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 Post subject: Core modding
PostPosted: Mon Mar 31, 2014 2:55 pm 
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Hi Twisty Puzzle fans,

This week, I presented three new puzzles that can all be built from the pieces of a Bermuda Minx. The only new parts are the cores, which all four have different geometries. I was quite surprised by the discovery that geometrically completely different puzzles can be built from the same pieces. The purpose of this thread is to discuss the concept of core modding.

First the four puzzles, see also the photo below.
The angle is measured between two adjacent axes.
Attachment:
Core mods.jpg
Core mods.jpg [ 80.06 KiB | Viewed 1292 times ]

I was also surprised by the almost total lack of response to my posts. I believe that the concept of core modding raises several questions.
    Is core-modding something new, or do there already exist other puzzles that are core mods of each other?
    Is this family of four complete, or are there more core mods of the Bermuda Minx?
    What would be a good definition of core modding?
    Can we come up with new puzzles that are the result of core modding?
    How much fudging is allowed in core modding?
    ... more questions ...

What do you think?

Oskar

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 Post subject: Re: Core modding
PostPosted: Mon Mar 31, 2014 3:36 pm 
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Sorry for such a short post but I think it's worth mentioning that Carl's Bubbloid series of puzzles use mostly interchangeable pieces with a different core.

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 Post subject: Re: Core modding
PostPosted: Mon Mar 31, 2014 4:00 pm 
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Brandon Enright wrote:
Sorry for such a short post but I think it's worth mentioning that Carl's Bubbloid series of puzzles use mostly interchangeable pieces with a different core.

Actually the only difference between the Bubbloid112 and Bubbloid122 is the core. All the other pieces are identical. And there is no fugging.

Same is true of the set Bubbloid123, Bubbloid223, and Bubbloid233 most of which I need to present.
And again this is true for the Bubblism512 and Bubblism521. This is the pentagonal prism version of the Bubbloid.
All 5 of these are off in queue to get tumbled by Brandon.

But none of these require any fudging. Would this still be considered "core modding"?

Carl

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 Post subject: Re: Core modding
PostPosted: Mon Mar 31, 2014 6:14 pm 
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Actually core modding is possible with and between *all* geometries if you use a ball-and-groove mechanism, because the outer parts don't need to touch each other, as long as they are fixed into grooves in a sperical core.

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 Post subject: Re: Core modding
PostPosted: Tue Apr 01, 2014 12:22 pm 
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wwwmwww wrote:
But none of these require any fudging. Would this still be considered "core modding"?
That is an interesting observation. Let us distinguish
1) non-fudged core modding
-Bubbloid112 --> Bubbloid122
-Bermuda Comet --> Bermuda Rhombdo
2) fudged core modding
-Bermuda Megaminx --> Bermuda Comet
-Bermuda Megaminx --> Bermuda Jumblix
So are there more instances of fudged core modding?
KelvinS wrote:
Actually core modding is possible with and between *all* geometries if you use a ball-and-groove mechanism, because the outer parts don't need to touch each other, as long as they are fixed into grooves in a spherical core.
That is a rather bold statement, which would require at least a single example to make it a valid conjecture. Let me pose it as a design challenge: design a functional puzzle with Rubik's Cube geometry that is core-modded into a functional puzzle with Megaminx geometry. Or am I misinterpreting your statement?

Oskar

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 Post subject: Re: Core modding
PostPosted: Tue Apr 01, 2014 1:05 pm 
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Oskar wrote:
KelvinS wrote:
Actually core modding is possible with and between *all* geometries if you use a ball-and-groove mechanism, because the outer parts don't need to touch each other, as long as they are fixed into grooves in a spherical core.
That is a rather bold statement, which would require at least a single example to make it a valid conjecture. Let me pose it as a design challenge: design a functional puzzle with Rubik's Cube geometry that is core-modded into a functional puzzle with Megaminx geometry. Or am I misinterpreting your statement?
This makes me think of the Moving Marble Puzzles. In some sense the marbles can the thought of as the pieces and the portion that holds the marbles can be thought of as the core. So to accept Oskar's challenge I'd envision a sphere with 6 toroidal paths removed near the surface. 2 are parallel to the x-y plane. 2 are parallel to the x-z plane. And 2 are parallel to the y-z plane. Each path is offset from its respective plane by either + or - half a marble diameter. And the marble diameters are chosen such that 8 fit exactly into each path.

