Patterns

 Roark and I have been playing with Rubik's Cube patterns lately. Between the two of us, he is the master. What I would like is a place to show our pattern algorithms. Maybe we can find shorter algorithms for some of them. First we need to identify the notation.

T = Top around

R = Right around

L = Left around

B = Bottom around

M = Middle vertical layer around

E = Middle horizontal layer around

S = Middle vertical layer between Front and Back

(x) = the x pattern whatever x may be. 

lowercase means 90 degrees instead of 180 degrees

^ = up

v = down

< = left

> = right

Checkerboard: M E S

RTL RTL (or RTR LTL) Family

Solid front; right and top stripes front to back: RTL RTL or RTR LTL. RTL RTL can be expressed as RT LR TL. It is the same 6 moves expressed as 3 2-move sequences instead of 2 3-move sequences. The middle moves, LR, can also be done R first, or RL. Expressed in groups of 3 it is RTR LTL. What exactly does this move do? It swaps the top right with the bottom left and the top left with the bottom right. That is what makes the stripes.

Stripe top to bottom on front; stripe front to back on right top solid: RTL RT(LM)

Checkerboard front; right and top solid: REL (turn the cube so the top is on the right) REL Checkerboard front; right and top solid: RTL RTL ME or RTLB TLTL or RTLT BLTL

Solid front; right and top checkerboard: RTL RTL S

H Family

H front; others solid: TM TM or MT MT or BM BM. Or if I'm doing it on a 1x3x3 in which M is not an easy move to do: RTR LBL or RTL RBL or RLT RLB (which is really the most like MT MT). Of course another option is to do something like T (MR)R T (MR)R, but I would rather do one of the 6-move sequences. Maybe. 

More about the 1x3x3. Name the corners I, J, K, and L starting at the top left and going clockwise. RTR swaps I and K. So does LBL. So RTR LBL flips the top and bottom edges and swaps two corners then swaps them back. 

RTL moves K>L>I>J and flips edges on the right, top, and left. RBL moves the corners back, flips the edges on the right and left back, and flips the bottom edge, leaving the top and bottom edges flipped.

Lazy H front; right solid; top solid: RE RE (this is just TM TM from a different angle)

H front; right and top stripes front to back: REL

H front; H right; top checkerboard: (sv e< m^ e>) x 2

H front; right Dot; top Stripe front to back: e< M e>

Dot Family

6 Dots: m^ e< mv e>. In other words, UFDG with middle layers.

4 Dots: Dot front; dot right; top solid: M e< M e>

Dot front; right stripe front to back; top solid: RER. This is one twist short of Lazy H.

Cross Family

Cross front; right checkerboard; top stripe left to right: (H) E S

Cross front; right solid; top stripe front to back: RE LE. On a 1x3x3 think of it as an I<>L, J<>K Double Swap: RTB RTB 

Cross front; right horizontal stripe; top solid: Whole cube clock and RE LE

Fish Family

Fish front; right and top solid: RT RT RT

Fish front; top and right stripes front to back: RT RT LT

Arrows front; top stripe front to back; right solid: RT RT LT E

Arrows front; top solid; right stripe front to back: RT RT LT M

Patterns that aren't opposite colors patterns Family
(Start with Blue front Yellow up)

6 dots: Front to Right to Bottom and Back to Left to Top: m^ e< mv e>

Blue H front with white edges; Red H right with yellow edges; Yellow X top with blue and orange edges: e> sv e< m^

Blue H front with green edges; Red H right with orange edges Yellow X top with white edges: e> M e< S 

Blue X front with green vertical and red horizontal edges; Red X right with yellow vertical and green horizontal edges; Yellow X top with white edges front back and orange edges left right: m^ e> mv E sv M

Cool Stripes F, T, B, D; Crosses R and L: fv (UFDG)x3 f^ cubevv fv (UFDG)x3 f^ (Flip front and back edges on top and bottom by flipping 2 at a time on top). "Cool stripes" are 3 different colors. The outer stripes are opposite colors in this algorithm.

