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 Post subject: Lollipop: a Complex 2D puzzlePosted: Sat Mar 09, 2013 2:43 am

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
Recently I made a "complex" 2D puzzle that can be played on webpage, called Lollipop. It can be found here:

http://nanma80.github.com/lollipop

The shape of the puzzle is a disk. Take the simpliest version with 3 axes for example. The outmost ring never flips. Each piece in second ring can be turned by only one axis. Each piece in the third ring in the third ring can be turned by two axes. The inner most ring, the core, can be turned by all three axes.

The puzzle with four axes is more complicated. For example, there is a ring where the pieces can be turned by opposite axes, and another ring where the pieces can be turned by three out of four axes.

The point is, for ANY subset of axes, the piece turned by and only by them can be found here. In a sense, this is the most "complete" puzzle with this number of axis in a 2D plane. All pieces are arranged by "type" into different rings.

The puzzle with three axes is pretty easy. The 4-axis version is not so trivial. Starting from 5-axis, it's seriously challenging. This puzzle supports a batch input through a textbox. For complicated puzzles this is indeed necessary.

This puzzle is obviously inspired by the Complex 3x3x3 puzzle proposed by Matt Galla, Carl Hoff, Andreas Nortmann, et al. I especially thank Matt for inspiring discussions. I'm looking forward to meeting you again to talk about puzzles!

 Attachments: Image 000.png [ 28.99 KiB | Viewed 4753 times ]

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Last edited by schuma on Sat Mar 09, 2013 3:06 am, edited 1 time in total.
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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Sat Mar 09, 2013 3:05 am

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
Hey Nan, these are great. I found the 5-axis version a bit tricky and quite fun. I just finished solving the 6-axis version and it was quite a bit harder to me.

For the 6-axis version I solved the rings in a somewhat odd order (outer ring is 1, inner circle is 13):
3, 2, 4, 5, (12 and 13's rotation), 11, 12, 13, 7, 9

The 7-axis one seems a bit too small. I'm not sure if I'll tackle it or not. I have a very hard time counting the rings / identifying a specific ring.

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Sat Mar 09, 2013 3:10 am

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
bmenrigh wrote:
Hey Nan, these are great. I found the 5-axis version a bit tricky and quite fun. I just finished solving the 6-axis version and it was quite a bit harder to me.

For the 6-axis version I solved the rings in a somewhat odd order (outer ring is 1, inner circle is 13):
3, 2, 4, 5, (12 and 13's rotation), 11, 12, 13, 7, 9

The 7-axis one seems a bit too small. I'm not sure if I'll tackle it or not. I have a very hard time counting the rings / identifying a specific ring.

Congrats on the solve of 6-axis!

Initially I didn't plan to include the 7-axis one. There are many problems: inner rings are too small, the colors are too similar, etc. But after I implemented the 6-axis, I thought, what to lose? It was really easy to extend to 7 axes. I just needed to write a config for it. So I made it. It's really experimental.

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Sat Mar 09, 2013 3:38 am

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
Let me add a comparison to justify the name...

 Attachments: Image 003.png [ 52.22 KiB | Viewed 4728 times ] lollipop.jpg [ 66.21 KiB | Viewed 4728 times ]

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Sat Mar 09, 2013 3:50 am

Joined: Fri Feb 18, 2011 5:49 pm
Location: New Jersey
I agree with Brandon, these are lots of fun to play with!

I think it's interesting how the choice in visual representation intuitively suggests a 1-piece-type-at-a-time solving method, unlike most twisty puzzles.

bmenrigh wrote:
For the 6-axis version I solved the rings in a somewhat odd order (outer ring is 1, inner circle is 13):
3, 2, 4, 5, (12 and 13's rotation), 11, 12, 13, 7, 9

For both the 5-axis and 6-axis one, I worked from the outside inwards until the last few rings which I did somewhat haphazardly. For the 6 axis puzzle, following your notation my last rings were 10, 13, 12+11, 9. The rest of the rings I was able to solve with my methods from the 5 axis version.

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Sat Mar 09, 2013 3:54 am

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
How many moves did you guys used? DKwan, you must have a pretty move count, I imagine. I tried the 5-axis and 6-axis before I implemented the move counter. I'll probably try them again just to see how wasteful I am.

