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 Post subject: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboids?
PostPosted: Sat Jul 20, 2013 9:34 pm 
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[Moderator]Talks about the L-Cube were the first comments about solving one of these cuboids. Today (July 26th) I decided to move the next few posts from the original topic to the solving forum. We started this thread earlier by talking about the X-Cube.[/Moderator]

Well I've been having some "fun" with the L-cube. I've encountered something I didn't expect to encounter on this puzzle. All the pieces you can't see are solved. No pieces came out and had to be resinserted.

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 Post subject: Re: Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid Series Relea
PostPosted: Sat Jul 20, 2013 10:54 pm 
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rline wrote:
Well I've been having some "fun" with the L-cube. I've encountered something I didn't expect to encounter on this puzzle. All the pieces you can't see are solved. No pieces came out and had to be resinserted.


I yelled at the screen saying "THAT"S IMPOSSIBLE" at first, but then I realized how to fix it. It's weird little situations like this that make cuboids and their cousins fun!

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 Post subject: Re: Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid Series Relea
PostPosted: Sat Jul 20, 2013 11:03 pm 
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themathkid wrote:
rline wrote:
Well I've been having some "fun" with the L-cube. I've encountered something I didn't expect to encounter on this puzzle. All the pieces you can't see are solved. No pieces came out and had to be resinserted.


I yelled at the screen saying "THAT"S IMPOSSIBLE" at first, but then I realized how to fix it. It's weird little situations like this that make cuboids and their cousins fun!

My thought wasn't "that's impossible", it was "oh no!"
I've also worked out how to fix it. It felt good too :lol: This L-cube is definitely worth the money, even if people don't want to go for the 3x3x5.

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 Post subject: Re: Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid Series Relea
PostPosted: Sat Jul 20, 2013 11:12 pm 
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rline wrote:
Well I've been having some "fun" with the L-cube. I've encountered something I didn't expect to encounter on this puzzle. All the pieces you can't see are solved. No pieces came out and had to be resinserted.
Well you made me scramble and solve my L-Cube in an effort to reproduce this state. :mrgreen: I was able to get the corners as shown, but not the flipped edge; I only got swapped edges. :( It is a fun little puzzle to solve. 8-)

rline wrote:
This L-cube is definitely worth the money, even if people don't want to go for the 3x3x5.
I hesitated to get the L-Cube at first, thinking it would be a subset of the other two, but it offers it's own challenge and I'm very happy I got it. I think it's a little easier than the X-Cube.

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 Post subject: Re: Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid Series Relea
PostPosted: Sat Jul 20, 2013 11:20 pm 
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Pete the Geek wrote:
I hesitated to get the L-Cube at first, thinking it would be a subset of the other two, but it offers it's own challenge and I'm very happy I got it. I think it's a little easier than the X-Cube.

Really? We must have a different X-cube method. 8-)

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 Post subject: Re: Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid Series Relea
PostPosted: Sun Jul 21, 2013 12:18 am 
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rline wrote:
We must have a different X-cube method. 8-)
:mrgreen: My method:
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 Post subject: Re: Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid Series Relea
PostPosted: Sun Jul 21, 2013 11:25 am 
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*mutter mutter* all this talk about L cubes.. :evil: Honestly.. put a sack of money down every time you mention one of these cubes will ya! :evil:


(yeah I just bought two *sigh* :roll: :lol: )


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 Post subject: How to solve Calvin's & Evgeniy's cuboid series?
PostPosted: Sun Jul 21, 2013 4:57 pm 
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There's a video solution for the X-cube for anyone interested. :)


Moderator Konrad:
I discussed it with rline and we thought it a good idea to start a separate solving thread.

I have preserved rline's original post in this thread

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 Post subject: Re:How to solve Calvin's & Evgeniy's cuboid series?
PostPosted: Mon Jul 22, 2013 11:42 am 
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Hi rline, I like your video (and I liked it in on Youtube :) ).
I had to smile a bit that you called three different piece types "edges" in the course of your tutorial.

I think you made a very good job making the X-Cube looking easy.

Probably many who are interested in cuboids will want to find their own solutions. Many (not all) ways lead to Rome in this case. :lol:

To all of those:
It may look a bit frightening if you look at a scrambled, shape-shifted X-Cube and I think it helps if you imagine how it is constructed in a logical way.

We start with a 5x5x5 and cut off the U and D layers:
Image

We sticker the inner layers u and d (WCA notation) like the cut off layers and remove further the corner/edge columns of the 5x5x3 cuboid:
Image

The remaining stuff are all inner pieces of the original 5x5x3.
Still, it makes sense to look at the new "cuboid" and assign proper piece names derived from the visual appearance of this new object:
Image

Maybe it helps to realize that the combination of two "corners" and one X-centre is the remainder of a 2x2x2 corner on the original 5x5x5:
Image

I highly recommend this puzzle and recommend too, figuring out your own way.

EDIT: Regarding my own method: I started with something more complex and made it much simpler afterwards.
There are similarities with rline's method (e.g. what rline calls the cuboid Corner Piece Series plays an important role in my method as well and the handling of a "corner parity" - odd permutation of corners), but there are differences too. I will not go into any details, because this is not the solving forum. We can start a solving topic, if somebody is interested.

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 Post subject: Re: How to solve Calvin's & Evgeniy's cuboid series?
PostPosted: Mon Jul 22, 2013 5:14 pm 
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Konrad wrote:
Hi rline, I like your video (and I liked it in on Youtube :) ).

Thanks Konrad! I appreciate any and all support :lol:

Konrad wrote:
Many (not all) ways lead to Rome in this case. :lol:

Yes I think that's very true. Someone asked me whether it could be solved as all center parts of a 5x5x5. I guess it could. Dan Fast (CBC) also said he had a different method, which I'm looking forward to seeing.

As usual, I love your graphics!

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 Post subject: Re: How to solve Calvin's & Evgeniy's cuboid series?
PostPosted: Tue Jul 23, 2013 10:06 am 
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rline wrote:
...Someone asked me whether it could be solved as all center parts of a 5x5x5. I guess it could. ....
This paradigm can certainly help to find useful move sequences. On the other hand, you cannot reuse any 5x5x5 centre sequences on a cuboid - and the X-Cube is even more special.

Before I discuss a centre 3-cycle as an example, I need to introduce a notation:

Image
As you recognize, I use a lower case letter for the white and yellow faces.
The reason is that we see here a stickered inner layer and I follow the (older) WCA notation where f was the single inner layer below F, and r the inner layer below R.
Whenever I turn the f layer (e.g. clockwise turn f) whatever cubies are in the F layer (when shape shifted) will turn together.

Now let us take a pure centre 3-cycle from the 5x5x5 like r' d' r U r' d r U' (a [3,1] commutator). The result is
Image

We cannot do exactly the same on the X-Cube, because sometimes outer and inner layers can be turned together, only.
If we do r' the following d' has to become (D' d') and we change the whole sequence to
r' (D'd') (Rr) U (R'r') (Dd) (Rr) U.
This produces a nice 3-cycle of X-Cube "corners" (corresponding to X-centres on a 5x5x5):
Image

Now we look at the same sequence when the white face is on top (face name lower case u)

Image
The picture shows the situation after r' (Dd)' (Rr)
The orange/green/yellow "corner" is nicely isolated in the U layer :lol: , but we cannot turn U independently. If we continue by (Uu) the result is not very useful!

BTW: You can see a few battered stickers on my photos. This happened very early as I mentioned in the other thread. Recently, it did not get any worse. I have dome nothing to the puzzle, the tensioning is OK for me.
I do not criticize the sticker thing much I'm just mentioning it. By no ways I would call this puzzle "cheap".