First question... does this puzzle fit your definition of Rubik's Cube geometry? Note face turns of 45 degrees would be allowed as edges could be exchanged with corners but one could restrict themselves to making only 90 degree turns and this would map perfectly to a Rubik's Cube.

To create the puzzle with Megaminx geometry one simply needs to create a torus which exactly holds 10 of the same sized marbles. Use this torus to cut 12 paths on a larger sphere. Each path would match the geometry of a face on a Megaminx.

This approach may require some fuding (using slightly smaller marbles) as I'm not certain everything would turn as expected if each marble was tight in its path and in constant contact with its neighbors. But in pinciple I think it could be argued this would be a solution to the challenge.

Being a mechanism guy I'm not as interested in moving marble puzzles as other twisty puzzles so this feels like cheating to me but I think its the type of thing KelvinS was proposing.

Carl

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 Post subject: Re: Core modding
PostPosted: Tue Apr 01, 2014 1:27 pm 
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Oskar wrote:
2) fudged core modding
-Bermuda Megaminx --> Bermuda Comet
-Bermuda Megaminx --> Bermuda Jumblix
So are there more instances of fudged core modding?
Just to make sure I'm on the same page...

Is it possible to make a Bermuda Megaminx, a Bermuda Comet, and a Bermuda Jumblix as seperate puzzles without fudging?

If so then the fudging is just the result of using a part in another puzzle that it wasn't specifically designed for but its "close enough" to actually work. The question then sort of becomes how close is close enough?

If these puzzles require fudging all by themselves... I haven't looked close enough to tell yet... then is the amount of fudging required to make the puzzle function similiar to the amount of fudging required to allow the puzzles to exchange pieces?

Which brings up another question... what is the best way to quantify the "amount of fudging"?

Very interesting topic... I need more time to think about it,
Carl

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 Post subject: Re: Core modding
PostPosted: Tue Apr 01, 2014 2:07 pm 
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wwwmwww wrote:
Is it possible to make a Bermuda Megaminx, a Bermuda Comet, and a Bermuda Jumblix as separate puzzles without fudging?
That is basically correct. Actually, Jumblix is a slightly fudged puzzle (angles of 60.89 and 59.55 deg), but we can ignore that for the moment as being relatively minor. Each of these puzzles can be "bermudized", c.f. Bermuda Cube and Bermuda Megaminx.

wwwmwww wrote:
If so then the fudging is just the result of using a part in another puzzle that it wasn't specifically designed for but its "close enough" to actually work.
That is correct. Mr Fok and Baiqiang serendipitously discovered these core mods, that happened to map on two puzzles that I had designed before.

As for your moving marbles puzzles example, I do not see how that answers Kelvin's statement. A Rubik's Cube does not have marbled, and unlike marbles, Rubik's corners and edges cannot be rotated in place.

Oskar

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 Post subject: Re: Core modding
PostPosted: Tue Apr 01, 2014 3:56 pm 
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Oskar wrote:
As for your moving marbles puzzles example, I do not see how that answers Kelvin's statement. A Rubik's Cube does not have marbled, and unlike marbles, Rubik's corners and edges cannot be rotated in place.
All depends on how one defines "Rubik's Cube Geometry".

