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Domain of the Cube Forum - Cube lovers returns
http://forum.cubeman.org
To promote mathematical discussions about the Rubik's Cube and related puzzles.enMegaminx "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 -0400Skewb Star Special Challenge/Competition, with Special Prize
http://forum.cubeman.org/?q=node/view/572
SKEWB STAR <br />
Special challenge/competition 24 October 2018<br />
by Peter Tchamitch<br />
www.petertchamitch.se<br />
<br />
Question 1:<br />
How many solutions are there to this puzzle?--in other words, in how many different ways<br />
is it possible to physically orientate a solved octahedron and a solved cube/skewb in relation<br />
to each other?<br />
<br />
Question 2:<br />
How many color-matchings (please see definition below) are there in total, in other words<br />
what is the sum of all the various color-matching values for all the various solutions?<br />
A “color-matching” is an instance of one of the sides of an octahedron-pyramid having theFri, 14 Jun 2019 04:04:04 -0400cubezzz.dyndns.org/drupal is once again active
http://forum.cubeman.org/?q=node/view/571
Hi folks,<br />
<br />
These old URLs should all work now:<br />
<br />
http://cubezzz.dyndns.org/drupal/?q=node/view/563#comment<br />
http://cubezzz.duckdns.org/drupal/?q=node/view/563#comment<br />
http://cubezzz.homelinux.org/drupal/?q=node/view/563#comment<br />
http://forum.cubeman.org/?q=node/view/563#comment<br />
<br />
MarkTue, 11 Jun 2019 00:00:55 -0400Optimal solutions to the Eliac puzzle
http://forum.cubeman.org/?q=node/view/570
The Eliac is a complex deep-cut 2-gen circle puzzle:<br />
<br />
<img src='https://i.imgur.com/b5lE2kw.png' width=300><br />
<br />
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 <a href='https://www.stringham.me/eliac/'>here</a>.<br />
<br />
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.Sat, 18 May 2019 17:13:03 -0400Remember to use http://forum.cubeman.org
http://forum.cubeman.org/?q=node/view/569
Hi folks,<br />
<br />
This is a notice that http://cubezzz.dyndns.org/drupal will probably stop working tomorrow. Please use http://forum.cubeman.org instead.<br />
<br />
The similar http://cubezzz.duckdns.org/drupal should also work.<br />
<br />
More news to come soon.Sun, 12 May 2019 20:58:33 -0400{4,3,3} 3 symmetry
http://forum.cubeman.org/?q=node/view/568
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). <br><br />
<br />
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.Sun, 24 Feb 2019 06:09:21 -0500The 2018 Computer Fewest Moves Challenge is Underway
http://forum.cubeman.org/?q=node/view/567
For the first time, the FMC will have solvers in the "NxNxN" category for up to 9x9x9 competing to solve 10 random scrambles in as few moves as possible. Also of note: There are now four solvers in the 5x5x5 section.<br />
<br />
For those who are interested, visit:<br />
<br />
http://cubesolvingprograms.freeforums.net/Thu, 18 Oct 2018 07:53:28 -0400Lower bound for the diameter of the 3-gen subgroup <U,F,R>
http://forum.cubeman.org/?q=node/view/566
What are the known bounds for the diameter of this subgroup? <a href='http://cubezzz.duckdns.org/drupal/?q=node/view/190'>This thread</a> gives a lower bound of 26 QTM but doesn't discuss HTM. I seem to recall a lower bound of 20 HTM from somewhere, but no upper bound. However, I recently found a position that requires 21 HTM:
<pre>U R F2 R U2 F2 U' F' R U F U R' F R2 U F R U2 R F'</pre>
Is this the first one known? Out of all 186624 positions with all pieces correctly permuted, this position and the inverse are the only ones requiring 21. Here's the full distribution:
<pre>
Depth PositionsSun, 02 Sep 2018 23:00:35 -0400