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 Post subject: Indicator Cube 4: The ATV, by EitanPosted: Fri Jun 14, 2013 4:20 pm

Joined: Wed Jan 07, 2009 6:46 pm
Location: San Francisco, CA
Hey Twisty Puzzlers!

It's been a while since I posted a new puzzle, mostly due to graduate school. But I just finished my first year of my master's degree, so it's puzzle time! I'm very pleased to present:

Indicator Cube 4: The ATV
Video
Shapeways: Coming in July (ish)

The Indicator Cube 4 is a 4x4 with geared wheels inside each edge piece. The wheels, whose axes are parallel to the turning axis of the puzzle, turn when you turn the outer layers. I believe that this is the first puzzle to have gears at this kind of orientation. In fact, this puzzle has a larger solution space than a 4x4, as opposed to most other geared puzzles, whose solution spaces are limited by the bandaging caused by the gears.

[Fuzzy modular math ahead. Bear with me.]

The gearing is 8:44 (or 2:11), which makes it look like the colors on the wheels just fly by. A full 360-degree turn of an outer layer causes the gears to turn 5.5 revolutions. Visually, the 5 full revolutions don't really make any difference, so a 360-degree turn of the outer layer causes a 180-degree turn of the wheels. This means that the wheels effectively turn half the speed of the outer layer.

The name "Indicator" refers to the way the wheels (kind of) indicate how many corners (modulo 8) have passed by a particular edge. The name "ATV" was Greg's clever idea. You see, it's a 4x4, with wheels.

I have also designed a 3x3 version of the puzzle ("Indicator Cube 3"), which I intend to print sometime this summer.

Thank you Bram, Eric, Greg, Oskar, and Tom for your advice while I was designing this puzzle.

I'm going to be doing a full overhaul of my Shapeways shop this summer, and this puzzle will be added during that process. For now, here are more pictures:

-Eitan

_________________
Eitan = "EIGHT-ahn"
Buy a Radio Cube 3! Only \$150 at Eitan's Shapeways Shop
Check out my video: Twisty Puzzles a la Vi

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 Post subject: Re: Indicator Cube 4: The ATV, by EitanPosted: Fri Jun 14, 2013 4:38 pm

Joined: Fri Feb 18, 2000 8:50 am
Location: chicago, IL area U.S.A
Wow, very cool!

I would imagine that solving it will involve a lot of 360-630 degree turns. Although theoretically, if one scrambles it in such a way that they never make more than a 180 degree turn, then it could be solved without ever doing a 360 degree turn.

-d

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 Post subject: Re: Indicator Cube 4: The ATV, by EitanPosted: Fri Jun 14, 2013 4:55 pm

Joined: Sun Apr 30, 2006 4:17 am
Location: Düsseldorf, Germany
Yeay!

A really cool puzzle. I'd like to order in WSF polished. Puzzles with small windows to deeper layers always are better in white - this is much better to recognise. And - you said, that your stickers are cut with a Silhouette Cameo. Great! I have one now, too. So I'll be glad to get your templates

Coooool!

_________________
Jade Club invitation: Please send your real name and your email address to jadeclub@tiex.de.
German Cube Day: gcd@tiex.de.
Anything else: puzzles@tiex.de.

My website: Frank's Puzzle Library

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 Post subject: Re: Indicator Cube 4: The ATV, by EitanPosted: Sat Jun 15, 2013 3:46 am

Joined: Wed Dec 29, 2004 7:57 am
Location: Στο Κάστρο του Αγίου Γεωργίου
Eitan, you left me flabberghasted. Cool!

_________________
.....................................
http://cube.helm.lu - http://gallery.helm.lu

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 Post subject: Re: Indicator Cube 4: The ATV, by EitanPosted: Sat Jun 15, 2013 4:06 am

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
And thank you for the preedited images:
http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=4078

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 Post subject: Re: Indicator Cube 4: The ATV, by EitanPosted: Sat Jun 15, 2013 7:39 am

Joined: Wed Dec 10, 2008 6:26 pm
Location: Boston area
Very cool! It seems that puzzles with windows into the interior is the next big trend in puzzle design.

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Visit Pitcher Puzzles where you can buy the IPP award-winning RotoPrism 2, Fracture-10, and many, many more.

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 Post subject: Re: Indicator Cube 4: The ATV, by EitanPosted: Sun Jun 16, 2013 8:48 pm

Joined: Wed Jan 07, 2009 6:46 pm
Location: San Francisco, CA
Good news: It's not a trivial puzzle! One theory that came up during design discussions (can't exactly remember with whom...) was that the puzzle would be as simple as solving the 4x4, followed by 360-degree turns until all the gears are solved. Well, below you will find some photographic evidence to the contrary!

