]>
Domain of the Cube Forum - Cube lovers returns
http://forum.cubeman.org
To promote mathematical discussions about the Rubik's Cube and related puzzles.enAll 3x3x3 involutions solved
http://forum.cubeman.org/?q=node/view/588
I optimally solved all 170,911,549,184 involutions in half-turn metric. The entire process took about 2.5 weeks to generate the 37GB solution file. <a href="https://github.com/Voltara/involutions">Source code</a> is available on GitHub.
<p>
Here are the total and 48-way symmetry reduced counts by distance:
<pre>
d Total Unique by symmetry
--------------------------------------
0 1 1
1 6 1
2 3 1
3 72 2
4 39 4
5 960 25
6 886 41
7 12708 292
8 19526 506Tue, 28 May 2024 17:14:31 -0400Does the STOP-cube have a second type of solution?
http://forum.cubeman.org/?q=node/view/587
You might ask: "What the heck is a STOP-cube?" and "Why would I care? Who are you anyways?"<br />
And those are all legit questions of course. <br />
<br />
My name is Ortwin, I am a long time member of the <a href="https://twistypuzzles.com/forum">twisty puzzle forum</a>. Currently I am looking for the answer to question regarding a specific sticker modification of a 3x3x3 cube, but there did not seem to be much interest over there in the question. Walter Randelshofer who is also a member of this forum recommended to post it into this community, and hereby I do.<br />
<br />
To get an idea what that "STOP-cube" is, you might want to have a quick look at the links to the topics in the twistypuzzle forum:Wed, 31 Jan 2024 00:10:54 -0500Diameter of the M24 Conway puzzle is 45
http://forum.cubeman.org/?q=node/view/586
<br><br><br />
<img src="http://www.maxhost.org/other/m24-conway-puzzle.jpg"><br />
<br><br><br />
<br />
This is a well know puzzle in which there are two moves, one which rotates the central "clock" by one position<br />
clockwise or counter-clockwise. <br><br />
The other switches or swaps each pair of numbers with matching colours. <br><br><br />
<br />
I decided to plug these values into GAP to investigate God's number for the underlying group for this puzzle <br><br />
as it still seemed be unknown or undocumented anywhere at least.<br />
<br />
Feeding these numbers into GAP we get:<br />
<br><br><br />
S := (1,24)(2,23)(3,4)(5,22)(6,11)(7,8)(9,10)(12,21)(13,14)(15,20)(16,17)(18,19);Wed, 08 Feb 2023 11:21:19 -0500Streamlined version of the solutions posted here on 22 September 2021
http://forum.cubeman.org/?q=node/view/585
It should probably have been stated more clearly in my previous post here on 22 September 2021 <br />
that all the proposed sequences and algorithms (in the presentation that was linked to in that post) <br />
are designed to solve the WTX and SSX** starting from a situation where one of the 12 solutions of<br />
the WT/SS portion of the cube is already in place and the remaining task is to move on from there <br />
to the other solutions in order to find the unique solution of the 12 which also results in the <br />
characteristic ”valleys” of the WTX/SSX being solved (there is of course a 1/12 chance that the <br />
starting solution just happens to be the right one) ** Please note the link at the bottom of the pageThu, 11 Nov 2021 10:29:58 -0500Proposed solutions to the Wolf Tooth Xtreme and Skewb Star Xtreme
http://forum.cubeman.org/?q=node/view/584
This post is a follow-up to my posts of 13 August 2019, ”Bonus Problem”, and 26 September 2019 , ”The latest on the Bonus Problem”<br />
<br />
Just to quickly recap: the problem in question was to find the best way to solve the custom hybrid cubes, the Wolf Tooth Xtreme and the Skewb Star Xtreme, which together constituted the Special Prize of the Skewb Star Special Challenge/Competition posted here on 14 June 2019<br />
<br />
The top four pages of the presentation <a href="https://www.petertchamitch.se/wtx_ssx.pdf" target="_blank">here</a> show the state of affairs at the time of the 13 August 2019 post, a state of affairs which was subsequently summarized in the first paragraph of the 26 September 2019 post; in the rest of that post I then outlined, without going into detail, a practical improvement to the previous ”standard method” and added at the end that ”it remains to be shown formally exactly why the improved system described above works”Wed, 22 Sep 2021 04:32:06 -0400Deficiency minus one presentation for the Tits Group
http://forum.cubeman.org/?q=node/view/583
Note that the simple group T (named for Jacques Tits) of order 17971200<br><br />
has a transitive permutation representation on 2304 points.<br><br />
<br><br />
<br />
A general formula for the number of edges in a n-cube is n.2^(n-1) to<br><br />
be found in this extract from "Beyond the Third Dimension" by Thomas Banchoff<br><br />
<a href="https://www.math.brown.edu/tbanchof/Beyond3d/chapter4/section05.html"> https://www.math.brown.edu/tbanchof/Beyond3d/chapter4/section05.html </a><br><br />
<br><br />
<br />
It is worth mentioning another source here for a general formula<br><br />
for the number of pieces of different types on a d-dimensional Rubiks' cubeSun, 02 May 2021 05:27:34 -0400A Generalization on the Shamir Method
http://forum.cubeman.org/?q=node/view/581
<p>
I have not posted in a very long time, but I have continued to work on ideas for a better
program to calculate God's Algorithm for the full cube. The time has long passed where a single
desktop class machine could make further progress on the problem as a whole. The search space is just
too large for that. Instead, I have been working on ideas for a program that could
at least visit all the positions in a single coset no matter how far the positions
in the coset are from Start.
</p>
<p>
I have such a program which works, but its performance is not acceptable. Therefore, I'm not going to report anything about it.
