Online since 2002. Over 3300 puzzles, 2600 worldwide members, and 270,000 messages.

TwistyPuzzles.com Forum
 It is currently Thu Apr 24, 2014 12:06 am

 All times are UTC - 5 hours

 Page 1 of 1 [ 13 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: Even Less Gears! by OSKARPosted: Sun Dec 12, 2010 10:41 am

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

Did you like the Gear Cube with 12 geared edges? And did you find Gear Cube Extreme harder to solve, even though it just has eight geared edges? Well, here is an even harder variation called "Even Less Gears!" with only four geared edges.

As Even Less Gears! has only four geared edges, four faces can make quarter turns like a Rubik's Cube, whereas the fifth and sixth face are coupled through the gears. However, one scrambled, more faces get coupled. The fact that sometimes faces are coupled and sometimes not, makes this puzzle arguably harder than Gear Cube Extreme.

One way of obtaining Even Less Gears! is by buying a Gear Cube from Mefferts and add a set of eight Shapeways-printed non-geared edges. Another alternative is to buy two Gear Cube Extreme from Mefferts and do some mix-and-match.

Here is a combinatorial question for you to solve.
How many essentially different variations does this puzzle have?
Note the term "essentially different". Replacing a single geared edge from Gear Cube by a non-geared one does not change the puzzle from a solving perspective, given the parity limitations of this puzzle. Nick Baxter's paper on the Burnside Lemma is probably a good place to start, if you want to solve the combinatorial question.

Variations to this question are
How many Gear Cube Extreme do you have to buy in order to build allpossible variations?
How much would that cost you?

Buy the non-geared edges from my Shapeways Shop.
Read more at the Shapeways Forum.
Check out the photos below.

Enjoy!

Oskar
Attachment:

Even Less Gears - prototype - view 1.jpg [ 53.21 KiB | Viewed 3098 times ]

Attachment:

Even Less Gears - prototype - view 2.jpg [ 52.1 KiB | Viewed 3098 times ]

Attachment:

Even Less Gears - prototype - view 3.jpg [ 48.58 KiB | Viewed 3098 times ]

_________________
.

Top

 Post subject: Re: Even Less Gears! by OSKARPosted: Sun Dec 12, 2010 10:55 am

Joined: Thu Sep 24, 2009 12:21 pm
Location: Chichester, England
I've been waiting for this for a while. I was going to make one for myself, if I ever got another Gear Cube Extreme. Could you ask Meffert about producing this?

_________________
3x3x3 single: 5.73 seconds.
3x3x3 average of five: 8.92 seconds.
3x3x3 average of twelve: 9.77 seconds.

Buy the Curvy Copter Skewb, NovaMinx, and more here!

Top

 Post subject: Re: Even Less Gears! by OSKARPosted: Sun Dec 12, 2010 10:57 am

Joined: Wed Feb 17, 2010 7:33 pm
What's next, a puzzle without gears?

But seriously, another great puzzle Oskar!

_________________
Selling White Dino Star
Tony Fisher wrote:
By midnight Rox will have revealed all her secrets, told everyone that she loves us and end up banning herself tomorrow when she reads it all back.

Transsexual and Proud!

Top

 Post subject: Re: Even Less Gears! by OSKARPosted: Sun Dec 12, 2010 12:20 pm

Joined: Sun May 17, 2009 1:33 pm
Location: USA, North America, Planet Earth, Solar system, Milky Way galaxy, Universe
Wow, this looks like a really neat puzzle (:
Is this variation easier or harder than the Gear Cube extreme? I'd imagine it to be easier but it does have some irregular 'bandaging' (?) on the gear parts.
great puzzle!

_________________
-sj

NEW VIDEOS-
3x3x3 stop-motion solve
Meffert's new Pyraminx Crystal solve
QJ 4x4x4 solve

Top

 Post subject: Re: Even Less Gears! by OSKARPosted: Sun Dec 12, 2010 12:25 pm

Joined: Fri Jul 16, 2010 8:25 pm
Location: Israel
Monopoly wrote:
Wow, this looks like a really neat puzzle (:
Is this variation easier or harder than the Gear Cube extreme? I'd imagine it to be easier but it does have some irregular 'bandaging' (?) on the gear parts.
great puzzle!

Oskar wrote:
did you find Gear Cube Extreme harder to solve, even though it just has eight geared edges? Well, here is an even harder variation called "Even Less Gears!" with only four geared edges.

_________________
Some of my collection for sale

The puzzles on the picture are not for sale.

