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Does Screw Cube jumble?
 Yes, it jumbles when following Bram's definition 10% [ 2 ] No, it does not jumble following Bram's definition 57% [ 12 ] Undecided, Bram's definition needs an update 33% [ 7 ]
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 Post subject: Screw Cube by ALEX and OSKARPosted: Fri Jul 27, 2012 1:17 pm

Joined: Mon Nov 30, 2009 1:03 pm
Hi Twisty Puzzles fans,

Screw Cube is an idea by Alex Polonsky. It is basically a 2x2x3 puzzle with eight identical corner pieces that can screw up and down the 1x2x2 base puzzle. As the corner pieces are blocked at the end of the thread after four turns, this makes this puzzle a sort-of Constrained Cube.

So, does this puzzle jumble?
-It is non doctrinaire? Check!
-It can be unbandaged? Check! (Just elongate the screw)
-It cannot be unbandaged into a doctrinaire puzzle? Check!
That means that this puzzle jumbles! Check?

Buy the puzzle at my Shapeways Shop.
Read more at the Shapeways Forum.
Check out the photos below.

Enjoy!

Oskar
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Last edited by Oskar on Sun Sep 02, 2012 2:46 pm, edited 1 time in total.

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Fri Jul 27, 2012 1:24 pm

Joined: Mon Jun 25, 2012 2:40 pm
Wow, this looks like a fun, untraditional solve. Another great new cube from you, well done!

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Fri Jul 27, 2012 1:35 pm

Joined: Sun Jan 02, 2011 6:48 pm
Nice, that's cool. It's interesting because it's a twistypuzzle, but you use a move that is normaly common in mechanical puzzles. I wouldn't call it jumbling, that's sure.

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Fri Jul 27, 2012 2:41 pm

Joined: Tue Jul 13, 2010 12:50 pm
I do not believe this puzzle should be classified as a jumbling puzzle, because the definition of "non-doctrinaire" is incorrect. "A twisty puzzle that does not returns to the same three-dimensional shape after each turn" should be instead "A twisty puzzle whose Jaap's Sphere does not return to the same configuration after each turn." Which would redefine bandaging (in the context of jumbling) as "pieces that would not otherwise swap using doctrinaire turns have done so and therefor interfere with the rotation of the puzzle."I think this more clearly defines bandaging and jumbling, and is a more solid mathematical definition.

Using this definition, the Screw cube does not jumble, as the rotation of the top and bottom layers do not alter the the configuration of the Jaap's sphere, and is therefor a doctrinaire puzzle.

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Fri Jul 27, 2012 3:26 pm

Joined: Sat Mar 22, 2003 9:11 am
Location: Marin, CA
This is not a jumbling puzzle, it's a puzzle with a novel form of bandaging. If you insist on unbandaging it, it turns into a puzzle with gaps, similar to the coca cola can puzzle.

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Fri Jul 27, 2012 4:48 pm

Joined: Sun Sep 26, 2004 8:04 am
Location: exeter,england
What ever it does or doesn't do,it looks awesome and I wait for it to be,hopefully,mass produced.

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Fri Jul 27, 2012 6:42 pm

Joined: Tue Mar 10, 2009 7:06 pm
Location: Nowhere in particular.
First off, fantastic puzzle!

In my mind, the big issue is: What constitutes bandaging? Does simply adding more threads to the screw mechanism create an unbandaged version of the puzzle? I thought about it for a little while, and I think I see two possibilities:
1. The puzzle does not jumble. Puzzles with a different number of threads are part of a "family" of screw puzzles, rather than being unbandaged variants of one another.
2. The puzzle does jumble. More threads constitutes a new form of unbandaging, and therefore a new type of jumbling.

Personally, I feel like the first one makes more sense. The second one just opens up too many new questions. (For example, if the threads were extended to allow for an additional half-turn, then would you need to split the pieces to accommodate for this? Is this type of puzzle even part of the same family?)

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Fri Jul 27, 2012 6:53 pm

Joined: Thu Oct 16, 2008 9:46 pm
Location: Littleton CO
I really like this idea and this puzzle. I think a hexagonal one could be made fairly easily building up from a cheese mech or something similar. I’d love to see more of these.