Cool Stripes R, L, T, D; Solid F and B: [Cool Stripes F, T, B, D; Crosses R and L] (L to F), E H. The outer stripes are opposite colors in this algorithm.

Cool Stripes on all 6 sides: [Cool Stripes R, L, T, D; Solid F and B] m^ R. The outer stripes are opposite colors in this algorithm.

Cool Stripes R, L, T, D; 8s on F and B: f^ R-handed (UFDG)x3 f^ (Flip top front and top back edges) F (L to F) RTLRTL. Adjacent stripes are opposite colors with this algorithm.

LINK to someone's Pretty Patterns Page.

F-Skewb FTO Adventures

I hadn't scrambled or solved the F-Skewb for years. A month ago the Czech kiddos were here and it got scrambled. When they left to go on their Idaho Family Reunion Adventure I figured I would solve it. Ha. It proved quite challenging. In fact I couldn't do it. I looked up my notes here in the blog and in my Solution Guide spreadsheet but it was all too vague. One thing did refer to the FTO so I thought if I would solve it, which I was confident that I could, it might help me remember the F-Skewb. Nope. I just ended up with 2 scrambled puzzles I couldn't solve instead of 1. Back to the notes. No help. So I forgot about them for a month and went back to the notes today starting with the FTO. Lo and behold, I solved it. 

Corners: Get 3 of one color. The other 3 are either solved or need an EPS to solve them.

Centers:

1. Get the white centers.
2. Solve the gray, blue, and red centers using go get it bring it home. Slice Face Slice' Face'. Make sure the whites are on the bottom back left or bottom back right so that white centers stay put. 
3. 3-cycle the green, orange, purple, and yellow centers home.

Edges: 3-cycle all the edges.

That's it! Easy peasy. Sorta. 

Now let's revisit my Solution Guide notes on how to solve the F-Skewb, or Dino Skewb.

1. White Edges
2. White Corners (Getting the corners now avoids nasty parity problems later)
3. Orient Yellow corners
4. Place middle layer edges each with an even number of turns (Corners may get twisted at this point. That is ok for now.)

In May 2020 in the blog I said, "This puzzle has 3 types of pieces. Experimenting with The Move and the FTO commutator brought it all back. Scramble time!"

And then:

Step 1: Simple twists solve the 4 little skew corners.

Step 2: Simple slices and The Move solve the 12 center pieces.

Step 3: The FTO commutator 3-cycles the ... uh ... edges(?) ... corners(?)

This looks much simpler than the notes in the Guide. Those notes don't even sound like me. Let's give this a go now that I remember how to do the FTO. 

It is finished. But the turning is so bad and it is so catchy that I don't ever want to scramble it again. Perhaps I should throw it away. Or lube the daylights out of it and see if it helps and if it doesn't then throw it away. Or at least attach a note to it explaining that it is not worth the effort.

Skewb Xtreme

When the kiddos were here this summer some puzzles got scrambled that I haven't solved for a long time, the Skewb Xtreme included. Today was the day to solve it. To begin I just solved it as if it were a Skewb. That is

1. 2 white corners opposite one another.
2. 2 skew yellow corners.
3. Permute the remaining corners all at once using the Move.
4. Twist the corners if necessary using something like Up Clock Down Replace Up Anti Down Goback.
5. 3-Cycle the Centers using (Up Forward Down Forward Up Goback Down Goback) x 2.

This was all well and good, but some of the Centers needed to flip and I couldn't remember my flipping algorithm. I tried looking things up in this blog and in the Solution Guides but didn't follow what I had said before. Sheesh. There was something about the Jing's Pyraminx that prompted me to dig it out and see if it helped. It did! It was scrambled so I solved it with the above steps. With everything in place the 4 edges needed to flip. It was obvious to me how to flip them. 