Top

 Post subject: Re: Even Less Gears! by OSKARPosted: Sun Dec 12, 2010 10:52 pm

Joined: Thu Aug 26, 2010 10:54 pm
Location: GD China
Does this mean that the fun of different combinations have different

Top

 Post subject: Re: Even Less Gears! by OSKARPosted: Mon Dec 13, 2010 1:53 pm

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
Easily understood but nobody made it before => genius.
Oskar wrote:
How many variations does this puzzle have?
144

Top

 Post subject: Re: Even Less Gears! by OSKARPosted: Wed Dec 15, 2010 1:33 am

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
Sorry for the double post. But I thought this deserves it.
Oskar wrote:
Here is a combinatorial question for you to solve.
How many essentially different variations does this puzzle have?
Note the term "essentially different". Replacing a single geared edge from Gear Cube by a non-geared one does not change the puzzle from a solving perspective, given the parity limitations of this puzzle.
Less then I expected.
There are no more than 7 different variants. These are:
• [] The cube without gears.
• [FR] The cube with a single gear.
• [FL BR]
• [FL FR BR]
• [FL FR BR BL] "Even less Gears"
• [UL UF UR UB DL DF DR DB] Gear Cube Extreme aka Anisotropic Cube
• [UL UF UR UB FL FR BR BL DL DF DR DB] Gear Cube (I don't dare to say "normal")
All other variants are identical in behaviour to one of these.

Top

 Post subject: Re: Even Less Gears! by OSKARPosted: Wed Dec 15, 2010 2:54 am

Joined: Mon Nov 30, 2009 1:03 pm
Andreas Nortmann wrote:
There are no more than 7 different variants. These are: <...> All other variants are identical in behaviour to one of these.
Sorry Andreas, but I have to disagree with you.

Even though I do not know the correct answer myself, I do know that there are at least two functionally different puzzles with three gear edges.
One with the three gear edges each in a different plane
Another where some or all of the gear edges are in the same plane
It is not too hard to prove that if all geare edges are in a different plane, they will always stay in a different plane.

Oskar

_________________
.

Top

 Post subject: Re: Even Less Gears! by OSKARPosted: Wed Dec 15, 2010 3:16 am

Joined: Tue Aug 24, 2010 8:11 am
Location: Taipei, Taiwan
Oskar wrote:
Even though I do not know the correct answer myself, I do know that there are at least two functionally different puzzles with three gear edges.
One with the three gear edges each in a different plane
Another where some or all of the gear edges are in the same plane
Oskar

I think the one with three gear edges each in a different plane is similar to the Gear Cube (12 gear edges).

_________________
http://cclx.webs.com/

Top

 Post subject: Re: Even Less Gears! by OSKARPosted: Wed Dec 15, 2010 6:37 am

Joined: Mon Jun 08, 2009 12:27 pm
Location: São Paulo - Brazil
Chilen wrote:
I think the one with three gear edges each in a different plane is similar to the Gear Cube (12 gear edges).

Looks like I got the difference. The first move is similar to the 12 geared cube, but when moved, some edges get aligned in the same plane, so it enables free moves on other layer. Am I correct, Oskar?

_________________
fbgrac

Top

 Post subject: Re: Even Less Gears! by OSKARPosted: Wed Dec 15, 2010 7:14 am

Joined: Mon Nov 30, 2009 1:03 pm
fbgrac wrote:
Am I correct, Oskar?
No. When three gears are in three different planes, they stay in three different planes. My question is whether that 3-gear puzzle has the same state space as the 12-gear version. Maybe Andreas is right after all. Analysis needed.

_________________
.

Top

 Post subject: Re: Even Less Gears! by OSKARPosted: Wed Dec 15, 2010 3:12 pm

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
I know that there are two different versions with 3 gears.
Oskar recognized correctly that one of them has one gear in every slice all the time. This means this specific variants allows only slice-moves, like the GearCube. There are similar arguments for every other variant which might be missing.
When somebody considers only which moves are allowed at which time, there are only those seven variants.

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 13 posts ]

 All times are UTC - 5 hours

Who is online

Users browsing this forum: Darren Grewe, Ghost_Cake, Google [Bot], Google Adsense [Bot], Pete the Geek, rakaCN and 7 guests

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forumYou cannot post attachments in this forum

Search for:
 Jump to:  Select a forum ------------------ Announcements General Puzzle Topics New Puzzles Puzzle Building and Modding Puzzle Collecting Solving Puzzles Marketplace Non-Twisty Puzzles Site Comments, Suggestions & Questions Content Moderators Off Topic