But let's take the 6 torodial path spherical puzzle I described above. Reduce the radius of the mables and the track such that neighboring marbles are no longer touching. Attach a rod to each marble that is radially pointed outward. One way to accomplish this would be to have a burried torodial path direcly under the first and this rod could be fixed through the center of a marble in each path. On the other end of some of these rods attach a heavily fudged shape which could either be a 3x3x3 corner or megaminx corner. These might look like your Illegal Cube corners. On the remainer of the rods attach a heavily fudged shape which could either be a 3x3x3 edge or megaminx edge. I'd make these long and narrow rectangular shapes. Imagine a 3x3x3 with a much thiner central slice layer. Or a Megaminx which has been pushed in the direction of a Kilominx but not so far that it has lost its edges.

Now design these fudged shapes such that they touch each other in either the 3x3x3 or Megaminx configuration while maintaining the proper spacing between the marbles they are attached to. I theory I believe this is all doable. In practice I suspect that if someone tried it they'd get a very poor turing puzzle. If you wanted rotating face centers too these could simply be attached to the spherical core with a screw and allowed to make point contact with the other fudged shapes. This might add some stability to the puzzle but I think you'd want a different shape for the 3x3x3 face center versus the megaminx face center.

In short I think this works on paper and if one allows alot of fuddging I suspect that one could create a fudged hybrid of just about any two puzzles that would be able to supply pieces that could be used to make either. But in practice I think this would be a very poor way to design puzzles. To get something that works well the amount of fudging needs to be minimized. And the closer the two puzzles are to each other the better.

I suspect you could design a 3x3x3 core which would work with your Illegal Cube pieces for example. But would that gain us anything?

Carl

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 Post subject: Re: Core modding
PostPosted: Tue Apr 01, 2014 4:11 pm 
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Oskar, this may be obvious to you guys, but not to me. Can I make a crazy comet using a helicopter core and unmodified bermudaminx parts?

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 Post subject: Re: Core modding
PostPosted: Tue Apr 01, 2014 4:29 pm 
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JasonSmith wrote:
Can I make a crazy comet using a helicopter core and unmodified bermudaminx parts?
Exactly! And two more puzzles when using two other different cores. Amazing, isn't it?

Oskar

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 Post subject: Re: Core modding
PostPosted: Tue Apr 01, 2014 5:19 pm 
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That is completely unexpected! I saw a picture of something like that on Facebook but I assumed the parts were modified.

I have a bag of helicopter cube cores... :)

I wonder what the best combination of bermuda puzzles is to get enough for a crazy comet?
Looking at this chart, it looks like at least 6 puzzles would have to be harvested just to get the face centers!

EDIT-- Digging into your individual puzzle announcements I see I am repeating previous information. Sorry! :)


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 Post subject: Re: Core modding
PostPosted: Tue Apr 01, 2014 5:53 pm 
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wwwmwww wrote:
Oskar wrote:
KelvinS wrote:
Actually core modding is possible with and between *all* geometries if you use a ball-and-groove mechanism, because the outer parts don't need to touch each other, as long as they are fixed into grooves in a spherical core.
That is a rather bold statement, which would require at least a single example to make it a valid conjecture. Let me pose it as a design challenge: design a functional puzzle with Rubik's Cube geometry that is core-modded into a functional puzzle with Megaminx geometry. Or am I misinterpreting your statement?
This makes me think of the Moving Marble Puzzles. In some sense the marbles can the thought of as the pieces and the portion that holds the marbles can be thought of as the core...

Yes Carl, that is *exactly* what I meant, except that some external piece (e.g., circular section of a spherical shell surrounding the core) would stick out from each marble, and these pieces would not necessarily touch each other. Then you can change the geometry just by changing the number and positions of the circular grooves around the core.

For example, the geometry of a 3x3x3 could be modeled with 9 intersecting circular grooves, 3 around each orthogonal axis. Then just change the number and position of grooves around the core to make any new geometry you want, without having to change the pieces that run around these grooves. Simple! :D

And in fact you could even mod the core further into non-spherical globular shapes to make an even wider range of wierd and asymmetric geometries with non-intersecting axes and even non-circular orbits. Thus the possibilities for core modding are endless with the ball-and-groove mechanism.

