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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Wed Jan 29, 2014 5:40 pm 
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I made this bandaged cube with the CT kit, but I haven't found it anywhere. The kit arrived today and I've solved this puzzle twice so far.
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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Sun Feb 09, 2014 2:24 pm 
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Anyone knows if CubeTwist is ever gonna release a 4x4x4 or 5x5x5 bandaged kit? Would love to buy one of those. ;)

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Fri Feb 21, 2014 11:10 am 
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Hi all! I just wanted to express my thanks to all the creators of all these wonderful bandaging patterns. I currently have $0 in my puzzle fund, so birthdays and bandaging are the only way I'm getting new puzzles at the moment. I love having hundreds of new puzzles at my disposal.

I have created a Google doc of all the named patterns I could find. I figure it might help someone in the future, rather than scrolling through pages after page. The document is editable, so if anyone has something to contribute, feel free!

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Fri Feb 21, 2014 2:24 pm 
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themathkid wrote:
I have created a Google doc of all the named patterns I could find. I figure it might help someone in the future, rather than scrolling through pages after page. The document is editable, so if anyone has something to contribute, feel free!

Good idea to make a Google Doc. I also made a word-doc with all the Bandaged Cubes I could find (83 bandaged 3x3x3 cubes total now). Following our idea, I made a Google Doc from the word-doc, so everyone can enjoy all 83 ones. (PS: The ones with "(Own)" in front of them are my own designs.)

Greetz,
Quuador

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Fri Feb 21, 2014 2:59 pm 
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Awesome guys! One of these days I need to get back to doing some of these bandaged puzzles, it's been quite a while.

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Fri Feb 21, 2014 7:12 pm 
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Quuador wrote:
Good idea to make a Google Doc. I also made a word-doc with all the Bandaged Cubes I could find (83 bandaged 3x3x3 cubes total now). Following our idea, I made a Google Doc from the word-doc, so everyone can enjoy all 83 ones. (PS: The ones with "(Own)" in front of them are my own designs.)

Greetz,
Quuador


Wow. Yours is so much better! Much cleaner and more consistent. I really appreciate the work you've put into this.

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Crazy2Face & Crazy3Face Puzzle Spreadsheet
Named 3x3x3 Bandaging Patterns


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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Fri Feb 21, 2014 9:26 pm 
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Thanks too for the Google Doc of all these puzzles. Here is a variation on Burgo's Double Block Clock:

Triple Block Clock
Attachment:
Triple Block Clock.png
Triple Block Clock.png [ 61.25 KiB | Viewed 652 times ]

This is the Double Block Clock with an additional block to prevent the blue and red faces from turning. Spoiler alert: a solution method follows, with algos hidden in invisible ink.
[x : y] = x y x' (conjugate)
[x, y] = x y x' y' (commutator)
Orange = F, Green = U
A = [U2 L : F]
C = [U, R]
G = [R2 U R'] : [U L F L' U2, R']
J = A' C' A' C2

1. Solve the 2x2x2 block around the yellow-red-blue corner. Pair the free edge and corner intuitively, then orient the pair correctly to join it with the yellow bandaged piece using the green face, and complete the block. From this point I suggest orienting the puzzle with orange = F and green = U.

2. Solve the edges. Use algos A and C (including repetitions and inversions) to solve the orange/blue edge. If the other three edges are in an even perm and none are flipped, they are either solved or can be solved with C or C'. Here are the other possible cases:
Even perm, flipped edges at FR and UR: G C' A2, then C or C' if necessary.
Odd perm, flipped edges at FR and UR: G' C A, then C or C' if necessary.
Odd perm, no flipped edges: A' C' G2 C' A2, then C or C' if necessary.

3. Permute the corners. Either they are in their correct positions or C3 permutes them.

4. Orient the corners. J twists UBR+ UBL-; this and its inverse can be used with fairly simple setup sequences to solve all possible orientations of the corners.


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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Sat Feb 22, 2014 5:29 am 
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Thanks for that Google doc! That's a much better resource than what I have managed to cobble together myself!

