Discussions on the mathematics of the cube

## The Special Prize of the Skewb Star Special Challenge/Competition of 14 June has been won but the challenge is still open

The winner of the Skewb Star competition posted here on 14 June is Jakub Stepo, who is
a member of the Cube Forum

The Special Prize has of course been sent to Mr. Stepo, but I would like to stress that the
challenge is still open and that everyone who sends in the correct answers by let´s say 31 December
2019 will have their names published here, as soon as the answers are received

After the tentative closing date of 31 December 2019, I was thinking of publishing here all the
actual worked solutions that may have been sent to me, and in this connection I can reveal ahead of time
that Jakub Stepo´s elegant and powerful solution will certainly be of great interest to Cube Forum

## 4x4 only two blocks from solved

Hello, I’m trying to solve the 4x4 for the first time but keep getiing the same mistake.
White is solved
Red is solved
Yellow is solved
Green is solved except left highest row: yellow/blue orange block
Bleu is solved except right highest row: orange/green/yellow block
Yellow is solved except the above two blocks.
These two blocks should be switch but I have no idea how.
If I start again, the same problem will appear.
Any ideas?

## Bonus problem related to the Skewb Star Special Challenge/Competition, with Special Prize, of 14 June 2019

So far, no one has sent in the answers to the two questions posed in the Skewb Star Special Challenge/Competition which I posted here on 14 June 2019, so I thought that I would avail myself of this window of opportunity to add a further bonus problem.

As I´m sure everyone immediately realized, the whole point of the Special Prize of the competition, the Skewb Star Xtreme, SSX, together with the Wolf Tooth Xtreme, WTX, is that solving these cubes is a practical application of knowing all of the solutions to the Skewb Star as well as how to alternate between them, in other words of having found a way to answer the two questions of the competition.

## New 5 spot pattern discovered for megaminx

Thanks to Tom's web program at twizzle I've discovered a new megaminx pattern. Quite a long time ago I realized that slice patterns could be adapted to the megaminx. The early results can be seen here: megaminx patterns

The notation to generate the 10 spot with Tom's program is (2L 3u')36. With more experimentation we should be able to find many more.

Mark

## An unsolved problem: how many solutions are there to the 8-Color Cube?

The 8-Color Cube is an extremely elegant problem, both in appearance and concept;

The cube is very easy to make at home: numbered stickers are available everywhere and the whole
construction process takes only about 15 minutes.

As you can see, Walter Randelshofer and myself have managed to find a number of extra solutions
separate from the pre-existing design solution with its ”Superflip Centre” variant, however the real
problem remains: how many solutions are there, in theory, to the 8-Color Cube?--this is the tough

## Skewb Star Special Challenge/Competition, with Special Prize

SKEWB STAR
Special challenge/competition 24 October 2018
by Peter Tchamitch
www.petertchamitch.se

Question 1:
How many solutions are there to this puzzle?--in other words, in how many different ways
is it possible to physically orientate a solved octahedron and a solved cube/skewb in relation
to each other?

Question 2:
How many color-matchings (please see definition below) are there in total, in other words
what is the sum of all the various color-matching values for all the various solutions?
A “color-matching” is an instance of one of the sides of an octahedron-pyramid having the

## cubezzz.dyndns.org/drupal is once again active

Hi folks,

These old URLs should all work now:

http://cubezzz.dyndns.org/drupal/?q=node/view/563#comment
http://cubezzz.duckdns.org/drupal/?q=node/view/563#comment
http://cubezzz.homelinux.org/drupal/?q=node/view/563#comment
http://forum.cubeman.org/?q=node/view/563#comment

Mark

## Optimal solutions to the Eliac puzzle

The Eliac is a complex deep-cut 2-gen circle puzzle:

The left circle rotates in increments of 90 degrees and the right circle rotates only by 180 degrees. There is a simulator of the puzzle here.

Using ksolve++ I made an optimal solver modified it slightly to turn it into a coset solver. The subgroup I used for the coset solver is the subgroup of positions where the 18 small triangles, 10 diamonds, and 2 squares are solved. There are 1600300800 arrangements of those 30 pieces and each coset has 3024000 solvable positions. Unfortunately since the puzzle is 2-gen, there isn't a good way to select a subgroup generated by a subset of the generators of the whole puzzle, which (as far as I can tell) is what is required in order to make the "pre-pass" trick work for sub-optimally solving cosets very quickly. So each coset needs to be solved optimally using a pure DFS, which takes quite a long time (about 1.5 hours on my laptop). Notice that the puzzle has a horizontal reflection symmetry so we only need to solve one coset in each symmetry class.

## Remember to use http://forum.cubeman.org

Hi folks,

This is a notice that http://cubezzz.dyndns.org/drupal will probably stop working tomorrow. Please use http://forum.cubeman.org instead.

The similar http://cubezzz.duckdns.org/drupal should also work.

More news to come soon.

## {4,3,3} 3 symmetry

Hello, I am new to this forum and this is my first post. I know that maybe its content will seem trivial to some of you, but I am afraid that I am not so well versed in mathematics and programming, so I try to do at least something within my limited capabilities (I am 15.34 at the moment).

Based on Dan Hoey’s calculations, I was able to calculate the number of essentially different positions up to symmetry of the four-dimensional analogue of the Rubik’s cube. However, it is quite probable that I have made some mistakes, as I have done it only by hand. Nevertheless, from the patterns observed I was able to make some interesting generalizations, presented later in this post.