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 Post subject: How to solve Calvin's & Evgeniy's cuboid series?
PostPosted: Wed Jul 24, 2013 3:49 am 
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Here is an outline, how I solve it:

1. Back to X-Cube shape - as in rline's tutorial I solve the inner 3x3 faces white and yellow at the same time. I find it very useful to view the puzzle as a strangely shaped 3x3x3 doing double layer turns only: Corners are a combination of 3 cubies in L-shape, edges are either I-shaped or L-shaped. You can use any known 3x3x3 move sequences.

2. U=white Solve the white face completely. This is very intuitive for anyone who has solved a single face on a3x3x3.

3. Solve the middle layer (E in WCA)

4. Solve the D layer. The working horse is a cuboid CPS. I hold the yellow face as f and do something like this [(Rr)2 U (Ll)2 U']x2. 3-cycle of corners between D and U
You can use cuboid X-centre 3-cycles as well: U=yellow B2 (r2 d' R2 d)x2 B2 If you do it on a 5x5x5, you'll see what it does.
Originally I placed all cubies at their correct location.
I started with the yellow edges first (using a pure 3x3x3 3-cycle)
I fnd rline's idea to reduce 2 corners and the edge inbetween to "reduced large edges" as on a 5x5x5 nice and it can save setup moves.

Where I over complicated things at first, was my handling of corner parity (two corners need to be swapped). I handled it like a swapping of two edge wings on a 5x5x5 and found only later that a 90 degree turn of a 3x3 baby face is easier. Later I saw that rline does the same.

EDIT: I have changed the title of this topic making it more general. If somebody wants to discuss any other related cuboids, this is the place to do it.

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 Post subject: Re: How to solve Calvin's & Evgeniy's cuboid series?
PostPosted: Wed Jul 24, 2013 5:44 pm 
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Konrad wrote:
Where I over complicated things at first, was my handling of corner parity (two corners need to be swapped). I handled it like a swapping of two edge wings on a 5x5x5 and found only later that a 90 degree turn of a 3x3 baby face is easier. Later I saw that rline does the same.
The tricky bit is ending up with two swapped edges at the end. They can be either whole babyface edges or just the single middle edge. Fixing one case using conventional cuboid methods produces the other case. This seems like a genuine X-Cube parity. We have an easy way to escape from this situation by [spoiler]taking advantage of the babyfaces that can be turned 90 degrees independent of the rest of the puzzle[/spoiler].

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 Post subject: Re: Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid Series Relea
PostPosted: Fri Jul 26, 2013 6:07 am 
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rline in post #1 wrote:
Well I've been having some "fun" with the L-cube. I've encountered something I didn't expect to encounter on this puzzle. All the pieces you can't see are solved. No pieces came out and had to be resinserted.

Attachment:
DSCF4396.png
As I mentioned in the other thread, I have admitted to my wife one of three cubes in the last parcel from Calvin, only. :lol: So, I had to wait for an opportunity to solve the L-Cube without the risk that my wife would see the L-Cube.
Yesterday I was at the library and instead of reading something I solved the L-Cube several times.
I found it surprisingly easy. OK, I screwed it up a few times during my first solve, because I made simple mistakes. What I mean: The strategy seemed to be straight forward.
Later we visited a wonderful concert in one of king Ludwig II. castles (Herrenchiemse on an island in lake Chiemsee). When we returned around midnight, I remembered an earlier post from rline (I made it the first in this thread today). I had not looked at the picture in detail before.
I was a bit shocked first (Right, I said "How is this possible?" to myself :roll: )

I had to go to bed not understanding how to fix this. :(
I the middle of my sleep, I woke up and knew the solution.

Many people will share this kind of experience. At least similar things happened to me quite often when I used to hunt bugs in Operating System code (actually ages ago :wink: )

Currently, I'm at the computer of my daughter in Munich (we have to do babysitting for our ill granddaughter).
So, I do not have my usual camera and computer equipment.
This photo should show clear enough that I constructed the same problem as in rline's picture:
Image

I think the fix is not completely obvious, if you encounter this situation by accident.
Interestingly, I have never seen the problem during a normal solve.
I'm not sure, but I assume that there is a 25% chance getting this kind of situation.
Can anybody prove me wrong or confirm this?

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 Post subject: Re: Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid Series Relea
PostPosted: Fri Jul 26, 2013 6:24 am 
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Konrad wrote:
This photo should show clear enough that I constructed the same problem as in rline's picture:
Image



From this state, treat the extra L cube faces as if they weren't there and use an algorithm that flip 2 edges (flipping the red/yellow and green/yellow edge)

Do you end up with 1 flipped edge? That is so cool if it does.

EDIT: R' U2' R2 U R' U' R' U2 L F R F' L' is the algorithm that does the trick.

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 Post subject: Re: Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid Series Relea
PostPosted: Fri Jul 26, 2013 4:13 pm 
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rubikcollector123 wrote:
...From this state, treat the extra L cube faces as if they weren't there and use an algorithm that flip 2 edges (flipping the red/yellow and green/yellow edge)

Do you end up with 1 flipped edge? That is so cool if it does.

EDIT: R' U2' R2 U R' U' R' U2 L F R F' L' is the algorithm that does the trick.

Sure enough this is a nice pattern.
Image
BTW, I use this to flip two opposite edges on a 3x3x3: (M' U)x3 (U M)x3 U2. (M = middle layer between L and R and turns like L - old WCA notation) With the setup R B it produces the identical result as your sequence.
This is not so bad either:
Image

Here is my method in a nutshell:
[spoiler]1. Build the inner 3x3x3 and do not care about the cubies on the two babyfaces just using usual 3x3x3 sequences. (F2L may be visually harder. I do it usually layer by layer). View the puzzle as a strangely shaped 3x3x3.
2. Solve the babyfaces
2a Edges first (like EPS from the Ultimate solution)
2b "Corners" with a pure 3-cycle (I use a [3,1] commutator)

I have never seen the strange situation rline has shown in his picture in an actual solve. With my method I will never see a single flipped edge in the last layer (like the red/yellow in the pictures).

EDIT: I mean that I orientate two 3x3x3 yellow edges at a time (yellow sticker on the yellow face). In case I see a single incorrectly orientated 3x3x3 edge, I re-orientate it together with the single L-shaped 3x3x3 edge.

When I awoke last night, I had realized that there are four 2x1x1 edges that can be swapped without immediate recognition before the babyfaces are solved. Additionally, one L-shaped edge exists that can be flipped without immediate recognition. (You could say babyface cubies hide the stickers of that edge.)
[/spoiler}

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Sat Jul 27, 2013 8:03 am 
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Hi rline and all other,

rline: I saw your video about x cube. Very nice video.

I don't own one of this series.
My question: Is the L cube more difficult than the x cube ?
Has it different mechanics ?
Or ist the L Cube a X Cube without 2 faces ?


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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Sat Jul 27, 2013 8:58 am 
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Andrea wrote:
Hi rline and all other,

rline: I saw your video about x cube. Very nice video.

I don't own one of this series.
My question: Is the L cube more difficult than the x cube ?
Has it different mechanics ?
Or ist the L Cube a X Cube without 2 faces ?
Hi Andrea,
I have not looked at the mechanism but I think they are all pretty close relatives. My impression is: The X-Cube is similar to a 5x5x3 and all others have just less 3x3 "babyfaces". (grigr posted about the I-Cube and T-Cube and one day later Calvin can offer these versions. We can safely assume that they all use the same mechanism with different piece types!)