Bad news: I don't know how to solve it from this point. (This isn't that big a deal for me.) Let the algorithm discussions.... BEGIN!

-Eitan

_________________
Eitan = "EIGHT-ahn"
Buy a Radio Cube 3! Only \$150 at Eitan's Shapeways Shop
Check out my video: Twisty Puzzles a la Vi

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 Post subject: Re: Indicator Cube 4: The ATV, by EitanPosted: Sun Jun 16, 2013 9:37 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Very very cool puzzle!!! I like it alot!! I'll be keeping an eye out for it on Shapeways.

Carl

_________________
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 Post subject: Re: Indicator Cube 4: The ATV, by EitanPosted: Mon Jun 17, 2013 2:03 am

Joined: Fri Nov 04, 2005 12:31 am
Location: Greece, Australia, Thailand, India, Singapore.
pirsquared wrote:
Good news: It's not a trivial puzzle! One theory that came up during design discussions (can't exactly remember with whom...) was that the puzzle would be as simple as solving the 4x4, followed by 360-degree turns until all the gears are solved. Well, below you will find some photographic evidence to the contrary!

Bad news: I don't know how to solve it from this point. (This isn't that big a deal for me.) Let the algorithm discussions.... BEGIN!

-Eitan

LOL What have you done again this time Eitan... what a brilliant way to mask a puzzle inside another puzzle.

Pantazis

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 Post subject: Re: Indicator Cube 4: The ATV, by EitanPosted: Mon Jun 17, 2013 5:13 am

Joined: Tue Jul 13, 2010 12:50 pm
I'm having a hard time visualising how the gears move, what does a simple (R2 U2)*X do?

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 Post subject: Re: Indicator Cube 4: The ATV, by EitanPosted: Mon Jun 17, 2013 5:23 am

Joined: Fri Nov 05, 2010 2:20 am
Location: Wherever
I just had a thought, why make the gear ratio be in neat increments? Why not do some weird ratios like 6:7? Or one where the ones inside are much slower than the outside like 44:8?
Or even weird ratios like Oskars variomatic cube? Non circular gears?
Amazing puzzle nevertheless!

_________________
A budding puzzle designer!

Check out my Shapeways shop!

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 Post subject: Re: Indicator Cube 4: The ATV, by EitanPosted: Mon Jun 17, 2013 8:48 am

Joined: Wed Jan 07, 2009 6:46 pm
Location: San Francisco, CA
Arkanoid0 wrote:
I'm having a hard time visualising how the gears move, what does a simple (R2 U2)*X do?

Can you write that out in normal notation? I don't know what "*X" means.

-Eitan

_________________
Eitan = "EIGHT-ahn"
Buy a Radio Cube 3! Only \$150 at Eitan's Shapeways Shop
Check out my video: Twisty Puzzles a la Vi

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 Post subject: Re: Indicator Cube 4: The ATV, by EitanPosted: Mon Jun 17, 2013 9:21 am

Joined: Fri Nov 05, 2010 2:20 am
Location: Wherever
pirsquared wrote:
Arkanoid0 wrote:
I'm having a hard time visualising how the gears move, what does a simple (R2 U2)*X do?

Can you write that out in normal notation? I don't know what "*X" means.

-Eitan

I think it means to do R2 U2 and repeat the sequence X times where X is any number you like.

_________________
A budding puzzle designer!

Check out my Shapeways shop!

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 Post subject: Re: Indicator Cube 4: The ATV, by EitanPosted: Mon Jun 17, 2013 10:23 pm

Joined: Fri Feb 18, 2011 5:49 pm
Location: New Jersey
pirsquared wrote:
Let the algorithm discussions.... BEGIN!

You can construct a commutator alg for reorienting the gears at the end by nesting a 4x4 edge 3-cycle with a single face turn. This might not be the shortest method, but I think it's reasonable for a solve and relatively easy to understand.

Here's a sample [8,1] alg in GB notation that should work:

D&2,R'2,D'&2,L'2,D&2,R'2,D'&2,L'2
D
L'2,D&2,R'2,D'&2,L'2,D&2,R'2,D'&2
D'

This will change the gear orientations of two edges, the lower FL edge and the upper RB edge (if I got it right).

You can replace the single turn D with D2, D', D4, etc... whatever number of turns is required to fix the orientation of the particular gear.

I think this is a really cool concept for a puzzle. It gives the edges a functionality that makes me think of super-cube centers on a 3x3, because they have an orientation that is affected by turns that do not permute the piece itself. Great job with both the concept and the design Eitan!

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