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.

New Ideas For The Tangram Cube

This time when I got to the long edges it occurred to me that to flip two of them it would be an easy thing to flip one of them, move the other to the same edge, flip it, then move the slice wherever it needs to go. If I got good at it I could even do it before moving the slice home in the first place, so that at most to solve the long edges it would take a max of 4 moves if they are permuted already, but if they are not then it should only take 3 moves. Namely flip the one that is not home, move the other home, flip it. See? If you don’t get it, here is an example:

Say the blue orange and the green yellow need to flip, and the blue orange is where the green yellow edge needs to be. Flip the blue orange, replace with the green yellow, flip the green yellow. That’s it. Orienting and permuting all at once.

The other new idea is to solve some of the centers while you are orienting little edges, if possible.

New Improved Strategy

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.

Tangram Cube

Instead of waiting years to solve my puzzles like I did before, I want to solve different ones on a semi-regular basis. Some of the puzzles are not so appealing and fun so will continue to just sit in the cabinet and look pretty. But some are more fun so I hope to get them out more.

As I was solving the Tangram Cube today it got down to this interesting 3-cycle.

The setup move turned out to be L W, so the "algorithm" is

L W 3-cycle W' L

where the 3-cycle is the one I documented a couple days ago.

L R W 3-cycle W' R L

would cycle them anti-clockwise.

Tangram Cube Fun

In August 2017 I bought a twisty puzzle—the Tangram Cube. I made several posts telling about solving it. The solution guide I presented. Recently, after a break from twisty puzzles for months, I started solving the puzzles in the case that were scrambled. Eventually I came across the Tangram Cube. I didn't even remember its name, let alone how to solve it. But I finally found my notes from 2017 in this blog, and was able to solve it. I've looked for a better way, a way in which I could easily solve the triangles (centers) near the beginning, and then use pure 3-cycles to solve other pieces, but I couldn't come up with anything. So here I present my current solution for the Tangram Cube.

Step 1. Solve the two little corners using at most one simple twist of W.

Step 2. Solve the six big corners 1 or more at a time by twisting edges or using Up Replace Down to get as many of them as possible then The Move to finish up. Use one of the Little Corners and one of the Edge turns with The Move.

Step 3. Solve the 3 long edges by moving the slice so they are in the correct spots, then if necessary flip two of them. Slide one to A, flip it, slide the other to A, flip it, slide if necessary. For example: K A K' A flips L and A. K A K A K flips L and R. Or you could use L or R as the flip spot and always only use 4 moves. If you need a pure flipper use (K A K' A) x 3 to flip L and A.

Step 4. Permute the 3 little edges using The Move with two Edges. (J A J' R) x 2 is a pure 3-cycle K1 to DE to YP.

Step 5. Orient the 3 little edges. (L A R) x 2 flips DE and YP. (J A J' R) x 2 (A K A K') x 2 is a pure flipper of K1 and YP.

Step 6. Solve the centers 1 or more at a time using (J A J' A) x 3 (W L W' L) x 3 which cycles Bottom > Back > Right. The setup move W' R W swaps the centers on the right and back so the cycle is reversed.

(J A J' A) x 3 is a 5-cycle. Right to Front to Left to Top to Back. 

If the 3-cycle is only going to solve one piece why not solve one piece using the shorter 5-cycle instead?

Now that I have re-figured out the puzzle, it is time to have some fun with it for a while before moving on to other scrambled puzzles in the cabinet. :)

2 Weeks???

Has it been that long since I did an Eyes Closed Solve on my first try? Yesterday I had another fail on the first try. This morning I got it right.

D' L F U L' F D R F D' F' U R' B' R' F' R D' B' R2
R1
PH
I A
4S DF
O
Pass	4
Chocolate	Vats
Gary	2	Doughnut	King

I'm thinking about going back to using only the F Perm on the corners and M2 as much as possible on the edges. But on this last solve look how much jumping back and forth there was on the edges. Maybe I should go back to using only the F Perm for awhile until I am good at it again. I dunno.

Well, I tried another solve and again messed up on the first try. On the second try I just did the corners then checked, and checked several times through the edges. No messups, but lots of looking at it to make sure I hadn't messed up. Sheesh.

D2 F L F U' B R' U2 F2 U' F U2 L D L2 B R F L' U' L U R D' R'
O K
He	Does	Promote	Compassion
2	Forgive	4	Jesus
U 2
VK OI	1	B4P

I have put the Tangram Cube away. And until I get confirmation that Josiah still wants to learn the Mirror Blocks, I am not solving it like I was every day. I am determined to get back to being able to solve the cube Eyes Closed on the first try consistently. 

Plus I want to start learning OLL for the 2x2x2.