In my view, the L-Cube is by no means harder than the X-Cube. With my method I will never encounter the kind of "parity" on the L-Cube shown in rline's or my pictures above. Probably rline uses a different method that he has encountered it at all. I have constructed the situation voluntarily from a solved state and it needed a bit of work. I have now solved it around 15 to twenty times and wondered at first that I have never seen any strange position. I'm quite confident that at least my method (maybe Pete's as well) avoids such situations completely.

The parity on the X-Cube cannot be avoided easily and you will recognize it very late. Otherwise you would need a lot of mental swapping of "corners" to see, if they are in an odd permutation.

Good luck and have fun!

BTW: I did not want to neglect your new simulator. I'm sure you did a great job.
I just have not yet had the time to look at it. Besides a few new puzzles, my granddaughters keep us pretty busy.
They'll travel to the US by tomorrow for 5 weeks :wink:

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Sat Jul 27, 2013 7:09 pm 
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First, I'm sorry I haven't responded yet. I wasn't actually subscribed to this topic(I think because it was split from the other one) so I wasn't aware of the updates.

Quote:
I had to go to bed not understanding how to fix this. :(
I the middle of my sleep, I woke up and knew the solution.

That's happened a handful of times for me. It's a wonderful experience!

Konrad wrote:
I was a bit shocked first (Right, I said "How is this possible?" to myself :roll: )
Konrad wrote:
Interestingly, I have never seen the problem during a normal solve.
Konrad wrote:
With my method I will never encounter the kind of "parity" on the L-Cube shown in rline's or my pictures above. Probably rline uses a different method that he has encountered it at all.

I encounter this parity on the L-cube probably 50% of the time. So yes, I'm quite sure it's due to the method I use. I've made a video using this method. I always try and think in terms of reduction these days, so my method is one of reduction. I won't hide the method since this is a solving thread.

L-Cube
1. Return to non-shapeshifted form (I don't call it "cuboid" form as it's not strictly a cuboid)
2. Reduce edges and corners
a. Attach babyface edges to their appropriate colour sticker on the main puzzle. [EPS]
b. Attach babyface corners to their appropriate colour sticker on the main puzzle. [CPS]
3. Solve puzzle as a 3x3x3, with reduced edges counting as a single edge and also for corners.
4. Fix the single flipped edge if it shows up.
a. Put the puzzle back into non-SS form. This is needed to do the next bit.
b. Flip each of the orange-blue pieces using EPS. This now means another reduced edge (the orange-blue reduced edge) has been flipped. So we have now 2 flipped edges.
c. Reduce corners again and solve reduced cube as a 3x3x3

Andrea wrote:
My question: Is the L cube more difficult than the x cube ?
Konrad wrote:
In my view, the L-Cube is by no means harder than the X-Cube.

Obviously the method makes a difference to the perception of the difficulty of the puzzle. My answer would be "yes, it is more difficult" but that could be due to the method I use.

Andrea wrote:
Has it different mechanics ?
Or ist the L Cube a X Cube without 2 faces ?
Konrad wrote:
I have not looked at the mechanism but I think they are all pretty close relatives.

Yes, the mechanism is the same for all puzzles. All that's happening is the piece type is being changed from puzzle to puzzle. It's a very clever design, and I echo Tony's post on the other thread that they should have released a DIY kit. Obviously financial concerns prevented this for them. But as an example, I made the T-cube last night. I might try and solve it using my reduction method, and then using Konrad's method, and see which is nicer.

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Sun Jul 28, 2013 3:31 pm 
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With this picture I want to clarify want I mean by "The L-Cube can be viewed as a 3x3x3 with strangely formed pieces":
Image

I have shaded the 3x3x3 edges.
5 1x1x1 edges
6 2x1x1 edges
1 L-shaped edge

Because we need to differentiate between baby faces and normal 3x3x3 edges, I use the notation similar to the one I proposed for the X-Cube above. We use the paradigm of a 5x5x5 cut down to the shape of the L-Cube (an X-Cube with only two baby faces remaining)

Regarding "flipped edges":
Image

How many 3x3x3 edges are "flipped" on the picture above?
You could get the impression to see three.
Actually, the two baby face edges are swapped not flipped.
They act like stickers on the invisible 1x1x1
This situation can be fixed by a pure flipping sequence as shown above.
Try on a normal 3x3x3 (M' U)x3 (U M)x3 U2 and you will get a flip of UF and UB.
So, just turn the L-shaped edge opposite to the flipped 1x1x1 (or 2x1x1) edge and do this move sequence.
Be careful to translate the 3x3x3 notation to double layer turns whenever a baby face layer is turned.

If you try to solve the baby faces in my picture above without flipping the yellow/red edge, you will always end with odd permutations either in the group of baby face edges or baby face corners.

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Sun Jul 28, 2013 4:19 pm 
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Konrad wrote:
With this picture I want to clarify want I mean by "The L-Cube can be viewed as a 3x3x3 with strangely formed pieces"...
Thanks Konrad. I really appreciate your explanations and illustrations. I've been rather stuck on the L-Cube lately, so your ideas are very helpful. I solved this puzzle early on with little difficulty, but now with what must be a more thorough scramble, I've been struggling - getting my money's worth - for days. Part of my difficulty is conceptual and it is important to have a good mental model such as "a 3x3x3 with strangely formed pieces". I also didn't get a chance to test out algorithms on the solved puzzle to really see what they do. Some of my favourite cuboid algorithms are doing things on the L-Cube that I don't understand.

One question I have is when you solve the 3x3x3, what do you do about the 3x3x3 edge between the two babyfaces -FL in your photo? If I were solving a 3x3x3 I would first put in the bottom corner to match the adjacent faces. In this case, this corner is covered by the babyfaces. Do I just find an L-shaped piece that has the bottom colour in the middle?

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Sun Jul 28, 2013 4:49 pm 
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Well I've held off "releasing" my L-cube video until now because I wondered whether my method was unduly complicating things, due to the way Konrad and Pete were talking about how it was a fairly simple solve. My method may well still be complicating things, but having seen Pete's
Quote:
I solved this puzzle early on with little difficulty, but now with what must be a more thorough scramble, I've been struggling - getting my money's worth - for days.

I decided that maybe I'll release it and take the criticism if it is turning something simple into something hard!! Anyway, it only uses the EPS and the CPS (U R U' L' U R' U' L) and its mirror. It should at least provide "a" method. So my L-Cube tutorial is here, for anyone interested.

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Sun Jul 28, 2013 5:19 pm 
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Pete the Geek wrote:
...Thanks Konrad. ....
You are welcome, Pete!
Pete the Geek wrote:
One question I have is when you solve the 3x3x3, what do you do about the 3x3x3 edge between the two babyfaces -FL in your photo?
This is the L-shaped edge. In the solved state, it has two blue/orange baby face edges on top. On a scrambled L-Cube these two can be any out of the set of 8 baby face edges.

When I do the second layer, I usually put the one L-shaped edge in, NOT considering its orientation. The other three second layer edges show their orientation clearly.
You can do the other three first and calculate the number of incorrectly oriented yellow edges after your favourite second layer edge sequence has placed the L-shaped edge, too.
Or you can just not care at first and fix it later (as described above) when you see a single incorrectly oriented yellow edge left over.
(I define an incorrectly oriented edge on a 3x3x3 as one that is in the correct layer (e.g. yellow) but its sticker does not match the layer-centre,)

I hope this makes sense. :)

EDIT: @rline: With my paradigm of "solving a 3x3x3 with strangely shape pieces" first, I could restrict myself to the Ultimate solution. I just find it visually easier to use a layer by layer method.

