P





Myke wrote:
very nice the 24 tile one is stabler then the 8 tile one so it would be easier to
play with the 24 tile one :) .


Thanks Myke! In fact, all of the Möbius Magics are 95% as stable as normal magics. But it is strongly advisable to reach Möbius Strip state only if there are enough tiles. If there are not enough tiles, playing it with the other possible shapes can be very safe and challenging... in fact, the one 8-tile I have has made all of my brain mucsles to reach Möbius Strip form!!! :?





Darren Grewe wrote:
Could you please tell me POG stands for I'm lost.
Looks awesome. Nice puzzle. I love M.C. Eschers work


Thanks Darren, I agree, Mr Escher is fantastic, I have a few sliding puzzles with his art too!
And don't worry about the POG... that is an inside joke LOL (I will tell you in private!)




Pantazis

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 Post subject:
PostPosted: Sat Jan 27, 2007 10:45 pm 
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Wow... this kind of makes me want to get into solving magics...

Up until now I was just interested in the polyhedron puzzles... but now the folding puzzles are applealing to me.

I'll work on the regular magic before attempting it in mobius form, hah, but seriously awesome build... er I guess awesome stringing would be the proper term for this?

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 Post subject:
PostPosted: Sun Jan 28, 2007 12:38 am 
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Pantazis,

I never commented on your magics puzzles before as I don't usually like to write those posts consisting simply of exclamations. 8-) But this one just broke my imagination. I am still grasping it. So, here is an exclamation: Wow! 8-)

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 Post subject:
PostPosted: Sun Jan 28, 2007 1:13 am 
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GarrettDickerson wrote:
Wow... this kind of makes me want to get into solving magics...
Up until now I was just interested in the polyhedron puzzles... but now the folding puzzles are applealing to me.
I'll work on the regular magic before attempting it in mobius form, hah, but seriously awesome build... er I guess awesome stringing would be the proper term for this?


Thanks! This is what I am trying to do, to make others interested in them! When I first held in my hands a Rubik's 8-tile Magic, it was impossible to not get intruiged by the ingenius way it was stringed... the movement is unbelievable!

And yes, starting from the most known magics is a good way to start! :)





Aleksey wrote:
Pantazis, I never commented on your magics puzzles before as I don't usually like to write those posts consisting simply of exclamations. 8-) But this one just broke my imagination. I am still grasping it. So, here is an exclamation: Wow! 8-)


Thanks Aleksey, this is very rewarding especially when it comes from someone I know for so long and has helped me in many ways! :)





And just to make things easier for all of you and to understand how all types of such magics are categorized, I present a nice chart:


Image


I hope things can be a bit more clear now! :)




Pantazis


PS Regarding the test tiles mentioned in the chart, some are rigid and some are complex. And of course, there *is* a possibility that some of them may come out in the future with a nice template! ;)
(After completing the chart I may even ask my supervisor to send a journal paper to the always interesting AMM...! LOL - seriously though, in the past I had seen many papers with much less work being published!)

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 Post subject:
PostPosted: Tue Jan 30, 2007 4:47 pm 
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Make a Master's Masters magic with like 20 lol and make them interlocking triangles!... i have a small magic obsession... i just love them, and seeing this is like... well lets say you like a rubiks cube.... then you walk up to a table, and sitting on it is a 20x20x20... its... exciting... All though this is the forst of your creations that I personally have seen, I am very impressed and I'd like to say that i could never hope to even attempt to do what you have done!

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 Post subject:
PostPosted: Wed Jan 31, 2007 10:44 am 
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FireWezul wrote:
Make a Master's Masters magic with like 20 lol and make them interlocking triangles!... i have a small magic obsession... i just love them, and seeing this is like... well lets say you like a rubiks cube.... then you walk up to a table, and sitting on it is a 20x20x20... its... exciting... All though this is the forst of your creations that I personally have seen, I am very impressed and I'd like to say that i could never hope to even attempt to do what you have done!


Thanks FireWezul!

Regarding the ability for someone to make magics, think of this:

Last year, around this time, I was studying the nice article regarding magics at the article section of this site. This is how it started. I never ever expected that I would come up with so many varieties of magics and theories, and if you had told me one year ago about the designs I have made now, I would probably have laughed!!!

:)



Pantazis

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 Post subject:
PostPosted: Wed Jan 31, 2007 2:28 pm 
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Are you finished yet?