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Sat Mar 09, 2013 4:54 am

Joined: Fri Feb 18, 2011 5:49 pm
Location: New Jersey
schuma wrote:
DKwan, you must have a pretty move count, I imagine.

Since I had solved 5 and 6 prior to the implementation of the move counter, I didn't make much of an effort to be efficient. I'm pretty sure my move counts were pretty horrible! I will probably have to put in a lot more time to come up with an efficient method.

One request with respect to move counts... can we have an "undo" button?

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Sat Mar 09, 2013 6:41 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
schuma wrote:
The puzzle with three axes is pretty easy.
Speak for yourself. LOL!!!! I've been playing with it for 10 minutes and so far the closest I've come to solved has the center two rings rotated by 120 degrees.

I trust that its safe to assume this initial post here wasn't when the puzzle was first revealed to everyone. If so it looks like Brandon solved 5 and 6 in the first 20 minutes.

GREAT puzzle. I really like the idea. I just wish I was a better solver.

Carl

P.S. UPDATE: Just solved 3. It only took me 205 moves. Which I'm going to guess is longer then the Devil's Algorithm for this puzzle. LOL!!!

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Sat Mar 09, 2013 7:26 pm

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
wwwmwww wrote:
schuma wrote:
The puzzle with three axes is pretty easy.
Speak for yourself. LOL!!!! I've been playing with it for 10 minutes and so far the closest I've come to solved has the center two rings rotated by 120 degrees.
The tricky thing about these puzzles is identifying what a "piece" is. Visually different rings have diffenet piece types. For example, on the 3-axis version, the 2nd ring from the outside has pieces that are made up of two colors and are centered on the axis. The 3rd ring from the outside has pieces that are two colors but they're centered between two axes.

Having a ring "rotated by 120 degrees" is really a 3-cycle of 3 pieces.

wwwmwww wrote:
I trust that its safe to assume this initial post here wasn't when the puzzle was first revealed to everyone. If so it looks like Brandon solved 5 and 6 in the first 20 minutes.
Yeah I had an unfair head start. I put maybe 1-2 minutes into solving the 3-axis version. Maybe 5 min into solving the 4-axis version. The 5-axis probably took me 1 hour from starting to figure it out to having it solved. The 6-axis version took me about 1.5 hours.

My guess is that these times are much longer than Dan and Nan took. Solving ability seems non-linear to me. I feel like I'm not anywhere near Dan or Nan in ability but I'm significantly better than many others.

wwwmwww wrote:
GREAT puzzle. I really like the idea. I just wish I was a better solver.
You definitely have whatever it takes. Most of the analyses you already do for puzzles are very similar to the analyses needed to solve.

wwwmwww wrote:
P.S. UPDATE: Just solved 3. It only took me 205 moves. Which I'm going to guess is longer then the Devil's Algorithm for this puzzle. LOL!!!
My technique never takes more than 19 moves, worst case. I'm solving in non-overlaping phases and god's could combine them all. The devil's alg is definitely small. Maybe 30.

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Sun Mar 10, 2013 12:18 am

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
wwwmwww wrote:
GREAT puzzle. I really like the idea. I just wish I was a better solver.

wwwmwww, I'm glad that you like this puzzle. I made it just because I like the concept of Complex 3x3x3 very very much.

The only drawback of Complex 3x3x3 is that it's too hard to solve. I want to bring this idea to more people, by making a simpler puzzle based on the same idea. That's why I'm going to 2D. But you guys have all the credits for coming up with the concept.

bmenrigh wrote:
The tricky thing about these puzzles is identifying what a "piece" is. Visually different rings have diffenet piece types. For example, on the 3-axis version, the 2nd ring from the outside has pieces that are made up of two colors and are centered on the axis. The 3rd ring from the outside has pieces that are two colors but they're centered between two axes.

You have a valid point. I've been thinking about it from the beginning. I could draw the boundaries of the "piece" to help the solvers. But it's both technically a bit complicated and breaking some symmetry of the appearance.

It's worth pointing out that the 4-axis version is very similar to 3x3x1. Although there are several types of additional pieces on 4-axis Lollipop than 3x3x1, if you solve Lollipop like a 3x3x1, 50% the chance, you'll see a special case.

