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 Post subject: 'bandaged' cmetrickPosted: Wed Aug 23, 2006 4:25 am

Joined: Sat Mar 22, 2003 9:11 am
Location: Marin, CA
Has anyone considered 'bandaging' the cmetrick by filling some of the holes so that they can't be rotated through? That might have some interesting possibilities.

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 Post subject: Posted: Mon Aug 28, 2006 9:36 am

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
Okay...
There are 9*6=54 center-holes in the middle of a spheres face. When you fill one hole then the five other holes can't be used to, and the whole sphere is bandaged.
There are 8*6*9=432 edge-holes which can be filled. Every filled hole results in 3 neighbors and their 4 opposite holes filled too. Effectively there are 6*9=54 edge-holes.
The center-holes are not necessary since their effect can be emulated by filling all 6 egde-holes of the sphere.
2**54=18*10**15 possibilities to bandage a CMetrick.

Do you agree, Bram?

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 Post subject: Posted: Mon Aug 28, 2006 1:51 pm

Joined: Sat Mar 22, 2003 9:11 am
Location: Marin, CA
No Andreas, if an edge-hole is filled you might as well fill all the other holes in that edge, and a face center hole might as well be bandaged if and only if all the edges around it are bandaged, so for each sphere there are 2 ** 12 ways of bandaging it at first pass, but that includes a huge number of duplicates, so the actual number is far less.

I think bandaging the 3x3 cmetrick is a little silly. Far better to start by bandaging the 2x2, which is a much purer distillation of the concept.

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 Post subject: Posted: Tue Aug 29, 2006 12:35 am

Joined: Wed Mar 15, 2000 9:11 pm
Location: Delft, the Netherlands
Bram wrote:
I think bandaging the 3x3 cmetrick is a little silly. Far better to start by bandaging the 2x2, which is a much purer distillation of the concept.

Also, the balls of the 3x3 are not all equal. If you plug a hole in one of the corner balls you can still go around it by doing a 3/4 turn the other way (assuming no other bandages block this movement). That option is not available on the centre ball because it has cogs on both sides.

In my opinion the 2x2 is much purer just because the balls are all equivalent.

_________________
Jaap

Jaap's Puzzle Page:
http://www.jaapsch.net/puzzles/

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 Post subject: Posted: Tue Aug 29, 2006 3:11 am

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
I agree with both of you. The opposite egde-holes are filled automatically only on the centre ball. On the corner balls there are Bram 2**12 possibilities with the mentioned duplicates.
What about the edge balls? Ohh. Forget that. I would rather start to analyze the Rainbow Cube...

Andreas

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