# Message #1378

From: Andrey <andreyastrelin@yahoo.com>

Subject: Re: Variations of Rubiks Cube puzzle

Date: Thu, 03 Feb 2011 10:47:31 -0000

Hi Alex,

It’s very interesting set of puzzles that you presented. I’ve tried "Grandmaster level". Not very difficult - it took only 1 hour to solve, but this puzzle is very unusual: if you take, for example, 2C piece and make "local" twists, you can’t flip it. You have to move it around the torus to change orientation! So it behaves like a part of non-orientable puzzle, while the torus itself is orientable surface! Very interesting effect. The same is true for 4C pieces: local twists can make 180-degree rotation of them, and for 90-degree you have to move it around the torus too.

Unfortunately, I haven’t algorithm for it: solution was almost intuitive. I first solved two outer rings of the square so only central 5x5 face was unsolved, then oriented all 2C and 4C pieces (by moving them to the torus boundary and retreiving from the back side), then positioned all 2C (by commutator like (F- I- H- E- H+ E+ I+ F+), where A..I are centers of the faces in order ABC//DEF//GHI). Unfortunately these commutators flip 4C pieces, so you have perform them twice. Last stage was positioning of 4C - and operation was like (I2 E+ I2 E+ I2 E2 I2) - it makes 3-cycle of 4Cs of E face.

Andrey

— In 4D_Cubing@yahoogroups.com, "puzzle314" <puzzle314@…> wrote:

>

> I am a new member. My name is Alex. I am a developer of the

> www.puzzlemystery.com <http://www.puzzlemystery.com> . I am working on

> variations of Rubik’s Cube puzzle.

>

> Recently I’ve added several 2D variations of the Rubik’s Cube

> puzzle <http://www.puzzlemystery.com/FlatRubikPuzzle.aspx> . The

> beginning level is pretty simple, but intermediate, advanced, master and

> grandmaster levels are very complicated. It appears easier to create

> than solve these puzzles. I would really appreciate if somebody could

> find solutions and send me the algorithms for these three levels.

>

> My next goal is to create 3D and then 4D Rubik’s Cube puzzles. I am

> only a beginner in 4D puzzles. There is one question I am trying to

> clear now: in order to twist a hyperface in MC4D, I should click on

> hypersticker. That allows me to make only one type of a twist. It is

> fine for 3D Rubik’s Cube where hyperface is a square and allows only

> one type of a twist. For 4D Rubik’s Cube the hyperface is a cube. It

> should allow 3 basic twists. How I can do it? Am I missing something?

>

> Alex

>