# Message #2028

From: Eduard <baumann@mcnet.ch>

Subject: Re: Super Puzzle Sunday!

Date: Sat, 18 Feb 2012 23:43:44 -0000

Thanks Nan,

Your hints for "Tetrahedron E0:0:1" are very valuable.

I never solved the 180°Rubik.

It is not so easy to see the equivalence between tetra E0:0:1 and Rubik 180°. How did you discover it? 4 1C triangles + 4 3C triangles ==> 8 180°corners; 12 1C quadrilaterals ==> 12 180°edges; 6 2C quadrilaterals ==> 6 180°faces. Are you right with your sentence "centers become 2C"?

I solved Tetrahedron E0:0:1 with 160 twists. You did it with 48.

I also solved the Tetrahedron E1:0:0.5 (easier).

— In 4D_Cubing@yahoogroups.com, "schuma" <mananself@…> wrote:

>

> Hi Ed,

>

> Tetrahedron E0:1:1 is certainly an interesting puzzle that is simple but not trivial.

>

> First, it is a sticker variation of the 180-degree-only Rubik’s cube. I don’t know if you have tried scrambling and solving the Rubik’s cube using only 180-deg turns. But puzzle 1 is nothing but that, except four corners become 1C, and the centers become 2C. As an result, we need to worry about the orientations of the Rubik’s cube centers. Based on this observation, I can borrow some algorithms from the Rubik’s cube.

>

> Here’s my procedure of solving puzzle 1:

>

> 1. The 2C pieces never moves, they only rotate. So they determine the global orientation of the puzzle.

>

> 2. Solve 3C and 1C triangles, free style. This is like solving all the corners on a 180 only Rubik’s cube. This step affects the orientations of 2C and the 1C quadrilaterals. I don’t have particular algorithms, but it is easy.

>

> 3. Fix orientations of 2C. If A and B denote two adjacent edges, the algorithm to flip the two 2C pieces on these two edges is [A,B]x3. This corresponds to [R2,U2]x3 on Rubik’s cube. This steps affects the

> 1C quadrilaterals.

>

> 4. 3-cycle 1C quadrilaterals. Let A, B, and C denote three edges that meet at one vertex. The algorithm is [A,B,A,C]x2. You can try it to see the effect. It’s a pure 3-cycle. It corresponds to [U2,F2,U2,R2]x2 on Rubik’s cube. This algorithm is also very useful on the edge-turning cube (Helicopter cube) and edge-turning dodecahedron. It is a [3,1] commutator with X=ABA, and Y=C.

>

> My general methodology is still SSSS, in your notation. But keep in mind that only the last step is necessarily a pure 3-cycle (doesn’t affect other types of pieces). The last but one step may affect the type of pieces to be solved in the last step, and so on. So the number of moves for each algorithm is not too high.

>

> Please let me know how you think of my method.

>

> Nan

>

> — In 4D_Cubing@yahoogroups.com, "Eduard" <baumann@> wrote:

> >

> > In the tracking for solvers for the new MagicTile vs 2 we have also place for non-monster puzzles.

> > These small puzzles are not automatically much simpler. The have clearly fewer pieces but often often not enough place to construct narrow sequences. I take as an example puzzle 1 := the spherical tetrahedron edge turning E 1:0:0. My method consists allways to search a small but sufficient set of sequences (SSSS) for the solving "with many twists". The normal Rubik’s Cube has typically 4 sequences: a 3 cycle foredges, a 3 cycle for corners, a rotator on place for edges and a rotator on place for corners. The opposite is having a large set of small sequences (LSSS; for solves "with minimal twist number"). For puzzle 1 I have found using blindly commutators of commutators one macro which moves only corners (a double switch where no corner stays fixed) and a macro which moves only inner faces (a double switch where no inner face stays fixed). I have no macro for edges only and no macro for outer faces only. I have no 3 cycles, no rotators.

> > Nan you certainly don’t use SSSS for small puzzles. Can you nevertheless tell us how you construct a sequence for outer faces or for edges in puzzle 1?

> >

> >

>