In other words, the number of permutations of 4-axis Lollipop is twice as much as 3x3x1. That's the only catch of 4-axis Lollipop.

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Sun Mar 10, 2013 12:54 am

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
DKwan wrote:
One request with respect to move counts... can we have an "undo" button?

Done. Thanks for the suggestion.

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Sun Mar 10, 2013 12:58 am

Joined: Fri Nov 04, 2005 12:31 am
Location: Greece, Australia, Thailand, India, Singapore.
Nice!!! Now you need to stop me from licking the screen!!!

Pantazis

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Sun Mar 10, 2013 1:02 am

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
schuma wrote:
DKwan wrote:
One request with respect to move counts... can we have an "undo" button?

Done. Thanks for the suggestion.

Awesome. I was using a regular expression to collapse move cancellations

Speaking of enhancements, it would be very nice if it was possible to highlight a ring. So if you're focusing on the 7th ring in, having it stand out in some way would be great. I'm thinking that making each piece in that ring much lighter, or possibly putting a black border around the inner and outer concentric circle that forms the ring would work.

I'm not sure what the interface would look like for selecting a ring to be highlighted though... Ideally something like shift-click of a piece in the ring would highlight the whole ring. Then you could toggle on or off any ring you wanted. I'm not sure if your code is actually aware of which ring the mouse is over at a given time though.

With ring highlighting 7 would be much more tractable.

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Sun Mar 10, 2013 2:24 am

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
Brandon, I just added a feature to "highlight" a ring. You can shift + click a ring to see what happens. I don't change any color, but make a ring three times broader than others.

Shift + click a blank space to reset this effect.

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Sun Mar 10, 2013 2:31 am

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
schuma wrote:
Brandon, I just added a feature to "highlight" a ring. You can shift + click a ring to see what happens. I don't change any color, but make a ring three times broader than others.

Shift + click a blank space to reset this effect.

Very nice! This addresses a different issue which was that since the rings are so thin on the 7-axis version I was going to suggest allowing you to hide outer rings. I don't think it's needed now.

The shift+click seems to not work in Firefox however I've been using Chromium for the puzzle anyways because it renders more smoothly.

It's too late for me to start on the 7-axis version but hopefully I'll be able to work on it tomorrow.

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Sun Mar 10, 2013 3:02 am

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
bmenrigh wrote:
The shift+click seems to not work in Firefox however I've been using Chromium for the puzzle anyways because it renders more smoothly.

It works on my Firefox on Mac OS X 10.8.2 and Windows 7. I don't know if it's a linux thing. For your information, I detect a mouse event and use e.shiftKey to check if it's a shift + click.

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Sun Mar 10, 2013 4:43 pm

Joined: Thu May 31, 2007 7:13 pm
Location: Bruxelles, Belgium
I don't have an html5 browser yet. So I haven't tested your program. But it looks interesting.
Sorry to ask a stupid question. But the pieces flip around axes on 2D plain rather than turning around the center of the circle, right?

I'm reluctant to update my browser, because the updating causes sometimes unpleasant side effects. As far as I don't have major problem, I avoid to update anything.
I'm sure I'm not the only one. Better to avoid new html5 functions unless it's absolutely necessary. This way more people can enjoy your puzzle

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Sun Mar 10, 2013 6:16 pm

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
gelatinbrain wrote:
Sorry to ask a stupid question. But the pieces flip around axes on 2D plain rather than turning around the center of the circle, right?

There's no such a thing as a stupid question. The flipping axes are in the plane, and the pieces can only flip by 180 degrees around these axes to get back to the plane. But my simulator also supports reorienting the whole disk by dragging it. The reorientation operation is rotation around the axis that is perpendicular to the plane, passing through the center of the disk. This rotation, though, is not necessary for solving, but purely for convenience.
gelatinbrain wrote:
I'm reluctant to update my browser, because the updating causes sometimes unpleasant side effects. As far as I don't have major problem, I avoid to update anything.
I'm sure I'm not the only one. Better to avoid new html5 functions unless it's absolutely necessary. This way more people can enjoy your puzzle

Totally understand your situation. We are all aware of the several technologies to visualize puzzles. Jaap uses pure javascript code, which works basically everywhere. But it has a lot of limitations. Your app is Java. I also made some puzzles using Java, but there are many people who don't have Java installed or not by default. html5 canvas and SVG are both options that older browsers don't support. There is a Rubik's cube simulator in CSS3. But even the latest Firefox and Chrome display it differently. And there are WebGL etc. I had a hard time choosing which technology to use. I have a feeling that nowadays more people use browsers supporting html5 canvas than others. And that's why I made the decision.