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Sun Feb 23, 2014 4:08 pm 
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Bandaged 3++

In between Bandaged 3+ and 3 Quads 3 Stripes lies what I call Bandaged 3++. I rate this one as very difficult.
Attachment:
Bandaged 3++.png
Bandaged 3++.png [ 58.62 KiB | Viewed 599 times ]
Spoiler alert: a solution method follows, with algos hidden in invisible ink.
Yellow = F, Blue = U, m = mirrored/reflected
A = B2 R' B R' U' B L U L F2 L' F2 L'
C = B' R U' B U B' R' B' R B2
Cm = L F' U L' U' L F L F' L2
G = [L F' L' U L U' F L'] [B' R U' B U B' R' B]
H = L F2 L F L' F L' F L F2 L2
Hm = B' R2 B' R' B R' B' R2 B2

1. Solve the quads and stripes. Intuitive; I find it easiest to leave the middle (white/red/green) stripe to last.

2. Permute the three unbandaged corners. Algo A does the cycle UBL->UFR->DFR->UBL and algo C swaps UBL<->UFR.

3. Align the corner orientations. After this step we want to have the three unbandaged corners with the same orientation. A third of the time this step can be skipped, otherwise use algo G, which twists UFR+ and DFR-, or its inverse.

4. Solve the five unbandaged edges. Algo H cycles FU->FR->FD->FU and its mirror Hm cycles RU->RF->RD->RU. Algo C twice flips FR and FD, and algo Cm twice flips RF and RD.

5. Orient the corners. Algo C four times twists the corners clockwise.


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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Sun Feb 23, 2014 8:16 pm 
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Hi Julian,
I solved your Tripple Block Clock, I used the Yellow face as U and did the backbone of the solve with Sunes. I haven't ironed out a complete method yet, but it makes for an interesting solve. I'll give the Bandaged 3++ a go later too. Thanks for the puzzles.
Burgo.

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Wed Feb 26, 2014 6:11 pm 
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Burgo, it's good to see you posting again in this thread. I was worried I had missed the party by a year or two! :)

I have enjoyed solving various puzzles in the list: Bandaged 3, Bandaged 3+, Bandaged Fortress, Pendulum, Big Block Clock, Bandaged Clock Jupiter, Alcatraz, Double Block Clock, and 3 Quads 3 Stripes so far. I particularly like Alcatraz and Double Block Clock. Thank you (and other contributors) for creating so many fun puzzles. I will gradually work my way through all the ones shown in this thread.

As Double Block Clock and Triple Block Clock both have only one permutation or orientation restriction beyond a regular Rubik's Cube - only one sixth of all corner perms are possible, like Big Block Clock - the group of states of Double Block Clock with a solved red-blue edge and Triple Block Clock are identical. In other words, if one has a solution for Triple Block Clock, one also has a solution for Double Block Clock: solve the red-blue edge, then solve the Triple Block Clock. I found 75% of edge cases very difficult to resolve, so I'll be interested to see your solution.


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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Thu Feb 27, 2014 5:45 am 
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Hi Julian,

Yes, these puzzles have quite a big permutation restriction due to the 3x2x1 block. The restriction is that once the F2L corners are placed, the LL corners are already permuted. It’s the same restriction we see on the `1x1x3 Block`.

The tricky part about `seeing this` in the `Double Block Clock` and `Triple Block Clock` is that the clock hand disguises it a little (because one LL edge is permanently placed). You can run some Sunes across the LL to permute the edges, and once the edges are solved, there may be an X pattern of corners.. which is just 3x Sunes away from correctly permuted (6x cycles of Sune bring it back to a full loop).

I Solved the bandaged blocks and the Orange Blue edge first (and orientated the other 5 edges at the same time). An example of how to reorientate edges is:
[Orange F, Yellow U] (reorient UL + UR): L2 D F D’ L’ (U) L D F’ D’ L2

[Red F, Yellow U (from now on)] I then solved the Red /Green F2L block. And permuted the LL with Sunes.
Orientation of LL Corners (examples):

{A} 4[UBL-CW UBR-CCW UFR-CCW UFL-CW]: U (U’ R U R’)x3 U (U’ R U R’)x3 U2 (R U R’ U’)x3 (Sune)x3

{B} 3[UBL-CCW UBR-0 UFR-CCW UFL-CCW]: U2 R U’ R’ U’ R U2 (Sune)x2 U2 R U’ R’ U’ (R U2 R’ U2)
3[UBL-CCW UBR-CCW UFR-CCW UFL-0]: (Sune) {B} (Sune Rev)

