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 Post subject: Indicator Cube 4: The ATV, by Eitan
PostPosted: Fri Jun 14, 2013 4:20 pm 
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Location: Evanston, IL
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)

Image

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. :P

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:

Image Image
Image Image
Image Image

-Eitan

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Buy a Radio Cube 3! Only $150 at Eitan's Shapeways Shop
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 Post subject: Re: Indicator Cube 4: The ATV, by Eitan
PostPosted: Fri Jun 14, 2013 4:38 pm 
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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 Eitan
PostPosted: Fri Jun 14, 2013 4:55 pm 
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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!

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 Post subject: Re: Indicator Cube 4: The ATV, by Eitan
PostPosted: Sat Jun 15, 2013 3:46 am 
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Eitan, you left me flabberghasted. Cool!

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 Post subject: Re: Indicator Cube 4: The ATV, by Eitan
PostPosted: Sat Jun 15, 2013 4:06 am 
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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 Eitan
PostPosted: Sat Jun 15, 2013 7:39 am 
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Very cool! It seems that puzzles with windows into the interior is the next big trend in puzzle design.

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

Image

-Eitan

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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 Eitan
PostPosted: Sun Jun 16, 2013 9:37 pm 
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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 Eitan
PostPosted: Mon Jun 17, 2013 2:03 am 
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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 Eitan
PostPosted: Mon Jun 17, 2013 5:13 am 
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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 Eitan
PostPosted: Mon Jun 17, 2013 5:23 am 
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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!

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

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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 Eitan
PostPosted: Mon Jun 17, 2013 9:21 am 
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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.

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