You are churning out puzzles like a new Tony Fisher :P

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 Post subject:
PostPosted: Wed Jan 31, 2007 8:42 pm 
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Pembo wrote:
Are you finished yet?


Well.. by having a final chart, the theoretical part for single closed-loop magics with standard stringing is finished.
Now, based on the information many designs can be made, for example adding extensions. The Magic Octopus is a fine example, and I had a lot of positive feedback as it gave some new twist to the closed-loop four tile magics.

I will definitely do more of them, different than the rest (as usual), because knowing all the construction possibilities is a big advantage.

Then, there are the bandaged magics. I was planning to make a couple of those, but the movement of the Möbius Magics was almost identical in some way. I may design a cute bandaged one, to have it as a reference!

One of my next designs though, will be some really twisted puzzle LOL
But I won't reveal yet any details of the fearsome "Flopping Cube"!!! ;)




Pembo wrote:
You are churning out puzzles like a new Tony Fisher :P


Wow... thanks for the compliment, but Tony is a true wizard. As for me, I am still in the Harry Potter (magic) status LOL





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 Post subject:
PostPosted: Wed Jan 31, 2007 11:00 pm 
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I don't see how you would string it. Would it be like the 2 tile's strings going
onto one tile only?

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 Post subject:
PostPosted: Thu Feb 01, 2007 8:33 am 
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kastellorizo wrote:
Wow... thanks for the compliment, but Tony is a true wizard. As for me, I am still in the Harry Potter (magic) status LOL
Pantazis


You're closer to Dumbledore if you ask me. :) (Except for that whole dead thing.)

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 Post subject:
PostPosted: Thu Feb 01, 2007 9:15 pm 
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Myke wrote:
I don't see how you would string it. Would it be like the 2 tile's strings going
onto one tile only?


You mean the Möbius Magics? there are two strings connecting three tiles at the same time. No exceptions. That is, it doesn't matter which tile you start from, you can getr an equivalent shape to the photos above by starting from any tile. For example, the tile that is presented as internal (or external) extension, can be changed to *any* tiles with a few manipulations.

In very few words: The Magic in its Möbius Strip form is a equivalent with a flat shape Magic (they are the same puzzle but a couple of moves away from each other).
So stringing it when it is flat is easier. If I was an octopus, I could probably string it while it was in Möbius Strip form too LOL

:P




xcool wrote:
You're closer to Dumbledore if you ask me. :) (Except for that whole dead thing.)


No no... white is not the true color of my hair... I just dyed them! :P
(plus, it would be very interesting to think of myself having a beard... hmmm... also, it is a festive season similar to Halloween right now in Greece LOL)




Pantazis

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 Post subject:
PostPosted: Fri Feb 02, 2007 11:26 pm 
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I just saw your webpage...


you're amazing

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 Post subject:
PostPosted: Mon Feb 05, 2007 5:23 pm 
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Uh... oh my... :shock: "amazing" doesn't even begin to cover it. You seriously surpassed anything that I've been able to conceive of a long time ago and for months now I've thought of you as a "Magic mod god in training", but I'd say this one removes the final barrier and upgrades your title to "Magic Mod God". In martial arts terms, you'd definitely be a 10th dan, ie. a Grand Master of Magics, and I'd say it's safe to say you can take your place among the puzzling greats of all time. Congratulations! :D Wow, now I've got to get to work on that resolution more than ever...


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 Post subject:
PostPosted: Tue Feb 06, 2007 10:01 am 
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FireWezul wrote:
I just saw your webpage...

you're amazing


Not me, the puzzles are amazing! ;)





Tim Browne wrote:
Uh... oh my... :shock: "amazing" doesn't even begin to cover it. You seriously surpassed anything that I've been able to conceive of a long time ago and for months now I've thought of you as a "Magic mod god in training", but I'd say this one removes the final barrier and upgrades your title to "Magic Mod God". In martial arts terms, you'd definitely be a 10th dan, ie. a Grand Master of Magics, and I'd say it's safe to say you can take your place among the puzzling greats of all time. Congratulations! :D Wow, now I've got to get to work on that resolution more than ever...


Tim, this counts double for me, since I regard you (the inventor of the "create the double cube" magic) as one of the very few magic experts of this forum. :)
(and I do have some knowledge of Judo and Tae Kwon Do, but definitely no dan yet!)



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