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

Naming and counting the pieces.

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 | | | | | | | |