So my method can be described as well
1. solve the 3x3x3 using your favourite 3x3x3 method (don't be confused by shape shifting :lol: ).
2. solve the baby faces using EPS, CPS

After the baby face edges are solved by EPS, the baby face corners will always be in an even permutation, meaning a few pure 3-cycles will do the job.

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Sun Jul 28, 2013 10:24 pm 
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rline, Konrad, thank you! Back to cuboid form:
Attachment:
L-Cube-Scrambled-Cuboid-Form_sm.png
L-Cube-Scrambled-Cuboid-Form_sm.png [ 248.63 KiB | Viewed 5419 times ]

The little detail of solving it from this state is still ahead of me, but I'm going to enjoy it like this for tonight! :mrgreen:

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Mon Jul 29, 2013 5:08 pm 
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Pete and all others interested:
Everybody who can solve a 3x3x3, can solve the puzzle to a position similar to this:
Image

You can avoid a single flipped edge on the last layer or solve one like this:
Image
Turn the L-shaped 3x3x3 edge up to the U face and flip two opposite edges in a pure way e.g. by (M' (Uu))x3 ((Uu) M)x3 U2
Image

Here is a photo series from scrambled to solved:
Image
White cross on u layer:

Image

White u layer solved:
Image

3x3x3 solved
Image

Baby face edges solved (I forgot the last turn L' on the photos):
Image

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Tue Jul 30, 2013 12:36 am 
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I was doing pretty well to get the 3x3x3 solved:
Attachment:
L-Cube-Scrambled-3x3-Solve_sm.png
L-Cube-Scrambled-3x3-Solve_sm.png [ 123.33 KiB | Viewed 5342 times ]


But then when I was solving the babyfaces this happened:
Attachment:
L-Cube-Scrambled-Babyface-Parity_sm.png
L-Cube-Scrambled-Babyface-Parity_sm.png [ 204.58 KiB | Viewed 5342 times ]
All the other edges are solved. :mrgreen: I'll try again tomorrow. All I can think to do is rotate one of the babyfaces 90° and resolve, but that's just a guess, not knowledge of the situation.

I can't believe I said this was easier than the X-Cube earlier in this thread! :shock:

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Tue Jul 30, 2013 1:03 am 
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Pete the Geek wrote:
I can't believe I said this was easier than the X-Cube earlier in this thread! :shock:

Well I'll admit I feel kind of vindicated in my assessment now! :lol:

What you've encountered in your picture is why I chose to solve it by reduction, to avoid that sort of thing.

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Tue Jul 30, 2013 4:14 am 
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@Pete: Well, when I have solved the 3x3x3, I will NEVER see a situation as in your picture again. You have permuted 3x3x3 pieces again. Obviously, you use different sequences to permute the baby face cubies. I solve them by very simple[1,1] commutators (EPS) for the edges and [3,1] for the corners. At the end of each of those, baby face pieces are permuted only.

I'll try to make some pictures later. Right now, I have to do other things.

BTW, right after my first solves in the library on last Thursday, I have swapped my X-Cube with the L-Cube. The X is now hidden between many others puzzles of my collection. The L-Cube lays in full daylight on my table and my wife has not recognized the difference :lol: That's the advantage that she is not so interested in my hobby and when scrambled, both look similar enough. :wink:

@rline: I have looked at the first part of your video and it looked frightening complicated to me. There must be an essential difference in our methods, because you think that reduction removes situations like in Pete's picture.
Probably, we will find out, why I think this is easier than the X, when I had the time to describe my "end game" solving the baby faces. This is the easiest part of it, because shape shifting can not confuse me any more.

When I swap back to the X-Cube again I'll try the same baby face strategy as on the L-Cube. Probably, this is fun too. :)

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Tue Jul 30, 2013 4:20 am 
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Quote:
@rline: I have looked at the first part of your video and it looked frightening complicated to me.

Hi Konrad

Thanks for watching! :)

I'm amazed (yes, literally amazed!) that you think a simple reduction method looks frighteningly complicated. It's just returning to cuboid shape first, then pairing outer edges with inner edges, as we might do on a 3x3x4 to reduce it to a 3x3x2. And then pairing outer corners to inner corners, as we might do on a 3x3x2. That's it. I'm not sure how that could be thought of as complicated. :?

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Tue Jul 30, 2013 4:51 am 
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I'll admit that I'm not very good at grasping a solution method showed in a video. :wink:

I have seen the first part of your video only, because I just thought: Solving a 3x3x3 is so much easier!!! :)

BTW, our fellow member robertpauljr (Bud Lengtat) said on Youtube
Quote:
You are amazing! When I get one of these I will start by looking for a way to do it without reducing! :D All that reducing, and re-reducing makes my head spin! I don't see how you keep it all straight. Anyway, it was a fun watch and I look forward to getting one of these someday. :D
I consider Bud an experienced solver.

I hope you can agree with this:
Solving a 3x3x3 is not a hard job for any of us. (Even with some confusing shape shifting aspect.) You will never encounter any strange situations as in the first picture of this topic.
If I convince you now, that the rest is easy (and I will never get to a strange situation as in Pete's picture again), would you not say that the overall method is easy?

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Tue Jul 30, 2013 5:14 am 
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Hi Konrad

This will probably be a strange conversation to many others. But to continue...

Quote:
Solving a 3x3x3 is so much easier!!! :)

But I didn't say it was harder. In fact, I haven't commented on your method at all. For all I know it's massively easier. I didn't try it.

Quote:
I consider Bud an experienced solver.

So do I :wink:

Bud and I have had many PMs over the time I've been on TP.

Quote:
Solving a 3x3x3 is not a hard job for any of us. (Even with some confusing shape shifting aspect.) You will never encounter any strange situations as in the first picture of this topic.

I agree with that. I've never disagreed with it. But where you see a flipped edge as a strange situation to be avoided if at all possible, I see it as a unique part of this cube, and its solve. It's definitely strange, but should we run from it? If it wasn't for that situation, this whole discussion on the L-cube, and people's views on how difficult it is, wouldn't have happened. Pete is a great case in point: he began saying it was easy, then recanted!

But I think the thing you're missing is that I'm not trying to convince anyone that "my method" is easier than any other method. It's just my method. That's it. I'm not promoting it as "the best method" or "easier than Konrad's" ( :lol: ). I'm just putting it out there. As far as I know I'm the only person who's uploaded a tutorial video on the L-cube. That's something.

Quote:
If I convince you now, that the rest is easy (and I will never get to a strange situation as in Pete's picture again), would you not say that the overall method is easy?

Sure. But I've never once said your method is hard. I guess I'm happy to be convinced, but it's not as though I've set out a challenge to you (or anyone else) saying "Find a better method than this!!"

In a recent PM (I'm sure Bud won't mind me quoting him on this) he wrote "I am baby stepping my way to achieving a new level of comfort with solving by reduction." He has been quite open with me that it's not his preferred method.

It's all perspective and is just about which method people prefer. Reduction vs non-reduction. I didn't think it was a competition! :lol: 8-)

I put out videos so that other people can be helped by them to solve a cube they couldn't solve (or just to watch them to see how I do it). If they don't get helped, so be it. If they don't like the method, they're more than welcome to come up with their own method. 8-)

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Tue Jul 30, 2013 9:03 am 
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Hi rline,

I hope you have not misinterpreted my comments. In no way I wanted to criticize you. I admire what you are doing and how you are doing it. I could not make such nice videos - beginning with the fact that I do not have the equipment. :roll:

As you have expressed yourself, the difficulty of a puzzle is a very personal perception.
(On the other hand there may be some agreement that a 2x2x1 is easier than a 3x3x3 :lol: )

In this case the debate started with the question "Is the L-Cube more difficult than the X-Cube?"
For me the answer is very clear: "No, the L-Cube is easier because it has 16 pieces less to solve."