{C} 3[UBL-0 UBR-CW UFR-CW UFL-CW]: U (R U' R') U2 (R U' R') U' (Sune) U (R U' R') U2 (R U' R') U' (Sune)
3[UBL-CW UBR-CW UFR-0 UFL-CW]: Sune U (R U' R') U2 (R U' R') U' (Sune) U (R U' R') U2 (R U' R') U'

{D} 2[UBL-0 UBR-CW UFR-0 UFL-CCW]: (R U R’ U’)x3 (Sune Rev) U R U’ R’ U2 R U’ R’ U’ (Sune)x2
2[UBL-0 UBR-CCW UFR-CW UFL-0]: (R U2 R’ U2) {D} (U2 R U2 R’)

Some combinations of these kinds of things will orientate the LL corners.

I think we’re both seeing the puzzle quite differently, and it seems that you might have a much more user friendly way to do the Corner Orientations.

EDIT: I just solved the Corner Orientations with your method, nice. The expanded notation for Julian's orientation sequence is:
[Orange F, Green U] Orientates (UBL + UBR): (U2 L F' L' U2) (R U R' U') (U2 L F' L' U2) (U R U' R')x2 and the sequence can be performed with the clock in either RB or RD positions.

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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)


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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Sun Mar 02, 2014 12:30 pm 
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Just wanted to share that I have solved the Bicube and Bandaged 3++ this weekend with my own methods. I can share my method if anyone is interested in either. The Bicube was very challenging. Lots of trial and error to find shape-preserving sequences and then a lot of pen-and-paper work to build useful 3-cycles. The Bandaged 3++ is longer but not much more difficult than 3 Quads, 3 Stripes, though the "2 bars swapped" / center orientation parity seems to happen more often and is very annoying.

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Sun Mar 09, 2014 7:58 am 
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@Burgo: Now that I've seen your way of flipping edges for the Triple Block Clock, I can see how I was making life more difficult for myself! :)

@Seth: It would be interesting to see your Bandaged 3++ solution, thanks. (I solve the stripes first, which avoids an odd perm of them later.) I am about to post another Bicube-related puzzle that you may also enjoy...


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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Sun Mar 09, 2014 8:36 am 
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Morse-X
Attachment:
Morse-X.png
Morse-X.png [ 48.69 KiB | Viewed 327 times ]
This one is another unbandaging of the Bicube. I call it Morse-X because we can see a pattern like Morse code for the letter X (dash-dot-dot-dash) on the F, U and R faces. All the stripes can move around all the faces. It can be difficult to get the puzzle back into shape, and of course there are extra edges to solve. I rate this as very difficult. My solution is in invisible ink below:

1. Get the puzzle back into shape. Let's name the stripe positions S1 to S6, going clockwise around the UFR corner in the diagram from S1 = white/green/orange. It is fairly easy to place stripes at S1, S3 and S5, and then not too difficult to place two of the others. If you then rotate the puzzle so that S4 is the last one to be placed, use the following routines, where the edges listed are the current position of the edge of the last stripe, which needs to move to DR:

BL: U' B' R' U
LD: R' F D F' R' F D' F' R
DB: U F R' F' U' R B R'
BD: F D' R F' R' F D F'
RB: R' F' U L' U' F U' R B' R' U

2. Solve the edges in between the stripes. The following routines move the named free edge to RB; rotate the puzzle as necessary. [x : y] = x y x'.

DB: [F2 D R : F2]
BD: [F R' D' F' : R2]
LB: [R' F D2 R' U' B2 U D' : R2]
BL: [U L F' D' F U' F D : R2]
DL: [U F' D F' D : R2]
LD: [R' F D2 B : R2]

3. Reduce the puzzle to the last stage of solving a Bandage Cube (Only the first algo of the six listed above is needed in combination with the following to solve the puzzle, but I give all six because they make for a more efficient solve.)

A = [F2 D2 R' B' R : D2]
C = [R2 B2 U' B : L2]

A swaps DB with LD
C swaps DB with DL

A C flips DB and DL
[A C]x2 twists the free corners URF+ DLB-

Now check the stripes. If they are in an odd permutation (an odd number of swaps is needed to solve them), do:

[F R' D2: F] R' D' F' R followed by C.