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Fri Jul 27, 2012 7:29 pm

Joined: Mon Aug 18, 2008 10:16 pm
Location: Somewhere Else
Ah, I support the idea of a six-sided version too. It could have a nut & bolt theme.

So... how many valid positions does it have?

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Fri Jul 27, 2012 7:32 pm

Joined: Sun Dec 26, 2010 12:21 am
Location: Buenos Aires, Argentina
I cannot for the life of me understand the concept of jumbling, doctrinaire and bandaging.

I thought jumbling meant being able to put pieces where they don't belong, like a corner in the place of an edge. Can you do that in this puzzle? I'm probably wrong though.

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Fri Jul 27, 2012 7:37 pm

Joined: Fri Feb 08, 2008 1:47 am
Location: near Utrecht, Netherlands
This is a very weird puzzle. It is bandaged not only because the pieces are limited in moving outwards, it is also bandaged because they only move so far down. This means that an infinitely long screw is not a proper unbandaging.

Perhaps this is not a twisty puzzle at all. Or perhaps the unbandaging is just not possible in 3D space.

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Sat Jul 28, 2012 2:51 am

Joined: Mon Apr 02, 2012 9:17 am
Oh man that would be a fun cube to review just because of the name. Hey Oskar did you see what did with your Cast Equa? Muhahahahahaha!!!!!

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Sun Jul 29, 2012 9:42 am

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Bram wrote:
This is not a jumbling puzzle, it's a puzzle with a novel form of bandaging.
I agree.
Bram wrote:
If you insist on unbandaging it, it turns into a puzzle with gaps, similar to the coca cola can puzzle.
Not sure I agree here though... unbandaging this gets complicated.
TomZ wrote:
This is a very weird puzzle.
I love weird.
TomZ wrote:
It is bandaged not only because the pieces are limited in moving outwards, it is also bandaged because they only move so far down. This means that an infinitely long screw is not a proper unbandaging.
Yes, I agree with this.
TomZ wrote:
Perhaps this is not a twisty puzzle at all.
Oh, I'd call this a Twisty Puzzle but I do think a perfect definition of Twisty Puzzle is all but impossible. As soon as you pin down a definition everyone sets out to break it. Oskar being the worst offender... that's a good thing.
TomZ wrote:
Or perhaps the unbandaging is just not possible in 3D space.
You can unbandage this in virtual 3D space by allowing pieces to move through each other. I can even think of ways that you could allow the outer layers to screw INTO the inner layer and MAYBE even through the inner layer over to the other side, on a physical model. This would add threads on the outside of the end layers so you'd lose your nice block shape and putting stickers on the threads would be a problem, but I'm pretty sure it could be done. But you'd still need an infinitely long puzzle to totally unbandage it.

Nice!!
Carl

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Sun Jul 29, 2012 11:12 am

Joined: Wed Nov 24, 2010 11:12 am
Location: Hong Kong/Beijing
I think you may have created a new type of twistypuzzle series ! Brilliant!

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Mon Jul 30, 2012 3:09 pm

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
What is the edge length?
What is its weight?

Thank you for posting edited images.

I am afraid I have nothing more to add.

Andreas

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Tue Jul 31, 2012 8:27 am

Joined: Sat Mar 22, 2003 9:11 am
Location: Marin, CA
TomZ wrote:
This is a very weird puzzle. It is bandaged not only because the pieces are limited in moving outwards, it is also bandaged because they only move so far down. This means that an infinitely long screw is not a proper unbandaging.

Puzzles with gaps tend to have this property. The classic 15 puzzle, for example, and noone says that it's bandaged.

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Tue Jul 31, 2012 12:41 pm

Joined: Mon Nov 30, 2009 1:03 pm
Andreas Nortmann wrote:
What is the edge length? What is its weight?
146 gram, 60x60x60 mm.

As for the poll,
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there is an overwhelming majority that agrees that this puzzle does NOT jumble. Also, there is a good majority for the view that Bram's current definition suffices. So I guess that that is settled.

I agree with Bram's view that this puzzle should be classified as a puzzle with a gap, like the 15 puzzle. So, it is a hybrid of a sliding piece puzzle and a twisty puzzle, like e.g. Twist & Slide.

