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 Post subject: Octo for tradePosted: Sat Apr 01, 2006 6:43 am

Joined: Fri Nov 04, 2005 12:31 am
Location: Greece, Australia, Thailand, India, Singapore.
Hi guys,

I have a couple of Octo duplicates (Taiwan version), which are sealed in their package (never opened).
I might place them on ebay, but I would prefer an interesting swap.

I also have some other duplicates (Rubik's Shells, Lockout, Octahedron, Alexander's Star), but it has to be a very special case for me to trade them. At the moment, I would like to use the Octo for swapping!

To get a view of this extremely cute and rare puzzle I have placed a "Spotlight" page here.

Peter

*EDIT*

I decided to list one on ebay!

http://cgi.ebay.com/ws/eBayISAPI.dll?Vi ... 6048397550

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 Post subject: Posted: Sat Apr 01, 2006 9:13 am

Joined: Tue Oct 07, 2003 10:00 pm
I think the number of combinations can't be right, it's much more than (8*4)! / (4!)^8 which is a naive upper limit... or do the pieces of one color differ?

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 Post subject: Posted: Sat Apr 01, 2006 10:09 am

Joined: Fri Nov 04, 2005 12:31 am
Location: Greece, Australia, Thailand, India, Singapore.
It's always the way you define and calculate it.
I regard each piece as different (even of the same color).

Now let's say I number each "barrel" elements as a group with order four.
Then we will have eight generators/permutations:

a0=(01,02,03,04)
a1=(11,12,13,14)
a2=(21,22,23,24)
a3=(31,32,33,34)
a4=(41,42,43,44)
a5=(51,52,53,54)
a6=(61,62,63,64)
a7=(71,72,73,74) (the last permution is not used for the calculations, as my assumptions are to keep one element invariant)

The big turning loop will be translated as the permutation

b=(01,11,21,31,41,51,61,71)(02,12,22,32,42,52,62,72)

If you plug this information to any program that generates permutation groups, it will give you order 265,252,859,812,191,058,636,308,480,000,000

Note that my condition to keep one element stabilised is my personal choice (just like holding this piece).

Now, if we want to calculate all combinations, where same colors are regarded as same pieces, then we will surely have less combinations.

Peter

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 Post subject: Posted: Sat Apr 01, 2006 10:40 am

Joined: Tue Oct 07, 2003 10:00 pm
Ok... though, viewing all pieces as different, I'd expect 31! (holding one fixed, permuting the other 31) and I realized your number is 30! only, do you know where this difference comes from (I gotta admit I've neither played with an Octo yet nor have I used those programs you mentioned)?

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 Post subject: Posted: Sat Apr 01, 2006 10:47 am

Joined: Wed Oct 31, 2001 4:19 am
Location: Manchester, UK
kastellorizo wrote:
a7=(71,72,73,74) (the last permution is not used for the calculations, as my assumptions are to keep one element invariant)

If you do that, surely you will never separate pieces 73 and 74.

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 Post subject: Posted: Sat Apr 01, 2006 10:48 am

Joined: Fri Nov 04, 2005 12:31 am
Location: Greece, Australia, Thailand, India, Singapore.
Well... it is actually two pieces that eventually won't change. To be more clear, I have chosen Nr 74 to be invariant. But that will mean Nr 73 will be forced to remain invariant as well.

As for GAP, it is not a new, but it is a quite useful program. The link hereprovides some GAP Rubik's Cube analysis, as well with some links (on the top) to download the software.

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 Post subject: Posted: Sat Apr 01, 2006 10:49 am

Joined: Fri Nov 04, 2005 12:31 am
Location: Greece, Australia, Thailand, India, Singapore.
LOL yes Mike you are right. You beat me on speed...!

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 Post subject: Posted: Sat Apr 01, 2006 12:11 pm

Joined: Sun Oct 16, 2005 10:00 am
How exactly does that octo function? I know that the colored parts rotate, but does the inner half of it twist along the outer part?

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 Post subject: Posted: Sat Apr 01, 2006 12:33 pm

Joined: Fri Nov 04, 2005 12:31 am
Location: Greece, Australia, Thailand, India, Singapore.
Korkow wrote:
does the inner half of it twist along the outer part?

Although it looks like it does, that is not the case.

The front and back side are actaully the ones that slide with respect to each other.
The front side contains half of the inner side, and half of the outer side. Same with the back side (which is symmetrical to the front side with respect to shape).

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 Post subject: Rainbow CubePosted: Sat Apr 01, 2006 8:57 pm

Joined: Sat Apr 01, 2006 8:55 pm
Location: Dallas, TX
I would like 2 Rainbow Cubes please. One for 7 and one for 14 colors. Please also I would like the additional stickering for 14.

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 Post subject: Re: Rainbow CubePosted: Sat Apr 01, 2006 11:35 pm

Joined: Fri Nov 04, 2005 12:31 am
Location: Greece, Australia, Thailand, India, Singapore.
sexualRubiks wrote:
I would like 2 Rainbow Cubes please. One for 7 and one for 14 colors. Please also I would like the additional stickering for 14.

Hi sexualRubiks!

I believe you should post your request here:
viewtopic.php?t=4485

Octo and Rainbow cubes are two different things, although excessively colorful and cutel!

Peter

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