4. Solve the last stage of the Bandage Cube


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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Mon Mar 10, 2014 10:07 pm 
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Julian wrote:
@Seth: It would be interesting to see your Bandaged 3++ solution, thanks. (I solve the stripes first, which avoids an odd perm of them later.) I am about to post another Bicube-related puzzle that you may also enjoy...


I haven't forgotten about this. I just need to make some pictures and clean up my notes a bit. I'll try to have it up in the next 48 hours.

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 Post subject: Re: Solving the Bandaged 3x3x3
PostPosted: Fri Mar 28, 2014 1:03 pm 
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Julian wrote:
@Seth: It would be interesting to see your Bandaged 3++ solution, thanks. (I solve the stripes first, which avoids an odd perm of them later.) I am about to post another Bicube-related puzzle that you may also enjoy...


Ok. I admit I forgot! But at least I eventually got around to it, right? I'm sure it's not an efficient method, but here goes:

Attachment:
Bandaged 3++ Edges.png
Bandaged 3++ Edges.png [ 81.19 KiB | Viewed 148 times ]


I always hold the puzzle with the three stripes at FR, FD, and RD [note: NOT like the picture!]. For the beginning phase, we will have red at F and white at R [so that the "unbandaged square" is at D]. After that square is reduced, we will have a 3 Quads / 3 Stripes. Let T be a 120-degree rotation of the puzzle about the ULB / DFR corners [such that the F face becomes R and R becomes D]. Using this allows us to almost exclusively use the F, R, and U faces for turning and makes everything easier to remember. X and Y are simple 2-move setups, but are used so often that I gave them their own letters. This also makes things easier to remember.

Sequences Used:
X = F'R
X' = R'F
Y = R'F
Y' = FR'

K = (XUX') (DFD2F'D') (XU'X') [Used for positioning D-face edges]
K Mirror = (YU'Y') (D'R'D2RD) (YUY')

M = (XUX') T (XUX') T' (YUY') T (YUY') T' [Used for orienting corners]
N = (XUX') T (XUY') T (XUX') T' (XU'X') T' [Used for cycling 2x1 bars CW about the DFR corner]
S = (XUX') T (YU2Y') T' (XU'X') [Swaps LB / UB edges + FD / FR bars]
T = 120-degree CW rotation of the puzzle about the DFR corner [F --> R, R--> D]
W = (XUY') T (XUY')(XU'X') T' [Used for orienting UL and UB edges]
Parity Fix = WTWT'WS [Swaps FD and FR bars]


1. Restore to the "solved" shape intuitively.
2. Correctly position the DFL corner.

- If it is at DFR, do S (FDF') TST' (FDF')
- If it is at UFL, do (FDF') S (FD'F)

3. Correctly orient the DFL corner.

- If it needs a CCW twist, do (FDF') (ST'ST) (FD'F')
- If it needs a CW twist, do (FDF') (STST') (FD'F)

4. Positions edges #4 and #5. Use combinations of T and S to move edge #4 into position #3. Check the orientation. The D color should show on the B face. If it doesn't, use WTS to flip it. Now use to K to swap (34), moving edge #4 correctly into position, correctly oriented. Now position edge #5 at position #1. The D color should show on the L face. If it doesn't, use WTS to flip it. Now use K mirror to swap (15), moving #5 correctly into position, correctly oriented.

NOTE: The puzzle is now a reduced 3 Quads / 3 Stripes. The rest is my solution for that puzzle. There are no reduction parities. Edges #4 and #5 will not be referenced again. A T or T' rotation of the puzzle is now ok - we no longer need to keep edges #4 and #5 on the D face. We do still need the bars at FD, FR, and RD, though [squares on F, R and D].

5. Position and orient remaining edges. Use S to swap edges LB and UB. You should need to do this at most twice to position all three edges. If edges are incorrectly oriented, use WTS to flip edges UL and UB.

6. Check the stripes / bars. If they need a 3-cycle, do N to cycle the CW or N' to cycle CCW. If a single swap is needed instead, do WTWT'WS to swap the FD and FR bars.

7. Orient the remaining two corners.

- If DFR needs a CCW twist, do M [STST']
- If DFR needs a CW twist, do [TST'S] M'

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