It is a little later in the day. I finally solved one first try start to finish eyes closed! It was less to remember and twist though as three of the top corners only needed to be twisted. Here is the scramble:
L F' L B' L' F' R F' L U R2 B2 L2 D' L' U' L D F' U2 L D2 B' D L

Another ECS Fail and Another Tangram Cube Pattern and Twisting Corners

First the bad news. On my first attempt at an ECS today I ended up with the back two layers solved and the front layer scrambled somewhat. I think what happened from the looks of it, and what was supposed to happen, is that in the M2 stage somewhere I forgot to F' once.

So now I've entered it in the spreadsheet and will give it another try.

U2 L2 U F2 D' R2 B2 D F' U R D L' B R' B2 D F2 R U B' R2 F U' B2
cycle 3UF
Christ	Vas	4	Our	ESCape
Yes!	Rejoice!	Praise!
Flip 1 & 3
1JG	ABA
Whites on bottom back

August 8, 2017
I gave it that nother try this morning first thing. Weird thing. When I opened my eyes it was all solved except one layer was 90° out. No idea.

Ha! I did it again with the same result. Only this time I figured out where I messed up. So obvious! On the last A I failed to put A back at the end by doing U.

By the way, let's talk about twisting corners. I used to for a long time twist two corners with RU'R' F'U'F D F'UF RUR' D'. And for awhile I used The Move x 6 with D's here and there. Actually if 3 corners need to twist this is probably my favorite way. Then with Roark I used The Move x 2 F The Unmove x 2 F'. But now I am using a method that I've known about for a long time but never used much. RUR'URU2R' L'U'LU'L'U2L.

Practice Practice Practice

Just did an eyes closed solve. I got confused the first time through and forgot at least one of the steps. It was a mess when I opened my eyes. Tried again, writing it out this time in the spreadsheet. Well, I just wrote the letters, even though I had sentences for part of it. During the solve my mind wandered some and I thought maybe I had skipped something but when I opened my eyes it was all solved. Phew.

The Tangram Cube is still fun and has my interest. I try to solve it once a day at least.

The Mirror Blocks Cube lessons with Josiah started last Monday. We got through the intro and the first step in solving it. I should solve it at least once a day too. I got some stickers for mine and am going to get a new one and more stickers. For now my old one is naked so I don't solve it by color, just by shape. That's OK, since that is where I need the most practice anyway.

I also gave the Lidbeck family a bunch of my puzzles. Skewb, Square-1, Super Square-1, Snakes, Magic, Pyraminx, the Tower thingy with all the shades of different colors of balls, and maybe more.

Tangram Cube Pattern

I recently got a Tangram Cube and had fun figuring it out. Once when I was just scrambling it I noticed a pattern developing. With a little effort I was able to fill in a few spots to make this.

Tangram Solution Strategy

On a solve recently I forgot to start with the little corners and instead started by solving the big corners to the little corners. No problem. When finished with the big corners one twist still solved the little corners. I like this because it makes for an easy to remember sequence of pieces to solve. Solve them by size starting with the largest!

Step 1 Solve the six big corners 1 or more at a time by twisting edges or using Up Replace Down to get as many of them as possible then The Move to finish up. Use one of the Little Corners and one of the Edge turns with The Move.

Step 2 Solve the two little corners using at most one simple twist of W. (It is now 5/3/2020 and I am not seeing how this can work. If the 6 big corners were solved in step 1 and then you do W, wouldn't that unsolve half the big corners that were solved in step 1?)

Step 3 Solve the three long edges by moving the slice so they are in the correct spots, then if necessary flip two of them. K A K A K flips L and R. You could flip L and A by moving them to R and flipping them there. Or R and A by moving them to L and flipping them there.

Step 4 Permute the three little edges using The Move with two Edges.

Step 5 Orient the three little edges. L R L R L A L A flips K1 and YP.

Step 6 Solve the six centers 1 or more at a time using (J A J' A) x 3 (W L W' L) x 3 which cycles Bottom > Back > Right. The setup move W' R W swaps the centers on the right and back so the cycle is reversed.

I'm still in that stage where I am learning new things every few solves. Today I started doing the 3 cycle of centers. The way I do it is by doing two 5 cycles. The second one puts two of the pieces back and results in a 3 cycle. So if you only need a 3 cycle you have to do the two 5 cycles. But what if you need a 5 cycle? Today that was the situation. I started with the first 5 cycle and before I started the second one noticed that after one 5 cycle all I needed was a 3 cycle. Get it? So in Step 6 if you need a 5 cycle think about this.

(J A J' A) x 3 cycles R>F>L>U>B. Right, Front, Left, Up, Back.