Oskar

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Tue Jul 31, 2012 1:26 pm

Joined: Mon Mar 30, 2009 5:13 pm
Oskar, I was just thinking:

Could you add such a screw motion in each of the 3 orthogonal axes rather than just one?

Or is that design already in progress?

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Tue Jul 31, 2012 3:13 pm

Joined: Wed May 13, 2009 4:58 pm
Location: Vancouver, Washington
KelvinS wrote:
Could you add such a screw motion in each of the 3 orthogonal axes rather than just one?
Like a cross cube or something else?

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Tue Jul 31, 2012 3:24 pm

Joined: Mon Mar 30, 2009 5:13 pm
GuiltyBystander wrote:
KelvinS wrote:
Could you add such a screw motion in each of the 3 orthogonal axes rather than just one?
Like a cross cube or something else?

No, I mean with genuine screw motion along all 3 axes, so that all 6 faces can independently twist in/out towards or away from the core, rather than just 2 faces in the Screw Cube presented above.

So the faces twist in/out rather than simply rotating, otherwise it should look like a normal proportional 3x3x3 cube.

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Wed Aug 01, 2012 12:02 am

Joined: Thu Oct 16, 2008 9:46 pm
Location: Littleton CO
I think if you added multiple layers (one more in this example), and enough thread, you could make it so that there are 2 inner layers on one part and 0 on another.
Does that make sense?
If yes, could you even do that?

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Wed Aug 01, 2012 4:56 am

Joined: Mon Mar 30, 2009 5:13 pm
eye2eye wrote:
I think if you added multiple layers (one more in this example), and enough thread, you could make it so that there are 2 inner layers on one part and 0 on another.
Does that make sense?
Yes, I had something similar in mind, where the screws are layered inside each other.

eye2eye wrote:
If yes, could you even do that?
I couldn't personally, but I'm sure Oskar could find a way to fudge the universe a little and make it work.

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Wed Aug 01, 2012 8:28 am

Joined: Mon Sep 29, 2008 9:41 am
Location: Spijkenisse, the Netherlands
Brilliant concept, I'd love to try it out some day!

And wouldn't 'removing the screw thread' just unbandage it into a regular 2x2x3? Or is that too simple?

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Thu Aug 02, 2012 8:23 am

Joined: Mon Aug 18, 2008 10:16 pm
Location: Somewhere Else

If instead of the screw mechanism, we placed a dial on each face going from 0 to 3, representing the heights, and used internal gearing to increase and decrease the dials, we could make a puzzle which solves identically to this one. Then, the unbandaging would be relatively simple - just allow the dial to go from 3 back to 0.

So I don't think we have a puzzle with gaps here - we have a gappy visualization of yet another gear puzzle.

You might also be able to use something similar to this to realize Kelvin's multi-axis puzzle - it wouldn't look as impressive, though.

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Thu Aug 02, 2012 8:55 am

Joined: Mon Mar 30, 2009 5:13 pm
Jared wrote:

If instead of the screw mechanism, we placed a dial on each face going from 0 to 3, representing the heights, and used internal gearing to increase and decrease the dials, we could make a puzzle which solves identically to this one. Then, the unbandaging would be relatively simple - just allow the dial to go from 3 back to 0.

So I don't think we have a puzzle with gaps here - we have a gappy visualization of yet another gear puzzle.

You might also be able to use something similar to this to realize Kelvin's multi-axis puzzle - it wouldn't look as impressive, though.

I don't think this idea is the same because "allowing 3 to go back to 0" effectively turns the screwing effect of this puzzle into simple rotation. The whole point of the screwing motion is that a complete rotation does *not* get back to the same state.

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Thu Aug 02, 2012 9:24 am

Joined: Mon Aug 18, 2008 10:16 pm
Location: Somewhere Else
Whoops, that should have been 0 to 4, but I see what you mean.

But, I think I disagree. The fact that 4 turns is a full rotation doesn't change anything. With the dials, you can still go from 0 to 4. In fact, you can make the dials go to any number at all. The only difference is a number showing, rather than a height.