A new trend is to support touch screen based devices, which means no "mouse over" events. It puts a lot more constraints. I'm still not convinced that I should limit myself to that when I make puzzles that may be mostly played by mouse.

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Sun Mar 10, 2013 6:44 pm

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
bmenrigh wrote:
It's too late for me to start on the 7-axis version but hopefully I'll be able to work on it tomorrow.

I changed the saturation of the colors a bit, so that the adjacent colors on the 7-axis version is not too close. I hope it helps you.

I also added the 1-axis and 2-axis versions for the sake of completeness...

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Sun Mar 10, 2013 9:31 pm

Joined: Thu Oct 16, 2008 9:46 pm
Location: Littleton CO
This is a wonderful little game! I've solved 1-3 axis versions a few times now. The third more than the rest. The only problem I have with the 3 axis version is that I have a bit of a hard time telling what's highlighted and what isn't. I don't know if anyone else has that problem, it could just be my screen. Thanks for sharing this!
P.s. I just solved the 4 axis version in 13 moves on my first try.

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Sun Mar 10, 2013 9:47 pm

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
eye2eye wrote:
This is a wonderful little game! I've solved 1-3 axis versions a few times now. The third more than the rest. The only problem I have with the 3 axis version is that I have a bit of a hard time telling what's highlighted and what isn't. I don't know if anyone else has that problem, it could just be my screen. Thanks for sharing this!
P.s. I just solved the 4 axis version in 13 moves on my first try.

Thanks! I don't have a very good way to highlight the colors without changing it too much either. The best I can do is to focus on one piece, and move the mouse in and out of the disk and see if the color changes...

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Mon Mar 11, 2013 1:16 am

Joined: Wed Jan 07, 2009 6:46 pm
Location: San Francisco, CA
I love the name of #7.

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Mon Mar 11, 2013 2:07 am

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
eye2eye wrote:
The only problem I have with the 3 axis version is that I have a bit of a hard time telling what's highlighted and what isn't. I don't know if anyone else has that problem, it could just be my screen.

I just changed the code a little bit. Now there are two checkboxes: highlight by color, or by drawing dots on the pieces. The default highlighting is still by color, but you can choose to use dots, or both.

Dots are pretty clear, but they don't look as clean.

 Attachments: Image 000.png [ 61.34 KiB | Viewed 4256 times ]

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Mon Mar 11, 2013 3:37 pm

Joined: Sat Apr 22, 2000 2:51 am
Location: New Ulm, Minnesota, USA
IMHO: You should highlight each piece with a hollow curved rectangle and a triangle for the center ring that way it would be easier to see the movement. I'll shut up an use the dots. Sorry about that.

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Mon Mar 11, 2013 3:40 pm

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
Darren Grewe wrote:
IMHO: You should highlight each piece with a hollow curved rectangle that way it would be easier to see the movement. I'll shut up an use the dots. Sorry about that.

Between the ring magnification, dots, and piece highlighting I'm having no trouble figuring out what moves. It might be worthwhile to explore darkening of colors instead of lightening them but I don't think any additional changes are needed.

The ability to hide the first N rings from outside to in or the first M rings from inside to out could be useful for the 6+ axis versions but so far I'm doing okay on the 7-axis as-is.

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Mon Mar 11, 2013 4:22 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
schuma wrote:
It's worth pointing out that the 4-axis version is very similar to 3x3x1. Although there are several types of additional pieces on 4-axis Lollipop than 3x3x1, if you solve Lollipop like a 3x3x1, 50% the chance, you'll see a special case.
Interesting... So the 4-axis Lollipop is equivalent to the Complex 3x3x1. I believe I see why. Does this mean that an 8-axis Lollipop would be equivalent to the Complex 3x3x3? I'm not sure about that as the Complex 3x3x1 is still basically a 2D puzzle. However if this is true then it should mean there exists a simple maping from the Rubik's Cube to a subset of the pieces on an 8-axis Lollipop. If so I'd be surprised to see that our beloved 3D puzzle maps to a 2D one so easily.