At least in theory anyway.

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 Post subject: Re: Core modding
PostPosted: Tue Apr 01, 2014 6:30 pm 
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KelvinS wrote:
For example, the geometry of a 3x3x3 could be modeled with 9 intersecting circular grooves, 3 around each orthogonal axis.
I'd say 2 around each orthogonal axis. A slice layer turn rotates the core.
JasonSmith wrote:
I have a bag of helicopter cube cores...
Are these available for purchase?
JasonSmith wrote:
Digging into your individual puzzle announcements I see I am repeating previous information. Sorry!
I remember seeing this but I was about to repeat this as well. I'll go hunt up the links and post them here. But if one is wanting a set of pieces that would be needs to make all the puzzles possible in this set of core modded puzzles Osker started this toppic over I believe one needs:

(A) Four cores. Two of which have been massproduced. The Mexaminx and the Helicopter Cube. Am I correct the oher two are only available through Shapeways currently?

(B) Some minimal set of the bermudaminx puzzles necessary to harvest for parts.

So just how many different puzzles can be built with such a set made this way? Off the top of my head I think there are more variations of the bermudaminx itself beyond just the 8 offered.

Carl

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 Post subject: Re: Core modding
PostPosted: Tue Apr 01, 2014 6:32 pm 
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Oskar wrote:
As for your moving marbles puzzles example, I do not see how that answers Kelvin's statement. A Rubik's Cube does not have marbled, and unlike marbles, Rubik's corners and edges cannot be rotated in place.

FYI, the "marbles" don't necessarily have to be spherical and rotatable within the grooves. :wink:

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 Post subject: Re: Core modding
PostPosted: Tue Apr 01, 2014 6:48 pm 
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wwwmwww wrote:
So just how many different puzzles can be built with such a set made this way? Off the top of my head I think there are more variations of the bermudaminx itself beyond just the 8 offered.


For reference, the Bermuda Cube parts could be mixed around into something like 28 different variations, possibly more. Bo Hu's simulator lists this many, at least.

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 Post subject: Re: Core modding
PostPosted: Tue Apr 01, 2014 7:27 pm 
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Ok here is the post I remembered:
http://twistypuzzles.com/forum/viewtopic.php?p=317020#p317020
There Oskar states:
Quote:
Four samples of Bermuda Earth is enough to build a Bermuda Comet. You need six if you want to replicate the original Crazy Comet.
Which doesn't quite answer the question I had. There are 4 axis systems/cores and Oskar has provided links to each in the first post. Scanning those threads I saw mention of these puzzles:

Bermuda Rhomdo
Crazy Rhomdo (regular)

Bermuda Comet
Regular Crazy Comet
many "Bermuda-ized" variations of Crazy Comet

Bermuda Jumblix
Jumblix
many "Bermuda-ized" variations of Jumblix

Does the Rhomdo geometry allow many "Bermuda-ized" variations as well? They weren't mentioned that I saw.

And the above list doesn't even count all the many "Bermuda-ized" variations of the Bermudaminx which is something like "28 different variations, possibly more" per themathkid and Bo Hu's simulator.

I assume each geometry has only one "regular" version.

themathkid, is the normal Megaminx one of the 28 variations you counted in Bo Hu's simulator?

So I have two open questions:

(1) How many "Bermuda-ized" and regular variations are there for each of these 4 geometries?
(2) What is the optimal set of Bermudaminx puzzles one should purchase if they wanted to be able to contrust ANY one of these possible puzzles?

Ideally, I'd like to see a list with proof it was complete and a table where each puzzle could have a row and the columns were for each of the different Bermudaminx pieces with the count needed of that part to construct each puzzle. If this gets created it probably should go in its own thread as to not take this thread off the more general topic of core modding.