It's a bit like the difference between a Rubik's Cube and a Bump Cube. Same thing, different look.

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Thu Aug 02, 2012 9:37 am

Joined: Mon Mar 30, 2009 5:13 pm
I think you did mean 0 to 3, representing 4 orientations.

Still, the only way to mimic the screw mechanism is to allow the numbers to count up or down continuously and indefinitely (representing an infinite screw), but not allow them to cycle back to 0 (representing simple rotation).

This could be simulated by coupling a counter to a latch mechanism that counts up or down indefinitely with clockwise or anticlockwise rotation.

However, the added complication with tge Screw Cube is that the screws are not infinite, so tge rotation is constrained after several rotations in each direction, as if the counter has both a lower and an upper limit on each individual piece.

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Thu Aug 02, 2012 9:55 am

Joined: Mon Aug 18, 2008 10:16 pm
Location: Somewhere Else
No, I meant 0 to 4. I forgot that the cube has five levels of rotation.

I think that maybe we're both right. I'm having trouble coming up with words to explain it though, so I hope this works: the only difference between your idea and mine is the length of the "screw". In your case, it's infinite, so the ends can't meet. But it's the same idea.

It's like how a straight line can be thought of as a circle of infinite radius.

Anyway, I prefer finite puzzles to infinite ones.

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Thu Aug 02, 2012 9:58 am

Joined: Mon Mar 30, 2009 5:13 pm
So is the 0 to 4 counting entire levels (complete rotations) rather than quarter turns?

That may explain the confusion...

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Thu Aug 02, 2012 10:02 am

Joined: Mon Aug 18, 2008 10:16 pm
Location: Somewhere Else
No, it was meant to be quarter turn levels. Sorry if I'm not making sense...

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Thu Aug 02, 2012 10:05 am

Joined: Mon Mar 30, 2009 5:13 pm
Then how can you count 5 quarter turns (0 to 4) as one rotation?

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Thu Aug 02, 2012 10:17 am

Joined: Mon Aug 18, 2008 10:16 pm
Location: Somewhere Else
I didn't. I only meant that that's the total number of levels in the actual cube.

And, 0 to 4 is 4 quarter turns. 0-1, 1-2, 2-3, 3-4.

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Thu Aug 02, 2012 10:26 am

Joined: Mon Mar 30, 2009 5:13 pm
So you're counting continuous rather than discrete quarter turns, so that 0 is the same as 4? I thought you meant 0 -> 1 -> 2 -> 3 -> 4 -> 0 -> 1 -> etc. with 5 discrete quarter turn states, rather than 1 -> 2 -> 3 -> 4 -> 1 -> etc., with 4 states.

Either way, my original comment stands, that allowing the numbers to cycle represents simple rotation rather than a screw. The numbers should continue counting up or down to a limit, and not cycle.

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Last edited by KelvinS on Thu Aug 02, 2012 10:41 am, edited 2 times in total.

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Thu Aug 02, 2012 10:37 am

Joined: Mon Aug 18, 2008 10:16 pm
Location: Somewhere Else
Even if they do count up and down to very large numbers, it doesn't matter, because it's trivial to just use 4n quarter turns to keep them in the limit.

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Thu Aug 02, 2012 10:53 am

Joined: Mon Aug 18, 2008 10:16 pm
Location: Somewhere Else
All the screw does is constrain the possible rotations. The only difference between the screw and (for example) TomZ's Constrained Cube is that it allows for 360 degrees or more for the range.

I still think we're both right. The only difference between our ideas is the size of the range of numbers (representing quarter turns). Like I said before, an infinite line is still a circle, just an infinitely large one.

One other thing to bear in mind is that when the puzzle is not looped, or is infinite, individual pieces can only reach 1/2 of all the possible positions, much like a Chess bishop can only reach half of the board. When you loop the puzzle with an odd number of positions in the loop (for example, 0 to 4), this restriction vanishes.

I wish someone more knowledgeable was here right now...

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Thu Aug 02, 2012 11:01 am

Joined: Mon Mar 30, 2009 5:13 pm
Again, the turns of a finite screw are limited, but they don't cycle. That is the key here.