Tangram Cube Solution Quandary

Before getting to the Tangram Cube a note about Eyes Closed Solving. I tried today and the first attempt I was a little off but thought I knew the problem, so I tried again on another cube that had the same scramble. Ended up even worse. Well, I put the same scramble on the two cubes so I could try again. Only one problem. The same scramble had different results. In other words, today I couldn't even scramble a cube accurately! (August 29, 2017. First thing this morning I got up, reviewed the puzzle a minute, closed my eyes, and solved it successfully. Yes!)

Now to the Tangram Cube! So in trying to do the solve again without notes today I discovered some new algorithms. For example, Step 5. Orient the 3 little edges. (J A J' R) x 2 A L A L flips K1 and YP. This is a simpler algorithm than the first one I came up with. I have replaced the former one in my solution post of a couple days ago. (August 30, 2017. Found an even better way today to flip K1 and YP! L R L R L A L A.)

Then I was just experimenting a little and found another better way to cycle 3 centers. I say better because it just uses The Move x 3 then another The Move x 3. So it only uses 24 moves instead of 28. But I'm not sure I quite have it figured out. And if I want to cycle backwards do I want to use 48 moves or do I want to learn the backwards cycle? Neither! I found a setup move that let's me cycle backwards. So here is what I have ended up with. I will revise the Solution post accordingly.

(J A J' A) x 3 (W L W' L) x 3 cycles Bottom > Back > Right
The setup move W' R W swaps the centers on the right and back so the cycle is reversed.

Tangram Cube Solution Plan

The way I see it everything is built around the two little corners so

Step 1. Solve the two little corners using at most one simple twist of W.

In order to establish the colors clearly I thought I would next solve the big corners. All was going well until it ended up that I needed to swap green and orange! No problem. Just twist one of the edges and it unsolved one corner and makes a 3-cycle needed.

In case someone stumbles upon this page and wonders what The Move is, you may recognize the term Edge Piece Series. Same thing. You twist a layer. Twist another layer that intersects the first layer. Twist the first layer back where it started. Twist the second layer back where it started. So it is a 4 twist sequence that 3-cycles something. It can be used one way or another in solving, as far as I know, every twisty puzzle out there. Well worth being familiar with. When I taught my grandson how to solve the Rubik's Cube I called it Al-Bob-Charlie. Move Al to Bob. Move Charlie to Al. Undo the first move. Undo the second move. He could solve all the edges and 3 of the corners using Al-Bob-Charlie and Up-Replace-Down.

Step 2. Solve the six big colors 1 or more at a time by twisting edges or using Up Replace Down to get as many of them as possible then The Move to finish up. Use one of the Little Corners and one of the Edge turns with The Move.

Step 3. Solve the 3 long edges by moving the slice so they are in the correct spots, then if necessary flip two of them. K A K A K flips L and R. You could flip L and A by moving them to R and flipping them there. Or R and A by moving them to L and flipping them there. If you need a pure flipper use (K A K' A) x 3 to flip L and A.

Step 4. Permute the 3 little edges using The Move with two Edges.

Step 5. Orient the 3 little edges. L R L R L A L A flips K1 and YP.

Step 6. Solve the centers 1 or more at a time using (J A J' A) x 3 (W L W' L) x 3 which cycles Bottom > Back > Right. The setup move W' R W swaps the centers on the right and back so the cycle is reversed.

Tangram Cube Initial Discoveries

I got a new puzzle yesterday from Speedcube Shop. I am checking it out.

Naming and counting the pieces.

• Two little corners that only rotate.
• Six big corners that can 3-cycle around the little corners. They can also swap around the long edges with an edge twist.
• Three long edges that can flip one at a time, and move around the cube with the inner slice.
• Three little edges that can move around with the slice, and swap one pair at a time with an edge twist. 
• Six center pieces that double swap with each edge twist, and 3-cycle with each corner twist.

I experimented a bit with The Move but didn't find anything immediately so moved on. May come back to it though. I tried finding a typical commutator 3-cycle. I look for a set of 3 moves that changes only 1 piece in one of the layers. Didn't find one yet. But going UpR(ight)C(orner) ReplaceT(op)E(dge) DownRC ReplaceF(ront)E UpRC ReplaceTE DownRC ReplaceFE...

Wait a minute. I thought I had a 3-cycle of little edges dialed in, but now in trying to put them back I have scrambled the centers. Well, all but the red one. What did I do?

It went downhill from there. Pretty soon it was pretty scrambled. But now, without really knowing how exactly, I've got it back to the 5-cycle. hmmmm.

August 25, 2017
Before I went to bed last night I decided to name things so I can track what I am trying and how it works. I am using some of the letters from my BLD solving. Here is what we have so far.