Oskar, you show diagrams on how to make the Bermuda Rhomdo, Bermuda Comet, and Bermuda Jumblix puzzles. Are these names then what you picked for these specific variations of the many possible? Or would you apply this name to all variations? Say a Bermuda Comet1, Bermuda Comet2, Bermuda Comet3, etc. for example. I'm guessing there are probably a 100+ different puzzles possible here and I'm trying to think what sort of naming scheme might be appropriate.

Oh and one last question... these pieces were designed only for the Bermudaminx I believe. So all the other geometries are fudged while the Bermudaminx isn't fudged... correct? I'm curious... could the fudging be equally destributed across all 4 geometries if they were redesigned for specifcally this purpose? And if they were, would the resulting puzzles turn any better? Things seem so close now that I'm not sure things would improve much if at all. I'm guessing Oskar is in the best position to answer this as he may be the only one to have handled all 4 geometries at this point.

Carl

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 Post subject: Re: Core modding
PostPosted: Tue Apr 01, 2014 7:51 pm 
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wwwmwww wrote:
And the above list doesn't even count all the many "Bermuda-ized" variations of the Bermudaminx which is something like "28 different variations, possibly more" per themathkid and Bo Hu's simulator.

I assume each geometry has only one "regular" version.

themathkid, is the normal Megaminx one of the 28 variations you counted in Bo Hu's simulator?



The 28 is for the Bermuda CUBES. Sorry. Didn't mean to confuse there.

I just noticed, via the simulator thread, that Bo Hu does have a simulator for the Bermudaminxes, but it currently only lists 12, one of which is the regular Megaminx. Surely there are more than this, so I doubt this is exhaustive. There are also simulators for the Jumblix and Crazy Comet, I cannot access the Crazy Comet one due to the MF8 board restrictions on downloading, but the Jumblix was uploaded separately by grigr and lists 12 variations.

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 Post subject: Re: Core modding
PostPosted: Wed Apr 02, 2014 2:23 am 
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wwwmwww wrote:
Does the Rhomdo geometry allow many "Bermuda-ized" variations as well?
Yes, all four puzzle have one "regular" version and many Bermudized version.
wwwmwww wrote:
(1) How many "Bermuda-ized" and regular variations are there for each of these 4 geometries?
(2) What is the optimal set of Bermudaminx puzzles one should purchase if they wanted to be able to contrust ANY one of these possible puzzles?
Those are interesting "knapsack" problems by themselves. Let me add another one.
(3) What is the optimal set of Bermudaminx puzzles one should purchase if they wanted to be able to contrust ALL one of these possible puzzles?
wwwmwww wrote:
Are these names then what you picked for these specific variations of the many possible? Or would you apply this name to all variations?
Let's call these specific ones "Oskar's Bermuda xxx".
wwwmwww wrote:
So all the other geometries are fudged while the Bermudaminx isn't fudged... correct?
Correct.
wwwmwww wrote:
could the fudging be equally destributed across all 4 geometries if they were redesigned for specifcally this purpose? And if they were, would the resulting puzzles turn any better?
My guess is that the answer to both questions is "yes". Especially the angles for Crazy Comet and Jumblix seem very close together. As for the original Jumblix, the fudging is so minor that does not notice that it is fudged.

Oskar

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 Post subject: Re: Core modding
PostPosted: Wed Apr 02, 2014 11:03 am 
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Oskar wrote:
Those are interesting "knapsack" problems by themselves. Let me add another one.
(3) What is the optimal set of Bermudaminx puzzles one should purchase if they wanted to be able to contrust ALL one of these possible puzzles?
I can't imagine wanting to make ALL of them but let me add another knapsack problem.
(4) What is the optimal set of Bermudaminx puzzles one should purchase if they wanted to be able to contrust ALL four of the "regular" versions? Is this set any different if one doesn't include the regular Megaminx as that one is already available as a mass produced puzzle?

This one is probably the easiest of the bunch to answer but I don't have time to dig into it now.

Carl

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