And I have added in a sense: "If somebody sees it the other way around, it may very well have to do with the method used".
When I compared your method with mine in a sense, I meant to explain why our opinion differs, not to criticize anything.

Peace! :) :) :) (I'm quoting Matt Galla :) aka allagem)

Here is my endgame.
First how I hold the puzzle and the used notation:

Image
As a reminder: I have chosen a notation derived from a 5x5x5.
The lower case face names correspond to an inner layer of a 5x5x5 and in this case to normal 3x3x3 faces.
Because in these two sequences we have never cubies in the outer layers R and L, r and l turns are identical to writing (Rr) and (Ll).

3 cycle of babyface edges.
r U r U = EPS = [r,U]
The picture shows the result on a solved puzzle in frontview / backview:

Image

3 cycle of babyface corners
r U' l' U r' U' l U = CPS = [r,[U':l']]
The picture shows the result on a solved puzzle in frontview / backview:
Image

In my perception, I have only two easy steps:
1. solve the 3x3x3
2. solve the baby faces

Regarding the one flipped edge:
On a 3x3x3 we can never have all edges at their correct locations and one edge flipped.
Most people are caught by surprise when they see your photo (on top of the topic) for the first time.
Remember my story when I came home last Thursday at midnight and did not understand it at first?
And I went to bed not understanding it yet.
Even more surprising was the fact that I had never encountered it myself before.
In the middle of my sleep, I understood that there is one L-shaped edge where you cannot see the orientation directly, and I knew how to fix your kind of parity.
Now I understand perfectly why I have never seen it:
On a normal 3x3x3 you will never see a single edge flipped, because it would mean an odd permutation within the group of stickers. This is mathematically impossible!
Everybody doing any 3x3x3 method will immediately look for some error made before - i.e. another flipped edge somewhere - when on the last layer one sticker only doesn't match the last layers centre.

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Wed Jul 31, 2013 12:41 am 
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Thank you for the help and ideas rline and Konrad.

My guess was correct and the swapped last-layer edges in my photo a few posts above was indeed fixed by turning a babyface 90° counter-clockwise and then resolving the edges. The rest of the solve was straightforward:
Attachment:
L-Cube-Solved-Comp_sm.png
L-Cube-Solved-Comp_sm.png [ 120.25 KiB | Viewed 5170 times ]

My puzzle was no doubt in a funky state, given all of the many algorithms I tried. In the end, reading Konrad's solution overview and watching rline's video gave me the concepts I needed to recognize the various corners and edges. The basics of my difficulty was that I was initially unable to differentiate between certain corners and edges. Once I learned to "see" them, it became more straightforward. Another big breakthrough was my realization that a certain cuboid algorithm was causing problems and that I could swap it for a different algorithm (essentially CPS).

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Wed Jul 31, 2013 4:32 am 
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Hi Konrad (and others!)
Konrad wrote:
Where I over complicated things at first, was my handling of corner parity (two corners need to be swapped). I handled it like a swapping of two edge wings on a 5x5x5 and found only later that a 90 degree turn of a 3x3 baby face is easier. Later I saw that rline does the same.

This quote was from one of the earlier posts, talking about the X-cube.

Ok. Onto the T-cube... I solved it as a 3x3x3 first, using your method. Now I have a corner parity (2 corners need to be swapped).
Attachment:
File comment: 2 corners to be swapped on T-cube
DSCF4446.jpg
DSCF4446.jpg [ 146.31 KiB | Viewed 5153 times ]

Now, I do what you and I did in your quote with the X-cube: turn a babyface 90 degrees, then re-solve edges (as well as 3-cycle home the corners to make clear the result). Now here's what I have:
Attachment:
File comment: after babyface turn
DSCF4453.jpg
DSCF4453.jpg [ 149.21 KiB | Viewed 5153 times ]

If I try and deal with this by using the 2nd orange-blue edge in picture (the solved one), I end up with what appears to be a single L-shaped edge flipped, which is in reality just two different babyface edges flipped. If I turn a babyface once again to deal with those swapped edges, then I land back at the swapped corners.

I've actually tried a few other techniques all to no avail.

I await your thoughts! :lol:

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Wed Jul 31, 2013 5:08 am 
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Hi Rline,

Parity in identical pieces in the inner 333 = swap 2 identical inner edges.
(You would achieve this by a 90* twist of either the white or yellow face).

Cheers,
Burgo.

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Wed Jul 31, 2013 7:18 am 
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Burgo wrote:
Hi Rline,

Parity in identical pieces in the inner 333 = swap 2 identical inner edges.
(You would achieve this by a 90* twist of either the white or yellow face).

Cheers,
Burgo.

Hi Burgo

Thanks for that. I think I tried exactly what you say here before I wrote, but I must have put something back wrong because it wouldn't fix anything. But now (later) I've gone and tried it again and it's worked nicely. So, thanks for that little contribution. I didn't know you'd been lurking this thread.

The only thing I don't really understand is why you referred to it as a parity in the inner 333, when the pieces affected were the outer pieces. Can you explain that to me please?

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Wed Jul 31, 2013 8:14 am 
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Hi Rline,

I don't own the puzzle, I only own the SmaZ 335, but, the outer edges sit on the inner edges and therefore must retain their parity. It is possible not to see a swap of identical pieces in the inner 333 (edges or corners in this case), but it will become visible in the outer pieces which all have a specific position.

I did add the brackets for fear that I hadn't provided enough information :) .
(PS if you don't mind me editing again, I really like the way these puzzles subtly disguise the identical and hidden pieces, they're really cool, I think I might get them after all).

Cheers,
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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Wed Jul 31, 2013 8:56 am 
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I think I have a nice paradigm to explain the parity issues.

Imagine a 3x3x3 that has sliding tiles (I don't even know, if such physical puzzle exists).
In the case of the L-Cube we would have 2 faces with such sliding tiles.
I'll use photos of a Super Cube with Pochmann stickers:
Image

Please, note that the Pochmann style stickers exist on the L-Cube baby faces only.
You can just shrink mentally the baby face cubies to 2D tiles still showing the locations they belong to.
All centres including the baby faces have no orientation on them. I edited the photos respectively.

The other faces would have plain colour stickers as usual and the baby face centres have no orientation.
A solved L-Cube looks like this:
Image
The two structured faces are those with sliding tiles.
Please note that I do not have spent the effort to edit the Pochmann stickers on the other faces!

Now let us discuss he parity issues on the L-Cube.

When we have solved the inner 3x3x3 the sliding tiles may be scrambled a lot, but when all tiles for edges are solved, necessarily the corner tiles are in an even permutation and can be solved by pure corner tile 3-cycles.
The grey shaded faces are scrambled tiles that do hide some 3x3 cubies:
The edge cubie with two tiles (L-shaped on the L-Cube) does not reveal its orientation.
If it is flipped another 3x3x3 edge must be flipped.
If we flip back the other cubie together with the edge with the two tiles (e.g. using the pure flipping sequence I have shown above) we would end with a parity of the sliding tiles (the baby face cubies on the L-Cube) because we would swap two tiles (two baby face edges)
Image

While solving the 3x3x3 we may encounter another parity issue, because two 3x3x3 edges may be swapped, because you cannot distinguish them (yellow/blue and yellow/orange in my pictures). You could end with an odd permutation of the 3x3x3 corners.