Up Back Down right-handed Up Forward Down left-handed (Replace the piece that that flipped with another that needed flipped) Up Back Down left-handed Up Forward Down right-handed (Put the second flipped piece back). Remember? After doing it with the Jing's Pyraminx it was an easy thing to do the same thing with the Skewb Xtreme to flip the Centers that needed to flip.

6. Flip Centers using the algorithm spelled out in the paragraph above.

And the Skewb Xtreme is solved. And all the Skewbs are solved. Happy day. 

Sierra Discovery Trail

 

This is a job for.............Super Floppy!

When the kiddos were here I ordered some puzzles one of which was a 3x3x1. I've had a floppy cube that I have no idea where it is now. I have a super floppy which when you have one edge isolated it will not turn. But now I have one which will. I used to think the floppy cube was unlike any other puzzle. But in the last couple days of fiddling it has occurred to me that it, especially the new one I got, is simply a middle layer of a 3x3 cube. I used to think it had a center, 4 edges, and 4 corners. But now I see that what I thought was the center is really like the core of the 3x3x3. And what I thought were edges I now see like centers of the 3x3x3. And what I thought were corners now I see like edges of a 3x3x3. I can play with it, scramble it, and solve it as if it is the layer between the front and back layers of the 3x3x3. You can do EPS with this thing! You can do Sune with this thing! It has become my latest favorite puzzle diversion. 

Spread the Love. The Puzzle Love that is.

This summer I had fun doing twisty puzzles with the Czech kiddos. Some of the puzzles even got to leave with them and travel around the world. The yellow Bump Cube and the Carbon Fiber 3x3x3 went with Annie. The Redi Cube and a Six Spot Cube went with Alex. A 2x2 Cube and the Rediminx went with David. Annie and Alex each mastered the ones they took along with them. David is great at the 2x2 using the 3-step method Solution Guide we made together. And we played a little with the Rediminx and I'm confident that he will be able to figure it out. Perhaps we can do some puzzling together in Google Meet.

Square-1 2022

 Updated in 2022

1. Back to Cube Shape

1. Star/28 or Star/1414 or 52/2214 or 52/2412 or 52/36 > 44/44 > 2T/2B > 2H/2H > Cube

2. Star/1414 > 52/Shield > Shield/Shield > 2T/2B > 2H/2H > Cube (Shield = 3212)

3. 2H/2T > RH/LH > 2H/2H > Cube (RH/LH = Top + Half)

2. Get all the white corners on top.

3. Corners First Algorithms that work with Square-1

1. 0 Pairs: R UiD R UDi R

2. 1 Pair: RURUi RURUi R with pair at bottom left

3. 2 Pairs: RUR UD RUR with pairs in front

4. 4 Pairs: RUR UD RUR U2D2 RUR UD RUR

5. 5 Pairs: (unpair on bottom back) R UiD R U2Di RUi RU RUi R

4. Edge Double Swap algorithm. u(=1) R U R ui(=-1) di R ui(=-2) d R ui(=-1) swaps UL with UB and DR with DB. To put it another way: (offset U) RUR (jiggle joggle) R (U back a corner) (little D) R (line up U)

5. To flip a middle layer piece (R U2) x 3

6. If one pair of edges need to swap at the end, there is a parity issue. Go to 44 44, swap 3 on top with 3 on bottom with R UD R (-1,-2) R (-2,4) R, backtrack to cube. Fix everything. 

The solution strategy in the old Solution Guide goes something like this.

1. Use the map to get it back to cube shape.

2. Get all the white corners on top.

3. Use Corners First algorithms for 1 pair and 2 pairs and even 0 pairs to solve the corners. Here is what the 2 pairs algorithm looks like in Square-1 notation. (0,-1) / (0,3) / (-2,-2) / (2,-1) / (0,1) swaps the front ones on top and the front ones on bottom. 

4. Solve Edges with this double swap algorithm. (1,0) / (3,0) / (-1,-1) / (-2,1) / (-1,0) swaps UL with UB, and DR with DB.

