Hi,

this posting is a direct follow-up to the thread about the skewbs.
Sadly there are way to much variants for the 3x3x3 to have all of them built.
I still work once in a while on further reducing the list of 3x3x3's worth to be built.
The last time I presented such an image was 2004. Time for an update:

Woah!
Thanks for posting these threads. I see that this is not all of them of course, but are these all the ones that you think are worth building?

Or am I wrong? (Probably wrong )

I did a quick search for your last image as I was curious to see how many have been added since 2004 and I found this thread.

http://twistypuzzles.com/forum/viewtopic.php?f=9&t=3217

Did you delete your old image? I would have left that piece of history. And since you say you are still trying to reduce the list may I ask if it still stands at 7336 variants?

Carl

No. I haven't precisely defined what a "variant worth building" means. The list is down to 5705. See the link below. Not all are worth to be built but so far I have no idea which are the ones.

That thread was my first presentation of the BandagingAnalyzer. I deleted those old programs because they were monolingual and outdated and there is a new one:
viewtopic.php?f=1&t=15993
which is bilingual.
The thread with the first image was hijacked by me:
viewtopic.php?p=18653#p18653

Andreas

To try to get rid of duplicate designs could you classify each puzzle with how many of each type of piece it has, then go through to check if two puzzles with the same pieces are copies or not?

You are still missing my favorite bandaged 3x3x3(I think), a fused cornerblock and a fused edge group.

The filtering program already did that.
If anybody is interested. I wrote an article for CFF about the filtering used for this list this program. It was published in CFF #79 but still left out many details.
To make a long story short:
Of all variants that can be transformed into each other by (1) twisting the layers and/or (2) twisting the whole puzzle and/or (3) mirroring the whole puzzle at most one is present in the resulting list.
If the variant has one or more implicit bonds the variant is deleted since there will be a variant on the list where this bond is explicit. A bond is implicit when it is not set but leaving it unset does not allow new moves.
If a unset bond does not change anything but open one or more dead ends the variant is omitted. This inspiration for this rule was given to my by Bram 7 years ago in the thread Carl linked to. Thank you Bram for that.
There are two more filtering criterias I found but have not generalized to other puzzles yet. There might be more ideas but I haven't had them so far.Please explain what a cornerblock and a fused edge group is.
Do they have size 1x2x3 or 1x1x3 or anything else?

Andreas

Edit: Corrected a quote.

Interesting... may I ask what seperates the 5705 from the original 7356? I didn't see that mentioned in the other thread.

Carl

The 1651 variants considered trivial

• have unfilled dead ends. Please see the help file attached to the program for an example or
• consist of nothing more than a single trivial path or
• have only a single permutation => After solving the bandaging signature the variant itself is solved.

or fulfill more than one condition.

A 2x2x2 block made of three centers, three edges, and a corner and a 1x1x3 block made from an edge and two corners. Do you have that one yet?

It is there.
It has 14 bonds and has the signature C00B40D85A0.
Use CTRL+F so search for it.