This would show you that you have to swap those two edges .
Image
Both kind of parities do exist on rline's first photo in this topic.

Now, how does this model explain the issues on the T-Cube?

Here is a picture of a solved T-Cube with sliding tiles:

Image

And here it is with permuted tiles:
Image

Now we have a lot more 3x3x3 pieces that cannot be distinguished.
E.g. the URF corner looks identical to the DRF corner.

So, the inner 3x3x3 can look solved but a hidden odd permutation of the 3x3x3 pieces can be displayed by an odd parity of tiles (baby face cubies).
BTW, you can always transform a baby face edge parity into a baby face corner parity.

I really hope that this "sliding tiles" paradigm helps to explain the understanding of these cuboids.
It explains nicely why baby face cubies can never be flipped ( a 2D tile can never flip).

EDIT:
The difference between the L-Cube and the T-Cube is this:
- When the inner 3x3x3 of the L-Cube is solved the two groups of baby face edges are either both in an even permutation or both in an odd permutation. A single 90° turn of a baby face will switch between these two states. An odd permutation of just one group can happen only, if something is wrong with the 3x3x3.
- On the T-Cube you can see a perfectly solved 3x3x3 but an odd permutation of just one group of baby face pieces.
This can be resolved by permuting the 3x3x3 pieces as suggested by Burgo.

This discussion persuades me to get the T-Cube and L-Cube as well.
Oh my, how can I explain this to my wife :lol:

EDIT2: I added a T-Cube picture more resembling a solved state.

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Wed Jul 31, 2013 5:04 pm 
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Hi Konrad,

I thought about it overnight: the difference between the L Cube and the T Cube is that the T cube has identical Corners and Edges. So the orientation of the centre by 90* can be hidden by a Corner Swap and Edge Swap. You can only do a `direct 2 edge swap` if you do either a `direct 2 corner swap` or `another 2 edge swap as well`, and the `2 edge + 2 corner swap` is associated with a 90* centre rotation (or parity change).

Cheers,
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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Thu Aug 01, 2013 8:40 am 
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Thanks, Burgo, for the precise explanation!

I want to visualize what Burgo explained (I'm going to use the same sliding tiles paradigm as in my post above):

Image
Please have in mind that faces with normal stickers do not carry Pochmann stickers. I have edited a few only.
I have made a 90 ° turn of the white face as displayed by the white Pochmann sticker and solved the Cube to a state where you would see a perfectly solved 3x3x3 on a T-Cube. The 3x3x3 remained in a state where we see an odd permutation of edges and an odd permutation of corners.
Now, which permutations of sliding tiles (baby face cubies on the T-Cube) have we got
1. a single swap of edge tiles = odd permutation as shown by the red arrow above
2. a 2-2 swap of corner tiles = even permutation.

This shows clearly that we cannot solve the tiles without changing something on the 3x3x3.
The EPS and CPS sequences shown in my post above are permutations of baby face cubies, but the 3x3x3 stays unchanged.

Now, why did the single 90° turn of a baby face was the solution for a corner parity on the X-Cube?
The 90° turn changes the parity of the edge group and the corner group on that baby face. Clearly I can now solve the corners, because their parity was switched from odd to even.
The odd parity of the edges can be switched by a single swap of baby face edges, which doesn't change any other visually different pieces.

Maybe I'll show the 8 move sequence when I swap the L-Cube with T-Cube (as you might remember I play with one of them at a time only :lol: )

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Fri Aug 02, 2013 2:43 am 
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Gentlemen,

I have really enjoyed following this conversation about parity! This meeting of some of the best twisty puzzle minds in the world has been an eye-opener for me!

Interestingly, for once, it is not because I didn't understand the discourse, it was enjoyable because I understood every step and every word. It is a marker of how much I have improved at doing these puzzles over the last few months. Also when Rline first converted a 2 corner swap into a 2edge swap I immediately visualised a pochmann super cube and said alloud SuperAntonioVivaldi's "law of the cube" that you cannot have 2 edges alone to swap. There must be another 2 pieces that are swapped over. The cube extensions are effectively super cube centres and have fixed positions but the inner cube has no such restrictions so anything that can swap edges in this area should fix the problem!

Now I'm desperate to actually receive my puzzles so I can finally have a play!

Keep up the conversation - this Newbie is finally graduating to an established twisty puzzler! Still a very long way before I reach your level of expertise! :shock:

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Last edited by Puzzlemad on Sat Aug 03, 2013 12:35 am, edited 1 time in total.

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Fri Aug 02, 2013 3:59 pm 
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Puzzlemad wrote:
....I have really enjoyed following this conversation about parity! ...
Keep up the conversation - this Newbie is finally graduating to an established twisty puzzler! ...:
Kevin, I take your post as a compliment to all who have contributed to this thread :) and I take it as an encouragement to explain how I solve the corner parity on the X-Cube.
Here is an example
Image
Two corners have to be swapped (the corners are in an odd permutation.)
After an U turn
Image
the parity of both - corners and edges on the U face - have switched. The corners are in an even parity and can be solved by a 3-cycle (b2 (r2 U l2 U')x2 b2)
Image
The edges are still in an odd permutation. They need to do 4-cycle to go back to their correct locations.
I do a simple move sequence to swap the parity to even:
(Ll)2 (Ff)2 U2 l2 U2 (Ff)2 (Ll)2 U2 = a [1:[1:[1:1]]] conjugate + U2
Please, note that I write (Ff) even in a sequence where no cubies at all are in the F layer. (If there would exist some F cubies they would turn together with the f layer.)
I'll do the same sequence on a 5x5x5 Super Cube to explain why this works.
Image
The green/red and green/orange edges have been swapped. Everything else seems unchanged. But on a 5x5x5 there is no such a thing that we get an odd permutation in one group of piece types only, right?
I'll use a 5x5x5 Super Cube (Pochmann stickers again) to show what happens:
Image
I do the same sequence as above (Ll)2 (Ff)2 U2 l2 U2 (Ff)2 (Ll)2 U2. EDIT: typo corrected. As noted by Kevin below.Image

Now I cut off all cubies that don't exist on an X-Cube (OK, OK I didn't use a saw, just Photoshop :lol: ) and have applied the stickers to the normally hidden inner faces of the 5x5x5:
Image
We see that we have swapped several pieces on the white face including two +-centres (=edges on the inner 3x3x3) besides the swap of two babyface edges on the green U layer.

We cannot see this on an X-Cube, because we have plain stickers and not the Pochmann style.
Image
We just get what we need - a single swap of edges. The permutation of X-Cube edges has become even and can be resolved (e.g. by two 3-cycles. (Here is a cuboid 3-cycle for a clockwise permutation of edges:
(r2 U')x2 (r2 U2)x2 (r2 U')x2 (r2 U2)x2 - the Ul edge remains fixed.)

My first parity fix wasn't much longer as the move count is concerned, but the thinking was more complex.

EDIT: I forgot the last U2 when writing (Ll)2 (Ff)2 U2 l2 U2 (Ff)2 (Ll)2 the second time. (Ll)2 (Ff)2 U2 l2 U2 (Ff)2 (Ll)2 U2 is correct. Thanks Kevin.

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Fri Aug 02, 2013 9:26 pm 
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Hi Kevin,
Puzzlemad wrote:
SuperAntonioVivaldi's "law of the cube" that you cannot have 2 edges alone to swap. There must be another 2 pieces that are swapped over.
The interesting thing in this case is that an `edge 2+2 swap` is actually only 2 edge 3cycles, so there is no parity change. Otherwise the parity would show on the L-cube, because it's possible to swap `2 yellow edges & 2 white edges`. But the parity only happens when corners and edges are involved and this becomes possible on the T-Cube. The L-Cube has too many `corner pieces` with specific positions on the inner 333 to cause external problems (when all the corners are in place, the parity of the edges can’t be out).