5. The above is in my Solution Guides Pre Fall 2013 spreadsheet. On June 27, 2015 I blogged "...today I set out to discover and document how to fix parity with a minimum of damage to the solve. Found it. When you make the swap of 3 pieces make sure you move the same number of yellows down that you move up. For example: / (3,3) / (–1,–2) / (–2,4) / backtrack"

 

Maple Leaf Skewb

 I decided to revisit an old puzzle and see if I could solve it. Grabbed the Maple Leaf Skewb. Instead of experimenting with it I just jumped right into a scramble. After fiddling around a teeny bit I decided to consult my notes. I found one brief entry that wasn't very helpful, but it pointed me in the right direction. Or maybe I am just not understanding what I said. Here's what I said in November 2020—

"The Maple Leaf Skewb took me the longest to figure out. I tried various things with varied success, but in the end came up with this strategy:

1. Move the central 3-sided parts to their centers.
2. Move the petals to their centers.
3. Solve the skewb.

You know the skewbish puzzles that have pieces that correspond to the squares of a skewb, only they need to be oriented by flipping sometimes? The algorithm is Up Back Down Switchhands Up Forward Down Replace Up Back Down Switchhands Up Forward Down Goback. When solving the pieces of the center squares I would sometimes want to flip the square. At first I would use the 14-move algorithm for flipping edges/centers of skewbish puzzles. After a while I realized that it wasn't necessary to do the whole thing and I just did half of it. 7 moves. Then I realized there was an easier way that only took 3 moves. Then I stumbled upon a way that is only 2 moves. Sweet. The 2 moves? Up Forward."

Steps 1 and 3 are pretty straightforward. Step 2... well, I ended up using a 3-cycle. (Up Around Down) (Over Around Back) (Up Around Down) (Over Around Back). 

Solved it again. See ya in another couple years. :)

Tangram Cube revisited

The F-Skewb caught my attention recently so I got it out and scrambled and solved it for the first time in a long time. I had to look up my strategy. It wasn't real easy to work with so I put it away and grabbed the Tangram Cube. The corners and long edges were not hard to solve, but the little edges and 6 little triangle centers stumped me, so I looked up my old posts from 2020 and 2017. Now I remember! Ha!

After solving it I wondered if I could figure out a quicker easier way to solve the last 6 little triangles. 

There is a double swap that is pretty easy. RLRL JW’ LRLR WJ’ Double Swaps top and left, and, front and bottom centers. 

(LJLJ’)x3 RLRL JW’ LRLR WJ’ 3-cycles bottom to right to left.

Here is the strategy I came up with in 2020:

1. Solve the two little corners. 1 twist max.
2. Solve the six big corners. Use Edge Flips, Up Replace Down, and The Move. 
3. Solve the three long edges, if necessary. If they are already permuted, but two need to flip, flip one, replace it with the other, flip it and move it back. If they are not yet permuted, flip-move-flip, in such a way that they end up in the correct places.
4. Permute the three little edges using The Move.
5. Orient the three little edges using (LAR)x2. This flips the edges at the top left and the back right. It also does a double swap of centers that are adjacent to said edges, so this could be used to solve some of the centers as you are orienting little edges.
6. Solve the remaining centers. (JAJ’A)x3 (WLW’L)x3 is a 3-cycle from Bottom to Back to Right. W’RW swaps Bottom and Right, so doing it before the 3-cycle let’s you go from Bottom to Right to Back.

Puzzle Adventures

The last few weeks I've been meeting up with Matthew and Cambria after school to help them learn how to solve 3x3x3 and 2x2x2 cubes. If they master the 2x2x2 and are up to the challenge, I want to help them learn how to solve it with their eyes closed. So I figured I better practice. 

I recently bought a new puzzle after watching the beginning of rline's tutorial. I didn't watch enough to learn how he does it. Just enough to want one! The Double Circle Cube. It was quite a challenge to solve, but I was able to work out commutators for all the little pieces and solve it. The algorithms are simple enough but repetitive so I sometimes lose track. Oh, and the setup moves can be really complex, so I have resorted to writing them down. At this point I want to try to figure out a way to build some of the edges at the beginning of the solve so I don't have to place as many individual pieces.

