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 Post subject: Puzzle Concept: 'Rolling' cubes.Posted: Thu Dec 12, 2013 11:31 am

Joined: Sun Nov 23, 2008 2:18 am
You have a cube sitting on one square of a square grid.
The cube may move to any empty square sharing an edge with its current square.
The cube moves by performing a 90 degree rotation about the edge between the square it is currently on and the square it is moving too.
For example, if the cube's d face is against the square the cube is sitting on and the f face is facing forward, than moving one square forward will put the f face against the grid and the u face facing forward.

Given this kind of movement, I have the following questions:
1. Given sufficient space in which to move around a given square of the grid, can the cube be placed onto the given square in all 24 orientations?
2. What is the minimal space needed to allow a cube to be placed onto a given square in all possible orientations?
3. Are any extra restrictions of orientation placed on the cube if the target square is along an edge of the grid or in a corner?
4. Are there any physical puzzles that use this kind of movement?
5. Would a 15 puzzle with this type of movement allow for the swapping of two cubes while having all cubes in the correct orientation?
6. How many states would a 15 puzzle with this kind of movement have?

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 Post subject: Re: Puzzle Concept: 'Rolling' cubes.Posted: Thu Dec 12, 2013 12:59 pm

Joined: Mon Apr 03, 2006 10:38 am
Location: Connecticut
Hi Jeffery,

Rolling Cube puzzles have been around for a while - here is a good article on the topic:
http://www.logicmazes.com/rc/precdnts.html

Jaap has an example puzzle here:
http://www.jaapsch.net/puzzles/eightcub.htm

And here is a research paper on the topic:
http://cccg.ca/proceedings/2007/05b5full.pdf

There is also a new puzzle out by the company Popular Playthings, called Tut's Tablet, which uses a rolling cube:
http://www.popularplaythings.com/index.php?id_product=70412&controller=product

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 Post subject: Re: Puzzle Concept: 'Rolling' cubes.Posted: Fri Dec 13, 2013 1:22 am

Joined: Sat Apr 21, 2007 11:21 pm
Location: Marin, CA
This reminds me of this puzzle I created for the release of the helicopter cube.

 Attachments: KEYPHRASE.1k.jpg [ 196.38 KiB | Viewed 533 times ]

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 Post subject: Re: Puzzle Concept: 'Rolling' cubes.Posted: Fri Dec 13, 2013 9:17 pm

Joined: Mon Aug 18, 2008 10:16 pm
Location: Somewhere Else
I remember that! I got a coupon for solving it.

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 Post subject: Re: Puzzle Concept: 'Rolling' cubes.Posted: Sat Dec 14, 2013 2:22 am

Joined: Sun Jul 14, 2013 11:10 pm
JasonSmith wrote:
This reminds me of this puzzle I created for the release of the helicopter cube.

What is this?

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 Post subject: Re: Puzzle Concept: 'Rolling' cubes.Posted: Wed Dec 25, 2013 8:39 pm

Joined: Thu Dec 15, 2011 10:04 pm
I believe that the QVoid iPad/iPhone app is an implementation of a rolling cube puzzle game.

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