Hi Konrad,
Attachment:
Konrads X-Cube Parity Fix.jpg
Konrads X-Cube Parity Fix.jpg [ 925.99 KiB | Viewed 4894 times ]
Something was bugging me about your diagram. I think the movement of internal pieces isn’t correct. I made a diagram of what happens on the `internal 333` and the `Real 555`. Those who can interpret the Real 555 won’t need the 333 part, but it’s there to illustrate.

Simply put, Konrad’s sequence is a domino parity fix, it's all double twists (180*) so there's no parity change, (the hidden RC edges in UL & UD are exchanged- I think Konrad’s diagram is slightly incorrect here- it's just a small mistake about which `unnoticed` pieces have moved). Now, why does a domino parity fix work? Because it uses a 2+2 swap of RC edges: 2 hidden RC edges (UL & DL) [which have 4 outer babyface edges- no outer parity change] `plus` 2 white RC edges (FL & FR) [which have only 2 outer babyface edges- outer parity change]. 2 inner RC edge swaps + 3 outer babyface edge swaps= inner unchanged, outer changed. Incidentally there is a corner X swap (which is 2 3cycles- no parity change, in the same way that a 2+2 edge swap is 2 3cycles- no parity change).

Why does it work? You can see on the real 555 and inner 333. Simply: it’s because the edges on the white and yellow faces `don’t have babyface pieces`. So: some edges have 2 babyface pieces `and` some edges have only 1 babyface pieces. 2+2 Swap 2 groups of identical RC pieces that are different types and you change the outer parity.

This is what changes the outer parity:
1. When the 2 RC edges and 2 RC corners are able to be swapped because they are identical. OR
2. When there can be a 2+2 RC edge swap involving [2 hidden RC edges with 2 Babyfaces ea and 2 RC edges with 1 babyface edge ea]. It has to be that full set of circumstances, because otherwise the edges are not available. (It can't be, for example, the identical 2 yellow and 2 white edges on the L-cube because they don't meet the criteria, the L-cube doesn't have enough hidden edges).

One fix (1) involves a necessary RC parity change, the other (2) does not, but it could be solved with the inner RC parity change method (in other words it is not necessary in this case to maintain parity on the inner 333).[Edit: it's not necessary on either the X or T Cubes to change the parity of the inner RC: read posts below vv.]

I cannot understand how a 90* twist of the babyface alone can resolve outer parity, as I believe has been discussed here, it must be associated with the movement of unidentifiable inner RC pieces in some way.

I hope I have that all correct and understandable,
Cheers,
Burgo.

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1st 3x3 solve Oct 2010 (Even though I lived through the 80s).
PB 3x3 55sec Jan 2011 (When I was a kid 1:30 was speedcubing so I'm stoked).
1st 3x3 Earth (nemesis) solve Jan 2011 My You Tube (Now has ALLCrazy 3X3 Planets with Reduction)


Last edited by Burgo on Sat Aug 03, 2013 3:44 am, edited 4 times in total.

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Fri Aug 02, 2013 9:44 pm 
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Thanks Konrad, Burgo, and Kevin.

I find these puzzles interesting for their apparent simplicity.

I'll admit I'm rapidly losing my understanding of what's going on with these things. :?

I think I'll just provide the photos of situations and let other people sort it all out :lol:

Today's picture is of the i-cube. This has only one babyface on the 3x3x3 and so Evgeny has called it the i-cube. I presume because the "dot" of the "i" is on top of the main part.

Anyway, I solved it mostly. But I've ended up with the picture below. The top face is the babyface. It has a 2+2 swap of edges so I'm guessing that there's no parity. I can convert that to a 2+2 swap of corners (obviously) by U2. I can also convert it to allthe U face solved with the u edges in a 2+2 swap.

So far I've tried quite a few things to "fix" it. I'm still thinking about it.

The difficulty as I can see is my inability to carry out an ordinary cuboid algorithms because of the shifted center.

Over to the experts. 8-)

Attachment:
DSCF4456.png
DSCF4456.png [ 715.71 KiB | Viewed 4886 times ]

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Fri Aug 02, 2013 9:56 pm 
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Hi Rline,

It's this puzzle here vv, we do talk vaguely of a method there:
http://www.twistypuzzles.com/forum/view ... =9&t=23063
I provided my full method for it in the AI 444 solving thread:
viewtopic.php?f=8&t=24349&start=15

Cheers,
Burgo.

_________________
1st 3x3 solve Oct 2010 (Even though I lived through the 80s).
PB 3x3 55sec Jan 2011 (When I was a kid 1:30 was speedcubing so I'm stoked).
1st 3x3 Earth (nemesis) solve Jan 2011 My You Tube (Now has ALLCrazy 3X3 Planets with Reduction)


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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Fri Aug 02, 2013 10:14 pm 
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Burgo wrote:
Hi Rline,

It's this puzzle here vv, we do talk vaguely of a method there:
http://www.twistypuzzles.com/forum/view ... =9&t=23063
I provided my full method for it in the AI 444 solving thread:
viewtopic.php?f=8&t=24349&start=15

Cheers,
Burgo.

Holy cow :shock: That's such an easy fix. I had no idea this puzzle was previously made and discussed. Your fix for my edges was a total of 12 moves. So in reality this puzzle is basically just a 3x3x3 with a potential extra 12 or so moves? Seems too easy.

Hmmm, thanks for posting back so quickly.

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Sat Aug 03, 2013 12:15 am 
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rline wrote:
Thanks Konrad, Burgo, and Kevin.

I find these puzzles interesting for their apparent simplicity.

I'll admit I'm rapidly losing my understanding of what's going on with these things.
I just had a short PM with Rline, I'll post what I wrote here because I think it might help to clarify what I said earlier:

1. All of these puzzles have identical pieces that can be exchanged and this may create an external edge or corner swap, which is a `parity in external pieces`.
2. All puzzles that get external babyface parity need to move internal RC pieces to change the external babyface parity.
3. With some puzzles (T-Cube) it matters if the inner puzzle's `parity` matches the outer puzzle's `parity`. (because more of the inner cube is visible so not enough identical pieces are available to overcome the situation without changing the inner `parity`). Inner parity can only be changed by twisting a yellow or white RC face by 90*. You can use (F2 R2)x3 to swap UR<>DR + FU<>FD, then 3cycle babyface edges and this doesn't alter parity, so the inner RC parity is unimportant.
4. With other puzzles (X-Cube) you can solve the outer part regardless of the inner puzzles `parity`. Parity of the external pieces can be resolved by doing a very particular 2+2 swap of inner RC edges (2 hidden edges and 2 white or yellow edges). Or alternatively you could use the parity change too, it wouldn't matter.
5. Other puzzles (L-Cube, I-Cube) you don't have enough indistinguishable pieces to create `parity` of the inner puzzle, so the outer puzzle won't get out of whack.

Hope that can clarify a bit,
Cheers,
Burgo.

_________________
1st 3x3 solve Oct 2010 (Even though I lived through the 80s).
PB 3x3 55sec Jan 2011 (When I was a kid 1:30 was speedcubing so I'm stoked).
1st 3x3 Earth (nemesis) solve Jan 2011 My You Tube (Now has ALLCrazy 3X3 Planets with Reduction)


Last edited by Burgo on Sat Aug 03, 2013 1:41 am, edited 1 time in total.