Crazy 2-face Bandaged Uranus

 After solving the 2-face bandaged Jupiter, rline shared that he loves 2-face bandaged Uranus. So I switched the Green from a 1 to a 0-face, and had a go.

At first I forgot that the edge between the 0 faces could be a problem. After becoming aware of the issue I solved all the green and white edges first. Then I used the white side to reduce edges. I kept the white/blue and white/green edges across from each other and put unreduced edges in the other spots on the white face to reduce them with 180° turns. That way I could easily solve the green/white edge later hopefully. After reducing all the edges I used the white face to reduce all the corners, making sure not to turn the green face. I put the other two white edges home relative to the blue and green ones. The blue and green edges did not line up with the blue and green centers yet. So I solved the white corners so I could turn the bottom so all the edges lined up with their centers. The good news is that getting it this far was fun, not frustrating. :) I ended up solving edges first, then permuting corners, then twisting corners. Having two 0-faces and a pink bandage piece certainly makes this a challenge.

Crazy 2-face Bandaged Jupiter

 rline came up with another Jupiter challenge. Swap out the edge bandaged piece for a center-edge bandaged piece, and add a 2-face. Strategy:

1. Reduce Edges (white up)

2. Reduce Corners (white down; pink up)

• Lots at a time, like the edges.
• If Up Replace Down doesn't put it oriented correctly, use it anyway then turn the pink out of the way and twist the corner.

3. Solve (blue down)

• First two layers minus RWB corner.
• Green edges then remaining corners.
• F (up forward down go back) F' to flip edges if necessary.

Crazy Jupiter Bandaged

 rline is back! Back into puzzling. Yesterday I sent him a box of puzzle pieces. A bunch of pieces from the kit Burgo sent me years ago that I have never done anything with. rline will get much more use out of them than I will. Also sent were a bunch of Crazy Tetrahedron pieces. Enough to build every Crazy Tetrahedron Planet and then some. 

He encouraged me to keep the pink pieces of the B4 kit so I could make some Crazy Bandaged Puzzles. His first challenge was based on Jupiter. The white face is a 0-face. All others are 1-faces. Plus there is a B4 Pink bandaged piece.

It was quite frustrating at first, and just about did me in. I was ready to take it apart, put the pinks away, and go back to something easier. Like a simple circle cube. That is all 0-faces. But I'm glad I persevered. I finally solved it, but every solve took hours to do. Then rline told me he can solve it in 20 minutes. What?!? After he posted a video I watched the master at work. Very methodical. Very nice. Very inspiring. I've been able to work out a strategy myself now that I can execute in under an hour. The only time I timed it it was 29 minutes, and since I was hurrying I messed up a few times which cost me some minutes. Here is my strategy—

1. Pink Block (white down)

3 pink edges on bottom.

Get pink corners just like white corners on a 3x3x3.

2. Reduce Edges (white up; start with pink down

Move 4 edges to the top so that a 90° twist reduces 3 of them. Twist. Repeat.

3. Reduce Corners (white & pink down; pink in back)

Unreduced corners in front with the inner of one matching the outer of the other. To get them there, twist the top and use one of the following moves (these are just the same moves that are used to solve the white corners of a normal 3x3x3)—

• Up Forward Down
• Up Replace Down
• (Up Forward Down Goback) (Up Forward Down)
• (Up Around Down Goback) (Up Forward Down)
• If the pink is blocking a move twist it up to the back of the side you want to twist up.

Turn the bottom to reduce a corner. Replace the corner with an inner that matches the outer than will come forward when you turn the bottom back.

If an outer and inner that belong together are on two sides of the same corner, get that color on the other side of the cube. Turn the bottom, twist the corner, turn the bottom back.