Or are the 8-axis Lollipop and the Complex 3x3x3 two totally different puzzles?

Carl

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Mon Mar 11, 2013 4:30 pm

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
wwwmwww wrote:
[...]So the 4-axis Lollipop is equivalent to the Complex 3x3x1. I believe I see why. Does this mean that an 8-axis Lollipop would be equivalent to the Complex 3x3x3? I'm not sure about that as the Complex 3x3x1 is still basically a 2D puzzle. However if this is true then it should mean there exists a simple maping from the Rubik's Cube to a subset of the pieces on an 8-axis Lollipop. If so I'd be surprised to see that our beloved 3D puzzle maps to a 2D one so easily.

Or are the 8-axis Lollipop and the Complex 3x3x3 two totally different puzzles?
I don't see the relationship between the Complex 3x3x3 and the 8-axis Lollipop so perhaps you can spell out the possible relationship / mapping better?

Last night Nan and Dan and I were discussing the possible relationship between the 6-axis Lollipop and the Complex 3x3x3 (especially the 180-degree turn Complex 3x3x3). Looking at the potential relationship(s) between the puzzles is fun and touches on a lot of theory stuff.

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Mon Mar 11, 2013 5:01 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
bmenrigh wrote:
I don't see the relationship between the Complex 3x3x3 and the 8-axis Lollipop so perhaps you can spell out the possible relationship / mapping better?
Arg... I was thinking about the 6 axis Lollipop. Seeing as the 4 axis Lollipop is the Complex 3x3x1 I just need to add 2 more axes. I think I took 4 and multiplied by 2.
bmenrigh wrote:
Last night Nan and Dan and I were discussing the possible relationship between the 6-axis Lollipop and the Complex 3x3x3 (especially the 180-degree turn Complex 3x3x3). Looking at the potential relationship(s) between the puzzles is fun and touches on a lot of theory stuff.
Well I was thinking about GuiltyBystander's visualization as seen here. With regards to the 6 faces(or axes) of the Complex 3x3x3(6 axis Lollipop) each piece is either a part of that face(axis) or it isn't so each piece can be thought of as being reduced to a 6 digit binary number. Though I guess you are correct the operations themselves are different. But if you are looking at an 180-degree turn Complex 3x3x3 where each operation is its own inverse as they are on the Lollipop I would think they could very easily reduce to the exact same puzzle. Do they?

Is Nan or Dan GuiltyBystander? I get real names and Forum IDs mixed up on occasion.

Carl

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Last edited by wwwmwww on Mon Mar 11, 2013 6:02 pm, edited 1 time in total.

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Mon Mar 11, 2013 5:25 pm

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
wwwmwww wrote:
Well I was thinking about GuiltyBystander's visualization as seen here. With regards to the 6 faces(or axes) of the Complex 3x3x3(6 axis Lollipop) each piece is either a part of that face(axis) or it isn't so each piece can be thought of as being reduced to a 6 digit binary number. Though I guess you are correct the operations themselves are different. But if you are looking at an 180-degree turn Complex 3x3x3 where each operation is its own inverse as they are on the Lollipop I would think the could very easily reduce to the exact same puzzle. Do they?
Dan and GuiltyBystander and I have had enough conversations about topics related to this over the last year that anything I say here is intrinsically going to involve their ideas and analyses as much as my own. I can't hope to do the topic justice by myself and I'm not sure where to even begin. I think a lot of this will get teased out in the upcoming deep-cut thread.

You're already getting at the idea for why the 6-axis Lollipop is different than the 180-degree Complex 3x3x3. It boils down to the operations being different (the axes have a different geometry in relation to each other).

Let's try to map the axes of the 6-axis Lollipop to a 180 degree cube. We'll call the 1 axis U which would make the 4 axis D. If we do a flip (reorientation) about 1 or 4 then that exchanges the 2 <-> 6 axes and the 3 <-> 5 axes. We could call these pairs 2=F, 6=B and 3=R, 5=L for example. The specifics of the pairs don't matter much.

Now imagine a flip about the 6, 3 axis. Per the above mapping that would be the B R axis which doesn't correspond to anything on the cube. There is no way to map operations with 6 axes of the 6-axis Lollipop onto the Complex 3x3x3 because the geometry of the axes don't match.