Holding the cube with yellow up and blue front:

L = long edge at FrontLeft
A = long edge at UpBack
R = long edge at RightDown

ED = little edge at LeftUp
K1 = little edge at FrontDown
YP = little edge at BackRight

J = corner at FUR. J or J up, and J' or J down.
W = corner at BDL. W' or W up, and W or W down.

K = move slice up. K or K up, and K' or K down.

Right now I have a 5-cycle of centers and two little edges are flipped.

Things finally fell into place after spending a lot of time today trying to figure out some cycles and swaps and flips. It is solved. But I need to experiment and document much more before I want to give it a good scramble. Here is what I've learned so far.

L R L R 3-cycles E and its adjacent centers to K, K to Y, and Y to E.
Of course similar 3-cycles can be accomplished using L and A, and A and R.

J A J' A 3-cycles big corners like you would expect The Move to do, plus it 5-cycles centers. Blue to yellow to red to orange to green to blue.
Using this and similar Moves you can cycle big corners from
Blue to Yellow to Green
Blue to Red to White
Red to Yellow to Green
Red to Blue to Orange
and on and on. I suppose solving the 8 corners would be an easy thing to do. The two small corners, J and W can be solved in at most 1 twist. The six big corners can probably be solved easily using The Move.

Another way to 3-cycle big corners is with the following algorithm.
(A W' A J A W A J') one time.
It also double-swaps centers blue-yellow, and red-white.

(A W' A J A W A J') two times swaps the centers back so results in a pure 3-cycle of big corners.

(A W' A J A W A J') three times would cycle the corners back home and double-swap the centers only.

August 26, 2017
In the table below last night I only finished two rows then filled in the J half of the puzzle 3-cycles but not their algorithms. I did not yet try them to see what is double-swapped. I went to bed. I'm ready to get back to it now. I haven't solved the cube with eyes closed since Wednesday and it is now Saturday! Yikes! I want to get back to that too. But first I want to work on this table some more.

Maybe not. I just reviewed what I wrote above and you know, if I could come up with an easy way to solve centers, and then find ways to solve the rest without messing up centers, it would surely be a much better approach. So I am going to take a break from the table and do some more experimenting and maybe document the other things I have found so far.

L R L R 3-cycles E and its adjacent centers to K, K to Y, and Y to E.
Of course similar 3-cycles can be accomplished using L and A, and A and R.

J A J' A 3-cycles big corners like you would expect The Move to do, plus it 5-cycles centers. Blue to yellow to red to orange to green to blue.
Using this and similar Moves you can cycle big corners from
Blue to Yellow to Green
Blue to Red to White
Red to Yellow to Green
Red to Blue to Orange
and on and on. I suppose solving the 8 corners would be an easy thing to do. The two small corners, J and W can be solved in at most 1 twist. The six big corners can probably be solved easily using The Move.

Another way to 3-cycle big corners is with the following algorithm.
(A W' A J A W A J') one time.
It also double-swaps centers blue-yellow, and red-white.

(A W' A J A W A J') two times swaps the centers back so results in a pure 3-cycle of big corners.

(A W' A J A W A J') three times would cycle the corners back home and double-swap the centers only.

(K A K' L) two times just moves centers. O>B>R and Y>W>G
(K L K' R) two times just moves centers. O>B>G and Y>W>R
(K A K' R) two times moves centers and edges. Edges OY>BW>GR

R L K L R K' flips L and A, and E and Y.

(K A K' A) two times cycles K>E>P. K and E flip; P rolls.

(K A K' A) three times flips L and A.

(K A K A) K' (A K A K) or
(K A K A K) two times cycles E>K>Y. K and E flip; Y rolls.

(J A J' R) x 2 (A K A K') x 2 flips YP and K1.

A ((L A L) J (L A L A) J') x 3 Pure Center 3-cycle B>R>G and with setup moves we could easily do B>R>O and B>R>W and G>W>B and G>W>O and G>W>R and B>O>Y and B>O>R and B>O>W and O>R>G and O>R>Y and G>Y>O and G>Y>B and G>Y>R and on and on and on.

Now that I found a center 3-cycle and have convinced myself I have all the algorithms I need, I have fully and intentionally scrambled it. I will not need to complete the table below. In the next post I will try to put just the algorithms I plan to use and how.

Tangram Cube	Corner 3-cycle	Double-swaps of centers
Algorithms		BY	RW	BG	WH	BW	RY	GO
A W' A J A W A J'	Yellow-blue-orange	x	x
A W A J A W' A J'	Yellow-blue-white					x	x
	Yellow-red-orange
	Yellow-red-white
	Blue-yellow-green
	Blue-yellow-white
	Blue-red-green
	Blue-red-white
	Red-blue-orange
	Red-blue-green
	Red-yellow-orange
	Red-yellow-green
	and on and on