4. 2x2x3 Block (white down)

The goal is to solve the pink, blue/red edge, blue/orange edge, red/white edge, and orange/white edge. It doesn't matter what order they are done in.

Use turns of the yellow, blue and orange faces to solve the orange/white. Yellow, blue and red faces to solve the red/white. 

To solve the red/blue edge—

1. Turn the blue then red to move the pink under the red center.
2. Turn the top to put the blue of the blue/red edge over the blue center.
3. Turn red then blue to move the pink back under the blue center.

5. Orient Edges 

Count the bad edges. Bad edges are edges that need to flip. An edge needs to flip if, holding the 2x2x3 block on the bottom left, you could not solve the edge using only turns of the top and right layers. 

If there are an odd number of bad edges, the pink edge needs to flip. With white down and blue on the right, and a bad edge at the top front do R2 U2 L F U2 Fi U R2. Doing this sequence maintains the 2x2x3 block and flips one of the bad edges.

If there are still bad edges to flip put blue down and yellow in front. Bad edges at the top/back and left/front can be flipped with Di (Up Forward Down) D.

6. Solve (blue down)

1. Finish the bottom two layers.
2. Permute edges. up forward down forward up around down. 
3. Permute corners if necessary by double swapping with setup moves and (Up Forward Down Goback) x 3. 
4. Orient corners. Right then Left up forward down forward up around down.

Using this strategy I solved it in under 20 minutes. It was a nice smooth solve with no mess-ups. 

Trip Memories — Wednesday June 16, 2021 — Capitol Reef; Moab

 After a full buffet breakfast at Ruby's Inn we set out for Capitol Reef. 

And to think, I thought Butch Cassidy was make-believe.

On our way to Capitol Reef we saw some bison.

The Castle

Marae saw a marmot maybe. I only saw the sign.

Trip Memories — Tuesday June 15, 2021 — Virgin River Gorge; Zion; Bryce

Tuesday morning we headed out from Mesquite, NV on our way to Bryce Canyon City via Zion National Park in Utah. The route began with a northeast section of Interstate 15 through the northwest corner of Arizona. I wasn't expecting any scenery so did not take any pictures, but now wish I had. It was an amazing stretch of highway, about 30 miles long through the Virgin River Gorge. There are Youtube videos people have posted, and a Wikipedia article about it. I wish I had known more about it before the trip.

Our Utah National Park adventure started with Zion National Park. 

As you can see we chose to do a drive-through of Zion. The plan had been to stop at vista points, but they were too crowded, so we just kept going. It was still and enjoyable drive with plenty of photo ops from the car. We did stop once and got a selfie just before leaving the Park.

The hour, give or take, drive from Zion to Bryce Canyon had a lot of wide open spaces. Google Photos' map says I took this around Hatch, UT. And the following photo in Dixie National Forest. Forest???

Bryce Canyon was our favorite Utah Park. There were lots of places to stop with short flat walks to vista points, and amazing scenery. But I'm getting ahead of myself. After turning off 89 onto 12 and going a couple miles, we came to a spot where we could get out and take pictures.

We stayed at Best Western Plus Ruby's Inn in Bryce Canyon City. It was too early to check in when we got there just after noon, so we drove into the Park.

First stop, Rainbow Point, which is at the end of the road. I guess the wildlife here is not all that wild. At least not this little critter.

Here is a wide angle shot of the view, followed by various other zooms and angles taken at this stop.

Next stop...

On to...

Followed by...

The next stop was dubbed Natural Bridge, but according to the interpretive sign posted at Natural Bridge, it isn't a bridge, but rather an arch. Whatever. It is cool looking to me whatever they want to call it.

Another short drive and we came to...

As far as I know we did not actually see Sheep Creek Swamp Canyon. Here's the deal. If you really want to see everything there is to see in the National Parks of Utah you have to hike. We were content to see what we could see from the car, or in the case of Bryce Canyon, from vista points you could drive to.

Our last stop in Bryce Canyon was...