I think the conclusion Dan and I have been pushed towards is that what fundamentally defines a twisty puzzle is 2 things. First is the geometry of the grips (axes) and what happens to them under the various operations. As I've quickly shown above, you can have geometries that share a lot of properties without being the same. The second is the piece types the puzzle has (the pattern of the grips define a piece type). In the case of a Complex puzzle, it's every piece type possible for the given geometry.

Another example is that the Complex Face-Turning-Dodecahedron (12 grips) is completely different than the Complex Edge-Turning Cube (also 12 grips). Yes the turns on the Dodecahedron are modulo-5 and on the cube modulo-2 but that's only one of the reasons why they're so different.

wwwmwww wrote:
Is Nan or Dan GuiltyBystander? I get read names and Forum IDs mixed up on occasion.

Sorry :-/

The mapping is
• Nan is schuma
• Dan is DKwan
• Landon is GuiltyBystander

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Mon Mar 11, 2013 10:02 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
bmenrigh wrote:
You're already getting at the idea for why the 6-axis Lollipop is different than the 180-degree Complex 3x3x3. It boils down to the operations being different (the axes have a different geometry in relation to each other).
Interesting...

So let's assume we make a 3D Lollipop puzzle. If we start with something which looks like the 4 axis Lollipop and rotate it about either axis we get a spherical Lollipop. At this point the puzzle would look more like an onion. Now if we add the 3rd axis so its perpendicular to the other 2 (and maybe a few more layers to the onion to account for the increased piece count). And I guess while we are at it we could enable 90 degree turns instead of just 180 degree rotations of the partial hemispheres (probably not the correct word) of the various onion layers.

Now have I made a Complex 3x3x3? Hmmm... Yes, I think I have. And I'm incorrect about needing to add more onion layers. The 4 axis Lollipop has 6 layers and the Complex 3x3x3 made in this fashion I believe shouldn't need more then 5 layers. With just 4 layers I can see how to make 7 of the 10 piece types.

The center shell, the ball core that always moves, is the imaginary core.
The outer shell, this never moves, is the real core.
One shell in from the outer one would be a spherical 3x3x3, it would contain the real face centers, the real corners, and the real edges.
One shell out from center shell would contain the imaginary face centers and the imaginary edges. It would look like a spherical 3x3x3 which was cut at a depth to remove the corners but each face move would move the slice layer with it.

Can I get the last 3 piece types into a 5th onion layer? If so what would it look like? If not, how many more onion layers do I need?

Carl

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Mon Mar 11, 2013 11:47 pm

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
I finally finished solving the 7-axis Complex Lollipop. It took 2400 moves according to the program but when I eliminate all repeated moves (11, 22, 33, etc. are the same as no move) it actually took 2346 moves.

Here is my move count progression after I finished each of the rings listed:
Code:
Ring 3 done
Ring 4: 146
Ring 5: 156
Ring 6: 240
Ring 7: 350
Ring 8: 484
Ring 9: 508
Ring 10: 532
Ring 11: 1076
Ring 13: 1686
Ring 14: 1894
Ring 15: 1992
Ring 16: 2092
Done: 2400

There is a ton of room for improvement. I'm expecting this to get crushed.

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Last edited by Brandon Enright on Wed Mar 13, 2013 2:13 am, edited 2 times in total.

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Tue Mar 12, 2013 12:04 am

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
bmenrigh wrote:
I finally finished solving the 7-axis Complex Lollipop. It took 2400 moves according to the program but when I eliminate all repeated moves (11, 22, 33, etc. are the same as no move) it actually took 2262 moves.

I don't remember my exact move count, but it's definitely ten times more than yours, mainly because of ring 11, and the fact that I don't care about the move count...

Good job!

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Tue Mar 12, 2013 1:04 am

Joined: Tue Feb 08, 2011 3:17 am
Location: Australia
Thanks for making this Nan,

Great puzzle. On the larger ones I am having a little difficulty with some colours looking too similar, particularly lighter greens and pinks/reds, perhaps some darker tones might help. What would really help me visually, would be to see the symetry, by making one half's dots white and keeping the other half's black, it would just more clearly show the line of symetry on the larger puzzles. When moving your mouse over it's just a little easy to double hit by accident, because so many dots are all black. Incidentally, I am just using dots, because that option doesn't change the colours.