Instead, I'm going to report on a plan for a new and similar program which I believe will have acceptable
performance. I have developed most of the pieces that will be required for this new program, but it will
take me a few months to put all the pieces together. The main idea in the new program is very old
and is not original with me. The idea borrows heavily from a message to the original Cube-Lovers mailing list
by Alan Bawden on 27 May 1987.
<a href="http://www.math.rwth-aachen.de/~Martin.Schoenert/Cube-Lovers/Alan_Bawden__Shamir's_talk_really_was_about_how_to_solve_the_cube!.html">Alan's message</a>
was based on a talk given by Adi Shamir.
</p>Sun, 19 Jul 2020 17:33:25 -0400Megaminx "cube in a cube" solved in 42 moves
http://forum.cubeman.org/?q=node/view/580
I've found a pattern for the megaminx which is analogous to the "cube in a cube" pattern for the Rubik's cube. It was originally found using a cyclically decomposable process, then many optimizations were applied. The software used to do this includes Twizzle (Tom Rokicki and Lucas Garron) and twsearch. To capture the video the extension nimbus was used on the google chrome web browser.<br><br />
The sequence of moves in SiGN notation is:<br />
BR2 U2' BR2' R2 U' F2 U2' L2 U' BL2 U2 BL2' U' L2' U' F2' U' R2' BR2 U2 BR <br />
BL2' L2' R2' U2 R2' U' F2' R2 F2 U' F2' U R2' F2 U R2 U' R2 L2 BL2 BR2<br><br />
The vidSun, 29 Mar 2020 15:29:53 -0400Jakub Stepo´s solutions to the two Skewb Star Competition problems
http://forum.cubeman.org/?q=node/view/579
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:
<p>Question 1<br>
========<br>
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.</p>Thu, 02 Jan 2020 06:45:14 -0500The latest on the Bonus Problem posted on 13 August 2019
http://forum.cubeman.org/?q=node/view/578
The so-called Standard Method referred to in the Bonus Problem post of 13 August 2019 involves<br />
finding the easiest or most convenient Skewb Star or Wolf Tooth solution, depending on how the<br />
SSX or WTX respectively were scrambled, and then, unless the characteristic valleys between the<br />
corners of the Skewb Xtreme just happen to be spontaneously solved, proceeding from there to the<br />
other Skewb Star or Wolf Tooth solutions in an orderly manner until the valleys are observed to be<br />
correct. No matter how orderly, this method still involves trial and error, and the Bonus Problem<br />
was basically asking for a way to eliminate that somehow. The SSX and WTX have only oneThu, 26 Sep 2019 15:12:00 -0400The Special Prize of the Skewb Star Special Challenge/Competition of 14 June has been won but the challenge is still open
http://forum.cubeman.org/?q=node/view/577
The winner of the Skewb Star competition posted here on 14 June is Jakub Stepo, who is<br />
a member of the Cube Forum<br />
<br />
The Special Prize has of course been sent to Mr. Stepo, but I would like to stress that the<br />
challenge is still open and that everyone who sends in the correct answers by let´s say 31 December<br />
2019 will have their names published here, as soon as the answers are received<br />
<br />
After the tentative closing date of 31 December 2019, I was thinking of publishing here all the<br />
actual worked solutions that may have been sent to me, and in this connection I can reveal ahead of time<br />
that Jakub Stepo´s elegant and powerful solution will certainly be of great interest to Cube ForumThu, 29 Aug 2019 05:43:13 -04004x4 only two blocks from solved
http://forum.cubeman.org/?q=node/view/576
Hello, I’m trying to solve the 4x4 for the first time but keep getiing the same mistake. <br />
White is solved <br />
Red is solved<br />
Yellow is solved<br />
Green is solved except left highest row: yellow/blue orange block<br />
Bleu is solved except right highest row: orange/green/yellow block<br />
Yellow is solved except the above two blocks.<br />
These two blocks should be switch but I have no idea how.<br />
If I start again, the same problem will appear.<br />
Any ideas?Tue, 27 Aug 2019 13:24:05 -0400Bonus problem related to the Skewb Star Special Challenge/Competition, with Special Prize, of 14 June 2019
http://forum.cubeman.org/?q=node/view/575
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.<br />
<br />
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.Tue, 13 Aug 2019 03:28:46 -0400New 5 spot pattern discovered for megaminx
http://forum.cubeman.org/?q=node/view/574
<img src='http://www.maxhost.org/other/5-spot-pattern-megaminx' width=600>
<p>
Thanks to Tom's web program at <a href="https://twizzle.cubing.net" target="_blank">twizzle</a> 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: <a href="http://www.cubeman.org/mega2.html" target="_blank">megaminx patterns</a>
<p>
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.
<p>
MarkWed, 19 Jun 2019 15:16:19 -0400An unsolved problem: how many solutions are there to the 8-Color Cube?
http://forum.cubeman.org/?q=node/view/573
The <a href="http://www.randelshofer.ch/rubik/virtual_cubes/rubik/eight-colored_faces/eightcolor_cube_1.html"target="_blank">8-Color Cube</a> is an extremely elegant problem, both in appearance and concept;<br />
<br />
The cube is very easy to make at home: numbered stickers are available everywhere and the whole<br />
construction process takes only about 15 minutes.<br />
<br />
As you can see, Walter Randelshofer and myself have managed to find a number of extra solutions<br />
separate from the pre-existing design solution with its ”Superflip Centre” variant, however the real<br />
problem remains: how many solutions are there, in theory, to the 8-Color Cube?--this is the toughMon, 17 Jun 2019 16:27:42 -0400