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Sat Aug 03, 2013 1:11 am 
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Puzzlemad wrote:
Interestingly, for once, it is not because I didn't understand the discourse, it was enjoyable because I understood every step and every word. It is a marker of how much I have improved at doing these puzzles over the last few months.
......
this Newbie is finally graduating to an established twisty puzzler! Still a very long way before I reach your level of expertise! :shock:

:shock: :shock: :shock:
I guess I spoke too soon! Sudden sound of conversation rocketing over my head!

At least I am understanding a greater proportion of the conversation than usual! :lol:

rline wrote:
I'll admit I'm rapidly losing my understanding of what's going on with these things :?

I'm so glad it's not just me! Maybe it will improve when I actually get a puzzle to play with - I blame you lot for forcing me to place another order with Calvin yesterday! My initial order only had the first 3 in the series because the I and the T cube had not come out but I couldn't resist and ordered the other 2 yesterday so as to not miss out on the fun!

Konrad,
Looking at your sequence on the 5x5 Pochman cube to me it looks like you have carried out the cuboid sequence to swap 2 pairs of opposite edges but left off the final U2 move. This means that in the 5x5 you have swapped the 2 centre edges and the 2 pairs of upper corners. This works for a standard cuboid but not for a super cuboid because of the effects on the front face. The front face of our puzzle in question is not "super" and so this is acceptable plus the corners on the puzzle are missing completely this makes your proposed sequence acceptable. However all of this does not remove the fact that it has obeyed the "law of the cube".

Burgo,
I'm afraid you lost me completely! :shock:
Talk of hidden puzzles!
Comparison with the AI!

I guess I really am still just a Newbie? :roll:
I guess I'll have to hope all that comes clear when I actually get the puzzles in my hands. :?

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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Sat Aug 03, 2013 1:35 am 
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Well Kevin, it seems that I was a bit out too: You should be able to solve the T-Cube without altering the parity.. I was able to do it by swapping the 2+2 edges that were on the puzzle but it had slipped my attention, I'll blame it on not having the puzzles :lol: , I had a feeling that something wasn't quite right there :roll: . You should be able to do it with (Ff2 Rr2) x3 and then 3cycling the babyface edges as for the 555 (Incidentally this exact same sequence will work on the X-Cube too). Not sure if I should edit the text above.. at least it shows my thinking, but it might be confusing, I'll possibly do it with strikethrough.

Puzzlemad wrote:
Konrad,
Looking at your sequence on the 5x5 Pochman cube to me it looks like you have carried out the cuboid sequence to swap 2 pairs of opposite edges but left off the final U2 move. This means that in the 5x5 you have swapped the 2 centre edges and the 2 pairs of upper corners. This works for a standard cuboid but not for a super cuboid because of the effects on the front face. The front face of our puzzle in question is not "super" and so this is acceptable plus the corners on the puzzle are missing completely this makes your proposed sequence acceptable. However all of this does not remove the fact that it has obeyed the "law of the cube".
No, Konrad has transcribed the movement of the outer Pochman 555 onto the inner 333, which is quite different: this actually disguises the fundamental change that is happening, and it really had me going for quite a while to figure out what it was :) . He will understand when he sees the Real 555.

Cheers,
Burgo.

_________________
1st 3x3 solve Oct 2010 (Even though I lived through the 80s).
PB 3x3 55sec Jan 2011 (When I was a kid 1:30 was speedcubing so I'm stoked).
1st 3x3 Earth (nemesis) solve Jan 2011 My You Tube (Now has ALLCrazy 3X3 Planets with Reduction)


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 Post subject: Re: How to solve Calvin's Puzzle-Aleh & Evgeniy 3x3x5 Cuboid
PostPosted: Sat Aug 03, 2013 6:24 am 
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Burgo wrote:
...
Puzzlemad wrote:
Konrad,
Looking at your sequence on the 5x5 Pochman cube to me it looks like you have carried out the cuboid sequence to swap 2 pairs of opposite edges but left off the final U2 move.
Sorry for my typo. My sequence is
(Ll)2 (Ff)2 U2 l2 U2 (Ff)2 (Ll)2 U2. I wrote it twice and had forgotten the U2 the second time.
I do not know where the misunderstanding with Burgo does come from.
The first seven moves in the form (Ll)2 F2 U2 l2 U2 F2 (Ll)2 do a double swap of 5x5x5 wedges (wedges = outer edges). The final U2 puts those wedges back. A lot of other changes remain invisible on the X-Cube because
a) Many pieces do not exist
b) There are no Super Cuboid stickers.

I'll use more photos to clarify things below.
Puzzlemad wrote:
This means that in the 5x5 you have swapped the 2 centre edges and the 2 pairs of upper corners. This works for a standard cuboid but not for a super cuboid because of the effects on the front face. The front face of our puzzle in question is not "super" and so this is acceptable plus the corners on the puzzle are missing completely this makes your proposed sequence acceptable. However all of this does not remove the fact that it has obeyed the "law of the cube".
No, Konrad has transcribed the movement of the outer Pochman 555 onto the inner 333, which is quite different: this actually disguises the fundamental change that is happening, and it really had me going for quite a while to figure out what it was :) . He will understand when he sees the Real 555.

Cheers,
Burgo.
Hi Burgo, I guess Kevin was right and we two need to find out where the misunderstanding has come from. :wink: I'm not familiar with the Real 5x5x5. Can you provide the Gelatinbrain number, please? I remember that you wrote in a PM long ago that you have solved it on Gelatinbrain :)

1. Notation: I used (old) WCA notation for a 5x5x5. l is the inner layer below L etc.
2. My sequence is (Ll)2 F2 U2 l2 U2 F2 (Ll)2 U2 performed on a Super 5x5x5 with Pochmann stickers. I made real photos and have photoshoped the last two pictures in my last post, only.
3. My mapping of a 5x5x5 to a 5x5x3: I glue together the pieces of two opposite outer layers (U and B) in my photos with the inner layers u and b.
Mentally I can shrink down the double size cubies to the normal size of one cubie.
Agreed so far?

I show real photos below. I have not even removed the background as usual, just merged front view and back view into one picture.
Here we start
Image
I show the result of my sequence in two steps.
First after (Ll)2 F2 U2 l2 U2 F2 (Ll)2
Image
and now after the U2 (that was missing above, sorry again!)
Image

How do I map this result onto the X-Cube?
The next two pictures are photoshoped! :wink:
First, I cut off all pieces not existing on the X-Cube
Image
Now I show how pieces are glued together in U&u and B&b (Note that they travelled always together in the turns of my sequence.) by some filtering in Photoshop:

Image

Yesterday, I tried to do a nicer editing of the very same result.
First with Pochmann stickers and then with plain white stickers
Quote:
Now I cut off all cubies that don't exist on an X-Cube (OK, OK I didn't use a saw, just Photoshop :lol: ) and have applied the stickers to the normally hidden inner faces of the 5x5x5:
Image
We see that we have swapped several pieces on the white face including two +-centres (=edges on the inner 3x3x3) besides the swap of two babyface edges on the green U layer.

We cannot see this on an X-Cube, because we have plain stickers and not the Pochmann style.
Image

Please note that I described a double swap of pieces that look identically on a 5x5x5, but look different on a 5x5x3.
The whole thing works on the X-Cube, because so many pieces are cut off from the original 5x5x5.

Now Burgo and I need to find out about the misunderstanding and what my sequence produces on a Real 5x5x5.

EDIT: I have changed a picture above and corrected the arrows indicating the swapping of pieces.

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