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Thu Aug 02, 2012 11:06 am

Joined: Mon Aug 18, 2008 10:16 pm
Location: Somewhere Else
That was my point. Turning it into a cycle unbandages the puzzle, for the definition of unbandaging being "removing a restriction to allow extra moves". The actual size of the cycle is irrelevant.

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Thu Aug 02, 2012 11:12 am

Joined: Mon Mar 30, 2009 5:13 pm
OK, now I see, but is that really unbandaging as we know it? Unbandaging is more like splitting one part into two independent parts, while you are suggesting to change overall symmetry from screw to rotation, however I don't see that as unbandaging.

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Last edited by KelvinS on Thu Aug 02, 2012 11:16 am, edited 2 times in total.

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Thu Aug 02, 2012 11:14 am

Joined: Mon Aug 18, 2008 10:16 pm
Location: Somewhere Else
I'm not sure. I think we need Bram again.

Does removing the constraints from the Constrained Cube count as unbandaging? I would say yes. What about making a Helicopter Cube a sphere, so that no pieces can catch on other pieces to block moves? I would say yes there too. But perhaps we need a clearer definition.

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Thu Aug 02, 2012 11:24 am

Joined: Wed May 13, 2009 4:58 pm
Location: Vancouver, Washington
Another similar comparison would be the 15 puzzle vs the coca cola can. The cola can can have pieces move all the way around, but the 15 puzzle is "bandaged" to not allow this. However, I doubt anyone would really call the 15 puzzle bandaged just because it doesn't allow those moves.

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Thu Aug 02, 2012 11:26 am

Joined: Mon Mar 30, 2009 5:13 pm
While unbandaging is a special way of removing certain constraints, I don't think every case of removing constraints can be classified as unbandaging.

For example, would you consider changing symmetry from cubic to dodecahedral as unbandaging? This is like going from screw to rotational symmetry. To me it's just replacing one type of constraint with another so that their movements are mutually exclusive.

For unbandaging, I think every form of one puzzle has to be a subset of another puzzle, but in this case the two sets intersect where you have simple rotation about the other two axes, then each puzzle has other configurations which aren't possible in the other, so it can't be a simple case of unbandaging.

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Last edited by KelvinS on Thu Aug 02, 2012 11:44 am, edited 2 times in total.

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Thu Aug 02, 2012 11:36 am

Joined: Mon Aug 18, 2008 10:16 pm
Location: Somewhere Else
I've often thought to myself that twisty puzzles are in fact sliding puzzles, but without holes... and with geometrical restrictions, of course.

If you "unbandage" a 15-puzzle by connecting both pairs of sides, you can fill in the hole, and then you have a twisty puzzle.

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Thu Aug 02, 2012 11:42 am

Joined: Mon Mar 30, 2009 5:13 pm
Jared wrote:
I've often thought to myself that twisty puzzles are in fact sliding puzzles, but without holes... and with geometrical restrictions, of course.

If you "unbandage" a 15-puzzle by connecting both pairs of sides, you can fill in the hole, and then you have a twisty puzzle.

That is very true, and in fact physical versions of this have been made with beeds running around tracks on a sphere. But in this case, all forms of the flat Puzzle are a subset of the spherical version. This is not the case with the screw cube vs classic rotational cube.

A true unbandaged version of the screw cube would allow rotational and translational movement to occur independently, and this would also be an unbandaged version of the classic rotational cube. So both screw and rotational cubes are special cases of this unbandaged cube, but neither the screw or rotational cubes are unbandaged forms of each other.

This is like in mathematics, where two types of statistical distribution are subsets of a more generalized ("unbandaged") form, but neither of those two distributions are subsets or generalized forms of each other.

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 Post subject: Re: Screw Cube by ALEX and OSKARPosted: Thu Aug 02, 2012 12:32 pm

Joined: Mon Aug 18, 2008 10:16 pm
Location: Somewhere Else
Just on the terminology end of things, perhaps "bandaged" should be reserved for combined pieces and "constrained" for all other forms of restricting moves?

This would have the side effect of having to rename "overhang bandaging" as "overhang constraints" or something, though. Though, I admit, I never liked the term "overhang bandaging"... it's just a mouthful.

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