I didn't think I would be very interested in these puzzles at first, and at first glance they looked really complex, but after a few twists it became very addictive.

Cheers,
Burgo.

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1st 3x3 solve Oct 2010 (Even though I lived through the 80s).
PB 3x3 55sec Jan 2011 (When I was a kid 1:30 was speedcubing so I'm stoked).
1st 3x3 Earth (nemesis) solve Jan 2011 My You Tube (Now has ALLCrazy 3X3 Planets with Reduction)

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Tue Mar 12, 2013 4:58 am

Joined: Sun Nov 23, 2008 2:18 am
jef
Very interesting concept, and I wish I could see well enough to play with the simulator. Here's hoping someone can figure out how to make physical Lollipops and given them a tactile solution.

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Wed Mar 13, 2013 12:16 am

Joined: Fri Feb 18, 2011 5:49 pm
Location: New Jersey
bmenrigh wrote:
There is a ton of room for improvement. I'm expecting this to get crushed.

Here's the counts for my first solve on the 7-axis:

Ring 3: 18
Ring 5: 48
Ring 6: 66
Ring 7: 150
Ring 8: 256
Ring 9: 278
Ring 10: 292
Ring 11: 648
Ring 13: 848
Ring 12: 950
Ring 14: 1114
Ring 15: 1226
Ring 16: 1432
Done: 1554

Still plenty of room for improvement though!

EDIT: I was pretty careful to avoid doing double-moves, but apparently I missed a few, so it "really" took 1548 moves.

Last edited by DKwan on Wed Mar 13, 2013 2:12 am, edited 3 times in total.

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Wed Mar 13, 2013 12:21 am

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
Excellent, great solve! I've made enough improvements to my routines that with a lot of effort I could probably reach 1500. I don't doubt you can get that count lower so I'm not sure what I'll do then

I have some layer-11 tricks that should help me a lot. It wouldn't surprise me if you actually used some of them in your solve though. I also have a lot of work to improve the non-macro free-form phase for rings 3 - 6.

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Prior to using my real name I posted under the account named bmenrigh.

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Wed Mar 13, 2013 1:24 am

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
After playing the crazy 7-axis puzzle, a forum member said he was ready to play the crazier 8-axis. I haven't configured it, but I created 30 rings that 8-axis requires, and took some snapshots. Note that the dots are not in the right places. I'm just giving you an idea about how it would look like.

The snapshots are 1:1 with no scaling.

Attachment:

Image 000.png [ 75.76 KiB | Viewed 3914 times ]

Attachment:

Image 001.png [ 74.25 KiB | Viewed 3914 times ]

Attachment:

Image 002.png [ 102.09 KiB | Viewed 3914 times ]

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Wed Mar 13, 2013 6:36 pm

Joined: Sat Aug 22, 2009 3:27 pm
Location: California
I absolutely loving it, I'm slowly working my way up on the numbers and it's really fun!

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hey look ^

Rest In Peace Frank

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Fri Mar 15, 2013 2:16 am

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
After solving the 7-axis version, bmenrigh has been looking forward for a larger Lollipop puzzle, the 8-axis one. While I hesitated, he stepped up and configured the 8-axis version, hopefully the last one in the Lollipop series.....

I've been checking the definition for a while. I think it is the correct puzzle. But no one has solved it though.

Since I called the 7-axis version eye exam, we call the 8-axis one Octometrist's Revenge.

I thank bmenrigh for his hard work. Without his passion it'll probably never be done.

I just want to remind you that many browser can zoom in a webpage that also applies to this puzzle. I definitely need to zoom in, in addition to shift + click to magnify a ring, to see what's going on on the 8-axis puzzle.

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 Post subject: Re: Lollipop: a Complex 2D puzzlePosted: Sun Mar 17, 2013 5:22 pm

Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
I just solved the 8-axis puzzle with 13970 moves. Although the final solution only took 38 minutes, it took me maybe 8 hours or so to find all the algorithms. There are some tricky rings, for example, 8, 23, 29. It took me quite a while to decide the order to solve them.

 Attachments: Image 001.png [ 79.78 KiB | Viewed 3596 times ]

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