## Jakub Stepo´s solutions to the two Skewb Star Competition problems

Submitted by Peter Tchamitch on Thu, 01/02/2020 - 06:45.For those who don´t know about this competition, please refer to my post of 14 June 2019 entitled "Skewb Star Special Challenge/Competition, with Special Prize", and to my Winner Announcement post of 29 August 2019, in which, as you can see, it was stated that the Special Prize had been awarded but that the challenge itself was to remain open until the New Year; well, the New Year has now arrived, so please find below Jakub Stepo´s solutions to the two competition problems:

Question 1

========

Let’s say that the cube is solved and ﬁxed in position. We have to ﬁnd out which positions are permissible while having solved cube.

## The latest on the Bonus Problem posted on 13 August 2019

Submitted by Peter Tchamitch on Thu, 09/26/2019 - 14:12.The so-called Standard Method referred to in the Bonus Problem post of 13 August 2019 involves

finding the easiest or most convenient Skewb Star or Wolf Tooth solution, depending on how the

SSX or WTX respectively were scrambled, and then, unless the characteristic valleys between the

corners of the Skewb Xtreme just happen to be spontaneously solved, proceeding from there to the

other Skewb Star or Wolf Tooth solutions in an orderly manner until the valleys are observed to be

correct. No matter how orderly, this method still involves trial and error, and the Bonus Problem

was basically asking for a way to eliminate that somehow. The SSX and WTX have only one

finding the easiest or most convenient Skewb Star or Wolf Tooth solution, depending on how the

SSX or WTX respectively were scrambled, and then, unless the characteristic valleys between the

corners of the Skewb Xtreme just happen to be spontaneously solved, proceeding from there to the

other Skewb Star or Wolf Tooth solutions in an orderly manner until the valleys are observed to be

correct. No matter how orderly, this method still involves trial and error, and the Bonus Problem

was basically asking for a way to eliminate that somehow. The SSX and WTX have only one

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

Submitted by Peter Tchamitch on Thu, 08/29/2019 - 04:43.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

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

Submitted by Rubikehv75 on Tue, 08/27/2019 - 12:24.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?

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

Submitted by Peter Tchamitch on Tue, 08/13/2019 - 02:28.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.

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

Submitted by cubex on Wed, 06/19/2019 - 13:52.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?

Submitted by Peter Tchamitch on Mon, 06/17/2019 - 15:27.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

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

Submitted by Peter Tchamitch on Fri, 06/14/2019 - 03:04.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

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

Submitted by cubex on Mon, 06/10/2019 - 13:12.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

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

Submitted by Ben Whitmore on Sat, 05/18/2019 - 16:13.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.

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.

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